<<

ISSN: 1402-1757 ISBN 978-91-7439-XXX-X Se i listan och fyll i siffror där kryssen är

LICENTIATE T H E SIS

Department of Civil, Environmental and Natural Resources Engineering1 Division of and Geotechnical Jens Johansson Impact of

ISSN 1402-1757 Impact of -Level Variations ISBN 978-91-7439-958-5 (print) ISBN 978-91-7439-959-2 (pdf) on Slope Stability Luleå University of 2014 Water-Level Variations on Slope Stability

Jens Johansson

LICENTIATE THESIS

Impact of Water-Level Variations on Slope Stability

Jens M. A. Johansson

Luleå University of Technology Department of Civil, Environmental and Natural Resources Engineering Division of Mining and

Printed by Luleå University of Technology, Graphic Production 2014

ISSN 1402-1757 ISBN 978-91-7439-958-5 (print) ISBN 978-91-7439-959-2 (pdf) Luleå 2014 www.ltu.se Preface

PREFACE This work has been carried out at the Division of Mining and Geotechnical Engineering at the Department of Civil, Environmental and Natural Resources, at Luleå University of Technology. The research has been supported by the Swedish Hydropower Centre, SVC; established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, The Royal Institute of Technology, Chalmers University of Technology and Uppsala University. I would like to thank Professor Sven Knutsson and Dr. Tommy Edeskär for their support and supervision. I also want to thank all my colleagues and friends at the university for contributing to pleasant working days.

Jens Johansson, June 2014

i Impact of water-level variations on slope stability

ii Abstract

ABSTRACT Waterfront- slopes are exposed to water-level fluctuations originating from either natural sources, e.g. extreme weather and tides, or from activities such as watercourse regulation for , freshwater provision, hydropower production etc. Slope failures and bank erosion is potentially getting trees and other vegetation released along with bank . When floating debris is reaching hydropower stations, there will be immediate risks of adverse loading on constructions, and clogging of spillways; issues directly connected to as energy production as dam safety. The stability of a soil slope is governed by slope geometries, stress conditions, and soil properties. External water loading, pore-pressure changes, and hydrodynamic impact from water flow are factors being either influencing, or completely governing the actual soil properties. As a part of this study, knowledge concerning water-level fluctuations has been reviewed; sources, geotechnical effects on slopes, and approaches used for modelling, have been focused. It has been found a predominance of research focused on coastal erosion, quantification of production, bio-environmentally issues connected to flooding, and effects on dams subjected to rapid drawdown. Though, also water-level rise has been shown to significantly influence slope stability. There seems to be a need for further investigations concerning effects of rapidly increased water pressures, loss of negative pore pressures, retrogressive failure development, and long-term effects of recurring rise-drawdown cycling. Transient water flow within soil structures affects pore-pressure conditions, strength, and deformation behavior of the soil. This in turn does potentially to soil-material migration, i.e. erosion. This process is typically considered in the context of embankment dams. Despite the effects of transient water flow, the use of simple limit- equilibrium methods for slope analysis is still widely spread. Though, improved accessibility of high computer capacity allows for more and more advanced analyses to be carried out. In addition, optimized designs and constructions are increasingly demanded, meaning less conservative design approaches being desired. This is not at least linked to economic as environmental aspects. One non-conservative view of slope-stability analysis regards consideration of negative pore pressures in unsaturated . In this study, three different approaches used for hydro-mechanical coupling in FEM-modelling of slope stability, were evaluated. A fictive slope consisting of a well- graded postglacial till was exposed to a series of water-level fluctuation cycles. Modelling based on classical theories of dry/fully saturated soil conditions, was put against two more advanced approaches with unsaturated-soil behavior considered. In

iii Impact of water-level variations on slope stability the classical modelling, computations of pore-pressures and deformations were run separately, whereas the advanced approaches did allow for computations of pore- pressures and deformation to be fully coupled. The evaluation was carried out by comparing results concerning stability, vertical displacements, pore pressures, flow, and model-parameter influence. It was found that the more advanced approaches used did capture variations of pore pressures and flow to a higher degree than did the classical, more simple approach. Classical modelling resulted in smaller vertical displacements and smoother pore- pressure and flow developments. Flow patterns, changes of soil governed by suction fluctuations, and changes of , are all factors governing as well water-transport (e.g. dissipation of excess pore pressures) as soil-material transport (e.g. susceptibility to internal erosion to be initiated and/or continued). Therefore, the results obtained underline the strengths of sophisticated modelling.

iv Abbreviations and symbols

ABBREVIATIONS AND SYMBOLS Symbol/ Definition Unit Abbreviation A1 Modelling approach 1 - A2 Modelling approach 2 - A3 Modelling approach 3 - ( ’ for drained conditions) kPa Soil weight kN/m3 3 Saturated soil weight kN/m Shear strain - 3 Unsaturated soil weight kN/m Strain increment (major principal-stress direction) - Volumetric strain increment - Strain increment (x-direction) -

Elastic strain increment (x-direction) -

Plastic strain increment (x-direction) - Volume change m3 , Displacements (x- and y-direction) m Initial lengths (x- and y-direction) m Head loss m Flow length m Horizontal side force kN

Horizontal side force, adjacent slice kN Modulus, initial stiffness kPa Modulus, secant (50% of deviatoric peak stress) kPa Oedometer modulus kPa Modulus, unloading/reloading kPa Young´s modulus kPa External water level - - Deviatoric strain (engineering notation) - Axial strain - Deviatoric strain (triaxial shear strain) - , Normal strains (x- and y-direction) - Principal strains - Volumetric strain - Elastic strain - strain - ̇ Plastic strain rate 1/s

v Impact of water-level variations on slope stability

̇ Visco-plastic strain rate 1/s FE(M) Finite element (method) - FOS Factor of safety - ( ) Yield function - Shear modulus kPa Ground surface - Gruondwater table - Acceleration of gravity m/s2 ( ) Plastic potential function -

, , van Genuchten´s empirical parameters - Suction pore-pressure head m Sensitivity ratio - Snesitivity score - Hydraulic gradient - Bulk modulus kPa Water bulk modulus kPa Hydraulic conductivity m/s

Saturated hydraulic conductivity m/s Relative hydraulic conductivity - 2 Intrinsic hydraulic conductivity m Length of slice base m LE(M) Limit-equilibrium (method) - Dynamic viscosity kPa s Normal force N - Poisson´s ratio - Specific volume - Effective normal force at slide base N PSH Pumped-storage hydropower - Gradient of the pore pressure kPa/m Preconsolidation pressure kPa Effective mean stress kPa Deviatoric stress kPa Specific discharge m/s

Horizontal flow m/day Vertical flow m/day Vertical flow, upward directed m/day Vertical flow, downward directed m/day Maximum flow m/day vi Abbreviations and symbols

Horizontal flow, rightward directed m/day Particle roundness - Rapid drawdown - Radius of slip surface (Swedish method) m

Initial radius of slip surface (log-spiral method) m 3 Water density kg/m Shear force at slice base N Slip surface - Degree of saturation - Effective degree of saturation - Maximum degree of saturation - Minimum degree of saturation - Residual degree of saturation - Saturated degree of saturation - Deviatoric stresses components kPa Total normal stress kPa Effective normal stress kPa Axial kPa Viscous stress component kPa Inviscid stress component kPa Major principal effective stress kPa Horizontal shear force N Shear stress kPa Maximum shear stress kPa

Shear strength kPa Water-pressure force N Pore pressure kPa Pore-air pressure kPa Pore-water pressure kPa Vertical deformation m Total volume m3 3 Pore volume m 3 Volume of solids m 3 Water volume m Water flow rate m/s Slice weight N Water load - Water-level fluctuation cycle - Angle of ( for drained conditions)

vii Impact of water-level variations on slope stability

Mobilized friction angle Friction angle at critical state Dilation component of the friction angle Geometrical interference component of friction angle Particle-pushing component of friction angle Inter-particle component of the friction angle Vertical side force N

Vertical side force, adjacent slice N Bishop´s parameter - Dilatancy angle Gradient operator -

viii Table of Contents

TABLE OF CONTENTS PREFACE ...... I ABSTRACT ...... III ABBREVIATIONS AND SYMBOLS ...... V TABLE OF CONTENTS ...... IX 1 INTRODUCTION ...... 1 1.1 Background ...... 1 1.2 Objectives ...... 4 1.2.1 Aim and objectives ...... 4 1.2.2 Method ...... 5 1.3 Scope and delimitations ...... 5 1.4 Outline ...... 6 2 WATER-LEVEL VARIATION – SOURCES, EFFECTS, AND CONSIDERATION ...... 7 2.1 Sources ...... 7 2.1.1 Long-term water-level variations ...... 7 2.1.2 Short-term water-level variations ...... 7 2.2 Effects ...... 10 2.3 Consideration ...... 11 3 SLOPE ANALYSIS ...... 15 3.1 Introduction ...... 15 3.2 Description and classification of soil ...... 15 3.3 Stress and strength ...... 16 3.3.1 Stress ...... 16 3.3.2 Particle arrangement...... 17 3.3.3 Strength and failure ...... 18 3.3.4 Angle of internal friction ...... 19 3.3.5 Factors governing internal friction – changed properties ...... 19 3.4 Slope-stability analysis ...... 22 3.4.1 Introduction ...... 22 3.4.2 Limit-equilibrium analysis ...... 23 3.4.3 Deformation analysis ...... 25 3.4.4 conditions ...... 26 4 MODELLING OF SOIL AND WATER ...... 29 4.1 Constitutive description of soil ...... 29 4.1.1 Stress ...... 29

ix Impact of water-level variations on slope stability

4.1.2 Strain ...... 29 4.1.3 Elastic response ...... 30 4.1.4 Unloading/reloading ...... 32 4.1.5 Plastic response ...... 32 4.1.6 Mohr-Coulomb model ...... 35 4.2 Hydraulic modelling ...... 38 4.2.1 Fundamentals ...... 38 4.2.2 Unsaturated soil ...... 38 4.2.3 Flow ...... 39 4.2.4 van Genuchten model ...... 40 4.3 Parameter sensitivity ...... 41 5 FEM-MODELLING ...... 43 5.1 Main aim ...... 43 5.2 Strategy ...... 43 5.3 Geometry, materials, and definition of changes ...... 44 5.4 Models used ...... 45 6 RESULTS AND COMMENTS ...... 47 6.1 Evaluation of FEM-modelling approaches ...... 47 6.1.1 General ...... 47 6.1.2 Stability ...... 47 6.1.3 Deformations, pore pressures and flow ...... 48 6.2 Parameter influence ...... 53 7 DISCUSSION ...... 57 8 CONCLUSIONS ...... 61 8.1 General...... 61 8.2 To be further considered ...... 62 REFERENCES ...... 65

APPENDED PAPERS: . J. M. Johansson and T. Edeskär, “Effects of External Water-Level Fluctuations on Slope Stability,” Electron. J. Geotech. Eng., vol. 19, no. K, pp. 2437–2463, 2014. . J. M. Johansson and T. Edeskär, “Modelling approaches considering impacts of water-level fluctuations on slope stability” To be submitted.

x Introduction

1 INTRODUCTION

1.1 Background Regarding the fact that an external water pressure acts stabilizing to a slope or to an embankment dam: “This is perhaps the o ly good thi g that water a do to a slope” (J. M. Duncan & Wright, 2005) There is a worldwide increasing need of land-use in costal/waterfront areas (e.g. Singhroy, 1995 among others). This trend, together with continuously changing site- specific conditions, brings more and more advanced and challenging geotechnical issues. It is necessary to monitor sites, to properly analyze data, and to evaluate potential risks concerning property, environmental, and human values. In case of unstable watercourse bank slopes, trees and other vegetation are potentially released along with bank landslides. In situations where the material released—floating debris— reaches downstream hydropower stations, there will be potential risks of damaging loads on constructions and clogging of spillways (e.g. Minarski, 2008; Åstrand & Johansson, 2011). The stability of a slope is utterly governed by soil properties, stress conditions, and slope geometries. Any change taking place of at least one of these factors, means slope- stability conditions being potentially affected. When it comes to changed soil properties, there are different scales. At a micro scale, the inherent properties of a soil are governed by its history; no matter if the soil is processed (crushed, filled etc.), or if it is naturally occurring; i.e. formed by weathering of , transported by erosive processes, and finally deposited from water, wind, or ice. Also at a larger scale— considering the soil skeleton—many different processes are governing the properties of the soil; e.g. particle-size distribution, soil-profile homogeneity, denseness etc. The properties of a soil is continuously affected by long-term processes, including e.g. transport and depositing (i.e. erosion and land-form development), and aging (i.e. weathering or other changed chemical or physical conditions). Any soil volume is continuously affected by hydrological conditions prevailing; present water is either influencing or completely governing the actual soil properties. At the scale of bank slopes and embankment dams, the structures are influenced by external water loads, development of pore pressures, and hydrodynamic impact from internal and external water flow. In Figure 1-1, some basic modes of water-level changes are defined; (A)

1 Impact of water-level variations on slope stability external erosion due to small waves or streaming water, (B) water-level drawdown, (C) water-level rise, and (D) water-level fluctuations.

Figure 1-1: Basic modes of water level change; streaming water (A), water level drawdown (B), raised water level (C), and fluctuating water level (D). Water loads (WL), positions of the ground- (GWT), and the external water level (EWL), are shown. Sources of water-level fluctuations (WLF’s) may e.g. include tidal water-level variations (e.g. Ward, 1945; Li, Barry, & Pattiaratchi, 1997; Raubenheimer, Guza, & Elgar, 1999), variations caused by wind waves (e.g. Bakhtyar, Barry, Li, Jeng, & Yeganeh-Bakhtiary, 2009), variations caused by other weather-related events (as heavy rainstorms and/or snow melting), and combinations of various phenomena (e.g. Zhang, 2013). Natural phenomena do also include time-dependent soil degradation in terms of e.g. weathering and structural changes. In addition, the stability of waterfront slopes is influenced by processes caused and driven by human activities. One such activity is regulation of watercourses, undertaken for water storage, enabling irrigation, freshwater provision, and/or hydropower production (e.g. Mill et al., 2010; Solvang, Harby, & Killingtveit, 2012). Despite the fact that regulation patterns seems to be critically connected to the stability of the banks, there is a clearly seen predominance of studies focusing on bio-environmental issues; i.e. endangered habitats

2 Introduction of plant and animal species. Moreover, among studies addressing geotechnical aspects of WLF’s, a large proportion have been directed to tidally driven issues; mostly aimed to describe relationships between an external sea-water level and level motions within the adjacent beach slope (e.g. Emery & Foster, 1948; Parlange et al., 1984; Nielsen, 1990; Thomas, Eldho, & Rastogi, 2013). Others have been addressing sediment-loading problems; river sediment budgets, changed river shapes caused by sedimentation etc. (e.g. Darby et al., 2007; Fox et al., 2007; R. Grove, Croke, & Thompson, 2013). Concerning WLF-effects specifically on slope-stability, the process of rapid drawdown is described and investigated by many authors (e.g. Lane & Griffiths, 2000; J. M. Duncan & Wright, 2005; Yang et al., 2010; Pinyol, Alonso, Corominas, & Moya, 2011; López-Acosta et al., 2013). Pore-pressure gaps and increased hydrological gradients are potentially occurring when water-level changes are rapidly coming about. Also water-level rise might cause problems, e.g. related to stress redistributions due to external loading, wetting induced issues such as loss of negative pore pressures, and seepage effects. Potential consequences might be loss of , soil structure collapse, and development of settlements and/or slope failure (Jia et al., 2009). Despite this fact, there are significantly less studies carried out on this topic. Quantification of slope stability is generally about two parts connected; (1) calculation of the factor of safety (FOS), and (2) determination of the location of the most critical slip surface. The development of methods for slope-stability analysis was initially about quantifications of behavior; this in the middle of the 19th century (Ward, 1945). The approach of assuming circular slip surfaces was introduced in 1916 and presented as a fully described method in the beginning of the 1920s (Krahn, 2003; J. M. Duncan & Wright, 2005). Numerous approaches for quantification of slope stability by using equilibrium equations have been presented. Such limit-equilibrium (LE) methods have been used for a long time (J. M. Duncan & Wright, 1980; Yu et al., 1998; Zheng et al., 2009) and have been more or less unchanged for decades (Lane & Griffiths, 1999). Despite well-known limitations of LE-analysis methods (e.g. Ward, 1945; Lane & Griffiths, 1999; Krahn, 2003) they have been widely used; largely due to their simplicity and usability. In parallel to the use of LE-approaches, application of continuum theories and material models has been brining use of methods based on deformations analysis, often numerically handled using finite-element (FE) analysis. Improved accessibility of high computer capacity allows for more and more advanced analyses to be performed. Optimized designs and constructions are increasingly demanded and less conservative design approaches are therefore often desired. This is not at least linked to economic and environmental aspects. One non-conservative view

3 Impact of water-level variations on slope stability in slope-stability analysis regards consideration of negative pore pressures in unsaturated soils. Taking into account negative pore pressures is generally associated with counting on extra contributions to the shear strength of the soil, resulting in extra slope stability. Though, there are still many unanswered questions when it comes to effects of considering peculiarities of unsaturated soil behavior (Sheng et al., 2013). Due to a worldwide expansion of watercourse regulation, with operational patterns directly governed by activities of energy balancing and freshwater provision, it is important to find reliable methods for analysis of stability effects on areas being exposed to the regulation.

1.2 Objectives 1.2.1 Aim and objectives The aim of this study is to identify and enlighten potential impacts on waterfront slopes subjected to water-level fluctuations, including evaluation of methods for slope- stability analysis. 1. Provide a review of the overall topic, capturing: . Sources of water-level fluctuations and known effects on slope stability . Fundamentals of mechanical properties of coarse grained soils; this with an emphasis on changes properties. . Advantages and disadvantages of methods available for slope-stability analysis (applicable to problems focused in this study).

2. Investigate potential impacts on a slope subjected to water-level fluctuations; this by FEM-modelling.

3. Evaluate approaches for FEM-modelling of impacts on a slope subjected to water-level fluctuations.

4. Evaluate potential benefits provided by parameter-influence analysis carried out in modelling work.

4 Introduction

1.2.2 Method The objectives were fulfilled by: 1. Conducting a literature review covering the topic of slope stability connected to water-level fluctuations.

2. Undertaking FEM-modelling for analysis of a slope subjected to water-level fluctuations; evaluating development of stability/safety, pore pressures, flow and deformations.

3. Performing a comparative study of different approaches used in FEM-modelling of a slope subjected to water-level fluctuations.

4. Performing a sensitivity analysis on the parameters used in the modelling carried out in (2) and (3).

1.3 Scope and delimitations The present study makes its starting point considering hydropower-production systems; this regards as well consequences as sources of issues. Though, both geotechnical aspects on the underlying processes and potential values of the findings are meant to be generally applicable and possibly extended in various directions. Some delimitations were done:

. Although as well the review part as the modelling part is primarily approached from a perspective of watercourse regulation, also other sources of water-level fluctuations are considered.

. The issues covered in the present work are approached focused on non- cohesive and low-cohesive embankment materials.

. In the FEM-modelling work done, some factors/conditions have been kept constant: - The soil material used is defined aimed to have properties being representative for glacial tills with an amount of fines in the lower range. - 10 water-level fluctuation cycles are considered - Only one rate is used for definition of water-level changes - Only one frequency is used for definition of water-level changes - The water-level fluctuation cycles are run without pauses. Consequently, excess pore pressures potentially developed are not necessarily dissipated.

5 Impact of water-level variations on slope stability

This allows for soil conditions to be varying by an increased number of water-level fluctuations run, and also for secondary effects linked to these non-constant conditions to be captured.

. The modelling part is based on a fictive case, i.e. focused on relative changes and differences. Though, input data for the soil model and the hydraulic model are based on values within ranges found representative. Since the result evaluation is comparative the exact values of the parameters chosen are not critical.

1.4 Outline The introduction (chapter 1) covers the overall background and objectives of the project. In chapter 2 the essence of the literature review regarding water-level fluctuations; sources, potential effects on slope stability, and considerations taken, is found (fully presented in Paper A). Chapter 3 covers some fundamentals on and slope-stability analysis. In chapter 4 basics of constitutive description of soils are presented along with details concerning the models used (in Paper B) for description of as well soil behavior as hydraulic properties. In chapter 5 the modelling work is described, and in chapter 6 the results are compiled. An overall discussion and conclusions drawn are presented in chapter 7 and chapter 8, respectively. The results/outcome from the review work is presented in chapter 7.

Paper A: A review concerning water-level fluctuations; sources, potential geotechnical effects on slope stability, and considerations taken. Paper B: A comparative study evaluating different approaches of hydro-mechanical coupling in FEM-modelling of impacts on a slope subjected to water-level fluctuations.

Besides what is presented in the present study, involvement in research on quantification of soil-particle shape has taken place. Work on implementation of 2D- image analysis on shape quantification was presented in (Rodriguez, Johansson, & Edeskär, 2012).

6 Water-level variation – sources, effects, and consideration

2 WATER-LEVEL VARIATION – SOURCES, EFFECTS, AND CONSIDERATION

2.1 Sources 2.1.1 Long-term water-level variations Sea-level rise is one of the most highlighted and debated direct effect of climate changes. The Bruun-theory (Bruun, 1988) is a generally accepted mathematical model developed for quantification of relationships between sea-level rise and coastal erosion. The model is assuming a closed material balance system between the shore and the offshore bottom profile. This kind of process is actually about the water-soil interface itself—not necessarily driven by water level changes—but could also be a consequence of water motion along the course; i.e. streaming/flowing. Though, a varied mean-level brings changed water-level ranges within which the short-term variations are occurring. In this sense, a rising sea level acts as an enabler of erosion (K. Zhang et al., 2004), whereupon consideration also of long-term changes are of importance. Hupp (1992) presented a channel-evolution cycle in a six-stage model describing the development from stable conditions, via some time limited landform changing stages, ending up with another stable state (Figure 2-1). These examples of long-term effects—as well coastal erosion as channel evolution—are showing clear consequences of water-soil interaction, entailing obvious effects on beaches/banks. Though, henceforth short-term water level variations will be focused.

2.1.2 Short-term water-level variations

Energy provision – water storage In the 1970s, the energy interest grew significantly due to uncertainties related to provision of oil. This was partly due to a generally spread reluctance to become dependent on other countries, partly due to concerns about the total global oil reserve Bardi (2009). The use of energy is growing worldwide; the rate of increased use and production is high as well in less developed countries, as in industrialized regions.

7 Impact of water-level variations on slope stability

Figure 2-1: Co eptual model o ha el evolutio . The illustrated y le i ludes the stages “pre- modi ied”, bei g o stable ature (Stage I), ollowed by stages bei g lasti g or limited time periods, i ludi g “ o stru tio ” (Stage II), “degradatio ” (Stage III), “threshold” (Stage IV), a d “aggradation” (Stage V). The y le e ds up with a stage o “re overy”, whi h o e is agai stable (Stage VI). The are representing the movement direction of the bed (vertically) and the banks (horizontally). The pictures are not to scale. (after Hupp, 1992)

Moreover, the use of renewable unregulated energy sources (non-fossil sources, naturally regenerated) is strongly growing. In 2011, as much as 19.0% out of the total global energy consumption, came from renewable energy sources (to be compared with 16.7% for 2010) (REN21, 2013). The significant growth of energy sources being totally dependent on the meteorological situation at a specific time, will increase the need for regulated (balanced) power (Catrinu, Solvang, & Korpås, 2010; Whittingham, 2008; Connolly, 2010). The concept is about storing energy being produced during periods when production of wind power (or other non-regulated sources) is exceeding the demand, and then letting the stored energy being discharged during periods of higher demands (Figure 2-2). The development and exploitation of non-regulated energy sources being planned, and the subsequent need of hydropower balancing, will necessarily require that flow magnitudes and water level heights, to a greater extent than until present, will vary in the future (Svenska Kraftnät, 2008). In addition to conventional hydropower, also pumped-storage hydropower (PSH) is a technique continuously growing. The system consists of two of different elevations. During off-peak electrical demand, water is pumped from a lower reservoir to a higher one; during on-peak demand, when the energy need is increasing, the water is discharged and energy is produced (C. Liu et al., 2010). The technology is well- established (Connolly, 2010), and is currently the only commercially proven large scale (>100MW) energy storage technology. In Rognlien (2012) some site-specific scenarios

8 Water-level variation – sources, effects, and consideration

Figure 2-2: Schematic sketch of the principle of storing energy produced during a period when production from wind power (or other non-regulated sources) is exceeding the demand, whereupon the stored energy is used during periods of higher demands. (Connolly, 2010) of practical implementation of PSH were discussed; examples included daily water- level variations in the order of 10 m. In 2011, there were about 170 pumped-storage plants operating in Europe and more than 50 new PSH-projects were expected to be either under construction or planned until 2020 (Zuber, 2011).

Other sources Natural water-level variations are related to meteorological and geological phenomena. Tide induced water-level fluctuations have been specifically studied for a long time. These kinds of variations are important to beach-sediment transport (e.g. Grant, 1948; J. R. Duncan, 1964; Nielsen, 1990; Li, Barry, Parlange, et al., 1997; Li, Barry, & Pattiaratchi, 1997). Besides actual sea-level variations and the mechanical material- transport processes, also the groundwater table on land is affected by the tidal changes (Emery & Foster, 1948; Chappell, Eliot, Bradshaw, & Lonsdale, 1979). Except tidally driven variations, there is also wind (i.e. strong winds, hurricanes etc.), changed atmospheric pressure (causing water movement), and submarine (generating waves sometimes propagating landward) (Pugh, 1987).

9 Impact of water-level variations on slope stability

2.2 Effects Drawdown of an external water level is usually impairing the stability of a slope. The process rapid drawdown is described and investigated by many authors (e.g. Lane & Griffiths, 2000; J. M. Duncan & Wright, 2005; Yang et al., 2010; Pinyol, Alonso, Corominas, & Moya, 2011). Pore pressure gaps and increased hydraulic gradients are potentially occurring as a consequence of rapid water-level changes. Such pore- pressure gaps combined with a decreased or fully vanished supporting water load, may lead to reduced slope stability. Studies on this phenomenon have been focused mostly on earth-fill dams, rather than on waterfront slopes in general. This predominance notwithstanding, the connection between rapid drawdown, vertical , and slope stability was generally highlighted in Yang et al. (2010). The study was based on laboratory testing of rapid drawdown in a column prepared with two soil layers; clayey over medium sand. Pore-pressure development was logged by time. The soil properties considered were—besides permeability—specific gravity, liquid limit, plasticity index, dry density, void ratio, porosity, and at saturation. Some of the results obtained are shown in Figure 2-3; pore pressures plotted against the depth, with different curves for different times elapsed. The results did clearly confirm potential outcomes of rapid drawdown; pore pressures remained high and increased gradients occurred. Consequences of rapid drawdown, including the fact that pore

Figure 2-3: Results from column rapid drawdown tests performed through a soil sample consisting of a finer soil layer (clayey sand) put over a coarser soil layer (medium sand). Pore-water pressures at different depths (elevations) are plotted at different times. The soil interface is represented by the dotted line. (Yang et al., 2010)

10 Water-level variation – sources, effects, and consideration pressures are potentially delayed compared to the external water level, have been shown to be outward seepage, tension cracks developed, and slope failure (Jia et al., 2009). Also rising of a water level might cause problems. In studies concerning the Three Gorges Dam site (e.g. Cojean & Caï, 2011), reduced slope stability has been noticed during periods of water-level rise. Generally, water-level rise has been shown to cause stress redistributions due to external loading (as well increases as reductions, in various directions), wetting induced issues such as loss of negative pore pressures, and seepage effects. These changes have been shown to cause loss of shear strength, soil structure collapse, development of settlements, and slope failure. In a large-scale slope model test reported, with the external water level being varied, vertical settlements at the crest were noticed (Jia et al., 2009). The deformation development was almost linear during the first period of water-level rising, and then continuously declining. The vertical settlements were assigned to wetting-induced soil collapse. Suction values did abruptly drop immediately when the water level reached the measure points. The horizontal total stresses were gradually increasing during the rise. In contrast, the vertical stresses were gradually reduced; asymptotically leveling out until the end of the rise. The authors suggested that the reduction of vertical stresses were caused by dissipation of entrapped air, together with gradually reduced stress concentrations (which were caused by the early observed differential settlements). The settlements were in turn explained by the wetting; i.e. entrapped air being replaced by water. Loss of negative pore-pressures and subsequent loss of shear strength did obviously immediately cause soil structure collapse/failure. Total stress changes were assigned to homogenization of the slope body; increased horizontal stresses caused by an increased water load, and vertical stresses stabilized due to stress-concentration dissipation. It was emphasized that a delayed change of pore pressure inside a slope—relative to the change of the adjacent external water level—results in significant movements of water within the slope body. Thus, the seepage forces were found to adversely affect the stability. The seepage- instability relationship was also confirmed in Tohari, Nishigaki, & Komatsu (2007).

