Modeling Fault Probability in Single Railroad Turnouts in Eastern Region, Sweden, with the Use of Logistic Regression Models

DEGREE PROJECT IN THE BUILT ENVIRONMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019

Modeling fault probability in single railroad turnouts in Eastern Region, Sweden, with the use of logistic regression models

A step from preventive to predictive preventive maintenance in railway maintenance planning

FILIPP ZAROV

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Modeling fault probability in single railroad turnouts in Eastern Region, Sweden, with the use of logistic regression models

A step from preventive to predictive preventive maintenance in railway maintenance planning

Filipp Zarov

Master thesis December 2019 School of Architecture and Built environment KTH Railway Group KTH Royal Institute of Technology Stockholm, Sweden

Abstract Turnouts are an important part of railway infrastructure for two reasons: infrastructure and maintenance. For the infrastructure they provide the flexibility to allow the formulation and branching of railway network and for maintenance they consume a large part of maintenance budget and have a prominent place in maintenance planning policy and activities. This is because as a “mechanical object”, a turnout often experiences malfunctions. The problem becomes even more complicated, since a turnout is composed of many different parts and each of them fails for very different reasons (e.g. switch blades vs crossing part). This is reflected in the different needs for maintenance activities, as railways are forced to pour in excessive amounts of resources to carry out emergency repairs, or to carry out unnecessary scheduled maintenance works in turnouts, which do not need to be inspected or repaired. Therefore, it is difficult to plan and organize maintenance activities in turnouts in an efficient manner. This raises the question of whether malfunctions in turnouts can be predicted and used as information for the maintenance planning process in order to optimize it and develop it into a more reliable preventive maintenance planning. The aim of this analysis is to attempt to model the probability of various malfunctions in turnouts as a function of their main geometric and operational characteristics by using logistic regression models and then input these results into the maintenance planning process in order to optimize it. First, it was important to objectify the railway track system and the turnout components, both in terms of parts and interrelationships. Furthermore, the process and basic elements of railway maintenance planning were defined, as well as arguments that motivate a turn towards preventive maintenance planning methodologies. This was done through a comprehensive literature study. The basis of this research was case studies, which described the relationship between geometrical and operational characteristics of turnouts and their wear, as well as risk-based modelling methods in railway maintenance planning. To create the analysis model, data from turnouts in eastern region provided by the Swedish Transport Administration were used, both from the point of view of describing the underlying causes of turnout malfunctions and to formulate an object-oriented database suitable for using in logistic regression models. The goal was a logit model that calculated the malfunction probability of a turnout, which could be used directly into a maintenance planning framework, which ranked maintenance activities in turnouts. The results obtained showed that although the model suffers from low correlation, different relationships between input variables and different functional errors were established. Furthermore, the potential of these analytical models and modeling structures was shown to be able to develop preventive, predictive railway maintenance plans, but further analysis of the data structure is required, especially regarding data quality. Finally, further possible research areas are presented. Keywords: maintenance planning, railway turnouts, malfunction probability modeling, object- oriented databases, logistic regression models Sammanfattning Spårväxlar är viktiga delar av järnvägens infrastruktur av två orsaker: infrastruktur och underhåll. För infrastrukturen ger de möjlighet till flexibla tillåter de formulering och grenning av järnvägsnät och för underhållet konsumerar de en stor del av underhållsbudgeten och de har en framträdande plats i underhållsplaneringspolitiken och aktiviteterna. Detta beror på att som ett ”maskinellt objekt”, har spårväxeln ofta fel. Problemet blir ännu mer komplicerat, eftersom en spårväxel består av många olika delar och var och en av dem bryts ner av mycket olika skäl (t.ex. tunganordning vs korsningsdel). Detta återspeglas i olika behov av underhållsaktiviteter. Eftersom järnvägarna tvingas hålla alltför stora mängder resurser för att utföra akuta reparationer eller för att utföra onödiga schemalagda underhållsarbeten i spårväxlar, som inte behöver inspekteras eller repareras. Därför är det svårt att planera och organisera underhållsaktiviteter för spårväxlarna på ett effektivt sätt. Detta ställer frågan om funktionsfel i spårväxlar kan förutsägas och användas som information till

2 underhållsplaneringsprocessen för att optimera den och utveckla den till en pålitligare förebyggande underhållsplanering. Syftet med denna analys är att försöka modellera sannolikheten för olika funktionsfel i spårväxlar som en funktion av deras huvudsakliga geometriska och operativa egenskaper med användning av logistiska regressionsmodeller och sedan mata dessa resultat in i underhållsplaneringsprocessen för att optimera den. För det första var det viktigt att objektifiera järnvägsspårsystemet och spårväxlarkomponenterna, både vad gäller delar och inbördes förhållanden. Dessutom definierades processen och grundelementen i järnvägsunderhållsplaneringen, samt att argument som motiverar förändring till förebyggande underhållsplaneringsmetoder. Detta gjordes genom en omfattande litteraturstudie. Grunden i denna analys var fallstudier, som beskrev förhållandet mellan geometriska och operationella egenskaper hos spårväxlar och deras förslitning samt riskbaserade modelleringsmetoder i järnvägsunderhållsplanering. För att skapa analysmodellen användes data från spårväxlar i östra regionen som tillhandahölls av Trafikverket, både ur synpunkten att beskriva de underliggande orsakerna till spårväxlarsfel och för att formulera en objektorienterad databas lämplig för användning i logistiska regressionsmodeller. Målet var en logitmodell som beräknade sannolikheten för fel i en spårväxel, som kunde användas direkt i en underhållsplaneringsram, som rangordnar lämpiga underhållsaktiviteter i spårväxlar. Erhållna resultat visade att även om modellen lider av låg korrelation, konstaterades olika samband mellan ingående variabler och olika funktionsfel. Vidare visades potentialen hos dessa analysmodeller och modelleringsstrukturer för att kunna utveckla förebyggande, förutsägbara järnvägsunderhållsplaner, men det krävs troligtvis ytterligare analys av datastrukturen, speciellt angående datakvaliteten. Slutligen presenteras ytterligare möjliga forskningsområden. Nyckelord: underhållsplanering, spårväxlar, felsannolikhet modellering, objektorienterad databas, logistiska regressionsmodeller Professional Acknowledgements Throughout the writing process of my master thesis, I received a great deal of support and assistance. I would like to thank 1) my supervisor Anders Lindahl, member of KTH railway group1 and transport planning division, as well as teacher in M.Sc. in Transport and Geoinformation technology for his invaluable support, teaching, guiding and assistance not only during the master thesis but also through the entire Master programme, 2) Arne Nissen2, responsible for managing Trafikverket railway maintenance databases, who kindly provided not only access to data related to railway traffic and turnout malfunctions from Ofelia and BIS databases in eastern region, but also actively supported and explained the variables and structure of the databases, 3) Carlos Casanueva Perez, associate professor in rail vehicle technology, department of Aeronautical and Vehicle engineering, CMG at ECO2 vehicle design and director of M.Sc. programme in railway engineering for his technical and practical advices, as well as for providing me with bibliographic material related to turnouts, 4) Fredrik Andersson, for being the inspiration behind this master thesis topic and helping formulating the basis of it and finally 5) anyone who directly or indirectly was involved in the implementation of this topic.

Personal Acknowledgements I would like to thank Marija Rubil, who wholeheartedly supported me through the whole process of realizing this master thesis, with her endless psychological and practical support, as well as helping me with the collection of critical reading material, which proved invaluable during the writing of this master thesis.

1 Education and project support 2 Trafikverket, Luleå, Spårtekniker, UHjsp

Table of Contents

1. Introduction ...... 6 Background ...... 6 Aims ...... 7 Method ...... 7 Limitations ...... 7 2. Literature review ...... 8 2.1. The railway wheel-track system – The dynamic interaction between rail infrastructure and rail vehicles – basic components of rail infrastructure ...... 8 2.1.1. Track structure in a nutshell ...... 8 2.1.2. Forces acting on a track ...... 8 2.1.3. Other factors that amplify the forces ...... 10 2.1.4. Track components ...... 10 2.1.5 Conclusions – Track system, loading and parts ...... 17 2.2. Turnouts ...... 17 2.2.1. Designation of a turnout ...... 18 2.2.2. Parts of a turnout ...... 18 2.2.3 Other important parts and aspects of a turnout ...... 23 2.2.4. Geometry and operational characteristics of a turnout ...... 26 2.2.5 Conclusions: Turnouts, parts and interaction between operational and geometrical characteristics ...... 31 2.3. Structural analysis of a rail track and turnout considerations ...... 32 2.3.1. Theoretical foundation and main parameters of track structural analysis ...... 32 2.3.2. From main parameters of structural analysis to stress calculations ...... 38 2.3.3. Structural considerations in a turnout...... 42 2.3.4. Conclusions: Structural considerations in railway infrastructure and turnouts ...... 47 2.4. Railway maintenance planning in Sweden and turnouts ...... 48 2.4.1. Railway market in Sweden, railway maintenance and Trafikverket ...... 48 2.4.2. Maintenance from Trafikverket’s perspective ...... 49 2.4.2.1. The maintenance plan 2019-2022 ...... 49 2.4.3. Maintenance planning considerations ...... 51 2.4.4. Classification of maintenance in relation to response- from corrective to predictive maintenance ...... 54 2.4.5. Modelling maintenance planning ...... 54 2.4.6. Conclusions: Maintenance planning, modeling and incorporation of asset degradation ...... 57 3. Methodology ...... 58 3.1. Fault risks in a turnout and data analysis: the case of east region in Sweden ...... 58

3.1.1. Turnouts in Sweden and Trafikverket’s perspective regarding turnout failures ...... 58 3.1.2. Creating an object- oriented synthetic database for analysis ...... 60 3.1.3. Data analysis of turnout malfunctions in eastern region – General trends ...... 60 3.1.4. Data analysis of turnout malfunctions in eastern region: relation between malfunctions and operational/geometric characteristics of turnouts ...... 61 3.1.5. Analysis of Causes of turnout malfunctions as recorded in Ofelia DB ...... 64 3.1.6. Conclusions: data analysis, database construction and results of analysis of turnout malfunctions in eastern region ...... 65 3.2. Modeling the probability of turnout faults by using logit models – An application to predictive maintenance planning ...... 66 3.2.1. Logistic regression – principles ...... 66 3.2.2. Modeling malfunction probability as a function of turnouts characteristics- separate influence of variables and statistical validation ...... 68 3.2.3. Modeling malfunction probability as a function of turnouts characteristics- Combined influence of variables and statistical validation ...... 69 3.2.4. Application of the model – an example ...... 69 3.2.5. Conclusions: modeling turnout malfunctions with logistic models ...... 70 4. Results ...... 71 5. Topics for further research ...... 75 Bibliography ...... 76 Appendix 1 ...... 80 Appendix 2 ...... 82 Appendix 3 ...... 83 Appendix 4 ...... 86 Appendix 5 ...... 87 Appendix 6 ...... 88 Appendix 7 ...... 91

1. Introduction Railway maintenance across Europe is one of the most important endeavors a national railway organization must undertake – with an increasing cost around EU. Sweden is not exception: according to Trafikverket’s maintenance plan 2019-2022 (Trafikverket, 2019) , for 2018 alone, around 8 billion Kr were disposed towards railway maintenance and by 2022 another 30 billion Kr will be disposed, with an increased expenditure each year. This includes not only preventive/remedial maintenance, but also reinvestments. In this grand scheme, one of the main points of focus is track infrastructure, with turnouts having a prominent position. Are turnouts important in the maintenance scheme and in railway network? Experts think so. Lichtberger (2005) underlines their importance, as they are prerequisite for the development of a highly productive network. However, they require high investment and large-scale maintenance, which makes them, as a premium component, expensive (1 meter of switch has up to 4 times higher cost than one meter of track). Atop of that, due to their structure, turnouts are prone to faults, which can seriously hinder rail operations. In the light of the rising maintenance requirements and costs, experts seek a way to optimize the planning of infrastructure maintenance, stressing the need for departing from corrective and preventive maintenance regimes (both are highly costly), as well as from ad-hoc planning principles and general KPIs, to predictive preventive maintenance (Zoeteman & Esveld, 2004). This approach comes from the risk analysis realm, where infrastructure faults are treated as probabilities, rather than certainties. This approach is highly promising, as it can truly optimize maintenance planning, for it can almost guarantee that maintenance intervention will occur neither after, nor before the damage but just when it needs to occur, Experts approach the optimization problems by frequently using mathematical models. In Sweden, rail infrastructure is old and exposed to high traffic volumes, which are expected to increase. That triggers the need for high maintenance and reinvestment costs and turnouts are no exception, given their special place in it. At the same time, maintenance optimization is a way of improving the financial result and effectiveness of maintenance. There are many models, which attempt it, mostly through the prism of track possession optimization and few from the perspective of risk analysis. So, what if the infrastructure is itself positioned at the center of modeling? That means modeling the probability of individual infrastructure to fail as a function of its attributes, can give rise to a bottom-up pattern of maintenance, which will be very effective, since it reflects the condition of the assets. A central argument of this thesis is that can be done with the use of logistic regression models. However, which properties of a turnout must be taken under consideration and which are the parts and mechanics of a turnout and rail infrastructure in general that must be considered? Can this approach be viable in terms of improving the maintenance? These thoughts comprise the core of this study. Background Railway engineering literature has established well both the structural analysis of a track, as well as the description of the parts of a turnout, mostly from the scope of national railway organizations. Maintenance optimization modeling has also several representatives (see Liden , 2015; Liden & Joborn, 2017 for examples). However, there is not a single compiled text regarding these practices and the practice of maintenance modeling in general, in combination with structural analysis of a trunout, as well as describing its parts. Therefore, references from Kerr (2003), Lichtberger (2005), Esveld (2001), as well as the AREMA practical guide for railway engineering (2003) are primarily used to establish a structural analysis of the turnout and its parts. Regarding the implementation of logit model in studying turnout faults, data about turnouts provided by Trafikverket for the east region in Sweden is used, which can be considered as the area under consideration. An attempt to use a risk analysis model in maintenance planning is done by Consilvio, et al. (2018), but no previous study of that kind exists for the area under consideration. As for logistic models, there is a sufficient body of literature , as well as practical applications in transport planning (see Ortuzar & Willumsen, 2001).

Aims The aims of this thesis is to 1) justify the need for a turn towards predictive preventive maintenance planning for the entire rail infrastructure – not only for turnouts, 2) to establish why turnouts are important in maintenance planning and why is important to forecast their faults, 3) to establish a framework for structural analysis of a turnout and 4) underline its peculiarities as a part of the track, 5) to examine what are the factors causing faults in turnouts and finally 6) to develop a logistic model which can be used to calculate the probability of a turnout to malfunction. To what degree aims are achieved is discussed on “Results” and “Topics for further research” chapters. Method Apart from using elements of structural engineering and applied railway engineering, the basic method is consisted of: I. Using turnouts failure data from 2018 for the east region in Sweden from two different maintenance databases: Ofelia and BIS. II. Combining them, along with inputs from Trafikverket technical documentation, a new synthetic database is constructed, where the malfunction is expressed with a binary manner (0-1) as the dependent variable and technical, geometrical and traffic characteristics are composing the independent variables. This will produce a logistic model, which will be able to forecast the probability of a turnout to malfunction or not. III. Statistical verification of the model. Limitations The thesis scope is restricted due to several factors:  Geography: Due to the difficulty and restrictions imposed by Trafikverket regrading handling and distribution of data, only data for the east region were provided.  Time: In order to conduct a thorough study of the topic this thesis is dealing with, more time is required, which obviously is not enough in the context of a master thesis.  Data quality: database building is a whole topic by its own. This process of building a complete database for the purpose of modelling requires cross-reference of many data sources and it is time consuming. As a result, database will contain only basic characteristics of a turnout.  Types of turnouts: For this thesis only simple turnouts (left or right-handed) are considered. There are many more types of them, which won’t be discussed extensively.  Interviews: For this master thesis, no interviews were conducted, as the input from Trafikverket was deemed sufficient. Furthermore, this is a topic based mostly on existing bibliography, technical documents and statistical data, rather than on data collected on site.

2. Literature review 2.1. The railway wheel-track system – The dynamic interaction between rail infrastructure and rail vehicles – basic components of rail infrastructure Turnout is a premium component of track infrastructure, meaning it has a configuration and parts that typical track does not. However, in terms of basic components and forces applied on it, it resembles a combination of a straight track and tracks on turns, without superelevation. Therefore, it is useful to revisit some key aspects of track parts and dynamics that are in play, in order to comprehend the loading environment in a turnout. The focus here is describing a ballasted track structure. 2.1.1. Track structure in a nutshell According to Selig & Waters (1994), a rail track must serve as a stable guideway with appropriate vertical and horizontal alignment. Therefore, each component of Figure 1: Schematic representation of the Wheel-track system. Source: the system must perform its specific (Lichtberger, 2005, p. Chapter 1) functions satisfactorily in response to the traffic loads and environmental factors imposed on the system. These points are made more clear by Lichtberger (2005), who stresses that the track consists not only of individual components which must be viewed separately, but it must be viewed as the "railway wheel-track" system as a whole (Figure 1). Finally, Edwards & Ruppert (2018) adopt an even wider perspective of the functions of a track. More specifically, a track has primary as well as secondary functions, which are 3:

Primary Secondary 1. Support and distribute train loads [R, S, FS, B] 6. Transmission of signal circuit[R] 2. Guide the vehicle[R,S,FS] 7. Broken rail detection[R] 3. Provide adhesion at wheel‐rail interface[R] 8. Path of ground return for traction power[R] 4. Provide a smooth running surface[R, S, FS] 5. Facilitate drainage[B] Table 1: Functions of a track. Source: (Edwards & Ruppert, 2018) 2.1.2. Forces acting on a track The main force applied on a track is the vertical wheel load (static or dynamic). The configuration and the components of the track itself are designed and arranged in such a way that allow the distribution and the reduction of the very high force of pressure in the wheel-rail contact point. Progressively, each layer distributes and reduces the initial load and as a result, the track remains in place (Figure 2). In reality, since a train moves on the track, the interaction between wheel and track is much more dynamic and multidimensional. According to Esveld (2001), in rail track litterature, the wheel-rail forces are applied vertically (Q is the denomination for the vertical force-z-direction), laterally to the track –to its sides ( Y for the lateral force - y-direction), and longitudinally –in parallel to the track ( T for the longitudinal force - x-direction). In addition, one must consider the internal longitudinal temperature forces, which may be present and are indicated with symbol N (Figure 3).

3 R = Rail, S = Sleeper, FS = Fastening System, B = Ballast

Esveld (2001) provides a more analytical insight of the causes and nature of track loads. He states that the forces acting on the track, as a result of train loads, are considerable and sudden and are characterized by rapid fluctuations. The loads can be considered from three main angles:  vertical  horizontal, transverse to the track  horizontal, parallel to the track In addition, loads can be divided according to their nature:  quasi-static loads as a result of the gross tare, the centrifugal force and the centering force in curves and switches, and cross winds  dynamic loads caused by: o track irregularities (horizontal and vertical) and irregular track stiffness due to variable characteristics and settlement Figure 2: Pressure distribution of the wheel force Q in the individual system components of the track. Source: of ballast bed and formation (Lichtberger, 2005, p. Chapter 2) o discontinuities at welds, joints, switches etc. o irregular rail running surface (corrugations) o vehicle defects such as wheel flats, natural vibrations, hunting. He adds that there are also the effects of temperature on CWR track, which can cause considerable longitudinal tensile and compressive forces, which in the latter case can result in Figure 3: Rail forces and displacements. Source: (Esveld, instability (risk of buckling) of the track. 2001, p. Chapter 1) Examining the loads from the perspective of their angle, Esveld (2001) states that the vertical rail force is the total vertical wheel load, which is made of the following components:

푄푡표푡 = (푄푠푡푎푡 + 푄푐푒푛푡푟 + 푄푤푖푛푑) + 푄푑푦푛 (1) 푞푢푎푠𝑖 − 푠푡푎푡𝑖푐 푓표푟푐푒푠

In which: 푄푠푡푎푡 : Static wheel load = half the static axle load, measured on straight horizontal track, 푄푐푒푛푡푟: Increase in wheel load on the outer rail in curves in connection with non-compensated centrifugal force, 푄푤푖푛푑 : Cross winds forces, 푄푑푦푛= dynamic wheel load components resulting from:  Sprung mass : 0-20 Hz  Unsprung4 mass: 20-125 Hz  Corrugations, welds, wheel flats: 0-2000 Hz The total horizontal lateral force exerted by the wheel on the outer rail is:

푌푡표푡 = (푌푓푙푎푛푔푒 + 푌푐푒푛푡푟 + 푌푤푖푛푑) + 푌푑푦푛 (2) 푞푢푎푠𝑖 − 푠푡푎푡𝑖푐 푓표푟푐푒푠

4 Unsprung mass: all the mass that is below the suspension of the train– weight of the wheel on the axle and parts of the track frame. Everything above the springs is sprung mass

In which: 푌푓푙푎푛푔푒 : Lateral force in curve caused by flanging against the outer rail, 푌푐푒푛푡푟 : Lateral force due to non-compensated centrifugal force, 푌푤푖푛푑 : Cross wind forces, 푌푑푦푛: Dynamic lateral force component; on straight track these are predominantly hunting phenomena. Finally, the horizontal longitudinal forces occur in the track as a result of:  Temperature forces, especially in CWR track. These forces can be considered as a static load  accelerating and braking  shrinkage stresses caused by rail welding  Rail creep (or creepage) 2.1.3. Other factors that amplify the forces Considering all these forces applied on the track, it is of utmost importance to set some requirements for the bearing strength and the quality of the track. According to Esveld (2001), these requirements depend largely on the loading parameters:  axle load: static vertical load per axle  tonnage borne: sum of the axle loads  running speed  Track horizontal and vertical geometry The static axle load level, to which the dynamic increment is added, in principle determines the required strength of the track. The accumulated tonnage is a measure that determines the deterioration of the track quality and as such provides an indication of when maintenance and renewal are necessary. Figure 4: Track Structure components (parallel The dynamic load component, which depends section). Source: (Selig & Waters, 1994) on speed and horizontal and vertical track geometry, also plays an essential part here (Esveld, 2001). In general, Esveld implies that as variables, speed, axle load and track geometry are closely related. Especially speed and track geometry increases the static forces applied on the track. 2.1.4. Track components Selig and Waters (1994), state that a track structure is consisted of two main parts:1) the superstructure and 2) the substructure (Figure 4, Figure 5). Superstructure is consisted of the following elements:  Rails  Fastening system  Sleepers (ties or corssties) Figure 5: Track Structure components (cross-section). Source: (Selig & Waters, 1994) The substructure on the other hand is consisted of:  Ballast  Subballast  Subgrade Finally they note that these parts are separated by the sleeper-ballast interface. The components of a track will be analyzed below.

2.1.4.1. Rails Rails are the longitudinal steel members that directly guide the train wheels evenly and continuously. They must have sufficient stiffness to serve as beams, which transfer the concentrated wheel loads to the spaced sleeper supports without excessive deflection between supports (Selig & Waters, 1994). In general, modern railways use the Vignole rail (or T-rail) as the rail of choice, come in sections, which size is measured in 푙푏푠/푦푎푟푑 or in 푘푔/푚푒푡푒푟. Rail brands (Figure 7) include the following information (Lichtberger, 2005) along with rail size: company, year of rolling, profile, steel sort. Figure 6: Schematic representation of the stress-strain The length of rail sections may also differ. diagram. Source: (Lichtberger, 2005, p. Chapter 3) Lichtberger (2005) states that it is possible to roll rails of 120 m length and to deliver them to the site, but standard rails used today are still only 60 m. In USA, rail sections are less than 39 feet (approximately 12 m) or 80 feet (approximately 24 m). He also states that greater rail section lengths have many advantages, in terms of productivity, economics and mechanical properties after installation. Finally, he states that the rails are always laid on the track with an inward inclination, but in switches they are usually laid without inclination. A big distinction between rail sections is the way of installation. According to Selig and Waters (1994), steel rail sections may be connected either by bolted joints or by welding. Bolted rails are most commonly used on curves to provide stress relief from thermally induced length changes Figure 7: Rail Branding in USA. Source: (Edwards & Ruppert, 2018) or on secondary lines. However, joints increase track deterioration in total (as many rail discontinuities) and increase maintenance costs. The other way is to use continuous welded rail (CWR). This approach is preferred on lines with high speed, with high axle loads, or with high traffic density. Rails can have a different gauge between them. The most important properties of a rail section are the ones given by the manufacturer. Every rail section has its own properties related to its internal geometry, resistance to angular acceleration (moment of inertia), tension stress limits etc. These properties are important for conducting a structural analysis of a track in relation to the rails and their capacity to accommodate loads without breaking (Figure 6, Table 2). Values related to the hardness of a rail and its tensile strength (how big loads can it accommodate before breaking) can be given by Brinell hardness and the tensile test respectively (see Lichtberger, 2005 for more details). In general, it can be said that heavier rail sections have bigger durability and higher tensile strength, which is also related to the quality of steel and existence of internal rail defects.

