1st Proctor Lecture of ISSMGE:

Accepted Manuscript 1st Ralph Proctor Lecture of ISSMGE Railroad performance with special reference to ballast and substructure characteristics Buddhima Indraratna PII: DOI: Reference:

S2214-3912(16)30011-3 http://dx.doi.org/10.1016/j.trgeo.2016.05.002 TRGEO 83

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Transportation Geotechnics

Please cite this article as: B. Indraratna, 1st Ralph Proctor Lecture of ISSMGE Railroad performance with special reference to ballast and substructure characteristics, Transportation Geotechnics (2016), doi: http://dx.doi.org/ 10.1016/j.trgeo.2016.05.002

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3rd ICTG 2016, The 3rd International Conference on Transportation Geotechnics

1st Ralph Proctor Lecture of ISSMGE Railroad performance with special reference to ballast and substructure characteristics Buddhima Indraratna* Distinguished Professor of Civil Engineering and Research Director, Centre for Geomechanics and Railway Engineering, University of Wollongong, Australia

Abstract Ballasted rail tracks are widely used throughout the world because they are economical, readily drained, and have sufficient load bearing capacity. Despite these advantages, geotechnical concerns such as ballast degradation, fouling (e.g. coal and subgrade soil), poor drainage of soft subgrade, pumping of clayey subgrade, differential track settlement and track misalignment due to excessive lateral movements exacerbate the cost of track maintenance. Globally, billions of dollars are spent annually on the construction and maintenance of rail tracks. Existing industry design standards are often unable to address these problems because they ignore true cyclic loading patterns, track vibrations, and the onset of plasticity and degradation of track materials. The mechanisms of ballast breakage and deformation, understanding the interface behaviour using geosynthetics, the need for effective track confinement using geocells, time-dependent drainage and filtration properties of track materials require further research to improve existing design guidelines. In view of this, large scale laboratory tests have been carried out using state-ofthe-art facilities designed and built at the University of Wollongong and in other proactive rail institutes worldwide in Europe, America, Japan and China. Based on these tests, various factors governing the stress-strain behaviour of ballast, the strength and degradation of ballast, the ability of various geosynthetics and synthetic energy absorbing mats to minimise ballast breakage and track settlement, the effectiveness of subballast as a granular filter and its stabilisation with geocell have been analysed. In Australia, field studies on instrumented tracks at Bulli (near Wollongong), Singleton and Sandgate (near Newcastle), have been carried out to assess the performance of railroad embankments stabilised with geosynthetic grids, rubber mats, and prefabricated vertical drains. This inaugural Ralph Proctor Lecture focuses on the current state of research encompassing deformation and degradation assessment of railroads and the benefits of geo-inclusions, highlighting examples of innovations from theory to practice, predominantly based on the own experience of the Author. © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Sociedade Portuguesa de Geotecnia (SPG).

Keywords: Railway ballast, Deformation, Degradation, Geosynthetics, Shock mats, Prefabricated vertical drains

* Corresponding author. Tel.: +61-2-4221-3046; fax: +61-2-4221-5474. E-mail address: [email protected] 1877-7058 © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Sociedade Portuguesa de Geotecnia (SPG).

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1. Introduction Ballasted rail tracks form the largest transportation networks in various parts of the world; they transport freight and bulk commodities between major cities, ports, mines and sources of agricultural goods, as well as commuters. To keep pace with the growth in populations and economies, and to help boost productivity, train speeds must increase in order to improve efficiency and reduce maintenance costs. As well as countries such as China, USA, Canada and India, Australia is playing a leading role in the development of heavy haul railway operations that include 3-4 kilometer long trains with axle loads exceeding 35 tonnes to optimise the efficiency of supply chains in the mining and agricultural sectors. Track structure is divided into superstructure and substructure, where the substructure consists of ballast, subballast and subgrade, and the superstructure consists of steel rails, fastening systems, and concrete or timber sleepers (ties). The efficiency and safety of ballasted railway track depends entirely on the complex interaction between these components as they respond to the cyclic loading imparted by moving trains. Although the superstructure components are predominantly elastic and their deformations are generally minimal, the granular substructure layers such as ballast and subballast often undergo significant deformation under the high cyclic stresses exerted by increasingly heavier and faster trains, and it is the substructure response that presents challenges to the track designer and subsequent maintenance upon construction. As the sharp corners of aggregates break and weaker particles are crushed under heavy cyclic loading, differential track settlement is almost inevitable (Selig & Waters, 1994), so when tracks are laid on stiff foundations such as hard rock terrains or concrete bridge decks, where large dynamic (impact) loads are encountered, these problems are often exacerbated. This in turn, leads to rapid fragmentation of ballast aggregates that affects the strength and drainage of track. Moreover, the ballast layer is fouled by upward migration of subgrade clay fines and the downward migration of coal spilling from wagons (Ebrahimi et al., 2012; Giannakos, 2010; Huang et al., 2009a; Indraratna et al., 2014c; Tennakoon et al., 2015), all of which seriously affect the drainage capacity of track. In severe cases, fouled ballast must be cleaned or replaced to maintain the desired track stiffness (resiliency), bearing capacity and alignment. This routine replacement of fouled ballast results in large stockpiles of waste ballast while the continuous replacement of used aggregates with fresh ballast demands additional quarrying. Therefore, to preserve the environment and minimise track maintenance, discarded ballast may be cleaned, sieved, and recycled. However, its shear behaviour must be investigated under field-loading and boundary conditions before the use. Since ballasted tracks have minimum lateral support, the lateral confining pressure must be increased to control lateral stability (Indraratna et al., 2014f; Indraratna et al., 2014g; Indraratna et al., 2014e; Lackenby et al., 2007). The ballast behaviour is affected by the overall characteristics of a granular mass such as the particle size distribution, the void ratio, and the relative density (Bian et al., 2016; Indraratna et al., 2016). While the properties of individual grains of ballast such as size, shape, and angularity govern its degradation under traffic loading, deformation is also influenced by the magnitude of wheel (or axle) load, the number of load cycles, frequency (equivalent to train speed) (Selig & Waters, 1994; Sun et al., 2014a; Sun et al., 2016), and the impact loads (Indraratna et al., 2014d; Nimbalkar et al., 2012a). The magnitude of the impact loads depends on the type and nature of surface imperfections on the wheels and rails, as well as on the track’s dynamic response (Auersch, 2006; Correia & Cunha, 2014; Gomes-Correia, 2001; Indraratna et al., 2014a; Jenkins et al., 1974; Le Pen et al., 2014b; Li & Davis, 2005; Mishra et al., 2014a). These impact loads are detrimental to other components of the track structure because designing for imperfections is difficult to incorporate, which is why assessing the behaviour of saturated clays (subgrade) under repeated train loading is necessary in the design of railroads. Furthermore, the soft estuarine clays located along the coastline in Australia have undesirable geotechnical properties such as low bearing capacity and high compressibility, which is why excessive settlement and lateral movement adversely affects the stability of rail embankments built on this soft compressible ground (Bergado et al., 2002; Indraratna & Redana, 2000; Indraratna et al., 2009a; Liu & Xiao, 2010; Preteseille et al., 2013). In conventional track design, ballast is regarded as an elastic medium where its degradation and associated plastic deformation is ignored. This problem stems from not understanding the complexity of particle breakage and fouling mechanisms and not having a proper constitutive model. This in turn leads to the application of overly simplified empirical approaches in the design and construction of track substructure, which then requires frequent remedial measures and costly maintenance. In the past, the effect of particle breakage on the mechanical behaviour of granular materials was studied adopting different modelling approaches (Been et al., 1991; Chávez & Alonso, 2003;

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Einav, 2007a, 2007b; Indraratna et al., 2014h; Indraratna et al., 2014c; Salim & Indraratna, 2004; Suiker & de Borst, 2003). Limited research has been carried out on the analytical and numerical modelling of ballast while considering plastic deformation associated with fouling, so the critical state of ballast must be analysed relative to fouling and particle breakage. The constitutive behaviour of granular materials has been studied by various researchers using the discrete element modeling approach (Ahmed et al., 2015; Huang & Tutumluer, 2011; Lu & McDowell, 2010; Mirghasemi et al., 2002; Thornton, 2000). This approach to model the track granular media is appealing as it can handle particles of different shapes and sizes. The use of planar geosynthetic products such as geogrid, geotextile or geocomposite (bonding geogrid with geotextile) has drawn more attention because they are economical and relatively easy to install. Several studies have already demonstrated that geogrid reinforcement reduces the settlement and degradation of ballast (Bathurst & Raymond, 1987; Brown et al., 2007; Indraratna & Salim, 2003; Indraratna et al., 2007b; Indraratna et al., 2010a; Qian et al., 2015). The main principle of geogrid reinforcement is to provide better interlocking that restricts the lateral movement of ballast. A layer of geogrid and geotextiles placed at the interface between ballast and subballast often gives encouraging results (Giroud & Han, 2004; Shin et al., 2002). Since the ballast-geogrid interface shear strength depends on the size of the apertures, the optimum value of A/D50 (the ratio of geogrid aperture size (A) to the mean particle size of ballast (D50)) is recommended to maximise the interface shear strength (Brown et al., 2007; Hussaini, 2013). As train speeds increase, the capacity of the track is often unable to withstand the substantially increased vibration and cyclic and impact loads, which is why the use of synthetic energy absorbing mats in rail track foundations has become increasingly popular (Baghsorkhi et al., 2015; Indraratna et al., 2014a). These mats are also called Under Sleeper Pads (USP) or Under Ballast Mats (UBM) when they are placed under the sleepers and beneath the ballast, respectively. The most common applications of these resilient mats in railways are to: (i) reduce structure-borne vibration and noise, and thus improve the vertical elasticity of the track substructure, (ii) reduce ballast degradation to improve the stability of the track foundation, and thus increase the service life of rail tracks (Nimbalkar et al., 2012a; Schneider et al., 2011; Sol-Sánchez et al., 2015a). In low lying coastal areas where the subgrade is generally saturated, fines can be pumped up as slurry into the ballast layer under cyclic loading if subballast is not provided with proper filtration properties; in fact this progressive entrapment of fine particles causes the subballast to undergo a large reduction in hydraulic conductivity. Subballast clogging and its related problems are generally ignored in conventional track design which is several. A number of empirical and analytical models of the filtration phenomenon in granular materials have been developed for embankment dams (Indraratna & Vafai, 1997; Indraratna & Raut, 2006; Locke et al., 2001; Sherard et al., 1984a, 1984b). However, since the loading system in a rail track environment is cyclic, unlike the steady seepage force that usually occurs, the influence of cyclic loading must be assessed in order to improve our understanding of the mechanisms of filtration, the interface behaviour, and the time-dependent changes to filtration that occur within the subballast as a filter medium. Moreover, the subballast layer is usually constructed from locally available materials, some of which have low shear strength and stiffness, and these poor quality materials cause excessive lateral spreading that leads to differential track settlement. Recent studies have shown that a geocell (three dimensional, polymeric cells, interconnected at the joint) can provide much better lateral track confinement than planar reinforcement (Indraratna et al., 2015; Leshchinsky & Ling, 2013b). Until today, only very limited field studies have been reported which quantify the relative performance of combined geosynthetics and shock mats (Hanson & Singleton Jr, 2006; Indraratna et al., 2010a; Indraratna et al., 2013c; Indraratna et al., 2014e; Indraratna et al., 2014g; Nimbalkar & Indraratna, 2016). Large scale experiments combined with full-scale field trials often represent an appropriate strategy for assessing track degradation. In view of this, extensive field trials on sections of instrumented railway track at Bulli and Singleton, New South Wales (NSW) in Australia have been carried out. To enable rail embankments to be constructed over soft clay terrain, prefabricated vertical drains (PVDs) are needed to eliminate excessive settlement and lateral movement (Indraratna et al., 2008; Indraratna et al., 2010c; Indraratna et al., 2012d). For a track section in the town of Sandgate (NSW), short PVDs were used to dissipate cyclic loads induced by pore water pressure, limit horizontal movement, and increase the bearing capacity of soft subgrade; this was then analysed under in-situ track conditions. This paper describes the results of these three full-scale field trials and a series of large scale laboratory tests supplemented by numerical analyses to assess the performance of ballasted tracks at increased speeds and axle loads, and to quantify

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the benefits of using geo-inclusions in track. The contribution made by various rail research institutions worldwide for improving heavy haul and HSR have been substantial in the past decade. Notable contributions have also been made by industry, e.g. SNCF (France). Table 1 provides a summary of major themes in rail geotechnics and selected key references. Table 1. Rail Geotechnics in a Nutshell – Key Themes. No. 1. 2.

Theme Description Basics of track substructure and rail embankments Load distribution in track, moving loads and dynamic track analysis

3.

Experimental studies on ballast: deformation and degradation

4.

Theoretical aspects and constitutive modelling of ballast and sub-ballast

5.

Track drainage and effects of ballast fouling

6.

Use of geosynthetics including geogrids, geotextiles and geocells

7.

Use of impact-attenuating synthetic mats

8.

Role of sub-ballast including capping layer and structural fills Subgrade performance, instability and implications on track response; Stabilisation of subgrade for railways

9.

10. 11.

Ballast bonding (polyurethane) for improved track resiliency Numerical modelling of track and DEM simulation

12.

Field Instrumentation and performance verification

13.

Specific design functions including transition zones

14.

Aspects of track maintenance and scheduling

15.

Track assessment using Image analysis Energy geotechnics and carbon footprint for track engineering Selected Practice Guides and Technical Specifications for ballasted tracks

16. 17.

