The effects of drainage on the behaviour of railway track foundation materials during cyclic loading

Railway track foundation materials play an essential role in ensuring the stability of the track structure and maintaining track geometry. During their operational life they are subject to repeated loading cycles, which under unfavourable conditions can result in the accumulation of unacceptably large plastic strains and a reduction in resilient stiffness. Both of these can significantly reduce the life of the track.

A number of studies have investigated the behaviour of railway track foundations under repeated loading (e.g. Brown et al., 1975; O'Reilly et al., 1991; Shahu et al., 1999; Chung Ip et al., 2012). It has generally been observed (Brown & Selig, 1991) that there is a threshold stress level above which significant accumulation of plastic strain and (in undrained conditions) generation of excess pore pressure occurs. Below this threshold stress, changes in cyclic strain and pore pressure are very small or negligible. A different approach has been adopted in investigating the dynamic response of soils to seismic loading (Georgiannou et al., 1991; Mortezaie & Vucetic, 2016), which identifies a threshold strain beyond which significant changes in stiffness, strength and pore pressure are observed. However, for railway foundations the applied stresses are more easily quantified than the resulting strains; hence the threshold stress approach is usually adopted.

Although a number of investigations have considered the effects of cyclic loading on soil behaviour, relatively few have addressed the combined effects of the horizontal and vertical stress changes to which railway track foundation soils are subjected, and result in principal stress rotation (PSR) (Brown, 1996). Field measurements have shown that, although vertical stress changes attenuate with depth, horizontal stress changes become more pronounced up to a certain depth below the sleeper base before then reducing with further increases in depth (Priest et al., 2010).

Laboratory studies where PSR has been considered show a higher rate of plastic strain accumulation than that exhibited when only the vertical stress is cycled (Chan & Brown, 1994; Momoya et al., 2007). In more recent work on saturated materials (Gräbe & Clayton, 2009), very large increases in permanent strain have been observed, associated with pore pressure increases, when PSRs have been applied in undrained conditions. Permanent deformations and pore pressures resulting from PSR were found to reduce as the clay content of the material was increased. In addition, the difference induced by PSR was greater at higher peak effective principal stress ratios. Gräbe & Clayton (2014) also observed that, in undrained loading of saturated materials, PSR caused the resilient modulus of the mixes investigated to reduce by some 20–26% compared with tests in which only the vertical stress was cycled. Cyclic changes in the direction of principal stresses are therefore likely to influence significantly the observed resilient behaviour of soils.

Owing to the limited amount of laboratory test data available, uncertainties remain in our understanding of the stress paths, drainage conditions and magnitudes of cyclic stress for which PSR may be important for the long-term performance of railway track foundations. The aim of the research reported in this paper was to investigate these, with an emphasis on the relative magnitudes of the cycles of shear and normal stress and on the drainage conditions – specifically, the time available for drainage between successive loading peaks, as governed by the permeability of the material and the drainage path length.

The laboratory tests were carried out using a hollow cylinder apparatus (HCA). In the HCA a rotation in the direction of principal stresses can be achieved by applying an axial twist (torque), which induces shear stresses on horizontal and complementary radial planes. However, because the thickness is finite, application of the torque results in non-uniform stress and strain distributions across the specimen wall. These non-uniformities and their effects can be reduced to acceptable levels by selecting an appropriate specimen geometry (Saada & Townsend, 1981; Sayao & Vaid, 1991) and adopting the Hight et al. (1983) framework of average stresses and strains for analysis (Zdravkovic & Jardine, 1997; Nishimura et al., 2007; Georgiannou et al., 2008; Cai et al., 2013). The specimens used in this research had an outer diameter of ∼100 mm, an inner diameter of ∼60 mm and a height of ∼200 mm, thereby satisfying the geometric criteria of both Saada & Townsend (1981) and Sayao & Vaid (1991).

In the tests reported in this paper, the stresses were corrected to take into account the effect of membrane restraint using the approach given by Tatsuoka et al. (1986; their equations (8)–(10)). Membrane penetration effects were insignificant, because the specimens were well graded, prepared at relatively high dry densities and tested at low effective stresses with constant inner and outer cell pressures. Keeping the inner and outer cell pressures equal also avoids stress/strain non-uniformities arising from changes in the curvature of the specimen wall.

The resilient modulus of a soil is the stiffness calculated from the recoverable (i.e. resilient) strains under repeated loading/unloading (equation (1)). In the HCA, it is equivalent to the resilient Young's modulus and is given the symbol E_r

where q_r is the cyclic deviator stress and ε_a,r is the recoverable axial cyclic strain.