Table 2: Moments of inertia and section modulus of rails. Source: (Lichtberger, 2005, p. Chapter 2)

2.1.4.2. Fastening systems According to Selig and Waters (1994), the connections between the sleeper and the rails are achieved by the fastening system, which have many variations. The purpose of the fastening system is to retain the rails against the sleepers and resist vertical, lateral, longitudinal, and overturning movements of the rail produced by forces exerted on the track and by changes in temperature. Figure 8: Typical fastening system in wooden ties. The fastening system to be used depends on the type Source: (Edwards & Ruppert, 2018) of sleeper (crosstie) which will be used and Selig and Waters (1994) describe these differences. With wooden sleepers, steel plates (tie plates) to distribute the rail force over the wood surface are used, which provides suitable bearing pressure and restrain lateral movements of the rail through friction. The size of sleeper plate is an important factor as it defines the stress applied on wooden sleepers. The other parts of the fastening system of this type are the spike fasteners (essentially big nails) and the rail anchors. Selig & Waters state that the spike fasteners restrain the sleeper plates horizontally. Longitudinal rail movement must be restrained by separate anchors clipped to the rails and placed against the sides of the sleepers in the cribs. They also note that driven spikes provide little rail uplift Figure 9: Cross-section of a fastening system in wooden ties. Source: (Edwards & Ruppert, 2018) restraint. Finally, they stress that this fastening system is used with jointed rails (Figure 8, Figure 9, Figure 10). Selig and Waters (1994) also provide an insight in the fastening system used in concrete sleepers, which have spring fasteners (elastic fastening system). They provide vertical and longitudinal restraint as well as lateral. The main components of that system are the clips (which secure the rail in all directions) and the rail pad assembly (mainly for load distribution). Pads are required between the rail seat and the concrete sleeper surface to fulfill the following functions (Selig & Waters, 1994): 1. Provide resiliency for the rail/sleeper system 2. Provide damping of wheel induced vibrations Figure 10: Standard permanent way, USA. Source: (Lichtberger, 2005, p. Chapter 4) 3. Prevent or reduce rail/sleeper contact attrition, and 4. Provide electrical insulation for the track signal circuits This type of fastening system is suitable for modern track and especially for a CWR track. In addition, the elastic downward pressure is essential for the smooth control of the rail's upward movement and high creep resistance (Lichtberger, 2005) (Figure 11). Finally, elastic fastening systems handle forces better, thus reducing the need for maintenance (Figure 12). Apart from the previous categorization, there is another way of categorizing fastening systems. According to Esveld (2001), fastening systems can be categorized as follows:  Direct fastenings entail that the rail and, if necessary, the baseplate are fixed to the sleeper using the same fasteners. Direct fastenings also include the fastening of track on structures without ballast bed and sleepers (Figure 10). Figure 11: Fastening system in a concrete sleeper. Source: (Edwards & Ruppert, 2018)

 Indirect fastenings entail that the rail is connected to an intermediate component, such as the baseplate, by other fasteners than those used to fix the intermediate component to the sleeper. The advantages of indirect fastenings are that the rail can be removed without having to undo the fastening to the sleeper and the intermediate component can be placed on the sleeper in advance (Figure 13). For Esveld (2001), indirect fastening has many more advantages, such as: Figure 12: Comparison of rigid and elastic rail fastenings. Source: (Lichtberger, 2005, p. Chapter 4)  The vertical load is distributed over a larger area of the sleeper. This lengthens the service life of the sleepers.  The horizontal load is absorbed better because of friction and because it is distributed over all the fastenings anchored in the sleeper. Baseplates are excellent for sustaining large lateral forces if large cant deficiencies are provided  The overturning moment causes less force on the fastenings in the sleeper  Baseplates have a high bending stiffness and grooves in the ribs provide good fastening locations for the rail  Baseplates give extra weight to the sleeper.  The only drawback of indirect fastening is the relatively high price. Figure 13: Cross section of the K permanent way. Source: (Lichtberger, 2005, p. Chapter 4)

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Figure 14: Indirect fastening to concrete sleepers (1), Vossloh 300 fastening system (2). Source: (Lichtberger, 2005, p. Chapter 4) 2.1.4.3. Sleepers (crossties) According to Lichtberger (2005), sleepers, ties or crossties have several important functions: 1. Establish and maintain track gauge. 2. Distribute and transmit forces to the ballast bed, such as, vertical, horizontal and longitudinal forces 3. Hold the rails in height, to the sides and in the longitudinal direction 4. to secure the track in cases of rail breakage and derailment 5. to dampen rail vibration and 6. to reduce the influence of sound and impact waves on the environment Figure 15: Forces on a baseplate. Source: (Esveld, 2001)

In bibliography it is stated that there are many types of sleepers, but here, wooden and concrete sleepers are going to be analyzed, which are the predominant ones (Selig & Waters, 1994). Wooden sleepers are produced from different types of wood. In Europe, wooden sleepers are made of oak or beech and they have dimensions of 16 × 26 × 260 푐푚, (height-width-length) while in USA, various species of wood are used with typical dimensions around 18 × 23 × 240 − 270 푐푚 (Lichtberger, 2005). Of course these dimensions vary from country to country, depending on the standards set by the national railways (see Table 3). Wooden sleepers are divided in the following categories of wood (Esveld, 2001):  Softwood sleepers (pine-wood)  hardwood sleepers (beech, oak, tropical varieties). This type is stronger and has a longer service life. Hardwood sleepers are used, for instance, in switches and crossings and where fastenings are applied without base plates. Esveld states that wooden sleepers (Figure 16) have to go a series of procedures before laid on the track. The total service life in years of some types of timber sleepers is: pinewood 20 - 25, beech 30 – 40 and oak 40 -60 (Esveld, 2001). In spite of all these procedure applied above, it is fair to mention that wooden sleepers are more elastic and lighter than concrete, but are more susceptible Figure 16: Wooden sleeper and baseplate. Source: to climate and environmental conditions. (Esveld, 2001) The other category of sleepers are the ones made from pre-stressed concrete. According to Esveld (2001), the development and use of concrete sleepers became significant after the Second World War owing to the scarcity of wood, the introduction of CWR track, and the improvements in concrete technology and pre-stressing techniques. As Kerr (2003) elaborates, the strength of concrete in tension is 1/10 of its compressive strength. At the same time steel is strong in both conditions but expensive. The combination of them, by placing steel wires to cover the tensile stresses, gave birth to reinforced concrete. However, that was not a viable alternative for concrete ties, as cracks under the rail seat and in the center part of the tie were formed, which led to penetration of the tie by water that corroded the metal reinforcement.

Table 3: Typical sleeper Dimensions. Source: (Selig & Waters, 1994) Kerr (2003) narrates that the tendency of conventional reinforced concrete to crack when subjected to vertical loads may be eliminated by subjecting the concrete of a beam, artificially, to a compression stress, a method which is called prestressing. For concrete ties, this eliminates the tensile stresses in the concrete, however should the vertical load be increased further and the prestressing force 푁표 remain the same, tensile stresses will occur in the concrete. When the beam cracks due to overloading, the crack will close when the load is removed, provided that no solid material penetrates the formed crack. The basic idea of prestressed concrete ties is demonstrated in Figure 17 and Figure 18. Figure 17: Principle of prestressed concrete ties. Source: (Edwards & Ruppert, 2018)

The advantages of concrete ties over wooden ones are the following (Lichtberger, 2005):  Longer life cycle and service life,  Less expensive than hardwood sleepers  Lower maintenance of the fastenings  Higher resistance to lateral displacement due to higher weight. Esveld adds also that:  heavy weight( 200-300 kg), useful in Figure 18: The effect of concentric prestressing on the connection with stability of CWR track. concrete beam stresses. Source: (Kerr, 2003)  great freedom of design and construction  relatively simple to manufacture. However, concrete ties have also disadvantages such as (Lichtberger, 2005):  susceptible to shock and impact:  difficult handling due to greater weight, and  maintenance of longitudinal level is somewhat more difficult because of the higher moment of inertia and the lower elasticity Esveld (2001) adds:  Less elastic than wood. On poor formation, pumping may occurs  Susceptible to corrugations and poor quality welds  Risk of damage from impacts (derailment, loading/unloading, tamping tines)  Dynamic loads and ballast stresses can be as much as 25% higher. Esveld also states that there are two basic types of concrete sleepers (Figure 19):  Twin-block sleeper. This type consists of two blocks of reinforced concrete connected by a coupling rod or pipe (synthetic pipe filled with reinforced concrete). Advantages of that design are well-defined bearing surfaces in the ballast bed and high lateral resistance in the ballast bed because of the double number of surface areas.  Monoblock sleeper. This is based on the shape of a beam and has roughly the same dimensions as a timber sleeper. it is considered to endure the higher and intensive loadings better than the twin-block sleeper. Advantages of that design are lower price, little susceptibility to cracking and that it can be prestressed. Regardless of the type of sleeper, its key parameters are a good bearing and bending capability: in other words, a sleeper should be able to bear the stress caused by load on a rail and be able to bend without braking. In addition, a second consideration is their spacing, which affects the magnitude of forces applied on them. Figure 19: Reinforced twin-block sleeper (up) and prestressed monoblock sleeper (down). Source: (Esveld, 2001)

2.1.4.4. Ballast and Subballast Selig and Waters (1994) define the ballast as the select crushed granular material placed as the top layer of the substructure in which the sleepers are embedded. They state that angular, crushed, hard stones and rocks, uniformly graded, free of dust and dirt, and not prone to cementing action have been considered good ballast materials, but no universal agreement exists as to proper specifications for the ballast material index characteristics. In addition, economics have to be considered when choosing ballast. Thus, a wide variety of materials have been used for ballast such as crushed granite, basalt, limestone, slag and gravel. Selig and Waters also enumerate the functions of ballast in detail, which are: 1. Resist vertical (including uplift), lateral and longitudinal forces applied to the sleepers to retain track in its required position 2. Provide some of the resiliency and energy absorption for the track 3. Provide large voids for storage of fouling material in Figure 20: Healthy track ballast. Source: the ballast, and movement of particles through the https://d1p2xdir0176pq.cloudfront.net/wp- ballast content/uploads/Graham-Ellis-Track-3.jpg 4. Facilitate maintenance surfacing and lining operations (to adjust track geometry) by the ability to rearrange ballast particles with tamping. 5. Provide immediate drainage of water falling onto the track 6. Reduce pressures from the sleeper bearing area to acceptable stress levels for the underlying material. In Figure 4 and Figure 5, the subdivisions of the ballast can be seen. Ballast gradation changes over time because of (Selig & Waters, 1994): 1. Mechanical particle degradation during construction and maintenance work, and under traffic loading 2. Chemical and mechanical weathering degradation from environmental changes 3. Migration of fine particles from the surface and the underlying layers. Figure 21: highly fouled ballast. Source: (Dersch & Thus the ballast becomes fouled and loses its open- Ruppert, 2018) graded characteristics so that the ability of ballast to perform its important functions decreases and ultimately may be lost. Subballast on the other hand, is the layer between the ballast and the subgrade. It fulfills two functions, which are also on the ballast list. These are (Selig & Waters, 1994): 1. Reduce the traffic induced stress at the bottom of the ballast layer to a tolerable level for the top of subgrade 2. Extend the subgrade frost protection More specifically, subballast layer fulfills also functions that ballast cannot and these are related to separating ballast and subgrade, migration of particles between the various layers, prevent subgrade attrition by ballast, shed water and permit drainage of extra water (Selig & Waters, 1994). According to Selig and Waters (1994), the most common and most suitable subballast materials are broadly - graded naturally occurring or processed sand-gravel mixtures, or broadly-graded crushed natural aggregates or slags. They must have durable particles and satisfy the filter/separation requirements for ballast and subgrade. In general, as discussed before the main key characteristics of any ballast layer is to distribute weights and facilitate drainage. Therefore ballast must have a specific height, big enough to absorb and distribute weights. As for the drainage function, it can be measured with ballast fouling index (Figure

20, Figure 21). This index measures health ballast, but also determine the hydraulic conductivity of it- in other words how much water can pass through the system. Fouling index can be measured in situ and defined as:

퐹1 = 푃4 + 푃200 (3)

Where: 푃4 is the percentage of particles passing 4.75 mm sieve and 푃200 is the percentage of particles passing a 0.075 mm sieve. The higher the index, the more fouled the ballast is and therefore the more water it holds, leading to the overall deterioration of the track. 2.1.4.5. Subgrade The final layer of track system is the subgrade. According to Selig and Waters (1994), the subgrade is the platform upon which the track structure is constructed. Its main function is to provide a stable foundation for the subballast and ballast layers. The influence of the traffic induced stresses extends downward as much as five meters below the bottom of the sleepers. This is considerably beyond the depth of the ballast and subballast. Hence the subgrade is a very important substructure component which has a significant influence on track performance and maintenance. For example subgrade is a major component of the superstructure support resiliency, and hence contributes substantially to the elastic deflection of the rail under wheel loading. In addition, the subgrade stiffness magnitude is believed to influence ballast, rail and sleeper deterioration. Finally, subgrade also is a source of rail differential settlement. They also mention that anything other than soils existing locally is generally uneconomical to use for the subgrade. 2.1.5 Conclusions – Track system, loading and parts It is vital to understand that trains and track infrastructure are a system: whatever happens to one affects the other and vice-versa. In this sense, trains apply forces on the track, vertical ,lateral and longitudinal. The purpose of a track is to handle these forces. The application of these forces is not static but dynamic, due to movement of train , geometry and track/wheel irregularities. Speed contributes to the increase of these forces. A typical ballasted track is comprised of several components; each of them is performing a key function. Different configuration of these components (e.g. size of rail section or type of sleeper) affect the performance of the track, creating a totally different loading environment each time. Also, each component has several key parameters which define its performance: rails have a certain stress limit, while sleepers have a maximum compression stress , affected by the sleeper spacing. These are important considerations when someone tries to understand how a ballasted track works and how different components affect track performance. These notions become even more important when someone considers a turnout: its geometry is different from a typical track, forces are applied differently and some of them are even more important, as they are crucial in turnout deterioration, like the lateral and longitudinal forces. Furthermore, the selection of components for a turnout can distinguish turnouts which fail and turnouts which are robust and perform their purpose. 2.2. Turnouts Railway turnouts can be considered as one of the most important parts of track infrastructure in railway networks. However, the terminology surrounds them is somewhat baffling, in the sense that the same device is referred as a “turnout”, a “switch”, a “set of points” or Switches and Crossings (S&C’s). So, for purposes of clarity, this device is going to be referred as a railway turnout (turnout for short or spårväxel in Swedish). That confusion comes from the fact that in reality, a railway turnout is comprised of several parts, with the main being the switch and the crossing. According to Kerr (2003, p. 1), main line tracks are Figure 22: A typical right hand turnout. Source: consisted of three major parts: the superstructure, the https://sc01.alicdn.com/kf/UT8yEAUXxNXXXagOFbXy substructure and special structures. Turnouts can be /202615050/UT8yEAUXxNXXXagOFbXy.jpg

17 categorized as a superstructure element. It must be noted that here only simple left or right handed turnouts are considered here. The devices in the railway superstructure that allow trains to change from one track to another are called switches5. The devices that allow trains to cross tracks are called crossings. This changing or crossing of tracks is a necessity to use the railway tracks in the most optimal way and to allow trains to be directed in different directions (Zwanenburg, 2007). The combination of a switch and a crossing constitutes a turnout (Figure 22). Esveld (2001, p. 333) states that turnouts are used to divide a track into two, sometimes three tracks and he purpose of crossings is to allow two tracks to intersect at the same level. A typical example of a left hand turnout is presented below (Figure 23). According to Lichtberger (2005), switches are of special importance for railways, as they are the prerequisite for the development of networks, i.e., for the branching and joining of tracks. He also states that the productivity and line speed of a railway is essentially influenced by the number and type of its switches. Finally, he notes that the structure of a switch is far more complicated and expensive than that of the track grid. According to Bianculli (2003, p. 114), switch origins are ancient, but in 1303 A.D., similar devices were used in forestry industry, in a similar manner as in railways for timber transport. Finally, Gridley Bryant, the builder of the Granite Railway in 1826, was credited with inventing the original track switch. Of course, today, a railway switch is a way more complicated railway device, which has been refined and enhanced over the course of 200 years, through the process of small incremental improvements, a process that was implemented in other parts of railway infrastructure. 2.2.1. Designation of a turnout According to Lichtberger (2005), turnouts are designated according to the following criteria:  Design type: single switch, double switch, single diamond crossing, double diamond crossing, etc.  Rail shape/profile: S49. S54, UIC60 etc.  Radius: 190, 300, 500, 1200 m  Ratio of inclination: this is the angle formed at the end of the switch by the tangent of the curve axis to the axis of the Main track; this angle is expressed by the ratio of Figure 23: A single left-hand Switch. Source: Lichtberger (2005) inclination of both axles to each other (1:9, 1:12, 1:18.5 etc.),  Direction of the branch track (to the left L, to the right R)  Type of blade (loose heel switch, flexing point or spring switch blade)  Type of sleepers:(wooden sleepers, steel sleepers or concrete sleepers) and  Type of crossing/frog (fixed vs movable crossing/frog). 2.2.2. Parts of a turnout As part of track superstructure, a turnout has many similarities with a straight or curved track. However, it has also some premium or special components, which cannot be found in any other part of the track superstructure. In addition, its geometry makes it a distinct part of track superstructure.

5 “Switches” is the American-English term. The same device is also more generally known as “turnout” or in the UK as “set of points”.

Figure 24: Cross-sectional drawing of switch blade and stock rail (asymmetric section). Source: (Esveld, 2001) According to Esveld (2001), a turnout is consisted of three major parts, presented based on their sequence along a turnout (Figure 26): 1. Switch blades 2. Closure rails 3. Crossing (or frog) Switch blades or switch According to Lichtberger (2005), the blade device or switch blades consists of the blades or tongue blades and the stock rails to which the blades cling. The initial point of the blade is called the switch tip and the end is referred to as the heel. The switch blades are connected by switch rods and operated as a unit (AREMA, 2003) with the help of a point machine. Geometrically, the switch blades Figure 25: relation between frog angle part is defined from the Point of Switch (PS) to the Heel of Switch (green angle), switch angle (red angle) and heel spread (blue line) in a (HS), where according to AREMA (2003) Point of switch (PS) is the turnout. Source: (Ruppert, 2017) location where the diverging or straight route is determined and Heel of switch (HS) is the location at which the switch point pivots about.

Figure 26: Parts of a turnout. Source: (Ruppert, 2017) Switch blades are mostly characterized by the angle they form with the stock rail, the geometry of their profile and their connection with the closure rails. Regarding the switch angle, it is the angle formed between the stock rail and the switch blades. According to Ruppert (2017), the angle of the switch blade is connected with the crossing/frog angle and with the heal spread, which according to Hay (1982) is the distance between the gauge sides of stock rail and the switch blades at the heel, in order to avoid an abrupt deflection (Figure 25). In addition, Esveld (2001) notices that the smaller the angle of the switch, the longer the switch blade is.

Regarding the geometry of their profile, as Hay (1982) states, the point itself is ground to a knife-edge and has a snug fit against the stock rail. Esveld (2001), describing the cross-section of a switch blade, states that in modern designs is an asymmetrical section that is lower than the standard rail profile. The asymmetric section also affects the moment of inertia of the blades: because of their asymmetric base, the moment of inertia is higher Figure 27: Standard rail section switch blades. Source: compared to a switch blade made of standard rail. Of http://www.ostpubs.com/wp- course, some railways still use switch blades made of content/uploads/2016/05/Beginning-End_00.jpg standard rails. Finally, an important aspect of the switch blades is the fact that they can have simple or complex geometry, in terms of how the turnout negotiates the curve. Turnouts with straight switch blades are referred to standard geometry, while turnouts with curved (clothoid) geometry are referred to tangent geometry. Regarding the connection with closure rails, AREMA (2003) states that the heel of each switch rail is connected to its lead rail by means Figure 28: Asymmetric rail section switch blades. Source: of special joint bars, or in some cases is https://thumbs.dreamstime.com/z/railroad-switch-rails- continuous, and the switch as a unit pivots about device-connection-railway-tracks-intended-transfer-train-one- way-to-another-turnouts-track-127254651.jpg these connections. These connections are placed on the heel block assembly. According to AREMA (2003), the heel block assembly maintains the correct distance between the gauge side of the stock rail and the gauge side of the points. It adds strength and rigidity. The block will be different for each switch and rail section. AREMA discusses two types of heel blocks: The conventional bolted heel block assembly, (Figure 29) permits movement of the point rails at the heel block. In the floating heel block the point flexes over its length. The floating heel block merely acts as a bearing point between point and stock rail to limit movement. Special plates are used under the heel block assembly. Lichtberger (2005) discusses the topic further. He states that blades can move, as a joint or a spring element is arranged at the heel Figure 29: Bolted heel block assembly. of the blade. On that remark, he distinguishes the blades into four Source: (AREMA, 2003) categories:  loose heels switches,  flexing blades with switch rail plates  spring switch blades  flexing blades without switch rail plates.

Figure 30: Cross-sectional drawing of T-rail switch blade (standard rail switch blade). Source: (Esveld, 2001)

In conclusion, modern switch blades have an asymmetric rail profile, which enhances the handling of forces and durability. In addition, they tend to be welded to the closure rails. Finally, switch rails vary in length from 11 to 39 ft. (3.3528- 11.8872 m) and even longer for high turnout numbers, depending on the weight of the rail and the curvature of the turnout (AREMA, 2003). Closure rails and stock rails According to AREMA (2003), closure rails are the rails connecting the switch blades with the crossing/frog of the turnout and stock rails are the outside rails in a turnout that the switch blades bear against. In cases of left or right handed turnouts, one of these rails serves as a contact for the closed blade and as a running rail for the open blade (Lichtberger, 2005). Two of these rails are straight, while the other two are curved (corresponding to the straight and diverging route). The curvature is expressed in radius in Europe or in degrees of curvature in USA (Hay, 1982)and depends of the number of frog/ratio or the inclination of the turnout. Stock and closure rails are made of standard rail steel. Finally, it should be noted that closure/stock rail section is defined geometrically from the Heel of the Switch to the Toe of Frog/crossing. These two points, according to AREMA (2003) are defined as:  Heel of Switch (HS) is the location at which the switch point pivots about  Toe of frog (TF) is the joint location ahead of the frog/crossing point connected to the closure rails. Also, regarding the connection of closure rails and frog/crossing Hay (1982) states that joint between closure rails and crossing/frog are one of the few in a turnout, but Esveld (2001) states that these are welded or if necessary glued. Crossing/Frog The last part of a turnout is called the crossing or frog. According to AREMA (2003), a frog is a device at the intersection of two running rails to permit the flange of a wheel moving along one rail to cross the other rail. A frog is comprised of the following parts (University of Wisconsin - Madison, 1899) based on Figure 31:

Figure 31: A detailed view of a turnout crossing/frog. Source: (University of Wisconsin - Madison, 1899)  The wedge shape part 퐴 is the frog Tongue  The extreme point of tongue 푎 is the point  The space 푏 between the ends 푐 and 푑 of the rails is the mouth  The rails comprising the mouth have a narrow point 푒 which is called throat  The curved ends 푓 and 푔 are the wings AREMA (AREMA, 2003) states that toe of the frog (TF) is the joint location ahead of the frog point connected to the closure rails, while Heel of frog (HF) is the joint location behind the point of frog. Hay (1982) suggests that the distance from frog toe to the point is the toe distance, while the distance from the point to the heel of the frog is called heel distance. Ruppert (2017) suggests that toe is simply the part from the joint ahead of the point to the point, while heel is the distance from point to the joint behind the point. Finally, as Lichtberger (2005) suggests, that the rails 푐 − 푔 and 푑 − 푓 are called the wing rails, which are the continuation of the two closure rails of the switch which are bent laterally leaving a flange groove. It can be stated that up to the throat of a frog, wing rails support the wheel, while from the throat to their end they guide the wheel flange. Special note about the frog point must be made. According to Ruppert (2017), in theory, the frog comes to a distinct point (THEO. PT), but in reality, it is rounded off to what is called a ½ inch point

(1/2 PF) in USA railway practice, because otherwise the impact of the wheels would destroy it. This point is not referred to the distance from Theoretical PT but where the width of this point is ½ inch (approx. 1,27 cm). Hay (1982) adds that for greater stability, the base of the point is continued into the throat and ground back from the theoretical point. So, for geometrical calculations, two points are used: the theoretical point and the ½ in. point of frog (actual point of frog). Turnout frogs or crossings are characterized by the mechanics of the point of more specifically by the way a frog is negotiating the gap between frog throat and the point as well as its geometry or more specifically the size of the frog angle or the frog number. Ruppert (2017) categorizes frogs into two big groups, depending on if they eliminate the gap or not: Fixed point and Movable point frogs (Figure 32). According to Esveld (2001), depending on the traffic load, different types of crossings are used. For normal to medium axle loads and speeds up to 200 km/h, rigid/fixed crossings are used. For higher axle loads and higher speeds, crossings with movable parts have to be used (for pictures, see Appendix 3, Figure 101):  Bolted Rigid frog: They are fabricated from machined rail pieces with specialized blocks and bolts to guide and support the assembly. Bolted-rigid frogs are generally limited to use in yard and industrial tracks, where traffic is fairly light on both sides, self-guarded frogs are not available, or the usage of second- hand frogs is desired.  Rail-bound Manganese (RBM) Frog: This Frog is made from high-strength manganese steel and held in place between the frog wing rails. It is the most common type of frog, used in many moderate to high speed and tonnage lines. It is also typically used for sidings, passing tracks, spurs, leads, etc.  Solid Manganese –Steel frog: In comparison Figure 32: Fixed vs movable point frogs. Source: (Ruppert, 2017) with RBM, this entire frog is a solid casting. These type of frogs are not that common (in North America) but some are used in transit service as alternative to RBM frogs.  Self-Guarded frog: This is a type of casted steel frog with raised “guard” cast onto wing rails: it eliminates the need for a guard rail opposite the frog but is only suitable for low-speed operation. In this type of frog, the frog flange is simply not strong enough to withstand high - speed operation. However, it is cost-effective, because it eliminates both the initial cost and the maintenance expense of two guard rails. It is commonly used in yard and industrial tracks. Finally, it is possible to be used on main lines, but only in cases where the speed is less than 30 m/h. All the frogs presented above are fixed-point frogs. This implies that they all have a gap in the running surface of the rail to allow a wheel flange to pass through, but this causes impact loads as the wheel tread jumps the gap. Therefore, loads are concentrated on the frog point and as a result, it suffers damage and wear. In that process, flangeway width and depth are also affected. These damages are typically addressed by welding and grinding maintenance activities to restore the point and the top surface. In order to address all these issues and mitigate the problem, eliminating the gap can be considered as a main strategy, which produced a completely new series of frogs: Frogs with movable point. Esveld (2001) provides a good review:  Swing Nose frog: In this type of frog, the entire point “swings” between the two guardrails to close the gap. It has a nose made out of a machined and heat-treated block. Smaller crossings of this type have an expansion joint in the heel to compensate for the difference in length after switching from one position to the other.  Crossing with movable wing rails or spring frog: This type is used for small turnouts and when the length of the turnout is restricted. The elimination of the gap is done by moving the wing rails instead of the point (AREMA, 2003).