2.3 Consideration The earliest used to take into account different degrees of submergence of a slope, involved stability charts (Morgenstern, 1963). In the following decades further investigations were done utilizing limit-equilibrium (LE) methods for expression of safety factors (Lane & Griffiths, 2000; Huang & Jia, 2009). Later, these kinds of problems have also been approached using finite-element (FE) tools (e.g. Lane & Griffiths, 2000; Pinyol et al., 2011).

11 Impact of water-level variations on slope stability

When it comes to cyclic recurring WLF’s, the fundamentals for each phase of rise and drawdown, respectively, are obviously the same as for these changes separately occurring. Though, there are important peculiarities linked to the recurrence. Since one of the key-issues of evaluating the effects of WLF’s on slope stability concerns description of groundwater motion, hydraulic modelling is highly important. Furthermore, any movement of the groundwater level is impacting the geotechnical conditions; the history of stress and strain changes is central. At the same time, soil deformations are affecting the pore pressure development. In order to describe this interaction, and for proper consideration of the behavior of unsaturated soils, fully coupled hydro-mechanical computations are needed (e.g. Galavi, 2010). In Huang & Jia (2009) it was stressed that fully coupled consolidation calculations should be further studied. Coupled hydro-mechanical behavior can possibly be considered in existing FE-codes. In such processes, calculations of deformations and groundwater flow with time-dependent boundaries have to be simultaneously carried out. Since as well saturated as partially saturated conditions have to be properly handled, consolidation has to be modeled also for unsaturated soils. For description of unsaturated soils, both elastic-plastic soil-skeleton behavior and suction dependency have to be considered. The latter concerns both degree of saturation and relative coefficient of permeability (e.g. Fredlund et al., 1994). Recent models considering influences of soil mechanical properties on the hydraulic behavior, are usually based on the dependency of soil-water characteristic curves (SWCC’s), on soil volume, soil density, or volumetric strain (Sheng, 2011). SWCC’s are relating suction and soil saturation for a specific soil material (examples are shown in section 4.2.4). Sheng (2011) did underline the importance of taking into account volume changes taking place along SWCC’s, when coupling hydraulic components with the mechanical components in constitutive models. The author stated that neglecting this volume change could mean inconsistent predictions of changes of volume and saturation. Among studies applying hydro-mechanical coupling, many have been addressing issues occurring in sediment-transfer systems. These are generally focused on sediment loading problems, sources of contributes to a river’s sediment budget, changed river shapes caused by sedimentation etc. (e.g. Darby et al., 2007; Fox et al., 2007; R. Grove, Croke, & Thompson, 2013). In Darby et al. (2007) a method for performance of a coupled simulation of fluvial erosion and was presented. The method did consider the dynamics of bank erosion involved coupling a fluvial-erosion model with FE-seepage analysis and LE-stability methods. The mass wasting was simulated to occur as a series of failure episodes. The study was limited to cohesive riverbanks, and mainly aimed to find a method to properly quantify bank derived sediment volumes.

12 Water-level variation – sources, effects, and consideration

Though, the modelling did involve both particle-size characterization and soil-strength consideration. The shortfall notwithstanding, some studies on large-scale reservoir fluctuations are found in the literature. For instance, it was found that the stability of a reservoir slope consisting of sand and , was more directly governed by hydraulic conductivities than by velocities of water-level changes (Liao et al., 2005). For evaluation of reservoir- fluctuation effects on a silty slope, the importance of negative pore pressures, friction resistance, and water-load support was highlighted in Zhan, Zhang, & Chen (2006). In that study, saturated-unsaturated seepage analysis was combined with LE-stability analysis. Also in Shen, Zhu, & Yao (2010) examination of “reservoir water-level fluctuation” did include analysis of only one cycle of rise and drawdown, carried out by means of LE-calculations. In Galavi (2010) hydro-mechanical theories used in FE- modelling were presented. Comparisons and evaluations performed showed good agreement between the results obtained from the numerical FE-computations performed using the FE-code 2D and those from analytical solutions. In Kaczmarek & Leśniewska (2011) effects of groundwater-level changes on a flood bank core were modeled. Stability and seepage were considered by FE-analysis. Though, the study was only briefly described and neither the input nor the outcomes were satisfactorily presented.

13 Impact of water-level variations on slope stability

14 Slope analysis

3 SLOPE ANALYSIS

3.1 Introduction Historically, methods for evaluation or determination of slope stability have been largely focused on theories regarding fine-grained soils. During the 1840s—related to the railway construction projects ran at that time—engineers were working on determination of the shear strength of clay (Ward, 1945). The analysis approach of assuming circular slip surfaces was introduced in 1916 (Petterson, 1955). Though, a fully described method was presented by Fellenius in the beginning of the 1920s (e.g. Krahn, 2003; J. M. Duncan & Wright, 2005). In 1945, Skempton was presenting a study named “A slip in the west bank of Eau Brink ”, including an illustration of a rotational slip surface within a slope mainly consisting of clay (Ward, 1945). During the past decades, engineering and research studies have brought knowledge and formulated theories within the area of soil mechanics. The understanding of different factors affecting slope stability (e.g. time dependent changes of soil behavior), has been continuously improved. This not at least due to known limitations of existing methods for evaluation of soil strength (e.g. laboratory and in situ testing methods) and development of new tools and instruments for measuring and observing slopes. All this together has successively formed the now available collection of experience and knowledge concerning slope behavior and slope failure. This applies for improved understanding of basic principles of soil mechanics, and improved analysis procedures. (J. M. Duncan & Wright, 2005)

3.2 Description and classification of soil The soil skeleton consists of three components. The solids consist of mineral grains and/or organic constituents. Moreover, free spaces between the solid grains—i.e. the pores/voids—are exhibiting properties (size and shape) depending on the geometrical properties of the solids. The pores are filled with fluids (often pore water), gas (often air), or a mixture of these two. The geotechnical properties of a soil volume are depending on minerals being present, content of organic material, content of water, manner of which the water is present, denseness of the soil particle arrangement, and size and shape of the particles. Different soil types are then grouped with respect to these characteristics.

15 Impact of water-level variations on slope stability

Soils are usually divided into two main groups; fine-grained soil and coarse-grained soil. This distinction is based upon the particle sizes; the diameters, d. The fractions clay and silt are sorted as fine-grained soils, whereas sand and are sorted as coarse-grained soils. Soils are also classified based upon the kind of forces being contributing to the soil strength. The grains in purely cohesive soils are held together by van der Walls forces, hydrogen bonds, and electro-static forces; the resultant makes up cohesive bonding. On the other hand, the strength of sand and gravel, i.e. frictional soils, is coming from mechanical inter-granular friction. Silt is sometimes with respect to strength properties called intermediate soils. (Craig, 2004)

3.3 Stress and strength 3.3.1 Stress

Classical theory In contrast to fine-grained soils (with strength coming from cohesive forces), the strength of a coarse grained soil mostly comes from contact forces between the individual grains. The mass of the soil particles, together with any additional forces from external loads, are getting normal forces acting at the particle contact areas. The resultant forces acting on a soil element are to be transmitted through the soil skeleton components, including also fluids and/or gases. The fundamental and well established principle of effective stress, , presented by Terzhagi in the 1920th, is expressed as:

(3.1) where is the total normal stress, and is the pore-water pressure. This equation is based upon the assumption that there are only two situations; (1) there is a pore pressure coming from the fully water filled pores, and (2) there is no pore pressure.

Unsaturated soil behavior In the middle of the 1950th, Bishop proposed an effective stress expression, considering also partially saturated or unsaturated soils:

( ) (3.2) where is the pore-air pressure, the pore-water pressure, and an experimentally determined matric-suction coefficient. This coefficient (Bishop’s parameter) could be related to the degree of saturation, . The experimental evidences of are sparse (Galavi, 2010), and the role of the parameter has been

16 Slope analysis generally questioned (Fredlund, 2006). The often used assumption of letting the matric-suction coefficient be replaced by the degree of saturation, i.e. , has been shown to require care to be taken. The validity of the assumption is highly dependent on the microstructure of the soil type being analyzed; more specifically the fraction of water filling the micropores, (Pereira et al., 2010). The deviation has been shown to be higher for fine-grained soils, especially those exhibiting high plasticity. Though, in PLAXIS (2012) the matric-suction coefficient is substituted with the effective degree of saturation, . Assuming air-pore pressure is being negligibly low, the effective stress expression (equation (3.2) becomes:

(3.3) Unsaturated soil behavior is further discussed in section 4.2. A number of proposals have been presented aiming to improve the accuracy regarding definition and description of stress-strain behavior and strength of unsaturated soils. Limitations of existing effective stress expression were indicated by e.g. Burland & Jennings (1962). The possibility to control the mechanical response of unsaturated soils by considering two stress-state variables, namely (1) the net stress, i.e. the difference between the total stress and the pore-air pressure, and (2) the suction, i.e. the difference between the pore-air pressure and the pore-water pressure, was firstly demonstrated by Fredlund & Morgenstern (1977). Moreover, a number of non-linear elastic constitutive models were developed based upon this. Subsequently, also elastic- plastic models have been proposed and developed (Sun et al., 2010). Many models are developed based on the Basic Barcelona Model (Alonso, Gens, & Josa, 1990). The subject of unsaturated soil was well reviewed in Sheng (2011).

3.3.2 Particle arrangement At a loose soil-particle arrangement, only a small lateral force is needed to get the soil particles rearranged into a denser configuration. Therefore, loose soils exhibit low resistance to volume decrease (contractancy) and deformations. Horizontal shearing of a dense coarse grained soil sample means stiff and almost elastic initial response. This since the soil particles of a dense soil are forced to “climb” over each other (in the direction against the applied vertical load), in order to get a rearrangement taking place. The soil undergoes volume increase (dilatancy). The response of shear stress, at increased shear straining, is conceptually shown in Figure 3-1. When shearing takes place without any further volume change, the critical state is reached.

17 Impact of water-level variations on slope stability

Figure 3-1: Shear stress/shear strain development for soils of different denseness. (after Hansbo, 1975)

3.3.3 Strength and failure Since the shear stress is directly dependent on the present effective normal stress, the shear strength is directly dependent on the effective normal stress at failure. One of the most known and used hypotheses for description of shear failure is Mohr-Coulomb´s theory, expressed by use of the strength parameters friction angle, and cohesion, (or and for drained conditions). Graphically, the failure criterion might be presented in the Mohr-Coulomb plane; either drawn as a straight line being a tangent to the shear stress/normal stress envelope (tangent parameters), or drawn from the origin to one specific stress point (secant parameters), see Figure 3-2. In the former case the strength parameters are valid only for a stress range around the touching point, whereas the ´-value in the latter case is only valid for one single stress state. According to the normally used tangent approach, the shear strength, is expressed:

(3.4) where c´ and ´ are valid for a limited effective stress range. The cohesion intercept, ’ obtained from the evaluation described is not to be confused neither with the “real” cohesion—i.e. the strength contribution originating from the inter-particle cohesive forces—nor the apparent cohesion, arising either from capillary tension stresses (negative pore pressure) or inter-granular cementation.

18 Slope analysis

Figure 3-2: The bold solid curve connecting the plotted stress points shows the actual shear stress-normal stress combinations of a specific soil. The thin solid line represents the envelope used for tangent approach evaluation of the strength parameters, whereas the dashed line represents the secant approach. (after Craig, 2004)

3.3.4 Angle of internal friction For a drained granular soil, the total angle of friction—i.e. the angle of friction mobilized during shearing, —is actually consisting of two main parts:

(3.5) where is the inter-particle sliding component and the geometrical interference component. The geometrical component is, in turn, consisting of two parts, namely

coming from the dilation phenomenon (particle climbing), and coming from particle pushing and rearrangement (Terzaghi et al., 1996). The final expression is moreover:

(3.6)

3.3.5 Factors governing internal friction – changed properties

Mineral composition and crushing properties The soil-particle minerals are affecting a coarse-grained soil by two factors; (1) the friction of the particle surface is directly dependent on the surface roughness (affecting the sliding component ), (2) the mineral hardness and strength is affecting the crushing properties of the individual particles (affecting the component ) (Terzaghi et al., 1996).

19 Impact of water-level variations on slope stability

Dilatancy The dilatancy angle, is used to describe volume increase during shearing. At low confining stresses, particles are moving as well through particle pushing as through particle climbing. This means an increased geometrical component (up to 30°) Terzaghi et al. (1996). According to Rowe´s theory (Rowe, 1962), the dilatancy phenomenon could be expressed:

( ) ( ) (3.7)

where and are the major and the minor principal stress, respectively, and is the rate of dilatancy (stresses and strains are further described in section 4.1). The index cv indicates critical state. The approach was based on results from compressional triaxial tests and the theory of Mohr circles. There are many studies that have been aimed to properly correlate the dilatancy angle to the friction angle. In Bolton (1986) it was stated that simple expressions are preferably used. One such simplification is the relationship (where is the friction angle at critical state). A simplified model is shown in Figure 3-3.

Figure 3-3: A soil volume subjected to a normal force, N and a horizontal shear force, T undergoes dilatancy. The dilatancy angle is denoted , the friction angle , and the friction angle at critical state . (after Axelsson, 1998) Even though this principle way of illustrating dilatancy is based on a number of assumptions, e.g. the particles being perfectly spherical (and of the same size), the fundamental mechanical effect is well described. Though, according to the definition of the critical state—i.e. that the dilatancy is zero—Bolton (1986) stated that the simple way of describing the dilatancy as above, means an overestimation of the difference

by approximately 20%, compared to the Rowe´s stress-dilatancy relationship, and suggested that the relation:

20 Slope analysis

(3.8) fits Rowe´s stress-dilatancy relationship well. In PLAXIS (2012) the definition of dilatancy angle is based on Rowe´s theory:

( ) (3.9)

where is the mobilized friction angle and is the friction angle at critial state.

Void ratio and grain size distribution Depending on to what extent the particles are interlocked and clamped by each other, the shearing resistance will vary. A simple measure of the soil-skeleton structure is the void ratio, , defined as the ratio of pore volume, and the volume of the solids, . At small void ratios of a coarse-grained soil, the total contact area between the particles is large; the friction angle is high. Therefore, in well-graded soils (e.g. glacial-tills), where smaller grains are filling the larger voids, friction angles are generally higher than in poorly graded soils (e.g. uniform ).

Particle shape Since Wadell (1932)—one of the first to put attention on how particle shape is affecting soil behavior—a number of studies have been carried out. In Krumbein (1941) as well the importance of considering the particle shape, as some methods for determination and analysis, were discussed. Connections and correlations between particle shape and mechanical behavior of soils—strength, stiffness/deformations, and hydraulic properties—are described and discussed in soil mechanics literature (e.g. Terzaghi et al., 1996; Guimaraes, 2002; Santamarina & Cho, 2004; Mitchell & Soga, 2005; Cho, Dodds, & Santamarina, 2006). Although there seems to be an agreement regarding the existing influence, the particle shape is rarely considered in designing of geotechnical structures. Even though particle shape—as an influencing factor—is mentioned in some guidelines and designing codes, e.g. Eurocode 7 and RIDAS (Swedenergy, 2008), it is not clearly described how to actually apply particle-shape information. (Johansson & Vall, 2011) In literature, the term shape is found to be used some inconsequently and there are significant variations in how different sub-quantities are used (Johansson & Vall, 2011). One common approach used for handling the complexity of particle-shape description,

21 Impact of water-level variations on slope stability is based on three sub-quantities of different geometric scales (Wadell, 1932; Krumbein, 1941; Mitchell & Soga, 2005). At large scale—i.e. when the particle diameters in different directions are described—the term sphericity is used. At an intermediate scale—for description of to what extent the particle boundary/perimeter is deviating from a smooth circle or ellipse—the sub-quantity roundness is used. To describe the smallest scale of the particle—the texture of the particle surface—roughness is used. For description of connections between soil-particle shape and the influenced properties, there are a number of empirical relationships developed. An often seen expression relating particle shape with strength is:

(3.10) where v is the friction angle at critical state, and is a quantity describing the roundness of the particles. This relation shows that the critical state friction angle is decreasing with increased roundness of the soil particles (Santamarina & Cho, 2004; Cho et al., 2006). Also void ratio is depending on the particle shape. At large strains, when the particle displacements are coming from particle rotation and inter-particle sliding, the void ratio is decreasing with increased roundness and increased sphericity (Cho et al., 2006). Since the strength properties are linked to void ratio (and/or porosity), also this relation affects the strength of the soil. The relevance of relationships between particle shape and mechanical soil properties, including the possibility to quantify the shape, was discussed in Rodriguez, Edeskär, & Knutsson (2013).

3.4 Slope-stability analysis 3.4.1 Introduction Among the factors causing reduced strength of a soils mass, increased pore pressure is very important. In addition to pore-pressure increase, also seepage—i.e. water flowing within the soil—might lead to washing out of soil particles, which moreover cause undermining of the soil (Ward, 1945). A lot attention has been put on natural events entailing an upward movement of the groundwater level; e.g. precipitation and subsequent infiltration (e.g. Lim et al., 1996; Tohari et al., 2007). Another phenomenon potentially resulting in strength loss is degradation and/or weathering; physical, chemical, and biological processes breaking down soil particles, rearranging the structures, and changing the properties of the entire soil mass (J. M. Duncan, 2005).

22 Slope analysis

The slope stability may also get reduced by increased shear stress due to changed loading conditions. The shear stress could be increased by (1) increased stresses acting in directions being driving; external loads at the top of the slopes, water pressure in cracks at the top of the slope, increased soil weight due to increased water content etc. The shear stress could also be increased by (2) factors making the resistant forces reduced; any kind of removal of soil at the bottom of the slope, and drop in water level at the slope base. (J. M. Duncan, 2005) As mentioned in previous sections, there are different approaches available for performance of stability analyses; limit-equilibrium methods, and deformation-analysis methods.

3.4.2 Limit-equilibrium analysis Limit-equilibrium (LE) methods have been used to analyze slope stability for a long time (J. M. Duncan & Wright, 1980; Yu et al., 1998; Zheng et al., 2009). These methods have been unchanged for decades (Lane & Griffiths, 1999). In J. M. Duncan & Wright (1980) it was emphasized that all equilibrium methods for slope-stability analysis have some characteristics in common: (1) The factor of safety (FOS) is defined as the ratio between the shear strength, and the shear stress required for equilibrium, . Using Mohr-Coulomb’s failure criterion and also applying Terzaghi´s expression for effective stress, the factor of safety becomes:

( ) ( )⁄ (3.11) where normal stress and pore pressure are denoted and u, respectively, and the strength parameters friction angle, and cohesion (expressed in terms of effective stresses, i.e. for drained situations) are denoted by , and , respectively. (2) It is to be assumed that the stress-strain characteristics of the soils are non-brittle, and that the same shear-strength value may be mobilized over a wide range of strains along the slip surface. (3) Some (or all) of the equilibrium equations are used to determine the average shear stress, and the slip surface normal stress; this in order to possibly use Mohr-Coulomb’s failure criterion for shear strength calculation. (4) Since the number of unknowns is larger than the number of equilibrium equations, explicit assumptions are to be involved. Among the single free-body procedures, i.e. the group of the LE-method that was first used, there are in turn sub-procedures being based on different approaches; e.g. the infinite slope procedure, the logarithmic spiral, and the Swedish circle method. For all of the single-free body procedures, homogenous soil profiles are preferred. External water

23 Impact of water-level variations on slope stability levels are considered as external loads, and the groundwater level determines from what level the soil will get saturated conditions. In Figure 3-4 the principles of some single free-body limit equilibrium procedures, are shown. In the infinite plane case, the slope inclination, the soil weight, and the strength parameters are needed for expression of the factor of safety. For the two other procedures, the shape of the assumed slip surface, the mass of the soil block bounded by the slip surface and the ground surface, and the location of the center, are to be determined. (J. M. Duncan & Wright (2005) (a) Infinite slope procedure (b) Logarithmic spiral (c) Swedish circle procedure procedure

Figure 3-4: Principle sketches of the basics of three single free-body limit-equilibrium procedures. The ground surfaces, GS and slip surfaces, SS are shown. Moreover, also slope inclination for the infinite slope case, ; the initial radius, for the logarithmic spiral case; and the constant radius, for the Swedish circle case, are presented.

Slice procedures Slices procedures were introduced already in the end of the 19th century (Ward, 1945). In order to simplify the process of determining the driving moments, and to make it possible to consider slip surfaces of more complex geometries, the soil block could be divided into vertical slices. Forces acting on a typical slice are weight, ; shear force on the slice base, (defined as , where is the shear strength and is the length of the slice base); effective normal force acting on the base, ; water pressure force acting on the base, ; vertical side force, ; horizontal side force, (see Figure 3-5). In the simplest slice procedure, often referred to as the ordinary method of slices, only overall moment equilibrium is considered. In Bishop´s simplified method also the equation of vertical force equilibrium of each slice is satisfied; in Bishop´s modified method, also side forces are considered. All these methods are restricted to circular slip surfaces. Moreover, there are methods where only the force equilibrium equations are satisfied; e.g. a method presented by Lowe and Karafiath in 1960 (J. M. Duncan &

24 Slope analysis

Wright, 1980). Methods satisfying as well moment equilibrium as force equilibrium (e.g. Morgenster a d Pri e’s method, Spe er’s method, and Ja bu’s ge eralized pro edure o slices) are applicable on slopes with slip surfaces of any geometry. When stability analyses are performed using LE-methods, consideration of pore-pressure situations are often considered by simplified methods (Huang & Jia, 2009). This might be done by assuming hydrostatic pore pressures (if there is no flow), use of flow-nets (for steady- state seepage), approximate charts (for transient/unsteady-state seepage), or pore- pressure ratios (J. M. Duncan, 1980)(as an alternative for steady-state seepage consideration or for analytical consideration of development of excess pore pressures due to consolidation).

Figure 3-5: A typical slice with acting forces. (J. M. Duncan & Wright, 1980) Still, it is worth mentioning that drawbacks and limitations of LE-methods have been known and evidenced for a long time. For instance, there are difficulties connected to accurate definition of the position of the slip surface (Ward, 1945), and there are numerical problems potentially met with Bishop´s modified method (J. M. Duncan, 1996). An illustrative example of what kind of reasoning being characteristically used to justify utilization of LE-analysis was seen in Tsai & Yang (2006); an LE-based study focused on prediction combined with consideration of rain-triggering effects. Several authors were referred to when it was stated: “the infnite is a preferred tool to evaluate landslides due to its simplicity and practicability”.

3.4.3 Deformation analysis As a consequence of known drawbacks of LE-procedures, together with a computational capacity being continuously improved, more accurate methods have been gradually more requested and developed. Numerical modelling approaches have

25 Impact of water-level variations on slope stability been most widely used based on finite-element (FE) methods; applied to the field of soil mechanics in the 1960s (J. M. Duncan, 1996). When using FE-methods the volume/area being analyzed is considered as a continuum whereupon it is discretized to a finite number of sub-volumes/sub-areas (elements) forming a mesh. In contrast to the fundamentals of LE-methods, a system analyzed with deformations-analysis approaches is not considered to necessarily be in equilibrium; neither in terms of forces nor moments. Besides consideration of stresses and geometrical conditions, stress-strain relationships are to be described. This is done by use of constitutive models considering different material properties. Moreover, the key-issue is to as reliably as possible define these constitutive relationships for a certain soil. When it comes to definition of stability in terms of safety factors, a procedure of simulating reduced strength until failure occurs is used. This method was firstly used in the 1970s (Zheng et al., 2009) and is usually referred to as the shear strength reduction technique. In PLAXIS 2D 2012 this is mathematically handled by expressing ratios of the strength parameters:

(3.12)

where is a controlling multiplier representing the safety factor; is the cohesion; is the friction angle; and the index reduced indicates values being successively decreased until failure occurs. For indication of global instability of soil slopes, the non- convergence of solutions is often used. This is indicated by the condition when a stress state at which the failure criterion and the global equilibrium can be simultaneously satisfied, is not found (Lane & Griffiths, 2000). The method is usable for constitutive models utilizing strength parameters that can be reduced. The safety factor is principally defined as in LE-approaches, i.e. by the ratio between the available shear strength and the shear stress at failure.

3.4.4 Drainage conditions Since soil strength is directly dependent on the presence of water and the interaction between the soil and the water, consideration of draining conditions is crucial for proper evaluation of different soil-mechanical behavior patterns. In a situation with fixed conditions—i.e. concerning water level, loading, inherent soil properties, and geometry—the pore pressure is hydrostatic. At occurrence of any changes, the pore- pressure situation is potentially affected. In coarse-grained soils, water is easily moving.

26 Slope analysis

This means that loading could be allowed without the pore-pressure state being changed; drained analysis is performed. In fine-grained soils, low permeability might mean a rate of drainage being lower than the rate of total stress change, meaning potential development of increased (excess, non-hydrostatic) pore pressures. Analogously, this could also be the case in coarse-grained soil if the total-stress is changed rapidly enough. In the two latter situations, undrained analysis is to be performed. Depending on what kinds of changes being expected and for what time- perspective the stability is assessed, either drained or undrained conditions are most critical. Therefore, both cases are to be considered; combined analysis is performed.

27 Impact of water-level variations on slope stability

28 Modelling of soil and water

4 MODELLING OF SOIL AND WATER

4.1 Constitutive description of soil 4.1.1 Stress For each specific stress state there are orthogonal stress directions in which the normal stresses display their maximum and minimum values; principal stresses, acting in the principal stresses directions. At the planes directed perpendicular to the principal stress directions, no shear stresses are acting. In two-dimensional (plane stress) situations there are two principal stresses; the major principal stress, and the minor principal stress, . In a three-dimensional situation the minor stress is denoted , and the intermediate principal stress gets the denotation . The average value of the principal stresses acting in a specific point within the soil mass is governing the volume change of a soil unit. It is termed mean pressure, p´, expressed as:

( ) (4.1)

The stress measure deviatoric stress is governing the shape change of a soil volume, for the triaxial case expressed :

√ ( ) (4.2)

where , and are the deviatoric normal stresses components; each defined as the difference between the mean pressure and the corresponding principal stress.

4.1.2 Strain Normal strain, which indicates the displacement in a specific direction, e.g. in the x- direction, is—according to engineering notations—defined as:

29 Impact of water-level variations on slope stability

(4.3) where is the strain, is the displacement, and is the initial length. Strains in other directions are analogously expressed. The shear strains are moreover (for small strains)—again according to engineering notation—determined by summing the ratios of displacements and initial dimensions perpendicular to the measured displacements, e.g.:

⁄ ⁄ (4.4) where is the shear strain component in the x:y-plane, is the displacement in the direction perpendicular to the length/dimension , ( and analogously related). In order to capture volume changes governed by isotropic compression, the volumetric strain increment, is expressed as:

(4.5) where the ratio of a negative change of the specific volume, and the initial specific volume, , is defined as a positive volumetric strain. Specific volume is defined as (where is the void ratio). The total volumetric strain is expressed as a sum of the principal strains ( ) or as a ratio of the volume change and the total volume ( ⁄ ).

Deviatoric normal strains are associated with shape changes. In the x-direction, is expressed as:

(4.6) with the variables defined above. Deviatoric normal strains in other directions are analogously expressed. In case of triaxial loading—with an axial strain, deviating from the two radial strains , the deviatoric axial strain, (also denoted ) becomes: ( ) (4.7)

4.1.3 Elastic response Stress-strain relationships for a soil are different for compression (volume change) and shearing (shape change). At axial or isotropic compression, axial (index: a) and/or

30 Modelling of soil and water volumetric strains (index: vol) are developed; in both cases the response is non-linear (Figure 4-1). The fundamental shear-response curves from as well direct shear testing (axis labels in brackets) as triaxial testing at drained conditions are presented in Figure 4-2.