Axial strains were measured locally on the specimen to eliminate errors associated with the misalignment of specimen ends, bedding and apparatus compliance (Jardine et al., 1984; Clayton & Khatrush, 1986; Cuccovillo & Coop, 1997). Global axial displacement was calculated from the axial actuator motor shaft encoder data. The change in the outer diameter of the specimen was measured using a linear variable differential transformer (LVDT) attached to a radial caliper. The change in the inner radius r_i was calculated from the change in the inner cell volume, assuming the specimen retained a cylindrical shape during deformation (Mamou, 2013). Global angular displacements were calculated from the torsional actuator shaft encoder data.

The axial force F and the torque T were measured using a combined load and torque cell located at the top of the specimen. The inner and outer cell pressures and the applied back pressure were controlled and measured by global digital systems (GDS) pressure/volume controllers. Pore pressures were measured independently at the top and bottom of the specimen using Druck PDCR810 pressure transducers.

The materials tested replicated gradings used in the construction of foundations (sub-ballast layers) for the South African Coal Line. These provide a baseline material for which previous laboratory test and field performance data are available in the literature (Gräbe & Clayton, 2009; Priest et al., 2010; Otter, 2011). The materials were represented by sand–clay mixes made up of varying proportions of Leighton Buzzard sand fractions B (LBSFB), C (LBSFC) and D (LBSFD); Hymod Prima clay (HPC); and Oakamoor HPF5 silica flour silt (Table 1).

Specimens were prepared by compaction to a target dry density of 2·15 Mg/m³ to replicate compaction of the material in the field. Table 2 summarises the dry densities, water contents and global void ratios achieved.

Each specimen was saturated prior to testing, to avoid complications of internal drainage and pore air compression in globally undrained conditions. In reality the water content of the soil comprising a railway track foundation is likely to vary as a result of changes in weather, climate and groundwater conditions. In many parts of the world, unsaturated conditions may well be the norm; however, saturated conditions represent a likely worst case and a convenient reference benchmark, and hence were adopted in the tests reported in this paper.

Specimens were flushed first with carbon dioxide (CO₂) to replace the air with a gas of greater solubility, and then with de-aired water. To dissolve any remaining gas, the back pressure was increased in stages together with the inner and outer cell pressures, so as to maintain a constant effective stress. On reaching a back pressure of at least 670 kPa, a period of time was allowed for any remaining gas to dissolve into the pore water. A final B-value in excess of 0·97 was taken to indicate a sufficient degree of saturation for a soil of relatively high stiffness (Black & Lee, 1973).

To replicate the confining stresses typical of railway track foundations in the field, specimens were tested from an initial isotropic effective stress (cell pressure minus back pressure) of 33 kPa (Gräbe, 2001). Each specimen was then subjected to cycles of axial stress of 0 to 30 kPa, together with cycles of shear stress of ±Δτ_θz, with a phase difference of 90°, as indicated in Fig. 1. The magnitude of the shear stress cycle Δτ_θz, and hence the degree of PSR, were gradually increased, to explore a range of stress changes potentially associated with a railway track foundation.

The peak magnitude of the applied cyclic change in shear stress Δτ_θz was initially set to the value indicated by the numerical analyses presented by Powrie et al. (2007) for a soil element near the bottom of a railway track foundation extending to a depth of 1 m below the sleeper base (|Δτ_θz| = 8·5 kPa). Thereafter, the magnitude of the peak cyclic shear stress was incremented until failure occurred. As a point of reference, the cyclic shear stress calculated by the numerical analyses of Powrie et al. (2007) for a soil element at a depth of 0·3 m below the sleeper base (corresponding to the bottom of a standard 0·3 m thick layer of ballast) was |Δτ_θz| ∼ 24 kPa.

Tests were carried out both under free-to-drain and undrained conditions. The objective of the undrained tests was to investigate the potential of the different sand–clay mixes to accumulate excess pore pressures, if unable to drain during load cycling. At the end of every undrained test stage and before the start of the next, specimens were allowed to drain so as to dissipate any accumulated excess pore pressure. The rest period varied depending on the clay content.

In the free-to-drain tests, the specimen was allowed to drain from the bottom during stress cycling. Pore pressures were measured at the top of the specimen, that is, the furthest point from the drainage boundary. No attempt was made to reduce the loading frequency to prevent the build-up of excess pore pressures, that is, to maintain fully drained conditions.