Key References Indraratna et al., 2011b; Iwnicki, 2006; Li et al., 2015; Miura et al., 1998; Mundrey, 2009; Selig & Waters, 1994 Choi, 2013; Correia et al., 2007a; Esveld, 2001; Ishikawa et al., 2011, 2014b; Kaewunruen & Remennikov, 2008; Momoya et al., 2005; Powrie et al., 2007; Remennikov & Kaewunruen, 2008; Yang et al., 2009 Aursudkij et al., 2009; Brown et al., 2007; Chen et al., 2014b; Correia et al., 2007b; Indraratna et al., 1998, 2005, 2014f; Ishikawa et al., 1997, 2011, 2014a; Kennedy et al., 2012; Lackenby et al., 2007; Le Pen & Powrie, 2011; Li & Selig, 1996; McDowell et al., 2003, 2004, 2005; Selig & Sluz, 1978; Suiker et al., 2005; Sun et al., 2016; Tutumluer et al., 2008; Woodward et al., 2014 Cui et al., 2013; Desai & Janardhanam, 1983; Einav, 2007a, 2007b; Indraratna et al., 2011b, 2012b, 2014b, 2014f; Knothe & Grassie, 1993; Rowe, 1962; Suiker & de Borst, 2003; Tennakoon et al., 2015; Yang et al., 2008; Zhai et al., 2004, 2009 Budiono et al., 2004; Darell, 2003; Dombrow et al., 2009; Ebrahimi et al., 2012, 2014; Feldman & Nissen, 2002; Giannakos, 2010; Hesse et al., 2014; Huang et al., 2009a; Indraratna et al., 2011a, 2013b; Trinh et al., 2012; Tutumluer et al., 2008 Brown et al., 2007; Chen et al., 2014a; Dash & Shivadas, 2012; Fernandes et al., 2008; Indraratna & Nimbalkar, 2013; Indraratna & Salim, 2003; Indraratna et al., 2010a; 2013a; 2014e; 2015; Leshchinsky & Ling, 2013; McDowell & Stickley, 2006; Mishra et al., 2014b; Qian et al., 2015; Raymond, 1986, 2002; Raymond & Ismail, 2003; Tatsuoka et al., 1992, 1996, 2008; Tutumluer et al., 2012 Alves Ribeiro et al., 2015; Auersch, 2006; Dahlberg, 2010; Hanson & Singleton Jr, 2006; Indraratna et al., 2014c, 2014e; Insa et al., 2014; Johansson et al., 2008; Kaewunruen & Remennikov, 2015; Markine et al., 2011; Marschnig & Veit, 2011; Nimbalkar et al., 2012; Paixão et al., 2015; Schneider et al., 2011; Sol-Sánchez et al., 2014, 2015b, 2015a; Wan et al., 2016 Chrismer & Davis, 2000; Fatahi et al., 2011; Fortunato et al., 2012; Haque et al., 2008; Indraratna et al., 2015; Radampola et al., 2008; Trani & Indraratna, 2010 Alves Costa et al., 2010; Cardoso et al., 2012; Correia & Cunha, 2014; Duong et al., 2013; Farris, 1970; Fatahi et al., 2015; Indraratna et al., 2010b; Li & Selig, 1996; Liu & Xiao, 2010; Miller et al., 2000; Potter & Cameron, 2005; Preteseille et al., 2013; Read et al., 1994; Selig & Sluz, 1978; Spriggs & Drechsler, 2011; Zhang et al., 2015 Dersch et al., 2010; Jubin, 2012; Keene et al., 2012, 2014; Kennedy et al., 2013; Woodward et al., 2007, 2014 Ahmed et al., 2015; Alves Costa et al., 2010, 2012; Chen et al., 2012; Correia & Cunha, 2014; D’Aguiar et al., 2012; Ferellec & McDowell, 2012; Huang et al., 2009b, 2010; Huang & Tutumluer, 2011; Indraratna et al., 2012a, 2014a; Lu & McDowell, 2006, 2010; McDowell et al., 2006; Ngo et al., 2014, 2015; Quinn et al., 2010; Suiker & de Borst, 2003; Tutumluer et al., 2007; Tutumluer et al., 2012 Alves Costa et al., 2012; Choi, 2013; Indraratna et al., 2010a, 2010b, 2014d; Kaewunruen & Remennikov, 2015; Le Pen et al., 2014b; Read et al., 1994; Sánchez et al., 2014; Schneider et al., 2011; Woodward et al., 2007 Coelho et al., 2011; Fernandes et al., 2012; Giner & López-Pita, 2009; Huang & Brennecke, 2013; Le Pen et al., 2014b; Li & Davis, 2005; Mishra et al., 2014a; Raymond, 1986; Varandas et al., 2014 Ebrahimi & Keene, 2011; Ferreira & Higgins, 1998; Higgins et al., 1999; Kaewunruen et al., 2015; Marschnig & Veit, 2011; Peng et al., 2011; Quiroga & Schnieder, 2012; Thom, 2007; Woodward et al., 2007; Zhang et al., 2013 Abadi et al., 2015; Ajayi et al., 2015; Fernlund, 2005; Le Pen et al., 2014a; Sun et al., 2014; Tutumluer et al., 2006, 2012 Åkerman, 2011; Chang & Kendall, 2011; Federici et al., 2008; Kaewunruen et al., 2015; Kiani et al., 2008; Schwarz, 2008; UIC, 2013, 2015; Westin & Kågeson, 2012 AREMA, 2003, 2015; British Standards Institution, 2003; Canadian National Railway, 2015; German Institute for Standardisation, 2008, 2013; Indian Railway Specification, 2004; International Union of Railways, 2008; IRPWM, 2004; Japanese Standards Association, 2014; Railtrack, 2000; Standards Australia, 2015

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2. Dynamic Track Analysis and Substructure Response The dynamic interaction between vehicles and track can be described using a mathematical model (shown in Fig. 1(a)) adopting distinct mass-spring-damper system with a discretely supported beam (Esveld, 2001). The track superstructure is separated from the substructure by the sleeper-ballast interface that importantly governs the load distribution with depth (Indraratna et al., 2011b). Many investigators have begun to study the interaction between track components and their individual characteristics separately. In comparison with the substructure, the characteristics of the superstructure components are better understood and their behaviour is more predictable. However, the properties of the substructure components are more non-homogeneous and have a very strong nonlinear stress-strain relationship, and that makes it difficult to predict how the substructure will behave when the dynamic characteristics of the loads are considered. Esveld (2001) describes the load-bearing function of the track that includes the dimensions of the different interfaces (Fig. 1(b). For a wheel load 100 kN, the greatest stress of 500 MPa occurs at the wheel-rail interface; this decreases by two orders at the rail-sleeper interface and then slowly decreases to about 300 kPa at the sleeper-ballast interface. The ballast-formation interface only receives about 50 kPa.

Fig. 1: (a). Dynamic Model of Vehicle-Track System (inspired by Esveld, 2001; Lei and Rose, 2008; Mishra et al., 2014a); (b) Principle of Load Transfer (modified after Esveld, 2001).

2.1. Substructure properties and its responses The load bearing capacity of a track system is determined by the vertical stresses imposed at the formation of the ballast bed and roadbed. The thickness of the ballast layer is calculated such that a reasonable stress is transferred to the formation, because overloading the ballast bed and formation causes the aggregates to degrade rapidly and at times initiate pumping fines from the formation to overlying granular strata, especially when the formation is saturated. These actions eventually reduce the quality of the track geometry and create problems such as undrained failure due to poor drainage. Track stiffness plays a significant role on track settlements and track geometry misalignments and irregularities (Banimahd et al., 2013; Brough et al., 2003; Burrow et al., 2007; Frost et al., 2004; Li & Selig, 1994; Sadeghi & Askarinejad, 2007; Woodward et al., 2014). The stiffness of substructure layers is different in that ballast and subballast are considerably stiffer than the subgrade. However, most existing design methods assume a homogeneous half-space for all the layers and omit the varying properties of distinctly different layers. This leads to underestimating the variations of stress in the substructure, and this is the reason why in track models such as

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ILLITRACK (Robnett et al., 1975), GEOTRACK (Chang et al., 1980) and KENTRACK (Huang, 1984), all the major components of track are characterised. Li and Selig (1998) used GEOTRACK multilayer track model to analyse the most important factors such as the thickness and stiffness of the ballast (granular) layer, and how the stiffness of the subgrade influences the variation of stress in the substructure for given loading conditions. Their results indicated that both the thickness and stiffness of the ballast significantly influence the subgrade stresses, as shown in Fig. 2 (a) and (b). Increasing the thickness of ballast reduces the subgrade stress and also distributes the stress more uniformly across the track. Similarly, with the same thickness of ballast, an increase in its stiffness from 140 MPa to 550 MPa significantly reduces the subgrade stresses.

Fig 2. Effect of ballast thickness (H) and stiffness (Eb) on the deviator stress at the ballast-subgrade interface; (a) Eb = 140 MPa; (b) Eb = 550 MPa (Li & Selig, 1998, with permission from ASCE)

However, above design method does not incorporate effect of high speed train and dynamic effects due to Rayleigh waves propagating in the track granular strata. As train speeds approach critical values rapid deterioration of the track, ballast and subballast can occur due to track critical velocity effects. To investigate these aspects, a 3D finite element analysis was used by Woodward et al. (2013) to model the development of Mach Cones (El-Kacimi et al., 2013) for high speed trains approaching the Rayleigh wave velocity of the subgrade. The results in Figs. 3 (a-c) show the response of a typical sleeper and development of Mach Cones as the train speed is increased incrementally. The Rayleigh wave velocity of the subgrade is approximately 70 m/s. Fig. 3 (a) shows that the transient vertical deflection is highly regular and the ground pattern is symmetrical when the train speed is 47 m/s. When the speed is 62 m/s approaches the ground Rayleigh wave speed, dynamic effects are developed rapidly and subsequent Mach Cones are shown in Fig. 3 (b). At train speed of 75 m/s, the track resonant velocity is achieved leading to large vertical transient deflection and development of full Mach Cone is observed as shown in Fig. 3 (c). A three dimensional dynamic non-linear finite element model (FEM) was developed by Banimahd et al. (2013) to study the track substructure response to train speed. It was found that when the train speed approaches and exceeds the subgrade stress wave velocity, large displacements occur as shown in Fig. 4(a) and (b). The results also indicate that the ballast with low stiffness results in higher displacement and more asymmetric displacement pattern than that with high stiffness (Woodward et al., 2007b). The comparison of numerical predictions by Banimahd et al. (2013) with field observations reported by Madshus et al. (2004) shows that the track displacement increases dramatically when the train speed approaches the Rayleigh wave velocity of subgrade. It is evident from the FEM and field results, the displacement response are essentially static when the train speed is half of Rayleigh wave velocity. However, when the train speed is equals the Rayleigh wave velocity of subgrade the maximum dynamic displacement may reaches more than 3 times the static displacement.

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Fig. 3. (a) Transient vertical deflection of typical sleeper (Left) and development of the ground Mach Cone and track dynamics (Right) at various train speeds using 3D finite element model; Speed = (a) 47 m/s; (b) 62 m/s; and (c) 75 m/s (reproduced from Woodward et al., 2013; with permission from ICOVP-2013).

V=70 m/s Ballast: Low stiffness

Wheel

V=70 m/s Ballast: High stiffness

Fig. 4. Simulated track displacement responses with variation of ballast stiffness: (a) low stiffness; and (b) high stiffness and (c) Maximum displacement with normalized train speed from simulated and field data (Reproduced from Banimahd et al., 2013, by kind permission of ICE Publishing)

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2.2. Impact loads and its responses The loading due to passage of trains generally forms regular harmonic stress patterns. However, abnormalities in the wheels and/or rails impart high impact stresses onto the tracks and accelerate deterioration of the track elements. These types of dynamic forces are either short or long in duration, whereas vehicle suspension plays almost no part. Short duration high frequency impact forces arising from discontinuities in the wheel or rail such as wheel flats and out of round wheels, dipped joints, surface discontinuity, and battered welds (Li et al., 2015) and in stiffness transition zones i.e. bridges and tunnels (Banimahd & Woodward, 2007). Uzzal et al. (2008) developed a dynamic analysis of rail track incorporating effect due to wheel flat. The results shown in Fig. 5(a) clearly indicate the presence of a very high wheel-rail contact forces due to wheel flat; these are generally referred to as P1 and P2 forces (Jenkins et al., 1974).

Fig 5. (a) Impact load due to wheel flat; and (b) displacement responses of ballast, sleeper and rail (modified after Uzzal et al., 2008)

The effect of wheel flat on the displacement of different track components (rail, sleeper and ballast) have been investigated by Uzzal et al. (2008). The results in Fig. 5 (b) clearly show noticeable displacements in the rail, sleeper, and ballast due to a significant wheel flat. Indeed, Uzzal et al. (2008) indicate that the impact forces created by wheel and rail irregularities affect not only the wheel and rail, but they also influence how the underlying track components, including the sleepers and ballast, respond to deflection. The effect of wheel flat on displacement responses of different track components (rail, sleeper and ballast) was investigated in the presence of a single rear wheel flat by Uzzal et al. (2008). The results in Fig. 5 (b) clearly show that there is a noticeable difference in displacement in the rail, sleeper and ballast due to rear wheel flat compared to that of flat-free front wheel. The result also shows that rail, sleeper and ballast are slightly lifted off or displaced, and this is attributed to the moving dynamic load that separates the track components at the interfaces. It is evident from study by Uzzal et al. (2008) that the impact forces created from wheel and rail irregularities not only affect the wheel and rail but also influence the deflection responses of underlying track components including sleeper and ballast.

3. Large-Scale Experimental Testing Ballast usually consists of blasted (quarried) rock aggregates originating from high quality igneous or metamorphic rock quarries. It consists of medium to coarse size aggregates (10 - 60 mm) that usually includes dolomite, rheolite, gneiss, basalt, granite, and quartzite. Ballast should possess angular particles of high specific gravity, high shear strength, high toughness and hardness, high resistance to weathering, and a minimum of hairline cracks (Jeffs & Tew, 1991; Selig & Waters, 1994).

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3.1. Static behaviour of ballast Although conventional triaxial equipment is often used to characterise the stress-strain behaviour of most geomaterials, testing relatively coarse agreegates in conventional geotechnical equipment often leads to misleading results (Indraratna et al., 1998), and therefore, large scale triaxial testing is needed to obtain the realistic strengthdeformation and degradation characteristics of ballast. With this in mind, the Author and co-workers, in collaboration with the Rail industry of NSW, have designed and built a large scale cylindrical triaxial apparatus (Fig. 6a) that can accommodate 300 mm diameter x 600 mm high specimens. The material tested was railway ballast that is commonly used in New South Wales (NSW), Australia. These dark, fine grained and very dense aggregates are made from crushed volcanic basalt, and have sharp angular corners (highly frictional), hence they are considered to be suitable for fresh ballast. The Mohr-Coulomb theory is often used to describe the shear behaviour of ballast. The non-linear strength envelope is curved, as shown in Fig. 6(b), but this non-linearity is more pronounced at smaller confining pressures. The non-linear strength envelope is associated with the dilatant behaviour of rock fragments at low normal stress, and normal stresses < 400 kPa are usually anticipated in a typical ballasted track (Indraratna et al., 2005a). Variations in the apparent friction angle (φp′) which correspond to the peak deviator stress are plotted in Fig. 6(b). In ballast where the confining pressure in tracks is low, the apparent friction angle is expected to be relatively high (φp′ > 50°), but the same material at a relatively high confining pressure indicates a reduced friction angle in the order of 40°.

(a)

(b)

Fig. 6. (a) cylindrical triaxial apparatus designed and built at University of Wollongong; (b) Mohr-Coulomb failure envelopes for ballast material (Indraratna et al., 1998; with permission from ASCE).

Figure 7(a) shows the principal stress ratio (σ′1/σ′3) versus axial strain plots, where the typical characteristics of most granular media indicate that the principal stress ratio decreases with an increasing confining pressure and the post-peak state is characterised by strain-softening behaviour. In Figure 7(b) the axial, radial and volumetric strains at failure [(εa)f, (εr)f, (εv)f] are plotted against confining pressure. It is obvious that at low confining pressures (σ′3 < 60 kPa), the specimen increases in volume (dilation) at failure. Apparently, this dilation is due to the radial expansion of the specimen (bulging) at low confining pressures. However, the initially dilatant behaviour (at low σ′3) changes to a compressive behaviour at higher confining pressures (σ′3 > 60 kPa). Axial strain at failure (εa)f increases non-linearly with an increasing confining pressure. Note that the radial strain at failure, (εr)f remains almost at a constant value. In general, this result is in acceptable agreement with the findings of Indraratna et al. (1993) for an array of rockfill materials.

