Chapter 2 Rural Road Network Problems

Contents

Contents ...... i

List of Figures ...... v

List of Tables ...... ix

List of Acronyms ...... xiii

Chapter 1

Introduction ...... 1

1.1 Rational ...... 1

1.2 Objectives ...... 4

1.3 Outline ...... 5

Chapter 2

Rural Road Network Problems ...... 7

2.1 Introduction ...... 7

2.2 Planning methodology ...... 8

2.2.1 Priority Ranking (PR)...... 8

2.2.2 Benefit/Cost Analysis (BCA) ...... 9

2.2.3 Centrality index ...... 10

2.2.4 Intensity of interaction ...... 11

2.2.5 Road density ...... 13

2.2.6 Accessibility Indicators (AI) ...... 14

2.2.7 Costs ...... 16

2.2.8 Accessibility index ...... 18

2.2.9 Facility based approach ...... 21

Rural Engineering Infrastructures Design and Public Facility Locations

2.2.10 Traffic Flow...... 22

2.3 Rural road network generation ...... 23

2.4 Solution techniques ...... 31

2.5 Multi-objective approach to the rural road network problem ...... 35

2.6 Discussion ...... 38

2.7 Summary ...... 42

Chapter 3

Local Conditions and Rural Road Constructions in Hilly Regions of Nepal ...... 45

3.1 Introduction ...... 45

3.1.1 Tectonic environment ...... 46

3.1.2 Geology ...... 48

3.1.3 Topography ...... 50

3.1.4 Climate ...... 51

3.1.5 Geography ...... 52

3.2 The five-zone mountain model ...... 54

3.3 Alignment selection and choice of cross section ...... 59

3.4 Impacts of roads construction on slopes ...... 61

3.5. Conclusions ...... 66

Chapter 4

Covering Based Rural Road Network Method ...... 69

4.1 Introduction ...... 69

4.2 Review of rural road planning models ...... 70

4.3 Use of location models in rural road network design ...... 73

4.4 Proposed rural road network method ...... 75

4.4.1 Identification of nodal points ...... 75

4.4.2 Defining the rural road network ...... 77

4.5 Application to the hilly regions of Nepal ...... 78 ii

4.6 Rural public facility location in hilly regions of Nepal ...... 82

4.6.1 Covering of settlements ...... 82

4.6.2 Covering of public facilities ...... 88

4.7 Linkage pattern of rural roads in hilly regions ...... 91

4.7.1 Data concerning the rural road networks under study...... 92

4.7.2 Existing pattern of the rural road linkages ...... 97

4.7.3 Rural road network formation ...... 104

4.8 Application to other rural infrastructure problems ...... 107

4.9 Conclusions ...... 107

Chapter 5

Rural Road Network Optimisation Models ...... 109

5.1 Introduction ...... 109

5.2 Covering aspects ...... 110

5.3 Rural road network models ...... 112

5.4 Prioritization of links ...... 118

5.4.1 Introduction ...... 118

5.4.2 Indicators for rural road evaluation ...... 118

5.4.3 Discussion...... 123

5.5 Models application and validation ...... 125

5.6 Conclusions ...... 139

Chapter 6

A Multi-Objective Analysis of the Rural Road Network Problem ...... 141

6.1 Introduction ...... 141

6.2 Multi-objective integer programming: basic concepts ...... 142

6.3 Objectives for the rural road network problem ...... 143

6.4 Multi-objective rural road model ...... 145

6.5 Application of the model ...... 147

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Rural Engineering Infrastructures Design and Public Facility Locations

6.5.1 Test instance data and solutions ...... 148

6.5.2 Analysis of the solutions ...... 149

6.6 Conclusions ...... 157

Chapter 7

Conclusions and Future Works ...... 159

7.1 Summary of conclusions ...... 159

7.2 Limitations and future works ...... 164

References ...... 167

Appendices ...... 175

A. Distance Matrix of 15 VDCs (Gorkha A) ...... 175

B. Short Distance Matrix of 15 VDCs (Gorkha A) ...... 182

C. Google Earth maps of case study regions ...... 189

D. Distance matrices of rural road networks of case study regions ...... 193

E. Suggested intervention in the test rural road network ...... 197

F. Bi-objective solutions of sample network for different budget levels ...... 209

G. Floyd-Warshall algorithm ...... 216

H. Prim’s Algorithm ...... 217

List of Figures

Figure 2.1: The accessibility planning cycle (Dixon-Fyle, 1998)...... 15

Figure 2.2: Link options from unconnected settlement (Singh, 2010)...... 19

Figure 2.3: System approach to rural road development (Kumar & Kumar, 1999)...... 23

Figure 2.4: Transport network generation model (Shrestha & Routray, 2002)...... 28

Figure 2.5: Rural road network generation using accessibility criteria (Singh, 2010)...... 30

Figure 2.6: The graph of a typical area (Makarchi & Tilloston, 1991)...... 33

Figure 2.7: The MST for the typical area (Makarchi & Tilloston, 1991)...... 34

Figure 3.1: Longitudinal geological subdivision of Nepal Himalaya (Gansser, 1964)...... 47

Figure 3.2: Physiographic features of Nepal (RAIDP, 2009)...... 53

Figure 3.3: Settlements and cultivated land in hill slopes of Nepal (Google Earth, 2013)...... 53

Figure 3.4: A Model for young fold mountains (Fookes et al., 1985)...... 55

Figure 3.5: A typical cross-section in cut and fill (DRILP, 2006)...... 63

Figure 3.6: width of cut vs volume of cut (slope 1º)...... 64

Figure 3.7: Slope vs volume of cut (2m width)...... 64

Figure 3.8: A typical cross-section in full cut (DRILP, 2006)...... 65

Figure 3.9: A typical Cross-section in mild slopes (DRILP, 2006)...... 65

Figure 4.1: Location of the VDC centre and rural roads network in the study area...... 79

Figure 4.2: Nodal villages obtained from the solution of the covering problem (case study). 81

Figure 4.3: MST of the rural road network (case study)...... 81

Figure 4.4: Settlements in case 1: Gorkha A...... 83

Figure 4.5: Settlements in case 2: Gorkha B...... 84

Rural Engineering Infrastructures Design and Public Facility Locations

Figure 4.6: Settlements in case 3: Lamjung A...... 85

Figure 4.7: Settlements in case 4: Lamjung B...... 86

Figure 4.8: Effect of coverage in service distance...... 88

Figure 4.9: Rural road network in the study area: Gorkha A...... 93

Figure 4.10: Rural road network in the study area: Gorkha B...... 93

Figure 4.11: Rural road network in the study area: Lamjung A...... 94

Figure 4.12: Rural road network in the study area: Lamjung B...... 94

Figure 4.13: Identified nodal points and MST of the rural road network (Gorkha A)...... 95

Figure 4.14: Identified nodal points and MST of the rural road network (Gorkha B)...... 95

Figure 4.15: Identified nodal points and MST of the rural road network (Lamjung A)...... 96

Figure 4.16: Identified nodal points and MST of the rural road network (Lamjung B)...... 96

Figure 4.17: Backbone and branch rural road network (Gorkha A)...... 98

Figure 4.18: Backbone and branch rural road network (Gorkha B)...... 100

Figure 4.19: Backbone and branch rural road network (Lamjung A)...... 101

Figure 4.20: Backbone and branch rural road network (Lamjung B)...... 103

Figure 4.21: Structure of backbone and branch road network...... 104

Figure 5.1: Rural road network for model application...... 126

Figure 5.2: Node numbering scheme for model RRNM-3 and model RRNM-4 with backbone and branch links...... 127

Figure 5.3: An optimal network intervention for a budget of NRs 400 million (RRNM-1). . 135

Figure 5.4: An optimal network intervention for a budget of NRs 600 million (RRNM-1). . 135

Figure 5.5: An optimal network intervention for a budget of NRs 30 million (RRNM-2). ... 136

Figure 5.6: An optimal network intervention for a budget of NRs 55 million (RRNM-2). ... 136

Figure 5.7: An optimal network intervention for a budget of NRs 400 million (RRNM-3). . 137

Figure 5.8: An optimal network intervention for a budget of NRs 600 million (RRNM-3). . 137

Figure 5.9: An optimal network intervention for a budget of NRs 140 million (RRNM-4). . 138

Figure 5.10: An optimal network intervention for a budget of NRs 300 million (RRNM-4)...... 138 vi

Figure 6.1: Rural road network for application of model...... 148

Figure 6.2: Pareto frontier for budget level NRs 400 millions...... 149

Figure 6.3: Pareto frontier for budget level NRs 600 millions...... 150

Figure 6.4: Decision options and surface level of links for budget level NRs 400 millions (contd. …)...... 151

Figure 6.4: Decision options and surface level of links for budget level NRs 400 millions. . 152

Figure 6.5: Decision options and surface level of links for budget level NRs 600 millions (contd. …)...... 152

Figure 6.5: Decision options and surface level of links for budget level NRs 600 millions. . 153

Figure 6.6: Map of the planning region...... 156

Figure 7.1: Proposed rural road network planning process...... 161

Figure 7.2: Proposed multi-objective rural road network planning process...... 163

Figure C1: Settlements and rural road network in the study area: Gorkha A ...... 189

Figure C2: Settlements and rural road network in the study area: Gorkha B ...... 190

Figure C3: Settlements and rural road network in the study area: Lamjung A ...... 191

Figure C4: Settlements and rural road network in the study area: Lamjung B ...... 192

vii

List of Tables

Table 2.1: Road density and distance to roads (United Nations, 1979) ...... 13

Table 2.2 Examples of Accessibility Indicators (AI) (Edmonds, 1998) ...... 15

Table 4.1: Coverage provided by the nodal points for a service distance of 4 km ...... 80

Table 4.2: Coverage of settlements using various covering distances ...... 87

Table 4.3: Coverage of the health centre by nodal points ...... 89

Table 4.4: Coverage of the market centre by nodal points ...... 89

Table 4.5: Coverage of schools by nodal points ...... 90

Table 4.6: Coverage of public facilities by nodal points ...... 90

Table 4.7: Location of nodal points and linkage to the nodal points-Gorkha A ...... 97

Table 4.8: Location of nodal points and linkage to the nodal points-Gorkha B ...... 99

Table 4.9: Location of nodal points and linkage to the nodal points-Lamjung A ...... 101

Table 4.10: Location of nodal points and linkage to the nodal points- Lamjung B ...... 102

Table 4.11: Rural road network linkage lengths ...... 105

Table 5.1: Scoring system for prioritization of new linkages (DoLIDAR, 2010) ...... 122

Table 5.2: Scoring system for prioritisation for upgrading and rehabilitation (DoLIDAR, 2010) ...... 122

Table 5.3: Traffic Unit (DoLIDAR, 2010) ...... 123

Table 5.4: Weight based on population, person-km, population per unit construction cost and gravity flow model ...... 129

Table 5.5: The intervention in the network link at different budget levels based on P1 (RRNM-1) ...... 130

Rural Engineering Infrastructures Design and Public Facility Locations

Table 5.6: The intervention in the network link at different budget levels based on P1 (RRNM-2) ...... 131

Table 5.7: The intervention in the network link at different budget levels based on P1 (RRNM-3) ...... 132

Table 5.8: The intervention in the network link at different budget levels based on P1 (RRNM-4) ...... 133

Table 6.1: Non-dominated solutions for budget level NRs 400 millions ...... 149

Table 6.2: Non-dominated solutions for budget level NRs 600 millions ...... 150

Table 6.3: Preferable solutions for budget level NRs 600 millions ...... 154

Table 6.4: Comparisons of preferable solutions for budget level NRs 600 millions ...... 155

Table D.1: Distance Matrix (km) for Network-Gorkha A ...... 193

Table D.2: Distance Matrix (km) for Network-Gorkha B ...... 194

Table D.3: Distance Matrix (km) for Network-Lamjung A ...... 195

Table D.4: Distance Matrix (km) for Network-Lamjung B ...... 196

Table E.1: The intervention in the network link at different level of budget based on P2 (RRNM-1) ...... 197

Table E.2: The intervention in the network link at different level of budget based on P3 (RRNM-1) ...... 198

Table E.3: The intervention in the network link at different level of budget based on P4 (RRNM-1) ...... 199

Table E.4: The intervention in the network link at different level of budget based on P2( RRNM-2) ...... 200

Table E.5: The intervention in the network link at different level of budget based on P3 (RRNM-2) ...... 201

Table E.6: The intervention in the network link at different level of budget based on P4 (RRNM-2) ...... 202

Table E.7: The intervention in the network link at different level of budget based on P2 (RRNM-3) ...... 203

Table E.8: The intervention in the network link at different level of budget based on P3 (RRNM-3) ...... 204

Table E.9: The intervention in the network link at different level of budget based on P4 (RRNM-3) ...... 205

Table E.10: The intervention in the network link at different level of budget based on P2 (RRNM-4) ...... 206

Table E.11: The intervention in the network link at different level of budget based on P3 (RRNM-4) ...... 207

Table E.12: The intervention in the network link at different level of budget based on P4 (RRNM-4) ...... 208

Table F.1: Solutions for budget level NRs 400 millions ...... 209

Table F.2: Solutions for budget level NRs 600 millions ...... 212

List of Acronyms

B/C Benefit Cost Ratio

BB Backbone and Branch

BCA Benefit Cost Analysis

CEA Cost Efficiency Analysis

CRND Continuous Road Network Design

DDC District Development Committee

DM Decision Maker

DoLIDAR Department of Local Infrastructure Development and Agricultural Roads

DRND Discrete Road Network Design

GIS Geographical Information System

HDM Highway Development and Management

IMT Intermediate Means of Transport

IRAP Integrated Rural Accessibility Planning

IRR Internal Rate of Return

KP Knapsack Problem

MBT Main Boundary Thrust

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Rural Engineering Infrastructures Design and Public Facility Locations

MCLP Maximal Covering Location Problem

MCT Main Central Thrust

MFT Main Frontal Thrust

MOP Multi Objective Problem

MPL Mathematical Programming Language

MST Minimum Spanning Tree

NDP Network Design Problem

NMT Non motorized transport

NPV Net Present Value

NRs Nepalese Rupees

O/D Origin and Destination

PR Priority Ranking

RED Road Economic Decision

RND Road Network Design

RRNM Rural Road Network Model

SAIPAL South Asian Institute for Policy Analysis and Leadership

SBD Suspension Bridge Division

STDS South Tibetan Detachment System

TRL Transport Research Laboratory

TU Traffic Unit

UNCHS United Nations Centre for Human Settlements

xiv

VDC Village Development Committee

ZoI Zone of Influence

Chapter 1

Introduction

1.1 Rational

Basic private and public infrastructures are essential for the operation and/or development of a society or enterprise. They are infrastructural facilities that support an entire structure of development. These infrastructural facilities refer to those basic services for functioning of primary, secondary and tertiary productive activities (Hirschman, 1958). The infrastructural facilities embrace all public services from law and order through education and public health to transportation, communications and water supply (Mabogunje, 1974; Kahn, 1979). In other words, these represent elements of basic needs, which communities would like to procure for better living. Regarding rural infrastructure facilities, Kahn (1979) asserts that they can be classified into three main types; namely,

(a) physical infrastructure – such as roads, water, rural electrification, storage and processing facilities; (b) social infrastructure – health and educational facilities, community centres, fire and security services; and (c) institutional infrastructure – credit and financial institutions, agricultural research facilities and social infrastructure.

The adequate provision of physical and social infrastructures will enhance the introduction and adoption of innovations offered by institutional infrastructure which is an important term used for judging the development level of a country.

Gramlich (1994) gives three different versions for the definition of infrastructures. From an economical standpoint, the first version consists in large capital-intensive natural monopolies such as highways and other transportation facilities, water and sewer lines, and communications systems. The second version focuses on ownership and is defined as the

Rural Engineering Infrastructures Design and Public Facility Locations tangible capital stock owned by the public sector. The third version includes successive human capital formed by investment in research and development.

Generally, when the research community refers to infrastructure, they mean roads, telecommunications, electrifications, and irrigations that are named as hard infrastructures. Other types of infrastructures are institutional and are named as soft infrastructures.

Soft infrastructures refer to the institutional environment or way in which business is done. It includes various services such as those relating to transport, finance, animal husbandry, and marketing. Soft infrastructure and hard infrastructure are interlinked and interact with one another. Wanmali and Islam (1997) state that investments in infrastructure and the associated provision of services, are integral to the process of development. The key role of hard infrastructures investment in improving agriculture production and facilitating the growth of soft infrastructure in developing countries in particular, is emphasized (Ahmed and Donovan, 1992). Wanmali and Islam (1995, 1997) and Stern (1989) argue that limiting infrastructure to hard infrastructure such as roads, telecommunications, electrifications and irrigations is narrow, and that soft infrastructure (also named social infrastructure) are also very important. However, for efficient development and operation of soft infrastructures, the role of hard infrastructures is vital.

In the context of developing countries, the majority of population is concentrated in rural areas. Poverty is largely a rural phenomenon. Most of the rural residents are not integrated into the mainstream of national life. They barely participate in the economic and social activities and, most often, they are surviving with a low level of quality of life. One of the factors of their low quality of life is the absence, or poor quality, of infrastructures. There are wide gaps in the availability of physical and social infrastructure between rural and urban areas. This is considered as an important issue in developing countries. However, the development of infrastructure in rural areas of such countries has been hampered due to lack of funds and proper planning methodologies. Moreover, the quality of soft infrastructure has been suffered heavily due to absence or poor quality of hard infrastructures such as road, water supply, electricity, and telecommunication infrastructures.

Planners and Geographers alike tend to use rural infrastructural development as a strategy to address the problems of rural areas. The term ‘development’ refers to the conscious action of using, in a co-coordinated way, the resources available to a given political unit (Bernstein,

1978). Accordingly, rural infrastructural development could imply the desirability of overcoming deprivation and low quality of rural life. It could also refer to the provision of bridges, hospitals, schools, electricity, and potable water, in areas where they are lacking. Rural infrastructural development is a positive action that aims to improve the welfare of people.

One of the major elements in infrastructure development in rural areas is related with accessibility and affordability of services to rural communities. The accessibility and affordability of services for the rural people is related to transport and communications infrastructure as there is a significant correlation between poverty and remoteness. Rural road construction is a intervention for raising living standards in poor rural areas (Gannon & Liu, 1997). Agricultural output from rural areas is a very significant component of the national economy in many developing countries. The rural transport systems require as much attention from transport planners as the inter-urban transport (Tolley & Turton, 1995). An adequate access to social services, such as medical and health services; proper nutritional care for the young; and education facilities to peasants, would determine to a large extent the improvement of social and economic welfare of the rural population (Howe & Richards (1984). These are also important determinants to ensure the continued self-sustaining momentum of the rural development efforts (Odoki et al., 2001). This can be improved only when the transport infrastructure is developed. Due to the lack of transport accessibility, basic goods and services do not reach to the majority of the rural population. This issue is more relevant in hilly regions of a developing country. With hilly and mountainous topography, better roads and optimal facility locations reduce isolation and economic vulnerability of rural residents. Enhancement of transport accessibility to settlements and various public facilities is important for the economic survival and welfare of rural communities.

In case of Nepal, the majority of the population is concentrated in mountainous hills of rural areas. The public facilities for the residents are scattered in different settlements. Many settlements of rural areas are not connected to the national road network due to the absence of road connectivity. It is difficult to get goods and public services and to participate in the economic and social activities because of the poor road connectivity, resulting in low quality of life. This has been happening due to lack of development of rural roads network covering the hill settlements and public facilities. The rural infrastructures which have been developed and are underdevelopment also have quality issues. A study (DoLIDAR, 2004) shows that

Rural Engineering Infrastructures Design and Public Facility Locations only 30% of Nepal is accessible by roads. More than 39% percent of the population in the hills is out of reach to roads within 4-hours walk. The road networks are mostly developed in plain regions and in few parts of hilly regions. Hence, there is a need to extend and develop the rural road networks particularly in the hilly regions of Nepal to integrate public facilities and settlements, connecting rural residents to the national network.

One of the main constraints in the development of rural infrastructure is the lack of sufficient funds in developing countries. Apart from the limited funds to build rural infrastructures (roads, water supply, electricity, telecommunication network) and public facilities, the lack of proper planning methodologies for development, improvement and management of rural infrastructures is also a major problem. Optimal use of available funds is a necessity and may help to develop and improve the present situation.

A research on the planning of rural infrastructures in a comprehensive and integrated manner is a dire need for rural development. However, the major life line infrastructure in rural areas of developing countries is rural roads and also, vital for development and operations of other hard and soft infrastructures. In this way, the topic of this work is envisaged and devoted to a planning methodology for rural road networks in hilly regions that considers the public facilities location and the rural road networks simultaneously.

1.2 Objectives

The main objective of this work is to investigate a rural infrastructure planning methodology considering connectivity to public facility locations.

Based on this objective, the following specific objectives are to be obtained:

 find a planning methodology to locate nodal points for rural infrastructure networks in rural areas,

 find a planning methodology to define a rural infrastructure network, and

 develop models that optimize rural road networks considering public facilities.

There are many works that extensively studied the development of infrastructure in the past. They were however studied independently without consideration of the others. Often, infrastructures have impact on each other. For example, location of facilities, both private and public, in order to serve residents, are constrained by the structure of the designed transportation network. When the network is designed improperly, residents get poor service

even when facilities are optimally located. As several evidences show there is significant interaction of the network with facility location, it is meaningful to determine the network design and facility locations simultaneously (Daskin and Owen, 1999; Melkote and Daskin, 2001). The study of these two issues together would assist decision makers on how to make an integrated choice, effectively, under limited fund constraints, namely, build schools, expand hospitals, or improve road links (Daskin and Owen, 1999). Therefore, it is important to investigate rural road network models where rural road networks are optimally designed considering existing and new public facility locations to achieve minimum cost comprising construction and operation costs.

Basically, the rural infrastructure planning methodology will be developed based on the rural road networks. This works aims to explore road network patterns in hilly regions in order to cover most of rural settlements and public facilities. A number of case studies will be conducted to explore the network pattern. The applicability and validity of the proposed models will be tested in a real network considering financial and geographic constraints. Furthermore, the application of the developed methodology may be adoptable to the development of rural water supply distribution networks, rural electrification networks, and telecommunication line distribution networks in rural areas.

1.3 Outline

This thesis is organized in seven chapters. A brief introduction and general description of the studies made in this thesis is presented in Chapter 1. General background, the underlying objectives, and the outline of the thesis are described in this chapter.

In Chapter 2, existing rural road models is reviewed from the literature as well as topographical condition of rural areas. Basic concepts of rural road planning are presented in this chapter. The concepts so far developed are found for plain areas. Also, in this chapter the covering aspects of the rural roads are addressed. This concept has been used to develop the proposed rural road network model.

Development of rural roads in hilly regions of Nepal with local conditions is addressed in Chapter 3. The five zone mountain model is reviewed in the chapter in the context of rural road development. Route location and rural road alignment is also discussed.

Rural Engineering Infrastructures Design and Public Facility Locations

Covering based rural road network is presented in Chapter 4. The shortcomings of the existing methods have been addressed in this chapter. A new model for rural road planning, the covering based rural road network model, is proposed in the context of hilly regions. Public facilities (e.g. health centres, schools, and rural markets) have been considered in the study. The model is tested in the road network of 15 Village Development Centres (VDCs) in hilly region of Gorkha district in Nepal. The linkage pattern of rural roads in hilly regions, the backbone and branch (BB) network, one of the outcomes of the study has been presented in this chapter. The application of the methodology developed in this chapter can be extended to other rural engineering infrastructures, such as, development of rural water supply distribution network, rural electrification network, and telecommunication line distribution network in rural areas.

Rural road optimisation models are presented in Chapter 5. A total of four models for rural road network optimisation are proposed. The first model Rural Road Network Model (RRNM-1) is introduced for upgrading of rural road network in plain or hilly regions. The second model RRNM-2 is a general purpose rural road optimisation model for new networks which can be in both plain and hilly areas. The third model RRNM-3 is introduced for upgrading rural road network links in hilly regions and core networks in plain areas. The fourth model RRNM-4 is introduced for new rural road network in hilly regions and core networks in plain areas. Different options of road surface (e.g. earthen, gravel, and asphalt) have been considered in the models RRNM-1 and RRNM-3. The network models have been tested in the road network considered in Chapter 4. Four prioritisation procedures have been introduced for the selection of rural roads links for intervention. An extensive study has been conducted on the applicability of the models with the prioritisation methods.

A multi-objective analysis of the rural road network has been introduced in Chapter 6. A Multi-objective Rural Road Network Model is proposed for the upgrade of rural road networks. The model is an extension to model RRNM-1 and model RRNM-3 developed in Chapter 5. It is a general model and can also consider BB network for hilly regions. The interaction between decision makers (DM) with her/his preference of decision and Pareto optimal solutions has been presented in this chapter.

Main conclusions are drawn in chapter 7, summarising the main findings of each chapter. Moreover, limitations and future research directions are also presented.

Chapter 2

Rural Road Network Problems

2.1 Introduction

The development of rural roads in developing countries has been increasingly realized by policy makers. For the systematic development of rural roads, some rural road planning models have bean used. There is a rich body of literature on transport network models, particularly focusing on urban problems. Hence, there are many advanced models for developments and improvement of urban transport networks. The urban transportation network planning models are mainly oriented towards choosing improvements or additions to an existing network, in order to reduce traffic congestion, energy consumption, and pollution control (Abdulaal & LeBlanc, 1978). Unlike urban transportation, rural transportation mainly deals with providing connectivity/accessibility to local settlements. As it is still in its developing phases, few papers deal with the subject of rural road network planning and development.

Transport for rural settlements typically encompasses the movement of rural people and their goods to meet their domestic, economic and social needs. This transport can be made by any means, along tracks, paths and roads. A research carried out by the World Bank and International Labour Organization (ILO) shows that transport in rural areas is carried out mostly on foot or with the aid of intermediate means of transport (IMT) (Edmonds et al. 1994). But, these people are generally isolated from the national network due to the absence of connectivity by a road to the main network. As a result, they have no or limited access to goods and services due to the absence or poor quality of physical access (transport) infrastructures.

The rural settlements are largely scattered in hilly regions mainly due to topographical

Rural Engineering Infrastructures Design and Public Facility Locations conditions. In such cases, connecting each and every settlements and facilities is impossible due to local conditions and the lack of resources. Therefore, the accessibility to the rural hill areas has to be defined in a different sense from the general term accessibility. The ground situation in the area is that the settlements and the facilities can be covered only within a specified distance from a road. Hence, the accessibility in those regions is to be understood in terms of coverage. This issue is emphasized in this study and the existing planning and development methods and models are reviewed on this basis.

The simplest approach to rural road planning is prioritisation of settlements based on their population and socioeconomic characteristics, and connecting them with the shortest road link. Most of the approaches are based on minimal spanning tree concept; inter settlement interaction approach, accessibility criteria, etc. These are said to be most appropriate and scientific approaches to rural road planning. Plenty of researches (e.g. Magnanti & Wong, 1984) consider road network design problem as a special case of network design problem (NDP). However, few works focus on rural road network developed for rural areas.

The following sections review the existing methods/models which deal with rural road network development problems. The relevant concepts and methods to this study are briefly discussed. The shortcomings in the existing models and methods are identified to the context of rural areas particularly focusing for hilly regions and proposed to address the problem in this study.

2.2 Planning methodology

In this section, some existing methodologies for rural road planning and development are reviewed. The review of the existing methodologies will give some background in order to identify some lacking issues. These issues can be incorporated in further development of methodology that will be more rational in specific contexts. The methodologies identified in literature are discussed in the following sub sections.

2.2.1 Priority Ranking (PR)

PR methods (‘Sufficiency Rating’) were used in the early 1950’s for planning maintenance and improvement of U.S. highways (Highway Research Board, 1952). This method is one of the first methods for evaluation of road links. This has been used for planning and

maintenance of highways. However, the concept has been proposed for adaptation for rural road projects (Carnemark et al., 1976).

PR is a weighted rating technique. An overall rating score Si is determined for each proposed project i by

(2.1)

Where, Wj is the weight of the j-th considered factor or characteristic; Xij is the score of the i- th project for the j-th factor; m is the number of factors. The higher the Si value, the more urgent is the project.

However, the method is complicated when benefits of projects are not independent. This is usually a case in rural road planning. The benefit in this case accrues from connection of unconnected settlements by a road and its connection with other roads rather than in monetary terms.

2.2.2 Benefit/Cost Analysis (BCA)

The conventional planning techniques in road planning consider Benefit/Cost Analysis (BCA). The BCA methodology has been adapted to rural road projects by Carnemark et al. (1976). In BCA, benefits are expressed in monetary units and compared with costs; the higher the benefit/cost ratio, the better the project. The main difficulty of BCA is the correct evaluation of all benefits in monetary units.

In areas of sparse development, the guiding principle of network planning has been to enhance savings in crop-production costs and to satisfy access needs for those farmers who will benefit from network improvements (UNCHS, 1985). This concept is known as the "producers' surplus approach". Generally, in resource-constrained developing countries, an extensive low-quality (earth or gravel-surfaced) local rural road network (farm-to-market feeder roads and farm-access roads) is preferred over high-quality roads. The approach illustrates the policy of reducing road-building cost, by providing low-quality roads, while enhancing accessibility levels for rural communities based on the benefit from the construction of rural road. This approach may be suitable for plain areas with high agricultural production. However, there are many settlements located in very low economic

Rural Engineering Infrastructures Design and Public Facility Locations potential (rural) areas and therefore it is difficult to estimate the benefit from the rural roads.

Shrestha (2003) has developed two computer-aided models for planning and prioritizing district transportation networks in Nepal for both developed and underdeveloped regions. The computer models use GIS for planning the district road network. A combination of the producer’s surplus and consumer’s surplus is used in the study. The prioritization of roads in the developed area is based on the economic net present value (ENPV), economic internal rate of return (EIRR), and the benefit cost ratio (B/C ratio); whereas the socio-economic criteria is used for underdeveloped area, supplemented with the economic analysis. In this study, most of the linkages to the rural settlements are not justified in economic grounds. Furthermore, the economic basis for selecting the rural road linkage avoids connecting the rural village settlements. This methodology is biased to choose links which connect heavily populated and economic centres.

In rural road planning, BCA also becomes more complicated when benefits of projects are not independent. Connection and accessibility are key concepts for the evaluation of rural road patterns (Oudheusden & Khan, 1987). Typically, in developing countries, a fixed budget for road development is allocated to a rural district. Hence, budget restrictions also should be considered in the evaluation of a rural road network. Usually, decision makers are expected to select the best road projects within the budget allocated.

2.2.3 Centrality index

The majority of the trips in rural areas are originated from one population centre and ended in another population centre. The centrality index can be used to assess the relative importance of settlements identified as transport nodes (Shrestha & Routray, 2002). Each settlement has different functions (service centres). The functions can be Education, Health, Business & Commerce, Industry institutions, and offices (Bank, Agriculture Service centre, Veterinary office, Post office, Telephone office, Electricity office, Cooperatives office). These functions attract the trips from other settlements hence, are included in the centrality index (DoLIDAR, 2010).

The centrality index of each settlement can be calculated as follows (Sarma, Routray & Singh, 1984; DoLIDAR, 2010):

(2.2)

Where,

th Cj = Centrality Index of the j market centre, th Wi = Weight of the j marketing functions,

th th Xij = Value of the i function (number of establishments or shops at the j market centre)

A settlement which has centres for marketing, clinics, schools and other commercial, social and welfare activities is called market centres.

The weight of a function can be obtained based on the median threshold population technique. According to the technique, the weight can be calculated as:

(2.3)

The median threshold population technique calculates the weight as follows. The forecast growth of the centrality index can be based on historical trend and opinion survey of knowledgeable persons. Also, an open ended discussion can be conducted with the informants on the development of market centres (Shrestha & Routray, 2002). Given the historical trend of urbanization pattern and evolving road networks, the prediction of urban growth can be pretty accurate. Nonetheless sometimes government institutions do not respond to the market dynamics fast enough. For example, relocation decisions of administrative offices entail serious political and social repercussions (Shrestha, 2003).

This index was also used for determining the hierarchy of the nodal points in Shrestha (2003) as network module for district road network planning and prioritisation.

2.2.4 Intensity of interaction

Settlements in a region interact among each other. If the intensity of interaction between two urban centres can be calculated, we can find the importance of a link between them. Furthermore, the hierarchy of settlements can also be fixed based on the settlement interaction. In addition to the population, the functions in a market centre play vital role to generate or attract trips. Normally educational institutions, hospitals and private clinics, wholesale shops and other industries should be included since those functions attract trips

Rural Engineering Infrastructures Design and Public Facility Locations

(Shrestha & Routray, 2002). A gravity model can be used to find the interaction between two nodal points. The population is multiplied with the centrality index. The centrality index can be considered as the weight of the population.

The distance between the urban centres plays an important role for generating trips following a distance decay function. The force of interaction between two settlements can be obtained by gravity model equation in the following form (Isard, 1960):

(2.4) Where,

Iij = Interaction between two nodal points i and j Wi = Weight/Centrality index of the node i Wj = Weight/Centrality index of the node j Pi = Population of the node i Pj = Population of the node j d = Road distance between i and j b = exponent of d

The Iij provides the preliminary indicative desire lines among the settlements. For the sake of simplicity the value of b can be considered as 1 (Shrestha & Routray, 2002).

Shrestha (2003) used Equation 2.4 to calculate the intensity of interaction between two nodal points and named it transport demand estimation model. However, the author sets the value of b as 2 in the study (Shrestha, 2003). Education, health related, commercial and industrial functions are included when calculating the index, as these functions attract trips from the hinterland settlements. In terms of trip generating capacity, the government institutions like administrative offices, district level court, and police station play an insignificant role in comparison to the other functions (Shrestha, 2003). However, from the accessibility point of view connectivity to these service/institutions may be important.

Mahendru et al. (1983, 1985) used the concept of settlement interaction, link efficiency, route efficiency, and network efficiency to generate, analyse, and evaluate alternative rural road linkage pattern. An Integrated area development approach was considered to develop the road network so that it serves the studied area in a balanced way. Gravity hypothesis was used to quantify the inter-settlement interaction based on level of socio-economic development, population, and spatial separation between settlements. Centrality score was

used as the composite index to quantify the level of socio-economic development. The interaction between two settlements was considered proportional to the difference in their centrality scores. Alternative networks were generated using various criteria like maximum link efficiency, minimum total link length, minimum total operating cost, and fully developed network. These were then compared regarding their total cost (which consisted of construction and operating costs) to arrive at the optimal network. In spite of its rational treatment of various aspects of rural road planning, there are some deficiencies in this approach. The Gravity hypothesis, used to model the hidden pattern of inter-settlement interaction, gives erroneous results when the centrality scores of interacting settlements are the same (in that case the interaction computed through the model is zero). The deterrence parameter, used in the model, was taken as the direct distance between the settlements, (Mahendru et al. 1985) and the one obtained from basic connectivity matrix (Srivastava 1989), which is not true for new road links in hilly and irregular topographical conditions.

2.2.5 Road density

In practice, road networks form a grid, and roads deviate to follow the best alignments for economical and simple construction. Roads also tend to concentrate near areas of high agricultural yield and market places. Moreover, road densities vary according to the access requirements of various crop types. Furthermore, the densities can vary depending on terrain conditions of rural areas.

Table 2.1: Road density and distance to roads (United Nations, 1979) Density (km/sq km) Average distance to road (km) Maximum distance to road (km) 0.500 0.50 1.0 0.200 1.25 2.5 0.100 2.50 5.0 0.050 5.00 10.0 0.025 10.00 20.0

UNCHS (1985) guideline has used the road density concept which is expressed as the number of kilometres of road per square kilometre to reflect the degree of difficulty of any given journey. The guidelines take it as a measure to indicate the average distance that a crop on a farm or a person travelling to a town must move before reaching a road (to obtain any mechanized mode of transportation). The concept is frequently used when planning the distance of farm-to-market roads in local-road networks. For a network in form of parallel roads, straight and evenly distributed in an area, the average distance from a road to the farms

Rural Engineering Infrastructures Design and Public Facility Locations can be as indicated in Table 2.1.

2.2.6 Accessibility Indicators (AI)

An Integrated Rural Accessibility Planning (IRAP, 2002) methodology is also being used for planning rural roads in developing countries. The IRAP is a local-level planning tool aiming to optimise the infrastructure investment on the basis of the most urgent needs of local communities (Howe, 1996). IRAP is based on the accessibility-activity approach and takes into account the access needs of households and the activities fulfilling these needs. In its basic sense, IRAP addresses household accessibility problems. It provides input to the rural accessibility planning process by the rating household need requirements for access as well rating the infrastructure on the basis of its ability to provide access. These inputs are useful to formulate strategies to reduce access problems at different budget requirements.

The IRAP is a process oriented approach that has the flexibility to solve traditionally considered transport-sector problems by either transport or non-transport means. For example, if water collection is a severe access need, the problem can be solved either by providing better footpaths or roads leading to the facility, or by bringing the water collection points closer to the users. In this way, the IRAP incorporates the mobility and sitting of service into the same framework. The main features of the IRAP framework are (Howe 1996): - It is needs-based in the sense that it covers all aspects of household needs - It is comprehensive in the sense of its ability to suggest solutions to the access problems, not just transport problems - It is sustainable because it is intended to be managed by local-level participation.

The IRAP methodology is based on household needs for access (Edmonds 1998, Dixon- Fyle 1998). The methodology starts by obtaining household data concerning accessibility for services like water and firewood collection, healthcare, education, etc. Various indicators are used to define the access needs for these services. Time or distance to the facilities offering these services is usually the main. The IRAP methodology provides two main outputs, the accessibility indicators and the accessibility profile (Figure 2.1), as explained as follows.

The first output of the household data collection exercise within the IRAP framework is the development of Accessibility Indicators (AI) for each of the access needs. AI is given as

(IRAP, 2002):

1. Data Collection 2. Data Encoding 3. Preparation of: Accessibility profiles Accessibility indicators Accessibility maps

8. Monitoring & The AP Cycle 4. Identification & Evaluation Prioritisation of Access problems

7. Project 6. Plan formulation 5. Defining Objectives and Implementation Targets

Figure 2.1: The accessibility planning cycle (Dixon-Fyle, 1998).

AI = number of households × time (or distance) to the facility (2.5)

Table 2.2 Examples of Accessibility Indicators (AI) (Edmonds, 1998) VILLAGE DISTRICT NATIONAL Water Number of %age of households with no %age of households with households × direct access to a water no direct access to a water Average collection supply × Average collection supply × Average time in the dry time in dry season collection time in the dry season season Health Number of %age of households in %age of households living households × time to villages with no health in villages with no health a health centre or centre × Average time to a centre × Average time to a clinic health centre health centre Education Number of primary %age of households with no %age of households with school age children × primary school in their no primary school in their time taken to get to village × Pupil/classroom village × Pupil/classroom the school ratio (or Pupil/teacher ratio) ratio (or Pupil/teacher ratio)

In the above equation, the number of households is representative of the population affected. The time (or distance) to the facility is representative of the burden to be borne by the population. The higher the value of AI the least will be the accessibility of a particular facility to a given population. In this way, the AI defines, in empirical terms, the inaccessibility of the

Rural Engineering Infrastructures Design and Public Facility Locations activities. Parameters other than number of households can also be used in the AI. Table 2.2 explains the range and importance of the parameters defining AI (IRAP, 2002). It contains the definition of AI at various levels of rural accessibility planning.

From Table 2.2 it is clear that the definition of AI is based on two factors: a) the affected population; for example households or number of school age children b) the burden; for example time taken to the facility or the distance to be covered

In this way, the AI defines two possible ways of solving the accessibility problem: - by reducing the size of the affected population; this can be done by improving the capacity of the facilities (increasing number of classes, etc.) - by reducing the distance or time for access; this can be done by improving the infrastructure (provision of roads) or enhancing supply of transport vehicles (IMT, NMT, etc.) The accessibility indicators AI are used to develop accessibility profiles of the areas covered in the IRAP study. These are the maps of the whole area under study redrawn to highlight the access problem of locations (for example villages) with reference to the burden they face. The accessibility profiles act as the planning tool in guiding the decision-makers regarding the best use of the resources.

Integrated Rural Accessibility Planning (IRAP, 2002) is a local level planning tool to prioritise rural infrastructure investments by looking at the access of rural household to basic services and facilities such as health services, schools, markets, and water supplies based on AI. This is a general method for a village level planning works of infrastructures. It is important to note that rural roads are one of the components only in planning exercise. This method is suitable for very low volume roads and village tracks. It requires heavy data collection and is usually very time consuming. However, presently, this method has been applied to many projects in developing countries in Asia such as Cambodia, Laos, Thailand, Philippines, Nepal, India, and Indonesia.

2.2.7 Costs

The costs associated with each link/network provide basis for comparison and selection of the link/network to upgrade/choose (Kumar & Tilloston, 1985; Makarchi & Tilloston, 1991). Each link/network will provide different levels of construction and travel costs. The optimum

network is the one for which the total cost, i.e. construction plus travel costs, are minimum (Kumar & Tilloston, 1985).

In Kumar and Tilloston (1985), construction costs have been taken as proportional to the lengths of links. Similarly, travel costs have been taken as proportional to a factor called "person-kilometre (km)". The person-km for a village node is defined as the product of population connected by the village node to its root node and the distance between that village node and its root node (root nodes are generally the settlements connected by a road or a point in the road). The factor has the following assumptions:

 The number of trips generated by a village node is proportional to its population  The travel costs are proportional to the distance travelled.

Thus the factor, person-km (multiplication of population and the distance travelled), will be proportional to the total travel costs.

In a rural road planning model, Makarchi and Tillotson (1991) also divided cost into two types. One type has been called construction costs and other type of cost has been called travel costs. The construction costs can be estimated with reasonable accuracy. However, the travel costs cannot be estimated with a satisfactory degree of accuracy. In a district of reasonably uniform topography, it seems reasonable to assume that the construction costs will be proportional to the lengths of the links (Makarchi & Tilloston, 1991). The travel costs are likely to be proportional to (i) the number of people connected by the link, and (ii) the distance travelled through the link to reach the destination (Makarchi & Tilloston, 1991). It is therefore argued that whatever the travel costs may be, they will be proportional to a factor called 'person-km' which is defined as the product of population connected by the link, and the distance between the village and the destination through the link, as defined by Kumar and Tilloston (1985).

These methodologies can be applied when the population of the settlements and the linear distance between them are known. This has a special advantage for rural areas where this simple data is often easily available. This method can still be used with actual costs where these are known.

Rural Engineering Infrastructures Design and Public Facility Locations

2.2.8 Accessibility index

In developing countries, the system of roads connecting rural settlements may be new construction, the up-gradating of existing paths/tracks and fair weather roads. Due to budget constraint, all these cannot be built/upgraded to a desired level. Therefore, there is a need to select the most efficient network which provides minimum basic access to all the settlements. The road links are required to be evaluated for their efficiency in terms of the level of accessibility provided. The accessibility provided by a road link is inversely proportional to the total amount of travel distance required for satisfying the missing functions in the settlement. The total travel can be computed by identifying various missing functions, per capita trips for these functions, location of functions in the region, length of connecting road link and the population of the settlement. Total travel through the connecting road link is the summation of travel, in terms of person-km, for various missing functions in the unconnected settlement. The lesser the amount of travel required, the more accessible will be the settlement (Singh, 2010).

Using this procedure, the road link offering maximum accessibility for each unconnected settlement can be determined. The developed network (based on person-km as the only criteria) seems to evolve maximum accessibility connectivity pattern for unconnected settlements. Settlements should be connected one at a time by considering and evaluating all the possible road link options in a given order. If this order is not taken into account then the possibility of inter connectivity among various unconnected settlements gets ignored. An indicator of accessibility is introduced in Singh (2010) which considers the settlements should be connected one at a time considering and evaluating all the possible road link options in an orderly manner. The indicator of accessibility can be obtained by dividing the total person- km of travel with the population of the unconnected settlement. The indicator now represents the average person lead for an unconnected settlement to access all its missing functions through the connecting road link. It can be used to compare the accessibility offered by various connecting road link options and the one which offers the maximum accessibility should be chosen first in the process of network development. Singh (2010) has formulated the index of accessibility as follows.