 Lift (jump) frog: an experimental category of frogs for heavy freight. It does not use moving parts for diverging route but rather lets the wheel “jump” over the straight rail as train diverges (Ruppert, 2017). Regarding the geometry or the size of a frog, it is characterized by two values, which are connected: the frog number and the frog angle. Recalling Figure 25, the frog angle is the green angle, which measures the spread or extent of diversion (Hay, 1982). Hay also states that a more common designation is the frog number N, which is the ratio between a unit spread and the axial distance from the theoretical point to the place where the unit spread is measured (Figure 33). According to Hay (1982), the frog number 푁 can be calculated as:

1 퐹 푁 = 퐴퐶/퐵퐷 (4) 푁 = 푐표푡 ( ) (5) 2 2 The frog angle on the other hand, can be calculated as:

1 퐹 = 2푎푟푐푡푎푛 ( ) (6) 2푁 It is common practice to use the frog number to characterize the whole turnout (e.g. #10 turnout, which means that the turnout has a #10 frog). Generally, the number of frog is connected with the speed in a turnout and with its size, as bigger frog number implies smaller frog angle, higher allowable speeds and bigger turnouts in Figure 33: Frog size calculation. Source: (Hay, 1982) overall (Table 4). According to AREMA (2003), though turnouts are generally available from No. 6 to No. 24 and more, most railways have limited the general use of turnouts to four to six designs for ease of standardization and part supply. AREMA also states that:

 Turnouts No. 10 and less are generally restricted for yard use, and few frog number angle(deg) railways will allow sizes under 8 or 9 except for special situations. 5 11.42118627 6 9.527283381 Turnouts for industries and sidings from main tracks are generally 7 8.17123356 restricted to no less than 10 to 12. 8 7.15266875 9 6.35966024  Turnout sizes 14-16 are used for medium-speed divergent moves and 10 5.724810452 some heavy traffic unit train facilities. 11 5.205124405 12 4.771888061  Turnout Numbers 20 and 24 are used for main line moves and 14 4.090816978 crossovers, allowing for higher speeds through the divergent leads. 15 3.818304866  Some railways are using No. 30’s and higher. These are used only in 16 3.579821216 18 3.182280542 special situations 20 2.864192368 24 2.386978848 Turnouts allowable speed is also related not only with the frog/turnout 30 1.909682508 number, but also with the shape of switch blades: straight, curved or Table 4: Relation between tangential geometry. frog/turnout number and frog angle. Source: (AREMA, 2003), 2.2.3 Other important parts and aspects of a turnout own edit So far, the main parts of a turnout were described. However, there are some extra parts that must be mentioned. The description starts from point of switch and ends at the heel of the frog. Ties and tie plates in a turnout For wooden ties, because of the divergence of the track, ordinary cross ties are not suitable, so special lengths of switch ties are necessary. These begin with standard-length crossties and increase by ½ foot lengths (approx. 15 cm) as the size and spread of turnouts requires. For increased stability, the crossties are usually continued under both tracks for several tie spaces beyond the heel of the frog. Immediately under the switch points the first two tie spaces are occupied by long timbers called head blocks. They

23 give stability at that point and act as a base on which to set the switch operating mechanism (Hay, 1982). Special designations are also made for ties under the heel block assembly (heel block ties) and those under the frog (frog ties) (AREMA, 2003). In comparison with wooden ties, concrete ties have the advantage that they can be shaped in any size, so turnouts have exactly the length of the tie they need every time. Also, fastening system on a concrete tie can be installed in any position, which possibly can eliminate many types of tie plates and give the opportunity to build turnouts in blocks. Finally it can be argued that concrete ties and fastening systems are used more and more for high speed applications (Esveld, 2001). Turnouts also utilize special type of plates in case of wooden crossties (AREMA, 2003) (see Appendix 3, Figure 102): Figure 34 Wooden vs concrete ties on a turnout. Source: http://www.ostpubs.com/wp-  Gauge plates are placed under the tip end and on content/uploads/2012/07/Turnouts_001.jpg the first tie ahead of the point of switch to hold the rails in proper gauge. https://sc01.alicdn.com/kf/UT8yEAUXxNXXXagOFbXy/2 02615050/UT8yEAUXxNXXXagOFbXy.jpg  Switch plates or slide chairs: They are used under the switch points for support, because of the geometry of the switch blades (they are below the top of the stock rail, especially at the point).  Rail braces: A rail brace is used to resist the lateral thrust on the point and stock rails. Rail braces bear against the outside of the stock rails. They are secured to the gauge and switch plates.  Heel block assembly: plates where heel of blades is found, giving strength and rigidity, as well as providing a point for blades to pivot around.  Turnout plates: Turnout plates are used immediately beyond the heel block assembly. These plates raise the switch end of the closure rail to the level of the heel of the switch point, where uniform riser plates were used under the switch  Hook Twin tie plates: Hook twin tie plates may be used through the closure rails or in locations where there is no room for standard tie plates  Frog plates: Hook twin tie plates are often used at the frog. Spring frogs use special slide plates to allow the wing rail to move on it. Some RBM frogs use toe plates to support wheel loads in this area. Newer style turnouts will often use full-length base plates under the frog. Rails and joints in a turnout Esveld (2001) argues that turnouts are in principle constructed of normal rails. Special profiles are used for the switch blades. The steel grade of the rails usually is the same as on plain track. Special grades like Head SpeciaI Hardened HSH rails improve the wear characteristic of the turnout. Hay (1982) adds that resistance to switch-point wear is obtained by the use of high carbon steel, by heat treating, by manganese-steel points and by use of replaceable manganese point inserts. It also fair to notice that manganese inserts are used in frogs. Modern crossings are now cast from manganese steel which is an advanced alloy that gets harder with use. This is an important property as the nose of the crossing can take high impact loads as train wheels pass through (Network Rail, 2012). Regarding the joints, Esveld (2001) states that all rail joints within the turnout are welded joints or, if necessary, glued insulated joints, as bolted and fish-plated joints should not be used in a modern design. Hay (1982) further argues that joints are being further removed from turnouts by continuously welding a part or all of the turnout. He adds that all joints are welded, except for insulated joints, including stock rail, switch points and connections to the frog. In case of joints existence, Ruppert (2017) mentions that in case of stock rails, they are staggered – the one will be longer than the other,

24 since opposing joints create a serious support and structural weakness of concern for rails and for crossties nearby. Point machine and switch rods According to Hay (1982), switch points are bound together in a unit by the use of switch rods. A head rod is placed vertically at the point ends, and 1-4 rods (according to AREMA (2003) up to 7) are spaced every two or three tie spaces from the point to a distance of 0.5 to 2/3 of the point length. The head rod extends under the stock rails and usually provides connections for the connecting or operating rods from the switch/point machine. AREMA (2003) adds that the Switch rods hold the switch points together at a fixed distance Figure 35: An electric point machine. Source: https://3.imimg.com/data3/VL/UM/MY- and they restrict the up and down movement of the points. 4827132/electric-point-machines-500x500.jpg Regarding the point machines, Esveld (2001) states that the turnout can be operated by different types of point machines e.g. electrically, hydraulically or pneumatically (Figure 35). It is also fair to mention that modern point machines comprise a part of the interlocking system and are controlled by Traffic Control Centers. Switch blades needs to be locked in place by means of switch locks. This is a necessity, as a fail to lock the blades can cause derailment. According to Lichtberger (2005), switch locks are the devices that secure the movable parts of a switch in their end position and allow the points to be thrown. Their tasks are:  to secure the end position of the switch blades by holding the closed point to the respective stock rail and the open point at a certain distance from the respective stock rail  to allow the points to be thrown Lichtberger distinguishes three types of locking devices: hook, clamp and inside locks. Esveld (2001) adds that the locking system can be either in the switch machine (internal locking) or in the track (external locking). In switches for medium and especially for high speed, several locking locations are necessary. He also adds that new developments Figure 36: Switch with integrated hydraulic for high speed or high capacity railway lines are integrated setting and locking system. Source: (Esveld, locking, switching, and detection systems (Figure 36). 2001) Switch heating As Lichtberger (2005) describes, in winter, snow and ice might impede the trouble-free operation of the movable parts of a switch in the area of the blade device, the movable point frog or the locks. That is why important switches are equipped with heaters. They produce heat in the area of the movable parts of a switch and thus keep them operational in winter. Ruppert (2017) adds that these devices can be powered by electricity or propane (Figure 37). Guardrails/check rails and switch point protectors The last components worth mentioning are the guardrails and the point protectors. As Ruppert (2017) mentions, points are subjected to damage and wear from wheel flanges due to thin section, lateral forces and wheel transfer from/to stock rail. Two approaches are either to use replaceable points of high-strength steel, which extend life and facilitate economic repair or to weld damaged points. Figure 37: Heating devices: electric (up) and propane (down). Source: (Ruppert, 2017)

A third option (perhaps a complementary one) is to use switch point protectors. Switch point protector increases the service life of switch points by absorbing the impact of passing car wheels. The protector momentarily defects the wheel flange so it misses the tip of the switch point. The protector is bolted to the inside of the straight stock rail leading into the switch. Figure 38: Switch point protector. Source: Normally the (Harmer Steel, 2014) protector is placed two inches (5.08 cm) ahead of the switch point tip, but the distance may vary due to speed and traffic conditions. This switch point protector is available in most standard rail sizes and is reversible to increase its useful service life. The face plate Figure 39: Another type of switch point can be manganese (Harmer Steel, 2014) (Figure 38). protector. Source: (Ruppert, 2017) Regarding the guradrails, according to AREMA (2003), they are used to prevent misrouting and derailing at the frog point and to prevent wheels from striking the frog point. They may be of either the adjustable or non-adjustable type. The guard rail captures the back of the flange on the wheel opposite the frog and guides the other wheel through the throat opening of the frog. Thus, the mid-point of the guard rail must be positioned ahead of the frog point to ensure that the wheel is properly tracking when it reaches the Figure 40: Guardrail/check rail. Source: (AREMA, 2003) throat of the frog. Lichtberger (2005) adds that a guard/check rains a compulsory element of any rigid diamond/frog (Figure 40). 2.2.4. Geometry and operational characteristics of a turnout It is difficult to establish a single methodology of defining the geometrical properties of a turnout as every railway organization has its own standards, unit measurements, mathematical formulas etc., which is also reflected across diferent railway design manuals and railway books. Also, in most cases, several standardized values are used which are related both with operational ang geometrical characteristics of a turnout . Nonetheless, these methodologies have several points in common, therefore an attempt to approach these points, but also to highlight some important differences will be made. It is also fair to mention that European and USA approach to turnout design is somewhat different. Effect of operational aspects over the geometry of a turnout It must be comprehended that the design of a turnout is an interaction between two aspects: operational and geometrical, as one gives rise to the other. From the perspective of operational perspective, the most important factors affecting the selection of a turnout are the location and use, the speed, and the type of motive power that is to be operated through it (AREMA, 2003; Hay, 1982). To these, the lateral acceleration and the change in lateral acceleration (the jerk) can be added as decisive parameters for the determination of geometric dimensions (Lichtberger, 2005). Esveld (2001) specifies that maximum values of lateral acceleration which is not compensated (푚/푠2), rate of acceleration change (푚/푠3) as well as entry and exit jerk (푚/푠3) can be considered as crucial factors in traditional turnout design method. According to Hay (1982), the curved lead of a turnout limits both the speed of safe operation and the length of rigid wheel base that may negotiate it without excessive binding or derailment. Therefore, the maximum comfortable (and safety) speed is limited to an equivalent of the permissible 3 in. of unbalanced superelevation (since turnout geometry includes no superelevation):

1 푒푎+3 2 푉푡 = ( ) (7) 0.0007퐷푡

Where 푉푡 is the permissible speed through the turnout, 푒푎 is the actual superelevation, usually 0 in and 퐷푡 is the degree of curve through the turnout (for curved switch points) and the degree of curve through the switch for straight points or the closure rails, whichever is the larger. The degree of curve through the switch is (푠/푙) × 100, where 푆=switch angle and 푙 =the length of the switch point. Lichtberger (2005) places his focus on lateral acceleration and the change of it, which is called the jerk. He states that the centrifugal force causes an uncompensated lateral acceleration, when a vehicle runs in a curve. It can be calculated according to the following formula

푉2 푎 = [푚 ] (8) 3.62∗푅 ⁄푠2 Where 푎 is the uncompensated lateral acceleration [푚 ] and R is the radius [m]. ⁄푠2 He states that the admissible uncompensated lateral acceleration is determined by the individual railways (ÖBB, DB AG 0,65 푚 , SBB 0,8 푚 ). On the other hand, when a vehicle enters a curve, ⁄푠2 ⁄푠2 it experiences a change in lateral acceleration, which is called jerk in every day usage. The jerk is calculated as follows (Lichtberger, 2005): 푉3 푚 푎푟 = 3 [ ⁄ 2] (9) 3.6 ∗푅∗퐿1 푠

Where 퐿1 is the axle base of a standard wagon (SBB 퐿1 = 18.9 m). Lichtberger states that the admissible value of the jerk is determined by the individual railways (ÖBB 1,0 푚 , SBB 1,2 푚 ). In general, ⁄푠2 ⁄푠2 according to Esveld (2001), a fundamental relationship connecting the lateral acceleration on a turnout, speed and the curvature of the diverging route in a turnout is the following:

푉2 푎 = (10) 푅 Here it is important to note a key difference between USA and European railway practices when it comes to define how sharp a curve is: In Europe, radius of a curve is by far the most predominant measure of defining a curve’s sharpness. The bigger the radius is, the smoother the curve is. By contrast, in USA railway practices, the degree of curve is used. As Figure 41: Chord and Arc definition. Source: (Dick & Ruppert, 2017) Hay (1982) puts it, railroad curves are usually designated in the USA by the degree of curvature (on subway and elevated lines and in Europe the radius is generally used instead). The degree of curvature/curve is variously defined as the amount of central angle subtended by a chord of 100 ft, by an arc of 100 ft, or by an arc of 100.007 ft. Hay notes that each of these gives approximately the same results. Also, he notes that the degree of curve may also be defined as the change in angular direction between two intersecting straight lines tangent to an arc of unit length (100 ft of chord or arc or 100.007 ft, of arc) as measured by the exterior deflection angle of the two tangents. In USA, railroads use the chord definition, while LRT and highway use the arc definition (AREMA, 2003). Dick (2017) presents the chord and arc definition as well. It is obvious that Degrees of Curve as well as Radius of a curve are related: Lower degree of curve implies bigger radius and therefore a more gradual curve. Same remark can be done Figure 42: Functions of a simple curve (left) and Degree of curve for radius alone: the bigger the radius of a (right). Source: (Hay, 1982)

27 curve, the more gradual a curve is. Finally, it can be stated that the smaller degrees of curve and the bigger the radius are, the smaller the lateral acceleration and jerk becomes, as well as the bigger the speed through the diverging route is. Defining the geometry of a turnout Geometry also affects the operational characteristics of a turnout, as their relationship is twofold. As said before, every national railway organization has its own methodology of determining the geometry of a turnout. Nonetheless, all methodologies are based on several similar points to begin with. For purposes of design, all methodologies use one or more of the points below, located in a turnout:  Point of Switch (PS)  Heel of switch (HS)  Point of intersection of the Turnout (PITO)  Point of frog/ Theoretical Point of frog In spite the fact that purely from a geometrical perspective a turnout extends from Point of Switch to the Heel of Frog, engineers tend to refer as a turnout all the superstructure lying on switch ties (from point of switch to the last switch tie (the last and biggest switch tie in a turnout). A good review of turnout geometry design is presented by Hay (1982). He states that turnouts are designed on the basis of the frog angle (or number), the length of the point, and the degree of the turnout curve. These in turn, give rise to an overall dimension, the lead, which is the distance between the point of switch and the point of frog. Either the theoretical or the actual lead may be under consideration. Here, another important difference between European and USA practice must be considered. Apart from difference between degrees of curve and radius measure, instead of using frog angle, European railways use the ratio of inclination, which is the angle formed at the end of the switch by the tangent of the Figure 43: Main points for turnout geometry calculation. Source: curve axis to the axis of the main track; this (Ruppert, 2017), own edit angle is expressed by the ratio of inclination of both axles to each other (1:9, 1:12, 1:18.5 etc.) (Lichtberger, 2005). AREMA (2003) adds that a common error for designers is to assume that the divergent route of lateral turnouts diverts from the main alignment (the straight side) at a rate equal to the frog number. This is incorrect as this number is based upon the axial distance with equal divergence on either side. This is different than the relative divergence between the two sides. Therefore the frog number does not equal the ratio of inclination. As Hay (1982) describes, on the basis of the theoretical rate of turning of a locomotive at the switch point and around the lead curve, too abrupt a deflection occurs at the point when the switch angle is greater than approximately ¼ of the frog angle. Particularly, ratios of 3 ½ :1 to 4:1 between the frog and switch angles are acceptable. Combining the point width with the heel spread, the length of the switch point can be found. Rather than producing a great variety of switch –point lengths, a few have been standardized within the ratio limit given above and adjustments made in the lead length and curvature accordingly. In a turnout design, one may start with the frog angle and compute the switch angle and then the length of switch point rail and by using a commercial point length and a standard heel spread of 6 ¼ in compute the switch angle s, which is determined by the following relation and according to Figure 44:

푠𝑖푛(푆) = (ℎ − 푡)/푙 (11)

Where 푆 is the switch angle, ℎ is heel spread, usually a standardized value (6 ¼ inches), 푡 is the switch point thickness, usually standardized value (1/4 inches) and 푙 is the length of switch-point rail in feet. The lead 퐿 (the length between the point of switch and the actual/theoretical point of frog) is the sum of 푙, 푏 and 푑. Triangle 1 is solved to obtain 푑 and 푒, using the frog angle 퐹 and the toe distance 푓 (obtained from design or manufacturer’s drawings). In triangle 2 the altitude is 푄 = 퐺 − (ℎ + 푒) and one angle is (퐹 + 푆)/2. This triangle is solved for 푏 and 퐶. Since 퐶 is the long chord of a curve with a central angle of 퐹 − 푆 and a radius equal to 퐺/2 + 푅 , then:

퐺 퐶 + 푅 = 1 (12) 2 2푠푖푛 [( )(퐹−푆)] 2 Solving for either for 퐶 (chord) or 푅 (radius) and substituting with 푄 = 퐺 − 푒 − ℎ (from Figure 44), the above equation becomes:

푄 퐶 퐶 = 퐹+푆 (13) 푅 = 퐹+푆 − 퐺/2 (14) 푠푖푛 ( ) 2푠푖푛 ( ) 2 2 The lead 퐿 thus computed is a theoretical lead. The actual lead in feet would be 퐿 plus the distance from the theoretical to the actual point of frog:

푁푃 퐴푐푡푢푎푙 푙푒푎푑 = 퐿′ = + 퐿 (15) 12 These relations hold whether the turnout is located on a curve or on a tangent. Since an infinite number of leads could result from a various combinations of switch-point lengths, angles and frog number or angle, the practice has been to adopt a few standard lengths of points in conjunction with various frog angles within the ratio limits previously discussed.

Figure 44: Turnout design. Source: (Pickels & Wiley, 1949, cited in Hay (1982) Geometry of switch blades From what was discussed previously, an important part for the geometry of a turnout are the blades. Blades can be straight, curved or vertex clothoids. As AREMA (2003) describes, some switch points are curved, but most are tangent. The location where the switch point meets the stock rails is known as the point of switch. The angle at this point is the switch angle. For straight points, this angle is fixed along the length of the points and is defined by the heel block distance, switch point thickness and switch length. For curved points, the point of switch (PS) represents the PC of a curve. With the exception of some advanced designs recently developed, there remains a slight angle deflected between the stock rail and the PC or PS of the curved point. The geometry of the switch points is crucial for the performance of turnouts along with radius/degree of curve and frog number/angle, especially for high-speed railways. The increase in axle loads as well as in speeds, led to the development of tangential geometry turnouts. This geometry concerns primarily the switch blades and secondary the turnout inclination or the frog angle (Figure 45).

Ruppert (2017) narrates that in standard geometry there is an angle immediately at the beginning of the switch point, which is translated into an abrupt change of direction (higher lateral forces, bigger damage and wear of switch blades, especially at their tip). As speeds increase, there is a need for trains to go faster and faster to the diverging route. So, tangential geometry turnouts were introduced. Instead of having an abrupt angle on the switch point, the switch point curves and becomes tangential to the straight track – instead of having an abrupt angle, trains are gradually making out a divert move, which means a much more smaller entry angle and much smoother change of course. This also allows higher speeds but also makes the length of the turnout even longer. Ruppert notes that higher speed rail and high speed freight will use tangential geometry- lower speeds (50 mph and below) use standard geometry. He notes also that tangent geometry turnouts decrease the high impact loads at the beginning of the switch point.

Figure 45: Standard VS tangential geometry in a turnout. Source: (Ruppert , 2017) Esveld (2001) adds that a modern design uses a tangential beginning of the turnout curve and today, mainly constant radius curves, clohoids, and a combination of these types of curves are used. In fact, the best design available today are vertex clothoids, a point made abundantely clear by Lichtberger (2005). He stresses that a circular curve in the branch of high-speed switches with large curves is not an ideal curve. The clothoid is more advantageous for the branch of a high-speed switch. The comparison between a vertex clothoid switch and a normal circular curve switch shows the following differences:  the vertex clothoid switch is shorter than the circular curve switch by about 15%. And  the space required for it is, therefore, smaller, and manufacturingis easier due to the shorter design Other geometrical aspects of the turnouts Regarding the existence of cant deficiency in a turnout, or superelevation for that matter, Esveld (2001) mentions that rails in the turnout can be placed vertically or inclined. In order to achieve a better curving behaviour a higher conicity is preferable and, therefore, vertical rails are recommended. The transition to the normal raili nclination takes place away from the turnout by slightly twisting the rails. Also AREMA (2003) notes that a turnout provides no superelevation through the lead curve. Finally, Hay (1982) adds that turnouts should not be placed on curves because of difficulties in maintaining adjustment and alignment. A structurally weak element would be introduced where lateral forces are usually a maximum. Further, a turnout to the outside of a curve introduces additional problems of reverse superelevation on the long turnout ties. Turnout performance In summary, key relations between operational and geometrical aspercts of a turnout are presented in Table 5. Also, relations between geometrical and operational characteristics of turnouts in Europe and USA are presented in Table 13 and Table 14 (see Appendix 3) It is obvious that the number of a turnout has a direct relation with a series of parameters in a turnout. In general, a bigger turnout number means:

Table 5: Relation between geometry and operational characteristics. Own edit

 Smaller frog angle  Bigger turnout lead  Increased distance between point of Switch (PS) and Point of intersection of turnout (PITO)- larger switch blades  Bigger frog (in length)  Bigger frog heel  Bigger turnout radius  Bigger diversion speed Same remarks can be done for the ratio of inclination (similar to frog number): bigger inclination leads to bigger radius, overall length and diverging speed. 2.2.5 Conclusions: Turnouts, parts and interaction between operational and geometrical characteristics This part presented turnouts, focusing on left and right handed turnouts, as part of superstructure and analyzed their parts and their role in the overall structure of a turnout. In addition, attention was given to their operational and geometrical characteristics and how these two aspects interact with each other. From the parts perspective, turnouts are extremely complicated, machine-like constructs, which justifies their overall high cost and their need for tactical maintenance. In addition, the most important parts were established: the switch and the crossing frog. Switch is responsible for diverting a train from a course to another and carry the train through the switch blades, while the crossing allows the train to cross tracks safely. Analysis of parts also showed that as constructs, turnouts are constantly developed to accommodate heavier and faster trains: special blade profile, transition towards CWR turnouts, use of techniques and special materials for more durable rails and parts, replacement of fixed with movable point frogs, use of advanced operating mechanisms linked to interlocking and traffic control systems, replacement of wooden with concrete sleepers and better fastening systems as well as use of premium components like heaters and point protectors constitute a modern turnout in terms of parts.

