A LABORATORY STUDY ON FLUIDIZATION OF SUBGRADE …

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A LABORATORY STUDY ON FLUIDIZATION OF SUBGRADE UNDER CYCLIC TRAIN LOADING

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2019-0350.R2

Manuscript Type: Article

Date Submitted by the Author: 15-Oct-2019

Complete List of Authors: Indraratna, Buddhima; University of Wollongong, Singh, Mandeep ; University of Wollongong, Centre for Geomechanics and Railway EngineeringNguyen, Thanh; University of Wollongong, Centre for Geomechanics and Railway EngineeringLeroueil, Serge; Université Laval, Abeywickrama, Aruni ; University of Wollongong, Centre for Geomechanics and Railway EngineeringKelly, Richard; University of Newcastle, School of Civil Engineering; SMECNeville, Tim; Australian Rail Track Corporation Ltd

Keyword: Fluidization, mud pumping, subgrade, cyclic triaxial test

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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A LABORATORY STUDY ON SUBGRADE FLUIDIZATION UNDER

UNDRAINED CYCLIC TRIAXIAL LOADING

Buddhima Indraratna1

Distinguished Professor of Civil Engineering,Founding Director, Centre for Geomechanics and Railway Engineering,

Director, Australian Research Council (ARC) Industrial Transformation Training Centre, ITTC-Rail

University of Wollongong, Wollongong City, NSW 2522, Australia

Mandeep Singh

PhD student, Centre for Geomechanics and Railway Engineering, University of Wollongong,

Wollongong City, NSW 2522, Australia

Thanh Trung Nguyen

Research Fellow, ARC Industrial Transformation Training Centre, ITTC-RailUniversity of Wollongong, Wollongong City, NSW 2522, Australia

Serge LeroueilProfessor of Geotechnical Engineering,

Université Laval, Quebec, Canada

Aruni Abeywickrama

PhD student, Centre for Geomechanics and Railway Engineering, University of Wollongong,

Wollongong City, NSW 2522, Australia

Richard Kelly

Conjoint Professor of Practice, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia,

Chief Technical Principal, SMEC, Brisbane, QLD, Australia

Tim Neville

Senior Geotechnical Engineer, Australian Rail Track Corporation Ltd.

Words: 5738; Figures: 14Submitted to: Canadian Geotechnical Journal

1Corresponding author: Buddhima Indraratna (e-mail: [email protected])

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Abstract

A long term issue that has hampered the efficient operation of heavy haul tracks is the

migration of fluidized fines from the shallow soft subgrade to the overlying ballast, i.e., mud

pumping. This paper presents a series of undrained cyclic triaxial tests, where realistic cyclic

loading conditions were simulated at low confining pressure that is typical of shallow

subgrade beneath a ballast track. Subgrade soil specimens with a low plasticity index

collected from a field site with recent history of mud pumping were tested at frequencies

from 1.0 to 5.0 Hz and a cyclic stress ratio (CSR) from 0.1 to 1.0. The experimental results

indicate that under adverse loading conditions of critical cyclic stress ratio (CSRc) and

frequency, there is upward migration of moisture and the finest particles towards the

specimen top, and this causes the uppermost part of the soil specimen to soften and fluidize.

Conversely, a smaller value of CSR tends to maintain stability of the specimen despite the

increasing number of loading cycles. It is noteworthy that for any given combination of CSR

and frequency, the relative compaction has a significant influence on the cyclic behaviour of

the soil and its potential for fluidization.

Keywords: Fluidization, cyclic triaxial test, mud pumping, subgrade.