In rural road planning, the road links are added to the existing network of road system so that each unconnected settlement gets connected to at least one road link. The connecting road link, emanating from the unconnected settlement, either joins a nearby

connected settlement or any intermediate node on the links of the existing road network. Therefore, the entire system of nodes can be divided into two categories: unconnected nodes (settlements) and connected nodes (i.e. connected settlements and intermediate nodes on the links of the existing road network). A link option is a road link between the unconnected and connected nodes (Figure 2.2). The unconnected settlements can be connected by upgrading the existing paths, tracks or un-surfaced roads to connected settlements.

If the total number of connected nodes in the existing road network is m then, theoretically, there can be these many link options offering connectivity to each unconnected settlement. However, many of these link options will be redundant as they will be intersecting the existing road network at many points and excessively large in length. Among these link options t h e one which offers maximum accessibility to the unconnected settlement should be chosen. The accessibility of a link option can be calculated by identifying the missing functions (services) k in the unconnected settlement, the total travel requirement of the unconnected settlement PK in terms of person-km to satisfy all its missing functions and the length of new road link option d as given below.

Existing road network

Intermediate Connected settlement nodes of link

m2 j m3 Intermediate m 1 nodes of link

Existing road Link options network

i Unconnected settlement

Figure 2.2: Link options from unconnected settlement (Singh, 2010).

(l) The total person–km of travel i.e. PKi , for an unconnected settlement i to access missing functions k through the link option l can be calculated from Equation (2.6).

(2.6)

k Here, Ti is the total number of trips originating from unconnected settlement i to access

Rural Engineering Infrastructures Design and Public Facility Locations

k(l) missing function k and di is the distance between the unconnected settlements i to the nearest function k through the link option l.

k(l) The di can be calculated using Equation (2.7).

(2.7)

l Here, dim is the length of link option l (i.e. the ground distance between the unconnected k settlement l and connected node m on the network) and dmj is the minimum distance between node m and the nearest node j on the network where the function k is present. If the function k k is present at node m then dmj will be zero.

l The accessibility index of link option l (i.e. Ai ) is calculated by dividing the total person-

(l) kilometre PKi with the population of the settlement Pi as given in Equation (2.8).

(2.8)

Here, Pi is the population of the unconnected settlement i .

It is assumed that the unconnected settlement access the first nearest function in its l neighbourhood, through the link option, to satisfy its missing functions. Higher value of Ai indicates lower accessibility of link option l, and vice-versa.

l In a physical sense, Ai represents the average distance the population has to cross to access all the missing functions in the unconnected settlement when it gets connected through the road link l. The link option with minimum index value (i.e. maximum accessibility) is the most preferred choice in developing the maximum accessibility network.

k The estimation of accessibility index, using Equation (2.8), requires the determination of Ti

k(l) k and di . Ti can be estimated by multiplying the settlement size P with the appropriate trip rate tk for each function, as given in Equation (2.9).

(2.9)

Here, the settlement size Pi can be the settlement’s i population, number of households etc. The trip rate tk represents trips per unit settlement size for missing

function k in the unconnected settlement.

For rural areas, appropriate trip rate models can be developed by correlating it with the socio-economic factors. The model form can be represented as shown in Equation (2.10).

(2.10) In absence of any such model, tk can be estimated for a few of the functions. For example, if the entire rural population is to be provided education up to high school standard by the end of planning horizon, then the trip rates to primary, middle and high school will be the proportion of the school going population in their corresponding age groups. However, the trip rates for marketing, health purpose etc will depend on the expected level of development in the area. These trip rates will be less in underdeveloped areas and more for the developed areas.

k(l) k l k The term di , has two components i.e. dmj and dim . Here, the term dmj can be estimated quite easily, as the location of facilities on the existing road network is known. The l other term dim , which is the length of new link option, will depend on its actual alignment on the ground. This alignment need not always to be a direct one and will primarily depend on the topography of the area. Topographic features such as water bodies, hills, costly structures, land type etc may cause deviation from straight alignment. Even for the network planning of a small number of unconnected settlements there will be many possible road link options and their alignment, depending on topography of the area. These link options needs to be analysed for their alignment, length, construction cost etc so that the least cost options could be selected (Singh, 2010). Furthermore, there is need of huge data for many functions to determine accessibility index of each link.

2.2.9 Facility based approach

In addition to market centres, in many rural areas additional access may be needed to various facilities like health, education, banks and administrative headquarters. To incorporate the access to these facilities, Kumar and Kumar (1999) have developed a facility based model to consider accessibility to those facilities in addition to the market centres. The model considers access of the village to market centres and some user friendly facility centres. About 93 percent of the rural trips are terminated either at the nearest market centre or at the nearest education facility. Thus, if road connections are provided to the nearest market centres and

Rural Engineering Infrastructures Design and Public Facility Locations nearest education centres, then about 93 percent of the travel demands of the rural population can be met (Kumar & Kumar, 1999).

2.2.10 Traffic Flow

The conventional transport planning process is based on the principle of subdividing the study area into smaller zones and subzones and studying the inter-zonal trip frequencies through OD matrix to decide linkage needs between various origins and destinations. This method may not be suitable for planning rural roads. Even planning rural roads at the district level, there will be around 1500 to 2000 rural settlements and it will require enormous amount of resource to collect trip frequency data for all the settlements to form the O-D matrix. Even if, the O-D pattern is made available, the observed trip frequencies will be very low and that would hardly justify the links in a network. The use of such data will be only to fix the relative priorities of the linkages (Mahendru et al. 1985). This shows that the use of conventional methods is not practical.

Furthermore, it is very difficult to estimate the traffic that will be served by a rural road involving construction of bridges and major upgrade. Population is considered as a good proxy for traffic in rural areas because traffic data generally is difficult to get (Kumar & Kumar, 1999).

Most of the literature on transport network design is concerned with the choice of improvements to, or additions of, links to an existing network either to reduce traffic congestion, energy consumption, pollution or other appropriate objective. However, the network design problem for rural road network in developing countries is somewhat different from that of developed countries. The networks are being planned around existing main roads and very few rural roads may still exist. Furthermore, in the rural areas of developing countries traffic flows are low and congestion may be assumed to have no effect on travel time (Makarchi & Tilloston, 1991). The specific objective is to connect all villages to the network regardless of their sizes (Makarchi & Tilloston, 1991).

A traffic simulation model was used by Athanasenas (1997) to evaluate rural road network design and alternative rural road investment strategies in the United States. An approach for cost-effective rural road management was identified by examining both deterministic and probabilistic traffic simulation models. The authors find difficulty in acquiring traffic data from the rural settlements and an estimation of trip generation from the rural villages.

Typically, acquiring traffic data and analysis is very difficult for rural areas and, moreover, the output of the effort is also less significant. Hence, rural road planning models circumvent this by using population (Kumar & Kumar, 1999) or person-km (Kumar & Tilloston, 1985; Makarchi & Tilloston, 1991; Singh, 2010).

2.3 Rural road network generation

One of the first works in rural road network generation is due to Swaminathan et al. (1982) which develop a system approach for rural road development by using the concept of graph theory (Figure 2.3). The market centres and main roads were considered as high- intensity electrical charges attracting the smaller charges at the nearby villages. This model used the minimum spanning tree (MST) for connecting the settlements to existing nearby roads or to the nearest market. In this model, weight was calculated for different alternative road connections for a village by using the gravity model to develop a complete road network plan that connects all the villages to nearby market centres by selecting links of maximum weight.

Figure 2.3: System approach to rural road development (Kumar & Kumar, 1999).

Later the guidelines prepared by UNCHS (1985) point to two main classes of network models

Rural Engineering Infrastructures Design and Public Facility Locations which can be utilized for network-building: (i) the "floating points" system where road junctions in the network are allowed to occur at any location in the plane and (ii) the "fixed point" system where junctions are confined to a finite set of locations (e.g. cities, market towns and villages). Models dealing with spanning-tree problems are particularly relevant for the latter case. A model developed by Mackinnon and Hodgson (1969), which attempts to maximize total flow in the network (estimated by gravity models) within the constraints of a given road mileage illustrates the application of this concept.

UNCHS (1985) suggested procedures for generation of network options for connectivity. Based on a set of simple evaluation criteria or indicators, options are reduced to a few which are considered for detailed engineering/economic evaluation. It also proposes to evaluate the road network by developing indicators based on graph-theoretic measure of connectivity in a network and/or gravity concept based measure of spatial accessibility. The guidelines indicate that the drawback of these measures is that they are limited to the analysis of topological properties of the network and do not deal with characteristics such as capacity, type of use and cost of construction. However, the procedure aims to identify the most accessible routes between settlements.

Kumar and Tilloston (1985) proposed the rural road network planning methodology based on minimization of total cost, which consisted of construction and travel costs. In this methodology, alternative networks are generated from a set of predetermined road links by providing connectivity to the rural settlements with different link options. The optimum network was selected as the one with minimum construction costs, which was generated using the MST. The model generates rural road network plans by providing an all weather road connection from each village to nearby main roads or market centre at the least cost. For providing road connections to the villages, the optimal rural road network is generated by minimisation of total transportation cost linking a pre defined set of villages, market centres, and main roads. The model can also minimise construction cost for a given level of effectiveness in the network. The model considers the accessibility provided to the villages as the benefit as a whole.

Trip generation, trip distribution and assignment are not as relevant to the planning of rural roads as is in conventional approaches to transportation planning. The necessary data neither exist nor are economically feasible to collect in rural areas. The methodology proposed by Kumar and Tilloston (1985) uses data known to be available from topographical maps,

published census data and local government departments. The aim of using this methodology in road networks planning is to produce a basic rural road network in which each village has road access to large centres for marketing, clinics, schools and other commercial, social and welfare activities. The market centres are considered to be attractors of traffic from adjacent villages.

This methodology has a model in which various villages, market centres, main roads and rural roads are considered as a "graph". The graph consists of a set of nodes and edges. Various villages, market centres and road junctions at main road are considered as nodes and the road links inter-connecting these nodes as edges. For this model, nodes are further sub-divided into village nodes, representing various villages to be connected, and root nodes, representing the possible destinations to which village nodes could be connected. The final network emerges in the form of various rooted trees.

Each network will provide different levels of construction and travel costs. If construction costs are reduced (by selecting links of minimum length) the distances to be travelled in order to reach root nodes may become very long with consequent increasing travel costs. On the other hand, if links providing the shortest distances to root nodes are selected, then each node will obtain more or less a direct connection to the root node, consequently increasing construction costs. The optimum network is the one for which the total cost, i.e. construction plus travel costs, are minimum. While in reality different networks will generate different trip patterns, the model adopts the simplification of a fixed trip matrix.

The model firstly generates a minimum construction cost network, and through an iterative process, reduces the total cost to a minimum. The network thus achieves the optimum. For normalising construction costs and the travel costs (are assessed in kilometres and person-km respectively) the model uses a conversion factor: "RC". The significance of this factor is that one unit of link length costs the same as the overall travel costs to RC people for one kilometre of travel over the life of the project. In other words, to save one kilometre of travel by RC people in reaching the root node, an extra investment of one kilometre of link length is justified. The optimum network generated depends on the value of RC.

Oudheusden and Khan (1987) proposed a rural road planning model for developing countries. Various approaches to the problem are assessed; a new network modelling approach is proposed and a combinatorial tree design problem is formulated as the basic decision model;

Rural Engineering Infrastructures Design and Public Facility Locations exact and heuristic methods are presented in the work. In the rural areas of developing countries, many households do not have adequate access to the local market centre, nor to the most basic retail and service businesses (including occasionally small industrial enterprises which are near the local market). After heavy tropical rainfall, many hamlets and small villages become completely isolated for weeks or months. Some can only be reached by road vehicles having to make very large detours. At those times of the year circuitous routes form the only available links with the regional exchange and distribution system. It seems logical, apart from necessary maintenance on existing earth road networks, to give priority to the construction of additional all-weather roads. These all-weather roads should connect as many hamlets and villages as possible to the local market. Actual travel times over the all-weather road network can be more or less neglected. Indeed, in the rainy season, rural people are accustomed to travel longer distances. The available, but always insufficient, funds should be utilized to save as many localities as possible from seasonal inaccessibility. This type of isolation being so undesirable, travel time considerations must remain secondary until all villages can be provided with all-weather roads. An adequate quantitative objective for the generation of useful rural road patterns is therefore the maximization of the number of villages that will be connected to the local market by all-weather roads. As the size of hamlets and villages varies, it is desirable to weight the different population concentrations and to maximize the total number of households to be connected. Usually, information on household numbers is available.

According to Oudheusden and Khan (1987), criteria to differentiate between rural communities other than population are normally less relevant. Typically, these localities have no specific function or facility which can generate additional traffic. In many cases, one can be satisfied with connecting such communities to a provincial highway as such a road normally gives good access to the local market(s). Rural roads in developing countries are rarely new. Most road projects upgrade existing tracks or roads.

To formulate the rural road decision model, the model considered an initial network N which includes all existing rural road segments and all possible new segments. Population concentrations or ‘villages’ is represented by vertices V of the initial network. No population is associated with edges E. In the model, connectivity is the only issue; optimal patterns of selected new roads (together with pertinent existing segments) will form a tree T in the network N. Oudheusden and Khan, (1987) has referred this problem as the Weighted Sub-tree Problem (WSP). It can be formulated as a mixed integer linear programming problem.

WSP seems a useful decision model for rural road planning in developing countries and can be seen as a special case of the Network Design Problems (Magnanti and Wong, 1984). These problems would become relevant if money were available to connect all villages. From the initial graph, N(V, E), decision makers select a spanning tree which include all villages, but there is not enough money for construction. The tree network N must then be realized in several stages, conforming to the allocation of funds to the district.

Kumar and Kumar (1999) developed a computer based user friendly model for systematic planning of rural road networks that increases the efficiency of available resources for rural roads. The model provides an all-weather road connection from each village to nearby market centres and education centres at the least cost. It uses a heuristic approach that minimises total transportation cost of the network.

For prioritisation of rural roads, generally two broad approaches are used: (a) sufficiency rating and (b) cost-benefit analysis. The cost benefit analysis consists of various costs and benefits associated with a road having to be evaluated in the same monetary terms, which is a difficult task. The model uses a simple parameter, that is, the population served with unit investment, for prioritising rural roads. As mentioned earlier, accessibility is considered as the main benefit of the investment in rural roads. Thus, the ratio of population served by a link and its construction cost can be taken as good proxy for the expected benefit from a rural road link. The link serving higher population per unit investment receives high priority. The priority for a rural road link can be calculated as follows:

(2.11)

Furthermore, in the same model, a facility based network generation method has been proposed which will be described as follows.

All the villages that are to be connected are to be considered unconnected nodes. The villages that fall on the main roads or junction of rural road links with main roads are considered as connected nodes. The roads links emanating from the connected nodes and that can be used for connecting any unconnected village are identified and their construction costs are estimated. The link having minimum construction cost among the various links emanating from the connected nodes is chosen. The chosen link is checked for the criteria of distance to a service centre. If the link does not meet the specified criteria, then further links (in the

Rural Engineering Infrastructures Design and Public Facility Locations increasing order of their construction costs) are selected and a link that satisfies the desired criteria at minimum cost is selected. The village node connected by the chosen link is included under the connected nodes.

However, some of the villages may not be connected due to lack of availability of facilities within the permissible fixed distance. In that case either new facilities are to be provided to meet the suggested criteria or the maximum distance of the particular facility is increased.

The process terminates when all the unconnected village nodes are connected to root nodes either directly or through other village nodes.

By combining the gravity model with the centrality index, and considering the existing rural transportation infrastructures as the basis, Shrestha and Routray (2002) has developed settlement based interaction models for rural road network generation (Figure 2.4) and implemented it in the Nawalparasi district of Nepal.

The nodal points and existing road network are identified first. We can identify the existing road network connecting the identified nodal points. Considering the nodal points and the road network, a shortest routes matrix for connecting different nodes in the network can be calculated. After identifying the shortest routes and locating the existing road network on a map, the missing linkages can be identified which are the candidate roads for construction or rehabilitation.

Determination of Function and Weight Preparation of Inventory of Existing to be included in the Centrality Index Roads, Tracks and Trails

Calculation of the Computation of Iij Population in Centrality Index Matrix the nodal points

Estimation of Desire lines for settlements to intersect with each other (It means eliminate the links which are obviously impracticable)

Network Generation

Figure 2.4: Transport network generation model (Shrestha & Routray, 2002).

Basically, the methods explained above are used for developed areas. There are separate

methods for developed and underdeveloped areas. However, most of the planning activities are similar to the developed areas (Shrestha, 2003, Shrestha, 1997). Generally, the underdeveloped areas have none or very few rural road links. Therefore, the basic issue in underdeveloped areas is to provide the accessibility within a reasonable time or distance.

For developing the district road networks in under developed areas based on the interaction model (Shrestha & Routray, 2002), the accessible areas (connected by rural roads) are delineated from the inaccessible areas. After delineating the accessible areas from the inaccessible areas, the gateway and hinterland nodal points are identified. The procedure of categorizing the nodal-points is similar to the developed areas. In the second stage, the gateway nodal points are connected with the nearest hinterland nodal points. The issue of shortest path may be less important in underdeveloped areas because there may be sometimes no other alternative options. Furthermore, the selection of the appropriate alignment is an important task from the engineering perspectives.

Singh (2010) has proposed rural road network planning method based on the accessibility concept and implemented using GIS technology. A new index of accessibility is designed which evaluates various link options according to their efficiency in accessing the missing functions in the unconnected settlement. This accessibility based approach of rural road planning also offers maximum benefit to the unconnected settlement in terms of access to various facilities or the main road network in a coordinated fashion by maintaining an integrated road system. New rural road links are added to existing roads in a prioritized manner. The link options can be either a completely new road alignment or the existing paths and tracks in the area.

The accessibility model takes each unconnected settlement at a time, considers all its connectivity options (i.e. connectivity with an already connected settlement or to the existing nearby road), and calculates their accessibility index. For each unconnected settlement, the link option with minimum index value (i.e. maximum accessibility) is identified. This process is repeated for all unconnected settlements. All the link options of various unconnected settlement are afterwards compared for their accessibility index values (discussed in 2.2.8). The link option, having minimum accessibility index value and its corresponding unconnected settlement, is identified. The first priority rural road link is to be added to the existing network.

Rural Engineering Infrastructures Design and Public Facility Locations

The list of connected and unconnected settlements and the existing road network is updated at this stage. The newly connected settlement now offers the service to other settlements in its neighbourhood, which can be accessed through the updated network, therefore, updating the distances from the facilities to the connected settlements.

Unconnected Update settlements

Take any unconnected settlement Link options from Connected settlement ‘l’ settlement

Distance of facility Distance of facilities from Existing road from connected node network unconnected settlement through link ‘d k’ k(l) mj options ‘di ’

Location of facility

Trip from Accessibility Index of link options for l unconnected unconnected settlement (Ai ) k settlement (Ti )

All link options No considered? No

Yes All Identify link option of min. unconnected Accessibility Index for each settlements settlement connected?

Identify link option of maximum Yes accessibility

Identify settlement to be connected

Update No All settlements No connected?

Yes

Stop

Figure 2.5: Rural road network generation using accessibility criteria (Singh, 2010).

At this stage, there are new link options between the newly connected settlement and the remaining unconnected settlements in its vicinity, which should be evaluated for their accessibility. For the remaining unconnected settlements, the link options of minimum index value (i.e. maximum accessibility) are identified. The accessibility index of these new link options is calculated and then compared with existing accessibility values of the link options for the unconnected settlements. Those unconnected settlements, which have smaller accessibility index values, are updated with the new link options and their index values. Again, the link option of lowest index value and its corresponding settlement is identified and added to the road network. This process is repeated until all the settlements get connected. The flow chart of the process explained above for rural road network generation using accessibility criteria is shown in Figure 2.5.

Wherever the generated road links matches with the existing rural roads, they overlap. It can be observed that, all the unconnected settlements got connected with only one road link, which offered maximum accessibility to the settlement. The road segments in the existing rural road network which are not important from accessing the missing functions of unconnected settlement can be identified. Moreover, it is possible to generate other type of rural road networks by modifying the link selection criteria. Construction cost can also be taken as criteria to generate the minimum construction cost rural road network.

Singh (2010) has also developed, a new method, using GIS which finds least cost road alignment between any two points based on topographic information of the area.

2.4 Solution techniques

Different authors have used different algorithms and solution techniques to solve the rural road network problem. Kumar and Tilloston, (1985) proposed an exact algorithm where village nodes are to be connected to root nodes through link options. Root nodes are considered as connected nodes of a partially constructed tree to which unconnected village nodes will eventually be connected. The nearest unconnected node to the connected nodes is selected and is connected it with a link. Then the village node is considered as a connected node to which other unconnected nodes can be connected. The process is repeated in succession for connecting the remaining unconnected nodes via links. The tree thus generated is the minimum construction cost network, requiring the minimum length of roads for connecting the village nodes to root nodes.

Rural Engineering Infrastructures Design and Public Facility Locations

The generation of a rural road network according to Kumar and Tilloston, (1985) for a particular value of RC is as follows. 1. Calculate the distance of village node from its root node (connected) and the population connected by that village node to its root node (multiplication of these two will give the person-km for that village node).

2. Now start from a village node which is connected to its root node. Alternatively, it could be connected via other possible village nodes and links. Calculate the total cost of each alternative connection for the node being connected, selecting the one that gives the least cost. 3. The selection of links is based upon the population connected by each village node and its distance from the root node. Both of these parameters change as soon as any link of the existing network is changed. Therefore, person-km of each node should bee calculated as soon as any link is replaced. 4. Repeat step (2) and (3) for all the nodes. 5. Repeat step (2) to (4), until no change occurs in the network.

In another rural road network problem, Oudheusden and Khan, (1987) has taken the rural road network problem as a WSP. For exact resolution, a special purpose algorithm of the enumerative type is required. Although the algorithm determines optimal solutions for an important range of WSP’s, and can be used as a heuristic for much larger problems, the approach is not recommended for rural road planning. The framework of rural planning requires a simple solution method which can be easily programmed on a microcomputer and even possibly be performed by manual calculations. Furthermore, the method should be appealing to planners. It should be based on principles which they can easily understand and to which they are accustomed. An exact, optimal solution for WSP is may not be required. The information needed is a small number of near-optimal network configurations which can be used as benchmark solutions for further deliberation. It seems sensible that a simple heuristic approach is a more suitable solution technique than one which guarantees optimality.

A very well known and simple heuristic for the classical 0-l Knapsack Problem (KP) (Dantzig, 1957), based on the ranking of utility/cost ratios of each project (Continuous KP solution approach) is used for WSP. Projects are added to the limit of the budget. Afterwards, the solution can possibly be improved by interchanging projects from out of the solution for those previously incorporated.

Oudheusden and Khan (1987) proposed two approaches; firstly, good solutions are determined on the basis of a quantitative network optimization model. Normally, this model incorporates (approximate) utility and cost figures which are used to compare and screen the various possibilities. Secondly, the proposed solutions can be modified by incorporating (minor) qualitative considerations. The different alternatives are often compared and discussed by a committee. In this stage, when time and expertise is available, more formal benefit/cost analysis or priority ranking can be attempted. These techniques may help to make the final selection from a few, carefully selected road patterns. It is a very common practice in developing countries.

Makarchi and Tilloston (1991) proposed two algorithms for a rural road network generation. The first algorithm finds the MST network in which exactly one link is selected from the link options for each unconnected node. They referred it as shortest spanning tree (SST). The MST network is the one which connects all the villages at minimum construction cost (i.e. minimum total length of road). The extra construction in this particular case is so small that virtually any saving in travel costs will justify this change to the obtained network. The algorithm for generating the MST network in this case divides the nodes into the connected set (initially the root nodes only) and the unconnected set.

52 53 54 55 31

29 30 32

51 28 6

2 3 33 50 27

34 4 26 7 49

24 35 8 9 25 48

14 36

23 10 11 13 22 37 47 16

12 15 17 38

21 18 19 20 39

40 45 44 43 42 41 Figure 2.6: The graph of a typical area (Makarchi & Tilloston, 1991).

Rural Engineering Infrastructures Design and Public Facility Locations

The graph of a typical area and the corresponding MST for the typical area is shown in Figure 2.6 and Figure 2.7 respectively.

52 53 54 55 31

29 30 32

51 28 6

2 3 33 50 27

34 4 26 7 49

24 35 8 9 25 48

14 36

23 10 11 13 22 37 47 16

12 15 17 38

21 18 19 20 39

40 45 44 43 42 41 Figure 2.7: The MST for the typical area (Makarchi & Tilloston, 1991).

The node of the unconnected set which is nearest to any member of the connected set using the link options is found and then taken from the unconnected set and added to the connected set, recording the link involved. The process iterates until all nodes are in the connected set, and the record of links used defines the MST.

The proxies for these costs are kilometres and person-km which are not directly comparable units, therefore, a conversion factor Lc is introduced, and this has been applied to the link lengths. Hence:

Total costs = person-kilometres + (Lc × kilometres) (2.12)

The value of Lc will determine whether any change to the network is worthwhile because it determines the trade off between construction and travel costs. A reduction in person-km is a benefit, and this has to be compared with the cost of extra kilometres. Replacement of one link by another is worthwhile only if the benefit exceeds the cost, that is, the change in

person-km exceeds Lc times the change in kilometres. It can be seen that there is a value for Lc which will determine the break-even point for each possible change. This is:

(2.13)

The factor Lc plays an important role in the second algorithm which makes changes to the SST network by considering every feasible replacement throughout the district under consideration. For each of these potential replacements the change in person-kilometres (benefits) and the change in kilometres (costs) are tabulated along with the Lc value which defines the break-even point for that replacement. This table of costs and benefits is then searched to find the highest benefit to cost ratio Lc which is available. Having established this value, the algorithm makes a second scan of the network, starting with the node closest to the destination and working to the furthest village node making substitutions whenever the substitution involves a benefit to cost ratio Lc at least as large as the maximum value found previously. At a first glance we expect just one substitution corresponding with the maximum Lc value found. However, replacing this link changes the route lengths for trips using that link and the number of trips on other links, and so further replacements may now meet the criterion, and more than one replacement may occur.

Now, a different spanning tree network is obtained and the process iterates by scanning this network exactly as before to make the next replacement(s). In each successive iteration, the value of Lc associated with each replacement falls. In principle, the process can terminate at the value for Lc which represents the true trade-off between construction costs and travel costs. However, the value is not known, and so the replacement algorithm proceeds to generate the full sequence of spanning tree networks starting with the MST and ending with the network which results if travel costs totally dominate construction costs.

The computations are linked by recursive equations. It has an objective function that minimises the total cost which is travel cost plus construction cost. The model evaluates the alternative links to unconnected villages from connected nodes (root nodes).

2.5 Multi-objective approach to the rural road network problem

Rural road construction and upgrading are generally related to economical and social issues in rural areas. Decision based on a single objective may not be realistic and the decision may not

Rural Engineering Infrastructures Design and Public Facility Locations be justified in the regional and socio-economic contexts. The problem hence may be dealt using multi-objective approaches. As follows, some works devoted to multi-objective approaches of road network planning will be presented. However, the literature on rural road network dealing with multi-objective approaches is very scarce.

Road network optimisation problems basically start from cost minimisation objective. In line with this, a model proposed in Janson et al., (1991) is based on an efficiency objective (the minimization of shipping costs). Traffic is assigned to the network according to the user- equilibrium principle. The model applies to previously selected routes and several planning periods.

An issue associated with road network optimisation is equity. Equity analysis is important and may be unavoidable. Equity concerns often influence transportation policy and planning decisions and most practitioners and decision-makers sincerely want to address these concerns. Feng and Wu (1999) proposed the basic model for highway investment planning to deal with the issues of both equity and efficiency. The model was later revised and expanded to deal with equity issues in highway investment planning (Feng and Wu, 2003). The work addresses horizontal (intraregional) and vertical (interregional) equity of the accessibility or travel cost for cities as well as the equity of budget allocation among the cities. In this study, more constraints and decision variables were added to the model to handle the exclusive and complementary properties among alternatives. In addition, adjustments for travel cost measures and objective functions are proposed to justify the horizontal and vertical equity.

As accessibility is a key factor in the quality of life and aptitude to development of regions, when maximising it, attention often must be paid to equity issues (i.e. the same level of accessibility across the regions in a territory). Spatial planning is generally indented to keep accessibility regional disparity at an acceptable level. In line with this, Antunes et al., (2003) has developed an accessibility-maximisation approach for inter-urban road network long-term planning and implemented it in an ongoing analysis of transformation of the Portuguese main road network.

Antunes et al., (2003) proposed a model which combines accessibility and equity objectives, and assumes travel demand to be elastic with regard to both trip distribution and traffic induction. Traffic is assigned to the network through an iterative all-or-nothing approach that takes into account the capacity of roads of different levels. However, the traffic congestion is

not an issue in rural road network links and a few numbers of links exist in the network in hilly regions.

Scaparra and Church, 2005 has proposed a model for rural road network design that involves two objectives while allocating a fix budget for a number of possible road projects: maximize all weather road connectivity among villages region and maximize route efficiency. The problem treated in the model is a bi-criterion optimization problem aimed at minimizing the sum of trip-weighted shortest path distances between all pairs of villages connected by all- weather roads (efficiency criterion) and maximizing the traffic flow volume provided by all- weather paved roads (connectivity criterion). The model seems suitable for plain areas of rural regions. However, for hilly regions, the objectives are to be defined in a different way. All the villages in hilly areas can not be connected but these can be covered within a specified distance. The connectivity and the accessibility terms could be defined in terms of covering within a specified distance.

Santos et al., (2009) has developed a multi-objective approach to long-term interurban multilevel road network planning. In addition to the efficiency objectives, the approach takes into account robustness and equity objectives. For achieving the objectives, two types of action have been proposed to be performed: the construction of a new road of a given level; and the upgrading of an existing road to a higher level. There is a strong need to upgrade rural road links to deliver goods and services in rural areas with minimum service level. The service levels are generally a single lane earthen road which needs to be upgraded with gravel or asphalt surfaces. Different road surface options are considered for improvement of rural road network in Heng et al. (2006). This kind of issue has rarely been handled in other works through optimization-based network planning models.

The other works related with multi-objective approaches used in road networks are the works by Friesz et al. (1993) and Tzeng and Tsaur (1997). They considered user costs and construction costs as simultaneous minimization objectives. The former also took into account the minimization of travel distance and the minimization of property expropriation. Ukkusuri et al., (2007) considered a robustness objective in addition to an efficiency objective (travel time minimization), and Cantarella and Vitetta (2006) considered environmental objectives (minimization of carbon monoxide emissions).

Rural Engineering Infrastructures Design and Public Facility Locations

Almost all of the works on road network problems addressing multi-objective issues are for highways. In case of rural road network development in rural areas, similar objectives may be relevant. However, the objectives related with connectivity and cost may be more relevant than the others.

2.6 Discussion

Although different models and methodologies have been developed by different authors for addressing rural road problems, they have some limitation to use in specific contexts. The following discussion will identify the limitations of the existing models and find a possible way of addressing the problem in a rational way.

The guideline (UNCHS, 1985) is more focused on agricultural development aspects. However, the concept of using spanning tree has been considered in the guideline. The concept has been extensively used for road network planning in many works. The density of road and distance to roads can be a good basis for plain areas. However for hill areas, the guideline would not be practical. In hill areas, provision of connectivity/accessibility in terms of covering may be more important than the access to the agricultural land.

The model developed by Kumar and Tilloston (1985) operates with the simple data of population and linear distances between the villages which can be very relevant to a study addressing the rural road network planning in hilly regions of a rural area. It gives useful information on relative construction and travel costs based on length of a link and population connected by the link. Person-km has been introduced to take in account travel costs in a link which could be a basis for selecting the optimum rural road network.

Oudheusden and Khan (1987) proposed quantitative and qualitative approaches which exist in decision making and can not be ignored the both. Based on these approaches, a WSP decision model was introduced to enable optimization of all-weather access to a local market or to a provincial road network, under budget constraint. This is a practical concept for many rural road situations in developing countries where funds are insufficient to connect all villages by roads.

A rural road network model proposed by Makarchi and Tilloston (1991) connects every village to the surrounding road network and which minimises the sum of the construction costs and the travel costs. However, they realised that the problem is complicated by the

lack of data on travel costs. As in Kumar and Tilloston (1985), the concept of person-km is utilised to take effect of travel costs. Connecting all the villages in the context of hilly regions may not be realistic.

In a user friendly rural road planning model, Kumar and Kumar (1999) has proposed a simple parameter to evaluate road links, the population served with unit investment. This approach is very simple and data can be collected easily. The link serving higher population per unit investment receives higher priority during evaluation. This can be a relevant parameter in this study also. Further, Kumar and Kumar (1999) has suggested road connections from each village to nearby market centres and education facilities at least cost as 93 percent of the rural trips are terminated either at the nearest market centres or at the nearest education facility. Identification of nodal points for a rural road network in rural areas is a difficult task as all the villages can not be connected by rural road links. This can be also a good basis for identification of nodal points for a rural road network in rural areas. Hence, this can be a related work to this study.

The IRAP methodology (IRAP, 2002) is useful to collect data for planning works in small areas. However, AI can be a useful tool for prioritisation of road links. Information is collected in settlement level. For a regional level planning, data from settlement level may not be relevant and could be a huge. The IRAP method may be suitable for VDC level transport planning based on household information. The method requires a huge volume of data which is time consuming and costly. It is not transport only method. Transport is the one of the component of IRAP process. It is highly participatory approach which may not be practical for a regional level planning. However, presently, this method has been applied to many projects in developing countries in Asia such as Cambodia, Laos, Thailand, Philippines, Nepal, India, and Indonesia.

In settlement based interaction model for rural road network planning (Shrestha & Routray, 2002); the central places and existing roads, tracks and trails are the basis for the rural road networking. The missing linkages can be identified based on present and potential nodal points and existing links and estimation of the transport demand by establishing relationship with centrality index and intensity of interaction in this method.

The method follows a participatory approach for rural road planning. The interaction between local governments (i.e. DDC in case of Nepal) is essential as the DDC endorses the plan in

Rural Engineering Infrastructures Design and Public Facility Locations final. The method seems a practical and participatory. However, how to identify the rural road nodal points in rural areas is not clear. The method is more focused on market centred approach. In rural areas, basically in hill areas, the connectivity/accessibility to the settlements and the service centres is more important. Furthermore, this method requires a heavy data collection to calculate centrality index of a nodal point.

The GIS based rural road network model (Singh, 2010) is based on accessibility concept and generates connectivity pattern for unconnected settlements based on travel costs in terms of person-km. The unconnected settlements need connectivity with at least one all weather road type to the existing regional roads so that it can have access to all its missing functions. This can be a very useful concept for rural road network planning. However, this method also requires huge data from settlements for each function (service) to calculate an index of accessibility accessing the missing functions in the unconnected settlement.

Most of the rural roads links can not be justified based on the conventional economic models such as BCA, ENPV, and EIRR. It is the most common problem in evaluation of rural roads in rural areas. However, there is need of connecting settlements in these areas by rural roads and rural roads are one of the most priority development activities in the rural areas. Hence, an alternative assessment tools is necessary to evaluate and develop rural road network in the rural areas considering social factors. Hence, connectivity/accessibility based rural road network model has been developed by different authors (Kumar & Tilloston, 1985; Oudheusden & Khan, 1987; Makarchi &Tilloston, 1991; Kumar & Kumar, 1999; IRAP, 2002; Shrestha & Routray, 2002; Singh, 2010) to address the problem of economic justification and formed bases for the development of rural road network in rural areas. Still there are some problems to adopt the models although they were developed for addressing the rural road network problems in rural areas. All of the models developed to address the problem of economic justification. These models can be applicable for plain areas. However, the problem may not be suitable for hilly areas due to topography and the settlement patterns in the hilly areas as the settlements and the public facilities are sparsely located in rural areas. This characteristic of settlement is more complicated in case of hilly regions. Hence, these models are also not sufficient to address the rural road network generation in hilly regions of rural areas.

Some models (Makarchi &Tilloston, (1991); Kumar & Kumar, 1999; Singh, 2010) propose the connection of all settlements in rural areas. However, connecting every settlement in a

rural area is not possible practically due to technical and the financial constraints even in plain areas. However, the settlements in remote areas should have access to the facilities of basic goods and services as delivery of services and goods to these settlements is a difficult task for local governments and local residents in these regions of the developing countries. This problem is more by many folds in hilly regions.

Some model requires collection of huge volume of data for economic evaluation of road links which is costly and time consuming but the outcome of the effort may not be so significant in case of rural roads. Prioritising the rural road links based on economic models is rarely justified (Shrestha, 2003). Even for some models (e.g. Singh, 2010) which addresses the rural road network problem based social factors need huge amount of data which may not be much useful in case of hilly regions.

Models based on agriculture potentiality (e.g. UNCHS, 1985) may also not be useful for prioritising the rural road links because agricultural potentials in rural areas, particularly in hilly regions are generally low. The models based on market centres (Kumar & Tilloston, 1985; Shrestha & Routray, 2002) may also not be effective for prioritisation of rural roads links. The prioritisation based on the market centre approach can discard many settlements from the access to roads.

Mostly, in developing countries, a fixed budget for road development is allocated to a rural district which restricts the budget restrictions. Hence, the implications of budget restrictions also should be considered in evaluation of a rural road network (Oudheusden & Khan, 1987). Decision makers have to select the best road projects within the budget allocated. The system of roads connecting rural settlements may be new construction, the up-gradating of existing paths/tracks and fair weather roads. Due to budget constraint, all these cannot be upgraded to a desired level. Hence, optimizations of access to rural settlements are necessary so that maximum benefits can be achieved in minimum costs within allocated budget. For example, models for rural roads in line with this concept are WSP decision model (Oudheusden & Khan, 1987) and improvement of rural road network with different surface level (Heng et. al, 2006). Further, rural road network decision model is a multi-objective problem (Scaparra & Church, 2005). This is a very relevant concept for this study.

From above discussion, we can say that rural road problems should be dealt more with social indicators rather than economic indicators. The primary social indicator is population (of settlements) covered by a rural road link. One of the advantages using this indicator is that

Rural Engineering Infrastructures Design and Public Facility Locations the population data can be easily obtained from census data. In line with this, populations covered by a road link (Kumar & Kumar, 1999) can be taken as the major indicator to be considered to take accounts the socio-economic benefits from the rural road links. The other factors can be costs (construction costs and travel costs). However, these factors can not be assessed precisely for rural areas. Hence, costs can be considered indirectly taking distances (construction cost) and the person-km (travel costs) (Kumar & Tilloston, 1985; Makarchi & Tilloston, 1991; Singh, 2010). Connectivity/accessibility can be taken as benefits from the rural roads as taken by previous models. This may be an amicable way of handling rural road problems.

Furthermore, it is clear that all the settlements in rural areas can not be connected by rural roads due to spatial and financial constraints. However, these settlements should have access to roads. Although all the settlements can not be connected, a rural road network can reach near to the settlements. Hence, connectivity/accessibility to rural hill settlements in rural areas is to be defined in a different way so that the rural road network can cover all the settlements within a justifiable distance from the network. This kind of issue has rarely been addressed in existing rural road network planning models. It is a main gap identified in rural road network generation in literature. The rural road network problems can be addressed in terms of coverage of settlements (population) and public facilities by links. This can be a realistic and practical way of solution of the problems.

2.7 Summary

Mostly, the rural road network models address the problems for plain areas. The problems of rural road network in hilly regions of rural areas are different from the problems in plain areas. The settlements and public facilities in hilly areas are sparsely populated. It is not practical and possible to connect all the settlements and public facilities by roads in rural areas.

A possible way of solution of this problem is definition of rural road network considering coverage of maximum settlements and public facilities within a specified distance. For this, nodal points in a network need to be identified so that the most of the settlements and public facilities can be covered. We need to develop basis for identification of nodal points as none of the existing methods discussed above has given the firm basis even for plain areas. Then,

the identified nodal points (obligatory points) can be connected by rural road links. This will form a covering based rural road network.

The prioritisation process of rural road network should be based on simple social indicators rather than complicated economic indicators focusing on the connectivity and accessibility of the settlements and the public services.

Maximisation of covering of settlements (population) and public facilities by roads is one of the major problems in rural areas. Also, minimisation of transportation cost in the road network is an issue. We need simple and more practical models to address rural road network problems in rural areas particularly for hilly regions of rural areas.

Chapter 3

Local Conditions and Rural Road Constructions in Hilly Regions of Nepal

3.1 Introduction

The study is related to rural road development particularly in the hilly regions of rural areas of Nepal. Rural road construction in reference to local condition of Nepal is briefly presented in this chapter.

Construction of roads is generally related with geological and geotechnical conditions of regions. The extents of these features are more in the context of slope stability and related geotechnical problems commonly encountered in hilly terrain. Hence, the background to the topography, geology, and climate of different regions will be presented. The geomorphology of mountain model (Fookes et al, 1985) is described in terms of landforms and erosion processes in the context of road construction in hilly region of Nepal.

Earthquakes, volcanic activity, erosion and rainfall are important natural factors which affect road construction on steep mountain slopes because they have direct links to many aspects of geology, slope stability and drainage. The problems of road construction become more difficult with increasing severity of these factors.

The most important geotechnical engineering problems in mountain areas are related with nature of near surface rocks and soil, slope stability and drainage. Aspects of these features are briefly explained in the following headings of tectonic movement, geology, topography, climates and geography.

Rural Engineering Infrastructures Design and Public Facility Locations

In addition to technical aspects, geographical situation of settlement distribution is also an important factor needs to be considered in rural road development. Hence, this is also discussed briefly.

3.1.1 Tectonic environment

Evolution of mountain belts has been closely associated with tectonic plate boundaries. Occurrence of earthquakes in these belts indicates mountain areas are still tectonically active. Seismic activity is often the triggering agent for catastrophic erosion and wide spread slope instability and consequently, sharp increase in sediment loads of mountain streams which is an additional factor of importance to road construction. The importance of these tectonic disturbances for road construction is reflected in the overall scale of mountain relief and the complexity of rock structures produced. Rates of slope erosion are generally at a maximum in areas of high relief.

The Himalayas is the largest mountain belt of the world, which extends for a total length of about 2400 km. The Nepal Himalayas is situated in the central part of the Himalayan Arc, located between the Kumaon Himalaya in the west and the Sikkim-Bhutan Himalaya in the east, and extends about 800 km. The Nepal Himalaya has been divided into the Indo-Gangetic Plain, Sub-Himalaya (Siwalik Group), Lesser Himalaya, Higher Himalaya, and Tibetan- Tethys Himalaya from south to north in sub-tectonic units. The different major geological units are separated by almost east-west running thrust systems that pass through the entire Himalayan region. These thrusts are Indus-Tsangpo Suture, South Tibetan Detachment System, Main Central Thrust, Main Boundary Thrust and Main Frontal Thrust, from north to south (Figure 3.1)(Ganssar, 1964).

Indus River

Tibetan-Tehtys Himalaya Kashmir

INDUS - TSANGPO SUTURE Higher Himalaya MFT Scale Lesser Himalaya 0 50 km

MBT Siwaliks

Samui River MCT: Main Central Thrust Shimia MBT: Main Boundry Thrust MFT: Main Frontal Thrust

Tsangoo River MFT INDUS - TSANGPO SUTURE

MCT Gange River MBT MCT MBT Kathmandu Gange River Thimpu Gandaki River

MFT

Kouhi River Brahmaputra River

Figure 3.1: Longitudinal geological subdivision of Nepal Himalaya (Gansser, 1964).

Indo-Gangetic Plain or Terai Plain The Indo-Gangetic Plain or Terai forms the southernmost tectonic unit of the Nepal Himalaya, having elevation from 100 to 200 m from mean sea level and is composed of alluvial deposits of Pleistocene to recent in age. The average thickness of the deposits is about 1.5 km.