In terms of operational characteristics, speed, acceleration and change of acceleration are the most important factors, which define the capacity and level of service of a turnout, while at the same time dictate the geometrical requirements of a turnout. In terms of geometry, design starts with several key points, some standardized dimensions and some key geometrical measures like the frog number or the ratio of inclination, which give rise to the overall dimensions of a turnout. At the same time, these geometrical characteristics set allowable speeds and accelerations undertaken by trains in a turnout: geometry of blades, frog number and ratio of inclination, type of rail, fastening system and sleeper characteristics, type of frog are some main parameters which should be considered. Therefore it was shown that operational characteristics interact with geometrical ones, and in conjunction with different set of selected parts and their characteristics define the performance of a particular turnout. 2.3. Structural analysis of a rail track and turnout considerations An important aspect of railway engineering is to analyze the response of track infrastructure to wheel loads of the rolling stock. This is done through a framework, called “track structural analysis”. One of its main goals is to identify some key parameters, related either to the structure as a whole or to components it is comprised of. Another aim is to determine the response either of the whole track or of its components to forces, loads and stresses. Finally, assuming a certain range of loads, the purpose is to determine if the track and its components can bear/withstand the loads and stresses caused by the

Figure 46: Longitudinal tie track (1) and cross-tie track (2). Source: (1) https://upload.wikimedia.org/wikipedia/commons/1/1e/Baulk_road_crossing.jpg, (2) https://upload.wikimedia.org/wikipedia/commons/8/88/Railroad_tieswoodconcrete.jpg planned traffic. Track structural analysis can be either static or dynamic and in this section, the former type is presented. For the presentation, a variety of sources are used, but the most central one is the books of Kerr (Kerr, 2003, p. Section IV), complemented by the books of Esveld (2001) and Lichtberger (2005). The method here is used and recommended by AREMA in the AREA manual (1991, section 22; referred in Kerr, 2002). For more on the method see Kerr (1976) and Kerr (2003) 2.3.1. Theoretical foundation and main parameters of track structural analysis According to Kerr (2003), attempts of analyzing the track structure began in 19th century and led to the development of analysis for two different types of track: The longitudinal –tie track and the cross-tie track. In the first case, the two metal rails are continuously supported by longitudinal ties, in the second case, the rails are supported discretely by cross-ties (Figure 46, Figure 47, Figure 48). The analysis of the first type of rail track evolved rather smoothly, while for the second it was more complicated due to the discrete nature of rail supports, which presents difficulties in terms of analysis but was surpassed by adopting the framework of longitudinal track analysis. According to Kerr (2003), Winkler (1867) was the first who proposed to analyze the stresses in the rails of a longitudinal-tie track by considering each rail as a continuously supported beam. The differential Figure 47: Longitudinal-tie track. Source: (Kerr, 2003, p. equation for the bending theory of an elastic beam Section IV) was established by the time:

푑4푤 퐸퐼 + 푝(푥) = 푞(푥) (16) 푑푥4 Mechanically, it represents the response of a beam attached to a base that consists of closely spaced linear springs. For this equation, according to Kerr (2003), Schwedler (1882, pp. 95-118), derived a solution, when a very long rail-tie beam is subjected to a concentrated wheel load 푃 at 푥 = 0, defining 푤(푥) (rail deflection) and 푀(푥) (rail bending moment). Figure 48: physical problem of the cross-tie support below In comparison with longitudinal track the rail base. Source: (Kerr, 2003, p. Section IV) analysis, cross-tie track analysis, which is the mainstream nowadays, faced issues in terms of analysis because it tried to analyze the track as a beam on many discrete supports, which was demanding in terms of computation. Therefore, it adopted the approach of longitudinal track analysis by assuming that for a cross-tie track the rails respond like a continuously supported beam. Kerr (2003) mentions that the work of Flamache (1904), Timoshenko (1915) and ASCE-AREA Special committee on stresses in Railroad Track headed by professor Talbot6 (1918), as well as evolution in rolling stock and track structure characteristics helped towards the acceptance of continuity assumption in cross-tie tracks. The model for cross-tie track (Figure 49) is similar to that of Winkler, with a crucial difference: now the rail is the only longitudinal element. The governing (equilibrium) equation is the same as in the case of longitudinal track: Figure 49: Analytical model for rail analysis in a cross-tie 퐼푉 퐸퐼푤 + 푘푤 = 푞 (17) track. Source: (Kerr, 2003, p. Section IV)

The difference however lies in what each terms represents. More analytically:  퐸퐼푤퐼푉: represents the contribution of rail bending  푘푤(푥):represents the “continuously distributed” upward pressure on the rail base (an assumption that also stands in the earlier Winkler’s model): 푝(푥) = 푘푤(푥) (18)

 푞: represents the vertical wheel loads.  퐸 is the Young’s modulus for rail steel7  퐼 is the moment of inertia of a rail8 with respect to its horizontal centroid axis  푘 is the vertical stiffness of the rail support (otherwise called as rail support modulus or track modulus). According to Kerr (2003), 푘 represents the effect of the cross-ties (their bending stiffness, their vertical compressibility in the rail-seat region and the tie spacing), fasteners, tie pads, ballast and subgrade, but does not include the rail response. In other words, how soft or stiff the track is. The rail support modulus plays an important role, as it affects the main parameters that describe the response of rail track to wheels: rail deflection, exerted pressure, bending moment of rail and rail seat force.

6 This special committee published five reports in total between 1918 and 1929 (ASCE - AREA, 1918), (ASCE-AREA, 1920), (ASCE-AREA, 1923), (ASCE-AREA, 1925), (ASCE-AREA, 1929) 7 Young's modulus is a mechanical property that measures the stiffness of a solid material, in essence how easily it is bended or stretched 8 According to Edwards (2018) the moment of inertia 퐼 is a quantity expressing a body’s tendency to resist angular acceleration. It is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation

The equilibrium equation can be used to derive these main parameters mentioned above. More specifically, for one wheel load 푃 that acts on a very long rail at 푥 = 0: Rail deflection function: describes the rail deflection around the wheel and along the rail:

푃훽 −훽|푥| 푤(푥) = 푒 [푐표푠(훽|푥|) + 푠𝑖푛(훽|푥|)], − ∞ < 푥 < +∞ (19) 2푘

휂(훽|푥|) With maximum deflection at position 푥 = 0:

푃훽 푃 4 푘 푤 = 푤(0) = = √ (20) 푚푎푥 2푘 2푘 4퐸퐼 Where :

4 푘 훽 = √ (21) 4퐸퐼

According to Edwards (2017) 훽 is the damping factor: it is important to the whole analysis because it takes into consideration the stiffness value 푘 and the flexural rigidity of the rail track structure. Pressure distribution function: pressure that the rail exerts on the ties (sleepers) around the wheel and along the rail. Combining (18) and (19):

푃훽 푝(푥) = 푒−훽|푥|[푐표푠(훽|푥|) + 푠𝑖푛(훽|푥|)] (22) 2

휂(훽|푥|) With maximum pressure at position 푥 = 0:

푃훽 푃 4 푘 푝 = 푝(0) = = √ (23) 푚푎푥 2 2 4퐸퐼

Bending moment of a rail: In terms of structural analysis, according to Megson (2019, p. Chapter 2), the moment of a force 퐹, about a given point 푂 is defined as the product of the force and the perpendicular distance 푎 of its line of action from the point, in other words 푀 = 퐹푎. A moment possesses both magnitude and a rotational sense. In short, Moment is the rotational effect a force exerts on a body. As an example, in Figure 50, the moment of the force 퐹 can be found by using the thumbs-up rule: it would be represented by a double-headed arrow through O with its Figure 50: Moment of a force about direction into the plane of the paper. a given point. Source: (Megson, 2019, p. Chapter 2) Rail is considered as a supported beam. According to Iremonger (Iremonger, 1982), a beam is not only in equilibrium as a whole but in addition, internal forces and moments maintain the static equilibrium of all parts of the beam. Therefore, if a wheel is considered, it applies a force downwards, which produces a sagging bending moment on the rail (Figure 51). In reality, the mechanics of bending moments are much more complicated, since all the forces being applied on Figure 51: Beam subjected to a pure sagging bending the rail have to be considered. In sort, a bending moment. Source: (Megson, 2019)

34 moment is defined as the resultant moment about the neutral axis of a beam or column, at any point along its span, of the system of forces that produce bending. (Gooch, 2007), or as the total algebraic sum of the moments of the external forces acting to any one side of the section considered. (Iremonger, 1982). Returning to track structural analysis, bending moment of a rail is described as:

푃 푀(푥) = −퐸퐼푤′′(푥) = 푒−훽|푥|[푐표푠(훽|푥|) − 푠𝑖푛(훽|푥|)], − ∞ < 푥 < +∞ (24) 4훽

휇(훽|푥|) With its maximum value being given by:

푃 푃 4 4퐸퐼 푀 = 푀(0) = = √ (25) 푚푎푥 4훽 4 푘

Finally, rail seat force is given by:

푃훽 퐹 ≅ 푎푝(푥 ) ≅ 푎 푒−훽푥푛[푐표푠(훽푥 ) + 푠𝑖푛(훽푥 )] = 퐹 휂(훽푥 ) 푥 > 0 (26) 푛 푛 2 푛 푛 푚푎푥 푛

휂(훽|푥|) where 푥1, 푥2, 푥3, … , 푥푛 are distances from the tie where 퐹푚푎푥 is exerted to neighboring ties, with maximum value given by:

푃훽 퐹 = 퐹 ≅ 푝(0)푎 = 푝 푎 = 푎 (27) 푚푎푥 1 1 2 Regarding 풌, Rail Support modulus, as Edwards (2017) states, it can be defined as:

푃 푘 = 푢 = (28) ∆ Where:  푘 or 푢: Track modulus (pounds/inch/inch)  푃: Wheel load per unit length of rail (pounds/inch)  ∆: one unit of track deflection (inch) Therefore track modulus is the amount of load in pounds on a 1-inch length rail required to deflect the track by 1-inch and it combines the stiffness of fasteners, ties, pads, ballast and subgrade into one term (Edwards & Ruppert, 2017). 푘 is a very important parameter in railway structural analysis, as it affects greatly all the main quantities describing the response of track to loads. Practically, it expresses the stiffness of the track. Edwards (2017) states that due to complexity of track system, the value of 푘 cannot be calculated from the properties of individual components, therefore field measurements are required. The estimation of 푘 can be even harder, as he mentions that several other Figure 52: Graphical presentation of η(βx) and μ(βx). factors can affect the value of 푘, such as: Source: (Kerr, 2003, p. Section IV)

 Deflection increases over time  Axial thermal forces  Track disturbance and climate  푘 can be varied even across short distances along the track. Nonetheless, railway bibliography mentions several methods of determination of 푘. One of them mentioned by Kerr (2002,2003) is an approach proposed by Timoshenko and Langer (1932) for one axle where 푤푚 = 푤0:

1 3 푃4 푘 = √ 4 (29) 4 퐸퐼푤푚

It is a very simple method and still recommended even in the most recent railway engineering texts. However, it requires special setup to be calculated (measurement of deflection). Graphically, functions of deflection, pressure, bending moment and rail seat force as well as forms of 휂 and 휇 (Figure 52) are shown are presented Figure 53: Rail deflections for different k-values with below, exhibiting really interesting remarks. constant wheel load and rail section (up) and for Furthermore, Kerr (2003) compares these different rail sections with constant k and wheel load parameters and the effect of different values of 푘 values (down) by one-axle rolling stock. Source: (Kerr, and for different rail sections on them. 2003, p. Section IV) Regarding deflection representation and analysis, it reveals that a short distance away from the wheels, on either side of them, the rails lifts, thus exerting upward forces on the fasteners. These forces are repeated with passing wheels and are amplified by the speed, loosening the cut spikes (when wooden ties with traditional fastening system are applied). So one main issue is that deflection has an important impact on rail fastening system of any kind. Furthermore, it must be noted that 푘 values have an immense impact on rail deflections (lower values imply Figure 54: Determination of rail-seat forces from the p(x) greater deflection), but rail sections do not curve, Source: (Kerr, 2003, p. Section IV) (Figure 53). Regarding the graphical representation of pressure, it is similar as deflection, but in essence multiplied by 푘. Kerr (2003) makes several remarks about pressure noticing that as 푘 increases, the maximum deflection decreases but the maximum pressure increases, which is important for ballast and subgrade when wooden ties are replaced with concrete ties. This results in stiffer track which means higher pressures to ballast and subgrade and therefore faster deterioration for both (Figure 53, Figure 55). Considering the rail seat forces (i.e. the vertical forces the rail exerts on the ties), Kerr (2003) mentions that due to the assumption of continuous support, the resulting contact pressure distribution 푝(푥) is also continuously distributed, but the rail seat forces act only on ties. Therefore, a rail-seat force is calculated by allocating the proper part of 푝(푥) curve to the tie under consideration (Figure 54). It is useful to note that Fn forces is directly related to wheel load, pressure and the spacing of ties and that rail seat forces will be a fracture of the wheel load, demonstrating the load distribution function of a track system (Figure 57).

Kerr (2003) suggests that according to rail seat force formula, 퐹푚푎푥 depends on tie spacing and wheel load. Tie spacing determines what percentage of wheel load the central tie will absorb: tighter spacing of ties means more even distribution of rail seat force and lesser force on the central tie. However, rail seat force is proportionate to wheel load: since 퐹푚푎푥 governs the size of tie plates, the pressure between ties and ballast (and ballast depth), by increasing wheel load the track will show increased deterioration, unless it has excess strength to absorb this increase in wheel loads. Also, 퐹푚푎푥 depends on 푘 values: higher values (stiffer track) means bigger maximum rail seat load (the tie below the wheel absorbs more wheel load). Finally, regarding to graphical representation of the bending moment of the rail, it is depicted in Figure 56. According to Kerr (2003) the largest rail bending moment 푀푚푎푥 occurs under the wheel and that its value increases with decreasing 푘 and increasing 퐸퐼. In fact, bending moment is seriously affected by soft Figure 55: Pressure distribution for different k values track, meaning small 푘 values. Also, Kerr stresses that with constant rail section (up) and with different rail that each bending moment distribution exhibits not sections for the same k value (down). Source: (Kerr, only positive, but also negative bending moments. 2003, p. Section IV) According to bending moment equation, the largest value of the negative moment is 20% of the positive 푀푚푎푥 at 푥 = 0 regardless of rail weight or rail support modulus 푘. Regions of negative bending moments play an important role in reducing 푀푚푎푥when two or three axle trucks are used. In general, bending moment is important, as it used to calculate the bending stress applied on a rail and thus to determine if a rail can handle specific loads (Figure 56). This analysis is concentrated around key measures regarding one-axle configurations, which is not the case for modern trains, but according to Kerr (2003) since the governing differential equation for

Figure 56: Rail bending moments caused by P for a range of k values (left) and for a range of rail sections (right). Source: (Kerr, 2003, p. Section IV) the rail is linear, the effect of the second axle may be included by superposition (addition) of the effects of the two wheel loads In general, the addition of another axle increases the railway deflection, pressure and rail seat force, but as 푘 value increases, the maximum deflection, Figure 57: Relationship between wheel load and maximum rail pressure and rail seat forces values start to seat force. Source: (Kerr, 2003, p. Section IV)

37 approach the values with one-axle trucks. For bending moments, this is more important, as the bending moments for two or more axles become smaller, which contributes to the overall health of rails (either with joints or CWR). 2.3.2. From main parameters of structural analysis to stress calculations

Having determined the 풘풎풂풙, 풑풎풂풙, 푴풎풂풙 and 푭풎풂풙, the next step in structural analysis of a track is to determine some key design strength criteria of its elements. This procedure is described by Edwards (2018). Usually these criteria are numerical and are either maintenance or strength criteria. More specifically, these criteria are the following: 1. Largest bending stress in rails 2. Largest bending stress in ties 3. Largest bearing stress between tie plate and tie (when plates are used) or largest bearing stress between rail and tie (if plates are not used) 4. Largest bearing stress between tie and ballast 5. Largest bearing stress between ballast (or subballast) and subgrade 6. Amount of track deflection under load It is important to mention that European and USA methodologies use different measurement systems: in Europe, metric system is used, where 1) Length: meters (m), centimeters (cm), millimeters (mm), 2) Area: square cm. and mm. (푐푚2, 푚푚2), 3) Pressure: Newtons/square cm or mm (푁 or ⁄푐푚2 푁 ). In comparison, in USA, imperial measures are used, where 1) Length: feet (1 ft = 30.48cm) ⁄푚푚2 and inches (1 in = 2.54 cm), 2) Area : square feet (푓푡2) and inch (𝑖푛2), 3) Pressure: pounds (or pounds- force) per square inch (psi or 푙푏/𝑖푛2). 2.3.2.1. Rail bending and axial thermal stress Regarding the rail and its bending stress, according to Kerr (2003), forces that are applied to rail result in three different types of stresses: Contact stresses (휎푐), Bending stresses (휎푏) and Axial stresses (휎표). These are summarized in Figure 58 and Table 6. Of great interest for the present analysis are bending stresses and axial thermal stresses. By itself, bending stress is used as an anchor point for the whole analysis. After it is found it is compared with the allowable bending stress, which is a combination of yield point of rail steel, the effect of thermal stress and wear/fatigue, are either parameters or values directly deducted from the initial yield point of rail steel. Kerr (2003) states that the purpose of determining the rail bending moments is to calculate the corresponding rail bending stresses. According to books on strength of materials, to a bending moment 푀(푥) some bending stresses are corresponded in the rail:

푀(푥)푧 휎 (푥, 푧) = (30) 푥 퐼

Contact stresses (휎푐) Bending stresses (휎푏) Axial stresses (휎표) Rail seat force ( a direct Caused by: Caused by: Caused by: result of wheel loads-not a - Wheel loads, static or - Wheel loads - Uniform temperature stress but force applied by dynamic - Non-uniform temperature changes the rail to the crosstie) changes - Acceleration/deceleration of trains - Rail Creepage

They affect: They affect: They affect: 퐹푚푎푥 affects: 1 ) Rail wear 1) Selection of rail size 1) Track buckling or pull- 1) Dimensions of tie 2) Rail fatigue and shelling 2) Rail section at poorly aparts 2) Size of tie-plate 3) Formation of plastic zone in maintained joint, which 2) Distribution of rail 3) Tie spacing contact regions and rail may plastically deform anchors 4) Depth of ballast layer corrugations

Table 6: Source and consequences of stresses. Source: (Kerr, 2003, p. Section IV)

Figure 58: Stresses in rail. Source: (Kerr, 2003, p. Section IV) As shown in Figure 59, where: 퐼 is the moment of inertia of the rail9, 푀(푥) is the bending moment of the rail and 푧 is the section modulus of the rail10. As it can be seen, geometric characteristics of the rail and especially moment of inertia of the rail play an important role in decreasing the bending stresses in a rail section. Regarding uniform thermal stresses in a rail section, Figure 59: Rail section properties. Source: (Kerr, Kerr (2003) suggests that they are more important, 2003, p. Section IV) especially in a CWR track, a case where a rail is fixed at both ends and is subjected to a temperature increase ∆푇0 ;then the axial displacement at both ends, as well as throughout the rail are zero. However, the corresponding axial forces 푁푡 are not zero (Figure 60). He analyzes further and states that when the thermal stresses 휎푡 are uniformly distributed over the cross section with area 퐴, the compression forces in the rail is:

푁푡 = −휎푡퐴 = −퐸퐴휀푡 (31)

Where: 휎푡=thermal stresses, 퐴 =cross sectional 11 area of rail, 휀푡 is the thermal strain or the amount of thermal expansion is defined as 휀푡 = ∆퐿/퐿 and 퐸 = Young’s modulus for steel12 Furthermore, he proves that: Figure 60: Axial (compression) forces in rail fixed at both ends. Source: (Kerr, 2003, p. Section VII) 푁푡 = −퐸퐴푎∆푇0 (32) Where 푎 is the coefficient of linear thermal expansion for steel. 2.3.2.2. Sleeper / crosstie bending stress Regarding a crosstie’s bending stress, the main parameter under consideration is the maximum bending stress that is applied on a tie and its bending capacity. A good review provided by Edwards (2018) using crosstie structural analysis postulated by Hay (1982). According to Edwards (2018), stress in a crosstie is concentrated under the rail and this can vary because ballast support can change overtime either due to traffic or to maintenance works. Thus, a tie

9 According to Edwards (2018) the moment of inertia 퐼 is a quantity expressing a body’s tendency to resist angular acceleration. It is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation 10 According to Edwards (2018) section modulus 푧 the ratio of the moment of inertia of the cross section of a beam undergoing flexure to the greatest distance of an element of the beam from the neutral axis. When comparing beams of the same material, the one with the largest section modulus will be the strongest 11 A force tending to pull or stretch something to an extreme or damaging degree 12 Young's modulus is a mechanical property that measures the stiffness of a solid material, in essence how easily it is bended or stretched

can end up in two conditions center bound track condition or end bound track condition (Figure 61). The former condition is a product of repeated load applications and can lead to broken ties at the center, while the latter is the case after tamping actions. Theoretically, Hay (1982, reffered in Edwards & Figure 61: Center bound track condition (up) and end Ruppert, 2018) approaches the issue of bending bound track condition (down), Source: (Edwards & moment and stress in a wooden sleeper by connecting Ruppert, 2018) wheel loads, and geometrical characteristics of a tie:

2푃 2푃 = 푠퐿 ⇔ 푠 = (33) 퐿 Connecting the wheel loads, the load per unit of length and length, where: 푠= load per inch of tie length, 푃= wheel load and 퐿=length of crosstie And:

퐿 = 퐿1 + 2퐿2 (34) Figure 62: basic dimensions of a crosstie. After, calculation of bending moment under center and rail Source: (Edwards & Ruppert, 2018) seat follow. It can be proved that:

퐹 퐹 퐿2 푀 = ( 푚푎푥)(퐿 − 2퐿 ) (35) and 푀 = − ( 푚푎푥 2) (36) 푐 4 1 2 푅 퐿

It must be noted that 퐹푚푎푥must account for adjacent wheels. Diagram of bending moments are presented in Figure 63. After calculating bending moments, the next step is to define the bending stress in a crosstie. For the calculation, the maximum bending moment is used. Recalling the equation (30) for rail, the bending stress in a tie can be calculated as:

Figure 63: Bending moments under the Rail seat and under center. Source: (Edwards & Ruppert, 2018)

푀푐 푆 = (37) 퐼 Or:

푆퐼 푀 = (38) 푐 Where: 푀=bending moment, 퐼= moment of inertia of the tie, 푐=distance from the neutral axis and 푆= wood fiber bending stress. These quantities can be found mostly geometrically or through the structural analysis of a tie, which is essentially a simple beam. Some of these geometrical aspects of a tie are presented in Figure 64. More specifically: Figure 64: Geometrical characteristics of a cross section of a tie. Source: (Edwards & Ruppert, 2018)

 퐼 = 푏ℎ3/12  푐 = ℎ/2 These quantities can be substituted in equation (38), thus giving: 푀 = 푏ℎ2푆/6 (39)

These formulas can be used to establish whether the existing ties can accommodate the existing loads in terms of either rail seat force, Figure 65: Effective contact area of a wooden crosstie. Source: bending moments or stresses, as every tie has an (Edwards & Ruppert, 2018) allowable rail seat force, an allowable bending moment and allowable bending tress. In terms of stress, wooden crossties have a different value for wood fiber bending stress limits. Which is also affected by the quality and type of wood, existence of defects and climate/temperature. The most important however are the geometrical characteristics of a tie, which play the most immense role in accommodating the rail seat forces. The approach is somewhat different for concrete crossties as they are prestressed, which affects the way of calculating the values said before. 2.3.2.3. Bearing stress between tie plate and crosstie Regarding the bearing stress between tie plates and tie as Edwards (2018) describes, the purpose of a tie plate (or any fastening system for that matter) is to reduce the contact pressure the rails exert on the wooden tie. Tie plates are usually standardized, but what differs between them is their length. Therefore, the key is to provide a tie plate area big enough to distribute the weight a rail exerts on a tie which means that the resulting pressure a plate exerts on a tie does not excess the bearing capacity of a tie. Tests indicate that wood fibers in ties have a certain bearing capacity, which should not be exceeded. That said:

퐹 휎푟푎푖푙−푡푖푒 = 푚푎푥 ≤ 푏푒푎푟𝑖푛푔 푐푎푝푎푐𝑖푡푦 표푓 푎 푡𝑖푒 (40) 푚푎푥 퐴 Where 퐴 is the surface provided by the tie plate. It is obvious that the most crucial characteristic of a tie plate is to distribute the rail seat force exerted on a tie, which is a function of the area of the tie plate. Similar function is provided by elastic fastening systems and especially the rail pads in concrete ties. 2.3.2.4. Bearing stress between crosstie and ballast Regarding the largest bearing stress between tie and ballast, the logic is similar as in the case of tie plates: to distribute 퐹푚푎푥 by using the area of a tie in such a way that the resulting pressure will not exceed the bearing stress of the ballast. However, according to Edwards (2018) these values assume different contact areas- effective areas or 퐿푒푓푓:

2  퐴 = 퐿푏 (wooden ties- this is the tie area delimited by the rails-an approximation) 푤 3  퐴푐 = 퐿푏 (concrete ties –the whole area of a concrete tie is taken into account) This is presented in Figure 65. Therefore, the pressure exerted from tie to ballast can be found by this simple formula:

푡푖푒−푏푎푙푙푎푠푡 퐹푚푎푥 휎푚푎푥 = (41) 퐿푒푓푓 푏

It must be noted that only one of the effective areas must be used for that calculation. 퐿푒푓푓 is approximately 1/3 of a wooden tie.