Figure 4-1: To the left the non-linearity is sown (curves for one-dimensional or isotropic compression); to the right the dissimilarity of the response of fine-grained and coarse-grained soils is shown (compression curves plotted in a logarithmic-linear diagram). (after Axelsson, 1998)

Figure 4-2: Response curves from shearing of soil at loose arrangement (curve 1), dense arrangement (curve 2), and critical arrangement (curve 3). Quantities for direct shearing are presented within brackets whereas the triaxial test notation is presented without. The strains are indexed e (elastic) and p (plastic). (after Axelsson, 1998) It is seen that the maximum deviatoric stress (or shear stress), mobilized during shearing, varies depending on the soil grain arrangement prior to loading. For a soil with dense grain arrangement—i.e. a soil that undergoes dilation during shearing—the maximum deviatoric stress is larger than the critical one. This maximum is reached at strains smaller than for as well loose as critically configured soils.

31 Impact of water-level variations on slope stability

The resistance against elastic straining is described by stiffness moduli. The description used in the Mohr-Coulomb’s elastic-perfectly plastic model, is presented in section 4.1.6.

4.1.4 Unloading/reloading Once a soil is unloaded, it will undergo swelling (corresponding to elastic deformations). The subsequent reloading of the same soil will result in a stress-strain response that coincides with the unloading path. To curve 1 in Figure 4-2 an unloading/reloading-curve (dashed), and a straight line that approximately represents the unloading/reloading-curve, is added.

4.1.5 Plastic response For stresses high enough, compression or shearing of a soil ends up with irreversible (plastic) strains. In such a situation, the total strains developed due to loading consist of as well elastic as plastic strain contributions (see Figure 4-2). The response is therefore said to be elastic-plastic. In the x-direction this is expressed as:

(4.8) where the total strain increment, consists of the elastic increment, and the plastic increment, . The strain increments in other directions are analogously expressed. The soil behavior related to elastic-plastic deformation is captured by the theory of plasticity. In order to properly take into account both elastic and plastic strains when analyzing or modelling soil behavior, the stress states at which plastic strains are developed, have to be defined. This limit—the yield criterion—is expressed by a yield function, f defining the stress limits in one, two, or multiple dimensions. For instance, regarding one-dimensional (or isotropic) compression, the yield function is depending on the effective mean pressure, ; more specifically the preconsolidation pressure, . For stresses higher than the preconsolidation pressure, there will be plastic strains developed. For multiaxial stress states, the yield functions can be expressed as e.g.

( ) or ( ) Geometrically, the yield criteria in the stress plane and the stress space are represented by a yield locus, and a yield surface, respectively. The yield criteria are expressed in different ways in different elastic-plastic constitutive models. Though, stress states entailing yield function values mean development of only elastic deformations. For these states the strains are determined using elastic stiffness moduli, in addition to values of mean stress and deviatoric stress.

32 Modelling of soil and water

At stress states causing the yield criteria being reached ( )—i.e. when plastic strains are developed—the strain magnitude is to be determined using a flow rule based on the gradient of the so called plastic potential function, . Moreover, the plastic strain increment, is expressed as a function of the partial differential of the plastic potential function, (differentiated with respect to the stress). Depending on the type of deformation being of interest, the strain increments are expressed in different ways. In Table 4-1 common strain-increment expressions are presented; including the plastic potential functions related to each expression. Table 4-1: Strain-increment expressions and plastic potential functions for different stress quantities. The plastic potential functions contain at least the variables presented in the table. Strain Stress quantity Plastic potential function, 2) increment 1)

Normal stress 3) ( ) (engineering notation)

Normal stress 4) ( ) (tensor notation)

Mean pressure ( )

Deviatoric stress ( )

1) The plastic multiplier, determines the magnitude of the plastic straining. 2) The plastic potential functions are depending on at least the variables presented in the table. Different constitutive models may involve addition variables. 3) Increments in other directions are analogously expressed by substitution of x. 4) General tensor notation. The partial differential of the plastic potential function is determining the direction of plastic straining. Since as well the yield function as the plastic potential function are functions of the stress state, there might be cases when . This special case is termed associated flow. This kind of flow is used when contractancy response is significant (e.g. in normally consolidated clays). Still, the general case—when , i.e. non-associated flow—is frequently used to describe the behavior of coarse-grained soil where both contractancy and dilatancy are possibly occurring. For elastic-plastic models there are different approaches for definition of the yield function. The classical way of describing elastic-plasticity is based on so called elastic- perfectly plastic theory. In these approaches the yield functions are assumed to be fixed, i.e. not influenced by the plastic straining itself. In contrast to this, there are also more sophisticated models which are considering yield property changes related to

33 Impact of water-level variations on slope stability development of plastic strains. As a consequence of strain dependency of the yield function, the stress limit at which plastic strains are initiated, changes. This means that the elastic range will either grow or shrink as a result of developed plastic strains. For as well one-dimensional as isotropic compression, hardening (grown elastic range) is simply described by an increased preconsolidation pressure, . This means that the yield function is also dependent on this quantity, i.e. ( ).

Time dependent strain In order to fully describe plastic yielding, time related phenomena are to be considered. This kind of yielding—i.e. permanent deformations developed over time, under constant effective stresses—is usually referred to as creep. In Tatsuoka (2007) it was emphasized that an increment of plastic strain, is caused by three phenomena; (1) plastic yielding, (2) viscous deformation (i.e. time-dependent yielding), and (3) inviscid cyclic loading effect. usually called creep. Historically, the viscous deformation part (creep) has mostly been considered as an issue in fine-grained soils; especially in highly plastic clays. For fine-grained soils creep is mainly caused by volumetric yielding; usually explained by “secondary consolidation”. However, when it comes to coarse-grained soils—i.e. where the deformations are mainly caused by shear yielding—the research has been relatively limited. The lack of studies performed on sand has been noticed and expressed by many authors, e.g. Murayama, Michihiro, & Sakagami (1984), Lade & Liu (1998) and Kuwano & Jardine (2002). Though, in the late 70s and early 80s, some researchers were carrying out experimental studies on creep characteristics of sand. Rheological models were formulated and evaluated, and it was suggested that creep behavior of sands could be expressed in terms of stresses and stress ratios; the findings were presented in e.g. Murayama et al. (1984). During recent years there have been some more studies carried out on time- dependent deformation on coarse-grained soils. Kuhn & Mitchell (1993) did propose a distinction to be made between two main groups of mechanisms to be considered when it comes to creep rate changing with time; deformation-dependent mechanisms and intrinsically time-dependent processes. Di Benedetto, Tatsuoka, & Ishihara (2002) presented how to consider also viscosity (i.e. creep behavior) in an elastic-plastic model used for description of the behavior of sand. As a fundamental part of the model presented, a distinction was made not only between elastic and plastic strains, but also between time-independent and time-dependent stresses. The instantaneous stress, was expressed as:

(4.9)

34 Modelling of soil and water where the inviscid stress component, is time-independent but still a function of the instantaneous irreversible (plastic) strain, and the viscous stress component, is a function of as well and its rate ̇ (i.e. ). Moreover, the “time-dependency” of is connected to the history of , rather than to the time, . The authors were stating—also based on earlier conclusions (Tatsuoka, 2000)—that the time, is not a relevant parameter for geomaterials. Since the plastic and the viscous strains are not independent of each other, Tatsuoka (2007) suggested a visco-plastic strain component being a part of a non-linear three-component rheology model (Figure 4-3). In Peng et al. (2012) a study on FEM-modelling of a dense sand loaded by a strip footing was presented. The study was mainly aimed to capture viscous behavior before peak strength being reached. The results were found to be in agreement with physical- test data. Though, the testing-time was in the order of hours.

Figure 4-3: A non-linear three-component rheology model considering the dependency between viscous and plastic strain: elastic strain rate denoted ̇ , and visco-plastic strain rate denoted ̇ . (after Tatsuoka, 2007)

4.1.6 Mohr-Coulomb model This section is focused on the model descriptions in PLAXIS (2012). This model was used for description of the soil behavior in the modelling work done in this study (Paper B). The Mohr-Coulomb model is an elastic-perfectly plastic constitutive soil model. The model is based on Coulomb´s friction law and describes the stress-strain relation either as fully elastic or fully (perfectly) plastic. The elastic behavior is described by Hook´s law i.e. by use of the parameters Young´s modulus, and Poisson´s ratio, . The Young´s modulus is generally expressing the relation between stress and strain, i.e. the stiffness. Due to the non-linearity of stress-strain response of soils, the stiffness is to be defined in different ways depending on the specific stress-strain state being analyzed.

For standard drained triaxial tests, the initial stiffness is usually denoted , defined as a tangent to the shear curve. Due to the very small range of linear elasticity of soils, this

35 Impact of water-level variations on slope stability modulus is not properly describing the stiffness of loaded soils. Therefore, the modulus

is instead used. This is a secant modulus intersecting the shear curve at the deviatoric stress corresponding to 50% of the peak value. Moreover, elastic unloading/reloading is described by the modulus . In Figure 4-4, the definitions of the moduli are principally shown.

Figure 4-4: The initial stiffness , the often used secant stiffness, , and the unloading/reloading stiffness, , defined. The unloading/reloading curve is represented with the long-dashed line. (modified after PLAXIS, 2012) Poisson´s ratio, expresses the ratio of strains developed perpendicularly to each other. For triaxial compression, the parameter expresses the ratio between lateral and axial strains. For one-dimensional compression, the relationship between Poisson´s ratio, and the horizontal and vertical effective stresses, is expressed as:

(4.10)

The stiffness can alternatively be described and defined by the shear modulus, defined as:

(4.11) ( )

or by the oedometer modulus, defined as:

( ) (4.12) ( )( )

36 Modelling of soil and water

Since the failure line defines the ultimate state up to which the developed strains are elastic, this fixed line is also representing the yield function, separating the two types of strain response (elastic and plastic). The full three-dimensional yield criterion consists of six yield functions; two functions in each plane of stress pairs. In terms of principal stresses, and with the major and the minor principal stresses ( and ), the yield functions are expressed as:

( ) ( ) ( ) ( ) (4.13) and

( ) ( ) ( ) ( ) (4.14)

Moreover, there are another four equations needed (analogously expressed, with all combinations of and ) to fully define the yield surface in three dimensions. The surface has the shape of a hexagonal cone, illustrated in Figure 4-5. In the plastic potential functions, which are parts of the flow rule (see Table 4-1) an additional plasticity parameter is used; the dilatancy angle, (discussed in section 3.3.5). The plastic potential functions are expressed as:

( ) ( ) ( ) (4.15) and

( ) ( ) ( ) (4.16)

Moreover, there are another four equations needed (analogously expressed, with all combinations of and ) for definition the whole yield surface.

37 Impact of water-level variations on slope stability

Figure 4-5: Mohr-Coulomb´s yield surface. (PLAXIS, 2012)

4.2 Hydraulic modelling 4.2.1 Fundamentals The degree of which a soil volume consist of pores is defined as porosity, , expressed as:

⁄ (4.17) where is the pore volume and is the total soil volume. The degree of which the total pore volume in a soil element is filled with water is defined as the degree of saturation, and according to classical soil mechanics expressed as:

⁄ (4.18) where is the water volume and is the pore volume.

Moreover, the soil unit weights are defined according to the input values of unsaturated weight, for the soil located above the level, and saturated weight, for the soil below.

4.2.2 Unsaturated soil

When considering unsaturated soil, the effective degree of saturation, is defined as:

( ) ( ) (4.19)

38 Modelling of soil and water

where is the degree of saturation and the indices max and min denote maximum and minimum values. The effective degree of saturation is used also for definition of actual soil unit weight, :

(4.20) ( ) where the indices denote unsaturated and saturated conditions.

4.2.3 Flow The rate of water flow, in saturated soil is according to Darcy´s law defined as:

(4.21) where is the hydraulic gradient (defined as the ratio between head loss, and the flow length ), ( ⁄ ), is the water density, is the acceleration of gravity, is the intrinsic permeability, and is the dynamic viscosity of the fluid (the water). In unsaturated soils, the hydraulic conductivity is reduced due to air present in the pores. This reduction is in PLAXIS 2D 2012 (Galavi, 2010) considered by expressing the specific discharge, , as:

( ) (4.22)

where is the gradient of the pore pressure causing the flow; is the vector of acceleration of gravity; and is the relative permeability, defined as:

⁄ (4.23) where is the tensor of permeability at a given saturation. Moreover, is in van

Genuchten model computed according to the dependency on , see equation (4.27).

Starting with the continuity equation—involving mass concentration ( ) and the divergence of the mass flux density of the residual water ( )—neglecting the compression of the solid particles as well as of the overall soil structure, the expression for transient flow becomes:

39 Impact of water-level variations on slope stability

( ) [ ( )] (4.24)

where is the bulk modulus of water, and other parameters as above. In case of steady-state flow there is no time dependence of the pore-pressure change, whereupon the left term in equation (4.24) is eliminated.

4.2.4 van Genuchten model For description of hydraulic behavior in the soil, va Ge u hte ’s model (van Genuchten, 1980) was used in the modelling work done in this study (Paper B). The important role of the hydraulic model is to properly define the degree of saturation, as a function of suction pore-pressure head, . This relation is expressed as:

(4.25) ( ) ( )[ ( | |) ]

where is the residual degree of saturation, is the saturated degree of saturation, is an empirical parameter describing air entry, and is an empirical parameter related to the water extraction from the soil (Galavi, 2010). The suction pore pressure head is defined as:

⁄ (4.26) where is the suction pore pressure and is the weight of the water. The relative permeability is expressed as:

( ) [ ( ) ] (4.27)

where is an empirical parameter. The hydraulic properties of a soil are often presented in soil-water characteristic curves (SWCC). In Figure 4-6 and Figure 4-7, SWCC’s for different values of the empirical parameters in van Genuchten´s hydraulic model are shown.

40 Modelling of soil and water

Figure 4-6: The effect of the parameter (linked to air entry) on the saturation-suction relationship. (Galavi, 2010)

Figure 4-7: The effect of the parameter (linked to water extraction) on the saturation-suction. relationship (Galavi, 2010)

4.3 Parameter sensitivity In order to evaluate to what extent the model parameters used are influencing the computation results, parameter-sensitivity analysis might be carried out. Parameter- sensitivity analysis might be useful for minimization of computation time; i.e. by identifying parameters being relevant for the result (significantly influencing). Sensitivity analysis might also be used for consideration of spatial in-situ variety of soil properties (Schweiger & Peschl, 2005), temporal changes (e.g. material deterioration

41 Impact of water-level variations on slope stability due to loading and aging), and/or uncertainties connected to the actual quantification (e.g. laboratory tests and field tests). In the stability-modelling performed in this study (Paper B), sensitivity analysis was used for comparison of the three analysis approaches evaluated. The parameter influence was investigated with respect to changed stability (FOS). For each parameter, a maximum and a minimum value were defined setting up an interval within which the reference value for each parameter was located. The theories used are based on the ratio of the percentage change of the result, and the percentage change of input (creating the output change); explained in e.g. U.S. EPA (1999). The sensitivity ratio –sometimes called elasticity (e.g. U.S. EPA, 2001)—is expressed as:

( ) ( ) ( )⁄( ) (4.28) ( ) where the output values are functions, of the input values , for which no index represents the reference input values and the indices U,L represents the changed ones; upper/lower. In order to increase the robustness of the analysis (PLAXIS, 2012) the sensitivity ratio was weighted by a normalized variability measure. This was done using a sensitivity score, , defined as the ratio of the range itself (or the standard deviation) and the reference value (U.S. EPA, 2001):

( ) (4.29)

where and defines the range limits, and is the mean (reference) value. The total sensitivity was then calculated as:

( ) (4.30) ∑ ( )

where and are the sensitivity scores connected to the upper and lower parameter value, respectively, and ∑ is the sum the sensitivity scores of all parameter combinations. Five model parameters were considered. In addition to the reference computation, one computation was run for each range boundary for each parameter (keeping the other parameters fixed), meaning 11 computations per stability case.

42 FEM-Modelling

5 FEM-MODELLING

5.1 Main aim The modelling work done (Paper B) was aimed to (1) investigate potential impacts on watercourse slopes subjected to recurring water-level fluctuations, (2) to find out whether there are important dissimilarities between a well-established modelling approach (based on the classical theory of saturated soil) and approaches that also consider unsaturated soil behavior, and (3) to analyze potential parameter-influence changes coming from the water-level changes. More details are presented in Paper B.

5.2 Strategy The following modelling strategies were used: Approach 1 (A1): Computations were performed using Terzaghi's definition of stress. Flow computations were run prior to the deformation computations; the results were then used in the deformation computations for the corresponding time step. The consolidation computations were based on excess pore pressures. Approach 2 (A2): For the fully coupled approach Bishop’s effective-stress equation was used. The consolidation computations were based on the Biot’s theory of consolidation (Biot, 1941); i.e. using total pore pressures with no distinction made between steady state and excess pore pressures. Approach 3 (A3): Computations were run like in A2, but with stability computations run without consideration of negative pore pressures. A fictive waterfront bank slope consisting of a well-graded postglacial till was simulated to be subjected to a series of water-level-fluctuation cycles (WLFC’s). Development of stability (in terms of factors of safety, FOS), vertical displacements, pore pressures, flow, and model-parameter influence, was investigated for an increased number of WLFC’s. The modelling was performed by use of the software PLAXIS 2D 2012 (PLAXIS, 2012), allowing for consideration of transient flow and performance of coupled hydro- mechanical computations. This FEM-code was used since it is well-established, and providing what is needed. Moreover, parameter-influence analysis was performed with

43 Impact of water-level variations on slope stability respect to FOS’s computed using the strength reduction technique. The parameter- influence development with an increased number of WLFC’s, was investigated. The bank was assumed to be infinite in the direction perpendicular to the model plane; i.e. 2D plain-strain conditions were assumed. The initial stress situation was determined by a Gravity loading computation; providing initial stresses generated based on the volumetric weight of the soil (this since the non-horizontal upper model boundary means that the K0-procedure is not suitable). Then a plastic nil-step was run, solving existing out-of-balance forces and restoring stress equilibrium. The WLFC’s were defined in separate calculation steps; one drawdown-rise cycle in each. Each WLFC was followed by a FOS-computation. In A3, each FOS-computation was preceded by a plastic nil-step; this to reset the stress situation in order to omit consideration of negative pore pressures. Sensitivity analysis was carried out for the three approaches. Five parameters were considered. Ranges used are presented in Table 5-2.

5.3 Geometry, materials, and definition of changes The model geometry was defined aimed to represent one half of a watercourse cross section. The model dimensions and mesh conditions were defined aimed to avoid (1) errors due to disturbances by the boundaries (due to too small model), (2) errors due to too coarse mesh, and (3) unreasonably time consuming computations due to too fine mesh. The slope height was set to 30 m, and the slope inclination to 1:2 (26.6°) (Figure 5-1); both measures considered to be representative for a watercourse slope consisting of a well-graded postglacial till, for Swedish conditions (properties presented in Table 5-1). 15-noded triangular elements were used. The mesh density was optimized by mesh quality checks done with the built in tool available in PLAXIS (2012) (the average element quality was 97%). Since the area around the position where the slope face and the external water level intersect was assumed to be most critical, extra care was taken regarding mesh density and quality in this region. The vertical model boundaries were set to be horizontally fixed and free to move vertically, whereas the bottom boundary was completely fixed. The left vertical boundary was assumed to have properties of a symmetry line, and the model bottom to represent a material being dense and stiff relative to the soil above. Therefore, as well the left vertical hydraulic boundary as the horizontal bottom, were defined as closed (impermeable). The right vertical boundary was defined to be assigned pore pressures by the head, simulating allowed in/out flow. Data-collection points were placed where interesting changes would be expected; at the crest, down along the slope surface, and

44 FEM-Modelling along a vertical line below the crest. The initial water-level position was set to +22.0 m (with the level of the watercourse bottom at ± 0 m), the level-change magnitude to 5.0 m (linearly lowered and raised), and the rate to 1.0 m/day. The water-level changes were run continuously; i.e. without allowing pore pressures to even out. Since the study was comparative, this was not mainly intended to reflect frequently occurring real situations.

Figure 5-1: Model geometry. Dimensions, initial water level (푊퐿푖푛푖푡푖푎푙), and the pre-defined data- collection points (A) at the crest, and (B) at the level +22 m, are shown in the figure.

5.4 Models used The soil was described using Mohr Coulomb´s model. This model was chosen for three reasons; (1) it is well-established and widely used by engineers, (2) as soon as the stability analysis is started (performed using the strength reduction technique), any model defined with the same strength parameters would behave like the Mohr- Coulomb model (i.e. stress dependent stiffness is excluded), (3) the study is comparative whereupon differences between the modelling approaches evaluated were focused rather than the accuracy of the soil description. The hydraulic properties were defined using the van Genuchten´s model (van Genuchten, 1980). The model is widely recognized and integrated in PLAXIS. Both models were described in chapter 4.

45 Impact of water-level variations on slope stability

Table 5-1: Model input data. Unit Value Comments General

Drainage type - - Drained 3 Unsaturated weight kN/m 19.00 Typical value 3 Saturated weight kN/m 21.00 Typical value Soil description

Young´s modulus kN/m2 40 000 2) Poisson´s ratio - 0.30 2) Cohesion kN/m2 8 Low, non-zero Friction angle ° 36 Typical value Dilatancy angle ° 3 Meeting the recommendation Hydraulic description

Model van Genuchten

Data set - - - Defined in order to be representative 1) Permeability, x m/day 0.05 Found to be representative (e.g. Lafleur, 1984) Permeability, y m/day 0.05 Found to be representative (e.g. Lafleur, 1984) Saturated degr. of sat. - 1.0 1) Residual degr. of sat. - 0.026 1) - - 1.169 Parameter linked to water extraction 1) - - 2.490 Parameter linked to air entry 1) - - 0 Parameter linked to pore connectivity 1) The data set was manually defined by using the parameters listed. The values of the parameters , , , , and were chosen based on examples in Galavi (2010), comments in Gärdenäs et al. (2006), and the pre-defined data set Hypres available in PLAXIS (2012). 2) Within ranges presented in Briaud (2013); Young´s modulus for a loose glacial till (10-150 MPa), and for a medium/compact sand (30-50 MPa), at .

NOTE: Since the result evaluation is comparative, the values of the parameters chosen are not critical.

Table 5-2: Soil parameters used in the sensitivity analysis (Min and Max), and the reference values. E (MPa) v (-) (°) c (kPa) (°) Min Ref Max Min Ref Max Min Ref Max Min Ref Max Min Ref Max 20 40 60 0.25 0.30 0.35 33 36 39 1 8 15 0 3 6

46 Results and comments

6 RESULTS AND COMMENTS

6.1 Evaluation of FEM-modelling approaches 6.1.1 General More details are presented in Paper B.

6.1.2 Stability In Figure 6-1 the failure plots from the three modelling approaches are shown; conditions at the initial stage (Init.), after one rapid drawdown (RDD), and after one WLFC (1); corresponding FOS-changes are presented in Figure 6-2; and FOS- developments at further cycling are presented in Figure 6-3.

Init. RDD 1

A1

A2

A3

Figure 6-1: Failure surfaces for the initial condition, after one rapid drawdown, and after one WLFC.

47 Impact of water-level variations on slope stability

1.80 1.70 A1

1.60 A2 FOS 1.50 A3 1.40 1.30 Init. RDD 1

Figure 6-2: FOS-values for initial conditions (Init.), after one rapid drawdown (RDD), and after one WLFC (1).

1.85 1.80

A1

1.75 A2 FOS 1.70 A3 1.65 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-3: FOS-developme t by i reased umber o WLFC’s. For all approaches the FOS-values were significantly decreasing due to the rapid drawdown, slightly increasing due to the first rise, and ending up exhibiting further increased values after 10 WLFC’s (with the initial conditions as reference values). Lower FOS-values were obtained using the approach assuming saturated conditions below the water-level, dry conditions above, and taking into account neither pore- pressure changes due to deformations, nor suction (A1), than using fully coupled flow- deformation computations, considering also suction forces (A2). Though, the lowest FOS-values were obtained using fully coupled flow-deformation computations, but with the negative pore pressures not considered in the stability analysis (A3).

6.1.3 Deformations, pore pressures and flow In Figure 6-4, vertical deformations developed at the crest (point A, Figure 5-1) are plotted. The values were registered in the middle of each WLFC, i.e. at the end of each drawdown.

48 Results and comments

-18.0 -19.0

-20.0 A1 -21.0

(mm) A2

y -22.0 u A3 -23.0 -24.0 1 2 3 4 5 6 7 8 9 10 Number of drawdowns Figure 6-4: Vertical deformations at the crest; readings from the end of each drawdown. The reference level before the first drawdown is 0 mm. The overall pattern is the same in all approaches; additional vertical deformations developed with an increased number of drawdowns. The rate is decreasing although a definitive asymptotical pattern cannot be seen.

Developments of the active pore pressure, consisting of contributions from as well steady state as excess pore pressure, are shown below. The values were registered in two different points; one located at the crest (point A in Figure 5-1), and one at the initial groundwater level (point B in Figure 5-1). In Figure 6-5, the values from point B are shown; only peak values are plotted. In Figure 6-6 the development in point A is shown. In both plots, only values from approach A2 are presented. The trends were similar in A3, whereas A1 is not relevant due to fully dry conditions above the water level.

-8

-7

(kPa ) (kPa -6

active active -5 p p

-4 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-5: Peak-pore pressure development from A2, registered in point B at the end of each WLFC; the development in between was found to be smooth/non-fluctuating.

49 Impact of water-level variations on slope stability

-80.4 -80.3

-80.2

-80.1 (kPa ) (kPa -80.0

active -79.9 p p -79.8 -79.7 -79.6 0 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-6: Pore-pressure development from A2, registered in point A. In Figure 6-7 a picture of the flow region—the area where the external water level and the slope surface intersect—is shown. Total (resultant) flow is represented by arrows. The picture shows the conditions prevailing after the first WLFC was run, but is qualitatively characteristic for the endpoints of all WLFC’s.

Figure 6-7: A sample picture of the area where the external water level and the slope intersect, showing the hydraulic conditions prevailing immediately after the first WLFC run in A1. The external water level is located at +22 m whereas the groundwater table within the slope is lower. The flow directions are presented by arrows.

50 Results and comments

In Figure 6-8 - Figure 6-13 flow conditions registered immediately after each WLFC are presented. Since the readings were taken at the end of each cycle, the external water level and the groundwater table are almost coinciding, meaning small absolute magnitudes of the flow values registered. The flow condition for each stage is presented as the deviation from the average value of the 10 cycles. Maximum total flow, and horizontal flow directed inwards (in to the slope), is presented in Figure 6-8 and Figure 6-9, whereas maximum vertical flow (upward, , and downward, ) is shown in Figure 6-10 and Figure 6-11. All of the maximum and minimum values are originating from the region being marked in Figure 6-7, except the values of . The latter ones are registered just below the groundwater table, approximately 10 m right (inwards) from the slope surface.

90%

60% A1

30% A2 0%

average) A3

|(deviation from from |(deviation -30% max

|q -60% 1 2 3 4 5 6 7 8 8 10 WLFC Figure 6-8: Maximum total flow; average ~0.1 m/day.

150% 100% A1

50% A2 0%

A3

average) (deviation from from (deviation

-50%

x, right x, -100% q 1 2 3 4 5 6 7 8 9 10 WLFC

Figure 6-9: Rightward directed horizontal flow; average ~0.08 m/day.

51 Impact of water-level variations on slope stability

200% 150% A1 100% 50% A2

0% A3

average) (deviation from from (deviation -50%

y, up y, -100% q 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-10: Maximum upward directed flow; average ~0.05 m/day.

200% 150%

100% A1 50% A2

(deviation from from (deviation 0% average)

A3

-50% y, down y,

q -100% 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-11: Downward directed flow; average ~0.05 m/day.

In Figure 6-12 and Figure 6-13, development of vertical flow, and horizontal flow,

—extracted from the same stress point in all approaches—are shown. The point is located approximately 1 m below the initial water level, 1 m to the right from the slope surface.

60%

40% A1

20% A2 average)

(deviation from from (deviation 0%

A3

y q -20% 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-12: Vertical flow; average ~0.05 m/day.

52 Results and comments

60%

40% A1 20% A2

average) 0%

(deviation from from (deviation A3

x

q -20% 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-13: Horizontal flow; average ~0.05 m/day. The flow magnitudes were found to be changing by increased number of cycles run. Larger flow changes were captured using the fully coupled flow-deformation computations (A2 and A3), compared to A1. The difference is particularly pronounced for the rightward directed horizontal flow, and the downward directed vertical flow, . Regarding and the results from A2 and A3 are to a large extent coinciding.