Sub-Himalaya (Siwalik Group) The Siwalik Group is delimited by the Main Boundary Thrust (MBT) to the north and the Main Frontal Thrust (MFT) to the south, and lies between the Lesser Himalaya and Indo- Gangetic Plain. About 6 km thick Neogene molasses sediments were accumulated into the foreland basin during middle Miocene to lower Pleistocene in age. The sediment comprises mudstone, sandstone and conglomerate.

Lesser Himalaya The Lesser Himalaya lies between the Siwalik Group to the south and the Higher Himalaya to the north. Both the southern and the northern limits of the Lesser Himalaya are represented by the thrust fault; the Main Boundary Thrust (MBT) and the Main Central Thrust (MCT), to the south and north, respectively. It is represented by thick piles of the sedimentary rocks and

Rural Engineering Infrastructures Design and Public Facility Locations low-grade metamorphic rocks, ranging from the Pre-Cambrian to Tertiary in age. Total thickness of the Lesser Himalayan rocks are exposed more than 14 km.

Higher Himalaya The Higher Himalaya is occupied by the high mountains, and lies between the Lesser Himalaya to south and the Tibetan-Tethys Himalaya to the north, which is separated by the Main Central Thrust (MCT) in the south and the South Tibetan Detachment System (STDS) in the north. The Higher Himalaya is comprised of high-grade metamorphic rocks of schist with granite bodies, pelitic gneisses and migmatites, and attains 6 to 12 km in thickness.

Tibetan-Tethys Himalaya The Tibetan-Tethys Himalaya is distributed in the northern part of the territory. The northern border of the Tethys Himalaya is represented by the fault South Tibetan Detachment System (STDS). About 10 km thick shallow marine sedimentary rocks were deposited from Cambrian to Cretaceous in age.

3.1.2 Geology

The near surface geology of the mountain belts is extremely variable and only broad observation can be made about distribution of typical rock types and structures. Tectonic upheaval from colliding plates resulted in the lateral contraction, uplift and folding of original sedimentary deposits to form the mountain ranges, followed by gravity slide processes which transported large masses of rock downslope towards the periphery of the mountain zone.

As the result of these mechanisms, two broad suites of rock types are commonly found in the mountain belts. In the central core volcanic and deep seated igneous rocks occur, mixed with the original sedimentary deposits, commonly thick shales, siltstones, and sandstones. Most of the original sedimentary rocks have been metamorphosed to varying degrees, the common results being slates, schists and gneisses with basic and intermediate lavas and pyroclassic volcanic rocks. In contrast, the periphery regions are characterised by lightly metamorphosed sedimentary rocks such as sandstones and limestones. These are often buried within or overlain by other metamorphic and igneous rocks transported from the central zone by gravity slide and nappe structures. The outcrop pattern of the rock types across a major fold mountain belt is therefore distinguished by considerable variation in lithology and structure and may be covered by a wide range of transported and in-situ residual soils.

The important engineering geological factors are the variations in rock types, structures and patterns of weathering and soil formation, and the slope erosion and instability features. The rock type may be the most important of these factors controlling slope stability on a regional scale. Brunsden et al, (1981) examined natural instability on five rock types in Nepal. They observed that gneiss that quartzite slopes were far more stable than slopes of schist, shale and phyllite. In practice, rock structure, topography and depth of weathering are rarely uniform over large areas of mountain train. However, road alignment selection according to rock types only may be impractical.

The mountains of Nepal have wide range of issues related to geological engineering. However, the problems are different in each physiographic province. Brief scenarios of engineering geological problems (Dahal and Hasegawa, 2008a) in various geomorphologic contexts are discussed below.

The Terai is made up of recent river deposits and consists of coarse sediment in the north, near to the base of Siwaliks Range, and fine in the south, near to the Indian border to Nepal. The elevation of Terai ranged from 70 m in eastern Nepal to 200 m in western Nepal with broad plain area. All rivers of Nepal drain to the Ganga River of India through the Terai. As a result, every year, Terai is facing extreme problems of floods and river bank erosion. Area near to the Siwaliks Range is also confronting problems of debris flows. Moreover, both small and large rivers have shown channel shifting nature in the last 300 years. Riverbeds in the Terai may rise at annual rates of 15 to 30 cm.

The Siwalik (Churia) Range is made up of sedimentary soft rocks such as mudstones, shale, sandstones, siltstones and conglomerates. These rocks are weak and easily disintegrable. The Upper Siwalik contains thick beds of conglomerates and they are loose and fragile. Similarly Lower Siwalik and Middle Siwalik have problem from alternating beds of mudstones and sandstone. In such alternating bands, mudstone tends to swell and can flow when saturated with water which results overhanging sandstone beds. Such overhang jointed sandstone beds easily disintegrate into blocks. Similarly, throughout Nepal, the rainfall within Churia Range is normally in the range of 2000 to 2500 mm per year. As a result, geological conditions and the climate render the Churia Range highly susceptible for landslides processes. Basically, rock failures, shallow slides and debris flows are common results of weathering process in Siwaliks.

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The Mahabharat Range belongs to the Lesser Himalayan Zone. It is the most important barrier of the monsoon clouds and it greatly influences the rainfall distribution pattern in Nepal. Almost in whole Nepal, southern face of Mahabharata Range gets extensive rainfall in comparison to Midland. The annual rainfall in Mahabharat Range area is comparatively higher and the frequency of high intensity rainfall is also high. Thus, these areas are getting extensive problem of floods, debris flows and shallow landslides.

Not only the rainfall but also geological conditions and very steep slopes play a major role to soil slips and debris flows in the Mahabharat Range. It is noticed that in the area which is made up of rocks such as limestone, dolomite marble and granites, the slopes are more stable in the Mahabharat Range. However, the area consisting of rocks such as phyllites, slates, intercalation of phyllites and quartzites render the terrain most prone to landslides.

The Midlands also belongs to the Lesser Himalayan Zone and are situated at north of the Mahabharat Range. It has a gentle topography compared to Churia and Mahabharat ranges. The slopes are also comparatively less steep than in other zones of Himalaya. Thick soil formations are found in slopes of the Midlands because of deeply weathered rocks.

Midlands is considered as rain shadow zone of the Mahabharat Range. Generally, it receives rainfall between 1000 to 2000 mm. This is the most inhabited and cultivated region in Nepal mountains.

The both Mahabharat Range and Midlands have many numbers of deep seated landslides. Many of them are still active and have slow moving creep. Most of the shallow landslides in Mahabharat Range and Midlands occur on deep seated landslides mass. These deep seated landslides are found as huge valley collapsing structures. The slip surface of such landslide has remarkable amount of clay mineral accumulation (Dahal and Hasegawa 2008b).

Basically, in lesser Himalayas, the construction of rural road is a major activity causing disturbance to the mountain slopes which are vulnerable to landslides. Hence, a proper selection of road alignment and design can reduce the vulnerability. However, such guidelines are rare to cover the slope complexity of the mountains.

3.1.3 Topography

From a geological viewpoint, the most important feature is the magnitude of relative relief and its relation to the density of system of dissection, since to a great extent this controls slope

steepness and stability. The influence of rock type and climate are also important, but the topography in which rates of uplift and denudation vary through the time of mountain building. The scheme of mountain landscape development was proposed first by Davis (1899). His system makes two assumptions, first that uplift greatly outpaces denudation until the mountain mass is tectonically stable, and second that rivers and streams are subject to two phases of activity. The first phase is one of rapid incision or down cutting while river actively excavate their channels. In the second phase down cutting is reduced when the major rivers are well adjusted to base levels of erosion and begin to develop flood plains. The river system produces dissected mountain landscape in which topography is characterized by an incising drainage network, frequent bare rock outcrops and steep valley side slopes. Beyond the limit of glacial activity these slopes are typically formed by number of near straight segments which increase in steepness and maintain their high angle to the edge of the main river valley. Once, a river forms a floodplain, slope development is largely independent of river activity and average slope angles are gradually reduced as the valley side slopes are denuded. In detail the form of mountain slope is largely controlled by different erosion of various rock types. In these high relief areas, landslides and surface water erosion are powerful erosion processes and are responsible for many of the geotechnical problems in road construction.

3.1.4 Climate

Mountain climates usually vary considerably over short distance because the effects of altitude modify the pattern of regional climate and create broadly vertical zones of climatic type. At the more local scale variations in relative relief, slope concentration and slope angles give rise to distinct micro-climates within this broader framework. Climatic factors influence the evolution of mountain slopes by controlling the relative rate of denudation. The importance of different weathering and erosion processes varies according to changes in mean annual temperature and rainfall.

At the regional scale the decrease in temperature with elevation is approximately linear but the variation of rainfall with elevation is more complex. As a general rule, rainfall increases with elevation upto certain altitudes usually between 1000 and 2000 m, but then decreases at higher altitudes. However, the effects of local topography and atmospheric conditions are also important. In the Nepal Himalaya, the most monsoon rain falls on the southern windward side of the of the foot hill ranges, increasing with altitude but sharply decreasing in the northern side of each successive range (Nayawa, 1974; Dhar & Bhattacharya, 1976). Such rain shadow

Rural Engineering Infrastructures Design and Public Facility Locations effects are common wherever mountain ranges from a barrier to rain bearing winds. It can be an advantage for a road alignment along the rain shadow slopes.

In relation to geotechnical construction problems, rainfall is usually the most important climatic index. However, the annual total is not necessarily the most important parameter. In temperate regions Radbruck-Hall and Varnes (1976) note that the frequency of slope failure increases substantially when seasonal rainfall is greater than 250 mm.

3.1.5 Geography

Nepal has area of 147181 square kilometres. The geography of Nepal is divided into three bands running the full breadth and comprising the Terai (southern plains), the Mid-Hills and the Mountains (Figure 3.2). Geography of Nepal comprises one of the most diverse climatic ranges and physical environments in the world. The altitude of the terrain varies from the Gangatic plains in Terai at 70 m to the Mount Everest at 8848 m (CBS, 2011), within a distance of 170 km. The Terai (23% of total area) is about 30 km wide and the altitude ranges from 70 m to 280 m high with fertile lowland. Then terrain slope increases rapidly from the end of Terai to the Himalayas. These slopes are the world’s steepest slopes, resulting in numerous untameable rivers, tributaries, plus countless streams separating large number of communities.

In the rugged terrain, trails criss-cross with numerous rivers. These topographic extremes are accompanied by extremes in climate from as high as 48ºC in the tropical Terai to as low as - 35ºC in the Himalayas. Melting snow in summer, compounded by very high precipitation during the monsoon from alpine altitudes further down, makes rivers swell beyond control. The hills (52% of total area) and Himalayas (25% of total area) comprise 87% of the area of the country.

Nepal has a total population of 26.5 million with 83% living in rural areas. 43% of the total population of Nepal lives in hills and 7% in mountains (CBS, 2011).

Figure 3.2: Physiographic features of Nepal (RAIDP, 2009).

Figure 3.3: Settlements and cultivated land in hill slopes of Nepal (Google Earth, 2013).

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Settlements in hilly regions of Nepal are scattered throughout the hill slopes. Generally, the ridge slopes have more populated settlements. The stream lines are surrounded by instability features like erosions, landslides, and generally covered by forests. Hence, population in valleys of streams are less due to steep slopes and the weak stability of hill slopes. This can be clearly seen in Figure 3.3. Mostly, valley slopes are barren lands due to a difficulty for cultivating. The stable land are either cultivated or inhabited in hilly regions of Nepal. Hence, the areas where people used to live and cultivate since long time are the stable areas. Thus, the numbers of settlements are concentrated in the upper hill slopes because they are less prone to instability problems. Besides settlements, the public facilities are also situated in the same hill slopes near to the ridgelines.

Road alignments which pass through ridges of hills cover most of the settlements and public facilities. Hence, it is necessary to take road alignment along the ridgeline as far as possible to connect or provide access to the settlements and the public facilities. However, it may be difficult to find such ideal alignments. Generally, road alignments may pass through near ridgelines. As the population are concentrated along the sides of ridgeline and the slope is also stable near to the ridgelines, it is a positive aspect of locating rural road alignment along the ridgelines of hill slopes.

3.2 The five-zone mountain model

The diversity of topography, geology and climate in mountainous terrain produce a wide range of landforms and related geological and geotechnical problems. Fookes et al., (1985) have proposed a simple model of fold mountain topography consisting of five main zones. The model is illustrated in Figure 3.4 and its units with typical landforms, materials and weathering processes associated with each zone are described below with emphasis on slope stability and earthworks, and drainage and river crossings.

Zone 1: Glacial and peri-glacial topography (typical of the High Himalaya). The rock and ice terrain of the high peaks.

Zone 2: Free rock faces and associated debris slopes (typical of the High Himalaya and highest elevations of the Middle Himalaya). Zone 2 is composed of immature rock fragments and coarse debris covered slopes. Exposed rock peaks, cliffs, ridges, screes, boulder cones and steep slopes mantled with coarse weathering products are the common landforms. Zone 2 scree extends down to the valley bottom. In mountainous areas, most of the rocky outcrops

are formed of strong jointed rock and subject to a number of instability processes. The most frequent are rockfalls, wedge, and toppling failures which are usually small and occur on rock face as a result of weathering. Slab failures, rock avalanches, and rock slides usually involve larger volumes of material and are typically associated with major joints and shear planes.

Zone 3: Degraded middle slopes and ancient valley floors (typical of parts of the Mahabharat Lekh and the of lower elevations of the Middle Himalaya). In comparison with zone 2 and 4, zone 3 topography is distinguished by generally lower average slope angles, a thicker soil cover and relict landforms which reflect the denudation history of the area. The important feature of this zone is that slope stability problems are greatly reduced and constraints on the choice of a road alignment and cross section are less severe than in zone 2 and 4. The zone may also provide sources for construction materials.

High altitude glacial and periglacial Rock face with rockfall 1 Degraded debris slide

Ancient high level Degraded sideslope Talus/scree Boulder field of erosion surface of former river Talluvium Talluvium cover to weatthered bedrock Incised gully Colluvium 2 Active lower slopes Colluvium

Tribucary valley 3 Rotational slide 4 3 Principal valley 4 5 4

Residual soil or weathered rock Floodplain deposits

Braided channel Debris slide with bar deposits Rockslope Fan Rapids

Alluvium

Young River terrace deposits

Figure 3.4: A Model for young fold mountains (Fookes et al., 1985).

Although a wide range of soil and rock materials may be encountered, they are common transported soils and in-situ residual soils. Colluvium is a loosely defined term for the characteristics transported slope debries and commonly consists of gravel and even larger

Rural Engineering Infrastructures Design and Public Facility Locations sized fragments in various stages of weathering bound together in a clayey matrix. In general, it has frictional strength and cohesion in wide ranges, reflecting the varied nature of the material during more advanced stages of weathering. Residual strengths can be very low in fine colluvial soils. Therefore, cuts and foundations must be carefully inspected in case the slope has experienced previous instability and contains relict shear surfaces.

Residual soils can be treated as two main types, completely weathered structureless soils, and soils which retain the relic structure of the original rock, the saprolites, of weathering grades 4 and 5. In saprolitic soils, discontinuities are preserved as planes of relative weakness. Rapid chemical weathering associated with preferred ground water movement along major joint planes may form clay and other weak infills or coatings, which have very low strength.

With time, these infills can substantially decrease the permeability along joint planes and form barriers to groundwater movement. This can lead to perched water tables and instability problems in the overlying soil. Beneath the soils, the weathered rock profile is characteristically thicker in zone 3 and a more complete sequence of the various weathering grades is found compared with the more active erosive slopes in zone 2 and 4.

Natural slides and mass wasting are relatively rare on zone 3 slopes. Failures caused by excavation occur mainly in the deep residual and colluvial materials on the ancient valley side slopes. These are often associated with the development of locally high groundwater levels or the reactivation of old slides initiated from zone 4 terrain. The topographic expression of these ancient slides is often subdued and masked by vegetation. In many cases they can only be identified by careful ground investigation during the reconnaissance and/or site investigation stages. The important natural erosion processes on zone 3 slopes are slow soil creep and surface water erosion. Bare slopes in both colluvial and residual soils, especially those with fine sand or silt grading, are highly susceptible to rilling and gully erosion. The colluviums is often more permeable than underlying residual soil or weathered rock and thin colluviums layers at the head of the cut slopes are prone to extensive ravelling under the action of surface and sub-surface water during heavy rains.

Zone 4: Active lower slopes (typical of many parts of the Mahabharat Lekh and some of the more confined slopes adjacent to the major rivers in the Middle Himalaya). The active valley side slopes of zone 4 form a large portion of the landscape. The topography is dominated by steeply sloping valley and gully side slopes covered with a mantle of transported soil

overlying weathered bedrock. High rates of erosion occur on these slopes and this zone generally creates the most serious problems for road construction.

Georges and high angle rock slope similar to zone 2 landforms occur at locations controlled by strong river undercutting. Where the average zone slope angle is greater than about 30, many of the steeper soil-covered slopes will have factors of safety little above unity and wide spread condition of potential instability exists.

Stability and drainage considerations strongly affect the choice of alignment and cross-section on zone 4 slopes. Various forms of shallow landslide and gully erosion are common in a great many rock types and different climatic settings. Debris slides, rockslides and mudslides are the three main types of shallow landslide. Debris slides are confined mainly to the upper layers of transported and residual soils. Intense rainfall is the main cause of natural instability on steep soil-covered slopes. But during construction the effect of all natural factors are usually of secondary importance when compared with over-steepening caused by excavation. Rockslides generally involve a greater thickness of material with the slide surface often located in the zone of weathered rock beneath the soil cover or along unfavourably oriented discontinuities close to the surface of the low-weathered rock. Mudslides are confined mainly to fine grained rocks and soils formed by deep penetrative weathering. They are commonly related to the presence of perennial near-surface groundwater.

Less frequently encountered are classical rotational slides and flow failures. Rotational slides are distinguished by shear surfaces at greater depth. Typical circumstances in which these slides occur are where erosion has undercut slopes in deep soils or in highly weathered rock slopes in which the loss of strength in the rock mass due to weathering outweighs the influence of moisture contents and rapidly moving debris-laden streams. Flows usually occur in natural soils and weak rock; they also develop where heavy rain or surface runoff is concentrated on large spoil tips formed during earthwork excavations.

Surface water erosion by gullies and rills is the second main process which affects the construction on zone 4 slopes. The common features of gully erosion are short lived peak discharge related to major rainstorms and a mixed bed load. Sediment concentrations are eroded and re-distributed in irregular fashion along the gully floor during each major flood.

Actively eroding mountain gullies are characterised by irregular, steep (10-45) longitudinal profiles and generally V shaped cross section with steep side-slope descending to the floor of

Rural Engineering Infrastructures Design and Public Facility Locations the channel. For a given size of drainage channel the density of the drainage network may be several times higher in zone 4 as compared with zone 3, an important factor in alignment selection since gully crossings are major cost items. Drainage pattern also bears heavily on the choice of alignment.

Rilling occurs on bare unvegetated slopes in certain fined grained rocks and soils. In contrast to gully erosion, it is more commonly related to human interference by removal of the natural vegetation cover by or by spoil tipping. Similarly, sub-surface erosion on natural slopes is rarely of direct concern to mountain roadwork as most of the engineering problems result from construction.

Zone 5: Valley floors (typical of the Low Himalaya and, to a lesser extent, the Middle Himalaya). The main features of interest are the tributary stream and gully crossings at the point where they flow into the major river valley. Road alignments following the margins of major rivers are a common choice in mountain areas where high velocities and sediment loads during floods would entail difficult and costly construction in mainly zone 5 terrains. These tributary stream outlets are commonly sites of abrupt changes in channel width and bed gradient and favoured locations for sediment deposition. Alluvial fans are the characteristics depositional landforms. Fan consist typically of gravel-clay size debris and occur most frequently where stream flow is ephemeral, in semi-desert and monsoonal areas, and where the ratio of depositional area to mountain catchment area is small. Single fans are usually conical in shape and have a maximum slope angle of 10.

Fans at the base of unstable mountain catchments are also associated with the deposition of coarser sediments (boulder and cobles) from debris flows. During period of rapid erosion on zone 4 slopes, sediment deposition can change stream bed levels by several meters in matter of hours or sometimes even minutes. A rapidly growing fan will deflect the main river channel and thus initiate erosion on the opposite bank.

The construction of rural roads is the major activity on mountain terrain. As road construction is largely related with regional geology along the alignment of roads, the five zone mountain model can be a good basis for planning and construction of rural roads in hilly region of Nepal. It provides a guide for rural road alignment selection and road cross section designs.

3.3 Alignment selection and choice of cross section

The general principle of locating any road corridor is the shortest length at the minimum gradient and an economy in river crossings and materials. The ideal corridor is along the mature slopes, stable terraces and plateaux of zone 3. Where it is necessary to traverse all the zones, there is the basic rule of corridor location: make distance in zone 3 and make height in zone 4, avoiding extended runs of the lines across zone 4 slopes. The art of the alignment engineer lie in searching out safe zones and linking these by stable corridors and river crossings. Generally, rural roads pass through zone 4 and zone 3.

Commonly the ruling gradient is in order of 1 in 15, the maximum permissible gradient 1 in 10, and the maximum radius of horizontal curves may be less than 20 m. The application of these standards usually means that the overall length of a mountain road ranges between two and four times the plan length between the end points. Cutting slopes may range up to 35 m high and even higher in zone 5 George locations and on steep rock slopes in zone 2. Retaining structures may be required up to say 15 m high and may have an aggregate length of 20% of the overall length of road (Fookes et al., 1985).

This guideline is equally useful for alignment selection of rural roads. However, the geometric standard for the road is much lower than the value stated above. The rural road standard (DoLIDAR, 2010) has further relaxed the road geometry for the rural roads as maximum average gradient in hill as 8%, maximum gradient as 12 and minimum radius of curvature as 10 m.

There are two traditional approaches to the choice of cross section in mountainous terrain: i) the earliest approach, which still survives, is to adopt full cut profile with side tipping of spoil throughout; ii) the second approach is to use principle of cut and fill balance borrowed from conventional road construction. Both of these approaches are unsuited for general application. The approach adopted must take note of the changing slope forms and characteristics of soil and rock. However, the sensitivity of cut mass in rural roads is important. The cut mass has a great impact on environment. The zonal model can be used as a basis for a rational approach to cross-section design.

If stability considerations are satisfied, there are two general principles: avoid structures and avoid rock cuts, both of which are costly, unless the alternative is clearly more expensive.

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Retaining structures are unavoidable on hill slopes greater than about 30, since above this slope angle many common fill materials will of marginal stability, keying in the base of an embankment becomes costly, and overburden soils are prone to shallow sliding. However, it may be possible to employ well founded and well placed rockfill on slopes up to about 45. Rock cuts will be unavoidable on slopes greater than 45. Earthworks problems arise when the only suitable cross section on potentially unstable slopes represents a major surplus or deficit of material. On such slopes the location of burrow and spoil disposal sites should be given as much attention as the alignment itself.

A zone 3 alignment is the most stable and economically desirable. Problems of alignment occur mainly at the zone boundaries. The most important decision is where to enter and leave zone 3. Instability from below the line is usually more difficult to handle than instability from above. At the higher boundary the alignment is at risk from rock fall. At the lower boundary zone 4, instability may give rise to major scarp face retreat, which is particularly difficult to guard against, and localised gully down-cutting, which can be more readily controlled.

Ridgehead route, also known as watershed or spine routes are a special case of zone 3 alignment, fringed entirely by zone 4, and have been widely adopted.

The objective of alignment within zone 3 will be to minimize cost by a cut and fill balance. Cuts and fills will generally be shallow, but where rockhead is also shallow, the vertical alignment should be assessed with care to avoid rock excavation wherever possible.

The aim of the alignment engineer in zone 4 is to search out stable ascent corridors to link zone 5 river crossings with zone 3 slopes where applicable. The efficient use of narrow ascent corridor often involves the vertical stacking of hairpin loops; alternatively known as switchbacks or zigzags is a contentious issue.

A bank of hairpin loops is particularly vulnerable to progressive instability which may develop upslope or down slope from even a minor failure in cut or fill. The cost of retaining structures, drainage, erosion control and stabilisation work is heavy. However, the use of hairpin banks minimise the overall road length and saving may be set against locally expensive construction at hairpin sites. If the ascent corridor is wide enough, then the hairpins can be split into small groups, offset from the groups immediately above and below to minimise the effects of progressive failures.

While setting out a hairpin loops in road alignments, hairpins can be located one above another in such a way that water diverted from the road uphill does not fall on the road segment downhill. This may prevent from progressive failures in the road segments in case of uphill road failure.

There are two principles of cross-section design in steep zone 4 slopes. Firstly, minimize the impact of the earthworks with shallow cuts and fills, secondly, make maximum use of sound rock at depth. In the compromise between these two conflicting requirements, walls and revetments are used extensively. Retained cut is preferable to retained fill since the cutting excavation will often expose rock for a stable formation. However, in rural roads, the volume of earthwork is to be minimised and not practical to go deep cutting producing heavy quantities of excavation which is difficult to manage. The first principle is appropriate for the rural roads.

Zone 5 is generally preferred to zone 4 for an alignment because of the much lower slope angles, although high flood levels in zone 5 may well be decisive factor. These zone 5 routes involve heavy and expensive construction but minimise overall length and geotechnical risk.

Bridge crossings and erosion protection are the expensive elements of zone 5 alignments. Crossing of the main stream may be necessary to avoid river undercutting, active debris fans, slides and cliffs and to minimise tributary crossings. However, alignment in zone 5 is not preferred for rural roads as the rural roads have generally unpaved surface and needs a huge numbers of cross drainage structures. Construction cost of rural roads is high in this zone.

A full fill cross section will normally be employed in zone 5 in order to avoid cutting into the toe of the zone 4 slopes, except where the encroaching embankment causes more severe problems than those of zone 4. The ideal elevation of the route should be just above the high flood level in order to minimise embanking work and simplify access for maintenance on the embankment face.

3.4 Impacts of roads construction on slopes

The construction of roads can have a huge impact on mountain slope. The massive cutting of the mountain slopes and careless disposal of the cut materials downhill, uncontrolled blasting of rock, quarrying and mining activities and improper water management has resulted in intensive soil loss from accelerated erosion, gullying and landslide in Nepal. Every kilometre

Rural Engineering Infrastructures Design and Public Facility Locations of road construction may bring about 100000 to 200000 tonnes of excavated materials. Additional 100 tonnes of slide materials can be added per kilometre annually in the case of unprotected cut slopes. The quantity of soil loss is 8000 metric tonnes per hectare per year as a result of careless construction of mountain roads. Similarly 1000 metric tonnes per hectare per year of soil loss occurs as a result of lack of maintenance of poorly constructed mountain roads (Deuja, 1994).

Rainfall is usually the most important climatic index. The annual total is not necessarily the most important parameter. In temperate regions, the frequency of slope failure increases substantially when seasonal rainfall is greater than 250 mm (Radbruch-Hall & Varnes, 1976). This causes a huge occurrence of landslides in mountain slope during monsoon season. It is estimated that 400-700 cubic meters of landslide occurs per km per year along the mountain roads, and 3000 to 9000 cubic meters of landslide occurs per km during the construction of mountain roads in Nepal (Deuja, 1994). The cut slope failure after construction can generate an average of 500 cum/km/year of debris. Up to 2000/cum/km/year can be generated during single storms with 10–20 years of recurrent intervals (TRL, 1997) in Nepal and India.

This shows a significant environment impact from roads construction in hilly region of Nepal. To reduce these impacts, the cut quantities in roads cross section need to be reduced. This is only possible when the width of cut and height of cut is reduced, resulting in the less quantity of excavation.

As the width of cut increases, the height of the cutting increases significantly which leads to the instability in the hill slope. The cut and throw of excavated materials have a significant environmental impact on loss of the agricultural and forest land and stability of valley slopes. Hence, the road cross-section should be such that the cut slope height becomes as lower as possible so that the cut slope is much more stable and safe. The excavated materials need to be used in construction as far as possible and the remaining materials need to be safely dumped so that it will not roll down to the downhill and cause erosion and landslides.

These show the need of cut and fill cross-sections for better cut mass management using the excavated materials as far as possible (Figure 3.5). Excavated stone blocks can be collected and used for constructing retaining structures.

A study shows slopes between 21 and 40 occupy 55.33 % of the total length of the road in hilly regions contributing the 53% of cut volume per kilometre of road construction (Shrestha, 2010).

VEGETATION COVER (BIO-ENGINEERING)

5.0m. 3:1- 6:1(V:H) 1.0m. SHOULDER 3.0m. CARRAGE WAY 0.2m. 0.8m. VEGETATION COVER EARTHEN DRAIN (BIO-ENGINEERING) 5% CROSS-SLOPE WITH SCOUR CHECK

1 0.4m. 0.5m

BACKFILL

H 0.3m.(min)

B=0.6H

Figure 3.5: A typical cross-section in cut and fill (DRILP, 2006).

Cut volume of excavation in cross-section is sensitive to width of cut and mountain slopes (Figure 3.6). There is a quadratic relation between the width of cut and the volume of cut for a slope. Increase in slope of hill further gives rise the quadric relation with volume of cut for a width of cut (Figure 3.7).

Rural Engineering Infrastructures Design and Public Facility Locations

0.8

0.7

0.6

0.5

0.4

0.3 Cut in 1 deg slope deg 1 slope (cum) in Cut 0.2

0.1

0 2 3 4 5 6 7 8 Width of cut (m)

Figure 3.6: width of cut vs volume of cut (slope 1º).

4 Cut in 2 m width width m 2 (cum) in Cut 3

0 0 10 20 30 40 50 Slope in degree

Figure 3.7: Slope vs volume of cut (2m width).

This study shows that the quantity of cut volume in rural roads is very sensitive to width of cut and the terrain slope in hilly regions. The higher volume of cut has serious impact on local environment. Hence, the efforts should be for the minimisation of volume of cut. For this exercise, we need to use the cut and fill cross-section (Figure 3.5 and Figure 3.9) as far as possible and minimising the use of cross-section Figure 3.8. This will minimise the cut width

and height of roads cross-section and less disturbance to the mountain slopes reducing the vulnerability of slopes.

VEGETATION COVER (BIO-ENGINEERING)

5.0m. 3:1- 6:1(V:H) 1.0m. SHOULDER 3.0m. CARRAGE WAY 0.2m. 0.8m. EARTHEN DRAIN 5% CROSS-SLOPE WITH SCOUR CHECK

0.4m.

Figure 3.8: A typical cross-section in full cut (DRILP, 2006).

VEGETATION COVER CL (BIO-ENGINEERING)

EXISTING GROUND

SLOPE VARIES CUT AREA 3:1 TO 6:1 (V:H) 5.0m. 1.0m. SHOULDER 3.0 CARRAGEWAY 0.2m. 0.8m. EARTHEN DRAIN 5% WITH SCOUR CHECK

VEGETATION COVER (BIO-ENGINEERING) 0.4m. FILL AREA 1 1.5

Figure 3.9: A typical Cross-section in mild slopes (DRILP, 2006).

Rural roads are one of the most demanded development infrastructures in hilly regions of Nepal. Nepal has 32580 km rural roads (DoLIDAR, 2010) in total in the country; among them only around 10000 km roads are operable. Most of the rural roads in hilly region are closed in the monsoon season (June to August) every year. Also, most of the hilly regions are out of connection with national transportation network during the monsoon season due to blockage

Rural Engineering Infrastructures Design and Public Facility Locations of rural road network because of surface condition of rural roads and landslides. A huge resource has been spent on the construction of rural roads especially in hills. However, most lacking part was planning and engineering. Thousands of kilometres of roads were constructed without much caring proper planning, engineering and environmental impacts. In the results, only few roads are in operation. These roads have created a lot of slope instability problems causing many landslides. Even the roads constructed under engineering supervision lack the care of the instabilities features during and after roads construction. This is due to weak geological materials and topography with steep slopes, numerous rivers, streams and water drains.

It is necessary to be aware of local geo-environment particularly in hilly regions of Nepal where infrastructures are to be built. The hilly regions of Nepal lies in the Himalaya and the Himalayas constitute one of the most tectonically active fold mountain belts and experience some of the highest rates of erosion in the world (TRL, 1997). The difficulties presented by conditions of adverse geology, topography and land use have made more acute in the humid sub tropical and humid warm temperature zones where rapid rock weathering and heavy rainfall act to induce land sliding and erosion. So the construction needs a proper consideration of local conditions of the region.

The knowledge on geo-mechanical behaviour of mountain geological materials in Nepal is still limited. This has resulted the development of infrastructure at high construction and maintenance costs, frequent damages due to harsh terrain, heavy monsoon rain, and a long construction time. Roads construction has a great impact on the local geology and topography. Many roads which were built without caring the local geology and topography had a huge post-construction impact in local environment. Soil erosion has been taken place in large quantity due to the roads constructed, causing slope instabilities in the natural slope integrity on the fragile geological conditions in the road corridors. These shows, road construction can have significant effects on slope stability, drainage, erosion and sediment supply to drainage networks. Further, it is very important to explore the knowledge on local environment before disturbing it.

3.5. Conclusions

The five zone mountain model is found useful to locate and assess the rural roads alignments in the hilly region of Nepal. The zonal model can be used as the framework for the analysis of

the geological and geomorphological processes, and consequences of roads construction. Mostly rural roads in the hill region of Nepal pass through corridors in the mountain zone 3 and zone 4. The mountain zone 3 is the best stable zone for locating and construction of rural roads in hilly regions. Most of the rural roads hill slopes lie in 20-40 with cut and fill cross- section with valley side retaining structures.

Post-construction impact of roads construction on environment can be very high in the hilly region of Nepal due to the excavated materials and the creation of mountain slope vulnerable to landslides. As the cut width in hill slope is very sensitive to the volume of quantity, the cut width needs to be reduced providing cut and fill road cross-sections, during engineering design and construction. Due consideration should be given to adopt appropriate cross- sections based on the terrain slope so that the volume of excavation could be minimised in construction of roads.

Mostly, settlements and public facilities are near ridgeline slopes (zone 3). This occurrence matches with stable slopes and requirement for road alignments passing through this zone. This fact gives an important background, technical as well as social, to formulate rural road network planning model for hilly regions of Nepal.

Chapter 4

Covering Based Rural Road Network Method

4.1 Introduction

The development or rural roads in developing countries is a priority of local governments and rural residents, as been realized by policy makers. For the development of rural roads network, a systematic planning methodology is required. There are currently several transportation networks planning models; however, they are mostly developed for the urban transportation network, in order to reduce traffic congestion, energy consumption, and pollution. Unlike urban transportation, rural transportation mainly deals with providing rural settlements accessibility to basic services. Also, local governments usually have insufficient funds and human resources/expertise. Hence, complex models are not practical for the rural (hilly) regions. This has led to the development of rural roads network in the hilly regions of Nepal to be largely based on intuitive judgment and ad hoc decisions. One of the major problems for the local government is the scarcity of funds for development of the rural infrastructure (including development of the road network). The optimal use of the scarce resources in rural region is one of the most challenging issues for decision makers in the absence of appropriate practical planning models. Therefore, there is a need for an effective and simple planning methodology for rural road networks.

Nepal has a rugged topography dissected by a number of streams and rivers, making a large part of the country inaccessible. The existing highway network connects only major cities and towns located mainly in the southern plain areas. However, a considerable portion of the population lives in the hilly and mountainous settlements, where commodities are transported

Rural Engineering Infrastructures Design and Public Facility Locations either by porters or by pack animals. Transporting goods even in the plain area is not efficient due to the lack of all weather road connections from road accessible points to hinterlands. Development professionals argue that inaccessibility is one of the main reasons for underdevelopment in the hilly region of Nepal.

Since the state has limited financial resources, it is necessary to mobilize local resources for construction and maintenance of transport infrastructure. A District Development Committee (DDC) has limited skills with which to plan and prioritize transport networks. Therefore, it is necessary to develop a suitable methodology, supporting tools and techniques that facilitate the development of sustainable rural road networks.

Due to difficult topographic conditions, the transport infrastructure needs a high level of investment. In view of this and the meagre financial resources within the DDCs, it is necessary to devise a methodology that provides a minimum level of accessibility with available resources. This chapter is devoted to explore a simple and practical model of rural road network formation for rural hilly regions in order to improve accessibility.

4.2 Review of rural road planning models

Different authors and agencies have developed rural road planning methodologies. Here are some concepts and methodologies developed in the past for rural road network planning.

One of the earlier works in rural road network development methods is by the UNCHS (1985) guideline. The guideline (UNCHS, 1985) has used the concept of using spanning tree, which has been extensively used for road network planning. Oudheusden and Khan (1987) proposed a WSP decision model to enable optimization of all-weather access to a local market or to a provincial road network, under budget constraint. A rural road network model proposed by Makarchi and Tilloston (1991) connects every village to the surrounding road network and minimises the sum of the construction costs and the travel costs. Kumar and Tilloston (1985) have proposed the SST to optimise rural road network. The method generates a sequence of spanning tree networks, each a progressively better solution than the previous SST network as travel costs (person-km) increase. Further, Kumar and Kumar (1999) has suggested road connections from each village to nearby market centres and education facilities at the least cost, a 93 percent of the rural trips either terminate either at the nearest market centres or at the nearest education facility.

Shrestha (1997) has developed the participatory district level rural road network based on district accessibility standards, nodal points, existing roads and trails, demand from the local people, and geographic characteristics. It is participatory in the sense that it involves the local people in every step of decision-making. By combining the gravity model with the centrality index, and considering the existing rural transportation infrastructures as the basis, Shrestha (2001) has implemented a settlement interaction based rural road network model in the Nawalparasi district of Nepal. He found the model could reduce the district level road length from 440 km, which was proposed by the previous transport plan, to 164 km, a reduction of more than sixty-two percent, without considerably reducing the level of accessibility.

Shrestha and Routray (2002) have proposed settlement based interaction model for rural road network planning. The central places and existing roads, tracks and trails are the basis for the rural road networking in the model (Shrestha & Routray, 2002). The missing linkages are identified based on present and potential nodal points and existing links and estimation of the transport demand by establishing relationship with centrality index and intensity of interaction in this method. The IRAP methodology (IRAP, 2002) has used concept of AI for prioritisation of road links from settlement based data.

Generally a road planning exercise needs the collection of huge volume of data for economic evaluation of road links which is costly and time consuming but the outcome of the effort may not be so significant in rural road planning. Prioritising the rural road links, based on economic models, is rarely justified (Shrestha, 2003). Traffic volume in a road link may be a main parameter for economic justification of the rural link. However, Athanasenas (1997) found difficulty in acquiring traffic data from the rural settlements and an estimation of trip generation from the rural villages. Also, traffic volume may be very low (lower than 25 vehicles per day) in a rural road link (Airey & Taylor, 1999). Hence, different alternative models have been employed for assessing rural road links in rural areas.

Some models proposed agriculture potentiality (UNCHS, 1985) as the basis for prioritising the rural road links. However, agricultural potentials in rural areas, particularly in hilly regions are generally low. Other models proposed market centres (Kumar & Tilloston, 1985; Shrestha & Routray, 2002) as the basis for prioritisation of links. The prioritisation of the road links based on the market centre approach can discard many settlements and public facility locations from the access to roads. Hence, market centred approach also may not be the most effective model for rural areas.

Rural Engineering Infrastructures Design and Public Facility Locations

Most of the rural road links can not be justified based on the conventional economic models such as BCA, ENPV, and EIRR (Oudheusden & Khan, 1987). Hence, alternative assessment tools were proposed by different authors to evaluate and develop rural road network in rural areas. These tools focus on the connectivity and accessibility of the settlements and the public services, as more importance than the economic aspects. Hence, connectivity/accessibility based rural road network model (Kumar & Tilloston, 1985; Oudheusden & Khan, 1987; Makarchi &Tilloston, 1991; Kumar & Kumar, 1999; IRAP, 2002; Shrestha & Routray, 2002; Singh, 2010) has been developed for the development of rural road network in rural areas.

Although these methods have been developed for rural road networks, however, have some deficiencies to apply to hilly regions of the rural areas. The participatory district level rural road network (Shrestha, 1997) doesn’t guarantee the development of an effective rural road network to cover most of the settlements and public facilities around it. Shrestha (2001) method requires defined nodal points for analysis of settlement interaction; however there is no basis for identification of the nodal points. The method is biased to the market centres and has no consideration for coverage of settlements and public facilities. The economic basis for selecting the rural road linkage avoids connecting the rural village settlements. They are biased to link heavily populated and economic centres. The method is more focused on market centred approach. Most of the linkages to the rural settlements are not justified in economic ground (Shrestha, 2003). Furthermore, this method requires heavy data collection to calculate centrality index of a nodal point. In rural areas, basically in hilly areas, the connectivity/accessibility to the settlements and the service centres is more important than the economic returns.

Some models (Makarchi &Tilloston, 1991; Kumar & Kumar, 1999; Singh, 2010) propose the connection of all settlements in rural areas. However, connecting every settlement in a rural area is not practical due to technical and financial constraints. Since, a characteristic of rural areas is sparsely located settlements and public facilities (even more in the case of hilly regions), it is not practical and possible to connect all the settlements and public facilities by rural roads. Hence, connectivity/accessibility to rural hill settlements should be defined in a different way. Although all the settlements can not be connected, a rural road network should bee as near to the settlements and public facilities as possible. Hence, the rural road networks should cover all the settlements within a justifiable distance from the network. A possible way to overcome the problem can be by introducing the concept of covering, which may cover the

maximum settlements and public facilities within a specified distance. This issue has not been dealt by the models discussed above and hence, are also not sufficient to address road network problems in hilly regions of rural areas. It is a major gap found in the literature. Therefore, rural road network problem needs to be dealt with covering aspects which is one of the objectives of this study, thus trying to overcome the short comings of existing rural road network models.

Mostly, current rural road network models address the problem for plain areas. However, problem faced in hilly regions of rural areas are different. On all the models and methodologies the most overlooked aspect is the covering. The methods rarely consider covering of rural settlements and public facilities.

As follows, definition and location of nodal points properly is needed in a rural road network. However, this is one of the challenging tasks for planners and engineers in fixing road alignment in rural areas. The nodal points need to be identified so that the most of the settlements and public facilities can be covered. However, none of the methods discussed above has given the basis for identification of nodal points even in plain areas. This kind of issue has not been dealt by any models in previous works. Then, nodal points are proposed to be connected in an optimised way to form a rural road network in the study region. Hence, we need a simple and a more practical model for rural road networks of hilly regions. This chapter proposes a covering based model so that most of the rural settlements and public facilities are covered within a specified service distance.

4.3 Use of location models in rural road network design

Facility location models have been studied extensively and intensively in the last decades (Drezner & Hamacher, 2004). Although the use of mathematical formulations of location analysis may be complex for practitioners in developing countries, several studies have proved the effectiveness of such models in the location decision-making process dealing with public facilities. Location allocation problems deal with decisions of finding the best or optimal configuration for the installation of one or more facilities in order to attend the demand of a population.

Location-allocation models were also used by Rahman and Smith (1999) to design optimal locations of health facilities in a rural area in Bangladesh. Using an integer-programming formulation, it considers the maximum allowable travel distance and number of facilities to be

Rural Engineering Infrastructures Design and Public Facility Locations located. These models were later extensively reviewed by the same authors (Rahman & Smith, 2000). The objectives and merits of these models in planning rural health facilities location were broadly illustrated and discussed in the later work.

In the work by Daskin and Dean (2004) formulations of three classical facility location models, location set covering model, maximal covering location model, and p-median model were broadly reviewed and considered as the key models for planning location of health care facilities. Numerous applications of those models in health care were identified.

Location analysis using location models is likely one of the most popular approaches to rural health facility location in developing countries. However, the use of location models in the definition of rural roads is rare. The transportation network design and location theory have been studied separately in the past. Recently, more research on developing models for integrating network design and facility location has been made.