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The variation of principal stress ratio at failure (σ′1/σ′3)f against confining pressure is plotted in Fig. 8(a), and selected rockfill data from previous studies are also plotted for comparison. Since the current tests were conducted at relatively low stress levels, the ballast exhibited a slightly higher stress ratio at failure compared to the results of rockfill (Charles & Watts, 1980; Marachi et al., 1972; Marsal, 1967; 1973). The variation of principal stress ratio at failure Rf (= σ′1/σ′3)f with effective confining pressure (σ′3), can be represented by the following non-linear model: Rf = c(σ′3)d

(1)

40

Axial, volumetric and radial strains at failure, (%)

where c and d are empirical coefficients. Effective Confining Stress 10 kPa 50 kPa 100 kPa

Stress ratio (σ '1 /σ '3 )

30

200 kPa 300 kPa

20

10

(a) 0 0

5

10

15

Axial strain, ε (%) a

20

25

-10 Dilation

-5

(εr )f

0 (εv )f

5

Compression

10

(b)

(εa )f

15 20 0

100

200

300

400

Effective confining stress, (kPa)

Fig. 7. (a) Variation of principal stress ratio with axial strain (data sourced from Indraratna et al., 1998; with permission from ASCE); (b) Variation of failure strains with confining pressure (data sourced from Indraratna et al., 1998; with permission from ASCE).

The effect of dilatancy on the principal stress ratio at failure is illustrated in Fig. 8(b), where the dilatancy at failure (Df) is defined by [1- (dεv/dεa)f]. Figure 8(b) shows that the relationship between stress ratio and dilatancy at failure is non-linear, and this relationship can be described by the following hyperbolic model:

Df =

1 k j+ Rf

(2)

In the above, Rf is the principal stress ratio at failure and j and k are empirical constants. The test data show a significant variation in shear behaviour at low levels of confining pressure (σ′3 < 60 kPa) compared to those at high confining pressures.

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40

40.0

c = 83 d = -0.47

20

Charles & Watts (1980)

Marachi et al. (1972)

10

Stress ratio at failure, R f = (σ'1 /σ' 3 )f

Rf = c(σ′3)d

30

1

Stress ratio at failure, (σ' /σ' )

3 f

(a) 30.0

(b) Df = 1- (dεv/ dεa)f = 1/(j+k/Rf) j = 0.46 k = 3.32

20.0

10.0

Marsal (1967, 1973)

0 1

10

100

1000

10000

Effective confining pressure, (kPa)

0.0 0.8

1.0

1.2

1.4

1.6

Dilatancy at failure, D

1.8

2.0

f

Fig. 8. (a) Variation of stress ratio at failure with confining pressure (modified after Indraratna et al., 1998; with permission from ASCE); (b) Influence of dilatancy on stress ratio at failure (modified after Indraratna et al., 1998; with permission from ASCE).

At low confining pressures the shear behaviour is influenced by volume expansion (dilation), leading to higher principal stress ratio at failure, while at higher confining pressure dilatancy is suppressed, resulting in a lower stress ratio at failure. This suggests that tracks should be maintained within an appropriate range of confinement to ensure higher stiffness and a lower settlement of ballast. These aspects are further investigated under cyclic loading and are discussed in the following section. 3.2. Assessment and implications of particle breakage Ballast degradation is a complex mechanism that usually begins with the breakage of asperities (sharp corners/projections), followed by complete crushing of weaker particles under further loading. To quantify the extent of degradation, Indraratna et al. (2005a) introduced a new Ballast Breakage Index (BBI) based on the particle size distribution (PSD) curves and BBI is calculated on the basis of changes in the fraction passing through a range of sieves, as shown in Fig. 9(a). An increase in the extent of particle breakage causes the PSD curve to shift towards the smaller particles size region on a conventional PSD plot, while an increase in the area A between the initial and final PSD, results in a greater BBI value. BBI has a lower limit of 0 and an upper limit of 1, so by referring to the linear particle size axis, BBI can be calculated by using the equation BBI = A/A+B, where A is the area defined previously, and B is the potential breakage or area between the arbitrary boundary of maximum breakage and the final particle size distribution. As shown in Fig. 9(b), Indraratna et al. (2005a) proposed that during cyclic loading, the pattern of ballast breakage could be categorised into three distinct zones: (i) the Dilatant Unstable Degradation Zone (DUDZ), (ii) the Optimum Degradation Zone (ODZ), and (iii) the Compressive Stable Degradation Zone (CSDZ), as shown in Fig. 9(b). These zones are defined by the level of effective confining pressure (σ′3) acting on the specimen. In the DUDZ zone (σ′3 < 30 kPa), specimens are characterised by limited particle-to-particle contact areas and undergo considerable degradation as a result of shearing and attrition of angular projections. In the ODZ region (σ′3 = 30 - 75 kPa), the particles are held together with enough lateral confinement to provide increased inter-particle contact areas, which in turn reduces the risk of breakage. At higher σ′3 (CSDZ region: σ′3 > 75 kPa), the particles are forced against each other, which limits any sliding or rolling, and therefore breakage is significantly increased. Due to the

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Fraction Passing

0.8

Ballast Breakage Index, BBI

large lateral confinement being applied to the samples in this region, volumetric compression is enhanced, which is partly due to an increase in particle breakage. 0.06 1.0 A = Shift in PSD qmax = 500 kPa (b) (a) B = Potential breakage 2.36 = Smallest sieve size 63 = Largest sieve size

0.6 Arbitary boundary of maximum breakage

0.4 Initial Gradation

0.2 0.0

Final Gradation

qmax = 230 kPa

0.04

0.02

(I)

0

10

20

30

40

50

60

70

Particle Size (mm)

(II)

(III)

0 0

50

100

150

200

250

Effective Confining Pressure (kPa)

Fig. 9. (a) Ballast breakage index (BBI) calculation method; (b) Effect of confining pressure on particle degradation (Reproduced from Indraratna et al., 2005a, by kind permission of ICE Publishing)

3.3. Assessment of end resistance offered by the shoulder ballast There are three components of lateral resistance, associated with the three interfaces between the ballast and sleeper: at the sleeper base, in the crib (between adjacent sleepers), and in the shoulder (at the sleeper end). The resistance from the ballast shoulder depends on the shoulder width and height (Fig. 10a). The relative contributions of the base, crib, and shoulder resistance are more complex than the equal (33% each) contributions that have been often suggested (ORE 1976). Le Pen et al (2015) investigated the relative the relative merits of increasing the ballast shoulder width and height on the lateral resistance through a series of model tests. The experiment modeled a one-third size sleeper end being pushed gradually into a shoulder formed of scaled ballast. The model ballast shoulder was confined between vertical wooden borders located well beyond the expected extent of the failure mechanism (which varied according to the shoulder size), as indicated in the plan view of the test setup shown in Fig. 10(b). Figs. 10(c) and 10(d) show the measured sleeper end resistance as a function of displacement when the height of the ballast shoulder (y) is raised. As anticipated, it is found that the lateral resistance increases with increase in the height of the ballast shoulder above the level of the sleeper top. These tests indicate that the peak resistance from the shoulder alone occurs at displacements between 20 and 40 mm. Beyond a certain threshold shoulder width (x between 600 and 800 mm for a shoulder height y = 0), the peak resistance and the deflection at which it occurs remain constant. In summary, a given volume of ballast increases the lateral resistance more effectively if it is used to increase the shoulder width rather than the shoulder height, up to the point at which the threshold width is reached. Beyond this, there is no benefit in extending the shoulder, but an increase in resistance can still be obtained by using additional material to raise the shoulder height. Limit equilibrium approach show that the resistance offered by a sleeper is at least one-third less than for isolated sleepers, when the overlapping of the failure mechanisms associated with adjacent sleepers is taken into account.

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13

Fig. 10. (a) Ballast shoulder and dimensions; (b) Plan view of experimental setup; Sleeper end resistance versus displacement plots: (c) Test for x=600 mm, y=0 mm; and (d) Test for x=600 mm, y=125 mm (Le Pen et al., 2014a; with permission from ASCE)

3.4. Influence of particle shapes and angularity The sizes and shapes of aggregates have long been recognised as the two major factors that affect the performance of ballast, but there have only been limited investigations into these effects (Le Pen et al., 2013; Moaveni et al., 2014). Particle size distribution (PSD) analysis has been one of the main methods used to determine the size of aggregates (Standards Australia, 1999). Sieving is a bulk approximation of particle size and cannot quantify the actual shape of particles, whereas an image-based analysis is more objective (Altuhafi et al., 2013). However, many studies are based on two dimensional (2D) or pseudo three dimensional (3D) scanning, which cannot provide comprehensive information about the form of individual particles (Cho et al., 2006; Le Pen et al., 2013; Moaveni et al., 2014). This section reports a recent study on a 3D assessment of particle size and shape where a 3D laser scanner was utilised. To facilitate 3D analysis, a modified measure called ‘ellipsoidness’ E is proposed (Sun et al., 2014b) and is shown in Fig. 11 (a&b).

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Percentage finer

100 80 60 40 20

Particle size (mm)

0 0.32 60

13.2-19 19-26.5 26.5-31.5 31.5-37.5 37.5-40 40-45 45-53 0.34

(a)

0.36

0.38

0.40

0.42

0.44

Average value

50 40 30 20 10 0.370

(b) 0.375

0.380 0.385 Ellipsoidness E

0.390

0.395

Fig. 11. Distribution of the ellipsoidness vs (a) percentage finer and (b) particle size (data sourced from Sun et al., 2014b); (c) Modified definition of Hardin’s breakage index, Br (Einav, 2007a; reprinted with permission from Elsevier)

The distribution of ellipsoidness (Fig. 11a) shows a greater variation between different sieve intervals than roundness, indeed the mean ellipsoidness exhibits a slight decrease as the particle size increases, which implies there should be more angularity in the larger particles (Fig. 11b). Even though there may be small variations in the particle surface irregularity of each sieve interval, they would still have significant influence on the mechanical response of granular soils (O’Sullivan et al., 2002). To effectively assess the amount of fragmentation within the representative volume of randomly compacted crushable granular materials, Hardin (1985) suggested the use of a relative breakage property based on the relative position of the current cumulative distribution from (a) an initial cumulative distribution, and (b) an arbitrary cut-off value of ‘silt’ particle size (of 0.074 mm). However, it is well recognised that the grain size distribution of compacted aggregates should be bounded by an ultimate distribution, attained under extremely large confining pressure and extensive shear strains. Therefore Einav (2007a) proposed to adjust the original definition of the relative breakage by Hardin (1985) to weigh from zero to one the relative proximity of the current grain size cumulative distribution from (a) an initial cumulative distribution, and (b) an ultimate cumulative distribution. This definition is presented in Fig. 11(c). 3.5. Influence of cyclic loading frequency on ballast behaviour The influence of train speed on the permanent deformation and degradation of ballast during cyclic loading was studied using the large scale cylindrical triaxial apparatus (Fig. 6a). These test specimens were isotropically consolidated to confining pressures (σ′3) of 10, 30, and 60 kPa. A range of frequencies varying from 5 Hz to 60 Hz was selected to simulate train speeds from about 40 to 400 km/h, and maximum cyclic deviator stresses (qmax,cyc) of 230 and 370 kPa were used to represent axle loads of 25 and 40 tonnes, respectively. Figure 12(a & b) presents the variation of axial strain (εa) with the number of cycles (N) for different frequencies (f) and amplitudes (qmax,cyc) of cyclic loading. A significant increase in εa with f was observed. For a particular value of f, εa increased rapidly to its maximum value (e.g, 30 % at N = 2 × 104 for f = 40 Hz), whereas at other frequency levels, εa rapidly increased during the initial cycles and then a permanent εa attained a stable value at large N. This

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sudden increase in εa at low values of N could be attributed to particle re-arrangement and corner breakage. Moreover, with an increase in f, higher values of N are needed to stabilise εa at a steady level.

(c) (a)

(b)

(d)

Range I Range II

Range II

Range III

Fig. 12. (a) Variation of axial strain (εa) versus number of cycles (N) for qmax,cyc of 230 kPa; (b) Variation of axial strain (εa) versus number of cycles (N) for qmax,cyc of 370 kPa; (c) Variation of ballast breakage index (BBI) with various frequencies (f); (d) Examples of ballast degradation (Sun et al., 2016; with permission from ASCE)

The results highlighted the existence of four regimes of permanent deformation based on the cyclic loads applied: (a) the zone of elastic shakedown showed no accumulation of plastic strain, (b) the zone of plastic shakedown is characterised by a steady-state response with a small accumulation of plastic strain, (c) a ratcheting zone that shows a constant accumulation of plastic strain, and (d) a plastic collapse zone where plastic strains accumulate rapidly and failure occurs in a relatively short time (Sun et al., 2016). Three different deformation ranges were observed in response to frequency of loading, namely, in Range I: plastic shakedown at f ≤ 20 Hz, in Range II: plastic shakedown and ratcheting at 30 Hz ≤ f ≤ 50 Hz, and in Range III: plastic collapse at f ≥ 60 Hz. A critical frequency can be identified where the risk of track failure is imminent. As shown in Fig. 12(c), the critical frequency range is between 20-40 Hz depending on the level of confinement (σ′3). Figure 12(c) shows that critical frequency decreases as particle breakage increases. The specimen undergoes ratcheting failure (Range II) when there is a significant particle breakage (BBI > 0.10) even at a relatively low value of frequency (i.e., f = 25 Hz). The tested ballast (latite basalt) showed distinct trends towards degradation corresponding to different deformation ranges during cyclic testing, as shown in Fig. 12(d). In Range I (f ≤ 30 Hz), particle degradation was in the form of attrition of asperities and corner breakage as shown in Fig. 12(d), but as the frequency increased (30 < f < 60 Hz) in Range II, a high degree of attrition resulting from increased vibration became predominant. At a very

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high frequency (f ≥ 60 Hz) in Range III, the coordination number decreased significantly, which would induce the particle splitting shown in Fig. 12(d). This implies the need to use geo-inclusions to arrest track deformation and these aspects are described in following sections. 3.6. Optimization of geogrids for given ballast gradations Large scale direct shear tests were carried to establish the role of geogrid aperture size (A) on the interface shear strength, and identify the best geogrid in terms of aperture size (A) for a given ballast gradation. Following the direct shear tests, model track tests were carried out using a novel large scale Process Simulation Prismoidal Triaxial Apparatus (PSPTA) to explore the deformation and degradation response of unreinforced and reinforced ballast under high-frequency cyclic loading (f = 20 Hz). The first phase of testing was carried out using the large scale direct shear box apparatus; it consists of two 300 x 300 mm square boxes, the upper immovable box is 100 mm deep and the lower, moveable box is 90 mm deep (Fig. 13a). Tests were carried out at normal pressures of 26.3, 38.5, 52.5 and 61.0 kPa, at a constant shear rate of 2.75 mm/min (Indraratna et al., 2012a). The second phase of testing was carried out using a novel PSPTA; its plan dimensions are 800 × 600 mm and it can accommodate 650 mm high samples (Fig. 13b). A vertical stress of 460 kPa was applied by a dynamic actuator, and a lateral pressure of 10 kPa was applied to the modified side wall that remained constant during the test. The physical characteristics and technical specifications of geogrids are listed in Table 2.