Free-to-drain tests investigated the susceptibility of the material to accelerated deterioration as a result of PSR, in conditions where the build-up or dissipation of any excess pore pressures was controlled by the consolidation characteristics of the soil (volumetric compressibility and permeability) and the drainage path length d in relation to the frequency of loading f. The loading frequency used in the tests was 0·0083 Hz or approximately 30 cycles per hour. It is difficult to relate this directly and in general terms to field conditions. An intensively trafficked route might experience up to 24 trains per hour, with rest periods of 2–3 min in between. However, a fast train travelling at 50 m/s would give bursts of axle loading at 8 Hz (which would be felt at a depth of ∼0·3 m below the sleeper base), or bogie loading at 4 Hz (which would be felt at a depth of about 1 m below the sleeper base; Powrie et al. (2007)), during each train passage.

The maximum drainage path length in the laboratory tests was 200 mm. Equality of the dimensionless group c_v/fd² for the same consolidation coefficient c_v between the laboratory and the field would suggest an equivalent train frequency of 13 per hour for a maximum field drainage path length of 0·3 m. It is considered that the free-to-drain tests probably represent a best-case field scenario, in that in reality the relevant frequency of loading (whether in terms of trains per hour or axles/bogies per second) would be higher and the maximum drainage path longer, so there would be less opportunity for excess pore water pressures to dissipate.

A summary of the stress cycles applied in all of the PSR tests carried out in this research is given in Table 3. The first letter identifies the drainage condition; U for undrained and F for free-to-drain tests. The second letter denotes the type of material (A, B or C); the number that follows is the magnitude of cyclic shear stress imposed on the specimen. Before each undrained test, the specimen was subjected to a free-to-drain cyclic PSR preloading stage to reduce the effects of specimen preparation on the subsequent results. The free-to-drain preloading stages of undrained tests are denoted by the letter P.

The accumulation of permanent strain with the number of cycles of increasing cyclic shear stress is illustrated in Figs 2, 3 and 4 for materials A, B and C, respectively. The different test stages (i.e. the different magnitudes of cyclic shear stress) are indicated by the letters (a) to (h). For materials B and C (Figs 3 and 4), in both undrained and free-to-drain conditions, there is a threshold cyclic shear stress beyond which the rate of increase in the plastic strain during each cycle accelerates, resulting in what might be described as fatigue failure as a result of the repeated loading (for example at stage (g) in Fig. 3 for the free-to-drain test). Below this cyclic shear stress threshold, the response of the specimens was stable over a large number of loading cycles with no unrestrained accumulation of axial strain (for example, stage (a) in Fig. 3 for the undrained test). Material A exhibited a cyclic shear stress threshold in free-to-drain conditions (stage (f), Fig. 2). When tested undrained, material A failed at the lowest cyclic shear stress applied (|Δτ_θz| = 8·5 kPa), suggesting that the cyclic shear stress threshold in undrained conditions was equal to or less than this value (stage (a), Fig. 2).

Previous strain-controlled experiments on clayey sands in undrained cyclic triaxial loading conditions have yielded similar observations in terms of a threshold strain, below which strain cycling results in stable behaviour, and above which strains (and pore pressures) accumulate with increasing number of loading cycles (Georgiannou et al., 1991).

Within the range of materials investigated in this research

• (a)

  undrained conditions were much more onerous than those in which drainage was able to occur (i.e. the cyclic shear stress threshold was much smaller in undrained conditions)

• (b)

  the magnitude of the cyclic shear stress threshold in given conditions (i.e. undrained or free to drain) increased with increasing clay content.

In free-to-drain conditions, where the rate of pore pressure dissipation was regulated by the permeability and the volumetric compressibility of the soil and the drainage path length, materials B and C (containing moderate amounts of fines) remained at least marginally stable over the range of increase in cyclic shear stress (stages (a) to (f), Fig. 3 and stages (a) to (g), Fig. 4) expected to occur at depths greater than about 0·3 m in the field (a typical minimum depth of ballast below sleeper soffit level on a ballasted railway track). Material A, however, failed when a cyclic shear stress of |Δτ_θz| = 23·5 kPa (stage (f), Fig. 2) was applied and suffered large strains at |Δτ_θz| = 20·5 kPa (stage (e), Fig. 2).

All of the materials tested appeared to be very sensitive to small changes in the extent of PSR once the cyclic strain threshold was exceeded, and the transition from stable behaviour to fatigue failure could be sudden. This implies that a currently stable railway track foundation will not necessarily be able to accommodate heavier traffic loads.