Two closely related papers by Melkote and Daskin (2001a; 2001b) developed a formulation for the network design, and outlined heuristic and optimal solution finding procedures. By generalizing the classical simple plant location problem, the integrated model of facility location and transportation network design was used to analyze the transportation planning scenarios. Sensitivity analyses for different cases were conducted throughout the papers to observe the performance of the integrated model. However, the model may be too complex and not practical for the rural hill areas, where the expertise on the subject and funds are usually a constraint.

There is also some literature dedicated to the theoretical study of rural road network planning usually focusing on the linkage development rather than taking on the entire rural road network definition. Some of the studies investigate the network design considering facility location. However, those studies provide a limited application by testing only on simulated networks. It was also concluded by Daskin and Owen (1999) that the interaction between the two areas is relatively unexplored. Rather than going for a complex model, the concept of a simple location-allocation model can be applied to find the obligatory points (control points) in a rural roads network. The task of identifying the optimal/best location for a facility in an area is the same as the task of identifying the appropriate locations of obligatory points in a rural road network so that the rural settlements are covered within a specified distance. Thus the identification of obligatory points can be dealt as a location analysis problem. The

optimum connection of the identified obligatory points will form the rural road network. Hence, the problem is addressed as a location analysis problem for which a solution procedure is presented in the following sections.

4.4 Proposed rural road network method

The proposed model is composed of two steps. The first step aims at identifying the nodal points (obligatory points) in a rural road network. In the second step, the model defines the rural road network that connects the nodal points. In the following subsections the model will be described in detail.

4.4.1 Identification of nodal points

In rural hills, villages are sparsely populated and most of the villages do not have access to the public facilities and services within a reasonable distance. Thus, identification of one or more nodes that can cover the most of the facilities in specified distances is necessary. Therefore, grouping of village settlements is necessary. One way of grouping the settlements is using the political boundaries to find an appropriate geographical location. However, fixing the location is difficult for the hilly and rugged terrains. Hence, an appropriate method is necessary to determine the location of such points.

The scattered villages in hill slopes are generally connected with foot trails and only some of them are connected by rural roads. The trails crisscross the hill slopes making the distance much greater than the Euclidian distance, hence, making impracticable the use of these distances. These trail networks provide access to the villages. Therefore, it is useful to study the trail networks in order to find a central nodal village (among the settlements within the specified boundary) from the accessibility point of view. The delineation of the political boundary can be the Village Development Committee (VDC) boundaries in case of Nepal. The VDCs are the lowest political units in Nepal. A transportation network within a VDC can be formed from which a distance matrix (with the actual distances of the foot trails between each settlement/village) can be obtained. Then, the shortest distance from each node to the other nodes can be found using the Floyd-Warshall algorithm (Floyd, 1962) (see Appendix G), thus obtaining the shortest path matrix. Then, the central village in the VDC can be found out which can be treated as the nodal point for the VDC. If a single node cannot cover the whole VDC settlements within the specified distance, one or more nodes can be added. In a similar fashion, the nodal points of the other VDCs can be found. For this purpose, we can use

Rural Engineering Infrastructures Design and Public Facility Locations a facility allocation model. The location of nodal points can be considered as a location problem. The identified nodal point(s) is/are the village(s) that cover(s) most of the remaining villages.

Within location theory, typical covering problems include: finding the minimum number of facilities needed to cover all demand nodes (the set covering problem) (Church & ReVelle, 1974), finding the location of a fixed number of facilities to maximize the number of covered demands (the maximal covering problem) (Church & ReVelle, 1974), and finding the locations of a fixed number of facilities to minimize the maximum distance between a demand node and the facility assigned to cover its demands (the p-centre problem) (Daskin & Owen, 1999).

As all the settlements can not be covered due to spatial and budget constraints, a relaxation over covering all the settlements is necessary. Therefore, effort should be placed in maximising the coverage of the settlements. Hence, for this context, in order to find the nodal points, the maximal covering problem seems to be the most appropriate model.

The classical Maximal Covering Location Problem (MCLP) (Church & ReVelle, 1974) is sated as follows. There are finite sets of facilities and users at a finite set of locations. These sets and locations are regarded as nodes on a network with arcs whose weights represent the distances between nodes. Maximum travelling distance for residents of the villages to get services from the allocated number of facilities is fixed. The objective is maximization of covering by the allocated facilities.

The MCLP is to maximise:

(4.1) Subject to:

(4.2)

(4.3)

(4.4)

(4.5)

Where, xj = 1 if a facility is located at j; xj = 0 otherwise. yi = 1 if demand from i is covered by a facility; yi = 0 otherwise.

Ni = {j│dij≤S}is the set of facilities which are eligible to provide cover to demand i n = number of demand points; ai = population of demand i; dij = shortest distance between i and j; p = number facilities to be located; and S = maximum service distance.

The maximum service distance influences the covering of settlements. Fixing a maximum service distance is a strategic decision. In planning to improve access through location of a facility, a catchment area needs to be defined. Since individual travel distance (travel time) influences their welfare, in order to avoid inequalities in the accessibility to public services, it is essential to consider the upper limit of travel distance of each citizen to reach the corresponding facility. The goal of minimising the total cost in this model should not be the only one considered, as that will give rise to locating facilities in populated areas which would penalize other isolated, low density, areas in the hilly regions. A desirable upper limit for travel distance (travel time) from any village to facility centre should not be exceeded (Rahman & Smith, 2000). However, determining the maximum service distance is a critical issue. In another study by Rahman and Smith (1999) Community Clinics are located by solving a MCLP using a maximum distance of 2 km between facilities and villages. The percentage of rural population covered was 99 % when the maximum service distance was relaxed to 4 km.

Determining the covering distance is an important preliminary step. This covering distance to be used may vary significantly with regards to the scenario under analysis.

4.4.2 Defining the rural road network

The obtained nodal points, existing rural roads, tracks and planned roads may be the basis for defining the rural road network. The possible linkages between the nodal points are to be established. These linkages are subjected to spatial and engineering constraints and are the

Rural Engineering Infrastructures Design and Public Facility Locations technically feasible. For most cases, due to varied topography, alternative linkage options are not available (even more in the case of hilly regions). All the possible alternative options of linkage between the two nodes are to be established and to be considered for further analysis of the rural road network.

The connection between the nodal points by the rural road links forms the basic network. A distance matrix connecting all the nodal points and the connecting points in the rural roads network is to be obtained. Afterwards, a Minimum Spanning Tree (MST) can be obtained, using Prim’s Algorithm (Prim, 1957) (see Appendix H), to connect each nodal point in the network. The MST network represents the minimum connection level necessary for the rural accessibility of a specified coverage distance. This MST forms the rural road network, and covers the most of the settlements and public facilities within the region in consideration.

4.5 Application to the hilly regions of Nepal

The applicability of the method is tested in the definition of the rural road network in 15 VDC of hilly region of Gorkha district (Nepal) as shown in Figure 4.1.

The VDCs lie in the north of the district headquarter in between the two rivers Burigandaki (in the east) and Daraundi (in the west) as shown in Figure 4.1. The district headquarter is the main service centre in the district and acts as a supply centre of goods and services to the VDCs of the district. The district headquarter is linked by a feeder road (a higher standard road) to the national highway network of the country.

Total population in the VDCs is 63437 inhabitants. The 15 VDCs cover an area of 244.2 square kilometre in the district, with a total of 219 villages. The number of villages, population and the area of the VDCs are shown in Table 4.1.

The location of existing road network and existing VDC centres in the area is shown in Figure 4.1. All the links in the network are earthen roads and operable only in dry seasons. Some of the links are earthen tracks only (impassable for vehicles). To analyze the situation, the distance matrix was obtained using the Floyd-Warshall algorithm. The nodal points of the 15 VDCs have been identified using the MCLP model. The corresponding distance matrix and short distance matrix of network of each VDC is shown in Appendix A and Appendix B.

The coverage by nodal points in each VDC is shown in Table 4.1. The second column of the

Table is VDC name, the third, fourth, and fifth columns show, respectively, the number of villages, the population, and the area of each VDC. The sixth column shows the number of villages covered by the nodal points and the seventh column shows the percentage of covered villages out of the total villages in the VDCs. Setting the maximum service distance as 4 km to the nodal point, the coverage by the nodal point varies from 54 % to 100 %. On average, 90 % coverage is achieved in the service distance.

The nodal points have been identified for 15 VDCs from the solution of the covering problem as shown in Figure 4.3. These nodal points can be the location of the obligatory points in the rural road network and form the basis for defining the nodes of the network.

Panchkhuwa Deurali

Pandrung Aru Pokhari

Source: RAIDP (2009) Masel

Tandrang Baguwa

Dhawa

Asrang

Borlang

Legend:

VDC Centre

District Headquarter

VDC Boarder Existing rural roads/tracks

Figure 4.1: Location of the VDC centre and rural roads network in the study area.

Rural Engineering Infrastructures Design and Public Facility Locations

Table 4.1: Coverage provided by the nodal points for a service distance of 4 km Coverage by node number of Area SN VDC villages Population (km2) Number % 1 Aarupokhari 13 5465 23.94 7 53.85 2 Asrang 13 3880 16.00 13 100.00 3 Baguwa 11 2246 6.34 11 100.00 4 Borlang 17 5383 29.95 13 76.47 5 Bunkot 24 7478 30.42 20 83.33 6 Dhawa 7 4040 16.05 6 85.71 7 Finam 18 3437 9.96 18 100.00 8 Masel 13 4408 14.96 11 84.62 9 Nareshwor 16 4501 13.13 14 87.50 10 Panchkhuwa 10 2422 9.69 10 100.00 11 Pandrung 13 3021 13.06 11 84.62 12 Takukot 16 4496 14.05 16 100.00 13 Taku lakuribot 16 2740 12.59 16 100.00 14 Tandrang 6 4928 15.83 5 83.33 15 Taple 26 4992 18.23 25 96.15 Total 219 63437 244.20 196

The next step is to identify the road linkages to the nodal point of the 15 VDCs. In the area, most of the nodal points have been found connected by rural roads links, as shown in Figure 4.1. The distance matrix of nodal points and the connecting nodes has been obtained considering spatial and technical constraints. Each nodal point is to be connected by at least a road link in the network. The MST is obtained using the Prim’s algorithm. The obtained MST is shown in Figure 4.3 and superimposed to Figure 4.2. This is the minimum level of rural road connectivity necessary to cover the hill area within the 4 km service distance.

Takumajhlakuribot

Panchkhuwa Deurali Taku

Pandrung Arupokhari Masel

Baguwa Tandrang

Nareswor Taple Asrang Dhawa

Finam

Borlang

Bungkot Legend Villages Identified nodes District Headquarter Rural Road Link Feeder Road

Figure 4.2: Nodal villages obtained from the solution of the covering problem (case study).

22 Link Length(km) 21 1-2 5.75 Legend 1-3 3.52 Nodal points 20 3-4 6.00 19 3-5 3.34 Intermediate points 5-6 3.44 Minimum Spanning Tree 17 6-7 5.70 18 7-8 2.69 12 8-9 4.20 13 7-10 4.12 14 11 10-11 2.49 16 11-12 1.74 6 10 11-13 0.70 13-14 1.50 2 7 14-15 7.73 15 14-16 7.35 5 13-17 2.78 8 17-18 5.57 1 17-19 2.10 3 19-20 1.20 9 20-21 3.28 21-22 5.12 80.32

Figure 4.3: MST of the rural road network (case study).

The implementation of method in the 15 VDCs of Gorkha district shows it is a simple and practical for identifying the appropriate obligatory points and the rural road network

Rural Engineering Infrastructures Design and Public Facility Locations development. After successful application of the method in the region, it is studied in other three regions. The result of the study have been used to analyse the rural public facility location and linkage patterns of rural road networks in hilly regions of Nepal, which will be presented in the following sections.

4.6 Rural public facility location in hilly regions of Nepal

Settlements in hilly regions of Nepal are highly scattered. Public facilities for these settlements are even more scattered and typically located at one of these settlements. Common rural public facilities are health centres, schools and market centres. These facilities were usually located on an ad-hoc basis and are connected by foot trails. Connection of these public facilities by rural roads is now an important issue for the government in order to deliver the government services properly. However, connection of all the facilities and the settlements by a rural road is not possible in the hilly region of country due to environmental, geographic, and budget constraints. Thus, one way of bringing the facilities in the reach of rural communities is by establishing of rural road network so that the public facilities will be within a convenient distance from the settlements. Hence, covering aspect of the public facilities is more relevant in the regional context. However, the covering distance to be used may be a political issue.

In order to further enhance the knowledge of the situation of hilly regions of Nepal, covering of settlements and public facilities has been studied for four regions. The study utilised the covering based model to analyse the situation. The study was conducted to establish rural road networks in four hilly regions of Gorkha (Gorkha A and Gorkha B) and Lamjung (Lamjung A and Lamjung B) districts of Nepal. The distance matrix and short distance matrix of Gorkha A network is shown in Appendix A and Appendix B as a sample. The distance matrix and short distance matrix of networks in the region Gorkha B, Lamjung A, and Lamjung B are calculated in the same way as in the case of Gorkha A.

4.6.1 Covering of settlements

The location of settlements in the four hilly regions is shown in Figure 4.4, Figure 4.5, Figure 4.6, and Figure 4.7. The regions consist of 1026 settlements in 63 VDCs (Table 4.2). The effect of covering using different service distance (from 2 km to 5 km in the intervals of 0.5 km) is presented in Figure 4.8. The figure shows that the coverage varies rapidly from 2 km service distance to 3.5 km service distance and then, increasing with lower increments

afterwards. In this case, when the service distance is 2 km, the coverage of settlement is only 50%. When the service distance is increased to 3 km, the coverage increases by 24% and covers 74% of the settlements. The coverage of settlement in 4 km and 5 km service distances are 89% and 96% respectively.

Thale Jhyalla Bhattagaon Kerabari Gairigaon TalloJaphdi Majhlakuribot Kamaltari Archale MathiloJaphdi Bhaledhunga Arukharka SiranLakuri BahungaonPokhariGaira TM1 Dandathok Dumreswara Lakure Takukot Palkhu Gyaji Aapswara Bhanjyang Lakure Mohoriya Bahakot Amile Khamgau Amile 1 Mulabari Mailung Sarkigaon MathiloMasar Dwaridhari Dandapari Churung Dandagaon Parigaon UppalloJarang Deurali Turturepani Keurepani Pandrung Arubot Ulte Baluwa Ratmate Sisneri TalloMasar Basi Bhalswara Dharapani TalloJarang Dhandagau Tunubote Pandegaon Saune Deurali Bhattagaon Gairichhap Ramche Dhakalgau Sapunge Majhthok Lamagaon Dandagau NirmalDiha Devkotagaon Sarkigaon GhoptegaonPahare Tallo Aru Sikhar Khatrithok Devisthan Tinkhande Lambagar Dandagaon Ghyampesal Kauchhani RajetarGaikhur Sarkigau Sarkigaon BarabiseSikhre Kayapani Darbare Banjaragaon Khanchok Majhthok D GairigauChisapan Pauwa Arubote Okhle Kubinde Dandabari Bohoragaon Bhyalgaon Holsimha Keureni Dharapani Majhthok N Dumsiri TalloKokhe Khatrigaon AgeShikhar Chhapthok Rithepani nareA Kamere Simle Upallokokhe Pokhrelgaon Dharampani Maithum Taribesi Lapse Gaikhur Pandegaon Aapchaur Ashokbari Ashrapani Kasinthok AhaleBhanjyang Kathekhola Tiwarigaon Taplebazar Baddanda NareB Bhogteni Deragau Baniyagaon Lapsibot AdhmareManpur Chautara Newargau Melbisauna AdhmaraPallo Bolang Khirpegau Aruswara Digau Kantheswara Aapswara Bandichaur Simalchaur Sunargau Magargaon Rajali Bhanjyang Pipalthok Hilekharka Ripgaon Sundardanda Jhingate HarraBisauni Waglegaon Thulkhetgau Chhatibane Luichiswara Kaphalchhap Thamdanda Nayagaon Dandagau Hatiya Finamgau Asranggaon Chhapthok Aultari PokhariBatta Kuwapani Okhlepani Baluwa Lakuriswara Bhantanagaon Mohoriyagaon Bhanjyang Bhagabatigau Narayanpur Alegau Airebhanjyang Dungagadebhanjyang lekhpakha Gairigau Nimjung

Ghatbesi Kotthok Khabdigau Birdigau Andherigau Polichhap Dandagau Basantegau Mahadevtar Rampur Pipaltar Chipleti Bhandarigau Jyadulchhabise Gairigau Hatiya Chhapthok Sunderpur Khabdibhanjyang Jyadulsimaltar Ludisusare Kuwapani Dharapani Lakuri Bhanjyang Siudepani Satbisetar Jogidanda Pokharidanda Mailung Maskichhan Bhagargau Apswara

Kyamuntar

Figure 4.4: Settlements in case 1: Gorkha A.

Rural Engineering Infrastructures Design and Public Facility Locations

Hansapur

Tallobhirsingh

Mathilobirsing Kubinde Furkedanda Nepane Chhabisetar Devisthan Birauta Balekhu Kupregau Chainpur Kwanje Chisapani Kerabari Kalimati Dharapani Dandagau Finam Nayagau Padukakharka Siureni Finamtar Bhogteni Byakharka Bhattagau Dhartipani Jaubari Kaule Kalimati Dhansar Thotneri Lagdi Besi Campus Magargau Mahipate Tham Kaldung Jaubari1 Arubot Thalajung Kaule Muge Thumka Sathimure Thuloswara Chilaune Upallogohore Okhle Arkul Jhimrek Deviswara Sanogohore Khanalthok Pateswara Ramche Ratmate Dhure Gohoredanda Kaldhunga Khabari Mallatar Parajuligau Bhandarigau Gaira Nibhare Kaldhunga Pam Lapse Sri1 Kapare Bhageri Dharamthali Guntar Bayapani Patalepani Thaneswara Bajredanda Tallopam Bhaledhunga Mukundagau Harmibhanjyang Jhargau Kapuswara Amp1 Sapkotagau Phattarbari Kutijung Harmikot Bhage Sarkigau Simle Sanodhodeni Pathivara Darmichaur Nawalpur Tallochitre Amp2 Chitrepokhari Damaigau Dakeswara Ampipal Aklesangu Patale TingauGairagau Jurithumka Kataharbari Simpani Baddagau Salbot Dumre Banspur Dandagau Pachyan Shikharbhorle Ratdanda Nawalpur1 Phaudargau Mathillogankhu Maibal Karkigau Jolahadadagau Kapreswara Dhansadanda Kholli Gairagau Raigau Ripgau Chilaunegau Sanotar Jhulungebajar Palumtar Chhoprak DmaigauMaltar Bohoragau Kyaureni Dharampani Alegau Phirfire Bogaligau Adhikaritar Kalomato Aathghare Jaisithok Ratmate Dhakare Phimaldanda Tallogankhu Magargau Falamkhani Majhgau Basnetgau Khairenipakho Panditgau Pokharibesi Baniyagau Nayasangu Chapbhanjyang Lapsichaur Khurpajung Aduwabari Kholipokhara Belbas Arubote Jarebar Baniyatar Bardanda Kolkot Amare Shivalingandanda Gairibari KhoplangBajar Hitikodhara Chorkate Nirkot Khoplangdanda Putalikhet Bhagori Bandre Neupanegau Lapsichaur Mahantadihi Khoplangbesi Ladikot Gaikhur Suparegau Belbas

Khadkagau Dhaukholagau Kamalbari Bharatbesi Amilichaur Satdobato Bagdanda Sarrobesi Kurechaur Jogibesi Ramche Mohoriya Maratbesi Panthabesi Serabajar Kosgade Kusuntar Chharchhare Ghaderikholagau Kumalgau

Lamgara

Figure 4.5: Settlements in case 2: Gorkha B.

Maldaneswara Tari Garantebajar Majhgau Tarebhitta Ramche Thumkagau Ghaderi Kaumati Kaltugau KallebesiDhokeedanda Chhapdanda Newargau Dasgau Bhirkuna-Tailu Kamrakhu Gairigau Okhari Bagar Betyani GurunManjyang Jorbisauna Salleri Kerabari Piwa Budkot Hadikholabajar Jaubaridanda Jogidanda Perjedanda Upalloalainche Bhaiswara Purano tso Talloalainche Sallabot Laurani Ghaderi Kamargau Sotidovan Uniswara Lamichhanegau Gauda Katheswara Alaichephat Pipalbhanjyang Chharmas Khaltagau Yuri Tsogau Dandathok Pyarjungbhanjyang Archalbot Majuwa Kolki Bharatbesi Patalekharka Lakhajung Pyarjung Kyamche Shikhar Dhidegau1 Pyarjungdanda Bhanjyang Dhidegau2 Jhagare Belghari Deurali Kaphalbote Bhotenigupha Sisneri Bharate Lamiswara Bakot Bigraha maswara Bastang Dhoke Sirubari Sirubarithulaghar Lamagau Semswara Bikharka Simlegau Ramche Kalleri Katrenidanda Kalghat Simghari Kuyele Sirubaribesi Sattale Kokegau Upalloborang Rithebot Dhape Talloborang Baguwa Kudule Koirale Bhirkharka Bhansar Lampata Patalepani Tinghare Kotod Kaurepani SattaleB Kuwapani Kaprechaur Deurali MajhigauB Chapswara Simleghari Bhansarbesi Ramche Sagrabas Adswara Daramdhunga Bhaisara Raginaskot Bandeswara Harrabotbagaincha Dandaban Majhigau Saunepani Bhagri Kolki Harrabot Gaudagau Panthedanda Khra Dauliyadanada Thakurgau Subbathok Lupgau B Bhalayakharka Naubise Pangre Dandakharka Amidanda Neupanedanda Lambato Lupgau Garebota Bohoragau Jeme Seltarbajar Bhatgau Gaitigau Sanobhati Pahure Seltar Phulbari Rimdanda Bhaisikholagau Aapchaur Chisapani Gaurigau Kalleri Kundanda Timure Tarkughat Thapaliyagau Salphedi Kumalgau Pantha Ghareghari Mangaltar Gaulitar Mejargau Satdobato Dhamilikuwa Tinpiple Altar Subatar Nayapauwa Batase Bangechaur Narimghat Parajuligau Garambesi

Saldaha Chepesangu

Figure 4.6: Settlements in case 3: Lamjung A.

Rural Engineering Infrastructures Design and Public Facility Locations

Bhutuha

Bhoteodar

Balithumbesi

Dharapani

Bhaktichowk

Ramadi

Shantanagar

Ghokreswara

Shivachok

Gairi

Balithumbesi A Balithumbesi

Udipur

Paundidhik

Khatrichaur

Shikra

Phedikuna

Pairechaur

Kusunde

Kuwargau

Balithum

Thapaghare

Tarkutar

Tarkukot

Kamargau

Ratanpur

Thamdanda

Shitalchautari

Phaliyasangu

Purandihi

Majuwa

Bahunthok

Pakhathok

Gyanibas

Nayagau

Nayagaupakha

Kamlukichhap

Tallobahunthok

ThuloDhimire

Thatichaur

Sundeerbajar

Gahateharre

Dhodeni

Khatrichhap

SanoDhimire

Gahate

Aarukharka

Parajuligau

Mulkot

Rakse

Khahare

Dhipichaur

Khaharedhad

Chamekharka

Khanyaswara

Handetar

Malekharka

Gahatelek

Bageswara

Bhakunde

Kamere

Nauswara

Dhadgau

Parewadanda

Pakhathok

Bajarkot

Dhitalgau

Khatrigau

Thakle

Kharetar

Kharbhanjyang

Bohoragau

Kolpani

Thaklebesi

Naruwal

Ghumauria

Kharibhanjyang

Bagedanda

Jogikula

Ranikuwa

Deurali

Jhakrikhet

Simle

Bagalegau

Muslephedi

Lakureswara

Khursane

Kaphalswara

Majhgau

Magarpatle

Gairigau

Suntaletar

Purkan

Basaulidanda

Jortichautara

Bhorleni

Danaigau

Duradanda

Mauranedanda

Saunepani

Purkan

Khatrigau

Simpani

Bahunbesi

Kokalegau

Barbot

Basaulagau

Archyalwani

Patale

Gausahar

Jamune

Kitinche

Lamjungdarbar

Pakheraswara

Dharapani

Panthipuranogau

Puranogau

Chaudia

Syauli

Simle

Pathebhanjyang

Lamapatal

Bhadarephedi

Dandakateri

Patale

Jyamire

Charghare

Kauseni

Badahare

Gharidanda

Rohotepani

Dhari

Dandagau

Deurali

Hattigade

SwaraDeurali

Kirtipur

Giregau

Devtapani

Chhaharepani

Chandrapatal

Dandagau

Misrigau

Kunchha

Gairigau

Shantibazar

Paundiphat

Khajegau

Barapole

Simalghari

Printibesi

Bhatuwa

Jaisigau

Adhikarigau

Syanse

Okhlepani

Dhaguwa

Majhgida

Puranokot

Jhagare

Khamarbot

Turlungkot

Koiralephant

Kalimasan

Phosre

Judikhet

Kankadanda

Gairiswara

Beltar

Baspani1

Dhuseni

Hile

Deurali

Sirwani

Kaneswara

Sindhuredhunga

Rampani

Kartapur

Upallokoiralephant

Baspani

Chaudanda

Pirsing

Sindure

Deurali

Phedi

Tallorayapali

Taple

Neta

Upallorayapali

Khamariswara

Makaiswara

Thuloswara

Bhusalthok

Chandigau

Ampchaur

Dhitalgau

Jita

Handikholagau

Swara

Dharmeswara

Jyamirkot

Shikhara

Jitasaptadhara

Jamune

Godargau

Majhgau

Manke

Gairigau

Jitakot

Chindegau

Dandagau

Kotgau

Thansingkot

Narinchaur

Manya

Kirtipur

Bardan

Sarankadihi

Jitatar

Tamakhani

Dhuseni

Simlegau

Besigau

Gobineri

Bhusaldihi

Khalak

Tiwarigaira

Kharekholagau

Tandrang

Ratmata

Saldanda

Khanaldihi

Jugepani

Sunargau

Kabrejhana

Taksar

Belbot

Sotipasal

Bagrebesi

Gothpani

Chamedanda

Bhadaure

Sunderdihi

Bagre

Sera

Poudeldihi

Chhatredhunga

Khadkagau

Pandegau

Punatandihi

Lamosoti

Chanaute

Gorkhalithan

Syaulibazar

Baharedihi

Sahudihi

Newarhatiya

Deurali

Kaure

Chardipasal

Bhusadihi

Lamachaur

Suryapal

Pokharithok

Kumalgau

Dhodre

Dhodrebesi

Saniswara

Amdanda

Bhorle

Sanokumalgau

Ranipani

Kodale

Samibhanjyang

Bhorle1

Ramgha

Jymiretar

Thulokumalgau

Simle

Shihale

Kharka

Chuderiswara

Gumba2

Dopahare

Mukunde

Phatandanda

Shikra

Jyamire

Bhorletar

Waglephant

Bhotegau

Gumba1

Shyamghalitar

Gumba

Khanalphant

Tallotar

Halesi

Thumka

Tharpu

Jaganpur

Parajuli

Tijam

Neupanebesi

Duipiple

Lamidanda Parajulibesi

Figure 4.7: Settlements in case 4: Lamjung B.

Table 4.2: Coverage of settlements using various covering distances Nos. Covered within (km) S.N. VDCs Villages 5 4.5 4 3.5 3 2.5 2 1 TakuLakuribot 16 16 16 16 16 16 16 15 2 Taku 16 16 16 16 13 11 10 9 3 Pandrung 13 10 9 9 7 6 5 5 4 Masel 13 12 11 11 10 8 7 7 5 Baguwa 11 11 11 11 11 11 11 9 6 Taple 26 26 25 25 22 21 17 15 7 Asrang 13 13 13 13 12 12 10 8 8 Nareswor 16 15 15 14 14 14 10 7 9 Finam 18 18 18 18 17 16 15 13 10 Panchkhuwa 10 10 10 10 9 9 7 6 11 Arupokhari 13 9 8 7 7 6 6 4 12 Tandrang 6 6 5 5 4 4 3 3 13 Dhawa 7 7 7 6 5 5 4 4 14 Borlang 17 15 14 13 11 10 9 6 15 Bungkot 24 21 21 20 18 16 15 13 16 Ghairung 23 20 18 17 16 15 12 10 17 Namjung 20 19 19 17 16 14 12 8 18 Tanglichowk 13 10 10 9 8 7 7 6 19 Fujel 19 19 19 17 16 14 11 9 20 Mirkot 13 16 16 13 11 9 6 5 21 Khoplang 24 18 16 15 12 9 8 7 22 Chhoprak 29 28 25 24 21 18 15 13 23 Ampipal 17 14 13 12 10 9 8 6 24 Harmi 16 15 14 13 12 11 9 8 25 Gankhu 20 20 20 19 18 16 13 10 26 Srinathkot 24 16 16 15 14 14 11 9 27 Jaubari 14 13 12 11 11 9 8 7 28 Thalajung 19 19 19 18 17 15 12 9 29 Kerabari 17 15 15 13 12 10 8 6 30 Dhamilikuwa 22 21 18 17 15 13 11 7 31 Chakratirtha 18 18 18 18 17 14 12 9 32 Bhalayakharka 14 13 12 11 10 9 8 7 33 Kolki 18 18 18 17 17 15 13 9 34 Pyarajung 11 11 11 11 10 9 7 5 35 Turture 16 16 16 16 16 13 12 7 36 Raginas 16 15 13 12 11 10 9 8 37 Bharate 20 20 20 20 19 17 13 11 38 Archalbot 12 12 12 12 12 12 11 8 39 Srimanjyang 14 14 14 14 14 14 12 11 40 Gauda 24 21 20 19 15 13 10 7 41 Pachowk 15 15 13 13 12 10 9 8 42 Ilampokhari 14 17 16 15 14 13 11 9 43 Nauthar 18 18 18 18 17 14 12 9 44 Sunderbajar 15 15 15 15 15 14 13 10 45 Bhoteodar 17 17 17 17 16 14 12 9 46 Udipur 14 13 11 10 10 9 8 6 47 Tarku 20 20 19 18 17 14 11 8 48 Gaushahar 33 33 32 27 25 18 15 9 49 Duradanda 14 14 14 14 14 14 12 12 50 Chandreswor 20 20 20 19 18 17 14 12 51 Puranokot 12 12 12 12 12 9 7 6 52 Sindure 14 14 13 12 10 9 8 7 53 Neta 7 7 7 7 7 7 6 5 54 Bangre 12 12 12 12 12 12 11 7 55 Bhorletar 18 18 18 17 16 12 11 7 56 Samibhanjyang 6 6 6 6 6 6 5 4 57 Ramgha 23 23 23 23 22 19 16 13 58 Suryapal 11 11 11 11 11 11 9 6 59 Taksar 16 16 16 16 16 15 13 11 60 Jita 19 19 19 19 18 14 11 11 61 Kunchha 13 13 13 13 13 12 10 7 62 Dhuseni 12 12 12 12 12 12 11 9 63 Parewadanda 11 11 11 11 11 9 8 5 Total villages 1026 982 951 911 850 758 646 516 % covered 100% 96% 93% 89% 83% 74% 63% 50%

Rural Engineering Infrastructures Design and Public Facility Locations

100%

90%

80% Distance (km) % of Coverage 5.00 96% 4.50 93% 70% 4.00 89% 3.50 83% 3.00 74% % of Coverageof % 2.50 63% 60% 2.00 50%

50%

40% 2.00 2.50 3.00 3.50 4.00 4.50 5.00 Distance (km)

Figure 4.8: Effect of coverage in service distance.

Relaxing the service distance allows covering much more settlements but the difficulty to achieve service rises accordingly, which is not desirable, as the accessibility provided by the nodal point will be decreased. Hence, it is better to add new nodal points rather than expanding the service distance to increase accessibility to the settlements and the public facilities.

The covering distance can be fixed as 4 km as more than 80% of the settlements are covered within 4 km walking distance as per the result obtained from the four case studies conducted in four hilly regions of Gorkha and Lamjung districts of Nepal. The value corresponds to the average human walking speed which is 5 km/hour. In the other words, the covering distance corresponds to the one hour walking distance which is reasonable in the context of hilly areas.

4.6.2 Covering of public facilities

The covering issue is not only important for the settlements but also to the service centres in rural hilly areas. Hence, existing public facilities (health centres, market centres and schools) in the study area has been analysed and presented as follows. The study was conducted in four regions (two regions in Gorkha district and two regions in Lamjung district). The study is limited to 56 VDCs and 904 settlements because data were not available for Ghairung, Namjung, Tanglichowk and Fujel VDCs in Gorkha A and Pachowk, Ilampokhari and Nauther

VDCs in Lamjung B regions (seven VDCs).

Based on the covering model, nodal points have been determined fixing the maximum service distance to 4 km. Then the coverage situation of public facilities has been evaluated and presented in the following sections.

Covered health centres

The health centres are sparsely scattered in the region, generally one health centre in each VDC (SAIPAL, 2010). According to the model, the coverage of the health centres by the nodal points has been found covered within the service distance of 4 km. The study has collected the health centre data of 56 VDCs in the four study regions. A total of 60 health centres has been found in the regions out of which 4 (7%) health centres are out of the 4 km covering distance. 93% of the total health centres are found covered with in the distance (Table 4.3).

Table 4.3: Coverage of the health centre by nodal points Numbers S.N. Region VDCs Settlements Covered Uncovered Total 1 Gorkha A 15 219 14 1 15 2 Gorkha B 11 193 10 3 13 3 Lamjung A 10 185 11 0 11 4 Lamjung B 20 307 21 0 21 Total 56 904 56 4 60 % covered/uncovered 93% 7%

Covered market centres

In the regions under study, a few market centres (18) have been identified. The data is based on central service map (SBD, 1989). All the market centres are found covered by the nodal points (Table 4.4).

Table 4.4: Coverage of the market centre by nodal points Numbers S.N. Region VDCs Settlements Covered Uncovered Total 1 Gorkha A 15 219 3 0 3 2 Gorkha B 11 193 2 0 2 3 Lamjung A 10 185 4 0 4 4 Lamjung B 20 307 9 0 9 Total 56 904 18 0 18 % covered/uncovered 100% 0%

Rural Engineering Infrastructures Design and Public Facility Locations

Covered schools

Schools are the major public facility in all the regions under study. Schools are scattered in different locations of a VDC as the settlements are scattered. The coverage of schools has been found lower when compared to the other public facilities. A total of 328 (89%) schools are identified in the four regions of study, out of which 293 has been found covered within the specified coverage distance. 35 (11%) schools are found outside the coverage distance (Table 4.5). This result is somehow similar to the coverage to the settlements by the nodal points 89% (Figure 4.8). It seems location of schools can be a good guide to fix a nodal point (obligatory point) within a VDC and to form a rural road network in a region. Location of schools can be easily identified in the map. However, the settlements are to be clustered in a definite location. The households of a settlement are highly scattered making difficult problem of that makes always a problem to locating the centroid of the scattered houses in the rural hilly areas.

Table 4.5: Coverage of schools by nodal points Numbers S.N. Region VDCs Settlements Covered Uncovered Total 1 Gorkha A 15 219 78 9 87 2 Gorkha B 11 193 49 20 69 3 Lamjung A 10 185 69 3 72 4 Lamjung B 20 307 97 3 100 Total 56 904 293 35 328 % covered/uncovered 89% 11%

Overall coverage

The total facility coverage is shown in Table 4.6. 90 % of the facilities are covered within 4 km covering distance and 10% facilities are found uncovered. The Table 4.5 and Table 4.6 are comparable. The facilities are dominated by the distribution of schools, which are found to be the dominant facilities in the rural areas.

Table 4.6: Coverage of public facilities by nodal points Numbers S.N. Region VDCs Settlements Covered Uncovered Total 1 Gorkha A 15 219 95 10 105 2 Gorkha B 11 193 61 23 84 3 Lamjung A 10 185 84 3 87 4 Lamjung B 20 307 127 3 130 Total 56 904 367 39 406 % covered/uncovered 90% 10%

This study has found the market centres well covered (100%), when the nodal points are fixed

according to the model presented above. Mostly (93%) health centres are also covered by the model in the regions. Schools are the least covered (89%) facilities and widely scattered in these regions. This also shows that definition of rural road network considering only market centres can not cover most of the settlements and other public facilities in hilly regions. However, most of the literature on planning of rural roads emphasize the construction of rural roads to connect market centres without considering the location of public facilities and settlements. This study shows that location of schools can be taken as a good basis of fixing the nodal points in the rural areas to define rural road network. When a bigger number of schools is covered, more settlements are also found to be covered. However, covering all the settlements and facilities in the region can be a costly endeavour. Hence, it is intended to maximise the coverage of settlements and public facilities by rural road in a reasonable service distance. The covering problem is a political and budgetary issue. However, covering can be improved adding more nodes in the least covered VDCs.

4.7 Linkage pattern of rural roads in hilly regions

There are many existing rural road networks in hills of Nepal developed in the past on public and community efforts. Most of the networks are in developing stages. The development of rural road network in the hill is constrained by its topography and geological condition (as is the case of the Himalayan region in Nepal). The developed network has formed a pattern of rural road network in hills. These developed patterns may give a ground for the development of a rural roads network model for hilly regions. For this purpose, the developed pattern of rural road networks in hills has been studied in this section. The developments of rural roads in the regions are guided by the location of settlements and public facilities. The facilities are the schools, health services, and market centres.

The settlements are scattered throughout the hill slopes in the studied regions. Generally, the ridge slopes have densely populated settlements. Population in valleys near streams are less due to steep slopes and the weak stability of hill slopes. Also, the stream lines are surrounded by instability features like erosions, landslides, and generally covered by forests. Mostly these areas are barren lands due to a difficulty for cultivating. The stable land are either cultivated or inhabited in the hilly regions of Nepal. Hence, the areas where people used to live and cultivate since long time are the stable areas. Thus, the numbers of settlements are concentrated in the upper hill slopes because they are less prone to instability problems. It is obvious that the nodal points of rural roads alignment are also concentrated in the hill slopes,

Rural Engineering Infrastructures Design and Public Facility Locations generally at ridgelines of hills. Hence, it is necessary to take road alignment along the ridgeline as far as possible to connect or provide accessibility to the settlements that there exist.

The road alignment through ridges of hills passes through stable slopes and covers most of the settlements. Besides settlements, the public facilities are also situated in the hill slopes near to the ridgeline of slopes. The same precedence has been found in the study of the location of public facilities (section 4.6). Hence, location of road alignment along the hill slopes is also equally beneficial to cover the public facilities in the hills. This is another positive aspect of the rural road alignment locating along a ridge of the hill slope.

4.7.1 Data concerning the rural road networks under study

Four rural road networks have been studied in hilly regions. All the rural road links to the identified nodal points have been considered as the alternative links. The nodal points were identified using covering based model as discussed in section 4.4. The existing and (few) new linkages to the nodal points have been shown in Figure 4.9, Figure 4.10, Figure 4.11, and Figure 4.12. The settlements, rural road networks in the four regions are marked in Google earth maps and presented in Appendix C. The distance matrix of the four networks has been formed and shown in Table D.1, Table D.2, Table D.3, and Table D.4 respectively in Appendix D. Each network has been solved for a MST for each region using Prim’s algorithm (Prim, 1957). The MST obtained for each network is shown in Figure 4.13, Figure 4.14, Figure 4.15, and Figure 4.16.

Takumajhlakuribot 22

21 Palkhu 20 Deurali Dwaridhari 19 Dhakalgau Khatrithok 17 18 13 12 M. Dubindanda 11 14 16 Taple bazar Pokhrelgau 10 Bhogteni 6 15 Digau 2 24 7 Thamdanda 5 Kuwapani 8 Gairigau 1 3 9 Legend Nodal points 23 Main nodes Hatiya Intermediate points 4

Figure 4.9: Rural road network in the study area: Gorkha A.

Hansapur

21 Chisapani

19 20

Kalimati Thalajung 22 15 16 Patalepani 12 23

11 17 10 Sarkigau 18 Ampipal Palumtar 13 8 Banspur

7 Chhoprak Kholipakha 6 9 14 3 Gaikhur 2 Legend 4 5 Nodal points Daukholagau Main nodes 1 Intermediate points

Figure 4.10: Rural road network in the study area: Gorkha B.

Rural Engineering Infrastructures Design and Public Facility Locations

Newargau Kamrakhu21 22 Okhari 18 Perjedanda 19 17 20 Upalloalainche Gauda Kamargau 8 Pyarjungbhanjyang 9

Bharate Bakot Lamagau 16 15 Kalleri 7 10 Daramdhunga Kotod Bhaisara 14 6 12 Harrabot 11 13 Seltarbajar Bhaisikholagau 5 Tarkughat Legend 2 1 Nodal points 4 Satdobato 3 Dhamilikuwa Main nodes Intermediate points

Figure 4.11: Rural road network in the study area: Lamjung A.

Jhakrikhet Bhakunde 5 4 Khatrigau Dandagau 6 Chandigau 20 25 Kharibhanjyang Sindhuredhunga Udipur 19 7 Gahatelek 3 Ranipani Swaradeurali 8 9 Baspani Bajarkot 18 26 Bagre 11 Nayagaupakha 22 Dhuseni 17 Bhorletar 27 28 Swara 23 21 Satrasayaphant MajhgidaKirtipur 44 Swara int 29 Archyalwani 10 Malekharka 24 16 Bhaktichowk 30 Rampani Khahare 2 Upallorayapali 31 12 Khatrichhap 13 Jita Gothpani Kharetar 32 Shantibazar Sundeerbajar 39 Amdanda 35 15 38 Sunargau Kunchha 14 Samibhanjyang 33 40 37 Paundidhik 1 Legend Gorkhalithan Kirtipur 41 Nodal points 34 Duipiple Main nodes 43 Sotipasal 36 Intermediate points 42 Thulokumalgau

Figure 4.12: Rural road network in the study area: Lamjung B.

Takumajhlakuribot 22

21 Palkhu 20 Deurali Dwaridhari 19 Dhakalgau Khatrithok 17 18 13 12 M. Dubindanda 11 14 16 Taple bazar Pokhrelgau 10 Bhogteni 6 2 7 15 Thamdanda Digau 5 Kuwapani 8 Gairigau 1 3 9 Legend Nodal points Main nodes

Hatiya Intermediate points 4

Figure 4.13: Identified nodal points and MST of the rural road network (Gorkha A).

Hansapur

21 Chisapani

19 20

Kalimati Thalajung 22 15 16 Patalepani 12 23

11 17 10 Sarkigau 18 Ampipal Palumtar 13 8 Banspur

7 Chhoprak Kholipakha 6 9 14 3 Gaikhur 2 Legend 4 5 Nodal points Daukholagau Main nodes 1 Intermediate points Figure 4.14: Identified nodal points and MST of the rural road network (Gorkha B).

95 Rural Engineering Infrastructures Design and Public Facility Locations

Newargau Kamrakhu21 22 Okhari 18 Perjedanda 19 17 20 Upalloalainche Gauda Kamargau 8 Pyarjungbhanjyang 9

Figure 4.15: Identified nodal points and MST of the rural road network (Lamjung A).

Jhakrikhet Bhakunde 5 4 Khatrigau Dandagau 6 Chandigau 20 25 Kharibhanjyang Sindhuredhunga Udipur 19 7 Gahatelek 3 Ranipani Swaradeurali 8 9 Baspani Bajarkot 26 Bagre 18 22 Dhuseni 17 11 Nayagaupakha Bhorletar 27 28 Swara 23 21 Satrasayaphant MajhgidaKirtipur 44 Swara int 29 Archyalwani 10 Malekharka 24 16 Bhaktichowk 30 Rampani Khahare 2 Upallorayapali 31 12 Khatrichhap 13 Jita Kharetar Gothpani 32 Shantibazar Sundeerbajar 39 Amdanda 35 15 38 Sunargau Kunchha 14 Samibhanjyang 33 40 37 Paundidhik 1 Legend Gorkhalithan Kirtipur 41 Nodal points 34 Duipiple Main nodes 43 Sotipasal 36 Intermediate points 42 Thulokumalgau

Figure 4.16: Identified nodal points and MST of the rural road network (Lamjung B).