(a)

(b)

Fig. 13. (a) Test setup of the large scale direct shear box apparatus; (b) Process Simulation Prismoidal Triaxial Apparatus (PSPTA) designed and built at University of Wollongong

Data from the direct shear tests are plotted in the form of variations in interface efficiency factor (α) with A/D50 ratio, where D50 (=35 mm) is the median particle size of ballast (Fig. 14a). The interface efficiency factor (α) is defined as the ratio of the shear strength of the interface to the internal shear strength of the soil (Koerner, 2012). Based on variations of α, the ratio A/D50 is classified into three zones: (i) the feeble interlock zone (FIZ), for an A/D50 ratio ranging from 0 to 0.95, relatively smaller particle interlocks and hence, the values of α are less than unity; (ii) the optimum interlock zone (OIZ), for an A/D50 ratio from 0.95 to 1.2, relatively larger particles interlock, leading to the values of α exceeding unity, and (iii) a diminishing interlock zone (DIZ), for an A/D50 > 1.2, where the values of α are greater than unity but the degree of interlocking decreases rapidly leading to a reduction in α as the A/D50 ratio increases. From these results, the optimum aperture size of geogrid can be treated as 1.15-1.3D50.

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Table 2. Physical characteristics and technical specifications of the geogrids used for the study (data sourced from Indraratna et al., 2012a). Geosynthetic type

Aperture shape

Aperture size (mm)

Rib thickness (mm)

Tult a (kN/m)

Jsec b (2% strain) (kN/m)

MD

CMD

MD

CMD

MD

CMD

MD

CMD

G1*

Square

38

38

2.2

1.3

30

30

525

525

G2*

Triangle

36

36

2.0

2.0

19

19

230

230

G3*

Square

65

65

1.7

1.5

30

30

550

600

G4+

Rectangle

44

42

1.0

1.0

30

30

500

500

G5#

Rectangle

36

24

1.0

1.0

55

30

500

350

G6*

Square

33

33

2.2

1.4

40

40

700

700

G7*

Rectangle

70

110

2.2

1.4

20

14

350

233

Note: * extruded type; + welded type; # knitted type; MD: Machine direction; CMD: Cross Machine direction; (manufacturer supplied values); b Secant modulus (manufacturer supplied values).

a

Ultimate tensile strength

0.6

(a) 0.45

A/D50 G1: 1.08 G2: 0.60 G3: 1.85 G4: 1.21

(b) z : distance above the subballast

0.3

0.15 LSRI=0 (unreinforced ballast) 0

-0.15 0.4

0.8

1.2

1.6

2

A/D50 Fig. 14(a) Interface efficiency factor ( α) versus A/D50, a dimensionless parameter (Indraratna et al., 2012a; reprinted with permission from ASTM International); (b) Variation of average LSRI with A/D50 (Indraratna et al., 2013a; reprinted with permission from Elsevier).

Data from the model track tests carried out using PST apparatus is presented in Fig. 14(b) in the form of variations of average lateral spread reduction index (LSRI) along the ballast depth. The LSRI is defined as the ratio of the difference in lateral displacement (δ) of unreinforced and reinforced ballast to the lateral displacement of unreinforced ballast. For geogrid placed at the subballast-ballast interface, the average LSRI increases from 0.06 to 0.25 as A/D50 increases from 0.6 to 1.20. This may be attributed to a better ballast-geogrid interlock attained as the geogrid aperture size increases for a given ballast size. However, with a further increase in A/D50 from 1.21 to 1.85, the average LSRI decreases from 0.25 to 0.20. For geogrid placed 65 mm above the subballast, the average LSRI follows an almost similar trend with A/D50 except that geogrid G2 exhibits a negative LSRI. 3.7. Effect of fouling (contamination) on ballast behaviour The process of accumulation of fines into the ballast voids is usually referred to as ballast fouling. This means the

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ballast layer should be designed and constructed as free draining material, but as it progressively becomes fouled the drainage capacity of the track diminishes. In the case of poor drainage, problems may occur in the track such as: (i) reduced ballast shear strength, stiffness, and load bearing capacity; (ii) increased track settlement; (iii) softening of the subgrade; (iv) the formation of slurry and clay pumping under cyclic loading; (v) ballast attrition by jetting action and freezing of water; and (vi) sleeper abrasion by water jetting (Tennakoon et al., 2012). Two common types of fouling are prevalent in Australia, namely, coal fouling (surface infiltration) due to coal spilling from wagons and clay pumping due to a softened and slurried subgrade. All these problems inhibit performance and demand additional track maintenance. Several fouling indices are used in practice to measure fouling. Selig and Waters (1994) defined the fouling index as a summation of the percentage of fouled material by weight passing through a 4.75 mm sieve and 0.075 mm sieve. They also proposed a percentage of fouling which is the ratio of the dry weight of fouled material passing through a 9.5 mm sieve to the dry weight of the total fouled ballast sample. However, these mass based indices deviate from accuracy when the fouling material has a different specific gravity, therefore the Percentage Void Contamination (PVC) was introduced as the ratio of the bulk volume of fouling material to the volume of voids of clean ballast (Feldman & Nissen, 2002). However, PVC does not consider the true effects of the void ratio, and the gradation and specific gravity of the fouling material, which is the main factor affecting ballast drainage, and subsequently the Void Contaminant Index (VCI) was proposed to incorporate the effects of the void ratio, the specific gravity and gradation of both fouling material and ballast (Indraratna et al., 2010b):

VCI =

( 1 + e f ) Gsb M f × × × 100 eb Gsf M b

(3)

Hydraulic Conductivity, k (m/s)

where eb is the void ratio of clean ballast, ef is the void ratio of fouling material, Gsb is the specific gravity of the ballast material, Gsf is the specific gravity of the fouling material, Mb is the dry mass of clean ballast, and Mf is the dry mass of the fouling material. For example, a value where VCI = 100% indicates that all the voids in the ballast are occupied by fouling material. More details of VCI, including the field determination procedures, are available elsewhere (Tennakoon et al., 2012). Figure 15(a) shows the unique large scale (500 mm diameter × 100 mm high) permeability test apparatus at the University of Wollongong, Australia. Using this device, the effects of non-plastic fines (coal) and plastic fines (clay) on the hydraulic conductivity of ballast have been assessed and the results are shown in Fig. 15(b). -1

Clay fouled ballast Coal fouled ballast

10

-2

10

-3

10

-4

hydraulic conductivity of coal fines

10

-5

10

-6

10

-7

10

-8

10

Hydraulic Conductivity of kaolin fines

-9

(a)

10 10

(b)

-10

0

20

40

60

80

100

Void Contaminant Index, VCI (%) Fig. 15. (a) Large scale permeability test apparatus, (b) Variation of hydraulic conductivity of clay and coal fouled ballast with Void Contaminant Index (modified after Tennakoon et al., 2012, with permission from ASTM).

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An increase of VCI by 5 % decreased the hydraulic conductivity of coal-fouled ballast by a factor of at least 200; clay fouled ballast remained unaffected, possibly due to the distribution of fouling material within the ballast voids. Coal fouling material usually settles to the bottom of the ballast layer, while clay fouling coats (lubricates) the ballast particles and decreases internal friction subsequently. At about 50% VCI, the hydraulic conductivities of fouled ballast approaches the same value, whereas clay fouled ballast shows a higher reduction in hydraulic conductivity than coal fouled ballast. 3.8. Influence of synthetic energy absorbing mats Impact forces occur due to imperfections in the wheels or rails such as such as wheel flats, rail corrugation, dipped rail, defective rail welds, insulation joints and the rail expansion gap. These irregularities are distinct in nature and can cause train wheels to impose impact forces onto the rail (Bian et al., 2013; Indraratna et al., 2014g). At bridge approaches, road crossings and track transitions where concrete slab tracks merge into ballasted track, or vice versa, these abrupt changes in stiffness lead to high impact forces that accelerate track degradation (Li & Davis, 2005). Therefore, installing rubber mats at these locations substantially attenuates the dynamic forces. Ballast particles undergo progressive deformation and degradation when subjected to large and undue stresses developed by repeated cyclic loading. On the other hand, the wheel and rail irregularities actually impart higher impact loads than the cyclic load exerted by moving wheels (Indraratna et al., 2010a). These two loading conditions were simulated by using the large scale testing apparatus designed and built at the University of Wollongong, Australia. Cyclic stresses were simulated using the process simulation prismoidal triaxial apparatus (PSPTA) shown in earlier Fig. 13(b) and impact loads were simulated using the high capacity drop weight impact test machine shown in Fig. 16(a). Large scale cylindrical triaxial apparatus has been widely used to study the shear strength of different types of soils, but this versatile equipment cannot simulate the actual behaviour of railways, because the intermediate principal stress cannot be controlled independently. The area of the prototype PSPTA replicates a unit cell of standard gauge Australian heavy haul track (Indraratna et al., 2015), and as such it realistically simulates the stress and appropriate boundary conditions. In a real rail track, ballast is not fully restrained laterally, particularly parallel to the sleepers (Indraratna et al., 2010a), so the vertical walls of this prismoidal chamber were built to simulate the free movement of ballast under cyclic loading.

(a)

(b)

Fig. 16. (a) High Capacity Drop Weight Impact Apparatus, (b) Cyclic load shear and volumetric strain responses (data sourced from Navaratnarajah et al., 2015; courtesy Proc. Int. Conf. Geotech. Eng. Colombo).

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A 10 mm thick under sleeper pad made from polyurethane was used for cyclic load testing, and three pieces of 10 mm thick resilient rubber mats were used either at the top and/or at the bottom of the ballast for the impact load test. The cyclic load test corresponded to a 25 tonne axle load with a frequency (f) of 15 Hz. Lateral confinement was applied by hydraulic jacks through movable vertical walls that simulated a low confining stress of 10 kPa. The longitudinal directions of the walls were locked in position to ensure plane strain conditions. In the impact load test, weak and hard subgrade conditions were simulated by 100 mm thick layer of compacted sand and a 50 mm thick steel plate, respectively (Indraratna et al., 2012b; Nimbalkar et al., 2012b). An impact load was applied by dropping a 5.81 kN (592 kg) free fall hammer onto the top of the test specimen.

(b)

(a)

Fig. 17. Impact load strain responses: (a) Shear strain; (b) Volumetric strain (data sourced from Nimbalkar et al., 2012a; with permission from ASCE)

The stress-strain and degradation of the ballast with and without the resilient rubber mats were analysed from the cyclic and impact tests, and the results are shown in this section. BBI was used to analyse the extent of particle breakage during cyclic and impact loading. As shown in Fig. 16(b), the shear and volumetric strains decreased by almost 30 % using under sleeper pad (USP) subjected to cyclic loading conditions. Rapid ballast deformation occurred up to around 10,000 load cycles, but the rate of deformation decreased with increasing load cycles as the ballast mass stabilised in the latter load cycles. The shear and dual volumetric strain from the impact tests are shown in Fig. 17. About 40 to 50% reduction in strain from the impact test occurred when resilient rubber pads were placed at the top and/or bottom of the ballast. These results indicated that the strains were higher when the base was a hard subgrade, such as a rail track on concrete deck of a bridge. The maximum reduction in strain occurred when the resilient pads were placed at the top and bottom of the ballast layer. The BBI of the ballast layer was assessed with depth by it into 3 equal layers 100 mm thick i.e.mm top, middle, and bottom. The results are shown in Tables 3 and 4 for cyclic and impact tests, respectively. The BBI results confirmed that ballast degradation decreases by more than 50 % when resilient pads (USP) are used under cyclic loading conditions. In the impact test, the BBI had the same trend as the cyclic test, in that the resilient rubber pads reduced ballast breakage significantly, as shown in Table 4. The BBI was higher when the subgrade was considerably stiffer. On average, there was up to 30 to 50 % reduction in ballast degradation from the impact test in weak and hard subgrade conditions, respectively. Table 3. Ballast breakage index (BBI) from cyclic load test (data sourced from Indraratna et al., 2014a) Resilient pad location

BBI Top

Centre

Bottom

Without Shock Mat

0.071

0.056

0.053

With USP

0.026

0.023

0.020

21

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000 Table 4. Ballast breakage index (BBI) from impact load test (data sourced from Nimbalkar et al., 2012a) Resilient pad location

BBI for hard subgrade

BBI for weak subgrade

Top

Centre

Bottom

Top

Centre

Bottom

Without resilient pad

0.131

0.099

0.28

0.069

0.048

0.123

Resilient pad at the top of ballast

0.104

0.075

0.257

0.042

0.035

0.09

Resilient pad at the bottom of ballast

0.122

0.085

0.181

0.061

0.041

0.066

Resilient pad at the top and bottom of ballast

0.081

0.067

0.124

0.024

0.017

0.045

3.9. Effects of Subballast and subgrade instability When subballast is considered as a filtration layer, it would prove inadequate because the design criteria are primarily based on the steady seepage loading that is common in embankment dams, therefore, seepage hydraulics through porous media must be influenced by the cyclic mechanical loading generated by passing trains. In this section, the effectiveness of subballast as a granular filter dependent on reducing its porosity and permeability over time is discussed. In current industry practices, subballast consists of typical road base material with particles ranging from 0.075 to 20 mm. To accommodate these coarser particles, a standard constant head permeameter had to be modified in order to carry out the simultaneous action of dynamic train loading and clay pumping. The thickness of the specimen reflects the typical depth of subballast used on actual rail track (Selig & Waters, 1994) while a diameter of 240 mm was chosen to minimise the effect of higher vertical seepage along the side of the cell. Figure 18 shows the key features of the permeameter.

Fig. 18. Schematic cross-section of experimental setup with controlled applied cyclic load and water head (Trani & Indraratna, 2010; with permission from ASCE).