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1. Introduction

The rapidly increasing demand for faster and heavier passenger and freight transport (Schut

and Wisniewski 2015; Correia et al. 2016; ARTC 2018) has led to the inevitable need for

more stable track foundations with lower maintenance costs. A common real-life scenario is

where low-lying coastal rail tracks are constructed on saturated subgrade soils (i.e. water

content often approaching the liquid limit). With continual passage of trains, excess pore

pressures (EPP) and plastic (residual) strains accumulate over time, which then leads to an

upward ejection of soil slurry to the overlying granular layers (ballast). This migration of

fines under repeated railway loading is commonly known as mud pumping. Although this

long standing dilemma for railway engineers has received much attention over the years, the

actual interpretation of the fluidizing mechanism has still remained mostly controversial. For

example, Takatoshi (1997) attributed this to the suction at the base of sleeper (tie) induced by

the difference in stiffness between ballast and sleeper, and the imperfect contact at their

interface to explain the migration of fines to the surface. On the other hand, subsequent

studies (Alobaidi and Hoare 1996; Muramoto et al. 2006; Duong et al. 2014; Chawla and

Shahu 2016) proposed the existence of an apparent relationship between the rising EPP and

the vulnerability of fines for infiltrating the upper granular layers. The process of fluidized

fines transported upwards from the soil (subgrade) often results in the fouling of overlying

ballast causing a reduction in the inter-particle friction (shear strength) and impeding the

drainage capacity (permeability) of the granular assembly (Selig and Waters 1994; Ionescu

2004; Tennakoon and Indraratna 2014). In order to reduce maintenance and enhance the

longevity of ballasted tracks, the cyclic response of EPP and undrained strains in relation to

this fluidization process must be addressed (Indraratna et al. 2011).

Past laboratory investigations (Boomintahan and Srinivasan 1988; Alobaidi and

Hoare 1996; Ghataora et al. 2006; Trinh et al. 2012; Duong et al. 2014) have used physical

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model testing of a rigid cell containing saturated subgrade and ballast subjected to cyclic

loading. Although this approach could simulate mud pumping in the laboratory, the rigid cell

boundary cannot regulate the confining pressure in the subgrade. A few studies (Ghataora et

al. 2006; Duong et al. 2014; Chawla and Shahu 2016) have also applied a certain ‘free

drainage’ condition at the simulated subgrade surface. However, in reality, the fouling and

degradation of the substructure materials may impede the free draining capability of the

ballast. Therefore, a more realistic testing program that enables both the drainage and

confining pressure to be effectively controlled is imperative when investigating this

phenomenon of fluidization or mud pumping.

A primary scope of this study is to demonstrate the occurrence of shallow subgrade

fluidization under cyclic loading subjected to a low confining pressure mimicking typical

track conditions. So in this study, cyclic triaxial testing was adopted to study the fluidization

behaviour of a selected subgrade soil subjected to undrained cyclic loading. The role of

loading characteristics such as the confining pressure, frequency, and cyclic stress ratio

(CSR) was examined considering a typical in-situ subgrade. The undrained cyclic response of

saturated soil has been abundantly documented in the literature (e.g. Ishihara et al. 1975;

Yasuhara et al. 1982; Vaid and Chern 1985; Hyodo et al. 1991; Yasuhara et al. 1992; Hyodo

et al. 1994; Yang and Pan 2017). In a nutshell, these studies suggest that a reduction in

effective stress caused by cyclic excess pore pressures that would generally result in either (i)

stabilization upon soil recompression, or (ii) failure induced after excessive deformation. In

traditional sense of shear failure mechanism, the stress path reaches the failure line (FL)

followed by unacceptable large axial strains (Fig. 1a).

The rapidly increasing undrained strains initiated during liquefaction and train-load

induced mud pumping seem to have common causative factors in relation to the build-up of

excess pore water pressure. While Castro and Poulos (1977) clearly distinguish the

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liquefaction and cyclic mobility phenomena on the basis of laboratory experiments, the

problem of mud pumping involves the migration of fines from the subgrade in addition to the

rapid increase in the pore pressures (Alobaidi and Hoare 1996; Nguyen et al. 2019). In the

case of seismic liquefaction, the ground accelerations determine the response of the overlying

structure, e.g., earth dams (Ambraseys and Sarma 1967). While the above mentioned tell-tale

observations can describe the dynamic response of liquefiable low-plastic or cohesionless

soils (Singh 1996; Bray and Sancio 2006; Boulanger and Idriss 2007; Bahadori et al. 2008),

they cannot be readily extended to explain the mud pumping phenomenon. Liquefaction

being a deep-seated phenomenon occurring under the action of dynamic accelerations with

the effective stresses dropping to zero, whereas mud pumping occurs at shallow depths (i.e.