Linkage pattern of rural road network has been studied for the MST networks and presented in the following section.

4.7.2 Existing pattern of the rural road linkages

The existing pattern of rural road linkages has been studied in the following four cases. All the cases lie in hilly regions of Nepal.

Case 1: Gorkha A

The rural road network is developed mostly in hilly topography. Figure C1 in Appendix shows, few links are along the valley/foot hills in the region. All the nodal points identified are at hills (Table 4.7). Almost all the nodal points are connected by existing links except link 14-15 and link 21-22 (Figure 4.13). The links 14-15 and link 21-22 are also in developing stage. All the linkages of network identified are in hill near to ridges of hills. None of the links along the valley/foot hills are in the MST.

Table 4.7: Location of nodal points and linkage to the nodal points-Gorkha A Node Road Link Route type SN VDC (Village) (existing) (to node) 1 Aarupokhari Dhakalgau Yes Hill 2 Asrang Thamdanda Yes Hill 3 Baguwa Pokhrelgau Yes Hill 4 Borlang Gairigau Yes Hill 5 Bunkot Hatiya Yes Hill 6 Dhawa Digau No Hill 7 Finam Sunderdanda Yes Hill 8 Masel Majhthok Yes Hill 9 Nareshwor Bhogteni Yes Hill 10 Panchkhuwadeurali Deurali Yes Hill 11 Pandrung Gairichhap Yes Hill 12 Takukot Takukot Yes Hill 13 Takumajhalakuribot Majhlakuribot No Hill 14 Tandrang M. Durbindanda Yes Hill 15 Taple Taplebajar Yes Hill 16 Ghairung Hatiya Yes Hill 17 Namjung Namjung Yes Hill 18 Tanglichowk Saddikhola Yes Hill 19 Fujel Bhedabari Yes Hill

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The identified network has a backbone link (links connecting nodes 1, 3, 5, 6, 7, 10, 11, 13, 17, and 19 in Figure 4.17) and 7 branch links. The branch links connect the other identified nodal points in the hill areas.

Takumajhlakuribot 22

Figure 4.17: Backbone and branch rural road network (Gorkha A).

Case 2: Gorkha B

In this case also, the rural road network is developed mostly in hilly topography. Most of the links are along the hills in the region (Figure C2 in Appendix). All the nodal points identified are in the hills (Table 4.8). Almost all the nodal points are connected by existing links except link 16-17 and link 17-18 (Figure 4.14). The link 16-17 is in the developing stage. The link 17-18 can be developed only after developing the link 16-17. All the linkages of network identified are near to ridges of hills except one link 1-14 in valley/foot hill in the MST. However, the MST can be modified to account for local conditions as follows.

The obtained MST connects all the nodes in the network. There are two categories of nodes in the network nodal points and intermediate points. The first category of points, the nodal points is important nodes which cover the settlements and the public facilities in the specified areas. The second categories of points, the intermediate points are only the connecting nodes introduced during the road network formation. The second category of nodes is not important in terms of connectivity and accessibility to settlements and public facilities. Hence, the

intermediate points can be removed from the network as far as possible to make the rural road network as short as possible (and more economical). In this way, after obtaining a MST of a road network, the above situation should be carefully judged. Furthermore, some important links can be retained in the network due to its importance. For example, some links can be strategically important within the region.

In this network, link 5-6 (7.53 km) to connect the strategically important node 7. Hence, it is better to retain links 5-6 and 6-8 (8.24 km) and remove links 1-14, 13-14, and 1-2 (total 17.1 km). This is short and better than the previous network. Now, link 5-6 is foot hill link. Link 22-23 is also not required since it doesn’t connect any nodal points.

Table 4.8: Location of nodal points and linkage to the nodal points-Gorkha B Road SN VDC Node Link Route type (Village) (existing) (to node) 1 Mirkot Dhaukholagau Yes Hill 2 Khoplang Kholipakha Yes Hill 3 Chhoprak Chhoprak Yes Hill 4 Ampipal Ampipal Yes Hill 5 Harmi Patalepani Yes Hill 6 Gankhu Banspur No Hill 7 Srinathkot Sarkigau No Hill 8 Jaubari Kalimati Yes Hill 9 Thalajung Thalajung Yes Hill 10 Kerabari Chisapani Yes Hill

The MST so obtained has a similar type of backbone links along a major ridgeline (links connecting nodes 4, 3, 6, 8, 10, 11, 12, 15, 16, 19, 20, and 21 in Figure 4.18) and 6 branch links. The branch links (2-3, 6-7, 8-9, 12-13, 16-17, 17-18, 20-22 in Figure 4.18) connect the identified nodal points in the region.

99 Rural Engineering Infrastructures Design and Public Facility Locations

Hansapur

21 Chisapani

19 20

Kalimati Thalajung 22 15 16 Patalepani 12 23

11 17 10 Sarkigau 18 Ampipal Palumtar 13 8 Banspur

7 Chhoprak Kholipakha 6 9 14 3 Gaikhur 2 Legend 4 5 Nodal points Daukholagau Main nodes Intermediate points 1 Backbone links Branch links

Figure 4.18: Backbone and branch rural road network (Gorkha B).

Case 3: Lamjung A

In this case, the rural road network is developed in foot hills and hills. Most of the linkages are developed along the valley/foot hills in the region (Figure C3 in Appendix). However, most of the nodal points identified are at hills (Table 4.9) except two (node 3 and node 4) in foot hills. In this case, 6 nodal points are connected by existing links and 5 are not yet connected. The link 17-18 is in developing stage. The links 18-19 and 18-22 can be developed only after developing the link 17-18. Only linkages 13-12, 12-9, 9-8, and 8-17 are near to ridges of hills. But, the MST (Figure 4.15) obtained from analysis of the road network shows that it is better to include links 9-10, 10-11, 8-7, 18-19, and 18-22 in the network to make an effective road network. However, these are new linkages in the network. Moreover, the MST did not included link 12-9 which is already developed.

As in case 2, the network (Figure 4.15) contains some intermediate points (nodes 5, 6, and 21) that can be removed. If link 12-9 (11.24 km) can be included in the network, we can remove nodes 14, 15, and 20 from the network. Then, we can remove links 13-14, 14-15-15-20, and 20-19 (total 18.72 km) in the network and the MST can be modified including the link 12-9. Though links 4-5 and 5-6 (the valley foot hills links) have been already developed, they are

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not effective in the network as it couldn’t connect the nodal points. Hence, links 4-5 and 5-6 can be removed from the MST network. The later MST network is recommended rather than the previous one as it is shorter.

Table 4.9: Location of nodal points and linkage to the nodal points-Lamjung A Road SN VDC Node Link Route type (Village) (existing) (to node) 1 Dhamilikuwa Dhamilikuwa Yes Hill 2 Chakratirtha Satdobato Yes Valley 3 Bhalayakharka Dharamdhunga No Hill 4 Kolki Bakot No Hill 5 Pyarjung Lamagaun No Hill 6 Turture Bhaisikholagau Yes Valley 7 Raginas Bhaiswara Yes Hill 8 Bharate Bharate Yes Hill 9 Archalbot Upalloalainche No Hill 10 Srimanjyang Newargau No Hill 11 Gauda Parjedanda Yes Hill

Newargau Kamrakhu21 22 Okhari 18 Perjedanda 19 17 20 Upalloalainche Gauda Kamargau 8 Pyarjungbhanjyang 9

Bharate Bakot Lamagau 16 15 Kalleri 7 10 Daramdhunga Kotod Bhaisara 14 6 12 Harrabot 11 13 Seltarbajar Bhaisikholagau 5 Tarkughat Legend 2 1 Nodal points 4 Satdobato Main nodes 3 Dhamilikuwa Intermediate points Backbone links Branch links Figure 4.19: Backbone and branch rural road network (Lamjung A).

The obtained MST has similar type of backbone links along a major ridgeline as in case 1 and 2 (links connecting nodes 1, 2, 13, 12, 9, 8, 17, and 18 in Figure 4.19) and 6 branch links along the secondary ridgelines.

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Case 4: Lamjung B

Also, in this case, the rural road network is developed in topography of hills and foot hills. Most of the links are along the hills in this region (Figure C4 in Appendix). Most of the nodal points identified are at hills (Table 4.10) except two nodes (node 2 and node 15) in the foot hills. In this case, all the nodal points are connected by existing road links. Most of the linkages are developed in hills of the region and are near to ridges of hills.

Table 4.10: Location of nodal points and linkage to the nodal points- Lamjung B Road SN VDC Node Link Route type (Village) (existing) (to node) 1 Sunderbajar Sunderbajar Yes Hill 2 Bhoteodar Bhaktichowk Yes Valley 3 Tarku Bajarkot No Hill 4 Udipur Nayagau Yes Hill 5 Gaushahar Jhakrikhet Yes Hill 6 Duradanda Archyalwami Yes Hill 7 Chandreswor Kirtipur Yes Hill 8 Puranokot Dandagau Yes Hill 9 Sindure Chandigau Yes Hill 10 Neta Swara Yes Hill 11 Bagre Bagre Yes Hill 12 Bhorletar Bhorletar Yes Hill 13 Samibhanjyang Amdanda No Hill 14 Ramgha Thulokumalgau Yes Hill 15 Suryapal Gorkhalithan Yes Hill 16 Taksar Sunargau Yes Hill 17 Jita Jita Yes Hill 18 Kunchha Shantibajar Yes Hill 19 Dhuseni Dhuseni Yes Hill 20 Parewadanda Kharetar Yes Valley

The MST has been obtained and can be seen in Figure 4.16. The network has been modified based on the judgement as in above cases. The MST now includes links 39-42, 38-30, 22-18 and 18-19 (total 22.04 km). The links 42-36, 36-37, 34-35, 24-16, and 16-12 (total 22.81 km) are removed from the network since these links don’t connect any nodal points. The modified MST is better than the previous one. In this region, node 1, 2, 3, 4 and 14 lies in feeder road (higher standard road) network. Hence, node 14 can be taken as the main connecting node rather than node 1.

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The modified MST has similar types of backbone link along a major ridgeline (links connecting nodes 14, 13, 12, 10, 8, 7, 6, 20, 19, 18, 21, 22, 28, 29, 30, 38, 39, 40 and 42 in Figure 4.20) and 11 branch links.

Jhakrikhet Bhakunde 5 4 Khatrigau Dandagau 6 Chandigau 20 25 Kharibhanjyang Sindhuredhunga Udipur 19 7 Gahatelek 3 Ranipani Swaradeurali Baspani 8 9 Kirtipur Bajarkot 26 Bagre 21 18 22 Dhuseni 17 11 Nayagaupakha Bhorletar 27 28 Swara 23 Satrasayaphant 44 Swara int 29 Majhgida Archyalwani 10 Malekharka 24 16 Bhaktichowk 30 Rampani Khahare Upallorayapali 2 31 12 Khatrichhap 13 Gothpani Jita Kharetar 32 Shantibazar Sundeerbajar 39 Amdanda 35 15 38 Sunargau Kunchha 14 Samibhanjyang 33 40 37 Paundidhik 1 Legend Gorkhalithan Kirtipur Nodal points 41 34 Main nodes Duipiple Intermediate points 43 Sotipasal 36 Backbone links 42 Thulokumalgau Branch links

Figure 4.20: Backbone and branch rural road network (Lamjung B).

In all the cases, it is noted that the backbone links passes through a major ridgeline which is between two rivers, on both sides of the ridge. The branch links pass along the secondary ridges emanating from the main ridge. The secondary ridges have also similar types of formation in between two streams. The streams are the tributaries of the main rivers. The structure of such network can be seen in Figure 4.21.

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Legend: BB Link Branch Link Stream River Nodal point

Figure 4.21: Structure of backbone and branch road network.

Both backbone and branch links mostly pass through the zone 3 of the mountain model (Section 3.2) and partly through the zone 4 of the mountain model. Zone 3 is the most stable zone in the hilly regions.

4.7.3 Rural road network formation

In the four case studies of rural road network, the MST linkages length is compared with the existing rural road linkage lengths. The MST network linkages lengths are found significantly lower than the original road linkages lengths. Table 4.11 shows the results obtained from the four case studies conducted in hilly regions of Gorkha and Lamjung districts of Nepal taking 4 km as the covering distance to the settlements and the public facilities.

The first column of Table 4.11 shows the four regions that are considered for the rural road network study. The second column in the table shows the original lengths of rural road network in the study regions, the third column shows the MST network length in the regions. The fourth column shows the reduced percentage of road length in the regions compared to the original network lengths.

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Table 4.11: Rural road network linkage lengths Total lengths MST lengths % of reduced Regions in km in km length Gorkha A 149 80 46% Gorkha B 128.5 84 35% Lamjung A 151 75 50% Lamjung B 204 124 39% Total 632.5 363

The total MST road linkage lengths are 43% of the total original road lengths for 4 km covering service distance. This shows that attention can be given to MST network which is less than 50% of the total road network in the hilly regions. Limited budget can be put to the important links (MST links) which are effective to cover settlements and public facilities. However, this can be subjected to further analysis for prioritization and setting the surface level of linkages based on the available budget.

It was found that the nodal points are connected by the existing roads, tracks and the trail. The trails can be replaced by the rural roads. The existing tracks can be upgraded to the standard rural roads. Most of the rural roads in the past were converted into standard rural roads from trails and tracks. The above analysis shows that the length of the rural roads network can be quite less than the existing network lengths. This shows that the methodology also gives an effective rural roads network in the hilly regions of Nepal. This can help to identify the most important rural road links to be developed in a hilly region at least to a minimum standard. Therefore, it gives an opportunity to decision makers to select the road links for intervention so that settlements and public facilities are better connected and covered. Furthermore, the scarce resource can be used more effectively in the important links rather than investing fund using ad-hoc or political basis. Investment in the proper rural roads links may enhance an effective quality of public services and improve accessibility in the rural areas.

In general, we find the road highway alignments along the major rivers. The rural road alignment is taken from the highway located at the bank of rivers to the ridgeline or from a point in a feeder road. One of the problems in locating the rural road alignment in hill is locating the transitional alignment from the existing road line at a river valley. This is one of the difficult tasks to locate the transitional part of rural road alignments in hilly regions. Generally, it lies in steep hill slopes. This can create instability problems in hill slopes mainly drainage, erosions, and landslides. The valley slope areas are more likely to have water drainage problems. Hence, locating the transitional alignment is a critical part in hill rural

105 Rural Engineering Infrastructures Design and Public Facility Locations road alignment selection works. There should be a strategy such that the transitional length of the road will be minimum and stable. The transitional section of the road carries the road head to that point in a main ridgeline from where a main ridge road alignment (backbone) can be formed.

From the main ridge road alignment (backbone), we can branch out a tree to connect identified nodal points with road links and cover the rural hill settlements and the public facilities. From these case studies, alignments along the ridgelines are found appropriate to cover the settlements and the public facilities effectively.

Furthermore, in a different context, the construction of roads in hills has a negative impact to the local environment, creating land slides and erosion to the natural slopes and valley side occupations and cultivation. This has resulted into the slide of the road itself in many circumstances. This damaging cost may become many times higher than the construction cost of the roads. This has not only washed out the excavated materials the cultivated lands, forests sometimes even whole village settlements. Most of the roads constructed in this way have created a serious environmental problem in hill districts of Nepal. In this way construction of rural roads in hilly regions has not only social and technical issues, but also environmental issues that should be carefully addressed during planning, design and construction of roads. Carefully planned rural roads alignment can minimise the problem reducing the volume of cut which cause disturbance to the local environment. One way of minimising the cut volume is to minimise the length of roads in hill slopes. Hence, the road network optimisation in the hilly regions is very important that will minimise the total length of road links in rural road networks and minimise environmental problems. The MST minimises the road lengths in a rural road network as shown above.

Now, a simple method for rural road network formation can be established. It can be stated as follows:

1. Identify and mark the backbone (main ridge) line in hills on a map, it will connect some of the nodal points, and 2. Identify and mark the branch (secondary ridge) lines in hills on the same map so that the remaining nodal points can be connected to the backbone line.

The MST is one level of optimisation of rural road network as it has given the road network length significantly less than the existing network ensuring better connectivity of the nodal

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points and covering settlements and public facilities. The covering based method explored in this study has been found practical for identifying the nodal points and the rural road network in hilly regions.

4.8 Application to other rural infrastructure problems

The rural road is a key element of rural infrastructures as it plays a vital role for the development and operation of other infrastructures. The other basic physical infrastructures are water supply, electricity and telecommunication which come at relatively high costs in rural communities. As scale, density, distance and purchasing power of rural communities tend to increase investment costs, inappropriate location of these facilities also drive the prices for these commodities up in rural areas. All the physical infrastructure problems stated above have some similar constraints and mitigation measures. The problems consist of locating water reservoirs and public water supply tap stands, locating electricity transformers and poles, locating public telephone booths and poles/terminals and defining the corresponding water distribution pipe network, electricity distribution wire network, and telecom wire network formation.

The rural infrastructure problems have similarities in the following respects:  Covering of settlements and public facilities,  Identification of an appropriate location of nodal points, and  Formation of distribution networks.

The proposed covering based method can therefore be used in electrical installation, pipe water distribution and telecommunication problems, in rural areas, to achieve the intended goals with a reduced cost and effective use of resources. Optimisation problems can be formulated on these infrastructures taking issues such as cost, efficiency, and/or reliability of the systems.

4.9 Conclusions

In order to define a rural road network, a model composed of two steps is proposed in this chapter. The covering model can be used to identify the village nodes (nodal points) which cover the settlements within the VDCs. These nodes can be taken as the obligatory points in a rural road network. The linkages to the nodes can form a basic rural roads network in the hilly

107 Rural Engineering Infrastructures Design and Public Facility Locations region of Nepal. This method provides a way of establishing the obligatory points in rural road alignment taking care of the covering of settlements and public facilities in rural hilly areas.

This model is useful in identifying the situation of coverage of settlements and public facilities by the nodal points in different service distances. The settlements and public facilities are concentrated along the ridgelines of hills. We can conclude that, for the rural hill region of Gorkha and Lamjung districts, only about 50% of settlements are covered within 2 km maximum service distance. If we increase the maximum service distance to 3 km, the coverage significantly increases to 74%. In the cases, almost 80 % of the settlements and the facilities are covered within 3.5 km of maximum service distance and 89% of the settlements were covered within 4 km service distance. Also, 4 km covering service distance can be taken as an appropriate service distance in hilly regions.

The refined network length is significantly decreased to 43 % for service distances of 4 km, ensuring better coverage, by using the MST.

The rural road network pattern can be defined by backbone and branch tree network in hilly regions of Nepal. The backbone links follows a main ridgeline and the branch tree network follows the secondary ridgelines of the main ridgeline of hills. The pattern has been developed in search of best routes to connect the rural hill settlements and public facilities considering better routes (cost minimisation).

The proposed model can be a practical and realistic approach for identifying obligatory points in rural road networks in hilly regions. The implementation of the model in the Gorkha and Lamjung districts of Nepal was able to confirm its applicability for the rural road network definition.

The covering based rural road network model is also adoptable to fix nodal points and form rural water supply distribution network, rural electrification grid extensions, and telecommunication network extensions.

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Chapter 5

Rural Road Network Optimisation Models

5.1 Introduction

Nepal has the majority of the population concentrated in rural areas of mountainous hills. The public facilities in the hills are scattered throughout different villages. Moreover, many residents of rural villages are not integrated in the national road network due to the absence or poor road connectivity. It is therefore difficult to get to public services and participate in economic and social activities. These factors have resulted in low quality of life of the Nepalese rural residents. Insufficient numbers of public facilities, transport accessibility to the facilities, and inappropriate location of the existing infrastructure in terms of covering are the other factors. The rural infrastructures which have been developed also face quality issues.

Only around 30% of Nepal is accessible by roads. More than 39% percent of the population in the hills is out of reach of all season roads within 4-hours walk (DoLIDAR, 2004). The road network is mostly developed in the plain regions and only in few parts of the hilly regions. Moreover, there is a lack of development of the rural road network that covers the villages and public facilities in the rural hilly regions. Hence, there is a need to extend and develop these roads (particularly in the hilly regions of Nepal) in order to integrate the rural facilities and the rural residents in the national network.

The development of infrastructures such as public facilities and road network has been extensively studied in the past, mostly independently from each other. This may not be enough as the location of facilities, in order to serve residents, is constrained by the structure of the designed network. When the network is designed improperly, residents get poor service even when facilities are located optimally. There is significant interaction of the network with

109 Rural Engineering Infrastructures Design and Public Facility Locations facility locations and it is therefore meaningful to determine the network design and facility location simultaneously (Daskin and Owen, 1999; Melkote and Daskin, 2001). However, the integrated model is complex for the rural infrastructures planning. In developing countries, funds spent on facilities are often fungible with funds for other development purposes. For example, we may have a choice between using funds to build a school, expand a hospital, or add a new road. The ability to move funds from one activity to another suggests that facility location models must account for alternative uses of these limited resources. It is particularly important that the models that support these decisions account for the possibility of improving the network, since network modifications may do more to reduce the average demand- weighted distance than will additional facilities. Such models would assist decision makers on how to make an effective choice under limited fund constraints (Daskin & Owen, 1999). It has been realized that these two issues, facility location and rural road network, have a direct impact on each other and should therefore be studied in a comprehensive and integrated manner.

Apart from limited financial resources to build rural roads and public facilities, the lack of proper planning methodology of these rural infrastructures is also a major problem (Heng et al., 2006). The models developed for the urban areas are often not suitable for the rural areas. Hence, a study on the planning of rural roads and public facility locations in an integrated manner, targeting optimized budget allocation is the main objective of this chapter. This chapter proposes rural road network models where rural road networks are designed considering public facility locations to achieve minimum total cost comprising construction and operation cost of the different road surface options (e.g. earthen, gravel, and bituminous) and public facilities (e.g. health centers, schools, and rural markets). The proposed model establishes the optimum location of nodal points which cover the facilities and establishes a rural road network considering financial and spatial constraints.

5.2 Covering aspects

In rural hills in Nepal, villages are sparsely populated and the main public facilities are not concentrated in the same location. Therefore, villages cannot easily access all types of facilities. Nevertheless, residents should have access to public facilities and services within a reasonable distance. Thus, identification of one or more nodes that can cover the most of the facilities in specified distances is necessary and usually it is a village from a group of villages. One way of grouping the settlements is based on the political boundary using the geographical

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centre of the boundary. However, the geographical centre may be less meaningful in the context of hilly terrains. Also, fixing the location of such centres is difficult for the hilly and rugged terrains. Hence, an appropriate method is necessary to locate such points.

Chapter 4 explored a covering model to determine the location of public facilities that may be more appropriate for hilly terrains. The scattered villages in hill slopes are generally connected with foot trails and only some of them are connected by rural roads. Mostly, the rural public facilities are connected by foot trails which constitute the accessibility network for the rural villages. The trails crisscross the hill slopes making for a distance much greater than the direct distance. Hence, it is not appropriate to use Euclidian distances. This trail network forms the base to locate an appropriate central village for facility location, from where distance to other villages or public facilities is to be minimum. Therefore, it is necessary to study the trail networks to find a nodal point (villages and facilities are treated as nodes). A distance matrix can be obtained after finding the actual distances of the foot trails between each settlement and facility.

The public facilities can be village development centres, health centre, schools, and market centres. The delineation of the area can be, for example, the Village Development Committee (VDC) boundaries, which are the lowest political units in Nepal.

Transportation network within a VDC can be assessed and the most effective village in terms of connectivity and covering in the VDC can easily be obtained (Shrestha et al., 2012). This can be treated as the nodal point for the VDC. If a single node cannot cover the whole VDC settlements and the facilities, other nodes may be added. In a similar fashion, the nodal points of the other VDCs can be obtained. For this, we need to generate the distance matrix of the villages and public facilities for each VDC. As the settlements in a VDC are sparsely populated, we cannot cover all the settlements with a public facility due to the requiring huge investments. An important choice for the decision maker is deciding what level of expenditure (how many facilities are to be used) can be justified by the resultant coverage (Church & ReVelle, 1974). As indicated above, one way to reduce the number of required facilities is to relax the constraint that all demand points must be covered. The typical covering problems include: finding the minimum number of facilities needed to cover all demand nodes (the set covering problem) (Church & ReVelle, 1974), finding the location of a fixed number of facilities to maximize the number of covered demands (the maximal covering problem) (Church & ReVelle, 1974), and finding the locations of a fixed number of facilities to

111 Rural Engineering Infrastructures Design and Public Facility Locations minimize the maximum distance between a demand node and the facility assigned to cover its demands (the p-centre problem) (Daskin & Owen, 1999). For this context, to find the nodal points, utilization of the maximal covering problem is more relevant. The shortest distance from each node to the other nodes needs to be calculated from the distance matrix. The shortest path matrix is obtained using the Floyd-Warshall algorithm (Floyd, 1962) thus providing the distance matrix.

The mathematical formulation of the covering based problem is explained in detail in Chapter 4. There is a finite set of facilities and demand points at a finite set of locations. These sets and locations are regarded as nodes of a network with arcs whose weights represent the distances between nodes. The maximum travelling distance for residents of the villages to get services from an allocated number of facilities needs to be defined. The objective of the problem is maximization of covering by the allocated facilities. The facilities are to be located in the villages from where remaining villages can be covered suitably.

The travel distance is a barrier influencing the decision making of residents of whether to travel to acquire services from a type of facility, at a certain location. This results in a constraint to where the facility should be located. Since individual travel distance (travel time) influences their welfare, and in order to avoid significant inequality in accessibility to public services, it is essential to consider the reasonable travel distance of each citizen to the facilities. Fixing a travel distance can be a political issue, however, 4 km in case of hilly region of Nepal is recommended in Chapter 4.

5.3 Rural road network models

The connection to the nodal points and facilities nodes by the rural roads links forms the basic network in the rural hills. A Minimum Spanning Tree (MST) is obtained by using the Prim’s Algorithm (Prim, 1957) to connect each nodal point in the network. The MST network is a minimum connection level necessary for a rural accessibility to cover the public facilities as identified in chapter 4.

The links in the network are technically feasible new links, existing tracks, potential links or roads in poor condition (which can be upgraded to all-weather roads) and can be considered as candidate links for improvement with options of road surface (earthen, gravel, or asphalt). The model to be developed aims to achieve the least total cost. The total cost includes all costs associated with construction/improvement and operation of a road network.

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The models can be divided into two cases. The first case concerns new road constructions and the second is directed at upgrading road links. Some new links construction may be necessary in the second case and thus can be included. As follows, two network models are proposed, each addressing one of the two cases.

We consider the residents and facilities to be on a number of village nodes of a road network, and the nodes are connected by road links as an undirected graph. The mathematical formulation considers a single surface in new constructions and different road surfaces options, for earthen, gravel, and asphalt in upgrading of links.

The model allows investigating the public resource allocation in order to attain minimum total cost. With an investment budget constraint, we intend to design the infrastructure by keeping total transportation costs to a minimum. However, the connectivity of network nodal points is more important in new constructions.

There are four models proposed for rural road networks, which will be discussed as follows:

Rural road network model 1(RRNM-1): Upgrading network

The network generally consists of existing road links which needs to be upgraded to a higher surface level. Few links can be new links and should be defined in constraints in case the new links are to be added to the existing network. The model sets a road surface with option of earthen, gravel and asphalt so that transportation cost in the network is a minimum in that budget level. It is a general purpose model applicable to both hills and plain networks.

Rural road network model 2 (RRNM-2): New network

The network is entirely formed of new links. This network can be a general network applicable for both plain and hill areas.

Rural road network model 3 (RRNM-3): Upgrading Hill/core network

The model is a special case of model 1. Backbone links are defined in the model so that backbone links are upgraded before upgrading the branch links in hills. In case of plain areas, a core network within a rural road network can be defined and can be treated as backbone links.

113 Rural Engineering Infrastructures Design and Public Facility Locations

Rural road network model 4 (RRNM-4): New Hill/core network

This model is a special case of Model 2. It consists of backbone links along the main ridges of hills and connects the branch links from the secondary ridges. The backbones are connected before connecting any branch links.

The models are formulated as follows. Residents are assumed on a number of village nodes of a given road network. The network is considered as an undirected graph G = (N, L). Where, N and L are the sets of village nodes and road links respectively. The following notations are used.

S is the set of road surface options S={s1, s2, s3} for earthen, gravel, and asphalt, respectively. is the weight of the link (i,j). is the travel cost per unit flow over surface type sS on link (i,j). is the distance from node i to node j. is the operating cost per unit flow of traveling over surface type s on link(i,j). is the operating cost on link (i,j) over surface type sS, where = . B is an available investment budget, and is the cost of improving link (i,j) with surface type s.

The decision variables in this model are: =1 if a link (i,j) is to be built with surface type s, 0 otherwise.

For new constructions, S will have a single surface; hence, notation s is not needed.

Budget constraints in this study are used to investigate different scenarios of decisions at different budget levels.

The model can be formed based on the Capacitated Facility Location/Network Design Problem (CFLNDP) (Melkote & Daskin, 2001) which seeks to minimize total transportation costs of the population subject to budget and spatial constraints and can be reformulated as (Heng et al., 2007):

RRNM-1: Minimise

(5.1)

114

The objective function of the model can be rewritten to consider the operating cost with weights to the links (Shrestha et al., 2012). Then, equation (5.1) can be restated as follows:

Minimise

(5.2)

Subject to:

(5.3)

(5.4)

 

   (5.5)

Equation (5.3) indicates that the improvement/construction expenditure is constrained to an investment budget. Constraints (5.4) define that one link is to be paved with only one type of surface. These constraints also guarantee all links are to be connected with one of the surface options. The model is suitable for links upgrading problems.

The objective function for new constructions is different. The objective of case 1 is to connect the links so that highly potential links are connected based on budget availability. Then, the model can be formulated as follows.

RRNM-2: Maximise

(5.6)

115 Rural Engineering Infrastructures Design and Public Facility Locations

Subject to:

(5.7)

 (5.8)

  (5.9)

The above models can select any links in the network when the constraints are met. These models are applicable to a general case.

In specific case of hilly regions, a typical network pattern has been identified in Chapter 4. In hilly regions, a rural road network consists of backbone links and branch links, later being connected to the former. Hence, the backbone links are to be connected or upgraded before connecting or upgrading the branch links. For plain areas, core network links can be defined and can be treated as backbone links as before. For this purpose, the branch links decision variables can be further defined as . The model will therefore have additional constraints.

Then, the model for rural road network upgrading problems with backbone and branch/core network can be rewritten as follows:

RRNM-3: Minimise

(5.10)

Subject to:

(5.11)

(5.12)

 

116

(5.13)

 



   (5.14)

Equations 5.10, 5.11, and 5.12 are the same as equations 5.2, 5.3, and 5.4. Here, the backbone link nodes are numbered first, and then branch links nodes. Where, m is the greatest node number in the backbone network. Hence, equation 5.13 guarantees that the secondary links can not be selected unless all the backbone links are selected.

Further, if we have to consider an intervention in branch links only after having higher surface level (asphalt or gravel) in backbone links, the following constraints can be imposed in the above model. In no case, the branch links have asphalt surface, unless all the links in the backbone are asphalt.

(5.15)

 



Similarly, the model can be modified for new networks, and rewritten as follows:

RRNM-4: Maximise

(5.16)

Subject to:

(5.17)

 (5.18)

  (5.19)

117 Rural Engineering Infrastructures Design and Public Facility Locations

  (5.20)

  (5.21)

The notations used in the above model represent the same as in the previous models.

5.4 Prioritization of links

5.4.1 Introduction

Fund available for rural road construction/upgrade is usually a constraint in developing countries. Hence, the available resources should be effectively used. For this, a prioritisation method is necessary. Based on a realistic and practical criterion, the rural road links in the network are to be prioritised for implementation.

There are many methods for prioritisation of road links. They are usually based on economic returns from the road linkages. The traditional feasibility indicators for economic evaluation of highway are Net Present Value (NPV), discounted benefit cost (B/C) ratio, and internal rate of return (IRR). These conventional methods are used for urban, and highways and higher standard roads where the economic return can be fairly estimated. However, in rural areas, the traffic volume is usually low and there is rarely significant economic activity. The traffic in rural roads in hilly regions may be lower than 25 vehicles per day (Airey & Taylor, 1999). The conventional economic indicator may therefore not be suitable for rural roads. Moreover, there is significant difficulty in quantifying the economic benefits and return from rural roads. Hence, a different approach is necessary to categorise and prioritise the road links in a network.

5.4.2 Indicators for rural road evaluation

Road links are generally prioritized on the basis of economic analysis. Basically traffic on the roads is the main parameter for evaluating the economic viability of roads. However, the traffic data of the rural roads are rarely available in districts. Maintaining the data in the districts may also be a costly endeavor. Moreover, as most of the rural hill roads have traffic less than 25 vehicles per day, most of the links may not viable on economic grounds. However, from a social point of view, rural villages and public facilities should be connected or covered in order to provide the accessibility of goods and services to be at least at a minimum level.

118

In this context, a practical methodology for prioritizing road works on low-volume and very low-volume roads in the rural areas of developing countries is relevant (Airey & Taylor, 1999). The methodology is based on a system for estimating future traffic on improved roads on the basis of readily available data. Moreover, the method accommodates the need to consider the opening of roads that may be currently impassable to motor traffic.

Two scenarios can be found: one for roads under operation (passable), and the other for impassable roads. The impassable roads can be of further two categories. The first category can be the new construction and the second is when the road is in poor condition. For impassable roads, lowest costs per head links were ranked highest. Here the problem is to quantify the number of trips in the links. There can be different trips such as district, agricultural and fishery trips. Airey and Taylor (1999) have given the indicative district trips also. However, the estimation of trips in the context of rural hills is still unworkable.

An alternative method is necessary to prioritize the road links in the network primarily based on social factors. The key social factor in the rural hill area is the population covered by a road link. The traffic generations in rural road links are due to population. Here, the role of other factors may not be significant. Hence, calculation of priority factor based on the population covered by links can be a realistic approach. The weight assigned based on population can be as comparable as trip generation in a link. When the traffic data and other data can be collected or is readily available, the weighting of links can be determined accordingly.

The gravity model has been used in many studies for traffic flow analysis in road links. An analogy can be made to the social sciences in a quantitative model of social interaction with the gravity model. A flow between any two population centres is directly proportional to the product of the populations or attractive forces of the two centres and inversely proportional to the difficulty between the two centres (Haynes & Fotheringham, 1984). That is,

(5.22)

More specifically, the simplest formulation is,

(5.23)

119 Rural Engineering Infrastructures Design and Public Facility Locations

Where, k and b are parameters to be determined empirically. For obtaining the data, population can be taken from census data, while the distance between population centres can be obtained from map measurement.

In Jung et al, (2008), the Korean highway system was investigated and it was found the gravity model as the metaphor of physical gravity in the system. The gravity model for the 2 Korean highway system was derived as T =f(P1P2/r ), where P denotes population.

The aim of a rural road planning methodology is to produce a basic rural road network in which each village has road access to large centres for marketing, clinics, schools, and other commercial, social and welfare activities. Such centres are called "market centres". The market centres are considered to be attractors of traffic from adjacent villages. The villages are considered to be generators of traffic which use the rural roads for trips to the market centres, either directly or via the existing main roads connecting the market centres. The construction costs can be taken as proportional to the lengths of links. Hence link lengths have been taken as a proxy for construction costs (Kumar and Tillotson, 1985). Similarly, travel costs can be taken as proportional to a factor called "person-km", which for a village node, is defined as the product of population connected by the village node to its root node and the distance between that village node and its root node (Kumar & Tillotson, 1985). The underlying assumptions involved in the adoption of this factor, are that:

 the number of trips generated by a village node is proportional to its population.  the travel costs are proportional to the distance travelled.

Thus the factor, person-km (multiplication of population and the distance travelled), will be proportional to the total travel costs. The methodology can be applied when only the population of the villages and linear distance between them are known. This is an advantage for rural areas where this simple data is often all that is available. It should be noted here that the method can still be used with actual costs when these are known.

Costs can be divided into two types. One type has been called construction costs and should include maintenance costs suitably discounted over the life of the road. In principle these costs can be estimated with reasonable accuracy. The other type of cost called travel costs, cannot be estimated with a satisfactory degree of accuracy. This limitation has led to a model which seeks to avoid dependence on the absolute value of travel costs. In a district of reasonably uniform topography it seems reasonable to suppose that the construction costs will

120

be proportional to the lengths of the links to be constructed (Makarchi & Tillotson, 1991). However, this can be complicated when there are different construction standards for roads carrying different levels of traffic. The model assumes that construction costs are proportional to the length of road constructed, but there is provision for a weighing factor to reflect different construction standards on some links. The travel costs are likely to be proportional to (i) the number of people connected by the link, and (ii) the distance travelled through the link to reach the destination. It is therefore argued that whatever the travel costs, they will be proportional to a factor called 'person-km' (Makarchi & Tillotson, 1991) which is defined as the product of population connected by the link, and the distance between the village and the destination through the link. Clearly this assumption can only be expected to apply over a region of similar agriculture, demographic structure, village type, and average income. The model is therefore aimed at relatively small uniform areas.

The model proposed by Kumar and Kumar, (1999) chooses the construction standards for a link on the basis of the population served by the link. Population is considered a good proxy for traffic in rural areas because traffic data generally is difficult to get. It is very difficult to estimate the traffic that will be served by a rural road involving construction of bridges and major upgrades. Road links can be ordered according to the population served and then road surface type for each category.

For prioritisation of rural roads, generally two broad approaches are used: (a) sufficiency rating and (b) cost-benefit analysis. The cost benefits analysis various costs and benefits associated with a road have to be evaluated in the same monetary terms, which is a difficult task. The model uses a simple parameter, that is, the population served with unit investment, for prioritisation of rural roads. As mentioned earlier, accessibility to people is considered as a benefit of the investment in rural roads. Thus, the ratio of population served by a link and its construction cost can be taken as good proxy for the expected benefit from a rural road link. The link serving higher population per unit investment receives higher priority. The priority for a rural road link can be calculated as follows:

Priority for a road link = Population served by the link/construction cost of the link.

DoLIDAR (2010) introduces Cost Efficiency Analysis (CEA) to prioritise new transport linkage. Criteria such as per capita cost and special social consideration (of inclusiveness) receive weights (points) relative to their perceived importance. Each road

121 Rural Engineering Infrastructures Design and Public Facility Locations link is then allocated to the number of points corresponding to the fulfilment of the particular criteria. The aggregate number of points that each intervention receives is computed by simply adding the points allocated per indicator. The result of this process leads to a ranking of the investment options. Four parameters are proposed to use for the prioritisation of the new transport linkages. The indicators are broadly based on socio- economic and technical data related to each individual road corridor and applicable for new linkages (Table 5.1).

Table 5.1: Scoring system for prioritization of new linkages (DoLIDAR, 2010) Parameter Scoring Unit Score Population per unit Cost Population/investment 55 Cost in 100000 Cultivated Land Cultivated Land/km 15 Population × Walking hour Population × Walking 20 hour /km Total Population of poor, Dalits and Population /km 10 marginalized Janjatis.

Population per unit cost has been taken as an important parameter for prioritisation of a linkage in DoLIDAR (2010). Population per unit cost is calculated from total population divided by investment cost in hundred thousand rupees i.e. number of person per 100000 Nepalese rupees (NRs). Further, it takes into account the accessibility parameter as population- distance in the form of population-hour, based on walking time to a road corridor. The population within the zone of influence (ZoI) area i.e. left and right of the proposed road alignment within 2 hours walking time in plain and 4 hours walking time in hills is considered. The cultivated land and the areas inhabited by poor and marginalized people within the ZoI are considered as a parameter for prioritization of roads in the manual.

The manual (DoLIDAR, 2010) has set a separate set of indicators for prioritisation for upgrading and rehabilitation of existing rural roads as shown in Table 5.2.

Table 5.2: Scoring system for prioritisation for upgrading and rehabilitation (DoLIDAR, 2010) Criteria Scoring Unit Score Traffic Unit TU 70 Cost Cost /km 20 Market/service Centrality Index 10 Total 100 centre

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Various types of vehicular and pedestrian traffic occupy the surface of rural transport linkage and impose different loads on the structure. Therefore, it is necessary to quantify the various traffic volumes in terms of a standard traffic unit, called Transport Unit (TU) or the Passenger Car Unit (PCU) which is defined as the traffic caused by a normal car, light van, jeep or a pick-up travelling at a speed of 40 km/h. A Passenger Car Equivalent is essentially the impact that a mode of transport has on traffic variables (such as headway, speed, density) compared to a single car. The composition of traffic and the respective traffic coefficients are taken from the Table 5.3.

Table 5.3: Traffic Unit (DoLIDAR, 2010) Type of Traffic Transport Unit (TU) Cars, light vans, jeeps and pick-ups 1.0 Light trucks up to 2.5 tonnes gross 1.5 Trucks up to 10 tonnes gross 3.0 Trucks up to 15 tonnes gross 4.0 4W Tractor towed trailers - standard 3.0 2W Tractor towed trailers - standard 1.5 Buses up to 40 passengers 3.0 Buses over 40 passengers 4.0 Bicycles 0.5 Rickshaws and tricycles carrying goods 1.0 Carts pulled/pushed by the human beings 2.0 Bullock carts with pneumatic tyre 6.0 Bulwheelslock carts with wooden wheels 8.0 Mule carts or horse drawn carts 6.0 Pack animals and mules 2.0 Pedestrians walking on the link 0.2 Porters walking on the link 0.4

The per km cost of upgrading and centrality index of each link in the rural road network is considered in the prioritisation of links. However, DoLIDAR (2010) recommends the direct benefit methods for the developed areas using the Net Present Value, Internal Rate of Return and Cost Benefit Ratio indicators for evaluating the rural roads.

5.4.3 Discussion

The quantification of economic indicators for prioritisation of rural roads is complex. Hence, prioritisation of rural roads in a network based on economic grounds is not practical in rural areas, due to the difficulty of estimating the correct economic benefit. Population served by a rural road link is taken as a good proxy to measure the benefit from the linkage. This measure is widely used in the literature to prioritise rural roads.

123 Rural Engineering Infrastructures Design and Public Facility Locations

Another main criterion for the evaluation and prioritisation of rural roads is construction cost. The cost of construction or upgrading should be justifiable in terms of benefits. But, it is also difficult to quantify its benefits. Hence, in many papers (e.g. Kumar & Kumar (1999)), cost of intervention with population is taken as the basis for prioritisation of links. The link which serves the most population is considered as a potential link in the rural areas. Therefore, population served by the link, that is population per unit investment, can be considered as an important indicator for prioritisation.

Another factor to be considered in the evaluation is travel cost by the population of the rural areas. However, this travel cost is difficult to quantify being a time consuming and costly work. A huge amount of travel data is needed to model the travel behaviour of the rural settlements, which is not practical. However, we need to include the effect of travel cost in the evaluation of rural road linkages. The travel cost can be more relevant than the construction cost of rural road link.

The travel cost is related to the distance from road head to a village and the population in the village. The higher the population, the greater the travel cost. Similarly, the greater the distance from village to the road head the greater the travel cost. The distance can be measured and population data can be obtained. However, it is difficult to estimate the travel cost. Hence, in many papers/works, indirect methods have been used to take the effect of travel cost in the evaluation of rural road linkages. The person-km has been used as indirect indicator by many researchers and can be taken as one of the most important parameter to evaluate the rural road links.

The Gravity model can also be used in traffic flow analysis. The main difficulty is the estimation of factor k and b in equation 5.23. The value of b is assumed as 2 in some studies (Jung et al, 2008, Shrestha, 2003) and k can be taken constant.