In undrained conditions, none of the materials in Figs 2–4 would be suitable for use within a depth of about 1 m below the sleeper base, with material A failing at the lowest level of cyclic shear stress (|Δτ_θz| = 8·5 kPa) considered.

The excess pore pressures generated during both undrained and free-to-drain tests are shown in Figs 5, 6 and 7 for materials A, B and C, respectively. The generation of significant excess pore pressures was always associated with the cyclic shear stress threshold being exceeded, in both undrained (stage (b), Fig. 6 and stage (c), Fig. 7) and free-to-drain conditions (stage (f), Fig. 5, stage (g), Fig. 6 and stage (h), Fig. 7). In principle, the maximum pore pressures generated should depend on the loading applied and whether the material yielded or remained elastic, while the degree of dissipation should depend on the permeability, stiffness, rest period and drainage path length, in accordance with conventional consolidation theory.

Prevention of drainage in the undrained tests led to the build-up of pore pressures that were unable to dissipate at generally lower magnitudes of cyclic shear stress, and contributed to the rapid failure of specimens as shown in Fig. 7, stage (c). The free-to-drain test specimens failed when the pore pressures generated became too large to dissipate between successive peak loads (for example stage (h), Fig. 7).

Graphs of volumetric strain against number of cycles for the free-to-drain tests are shown in Figs 8, 9 and 10 for materials A, B and C respectively. Volumetric strains were always compressive, and mirrored the axial strain behaviour in that they were generally reasonably stable within a given magnitude of cyclic shear stress until the cyclic shear stress threshold was reached. At this point, much larger volumetric strains started to develop with continued cycles of shear stress. The volumetric compressibility of material A was similar to that of material B, while material C (14% clay) was volumetrically slightly stiffer.

Increasing the clay content resulted in the development of smaller pore pressures under any given set of stress and drainage conditions (for example stage (f) in Figs 5–7). Although increasing the clay content of the mix would be expected to reduce the permeability and hence inhibit the dissipation of excess pore pressures between successive load peaks, the data suggest that the dominant (and beneficial) effect was an accompanying increase in volumetric stability (if not stiffness), which is possibly a result of the wider range of grain sizes in the mix.

The changes in resilient modulus with the number of stress cycles are shown for undrained conditions in Figs 11–13, and for free-to-drain conditions in Figs 14–16, for materials A to C. For a given magnitude of cyclic shear stress in undrained conditions, the resilient modulus typically remained reasonably steady until the cyclic shear stress threshold was reached, at which point it started to reduce rapidly (stage (b), Fig. 12 and stage (c), Fig. 13). However, material A failed at the lowest level of cyclic shear stress (Δτ_θz = 8·5 kPa) and therefore showed a continuous decrease in resilient modulus from the outset (stage (a), Fig. 11).

In free-to-drain conditions the resilient modulus increased with the number of cycles and increasing cyclic shear stress magnitude until the cyclic shear stress threshold was reached, when again a rapid degradation in resilient modulus occurred (stage (f), Fig. 14, stage (g), Fig. 15 and stage (h), Fig. 16).

These data suggest that below the cyclic shear stress threshold, changes in the amount of in-cycle PSR will have little effect on the resilient modulus of the foundation and, depending on the drainage conditions, may even increase it (for example stages (a) to (b), Fig. 13 and stages (a) to (g), Fig. 16). This implies that the response of a railway track foundation to cyclic shear stresses only becomes critical when the cyclic threshold stress of the soil is exceeded. However, deterioration may then be rapid and its onset may occur with little or no warning in terms of prior stiffness change (e.g. stage (f), Fig. 10, although plastic strains had started to accumulate at stage (e) in this case).

Figure 17 shows stress paths in terms of deviator stress q, defined in the conventional way as

against mean effective stress p′ for the undrained test stages on materials A, B and C that caused failure (test stages UA8·5, UB11·5 and UC14·5, respectively). The move towards the critical stress ratio (as identified by Gräbe & Clayton (2009)) with increasing number of load cycles as pore pressures build up is apparent.

The effect of increasing the clay content on the cyclic stress threshold of the mixes is illustrated for both undrained and free-to-drain conditions in Fig. 18. Increasing the clay content from 7%, through 11% to 14%, increased the cyclic shear stress threshold of the mix in both undrained and free-to-drain conditions. The cyclic shear stress threshold was greater in free-to-drain conditions than undrained.