2.3.2.5. Bearing stress between ballast and subgrade Regarding the largest bearing stress between ballast (or subballast) and subgrade, the practice dictates that the stress exerted by the ballast on the subgrade must not exceed the allowable bearing stress of the subgrade, which is connected with the ballast height. Edwards (2018) suggests the use of Talbot committee formula (ASCE-AREA, 1920) in order to solve the problem. According to Bathurst & Kerr (1999), it is an empirical formula based on measurements of vertical stress versus depth. Then, a best-fit curve was drawn and the expression for the vertical stresses was chosesn, namely:

1.25 푝푐 = 16.8푝푎/ℎ (42)

Where 푝푐 is the subgrade stress under tie centerline , 푝푎 is the pressure at tie face (maximum rail seat load/tie bearing area) and ℎ is the support ballast thickness. The same equation can be solved for ℎ, thus producing the following equation:

16.8푝 0.8 ℎ = ( 푎) (43) 푝푐 They also mention that various similar formulas were developed by either national railway organizations or by individual researchers. 2.3.3. Structural considerations in a turnout In this paragraph, several critical issues regarding the structural characteristics of a turnout will be discussed, on the basis of the earlier chapter regrading the structural analysis of a rail track. 2.3.3.1. Forces acting on the diverging route Earlier, it was discussed that from the standpoint of forces applied on the track, there are three kinds of them (Esveld, 2001):  Vertical  Horizontal, transverse to the track (lateral forces)  Horizontal, parallel to the track (longitudinal/axial forces) Examining a typical right-handed turnout, the situation with force application is more intriguing than a typical rail track: while Figure 66: Forces applied on a turnout. for the straight route, the application of forces is more or less the Own edit same as in the case of a straight track (with the exception of more discontinuities causing the development of dynamic forces), for the diverging route it can be assumed that because of the curve, there is an amplification of all forces, espcially in the outer rail, of vertical, lateral and axial forces, as well as of their dynamic component (Figure 66, Figure 67, Figure 68). This is not happening only because of discontinuties, but also because of the special wheel-rail interaction on a curve, the hunting motion as well as the existence of centrifugal force:

푚푣2 퐹 = (44) 푐 푅 It has to be noted that turnouts do not employ cant deficiency to counteract the extra forces being developed on a turnout curve; therefore they have to deal with these forces through their geometric Figure 67: Right-handed (left) and left design, acceptable speeds and proper design of the vehicle/track, handed (right) turnout, outer rail (red). especially at high-speed turnouts. Own edit Vertical forces When vertical forces are considered, wheel load, speed, radius of curve, track width, geometry of vehicle in relation to the track, increase of wheel load in connection with centrifugal force as well as cross wind force have to be taken into account for the calculation of maximum vertical forces, which is

applied on the outer rail. Depending also on the circumstances, there is an inherent tilting risk, which can occur over the outer rail at high speeds, great cross wind and due to off-loading of the inner rail (Esveld, 2001). He states that In view of the large number of load repetitions, the dynamic wheel load can be considered as a fatigue load, so static wheel load must be multiplied by a dynamic factor. Vertical loads also bend the track upward about 2 m in front of and behind a wheel. These forces act on fastenings and sleepers (Esveld, 2001). Lateral forces In case of a curve without superelevation, for lateral forces, lateral force caused by flanging in connection to the wheel load, centrifugal force, track width, speed, radius of curve and cross winds have to be taken into account. Again, the maximum lateral force is applied on Figure 68: Quasi-static vehicle forces in a curve. the outer rail. Excessive lateral forces can cause Source: (Esveld, 2001) derailment. More specifically, derailment can occur if the 푙푎푡푒푟푎푙/푣푒푟푡𝑖푐푎푙 force ratio increases in value because of high lateral forces Y acting on the outer rail

or low wheel loads Q in the case of unloaded wheels (Esveld, 2001). As Esveld (2001) explains, in the situation is drawn where the forces are acting on the rail and where flange climbing is about to begin. From the equilibrium conditions the normal force N (product of Lateral and vertical force applied by the wheel) and the tangential force S in the contact area can be expressed as: 푁 = 푌푠𝑖푛훽 + 푄푐표푠훽 (45)

푆 = 푄푠𝑖푛훽 − 푌푐표푠훽 (46)

He states that flange climbing can be prevented or stopped if the shearing force satisfy this relationship: 푓푁 ≤ 푆 (47)

Where 푓 is the friction coefficient. Geometry of rails and especially in switch blades can be crucial in preventing a derailment. In the total lateral force, a dynamic factor must be also included. Lateral forces can not only cause derailment but also can cause the sleepers to move in the ballast bed, possibly causing permanent deformation, therefore the track frame must Figure 69: Quasi-static vehicle force in a have a reliable horizontal track stiffness. Another important curve. Source: (Esveld, 2001) remark comes from Hay (1982) regarding the relation between Lateral and Vertical forces: the L/V ratio. He states that this is the ratio of lateral component to the vertical component of the wheel load and plays an immense role in derailments, especially on curves. According to this relation, the tendency towards derailment increases as the ratio increases, because of increased lateral pressure against the outer rail, causing a wheel flange to climb or overturn the rail. Longitudinal forces Longitudinal or axial forces are of most importance for a turnout, just as the lateral forces. Two of the most severe are the effects of temperature change and track creepage. Kerr (2003) makes some very interesting remarks about axial forces in a turnout, caused by change of temperature. Considering a left or right hand turnout, it consists of a tangent track that branches out into another track. During the summer, this track configuration is subjected to a uniform temperature rise ∆푇0 above neutral (stress-

free temperature). The generated axial compression forces are shown in Figure 70. He describes that on the left side of the turnout region, each of the two rails is subjected to the thermal force 푁푡. On the right side of the turnout region, there are two tracks and each of the four rails is subjected to a force 푁푡. Thus, the 4 푁푡’s from the right side have to be converted into 2 푁푡’s on the left side of the turnout region. Figure 70: Axial rail forces in a turnout caused by ∆푇0. Source: (Kerr, 2003, p. Section VII) Note that the two inner rails on the right side essentially terminate at the frog. Therefore, the axial forces have to transfer to the outer stock rails, utilizing the switch ties and the longitudinal track resistance between the rail-tie structure and the ballast. This is indicated in Figure 70 by the dashed force-flow arrows. The result is an increase of the axial forces in the outer rails in the frog region. This force situation may lead to lateral buckling of the entire rail-tie structure in the turnout, especially in cases when the fastening system is wear or weakened by traffic. He also notes that another aspect to be considered is shown in Figure 71. When the rail temperature increases by Figure 71: Lateral track force in a turnout ∆푇0, the branched-out track exerts a lateral force ∆푁 on the region. Source: (Kerr, 2003, p. Section VII) main line, pushing the turnout region sideways. This might get the track out of line and trigger a buckling mode. Rail creep or creepage is another important factor which produces longitudinal or axial forces affecting the track. Esveld (2001) describes this phenomenon as the gradual displacement in the running direction of either the rails relative to the sleepers or of the rails plus sleepers relative to the ballast bed. Kerr (2003) states that forces due to rail creep, are more difficult to determine, as they are caused even by vehicles moving at a constant speed. The rail-driving mechanism is generated by the interaction of the moving wheels with the rails, while they load and then unload the rails. To date there is no generally accepted theory for phenomena of this type. Oldknow (2017;cited in Edwards & Ruppert, 2018) explains that creepage at the wheel-rail interface is related to all of the following: locomotive adhesion, braking, vehicle steering, curving forces , wheel and rail wear, rolling contact fatigue, thermal defects , noise and corrugation. Another remark he makes is that sometimes, forces give rise to creepage (e.g. traction, braking steering), but other times, creepage gives rise to forces (e.g. curving). Esveld (2001) supports that Creep has the following disadvantages:  Increase in CWR forces  Too large or too small expansion gaps in jointed tracks  Non uniform rail creep resulting in misalignment of the Figure 72: Schematic layout of standard sleepers due to which horizontal bending moments are exerted and radial boogies: (a) Parallelogrammed on the rail bogies, (b) radial bogies. Source: (Hay,  Displacement of sleepers resulting in disturbance of the 1982) stability of the track in the ballast bed Esveld also argues that the cause of creep is to be found in the bending wave movement of the track close to the wheel. More details about creepage are described also by Oldknow (2017). One of his remarks, especially important for turnouts and curves in general is the rise of lateral creepage, which is related to the radius of the curve, as well as the type of bogies. Radial bogies can decrease creepage on the diverting route of the turnout (Figure 72).

2.3.3.2. Effect of joints and discontinuities on structural analysis measures Forces acting on a turnout also affect deflections, pressures, bending moments and rail seat forces, especially at parts of a turnout with discontinuities, mainly joints, switch blades and the frog. Kerr (2003) analyzes the effect of a poorly maintained joint on these values (see Kerr (2003, pp. 98-100). What can be found is that in case of a poorly maintained joint and with 푘 = 3000 푙푏/𝑖푛2, rail section 132 RE with 퐼 = 87.9, 푃 = 30000 푙푏 and 푎 = 20 𝑖푛, is that for maximum values: 푊푗표푖푛푡 = 4 × 푊푟푎푖푙, 푃푗표푖푛푡 = 4 × 푃푟푎푖푙, 푀푗표푖푛푡 = 4 × 푀푟푎푖푙, 퐹푚푎푥−푗표푖푛푡 = 3 × 퐹푚푎푥−푟푎푖푙. Furthermore, Kerr elaborates that even in cases of well-maintained joints, rail seat forces and deflections will still be larger than Figure 73: Pressure distribution at joints. Source: (Kerr, 2003) away from the joint because according to AREA13 the vertical bending stiffness of two joint bars is only about one third of the corresponding rail stiffness. The result is that at joints, wheel ‘’dips’’ in that area causing dynamic vertical forces as well as static rail seat forces. This is why the use of joints should be avoided when using concrete ties, as 푘 values are higher than in wooden ties. By extend, it can be argued that the same situation, even more serious, happens at turnouts: even when CWR rails are used, turnout has some distinct points of discontinuity, mainly at switch blades and at the frog area (between toe throat and frog point), where discontinuities and geometric irregularities give rise to higher structural measures than in cases of standard rail. Also, the facts that this is a turn and in turns vertical, lateral and axial forces are higher, with a higher dynamic component and with the existence of centrifugal force the overall infrastructure deteriorates faster, must also be taken into account.

Figure 74: Dynamic loads calculated in turnout blades (A), rail (B) and crossing nose (C). Source: (Saura, et al., 2018)

2.3.3.3. Moment in sleepers and fastening system stress on a turnout Moments applied on crossties in a turnout also vary greatly from the crossties of a typical straight track, on both routes. This is happening because the inner closure rails transferring the wheel loads converge at the center of the ties supporting the frog as wheel loads move progressively from the point of switch to the point of frog. This is also happening because the length of sleepers vary from point of switch to the last switch tie. This implies that moments applied on crossties vary, but not the moment of inertia of each tie. Situation also varies for the fastening system in each crosstie, as loads being applied from the wheel to rail and from there to the fastening system vary, due to existence of extra

13 AREA Manual for railway Engineering 1995, Chapter 4

45 lateral and dynamic forces. Therefore, one must be aware of the variation of moments as well as the variation of stresses applied on ties and the fastening system across the entire turnout structure. 2.3.3.4. Settlement behaviour of switches The typical settlement14 behaviour of switches is shown in Figure 75. A high point develops in the area of the long sleepers, whereas the blade device is subject to the greatest settlement. As switches are passed mainly in the main track, defects in cross level occur in the area of the long sleepers These geometric defects are mainly Figure 75: Settlement behavior of two switches. caused by discontinuous supporting surfaces of the Source: (Lichtberger, 2005) switch sleepers and by sleeper cavities (Lichtberger, 2005). It can be argued that in railway engineering, settlement is related to the track stiffness and the mechanical properties of the ballast, apart from the loads being applied, which also affects deflection. It can also be argued that biggest settlement happens in the area of switch blades due to the fact that the abrupt change of trajectory of a train creates extra dynamic forces as well as the geometry of the turnout itself exerts additional strain on the foundations of a turnout. Geometric design of a tunrout as well as proper construction of ballast and subgrade layer can raduce settlement . 2.3.3.5. Geometric design of switch blades and reduction of lateral forces Geometric design of switch blades as well as the turnout number affects the lateral forces applied on the outer rail of the turnout. Here the effect of tangentail turnout design will be discussed. A good discussion about the topic is presented by Ruppert (2017). According to Table 15, (see Appendix 3) several conclusions can be drawn. The advantages of a tangential geometry turnout, in comparison with a standard turnout are the following:  Bigger diversion speed. Because the change of direction is not so abrupt but very gradual, trains can take the diverging route in a turnout at bigger speeds than in a standard geometry turnout.  Lateral forces are significantly decreased, as well as L/V ratio  Lateral forces have a better distribution in a turnout. Ruppert (2017) points out that the energy required to divert the train is the same, regardless of the design. What happens when standard vs tangential geometry is implemented is how that energy is distributed across of the turnout (Figure 76). In a tangential turnout, the energy distribution is better, thus there is a reduction of the wear of the track and of the turnout in total. Regardless of that however, the faster a train goes, the bigger the lateral force become.

Figure 76: Lateral forces in a turnout with typical and pseudotangential geometry. Source: (Ruppert , 2017)

14 In civil engineering terms, settlement can be defined as the downward move of soil due to stresses applied on the ground from the structure

2.3.3.6. Kinematics vs dynamics in a turnout As Esveld (2001) comments, traditional turnout design methods assume that vehicle response is determined by kinematics rather than dynamics. Turnouts or crossovers - particularly for high-speed applications - are generally designed based on several parameters derived from the kinematic acceleration, mainly acceleration and change of acceleration. However, he states that vehicle response is clearly dynamic. As shown in Figure 77, simple kinematic15 considerations will underestimate actual response. Figure 77: Kinematic Vs dynamic response. Source: Field measurements confirm that passenger (Esveld, 2001) compartment lateral accelerations in turnouts can go up to twice the kinematic values (Weigend , 1983; cited in Esveld, 2001). Therefore Esveld suggests that turnout design has to be considered as a vehicle/track interaction problem, approached through simulation techniques. 2.3.4. Conclusions: Structural considerations in railway infrastructure and turnouts A track structural analysis is the cornerstone of rail track analysis. It describes the response of track to loads. Several important key parameters are derived: deflection, bending moment, pressure and rail seat force values. These parameters are later used to derive maximum stress values and compare them with the allowable levels of each track part. This procedure can determine if a track part is suitable to be used and handle the loads, which is closely related to the properties and type of each part: different rail section, fastening system, sleepers (wooden or concrete) ballast material and condition have different tolerance and a successful combination of them can determine the overall structure health. In the light of points mentioned above, it is even more crucial to calculate the tolerance of every component when turnouts are examined, as they contain special parts and particular geometry, which is differentiated from a typical track. In addition to typical structural considerations, turnouts face extra special topics: the importance of lateral and longitudinal forces, increased dynamic loading due to discontinuities, settlement and interaction between geometry/operation and loading values are the main concerns, mainly from the standpoint of stresses which can cause malfunctions. This configuration of type of parts, operational and geometrical characteristics of a turnout, as well as some overall attributes every turnout shares give rise to specific structural considerations. As shown, forces applied on a turnout can be considered higher, not only because of the overall geometry of a turnout (curve without superelevation) but also because of the inherent discontinuities a turnout possesses (mainly in switch blades and in the crossing). In addition, the existence of movable parts presents some issues in terms of potential failures. Finally, it was shown that the main structural parameters could be much higher than the ones met at a straight track, posing durability and risk issues to the turnout. The calculation of stress values is important, as these values can and should be used as input in infrastructure maintenance models, such as the one proposed in this thesis. Unfortunately, this requires the deployment of sensors in turnouts for data collection, construction of appropriate databases and development of a structural analysis methodology, especially for turnouts. Unfortunately, such a methodology (for semi-static turnout structural analysis) is not in place. Therefore, it would be useful for such a methodology to be developed for turnouts as well.

15 Branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion.

2.4. Railway maintenance planning Consultancies: Construction and e.g. SWECO, Maintenance in Sweden and turnouts WSP etc. entrepreneurs: e.g. In this chapter, aspects of railway Infranord etc. maintenance planning practice in Sweden, the Swedis role and impact of maintenance plan 2019- h 2022, key issues of maintenance planning, the Railway transition towards predictive preventive Market maintenance regime, modeling of maintenance as well as the importance of turnouts in the maintenance plan are discussed. Authorities: e.g. Trafikverket, SL 2.4.1. Railway market in Sweden, public transport etc. railway maintenance and Trafikverket Figure 78: Organization of Swedish railway Market. Source: Railway maintenance planning and (Lindahl, 2018) execution, as well as setting acceptable design and operational standards across railway infrastructure and rolling stock is one of the most important procedures undertaken by any national railway organization. Of course, every country has its own system, depending on how nationalized or deregulated its railway market is. This affects who is doing the maintenance and who sets the standards. Swedish railway market is one of the most deregulated across the Europe. According to Lindahl (2018) three types of actors can be met in Swedish rail market: authorities, corporations specialized in construction and maintenance and consultancies (Figure 78). All these entities have to cooperate to insure day-to-day operation of the traffic (Fröidh, et al., 2011). The most important of all in terms of influence and operations is the Swedish Transport Administration (Trafikverket). According to Fröidh (2011), the Swedish Transport Administration’s main task is to be responsible for the construction, operation and maintenance of state- administered roads and railways. It is also Figure 79: Trafikverket maintenance strategy. Source: responsible for long-term planning of https://www.trafikverket.se/resa-och-trafik/underhall-av-vag-och- transport system for road traffic, railway jarnvag/Genomfora-och-folja-upp-underhall/ (own edit) traffic, shipping and air transport and for (some) procurement of interregional public transport, It is important to note that Trafikverket is also responsible for producing technical documentation and setting standards in railways. In addition, railway maintenance is planned, but not executed by Trafikverket, but by contractors such as Infranord16, which belong to construction and maintenance entrepreneurs. Due to recent event however17, it seems that Trafikverket will regain part of the maintenance work from the contractors (Tenfält, 2019).

16 Company Owned by the Swedish State which conducts construction, operation and maintenance, formed from Banverket Produktion 17 Security/Cybersecurity Concerns

2.4.2. Maintenance from Trafikverket’s perspective Trafikverket plans for maintenance activities across the entire Swedish rail network it owns and manages. According to Trafikverket’s website (Trafikverket, 2015), the maintenance strategy is divided into the following steps (Figure 79):  Check the condition of the railway: Trafikverket carries out inspections (about 1 million of them) every year (maintenance and security inspections), in order to access the state of rail infrastructure.  Plan maintenance measures: Measures are planned for long and short term. For long term perspective in National plan 2014-2025, for short term through Trafikverket’s business planning, which results in rolling three-year plan (currently maintenance plan 2019-2022). Maintenance choices are made based on minimum disruption of train traffic and different parameters, such as technical material lifespan define where and when action needs to be taken.  Remedial and preventive maintenance: Maintenance can be divided into four levels:  Emergency interventions and directed maintenance (remedial)  Minor maintenance measures (prevention)  Reinforced measures (prevention)  Reinvestments (prevention)  Order and procurement of maintenance: Maintenance work is carried out by contractors, while procurement of new contracts is based on maintenance strategy and focuses on minimizing disruptions, for example through more preventative maintenance than remediation.  Implementation of maintenance: Trafikverket has been working on implementing measures under so-called maintenance windows, which contribute to more efficient maintenance.  Follow up: The maintenance agreements between Trafikverket and contractors set requirements that the contractor must comply with, In order to enforce their upholding, continuous inspections are carried out. 2.4.2.1. The maintenance plan 2019-2022 According to Trafikverket’s website (Trafikverket , 2019), the maintenance plan for 2019-2022 reports on how the Swedish Transport Administration plans during the period to prioritize and use allocated funds for road and rail maintenance measures, and the effects these measures will have. For railways, during 2019-2022, a large number of measures will be implemented that increase the robustness of the railway network. More money for action means increased scope for preventative maintenance, which provides an increased long-term effect compared to remedial maintenance. The maintenance plan for 2019-2022 (Trafikverket, 2019) uncovers more details regarding maintenance of railway network (see Appendix 1). According to the plan, railway maintenance operations are divided into:  basic maintenance (the basis of the maintenance plan) ,  reinvestments (replacement of parts of railway system)  Smaller replacements (preventive measures of parts or components in the rail infrastructure. They are planned and less extensive, not included in the basic maintenance contracts)  Operating costs (costs, which are directly attributable to the function of the physical infrastructure). The development of traffic for 2019-2022 suggests traffic increase, thus greater wear and thus faster degradation of the plant, resulting in higher maintenance costs. More specifically, an increase in traffic affects access to the facility for track work, resulting in increased costs due to quality deficiencies, longer shift times and increased total time spent. To counteract the effects of traffic on working hours, the so-called maintenance windows18 are introduced.

18 In order to create scope for necessary preventive maintenance work and measures that need to be taken to defects discovered in the facilities in connection with inspections, the Swedish Transport Administration intends to reserve capacity in the railway network – known as service/maintenance windows (Trafikverket, 2018)

Pressures due to EU legislation also arise for Swedish railways. Due to SERA19 directive, the Swedish Transport Administration must announce upcoming major shutdowns of the railway network more than two years in advance. In addition, in 2018, a new Swedish government law obliges Trafikverket to compensate the railway companies for the costs they have to pay their customers for delays in train traffic, which will increase administration expenditure by around 200 million euros per year, which may affect the planning of actions. During the period, the Swedish Transport Administration will carry out a large number of reinvestments which aims to ensure the robustness of the rail network, both on short and long term. Amongst other categories of infrastructure, in track reinvestments, it is stated than “more and more track and rail changes are possible, with focus on removing and avoiding speed reductions on the larger lanes. Turnout replacement rate will also increase significantly from 2019 onwards. The focus is also on removing and preventing speed reductions. The increased rate of reinvestment overall, it prevents maintenance costs from increasing, for example by investing in replacing jointed rails with CWR rails”. Some key remarks of the Maintenance plan 2019-2022 are summarized below: 1. Maintenance policy and planning are dependent on ad-hoc legislation (European and National) 2. Trafikverket is the organization responsible for making maintenance plans by following also the existing legislation and framework. 3. Maintenance is categorized into remedial and preventive. Trafikverket intends on expanding the percentage of the latter. 4. Trafikverket uses rather simple measures, which give a hint when maintenance should be done (rather empirical or technical). 5. Trafikverket recognizes the volume of traffic as a factor of infrastructure deterioration, expecting its increase. 6. Pressure due to EU and national legislation as well as agreements between Trafikverket and railway companies exert pressure on maintenance planning and the costs incurred from train delays. 7. The way that priorities are made are somewhat ad-hoc, drawn from legislation guidelines and general indicators which are too simple to describe infrastructure deterioration. 8. Financially, priority is given to reinvestments and basic maintenance. Increasingly, most reinvestment will be directed towards track infrastructure (see Appendix 1, Figure 97). 9. Maintenance contractors will be affected by maintenance levels introduced later and are binded by response times (shorter for important routes and metropolitan areas) (see Appendix 1, Figure 98). Finally, maintenance plan 2019-2022 includes many maintenance measures and a selection of planned major maintenance measures is presented in it, as well as in form of maps. From the analysis of major maintenance actions presented on maps, 20 - 40% of them are dedicated either turnouts or crossings (see Appendix 1, Table 11). Therefore, in the budgetary, as well as in the importance sense, turnouts/crossings and track maintenance actions in general hold a significant amount, marking their importance in the final robustness of the entire swedish rail network.