Most of the methodologies do not categorise the indicators for new linkages and the existing linkages for upgrading or rehabilitation. However, DoLIDAR (2010) has treated the prioritisation works differently for the new linkages and the existing linkages which are to be considered for rehabilitation and upgrading. In many papers, it has been found that the travel cost has been taken in the form of person-kilometre and as a basic indicator to take into account the travel cost. This has been taken into consideration in the manual in the form of population hour. However, the weight assigned to the indicator was 20% considerably

124

less when compared to population per investment (55%). The remaining weight was assigned to the cultivated land and the marginalized poor population as 15% and 10% respectively.

In literature, same indicators have been adopted for evaluation of new and upgrading linkages. However, DoLIDAR (2010) manual has given separate indicators for evaluation of upgrading linkages.

For the rehabilitation and upgrading of rural roads, DoLIDAR (2010) focuses on the economic benefits based on traffic volume in the road links. For the traffic indicator, it has given 70 % weight and for cost of upgrading 20% and for centrality index 10%. However, the collection of traffic and travel data is not practical in rural areas of hilly regions. Furthermore, in rural areas traffic are significantly less but a good accessibility to the settlements is still important. Hence, indicators based on the traffic unit are not suitable for the prioritisation for upgrading and rehabilitation of rural roads in most of the hilly regions. The same prioritisation indicators for new linkages are suitable for prioritisation of roads to upgrade.

DoLIDAR (2010) has attempted to consider important parameters; however, it is still complicated and not practical for rural hill areas. The cultivated land, centrality index, traffic units may not be easily available data and although it can be collected, the role of these indicators may not be significant. Hence, the parameters for prioritisation of rural roads links can be further simplified using simple parameters like population, construction/maintenance cost and person-km.

The benefit from the rural roads is associated with the accessibility to the public services and the rural settlements. Most of the methods are based on the accessibility to the market centres. However, the indicator addressing coverage issues of settlements and public facilities in rural areas is still lacking.

5.5 Models application and validation

The applicability of the proposed models is tested in the rural road network formed in Chapter 4 in 15 VDC of the hilly region in Gorkha district of Nepal as shown in Figure 5.1.

125 Rural Engineering Infrastructures Design and Public Facility Locations

Figure 5.1: Rural road network for model application.

Figure 5.1 shows the MST of rural road network in 15 VDCs of the district. This can be taken as the minimum level of connectivity necessary for the region as it connects all the nodal points which cover most of the settlements and public facilities within 4 km walking distance.

Prioritisation of links is necessary to implement a link in a network for both types of links either new or upgrading of the existing network. The simple parameters of prioritisation for rural roads as discussed in the previous section 5.4 are used here. Prioritisation weight from four methods has been calculated separately as follows:

(i) Population served by links (P1), (ii) Person-km (P2), (iii) Population served/km (P3), and (iv) Gravity flow model (P4).

The weight calculated for each link is given in Table 5.4 and treated as number of trips for the cost optimization purpose. Operating cost per unit flow over earthen, gravel, and asphalt surface are taken NRs 50.64, NRs 45.64, and NRs 36.79 (Tech Studio of Engineering, 2011) (NRs is Nepalese Rupees, 1 Euro ≈ NRs 110). The upgrading cost from earthen surface level to gravel surface level is taken as NRs 5 million per kilometre and from gravel surface level to asphalt surface level as 10 million per kilometre.

126

The mathematical models were solved using MPL for Windows 4.2 as the modelling language with CPLEX 10.0’s solver. The analysis is conducted to different budget levels. The node numbering in the network is rearranged as shown in Figure 5.2 for the model RRNM-3 and model RRNM-4. These models have backbone links (nodes 1 to 10) as seen in Figure 5.2.

9 19 15 8 7 16 18

4 6 11 5 17

3 13 1 2 14 Legend Nodal points Main nodes Intermediate points Backbone links 12 Branch links

Figure 5.2: Node numbering scheme for model RRNM-3 and model RRNM-4 with backbone and branch links.

The four method of prioritisation were applied in each model. The intervention in the network link at the different budget levels is shown in Table 5.5 (RRNM-1), Table 5.6 (RRNM-2), Table 5.7 (RRNM-3), and Table 5.8 (RRNM-4) based on prioritisation method P1 (population served by link). As per budget availability, the decision maker can select a set of links for intervention from these tables according to the rural road network model. Only four tables are presented here as an example. The output of these models RRNM-1, RRNM-2, RRNM-3, and RRNM-4 based on remaining prioritisation methods P2 (person-km), P3 (population served/km), and P4 (Gravity flow model) are presented in Appendix E as follows.

Table E.1 to Table E.3 shows the intervention (upgrading) in the network according to RRNM-1 under budget level NRs 10 millions to NRs 55 millions in intervals of 5 millions.

127 Rural Engineering Infrastructures Design and Public Facility Locations

The model suggests different road surface level for different links. Similarly, RRNM-2 is used to analyse the network for budget levels NRs 10 millions to NRs 55 millions and the output of the model is presented in Table E.4 to Table E.6 for the four prioritisation methods for intervention.

In a similar fashion, the output of the RRNM-3, based on the four methods of prioritisation is shown in Table E.7 to Table E.9 from budget level NRs 60 millions to NRs 220 millions. The model suggests different road surface level for different links as in RRNM-1. Finally, RRNM- 4 is used to analyse the network and the outputs are presented in Table E.10 to Table E.12. In this case, budget level has been started from NRs 140 millions to NRs 400 millions to verify the output of the model based on the same four methods of prioritisation.

Figure 5.3 to 5.10 illustrate an optimized network intervention for different budget levels.

128

Table 5.4: Weight based on population, person-km, population per unit construction cost and gravity flow model Links after % of % of % of new Population Person-km Population Gravity population cumulative population % of BB S.N. Links length served (cumulative) served/km Flow served p-km served/km flow scheme 1 1-2 5.75 4501 25,881 783 3,509,997 7.10 1.9 2.02 51.74 1-11 2 1-3 3.52 58936 1,364,905 16,743 6,784,469 92.90 100 43.23 00.00 1-2 3 3-4 6.00 7478 44,868 1,246 2,127,380 11.79 3.29 3.22 31.36 2-12 4 3-5 3.34 51458 1,112,582 15,407 4,657,089 81.12 81.51 39.78 68.64 2-3 5 5-6 3.44 48021 940,712 13,960 1,856,578 75.70 68.92 36.04 27.37 3-4 6 6-7 5.70 43029 775,520 7,549 957,603 67.83 56.82 19.49 14.11 4-5 7 7-8 2.69 9263 47,526 3,443 275,158 14.60 3.48 8.89 4.06 5-13 8 7-10 4.12 33766 482,729 8,196 512,915 53.23 35.37 21.16 7.56 5-6 9 8-9 4.20 5383 22,609 1,282 1,184,016 8.49 1.66 3.31 17.45 13-14 10 10-11 2.49 31520 343,613 12,659 996,213 49.69 25.17 32.68 14.68 6-7 11 11-12 1.74 4408 7,670 2,533 553,313 6.95 0.56 6.54 8.16 7-15 12 11-13 0.70 27112 257,458 38,731 442,900 42.74 18.86 100.00 6.53 7-8 13 13-14 1.50 8968 80,902 5,979 135,176 14.14 5.93 15.44 1.99 8-16 14 13-17 2.78 18144 157,578 6,527 307,724 28.60 11.54 16.85 4.54 8-9 15 14-15 7.73 4040 67,450 523 58,823 6.37 4.94 1.35 0.87 16-17 16 14-16 7.35 4928 36,221 670 76,353 7.77 2.65 1.73 1.13 16-18 17 17-18 5.57 5465 30,440 981 92,170 8.61 2.23 2.53 1.36 9-19 18 17-19 2.10 12679 76,697 6,038 215,554 19.99 5.62 15.59 3.18 9-10 19 19-20 1.20 10257 50,071 8,548 5,695,718 16.17 3.67 22.07 83.95 10-20 20 20-21 3.28 7236 37,763 2,206 1,379,806 11.41 2.77 5.70 0.34 20-21 21 21-22 5.12 2740 14,029 535 469,934 4.32 1.03 1.38 6.93 21-22

129 Rural Engineering Infrastructures Design and Public Facility Locations

Table 5.5: The intervention in the network link at different budget levels based on P1 (RRNM-1)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

1 3 3 5 6 7 8

(NRs) 1

10 11 11

13 13 14 14 17 17 19 20 21

in millions 5.75 3.52 6 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 100 A A A

200 A A A A A A G

300 A A A A A A A G A A

400 A A A A A A A A A A A A G

500 A A A A A A A A G A A A A A A A

600 A A A A A A A A A A G A A A A A A A

700 A A A A A A A A A A A A A A A A A A

800 A A A A A A A A A A A A A A A A A A A A Note: A = Asphalt G = Gravel

130

Table 5.6: The intervention in the network link at different budget levels based on P1 (RRNM-2)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

(NRs) -

1 1 3 3 5 6 7 8

10 11 11

13 13 14 14 17 17 19 20 21

in millions 5.75 3.52 6.0 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 10 E E

15 E E

20 E E

25 E

30 E E E

35 E E E

40 E E E

45 E E E E

50 E E E E E

55 E E E E E = Earthen (Selected Link)

131 Rural Engineering Infrastructures Design and Public Facility Locations

Table 5.7: The intervention in the network link at different budget levels based on P1 (RRNM-3)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 100 A A A A

200 A A A A A A A

300 A A A A A A A A G G A

400 A A A A A A A A A A A A A A

500 A A A A A A A A A A A A A A A A

600 A A A A A A A A A A A A A A G A A A

700 A A A A A A A A A A A A A A A A A A A

800 A A A A A A A A A A A A A A A A A A A A G Note: A = Asphalt G = Gravel

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Table 5.8: The intervention in the network link at different budget levels based on P1 (RRNM-4)

Links and Distance (km)

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

Budget -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

(NRs) in millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 140 E E E E E E E E E 160 E E E E E E E E E E E E 180 E E E E E E E E E E E E 200 E E E E E E E E E E E E E E 220 E E E E E E E E E E E E E E E 240 E E E E E E E E E E E E E E E 260 E E E E E E E E E E E E E E E E 280 E E E E E E E E E E E E E E E E 300 E E E E E E E E E E E E E E E E 320 E E E E E E E E E E E E E E E E E E 340 E E E E E E E E E E E E E E E E E E E 360 E E E E E E E E E E E E E E E E E E E 380 E E E E E E E E E E E E E E E E E E E E 400 E E E E E E E E E E E E E E E E E E E E Note: E = Earthen (Selected Link)

133 Rural Engineering Infrastructures Design and Public Facility Locations

As per the availability of the budget, the decision maker can select a set of links for intervention. From RRNM-1, for example, the suggested intervention can be found as shown in Figure 5.3 for a budget level of NRs 400 millions and Figure 5.4 for a budget of NRs 600 millions based on the four prioritisation methods separately.

Similarly, the output of the RRNM-2, based on the four methods of prioritisation is plotted in Figure 5.5 for budget level NRs 30 millions and in Figure 5.6 for budget level NRs 55 millions. In this case, the network is assumed as entirely new.

Similarly RRNM-3 is used to analyse the network. In this case, budget level ranges from NRs 100 millions to NRs 800 millions to verify the output of the model based on the same four prioritisation methods. The suggested links with road surface is shown in Figure 5.7 for the budget level NRs 400 millions and Figure 5.8 for the budget level NRs 600 millions. It can be seen that the model has selected the backbone links first and branch links afterwards.

Finally, RRNM-4 is used to analyse the network for budget levels NRs 140 millions to NRs 400 millions. The suggested links for the four prioritisation methods for intervention are shown in Figure 5.9 (budget 140 millions) and Figure 5.10 (budget 300 millions). It clearly shows that only backbone links are selected when the budget level is low (140 millions).

Looking to the Table 5.5, it is seen that the selected links have mostly asphalt surfaces. This is due to saving from lower operation cost in asphalt surfaces as operating rate for gravel is high (NRs 45.54) compared to asphalt (NRs 36.79).

134

20 19 Note: All thick lines represent Asphalt surface, thick lines with zigzag lines represent Gravel surface, 17 and thin solid lines represent road links with earthern surface. 18 12

13 11 14

6 10

15 2 7

8 Legend: 5 Nodal points Main nodes

1 Intermediate points 3 9 Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 Gravel Surface 4 Links

Figure 5.3: An optimal network intervention for a budget of NRs 400 million (RRNM-1).

20 19 Note: All thick lines represent Asphalt surface, thick lines with zigzag lines represent Gravel surface, 17 and thin solid lines represent road links with earthern surface. 18 12

13 11 14

6 10

15 2 7

Legend: 8

5 Nodal points Main nodes

1 Intermediate points 3 9 Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 Gravel Surface 4 Links

Figure 5.4: An optimal network intervention for a budget of NRs 600 million (RRNM-1).

135 Rural Engineering Infrastructures Design and Public Facility Locations

20 19

18 12

13 11 14

6 10

15 2 7

8 Legend: 5 Nodal points

1 Main nodes 9 3 Intermediate points Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 4 Links

Figure 5.5: An optimal network intervention for a budget of NRs 30 million (RRNM-2).

20 19

18 12

13 11 14

6 10

15 2 7

8 Legend: 5 Nodal points Main nodes 1 3 9 Intermediate points Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 4 Links Figure 5.6: An optimal network intervention for a budget of NRs 55 million (RRNM-2).

136

20 10

Note: All thick lines represent Asphalt surface, thick lines with zigzag lines represent Gravel surface, and thin solid lines represent road links with earthern surface. 15 9 19

8 7 16 18

6 4

17 11 5

Legend: 3 13 Nodal points 14 Main nodes

1 Intermediate points 2 Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 Gravel Surface 12 Links Figure 5.7: An optimal network intervention for a budget of NRs 400 million (RRNM-3).

20 10

Note: All thick lines represent Asphalt surface, thick lines with zigzag lines represent Gravel surface, and thin solid lines represent road links with earthern surface. 15 9 19

8 7 16 18

6 4

17 11 5

Legend: 3 13 Nodal points 14 Main nodes

1 2 Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 Gravel Surface 12 Links Figure 5.8: An optimal network intervention for a budget of NRs 600 million (RRNM-3).

137 Rural Engineering Infrastructures Design and Public Facility Locations

20 10

19 15

8 7 16

4 6

17 11 5

13 Legend: 3 Nodal points

1 Main nodes 2 14 Intermediate points Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 12 Links

Figure 5.9: An optimal network intervention for a budget of NRs 140 million (RRNM-4).

20 10

19 15

8 7 16

4 6

17 11 5

3 Legend: Nodal points

1 Main nodes 14 2 Intermediate points Prioritised by P1 Prioritised by P2 Prioritised by P3 Prioritised by P4 12 Links

Figure 5.10: An optimal network intervention for a budget of NRs 300 million (RRNM-4).

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The implementation of the proposed models in the 15 VDCs of Gorkha district show they can be a practical and realistic approach for the integrated facility location and rural road networks development in rural areas, particularly in the hilly region of Nepal.

The output of three methods P1, P2, and P3 are somehow similar. All the methods have population served as the key parameter. In hilly areas, the accessibility problem is the main and then others. Hence, the P2 method which considers population and distance can be more realistic parameters for prioritisation for new networks. The third method P3 takes account the population and the cost of construction (indirectly by taking distance) and may be a realistic parameter for upgrading of rural roads in hilly regions.

5.6 Conclusions

The important indicators for prioritisation of rural road links identified are population served by a road link, person–km, population per unit intervention cost, and gravity flow. For hilly regions, the same indicators for prioritisation of rural road links for new linkages and upgrading/rehabilitation, are also applicable. Taking too many indicators makes the prioritisation process complex and the role of the indicators in rural areas of hilly region may not be significant. Hence, consideration of a few significant indicators makes the process more simple, practical, and possibly sufficient for the rural roads prioritisation.

In this chapter, it was studied the problem of designing a rural transportation network to provide better accessibility to public services for the rural residents around the network along with cost-effective road improvement. The proposed models provide a portfolio of suggested links for road network improvements, and offers solutions for different budget levels, optimizing the transportation cost in a rural road network with different types of road surface (earthen, gravel, or asphalt). The proposed models can be a more practical and realistic approach for the study and development of rural road networks in rural areas, particularly in hilly regions such as Nepal.

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Chapter 6

A Multi-Objective Analysis of the Rural Road Network Problem

6.1 Introduction

As seen in previous chapters, several objectives may be used for rural road networks definitions/upgrading. The rural road construction and network upgrading are generally related to economical and social issues. Therefore, decision based on a single objective may not be realistic and the corresponding decisions may not be correctly justified. As if the different objectives are to be addressed simultaneously, it becomes a Multi-objective approach. In this chapter, the rural road network problem is tackled using a multi-objective approach.

In single-objective approaches, the optimal solution can be obtained by ordering all the feasible solutions based on the objective function value. In multi-objective approaches, the concept of optimal solution is substituted by the notion of Pareto optimality. In multi- objective, the most preferred solution (the solution found to be interesting to the DM) is identified, rather than looking for the optimal solution.

As follows, basic concepts regarding multi-objective models will be presented. Then, a multi- objective approach will be applied to a rural road network model for link selection and upgrade. There are two types of approaches for multi-objective problems: interactive and non- interactive (Alves & Clímaco, 2006). The non-interactive method of analysis is used for this study. However, as the role of DM is crucial and depends on the local situation and strategy, the DM is to be well informed during analysis of the problems.

141 Rural Engineering Infrastructures Design and Public Facility Locations

6.2 Multi-objective integer programming: basic concepts

A general multi-objective integer programming problem consists of a number of objectives subject to a set of constraints. The problem can be written as:

(MOP)

(6.1)

…

(6.2)

Subject to:

(6.3)

K is the number of objectives. ⊂ ℝ denotes the non-convex set of feasible solutions defined by the set of functional constraints, ≥ 0 and integer for ⊆ {1, 2, ..., }. is assumed compact (closed and bounded) and non-empty.

A solution is efficient for the MOP if and only if there is no such that ≥

for all {1, 2, ..., } and > for at least one .

Let ⊂ ℝ be the image of the feasible region in the objective functions space. A point is called non-dominated if it corresponds to an efficient solution . The terms efficient, non-dominated and Pareto optimal are often used indistinctively as synonymous (Alves & Clímaco, 2009).

A non-dominated point (solution) is called unsupported if is dominated by a convex combination (not belonging to ) of other non-dominated points (belonging to ). As the feasible region is non-convex, unsupported non-dominated solutions may exist. Thus, unlike in multi-objective linear programming, the set of non-dominated solutions of MOP cannot be fully obtained by varying the parameter on the weighted sum of the objective functions:

(MOP )

(6.4)

142

Subject to: (6.5)

Where ℝ

Even if the complete parameterization of is attempted, unsupported non-dominated solutions cannot be reached. One way to overcome this is by adding additional constraints into MOP , imposing bounds on the objective function values (Soland, 1979):

(MOP α)

max (6.6)

Subject to: (6.7)

≥ = 1, 2, ..., (6.8) where, and ℝ .

Every solution obtained by MOP , is non-dominated and there is always an such that MOP , returns a specific non-dominated solution. Thus, MOP α allows to determine the complete set of non-dominated solutions of MOP. This method is called weighted sum and any parameterization of can be used to obtain solutions.

The ideal values are defined by the maximum objective function values over the set of efficient solutions , and can be obtained by individually optimizing each objective function. The resulting ideal point is usually not feasible, otherwise no conflict exists between criteria and the solution is optimal.

6.3 Objectives for the rural road network problem

Multi-objective problems have been dealt for many areas, also in road network planning problems. However, there are still few works on the area. Furthermore, works addressing the rural road network case are even rarer. Looking at objectives, works in the literature can be grouped according to:

 cost minimisation (Janson et al., 1991; Friesz et al. , 1993; Tzeng & Tsaur, 1997),  equity (Feng & Wu, 2003; Meng & Yang, 2002, Antunes et al., 2003),  robustness (Lo & Tung, 2003; Ukkusuri et al., 2007),

143 Rural Engineering Infrastructures Design and Public Facility Locations

 accessibility maximisation (Antunes et al., 2003),  connectivity maximisation (Scaparra & Church, 2005),  minimization of travel distance (Friesz & Harker, 1983; Ukkusuri et al., 2007),  minimization of property expropriation (Friesz & Harker, 1983),  minimization of carbon monoxide emissions (Cantarella & Vitetta, 2006) and  other relevant objectives (e.g. route efficiency) (Scaparra & Church, 2005).

A number of articles address multi-objective road network design models. Friesz & Harker, (1983) took into account the minimisation of travel distance and the minimization of property expropriation. Friesz et al. (1993) and Tzeng &Tsaur (1997) contemplated user costs and construction costs as simultaneous minimization objectives. Feng and Wu, (2003) considered horizontal (across all the population centres) and vertical (across the centres of the same region) equity objectives. The model presented in Antunes et al., (2003) combines accessibility and equity objectives. Scaparra and Church, (2005) has considered a model for rural road network design that involves two objectives while allocating a fix budget for a number of possible road projects: maximize all weather road connectivity among villages region and maximize route efficiency. Ukkusuri et al., (2007) considered a robustness objective in addition to travel time minimization as an efficiency objective.

The traditional approach to road network planning consists of finding minimum cost approach capable of accommodating given traffic flows (Janson et al., 1991). But, it does not recognize the interdependence between road quality and traffic flows and other socio economic factors such as accessibility issue (Antunes et al., 2003). However, the minimum-cost objectives have always prevailed in most studies and the minimum cost objective can be one of the important objectives for rural road network planning problems. Minimum cost consideration in rural road network problems can be construction costs and travel costs (Kumar & Tilloston, 1985; Makarchi & Tilloston, 1991). However, for upgrading of rural road network, the operation cost in a network can be a good measure of rural road network optimisation. It gives the measure of time, difficulty, distance and costs when the road links are used.

Antunes et al., (2003) has developed an accessibility-maximisation approach for inter-urban road network long-term planning. Accessibility is a key factor in the quality of life of rural population and aptitude to development of regions, this issue is more prominent in rural areas. However, all the settlements (population) cannot be connected in hilly areas. But, most of the settlements can be covered within a reasonable distance. This issue has been taken in

144

consideration in covering based rural road network model. The concept has been dealt in detail in Chapter 4. It is a social issue that the population covered in a region to be maximised. This can be another important objective to be considered in rural road network development and upgrading. Measure of accessibility in terms of spatial measurement in plan is less relevant in case of hilly regions. It is more significant that whether a road link can cover the settlements and population of the region considered. Hence, population covered can be taken as the best indicator for the maximisation of accessibility in the hilly regions of Nepal. Higher the population covered, better will be the accessibility.

Although the works discussed above are relevant, the objectives may vary for rural road network in rural regions. In this context, cost and accessibility related objectives may be more relevant. Hence, two objectives are considered for rural road optimization problem in this study: minimisation of user operation cost and maximisation of population covered by a network. The first one corresponds to an efficiency objective and the second corresponds to a social objective.

The type of roads in rural areas is typically earthen which may need to be upgraded to gravel or asphalt surfaces. Three levels of road surface (earthen, gravel, or asphalt) are considered in this study (such as dealt in Chapter 5).

Here, a multi-objective analysis is performed in order to increase the knowledge on rural road network problem, when limited funds are available.

6.4 Multi-objective rural road model

In this study, two objectives are considered for decision making, model becomes a bi- objective problem, thus the special case of the multi-objective optimisation problem (MOP) where two objectives are considered (k=2).

The first objective under study is user operation cost minimisation. The links with lower operation cost to users are likely to be selected for upgrading from lower surface level (from earthen or gravel) to upper surface levels (gravel or asphalt). Links with high traffic volume are also likely to be selected since higher cost saving can be achieved. However, traffic volume in rural areas is generally low and difficult to estimate. Hence, the operation cost generally depends on the link length (distance) and the operating cost per unit flow of travelling over a surface. The formulation of model was discussed in Chapter 5.

145 Rural Engineering Infrastructures Design and Public Facility Locations

The second objective intends to maximise the population linked. The higher the population covered by the link, more likely it is to be selected for upgrading to higher surface levels (even if the link length is higher and the operation cost is also higher). It is considered as social objective. Here, is the population served by link (i, j).

An objective function of the model can be written to consider the operating cost with weights to the links. Then, the equation (5.1) can be restated as the first objective.

Minimise

(6.9)

The second objective is to maximise the population coverage by the selected links. Maximise

(6.10)

Subject to:

(6.11)

(6.12)

 

   (6.13)

Equation (6.11) indicates that the improvement/construction expenditure is constrained to an investment budget. The term of link construction expenditure is to be spent to build only one link, either (i, j) or (j, i) (as the graph is undirected). Constraints (6.12) define that one link is paved with only one type of surface. These constraints also guarantee all links are to be connected with one of the surface options.

For a special case, the model can be modified to consider additional constraints. For example, two types of links typically exist in hilly regions, backbone and branch links (Section 4.7). The backbone links can be defined in the model as constraints and the backbone links are upgraded before upgrading the branch links. Due importance can be given to the back bone

146

links before intervening the branch links. Then, the following constraints can be added to the previous model to consider the backbone and branch concept in the model.

(6.14)

 

   (6.15)

   (6.16)

Here, the backbone link nodes are numbered first, then secondary link nodes (see Chapter 5). Where, m is the greatest node number in the backbone network. Hence, equation 6.14 assumes that the secondary branch links can not be selected unless all the backbone links are selected.

The node numbering in the network should be rearranged for this case (e.g. Figure 5.2, where the links connecting the nodes 1 to 10 are backbone links and the remaining are branch links).

6.5 Application of the model

The applicability of the multi-objective model is tested in the same rural road network considered in Chapter 5.

For the test instance, the parameter of prioritisation is taken as person-km as discussed in Chapter 5. However, the analysis can be performed to other parameters also. The same weight calculated for each link is taken from Table 5.4. Since, the data of flow in each link is not available for this network, the number of trips is not considered in this analysis. The trip data can be considered for the realistic cost optimisation analysis. However, it is difficult to estimate trip data for rural regions (particularly for hilly regions) Operating cost per unit flow over earthen, gravel, and asphalt surface of the links are also taken as NRs 50.64, NRs 45.64, and NRs 36.79 respectively (drawn from Tech Studio Engineering, 2011) as before. The upgrading cost from earthen surface level to gravel surface level is taken as NRs 5 million per kilometre and from gravel surface level to asphalt surface level as 10 million per kilometre.

147 Rural Engineering Infrastructures Design and Public Facility Locations

6.5.1 Test instance data and solutions

The mathematical models were solved using the weighted sum method (see section 6.2) with MPL for Windows 4.2 as the modelling language and CPLEX 10.0’s Mixed Integer Programming as the solver. An analysis can be conducted in different budget level constraints.

Figure 6.1: Rural road network for application of model.

Solution of rural road network multi-objective model is obtained for budget level NRs 400 millions and NRs 600 millions. The details of the solutions of the model are presented in Appendix Table F.1 for budget level NRs 400 millions and in Appendix Table F.2 for budget level NRs 600 millions.

The model gives a lot of solutions as shown in Table F.1 and Table F.2. The decision maker can prefer any solution from the Table F.1 and Table F.2. However, she/he may be interested in some efficient solutions so as to achieve the objectives. Data concerning these solutions is (non-dominated solutions) is presented in the Tables F.1 and Table F.2 in the Appendix. In the tables, the letter “a” stands for asphalt, “g” stands for gravel, and “e” stands for earthen surface level of the road links.

148

6.5.2 Analysis of the solutions

The non-dominated solution sets have been identified for the bi-objective models. The set of solutions obtained are the unique solutions. This reflects such a decision maker's preference, i.e. all objectives have the same importance, and closer all objectives to the ideal point, the better. The Pareto optimal solutions, distributed along the Pareto frontier, provide information about alternative solutions for the decision maker to choose from.

Table 6.1: Non-dominated solutions for budget level NRs 400 millions

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s1 73,060 396,592 g g g g g g g g g g g g g g g g g g g g e s3 70,690 395,292 g g g a g g g g g g a a g g e g g g g g g s5 69,981 393,867 g a g g g g g g g g g g g g g g e g g g g s8 69,936 390,884 g a g g g g g g a g e a g g e g g g g g g s10 69,740 388,939 g a g g g g g g g g g g g g a e e g g g g s20 68,717 378,985 g g g g g a g a g g g g a a g e g e g g e s22 66,001 377,658 e a a g a g a a a a a g a g e e e g g g e s28 61,005 372,275 e a g a a a a a e a g g a g e e e g g g e s48 60,302 361,601 e a e a a a g a e a g a a a a e e g g e e s61 60,208 357,193 e a e a a a g a e a e a g a a e e a a e e

400,000 s3 s5 s1 s8

390,000 s10 (max.) 2 380,000 s20 s28 s22 370,000

s48 360,000 s61

PopulationCovered, Z 350,000

340,000 60,000 62,000 64,000 66,000 68,000 70,000 72,000 74,000

User Operation Cost, Z1 (min.)

Figure 6.2: Pareto frontier for budget level NRs 400 millions.

149 Rural Engineering Infrastructures Design and Public Facility Locations

Solutions shown in Table 6.1 are the non-dominated solutions (drawn from Table F.1) for budget level NRs 400 millions. Similarly, the non-dominated solution (obtained from Table F.2) for the budget level NRs 600 millions is shown in Table 6.2. The Pareto frontier for budget level NRs 400 millions is shown in Figure 6.2. Pareto frontier for the same network but for budget level NRs 600 millions was also obtained is shown in Figure 6.3.

Table 6.2: Non-dominated solutions for budget level NRs 600 millions

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s1 73,034 399,332 g g g g g g g g g g g g g g g g g g g g g

s2 72,776 396,592 g g g g g g g g g g g g g a g g g g g g e s3 70,110 395,292 g a g g g g g g g g g g g g e g g g g g g s8 69,981 393,867 g a g g g g g g g g g g g g g g e g g g g s18 62,913 390,791 e g a a a a a a a a g a a a e a g a a g g s29 60,239 389,366 e a g a a a g a g a g a g a g g e a a g g s30 59,951 389,356 g a g a a a g a a a a a g a g a g a a e e s35 59,667 388,484 g a g a a a g a e a g a g a a a e a g a g

410,000

s1 400,000 s2 s30 s3

390,000 s8 (max.)

2 s29 s18 s35 380,000

370,000

360,000 PopulationCovered, Z 350,000

340,000 59,000 61,000 63,000 65,000 67,000 69,000 71,000 73,000 75,000

User Operation Cost, Z1 (min.)

Figure 6.3: Pareto frontier for budget level NRs 600 millions.

The decision options on intervention in the rural road network with different surface levels for budget NRs 400 millions and NRs 600 millions are shown in Figure 6.4 and Figure 6.5. There are ten decision options for the first budget level and eight decision options for the second budget level.

150

s1 s3

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 14 11 14 16 16

6 6 15 15 2 7 2 7 Legend: Legend: 5 8 5 8 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate point 1 Intermediate point 1 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

s5 s8

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 14 11 14 16 16

6 6 15 15 2 7 2 7 Legend: Legend: 5 8 5 8 Nodal points Nodal points 9 Main nodes 9 Main nodes 1 Intermediate point 1 Intermediate point 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

s10 s20

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 14 11 14 16 16

6 6 15 15 2 7 2 7 Legend: Legend: 5 8 5 8 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate point 1 1 Intermediate point 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

Figure 6.4: Decision options and surface level of links for budget level NRs 400 millions (contd. …).

151 Rural Engineering Infrastructures Design and Public Facility Locations

s22 s28

22 22

21 21

20 19 20 19

12 12 17 18 17 18

13 13 11 14 11 16 16

6 6 15 15 2 7 2 7 Legend: 8 Legend: 5 8 5 Nodal points Nodal points 9 9 Main nodes Main nodes Intermediate point 1 1 Intermediate point 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

s48 s61

22 22

21 21

20 19 20 19

12 12 17 18 17 18

13 13 11 14 11 14 16 16

6 6 15 15 2 7 2 7 8 Legend: 8 Legend: 5 5 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate point Intermediate point 1 1 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

Figure 6.4: Decision options and surface level of links for budget level NRs 400 millions.

s1 s2

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 14 11 14 16 16

6 6 15 15 2 7 2 7 8 Legend: 8 Legend: 5 5 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate link Intermediate link 1 1 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

Figure 6.5: Decision options and surface level of links for budget level NRs 600 millions (contd. …).

152

s3 s8

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 11 14 16 16

6 6 15 15 2 7 2 7 Legend: 8 Legend: 5 8 5 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate link Intermediate link 1 1 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

s18 s29

22 22

21 21

20 19 20 19

12 17 18 12 17 18

13 13 11 11 14 16 16

6 6 15 15 2 7 2 7 8 Legend: 8 Legend: 5 5 Nodal points Nodal points 9 Main nodes 9 Main nodes Intermediate link 1 Intermediate link 1 3 Asphalt surface 3 Asphalt surface Gravel surface Gravel surface Earthen link Earthen link

4 4

s30 s35

22 22

21 21

20 19 20 19

17 18 12 17 18

13 13 11 14 11 16 16

4 4

Figure 6.5: Decision options and surface level of links for budget level NRs 600 millions.

153 Rural Engineering Infrastructures Design and Public Facility Locations

To compare the different decision options, we need to calculate the tradeoffs between the values of the two objective functions for the non-dominated set. We can therefore examine how much we have to penalize the value of one objective function, in order to improve the objective value of the other. In this model, all tradeoffs will be positive; the increase of one objective function will increase the other. However, for this case, we search for solutions with lower value for the first objective, operation cost minimisation (Z1) and higher values for the second objective, population covered (Z2). Also, we may be interested in higher tradeoffs, meaning that the increase of a value of Z1 is intended to produce the biggest increment possible on the value of Z2. On the other hand, when we observe solutions with better value for Z1 and worse value for Z2, we may choose smaller tradeoffs.

In this way, the bi-objective model identifies alternative solutions that allow the DM to compare the values of the two objectives. The DM will know a set of solutions with lower operation costs and higher population covered and will be able to analyze the tradeoffs between the two objectives. According to the DM preferences, she/he can choose a final solution that reflects her/his judgement.

For illustration purposes, four solutions has been chosen to conduct a thorough analysis, the DM may be interested in the non dominated solutions of the model which lies in the region where it has the lowest operation cost and higher population coverage space of the solution space (for budget level NRs 600 millions), as shown in Table 6.4.

Table 6.3: Preferable solutions for budget level NRs 600 millions

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s18 62,913 390,791 e g a a a a a a a a g a a a e a g a a g g s29 60,239 389,366 e a g a a a g a g a g a g a g g e a a g g s30 59,951 389,356 g a g a a a g a a a a a g a g a g a a e e s35 59,667 388,484 g a g a a a g a e a g a g a a a e a g a g

Then the DM can make comparisons of improvements in population covered, with increase in operation cost, as shown in Table 6.4.

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Table 6.4: Comparisons of preferable solutions for budget level NRs 600 millions Increase in % Solutions Z1 Z2 Operation Population cost coverage s35 59,667 388,484 s30 59,951 389,356 0.48 0.22 S29 60,239 389,366 0.48 0.00 s18 62,913 390,791 4.44 0.37

Solution s35 has the lowest operating cost among the solutions. However, the solution covers the least population which is not intended. The solution with the second lowest operation cost is s30 where the operation cost is increased by 0.48% and the population covered by this solution is 0.22% more than by s35. The next solution to s30 is s29 with operation cost 0.48% higher than solution s30. Though operation cost is increased, there is no significant increase in population coverage which may not be considered positive in decision making. The last solution s18 has 4.44% increases in operation cost which is significantly higher than the previous solutions and the population coverage increase is only 0.37% which is not so significant. So, solution s30 can be an interesting solution in terms of trade off for the budget level of NRs 600 millions.

Besides these analytical results, the connectivity of the network is also to be looked with respect to public facility location and market centres. In general practice, there is a strategy to connect market centres during rural road network formation (Shrestha, 2003). Usually, most of the public facilities are situated in market centres. These factors are also to be considered during decision taking.

In this region (Figure 6.6), an important market centre is situated at node 13 although it doesn’t serve as a nodal point. It consists of important public facilities such as college, health post, agricultural extension services, bank, post office, and police station. Hence, the road links between node 1 (main node) and node 13 (main market centre) are to be improved with a higher surface level. There is another important market centre near to nodal point 16, which has similar public service centres. Although the market centre is not in this region, however, strategically it is a gateway to the northern part of the district. Hence, it is better to improve links between node 13 and node 16 with higher surface levels.

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Palakhu Bhanjyang Lakure 21 20 Panchkhuwa Deurali Pandrung Dandapari 19 Jarang Aru Pokhari Ramche 18 17 Sisneri Masel Arughat 12 13 Ghyampesal 11 14 Tandrang Baguwa Kubinde 16 Sarkigaun 10 Dukhuwa 2 Dandabesi Pokharel Chautara Digaun 7 Ripgaun Dhawa 5 15 6 Okhalepani Baluwatar Asrang 8 Chhapthok 3 1 9 Central Places Narayanpur Borlang Ghatbesi First grade place Birdigaun Second grade place Chhapthok Mahadevtar Third grade place Legend Fourth grade place 4 Satbisetar Prithvi Narayan District headquarter Fifth grade place Mailung VDC headquarter Sixth grade place Masel Other settlement Khabari Other settlement River/Stream Kyamuntar VDC boarder Rural road network

Figure 6.6: Map of the planning region.

Among the nodal points, the settlements around node 12 are heavily populated. This factor can also be considered during improvements of links. This shows that link 11-12 is a potential link to be improved to a higher surface level.

Considering the above rational situations, solution s29 and s30 may be the most preferred solutions. Both solutions cover the important market centres and heavily populated areas in this region. This analysis shows that it is possible to provide the DM with some interesting alternatives rather than a unique solution to the problem. Also, there are some possibilities in decisions to improve the value of one objective without a major increase on the value of the other one.

In this way, the DM may have a considerable set of different solutions that allow varying the population covered by the rural road network significantly without major increase of the operation costs. In this situation, the DM is presented with a set of alternatives that make it possible to improve simultaneously the value of costs and the value of service. The DM should analyze those solutions that dominate the original one, comparing the improvements on the values of both objectives. However, the final choice of the solution to be implemented

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belongs to the DM that should analyze the model, compare the different solutions, and reflect and clear some ambiguities that she/he might have.

Similarly, solutions of the multi-objective model with backbone and branch links can be obtained and analysed which may bee suitable for rural road network in hilly regions.

6.6 Conclusions

This chapter considered the rural road network problem as a multi-objective problem. A model is proposed for general rural road networks. Adding some constraints, the model can also be used for backbone and branch rural networks in hilly regions. The first model has been tested in the rural road network which was considered for Chapter 5.

The proposed model minimizes the operation costs in the first objective and maximises population covered in the second objective subject to a budget constraint.

We can obtain all Pareto optimal solutions, which could be interesting to DM, with different optimal alternatives distributed along the Pareto frontier. This approach was found to be suitable for a correct analysis of rural road networks.

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Chapter 7

Conclusions and Future Works

7.1 Summary of conclusions

Rural areas have sparsely located settlements and public facilities. This is more relevant in hilly regions. The delivery of services and goods to the settlements is therefore a difficult task for local governments of developing countries.

Often, in these regions, the major infrastructures in dire need are rural roads. Thus, different models have been developed for assessing rural road links in rural areas, mostly based on economic viability. Most of the rural road links, especially in hilly regions, can not be justified based on the conventional economic ground. However, settlements in these areas must be connected and are one of the most important development activities in rural areas. Hence, an alternative method for rural road network planning method needs to be envisaged. Hence, covering based rural road network model focusing on the connectivity of settlements and public services (typically considered import than the economic aspects) is developed.

Connecting every settlement in rural area is not possible in practice due to technical difficulties and financial constraints. However, settlements in remote areas should have access to the facilities of basic goods and services, even though connectivity of all settlements in rural areas is infeasible. Hence, the network problem was dealt in terms of covering of settlements and public facilities within a specified distance. A method was developed to identify the nodal points in rural road network so that most of the settlements can be covered.

The five zone mountain model with typical landforms, glacial and peri-glacial topography (High Himalaya), free rock faces and associated debries slopes (High Himalaya and highest elevations of the Middle Himalaya), degraded middle slopes and ancient valley floors (parts of the Mahabharat Lekh and the lower elevations of the Middle Himalaya), active lower

159 Rural Engineering Infrastructures Design and Public Facility Locations slopes (many parts of the Mahabharat Lekh and some of the more confined slopes adjacent to the major rivers in the Middle Himalaya), and valley floors (the Low Himalaya and, to a lesser extent, the Middle Himalaya) was found useful to assess the rural roads alignments in the hilly region of Nepal. The zonal model can be used as the framework for the analysis of the geological and geomorphological processes, and consequences of roads construction. Mostly rural roads in the hilly regions of Nepal pass through hill slopes of 20-40corridors in the mountain zone 3 and zone 4. Cut and fill road cross-sections with valley side retaining structures are the most common.

Post-construction impact of roads construction on environment is found high in the hilly region of Nepal due to the excavated materials and the creation of mountain slope vulnerable to landslides. As the cut width in hill slope is very sensitive to the volume of excavated quantity, it is necessary to reduce cut widths providing cut and fill road cross-sections, during engineering design and construction.

A two step method was found effective to define rural road network in hilly regions. It was proposed as a covering based rural road network model (shown in Figure 7.1). In the first step, the nodal points were identified which covered the settlements and public facilities within a specified boundaries (VDCs boundaries in Nepal) in a region. These nodal points were taken as the obligatory points in a rural road network. Then, in the second step, the model established the linkages to the nodal points to form a basic road network in the specified region. The MST connecting the identified nodal points was used as a basic rural road network for the hilly regions.

A typical rural road network configuration was identified within the networks in hilly regions of Nepal. The pattern was defined by backbone and branch (BB) network. The backbone network follows a main ridgeline (between two rivers) and the branch network, emanating from the main ridgeline, follows the secondary ridgelines (between two streams which are tributaries of the main rivers).

This model was used for analysis of coverage situation of settlements and public facilities by the nodal points in different service distances in four hilly regions of Gorkha and Lamjung districts of Nepal. It was concluded that only about 50% of settlements were covered within a maximum service distance of 2 km. When the maximum service distance was increased to 3 km, the coverage significantly increased to 74%. 89% of the settlements were covered within

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4 km of maximum service distance. The 4 km covering service distance was identified as a reasonable maximum service distance in the regions.

Defining political boundary Define nodal points within which the settlements and public facilities are to be covered. Obtaining distance matrix and short distance matrix (Floyd-Warshall algorithm). Defining nodal points using MCLP

Obtain rural road network All the nodal points are connected by rural road links (MST network) (Prim’s algorithm) so that most of the settlements and public facilities are covered.

Backbone network can be General network Backbone/core defined in hilly areas and

network core networks in plain areas. Covering based rural road based model rural Covering network

RRNM-1 RRNM-2 RRNM-3 RRNM-4 A rural road network problem (existing) (new) can be one of the four models (existing) (new) based on new or existing networks.

Prioritisation of rural road Prioritisation of rural road network links links can be done based on (W ) population covered by a link, ij person-km, population/investment, gravity flow model, and other methods

Portfolios of links at various budget levels Identify the suitable interventions for with different surface levels improvement of accessibility

Rural road network decision network road Rural models

Figure 7.1: Proposed rural road network planning process.

161 Rural Engineering Infrastructures Design and Public Facility Locations

The road network length was found significantly less to (43 % of the existing network length) for maximum service distances of 4 km, ensuring better coverage of settlements and public facilities in the case study regions. This has been taken as the minimum level of connectivity/coverage necessary.

The covering based network concept was also found applicable to find nodal points and establish water supply distribution networks, rural electrification grid extensions, and telecommunication network extensions.

Four models were found appropriate for the rural road network in rural areas and proposed as rural road network decision models (shown in the second part of Figure 7.1). Among them, two models (RRNM-1 and RRNM-2) are appropriate for general purpose (can be used in both plain and hilly road networks) models. The other two models (RRNM-3 and RRNM-4) are appropriate for hilly regions introducing the BB network configuration. However, core network within a network in plain regions can also be defined and the concept of BB network is used. RRNM-2 and RRNM-4 models were proposed for a new network with a single surface (either of earthen, gravel or asphalt). RRNM-1 and RRNM-3 models were proposed for upgrading of existing rural road networks.