6.2 Parameter influence The sensitivity analysis performed in the study presented in Paper B did provide parameter-influence values; total sensitivity ( ). In Figure 6-14 -values (on the y-axis) for each of the five parameters at initial state (Init.), after one rapid drawdown (RDD), and after one WLFC (1), are shown. (A1) (A2) (A3) 70% 70% 70% 60% 60% 60% 50% 50% 50% Init. 40% 40% 40% 30% 30% 30% RDD 20% 20% 20% 1 10% 10% 10% 0% 0% 0% ν c φ ψ E ν c φ ψ E ν c φ ψ E

Figure 6-14: The influence (in terms of total sensitivity) of each parameter, with respect to safety (in terms of FOS). The stiffness parameters are influencing the stability significantly less than are the strength parameters. The cohesion, exhibits the highest influence in all approaches; followed by the influence of the friction angle, and the dilatancy angle, . The

53 Impact of water-level variations on slope stability influence of as well Poisson’s ratio, as of Young’s modulus, is slightly increasing during further cycling; though remaining below 3% and 2%, respectively. Therefore, the stiffness parameters are excluded from the presentation of the further sensitivity development, presented in Figure 6-15 - Figure 6-17.

60% 58% A10 56% A1 A3 0 A2 54% A20 A3 52%

Sensitivity (cohesion) Sensitivity 50% 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-15: Sensitivity development for cohesion, c. The dotted lines are showing the initial values for each modelling approach (A10, A20, and A30).

40% 38% A2 A1 36% 0 A30 A2 34% A3 32% A10

Sensitivity (frictionangle)Sensitivity 30% 1 2 3 4 5 6 7 8 9 10 WLFC Figure 6-16: Sensitivity development for friction angle, . The dotted lines are showing the initial values for each modelling approach (A10, A20, and A30).

54 Results and comments

9% A3 A20 0 A10 8% A1 7% A2 6% A3

5%

Sensitivity (dilatancy angle) (dilatancy Sensitivity 1 2 3 4 5 6 7 8 9 10

WLFC Figure 6-17. Sensitivity development for dilatancy angle, . The dotted lines are showing the initial values for each modelling approach (A10, A20, and A30). It is clear that the sensitivity values are depending on the stage at which the safety is evaluated, i.e. on the numbers of WLFC’s run. For cohesion, the qualitative trend is the same in all cases; maximum influence at drawdown and then declining with increased number of WLFC’s. In A1 the sensitivity of cohesion gets lower than the initial value after 5 WLFC’s; in A2 this occurs at 2 WLFC’s, and in A3 the initial value is not reached at all during the 10 cycles. For the friction angle, the pattern is opposite; minimum values at drawdown and then increasing. For this parameter, the initial values are exceeded in all approaches; in A1 and A2 after 3 WLFC’s, and in A3 after 6 WLFC’s. The total change of the influence of cohesion during 10 cycles, seems to be similar in all approaches. The increase of the friction-angle influence in A2 seems to be fading out slower than in A1 and A3. When it comes to the dilatancy angle, the patterns are more scattered. In all cases the sensitivity values are decreased after the first drawdown (Figure 6-14), whereas the further development is almost constant. Though, the absolute magnitudes (and the variations) of the dilatancy-angle influence are very small, and further conclusions are not reasonably drawn.

55 Impact of water-level variations on slope stability

56 Discussion

7 DISCUSSION Concerning objective 1 (Review): Fast growing use of non-regulated energy sources and pumped-storage hydropower would potentially entail water levels in regulated watercourses being fluctuating more in the future than until present. This is the view among many authors (e.g. Catrinu, Solvang, & Korpås, 2010; Whittingham, 2008; Connolly, 2010; Zuber, 2011). Since production of floating debris due to bank erosion and slope failure is a current matter (e.g. Åstrand & Johansson, 2011), an increased degree of fluctuating water level will probably worsen the situation in locations being exposed. This hypothesis is substantiated by statements made in K. Zhang et al. (2004), speaking of varied mean water levels—changed water-level ranges within which the short-term variations are occurring—as enablers of erosion. Such changes could directly mean reduced slope stability. There is a lack of studies that actually evaluate recurring water-level variations. Though, there have been a few addressing issues connected to drawdown (e.g. Yang et al., 2010; Pinyol, Alonso, Corominas, & Moya, 2011), and rise (e.g. Jia et al., 2009; Cojean & Caï, 2011). Thus, it is reasonable to assume that at least the issues noticed for single drawdowns and rises (pore-pressure gaps, suction loss, effects of rapidly increased water pressures in pores and discontinuities, harmful flow patterns, soil material migration, retrogressive failure development etc.), also would be faced as a consequence of many changes being cyclic recurring. Moving water, altering hydraulic gradients, and cyclic loading, are all factors potentially entailing soil degradation and changed soil properties. This in turn could mean strength reduction and stability issues (J. M. Duncan, 2005). When it comes to proper description of soils, there seems to be factors that could be incorporated in modelling for improved accuracy. For instance, particle shape for consideration of degradation potential (Cho, 2006; JM Rodriguez, 2013), and creep for more detailed description of long-term deformations (Tatsuoka, 2007). In studies addressing flow modeling issues, soil material characteristics are only in exceptional cases specified. Also when fundamental soil characteristics are fairly described, like in e.g. Yang et al. (2010), strength/stiffness properties are rarely

57 Impact of water-level variations on slope stability considered. Therefore, the coupling between soil deformation, pore-pressure development, and water flow conditions are often overlooked and/or missed. Given the important and critical connections involving pore pressures, soil strength, soil-deformation development, (and so on)—stated in Huang & Jia (2009), Galavi (2010), and Sheng (2011)—it seems to be unreasonable to use simple limit- equilibrium methods for analysis of slopes subjected to water-level fluctuations. Concerning objective 2 (Impacts on a slope subjected to water-level fluctuations—FEM-modelling): The modelling performed in this study—given the specific conditions of soil properties, slope geometry, and pattern of water-level changes—showed that the water-level fluctuations resulted in growing stability and development of vertical deformations at the slope crest. The stability increase is to assign to the fact that the groundwater table is dropping (remained at a lower level) for each WLFC. Though, since rapid changes of pore pressures and flow rates were noticed within the slope, other upcoming issues could probably occur as well suddenly as in the long term. The development of the pore-pressure peak values (registered at the initial water level, point B in Figure 5-1) shows how the pore pressure at the end of each WLFC, slowly becomes more and more negative. This increase of the negative pore pressure indicates that the groundwater table is dropping for each cycle, contributing to an increased stability. This in turn means that equilibrium between groundwater level and external water level was not reached during the ten cycles. If such fluctuations are taking place for a long time, negative pore pressures could falsely remain high. If then the fluctuation stops, the water levels would go back to equilibrium, and the extra shear strength would be lost. This phenomenon of suction loss would potentially get consequences similar to those noticed in situations of wetting-induced strength loss presented in e.g. (Jia et al. (2009). The pore-pressure development registered both in point A and B did show asymptotic patterns. Also the deformation increase was fading out. This might indicate that the slope was approaching a state where only elastic strains were developed at further WLFC’s. In situations where internal erosion is taking place, the soil is definitely getting changed properties. Since e.g. hydraulic conductivity has been shown to significantly affect the stability of reservoir slopes consisting of sand and silt (Liao et al., 2005), material changes would be preferably considered in long-term modelling. Despite the fact that the absolute magnitudes of differences identified in this study were small—FOS-values, pore pressures, flows etc.—these do nonetheless demonstrate

58 Discussion important dissimilarities concerning the ability to capture/simulate real soil-water interactions and changes. Further investigations of processes taking place within slopes being subjected to recurrent WLF’s, would desirably be conducted. For instance by laboratory/scale tests like what was presented in Jia et al. (2009), combined with moelling. The results obtained in this study are reflecting effects occurred under the specified conditions of hydraulic conductivity, rate of water-level change, and slope geometry. Since these factors are unquestionably affecting processes taking place within a watercourse slope, it would be reasonable to include variation also of such non- constitutive parameters in further studies. Concerning objective 3 (Evaluation of FEM-modelling approaches): Lower FOS-values were obtained using the classical approach, A1 than those obtained using approach A2. This could be reasonably explained by the consideration taken to the contribution of suction forces to the stability in A2; i.e. due to higher effective stresses. The fact that the lowest FOS’s were obtained by using A3, would suggests that this approach was most conservative in this study, in the sense of not overestimating the stability. This is unexpected since suction was not considered at all in A1, whereas suction was considered throughout the entire cycle in A3, until the FOS-computation was run. Anyhow, whether the unexpected result is connected to the nil-steps computed in A3 done in order to neglected suction, or to unrealistic computation of the soil weight above the water level, the FOS result of A3 is to be treated with caution. Use of A1 resulted in smaller vertical crest deformations compared to the other approaches. This suggests that the two-way interaction between pore pressure changes and deformation development in the fully coupled computations (A2 and A3), could capture conditions that bring larger deformations. This means a potential underestimation in A1. Moreover, the flow developments registered in A2 and A3 were significantly more fluctuating than those in A1; as well horizontally as vertically. The difference was seen to be particularly pronounced for the rightward directed horizontal flow, and the downward directed vertical flow. In addition, the fluctuating negative pore pressure registered at the crest does underline that central information about processes taking place in the slope is well captured in A2. Since changes such as those mentioned in turn are governing as well water-transport (e.g. efficiency of dissipation of excess pore pressures), as soil-material transport (i.e. susceptibility to

59 Impact of water-level variations on slope stability internal erosion to be initiated and/or continued), modelling approaches not being fully coupled are probably not suitable for analysis of processes being governed by fluctuating flows, altering hydraulic gradients, unloading/reloading etc. In that sense— in agreement with what was concluded in Sheng et al. (2013)—there seems to be situations where approaches considering unsaturated soil behavior is not necessarily less conservative than are classical ones. Since hydraulic models do rely on empirical soil-specific parameters, there are potential uncertainties connected to the level of accuracy at which these have been quantified. Still, this uncertainty is to be related to the extra information possibly obtained at consideration of specific features of unsaturated soils. Concerning objective 4 (Parameter-sensitivity analysis): The parameter-sensitivity analysis results obtained using A1 seems to be quantitatively more comparable to those obtained using A3 than to those obtained using A2. This suggests that consideration of suction at stability computation (only true in A2), does directly affect the parameter influence on the results. However, major differences were not found. Since the sensitivity was computed with respect to FOS determined by using the strength reduction technique, the low and insignificantly changing sensitivity values of the stiffness parameters were expected. The non-constant sensitivity values of the dilatancy angle, might indicate that the occurrences of plastic strains are somewhat different in the different stages. It might be useful to consider parameter influence for evaluation of the accuracy needed for definition of model input data; as well absolute magnitudes, as the development patterns. Moreover, when making up modelling/design strategies, parameter changes (e.g. by time or by external changes taking place), could be valuably included.

60 Conclusions

8 CONCLUSIONS

8.1 General Concerning objective 1 (Review): . It seems to be consensus among researchers and experts that the fast growing use of non-regulated energy sources and pumped-storage hydropower, will entail water levels in regulated watercourses being fluctuating more in the future than until present. . Water-level changes have been shown to significantly influence slope stability; failure due to suction loss, effects of rapidly increased water pressures (as well in pores as in discontinuities), potentially harmful flow patterns, internal erosion, and retrogressive failure development. . Moving water, altering hydraulic gradients, soil-material transport, and cyclic external loading, are all factors potentially entailing soil degradation, property changes, strength reduction, and stability issues. . Given the important and critical connections involving pore pressures, soil strength, and soil-deformation development, it is not reasonable to use simple limit-equilibrium methods for analysis of slopes subjected to water-level fluctuations. Concerning objective 2 (Impacts on a slope subjected to water-level fluctuations—FEM-modelling): . Water-level fluctuations resulted in growing stability, development of vertical deformations at the slope crest, and rapidly fluctuating flows (as well horizontal as vertical) within the slope. . Even though the stability might remain unchanged or even increase due to fluctuations of an external water level, rapid changes of pore pressures and flow within the slope, could mean upcoming issues as well suddenly as in the long term. Concerning objective 3 (Evaluation of FEM-modelling approaches): . Modelling assuming strictly saturated or dry conditions resulted in—restricted to slope stability in terms of safety factors—higher conservatism compared to

61 Impact of water-level variations on slope stability

modelling considering also the behavior of unsaturated soil and fully hydro- mechanical coupling. . Modelling considering the behavior of unsaturated soil and fully hydro- mechanical coupling, but with suction neglected at stability computation, was shown to give safety factors even lower than did classical modelling. Whether this was due to the saturation-suction relation in the hydraulic model used, or due to the nil-steps run prior to the FOS-computations, the importance of being careful when complex situations are designed, is however underlined. . Advanced modelling seems to allow for rapid changes of pore pressures and flow to be more realistically described than do classical modelling. Since such changes in turn are governing as well water-transport (i.e. the efficiency of dissipation of excess pore pressures), as soil-material transport (i.e. susceptibility to internal erosion to be initiated and/or continued), simplified modelling approaches are not suitable for analysis of processes being governed by fluctuating flows, altering hydraulic gradients, unloading/reloading etc. Concerning objective 4 (Parameter-sensitivity analysis): . The influence of the parameters on the slope stability was found to be changing as a result of WLFC’s taking place. . For evaluation of the accuracy needed for modelling-input data, it might be useful to consider parameter influence; as well total values, as the development patterns. Moreover, when making up modelling/design strategies, inclusion of parameter changes (e.g. by time or by external changes taking place), could be valuable.

8.2 To be further considered In order to properly simulate groundwater flow—capturing also effects besides critical development of pore-pressures, flow patterns, and subsequent stability changes— consideration should be taken to:

. Use of a more advanced constitutive soil model (e.g. the Hardening soil model PLAXIS, 2012) would potentially reduce inaccuracy coming from e.g. improper description of plastic deformations and stiffness changes. The water- level fluctuation effects would also be investigated using models based on the Basic Barcelona Model (Alonso, Gens, & Josa, 1990). . Incorporate varied hydraulic conductivity in sensitivity analyses.

62 Conclusions

. Vary frequencies and rates of water-level changes, slope geometries etc. (in previous studies simple approaches are used focusing on one or a few cycles), for further investigation. . Design a modelling approach for application to long-term effects of WLF’s on potential debris production along regulated watercourses. . Indirect consider internal-erosion in embankments (dams and/or watercourse banks), by incorporating parameter changes in the modelling. . Further investigate processes taking place within slopes being subjected to recurrent WLF’s, e.g. by laboratory/scale tests like what was presented in Jia et al. (2009) .

63 Impact of water-level variations on slope stability

64 References

REFERENCES Alonso, E. E., Gens, A., & Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, vol. 40, no. 3, pp. 405–430. Axelsson, K. (1998). Introduktion till Jordmekaniken jämte jordmaterialläran. Luleå: Division of Mining and Geotechnical Engineering, Luleå University of Technology. Bakhtyar, R., Barry, D. A., Li, L., Jeng, D. S., & Yeganeh-Bakhtiary, A. (2009). Modeling sediment transport in the swash zone: A review. Ocean Engineering, vol. 36, no. 9-10, pp. 767–783. Bardi, U. (2009). Peak oil: The four stages of a new idea. Energy, vol. 34, no. 3, pp. 323– 326. Biot, M. A. (1941). General Theory of Three-Dimensional Consolidation. Journal of Applied Physics, vol. 12, no. 2, pp. 155. Bolton, M. D. (1986). The strength and dilatancy of sands. Geotechnique, , no. I. Briaud, J. (2013). Geotechnical Engineering: Unsaturated and Saturated Soils. John Wiley & Sons, Inc. Bruun, P. (1988). The Bruun rule of erosion by sea-level rise: a discussion on large-scale two-and three-dimensional usages. Journal of Coastal Research, vol. 4, no. 4, pp. 627– 648. Burland, J. B., & Jennings, J. E. B. (1962). Limitations to the Use of Effective Stresses in Partly Saturated Soils. Géotechnique, vol. 12, no. 2, pp. 125–144. Catrinu, M. D., Solvang, E., & Korpås, M. (2010). Pe spectives on hyd opowe ’ s ole to balance non-regulated renewable power production in Northern and Western Europe. In HYDRO 2011, okt 17 - okt 20. Prague. Chappell, J., Eliot, I., Bradshaw, M., & Lonsdale, E. (1979). Experimental control of beach face dynamics by watertable pumping. Engineering , vol. 14, no. 1, pp. 29–41. Cho, G.-C., Dodds, J., & Santamarina, J. C. (2006). Particle Shape Effects on Packing Density, Stiffness, and Strength: Natural and Crushed Sands. Journal of Geotechnical and Geoenvironmental Engineering, vol. 132, no. 5, pp. 591–602. Cojean, R., & Caï, Y. J. (2011). Analysis and modeling of slope stability in the Three-Gorges Dam reservoir (China) — The case of Huangtupo landslide. Journal of Mountain Science, vol. 8, no. 2, pp. 166–175. Connolly, D. (2010). A Review of Energy Storage - For the integration of fluctuating renewable energy. PhD thesis, University of Limerick., Limerick, Ireland. Craig, R. F. (2004). C aig’s soil mechanics. CRC Press. Darby, S. E., Rinaldi, M., & Dapporto, S. (2007). Coupled simulations of fluvial erosion and mass wasting for cohesive river banks. Journal of Geophysical Research, vol. 112, no. F3, pp. F03022.

65 Impact of water-level variations on slope stability

Di Benedetto, H., Tatsuoka, F., & Ishihara, M. (2002). Time-dependent shear deformation characteristics of sand and their constitutive modelling. Soils and foundations, vol. 42, no. 2, pp. 1–22. Duncan, J. M. (1996). State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes. Journal of Geotechnical Engineering, vol. 122, no. 7, pp. 577–596. Duncan, J. M., & Wright, S. G. (1980). The accuracy of equilibrium methods of slope stability analysis. Engineering Geology, vol. 16, no. 1-2, pp. 5–17. Duncan, J. M., & Wright, S. G. (2005). Soil Strength and Slope Stability. Hoboken, New Jersey: John Wiley & Sons, Inc. Duncan, J. R. (1964). The effects of water table and tide cycle on swash-backwash sediment distribution and beach profile development. Marine Geology, vol. 2, no. 3, pp. 186–197. Emery, K., & Foster, J. (1948). Water tables in marine beaches. Journal of Marine Research, vol. 7, pp. 644–654. Fox, G. A., Wilson, G. V, Simon, A., Langendoen, E. J., Akay, O., & Fuchs, J. W. (2007). Measuring streambank erosion due to ground water seepage: correlation to bank , precipitation and stream stage. Earth Surface Processes and Landforms, vol. 32, no. 10, pp. 1558–1573. Fredlund, D. G. (2006). Unsaturated Soil Mechanics in Engineering Practice. Journal of Geotechnical and Geoenvironmental Engineering, vol. 132, no. 3, pp. 286–321. Fredlund, D. G., & Morgenstern, N. (1977). Stress state variables for unsaturated soils. Journal of Geotechnical and Geoenvironmental Engineering, vol. 103, no. GT5, pp. 447– 466. Fredlund, D. G., Xing, A., & Huang, S. (1994). Predicting the permeability function for unsaturated soils using the soil-water characteristic curve. Canadian Geotechnical Journal, vol. 31, no. 4, pp. 533–546. Galavi, V. (2010). Internal Report - Groundwater flow, fully coupled flow deformation and undrained analyses in PLAXIS 2D and 3D. Grant, U. (1948). Influence of the water table on beach aggradation and degradation. Journal of Marine Research, vol. 7, pp. 650–655. Guimaraes, M. (2002). fines and ion removal from clay slurries - fundamental studies. Georgia Institute of Technology. Gärdenäs, A. I., Šimůnek, J., Jarvis, N., & van Genuchten, M. T. (2006). Two-dimensional modelling of preferential water flow and transport from a tile-drained field. Journal of , vol. 329, no. 3-4, pp. 647–660. Hansbo, S. (1975). Jordmateriallära. Uppsala: Almqvist & Wiksell. Huang, M., & Jia, C.-Q. (2009). Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage. Computers and Geotechnics, vol. 36, no. 1-2, pp. 93–101. Hupp, C. (1992). Riparian vegetation recovery patterns following stream channelization: a geomorphic perspective. Ecology, vol. 73, no. 4, pp. 1209–1226.

66 References

Jia, G. W., Zhan, T. L. T., Chen, Y. M., & Fredlund, D. G. (2009). Performance of a large- scale slope model subjected to rising and lowering water levels. Engineering Geology, vol. 106, no. 1-2, pp. 92–103. Johansson, J. M. A., & Vall, J. (2011). Friktionsjords kornform. pure.ltu.se. Luleå Univeristy of Technology, Luleå. Kaczmarek, J., & Leśniewska, D. (2011). Modelling Events Occurring in the Core of a Flood Bank and Initiated by Changes in the Groundwater Level, Including the Effect of Seepage. Technical Sciences, vol. 14, no. 14. Krahn, J. (2003). The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses. Canadian Geotechnical Journal, vol. 40, no. 3, pp. 643–660. Krumbein, W. C. (1941). Measurement and Geological Significance of Shape and Roundness of Sedimentary Particles. SEPM Journal of Sedimentary Research, vol. Vol. 11, no. 2, pp. 64–72. Kuhn, M. R., & Mitchell, J. K. (1993). New Perspectives on Soil Creep. Journal of Geotechnical Engineering, vol. 119, no. 3, pp. 507–524. Kuwano, R., & Jardine, R. (2002). On measuring creep behaviour in granular materials through triaxial testing. Canadian Geotechnical Journal, vol. 1074, pp. 1061–1074. Lade, P. V., & Liu, C.-T. (1998). Experimental Study of Drained Creep Behavior of Sand. Journal of Engineering Mechanics, vol. 124, no. 8, pp. 912–920. Lafleur, J. (1984). Filter testing of broadly graded cohesionless tills. Canadian Geotechnical Journal, vol. 21, no. 4, pp. 634–643. Lane, P. A., & Griffiths, D. V. (1999). Slope stability analysis by finite elements. Géotechnique, vol. 49, no. 3, pp. 387–403. Lane, P. A., & Griffiths, D. V. (2000). Assessment of Stability of Slopes under Drawdown Conditions. Journal of Geotechnical and Geoenvironmental Engineering, vol. 126, no. 5, pp. 443–450. Li, L., Barry, D. A., Parlange, J.-Y., & Pattiaratchi, C. B. (1997). Beach water table fluctuations due to wave run-up: Capillarity effects. Research, vol. 33, no. 5, pp. 935–945. Li, L., Barry, D. A., & Pattiaratchi, C. B. (1997). Numerical modelling of tide-induced beach water table fluctuations. Coastal Engineering, vol. 30, no. 1-2, pp. 105–123. Liao, H., Ying, J., Gao, S., & Sheng, Q. (2005). Numerical Analysis on Slope Stability under Variations of Reservoir Water Level. In Landslides (pp. 305–311). Springer Berlin Heidelberg. Lim, T., Rahardjo, H., Chang, M., & Fredlund, D. G. (1996). Effect of rainfall on matric suctions in a residual soil slope. Canadian Geotechnical Journal, vol. 33, no. 4, pp. 618– 628. Liu, C., Li, F., Ma, L.-P., & Cheng, H.-M. (2010). Advanced materials for energy storage. Advanced materials, vol. 22, no. 8, pp. E28–E62. López-Acosta, N. P., Fuente de la, H. A., & Auvinet, G. (2013). Safety of a protection levee under rapid drawdown conditions. Coupled analysis of transient seepage and stability. In

67 Impact of water-level variations on slope stability

Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013 (pp. 3305–3308). Mill, O., Dahlbäck, A., Wörman, S., Knutsson, S., Johansson, F., Andreasson, P., … Glavatskih, S. (2010). Analysis and Development of Hydro Power Research - Synthesis within Swedish Hydro Power Centre. Stockholm. Minarski, R. (2008). Assessment of the potential amount of floating debris in Lule river. Luleå University of Technology. Mitchell, J., & Soga, K. (2005). Fundamentals of soil behavior. John Wiley & Sons, Inc. Morgenstern, N. (1963). Stability Charts for Earth Slopes During Rapid Drawdown. Géotechnique, vol. 13, no. 2, pp. 121–131. Murayama, S., Michihiro, K., & Sakagami, T. (1984). Creep characteristics of sand. Soils and foundations, vol. 24, no. 5. Nielsen, P. (1990). Tidal dynamics of the water table in beaches. Water Resources Research, vol. 26, no. 9, pp. 2127–2134. Parlange, J., Stagnitti, F., Starr, J., & Braddock, R. (1984). Free-surface flow in porous media and periodic solution of the shallow-flow approximation. Journal of Hydrology, vol. 70, no. 1-4, pp. 251–263. Peng, F.-L., Tan, K., & Tan, Y. (2012). Simulating the Viscous Behavior of Sandy Ground by FEM. In GeoCongress 2012 (pp. 2167–2176). Reston, VA: American Society of Civil Engineers. Pereira, J.-M., Coussy, O., Alonso, E. E., Vaunat, J., & Olivella, S. (2010). Is the degree of sat ation a good candidate fo Bishop’s pa amete ? In A. Gens (Ed.), Alonso, E.E., Gens, A. (eds.) Unsaturated Soils—Proceedings of 5th International Conference on Unsaturated Soils (pp. 913–919). , Barcelona, Spain, September 2010: CRC Press. Petterson, K. E. (1955). The Early History of Circular Sliding Surfaces. Géotechnique, vol. 5, no. 4, pp. 275–296. Pinyol, N. M., Alonso, E. E., Corominas, J., & Moya, J. (2011). Canelles landslide: modelling rapid drawdown and fast potential sliding. Landslides, vol. 9, no. 1, pp. 33–51. PLAXIS. (2012). PLAXIS 2D 2012. Delft, Netherlands.: Available at: http://www.plaxis.nl/. Pugh, D. T. (1987). Tides, Surges and Mean Sea-Level. Marine and Geology (Vol. 5, p. 301). John Wiley & Sons, Inc. R. Grove, J., Croke, J., & Thompson, C. (2013). Quantifying different riverbank erosion processes during an extreme flood event. Earth Surface Processes and Landforms, vol. 1406, no. February, pp. n/a–n/a. Ramalho, R. S., Quartau, R., Trenhaile, A. S., Mitchell, N. C., Woodroffe, C. D., & Ávila, S. P. (2013). Coastal evolution on volcanic oceanic islands: A complex interplay between volcanism, erosion, sedimentation, sea-level change and biogenic production. Earth- Science Reviews, vol. 127, pp. 140–170. Raubenheimer, B., Guza, R. T., & Elgar, S. (1999). Tidal water table fluctuations in a sandy ocean beach. Water Resources Research, vol. 35, no. 8, pp. 2313–2320. REN21. (2013). Renewables 2013: Global Status Report.

68 References

Rodriguez, J., Edeskär, T., & Knutsson, S. (2013). Particle Shape Quantities and Measurement Techniques–A Review. Electronical Journal of Geotechnical Engineering, vol. 18, pp. 169–198. Rodriguez, J., Johansson, J., & Edeskär, T. (2012). Particle shape determination by two- dimensional image analysis in geotechnical engineering. In Nordic Geotechnical Meeting, NGM 2012, 16, 9-12 May, 2012. (pp. 207–218). Rognlien, L. M. (2012). Pumped storage hydropower development in Øvre Otra, Norway. Norwegian University of Science and Technology. Rowe, P. W. (1962). The Stress-Dilatancy Relation for Static Equilibrium of an Assembly of Particles in Contact. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 269, no. 1339, pp. 500–527. Santamarina, J. C., & Cho, G. C. (2004). Soil behavio : he ole of pa ticle shape, pp. 1– 14. Schweiger, H. F., & Peschl, G. M. (2005). Reliability analysis in geotechnics with the random set finite element method. Computers and Geotechnics, vol. 32, no. 6, pp. 422– 435. Shen, Y., Zhu, D., & Yao, H. (2010). Critical slip field of slope in process of reservoir water level fluctuations. Rock and Soil Mechanics, vol. 31, no. S2, pp. 179–183. Sheng, D. (2011). Review of fundamental principles in modelling unsaturated soil behaviour. Computers and Geotechnics, vol. 38, no. 6, pp. 757–776. Sheng, D., Zhang, S., & Yu, Z. (2013). Unanswered questions in unsaturated soil mechanics. Science China Technological Sciences, vol. 56, no. 5, pp. 1257–1272. Singhroy, V. (1995). Sar integrated techniques for geohazard assessment. Advances in Space Research, vol. 15, no. 11, pp. 67–78. Smith-Konter, B., & Pappalardo, R. T. (2008). Tidally driven stress accumulation and shear fail e of ncelad s’s tige st ipes. Icarus, vol. 198, no. 2, pp. 435–451. Solvang, E., Harby, A., & Killingtveit, Å. (2012). Increasing balance power capacity in Norwegian hydroelectric power stations. Sun, D., Sun, W., & Xiang, L. (2010). Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation. Computers and Geotechnics, vol. 37, no. 5, pp. 678–688. Swedenergy. (2008). RIDAS. Svenska Kraftnät. (2008). Storskalig utbyggnad av vindkraft (Vol. 1). Tatsuoka, F. (2000). Some new aspects of time effects on the stress-strain behaviour of stiff geomaterials, Keynote Lecture. The Geotechnics of Hard Soils-Soft Rocks, Proc. of Second Int. Conf. on Hard Soils and Soft Rocks, Napoli, 1998, vol. 2, pp. 1285–1371. Tatsuoka, F. (2007). Inelastic deformation characteristics of geomaterial. In Soil Stress- Strain Behavior: Measurement, Modeling and Analysis (Vol. 146, pp. 1–108). Springer Netherlands. Terzaghi, K., Peck, R., & Mesri, G. (1996). Soil mechanics in engineering practice (p. 1565).