19 Single European Railway Area

2.4.3. Maintenance planning considerations In this part, main maintenance planning considerations and problems are presented. 2.4.3.1. The core aim of maintenance planning Track sections need to be closed every now and again for track maintenance and upgrades in order to ensure a satisfactory level of safety, comfort and future availability. Therefore, choosing the most suitable times for closing tracks for maintenance, so called track possessions, is a tough challenge that all infrastructure managers face today (Forsgren, et al., Figure 80: The vicious cycle of traffic, maintenance and 2013). This means that traffic and maintenance costs. Source: (de Vre, et al., 2016) activities have to be coordinated, since they are mutually exclusive. This is the reason that this planning conflict becomes crucial on lines with high traffic density and/or around the clock operation - especially when both traffic demand and maintenance needs are increasing, which is the case in many European countries. Hence, large benefits can be realized if planning, scheduling and effectuation can be improved. (Lidén & Joborn, 2017). Therefore, the planning of maintenance activities in coordination with the traffic and its evolution, taking into account the economics and time needed for maintenance execution, can be considered as the core of maintenance planning in railways (Figure 80). However, according to Lidén and Joborn (2017), there has been very little research about how to model or solve integrated planning problems such as coordination of maintenance and traffic. This fact is also reflected in bibliography, where no complete works or a unified body of articles related to the topic exists. 2.4.3.2. The role of timetable planning Railway timetable planning is a basic task in every railway organization. Its purpose is to organize all the activities performed on a rail network, namely passenger and freight train traffic, as well as maintenance activities for a specific time period, usually a year. Nelldal & Lindahl (2011, p. chapter 5) describe the process of timetable building in Sweden, stating that the planning process for the train plan is continuous and it takes about a year to construct a complete train plan for the next year. During the planning, room must also be left when drawing up the plan to allow track maintenance, conversions and extensions. They also mention that timetable arrangements for track works are regulated partly in the overall track works plan that is part of the train plan, and partly in the specific contracts that apply for four weeks at a time. Therefore, train timetable plan and organizes maintenance work across the rail network. A second remark is that maintenance can be planned on a strategical level (for the long term) and on a tactical-operational level (short/very short term). 2.4.3.3. Track possession vs maintenance windows The basic principle in railway maintenance planning is to find a proper time for maintenance, so traffic is disturbed as less as possible. Typically, this is done through track possessions (the actual reservations for specific work tasks which might be smaller geographically and/or in time according to Lidén (2016)). More specifically, all non-train activities that require secure access to the railway infrastructure must obtain a (work) possession (RailNetEurope, 2013; reffered in Lidén & Joborn, 2016)). If the possession will be in conflict with or influence a train path we call it a “major possession”, while those not affecting the train operation are called “minor possessions” (Lidén, 2015). According to Lidén (2015), the planning of possessions is often labelled “capacity planning” and is representative for most European countries, performed also by Sweden, following roughly the same steps.

As Lidén & Joborn (2016) describe, up to now, the planning regime adopted in Sweden has been to let the maintenance contractors apply for these work slots, which usually is done as late as possible. If no room is reserved for maintenance in the timetable it can be difficult to find suitable possessions, which forces the contractors to perform their work on odd times and/ or divide the tasks into small chunks which leads to inefficiency and cost increases. If the work cannot be split into smaller tasks, then the timetable must be altered and train operations rescheduled. Figure 81: illustration of traffic without (above) and with (below) a To increase the possibility for maintenance window that closes the line. Time is on x axis and distance on suitable work possessions, Lidén y axis. Dashed lines indicate rejected trains. The central and peripheral states that a new planning regime is durations are marked with grey boxes. Detailed stopping and runtime supplements are not shown. Source: (Lidén & Joborn, 2016) now being introduced in Sweden, called maintenance windows (predetermined train free slots in the timetable), where the infrastructure manager will propose regular, 2–6 h train free slots before the timetable is constructed ( Figure 81). Thus, the maintenance windows are given as input to the yearly timetable process. In addition, the maintenance windows will be dimensioned and constructed before the procurement of maintenance contracts and will remain more or less unchanged during the contract period, giving stable planning and quotation conditions for the contractors. Therefore, Lidén suggests that maintenance planning situation will be changed from many, small and fragmented work possessions squeezed into an already published timetable to few, large and regular maintenance windows preplanned before the timetable is constructed and the maintenance contracts procured. This will affect the effectiveness, cost, planning burden, robustness and punctuality of the maintenance work, since the size of a maintenance window determines the total maintenance cost and the total maintenance cost is inversely proportional to the temporal window size. ( see Lidén & Joborn, 2016 for more). Note that the construction of maintenance windows is a long term planning problem and it must be based on reasonable predictions about the maintenance work volumes as well as the traffic demand for period lengths of 5-10 years, taking into account the duration of maintenance contracts, which in Sweden are 5+2 years (Lidén & Joborn, 2016). 2.4.3.4. Maintenance work shifts Lidén and Joborn (2016) suggest that a maintenance work shift typically consists of three parts (Figure 82): 1. Preparation: Crew and equipment must be transported to the working site, where the resources will be organized, prepared and set up. The working area must be secured, by proper signaling and electrification measures which includes registration and acknowledgement from the traffic control centre(s). 2. Maintenance: The actual work task(s) Figure 82: Division of work time and the three window size cases. can be of varying type, where some Source: (Lidén & Joborn, 2016)

tasks (e.g. inspection and vegetation clearance) require short times, say 1/2 -1 h, while others (e.g. welding, switch machine work) take longer to finish, say 2-6 h. 3. Termination: When the maintenance task has been finished, the site must be cleared, resources and safety measures removed and finally the responsibility handed back to the traffic control centre(s). They also label preparation and termination as overhead time, while the actual maintenance job is called task time. They state that together they form the shift time and the sum of all shifts is called work time. Finally, they distinguish between the following cases regarding window size:  Short - when the task must be divided into two or more possessions,  Nominal - when precisely one task can be performed per possession, and  Long - when more than one task can be performed within the same possession. 2.4.3.5. Main categorization of maintenance planning problems Lidén (2015) performs an extensive categorization of maintenance topics and their scopes. Regarding the scope, it categorizes it into three major classes: 1. In the strategic class, problems concerning dimensioning, localization and organization are listed, with time horizons of one to several years. 2. In the tactical class, scheduling, timetabling and construction of plans are included covering a medium long time horizon (weeks to year). 3. In the operational class, problems concerning implementation and effectuation are listed, covering short time horizons (hours to month), usually handling the real resources. In strategic problems the following are included:  Maintenance dimensioning: It is a question of dimensioning the maintenance volumes and allocate them over the infrastructure network while considering traffic volumes, safety, reliability, economy, etc for the purpose of establishing infrastructure quality levels together with policies for maintenance and renewals  Contract design: How the maintenance contracts are designed and split in terms of scope, form and terms with concerns over cost, quality and efficiency.  Maintenance resource dimensioning and localization: The dimensioning and localization of maintenance resources in an efficient way, in order to guarantee adequate maintenance service levels In tactical problems, the following are included:  Possession scheduling: the focal point for coordination with the traffic and there are several sub problems lying in this realm:  Major possession scheduling: a key planning problem regarding railway infrastructure maintenance since it (1) has a fundamental impact on the traffic capacity, (2) frames the work planning and cost conditions, and (3) is conducted all the way from freight corridor to timetable revision planning.  Regular possession pattern construction: construction of prescheduled patterns of well-sized train-free slots that give access to every part of the infrastructure with sufficient intervals.  Possession and work coordination: planning of coordination of possessions in terms of their relationship, timing etc.  Timetable compression. guarantee a certain traffic free time during timetable construction for ad hoc maintenance work later in the planning process. Can be treated as sub-problem of normal train timetable construction.  Maintenance vehicle and team routing: planning of efficient use of specialized maintenance machines and teams, which must consider the work tasks to be performed, transportation from and to depots, interruptions, other train traffic, crew requirements, machine service needs and coordination with other tasks.

 Rescheduling: planning of rescheduling of maintenance activities due to change in budget or in cases of urgent repairs. It addresses questions such as which jobs to change or cancel, how to reschedule resources, the best way to get back to the master plan etc. Finally, in operational problems, the following are included:  Maintenance project planning: Planning of production and coordination regarding equipment, crew and material handling in relation to time schedule documentation and legislation  Work timing and resource scheduling: construction of efficient inspection work tours, which fulfill the prescribed requirements as well as planning of efficient selection of the exact timing of each maintenance action, taking into account factors such as work loads, time limits etc.  Track usage planning: planning of detailed track usage plan at large stations and railway yards, in order to know when tracks are free from rolling stock and available for maintenance, for the benefit of both for operators and contractors In addition, several other aspects of planning include robustness and scenario planning, as well as real-time maintenance/operational control. 2.4.4. Classification of maintenance in relation to response- from corrective to predictive maintenance Earlier, remedial/corrective and preventive maintenance were mentioned and briefly discussed. However, this categorization is limited, in terms of how maintenance responds to faults. According to Consilvio et al. (2018), maintenance can be categorized further in these terms:  Corrective (unplanned) maintenance: performed when a fault occurs.  Planned maintenance: performed on a regular fixed time schedule.  Condition-based maintenance: performed only when necessary, based on the continuously monitored asset conditions.  Predictive maintenance: performed only when necessary, based on model estimations suitably integrated by few measures. In particular, the aim of predictive railway maintenance is to minimize the probability of the occurrence of the so-called mission-critical faults during train service. A strong argument regarding maintenance types emerges here by Consilvio et al. (2018): While on one hand, unplanned corrective maintenance activities performed when a fault is occurred are expensive and would cause low service quality, on the other hand, preventive maintenance that does not consider the actual asset condition is often unnecessary and turns out to generate avoidable costs. In a predictive maintenance framework however, the interventions are planned by taking into account the forecast degradation state of railway assets and performed when a given threshold is reached, thus minimizing the probability of both sudden and unnecessary operations. This guarantees low fault probabilities and the best cost reduction, because maintenance is performed exactly when necessary and requires a limited number of monitoring measures. Such an approach can be traced well into the realm or risk-based maintenance planning. Finally, it is important to note that authors agree about moving from a planned preventive maintenance to a predictive preventive maintenance (Zoeteman & Esveld, 2004, reffered in Consilvio, et al., 2018). 2.4.5. Modelling maintenance planning From bibliography, it seems that maintenance planning can be approached mathematically, through modelling, and more specifically, it is related to the main problems derived from maintenance planning, mainly on tactical level. These approaches obviously concern preventive and predictive maintenance. It could be argued that the most elemental consideration of mathematics in maintenance planning would be to consider the technical life of infrastructure under study or millions of tons that a certain infrastructure has served up to a certain time point in order to plan maintenance, an approach however which ignores many other aspects, such as economics or the very complex mechanics of infrastructure. Another approach can be undertaken through pure train traffic capacity and timetable work (Lidén, 2015).

Preventive maintenance planning is usually approached through the prism of optimization or life cycle analysis. Especially for cases of optimization, according to Consilvio, et al. (2018) it was used to be approached by cost minimization, in order to reduce the overall maintenance budget. An example of optimization is to find a pattern of maintenance windows that allows for a wanted train traffic to be run and that minimizes the total cost for train operations and maintenance (see Lidén & Joborn, 2017). However, according to Lidén (2015, cited in Consilvio, et al., 2018), nowadays, the aim of predictive maintenance scheduling is to minimize time duration and overall maintenance costs, planning the preventive maintenance activities and assigning them to the different working teams, but also to maximize the system reliability and availability, at the same time, issues that were seen in the main topics and scopes of railway maintenance. Finally another family of approaches are those which use simulation models for studying how network capacity, delays, etc, depend on the state of each track section, degradation, maintenance and train traffic (Lidén, 2015). According to Consilvio et al. (2018), in regard to relevant research, preventive maintenance problems in a large-scale railroad network involve hundreds of activities and very complex relationships among them, which generates a larger number of side constraints. In addition, such optimization problems have been proven to be Non-deterministic Polynomial-time Hard (NP-Hard) problems20, thus, requiring too long time to be solved and, for this reason, many scheduling heuristic21 techniques have been used for managing preventive maintenance activities (Soh, et al., 2012, reffered in Consilvio, et al., 2018), mainly based on Genetic algorithms, Ontology-based modelling, Strategic gang scheduling and other specific heuristic approaches. In their approach, they use conditional probability followed by a maintenance optimization algorithm. To sum up, regardless of the approach taken, the process of maintenance planning modelling is roughly divided in two discrete but interconnected parts:  Infrastructure failure occurrence: can be described either as a probability of fault occurrence or as measured level of deterioration, compared with some critical value. In most cases, the state of deterioration of a specific infrastructure is related to a degradation model, which can have different forms (linear, exponential, Weibull distribution etc.). In addition, infrastructure faults and degradation can be related to time aspects of maintenance (e.g. interval between maintenance activities etc.). Finally, deterioration level is measured relatively easily for some infrastructure, like track, but difficult to be measured for other rail assets, such as signaling equipment or electrical equipment, since their deterioration does not progress continuously and failures seem to occur suddenly (Consilvio, et al., 2018).  Maintenance planning optimization: having calculated the state of infrastructure, assignment of maintenance activities, teams and equipment to specific network paths follows. The key aspect of this process is that this assignment is done under the prism of optimization, meaning that aspects such as time, budget or some other key parameter(s) must be optimized. The latter example set by Consilvio, et al. underlines the departure from classical approaches to the topic of maintenance planning which enters the realm of risk analysis, probabilities and an asset- oriented maintenance planning. 2.4.5.1. Track system maintenance measures and life As Lichtberger (2005) describes, track systems, like any other industrial plant, have to be maintained. Apart from the static and dynamic requirements of operational loads the track geometry is subject to atmospheric influences and other external stresses (chemical, vegetative). The life cycle of the structural elements of the track is limited, depending on stress and length of use; - they have to be replaced after this period has elapsed. He states that typically certain maintenance cycles/ service life periods approximately apply to normal main tracks of high stress / track components (see Appendix 2, Table 12 ). Turnouts however are exposed to even bigger wear. Lichtberger (2005) stresses that the

20 A class of problems to solve which, a polynomial-time algorithm has never been found. 21 A heuristic technique, is any approach to problem solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals.

55 lifetime of switches on wooden sleepers amounts to approximately 20 years, on concrete sleepers is 30 years. When diamonds are subject to extreme stress, they are replaced up to 3 times a year. Usually, the average lifetime of a switch diamond can be expected to be 5 years. There remarks show also that some components of the turnouts must be maintained frequently, posing an extra issue to the overall maintenance planning. In addition, a typical measure for track infrastructure wear is million tons of traffic. Figure 83: Degradation curve with indication of the lost In all, Lichtberger (2005) states that maintenance "life time". Source: (Zwanenburg, 2007) is triggered not only by certain value of maintenance cycles, but also from certain geometrical value deviations, an important aspect for turnouts. 2.4.5.2. Infrastructure degradation: The Swiss experience with turnout failures A more comprehensive analysis of railway infrastructure degradation and more specifically of turnout malfunctions comes for Switzerland, and more particularly from the work of Zwanenburg (2007), whose research is focused more on the expected lifetime of railway turnouts, their maintenance and renewal, as well as LCC analysis. More specifically, in his project, the focus is on understanding the phenomenon of wear and degradation of S&C and its components and relates it to parameters, which influence this degradation and wear. To achieve this, multiple SBB databases are combined to find relations between different track parameters and train parameters on one side and the carried out maintenance and renewals on the other side.

Figure 84: Linear, progressive, regressive and instantaneous degradation curves. Source: (Zwanenburg, 2007) He states that turnout has moving parts, which make it a machine rather than a type of infrastructure. Second, turnouts are subjected to high, concentrated, dynamic forces, mainly due to the flangeway opening at the frog, which a train wheel has to “jump” and the fact that the curved direction has a small radius without cant, which causes high lateral forces. These conditions lead to special maintenance and renewal necessities due to degradation caused by running trains. Its speed depends on:  Train properties, mainly loads, speed and condition of the rolling stock  Track properties, mainly support condition, quality of materials, installation quality of switches, track geometry, state of track material etc. Besides of these remarks, he also mentions horizontal relations between different aspects of turnouts, for example track geometry and the state of the material relation, which goes both ways. Therefore, the view of LCC and the concept of degradation process lie at the core of his analysis. Especially in degradation process, many degradation phenomena can occur (according to Pro Rail at least 75), related to mechanical parts of turnouts (ProRail, 2000, cited in Zwanenburg, 2007). Zwanenburg notes that they are related to geometry degradation, wear of material of structural failure, like cracks. Also, the way this wear or degradation occurs is always different: a new component has a initial quality 푄푖 and traffic causes a gradual degradation. He states that the degradation line can have various shapes, depending on train and track properties mentioned earlier (Figure 84). In the light of LCC and quality level, Zwanenburg states that the replacement or maintenance action takes place before the minimum allowable quality limit 푄푚푖푛 is reached. This is always the case, due

56 to several reasons, like inspection timing in relation to component condition, issues of maintenance possessions, optimization of the use of equipment and personnel etc. This implies that early replacement means economically a loss of productivity of the assets and also the replacement occurs before the actual end of life (Figure 83). The main point of Zwanenburg’s research is to examine several rules of thumb inside the railway industry regarding maintenance of turnouts in conjunction with data from SBB databases. These rules are:  Turnouts located in high density traffic tracks show higher deterioration rates than those in track of lower density traffic.  Curved turnouts are exposed to higher dynamic forces and have therefore a shorter lifetime than turnouts in plain track  Turnouts with smaller angle (bigger inclination) show less wear than those with bigger angle (smaller inclination) He concluded that the first rule of thumb is true, in the second, the surprising result was obtained, that the average replacement age of a curved switch was exactly the same as that of a normal standard turnout and for the third rule, no relationship was established, which was attributed to geography of turnouts ( in SBB network, 1:9 switches -with a big angle- are normally part of stations or connect sidings to main tracks, while 1:15 switches are normally integrated in plain track and know a heavy load and normal speed in both directions), thus turnouts are exposed to different traffic. Furthermore, he adds that a general trend was found that the average replacement age increased slightly during the evaluation period (1997-2005). This is mainly due to the introduction of better materials and maintenance procedures and will continue through introduction of even better materials.

2.4.6. Conclusions: Maintenance planning, modeling and incorporation of asset degradation In Sweden, Trafikverket is the main organization, responsible for railway maintenance planning, setting the standards for contractors and producing technical documentation, amongst them for turnouts as well. It employs a cyclic maintenance strategy (observation – preventive intervention – monitoring through KPI’s). Also it introduced the maintenance windows in timetable planning, exclusively for maintenance. Trafikverket’s strategy emphasizes on preventive maintenance, not only because of the increased traffic forecasts, but also because of the EU and national legal framework. Its strategy for the coming years is described through the maintenance plan 2019-2022, where apart from basic maintenance, big amounts are also directed towards reinvestments, particularly towards track infrastructure renewal, where turnout maintenance holds a prominent place, underlining their importance. It has to be noted that there is a correlation between amounts being spent on maintenance and the increase of traffic. However, in spite of moving towards preventive maintenance and towards maintenance windows from possessions, Trafikverket does not employ predictive maintenance, which poses a question of whether resource management and maintenance quality are on an equilibrium. This question in turns, casts doubt on whether the core aim of maintenance planning is followed, if the introduction of maintenance windows is arguably the best method of dealing with maintenance (particularly in cases of infrastructure such as turnouts which have a higher risk to malfunction), especially when one considers the structuring of maintenance through the timetable, and if the existing maintenance monitoring indicators are enough, given the fact that turnouts need more frequent maintenance and are susceptible to more frequent failures. In this process, the actual maintenance work structure has to be also considered. Clearly, from this scope, the maintenance of turnouts in this framework is related with the strategic and tactical problems of maintenance planning. These approaches and framework being followed in practice, pose an abysmal strain, in terms of resource management, maintenance time planning and quality of maintenance work, especially for turnouts. Therefore it can be argued that a better approach is to move towards predictive preventive maintenance, especially for critically important railway infrastructure, through the usage of risk-based

57 models. However, a framework must be established in order to clarify which factors contribute to turnout degradation. Furthermore, its parts must be well understood and structural mechanics clarified. In general, the process of devising a preventive predictive maintenance planning model is divided into two successive parts: the first is to define a model for infrastructure degradation, which can be either a direct measure of state of infrastructure or probability of malfunction. Then, this is a measure which is used as an input for optimizing maintenance planning, which is essentially a problem of assignment of maintenance activities on a rail network, in a way which minimizes/optimizes a particular measure (e.g. time or money). This is exactly what will be attempted in this thesis: the development of a model which will be asset- oriented, describing the probability of a turnout to malfunction and using that probability of each turnout to form a maintenance plan for turnouts using a bottom up- approach: fault probabilities give rise to maintenance patters

3. Methodology This part of master thesis lays down the methodology followed for the formulation of predictive maintenance model, with the turnout malfunction probability lying in its heart. First, a thorough analysis of turnout data available for eastern region in Sweden was examined in order to pinpoint the causes behind malfunctions in turnouts, while an Object oriented Database (OODB) relating turnout failures with their characteristics is constructed. Then, the model used to calculate the probability of turnout malfunction on the basis of OODB data is formulated and assessed. Finally, the results of this model are used as input to a maintenance planning model, solely based on the probability of malfunction. 3.1. Fault risks in a turnout and data analysis: the case of east region in Sweden In this section, malfunctions in turnouts will be analyzed. The basis of analysis is consisted of findings and notes made by A. Nissen for turnouts in swedish rail network and of course findings from data analysis performed on Ofelia and BIS datasets for eastern region in Sweden. The main purpose is to land to a conclusion regarding the nature of malfunctions and their causes in turnouts. This analysis complements and expands the scope of the Swiss experience in turnout malfunctions presented by Zwanenburg earlier. 3.1.1. Turnouts in Sweden and Trafikverket’s perspective regarding turnout failures Trafikverket has an extensive collection of technical documentation regarding turnouts, their technical details and standardization. In addition, as discussed earlier, turnouts are of utmost importance for the current maintenance plan. Apart from these remarks, for maintenance recording purposes, Trafikverket has three main databases at its disposal: 1. OFELIA: According to Trafikverket (2019), in Ofelia database, maintenance contractors report the actions taken in connected with a registered fault symptom by the traffic management. The contractor reports information about the actual error, cause and action taken and concludes the fault report. This database cab be used for purposes of maintenance, replacement and upgrade as well as for statistical analysis and investigations 2. BESSY: Bessy is another IT database for planning and conducting inspections on Trafikverket’s railway facilities. It is used together with another It system called “inspection plan” (Besiktningsplan) (Trafikverket, 2019). 3. BIS (Baninformation): BIS is Trafikverket’s computer system for storing and retrieving information on track related facilities and events (Trafikverket, 2018) It must be noted that for analysis purposes, Ofelia and BIS databases were used extensively in combination. Unfortunately, the format as well as the quality of data inside them is quite ambiguous – their format is not suitable for implementing the particular type of model proposed here. Therefore,

58 several actions needed to be taken in order to produce a synthetic database suitable for this task. The topic of creating such a database, as well as the results and implications will be discussed below. Regarding the state of malfunctions in turnouts, more information is provided by Arne Nissen, who represented Trafikverket for this master thesis, is responsible for Ofelia, Bessy and BIS databases and provided data for the Eastern Region. According to him (Nissen, 2019), the quality of maintenance data is not good and Trafikverket needs to work on them to improve their quality. However, he states that when it comes to turnouts, the basic reasons for train – disturbing failures are the following: 1. Weather conditions, particularly snow and ice 2. Control device issues (kontrollanordning): Turnout is not under control because locking devices for switch blades (tungkontrollkontakter) do not give green signal 3. Point device issues (tunganordning): Mechanical problems that prevent the motor from working 4. Failure in actuation, locking and detection (omläggningsanordning) : misaligned or burnt contact fingers etc.) Furthermore, he adds that turnouts with double slip and turnouts with movable frogs have nearly double frequency of failures and that is because of more point motors. Therefore, according to Nissen, the main reasons for turnout failures are actually related more with electromechanical and weather, rather than structural or wear and tear issues. This is an important remark, as it sets an area for future research and reference. 3.1.1.1. Types of turnouts used in swedish rail network There are many types of turnouts implemented in Swedish rail network and that is the case for eastern region. However, in order to provide some data homogeneity only simple turnouts (EV – enkel växel) were chosen. According to Nissen (2019), There are 4 main types of simple turnouts deployed: 1. 60E : turnouts that were introduced in 2014 2. UIC/BV50: turnouts that were introduced in 1988 3. SJ series: the most important is SJ50 turnout type which was produced until 1988. 4. SJ series: they include smaller turnouts SJ 34,41,43, which are not exposed to serious traffic (they serve primarily side tracks). In general, SJ series are the oldest ones amongst all turnout types (some of them are almost 90 years old). The presentation above implies that turnouts can be categorized in terms of usage. According to Trafikverket (Trafikverket, 2016), turnouts utilized in swedish rail network are divided into three main categories:  Standard category (Standardsortiment): The turnout models selected by Trafikverket to be used for the insertion of newly manufactured turnouts. When a new turnout is to be installed, in the case of new production or when rebuilding / replacing an existing infrastrucutre, it is from these switches that the choice is made.  Management category (Sortiment förvaltning): Turnout models that are no longer included in Trafikverket’s standard category, but where there is a secure supply of parts and expertise, as well as access to documentation and drawing documentation. No new production of complete turnouts occurs for this category. This group currently has the largest number of turnouts in the infrastructure.  Decommissioning category (Sortiment avveckling): Turnouts that exist in the Swedish Transport Administration's facility where new manufacturing has ceased. For these turnouts, there is no secure supply of parts or skills, nor satisfactory documentation or drawing documentation. The strategy for these turnouts is to gradually replace them with switches from the management or standard range. Therefore it could be said that while 60E, UIC, BV50 belong to the two former categories, most of SJ turnouts are under decommissioning.