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A cyclic wheel load simulating a typical heavy haul train was replicated in the modified permeameter, by imposing a uniform cyclic stress via a dynamic load actuator over a specified number of cycles, and at a desired frequency. Every specimen was subjected to a minimum stress of 30 kPa and a maximum stress of 70 kPa, which is comparable to the vertical stress measurements induced by heavy haul freight trains. The methodology of this experiment has been discussed elsewhere by (Trani, 2009). The evolution of permanent granular filter deformation has been studied over a large number of load cycles (Indraratna et al., 2007a). Based on the laboratory data, a timedependent total reduction in porosity function as the collective effect of one dimensional compression and the accumulation of fines within the filter can be represented as:

∆nT =

(

ε f 1 − e −t f

(

ks

1 − n0 + ε f 1 − e

)

−t f k s

)

+ Fa

(

1 + ε f 1 − e −t f 1+ ε f

ks

) (1 − e

−t f k s

)

(4)

where n0 is the initial filter porosity, εf = the shakedown plastic strain obtained from a one dimensional cyclic consolidation test on a fully saturated specimen, t = time (sec), f = frequency (Hz), and ks = scaling factor equal to Nmax/10, where Nmax is the maximum number of cycles used in the model. Fa = dimensionless depth dependent accumulation factor which creates an apparent threshold amount of fines that could occupy the voids in between the filter grains at a given depth and is related to the slurry concentration and the loading rate. The proposed function considers the reduction of porosity with time that depends on the compaction energy (natural or imposed stress state) through the parameter εf. The Kozeny-Carman equation (Carman, 1938; Kozeny, 1927) forms the basis of the derivation of the formulation used to predict deterioration in the hydraulic conductivity of the granular filter specimens. A decreased hydraulic conductivity as a result of time based compression and clogging can be represented as: kt = k 0

(1 − n0 )2  d e2.t n03

(n0 − ∆nT )3   2  2  d e.0 (1 − (n0 − ∆nT )) 

(5)

where k0 = initial hydraulic conductivity, de.0 = initial effective diameter of the granular filter, and the effective diameters de.0 and de.t are the geometric-weighted harmonic mean of their respective PSDs. The practical design implications are described below. Figure 19 illustrates the capability of the proposed Eqs. (4) & (5) to predict the extent of filter clogging with respect to its effect on drainage capacity at a particular time. If the porosity (Fig. 19(a)) of a particular layer is known without knowing when it occurred, the point in time when the corresponding permeability of the layer in question can be estimated, as shown in Figs. 19(b,c,d). 3.10. Use of geocells to eliminate the rick of subballast and subgrade instability effects The PSPTA chamber was used to investigate the performance of reinforced and unreinforced subballast (crushed basalt) during cyclic loading. In order to simulate field conditions, vertical walls were allowed to move laterally parallel to the sleepers , but were restricted from moving in the direction of train passage. In the field, only a small confining pressure exerted by the ballast shoulder and sleepers (5 kPa ≤ σ′3 ≤ 30 kPa), is usually available (Indraratna et al., 2010a; Indraratna & Nimbalkar, 2011; Nimbalkar & Indraratna, 2015; Trani & Indraratna, 2012). Accordingly, a low confining pressure was applied to the specimen. A mean stress was applied to the specimen (σmean =102 kPa) through a servo-hydraulic actuator at a rate of 1 mm/min, which was transmitted to the subballast through a 100 mm diameter steel ram and a top solid platen (800 mm long, 600 mm wide and 12 mm thick). Considering a 30 tonne axle load, a cyclic loading with a maximum of σmax,cyc = 166 kPa and minimum of σmin,cyc = 41 kPa were applied to the specimen in a stress controlled fashion. The experiments were carried out up to the total number of cycles of N = 500,000 cycles, at different frequencies of f = 10, 20 and 30 Hz to simulate train speeds (V) of about 73, 145, and 218 km/h.

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Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

10

20

30

40

50

0.01

0.10

36 Experimental data n 0 -- Eq. (13) n0 Eq.(4) (13)

Porosity [%]

34 Layer 4

1 = bottom layer

   

32

de is the geometric weighted harmonic mean of the new PSD from combined m ass of filter and accumulated fines




Layer 2

28

30

1.E-03

Experimental data Eq. (5) (18)

1.E-04

32

28

(4)

1.E-03 Hydraulic conductivity [m/s]

34

5 = top layer

30

1.E-04

 1.E-05

1.E-05

  

1.E-06

5 = top layer

1 = bottom layer

1.E-06




1.E-07 0

(c)

1.00 36

Porosity [%]

0

(b)

de [mm]

Time [hr]

10

20 30 Time [hr]

40

50

0.01

0.10 de [mm]

Hydraulic conductivity [m/s]

(a)

1.E-07 1.00

(d)

Fig. 19. Porosity based family of curves: circled numbers represent the filter layers; n0 = 34.96%, k0 = 3.66x10-4 m/s, εf = 0.009, V0 = 1.44x10-3 m3, ρa = 2,700 kg/m3, Nmax = 763,500 cycles, f = 5 Hz (reproduced from Trani and Indraratna, 2012; with permission from AGS).

Figure 20(a) shows the variation of axial deformation (SV) at different confining pressures (σ′3) at a given number of cycles (N) = 500,000. At very low confinining pressure (σ′3 ≤ 15 kPa), unreinforced subballast experiences substantial vertical deformation (about SV = 180 mm), however the experimental results indicated that the magnitude of SV decreased when increasing σ′3. Nevertheless, the use of geocell helped to improve the performance of subballast under cyclic loading. The behaviour was more profound at lower confining pressure (σ′3 ≤ 15 kPa), because during cyclic loading, the geocell assembly confined the encapsulated subballast. In effect, the geocell arrested the subballast from spreading laterally, acting as a stiff mattress to transfer the load over a wider area; as a consequence, it could reduce the total and differential settlement. Fig. 20(a) also shows that the magnitude of vertical deformation increased significantly as the frequency increased (f ≥ 20 Hz), but the geocell mattress successfully reduced the vertical deformation of subballast, particullarly at higher frequencies by about 20-25 %. There was a marginal difference at higher confining pressure (σ′3 = 30 kPa), which highlights the effectiveness of geocell at lower confining pressures and higher frequencies. An analytical model could be developed to understand the performance of cellular confinement and its impact on the infill. The hoop stress of geocells provided additional confining pressure, which helped to control the subballast from spreading laterally, hence the settlement. The magnitude of additional confinement can be predicted by (Indraratna et al., 2015):

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Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

∆σ 3' = ∫

N = Nlim

N =1

[

]

 a ' b '    1 + sin ψ m  2M m (1 −ν g )k + ν g  ν gσ cyc dN ⋅ ⋅ − + ε 1P,1  +   ×  D (1 + ν g )(1 − 2ν g )  dM R  N N    1 − sin ψ m 

(6)

where Mm is the mobilised geocell modulus at a different number of cycles, aˊ and bˊ are the empirical coefficients representing the stable and unstable zone, D is the diameter of an equivalent circular area of the geocell pocket, νg is the Poisson’s ratio of geocell, k is the ratio (k = εcp/ε3p = 0.45), ψm is the mobilized dilation angle, Nlim is the number of cycles required to attain the stable zone. Figure 20(b) shows the value of additional confining pressure (∆σ′3) predicted by using Eq. [6]. The value of ∆σ′3 was at its maximum at very low confining pressure (σ′3 ≤ 15 kPa) and particularly at a higher frequency (f ≥ 20 Hz). As shown here, the degree of ∆σ′3 decreased markedly as the confining pressure (σ′3 ≥ 20 kPa) increased, because, no significant tensile strength had been mobilised in the geocell mattress. Similar behaviour occurred at a confining pressure of σ′3 = 30 kPa. It can be concluded that this confining pressure was enough to minimise any excessive lateral spreading of subballast (Indraratna et al., 2015).

(kPa)

200

3

160

Additional confinement,

N=500,000 cycles

120

80

40

(a)

(b)

0 0

5

10

15

Confining pressure,

20

25

'3 (kPa)

Fig. 20. (a) Effect of confining pressure on vertical deformation of unreinforced and reinforced sub-ballast; (b) Effect of confining pressure and frequency on developed additional confining pressure in reinforced subballast (data sourced from Indraratna et al., 2015; with permission from ASCE)

Leshchinsky and Ling (2013a) assessed the effectiveness of geocell confinement through a series of large scale model tests and finite element procedures. The geocell was placed in two different configurations: centrally located in the embankment, and two layers in the embankment as shown in Fig. 21 (a &b). All of these configurations were loaded under both monotonic and cyclic conditions on separate occasions to demonstrate the behavior of the embankment in both unconfined and confined conditions (Fig. 21(c)). The cyclic tests consisted of 50,000 cycles of loading at a frequency of 5 Hz, with sinusoidal loading cycles representative of vibrations that might occur from wheel loads. The loading amplitude for the unreinforced test was between 35 and 175 kPa, which was 20% of the maximum load attained from the monotonic test. The loading amplitude for both of the reinforced configurations was between 70 and 350 kPa, representative of realistic load. The geocell in both configurations encountered only cosmetic damage from the cyclic loading (Fig. 21(d)). A commercially available FE software was used in the analysis. The model tests were simulated using material properties attained from laboratory tests and the geometry and boundary conditions, and the stress and deformation behavior was compared. As shwon in Fig. 21(a), use of geocell confinement reduced the amount vertical deformation that occurred in the embankment under repeated loading. It was shown that the comparison of vertical displacement to vertical load matched reasonably well at least

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

25

for the unreinforced configuration. i.e. Test 4 (Fig. 22(a)). Generally, the cyclic hardening encountered by both of the reinforced models in the later loading stages was captured (as implied by the flattening of the curves in the later cycles), whereas the unreinforced configuration (Test 4) still underwent some cyclic deformation in both the experiment and the simulation. The actual simulated amounts of lateral displacement from the FE analysis did not match entirely, although they were reasonable (Fig. 22(b)). Thus, the experimental results and simulations demonstrate the benefits of using the geocell confinement in the gravel.

Fig 21 (a) Cross-section of reinforcement configurations; (b) Schematic of testing apparatus; and (c) Cosmetic damage to geocell consisting of only minor bending and scraping (Leshchinsky & Ling, 2013a; with permission from ASCE)

Fig 22 Cyclic loading curves: (a) vertical settlement; and (b) lateral deformation at crest (Leshchinsky & Ling, 2013a; with permission from ASCE)

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3.11. Use of geosynthetic vertical drains for soft subgrade drainage Low lying areas containing thicker layers of soft clays can sustain high excess pore water pressures during repeated train loading. In such soils with low permeability, any increase in excess pore pressures has an adverse effect on the effective load bearing capacity of track foundations, because under certain circumstances, clay pumping beneath rail tracks may pump the soil upwards and foul the ballast layer and promote undrained shear failure (Chang, 1982; Indraratna et al., 1992). Prefabricated vertical drains (PVDs) can be used to dissipate excess pore pressures by radial consolidation before they can develop to critical levels. These PVDs continue to dissipate excess pore water pressures even after the passage of trains (i.e. after the cyclic load ceases) (Indraratna et al., 2009a). Tests were carried out using the large scale cylindrical triaxial equipment that was modified to measure the excess pore water pressure at various locations inside the specimen (Fig. 23a). The soil specimens were prepared under anisotropic consolidation with an effective vertical stress of 40 kPa (K0 = 0.60 representing the in-situ stress), where Ko is the ratio of the effective horizontal to the effective vertical stress. A cyclic stress ratio (CSR) of 0.65 was chosen, where CSR is defined as the ratio of the cyclic deviator stress qcyc to the static deviator stress at failure qf (ASTM, 2002). The term Critical Cyclic Stress Ratio (CCSR) is defined as the level of cyclic deviator stress above which a sample would experience failure after a certain number of loading cycles (Ansal & Erken, 1989). A sinusoidal cyclic load was applied to the specimen under stress-controlled conditions at a frequency of 5 Hz (simulating a 100 km/hr train speed) with a maximum cyclic amplitude of 25 kPa. PVD

30 cm

T3

T2

T1

60 20 T4

T5

4 20

T6 8

1.5

Excess pore pressure ratio, u *

0.6

T6

0.4

T1 T5 T2 T4

0.2

T3 With PVD 0 0

(a)

1000

2000 N (Cycles)

3000

4000

(b)

Fig. 23. (a) Locations of the pore pressure transducers at different positions from the PVD inside the soil sample; and (b) Excess pore pressures generated inside the soil sample at different locations from the PVD with the application of cyclic loads (Indraratna et al., 2009a; with permission from ASCE)

The excess pore water pressure ratio (u*) is defined as excess pore water pressure normalised to an initial effective pressure (Miller et al., 2000; Zhou & Gong, 2001). Fig. 23b shows the excess pore pressure ratio (u*) versus the number of loading cycles (N) under a partially drained condition with PVD. The six transducers highlights effect of length of the drainage path on the development of excess water pore pressure. As loads were applied repeatedly, the PVD reduced any build up of excess pore water pressure and also accelerated dissipation during the rest period. A soft formation beneath a rail track stabilised by radial drainage (PVD) can be subjected to

27

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

higher levels of cyclic stress than the critical cyclic stress ratio, without causing undrained failure. 4. Theoretical concepts, granular mechanics and constitutive modeling Ballast accumulates plastic deformation under cyclic loading, but despite this being well known, very limited efforts have been made to develop realistic constitutive stress-strain relationships, particularly modelling the deformation and degradation of ballast. In the case of rail ballast, the progressive changes in the particle geometry due to internal attrition, grinding, splitting and crushing (i.e. degradation), further complicates the stress-strain relationships. Thus there is a lack of realistic constitutive modelling, which includes the effect of particle breakage during shearing. In this section, constitutive modeling of ballast is described. 4.1. Effect of ballast breakage The first continuum mechanics-based constitutive model for rail ballast to capture breakage was developed by Salim and Indraratna (2004), using the critical state concept and the theory of plasticity with a kinematic-type yield locus. The theoretical formulation relates the deviator stress ratio at any stage of shearing with the basic friction angle, dilatancy, and energy consumption due to particle breakage. The increments of plastic distortional (δεsp) and volumetric (δεvp) strains are given by Salim and Indraratna (2004): po ( i )   p  * 2ακ   ( 9 + 3M − 2η M )ηδη   1 − p p  cs   cs ( i )  δε sp =  2p  9M 2 (1 + ei )  o − 1 ( M − η * )  p 

(7)

βδ Bg  9 ( M −η ) δε vp   6 + 4M  9 − 3M = + δε sp 9 + 3M − 2η * M pδε sp  9 + 3M − 2η * M   6 + M 

(8)

In the above, parameter p is the effective mean stress and pcs is the value of p on the critical state line at the current void ratio. The subscript i indicates the initial value at the start of shearing. The parameter η is the stress ratio (=q/p), q is the deviator stress, η* = η (p/pcs), M is the critical state stress ratio, ei is the initial void ratio, κ is the negative slope of compression curve (e-lnp). α and β are dimensionless constants. χ and µ are the material constants defining the rate of ballast breakage. -8.0 Test data for crushed basalt (Indraratna and Salim 2001)

σ3 = 300 kPa

1200

200 kPa

800

100 kPa 50 kPa

400

(a) 0

εv (%)

Model prediction

1600

Test data for crushed basalt (Indraratna and Salim 2001)

-6.0

Volumetric strain,

Distortional stress, q (kPa)