69 Impact of water-level variations on slope stability

Thomas, A., Eldho, T. I., & Rastogi, a. K. (2013). A comparative study of point collocation based MeshFree and finite element methods for groundwater flow simulation. ISH Journal of , , no. January 2014, pp. 1–10. Tohari, A., Nishigaki, M., & Komatsu, M. (2007). Laboratory Rainfall-Induced Slope Failure with Moisture Content Measurement. Journal of Geotechnical and Geoenvironmental Engineering, vol. 133, no. 5, pp. 575–587. Tsai, T.-L., & Yang, J.-C. (2006). Modeling of rainfall-triggered shallow landslide. Environmental Geology, vol. 50, no. 4, pp. 525–534. U.S. EPA. (1999). TRIM, Total Risk Integrated Methodology, TRIM FATE Technical Support Document, Volume I: Description of Module. U.S. EPA. (2001). Risk Assessment Guidance for Superfund (RAGS) Volume III - Part A: Process for Conducting Probabilistic Risk Assessment (2001) - Appendix A (Vol. 3, pp. 1– 37). Wadell, H. (1932). Volume, Shape, and Roundness of Rock Particles. The Journal of Geology, vol. 40, no. 5, pp. 443–451. Van Genuchten, M. T. (1980). A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Society of America Journal, vol. 44, no. 5, pp. 892–898. Ward, W. H. (1945). The Stability of Natural Slopes. The Geographical Journal, vol. 105, no. 5/6, pp. 170. Whittingham, M. (2008). Materials challenges facing electrical energy storage. Mrs Bulletin, vol. 33, no. 04, pp. 411–419. Yang, H., Rahardjo, H., & Xiao, D. (2010). Rapid Drawdown of Water Table in Layered Soil Column. In Geoenvironmental engineering and geotechnics: progress in modeling and applications (pp. 202–209). Shanghai, China: American Society of Civil Engineers (ASCE). Yu, H. S., Salgado, R., Sloan, S. W., & Kim, J. M. (1998). Limit Analysis versus Limit Equilibrium for Slope Stability. Journal of Geotechnical and Geoenvironmental Engineering, vol. 124, no. 1, pp. 1–11. Zhan, T., Zhang, W., & Chen, Y. (2006). Influence of reservoir level change on slope stability of a silty soil bank. In The Fourth International Conference on Unsaturated Soils, ASCE, April 2–4 (pp. 463–472). Zhang, C. (2013). Non-Tidal Water Level Variability in Lianyungang Coastal Area. Advanced Materials Research, vol. 610, pp. 2705–2708. Zhang, K., Douglas, B. C., & Leatherman, S. P. (2004). Global Warming and Coastal Erosion. Climatic Change, vol. 64, no. 1-2, pp. 41–58. Zheng, H., Sun, G., & Liu, D. (2009). A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique. Computers and Geotechnics, vol. 36, no. 1-2, pp. 1–5. Zuber, M. (2011). Renaissance for Pumped Storage in Europe. RenewableEnergyWorld.com (publ. augusti 20, 2011). Retrieved October 02, 2012, from

70 References

http://www.renewableenergyworld.com/rea/news/article/2011/08/renaissance-for- pumped-storage-in-europe Åstrand, S., & Johansson, N. (2011). Drivgods vid extrema tillfällen, Elforsk, Rapport 11:32. Stockholm.

71

Paper A

Effects of External Water-Level Fluctuations on Slope Stability

J. M. Johansson and T. Edeskär

Electronic Journal of Geotechnical Engineering vol. 19, no. K, pp. 2437–2463, 2014.

 (IIHFWVRI([WHUQDO:DWHU/HYHO )OXFWXDWLRQVRQ6ORSH6WDELOLW\

Jens M. A. Johansson 'HSDUWPHQWRI&LYLO(QYLURQPHQWDODQG1DWXUDOUHVRXUFHVHQJLQHHULQJ /XOHn8QLYHUVLW\RI7HFKQRORJ\7HO6(±/XOHn6ZHGHQ HPDLOMHQVPDMRKDQVVRQ#OWXVH  Tommy Edeskär $VVLVWDQWSURIHVVRU 'HSDUWPHQWRI&LYLO(QYLURQPHQWDODQG1DWXUDOUHVRXUFHVHQJLQHHULQJ /XOHn8QLYHUVLW\RI7HFKQRORJ\7HO6(±/XOHn6ZHGHQ HPDLOWRPP\HGHVNDU#OWXVH

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³VLPSOLFLW\´DQG³DSSOLFDELOLW\´²SURPRWLQJ XVH RI OLPLWHTXLOLEULXP PHWKRGV²VKRXOG PRUH RIWHQ EH VHW LQ UHODWLRQ WR DFFXUDF\ DQG UREXVWQHVVSURYLGHGE\XVHRIPHWKRGVFRQVLGHULQJDOVRGHIRUPDWLRQV KEYWORDS: :DWHUOHYHOIOXFWXDWLRQVUHVHUYRLUVORSHVWDELOLW\

-2437 -  Vol. 19 [2014], Bund. K 2438

INTRODUCTION ,Q-0'XQFDQ :ULJKW  LWZDVUHPLQGHGWKDWDQH[WHUQDO ZDWHU SUHVVXUH DFWV VWDELOL]LQJWRDVORSHRUWRDQHPEDQNPHQWGDP³7KLVLVSHUKDSVWKHRQO\JRRGWKLQJWKDWZDWHU FDQGRWRDVORSH´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

FDSDFLW\ PRUH VRSKLVWLFDWHG DQG DFFXUDWH PHWKRGV KDYH EHHQ LQFUHDVLQJO\ UHTXHVWHG DQG GHYHORSHG 6XFK GHIRUPDWLRQDQDO\VLV PHWKRGV EDVHG RQ DFWXDO OLPLW FRQGLWLRQV DUH RIWHQ KDQGOHGE\XVHRIILQLWHHOHPHQWV )( WRROV ,QWKLVSDSHUJHRWHFKQLFDOHIIHFWVRIZDWHUOHYHOIOXFWXDWLRQRQVORSHVWDELOLW\DUHDGGUHVVHG UHOHYDQW LQWHUGLVFLSOLQDU\ ILQGLQJV DUH SUHVHQWHG DGYHQWXURXV VLPSOLILFDWLRQV DQGRU LQDGYHUWHQFLHVDUHXQGHUOLQHGDQGSRWHQWLDOLPSURYHPHQWDUHDVDUHLGHQWLILHG,QRUGHUWRPDNHLW SRVVLEOH WR SXW ILQGLQJV RQ ³ZDWHUOHYHO IOXFWXDWLRQV´ LH VRXUFHV SRWHQWLDO VRLO PHFKDQLFDO FRQVHTXHQFHVDQGVORSHVWDELOLW\HIIHFWV LQUHODWLRQWRWKRXJKWVDQGRXWORRNVRQDFWXDODQDO\VLV VRPHIXQGDPHQWDOVRIVORSHVWDELOLW\DQDO\VLVSURFHGXUHVDUHDOVRFRYHUHG WATER LEVEL VARIATION – MODES AND SOURCES

General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³EHKLQG´WKHVORSHVXUIDFHKDVWREHSURSHUO\H[SUHVVHG

Long-term natural variations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³XSSHU ERXQG´ LV FRUUHFW  FP LQ WKH VW FHQWXU\ EDVHG RQ ,3&&¶V SUHGLFWLRQSUHVHQWHGLQWKH³7KLUG$VVHVVPHQW5HSRUW´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ol. 19 [2014], Bund. K 2440

Figure 1: %DVLFPRGHVRIZDWHUOHYHOFKDQJHIORZLQJZDWHU $ ZDWHUOHYHOGUDZGRZQ % UDLVHGZDWHUOHYHO & DQGIOXFWXDWLQJZDWHUOHYHO ' ,QWKHSLFWXUHVSULQFLSOH ZDWHUORDGV :/ DVZHOODVWKHSRVLWLRQVRIWKHJURXQGZDWHUWDEOH *:7 DQGWKH H[WHUQDOZDWHUOHYHO (:/ DUHVKRZQ

GHVFULELQJ WKH GHYHORSPHQW IURP VWDEOH FRQGLWLRQV YLD VRPH WLPH OLPLWHG ODQGIRUP FKDQJLQJ VWDJHVHQGLQJXSZLWKDQRWKHUVWDEOHVWDWH VHH)LJXUH 7KHVHH[DPSOHVRIORQJWHUPHIIHFWV² DV ZHOO FRDVWDO HURVLRQ DV FKDQQHO HYROXWLRQ²DUH VKRZLQJ FOHDU FRQVHTXHQFHV RI ZDWHUVRLO LQWHUDFWLRQ HQWDLOLQJ REYLRXV HIIHFWV RQ WKH EHDFKEDQN 7KRXJK KHQFHIRUWK VKRUWWHUP ZDWHU OHYHOYDULDWLRQVZLOOEHIRFXVHG

Short-term natural variations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ol. 19 [2014], Bund. K 2441

Figure 2: &RQFHSWXDOPRGHORIFKDQQHOHYROXWLRQ 7KHLOOXVWUDWHGF\FOHLQFOXGHVWKHVWDJHV³SUHPRGLILHG´EHLQJRIVWDEOHQDWXUH 6WDJH, IROORZHGE\ VWDJHVEHLQJODVWLQJIRUOLPLWHGWLPHSHULRGVLQFOXGLQJ³FRQVWUXFWLRQ´ 6WDJH,, ³GHJUDGDWLRQ´ 6WDJH,,,  ³WKUHVKROG´ 6WDJH,9 DQG³DJJUDGDWLRQ´ 6WDJH9 7KHF\FOHHQGVXSZLWKDVWDJHRI³UHFRYHU\´ZKLFK RQHLVDJDLQVWDEOH 6WDJH9, 7KHDUURZVDUHUHSUHVHQWLQJWKHPRYHPHQWGLUHFWLRQRIWKHEHG YHUWLFDOO\  DQGWKHEDQNV KRUL]RQWDOO\ 7KHSLFWXUHVDUHQRWWRVFDOH DIWHU+XSS 

Watercourse regulation (QHUJ\EDODQFLQJ %HVLGHV WKH HIIHFWV EHLQJ LPPHGLDWHO\ UHODWHG WR FOLPDWH DQG ZHDWKHU WKHUH DUH DOVR RWKHU FOLPDWHOLQNHGSKHQRPHQDLQIOXHQFLQJVORSHVWDELOLW\7KHHQHUJ\GHPDQGLVJOREDOO\LQFUHDVLQJ DQGWKHXVHRIUHQHZDEOHXQUHJXODWHGHQHUJ\VRXUFHV QRQIRVVLOVRXUFHVQDWXUDOO\UHJHQHUDWHG LV VWURQJO\JURZLQJ,QDVPXFKDVRXWRIWKHWRWDOJOREDOHQHUJ\FRQVXPSWLRQFDPH IURPUHQHZDEOHHQHUJ\VRXUFHV WREHFRPSDUHGZLWKIRU 0RUHRYHUWKHVKDUHRI ³PRGHUQ UHQHZDEOHV´ LH ELRPDVV ZLQG VRODU JHRWKHUPDO KHDW KRW ZDWHU ELRIXHOV DQG K\GURSRZHU  ZDV ELJJHU WKDQ WKH VKDUH RI ³WUDGLWLRQDO ELRPDVV´ FRPEXVWHG LQ LQHIILFLHQW DQG SROOXWDQWV\VWHPV  5(1  $V D FRQVHTXHQFH RI WKH WUHQGV RI HQHUJ\ FRQVXPSWLRQ LQ WKH UHFHQW \HDUV LQFUHDVLQJO\ DWWHQWLRQKDVEHHQJLYHQWRWKHLPSRUWDQFHRIXVH RIK\GURSRZHUUHVHUYRLUV IRUHQHUJ\VWRUDJH HJ &RQQROO\   7KH XQGHUO\LQJ UHDVRQ²LH DQ LQFUHDVHG QHHG RI HQHUJ\ EDODQFLQJ² FRPHV IURP WKH JURZWK RI QRQUHJXODWHG HQHUJ\ VRXUFHV HJ ZLQG DQG VRODU  :KLWWLQJKDP 0LOOHWDO&RQQROO\ %HVLGHVSRZHUGLVWULEXWLRQLVVXHV LQFOXGLQJHJJULG GHVLJQ DQGWKHHFRQRPLFDQGSROLWLFDODVSHFWVLWKDVEHHQVWDWHGWKDWDOVRRWKHUHIIHFWVRQWKH K\GURSRZHUV\VWHPVDUHWREHH[SHFWHG 'DKOElFN 5HJDUGLQJZLQGSRZHUGHYHORSPHQW DQG H[SORLWDWLRQ EHLQJ SODQQHG DQG WKH IROORZLQJ QHHG RI K\GURSRZHU EDODQFLQJ LW ZDV FRQFOXGHGWKDW³WKLVQHFHVVDULO\UHTXLUHWKDWIORZPDJQLWXGHVDQGZDWHUOHYHOKHLJKWVWRDJUHDWHU H[WHQWWKDQSUHYLRXVO\ZLOOYDU\EHWZHHQWKHH[LVWLQJOLPLWV´ 6YHQVND.UDIWQlW 'LIIHUHQW SHUVSHFWLYHV RI SRWHQWLDO LVVXHV UHODWHG WR PRUH DFWLYHO\ RSHUDWHG K\GURSRZHU SODQWV FDXVLQJ LQFUHDVHG ZDWHUOHYHO YDULDWLRQV LQ LPSRXQGPHQWVUHVHUYRLUV DUH FRQWLQXRXVO\ XSGDWHG WKURXJK UHVHDUFKZLWKLQ&('5(1 &HQWUHIRU(QYLURQPHQWDO'HVLJQRI5HQHZDEOH(QHUJ\ ,WLVKLJKO\ Vol. 19 [2014], Bund. K 2442

H[SHFWHGWRJHWLQFUHDVHGYDULDWLRQVRIWKHUHVHUYRLUZDWHUOHYHOVKRXUWRKRXUGD\WRGD\DQGRU VHDVRQDOO\ 6YHQVND(QHUJLP\QGLJKHWHQ0LOOHWDO6ROYDQJHWDO  1XPHURXV VWXGLHV KDYH EHHQ FDUULHG RXW UHODWHG WR WKH 7KUHH *RUJHV 3URMHFW 6LJQLILFDQW ZDWHUOHYHO FKDQJHV KDYH EHHQ WDNLQJ SODFH IROORZLQJ WKH UHJXODWLRQ DFWLYLWLHV DQG ODUJH DUHDV DORQJWKHUHVHUYRLU ZLWKDOHQJWKRIDSSUR[LPDWHO\NP KDYHEHHQLQIOXHQFHGHQGLQJXSZLWK ODQGVOLGHV HJ&RMHDQ &Dw+XHWDO  3XPSHGK\GURSRZHUVWRUDJH ([LVWLQJGUDZEDFNVDQGOLPLWDWLRQVRIGLIIHUHQWHQHUJ\VWRUDJHPHWKRGV²UHJDUGLQJDVZHOO VFDOH DV DSSOLFDELOLW\²DUH FRQWLQXRXVO\ LGHQWLILHG DQG FRPSDUHG 7KH VLPSOH HQHUJ\VWRUDJH WHFKQRORJ\SXPSHGK\GURSRZHUVWRUDJH3+6 RUSXPSHGK\GURHOHFWULFVWRUDJH3+(6 KDVEHHQ LQ XVH VLQFH  &RQQROO\   $ 3+6V\VWHP FRQVLVWV RI WZR UHVHUYRLUV RI GLIIHUHQW HOHYDWLRQV'XULQJRIISHDNHOHFWULFDOGHPDQGZDWHULVSXPSHGIURPWKHORZHUUHVHUYRLUWRWKH KLJKHURQHGXULQJRQSHDNGHPDQGZKHQWKHHQHUJ\QHHGLVLQFUHDVLQJWKHZDWHULVGLVFKDUJHG WKURXJK HOHFWULFLW\ JHQHUDWLQJ WXUELQHV & /LX HW DO   ,Q 'HDQH HW DO   LW ZDV H[SUHVVHGWKDW³3+(6LVFXUUHQWO\WKHRQO\FRPPHUFLDOO\SURYHQODUJHVFDOH !0: HQHUJ\ VWRUDJHWHFKQRORJ\´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– EFFECTS AND CONSIDERATIONS

Analysis of slope stability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ol. 19 [2014], Bund. K 2443

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³$VOLSLQWKHZHVWEDQNRI(DX %ULQN&XW´LQFOXGLQJDQLOOXVWUDWLRQRIDURWDWLRQDOVOLSVXUIDFHZLWKLQDVORSHPDLQO\FRQVLVWLQJ RI FOD\ SUHVHQWHG E\ 6NHPSWRQ LQ  $Q DSSURDFK RI DFWXDOO\ DVVXPLQJ D FLUFXODU VOLS VXUIDFHVZDVLQWURGXFHGLQDQGLQWKHEHJLQQLQJRIWKHV)HOOHQLXVSUHVHQWHG D IXOO\ GHVFULEHGDQDO\VLVPHWKRG .UDKQ-0'XQFDQ :ULJKW /DWHUWKLVPHWKRGKDV EHHQUHIHUUHGWRDVWKH׋ PHWKRGRUWKH6ZHGLVKFLUFOHPHWKRG,Q)LJXUHDVFKHPDWLFVNHWFK RIDFLUFXODUVOLSVXUIDFHRIDZDWHUIURQWVORSHLVVKRZQ7KHUHDUHGLIIHUHQWDSSURDFKHVXVHGIRU TXDQWLWDWLYHVWDELOLW\DQDO\VLVOLPLWHTXLOLEULXPPHWKRGV /( DQGGHIRUPDWLRQDQDO\VLVPHWKRGV RIWHQXWLOL]LQJILQLWHHOHPHQWV )(  /LPLWHTXLOLEULXPDQDO\VLV /(PHWKRGV KDYH EHHQ XVHG WR DQDO\]H VORSH VWDELOLW\ IRU D ORQJ WLPH - 0 'XQFDQ  :ULJKW

DVVXPSWLRQVDUHWREHLQYROYHG

Figure 3: 6FKHPDWLFVNHWFKRIDZDWHUIURQWVORSH +LJKPHDQDQGORZZDWHUOHYHOV +0DQG/ SRVLWLRQVRIWKHYDU\LQJJURXQGZDWHUWDEOH *:7 WKH UDQJHZLWKLQZLWFKWKHVKRUHOLQHLVPRYLQJDUHVKRZQ0RUHRYHUDILFWLYHSRWHQWLDOVOLSVXUIDFHLVGUDZQ 0RGLILHGDIWHU/LHWDO 

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VVLPSOLILHGPHWKRGDOVRWKHHTXDWLRQRIYHUWLFDOIRUFHHTXLOLEULXPRIHDFK VOLFHLVVDWLVILHGLQ%LVKRSVPRGLILHGPHWKRGDOVRVLGHIRUFHVDUHFRQVLGHUHG$OOWKHVHPHWKRGV DUH UHVWULFWHG WR RQO\ FLUFXODU VOLS VXUIDFHV 0RUHRYHU WKHUH DUH PHWKRGV LQ ZKLFK RQO\ IRUFH HTXLOLEULXPHTXDWLRQVDUHVDWLVILHGHJDPHWKRGSUHVHQWHGE\/RZHDQG.DUDILDWKLQ - 'XQFDQ :ULJKW 0HWKRGVVDWLVI\LQJDVZHOOPRPHQWHTXLOLEULXPDVIRUFHHTXLOLEULXP HJ0RUJHQVWHUQDQG3ULFH¶VPHWKRG6SHQFHU¶VPHWKRGDQG-DQEX¶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ol. 19 [2014], Bund. K 2445

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

F WDQ ׋ Ȉ0VI    FUHGXFHG WDQ ׋௥௘ௗ௨௖௘ௗ

ZKHUH 0VI LV D FRQWUROOLQJ PXOWLSOLHU UHSUHVHQWLQJ WKH VDIHW\ IDFWRU F LV WKH FRKHVLRQ ׋LVWKH IULFWLRQDQJOHDQGWKHLQGH[³UHGXFHG´LQGLFDWHVYDOXHVEHLQJVXFFHVVLYHO\GHFUHDVHGXQWLOIDLOXUH RFFXUV +RZHYHU WKH GHILQLWLRQ RI DFWXDO IDLOXUH LV QRW DOZD\VREYLRXVDQGWKHUHDUHPDQ\ GLIIHUHQW DSSURDFKHV WR XWLOL]H 7KRXJK WKH ³QRQFRQYHUJHQFH RI VROXWLRQV´ LV RIWHQ XVHG IRU LQGLFDWLRQRIJOREDOLQVWDELOLW\RIVRLOVORSHV7KLVLVLQGLFDWHGE\ZKHQDVWUHVVVWDWHFDQQRWEH IRXQGWRVLPXOWDQHRXVO\VDWLVI\WKHIDLOXUHFULWHULRQDQGWKHJOREDOHTXLOLEULXP /DQH *ULIILWKV   /(DQG)(±SURVFRQVGLIIHUHQFHV $PRQJWKHODUJHQXPEHURISUHYLRXVVWXGLHVRQYDULRXVVORSHVWDELOLW\LVVXHVDVLJQLILFDQW VKDUHLVEDVHGRQ/(DQDO\VLV6WLOOLWLVZRUWKPHQWLRQLQJWKDWGUDZEDFNVDQGOLPLWDWLRQVRI/( PHWKRGV KDYH EHHQ NQRZQ DQG HYLGHQFHG IRU D ORQJ WLPH )RU LQVWDQFH WKHUH DUH GLIILFXOWLHV FRQQHFWHG WR DFFXUDWHO\ GHILQH WKH SRVLWLRQ RI WKH VOLS VXUIDFH :DUG   DQG WKHUH DUH QXPHULFDO SUREOHPV SRWHQWLDOO\ PHW ZLWK %LVKRSV PRGLILHG PHWKRG - 0 'XQFDQ   $Q LOOXVWUDWLYH H[DPSOH RI ZKDW NLQG RI UHDVRQLQJ WKDW LV FKDUDFWHULVWLFDOO\ MXVWLI\LQJ XVH RI /( DQDO\VLV ZDV VHHQ LQ 7VDL 

HUURUV FRQQHFWHG WR WKH DQDO\VLV DSSUR[LPDWLRQV PLJKW EH VLJQLILFDQW ,W KDV EHHQ VKRZQ WKDW IRUFHHTXLOLEULXPSURFHGXUHVPD\JLYHVDIHW\IDFWRUYDOXHVEHLQJ³VLJQLILFDQWO\DIIHFWHGE\WKH DVVXPHGVLGHIRUFHLQFOLQDWLRQ´WKH\PD\GHYLDWHIURPWKRVHFDOFXODWHGE\PHWKRGVVDWLVI\LQJDOO HTXLOLEULXP HTXDWLRQV E\ DERXW   RYHUHVWLPDWLRQ  7KH OLQN H[LVWLQJ EHWZHHQ /( DSSUR[LPDWLRQV DQG SRWHQWLDO HUURUV LV JHQHUDOO\ NQRZQ DQG UHFRJQL]HG E\ PDQ\ DXWKRUV HJ :DUG/DQH *ULIILWKV.UDKQ 7KHDFFXUDF\RI/(UHVXOWVKDVWKHUHIRUHEHHQ VWXGLHGDQGHYDOXDWHGLQPDQ\FRQWH[WV6RPHHYDOXDWLRQVKDYHEHHQPDGHE\PHDQVRIGLUHFW TXDQWLWDWLYHFRPSDULVRQVEHWZHHQWKHUHVXOWVDFKLHYHGIURP/(DQDO\VLVDQGWKRVHIURPPHWKRGV FRQVLGHULQJDOVRVWUDLQVDQGGHIRUPDWLRQV HJ

Water-level drawdown :KHQDQH[WHUQDOZDWHUOHYHOLVORZHUHGWKHVKRUHOLQH DORQJZKLFKWKHZDWHUOHYHOLQWHUVHFWV ZLWKWKHEHDFKIDFH PRYHVLQWKHGLUHFWLRQRXWZDUGVIURPODQG6XUILFLDOZDWHUIORZRFFXUVDQG VR PLJKW GR VXUILFLDO VRLOPDWHULDO WUDQVSRUW LH H[WHUQDO HURVLRQ 7KH HURVLRQ SURFHVVHV KDYH FKDUDFWHULVWLFV EHLQJ GHSHQGHQW RQ WKH VRLO SURSHUWLHV HJ JUDLQ VL]H GHQVHQHVV GHJUHH RI VDWXUDWLRQHWF *UDQW-5'XQFDQ (YHQWKRXJKVHGLPHQWHURVLRQSURFHVVHVDUH H[WHQVLYHO\VWXGLHGLWZDVFRQFOXGHGLQ%DNKW\DUHWDO  WKDW³0RVWUHVHDUFKLQWKLVDUHD Vol. 19 [2014], Bund. K 2447

GHDOVZLWKWKHODUJHVFDOH WLGH SUREOHPRIVHDDQGDTXLIHULQWHUDFWLRQDQGOHVVDWWHQWLRQKDVEHHQ GHYRWHGWRWKHUHVSRQVHRIEHDFKJURXQGZDWHUWRWKHVZDVKPRWLRQV´ :KHQ LW FRPHV WR VORSH VWDELOLW\ DV ZHOO ODUJHVFDOH GUDZGRZQ HIIHFW RI FKDQJHG H[WHUQDO ORDGLQJVLWXDWLRQVDVK\GURG\QDPLFSKHQRPHQDZLWKLQWKHVORSHDUHWREHFRQVLGHUHG'UDZGRZQ RIDQH[WHUQDOZDWHUOHYHOLVXVXDOO\LPSDLULQJWKHVWDELOLW\VLWXDWLRQ7KHSURFHVVRIKDYLQJWKH ZDWHUOHYHOUDSLGO\ORZHUHGLVGHVFULEHGDQGLQYHVWLJDWHGE\PDQ\DXWKRUV HJ/DQH *ULIILWKV -0'XQFDQ :ULJKW

Figure 45HVXOWVIURPFROXPQUDSLGGUDZGRZQWHVWVSHUIRUPHGWKURXJKDVRLOVDPSOH FRQVLVWLQJRIDILQHUVRLOOD\HU FOD\H\VDQG SXWRYHUDFRDUVHUVRLOOD\HU PHGLXPVDQG  3RUHZDWHUSUHVVXUHVDWGLIIHUHQWGHSWKV HOHYDWLRQV DUHSORWWHGDWGLIIHUHQWWLPHV7KH VRLOLQWHUIDFHLVUHSUHVHQWHGE\WKHGRWWHGOLQH

Water-level rise $OVR ULVLQJ RI D ZDWHU OHYHO PLJKW FDXVH SUREOHPV DPRQJ VWXGLHV FRQFHUQLQJ WKH 7KUHH *RUJHV'DPVLWH HJ&RMHDQ &Dw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ol. 19 [2014], Bund. K 2449