3.1.2. Creating an object- oriented synthetic database for analysis The basic database used for the creation of the synthetic database was Ofelia. Unfortunately, this database is event – oriented: that means it registers malfunction events on swedish rail network which referred to specific type of infrastructure, times of repair and response, type of subsystem that malfunctioned and actions taken to repair the damage. There are little to none technical data related to the actual type of infrastructure that malfunctioned in order to relate them to the malfunction event. Therefore, relevant data needed to be either extracted from Ofelia entries (e.g. the description of turnout contains information about the Figure 85: Creation of a synthetic object-oriented turnout like rail section, radius, inclination etc.), added from database. Own edit other databases (e.g. BIS infrastructure database contains relevant info, which can be associated with entries in Ofelia), estimate them through technical documentation - Trafikverket provides an abundance of technical documentation which describe turnout technical characteristics - (Trafikverket, 2015; Trafikverket, 2015; Trafikverket, 2015; Trafikverket, 2016; Trafikverket, 2016) or incorporate them from external sources (A. Nissen provided traffic data for rail network in eastern region). This combination allows the creation of a synthetic database, which is now object oriented: the malfunction is related to a specific type of infrastructure and its technical/operational characteristics-namely turnouts and is suitable for malfunction analysis (Figure 85). Furthermore, this database can be used for the proposed modeling framework. However, as mentioned earlier, problem lies in the fact that some data are ambiguous to their quality, which poses serious questions regarding the validity of the entire database. This poses another important topic for future research. 3.1.3. Data analysis of turnout malfunctions in eastern region – General trends This data describes turnout malfunctions in terms of absolute numbers, effect on railway operations, seasonal variation and in relation to maintenance actions response. 3.1.3.1. Train disturbing fails In Eastern region (Figure 86), for 2018 3384 faults were recorded. Of them, 964 (28%) disturbed the traffic and were related to different events and infrastructure, so for eastern region, 1 out of 3 faults were disturbing to the traffic. It is important to note that out of them, 861 (90%) were related to turnouts, which signifies their importance both for smooth railway operations and for maintenance activities. Other events of statistical significance were reverse movements in a turnout, faults in positioning system and track related incidents (Appendix 4, Figure 104). 3.1.3.2. Trains delayed and additional delay due to turnout malfunction Naturally, as a result of a fault in a turnout, trains are getting delayed. During 2018, in 52% of cases due to faults, 1-2 trains were delayed22. This indicator Figure 86: Maintenance actions in eastern region for underlines the effect of a fault, and in most cases it period 2019-2022. Source: (Trafikverket, 2019)

22 Number of trains delayed more than 3 min

60 doesn’t affect many trains, partially because fault is remedied fast and partially because it is not serious. Of course, there are cases of more serious faults (around 12.5%), where 10 or more trains were delayed. Same remarks can be done about extra delays23 observed due to faults in turnouts: in 76% of cases, trains were delayed 1 hr, while a 7% more than 4 hrs. Again, this implies that faults are remedied fast, but some of them can take days to be remedied. Also they cost a lot in terms of time and money (Appendix 4, Figure 103). 3.1.3.3. Faults in turnouts during months of the year Another important feature of faults is that they variate during the months of the year. It is clear from the data that faults are increased during the later months of autumn and are picking up during winter months. That can be attributed to the weather conditions: snow and ice, as well as changes in temperature make the parts of a turnout more prone to damage, especially the switch and the crossing part (when it is movable), due to freezing and clogging the movable parts (Figure Figure 87: Train disturbing fails over the course of the year. 87). Source: (Trafikverket, 2018), 2018, Own edit 3.1.3.4. Duration of repairs and response time for malfunction repairs Regarding the duration of repairs in turnouts, most of them are done within the hour (45%), however a 15% of them can take more than a day. This 15% is a considerable amount and can affect the traffic speed and scheduling in a serious way. On the other hand, examining the response times, it is clear that in 52% of cases, response in less than 30 min, which shows an effectiveness when it comes to response due to turnout malfunctions (Appendix 4, Figure 103). 3.1.4. Data analysis of turnout malfunctions in eastern region: relation between malfunctions and operational/geometric characteristics of turnouts So far, the general trends in turnout faults for the Easter region have been analyzed. Arguably, the majority of faults were related to turnouts. Furthermore, trends show that most of the faults are treated as soon as possible, causing minimum disturbance of the traffic, but some of them can cause abysmal delays and take more than 1 day to repair, underlining the complexity of the turnouts. However, these remarks apply for all the types of turnouts, either simple or with more complex geometry (e.g. turnouts divided into 3 tracks). The following analysis focuses exclusively on simple turnouts, with a straight and a diverging track, not placed on curves. What analysis will take into account are the operational and geometrical/structural characteristics in all cases in relation to malfunction existence in turnouts. Note that here the different attributes are not the cause of failures per se, but rather characterize the turnouts where malfunctions appeared. 3.1.4.1. Turnout models/rail profile and malfunctions The relationship between rail profiles of turnouts and malfunctions are presented in Figure 88. It seems that most of disturbing fails are related to turnouts which employ 60E and UIC60 profiles. In fact, the bigger the rail size becomes, the more malfunctions turnouts experience. This is a controversy, since bigger rail sizes have a bigger moment of inertia and are more durable in general. This can be attributed to the fact that these are the most modern profiles and Figure 88: Rail profiles and failures in turnouts. Source: Trafikverket implements them in main line tracks (Trafikverket, 2018), own edit

23 Additional delay (more than 3 min)

– so naturally they are exposed to bigger traffic cumulatively. This can be confirmed in part by the findings regarding malfunctions and types of track. 3.1.4.2. Turnout malfunctions and radius It is clear from the data that radius has a progressively positive effect on malfunctions: the bigger the radius is, the less the malfunctions are. This can be attributed in part to the effect of geometry and distribution of forces and repetitive loads and in part to the fact that turnouts with big radius are the minority in Figure 89: Turnout malfunctions and radius. Source: comparison with smaller ones. Apart from that, (Trafikverket, 2018), own edit an interesting trend rises: up to radii of 600 m. the trend is clearly declining but then for radii between 600-800 m it regresses to higher values. It is not clear why, but speculations here are maintenance as well as types of track play a role (Figure 89). 3.1.4.3. Turnout malfunctions and inclination Analysis of inclination of turnouts show that smaller inclinations (smaller angle in the frog area or between intersecting tracks) have a tremendously positive effect on malfunctions. Again this is attributed to the role of geometry in distributing forces as well as reducing the acceleration values on the turnout (inclination is related to radius) (Figure 90). 3.1.4.4. Fixed vs movable crossing and turnout malfunctions The analysis of the effect of crossing’s type on malfunctions did not show any clear relation. Nissen (2019) mentioned that movable crossing experience double frequency of failures in comparison with fixed ones, but data show that most of failures are related to fixed crossings and Figure 90: Turnout failures and inclination. Source: that the ratio of disturbing to non-disturbing (Trafikverket, 2018), own edit failures is almost identical. That concludes the need for further research on the topic, which also requires significantly better quality of data (Appendix 5, Figure 105) 3.1.4.5. Wooden Vs Concrete sleepers and turnout malfunctions The advancements of recent years globally show that prestressed concrete ones increasingly replace wooden sleepers. This is the cases, as concrete is a more flexible material, widely used and suitable for high speed applications. In terms of malfunctions, it seems that disturbing failures in turnouts are more than non-disturbing ones. Furthermore, and this is surprising is that turnouts with concrete sleepers fail more than ones with wooden ones. Data and results can be characterized as sketchy at least and must be approached with caution. Nonetheless, a possible explanation might be that CWR development has not kept up with the types of sleepers – a necessary condition for concrete sleepers to be applied (Appendix 5, Figure 105). 3.1.4.6. Straight Vs curved blades and turnout malfunctions Another finding from data analysis is that turnouts with curved blades face far less malfunctions in comparison with these having straight ones. In part this can be explained by the fact that curved blades (just as bigger radius and smaller inclination) ensure the better handling of loads and accelerations. However, these findings can also be attributed to the fact that turnouts which are equipped with curved blades are far less in comparison with ones equipped with straight ones (Figure 91).

3.1.4.7. Machined Vs RBM Crossing and turnout malfunctions Another surprising discovery was related to Machined Vs RBM crossings and malfunctions – and this is also something that must be approached with caution – is the fact that machined rail crossings appear to have fewer malfunctions in comparison with RBM crossings. This can be explained in part by the fact that the most of main line applications naturally involve RBM crossings – machined rail crossings are placed on side tracks and are Figure 91: Straight vs curved blades and turnout malfunctions. considered as outdated type of crossing. This is Source: (Trafikverket, 2018), own edit somewhat reinforced by the fact that ratio of disturbing to non –disturbing malfunctions is actually higher in machined crossings in comparison to RBM crossings (Appendix 5, Figure 106). 3.1.4.8. Service years and turnout malfunctions In this analysis, service years are defined as the number between year of installation and 2018. However, the results are peculiar: malfunctions are not increased as years go by but rather follow and diminishing and regressive cycle every 20 years. It is unsafe to speculate regarding the origins of this trend. However, one possible explanation is that maintenance and LCC analysis plays an important role here. Also, it must be noted that more research and data configuration is required as to why this is happening (Appendix 5, Figure 106). 3.1.4.9. Mbrt’s of traffic and malfunctions The effect of traffic on turnout malfunctions has been one of the most controversial topics of this research. While there is a positive trend as traffic increases, there are peakings between 2-4 and 10-12 Mbrt’s. The thinking was to explore the effect of cumulative traffic on malfunctions. Figure 92: Cumulative traffic in Mbrt's and turnout malfunctions. However, these data should be also examined Source: (Nissen, 2019), own edit with caution, as this is extremely aggregated (expressing Mbrt’s in track parts and not on specific lines. Furthermore, the effect of tactical maintenance is ignored. Finally, they cover part of the service period of most of turnouts as many of them were installed way before 2013. In all, more specialization/adaptation as well as more disaggregated data is required for the effect of traffic on malfunctions to be studied properly (Figure 92). 3.1.4.10. Turnout heating output and malfunctions Turnout heating is important, especially in Sweden and especially during winter time for movable parts of a turnout, like blades or movable crossings. Analysis of data shows that as the heating output of these devices increases, the malfunctions decrease. However, in absolute numbers, malfunctions tend to increase until the threshold of 10-15 KW – this can be explained in part by the fact that heaters are more effective above a certain threshold, which can be also related to the temperatures during winter (Figure 93). Figure 93: Turnout heating output and malfunctions. Source: (Trafikverket, 2018), own editing

3.1.4.11. Year periods and turnout malfunctions It comes as no surprise that most of malfunctions are observed during winter, when snow and ice block movable parts of the turnout, in cases of extreme weather conditions or due to excessive icing. Therefore, the trend shows a decline as seasons move towards the summer (Appendix 5, Figure 106). Figure 94: Allowable speeds and Turnout malfunctions. Source: 3.1.4.12. Allowable speed and turnout (Trafikverket, 2018), own editing malfunctions The last operational characteristic examined was the allowable speed, as the actual speed of the rolling stock during the time of malfunction could not be found. The trend is clear here: bigger speeds create more malfunctions as dynamic loads increase on a turnout (Figure 94). 3.1.5. Analysis of Causes of turnout malfunctions as recorded in Ofelia DB Apart from turnout malfunction record, Ofelia database provided also the recorded reasons of failure by turnout part. It has to be noted that only train disturbing failures were used towards the end of analysis. In general, analysis of failures of subparts of simple turnouts showed the following (Figure 95):  Switch/turnout (spårväxel): 55%  Control device24 (Kontrollanordning): 19%  Actuation, locking and detection (omläggningsanordning) :  Point device (Tunganordning): 5%  Switch heating (Växelvärme): 4%  Crossing (Korsning): 2%  Snow protection/shelter (Snöskydd): Figure 95: Parts of turnouts that failed. Source: (Trafikverket, 2018), 1% own edit It is obvious from the analysis that failures are related mostly with the turnout itself from a generic perspective, but also with mechanical/ movable parts of a turnout, as well as with parts exposed to serious loads, like the crossing. Furthermore, it seems that common causes are related to electromechanical issues in movable/electrical parts of turnout. The categories of failures presented in Figure 95 were able to be analysed further: 1. Switch/turnout (spårväxel): Surprisingly, in that category, 49% of causes were not possible to define. Apart from that the second most frequent cause was bad connection(16%) , followed by interruption (9%) and nothing wrong (6%). The rest of cases were mostly related to wear and tear, material failure or rust as reasons of malfunction (Appendix 6, Figure 107). 2. Control device (Kontrollanordning): In this category, four main causes can be detected: Interruption (33%), Bad connection (27%), not possible to define (18%) and material failure (15%). Wear and tear, deformation and rust were minor percentage. (Appendix 6, Figure 108). 3. Actuation, locking and detection (omläggningsanordning): In this category, two main causes emerge: Not possible to define (39%) and interruption (27%). These are followed by material failure (10%), wear (8%) and deviating temperature/bad connection with 4% respectively (Appendix 6, Figure 108).

24 Referring primarily to control rods which control the switch blades

4. Point device (Tunganordning): This category has very diversified causes of failure: Many of them were not possible to define (38%) but rust (15%), interruption (12%) and deformation (8%) as well as wear (8%) were amongst the main causes following. Causes like material failure, rail damage, tampering/theft, deviating temperature and bad connection earned a 4% respectively (Appendix 6, Figure 108). 5. Switch heating (Växelvärme): In this category half of causes were related to interruption, followed by short circuit (20%), deformation (10%), not possible to define (10%) insulation and material failure (5% respectively). It is obvious that the prevailing causes here were electrical, rather than mechanical or structural (Appendix 6, Figure 108). 6. Crossing (Korsning): Crossing failures are one of the few groups where failures are related exclusively to structural issues. More specifically, Rail cracks (56%) represent the majority of cases, while all the rest, like deformation, rail fracture, rail damage and wear, earn a respectful 11% each (Appendix 6, Figure 108). 7. Snow protection/shelter (Snöskydd): This is the smallest group of subparts of a turnout and respectively the smallest diversification amongst causes. The most common reason of failures are related to incorrect operation (66%), while poor track position represents the rest of cases (Appendix 6, Figure 108). 3.1.6. Conclusions: data analysis, database construction and results of analysis of turnout malfunctions in eastern region Currently, Trafikverket employs several maintenance databases in order to keep a record regarding infrastructure and its malfunctions. However, it does not employ an objected-oriented infrastructure fault database, which is prerequisite for a proper risk and correlation analysis between the actual failures and the operational/geometrical characteristics of turnouts it employs on its network. For that end, an appropriate database was created, by using Ofelia and BIS databases, as well as technical specifications regarding turnouts. This database can be used not only for modelling of malfunctions in tunrouts, but also for purposes of meaningful statistical analysis. However, in that case, data availability and its origins can determine if a database can serve or not its purpose effectively. From the data analysis, as well as examining similar experiences from other countries like Switzerland, it seems that malfunctions has several common causes. Nissen (2019) calls for snow-icing and electromechanical issues in movable parts of the turnout as the main causes. In the previous chapter, Zwanenburg (2007), by studying turnouts wear in Swiss rail network calls for train and track properties as the main factors of wear and consequently of faults. Furthermore, he proves several variables well known to railway industry that affect degradation to be true, but his results are not without faults. However he defends them by stating that factors related to geography can play a significant role in the quality of results. Finally, statistical analysis of the synthetic as well as Ofelia databases was conducted. The findings in general confirm the findings of Zwanenburg, as well as these that can be drawn from the theory surrounding railway engineering and the analysis of turnouts, in the sense that it appears to be a correlation between turnout malfunctions and most of geometrical and operational characteristics of a turnout. However, several variables did not show the promising relation, due to many factors, which can be attributed mostly to the quality and type of data. For example, while statistical analysis shows that there is a relation between speed, inclination, traffic and malfunctions, relations between malfunctions and quantitive variables, like type of frog or sleeper could not be established. This underlines the need for better databases with more detailed variables to be examined and related with malfunctions, an important topic which will be discussed at the end of the thesis. Reasons of faults in turnouts in eastern region were also analysed. In general, what results show is that turnout in general suffers a lot of them, but also subparts which are related to movable parts of the turnout experience a lot of them. Therefore the reasons are more related to electromechanical causes than to structural ones. Nonetheless, parts like crossing or point device are also experiencing structural faults like rail cracks or damage. This underlines the need for incorporating more characteristics of these subparts in any risk analysis, an issue closely related to database building. These remarks, set the frame for establishing the basic category of variables, characteristics required for risk analysis, as well as proper statistical analysis of a turnout (Table 7). For this master thesis, only

65 the two former categories could be studied. The next and last part examines the incorporation of these variables in a probabilistic model for studying malfunctions. The model chosen for this task is a logistic regression model, which expresses the probability of malfunction as a function of turnout characteristics.

Table 7: Main factors contributing to turnout malfunctions. Own edit. 3.2. Modeling the probability of turnout faults by using logit models – An application to predictive maintenance planning This last part will attempt to answer the question of whether malfunctions in a turnout can be modeled using a binary logit model. Logit models are ideal for modeling discrete variables, instead of continuous like in regression models, and this is the case with turnout malfunctions. Of course, this creates many questions regarding the interpretation of the outcome. These issues will be discussed analytically at the end of this thesis. 3.2.1. Logistic regression – principles Logistic regression model bibliography is well established and known. However, it is fitful to provide some of its main characteristics. The works of Washington, et al. (2011)as well as Foltz (2015) will be used towards this end. As Washington et al. (2011) narrate, regression models are developed on the basis that the dependent variable is continuous. However, there are numerous cases when the dependent variable is discrete – the gender of a person, current passing through a circuit, categorical outcomes are some examples. More specifically, logistic regression models are addressing cases where the outcome variable is binary: train disturbing (1) and non- train disturbing faults (0) are the case with turnouts: as a variable, malfunction of a turnout is a binary variable, which means it can have only two states. Furthermore, this model is appropriate, as it connects the outcome (probability of a turnout to malfunction or not to malfunction) with its characteristics – operational and geometrical. Finally, the probability of malfunction can be directly related to the degree of infrastructure degradation. These three reasons justify the selection of a binary logit model for the analysis of malfunctions in a turnout. The goal of logistic regression, much like linear regression, is to identify a well fitting, defensible model that describes the relationship between a binary dependent variable and a set of independent or explanatory variables. As usual, an often unstated assumption is that the independent variables directly or indirectly influence the outcome, and that the independent variables are used to either explain or predict outcomes—depending upon the particular study objectives (Washington, et al., 2011). In the case of turnouts, the main underlying assumption is that the presence of a fault in turnouts is a function of several internal characteristics (see conclusions in the previous chapter).

Logistic regression models are related first with probabilities, odds and odd ratios. As Foltz (2015) explains, the probability of an event to occur as well, the odds, as well as the odds ratio are:

푂푢푡푐표푚푒푠 표푓 푖푛푡푒푟푒푠푡 푃(표푐푐푢푟푟푖푛푔) 푃 = (48) 푂푑푑푠 = (49) 퐴푙푙 푝표푠푠푖푏푙푒 표푢푡푐표푚푒푠 푃(푛표푡 표푐푐푢푟푟푖푛푔)

푂푑푑 푂푑푑푠 푟푎푡𝑖표 = 푠1 (50) 푂푑푑푠0 Washington et al. (2011) state that odds are related to probability but are conceptually and numerically different, describing likelihood of events. For example, suppose that the probability that a crash at an intersection involves a rear-end collision is P = 0.1. It follows that the probability that a crash does not involve a rear end collision is 1 – P = 0.9. At the same time, the likelihood (odds) that a crash is a rear-end collision 1 in 9 (1/9), or equivalently that the odds that a crash is not a rear-end collision is 9 to 1 (9/1). So basically odds compare probabilities. Odds ratios are useful for comparing the likelihood of two events. Continuing from the previous example, one might ask which crash is more likely, a rear-end or sideswipe (suppose the odds of a sideswipe crash are 1 in 4)? Computing the odds ratio gives, 1:9/1:4 = 4/9 suggesting that the odds of a rear-end crash compared to a sideswipe crash are 4 in 9 (i.e., 4 rear-end crashes corresponds with the occurrence of 9 sideswipe crashes on average). One can ask what probabilities, odds and odd ratios have to do anything with the logistic regression. As Foltz (2015) describes the dependent variable is binary – 0 and 1. What has to be done is to link the probabilities that exist between 0 and 1 to the independent variables. The dependent variable in logistic regression follows the Bernoulli distribution, having an unknown probability p. Bernoulli distribution is a special case of binomial distribution where 푛 = 1, success is 1 and failure is 0 and therefore the probability of success is 푝, while failure is 푞 = 1 − 푝. Having said that, in logistic regression, an unknown p for any given linear combination of the independent variables is estimated. In other words, the independent variables have to be somehow linked with the Bernoulli distribution – this link is called the logit. As Foltz (2015) explains, in logistic regression, the goal is to estimate p for a linear combination of independent variables, since p is unknown in comparison to binomial distribution problems. To tie together the linear combination of variables and the probabilities between 0 and 1, the natural log of the odds ratio, the logit, is used. As Washington et al. (2011) denote it:

푃푖 푌푖 = 퐿표푔𝑖푡(푃푖) = 푙푛 ( ) = 훽0 + 훽1훸1 + ⋯ + 훽휅훸휅 (51) 1−푃푖

By essentially solving for 푃푖, the result is:

푒훽0+훽1훸1+⋯+훽휅훸휅 푃 = (52) 푖 1+푒훽0+훽1훸1+⋯+훽휅훸휅 Assumptions regarding the data structure of logit models are not far off from linear regression models. According to Schreiber-Gregory (2018), logistic regression is quite different from linear regression, as it does not make several of the key assumptions that linear and general linear models are relied on. However, logistic regression still shares some assumptions with linear regression, with some additions of its own:  Binary dependent variable: Binary logistic regression requires the dependent variable to be binary.  Observation independence: Logistic regression requires the observations to be independent of each other. In other words, the observations should not come from repeated measurements or matched data.  No multicollinearity: Logistic regression requires there to be little or no multicollinearity among the independent variables. This means that the independent variables should not be too highly correlated with each other.

 Assumption of linearity of independent variables and log odds: Logistic regression assumes linearity of independent variables and log odds. Although this analysis does not require the dependent and independent variables to be related linearly, it requires that the independent variables are linearly related to the log odds.  Large sample size: Logistic regression typically requires a large sample size. A general guideline is that you need at minimum of 10 cases with the least frequent outcome for each independent variable in your model. For example, if you have 5 independent variables and the expected probability of your least frequent outcome is .10, then you would need a minimum sample size of 500 (10*5 / .10). These assumptions in part define also the way to evaluate a possible logit model through different measures similar to ones used in linear regression models. For the overall goodness of fit of model, McFadden’s, as well as Cox and Snell’s 푅2 (uncorrected/corrected) are typical measures (Allison, 2014). For the statistical significance of parameters chi-square goodness of fir test can be used to produce the p-values. Finally, multicollinearity detection can be done by using either correlation matrix (coefficients smaller than 0.8 indicate low multicollinearity) or Variance infliation factor (VIF), which should be lower than 10. 3.2.2. Modeling malfunction probability as a function of turnouts characteristics- separate influence of variables and statistical validation Having established the model that will be used, it is clear that for turnout malfunctions, the probability of breakdown as a function of geometric/operational characteristics will be modelled. For this purpose, the object – oriented turnout fault database is used. After tests, it was determined that results are better when outliers are included in the modelling process. For the modelling process, the RegressItLogistic excel add-on (Nau, 2019) was used. First, the independent variables were used separately to predict the probability of a turnout fault. The variables used as well as their results are presented below It can be said that arguably, the structure of database, as well as the quality of data played an immense role in these results. For most of the variables, no significant relation between them and breakdowns could be established. However, it is worth noticing that while inclination was significant, and had exactly the desirable effect on breakdowns, there is a paradox: as fraction becomes bigger (smaller denominator), the probability of breakdown diminishes, meaning that turnouts with smaller inclinations have a bigger probability of failure. Allowable speed was one of the few variables, which performed as expected: higher speeds resulted in higher probability of breaking down. The effect of concrete sleepers on failures was an ambivalent topic, since it had to be known if turnout employed joints or not. Finally, a surprise was the influence of type of track, especially that of normal main track versus side track: while on normal track the probability increased, on a side track the probability diminishes.