2000

σ3 = 50 kPa

Model prediction

-4.0

Dilation

-2.0

100 kPa

0.0 2.0

200 kPa 4.0

300 kPa

Contraction

6.0

(b)

8.0 0.0

5.0

10.0

15.0

Distrortional strain,

20.0

εs (%)

25.0

0.0

5.0

10.0

15.0

20.0

25.0

Distrortional strain, εs (%)

Fig. 24. Model predictions for (a) stress-strain and (b) volume change behaviour (Salim and Indraratna, 2004; © 2008 Canadian Science Publishing or its licensors. Reproduced with permission)

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Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

This model was verified using large scale triaxial laboratory results (Fig. 24). The constitutive model contained eleven parameters that could be evaluated using the results of drained triaxial tests and an assessment of particle breakage. Since then, constitutive models for ballast have been attempted by various researchers (Yang et al., 2008; Zhai et al., 2004). 4.2. Ballast breakage and implications on critical state behaviour An elastoplastic state dependent constitutive model under triaxial monotonic loading was formulated to capture the dependency of critical state behaviour on particle breakage (Ahmed et al., 2015; Indraratna et al., 2014h). Particle breakage during triaxial shearing was modelled by a nonlinear function which linked the Ballast Breakage Index (BBI) described in detail by Lackenby et al. (2007), with the accumulated plastic deviatoric strain and initial effective mean stress. Hence, it is now possible to predict the evolution of BBI at each stage of loading, such that BBI is captured in the CSL in both q-p' and v-lnp' planes. Figure 25(a) shows the critical states for ballast on the q-p' plot, and the corresponding BBI at these critical state points. The CSL in the q-p' plane is non-linear. As expected, there was more breakage as p' increased, and the drop in q was more pronounced as p' increased. The critical state stress ratio Mc = (q/p')c is not a constant for ballast and is plotted as a function of the BBI in Fig. 25(b). As particle breakage increases, Mc decreases and can be represented by: (9)

M c = M c 0 − [1 − exp(− α ⋅ BBI )]

where α is the model parameter and Mc0 = critical state stress ratio for BBI = 0. The specific volume and effective mean stress obtained by the tests are plotted in Fig. 26(a). The results indicate that the CSL would change location in the v-lnp' plane with an increase of BBI. The CSL in the v-lnp' plane becomes a critical state surface when the extra dimension of BBI is added (Fig. 26b). The CSL shown as a dashed line in Fig. 26(b) corresponds to the current value of BBI, and it is assumed to have a constant slope. As the effective mean stress increases, the BBI increases. The critical state surface cannot exist for stress levels above a certain limit which depends on the current value of BBI. Thus, the critical state surface in the v-lnp'-BBI space can be represented by:

vc = Γref − a ⋅ exp (b ⋅ BBI ) − λ ln p'

(10)

where гref, a and b are material constants controlling the rate at which CSL evolves with particle breakage. A unified function is thus proposed to represent particle breakage during shearing under triaxial conditions: BBI =

θb [1 − exp(−ν bε sp )] ωb − ln pi '

(11)

where θb, νb and ωb are material constants characterising the breakage of aggregates, and pi' is the initial effective mean stress that is used to consider the effect of confining pressure under triaxial conditions. Accounting for the critical state constitutive framework, the following state-dependent dilatancy relationship for ballast is proposed:

{

(

) }

D = δε vp δε sp = Ad  M c0 − (1 − e−α ⋅BBI ) ⋅ exp kd υ − Γref + a ⋅ exp ( b ⋅ BBI ) + λ ln p ' − η

(12)

where D is dilatancy linked to the non-associated flow rule, δεvp is the plastic volumetric strain increment, δεsp is the increment of plastic distortional strain, and kd is the model parameter. All parameters can be evaluated by triaxial data.

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

(a)

29

(b)

Fig. 25. Monotonic triaxial tests results on ballast: (a) critical state points on q-p’ plane; (b) evolution of Mc with BBI (Indraratna et al., 2014h; © 2008 Canadian Science Publishing or its licensors. Reproduced with permission).

(a)

(b)

Fig. 26. Monotonic triaxial tests results on ballast: (a) critical state points on q-p’ plane; (b) critical state surface in compression-breakage space (Indraratna et al., 2014h; © 2008 Canadian Science Publishing or its licensors. Reproduced with permission).

Figure 27 shows the predicted stress-strain and volume change employing the current model, compared to laboratory observations. The model parameters used were: G = 8 MPa, ν = 0.3; θb = 0.33, νb = 11.5, ωb = 6.4, Mc0 = 2.6, гref = 2.41, λ = 0.105, α = 4.287, a = 0.2, b = 1.87, kp = 1.05, Bm = 0.017, Ad = 0.8 and kd = 1.6. Here the elastic parameters are assumed to be constant with breakage, and the model predictions without any breakage are also shown for comparison. Figure 27(a) indicates that particle breakage reduces the shear strength of ballast, but as the confining pressure increases, this reduction in strength is more pronounced due to higher particle breakage (Chen et al., 2015b). Figure 27(b) shows there is only a small difference in volumetric strain between the model prediction with particle breakage and the one without particle breakage for a small confining pressure (σ3' = 60 kPa). The

30

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

particle breakage causes the specimens to be more compressive, and as the confining pressure increases, this effect is more pronounced (Fig. 27(b)).

(a)

(b)

Fig. 27. Model predictions compared with experimental results of drained triaxial shearing: (a) stress-strain response and (b) volume change behaviour (data sourced from Indraratna et al., 2014h; © 2008 Canadian Science Publishing or its licensors. Reproduced with permission).

4.3. Effect of clay fouling In this section, a bounding surface plasticity model is proposed to simulate the nonlinear stress-strain behaviour of ballast with varying degrees of fouling. The bounding surface framework introduced by (Dafalias & Herrmann, 1982) is extended to clay-fouled ballast. The model adopting a non-associated flow rule within a Critical State (CS) framework was validated with a series of monotonically loaded drained triaxial tests. The model describes strainsoftening and stress-dilatancy with 12 parameters determined from the results of large scale laboratory testing as described by Indraratna et al. (2013d). The increments of plastic strain (δεvp, δεsp) are given by:

1 h

(13)

1 h

(14)

δ εvp = npδ p + nqδ q mp δ εsp = npδ p + nqδ q mq

where mp, mq are the plastic flow directional unit vectors (i.e. unit vectors normal to the plastic potential) along the p' and q axes, the parameter h is the plastic modulus, and np, and nq are the loading direction unit vectors (i.e. unit vector normal to the loading or bounding surface). Here, the non-associated flow rule is modified as:

δ εvp = Mf −η δ εsp

(15)

where η is the stress ratio and Mf is equal to (1+kdξ)M. kd is a material parameter which varies with the confining pressure and the Void Contaminant Index (VCI), and ξ is the state parameter. The numerical model predictions using Eqs. (14)-(15) are compared to the laboratory results for clay-fouled ballast with a VCI = 0%, 50% and 80% at various confining pressures. A series of triaxial tests were carried out for VCI = 0%, 50%, and 80% and the results

Buddhima Indraratna / Procedia Engineering 00 (2016) 000–000

31

are presented in Fig. 28. It is evident that the constitutive model correctly simulated the strain softening and stressdilatancy relations of clay-fouled ballast at different ranges of fouling (0 ≤ VCI ≤ 80%) at a relatively low confining pressure of 10 kPa. The volumetric strain of fouled ballast, as predicted by this model is also in good agreement with the experimental data. The model captures the increased deviator stress and overall volumetric decrease (reduced dilation) with an increase in confining pressure to 30 kPa and 60 kPa (Fig. 28).

(a)

(b)

Fig. 28. Model validation for (a) deviator stress and (b) volumetric strain response of clay-fouled ballast at confining pressure (σ′3) of 10 kPa. (Tennakoon et al., 2015; reprinted with permission from Elsevier)

As described by Indraratna et al. (2013d), the overall volumetric response of clay-fouled ballast is initially compressive but depending on the VCI, subsequent dilation occurs, unlike clean ballast. Furthermore, an increased level of fouling (VCI ≥ 25%) leads to a decrease in the rate and magnitude of dilation at high axial strain. Therefore, it is evident that this model can predict the reduced maximum compression and suppressed dilation at large strains at increasing levels of fouling. 4.4. Effect of coal fouling The Critical State Soil Mechanics (CSSM) framework has been used to characterise the behaviour of coal-fouled ballast. Earlier studies suggested that the void ratio may not serve as a consistent basis for comparison purposes because fine particles may become trapped in the voids and remain inactive in the force chain of the solid skeleton (Mitchell & Soga, 2005; Ni et al., 2004; Thevanayagam & Mohan, 2000). An alternative variable such as the intergranular specific volume has been proposed to unify the Critical State Line (CSL) of coal-fouled ballast. The intergranular specific volume υg (= 1 + eg) of coal-fouled ballast is then used to unify the intergranular specific volume-log confinement lines for varying levels of coal fouling. The increments of plastic distortional (δεsp) and volumetric (δεvp) strains are given by (Indraratna et al., 2014c):

p'   p'   2ακ g  '  1 − 'o (i ) ηδη    pcs   pcs (i )  δε sp =  2p '   B C M 2υ gi  'o − 1 ( M − η *) + '  χ + µ ( M − η *)  + ' ξ + θ ( M − η *)   p p   p 



 B C  χ + µ ( M −η *) +  '  ξ + θ ( M − η *)  δε sp '  p  p  

δε vp = ( M − η ) +  

(16)

(17)

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Equations (16) and (17) show the evolution of ballast and coal particle breakages during monotonic shearing captured through separate terms, but both linked to the initial intergranular specific volume. These equations also represent the plastic strains that are affected by change in the fines and the overall change in volume of the sample. Figure 29 (a&b) shows the stress-strain and volume change predictions for coal-fouled ballast, compared to the experimental data. Since the confining pressures used in the laboratory experiments were small (σ′3 ≤ 240 kPa) compared to the compressive strength of the parent rock in the vicinity of 130 MPa (Indraratna et al., 2009b), a fraction of the imparted energy would be consumed in ballast breakage. Another fraction of energy was consumed in the breakage of coal. The effect of particle breakage appears to be small due to the ballast being subjected to relatively low stresses (Fig. 29). For the observed range of particle breakage, the present model can provide an acceptable match with the experimental data for coal-fouled ballast. The effects of contaminated ballast have also been discussed by Huang and Tutumluer (2011) and are elaborated in the following section.

Fig. 29. Model validation for (a) deviator stress and (b) volumetric strain response of clay-fouled ballast at confining pressure (σ′3) of 30 kPa, 120 kPa, 240 kPa (Indraratna et al., 2014c; reprinted with permission from Elsevier)

5. Numerical simulation of discrete track elements using DEM

5.1. Effect of ballast breakage on track stability The discrete element method (DEM) developed by (Cundall & Strack, 1979) has been widely used to study shear behaviour of fresh and fouled ballast (Huang & Tutumluer, 2011; Lobo-Guerrero & Vallejo, 2006). This pioneering work on DEM application to rail ballast was initiated by McDowell and Bolton (1998) at Cambridge University, and then by McDowell and co-workers at Nottingham University (Lu & McDowell, 2008; Lu & McDowell, 2010; McDowell et al., 2006). In DEM, the force-displacement law comes from the contact forces that are applied on two particles in contact with the relative deformation between them. This irregularly shaped ballast can be modelled by connecting and overlapping many balls of different sizes and positions together using a clump approach (Itasca, 2008). In this analysis, the cyclic shearing behaviour of railway ballast under a range of confining pressures is modelled. The ballast is simulated using a particle consisting of a ten-ball triangular clump with eight asperities (Fig. 30a). The triaxial sample containing 618 particles (each of the ten balls in the clump is 16.33 mm in diameter and each asperity is 6 mm in diameter) is shown in Fig. 30b. For the cyclic triaxial test simulations, a servo-control was applied to the top and bottom walls to maintain the required loading. Following Lackenby et al. (2007), samples

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under confining pressures ranging from 10 kPa to 240 kPa were simulated and sinusoidal load pulses were applied to the samples with a minimum deviatoric stress of 45 kPa being set for each test. Three different magnitudes of maximum deviatoric stress were used: 230 kPa, 500 kPa, and 750 kPa. The frequency of the cyclic load was 4 Hz. Details of the modelling procedure can be found in Lu and McDowell (2008).

Fig. 30. (a) ten-ball triangular clump with eight small balls (asperities) bonded as a ballast particle model and (b) assembly of ten-ball triangular clumps with eight small balls (asperities) bonded in the triaxial cell (Reproduced from Lu & McDowell, 2010, by kind permission of ICE Publishing)

Figure 31 presents the number of asperities broken off and the number of broken parallel bonds between clumps after 100 cycles for the simulations. Indraratna et al. (2005a) and Lackenby et al. (2007) indicated that ballast degradation behaviour under cyclic loading can be categorised into three distinct zones: the DUDZ, the ODZ, and the CSDZ, as described earlier in Section 3.2. These three distinct zones are included in the simulation, as shown in Fig. 31(a) by Lu and McDowell (2010). Regarding the parallel bonds between clumps (which simulate small scale asperities), Fig. 31(b) shows that a large number of parallel bonds between clumps broke under a low confining pressure (DUDZ) and the number of broken parallel bonds decreased as the maximum deviator stress decreased and the confining pressure increased. Figures 31(a) and 31(b) indicate that the fracture of small angular projections (modelled by bonding asperities) and the grinding off of very small asperities (modelled by a parallel bond between clumps) dominate behaviour in the DUDZ. The fracture of small angular projections and grinding off of small-scale asperities in the DUDZ is accompanied by significant particle rolling and sliding. Fig. 31(b) shows that unlike the other zones, fewer parallel bonds between clumps break off. However, more asperities break off in the CSDZ than in the ODZ as shown in Fig. 31(a). In general, Figs 31(a) and 31(b) suggest that the cyclic degradation behaviour is dominated by asperity fracture (i.e. the fracture of small angular projections), simulated here by bonding small balls to the clumps.