The relevant indicators for prioritisation of rural road links are also identified as population served by a road link, person–km, population per unit intervention cost, and gravity flow model based on socioeconomic aspects.

The models provided a portfolio of suggested links for road network improvements, and offered solutions for different budget levels optimizing the transportation cost in a rural road network with different types of road surface (earthen, gravel, or asphalt) for upgrading.

A multi-objective approach was introduced for solving a rural road network upgrading problem with surface level of earthen, gravel and asphalt. A multi-objective model was proposed for general networks. Adding some constraints, the model can also be used for backbone and branch rural networks in hilly regions. The model considers two objectives, minimizes the user operation costs in the first objective and maximises population covered in the second objective subject to a budget constraint.

162

All Pareto optimal solutions were obtained, which could be interesting to DM, with different optimal alternatives distributed along the Pareto frontier. This approach was found to be suitable for a pragmatic analysis of rural road networks.

The proposed planning process, for rural road networks in rural areas by the multi-objective approach is summarised in a flow chart (Figure 7.2). The first part of the planning process (covering based rural road network model) can be the same as in Figure 7.1.

Backbone network can be General network Backbone/core defined in hilly areas and network core networks in plain areas.

A rural road network upgrading problem can be Multi-objective rural road network decision dealt with two objectives: model  Minimisation of operation cost, and  Maximisation of population covered.

Prioritisation of rural road Prioritisation of rural road network links links can be done based on population covered by a link, (Wij) person-km, population/investment, gravity flow model, and other methods

Set of alternative solutions: Pareto optimal Identify the suitable interventions for solutions with different surface levels. improvement of accessibility

Figure 7.2: Proposed multi-objective rural road network planning process.

The study explored the covering based rural road network method which identifies nodal points that cover settlements and public facilities and forms a basic level of road network connecting the nodal points in a region to improve physical access optimising scare resources. The study also explored different rural road network models for new network construction and upgrading. The methodology developed was tested in real road networks of Gorkha and Lamjung districts of Nepal considering settlements and public facility locations and confirmed its applicability. The models were found simple, practical, and realistic in the context of rural areas of developing countries like Nepal.

163 Rural Engineering Infrastructures Design and Public Facility Locations

7.2 Limitations and future works

Some limitations were identified during the development of the work presented in this thesis which will be enumerated, as follows and may be also useful for future consideration.

Traffic in any road network link is an important indicator of construction and upgrading process of any network. However, traffic generation estimation in rural area is a complex problem and exist very few works on the subject. The available works are not sufficient to analyse and estimate traffic flow in network links. A scientific method of traffic generation was not found for rural road network.

During the implementation of models, the network has been assumed as connected in a single node to a main road (higher level road). However, the network can have connections in different nodes with the main roads. This affects the traffic flow pattern. This limitation is also related with the traffic trip estimation problem.

Encountered limitations and ideas led to consider some future work and to identify promising research directions as follows.

A scientific method of traffic generation estimation in rural areas has been found a promising area of study in rural road network. In the same area of traffic studies, the traffic flow pattern in case of multi node connection to main roads is also identified as a problem that can be studied in future.

The road network models have been developed with objectives of maximising population coverage (accessibility maximisation) and minimisation of transportation cost. The whole network may be blocked when one of the main linkages is blocked due to some reason such as landslides. To minimise this situation, an objective of robustness can be considered in rural road network models and recommended for further studies.

Reliability is another issue in planning of distribution networks particularly in water, electricity and telecommunication distribution networks. Long length of distribution lines increases the probability of occurrence of a failure in distribution lines which leads to a low system reliability. Reliability is an essential factor in distribution networks particularly in rural areas which is low and should be maximised. This is one of the promising issues that can

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be considered in study and design of rural infrastructures particularly in water distribution system, electricity distribution lines, and telecommunication lines.

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Research Laboratory Limited, Crowthorne, Berkshire, United Kingdom Tzeng, G. H., and Tsaur, S. H. (1997). Application of multiple criteria decision making for network improvement. J. Adv. Transp., 31(1), 49–74. Tzeng, G. H., and Tsaur, S. H. (1997). Application of multiple criteria decision making for network improvement. J. Adv. Transp., 31(1), 49–74. Ukkusuri, S. V., Mathew, T. V., and Waller, S. T. (2007). Robust transportation network design under demand uncertainty. Comput. Aided Civ. Infrastruct. Eng., 22(1), 6–18. UNCHS (United Nations Centre for Human Settlements), (1985). Guidelines for the Planning of Rural Settlements and Infrastructure: Road Networks. Nairobi, Kenya. Wanmali S. and Islam Y., (1995). Rural Service, Rural Infrastructure, and Regional Development in India. Geographical Journal, Vol. 161, No. 2, 149-166. Wanmali S. and Islam Y., (1997). Rural Infrastructure and Agriculture Development in Southern Africa: A Centre-Periphery Perspective. Geographical Journal, Vol. 163, No. 3, 259-269. Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Proc.-Inst. Civ. Eng., 1(36), 325–378.

174

Appendices

A. Distance Matrix of 15 VDCs (Gorkha A)

Takumajhlakuribot Distance Matrix (km)

Thale Bhattagaon Jhyalla TalloJaphdi Gairigaon Kerabari Archale Majhlakuribot Kamaltari MathiloJaphdi Arukharka Majhlakuribot SiranLakuri Bahungaon Dumreswara Aapswara 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 0.35 1.25 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.35 0 1.1 0.6 0.9 0 0 0 0 0 0 0 0 0 0 0 3 1.25 1.1 0 0 0 0.65 0 0 0 0 0 0 0 0 0 0 4 0 0.6 0 0 0.8 0 0.7 0.8 0 0 0 0 0 0 0 0 5 0 0.9 0 0.8 0 0.45 0 0.55 0 0 0 0 0 0 0 0 6 0 0 0.65 0 0.45 0 0 0.8 1.92 0 0 0 0 0 0 0 7 0 0 0 0.7 0 0 0 0.9 0 0 0.9 0 0 0 0 0 8 0 0 0 0.8 0.55 0.8 0.9 0 1.7 0.92 0 0 0 0 0 0 9 0 0 0 0 0 1.92 0 1.7 0 0 0 0 0 1.7 0 0 10 0 0 0 0 0 0 0 0.92 0 0 0 0.4 0.35 0 0 0 11 0 0 0 0 0 0 0.9 0 0 0 0 0.75 0 0 0 1.18 12 0 0 0 0 0 0 0 0 0 0.4 0.75 0 0.6 0 0.51 0 13 0 0 0 0 0 0 0 0 0 0.35 0 0.6 0 0.46 0 0 14 0 0 0 0 0 0 0 0 1.7 0 0 0 0.46 0 0.45 0 15 0 0 0 0 0 0 0 0 0 0 0 0.51 0 0.45 0 0.45 16 0 0 0 0 0 0 0 0 0 0 1.18 0 0 0 0.45 0

Taku Distance Matrix (km)

Bhaledhunga PokhariGaira Takukot Dandathok Palkhu Mohoriya Bhanjyang Bahakot Mailung MathiloMasar Dandagaon Keurepani Turturepani Ulte TalloMasar Bhalswara 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 0.72 1.03 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.72 0 0 0.47 0 0 0 0 0 0 0 0 0 0 0 0 3 1.03 0 0 0.82 1.27 0.7 0 0 0 0 0 0 0 0 0 0 4 0 0.47 0.82 0 0.73 0 0 0 0 0 0 0 0 0 0 0 5 0 0 1.27 0.73 0 1.55 0.65 0 1.14 0 0 0 0 0 0 0 6 0 0 0.7 0 1.55 0 0 0 0 0 0 1.22 0 0 0 0 7 0 0 0 0 0.65 0 0 0.51 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0.51 0 0.75 0 0 0 0 0 0 0 9 0 0 0 0 1.14 0 0 0.75 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0.91 0 0.73 0 0 0 11 0 0 0 0 0 0 0 0 0 0.91 0 1.01 0.93 0 1.44 0 12 0 0 0 0 0 1.22 0 0 0 0 1.01 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0.73 0.93 0 0 0.87 0.51 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0.87 0 0 0.85 15 0 0 0 0 0 0 0 0 0 0 1.44 0 0.51 0 0 1.65 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0.85 1.65 0

175 Rural Engineering Infrastructures Design and Public Facility Locations

Pandrung Distance Matrix (km)

Sarkigaon Dwaridhari Parigaon UppalloJarang Pandrung Basi TalloJarang Saune Ramche Gairichhap Lamagaon Pahare Tinkhande 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 0.53 0 1.19 0 0 0 0 0 0 0 0 0 2 0.53 0 0 0 0.61 0 0 0 0 3.26 0 0 0 3 0 0 0 0.49 0 0 0 0 0 0 0 0 0 4 1.19 0 0.49 0 0 0 3.24 0 0 0 0 0 0 5 0 0.61 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0.95 0 0 0 0 0 0 7 0 0 0 3.24 0 0.95 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0.47 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 1.65 0 10 0 3.26 0 0 0 0 0 0.47 0 0 0.76 1.75 0 11 0 0 0 0 0 0 0 0 0 0.76 0 0 0 12 0 0 0 0 0 0 0 0 1.65 1.75 0 0 1.13 13 0 0 0 0 0 0 0 0 0 0 0 1.13 0

Masel Distance Matrix (km)

NirmalDiha Sapunge Bhattagaon Pandegaon Majhthok Sarkigaon Devkotagaon Khatrithok Devisthan Ghyampesal Dandagaon Ghoptegaon Kayapani 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 3.27 0 0 0 0 0 0 0 0 0 0 0 2 3.27 0 0 0 1.96 0 0 0 0 0 0 0 0 3 0 0 0 0.65 0.8 0 0 0 0 0 0 0 0 4 0 0 0.65 0 0.89 0 0 0 0 0 0 0 0 5 0 1.96 0.8 0.89 0 0.59 0 1.05 0 0 0 0 0 6 0 0 0 0 0.59 0 0 0.91 0 0 0 0 0 7 0 0 0 0 0 0 0 0.31 0 0 0 0 0 8 0 0 0 0 1.05 0.91 0.31 0 1.55 0 0 0 0 9 0 0 0 0 0 0 0 1.55 0 0 1.09 0 0 10 0 0 0 0 0 0 0 0 0 0 0.97 0 0 11 0 0 0 0 0 0 0 0 1.09 0.97 0 1.3 0 12 0 0 0 0 0 0 0 0 0 0 1.3 0 2 13 0 0 0 0 0 0 0 0 0 0 0 2 0

Baguwa Distance Matrix (km)

Sikhre Banjaragaon Khanchok Bhyalgaon Khatrigaon Pokhrelgaon Kasinthok Dharampani Rithepani Kathekhola Pandegaon 1 2 3 4 5 6 7 8 9 10 11 1 0 0.4 0 0 0 0 0 0 0 0 0 2 0.4 0 1.72 0 0 0 0 0 0 0 0 3 0 1.72 0 0.67 0 1.36 0 0 1.38 0 0 4 0 0 0.67 0 0.61 0 0 0 0 0 0 5 0 0 0 0.61 0 0.64 0.81 0 0 0 0 6 0 0 1.36 0 0.64 0 1.65 0.29 0 1.35 0 7 0 0 0 0 0.81 1.65 0 0 0 0 0 8 0 0 0 0 0 0.29 0 0 0.35 0.69 0 9 0 0 1.38 0 0 0 0 0.35 0 0 0.58 10 0 0 0 0 0 1.35 0 0.69 0 0 0.67 11 0 0 0 0 0 0 0 0 0.58 0.67 0

176

177 Rural Engineering Infrastructures Design and Public Facility Locations

Asrang Distance Matrix (km)

Magargaon Jhingate Kaphalchhap Ripgaon HarraBisauni Waglegaon Thamdanda Asranggaon Okhlepani Nayagaon PokhariBatta Bhantanagaon Mohoriyagaon 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 0 1.35 0 0.87 0 1.07 0 0 0 0 0 0 2 0 0 0.36 0 0 0 0 0 0 0 0 0 0 3 0 0.36 0 0 0 0 0.99 0 0 0 1.18 0 0 4 0 0 0 0 0.54 0 0.49 0 0 0 0 0 0 5 0.87 0 0 0.54 0 0 0.53 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0.91 0 0 0 7 1.07 0 0.99 0.49 0.53 0 0 0.94 0 0 0 0 1.33 8 0 0 0 0 0 0 0.94 0 1.13 0 0 0 0 9 0 0 0 0 0 0 0 1.13 0 0.71 0 0 0 10 0 0 0 0 0 0.91 0 0 0.71 0 0 0 0 11 0 0 1.18 0 0 0 0 0 0 0 0 0.58 0 12 0 0 0 0 0 0 0 0 0 0 0.58 0 0 13 0 0 0 0 0 0 1.33 0 0 0 0 0 0

Nareswor Distance Matrix (km)

NareB nareA Rajetar Gaikhur Sarkigau Gairigau Chisapan AgeShikhar Holsimha Dumsiri Kamere Aapchaur Lapse Bhogteni Tiwarigaon Newargau 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 2.54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2.54 0 0 0 0 0 0 0 0 0 0 2.91 0 0 0 0 3 0 0 0 0.3 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0.3 0 0.44 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0.44 0 0 0.37 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0.61 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0.37 0.61 0 1.77 0 0 0 0 0 1.77 0 0 8 0 0 0 0 0 0 1.77 0 0 0 0 0.57 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0.36 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0.36 0 0 0 0.55 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 0 1.03 0 0 0 12 0 2.91 0 0 0 0 0 0.57 0 0 0 0 0 1.4 0 0 13 0 0 0 0 0 0 0 0 0 0.55 1.03 0 0 0 0.72 0 14 0 0 0 0 0 0 1.77 0 0 0 0 1.4 0 0 1.04 0.72 15 0 0 0 0 0 0 0 0 0 0 0 0 0.72 1.04 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0.72 0 0

Tandrang Distance Matrix (km)

Okhle Kubinde Dandabari M. Dubindanda M. Nange Maithum 1 2 3 4 5 6 1 0 0.84 0 0 0 0 2 0.84 0 3 3.9 0 0 3 0 3 0 0.9 0 0 4 0 3.9 0.9 0 0 1.68 5 0 0 0 0 0 2.4 6 0 0 0 1.68 2.4 0

178

Finam Distance Matrix (km)

Kantheswara Aruswara Melbisauna Lapsibot Khirpegau Sunargau Hatiya Pipalthok Sundardanda Hilekharka Thulkhetgau Luichiswara Finamgau Aultari Kuwapani Lakuriswara Bhagabatigau Dungagadebhanjyang 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 0 1.17 0 0 0 0.68 0 0 0 0 0 0 0 0 0 0 0 0 2 1.17 0 0.45 0 0 0 0 0 1.28 0 0 0 0 0 0 0 0 0 3 0 0.45 0 0.83 0 0 0 0 0 1.04 0 0 0 0 0 0 0 0 4 0 0 0.83 0 0.33 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0.33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0.68 0 0 0 0 0 0.38 0.52 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0.38 0 0.81 0 0 0 0 0.91 0 0 1.53 0 0 8 0 0 0 0 0 0.52 0.81 0 0.58 0 0 0 0.75 0 0 0 0 0 9 0 1.28 0 0 0 0 0 0.58 0 0.54 0.34 0.7 0.52 0 0 0 0 0 10 0 0 1.04 0 0 0 0 0 0.54 0 0 0.62 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0.34 0 0 0.47 0.52 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0.7 0.62 0.47 0 0 0.22 0 0 0 0 13 0 0 0 0 0 0 0.91 0.75 0.52 0 0.52 0 0 0 0.51 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0.22 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0.51 0 0 1.06 0 0 16 0 0 0 0 0 0 1.53 0 0 0 0 0 0 0 1.06 0 0 1.41 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.06 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.41 1.06 0

Panchkhuwa Deurali Distance Matrix (km)

Amle Khamgau Gyaji Lakure Amle B Mulabari Deurali Baluwa Arubot Dharapani 1 2 3 4 5 6 7 8 9 10 1 0 1.25 0 0 0 0 0 0 0 0 2 0 0 0.85 0 0 0.63 0 0 0 0 3 0 0.85 0 0 1.71 1.08 0 0 0 0 4 0 0 0 0 1.44 0 0 0 0 0 5 0 0 1.71 1.44 0 0 2.62 0 0 0 6 0 0.63 1.08 0 0 0 1.25 0 0 0 7 0 0 0 0 2.62 1.25 0 0.44 0 1.44 8 0 0 0 0 0 0 0.44 0 0.97 0 9 0 0 0 0 0 0 0 0.97 0 0.71 10 0 0 0 0 0 0 1.44 0 0.71 0

Dhawa Distance Matrix (km)

Chautara Baddanda Rajalibhanjyang Digau Bolang Dandagau Baluwa 1 2 3 4 5 6 7 1 0 1.3 0 0 0 0 0 2 1.3 0 2.35 0 0 0 0 3 0 2.35 0 1.25 0 0 0 4 0 0 1.25 0 1.46 1.41 3.17 5 0 0 0 1.46 0 0 3.24 6 0 0 0 1.41 0 0 1.69 7 0 0 0 3.17 3.24 1.69 0

179 Rural Engineering Infrastructures Design and Public Facility Locations

Arupokhari Distance Matrix (km)

Lakure Dandapari Ratmate Churung Sisneri Deurali Dhakalgau Tunibote Dhadagau Lamabagar Dadgau Kauchini Tallo Aru 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 1.18 0 0 0 0 0 0 0 0 0 0 0 2 1.18 0 1.84 0 0 0 0 0 0 0 0 0 0 3 0 1.84 0 0 0.65 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3.72 0 0 0 0 0 0 5 0 0 0.65 0 0 1.8 0 0 0 0 0 0 0 6 0 0 0 0 1.8 0 3.74 0 0 0 0 0 0 7 0 0 0 3.72 0 3.74 0 0.87 0 0 2.6 0 0 8 0 0 0 0 0 0 0.87 0 1.55 0 0 0 0 9 0 0 0 0 0 0 0 1.55 0 2.13 1.32 0 0 10 0 0 0 0 0 0 0 0 2.13 0 0 0 0 11 0 0 0 0 0 0 2.6 0 1.32 0 0 0 0.78 12 0 0 0 0 0 0 0 0 0 0 0 0 1 13 0 0 0 0 0 0 0 0 0 0 0.78 1 0

Borlang Distance Matrix (km)

Narayanpur Lekhapakha Bhanjyang Alegau Chhapthok Gairigau Birdigau J. Simaltar Polichhap Airebhanjyang Ghatbesi Pipaltar Sundeerpur Mahadevtar Satbisetar Apswara Kyamuntar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 0 0.71 1.46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.71 0 1.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1.46 1.05 0 0.5 0 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0.5 0 0 0.71 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 1.67 0 0 0 0 0 0 0 6 0 0 1 0.71 0 0 1.16 0 1.41 2.52 0 2.35 2.11 0 0 0 0 7 0 0 0 0 0 1.16 0 2.35 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 2.35 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 1.41 0 0 0 0 0 0.69 0 0 0 0 0 10 0 0 0 0 1.67 2.52 0 0 0 0 3.15 0 0 2.88 0 0 0 11 0 0 0 0 0 0 0 0 0 3.15 0 0 0 1.71 0 0 0 12 0 0 0 0 0 2.35 0 0 0.69 0 0 0 1.43 1.87 0 0 0 13 0 0 0 0 0 2.11 0 0 0 0 0 1.43 0 0 0.95 2.85 0 14 0 0 0 0 0 0 0 0 0 2.88 1.71 1.87 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0.95 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 2.85 0 0 0 1.06 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.06 0

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181 Rural Engineering Infrastructures Design and Public Facility Locations

B. Short Distance Matrix of 15 VDCs (Gorkha A)

Takumajhlakuribot Short Distance Matrix (km)

Thale Bhattagaon Jhyalla TalloJaphdi Gairigaon Kerabari Archale Majhlakuribot Kamaltari MathiloJaphdi Arukharka Majhlakuribot SiranLakuri Bahungaon Dumreswara Aapswara 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 0.35 1.25 0.95 1.25 1.7 1.65 1.75 3.45 2.67 2.55 3.07 3.02 3.48 3.58 3.73 2 0.35 0 1.1 0.6 0.9 1.35 1.3 1.4 3.1 2.32 2.2 2.72 2.67 3.13 3.23 3.38 3 1.25 1.1 0 1.7 1.1 0.65 2.35 1.45 2.57 2.37 3.25 2.77 2.72 3.18 3.28 3.73 4 0.95 0.6 1.7 0 0.8 1.25 0.7 0.8 2.5 1.72 1.6 2.12 2.07 2.53 2.63 2.78 5 1.25 0.9 1.1 0.8 0 0.45 1.45 0.55 2.25 1.47 2.35 1.87 1.82 2.28 2.38 2.83 6 1.7 1.35 0.65 1.25 0.45 0 1.7 0.8 1.92 1.72 2.6 2.12 2.07 2.53 2.63 3.08 7 1.65 1.3 2.35 0.7 1.45 1.7 0 0.9 2.6 1.82 0.9 1.65 2.17 2.61 2.16 2.08 8 1.75 1.4 1.45 0.8 0.55 0.8 0.9 0 1.7 0.92 1.8 1.32 1.27 1.73 1.83 2.28 9 3.45 3.1 2.57 2.5 2.25 1.92 2.6 1.7 0 2.51 3.41 2.66 2.16 1.7 2.15 2.6 10 2.67 2.32 2.37 1.72 1.47 1.72 1.82 0.92 2.51 0 1.15 0.4 0.35 0.81 0.91 1.36 11 2.55 2.2 3.25 1.6 2.35 2.6 0.9 1.8 3.41 1.15 0 0.75 1.35 1.71 1.26 1.18 12 3.07 2.72 2.77 2.12 1.87 2.12 1.65 1.32 2.66 0.4 0.75 0 0.6 0.96 0.51 0.96 13 3.02 2.67 2.72 2.07 1.82 2.07 2.17 1.27 2.16 0.35 1.35 0.6 0 0.46 0.91 1.36 14 3.48 3.13 3.18 2.53 2.28 2.53 2.61 1.73 1.7 0.81 1.71 0.96 0.46 0 0.45 0.9 15 3.58 3.23 3.28 2.63 2.38 2.63 2.16 1.83 2.15 0.91 1.26 0.51 0.91 0.45 0 0.45 16 3.73 3.38 3.73 2.78 2.83 3.08 2.08 2.28 2.6 1.36 1.18 0.96 1.36 0.9 0.45 0

Taku Short Distance Matrix (km)

Bhaledhunga PokhariGaira Takukot Dandathok Palkhu Mohoriya Bhanjyang Bahakot Mailung MathiloMasar Dandagaon Keurepani Turturepani Ulte TalloMasar Bhalswara 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 0.72 1.03 1.19 1.92 1.73 2.57 3.08 3.06 4.87 3.96 2.95 4.89 5.76 5.4 6.61 2 0.72 0 1.29 0.47 1.2 1.99 1.85 2.36 2.34 5.13 4.22 3.21 5.15 6.02 5.66 6.87 3 1.03 1.29 0 0.82 1.27 0.7 1.92 2.43 2.41 3.84 2.93 1.92 3.86 4.73 4.37 5.58 4 1.19 0.47 0.82 0 0.73 1.52 1.38 1.89 1.87 4.66 3.75 2.74 4.68 5.55 5.19 6.4 5 1.92 1.2 1.27 0.73 0 1.55 0.65 1.16 1.14 4.69 3.78 2.77 4.71 5.58 5.22 6.43 6 1.73 1.99 0.7 1.52 1.55 0 2.2 2.71 2.69 3.14 2.23 1.22 3.16 4.03 3.67 4.88 7 2.57 1.85 1.92 1.38 0.65 2.2 0 0.51 1.26 5.34 4.43 3.42 5.36 6.23 5.87 7.08 8 3.08 2.36 2.43 1.89 1.16 2.71 0.51 0 0.75 5.85 4.94 3.93 5.87 6.74 6.38 7.59 9 3.06 2.34 2.41 1.87 1.14 2.69 1.26 0.75 0 5.83 4.92 3.91 5.85 6.72 6.36 7.57 10 4.87 5.13 3.84 4.66 4.69 3.14 5.34 5.85 5.83 0 0.91 1.92 0.73 1.6 1.24 2.45 11 3.96 4.22 2.93 3.75 3.78 2.23 4.43 4.94 4.92 0.91 0 1.01 0.93 1.8 1.44 2.65 12 2.95 3.21 1.92 2.74 2.77 1.22 3.42 3.93 3.91 1.92 1.01 0 1.94 2.81 2.45 3.66 13 4.89 5.15 3.86 4.68 4.71 3.16 5.36 5.87 5.85 0.73 0.93 1.94 0 0.87 0.51 1.72 14 5.76 6.02 4.73 5.55 5.58 4.03 6.23 6.74 6.72 1.6 1.8 2.81 0.87 0 1.38 0.85 15 5.4 5.66 4.37 5.19 5.22 3.67 5.87 6.38 6.36 1.24 1.44 2.45 0.51 1.38 0 1.65 16 6.61 6.87 5.58 6.4 6.43 4.88 7.08 7.59 7.57 2.45 2.65 3.66 1.72 0.85 1.65 0

182

Pandrung Short Distance Matrix (km)

Sarkigaon Dwaridhari Parigaon UppalloJarang Pandrung Basi TalloJarang Saune Ramche Gairichhap Lamagaon Pahare Tinkhande 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 0.53 1.68 1.19 1.14 5.38 4.43 4.26 7.19 3.79 4.55 5.54 6.67 2 0.53 0 2.21 1.72 0.61 5.91 4.96 3.73 6.66 3.26 4.02 5.01 6.14 3 1.68 2.21 0 0.49 2.82 4.68 3.73 5.94 8.87 5.47 6.23 7.22 8.35 4 1.19 1.72 0.49 0 2.33 4.19 3.24 5.45 8.38 4.98 5.74 6.73 7.86 5 1.14 0.61 2.82 2.33 0 6.52 5.57 4.34 7.27 3.87 4.63 5.62 6.75 6 5.38 5.91 4.68 4.19 6.52 0 0.95 9.64 12.57 9.17 9.93 10.92 12.05 7 4.43 4.96 3.73 3.24 5.57 0.95 0 8.69 11.62 8.22 8.98 9.97 11.1 8 4.26 3.73 5.94 5.45 4.34 9.64 8.69 0 3.87 0.47 1.23 2.22 3.35 9 7.19 6.66 8.87 8.38 7.27 12.57 11.62 3.87 0 3.4 4.16 1.65 2.78 10 3.79 3.26 5.47 4.98 3.87 9.17 8.22 0.47 3.4 0 0.76 1.75 2.88 11 4.55 4.02 6.23 5.74 4.63 9.93 8.98 1.23 4.16 0.76 0 2.51 3.64 12 5.54 5.01 7.22 6.73 5.62 10.92 9.97 2.22 1.65 1.75 2.51 0 1.13 13 6.67 6.14 8.35 7.86 6.75 12.05 11.1 3.35 2.78 2.88 3.64 1.13 0

Masel Short Distance Matrix (km)

NirmalDiha Sapunge Bhattagaon Pandegaon Majhthok Sarkigaon Devkotagaon Khatrithok Devisthan Ghyampesal Dandagaon Ghoptegaon Kayapani 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 3.27 6.03 6.12 5.23 5.82 6.59 6.28 7.83 9.89 8.92 10.22 12.22 2 3.27 0 2.76 2.85 1.96 2.55 3.32 3.01 4.56 6.62 5.65 6.95 8.95 3 6.03 2.76 0 0.65 0.8 1.39 2.16 1.85 3.4 5.46 4.49 5.79 7.79 4 6.12 2.85 0.65 0 0.89 1.48 2.25 1.94 3.49 5.55 4.58 5.88 7.88 5 5.23 1.96 0.8 0.89 0 0.59 1.36 1.05 2.6 4.66 3.69 4.99 6.99 6 5.82 2.55 1.39 1.48 0.59 0 1.22 0.91 2.46 4.52 3.55 4.85 6.85 7 6.59 3.32 2.16 2.25 1.36 1.22 0 0.31 1.86 3.92 2.95 4.25 6.25 8 6.28 3.01 1.85 1.94 1.05 0.91 0.31 0 1.55 3.61 2.64 3.94 5.94 9 7.83 4.56 3.4 3.49 2.6 2.46 1.86 1.55 0 2.06 1.09 2.39 4.39 10 9.89 6.62 5.46 5.55 4.66 4.52 3.92 3.61 2.06 0 0.97 2.27 4.27 11 8.92 5.65 4.49 4.58 3.69 3.55 2.95 2.64 1.09 0.97 0 1.3 3.3 12 10.22 6.95 5.79 5.88 4.99 4.85 4.25 3.94 2.39 2.27 1.3 0 2 13 12.22 8.95 7.79 7.88 6.99 6.85 6.25 5.94 4.39 4.27 3.3 2 0

Baguwa Short Distance Matrix (km)

Sikhre Banjaragaon Khanchok Bhyalgaon Khatrigaon Pokhrelgaon Kasinthok Dharampani Rithepani Kathekhola Pandegaon 1 2 3 4 5 6 7 8 9 10 11 1 0 0.4 2.12 2.79 3.4 3.48 4.21 3.77 3.5 4.46 4.08 2 0.4 0 1.72 2.39 3 3.08 3.81 3.37 3.1 4.06 3.68 3 2.12 1.72 0 0.67 1.28 1.36 2.09 1.65 1.38 2.34 1.96 4 2.79 2.39 0.67 0 0.61 1.25 1.42 1.54 1.89 2.23 2.47 5 3.4 3 1.28 0.61 0 0.64 0.81 0.93 1.28 1.62 1.86 6 3.48 3.08 1.36 1.25 0.64 0 1.45 0.29 0.64 0.98 1.22 7 4.21 3.81 2.09 1.42 0.81 1.45 0 1.74 2.09 2.43 2.67 8 3.77 3.37 1.65 1.54 0.93 0.29 1.74 0 0.35 0.69 0.93 9 3.5 3.1 1.38 1.89 1.28 0.64 2.09 0.35 0 1.04 0.58 10 4.46 4.06 2.34 2.23 1.62 0.98 2.43 0.69 1.04 0 0.67 11 4.08 3.68 1.96 2.47 1.86 1.22 2.67 0.93 0.58 0.67 0

183 Rural Engineering Infrastructures Design and Public Facility Locations

184

Asrang Short Distance Matrix (km)

Magargaon Jhingate Kaphalchhap Ripgaon HarraBisauni Waglegaon Thamdanda Asranggaon Okhlepani Nayagaon PokhariBatta Bhantanagaon Mohoriyagaon 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 1.71 1.35 1.41 0.87 4.76 1.07 2.01 3.14 3.85 2.53 3.11 2.4 2 2.42 0 0.36 1.84 1.88 5.04 1.35 2.29 3.42 4.13 1.54 2.12 2.68 3 2.06 0.36 0 1.48 1.52 4.68 0.99 1.93 3.06 3.77 1.18 1.76 2.32 4 1.41 1.84 1.48 0 0.54 4.18 0.49 1.43 2.56 3.27 2.66 3.24 1.82 5 0.87 1.88 1.52 0.54 0 4.22 0.53 1.47 2.6 3.31 2.7 3.28 1.86 6 4.76 5.04 4.68 4.18 4.22 0 3.69 2.75 1.62 0.91 5.86 6.44 5.02 7 1.07 1.35 0.99 0.49 0.53 3.69 0 0.94 2.07 2.78 2.17 2.75 1.33 8 2.01 2.29 1.93 1.43 1.47 2.75 0.94 0 1.13 1.84 3.11 3.69 2.27 9 3.14 3.42 3.06 2.56 2.6 1.62 2.07 1.13 0 0.71 4.24 4.82 3.4 10 3.85 4.13 3.77 3.27 3.31 0.91 2.78 1.84 0.71 0 4.95 5.53 4.11 11 3.24 1.54 1.18 2.66 2.7 5.86 2.17 3.11 4.24 4.95 0 0.58 3.5 12 3.82 2.12 1.76 3.24 3.28 6.44 2.75 3.69 4.82 5.53 0.58 0 4.08 13 2.4 2.68 2.32 1.82 1.86 5.02 1.33 2.27 3.4 4.11 3.5 4.08 0

Nareswor Short Distance Matrix (km)

NareB nareA Rajetar Gaikhur Sarkigau Gairigau Chisapan AgeShikhar Holsimha Dumsiri Kamere Aapchaur Lapse Bhogteni Tiwarigaon Newargau 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 0 2.54 8.9 8.6 8.16 8.4 7.79 6.02 9.52 9.16 9.64 5.45 8.61 6.85 7.89 7.57 2 2.54 0 6.36 6.06 5.62 5.86 5.25 3.48 6.98 6.62 7.1 2.91 6.07 4.31 5.35 5.03 3 8.9 6.36 0 0.3 0.74 1.72 1.11 2.88 5.55 5.19 5.67 3.45 4.64 2.88 3.92 3.6 4 8.6 6.06 0.3 0 0.44 1.42 0.81 2.58 5.25 4.89 5.37 3.15 4.34 2.58 3.62 3.3 5 8.16 5.62 0.74 0.44 0 0.98 0.37 2.14 4.81 4.45 4.93 2.71 3.9 2.14 3.18 2.86 6 8.4 5.86 1.72 1.42 0.98 0 0.61 2.38 5.05 4.69 5.17 2.95 4.14 2.38 3.42 3.1 7 7.79 5.25 1.11 0.81 0.37 0.61 0 1.77 4.44 4.08 4.56 2.34 3.53 1.77 2.81 2.49 8 6.02 3.48 2.88 2.58 2.14 2.38 1.77 0 4.64 4.28 4.76 0.57 3.73 1.97 3.01 2.69 9 9.52 6.98 5.55 5.25 4.81 5.05 4.44 4.64 0 0.36 1.94 4.07 0.91 2.67 1.63 3.39 10 9.16 6.62 5.19 4.89 4.45 4.69 4.08 4.28 0.36 0 1.58 3.71 0.55 2.31 1.27 3.03 11 9.64 7.1 5.67 5.37 4.93 5.17 4.56 4.76 1.94 1.58 0 4.19 1.03 2.79 1.75 3.51 12 5.45 2.91 3.45 3.15 2.71 2.95 2.34 0.57 4.07 3.71 4.19 0 3.16 1.4 2.44 2.12 13 8.61 6.07 4.64 4.34 3.9 4.14 3.53 3.73 0.91 0.55 1.03 3.16 0 1.76 0.72 2.48 14 6.85 4.31 2.88 2.58 2.14 2.38 1.77 1.97 2.67 2.31 2.79 1.4 1.76 0 1.04 0.72 15 7.89 5.35 3.92 3.62 3.18 3.42 2.81 3.01 1.63 1.27 1.75 2.44 0.72 1.04 0 1.76 16 7.57 5.03 3.6 3.3 2.86 3.1 2.49 2.69 3.39 3.03 3.51 2.12 2.48 0.72 1.76 0

Tandrang Short Distance Matrix (km)

Okhle Kubinde Dandabari M.Dubindanda M.Nange Maithum 1 2 3 4 5 6 1 0 0.84 3.84 4.74 8.82 6.42 2 0.84 0 3 3.9 7.98 5.58 3 3.84 3 0 0.9 4.98 2.58 4 4.74 3.9 0.9 0 4.08 1.68 5 8.82 7.98 4.98 4.08 0 2.4 6 6.42 5.58 2.58 1.68 2.4 0

185 Rural Engineering Infrastructures Design and Public Facility Locations

Finam Short Distance Matrix (km)

Kantheswara Aruswara Melbisauna Lapsibot Khirpegau Sunargau Hatiya Pipalthok Sundardanda Hilekharka Thulkhetgau Luichiswara Finamgau Aultari Kuwapani Lakuriswara Bhagabatigau Dungagadebhanjyang 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 0 1.17 1.62 2.45 2.78 0.68 1.06 1.2 1.78 2.32 2.12 2.48 1.95 2.7 2.46 2.59 5.06 4 2 1.17 0 0.45 1.28 1.61 1.85 2.23 1.86 1.28 1.49 1.62 1.98 1.8 2.2 2.31 3.37 5.84 4.78 3 1.62 0.45 0 0.83 1.16 2.3 2.68 2.16 1.58 1.04 1.92 1.66 2.1 1.88 2.61 3.67 6.14 5.08 4 2.45 1.28 0.83 0 0.33 3.13 3.51 2.99 2.41 1.87 2.75 2.49 2.93 2.71 3.44 4.5 6.97 5.91 5 2.78 1.61 1.16 0.33 0 3.46 3.84 3.32 2.74 2.2 3.08 2.82 3.26 3.04 3.77 4.83 7.3 6.24 6 0.68 1.85 2.3 3.13 3.46 0 0.38 0.52 1.1 1.64 1.44 1.8 1.27 2.02 1.78 1.91 4.38 3.32 7 1.06 2.23 2.68 3.51 3.84 0.38 0 0.81 1.39 1.93 1.43 1.9 0.91 2.12 1.42 1.53 4 2.94 8 1.2 1.86 2.16 2.99 3.32 0.52 0.81 0 0.58 1.12 0.92 1.28 0.75 1.5 1.26 2.32 4.79 3.73 9 1.78 1.28 1.58 2.41 2.74 1.1 1.39 0.58 0 0.54 0.34 0.7 0.52 0.92 1.03 2.09 4.56 3.5 10 2.32 1.49 1.04 1.87 2.2 1.64 1.93 1.12 0.54 0 0.88 0.62 1.06 0.84 1.57 2.63 5.1 4.04 11 2.12 1.62 1.92 2.75 3.08 1.44 1.43 0.92 0.34 0.88 0 0.47 0.52 0.69 1.03 2.09 4.56 3.5 12 2.48 1.98 1.66 2.49 2.82 1.8 1.9 1.28 0.7 0.62 0.47 0 0.99 0.22 1.5 2.56 5.03 3.97 13 1.95 1.8 2.1 2.93 3.26 1.27 0.91 0.75 0.52 1.06 0.52 0.99 0 1.21 0.51 1.57 4.04 2.98 14 2.7 2.2 1.88 2.71 3.04 2.02 2.12 1.5 0.92 0.84 0.69 0.22 1.21 0 1.72 2.78 5.25 4.19 15 2.46 2.31 2.61 3.44 3.77 1.78 1.42 1.26 1.03 1.57 1.03 1.5 0.51 1.72 0 1.06 3.53 2.47 16 2.59 3.37 3.67 4.5 4.83 1.91 1.53 2.32 2.09 2.63 2.09 2.56 1.57 2.78 1.06 0 2.47 1.41 17 5.06 5.84 6.14 6.97 7.3 4.38 4 4.79 4.56 5.1 4.56 5.03 4.04 5.25 3.53 2.47 0 1.06 18 4 4.78 5.08 5.91 6.24 3.32 2.94 3.73 3.5 4.04 3.5 3.97 2.98 4.19 2.47 1.41 1.06 0

Panchkhuwa Deurali Short Distance Matrix (km)

Amle Khamgau Gyaji Lakure B Amle Mulabari Deurali Baluwa Arubot Dharapani 1 2 3 4 5 6 7 8 9 10 1 0 1.25 2.1 5.25 3.81 1.88 3.13 3.57 4.54 4.57 2 1.25 0 0.85 4 2.56 0.63 1.88 2.32 3.29 3.32 3 2.1 0.85 0 3.15 1.71 1.08 2.33 2.77 3.74 3.77 4 5.25 4 3.15 0 1.44 4.23 4.06 4.5 5.47 5.5 5 3.81 2.56 1.71 1.44 0 2.79 2.62 3.06 4.03 4.06 6 1.88 0.63 1.08 4.23 2.79 0 1.25 1.69 2.66 2.69 7 3.13 1.88 2.33 4.06 2.62 1.25 0 0.44 1.41 1.44 8 3.57 2.32 2.77 4.5 3.06 1.69 0.44 0 0.97 1.68 9 4.54 3.29 3.74 5.47 4.03 2.66 1.41 0.97 0 0.71 10 4.57 3.32 3.77 5.5 4.06 2.69 1.44 1.68 0.71 0

Dhawa Short Distance Matrix (km)

Chautara Baddanda Rajalibhanjyang Digau Bolang Dandagau Baluwa 1 2 3 4 5 6 7 1 0 1.3 3.65 4.9 6.36 6.31 8 2 1.3 0 2.35 3.6 5.06 5.01 6.7 3 3.65 2.35 0 1.25 2.71 2.66 4.35 4 4.9 3.6 1.25 0 1.46 1.41 3.1 5 6.36 5.06 2.71 1.46 0 2.87 3.24 6 6.31 5.01 2.66 1.41 2.87 0 1.69 7 8 6.7 4.35 3.1 3.24 1.69 0

186

Arupokhari Short Distance Matrix (km)

Lakure Dandapari Ratmate Churung Sisneri Deurali Dhakalgau Tunibote Dhadagau Lamabagar Dadgau Kauchini Aru Tallo 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 1.18 3.02 12.93 3.67 5.47 9.21 10.08 11.63 13.76 11.81 13.59 12.59 2 1.18 0 1.84 11.75 2.49 4.29 8.03 8.9 10.45 12.58 10.63 12.41 11.41 3 3.02 1.84 0 9.91 0.65 2.45 6.19 7.06 8.61 10.74 8.79 10.57 9.57 4 12.93 11.75 9.91 0 9.26 7.46 3.72 4.59 6.14 8.27 6.32 8.1 7.1 5 3.67 2.49 0.65 9.26 0 1.8 5.54 6.41 7.96 10.09 8.14 9.92 8.92 6 5.47 4.29 2.45 7.46 1.8 0 3.74 4.61 6.16 8.29 6.34 8.12 7.12 7 9.21 8.03 6.19 3.72 5.54 3.74 0 0.87 2.42 4.55 2.6 4.38 3.38 8 10.08 8.9 7.06 4.59 6.41 4.61 0.87 0 1.55 3.68 2.87 4.65 3.65 9 11.63 10.45 8.61 6.14 7.96 6.16 2.42 1.55 0 2.13 1.32 3.1 2.1 10 13.76 12.58 10.74 8.27 10.09 8.29 4.55 3.68 2.13 0 3.45 5.23 4.23 11 11.81 10.63 8.79 6.32 8.14 6.34 2.6 2.87 1.32 3.45 0 1.78 0.78 12 13.59 12.41 10.57 8.1 9.92 8.12 4.38 4.65 3.1 5.23 1.78 0 1 13 12.59 11.41 9.57 7.1 8.92 7.12 3.38 3.65 2.1 4.23 0.78 1 0

Borlang Short Distance Matrix (km)