Statistical Expected Expected Influence on Variable name Coefficient R2 Adj R2 z-stat P-value significance sign breakdown Inclination -6.118865102 0.003567373 0.001624812 -2.689663332 0.007152414 Yes yes No Max_allowable_speed 0.004992293 0.002233558 0.000290998 2.142486749 0.032154334 Yes yes Yes Radius 0.000170072 0.001171365 0.00000 1.561814229 0.118331759 No No No Rail size 0.018070824 0.001361248 0.00000 1.664614814 0.095989628 No No No Service_time 0.00146745 0.000059 0.000000 0.349962727 0.72636667 No Yes No Total_heat_output__KW____Heating 0.002867498 0.0000422 0.00000 0.294871846 0.76809178 No Yes No _turnouts Traffic__Mbrt_year____2013_2017 -0.000420739 0.0000187 0.0000000 -0.19588665 0.844698887 No No No Concrete_sleeper 0.235228291 0.001988148 0.0000456 2.008524685 0.044587566 Yes Ambivolent Ambivolent Curved_blades 0.225887412 0.0006639 0.0000000 1.181008676 0.237599277 No No No Fixed_crossing 0.017348638 0.0000016 0.0000000 0.057061679 0.954496063 No Yes Ambivolent Movable_crossing -0.017348638 0.0000016 0.0000000 -0.057061679 0.954496063 No Yes No Machined_rail_crossing -0.001929757 0.00000016 0.00000000 -0.017970912 0.985662058 No No No RBM_crossing 0.001929757 0.00000016 0.00000000 0.017970912 0.985662058 No No No Normal_main_track 0.348556976 0.00284469 0.00090213 2.374375716 0.017578653 Yes Yes Yes Diverting_main_track -0.22697521 0.001125785 0 -1.504281389 0.132508929 No Ambivolent Ambivolent Side_track -1.466540728 0.00411572 0.00217316 -2.408807223 0.016004749 Yes yes Yes Straight_blades -0.225887412 0.000663934 0 -1.181008676 0.237599277 No No No Winter 0.021752073 0.0000193 0.0000000 0.19929889 0.842028947 No Yes No Table 8: Separate Influence of variables on turnout breakdowns. Own edit

3.2.3. Modeling malfunction probability as a function of turnouts characteristics- Combined influence of variables and statistical validation The situation is rather different when a series of dependent variables try to explain the variation of one dependent variable. The first observation is that more variables became relevant: For example, machined rail crossing has now a statistical significance and affects the probability of a breakdown positively. Another variable, previously unimportant, is heat output in turnout heaters: it seems that the bigger the output is, the smaller the failure probability becomes. In addition, in conjunction, variables explain a bigger portion of dependent variable’s variability, which is indicated by a bigger푅2. Still, this model is far from perfect: the 푅2 value is still small and not many variables seem capable to explain the probability of malfunction accurately (Table 9, Error! Reference source not found., Figure 109 - Figure 112. That does not mean however that these kinds of models do not have any true potential in explaining turnout malfunctions. In fact, this is a risked-based model, which treats the malfunction as a probability, rather than a certainty. In fact, the whole concept raises a series of questions that will be discussed in the end. Regardless of the case, it was clear that turnout inclination plays an important role in all cases. Other variables were also shown to have an impact, for example allowable speed, the existence or not of machined rail crossing, type of sleeper and total heating output of heating systems. Surprisingly in both cases, service years and traffic volume did not show to have any impact or being statistically significant. That can be explained however by the fact that maintenance cycles were not taken into account and traffic volume data was very aggregated and bad. Turnout failure model R-squared (McFadden) Adj.R-Sqr. RMSE Mean # Fitted ROC area Critical z Conf. level 0.013020199 0 0.456931 0.305439 1673 0.567322 1.959963985 0.95 Statistical Expected Expected Influence Variable Coefficient z-statistic P-value significance sign on breakdown Constant 2.05430 0.959277902 0.337418764 No - - Concrete_sleeper 1.06152 2.723466147 0.006460084 Yes Ambivolent Ambivolent Curved_blades 0.20401 0.934741554 0.349921506 No No No Inclination_nmr -17.09269 -1.982115173 0.047466352 Yes Yes No Machined_rail_crossing 0.42019 2.238339888 0.025198899 Yes Yes Yes Max_allowable_speed -0.01281 -0.993475452 0.320478308 No No No Movable_crossing -0.04885 -0.10389372 0.917253691 No Ambivolent Ambivolent Normal_main_track 0.20324 1.206462388 0.227639253 No Yes Yes Radius -0.00003 -0.080183818 0.93609106 No Yes Yes rail_size -0.02705 -0.801316865 0.42294823 No Yes Yes Service_time 0.00581 0.99811908 0.318221619 No Yes Yes Total_heat_output__KW_ -0.02888 -1.955816675 0.050486754 Yes Yes Yes ___Heating_turnouts Traffic__Mbrt_year____20 0.00054 0.231388366 0.817013102 No Yes No 13_2017 Winter 0.01321 0.118921606 0.905337464 No Yes No Table 9: Modeling results for combined variables. Own edit 3.2.4. Application of the model – an example Having determined the parameters of the model, now it is feasible to estimate the probability of a turnout to malfunction. The model will be:

푒푉 푃 = (53) 푓푎푢푙푡 1+푒푉 Where:

푉 = 2.05430 + 1.06152 × CNCRTSLPR + 0.20401 × 퐶푅푉퐷퐵퐿퐷푆 − 17.09269 × 퐼퐶퐿푁푇푁

+ 0.42019 × 푀퐶푁퐷푅퐿퐶푅푆푁퐺 − 0.01281 × 푀푋퐴퐿푊퐵퐿푆푃퐷 − 0.04885 × 푀푉퐵퐿퐶푅푆푁퐺

+ 0.20324 × 푁푅푀퐿푀푁푇푅퐾 − 0.00003 × 푅퐷푆 − 0.02705 × 푅퐿푆퐼푍퐸 + 0.00581

× 푆푅푉퐶퐸푇퐼푀퐸 − 0.02888 × 푇푇퐿퐻푇푂푇푃푇 + 0.00054 × 푇푅퐹퐶 + 0.01321 × 푊푁푇푅

It has to be noted that although the basis of a logit model is the link between probabilities and a combination of linear parameters, V here can be considered as a type of function that describes the degradation of a turnout or its state and according to the model, the degradation is considered to be linear, which cannot be always the case, as Zwanenburg (2007) shows. Taking as an example, two turnouts subjected to different operational and geometrical characteristics but to the same season of the year are going to be compared. The results are presented in Table 10.

Table 10: Characteristics of two turnouts and their probabilities of failure. Own edit

It is clear that from the prevailing traffic conditions as well as its geometrical characteristics, the turnout 1 is in bigger risk of malfunction, since it is located in a main line with heavy traffic, Turnout 2, which is located on a side track and does not experience heavy traffic, has a lower probability of failure. Therefore, in terms of maintenance priority, turnout 1 is first. If e.g. 100 turnouts are evaluated, their probabilities can create a bottom-up maintenance plan, instead of an ad-hoc one (Figure 96). This is clearly seen in the theoretical example presented above. By inputting the characteristics of turnout in the model, a maintenance pattern emerges. The roughest interpretation of the probability is that it acts as a ranking indicator, which shows which turnouts must be maintained first: Considering also their geographical distribution, it is possible to group the maintenance work into three main groups. Group 1 contains turnouts that need to be maintained first, group 2 second and group 3 last or not even maintained. This has implication in terms of optimizing economics as well as maintenance timetable graph, which interferes with regular railway timetable. 3.2.5. Conclusions: modeling turnout malfunctions with logistic models This model proves that is preliminary feasible to develop a risk –based model for turnouts, which will define the maintenance priorities for companies and public entities responsible for turnout and railway maintenance. Theoretically, this approach can be adopted for every type of infrastructure on the railway network, where from probabilities about a series of individual components, big maintenance patterns emerge. Nonetheless, it must be noted that the meaning of the probability is not clear, in the sense that if a turnout needs immediate inspection and repairs or not. As a result, probabilities must be ideally associated with specific states of a turnout, which can be derived empirically. Also, another important aspect is the data quality used for modeling and its impact on the results: from the experiments conducted it is obvious that rough, aggregated data is not the best approach. Furthermore, the validity of some types of data is questionable. As a result, the model suffers from accuracy and variability explanation issues, which makes it an interesting testbed for future developments, but not an applicable model in present. In conclusion, this is an interesting topic, which poses way too many research issues, as well as challenges set forth to researchers and organizations/companies of interest, like Trafikverket, maintenance companies as well as consultancies across Sweden.

Figure 96: Planning of maintenance work in turnouts through use of logistic models. Source: Own edit The process itself however did not produced the expected results in terms of reliability and that can be attributed to several key factors. The first was obviously the quality of data, which was not the best, therefore better data quality could yield better results. The second reason lies with the nature of malfunctions and the model itself: Each malfunction does consider primarily a specific part of the turnout: some of them are related to point machine, while others with the crossing/frog e.t.c. At the same time, the logistic model tries to model the malfunction probability of a turnout, by examining turnout as a single unit. In reality however, turnout is a machine, a collection of parts and each part is exposed to a different degree of degradation and fails for totally different reasons. The result is that there is such a variability, that no effective model that characterizes the turnout as a single unit can be established effectively. Finally, another factor is the form of degradation model: by default when one uses a logistic model, it assumes that the degradation function (which is comprised of all characteristics of a turnout) is linear, which as Zwanenburg showed is not always the case, especially when the different parts of a turnout are considered. 4. Results It is important to understand that a typical ballasted track should be perceived as a system which is derived from the interaction of rolling stock and rail infrastructure: rolling stock movement on track applies forces on the track infrastructure and as a result the infrastructure deteriorates. In addition, the resulted loading environment of a track is extremely dynamic which implies extreme loading conditions and variability. To deal with that kind of loading environment and deterioration, a typical ballasted track is comprised of several components; each of them is performing a key function. Different

71 configuration of these components (e.g. size of rail section or type of sleeper) affect the performance of the track, creating a totally different loading environment each time. In addition, each component has several key parameters, which define its performance and longevity: rails have a certain stress limit, while sleepers have a maximum compression stress, affected by the sleeper spacing. These are important considerations when someone tries to understand how a ballasted track works and how different components affect track performance. In their turn, turnouts are part of the track infrastructure, labeled as special trackwork, play an important role by allowing network branching. From the parts perspective, turnouts are extremely complicated, machine-like constructs, which justifies their overall high cost and their need for tactical maintenance. In addition, the most important parts were established: the switch and the crossing frog. Switch is responsible for diverting a train from a course to another and carry the train through the switch blades, while the crossing allows the train to cross tracks safely. Analysis of parts also showed that as constructs, turnouts are constantly developed to accommodate heavier and faster trains: special blade profile, transition towards CWR turnouts, use of techniques and special materials for more durable rails and parts, replacement of fixed with movable point frogs, use of advanced operating mechanisms linked to interlocking and traffic control systems, replacement of wooden with concrete sleepers and better fastening systems as well as use of premium components like heaters and point protectors constitute a modern turnout in terms of parts. In terms of operational characteristics, speed, acceleration and change of acceleration are the most important factors, which define the capacity and level of service of a turnout, while at the same time dictate the geometrical requirements of a turnout. In terms of geometry, design starts with several key points, some standardized dimensions and some key geometrical measures like the frog number or the ratio of inclination, which give rise to the overall dimensions of a turnout. At the same time, these geometrical characteristics set allowable speeds and accelerations undertaken by trains in a turnout: geometry of blades, frog number and ratio of inclination, type of rail, fastening system and sleeper characteristics, type of frog are some main parameters which should be considered. Therefore, it was shown that operational characteristics interact with geometrical ones, and in conjunction with different set of selected parts and their characteristics define the performance of a particular turnout. In terms of structural integrity, performance of a rail track infrastructure is usually evaluated through a structural analysis framework, which describes the response of track to loads. Several important key parameters are derived: deflection, bending moment, pressure and rail seat force values. These parameters are later used to derive maximum stress values and compare them with the allowable levels of each track part. This procedure can determine if a track part is suitable to be used and handle the loads, which is closely related to the properties and type of each part: different rail section, fastening system, sleepers (wooden or concrete) ballast material and condition have different tolerance and a successful combination of them can determine the overall structure health. In cases when turnouts are examined, structural analysis raises some extra concerns, as turnouts contain special parts and particular geometry, which is differentiated from a typical track. In addition to typical structural considerations, turnouts face extra special topics: the importance of lateral and longitudinal forces, increased dynamic loading due to discontinuities, settlement and interaction between geometry/operation and loading values are the main concerns, mainly from the standpoint of stresses which can cause malfunctions. The configuration of type of parts, operational and geometrical characteristics of a turnout, as well as some overall attributes every turnout shares give rise to specific structural considerations. As shown, forces applied on a turnout can be considered higher, not only because of the overall geometry of a turnout (curve without superelevation) but also because of the inherent discontinuities a turnout possesses (mainly in switch blades and in the crossing). In addition, the existence of movable parts presents some issues in terms of potential failures. Finally, it was shown that the main structural parameters could be much higher than the ones met at a straight track, posing durability and risk issues to the turnout. All in all, the calculation of response of turnouts to the loading environment is important and should be incorporated in infrastructure maintenance models, such as the one proposed in the master thesis, but unfortunately, such a methodology (for semi-static turnout structural analysis) is not in place. Therefore, it would be useful for such a methodology to be developed for turnouts as well.

In Sweden, Trafikverket is the main organization, responsible for railway maintenance planning, setting the standards for contractors and producing technical documentation, amongst them for turnouts as well. It employs a cyclic maintenance strategy (observation – preventive intervention – monitoring through KPI’s). Also it introduced the maintenance windows in timetable planning, exclusively for maintenance. Trafikverket’s strategy emphasizes on preventive maintenance, not only because of the increased traffic forecasts, but also because of the EU and national legal framework. Its strategy for the coming years is described through the maintenance plan 2019-2022, where apart from basic maintenance, big amounts are also directed towards reinvestments, particularly towards track infrastructure renewal, where turnout maintenance holds a prominent place, underlining their importance. It has to be noted that there is a correlation between amounts being spent on maintenance and the increase of traffic. However, in spite of moving towards preventive maintenance and towards maintenance windows from possessions, Trafikverket does not employ predictive maintenance, which poses a question of whether resource management and maintenance quality are on an equilibrium. This question in turns, casts doubt on whether the core aim of maintenance planning is followed, if the introduction of maintenance windows is arguably the best method of dealing with maintenance (particularly in cases of infrastructure such as turnouts which have a higher risk to malfunction), especially when one considers the structuring of maintenance through the timetable, and if the existing maintenance monitoring indicators are enough, given the fact that turnouts need more frequent maintenance and are susceptible to more frequent failures. In this process, the actual maintenance work structure has to be also considered. Clearly, from this scope, the maintenance of turnouts in this framework is related with the strategic and tactical problems of maintenance planning. These approaches and framework being followed in practice, pose an abysmal strain, in terms of resource management, maintenance time planning and quality of maintenance work, especially for turnouts. Therefore it can be argued that a better approach is to move towards predictive preventive maintenance, especially for critically important railway infrastructure, through the usage of risk-based models. However, a framework must be established in order to clarify which factors contribute to turnout degradation. Furthermore, its parts must be well understood and structural mechanics clarified. In general, the process of devising a preventive predictive maintenance planning model is divided into two successive parts: the first is to define a model for infrastructure degradation, which can be either a direct measure of state of infrastructure or probability of malfunction. Then, this is a measure which is used as an input for optimizing maintenance planning, which is essentially a problem of assignment of maintenance activities on a rail network, in a way which minimizes/optimizes a particular measure (e.g. time or money). Zwanenburg (2007), by studying turnouts wear in Swiss rail network calls for train and track properties as the main factors of wear and consequently of faults. Furthermore, he proves several variables well known to railway industry that affect degradation to be true, but his results are not without faults. However, he defends them by stating that factors related to geography can play a significant role in the quality of results. Therefore, the degree of degradation of turnouts and the construction of a degradation model are related with the geometrical and operational characteristics of turnouts. In methodology part, findings regarding turnouts were interesting but also surprising. Using the existing literature as well as the input from Trafikverket as guide, an attempt to derive conclusions regarding the nature of malfunctions in turnouts in eastern region was made. As a basis, Trafikverket’s databases Ofelia and BIS were used, but for proper analysis, a synthetic Object oriented database had to be constructed. This database can be used not only for modelling of malfunctions in tunrouts, but also for purposes of meaningful statistical analysis. However, in that case, data availability and its origins can determine if a database can serve or not its purpose effectively. From the data analysis, it seems that malfunctions has several common causes. Nissen (2019) calls for snow-icing and electromechanical issues in movable parts of the turnout as the main causes. The statistical analysis of the synthetic as well as Ofelia databases was conducted. The findings in general confirm the findings of Zwanenburg and Trafikverket, as well as these that can be drawn from the theory surrounding railway engineering and the analysis of turnouts, in the sense that it appears to be a correlation between turnout malfunctions and most of geometrical and operational characteristics of a turnout. However, several variables did not show the promising relation, due to many factors, which can be attributed mostly to the quality and type of data. For example, while statistical analysis shows that there is a relation between

73 speed, inclination, traffic and malfunctions, relations between malfunctions and quantitive variables, like type of frog or sleeper could not be established. This underlines the need for better databases with more detailed variables to be examined and related with malfunctions. Reasons of faults in turnouts in eastern region were also analysed. In general, what results show is that a turnout suffers a lot of malfunctions, but also subparts which are related to movable parts of the turnout experience a lot of them. The reasons were found to be more related to electromechanical causes than to structural ones. Nonetheless, parts like crossing or point device are also experiencing structural faults like rail cracks or damage. This underlines the need for incorporating more characteristics of these subparts in any risk analysis, an issue closely related to database building. These remarks, set the frame for establishing the basic category of variables, characteristics required for purposes of modelling, as well as proper statistical analysis of a turnout (Table 7). For this master thesis, only the effect of operational and geometrical categories could be studied and incorporated into the modelling process. For the modelling process, a binary logit model was used, as through its structure the probability of malfunction could be directly related to geometrical and operational characteristics of a turnout. Furthermore, the linear function serves a form of degradation model for a particular turnout. First, the malfunction probability was calculated and after it was used to rank the turnouts in terms of maintenance priority. It was proved that is preliminary feasible to develop a risk –based model for turnouts, which will define the maintenance priorities on the basis of the state of each turnout which is related to its characteristics, for companies and public entities responsible for turnout and railway maintenance. Theoretically, this approach can be adopted for every type of infrastructure on the railway network, where from probabilities about a series of individual components, big maintenance patterns emerge. However, in terms of statistical significance and behavior, the explanatory variables did not have always the expected behavior, which it is assumed to be connected with data and modelling structure issues (Appendix 7) Finally, the process itself did not produced the expected results in terms of reliability and that can be attributed to several key factors. The first was obviously the quality of data, which was not the best; therefore, better data quality could yield better results. The second reason lies with the nature of malfunctions and the model itself: Each malfunction does consider primarily a specific part of the turnout: some of them are related to point machine, while others with the crossing/frog etc. At the same time, the logistic model tries to model the malfunction probability of a turnout, by examining turnout as a single unit. In reality however, turnout is a machine, a collection of parts and each part is exposed to a different degree of degradation and fails for totally different reasons. The result is that there is such a variability, that no effective model that characterizes the turnout as a single unit can be established effectively. Finally, another factor is the form of degradation model: by default when one uses a logistic model, it assumes that the degradation function (which is comprised of all characteristics of a turnout) is linear, which as Zwanenburg showed is not always the case, especially when the different parts of a turnout are considered.

5. Topics for further research The approach chosen here to treat turnout malfunctions, poses some serious topics for further research:  From logit models to Nested logit models. This topic concerns the form of risk models themselves. In spite of the promising results, it can be argued that logistic regression models of that kind (binary response) treat turnouts as a simple mass, where every detail is associated with the probability of a turnout to fail. If the language of discrete choice models is used, that means that a turnout has a unified disutility to malfunction. In reality, this is partially true, because every time a turnouts fails, it does not fail as a whole but some of its parts: can be the point machine, or switch blades or the crossing etc. therefore, not only the turnout has a probability to fail, but also one of its components. This is where the nested logit structure comes in. The derivation of the nested logit model is based on the assumption that some of the alternatives share common components in their random error terms. That is, the random term of the nested alternatives can be decomposed into a portion associated with each alternative and a portion associated with groups of alternatives (Koppleman & Bhat, 2006). In other words, the malfunction disutility that a turnout has, is the sum of malfunction disutilities that each component has. Therefore NL structures can be considered as good candidates for better, more robust risk analysis models.  Object – oriented databases. It is clear that existing maintenance databases regarding incidents are inadequate: they are centered around the incident and not the object itself – for example, Ofelia database contains data regarding the incident, but not enough data regarding the infrastructure itself, making it difficult to associate the incident with the characteristics of the infrastructure itself. Therefore, an imperative step is to go towards this direction, which will help the development of risk-based models.  Data communication. Another important topic is that many times, only the person who creates and manages the database understands all the entries, all the fields, the data structure itself. But if a person who had not any contact with it attempts to use it, it will require significant time for him to comprehend it, which poses a significant strain to him and to the person/organization who manages it, diminishing the productivity of everyone. A database should be able to communicate its contents with accuracy and efficiency. Databases of technical content should include footnotes and schematics as minimum to communicate their content efficiently.  Development of DSS for turnouts. This topic has to do with the creation of integrated computer packages, which can assist in the decision making process of maintenance planning for turnouts and for other infrastructure: robust mathematical base, variety of functions and interconnection with other software are some key components for a successful DSS packages.  Further analysis of the effect of variables to turnout malfunctions. This is a necessary step towards a deep understanding of the reasons behind the failures in turnouts: obviously geography and data quality play an important role in this process, but comprehending the subparts of a system and how they work is also crucial. Therefore, analyses similar to that for turnouts must be done for the main parts of the turnout.  Data quality and variety. An important prerequisite for the development of robust models and databases. Apart from typical descriptive data, sensor, maintenance and traffic data should be also collected and imported into databases as well as data related to structural aspects of turnouts. Data must also be checked for errors.  Incorporation of maintenance part: In this model, only operational and technical characteristics were used to predict the probability for a turnout to malfunction. However, maintenance characteristics are also playing an important role in the appearance of malfunctions, by essentially postponing the time of malfunction or the appearance of another. Therefore, it is crucial this impact to be examined and analyzed.  Compartmentalization of modelling: It seems that every single main component of turnouts wears out differently and the set of variables affecting it are different as well. Therefore, separate models for each main parts could be developed.  Degradation function: The use of different forms of degradation models should also be examined.

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Appendix 1

Figure 97 : Financial framework for rail maintenance in 2019-2022, by type of maintenance, SEK million (left), Distribution of reinvestments (right). Source: (Trafikverket, 2019), own edit

Figure 98: Response time for the contractor during rush hour (left), Maintenance levels introduced in the coming years (right). Source: (Trafikverket, 2019)

Figure 99: Maintenance actions in eastern region. Source: (Trafikverket, 2019)

Turnout and Percentage of turnouts/crossings Transport flow/region Actions crossings action over the sum of actions actions per region/transport flow

Hallsberg–Luleå‐Riksgränsen 30 12 40% Stockholm–Örebro 6 1 17% Stockholm–Oslo 14 7 50% Stockholm–Göteborg 19 8 42% Stockholm–Malmö 23 8 35% Gävle–Kil–Göteborg 14 3 21% Malmö–Oslo 14 3 21% Region Nord 18 4 22% Region Mitt 38 9 24% Region Stockholm 19 6 32% Region Öst 27 6 22% Region Väst 36 12 33% Region Syd 21 6 29% Total 279 85 30% Table 11: Analysis of major maintenance measures for turnouts/ crossings. Source: (Trafikverket, 2019), own editing

Appendix 2

Maintenance action Maintenance cycles Life periods tamping 40-70 mio. T 4-5 years grinding 20-30 mio.T 1-3 years cleaning 150-300 mio. T. 12-15 years rail replacement 300-1000 mio. T. 10-15 years replacement of wooden sleepers 250-600 mio T. 20-30 years replacement of concrete sleepers 350-700 mio. T. 30-40 years rail fastenings 100-500 mio. T. 10-30 years replacement of ballast 200-500 mio. T. 20-30 years rehabilitated subsoil >500 mio. T. > 40 years Table 12: Typical maintenance cycles and service life periods apply to normal main tracks of high stress / track components. Source: (Lichtberger, 2005)

Appendix 3

Figure 100: Turnout dimensions and parts. Source: (Ruppert, 2018)

Figure 101: Bolted rigid frog (1), RBM Frog (2), Self-Guarded Frog (3), Solid Manganese-steel frog (4), Swing nose frog (5), Movable point frog (6), spring frog (7), lift (jump) frog (8). Source: (Ruppert, 2017)

Figure 102: From left to right and up to down: gauge plates, switch plates, rail braces, heel block assembly, turnout plates, hook twin tie plates, and frog plates. Source: (AREMA, 2003)

Table 13 Geometry of turnouts in USA. Source: (Ruppert , 2017)

Table 14: Typical switches on European railways. Source: (Lichtberger, 2005)

Table 15: Turnout performance comparison between standard, pseudotangential and tangential turnout. Source: (Ruppert , 2017)

Appendix 4

Figure 104: Train disturbing failures by cause/type of infrastructure. Source: (Trafikverket, 2018), own edit

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3 4

Figure 103: Number of trains got delayed due to Turnout malfunctions (1), Additional Train delay due to turnout malfunction (2), Duration of repairs in turnouts (3), Response time for turnout faults (4). Source: (Trafikverket, 2018), own edit

Appendix 5

1 2

3 4

Figure 105: Graphs for eastern region related to turnout malfunctions and: rail size (1), Type of track (2), type of crossing (3,4), Type of sleepers (5,6). Source: (Trafikverket, 2018), own editing

5 6

Figure 106: Graphs for eastern region related to turnout malfunctions and: type of fixed crossing (7,8), Turnout service years (9), season (10). Source: (Trafikverket, 2018), own editing

Appendix 6

Figure 107: Parts of turnout that failed: turnout. Reasons behind failure. Source: (Trafikverket, 2018), own editing

Figure 108: Parts of turnout that failed: point device (2), Actuation locking and detection (3), switch heating (4), control device (5), crossing (6) and snow protection (7). Reasons behind failure. Source: (Trafikverket, 2018), own editing

Appendix 7

Figure 109: Effect of concrete sleepers (1), curved blades (2), inclination (3), machined rail crossing (4) on turnout fault probability. Own edit

Figure 110: Effect of max allowable speed (5), movable crossing (6), and normal main track (7) on turnout fault probability. Own edit

Figure 111: Effect of radius (8), rail size (9), and service time (10) on turnout fault probability. Own edit

Figure 112: Effect of heating output (KW) Traffic 2013-2017 (Mbrt’s) (12) and winter (13), on turnout fault probability. Own edit

TRITA TRITA-ABE-MBT-19747