low confining pressure) due to the repetitive (cyclic) loading applied over a considerable

period of time at the subgrade-ballast interface as a result of long freight or heavy haul trains

(Duong et al. 2013; Hudson et al. 2016; Wheeler et al. 2017). Additionally, the heavy haul

train loading frequency range adopted to examine the cyclic behaviour of a subgrade soil (>

1.0 Hz) is significantly larger than that used for investigating liquefaction under seismic loads

(Muramoto et al. 2006; Indraratna et al. 2010; Trinh et al. 2012; Duong et al. 2014; Yang and

Pan 2017).

As shown later in this paper, the stress paths followed by laboratory soil specimens

that are vulnerable to fluidization (mud pumping) indicate a sharp drop in the cyclic deviator

stress due to strain softening as a result of large axial strains, but are accompanied by a non-

zero effective stress towards the failure line (Fig. 1b). In this regard, the scope of this paper

covers a testing scheme that aims to further clarify the mechanism of mud pumping, where

fluidized fine-grained soil (soft subgrade) tends to migrate upwards under a critical cyclic

stress ratio (CSR) subjected to a given frequency (f) of repeated loading over a significant

number of loading cycles, N.

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2. Experimental investigation

2.1 Soil properties

To investigate the cyclic behaviour of soil prone to mud pumping, natural soil samples were

obtained from a field site near the city of Wollongong that has had a history of mud pumping

(Fig. 2a). Laboratory tests were conducted to determine its properties such as the density,

particle size distribution (PSD) (see Fig. 2b), Atterberg limits and specific gravity (Table 1).

These tests classified the soil as a low plastic clay, CL of plasticity index of about 11 (ASTM

D2487-17 2017) with a clay content (finer than 4 m) of approximately 12% and an overall

fine fraction (< 75 m) of nearly 30%. The particle gradation also shows a large amount of

medium to coarse sand (Fig. 2b). The current natural soil has a relatively broad gradation

with a very high coefficient of uniformity and a filter ratio (i.e., D15coarse/D85fine) of about 5.8,

which indicates the soil is very susceptible to internal instability when excess pore pressure is

increasing (Skempton and Brogan 1994; Locke and Indraratna 2002; Kézdi 2013). Data

presented in Fig. 3 shows that mud pumping incidents are identified mostly for fine grained

soils having a low to moderate plasticity index (i.e., PI < 26) (Ayres 1986; Raymond 1986;

Alobaidi and Hoare 1996; Muramoto et al. 2006; Liu et al. 2013; Duong et al. 2014; Chawla

and Shahu 2016).

The samples of natural subgrade soil were reconstituted to produce test specimens of

different compacted dry densities (d), i.e., d = 1600, 1680 and 1790 kg/m3, and then tested

to investigate how the density could influence its cyclic response. The remoulded specimens

were 50 mm in diameter and had a height to diameter ratio of 2. The sample was prepared by

moist tamping to reduce the possibility of particle segregation (Ladd 1978) which has also

been adopted in previous studies (Lo et al. 2010). Additionally, non-linear undercompaction

criterion (Fig. 4) proposed by Jiang et al. (2003) was employed to achieve uniform density

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test specimens to ensure repeatability in the tests.

The in-situ dry density of the subgrade soil after subsequent mud pumping (i.e. 1803

kg/m3), was close to the maximum dry density defined by the laboratory Standard Proctor

compaction test conducted in accordance with ASTM D698 (Table 1). This implies that

subgrade mud pumping may still occur even if the subgrade had reached a relatively high

state of compaction (the relative compaction, RC ≈ 99%). Relative compaction is the

percentage ratio of the compacted density to the maximum dry density. Specimens of

relatively low dry density (i.e., 1600 kg/m3) were also tested because of disturbance caused

by past instabilities and/or the loosening of shallow subgrade during track construction. The

void ratios corresponding to this range of density are shown in Table 2 and the relative

compaction (RC), i.e. the ratio of the current specimen dry density to the maximum

laboratory-measured dry density is also noted.