Narayanpur Lekhapakha Bhanjyang Alegau Chhapthok Gairigau Birdigau J.Simaltar Polichhap Airebhanjyang Ghatbesi Pipaltar Sundeerpur Mahadevtar Satbisetar Apswara Kyamuntar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 0 0.71 1.46 1.96 6.65 2.46 3.62 5.97 3.87 4.98 8.13 4.56 4.57 6.43 5.52 7.42 8.48 2 0.71 0 1.05 1.55 6.24 2.05 3.21 5.56 3.46 4.57 7.72 4.15 4.16 6.02 5.11 7.01 8.07 3 1.46 1.05 0 0.5 5.19 1 2.16 4.51 2.41 3.52 6.67 3.1 3.11 4.97 4.06 5.96 7.02 4 1.96 1.55 0.5 0 4.9 0.71 1.87 4.22 2.12 3.23 6.38 2.81 2.82 4.68 3.77 5.67 6.73 5 6.65 6.24 5.19 4.9 0 4.19 5.35 7.7 5.6 1.67 4.82 6.29 6.3 4.55 7.25 9.15 10.2 6 2.46 2.05 1 0.71 4.19 0 1.16 3.51 1.41 2.52 5.67 2.1 2.11 3.97 3.06 4.96 6.02 7 3.62 3.21 2.16 1.87 5.35 1.16 0 2.35 2.57 3.68 6.83 3.26 3.27 5.13 4.22 6.12 7.18 8 5.97 5.56 4.51 4.22 7.7 3.51 2.35 0 4.92 6.03 9.18 5.61 5.62 7.48 6.57 8.47 9.53 9 3.87 3.46 2.41 2.12 5.6 1.41 2.57 4.92 0 3.93 4.27 0.69 2.12 2.56 3.07 4.97 6.03 10 4.98 4.57 3.52 3.23 1.67 2.52 3.68 6.03 3.93 0 3.15 4.62 4.63 2.88 5.58 7.48 8.54 11 8.13 7.72 6.67 6.38 4.82 5.67 6.83 9.18 4.27 3.15 0 3.58 5.01 1.71 5.96 7.86 8.92 12 4.56 4.15 3.1 2.81 6.29 2.1 3.26 5.61 0.69 4.62 3.58 0 1.43 1.87 2.38 4.28 5.34 13 4.57 4.16 3.11 2.82 6.3 2.11 3.27 5.62 2.12 4.63 5.01 1.43 0 3.3 0.95 2.85 3.91 14 6.43 6.02 4.97 4.68 4.55 3.97 5.13 7.48 2.56 2.88 1.71 1.87 3.3 0 4.25 6.15 7.21 15 5.52 5.11 4.06 3.77 7.25 3.06 4.22 6.57 3.07 5.58 5.96 2.38 0.95 4.25 0 3.8 4.86 16 7.42 7.01 5.96 5.67 9.15 4.96 6.12 8.47 4.97 7.48 7.86 4.28 2.85 6.15 3.8 0 1.06 17 8.48 8.07 7.02 6.73 10.21 6.02 7.18 9.53 6.03 8.54 8.92 5.34 3.91 7.21 4.86 1.06 0

187 Rural Engineering Infrastructures Design and Public Facility Locations

188

C. Google Earth maps of case study regions

Figure C1: Settlements and rural road network in the study area: Gorkha A

189 Rural Engineering Infrastructures Design and Public Facility Locations

Figure C2: Settlements and rural road network in the study area: Gorkha B

190

Figure C3: Settlements and rural road network in the study area: Lamjung A

191 Rural Engineering Infrastructures Design and Public Facility Locations

Figure C4: Settlements and rural road network in the study area: Lamjung B

192

D. Distance matrices of rural road networks of case study regions

Table D.1: Distance Matrix (km) for Network-Gorkha A

Node

Gorkha HQ Bhogteni pointInt. Hatiya Kuwapani Taple pointInt. Thamdanda Gairigau Pokhrelgau pointInt. Khatrithok pointInt. pointInt. Digau M. Dubindanda pointInt. Dhakalgau Deurali Dwaridhari Palkhu Takumaj pointInt. pointInt. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 0 5.75 3.52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5.75 0 0 0 0 3.51 0 0 0 0 0 19.8 0 0 0 0 0 0 0 0 0 0 0 0 3 3.52 0 0 6 3.34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13.84 0 5 0 0 3.34 0 0 3.44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 3.51 0 0 3.44 0 5.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 5.7 0 2.69 0 4.12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 2.69 0 4.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 4.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.35 0 10 0 0 0 0 0 0 4.12 0 0 0 2.49 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 2.49 0 1.74 0.7 0 0 0 0 0 0 0 0 0 0 0 12 0 19.8 0 0 0 0 0 0 0 0 1.74 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0.7 0 0 1.5 0 0 2.78 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 1.5 0 7.73 7.35 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 7.73 0 0 0 0 0 0 0 0 0 8 16 0 0 0 0 0 0 0 0 0 0 0 0 0 7.35 0 0 0 0 0 0 0 0 0 9.95 17 0 0 0 0 0 0 0 0 0 0 0 0 2.78 0 0 0 0 5.57 2.78 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.57 0 0 0 0 0 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.78 0 0 1.2 0 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.2 0 3.28 0 0 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.28 0 5.12 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.12 0 0 0 23 0 0 0 13.84 0 0 0 0 4.35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8.5 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 9.95 0 0 0 0 0 0 8.5 0 Notes: Int. point = Intermediate point Bold letters = nodal point Normal letters = Intermediate point

193 Rural Engineering Infrastructures Design and Public Facility Locations

Table D.2: Distance Matrix (km) for Network-Gorkha B

Node

Start point Dhaukholaga u pointInt. Gaikhur pointInt. pointInt. Palumtar pointInt. Kholipakha Ampipal Patalepani pointInt. Chhoprak pointInt. Thalajung pointInt. Sarkigau Banspur Chisapani pointInt. Hansapur Kalimati pointInt. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 0 6.5 0 0 0.92 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 6.5 0 4.64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 4.64 0 1.68 0 3.36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0.92 0 0 0 0 7.53 0 0 7.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 3.36 0 0 7.53 0 5.94 8.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 5.94 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 8.24 0 0 2.6 2.56 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 7.01 0 0 2.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 2.56 0 0 1.15 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 1.15 0 5.78 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 5.78 0 3.6 0 6.5 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 3.6 0 6.6 0 0 0 0 0 0 0 0 0 14 4 0 0 0 0 0 0 0 0 0 0 0 6.6 0 0 0 0 0 0 0 0 0 17.3 15 0 0 0 0 0 0 0 0 0 0 0 6.5 0 0 0 4.4 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.4 0 6.75 0 3.87 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.75 0 3.62 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.87 0 0 0 1.13 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.13 0 5.8 5 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.8 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 3.74 23 0 0 0 0 0 0 0 0 0 0 0 0 0 17.3 0 0 0 0 0 0 0 3.74 0

194

Table D.3: Distance Matrix (km) for Network-Lamjung A

Start (Tarkughat) point Bhaisikholagau Dhamilikuwa Satdobato pointInt. (Seltarbajar) pointInt. (Kotod) Bakot pointInt. (Gauda) pointInt. (Pyarajungbhanjyang) Lamagau Dharmadhunga Bhaiswara pointInt. (HarrabotBend) pointInt. (Harrabot) pointInt. (Kalleri) Bharate Parjedanda pointInt. (Okhari) Upalloalainche pointInt. (Kamargau) pointInt. (Kamarkhu) Newargau Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 0 1.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1.1 0 2.92 0 0 0 0 0 0 0 0 0 2.35 0 0 0 0 0 0 0 0 0 3 0 2.92 0 6.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 6.39 0 4.23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 4.23 0 4.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 4.5 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 13 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 7 0 2.38 0 0 0 0 0 0 0 1.56 0 0 0 0 0 9 0 0 0 0 0 0 0 2.38 0 1.45 0 11.29 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 1.45 0 13.5 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 13.5 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 11.29 0 0 0 4.98 0 0 0 0 0 0 0 0 0 13 0 2.35 0 0 0 0 0 0 0 0 0 4.98 0 2.18 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 2.18 0 4.55 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 4.55 0 12.5 0 0 0 3.49 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12.5 0 10.5 0 0 0 0 0 17 0 0 0 0 0 0 0 1.56 0 0 0 0 0 0 0 10.5 0 3.45 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.45 0 8.6 0 0 6.7 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8.6 0 8.5 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.49 0 0 0 8.5 0 2.72 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.72 0 11 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.7 0 0 11 0

195 Rural Engineering Infrastructures Design and Public Facility Locations

Table D.4: Distance Matrix (km) for Network-Lamjung B

Node Paudidhik Bhaktichowk Udipur Bhakunde Jhakrikhet Khatrigau Kharibhanjyang Gahatelek Nayagau Malekharka Bajarkot Khahare Khatrichhap Suderbajar Kharetar Satrasayaphant Archalwami Swaradeurali Sinduredhunga Dandagau Kirtipur Baspani Dhuseni Majhgida Chandigau Ranipani Bagre Int Swara Swara Upallorayali Rampani Shanibajar Kunchha Kirtipur Jita Sotipasal Sunargau Gothpani Amdanda Samibhanjyang Gorkhalithan Thulokumalgau Duipiple Bhorletar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 1 0 3.37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3.37 0 5.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 5.39 0 6.81 0 0 0 0 5.89 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 6.81 0 2.59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 2.59 0 5.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 5.3 0 3.07 0 0 0 0 0 0 0 0 0 0 0 0 3.22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 3.07 0 2.18 0 0 2.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 2.18 0 2.18 5.62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 5.89 0 0 0 0 2.18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 5.62 0 0 10 0.82 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 2.5 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0.82 0 0 0.6 0 0 3.23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0.6 0 1.24 2.13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 1.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 2.13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.6 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 3.23 0 0 0 0 2.46 0 0 0 0 0 0 4.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.46 0 3.71 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.71 0 7.08 0 0.91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7.08 0 3.24 0 0 0 0 3.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0 0 3.22 0 0 0 0 0 0 0 0 0 0 0 0 3.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.91 0 0 0 4.44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.44 0 3 0 0 0 0 3.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.34 0 0 0 0 0 0 2.1 0 0 0 0 0 0 5.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.27 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.46 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 3.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.2 0 0 0 0 3.8 0 0.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6 0 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.4 0 0 0 0 0.7 0 1.9 0 0 0 0 0 0 0 0 0 0 0 0 0 31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.9 0 3.4 0 0 2.4 0 0 5.65 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.4 0 1.9 0 0 0 0 0 0 0 0 0 0 0 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.9 0 7.4 0 0 0 0 0 0 0 0 0 0 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.3 1.68 0 0 0 0 0 0 0 0 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.4 0 0 5.3 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.7 0 0 4.28 0 0 0 4.5 4 0 0 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.28 0 1.28 0 0 0 0 0 0 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.7 0 0 0 0 0 1.28 0 3 0 0 0 0 0 39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 4.19 4.87 0 0 41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.5 0 0 0 4.19 0 0 0 0 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4.87 0 0 0.59 0 43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.59 0 10.3 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10.3 0

196

E. Suggested intervention in the test rural road network

Table E.1: The intervention in the network link at different level of budget based on P2 (RRNM-1)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

1 3 3 5 6 7 8

(NRs) 1

10 11 11

13 13 14 14 17 17 19 20 21

in millions 5.75 3.52 6 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 100 A A G

200 A A A A G G G

300 A A A A A A A G A A

400 A A A A A A A A A A A A

500 A A A A A A A A A A A A A A G

600 A A A A A A A A G A A A A A A A A

700 A A A A A A A A A A A A A A A A A A

800 A A A A A A A A A A A A A A A A A A A A Note: A = Asphalt G = Gravel

197

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.2: The intervention in the network link at different level of budget based on P3 (RRNM-1)

Links and Distance (km)

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

1 1 3 3 5 6 7 8

10 11 11

13 13 14 14 17 17 19 20 21

Budget (NRs) in millions 5.75 3.52 6.0 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 100 A A G A G

200 A A A A A A G A

300 A A A A A A G A A A A

400 A A A A A A A A A A

500 A A A A A A A A A A A A A A A

600 A A A A A A A A A A A A A A G A A A

700 A A A A A A A A A A A G A A A A A A A

800 A A A A A A A A A A A A A A A A A A A Note: A = Asphalt G = Gravel

198

Table E.3: The intervention in the network link at different level of budget based on P4 (RRNM-1)

Links and Distance (km)

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

Budget (NRs) 10

------

1 1 3 3 5 6 7 8

10 11 11

in millions

13 13 14 14 17 17 19 20 21

5.75 3.52 6 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 100 A A G A

200 A A A A A

300 A A A A A A A A

400 A A A A A A A A G A A

500 A A A A A A A A A A A A A

600 A A A A A A A A A A A A G A A A A A

700 A A A A A A A A A A A A A A G A A A A A

800 A A A A A A A A A A A A A A A A A A A A Note: A = Asphalt G = Gravel

199

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.4: The intervention in the network link at different level of budget based on P2 ( RRNM-2)

Links and Distance (km)

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

Budget -

1 1 3 3 5 6 7 8

10 11 11

13 13 14 14 17 17 19 20 21

(NRs) in millions 5.75 3.52 6.0 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 10 E E

15 E E

20 E E

25 E

30 E E

35 E E E

40 E E E

45 E E E

50 E E E E E

55 E E E Note: E = Earthen (Selected Link)

200

Table E.5: The intervention in the network link at different level of budget based on P3 (RRNM-2)

Links and Distance (km)

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

Budget -

1 1 3 3 5 6 7 8

10 11 11

13 13 14 14 17 17 19 20 21

(NRs) in millions 5.75 3.52 6.0 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 10 E E

15 E E

20 E E E

25 E E E

30 E E E E

35 E E E E

40 E E E E

45 E E E E

50 E E E E E

55 E E E E E Note: E = Earthen (Selected Link)

201

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.6: The intervention in the network link at different level of budget based on P4 (RRNM-2)

Links and Distance (km)

2 3 4 5 6 7 8 9 11 12 13

14 17 15 16 18 19 20 21 22

------

Budget -

1 1 3 3 5 6 7 8

10 11 11

13 13 14 14 17 17 19 20 21

(NRs) in millions 5.75 3.52 6.0 3.34 3.44 5.7 2.69 4.12 4.2 2.49 1.74 0.7 1.5 2.78 7.73 7.35 5.57 2.1 1.2 3.28 5.12 10 E E

15 E

20 E

25 E E

30 E E E

35 E E E E

40 E E E E

45 E E E E

50 E E E E

55 E E E E E Note: E = Earthen (Selected Link)

202

Table E.7: The intervention in the network link at different level of budget based on P2 (RRNM-3)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 100 A A G A

200 A A A A A A A

300 A A A A A A A A G A G

400 A A A A A A A A A A G A A A

500 A A A A A A A A A A A A A A A

600 A A A A A A A A A A A G G A A A A A

700 A A A A A A A A A A A A G A A A A A A

800 A A A A A A A A A A A A A A A A A A A A Note: A = Asphalt G = Gravel

203

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.8: The intervention in the network link at different level of budget based on P3 (RRNM-3)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 100 A A A A

200 A A A A A A A A A

300 A A A G A A A A A G A A

400 A A A A A A A A A A A A A A

500 A A A A A A A A A A A A A A A A

600 A A A A A A A A A G A A A A A A A A

700 A A A A A A A A A A A A A A A G A A A A

800 A A A A A A A A A A A A A A A G A A A A A Note: A = Asphalt G = Gravel

204

Table E.9: The intervention in the network link at different level of budget based on P4 (RRNM-3)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 100 A A A G

200 A A G G G G A G G A

300 A A A G G A A G G A A A

400 A A A G G A A G G A A A G A A

500 A A A A A A A A G A A A A A A

600 A A A A A A A A A A A A A A G A A A

700 A A A A A A A A A A A A A A A G A A A A

800 A A A A A A A A A A A A A A A G A A A A A Note: A = Asphalt G = Gravel

205

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.10: The intervention in the network link at different level of budget based on P2 (RRNM-4)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 140 E E E E E E E E E 160 E E E E E E E E E E E 180 E E E E E E E E E E E E E E 200 E E E E E E E E E E E E E E 220 E E E E E E E E E E E E E E 240 E E E E E E E E E E E E E E E 260 E E E E E E E E E E E E E E E 280 E E E E E E E E E E E E E E E E 300 E E E E E E E E E E E E E E E E 320 E E E E E E E E E E E E E E E E E E 340 E E E E E E E E E E E E E E E E E E 360 E E E E E E E E E E E E E E E E E E E 380 E E E E E E E E E E E E E E E E E E E E 400 E E E E E E E E E E E E E E E E E E E E Note: E = Earthen (Selected Link)

206

Table E.11: The intervention in the network link at different level of budget based on P3 (RRNM-4)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 140 E E E E E E E E 160 E E E E E E E E E E E 180 E E E E E E E E E E E E E 200 E E E E E E E E E E E E E E E 220 E E E E E E E E E E E E E E 240 E E E E E E E E E E E E E E E 260 E E E E E E E E E E E E E E E E 280 E E E E E E E E E E E E E E E E 300 E E E E E E E E E E E E E E E E E E 320 E E E E E E E E E E E E E E E E E E 340 E E E E E E E E E E E E E E E E E E E 360 E E E E E E E E E E E E E E E E E E E 380 E E E E E E E E E E E E E E E E E E E E 400 E E E E E E E E E E E E E E E E E E E E Note: E = Earthen (Selected Link)

207

Rural Engineering Infrastructures Design and Public Facility Locations

Table E.12: The intervention in the network link at different level of budget based on P4 (RRNM-4)

Links and Distance (km)

Budget

2 3 4 5 6 7 8 9 14 20

17 18 21 22

10 11 12 13 15 16 19

------

- - - -

------

(NRs) in -

1 2 3 4 5 6 7 8

9 1 2 5 7 8 9

13 10

16 16 20 21

millions 3.52 3.34 3.44 5.7 4.12 2.49 0.7 2.78 2.1 5.75 6 2.69 4.2 1.74 1.5 7.73 7.35 5.57 1.2 3.28 5.12 140 E E E E E E E E 160 E E E E E E E E E E E E 180 E E E E E E E E E E E 200 E E E E E E E E E E E E 220 E E E E E E E E E E E E E 240 E E E E E E E E E E E E E E 260 E E E E E E E E E E E E E E E 280 E E E E E E E E E E E E E E E E E 300 E E E E E E E E E E E E E E E E E E 320 E E E E E E E E E E E E E E E E E E 340 E E E E E E E E E E E E E E E E E E E 360 E E E E E E E E E E E E E E E E E E E 380 E E E E E E E E E E E E E E E E E E E E 400 E E E E E E E E E E E E E E E E E E E E Note: E = Earthen (Selected Link)

208

F. Bi-objective solutions of sample network for different budget levels

Table F.1: Solutions for budget level NRs 400 millions

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s1 73,060 396,592 g g g g g g g g g g g g g g g g g g g g e s2 70,815 395,292 g g g a g g g g g g g g g g e g g g g g g s3 70,690 395,292 g g g a g g g g g g a a g g e g g g g g g s4 70,660 395,292 g g g a g g g g g g g a g g e g g g a g g s5 69,981 393,867 g a g g g g g g g g g g g g g g e g g g g s6 70,044 392,552 g a g g g g a g g g a g g g e g g g g g e s7 70,017 391,854 g a e g g g g g g g g g g g g g g g g g g s8 69,936 390,884 g a g g g g g g a g e a g g e g g g g g g s9 70,021 389,996 g a g g g g g g g g e g g g g e g g g g g s10 69,740 388,939 g a g g g g g g g g g g g g a e e g g g g s11 70,208 387,814 g a e g g g g g g g g g g g e g g g g g g s12 69,777 386,926 g a e g g g g g g g g g g g a e g g g g g s13 70,375 385,956 g g g g g a g g g g e g g g e e g g a g a s14 70,491 384,981 g g g g g a g g e g g g g g e e g g g g g s15 70,634 383,973 a g g a g g g g e g g g g g g g g g g e e s16 69,957 382,945 e a e g g g g g g g e g g g g g g g a a g s17 69,899 381,981 g a e g g g g g g g e g g g g g e a g g a s18 70,260 381,000 e g g a g g g g e g e g a a e g a a a g g s19 70,280 379,971 g g g g g a a g g g a g e g g e e g g g g s20 68,717 378,985 g g g g g a g a g g g g a a g e g e g g e s21 69,945 377,993 g a g g g g e g g g e g g g g e a g a g e s22 66,001 377,658 e a a g a g a a a a a g a g e e e g g g e s23 70,274 376,999 g g g a g g g g g g e g a a g e g a e g e s24 70,449 375,980 g g g a g g g g g g e g a a e e g a a e e s25 70,105 374,982 e g g g g a g g g g e g a g g g e a a e e s26 70,365 373,977 e a e g g g g g g g e g g g e e g g g g g s27 69,665 372,969 e g e a g g g g g a e g g a g a g a a e e s28 61,005 372,275 e a g a a a a a e a g g a g e e e g g g e s29 69,859 371,980 e a g g g g e g e g g g g a g g e g g g e s30 68,606 371,237 e g e a a g a g a g e g g g e e a a g g e s31 69,192 370,986 e a g g g g g g e a a g a a g g e g e g e s32 69,277 369,967 e a g g g g g g e a g g a a e g e a g e e s33 69,996 368,996 e a g g g g e g a g e g g g g e a g g e g s34 64,203 368,772 e a a a a g a a e g g g e g e e a g g g e s35 67,805 367,992 e a e a g g g g a g g g e g g e e g g g g s36 67,402 367,197 e g e a a g a a a g e g e g e g a g g g e s37 69,926 366,997 g a g g g g e g g g g g a e g e g a g a g s38 65,404 366,984 e a e a g g a a a a g g a a g e e a g e e s39 69,850 365,981 g a g g g g e g e g e a a g e a g g e g g s40 69,406 365,955 a a a g g g a g a a a g e g e e e g g e e s41 63,806 365,252 e a e a a g a a a a g g e g g e e g g g e s42 68,382 364,984 g a g g g g g a a a a a g e e e g g g e g 209

Rural Engineering Infrastructures Design and Public Facility Locations

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s43 61,104 364,797 e a e a a a a a e a g g a g e e e g g g e s44 69,626 363,969 a a e g g g a g e g a a g a e g e a e g e s45 68,049 362,993 e a g g g g a a g a e a g a e e e g e g e s46 65,604 362,222 g g e a a a e g a g a g a a g e e g g e e s47 68,263 361,968 e a g g g g g a e a e a g e g e g g g g a s48 60,302 361,601 e a e a a a g a e a g a a a a e e g g e e s49 60,503 361,601 e a e a a a a a e a g a a g a e e g g e e s50 69,814 360,999 e a g g g g g g e a a g e g e g e g g e e s51 67,461 359,996 g a g a g g e g e g g g g a e e e a e a g s52 67,002 359,923 e g e a a g a a a a a g a g e e e g e g e s53 60,704 359,574 e a e a a a e a e a g g a g a e e g g g e s54 68,372 358,991 g a e g g g g a e a e g a g g e e e g g g s55 62,405 358,604 e a a a g a e a e a e a a a e e e a a a e s56 61,602 358,580 e a e a a a a g e a g g a a a e e g e g e s57 61,802 358,580 e a e a a a a g e a g g a a g e e a e g e s58 66,769 357,972 a a g g g a g g g a e g g g e g g e e e e s59 66,403 357,457 e g a a a g a a e a e g a a g e g e g e e s60 64,002 357,375 e g a a a a a a g g e a a a g e e e g e e s61 60,208 357,193 e a e a a a g a e a e a g a a e e a a e e s62 60,902 357,133 e a e a a a g a a a e g a g g e e e g a e s63 65,203 357,133 e a e a g g a a a a e a g a a e e e g g e s64 68,275 356,970 g a e g g g e a a a e g e g e a e g a g e s65 69,635 355,969 e a e g g g g g a a e a g g e g g e e g g s66 67,605 355,408 e g a g g a e a e a e a g a a e e a a e e s67 63,000 355,019 e a a g a a e a a a e a e a e e e g g g e s68 68,428 354,994 e a e g g g g a e a a a g g e g g e e g g s69 64,604 354,058 e a e a a g g a e g g g e g e e a g g e e s70 68,405 353,998 e g e g a a a g a g g g e g e e a e g g e s71 68,194 353,998 e a e g g g g a a a a a e a e e g e g g e s72 69,004 353,676 e g a g a g e a e a e g e a g e e g g g e s73 60,805 353,423 g a e a a a g a e a g g g g a e e e g e e s74 68,572 352,995 a a g g g g g a g g a a e a e e e e e g a s75 63,603 352,633 e g e a a a a a e a g a e g a e e a g e e s76 66,606 352,633 e g e g a a a a e a g g e g g e e g g e e s77 66,204 352,360 e g e a g a e a e g g g a a a e g e g g e s78 62,801 352,338 e a e a g a e a e a a a g g a e e g g e e s79 68,000 352,283 g g e a a g e g a a g g g g a e e e g e g s80 67,805 352,273 e g a a a g e g e a g g e a e e a a g e e s81 65,005 352,118 e g e a a a g a e g a g g g e e e e g g e s82 69,603 352,013 e g e g a g e a a g e g e g a g e g g e g s83 68,334 351,997 e a a g g g a a a a a g g e e e e g e g g s84 62,302 351,992 e a g a g a a a e a e a a a a e e e g e e

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Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s85 67,204 351,745 g a e g g a g g a g g g a a e e e e e g e s86 70,602 351,736 e g g g a g e g e a g g e a e g e g g e e s87 63,201 351,581 e a e a a g e a a a e a e a a e e g g g e s88 62,604 351,421 e a e a a a g g e a e g e g e e e g g g e s89 62,201 351,344 e a e a g a a a e a g a a a a e e a e e e s90 64,805 351,279 e a g g a a g g e a g g e g e e a g e e e s91 70,400 351,273 e a e g g g a g a g g g e g e e e e g g g s92 61,205 351,067 a a e a a a e a e a g g e g e e e g g g e s93 67,899 351,000 e a g a g g g g g g g e g g e g g e g g g s94 68,804 350,941 g g g a g g e a e a e g e g a e e g g e e s95 61,402 350,786 g a e a a a g a e g e g g e a e e g g g e s96 63,403 350,606 e g e a a a e a e a g a e a a e e a g g e s97 68,162 349,974 g a e g g g g a a a a a g a e e g e e e e s98 60,603 349,612 e a e a a a a a e a g a e g a e e g e g e s99 62,001 349,612 e a e a a a a g e a a g e g a e e g e g e s100 62,105 349,502 e a e a a a g g a a g g e a e e a e a e g s101 68,205 349,393 e g e g a a g g e a a g g e e e e g g g g s102 61,705 349,383 a a e a a a g a e g a g a g e e e e g e e s103 62,501 348,989 e a g a a a g e g a e a g a g e g g g g e s104 68,896 348,967 g a g g g g e a a g a g g e g g e g e e g s105 60,405 348,922 e a e a a a a a e a a g a a a e e e g e e s106 65,802 348,835 e a e g a g e a e a g g e a a e g g g e e s107 69,207 348,740 a g e g a g a a a a e g e g e g e a e e e s108 70,206 348,659 e g e a g g a e g a g g g a a e g a g g g s109 66,804 348,593 e g e g a a a a e g a a e a e e e a g e e s110 61,302 348,480 e a g a a a e a g a g g g g e e e e g e e s111 61,901 348,259 e a a a a a e g e a g g g a e e e a e e a s112 64,400 348,238 e g e a a a e a a a a g g g e e e e g g e s113 61,502 348,007 g a g a a a a a e g e g a e g e e g e g e s114 69,801 348,007 g g a g a g g a e g e g a e g e e g e g e s115 70,001 347,996 e a e g g g g g g a g g e e e g e g g g e s116 67,859 347,996 e a e a g g g g a g a e a g e g e g g g e s117 60,176 347,930 e a e a a a e a e a e a a a a e e a a e e

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Rural Engineering Infrastructures Design and Public Facility Locations

Table F.2: Solutions for budget level NRs 600 millions

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s1 73,034 399,332 g g g g g g g g g g g g g g g g g g g g g s2 72,776 396,592 g g g g g g g g g g g g g a g g g g g g e s3 70,110 395,292 g a g g g g g g g g g g g g e g g g g g g s4 72,922 394,924 g g g g g g g g g g e a g g g g g g g g g s5 72,534 394,831 e g g g g g g g g a g g g g g g g g g g g s6 72,568 394,404 g g g g g g g g g a a g g g g e g g g g g s7 70,202 393,949 g g g g g a g g e g g g g g g g g g g g g s8 69,981 393,867 g a g g g g g g g g g g g g g g e g g g g s9 72,872 392,552 a g g g g g g g g g g g g g e a a g g g e s10 72,892 392,184 g g g g g g g g g g e g g g g a g g g g e s11 69,867 392,096 a a g g g g g g g g g g g g g g g g g e g s12 72,581 392,091 e g g g g g g g g g g a a g a g g g g g e s13 72,764 391,854 g g e g g g g g g g g a a g g a g g g g g s14 70,034 391,664 g a g g g g g g g g a g g g g e g g g g e s15 69,595 391,209 a g g g g a g g e g a g g g a g a g g a e s16 69,911 391,127 a a g g g g g g g g g g g g g g e g g g e s17 70,114 390,884 g a g g g g g g g g e g g g e g g g g g g s18 62,913 390,791 e g a a a a a a a a g a a a e a g a a g g s19 72,955 390,423 e g g g g g g g g g e g g g g g g a g g g s20 70,198 390,364 g a g g g g g g g g a g g g e e g g g g g s21 69,839 390,069 g a g g g g e g g g g g g g g g g g g a a s22 69,172 389,996 a a a g g g a g g g e g g g a e a g g g a s23 70,026 389,909 g a g g g g g g e g a g g g e g a g g g g s24 69,896 389,903 e a a g g g g g g g g g g g g e g g g g g s25 70,172 389,827 g a g g g g g g g g g g g g e g e g g g g s26 69,958 389,541 g a g g g g g g e g e g g g g g g g g g g s27 69,903 389,459 g a g g g g a g g g e g g g g g e g g g g s28 69,661 389,448 e a a g g g g g e g g g g g g a g g g g g s29 60,239 389,366 e a g a a a g a g a g a g a g g e a a g g s30 59,951 389,356 g a g a a a g a a a a a g a g a g a a e e s31 71,205 389,114 a g e g g g g g a a g g a a a a a a a a e s32 69,473 389,075 g a g g g g a g g g g g g g a g g g e g a s33 69,661 389,021 a a a g g g g g e g a g g g g e a g g g g s34 69,740 388,939 g a g g g g g g g g g g g g a e e g g g g s35 59,667 388,484 g a g a a a g a e a g a g a a a e a g a g s36 70,001 388,144 g a g g g g g g a g e g a g e g g g g g e s37 70,155 388,056 g a g g g g g g g g g g g g e g g g g e g s38 70,190 388,051 e a g g g g g g g g g g g g e g g g g g e s39 69,689 387,814 a a e g g g g g a g g g a g e a a g g g g s40 72,910 387,688 g g a g g g g g g g e g g g g g g g g e g s41 69,830 387,683 e a a g g g g g g g e g g g g g g g g g e s42 70,225 387,624 g a g g g g g g g g a g g g e e g g g g e

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Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s43 70,018 387,595 e a g g g g g g g g g g g g g g g g g e g s44 73,010 387,446 g g e g g g g g g g e g g g g g g g g a a s45 70,072 387,353 e a e g g g g g g g g g g g g g g g g g g s46 59,752 387,329 a a g a a a e a g a a a g a a g g a a g e s47 69,873 387,256 g a a g g g g g g g e g g g g e g g g g e s48 60,131 387,169 g a g a a a g a e a g a g a e a a a g g e s49 69,750 387,163 e a g g g g g g g g a g g g a e g g g g e s50 60,229 387,087 g a g a a a g a g a g a g a e a e a a g e s51 70,115 386,926 g a e g g g g g g g g g g g g e g g g g g s52 69,810 386,801 g a a g g g g g e g e g g g g g g g g g e s53 67,366 386,719 g a a a g g g g a g e g g g g g e g g g e s54 69,916 386,708 e a g g g g g g e g a g g g g g a g g g e s55 69,767 386,653 g a a g g g g g g g a g g g g g g e g g a s56 69,345 386,626 e a a g g g g g g g a a a g a g e g g g e s57 60,125 386,471 g a e a a a g a e a a a g a g a g g g a a s58 60,390 386,389 g a e a a a g a a a a a g a g g e g g g g s59 69,969 386,383 e a g g g g a g g g e a g g e g g g g g g s60 60,189 386,335 g a g a a a g a g a g a a a g g g g e a e s61 60,185 386,324 g a g a a a a a g a a a e a e a g g a g a s62 60,458 386,281 g a g a a a g a e a g a g a g e g g g g e s63 60,341 386,199 g a g a a a a a a a g a g a g e e g g g e s64 69,858 386,029 g a g g g g e g g g a a g g e a g g g g g s65 60,593 385,956 g a g a a a g a g a e a g a e e g g g g g s66 70,090 385,863 e a g g g g g g g g a a g g e e g g g g a s67 69,539 385,744 g a g g g g g g e g a a g g a g e g a g e s68 60,151 385,661 g a g a a a e a a a e a g a g g g a g g g s69 60,173 385,568 e a g a a a e a g a a a g a g a g g g g a s70 69,986 385,501 g a g g g g g g e g e a g g e g g g g g a s71 60,456 385,495 e a g a a a g a g a e a g a g e g g g g g s72 60,220 385,436 g a a a a a g a g a g a e a g e g g g g a s73 69,917 385,419 a a g g g g g g g g e a g g e g e g g g a s74 60,361 385,408 e a g a a a g a e a g a g a e a g g g g a s75 69,926 385,326 e a a g g g g g g g a a g g e g e g g g g s76 70,056 385,316 g a g g g g g g g g a a g g e g g g g e e s77 60,235 385,141 g a g a a a e a a a a a g a g e g a g g g s78 73,018 385,074 a g e g g g g g g g a a g g e g a g g g e s79 69,898 385,035 g a g g g g g g a g a a g g e g g g e g a s80 70,116 384,981 g a g g g g g g e g a a g g e e g g g g g s81 69,467 384,948 a a a g g g g g a g e a a g g g g g g e e s82 69,920 384,899 a a g g g g g g g g a a g g e e e g g a a s83 59,839 384,855 e a g a a a g a g a g a g a a g a a g e e s84 60,195 384,706 g a e a a a g a a a e a g a g a g g g g e

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Rural Engineering Infrastructures Design and Public Facility Locations

Links

1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s85 60,229 384,667 a a a a a a g a g a e a g g g g a g e g g s86 59,958 384,618 g a e a a a g a g a a a g a a g g a g e g s87 69,733 384,613 a a g g g g g g e g e a g g g e a g g g g s88 62,587 384,604 a a g a a g e a g a g a g a a a e g g a g s89 60,066 384,574 e a g a a a g a a a g a g a g g a a e g g s90 69,927 384,531 g a g g g g g g g g e a g g g e e g a g g s91 60,173 384,520 e a a a a a g a e a g a g a g e g a g g g s92 69,862 384,444 g a g g g g g g e g a a g g e g e a g a g s93 69,624 384,428 g a g g g g g g g g a a g g a e g g g e e s94 59,940 384,186 a a e a a a g a g a a a g a a e g a g g e s95 60,066 384,147 a a g a a a g a g a a a g a g e a a e g g s96 69,446 384,076 g a g g g g g g e g e a g g a g e g a a g s97 59,928 383,983 e a g a a a g a e a g a g a a g e a g g a s98 60,268 383,973 g a g a a a g a e a g a g a g g g a g e e s99 60,404 383,913 g a g a a a g a g a g a g a g g g e g g e s100 60,433 383,891 g a g a a a g a g a g a g a g g e g g e e s101 69,452 383,731 g a e g g g g g e g a a g g g a a a g a e s102 62,877 383,692 a a g a a g a a e a g g g a g a a g e g g s103 69,980 383,649 g a e g g g g g g g a a g g g g e g g g e s104 69,940 383,643 e a g g g g g g g g e a g g e g g a g g e s105 60,118 383,610 g a g a a a g a g a g a g a g g e a e a a s106 60,182 383,584 a a g a a a g a g a g a e a e a a g g g e s107 60,018 383,556 g a g a a a g a e a g a g a a e e a g g g s108 60,394 383,406 g a e a a a g a a a e a g a e g g a g g g s109 63,582 383,313 e a e g a a a a g g a a g g e g g a g a g s110 60,117 383,289 a a g a a a e a g a g a g a e a g a a g e s111 70,012 383,216 g a g g g g g g g g e a g g e e a g g g e s112 69,688 383,187 e a g g g g g g a g e a g g g g a g g e a s113 60,450 383,128 g a a a a a g a g a a a g a e e g g g e g s114 70,162 383,123 e a g g g g g g g g a a g g e e g g g g e s115 69,820 382,945 e a e g g g g g a g e a a g g g g g g g g s116 60,200 382,921 g a g a a a e a g a e a g a g g g a a g e s117 70,080 382,886 g a e g g g g g a g a a g g e e g g a g g s118 59,872 382,833 g a g a a a e a g a a a g a a a g g g e g s119 60,278 382,828 e a g a a a e a g a g a g a g g a g a g e s120 69,744 382,761 a a g g g g g g e g e a g g e g g a g a e s121 60,305 382,755 e a g a a a g a g a e a g a g e g a a g e s122 69,702 382,696 a a g g g g a g g g a a e g g e g g g a e s123 69,913 382,679 g a g g g g g g g g e a g g e a e g g g e s124 69,817 382,668 e a g g g g g g e g a a g g e a a g g g e s125 60,569 382,613 g a g a a a g a g a g a g a e g g e g g g s126 69,694 382,591 g a e g g g e g g g g a g g g a g g g a g

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1-3 3-4 3-5 5-6 6-7 7-8 7-10 8-9 10-11 11-12 11-13 13-14 13-17 14-15 14-16 17-18 17-19 19-20 20-21 21-22 Solutions Z1 Z2 1-2 s127 69,954 382,586 e a g g g g g g g g a a g g e a e g g g e s128 69,861 382,518 g a e g g g g g a g e a g g g e g g g a g s129 69,862 382,431 g a e g g g a g e g a a g g e a g g g g g s130 69,963 382,425 e a e g g g g g g g a a g g g e g g g a g s131 60,234 382,401 g a a a a a e a a a g a g a g e g g g g e s132 60,651 382,349 g a e a a a g a g a g a g a e g e g g g g s133 69,777 382,305 g a g g g g g g e g e a g g g g a g g e g s134 69,922 382,300 e a g g g g g g e g e a g g g g g g g g e s135 60,192 382,295 g a a a a a g a g a g a g a e a g g e g e s136 60,382 382,245 g a g a a a g a g a e a g a g g g e g g g s137 70,143 382,241 g a g g g g g g e g a a g g e e g g g g e s138 60,109 382,218 e a g a a a g a g a e a g a a g e g g g e s139 60,057 382,212 e a g a a a g a e a g a g a a g g g a e g s140 70,170 382,159 g a g g g g g g g g a a g g e e e g g g e s141 69,843 382,152 e a g g g g a g g g a a g g g g g e g g g s142 69,782 382,130 e a g g g g g g g g a a g g g a e g g e g s143 69,490 382,063 g a e g g g a g e g e a g g g g a a a a g s144 60,357 381,981 g a e a a a g a a a e a g a g g e g g g a s145 69,760 381,970 e a e g g g a g e g a a g g g g g a g g g s146 60,269 381,946 g a a a a a e a e a g a g g g g a a g g e s147 60,402 381,916 g a g a a a g a g a e a e a e g g a g g g s148 60,470 381,878 g a e a a a g a g a g a g a g g g g g e e s149 60,338 381,864 a a g a a a e a g a g a g a g g e g g g e s150 69,723 381,834 e a g g g g g g g g a a g g g a g g e g e s151 69,614 381,823 e a a g g g g g g g a a e g e g a a g g a s152 69,896 381,791 a a g g g g g g g g e a g g g e e g g g e s153 69,866 381,780 e a g g g g g g e g g a g g g e a g a g e s154 60,225 381,725 g a g a a a g a a a g a a a g e a e g g g s155 70,034 381,698 e a g g g g g g g g a a g g g e e g g g e s156 69,782 381,621 a a g g g g e g g g e a g g e g g g a a a s157 60,232 381,597 g a e a a a g a a a g a g a g g g g e a a s158 60,146 381,543 g a e a a a g a e a g a g a a e g g g g a s159 70,085 381,528 e a g g g g e g g g a a g g e g g g g g g s160 60,511 381,461 g a e a a a g a g a g a g a g e e g g g a s161 70,040 381,455 e a g g g g g g g g e a g g e e a g g g g s162 60,340 381,407 a a g a a a g a g a a a g a g e g g e g e s163 60,385 381,396 g a g a a a g a a a a a e a e e g a a g g s164 69,592 381,336 g a g g g g g g e g e a g g a g e g g g e s165 69,353 381,270 a a g g g g g g e g g a g g a g g e g a a s166 59,373 381,243 e a a a a a a a e a g a a a a a e a a a e s167 69,716 381,243 e a a g g g g g e g a a g g g g e g g a e

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Rural Engineering Infrastructures Design and Public Facility Locations

G. Floyd-Warshall algorithm

The Floyd-Warshall Algorithm (Floyd, 1962) is an algorithm to find all-pairs shortest paths on a graph. That is, it is guaranteed to find the shortest path between every pair of vertices in a graph. The graph may have negative weight edges, but no negative weight cycles (for then the shortest path is undefined).

A brief description of the algorithm is as follows.

Let dist(k,i,j) be the length of the shortest path from i and j that uses only the vertices as intermediate vertices. The following recurrence:

k = 0 is the base case - dist(0,i,j) is the length of the edge from vertex i to vertex j if it exists, and otherwise. dist(k,i,j) = min(dist(k - 1,i,k) + dist(k - 1,k,j),dist(k - 1,i,j)): For any vertex i and vertex j, the length of the shortest path from i to j with all intermediate vertices simply does not involve the vertex k at all (in which case it is the same as dist(k - 1,i,j)), or that the shorter path goes through vertex k, so the shortest path between vertex i and vertex j is the combination of the path from vertex i to k, and from vertex k to j.

After N iterations, there is no need anymore to go through any more intermediate vertices, so the distance dist(N,i,j) represents the shortest distance between i and j.

The pseudo code of the algorithm below assumes an input graph of N vertices. for i = 1 to N for j = 1 to N if there is an edge from i to j dist[0][i][j] = the length of the edge from i to j else dist[0][i][j] = INFINITY for k = 1 to N for i = 1 to N for j = 1 to N dist[k][i][j] = min(dist[k-1][i][j], dist[k-1][i][k] + dist[k-1][k][j])

This will give the shortest distances between any two nodes, from which shortest paths may be constructed. This algorithm can be used to calculate the shortest distance from each node to the other nodes in order to identify the nodal point(s) for rural road network.

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H. Prim’s Algorithm

A brief description of the Prim’s Algorithm (Prim, 1957) is described below.

At first a peak is chosen in random order ,which for simplicity we accept it as V(1).This way two sets of pointers are initialized, the O={1} and P={2...n}.

The O set will always contain the pointers of those peaks which are terminally attached in the

T tree. The V(1) peak has already been attached in the T tree. The P set contains the rest of the pointers for the peaks, P={1...n}-O which are those pointers who have not been terminally connected with a node of T, that means they are not attached in the tree.

In every execution of the Prim Algorithm, a new peak will be connected to the T tree, not always with their numbering order, for example the V(4) peak can be connected to the tree before the V(2) peak. The corresponding pointer of the newly connected peak will be deleted from P set and will be inserted to the O set. When all peaks are connected there will be O={1,...n} and P=0. This means the end of the algorithm.

The new peak every time will be chosen by using greedy method, among all sides of G which connect peaks already inserted in the T (pointers in the O set ) tree with the rest of the peaks

(pointers in the P set ), we choose one with minimum cost. If the chosen one is e(ij) then i belongs in the O set, V(i) peak is already in the T tree, j belongs in the P set , and V(j) peak has not been attached in the T tree yet. We put V(j) in the T tree, we change the O set by putting the j pointer, and we also change the P set by removing the j pointer.

The pseudo code of the algorithm is as follows.

INPUT :n,c[e(ij)],i,j belonging to {1,...,n}. OUTPUT :p(j) j=2,...,n (pointer of peaks j father in the T tree). Steps

1. : (initializations).

O={1} (V(1) root of the T tree). P={2,...,n}

For every j belonging to P :e(j):=c[e(j1)] , p(j)=1

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( all peaks connected to the root. By definition of the cost function: e(j)=infinite when V(j) does not connect to V(1).).

2. Choose a k for which e(k)<=e(j) for every j belonging to P.In case of tight choose the smaller one. Exchange the O set with the set produced by the union of the O set and {k} . Exchange the P set with the set produced by the difference of the P set and {k}. (P<-P-{k}) If P=0 then stop.

3. For every j belonging to P compare e(j) with c[e(kj)]. If e(j) >c[e(kj)] exchange e(j) <-c(e(kj)). Go back to Step 1.

This algorithm will give a MST connecting each nodal point in the region; hence can be used to define the rural road network in the region of rural areas.

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