The right-hand scale on Fig. 18 indicates the equivalent depth below sleeper base level at which the cyclic stress on the left-hand scale is reached, according to the finite-element analyses presented by Powrie et al. (2007). For a foundation material to perform acceptably, there would need to be an adequate margin between the cyclic shear stress threshold and the cyclic stress imposed at the depth at which the material was to be used.

In undrained conditions, all of the materials tested are acceptable for use at depths greater than 1 m below the sleeper base. Drainage reduces the minimum depth at which a material will remain below the cyclic threshold stress; subject to the applicability of the drainage conditions in the laboratory tests to a given field situation, materials with a clay content of more than about 10% may be suitable for use immediately below the ballast (a depth of 0·3 m below the sleeper base).

 Figures 19 and 20 summarise how the resilient modulus varies with clay content and the magnitude of the shear strain cycle in undrained and free-to-drain conditions. Below the cyclic shear stress threshold, the resilient stiffness tended to equalise with increasing magnitude of cyclic shear stress over the range of clay contents investigated (for example Fig. 20, stages (b) to (f)) for 7%, 11% and 14% clay). The influence of the clay content on the resilient modulus for a given magnitude of applied shear stress became more significant once the cyclic stress threshold was exceeded (for example Fig. 19, stage (b) for 11% and 14% clay); this is inescapable given the dependence of cyclic shear stress threshold on clay content. However, as long as the cyclic stress threshold of the mix is not exceeded, varying the clay content between 7% and 14% should have only a second-order effect on the resilient modulus over the lifetime of a railway track foundation.

• (a)

  The ability of the soil within a railway track foundation to respond resiliently, without the development of excessive plastic settlements, depends on the magnitude of the cyclic shear stress applied by train loading remaining below a certain threshold value.

• (b)

  Below the cyclic shear stress threshold, the response of soils containing a range of sand, silt and clay materials was stable over a large number of loading cycles. In undrained conditions, cyclic changes in shear stress below the threshold value had no significant effect on the resilient stiffness of the soils tested. In free-to-drain conditions, the resilient stiffness increased with number of cycles and with increasing shear stress below the threshold level.

• (c)

  Once the cyclic shear stress threshold was exceeded, a rapid reduction in stiffness and stability ensued. The soils tested were sensitive to even small changes in the magnitude of cyclic shear stress near the cyclic shear stress threshold. Small increases in cyclic shear stress could trigger the rapid deterioration of a previously stable sand–clay mix. The fact that a railway track foundation is currently stable may therefore not be a reliable indicator of its ability to accommodate significantly heavier traffic.

• (d)

  The deterioration in resilient modulus and material stability was generally associated with the generation of large excess pore water pressures, even in free-to-drain conditions in which there had been no significant excess pore pressure generation at lower cyclic shear stresses. In free-to-drain conditions, instability was associated with the development of substantially increased compressive volumetric strains.

• (e)

  The cyclic shear stress threshold in both undrained and free-to-drain conditions increased as the clay content of the soil was increased from 7% to 14%. Increasing the clay content also reduced the excess pore pressure generation in both undrained and free-to-drain conditions. The cyclic shear stress threshold reduced dramatically when specimen drainage was prevented. Thus internal or external drainage is likely to play an important role in the continuing stability of railway foundations in the field.

• (f)

  For the materials tested, the cyclic shear stress threshold in free-to-drain conditions was generally similar to or less than the cyclic shear stress in the soil immediately below a 0·3 m deep ballast bed, but comfortably greater than the cyclic shear stress at a depth of 1 m below the sleeper base. In undrained conditions, the cyclic shear stress threshold was generally similar to the likely cyclic shear stress at a depth of 1 m below the sleeper base. These factors would need to be taken into account in assessing the suitability of a natural or engineered railway track foundation material, either within the sub-ballast zone (a depth of 0·3 m to 1·0 m below the sleeper base) or below it.

The research was carried out with the financial support of the Engineering and Physical Sciences Research Council (grant number EP/H044949/1, Railway Track for the 21st Century).

B

Skempton's pore water pressure coefficient

c_v

consolidation coefficient

E_r

resilient Young's modulus

F

axial force

N

number of cycles

p′

mean effective stress = (σ′₁ + σ′₂ + σ′₃)/3

q

deviator stress = $1/2σ′1−σ′22+σ′1−σ′32+σ′2−σ′32$

q_r

cyclic deviator stress

r_i

inner radius

T

torque

Δu

excess pore pressure

Δσ_z

axial stress

Δτ_θz

shear stress

ε_a

axial strain

ε_a,r

recoverable axial cyclic strain

ε_vol

volumetric strain