WRKRPRJHQL]DWLRQRIWKHVORSHERG\LQFUHDVHGKRUL]RQWDOVWUHVVHVFDXVHGE\DQLQFUHDVHGZDWHU ORDGDQGYHUWLFDOVWUHVVHVJUDGXDOO\UHWXUQLQJWRWKHVWDUWYDOXHV,WZDVHPSKDVL]HGWKDWDGHOD\HG FKDQJH RI SRUH SUHVVXUH LQVLGH D VORSH²UHODWLYH WR WKH FKDQJH RI WKH DGMDFHQW H[WHUQDO ZDWHU OHYHO²UHVXOWVLQVLJQLILFDQWPRYHPHQWVRIZDWHUZLWKLQWKHVRLOVORSHERG\7KXVWKHVHHSDJH IRUFHVZHUHIRXQGWRDGYHUVHO\DIIHFWWKHVWDELOLW\7KHVHHSDJHLQVWDELOLW\UHODWLRQVKLSZDVDOVR FRQILUPHGLQ7RKDUL1LVKLJDNL .RPDWVX  

Water-level fluctuation: drawdown-rise combinations :KHQLWFRPHVWRF\FOLFZDWHUOHYHOIOXFWXDWLRQVWKHIXQGDPHQWDOVIRUHDFKSKDVHRIULVHDQG GUDZGRZQUHVSHFWLYHO\DUHREYLRXVO\WKHVDPHDVIRUWKHVHFKDQJHVRFFXUULQJVHSDUDWHG7KRXJK WKHUHDUHLPSRUWDQWSHFXOLDULWLHVOLQNHGWRUHFXUUHQFHLHDFWXDOF\FOLQJ6LQFHRQHRIWKHNH\ LVVXHVRIHYDOXDWLQJWKHHIIHFWVRIF\FOLFZDWHUOHYHOIOXFWXDWLRQV RQ VORSH VWDELOLW\ FRQFHUQV ZDWHUIORZSDWWHUQV²QRWDWOHDVWGHVFULSWLRQRIJURXQGZDWHUPRWLRQ²K\GURORJLFDOPRGHOLQJLV KLJKO\ LPSRUWDQW )XUWKHUPRUH DQ\ PRYHPHQW RI D JURXQGZDWHU OHYHO LV LPSDFWLQJ WKH JHRWHFKQLFDOFRQGLWLRQVWKHKLVWRU\RIVWUHVVDQGVWUDLQFKDQJHVLVFHQWUDO&RQVLGHUDWLRQRIVXFK GHYHORSPHQWFRQFHUQVK\GURPHFKDQLFDOFRXSOLQJ

Hydrological modeling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

LQILOWUDWLRQ DQG ZDWHU YROXPH UHGXFWLRQ ZKHUHDV RXWJRLQJ ZDWHU YROXPHV PRVWO\ PRYH RQ VDWXUDWHGVRLOJHWH[WUDZDWHUDGGHGIURPWKHHIIOXHQW]RQHDQGWKHUHIRUHEHFRPHDFFHOHUDWLQJ,W KDVEHHQVXJJHVWHGWKDWUDSLGIOXFWXDWLRQVRIDSKUHDWLFOHYHOZLWKLQDVDQG\EHDFKVZDVK]RQHLV JRYHUQHG E\ RFFXUUHQFH RI ORFDO MXPSV LQ SRUHSUHVVXUHV 7XUQHU  1LHOVHQ   7KXV WKH DXWKRUVGLGVXJJHVWWKDWSKUHDWLFOHYHOFKDQJHVDUHFDXVHGE\GRZQZDUGLQILOWUDWLRQUDWKHUWKDQ E\ XSZDUG ZDWHU IORZ )XUWKHUPRUH LW ZDV VWUHVVHG WKDW FRQFOXVLRQV LQ SUHYLRXV VWXGLHV² VXJJHVWLQJWKDWVDWXUDWLRQFKDUDFWHULVWLFVRIDVRLOEHGLVYDU\LQJ LHLVDOWHULQJEHWZHHQZHWDQG GU\ DWZDWHUWDEOHIOXFWXDWLRQV²PLJKWEHZURQJ $QREYLRXVIDFWLVWKDWWKHJURXQGZDWHU WDEOH LV ODJJLQJ EHKLQG WKH H[WHUQDO ZDWHU OHYHO (PHU\ )RVWHU&KDSSHOOHWDO ,Q/L%DUU\ 3DWWLDUDWFKL  LWZDVFODLPHG WKDWWKHUHDUHLPSRUWDQWGUDZEDFNV LQ IRUPHUO\ GHILQHG PRGHOV XVHG IRU GHVFULSWLRQ RI JURXQGZDWHU EHKDYLRU 7KH\ VWUHVVHG WKDW PDQ\ PRGHOV DUH EDVHG RQ WKH RQHGLPHQVLRQDO %RXVVLQHVT¶VHTXDWLRQ²LHVKDOORZIUHHZDWHUIORZWKHRU\ HJ3DUODQJHHWDO1LHOVHQ  ²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³+LJKFRVWVLQ FUHDWLQJDJULGPHVKORZ DFFXUDF\RISUHGLFWLRQGLIILFXOW\LQDGDSWLYHDQDO\VLVDUHIHZRIWKH VKRUWFRPLQJVRIWKHVHPHWKRGV´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ol. 19 [2014], Bund. K 2451

GHJUHHRIVDWXUDWLRQDQGUHODWLYHFRHIILFLHQWRISHUPHDELOLW\ HJ)UHGOXQGHWDO 5HFHQW PRGHOVFRQVLGHULQJLQIOXHQFHVRIVRLOPHFKDQLFDOSURSHUWLHVRQWKHK\GUDXOLFEHKDYLRUDUHXVXDOO\ EDVHGRQWKHGHSHQGHQF\RIWKHVRLOZDWHUFKDUDFWHULVWLFFXUYHVRQVRLOYROXPHVRLOGHQVLW\RU YROXPHWULFVWUDLQ 6KHQJ ,QWKLVVWXG\²DUHYLHZRISULQFLSOHVRIPRGHOLQJXQVDWXUDWHG VRLOV²LWZDVDOVRFRQFOXGHGWKDW³ZKHQFRXSOLQJWKHK\GUDXOLFFRPSRQHQWZLWKWKHPHFKDQLFDO FRPSRQHQWLQDFRQVWLWXWLYHPRGHOLWLVUHFRPPHQGHGWRWDNHLQWRDFFRXQWWKHYROXPHFKDQJH DORQJ VRLO±ZDWHU FKDUDFWHULVWLF FXUYHV 1HJOHFWLQJ WKLV YROXPH FKDQJH FDQ OHDG WR LQFRQVLVWHQW SUHGLFWLRQRIYROXPHDQGVDWXUDWLRQFKDQJHV´ 7KHUHDUHYHU\IHZVWXGLHVDSSO\LQJK\GURPHFKDQLFDOFRXSOLQJIRXQGLQWKHOLWHUDWXUH7KH PDLQDLPVRIVXFKVWXGLHVKDYHRIWHQEHHQWRDGGUHVVLVVXHVRFFXUULQJLQWKHIOXYLDOHQYLURQPHQW LH LQ WKH VHGLPHQW WUDQVIHU V\VWHP  7KHVH DUH JHQHUDOO\ FRQQHFWHG WR VHGLPHQW ORDGLQJ SUREOHPV VRXUFHV RI FRQWULEXWHV WR D ULYHU¶V VHGLPHQW EXGJHW FKDQJHG ULYHU VKDSHV FDXVHG E\ VHGLPHQWDWLRQ HWF HJ 'DUE\ HW DO  )R[ HW DO  5 *URYH &URNH  7KRPSVRQ  ,Q'DUE\HWDO  LWZDVSUHVHQWHGDPHWKRGIRUSHUIRUPDQFHRIDFRXSOHGVLPXODWLRQ RIIOXYLDOHURVLRQDQGPDVVZDVWLQJ7KHPHWKRGXVHGWRFRQVLGHUWKHG\QDPLFVRIEDQNHURVLRQ LQYROYHGVLPXODWLRQVFRXSOLQJDIOXYLDOHURVLRQPRGHOZLWK)(VHHSDJHDQDO\VLVDQG/(VWDELOLW\ PHWKRGVWKHPDVVZDVWLQJZDVVLPXODWHGWRRFFXUDVDVHULHVRIIDLOXUHHSLVRGHV(YHQWKRXJK WKDW VWXG\ ZDV OLPLWHG WR FRKHVLYH ULYHUEDQNV DQG PDLQO\ DLPHG WR ILQG D PHWKRG WR SURSHUO\ TXDQWLI\EDQNGHULYHGVHGLPHQWYROXPHVWKHWHVWLQJDQGPRGHOLQJGLGLQYROYHERWKSDUWLFOHVL]H FKDUDFWHUL]DWLRQDQGVRLOVWUHQJWKFRQVLGHUDWLRQ 7KHVKRUWIDOOQRWZLWKVWDQGLQJVRPHVWXGLHVRQODUJHVFDOHUHVHUYRLUIOXFWXDWLRQVDUHIRXQGLQ WKHOLWHUDWXUH)RULQVWDQFHLWZDVIRXQGWKDWWKHVWDELOLW\RIDUHVHUYRLUVORSHFRQVWLWXWHGE\VDQG DQG VLOW ZDV PRUH GLUHFWO\ JRYHUQHG E\ K\GUDXOLF FRQGXFWLYLWLHV WKDQ E\ ZDWHUOHYHO FKDQJH YHORFLWLHV /LDRHWDO )RUHYDOXDWLRQRIUHVHUYRLUIOXFWXDWLRQHIIHFWVRQDVLOW\VORSHWKH LPSRUWDQFHRIQHJDWLYHSRUHSUHVVXUHVIULFWLRQUHVLVWDQFHDQGZDWHUORDGVXSSRUWZDVKLJKOLJKWHG LQ =KDQ =KDQJ  &KHQ   ,Q WKDW VWXG\ VDWXUDWHGXQVDWXUDWHG VHHSDJH DQDO\VLV ZDV FRPELQHGZLWK/(VWDELOLW\DQDO\VLV$OVRLQ6KHQ=KX 

Seepage – internal erosion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ol. 19 [2014], Bund. K 2452

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³URRI´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²EXLOW IRU ORQJWHUPVWRUDJHRIGHSRVLWHGZDVWHPDWHULDOSURGXFHGLQWKHPLQLQJLQGXVWU\²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ol. 19 [2014], Bund. K 2453

$OVRPRUHUHFHQWO\GHYHORSHGQDWXUDOGDPPLQJIRUPDWLRQVKDYHEHHQLQYHVWLJDWHG,Q0H\HU HW DO   D ODQGVOLGH EORFNDJH²D GDP FRQVWLWXWHG E\ VRLO RULJLQDWLQJ IURP D GHEULV DYDODQFKH²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|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¶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¶6XOOLYDQ 7KHODWWHUDOWHUQDWLYHIRUHURVLRQVLPXODWLRQZDVKLJKOLJKWHG DOVR LQ 5HERXO HW DO   $FFRUGLQJ WR WKH DXWKRUV D FHQWUDO SDUW RI PRGHOLQJ WUDQVSRUW SURFHVVHVLQJUDQXODUPDWHULDOVLVWRFRPSXWHWKHFXPXODWLYHFRQVWULFWLRQVL]HGLVWULEXWLRQ &6'  LHWKHYRLGQHWZRUNJHRPHWULHV7KHPRGHOSURSRVHGRQO\UHTXLUHVLQIRUPDWLRQDERXWSDUWLFOH Vol. 19 [2014], Bund. K 2454

VL]H GLVWULEXWLRQ DQG H[WUHPH YRLG UDWLRV RI WKH VRLO PDWHULDO (YHQ WKRXJK OLPLWDWLRQV ZHUH LGHQWLILHG WKH PHWKRGRORJ\ ZDV IRXQG SURPLVLQJ ,Q 6KLUH  2¶6XOOLYDQ   LQWHUQDO VRLO VWDELOLW\ZDVPLFURPHFKDQLFDOO\DVVHVVHGE\'(0PRGHOLQJZKHUHDVWKHDSSURDFKLQ5HERXOHW DO   FRQFHUQHG SUREDELOLVWLF GHWHUPLQDWLRQ RI &6' %RWK VWXGLHV ZHUH EDVHG RQ WKH DVVXPSWLRQ RI SHUIHFWO\ VSKHULFDO SDUWLFOHV ,Q +LFKHU   SUHGLFWLRQV RI WKH PHFKDQLFDO EHKDYLRU RI JUDQXODU PDWHULDOV EHLQJ VXEMHFWHG WR SDUWLFOH UHPRYDO ZHUH PDGH 7KH QXPHULFDO PRGHOSUHVHQWHGZDVFRQVLGHULQJVWUHVVVWUDLQUHODWLRQVKLSVHODVWLFLW\DQGSODVWLFLW\RIVRLO WKH ODWWHUXVLQJ0RKU&RXORPESODVWLFODZ DQGVOLGLQJUHVLVWDQFHFRQQHFWHGWRYRLGUDWLR7KHPRGHO ZDVDSSOLHGRQLQWHUQDOHURVLRQSURFHVVHVDQGWKHUHVXOWVREWDLQHGZHUHIRXQGWREHLQDJUHHPHQW ZLWKUHDOREVHUYDWLRQVGRQH,WLVZRUWKPHQWLRQLQJWKDWPRGHOLQJDSSURDFKHVEDVHGRQDVVXPLQJ VRLOSDUWLFOHVWREHVSKHULFDOO\VKDSHGPLJKWLPSRUWDQWO\UHGXFHWKHUHOLDELOLW\RIWKHUHVXOWVWKHUH DUHHIIHFWVRISDUWLFOHVKDSHRQPHFKDQLFDOSURSHUWLHVRIVRLOV&KRHWDO  7KHUHOHYDQFHRI VXFKUHODWLRQVKLSVLQFOXGLQJWKHSRVVLELOLW\WRTXDQWLI\WKHVKDSHZDVSUHVHQWHGLQ5RGULJXH]  (GHVNlU  DQG5RGULJXH](GHVNl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³ILUVW´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³HURVLRQFDSDFLW\´RI ZDWHU PRYLQJ ODQGZDUG DQG WKDW RI ZDWHU PRYLQJ RXWZDUG IURP D VORSH EHLQJ H[SRVHG WR D IOXFWXDWLQJ ZDWHU OHYHO DQ DFWXDOLW\ UHODWHG WR GHJUHH RI VDWXUDWLRQ H[SODLQHG LQ - 5 'XQFDQ   7KRXJK IRU DSSOLFDWLRQ RQ UHVHUYRLUEDQN VORSHV WKLV WKHRU\ RI H[WHUQDOHURVLRQ VXVFHSWLELOLW\ EHLQJ UHGXFHG ZLWK LQFUHDVHG GHJUHH RI VDWXUDWLRQ  KDV WR EH PHUJHG DQG EDODQFHG ZLWKZKDWLVWKHFDVHIRUVXIIXVLRQDQGRWKHUVHHSDJHSURFHVVHV 5HJDUGLQJWKHODUJHVFDOH²LHLQVLWXDWLRQVZLWKKLOOVLGHVLQVWHDGRIEHDFKHVDQGZDWHUOHYHO FKDQJHVRIUHJXODWHGZDWHUFRXUVHVLQVWHDGRIZDYHVDQGWLGHV²WKHUHDUHIHZVWXGLHVWKDWVWLFNWR DFWXDOIOXFWXDWLRQ$PRQJWKHRQHVWKDWDFFRUGLQJWRWKHSDSHUWLWOHVDLPWRFRQVLGHU³YDULDWLRQV´ DQG³IOXFWXDWLRQV´PRVWDWWHQWLRQKDVDQ\ZD\QRUPDOO\EHHQSXWRQWKHGUDZGRZQSKDVH HJ Vol. 19 [2014], Bund. K 2455

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²QHHGHGWR EHIXOILOOHGIRULQWHUQDOHURVLRQWRRFFXULQHPEDQNPHQWGDPV²ZRXOGSUREDEO\EHDSSOLFDELOLW\ DOVRRQQDWXUDOVWUHDPEDQNV2QFHKDYLQJWZRZDWHUOHYHOVRIGLIIHUHQWHOHYDWLRQV SRWHQWLDOO\ FRQQHFWHG  SUHVHQW LQ VRLO WKHUH ZLOO EH JUDGLHQWV SRWHQWLDO VHHSDJH IORZV  )XUWKHUPRUH SRWHQWLDOZDWHUSDWKVDUHXQGRXEWHGO\SUHVHQWLQDQ\SRURXVPDWHULDOVDQGIORZVWKURXJKDQ\VRLO YROXPHPD\OHDGWRHURVLRQRIILQHJUDLQHGIUDFWLRQV,QDVRLOYROXPHZKHUHIORZLQJZDWHULV SUHVHQWWKHUHDUH E\GHILQLWLRQ ³H[LWV´0RUHRYHUWKHJHRORJ\DQGWKHSDUWLFOHVL]HGLVWULEXWLRQ GRJRYHUQZKHWKHUWKHVHSRWHQWLDOH[LWVDUH³XQSURWHFWHG´RUQRW(YHQWKRXJKHPEDQNPHQWGDP FRQGLWLRQV JHQHUDOO\ PHDQ SRWHQWLDO SUHVHQFH RI YHU\ KLJK K\GUDXOLF JUDGLHQWV DOVR QDWXUDO FRQGLWLRQVZRXOGEHRILQWHUHVWQRWDWOHDVWFRQVLGHULQJJUDGLHQWFKDQJHVVWUHVVUHGLVWULEXWLRQV UHFXUUHQFHDQGORQJWHUPHIIHFWV $FFRUGLQJ WR VRPH ILQGLQJV FRQFHUQLQJ WKH SURSHUWLHVSHFXOLDULWLHV RI QDWXUDO JHRORJLFDO IRUPDWLRQV VHUYLQJ DV K\GUDXOLF EDUULHUV LV LQWHUHVWLQJ 7KRXJK ORQJWHUP VWDELOLW\ RI VXFK IRUPDWLRQV LV SHUKDSV QRW DOZD\V D FRQVHTXHQFH RI H[WUDRUGLQDU\ JRRG HURVLRQUHVLVWLQJ FRQGLWLRQVEXWSRVVLEO\VRPHWLPHVDUHVXOWRIFKDQJHGSDWWHUQVRISKUHDWLFOLQHFRQQHFWLRQV HJ -DQW]HU 7RWKLVGLVFXVVLRQVKRXOGEHDGGHGDOVRWKHLQWHUHVWLQJWKRXJKWVSUHVHQWHGLQ&RVWD  6FKXVWHU   LH WKDW SHFXOLDULWLHV RI QDWXUDO GDPV HJ KRPRJHQHLW\  DUH SRWHQWLDOO\ LQFUHDVLQJ WKH VXVFHSWLELOLW\ WR LQWHUQDO HURVLRQ +RZHYHU VWDWLRQDU\ FRQGLWLRQV VHHQ LQ QDWXUDO K\GUDXOLFEDUULHUVDUHQRWFRPSDUDEOHWREDQNVORSHVIDFLQJIOXFWXDWLQJZDWHUWKHODWWHUFRQGLWLRQV PHDQ JUDGLHQW FKDQJHV DQG KRUL]RQWDO IORZV 0RUHRYHU DOO WKH FRPSRQHQWV QHHGHG WR LQLWLDWH DQGODWHUFRQWLQXH LQWHUQDOHURVLRQOLNHSURFHVVHVDUHSRWHQWLDOO\SUHVHQW (YHQWKRXJKLQWHUQDOHURVLRQKDVEHHQDWRSLFRIUHVHDUFKIRUD ORQJ WLPH WKHUH DUH VWLOO XQVROYHGLVVXHVFRQQHFWHGWRWKHFRPSOH[LW\RIWKHSURFHVVHVSHFLDOO\ZKHQLWFRPHVWRSK\VLFDO GHVFULSWLRQDQGPRGHOLQJ,WLVREYLRXVWKDWLQVWXGLHVIRFXVHGRQ³LQWHUQDOHURVLRQ´LQWKHFRQWH[W RI PDQPDGH HPEDQNPHQW GDPVWKH FRPSOH[LWLHV DQG WKH ODFN RI UHOLDEOH VLPXODWLRQ PHWKRGV KDYH EHHQ UHSHWLWLYHO\ DQG FOHDUO\ VWUHVVHG 2Q WKH RWKHU KDQG ZLWKLQ WKH ILHOG RI HURVLRQ DQG VHGLPHQWDWLRQRIVWUHDPEDQNV²UHVHDUFKWKDWLVJHQHUDOO\DLPHGWRTXDQWLI\VHGLPHQWSURGXFWLRQ DQGVXEVHTXHQWLVVXHV ²WKHUHDUHQXPHURXVUHSRUWHGDSSURDFKHVFRQVLGHULQJ³VHHSDJHHURVLRQ´ 7KHYLHZVRIKRZWKHHURVLRQVKRXOGEHGHVFULEHGDQGVLPXODWHGVHHPWREHGLIIHUHQW7KLVLV SUREDEO\ EHFDXVH RI WKH IDFW WKDW WKH XOWLPDWH JRDOV DUH QRW WKH VDPH VHGLPHQW TXDQWLILFDWLRQ YHUVXVSK\VLFDOGHVFULSWLRQRIVRLOPDWHULDOPLJUDWLRQ,QWXUQSHUKDSVWKLVH[SODLQVWKHVHYHUH ODFNRILQWHUGLVFLSOLQDU\H[FKDQJHRINQRZOHGJHDQGDYDLODEOHPHDVXUHV Vol. 19 [2014], Bund. K 2456

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ƒ 7KHODFNRIVWXGLHVDGGUHVVLQJVORSHVWDELOLW\LVVXHVUHODWHGWRZDWHUFRXUVHUHJXODWLRQ²LH WKH SUHGRPLQDQFH RI VWXGLHV RQ SXUH ELRHQYLURQPHQWDO LVVXHV²LV FRQWULEXWLQJ WR DQ XQEDODQFHGSLFWXUH5HODWLRQVKLSVEHWZHHQHIIHFWVRIK\GURORJLFDOFKDQJHVRQVORSHVWDELOLW\ DQGKXPDQVDIHW\²LHWKHFHQWUDOUROHRIJHRWHFKQLFDOSHUVSHFWLYHV²VKRXOGEHFODULILHG ƒ 6LQFHZDWHUOHYHOULVH QRWRQO\GUDZGRZQ KDVEHHQVKRZQWRVLJQLILFDQWO\LQIOXHQFHVORSH VWDELOLW\ WRJHWKHU ZLWK WKH REYLRXV ODFN RI VWXGLHV LW ZRXOG EH GHVLUDEOH WR IXUWKHU LQYHVWLJDWHWKHSURFHVVHVRIVXFWLRQORVVHIIHFWVRIUDSLGO\LQFUHDVHGZDWHUSUHVVXUHV DVZHOO LQSRUHVDVLQRWKHUGLVFRQWLQXLWLHV UHWURJUHVVLYHIDLOXUHGHYHORSPHQWHWF ƒ 0DQ\RIWKHVWXGLHVLQWHQGHGWRHYDOXDWHHIIHFWVRIZDWHUOHYHOIOXFWXDWLRQVDFWXDOO\DUHQRW ,QRUGHUWRIXOO\FRQVLGHUDOWHULQJK\GUDXOLFJUDGLHQWVVWUHVVVWUDLQFKDQJHVDQGZDWHUIURQW LQIOXHQFH ]RQHV ORQJWHUP YLHZV VKRXOG EH FHQWUDO DQDO\VLV RI VHYHUDO ULVHGUDZGRZQ F\FOHVGHWDLOHGGHVFULSWLRQRIVRLOPDWHULDOVDQGPRUHDWWHQWLRQSXWRQFRQVWLWXWLYHPRGHOV XVHGLVQHHGHG ƒ 7KH FRXSOLQJ EHWZHHQ VRLO GHIRUPDWLRQ SRUHSUHVVXUH GHYHORSPHQWDQGZDWHUIORZ FRQGLWLRQV DUH RIWHQ GHOLEHUDWHO\ RYHUORRNHG RU LQFLGHQWDOO\ PLVVHG 5HJDUGLQJ DV ZHOO JHQHUDO SRUHSUHVVXUH FRQVLGHUDWLRQ DV VSHFLILF VHHSDJH PRGHOLQJ LQWHUGLVFLSOLQDU\ DSSURDFKHVZRXOGEHEHQHILFLDOIRUIXUWKHULPSURYHPHQWV ƒ ,QRUGHUWRUHOLDEO\LQFRUSRUDWHHIIHFWVRIVHHSDJHRQVRLOSURSHUW\FKDQJLQJDVZHOODFXWH HIIHFWVDVORQJWHUPFKDQJHVKDVWREHFRQVLGHUHG7KHUHIRUHHIIHFWV RI ZDWHUOHYHO IOXFWXDWLRQV RQ VORSH VWDELOLW\ DUH KLJKO\ GHSHQGHQW RQ GHVFULSWLRQPRGHOLQJ RI LQWHUQDO HURVLRQ ƒ *LYHQ WKH LPSRUWDQW DQG FULWLFDO FRQQHFWLRQV LQYROYLQJ SRUH SUHVVXUH VRLO VWUHQJWK VRLO GHIRUPDWLRQGHYHORSPHQWSRUHSUHVVXUHFKDQJH DQGVRRQ DQDO\VHVKDYHWREHSHUIRUPHG XVLQJUREXVWVLPXODWLRQDSSURDFKHV7KHWHUPV³VLPSOLFLW\´DQG³DSSOLFDELOLW\´ SURPRWLQJ Vol. 19 [2014], Bund. K 2457

XVH RI /(PHWKRGV  DUH WKHUHIRUH WR EH UHODWHG WR DFFXUDF\ DQG UREXVWQHVV RI PHWKRGV FRQVLGHULQJDOVRGHIRUPDWLRQVHVSHFLDOO\IRUV\VWHPVRIVRLODQGPRYLQJZDWHU

ACKNOWLEDGEMENTS 7KLVZRUNZDVFDUULHGRXWDW/XOHn8QLYHUVLW\RI7HFKQRORJ\DQGVXSSRUWHGE\WKH6ZHGLVK +\GURSRZHU&HQWUH 69& DQRUJDQL]DWLRQHVWDEOLVKHGE\WKH6ZHGLVK(QHUJ\$JHQF\(OIRUVN DQG 6YHQVND .UDIWQlW WRJHWKHU ZLWK /XOHn 8QLYHUVLW\ RI 7HFKQRORJ\ 7KH 5R\DO ,QVWLWXWH RI 7HFKQRORJ\&KDOPHUV8QLYHUVLW\RI7HFKQRORJ\DQG8SSVDOD8QLYHUVLW\3DUWLFLSDWLQJDJHQFLHV FRPSDQLHV DQG LQGXVWU\ DVVRFLDWLRQV DUH $OVWRP +\GUR 6ZHGHQ $QGULW] +\GUR (QHUJLP\QGLJKHWHQ (21 9DWWHQNUDIW 6YHULJH )DOX (QHUJL RFK 9DWWHQ )RUWXP *HQHUDWLRQ +ROPHQ(QHUJL-lPWNUDIW-|QN|SLQJ(QHUJL.DUOVWDGV(QHUJL0lODUHQHUJL1RUFRQVXOW3|\U\ 6ZHG3RZHU 6NHOOHIWHn .UDIW 6ROOHIWHnIRUVHQV 6WDWNUDIW 6YHULJH 6YH0LQ 6YHQVND .UDIWQlW 6ZHFR,QIUDVWUXFWXUH6ZHFR(QHUJXLGH8PHn(QHUJL9DWWHQIDOO9DWWHQNUDIW9*3RZHU:63 DQGc) REFERENCES  $O7DLH / 3XVFK 5  .QXWVVRQ 6   +\GUDXOLF SURSHUWLHV RI VPHFWLWH ULFK FOD\ FRQWUROOHGE\K\GUDXOLFJUDGLHQWVDQGILOWHUW\SHV$SSOLHG&OD\6FLHQFHYROSS±  $U\DO . 3   6ORSH VWDELOLW\ HYDOXDWLRQV E\ OLPLW HTXLOLEULXP DQG ILQLWH HOHPHQW PHWKRGV1RUZHJLDQ8QLYHUVLW\RI6FLHQFHDQG7HFKQRORJ\  %DNKW\DU5%DUU\'$/L/-HQJ'6 