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Fig. 31. (a) number of broken asperities; and (b) number of broken parallel bonds between clumps against confining pressure (Reproduced from Lu & McDowell, 2010, by kind permission of ICE Publishing)

Fig 32 (a) Deformed triaxial sample with three geogrid layers (b) Contact force distribution and geogrid after partial horizontal and vertical unloading (Reproduced from McDowell et al., 2006, by kind permission of ICE Publishing)

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McDowell et al. (2006) reported DEM simulation of cyclic triaxial loading response of geogrids. Laboratory tests revealed that considerably higher deviatoric stresses are necessary to produce the same deviatoric strains as for samples without geogrids. This effect cannot be explained by an apparent confining pressure caused by the stiffness of the geogrid alone; it is the aggregate-geogrid interlock that is responsible. To investigate this effect, the ballast model containing three layers of geogrid at one-quarter depth, mid-depth and three-quarters depth is numerically simulated using DEM. To quantify the interlocking effect a force ratio β was defined as the ratio of the average contact force inside a cuboid whose boundaries were around the four intact closed apertures at mid-depth and 1 cm above and below mid-depth (see Fig. 32(a)) to the average force in the same 2 cm height interval but across the entire cross-section enclosing the entire layer of geogrid. The confining pressure was approximately 10 kPa and nine cycles of deviatoric stress were applied: first, axial stress was cycled between 10 kPa and 20 kPa for 3 cycles, then between 10 kPa and 30 kPa for 3 cycles, and finally between 10 kPa and 40 kPa for 3 cycles. On loading, maxima in the force ratio β occur at the geogrids, but the minima that occur on unloading are much greater, with local maxima in between the grids. This again can be explained in terms of particle–geogrid interlock: in the immediate vicinity of the geogrid, interlocking occurs across the entire cross-section, which results in relatively low β values, in the order of 1.2. However, in between the geogrid layers the interlocking effect is restricted to the central part of the crosssection, and contact forces considerably reduce near to the model boundaries, leading to high β values. This bridging effect between geogrid layers is evident in Fig. 32(b). The particle contact forces clearly reduce near the boundaries in between the geogrid layers. The influence of the geogrid appears to extend to approximately 10 cm either side of the grid. It should be noted that the axial and radial displacements using only one geogrid at mid-depth were found to be approximately 50% higher than those using the three layers of geogrid, demonstrating that multiple layers of geogrid may be useful in certain applications. 5.2. Effect of coal fouling on track stability In this DEM analysis, nine different ballast particles were generated, as shown in Fig. 33a. A geogrid having 40 mm × 40 mm aperture size, similar to that conducted in the laboratory, was modelled in DEM by bonding small spherical balls together (i.e. spheres with a 2 mm radius at the rib and a 4 mm radius at the junction), as shown in Fig. 33b. These balls were linked together by parallel bonds that represent the tensile strength of the geogrid. The large scale shear box (300 mm long × 300 mm wide × 200 mm high) was modelled in DEM with rigid walls to simulate fresh and fouled ballast (VCI = 40%), as shown in Fig. 33c-d. Ballast fouling is a result of fine particles that accumulate and clog the pores between the aggregates. In this study, fouled ballast was simulated in DEM by adding a predetermined amount of fine particles into the voids to create varying levels of VCI. Fouled ballast (VCI = 40%) was simulated by adding up to 150,000 of 1.0 mm balls into the pore spaces of fresh ballast (Fig. 33d). A linear contact model was applied for the DEM model in the current analysis. A series of direct shear tests were conducted in the laboratory, and DEM simulations were carried out to investigate the shear stress-strain behaviour of fresh and fouled ballast reinforced by geogrid. While details of the tests and laboratory results were presented and discussed elsewhere by (Indraratna et al., 2014b), some of these results are reproduced here to compare and validate the proposed DEM model.

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Fig. 33. (a) ballast particles; (b) simulated geogrid; (c) direct shear test for fresh ballast; (d) direct shear test for 40%VCI-fouled ballast (modified after Indraratna et al., 2014b; with permission from ASCE)

Figure 34 presents comparisons of the shear stress-displacement and volumetric change of the fresh and fouled ballast measured in the laboratory, and those obtained from the DEM simulations. The predicted results at any particular normal stress agree reasonably well with the experimental results, showing that the proposed DEM model can capture the shear stress-displacement response of fresh and fouled ballast. As expected, fresh ballast experienced the highest shear stress and lowest volumetric dilation than the fouled ballast. Also, the DEM simulation shows a somewhat higher dilation than the laboratory results for σn = 27 kPa in a shear displacement range of 10-25 mm (i.e. 4-8% shear strain). This difference was primarily due to particle breakage that was not captured accurately in the current DEM analysis. The laboratory results also show a sudden drop in shear stress at a displacement of 10-25 mm, before picking up the load again, which further supports the initiation of particle degradation at this level of shear strain.

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160

Fresh ballast

40% VCI fouled ballast

Shear stress (kPa)

140

σn=75kPa

120

σn=75kPa

100

σn=51kPa

80

σn=51kPa

60 40

σn=27kPa

20

σn=27kPa (b)

(a)

Vertical displacement (mm)

0

σn(kPa)

σn(kPa)

Lab. DEM

27 51 75

10 8

Lab. DEM

σn=27kPa

27 51 75

σn=27kPa σn=51kPa

6

σn=51kPa

σn=75kPa

4

σn=75kPa

2

Dilation

Dilation

Compression

Compression

0

0

5

10

15

20

25

30

35

Horizontal displacement (mm)

40

0

5

10

15

20

25

30

35

40

Horizontal displacement (mm)

Fig. 34. Comparisons of shear stress and vertical displacement versus shear displacement between experimental data and DEM simulation (modified after Ngo et al., 2014; reprinted with permission from Elsevier)

The ‘in-situ’ track conditions including clean, partially fouled, and fouled in different ballast layer arrangements can also be modeled in DEM. The simulations of shoulder fouling and track center fouling were carried out under repeat loading. Only the half width of the track was modeled due to symmetry. A tie was placed on top of a 0.5 m thick section of ballast. The compaction was simulated by creating a DEM block element that covered the top of the ballast and pushed downwards with a force of 100 kN until there was no further particle movement. The half ballast section was then divided into four parts (0, 1, 2, and 3) called the shoulder bottom, center bottom, shoulder top, and center top, respectively. These parts were assigned with different surface friction angles to represent different fouling scenarios in DEM. Fig. 35 is a snapshot of the half-track DEM model.

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Fig. 35. Half-track DEM model with different parts fouled by coal dust (Huang & Tutumluer, 2011; reprinted with permission from Elsevier)

Fig. 36 shows the DEM predictions of ballast settlement after 120 cycles under different fouling scenarios. After the first hundred cycles of traffic, clean ballast indicated the smallest amount of settlement, which means that fouling increases track settlement potential. In other words, a fouled track portion will accumulate more settlement than clean track within a relatively short amount of time, which may lead to scenario often referred to as a ‘‘hanging tie’’. This phenomenon is illustrated elsewhere by Huang and Tutumluer (2011). Without any lateral resistance from the interface between the tie and ballast, the track is prone to buckling. Of all the fouling scenarios, shoulder fouling has a more detrimental effect on track settlement; and in the case of partial fouling or full fouling, there is more settlement with shoulder fouling than centre track fouling.

Fig. 36. DEM track settlement predictions for different fouling scenarios (Huang & Tutumluer, 2011; reprinted with permission from Elsevier)

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5.3. Effects of geogrids on track stability (DEM approach) To reduce the lateral movement of ballast and optimise performance, the track can be reinforced with geogrid. Experimental process simulation results proved that a square geogrid with aperture size of 65 mm reduced lateral displacement best of all when placed 130 mm above the subballast [Section 3.6]. To better understand geogrid reinforcement from a micro mechanical view, the square geogrid model using PFC3D was placed at 130 mm above the subballast (Chen et al., 2015a). Figure 37(a) shows the contact force distributions at peak load in the GIZ (geogrid influence zone), and indicate how the applied load was transferred to the sample.

(a)

(b)

Fig. 37. Mechanism of contact force chains developed at maximum load (Maximum contact force = 4618 N) and GIZ (geogrid influence zone) (Chen et al., 2015a; reprinted with permission from Elsevier)

It was evident that placing the geogrid 130 mm above the base resulted in more interlocking in terms of confining most of the ballast across the entire section of geogrid, so that the geogrid-ballast system essentially acted like a beam in bending. Moreover, the GIZ is defined based on the orientation of contact force chains parallel to the geogrid layer, as shown in Fig. 37(b), where it gradually decreases from 225 mm at the fixed side to 130 mm at the movable side; this means the increased confinement is non-uniform along the length of the sample. 6. Applications to case studies and performance verification

6.1. Field study on instrumented track at Bulli In order to investigate stresses induced by moving trains and vertical and lateral track deformation, a field trial was carried out on instrumented track in the town of Bulli, north of Wollongong City. The instrumented section of track was 60 m long and was divided into four equal sections. Fresh and recycled ballast was used during construction, and a geocomposite (biaxial geogrid + nonwoven geotextile) layer was placed at the ballast-subballast interface. The technical specifications of various materials used during construction are reported elsewhere (Indraratna et al., 2013b; Indraratna & Nimbalkar, 2015). Vertical (Sv) and lateral (Sh) deformations were measured by settlement pegs and electronic displacement transducers, respectively and they are plotted against the number of load cycles, as shown in Fig. 38. These results indicate that the relationship between deformation and the number of load cycles is non-linear. The rate of increase of Sv diminishes as the number of load cycles increase. Recycled ballast experienced less deformation because it had moderately graded particle size distribution compared to the very uniform fresh ballast. Recycled ballast often has less breakage because the individual ballast particles are less angular, which in turn prevents corner breakage resulting from high contact stresses. The results of the field trial indicate that the geocomposite reduced the vertical deformation of fresh ballast by 33% and recycled ballast by 9% (Fig. 38a). It also reduced the lateral deformation of fresh ballast by about 50% and recycled ballast by 11% (Fig. 38b). The apertures of the geogrid offered strong mechanical interlocking with the ballast, and the load

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0

(a)

Average lateral deformation of ballast, (Sh)avg (mm)

Average vertical deformation of ballast, Sv (mm)

bearing capacity of the ballast layer was improved by the geocomposite layer. This substantially reduced settlement of track under repeated train loading during the monitoring period. Fresh ballast (uniformly graded) Recycled ballast (broadly graded) Fresh ballast with geocomposite Recycled ballast with geocomposite

3

6

9

12

15

18 0

5

1x10

5

5

2x10

5

3x10

4x10

5

5x10

5

6x10

5

5

7x10

8x10

5

-0

(b) (a)

-2

Fresh ballast (uniformly graded) Recycled ballast (broadly graded) Fresh ballast with geocomposite Recycled ballast with geocomposite

-4 -6 -8 -10 -12 -14

9x10

0

5

1x10

5

2x10

Number of load cycles, N

5

3x10

5

4x10

5

5x10

5

5

6x10

7x10

Number of load cycles, N

Fig. 38. Average deformations of the ballast layer: (a) vertical; (b) lateral (Indraratna et al., 2010a; with permission from ASCE).

6.2. Field study on instrumented track at Singleton A field trial was also undertaken on instrumented sections of track near the town of Singleton, close to Newcastle, in order to investigate the performance of different types of geosynthetics to improve overall track stability. Eight experimental sections of track were constructed on three types of subbases, including; (i) relatively soft alluvial deposits (silty clay); (ii) hard rock (intermediate siltstone); and (iii) a concrete bridge deck supported by a piled abutment. A layer of synthetic (rubber) mat was placed on a bridge deck (Fig. 39a) while a layer of geosynthetics was installed in sections of track located on soft alluvial deposits and hard rock. The properties of geosynthetics and rubber mats are given by (Indraratna & Nimbalkar, 2015). 0

(a)

Vertical Deformation of Ballast, Sv (mm)

Vertical Deformation of Ballast, Sv (mm)

0

6

12

18

24

30 0.0

Section A Section 1 Section 2 Section 3 Section 4 4.0x10

4

8.0x10

4

5

1.2x10

5

1.6x10

5

2.0x10

Number of Load Cycles, N

5

2.4x10

5

2.8x10

(b)

6

12

18

24

30 0.0

Section C Section 5 4

4.0x10

4

8.0x10

1.2x10

5

1.6x10

5

5

2.0x10

5

2.4x10

2.8x10

Number of Load Cycles, N

Fig. 39. Vertical deformation of ballast layer plotted versus number of load cycles in semi-logarithmic scale for (a) soft embankment; (b) hard rock (Reproduced from Indraratna et al., 2014e, by kind permission of ICE Publishing)

5

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Figures 39(a) and 39(b) show the variation of vertical deformation (Sv) of the ballast against the number of load cycles, and they indicate that vertical deformations increased as the subgrade became weaker, i.e., Sv was smaller at section B and larger than section A. Vertical deformations of the reinforced sections were 10-32% smaller than those without reinforcement. This pattern is similar to that observed in the laboratory (Brown et al., 2007; Indraratna & Nimbalkar, 2013), and can be attributed mainly to the frictional interlock between ballast aggregates and geogrids. It is also apparent that geogrid generally reduces track deformation more effectively over softer subgrades. Particle breakage was quantified in terms of the Ballast Breakage Index (BBI) and its values are shown in Table 5. As expected, BBI was highest at the top of the layer, and decreased with depth. The largest values of BBI obtained at hard rock verified that particle breakage was influenced by the type of subgrade. Ballast degradation is more pronounced with a stiff subgrade (e.g. rock) than with a relatively weak subgrade, a result that agrees with the laboratory findings reported earlier (Section 3.8). The ballast breakage index (BBI) at concrete bridge deck is the lowest, which suggests that rubber mats can effectively reduce particle degradation when placed above a concrete deck. Table 5. Assessment of ballast breakage (data sourced from Indraratna et al., 2014g) Sr.

Subbase type

Ballast breakage index, BBI

No.

Top layer

Middle layer

Bottom layer

1

alluvial deposit (silty clay)

0.17

0.08

0.06

2

concrete bridge deck

0.06

0.03

0.02

3

Hard rock (siltstone)

0.21

0.11

0.09

6.3. Field study at Sandgate: use of short prefabricated vertical drains in railway track The Sandgate Rail Grade Separation Project site was located near the City of Newcastle. In this area, the thickness of soft compressible soil varies from 4 m to 30 m, and it overlies a layer of soft residual clay followed by bedrock. Due to time constraints, the construction of the rail track began immediately after the vertical drains were inserted into the clayey subgrade, and a train load (25 ton axle load) at low speed was used initially as the external surcharge. In this finite element analysis (Indraratna et al., 2010c), an equivalent dynamic loading was considered using the impact factor method, i.e. a static pressure of 104 kPa with an impact factor of 1.3 was applied (Standards Australia, 1999). The over consolidated crust and fill layer were simulated by the Mohr-Coulomb model, and the soft clays were conveniently modelled using a soft soil constitutive model. The soil parameters used in FE analysis are given in Table 6. Fig. 40 shows a vertical cross section of mesh discretisation of the formation beneath the rail track. This 2D plane strain analysis used triangular elements with six displacement nodes and three pore pressure nodes. An equivalent plane strain analysis with an appropriate conversion from axisymmetric to 2-D was also used to analyse the multi-drain analysis (Indraratna et al., 2005b). Table 6. Selected parameters for soft soil layer used in the FEM (data sourced from Indraratna et al., 2010c). Soil layer

Depth of layer (m)

Model

c

φ

e0

λ /(1+e0)

κ/(1+e0)

kv

kh -4

(kPa)

(×10 m/day)

(×10-4 m/day)

Soft soil-1

1.0-10.0

Soft Soil

10

25

2.26

0.131

0.020

0.70

1.4

Soft soil-2

10.0-20.0

Soft Soil

15

20

2.04

0.141

0.017

0.75

1.5

Note: c is cohesion, φ is friction angle, e0 is initial void ratio, λ & κ are critical state parameters. kh & kv are coefficients of horizontal & vertical permeability, respectively.