 &RMHDQ 5  &Dw < -   $QDO\VLV DQG PRGHOLQJ RI VORSH VWDELOLW\ LQ WKH 7KUHH *RUJHV 'DP UHVHUYRLU &KLQD  ² 7KH FDVH RI +XDQJWXSR ODQGVOLGH -RXUQDO RI 0RXQWDLQ 6FLHQFHYROQRSS±  &RQQROO\'  7KHLQWHJUDWLRQRIIOXFWXDWLQJUHQHZDEOHHQHUJ\XVLQJHQHUJ\VWRUDJH 3K'WKHVLV8QLYHUVLW\RI/LPHULFN/LPHULFN,UHODQG  &RQQROO\'/XQG+0DWKLHVHQ%93LFDQ( /HDK\0  7KHWHFKQLFDODQG HFRQRPLF LPSOLFDWLRQV RI LQWHJUDWLQJ IOXFWXDWLQJ UHQHZDEOH HQHUJ\XVLQJHQHUJ\VWRUDJH 5HQHZDEOH(QHUJ\YROSS±  &RVWD -  6FKXVWHU 5   7KH IRUPDWLRQ DQG IDLOXUH RI QDWXUDO GDPV *HRORJLFDO 6RFLHW\RI$PHULFD  'DKOElFN 1   8WYHFNOLQJVEHKRY LQRP UHJOHUNUDIWVRPUnGHW XU HWW YDWWHQNUDIWSHUVSHNWLY6WRFNKROP  'DUE\6(5LQDOGL0 'DSSRUWR6  &RXSOHGVLPXODWLRQVRIIOXYLDOHURVLRQDQG PDVVZDVWLQJIRUFRKHVLYHULYHUEDQNV-RXUQDORI*HRSK\VLFDO5HVHDUFKYROQR) SS)  'HDQH - 3 Ï *DOODFKyLU % 3  0F.HRJK ( -  7HFKQRHFRQRPLF UHYLHZ RI H[LVWLQJDQGQHZSXPSHGK\GURHQHUJ\VWRUDJHSODQW5HQHZDEOHDQG6XVWDLQDEOH(QHUJ\ 5HYLHZVYROQRSS±  'RQDOG , %  &KHQ =   6ORSH VWDELOLW\ DQDO\VLV E\ WKH XSSHU ERXQG DSSURDFK IXQGDPHQWDOVDQGPHWKRGV&DQDGLDQ*HRWHFKQLFDO-RXUQDOYROQRSS±  'XQFDQ-0  6WDWHRIWKH$UW/LPLW(TXLOLEULXPDQG)LQLWH(OHPHQW$QDO\VLVRI 6ORSHV-RXUQDORI*HRWHFKQLFDO(QJLQHHULQJYROQRSS±  'XQFDQ - 0  :ULJKW 6 *   7KH DFFXUDF\ RI HTXLOLEULXP PHWKRGV RI VORSH VWDELOLW\DQDO\VLV(QJLQHHULQJ*HRORJ\YROQRSS±  'XQFDQ - 0  :ULJKW 6 *   6RLO 6WUHQJWK DQG 6ORSH 6WDELOLW\ +RERNHQ 1HZ -HUVH\-RKQ:LOH\ 6RQV,QF  'XQFDQ-5  7KHHIIHFWVRIZDWHUWDEOHDQGWLGHF\FOHRQVZDVKEDFNZDVKVHGLPHQW GLVWULEXWLRQDQGEHDFKSURILOHGHYHORSPHQW0DULQH*HRORJ\YROQRSS± (PHU\. )RVWHU-  :DWHUWDEOHVLQPDULQHEHDFKHV -RXUQDO RI 0DULQH 5HVHDUFKYROSS±  )HOO50DF*UHJRU36WDSOHGRQ' %HOO*  *HRWHFKQLFDOHQJLQHHULQJRIGDPV /RQGRQ7D\ORU )UDQFLV  )HOO 5 :DQ & ) &\JDQLHZLF] -  )RVWHU 0   7LPH IRU 'HYHORSPHQW RI ,QWHUQDO (URVLRQ DQG 3LSLQJ LQ (PEDQNPHQW 'DPV -RXUQDO RI *HRWHFKQLFDO DQG *HRHQYLURQPHQWDO(QJLQHHULQJYROQRSS±  )RVWHU 0  )HOO 5   $VVHVVLQJ (PEDQNPHQW 'DP )LOWHUV 7KDW 'R 1RW 6DWLVI\ 'HVLJQ&ULWHULD-RXUQDORI*HRWHFKQLFDODQG*HRHQYLURQPHQWDO(QJLQHHULQJYROQR SS±  )R[*$:LOVRQ*96LPRQ$/DQJHQGRHQ(-$ND\2 )XFKV-:   0HDVXULQJVWUHDPEDQNHURVLRQGXHWRJURXQGZDWHUVHHSDJHFRUUHODWLRQWREDQNSRUHZDWHU Vol. 19 [2014], Bund. K 2459

SUHVVXUH SUHFLSLWDWLRQ DQG VWUHDP VWDJH (DUWK 6XUIDFH 3URFHVVHV DQG /DQGIRUPV YRO  QRSS±  )UHGOXQG' 0RUJHQVWHUQ1  6WUHVVVWDWHYDULDEOHVIRUXQVDWXUDWHGVRLOV-RXUQDO RI*HRWHFKQLFDODQG*HRHQYLURQPHQWDO(QJLQHHULQJYROQR*7SS±  )UHGOXQG ' ;LQJ $  +XDQJ 6   3UHGLFWLQJ WKH SHUPHDELOLW\ IXQFWLRQ IRU XQVDWXUDWHGVRLOVXVLQJWKHVRLOZDWHUFKDUDFWHULVWLFFXUYH&DQDGLDQ*HRWHFKQLFDO-RXUQDO YROQRSS±  *DODYL9  ,QWHUQDO5HSRUW*URXQGZDWHUIORZIXOO\FRXSOHGIORZGHIRUPDWLRQDQG XQGUDLQHGDQDO\VHVLQ3/$;,6'DQG'  *UDQW 8   ,QIOXHQFH RI WKH ZDWHU WDEOH RQ EHDFK DJJUDGDWLRQ DQG GHJUDGDWLRQ -RXUQDORI0DULQH5HVHDUFKYROSS±  +LFKHU 3<   0RGHOOLQJ WKH LPSDFW RI SDUWLFOH UHPRYDO RQ JUDQXODU PDWHULDO EHKDYLRXU*pRWHFKQLTXHYROQRSS±  +X;7DQJ+/L& 6XQ5  6WDELOLW\RI+XDQJWXSRULYHUVLGHVOXPSLQJPDVV ,,XQGHUZDWHUOHYHOIOXFWXDWLRQRI7KUHH*RUJHV5HVHUYRLU-RXUQDORI(DUWK6FLHQFHYRO QRSS±  +XDQJ0 -LD&4  6WUHQJWKUHGXFWLRQ)(0LQVWDELOLW\DQDO\VLVRIVRLOVORSHV VXEMHFWHGWRWUDQVLHQWXQVDWXUDWHGVHHSDJH&RPSXWHUVDQG*HRWHFKQLFVYROQRSS ±  +XSS&  5LSDULDQYHJHWDWLRQUHFRYHU\SDWWHUQVIROORZLQJVWUHDPFKDQQHOL]DWLRQD JHRPRUSKLFSHUVSHFWLYH(FRORJ\YROQRSS±  ,NDUG 6 - 5HYLO D 6FKPXW] 0 .DUDRXOLV 0 -DUGDQL D  0RRQH\ 0   &KDUDFWHUL]DWLRQ RI )RFXVHG 6HHSDJH 7KURXJK DQ (DUWKILOO 'DP 8VLQJ *HRHOHFWULFDO 0HWKRGV*URXQGZDWHU  ,YHUVRQ50  /DQGVOLGHWULJJHULQJE\UDLQLQILOWUDWLRQ:DWHU5HVRXUFHV5HVHDUFK YROQRSS±  -DQW]HU ,   &ULWLFDO +\GUDXOLF *UDGLHQWV LQ 7DLOLQJV 'DPV &RPSDULVRQ $QDORJLHV &RPSDULVRQWRQDWXUDODQDORJLHV/XOHn8QLYHUVLW\RI7HFKQRORJ\  -LD*:=KDQ7/7&KHQ<0 )UHGOXQG'*  3HUIRUPDQFHRIDODUJH VFDOHVORSHPRGHOVXEMHFWHGWRULVLQJDQGORZHULQJZDWHUOHYHOV(QJLQHHULQJ*HRORJ\YRO QRSS±  .DF]PDUHN -  /HĞQLHZVND '   0RGHOOLQJ (YHQWV 2FFXUULQJ LQ WKH &RUH RI D )ORRG %DQN DQG ,QLWLDWHG E\ &KDQJHV LQ WKH *URXQGZDWHU /HYHO ,QFOXGLQJ WKH (IIHFW RI 6HHSDJH7HFKQLFDO6FLHQFHVYROQR  .HQQH\ 7 &  /DX '   ,QWHUQDO VWDELOLW\ RI JUDQXODU ILOWHUV &DQDGLDQ *HRWHFKQLFDO-RXUQDOYROQRSS±  .UDKQ-  7KH50+DUG\/HFWXUH7KHOLPLWVRIOLPLWHTXLOLEULXPDQDO\VHV &DQDGLDQ*HRWHFKQLFDO-RXUQDOYROQRSS±  /DIOHXU-0O\QDUHN- 5ROOLQ$/  )LOWUDWLRQRI%URDGO\*UDGHG&RKHVLRQOHVV 6RLOV-RXUQDORI*HRWHFKQLFDO(QJLQHHULQJYROQRSS± Vol. 19 [2014], Bund. K 2460

 /DQH 3 $  *ULIILWKV ' 9   6ORSH VWDELOLW\ DQDO\VLV E\ ILQLWH HOHPHQWV *pRWHFKQLTXHYROQRSS±  /DQH3$ *ULIILWKV'9  $VVHVVPHQWRI6WDELOLW\RI6ORSHVXQGHU'UDZGRZQ &RQGLWLRQV-RXUQDORI*HRWHFKQLFDODQG*HRHQYLURQPHQWDO(QJLQHHULQJYROQRSS ±  /L / %DUU\ ' $ 3DUODQJH -<  3DWWLDUDWFKL & %   %HDFK ZDWHU WDEOH IOXFWXDWLRQVGXHWRZDYHUXQXS&DSLOODULW\HIIHFWV:DWHU5HVRXUFHV5HVHDUFKYROQR SS±  /L / %DUU\ ' $  3DWWLDUDWFKL & %   1XPHULFDO PRGHOOLQJ RI WLGHLQGXFHG EHDFKZDWHUWDEOHIOXFWXDWLRQV&RDVWDO(QJLQHHULQJYROQRSS±  /L / %DUU\ ' 6WDJQLWWL ) 3DUODQJH -<  -HQJ '6   %HDFK ZDWHU WDEOH IOXFWXDWLRQV GXH WR VSULQJ±QHDS WLGHV PRYLQJ ERXQGDU\ HIIHFWV $GYDQFHV LQ :DWHU 5HVRXUFHVYROQRSS±  /LDR +

 3XJK'7  7LGHV6XUJHVDQG0HDQ6HD/HYHO0DULQHDQG3HWUROHXP*HRORJ\ 9RO S -RKQ:LOH\ 6RQV,QF  5 *URYH - &URNH -  7KRPSVRQ &   4XDQWLI\LQJ GLIIHUHQW ULYHUEDQN HURVLRQ SURFHVVHVGXULQJDQH[WUHPHIORRGHYHQW(DUWK6XUIDFH3URFHVVHVDQG/DQGIRUPVYRO QR)HEUXDU\SSQD±QD  5DPDOKR564XDUWDX57UHQKDLOH$60LWFKHOO1&:RRGURIIH&' ÈYLOD6 3   &RDVWDO HYROXWLRQ RQ YROFDQLF RFHDQLF LVODQGV $ FRPSOH[ LQWHUSOD\ EHWZHHQ YROFDQLVPHURVLRQVHGLPHQWDWLRQVHDOHYHOFKDQJHDQGELRJHQLFSURGXFWLRQ(DUWK6FLHQFH 5HYLHZVYROSS±  5DXEHQKHLPHU%*X]D57 (OJDU6  7LGDOZDWHUWDEOHIOXFWXDWLRQVLQDVDQG\ RFHDQEHDFK:DWHU5HVRXUFHV5HVHDUFKYROQRSS±  5HERXO 1 9LQFHQV (  &DPERX %   $ FRPSXWDWLRQDO SURFHGXUH WR DVVHVV WKH GLVWULEXWLRQ RI FRQVWULFWLRQ VL]HV IRU DQ DVVHPEO\ RIVSKHUHV &RPSXWHUV DQG *HRWHFKQLFV YROQRSS±  5(1  5HQHZDEOHV*OREDO6WDWXV5HSRUW  5RGULJXH]- (GHVNlU7  &DVHRIVWXG\RQSDUWLFOHVKDSHDQGIULFWLRQDQJOHRQ WDLOLQJV-RXUQDORI$GYDQFHG6FLHQFHDQG(QJLQHHULQJ5HVHDUFKYROQRSS±  5RGULJXH] - (GHVNlU 7  .QXWVVRQ 6   3DUWLFOH 6KDSH 4XDQWLWLHV DQG 0HDVXUHPHQW7HFKQLTXHV±$5HYLHZ(OHFWURQLFDO-RXUQDORI*HRWHFKQLFDO(QJLQHHULQJYRO SS±  5RJQOLHQ / 0   3XPSHG VWRUDJH K\GURSRZHU GHYHORSPHQW LQ ‘YUH 2WUD 1RUZD\ 1RUZHJLDQ8QLYHUVLW\RI6FLHQFHDQG7HFKQRORJ\  5|QQTYLVW + )   $VVHVVLQJ WKH 3RWHQWLDO IRU ,QWHUQDO (URVLRQ LQ *ODFLDO 0RUDLQH &RUH (PEDQNPHQW 'DPV ,Q ,QWHUQDWLRQDO &RQIHUHQFH RQ 6PDOO +\GURSRZHU .DQG\ 6UL /DQND2FWREHU  6KHQ<=KX' 

6WRMVDYOMHYLF-'-HQJ'66H\PRXU%5 3RNUDMDF '   +LJKHU RUGHU DQDO\WLFDOVROXWLRQVRIZDWHUWDEOHIOXFWXDWLRQVLQFRDVWDODTXLIHUV*URXQGZDWHUYRO QRSS±  6ZDWKL% (OGKR7,  *URXQGZDWHUIORZVLPXODWLRQLQFRQILQHGDTXLIHUVXVLQJ 0HVKOHVV /RFDO 3HWURY*DOHUNLQ 0/3*  PHWKRG ,6+ -RXUQDO RI +\GUDXOLF (QJLQHHULQJ YROQRSS±  6YHQVND (QHUJLP\QGLJKHWHQ   9DWWHQNUDIWHQ RFK HQHUJLV\VWHPHW(5  (VNLOVWXQD6ZHGHQ  6YHQVND.UDIWQlW  6WRUVNDOLJXWE\JJQDGDYYLQGNUDIW 9RO   7HR + 7 -HQJ ' 6 6H\PRXU % 5 %DUU\ ' D  /L /   $QHZ DQDO\WLFDO VROXWLRQIRUZDWHUWDEOHIOXFWXDWLRQVLQFRDVWDODTXLIHUVZLWKVORSLQJEHDFKHV$GYDQFHVLQ :DWHU5HVRXUFHVYROQRSS±  7KRPDV$(OGKR7, 5DVWRJLD.  $FRPSDUDWLYHVWXG\RISRLQWFROORFDWLRQ EDVHG0HVK)UHHDQGILQLWHHOHPHQWPHWKRGVIRUJURXQGZDWHUIORZVLPXODWLRQ,6+-RXUQDO RI+\GUDXOLF(QJLQHHULQJQR-DQXDU\SS±  7RKDUL $ 1LVKLJDNL 0  .RPDWVX 0   /DERUDWRU\ 5DLQIDOO,QGXFHG 6ORSH )DLOXUH ZLWK 0RLVWXUH &RQWHQW 0HDVXUHPHQW -RXUQDO RI *HRWHFKQLFDO DQG *HRHQYLURQPHQWDO(QJLQHHULQJYROQRSS±  7VDL 7/ 



  ‹HMJH 



Paper B

Modelling approaches considering impacts of water-level fluctuations on slope stability

J. M. Johansson and T. Edeskär

To be submitted

Modelling approaches considering impacts of water-level fluctuations on slope stability

Jens M.A. Johansson1; Tommy Edeskär2

Abstract Waterfront slopes are affected by water-level fluctuations originating from as well natural sources (e.g. tides and wind waves), as non-natural sources such as watercourse regulation involving daily or hourly recurring water-level fluctuations. Potentially instable slopes in populated areas means risks for as well property as human lives. In this study, three different approaches used for hydro-mechanical coupling in FEM-modelling of slope stability, have been evaluated. A fictive slope consisting of a till-like soil material has been modeled to be exposed to a series of water- level fluctuation cycles (WLFC’s). Modelling based on assuming fully saturated conditions, and with computations of flow and deformations separately run, has been put against two approaches being more sophisticated, with unsaturated-soil behavior considered and with computations of pore-pressures and deformations simultaneously run. Development of stability, vertical displacements, pore pressures, flow, and model-parameter influence, has been investigated for an increased number of WLFC’s. It was found that more advanced approaches did allow for capturing larger variations of flow and pore pressures. Classical modelling resulted in smaller vertical displacements, and smoother development of pore-pressure and flow. Flow patterns, changes of soil density (linked to volume changes governed by suction fluctuations), and changes of hydraulic conductivity, are all factors governing as well water- transport (e.g. efficiency of dissipation of excess pore pressures) as soil-material transport (i.e. susceptibility to internal erosion to be initiated and/or continued). Therefore, the results shown underline potential strengths of sophisticated modelling. Parameter influence was shown to change during water-level cycling.

Key words: Hydro-mechanical coupling; Water-level fluctuations; Slope stability; Unsaturated soil; FEM-analysis; Parameter influence

1 Introduction When it comes to recurring water-level fluctuations in watercourses and reservoirs, effects of hydrological changes on slope stability are often overlooked. There is a predominance of studies focused on bioenvironmental issues [1]. The activity of watercourse regulation for water storage, enabling irrigation, freshwater provision, and hydropower production, often means occurrence of water-level fluctuations (e.g. [2–4]). The growing use of non-regulated energy sources (e.g. wind and solar) [5, 2, 6, 7]—bringing significant emphasis put on wind-power development and exploitation—entails a need of energy balancing by water storage in reservoirs. According to [8], this will necessarily require that flow magnitudes and water level heights, to a greater extent than until present, will vary in the future. It is highly expected to get increased variations of the reservoir water levels; hour to hour, day to day and/or seasonally [9, 2, 4]. The process of rapid drawdown is described and investigated by many authors e.g. [10–13]. Also water- level rise might cause problems. In studies concerning the Three Gorges Dam site (e.g. [14]), slope stability reductions registered during periods of water-level rise, have been reported. Rise of water levels has been shown to cause stress redistributions due to external loading, wetting induced loss of negative pore pressures, and seepage effects. Subsequently, these changes have been shown to potentially cause loss of shear strength, soil structure collapse, and development of settlements and/or slope failure [15]. It has been emphasized that a delayed change of pore water pressure inside a slope—relative to the external water level—may result in significant movements of water within the slope; creating seepage forces being adversely affecting the stability [15]. Despite well-known limitations of limit-equilibrium methods (LEM) (e.g. [11, 16]), these are well established and widely used. For capturing important relations between pore pressure, soil strength, and

1 Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology 2 Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology

1 soil-deformation development, the use of finite-element methods (FEM) have been more and more spread. Long-term perspectives are important for consideration of altering hydraulic gradients, stress-strain changes, and development of influenced waterfront zones. Still, reliable relationships between soil deformation, pore-pressure development, and unsteady water-flow conditions are often deliberately overlooked or incidentally missed [1]. Though, improved accessibility of high computer capacity allows for more and more advanced analyses to be performed. In addition, optimized designs and constructions are increasingly demanded and less conservative design approaches are therefore often desired. This is not at least linked to economic and environmental aspects. One non-conservative view in slope-stability analysis regards consideration of negative pore pressures in unsaturated soils. Taking into account negative pore pressures is generally associated with counting on extra contributions to the shear strength of the soil, resulting in extra slope stability. The well-known and widely used Terzaghi´s equation of effective-stress ( – u) is simply based upon the difference between the total stress, and the pore pressure, u. The equation implies that there are only two possible soil conditions; (1) presence of pore pressure coming from fully water filled pores, and (2) no pore pressure. The validity of this expression is widely accepted in saturated soil mechanics, but has since a long time been found to not be applicable for partly saturated conditions, e.g. [17]. The possibility to control the mechanical response of unsaturated soils by considering two stress-state variables—(1) net stress, i.e. the difference between the total stress and the pore-air pressure, and (2) suction, i.e. the difference between the pore-air pressure and the pore-water pressure—was firstly demonstrated by [18]. Though, the earliest effective-stress equation for consideration of a varying degree of saturation and suction was presented by Bishop in the end of the 1950th. For description of the amount of water being present in unsaturated soils, soil-water characteristic curves (SWCC) are important. The degree of saturation, (among other alternatively use quantities) appears to most closely control the behavior of unsaturated soil [19]. For proper consideration of the behavior of unsaturated soils, fully coupled hydro-mechanical computations are needed (e.g. [20–22]). Among studies with hydro-mechanical approaches applied, many are addressing sediment-loading problems; sources, changed river shapes caused by sedimentation etc. (e.g. [23–25]). Consequently, the slope-stability part is often either absent or considered by using LEM-approaches (e.g. [26–28]). There are a few studies addressing effects of large-scale reservoir water-level fluctuations on slope stability; e.g. [29] where saturated-unsaturated seepage analysis was combined with LEM-stability analysis, and [30] where evaluation of the approach of analyzing stability using critical slip fields. The complexity of how factors such as drawdown rate, permeability, and slope height actually do influence the stability of a slope subjected to drawdown, was discussed in [20]. In [31] it was emphasized the misconception concerning that analysis approaches considering principles of unsaturated soil mechanics are always less conservative than are classical ones. It was stated that the overall subject is at its early stage, that there are numerous areas in which practical application of the principles of unsaturated soil mechanics are central, and that as well experimental as theoretical advances are expected. The present study is aimed to evaluate results from three approaches of hydro-mechanical coupling in FEM-modelling of slope stability; (1) semi-coupled modelling, (2) fully coupled modelling, and (3) fully coupled modelling, but with negative pore pressures neglected in stability computations. In (1) flow computations were run prior to those of deformations, and Terzaghi’s effective-stress definition was used. In (2) pore-pressure development and deformations were simultaneously computed, utilizing Bishop’s effective-stress definition, considering also the behavior of unsaturated soils. Approach (3) is similar to (2), but with suction effects in stability computation neglected. A fictive waterfront bank slope consisting of a well-graded postglacial till, typical for Swedish conditions, was modeled to be subjected to a series of water-level-fluctuation cycles (WLFC’s). Development of stability (in terms of factors of safety, FOS), vertical displacements, pore pressures, flow, and model-parameter influence, was investigated for an increased number of WLFC’s. The modelling was performed by use of the software PLAXIS 2D 2012 [32], allowing for consideration of transient flow and performance of coupled hydro-mechanical computations. Moreover, parameter-influence analysis was performed with respect to FOS’s calculated using the strength reduction technique; i.e. the parameter-influence development with an increased number of WLFC’s was investigated.

2

2 Methodology 2.1 Model design and preparations 2.1.1 Geometry, materials, and definition of changes

The model geometry was defined aimed to represent one half of a watercourse cross section. The slope height was set to 30 m, and the slope inclination to 1:2 (26.6°) (Figure 2-1); both measures considered to be representative for a watercourse slope consisting of a well-graded till, typical for Swedish conditions (properties presented in Table 1). 15-noded triangular elements were used. The vertical model boundaries were set to be horizontally fixed and free to move vertically, whereas the bottom boundary was completely fixed. The left vertical boundary was assumed to have properties of a symmetry line, and the model bottom to represent a material being dense and stiff relative to the soil above. Therefore, as well the left vertical hydraulic boundary as the horizontal bottom, were defined as closed (impermeable). The right vertical boundary was defined to be assigned pore pressures by the head, simulating allowed in/out flow. Data-collection points were placed where interesting changes would be expected; at the crest, down along the slope surface, and along a vertical line below the crest. The initial water-level position was set to +22.0 m (with the level of the watercourse bottom at ± 0 m), the level-change magnitude to 5.0 m (linearly lowered and raised), and the rate to 1.0 m/day. In [33] situations with daily magnitudes of water-level variations in pumped-storage hydropower (PSH) in the order of 10 m were discussed, and in [20] a rate of 1 m/day was used in rapid drawdown analysis. Since this study is comparative, the rate used was chosen in order to create a stability reduction at drawdown, avoid failure, and still be within a relevant and representative range. The water-level changes were run continuously; i.e. without allowing pore pressures to even out.

Figure 2-1: Model geometry. Dimensions, initial water level (WLinitial), and the pre-defined data-collection points—one at the crest (A) and one at the level +22 m (B)—are shown in the figure.

3

Table 1: Model input data used. Unit Value Comments General

Drainage type - - Drained 3 Unsaturated weight kN/m 19.00 Typical value 3 Saturated weight kN/m 21.00 Typical value Soil description

Young´s modulus kN/m2 40 000 2) Poisson´s ratio - 0.30 2) Cohesion kN/m2 8 Low, non-zero Friction angle ° 36 Typical value Dilatancy angle ° 3 Meeting the recommendation Hydraulic description

Model van Genuchten

Data set - - - Defined in order to be representative 1) Permeability, x m/day 0.05 Found to be representative (e.g. Lafleur, 1984) Permeability, y m/day 0.05 Found to be representative (e.g. Lafleur, 1984) Saturated degr. of sat. - 1.0 1) Residual degr. of sat. - 0.026 1) - - 1.169 Parameter linked to water extraction 1) - - 2.490 Parameter linked to air entry 1) - - 0 Parameter linked to pore connectivity 1) The data set was manually defined by using the parameters listed. The values of the parameters , , , , and were chosen based on examples in [22], comments in [35], and the pre-defined data set Hypres available in PLAXIS 2D 2012 [36]. 2) Within ranges presented in [37]; Young´s modulus for a loose glacial till (10-150 MPa), and for a medium/compact sand (30-50 MPa), at - .

NOTE: Since the result evaluation is comparative, the values of the parameters chosen are not critical.

2.2 Modelling strategy 2.2.1 Approaches evaluated

Approach 1 (A1): The computations were performed using Terzaghi's definition of stress, i.e. [ ], where is the normal stress, is the effective normal stress, and is the pore pressure consisting of steady-state pore pressure (from the phreatic level or groundwater flow computations) and excess pore pressure (coming from undrained behavior or consolidation; i.e. temporal pore-pressure changes governed by the WLF’s and captured by consideration of transient water flow). In this semi-coupled approach, flow computations were run prior to the deformation computations. Pore pressures from the flow computations were, for each time step, used in the deformation computation for the corresponding time step. The consolidation computations were based on excess pore pressures.

Approach 2 (A2): For the fully coupled approach Bishop’s effective-stress equation was used. The consolidation computations were based on the Biot’s theory of consolidation [38]; i.e. using total pore pressures with no distinction made between steady state and excess pore pressures.

Approach 3 (A3): Computations run like in A2, but with stability computations run without consideration of negative pore pressures.

4

2.2.2 Behavior of unsaturated soil

For the fully coupled approaches (A2 and A3), Bishop’s effective-stress equation was used, allowing for capturing the unsaturated soil behavior:

( ) (2.1) where is the pore-air pressure, the pore-water pressure, and the experimentally determined matric- suction coefficient being related to the degree of saturation, . The experimental evidences of are sparse [22], and the role of the parameter has been generally questioned [19]. In PLAXIS 2D 2012 the matric- suction coefficient is substituted with the effective degree of saturation, , defined as:

( ) ( ) (2.2) where is the degree of saturation and the indices max and min denote maximum and minimum values. Moreover, in this study the air-pore pressure is assumed to be negligibly low, whereupon the effective stress is simply expressed as:

(2.3) The effective degree of saturation is used also for definition of actual soil unit weight, :

( ) (2.4) where the indices denote unsaturated and saturated conditions.