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20 m 20m 104 @ 2.5 width (including impact factor impact of 1.3) 104kPa kPa @m2.5m width (including

factor of 1.3) Crust Crust

1 1m m

99m m

Soft Soil Layer 1 1 Soft Soil

Soft2Soil 2 Soft Soil Layer 10 10mm

6565m m

Fig. 40. Vertical cross section of rail track and foundation (Indraratna et al., 2010c; with permission from ASCE).

The field results were known only after one year, so all the predictions could be categorised as Class A (Lambe, 1973). The calculated and observed consolidation settlements at the centre line are presented in Fig. 41(a); the predicted settlements match the field data very well. The in-situ lateral displacement after 180 days at the toe of rail embankment is shown in Fig. 41(b). As anticipated, maximum displacements are measured within the top layer, i.e. the softest soil below the 1 m crust. Lateral displacement is restricted to the topmost compacted fill (depth 0-1 m). The Class A predictions of lateral displacements also agree well with the field data. The ability of PVDs to reduce the effects of undrained cyclic loading by reducing lateral movement is amply justified by the results of field trial and finite element predictions. 0

0

0

10

Lateral movement (mm) 20

30

Crust

0.05 0.1

Depth (m)

S e t tle m e n t ( m )

-4

Field Data Prediction-Class A

0.15

-8 Soft Soil 1

-12

Soft Soil 2

0.2 -16

0.25 0

50

100

150 Time (days)

200

250

Field Data Prediction-Class A (PVD Spacing @2m)

300 -20

Fig. 41. (a) Predicted and measured settlements at the centre line of rail tracks; (b) Lateral displacement at the embankment toe at 180 days (Indraratna et al., 2010c; with permission from ASCE)

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6.4. Case history: transition zones in railway track Transition zones, where track stiffness changes abruptly, create accelerated deterioration of track geometry. These zones, for example: bridge or tunnel approaches, road and culvert crossings, and ballasted to slab track transitions often require frequent maintenance. It also increases the wear and tear of vehicle components, track (rail and sleeper) and structures (bridge, culvert, cross roads) and decrease the passenger ride quality. The localized problems in these zones lead to speed restrictions and delays of train service (Banimahd et al., 2012; Coelho et al., 2009; D’Aguiar et al., 2014; Le Pen et al., 2014b; Li & Davis, 2005; Momoya et al., 2015; Paixão et al., 2014; Sañudo et al., 2016; Seara & Correia, 2010; Thompson & Woodward, 2004; Varandas et al., 2011; Woodward et al., 2007a). To mitigate these issues, railway industries and researchers have spent great deal of time and effort. Li and Davis (2005) have investigated the transition zone of bridge approach in order to identify and evaluate appropriate mitigation methods. Four bridges on heavy haul coal corridor (36 ton axle load) were selected for the study. All four bridges are located on the same track supporting a significant traffic at approximately 180 million gross tons (MGT) per year. The approaches to the four bridges were built with four different types of foundations viz., (i) hot mix asphalt (HMA) layer, (ii) geocell confined subballast layer, (iii) cement stabilised backfill and (iv) controlled standard track construction. The results show that all four transition zones experienced severe track geometry degradation soon after the train operation commenced. Fig. 42 (a) illustrates the comparison of track settlement at track on bridge, at approach and at open track locations. The settlement of the bridge approach is approximately 3 times that of track on bridges. Fig. 42 (b) shows the variation of settlement in both (left and right) approaches. This differential settlement further increase the dynamic vehicle-track interaction and cause accelerated damages. Li and Davis (2005) also reported that the track geometry degradation came mainly from ballast and subballast layers, with additional contribution from subgrade layer.

Fig. 42. (a) Comparison of track settlements from average of all four bridges; (b) Track settlement at the approach area (modified after Li and Davis, 2005; with permission from ASCE)

A similar results are obtained from (Coelho et al., 2009; Varandas et al., 2011) at a track monitoring site consisting of transition zone between an embankment and a piled concrete culvert as shown in Figs. 43 (a) and (b). Significant increase of the transmitted force was observed at the sleeper in transition zone compared to sleeper before the transition zone (Fig. 43 (a)). Coelho et al. (2009) concluded that the reduction in track support stiffness was considerable, with observed vertical displacements (Fig. 43 (b)) at the approach slab is about eight times higher than that on the normal track.

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Fig. 43. (a) Force transmitted through sleeper to the ballast (reproduced from Varandas et al., 2011; reprinted with permission from Elsevier); (b) Maximum vertical deflection of track against the distance from the center of culvert measured during passage of an IDD and ISD train (reproduced from Coelho et al., 2009; by kind permission of Delft University of Technology and the Authors of the original paper)

Seara and Correia (2010) simulated the implications and problems of transition zones using the finite element software DIANA to find the optimum stiffness ratio with respect to two adjoining wedges as shown in Fig. 44(a), where wedge 1 is beside the stiff abutment. The track settlement obtained for a 100 kN moving wheel load at a speed of over 300 km/h from the embankment zone to the concrete bridge deck is shown in Fig. 44 (b) for varying stiffness ratio (E1/E2 =1.195- 2.0) in relation to the overall embankment stiffness (60-100 MPa) . The results show a significant difference in settlement between the embankment zone and the approach to the abutment. This FEM model categorically demonstrates why appropriate stiffness values of the rail (granular) embankment, transition zone and concrete bridge deck should be optimised to ensure that undue differential settlement, and associated potential impact and damage can be minimised as much as possible.

Fig. 44. (a) Global view of numerical model; (b) Settlement along the track (Seara & Correia, 2010; courtesy Escola de Engenharia da Universidade do Minho)

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7. Conclusions

This inaugural Ralph Roscoe Proctor paper presented a geotechnical perspective of railroad performance with special reference to the deformation and degradation of granular materials and track substructure through large scale laboratory tests, analytical and numerical modeling and the findings from full-scale field investigations. The paper elaborated on the detailed stress-strain behavior under both static and cyclic loading and the volumetric response and degradation of ballast with implications on design and performance of tracks. The results also indicated that geosynthetic grids, geocells, synthetic mats and prefabricated vertical drains effectively reduce the deformation of granular media and subgrade. The large scale triaxial tests revealed that the Ballast Breakage Index (BBI) had a profound effect on the magnitude of the resilient modulus (MR). Permanent deformation and degradation increased with the frequency and magnitude of load cycles. Three different deformation mechanisms were observed in response to the frequency of loading, namely, in Range I: plastic shakedown at f ≤ 20 Hz; in Range II: plastic shakedown and ratcheting at 30 Hz ≤ f ≤ 50 Hz, and in Range III: plastic collapse at f ≥ 60 Hz. A 3D laser scanning method was found to be appropriate to quantitatively assess the size and shape of ballast. A new shape index called ‘ellipsoidness’ was introduced to better represent the particle shape index. The detrimental effect of fouling on the track drainage was also examined using a new parameter, the Void Contaminant Index (VCI) to replace the previous Fouling Index (FI) and Percentage Void Contamination (PVC) index. The VCI could accurately capture ballast fouling because it could incorporate the effects of void ratios, specific gravities, and gradations of both fouling material and ballast. Even a small increase in the VCI at the initial stage leads to a significant decrease in the hydraulic conductivity of fouled ballast, but beyond a certain limit of VCI (50% for coal fouled ballast and 90% for sand fouled ballast) the hydraulic conductivity converged to that of the fouling materials itself. The elasto-plastic constitutive models can successfully apply a continuum mechanics-based approach to ballast that can capture the effects of particle breakage and ballast fouling due to coal and clay. These models described in the paper adopted the critical state concept and the theory of plasticity with a kinematic-type yield locus. The modified stress dilatancy formulation related triaxial shearing with energy consumption due to particle breakage and the use of an alternative variable such as the intergranular specific volume to unify the critical state line. The discrete element method or DEM considers bonding small balls in clumps to represent angularity of particles, and it showed that cyclic degradation was dominated by asperity fracture (i.e. the fracture of small angular projections). These simulations could capture the behaviour of real ballast in terms of axial and volumetric strain and degradation under both monotonic and cyclic loading. A ‘half-track’ DEM simulation revealed that fouling could lead to problems on the track such as ‘‘hanging tie’’. In addition, the simulations revealed a useful micromechanical insight into the monotonic and cyclic behaviour of ballast. The large scale direct shear tests revealed that geogrids can increase the shear strength of ballast while reducing its dilation, while interlocking between the ballast and geogrid increases the peak shear stress associated with internal confinement. This frictional interlock also helps to reduce the lateral deformation of ballast; however, the benefits gained from using geogrid are reduced in coal fouled ballast because the coal fines acted like void filler and coats the surfaces of ballast aggregates, which in turn reduces inter-particle friction and the subsequent interface shear strength. It was also observed through shear box testing that the optimum geogrid aperture to maximise the interface shear strength was 1.2D50. The Lateral Spread Reduction Index (LSRI) can be used to assess the deformation of ballast reinforced with geogrid-reinforced ballast. It was shown that LSRI was influenced by the type of geogrid. Ballast breakage and associated settlements decreased significantly with an increase in LSRI. The large scale impact tests revealed that the synthetic rubber mats could decrease the strains induced in ballast by impact as much as 50 %. In fact, impact causes most damage to ballast, especially under high repetitive loads; even a few impact blows can cause considerable damage to ballast (i.e. BBI > 17 %) when a stiff subgrade is present. However, when a shock absorbing mat was placed at the top and bottom of a ballast layer, the reduction in particle breakage over a stiff subgrade approached 50 %. A semi-empirical mathematical model could be used to predict the filtration and drainage of saturated subballast under cyclic train loading. A suitable granular filter for a given base soil must satisfy the constriction-based filtration

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criterion. When applied to the railway sector where a degree of plastic deformation to an anticipated cyclic load generated from passing traffic is expected, a relatively relaxed criterion can be adopted, whereby the original size of Dc35 is 2-3 times the size of d85sa. It is also suggested that the coefficient of uniformity of the filter is kept within the range of 3 to 6. A large scale prismoidal triaxial was used to investigate unreinforced and geocell-reinforced subballast under low confining pressure and subjected to cyclic loading. The results showed that geocell effectively reduced axial deformation in the specimen, particularly at lower confining pressures (σ′3 ≤ 15 kPa) and higher frequencies (f ≥ 20 Hz). The results also revealed that the values of friction angle (φm) and dilatancy angle (ψm) changed during cyclic loading. These results confirmed that geocell could be used as a practical and useful technique to improve track resiliency and corresponding train speed, by effectively controlling the stiffness of subballast. The ‘field’ performance of ballasted rail tracks with geosynthetic reinforcement was investigated, where different types of ballast and geosynthetic reinforcements were installed and monitored. The results of the Bulli study indicated that using geocomposite as reinforcing elements for recycled ballasted tracks was a feasible and effective alternative, while the Singleton study showed that geogrid increased its influence on track behaviour as the subgrade became weaker. The geogrids can certainly reduce the vertical deformation of ballast; the obvious benefits being improved track stability and a reduction in maintenance costs. Transient deformation of the ballast layer also decreases when geosynthetics are used, while the placement of synthetic rubber mats also help to mitigate excessive ballast degradation. A Class A FEM prediction of track behaviour compared to field data proved that short vertical drains could increase track stability by significantly decreasing the build-up of excess pore water pressure during the passage of trains, and helping to facilitate the dissipation of excess pore water pressure during the rest period. In this way, the dissipation of pore water pressure increases track stability for the next loading stage. Both the predictions and the field data showed that lateral displacement could be effectively curtailed by the use of vertical drains. Better understanding of such a performance would allow for safer and more effective design and analysis of ballasted rail tracks with geosynthetic reinforcement. 8. Acknowledgements

As the inaugural Ralph Proctor Lecturer, my sincere thanks go to all the members of the TC202 of ISSMGE and its Executive Committee under the leadership of former Chair, Prof Antonio Gomes Correia and current Chair, Prof Erol Tutumluer, for selecting me for this prestigious presentation. I am particular grateful to Dr. Sanjay Shrawan Nimbalkar, A/Prof Cholachat Rujikiatkamjorn and Sinniah Navaratnarajah (doctoral student), for their help and technical contributions during the preparation of this paper. Over the years, the assistance of David Christie (formerly Senior Geotechnical Consultant, RailCorp), Tim Neville (ARTC) and Michael Martin (Aurizon/QLD Rail) is gratefully acknowledged. A number of past doctoral students, including Dr Wadud Salim (large scale testing and constitutive modelling), Dr Daniela Ionsecu (large scale testing and ballast characterisation), Dr Joanne Lackenby (particle breakage assessment), Dr Dominic Trani (drainage and filtration of subballast), Dr Behzad Fatahi (native vegetation for subgrade stability), Dr Nayoma Tennakoon (effects of ballast fouling), Dr Pramod Thakur (effects of particle angularity), Dr Karim Hussaini (use of geogrids in track), Dr Qideng Sun (mathematical modelling of ballast behaviour), Dr Mehdi Biabani (use of geocells in track), Dr Ni Jing (cyclic instability of subgrade), Dr Trung Ngo (DEM modelling of track), Dr Ashok Raut and Dr Mark Locke (filtration and drainage in porous media) and a few current doctoral students (Yifei Sun, Chamindi Jayasuriya, Rakesh Mallisetty) have contributed to the contents of this paper. I wish like to thank a number of technical staff at University of Wollongong, namely, Alan Grant, Cameron Neilson and Ian Bridge whose assistance during the development of large-scale testing facilities was invaluable. I am also grateful to my past and present colleagues, A/Prof Hadi Khabbaz, Dr Mohammad Shahin, Dr Cheng Chen, Dr Pongpipat Anantanasakul, Dr Jayan Vinod and Dr Ana Heitor for their assistance and contributions to the contents of this paper directly or indirectly. I wish to thank the Australian Research Council, CRC for Railway Engineering and Technologies, CRC for Rail Innovation, RailCorp (now Sydney Trains), Australian Rail Track Corporation, and Queensland Rail National (now

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Aurizon) for their continuous support in terms of research funding and technical assistance during numerous projects over the past two decades. A significant portion of the contents have been reproduced with kind permission from the Journal of Geotechnical and Geoenvironmental Engineering ASCE, International Journal of Geomechanics, ASCE, Proceedings of the Institution of Civil Engineers – Ground Improvement, ASTM Geotechnical Testing Journal, Géotechnique and Canadian Geotechnical Journal among others. 9. References Abadi T, Le Pen L, Zervos A, Powrie W. Measuring the area and number of ballast particle contacts at sleeper/ballast and ballast/subgrade interfaces. The International Journal of Railway Technology. 2015;4(2):45-72. Ahmed S, Harkness J, Le Pen L, Powrie W, Zervos A. Numerical modelling of railway ballast at the particle scale. International Journal for Numerical and Analytical Methods in Geomechanics. 2015;40(5):713-37. Ajayi O, Le Pen L, Zervos A, Powrie W. 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