2.2.3 Models used

The constitutive behavior of the soil was described by Mohr-Coulomb’s elastic-perfectly plastic model. This model was chosen for three reasons; (1) it is well-established and widely used by engineers, (2) as soon as the stability analysis is started (performed using the strength reduction technique), any model defined with the same strength parameters would behave like the Mohr-Coulomb model (i.e. stress dependent stiffness is excluded), (3) the study is comparative whereupon differences between the modelling approaches evaluated are focused rather than the accuracy of the soil description. For other permissions/claims, models like e.g. the Hardening soil model [32] (allowing for description of more realistic elastic-plastic behaviors), or the Basic Barcelona Model [39] (specifically developed for description of the stress-strain behavior in unsaturated soils), could have been used. The soil was defined by the variables listed in Table 1. The elastic behavior is described by the parameters Young´s modulus, and Poisson´s ratio, . The full three-dimensional yield criterion consists of six yield functions; two functions in each plane of stress pairs. Each yield function depends on one stress pair (one combination of the principal effective stresses), the friction angle, and the cohesion, . These are defining the ultimate state up to which the strains are elastic; for stress conditions entailing that the yield function is reached, the strain response becomes perfectly plastic. For these conditions the strain magnitudes are determined using flow rules based on plastic potential functions. These are—similar to the yield functions—depending on the stress state, but are consisting of three plastic parameters; in addition to the friction angle, and the cohesion, , also the dilatancy angle, . This parameter is used for description of additional resistance against shearing, originating from dilatant behavior. For description of hydraulic behavior in the soil, van Genuchten’s model [40] was used. The important role of the hydraulic model is to properly define the degree of saturation, as a function of suction pore- pressure head, . This relation, often presented in soil-water characteristic curves (SWCC), is expressed:

(2.5) ( ) ( )[ ( | |) ]

5

where is the residual degree of saturation, is the saturated degree of saturation, is an empirical parameter describing air entry, and is an empirical parameter related to the water extraction from the soil. The relative permeability, ( ) is expressed as:

( ) [ ( ) ] (2.6)

where is an empirical parameter. The relative permeability is in the flow computation reducing the permeability according to ( ⁄ ) where is the saturated permeability.

2.2.4 Factor of safety

The strength reduction (or phi/c-reduction) technique is based on FOS’s defined as the ratio between the available shear strength and the shear stress at failure. In PLAXIS 2D 2012 this is mathematically handled by expressing ratios of the strength parameters:

(2.7)

where is a controlling multiplier representing the safety factor; c is the cohesion; is the friction angle; and the index reduced indicates values being successively decreased until failure occurs. For indication of global instability of soil slopes, the non-convergence of solutions is often used. This is indicated by the condition when a stress state at which the failure criterion and the global equilibrium can be simultaneously satisfied, is not found [10].

2.2.5 Parameter-sensitivity analysis

The parameter influence was investigated with respect to changed FOS. For each parameter, a maximum and a minimum value were defined spanning a representative interval within which the reference value for each parameter (presented in Table 1) was located. The theories used are based on the ratio of the percentage change of the result, and the percentage change of input (creating the output change); explained in e.g. [41]. The sensitivity ratio [42] is expressed as:

( ) ( ) ( )⁄( ) (2.8) ( ) where the output values are functions, of the input values, for which no index represents the reference input values and the index U,L represents the changed ones; upper/lower. In order to increase the robustness [32] of the analysis, the sensitivity ratio was weighted by a normalized variability measure. This was done using a sensitivity score, , defined as the ratio of the range itself and the variable mean value [42]:

( ) (2.9)

where and define the range limits, and is the mean (reference) value. The total sensitivity was then calculated as:

6

( ) (2.10) ∑ ( )

where and are the sensitivity scores connected to the upper and lower parameter value, respectively, and ∑ is the sum the sensitivity scores of all parameter combinations. Five model parameters were considered in the analysis; the variation boundaries are presented in Table 2. For each parameter, one computation was run for each range boundary, keeping the other parameters fixed. This was giving the sensitivity ratios (eq. 2.8) and the sensitivity scores (eq. 2.9). The total scores (eq. 2.10) were then plotted.

Table 2: Soil parameters used in the sensitivity analysis (Min and Max), and the reference values.

E (MPa) v (-) (°) c (kPa) (°) Min Ref Max Min Ref Max Min Ref Max Min Ref Max Min Ref Max 20 40 60 0.25 0.30 0.35 33 36 39 1 8 15 0 3 6

2.3 Computations The computations were performed in PLAXIS 2D 2012 [32]. This FEM-code was used since it is well- established and providing what was needed. The bank was assumed to be infinite in the direction perpendicular to the model plane; i.e. 2D plain-strain conditions were assumed. A1 was performed in Classical calculation mode whereas A2 and A3 were run in Advanced mode. The initial stress situation was determined by a Gravity loading phase; providing initial stresses generated based on the volumetric weight of the soil (this since the non-horizontal upper model boundary means that the K0-procedure is not suitable). Then a plastic nil-step was run, solving existing out-of-balance forces and restoring stress equilibrium. The WLFC’s were defined in separate calculation steps; one drawdown-rise cycle in each. Each WLFC was followed by a FOS-computation. In A3, each FOS-computation was preceded by a plastic nil-step; this to restore the stress equilibrium in order to omit consideration of negative pore pressures. Sensitivity analyses were carried out for the three approaches.

3 Results and comments 3.1 Stability In Figure 3-1 the failure plots from A1 are shown; conditions at the initial stage (Init.), after one rapid drawdown (RDD), and after one WLFC (1). Fully developed failure surfaces were found for all WLFC’s in all of the approaches.

Init. RDD 1

Figure 3-1: Failure surfaces for the initial condition, after one rapid drawdown, and after one WLFC, for approach A1.

The changed failure-surface geometry—moved upward at drawdown—shows the supporting effect of the external water level. Since the slope was stable also after the drawdown, the reference parameter values and geometry used was found to be suitable for further analysis. The FOS-development is presented in Figure 3-2.

7

1.80 1.85

1.70 1.80

A1 A1 1.60 1.75

FOS A2 FOS 1.50 A2 1.70 A3 1.40 A3 1.65 1.30 1 2 3 4 5 6 7 8 9 10 Init. RDD 1 WLFC

Figure 3-2: FOS-values for initial conditions (Init.), after one rapid drawdown (RDD), and after one WLFC (1) (picture to the left); and development by additional WLFC’s (picture to the right).

For all approaches—with the initial conditions as references—the FOS-values were significantly decreasing due to the rapid drawdown (about 17% for A1, and 16% for A2 and A3), slightly increasing due to the first WLFC (3% for A1 and 2% for A2 and A3), and ending up exhibiting further increased values after 10 WLFC’s (a total increase of 6 % for A1, and 5% for A2 and A3). The results show that the stability growth continues during the entire period studied. Lower FOS-values were obtained using the approach assuming saturated conditions below the water- level, dry conditions above, and taking into account neither pore-pressure changes due to deformations, nor suction (A1), than using fully coupled flow-deformation computations, considering also suction forces (A2). This is reasonably explained by the consideration taken to the contribution of suction forces to the stability. The lowest FOS-values were obtained in A3; i.e. fully coupled flow-deformation computations, but with the negative pore pressures not considered in the stability analysis. These FOS-values were found to be even lower than those obtained in A1; this although suction was neglected also in A1.

3.2 Deformations, pore pressures and flow In Figure 3-3, vertical deformations developed at the crest (point A, see Figure 2-1) are presented. The values were registered in the middle of each WLFC, i.e. at the end of each drawdown.

-18.0 -19.0 -20.0 A1 -21.0 A2

(mm) -22.0

y -23.0 A3 u -24.0 1 2 3 4 5 6 7 8 9 10 Number of drawdowns Figure 3-3: Vertical deformations at the crest; readings from the end of each drawdown. The reference level before the first drawdown is 0 mm.

The overall pattern is the same in all approaches; additional vertical deformations are developed with an increased number of drawdowns. The rate is decreasing although a definitive asymptotical pattern cannot be seen. Utilization of A1 seems to give less deformations developed compared to both A2 and A3. This was found to be true at all depths vertically below point A (see Figure 2-1). The development of the active pore pressure, (consisting of contributions from as well steady state as excess pore pressure) measured in A2, is shown in Figure 3-4. The developments were registered in two different points; one located at the crest (point A in Figure 2-1), and one at the initial groundwater level (point B in Figure 2-1).

8

-8

-80.4

-7 -80.2

(kPa (kPa )

(kPa ) (kPa

-6 -80.0

active -5 active

p p -79.8 -4 p -79.6 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 WLFC WLFC Figure 3-4: Pore-pressure development from A2, registered in point B (picture to the left), and in point A (picture to the right).

For point B only peak-values are presented, registered at the end of each WLFC. The development in between was found to be smooth/non-fluctuating. The development of the peak values shows how the active pore pressure—at the end of each WLFC—slowly becomes more and more negative; an increase exhibiting a higher rate between 1 and 5 WLFC’s than for further cycling, seeming to be asymptotically fading out. The increase of the negative pore pressure indicates that the groundwater table is dropping for each cycle. To the right, suction effects above the water level is clearly seen. Also in this plot there is a fading out pattern. In Figure 3-5 a typical picture of the flow region—the area where the external water level and the slope surface intersect—is shown. The external water level is back to the level +22, immediately after one WLFC has been run, whereas the groundwater table is lagging behind.

Figure 3-5: A sample picture of the area where the external water level and the slope intersect, showing the hydraulic conditions prevailing immediately after the first WLFC run in A1. The external water level is located at +22 m whereas the groundwater table within the slope is lower. The flow directions are presented by arrows.

In Figure 3-6, Figure 3-7 and Figure 3-8 flow conditions immediately after each WLFC are plotted. Since the readings were taken at the end of each cycle, the external water level and the groundwater table are almost coinciding, meaning small absolute magnitudes of the flow values registered. The flow condition for each stage is presented as the deviation from the average value of the 10 cycles. Maximum total flow, and horizontal flow directed inwards (in to the slope), is presented in Figure 3-6, whereas maximum vertical flow (upward directed, , and downward directed, ) is shown in Figure 3-7. All of the maximum and minimum values are originating from the region being marked in Figure 3-5, except the –values. The latter ones are registered just below the groundwater table, approximately 10 m right (inwards) from the slope surface.

9

90% 200%

60% 150%

100% A1 30% 50% A2 0%

0% A3

average)

average)

(deviation from

|(deviation from from |(deviation -30% -50%

max -60%

x, right x, -100% |q 1 2 3 4 5 6 7 8 8 10 q 1 2 3 4 5 6 7 8 9 10 WLFC WLFC Figure 3-6: Maximum total flow in the slope; average ~0.1 m/day (picture to the left), and rightward directed horizontal flow; average ~ 0.08 m/day (picture to the right).

200% 200%

150% 150%

100% 100% A1 50% 50% A2

average) 0%

0% (deviation from

average)

(deviation from A3

-50% -50%

y, up y, q y, down y, -100%

-100% q 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 WLFC WLFC Figure 3-7: Maximum upward directed flow (picture to the left), and downward directed flow (picture to the right); both averages ~0.05 m/day.

The flow magnitudes were found to change from one stage to another; i.e. by increased number of cycles. Larger flow changes were captured using the fully coupled flow-deformation computations (A2 and A3), compared to in A1. The difference is particularly pronounced for the rightward directed horizontal flow, and the downward directed vertical flow, . Regarding and , the results from A2 and A3 are to a large extent coinciding. In Figure 3-8, development of vertical flow, and horizontal flow, —extracted from the same stress point in all approaches—are shown. The point is located approximately 1 m below the initial water level, 1 m to the right from the slope surface.

60% 60%

40% 40% A1

20% 20% A2

average)

average)

(deviation from

(deviation from 0%

0% A3

y y

x x q -20% q -20% 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 WLFC WLFC Figure 3-8: Vertical flow (picture to the left), and horizontal flow (picture to the right); both averages ~0.05 m/day.

Again, larger flow deviations were captured in A2 and A3, compared to in A1.

10

3.3 Parameter influence

The sensitivity analysis did provide parameter-influence values; total sensitivity ( ). In Figure 3-9 the total sensitivity values (on the y-axis) for each of the five parameters at initial state (Init.), after one rapid drawdown (RDD), and after one WLFC (1), are shown.

(A1) (A2) (A3) 80% 80% 80%

60% 60% 60% Init. 40% 40% 40% RDD 20% 20% 20% 1

0% 0% 0% ν c φ ψ E ν c φ ψ E ν c φ ψ E

Figure 3-9: The influence (in terms of sensitivity) of each parameter, with respect to safety (in terms of FOS).

The stiffness parameters are influencing the stability significantly less than are the strength parameters. The cohesion, exhibits the highest influence in all approaches; followed by the influence of the friction angle, and the dilatancy angle, . The influence of as well Poisson’s ratio, as of Young’s modulus, is slightly increasing during further cycling; though remaining below 3% and 2%, respectively. Therefore, the stiffness parameters are excluded from the presentation of further sensitivity development, presented in Figure 3-10. ( ) ( ) ( ) 60% 40% 9% A20 A3 A1 58% 38% 0 0 8% A10 A2 56% 36% 0 A30 7% A30 54% 34%

Sensitivity A20 6% 52% 32% A10 50% 30% 5% 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 WLFC WLFC WLFC A1 A2 A3

Figure 3-10: Sensitivity development. The dotted lines are showing the initial values for each modelling approach (A10, A20, and A30).

It is clear that the sensitivity values are depending on the stage at which the safety is evaluated, i.e. on the numbers of WLFC’s run. For cohesion, the qualitative trend is the same in all cases; maximum influence at drawdown and then declining with increased number of WLFC’s. In A1 the sensitivity of cohesion gets lower than the initial value after 5 WLFC’s; in A2 this occurs at 2 WLFC’s, and in A3 the initial value is not reached during the 10 cycles. For the friction angle, the pattern is opposite; minimum values at drawdown and then increasing. For this parameter, the initial values are exceeded in all approaches; in A1 and A2 at 3 WLFC’s, and in A3 at 6 WLFC’s. The total change (decrease) of the influence of cohesion

11

(during 10 cycles) seems to be similar in all approaches, whereas the increase of the friction-angle influence in A2 seems to be fading out slower than in A1 and A3. When it comes to the dilatancy angle, the patterns are more scattered. In all cases the sensitivity values are decreased after the first drawdown, whilst the further development is almost constant. Though, the absolute magnitudes (and the variations) of the dilatancy-angle influence are very small, and further conclusions are not reasonably drawn.

4 Discussion Despite the fact that the absolute magnitudes of differences identified in this study were small—FOS- values, pore pressures, flows etc.—these do nonetheless demonstrate important dissimilarities concerning the ability to capture/simulate real soil-water interactions and changes. The results of FOS-development show that the stability growth continues during the entire period studied; though not smoothly. The stability increase is to assign to the fact that the groundwater table is dropping (remained at a lower level) for each WLFC; this was also confirmed by the pore-pressure developments discussed. Lower FOS-values were obtained using the classical approach, A1 than those obtained using approach A2. This could be reasonably explained by the consideration taken to the contribution of suction forces to the stability in A2. The fact that the lowest FOS’s were obtained by using A3, would suggests that this approach is most conservative in this study, in the sense of not overestimating the stability. This is unexpected since suction was not considered at all in A1, whereas suction was considered throughout the entire cycle in A3, until the FOS-computation was run. Anyhow, whether the unexpected result is connected to the nil-steps computed in A3 done in order to neglected suction, or to unrealistic computation of the soil weight above the water level, the FOS result of A3 is to be treated with caution. Use of A1 resulted in smaller vertical crest deformations compared to the other approaches. This suggests that the two-way interaction between pore pressure changes and deformation development in the fully coupled computations (A2 and A3), could capture conditions that bring larger deformations. This means a potential underestimation in A1. Moreover, the flow developments registered in A2 and A3 were significantly more fluctuating than those in A1; as well horizontally as vertically. The difference was seen to be particularly pronounced for the rightward directed horizontal flow, and the downward directed vertical flow. In agreement with what was stated in [31], also the outcomes from the present study show that there seems to be situations where computations taking into account unsaturated soil behavior, is not necessarily less conservative than are classical ones. The parameter-sensitivity analysis results obtained using A1 seems to be quantitatively more comparable to those obtained using A3 than to those using A2. This suggests that consideration of suction at stability computation (only true in A2), does directly affect the parameter influence on the results. However, major differences were not found. Since the sensitivity was computed with respect to FOS determined by using the strength reduction technique, the low and insignificantly changing sensitivity values of the stiffness parameters were expected. The non-constant sensitivity values of the dilatancy angle, might indicate that the occurrences of plastic strains are somewhat different in the different stages. Though, the influence is significantly lower than for friction angle and cohesion, and also less changing. It might be useful to consider parameter influence for evaluation of the accuracy needed for definition of model input data; as well absolute magnitudes, as the development patterns. Moreover, when making up modelling/design strategies, parameter changes (e.g. by time or by external changes taking place), could be valuably included. The results obtained in this study are reflecting effects occurred under the specified conditions of hydraulic conductivity, rate of water-level change, and slope geometry. Since these factors are unquestionably affect processes taking place within a watercourse slope, it would be reasonable to include variation also of such non-constitutive parameters in further studies. Since fully coupled flow-soil deformation modelling to a higher degree describes real soil-water interaction, results from semi-coupled approaches (like A1) are probably not optimal for analysis of processes being governed by fluctuating flows, altering hydraulic gradients, unloading/reloading etc. Since hydraulic models do partly rely on empirical soil-specific parameters there are potential uncertainties connected to the level of accuracy of these. Still, this uncertainty is to be related to the extra information

12 possibly obtained at consideration of specific features of unsaturated soils. Flow patterns, changes of denseness, and non-constant values of the hydraulic conductivity, are all factors being valuable for proper modelling. Not at least since such changes in turn are governing as well water-transport (i.e. the efficiency of dissipation of excess pore pressures), as soil-material transport (i.e. susceptibility to internal erosion to be initiated and/or continued).

5 Concluding remarks . The soil structure seems to become more stable due to the first WLFC, and the stability growth continues during the entire period studied. This for all approaches. . Modelling assuming strictly saturated or dry conditions (classical, like in A1) resulted in—restricted to slope stability in terms of safety factors—higher conservatism compared to modelling considering also the behavior of unsaturated soil and fully hydro-mechanical coupling (advanced, like in A2). . Modelling considering the behavior of unsaturated soil and fully hydro-mechanical coupling, but with suction neglected at stability computation (A3) resulted in lower safety factors even compared to classical modelling (A1). This might be explained by errors due to the saturation-suction relation in the hydraulic model used, or to the nil-step computations run in order to get the negative pore pressure neglected. . Advanced modelling seems to allow for rapid changes of pore pressures and flow to be more realistically captured compared to classical modelling. Such changes in turn are governing as well water-transport (i.e. the efficiency of dissipation of excess pore pressures), as soil-material transport (i.e. susceptibility to internal erosion to be initiated and/or continued). . The influence of the parameters were changing as a result of WLFC’s taking place; decreased influence of cohesion, increased influence of the friction angle, scattered patterns of the influence of the dilatancy angle.

5.1 To be further considered In order to capture effects of water-level variation frequencies, rates, slope geometries etc., on slope stability, investigations should be performed using advanced modelling approaches, and considering real long-term perspectives. Use of a more advanced constitutive soil model (e.g. the Hardening soil model [32]) would potentially reduce inaccuracy coming from e.g. improper description of plastic deformations and stiffness changes. The water-level fluctuation effects would also be investigated using models based on the Basic Barcelona Model [39]. Parameter influence would be preferably considered when evaluating the accuracy needed for modelling-input data, as well as when making up modelling/design strategies. Investigations of processes taking place within slopes being subjected to recurrent WLF’s, would desirably be conducted. For instance by laboratory/scale tests combined with modelling.

6 Acknowledgements The research has been supported by the Swedish Hydropower Centre, SVC; established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, The Royal Institute of Technology, Chalmers University of Technology and Uppsala University. Participating agencies, companies and associations are: Alstom Hydro Sweden, Andritz Hydro, Energimyndigheten, E.ON Vattenkraft Sverige, Falu Energi och Vatten, Fortum Generation, Holmen Energi, Jämtkraft, Jönköping Energi, Karlstads Energi, Mälarenergi, Norconsult, Pöyry SwedPower, Skellefteå Kraft, Sollefteåforsens, Statkraft Sverige, SveMin, Svenska Kraftnät, Sweco Infrastructure, Sweco Energuide, Umeå Energi, Vattenfall Vattenkraft, VG Power, WSP and ÅF.

13

7 References [1] J. M. A. Johansson and T. Edeskär, “Effects of External Water-Level Fluctuations on Slope Stability,” Electron. J. Geotech. Eng., vol. 19, no. K, pp. 2437–2463, 2014. [2] O. Mill, A. Dahlbäck, S. Wörman, S. Knutsson, F. Johansson, P. Andreasson, J. Yang, U. Lundin, J.-O. Aidanpää, H. Nilsson, M. Cervantes, and S. Glavatskih, “Analysis and Development of Hydro Power Research - Synthesis within Swedish Hydro Power Centre,” Stockholm, 2010. [3] N. Dahlbäck, “Utvecklingsbehov inom reglerkraftsområdet ur ett vattenkraftperspektiv,” Stockholm, 2010. [4] E. Solvang, A. Harby, and Å. Killingtveit, “Increasing balance power capacity in Norwegian hydroelectric power stations,” 2012. [5] M. Whittingham, “Materials challenges facing electrical energy storage,” Mrs Bull., vol. 33, no. 04, pp. 411–419, Jan. 2008. [6] D. Connolly, “A Review of Energy Storage Technologies - For the integration of fluctuating renewable energy,” PhD thesis, University of Limerick., Limerick, Ireland, 2010. [7] REN21, “Renewables 2013: Global Status Report,” 2013. [8] Svenska Kraftnät, “Storskalig utbyggnad av vindkraft,” 2008. [9] Svenska Energimyndigheten, “Vattenkraften och energisystemet-ER 2008:24,” Eskilstuna, Sweden, 2008. [10] P. A. Lane and D. V. Griffiths, “Assessment of Stability of Slopes under Drawdown Conditions,” J. Geotech. Geoenvironmental Eng., vol. 126, no. 5, pp. 443–450, May 2000. [11] J. M. Duncan and S. G. Wright, Soil Strength and Slope Stability. Hoboken, New Jersey: John Wiley & Sons, Inc., 2005. [12] H. Yang, H. Rahardjo, and D. Xiao, “Rapid Drawdown of Water Table in Layered Soil Column,” in Geoenvironmental engineering and geotechnics: progress in modeling and applications, 2010, pp. 202–209. [13] N. M. Pinyol, E. E. Alonso, J. Corominas, and J. Moya, “Canelles landslide: modelling rapid drawdown and fast potential sliding,” Landslides, vol. 9, no. 1, pp. 33–51, May 2011. [14] R. Cojean and Y. J. Caï, “Analysis and modeling of slope stability in the Three-Gorges Dam reservoir (China) — The case of Huangtupo landslide,” J. Mt. Sci., vol. 8, no. 2, pp. 166–175, Mar. 2011. [15] G. W. Jia, T. L. T. Zhan, Y. M. Chen, and D. G. Fredlund, “Performance of a large-scale slope model subjected to rising and lowering water levels,” Eng. Geol., vol. 106, no. 1–2, pp. 92–103, May 2009. [16] J. Krahn, “The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses,” Can. Geotech. J., vol. 40, no. 3, pp. 643–660, Jun. 2003. [17] J. B. Burland and J. E. B. Jennings, “Limitations to the Use of Effective Stresses in Partly Saturated Soils,” Géotechnique, vol. 12, no. 2, pp. 125–144, Jan. 1962. [18] D. G. Fredlund and N. Morgenstern, “Stress state variables for unsaturated soils,” J. Geotech. Geoenvironmental Eng., vol. 103, no. GT5, pp. 447–466, Jul. 1977. [19] D. G. Fredlund, “Unsaturated Soil Mechanics in Engineering Practice,” J. Geotech. Geoenvironmental Eng., vol. 132, no. 3, pp. 286–321, Mar. 2006. [20] M. M. Berilgen, “Investigation of stability of slopes under drawdown conditions,” Comput. Geotech., vol. 34, no. 2, pp. 81–91, Mar. 2007. [21] M. Huang and C.-Q. Jia, “Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage,” Comput. Geotech., vol. 36, no. 1–2, pp. 93–101, Jan. 2009. [22] V. Galavi, “Internal Report - Groundwater flow, fully coupled flow deformation and undrained analyses in PLAXIS 2D and 3D,” 2010. [23] S. E. Darby, M. Rinaldi, and S. Dapporto, “Coupled simulations of fluvial erosion and mass wasting for cohesive river banks,” J. Geophys. Res., vol. 112, no. F3, p. F03022, Aug. 2007. [24] G. A. Fox, G. V Wilson, A. Simon, E. J. Langendoen, O. Akay, and J. W. Fuchs, “Measuring streambank erosion due to ground water seepage: correlation to bank pore water pressure, precipitation and stream stage,” Earth Surf. Process. Landforms, vol. 32, no. 10, pp. 1558–1573, Sep. 2007. [25] J. R. Grove, J. Croke, and C. Thompson, “Quantifying different riverbank erosion processes during an extreme flood event,” Earth Surf. Process. Landforms, vol. 1406, no. February, p. n/a–n/a, Feb. 2013. [26] M. Rinaldi and N. Casagli, “Stability of streambanks formed in partially saturated soils and effects of negative pore water pressures: the Sieve River (Italy),” , pp. 253–277, 1999. [27] A. Simon, A. Curini, S. E. Darby, and E. J. Langendoen, “Bank and near-bank processes in an incised channel,” Geomorphology, vol. 35, no. 3–4, pp. 193–217, Nov. 2000. [28] a. Samadi, E. Amiri-Tokaldany, and S. E. Darby, “Identifying the effects of parameter uncertainty on the reliability of riverbank stability modelling,” Geomorphology, vol. 106, no. 3–4, pp. 219–230, May 2009. [29] T. Zhan, W. Zhang, and Y. Chen, “Influence of reservoir level change on slope stability of a silty soil bank,” in The Fourth International Conference on Unsaturated Soils, ASCE, April 2–4, 2006, pp. 463–472.

14

[30] Y. Shen, D. Zhu, and H. Yao, “Critical slip field of slope in process of reservoir water level fluctuations,” Rock Soil Mech., vol. 31, no. S2, pp. 179–183, 2010. [31] D. Sheng, S. Zhang, and Z. Yu, “Unanswered questions in unsaturated soil mechanics,” Sci. China Technol. Sci., vol. 56, no. 5, pp. 1257–1272, Apr. 2013. [32] PLAXIS, “PLAXIS 2D 2012.” Available at: http://www.plaxis.nl/, Delft, Netherlands., 2012. [33] L. M. Rognlien, “Pumped storage hydropower development in Øvre Otra, Norway,” Norwegian University of Science and Technology, 2012. [34] J. Lafleur, “Filter testing of broadly graded cohesionless tills,” Can. Geotech. J., vol. 21, no. 4, pp. 634–643, Nov. 1984. [35] A. I. Gärdenäs, J. Šimůnek, N. Jarvis, and M. T. van Genuchten, “Two-dimensional modelling of preferential water flow and pesticide transport from a tile-drained field,” J. Hydrol., vol. 329, no. 3–4, pp. 647–660, Oct. 2006. [36] PLAXIS, “PLAXIS 2D 2012,” PLAXIS Material Models Manual 2012, 2012. [Online]. Available: http://www.plaxis.nl/files/files/2D2012-3-Material-Models.pdf. [Accessed: 15-Mar-2014]. [37] J. Briaud, Geotechnical Engineering: Unsaturated and Saturated Soils. John Wiley & Sons, Inc., 2013. [38] M. A. Biot, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., vol. 12, no. 2, p. 155, 1941. [39] E. E. Alonso, A. Gens, and A. Josa, “A constitutive model for partially saturated soils,” Géotechnique, vol. 40, no. 3, pp. 405–430, Jan. 1990. [40] M. T. van Genuchten, “A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils,” Soil Sci. Soc. Am. J., vol. 44, no. 5, pp. 892–898, 1980. [41] U.S. EPA, “TRIM, Total Risk Integrated Methodology, TRIM FATE Technical Support Document, Volume I: Description of Module,” 1999. [42] U.S. EPA, “Risk Assessment Guidance for Superfund (RAGS) Volume III - Part A: Process for Conducting Probabilistic Risk Assessment (2001) - Appendix A,” 2001.

15