2.2 Cyclic triaxial test

A series of cyclic triaxial tests at low confining stress was conducted on the reconstituted

specimens in undrained condition. Since the in-situ subgrade stresses are anisotropic (Wood

1991; Cai et al. 2018), a ratio of horizontal to vertical stress of 0.6 was determined for the

tested soil based on a previous study (Indraratna et al. 2009). A one-way stress-controlled

loading scheme (ASTM D5311-92 2004) was applied to model the real-life cyclic stress state

induced by train passage. The cyclic behaviour of the subgrade samples was examined using

a cyclic triaxial system, set up on an axially stiff loading frame with an electro-mechanical

actuator.

The cyclic stress ratio (CSR) is the ratio of the applied cyclic stress ( ) to twice the 𝜎𝑑

effective confining pressure ( ), as follows:𝜎′𝑐

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𝐶𝑆𝑅 =𝜎𝑑

2𝜎′𝑐[1]

An effective confining pressure of 15 kPa was used in this study in line with previous studies

(Indraratna et al. 2010; Liu and Xiao 2010; Trinh et al. 2012). Due to the fact that track

usually experiences varying magnitudes of stress for different axle loading (e.g., 15-35

tonnes), varying values of CSR were used by selecting different combinations of in order 𝜎𝑑

to represent the realistic loading conditions. Several authors (Liu and Xiao 2010; Milne et al.

2017) compute the vehicle passing frequency with respect to the vehicle speed and carriage

length [f = vT/lc; where vT = train speed (in m/s) and lc = length of the carriage (in m)].

However, some researchers compute the frequency acting on the ballast with respect to the

characteristic axle length (Indraratna et al. 2018). Powrie et al. 2007, reported that for a train

passing at 50 m/s (i.e., 180 km/h), the frequency acting at 1.0 m below the sleeper base is 4.0

Hz (Mamou et al. 2017). Therefore, the tested frequency range (1.0 Hz to 5.0 Hz) would

correspond to approximately 45 km/h to 225 km/h, train speeds. Interestingly, Wheeler et al.

(2017) observed the pumping of fines with train speeds as low as 40 km/h. Thus, the tested

frequency range (1.0 Hz to 5.0 Hz) is in-line with the expected frequencies acting on the

problematic subgrade (with 225 km/h representing the upper bound, for current Australian

conditions).

To ensure consistent testing conditions, the following parameters were controlled and

applied during the experimental program:

A back pressure of 400 kPa was applied over 24 hours to ensure that Skempton’s B-

value > 0.95 was achieved for saturating the test specimens, and the associated water

contents were determined according to the volume change of water inflow. The

corresponding average water contents at the three different compacted levels are also

given in Table 2.

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A sinusoidal wave form of cyclic load was applied, and the excess cyclic pore pressure

was measured using a pore pressure transducer located at the bottom of the test specimen;

Depending on the cyclic stress ratio (Eq.1), the applied cyclic stress was varied from an

initial deviatoric stress of 10 kPa to a value of 10 +d kPa, where d is the cyclic deviator

stress in the axial direction.

During the phase of cyclic shearing, the cell pressure was kept constant at 450 kPa while

the back pressure was at 435 kPa. The top and bottom drainage valves were kept closed

during the cyclic loading stage to simulate the undrained condition.

Testing was halted when the residual axial strains reached either 5% or when the number

of cycles reached 50,000. (In parts of Australia, the heavy-haul trains can be as long as

2.8 km (BITRE 2011), therefore, a four axle carriage, with 20.0 m carriage length, causes

about 280 loading cycles with every passage. The following study simulates roughly 180

continuous passes of the train, however, without any rest period. However, the provision

of rest periods would result in alleviating the generated excess pore pressures (Sakai et al.

2003; Mamou et al. 2017).

Membrane correction for undrained testing was applied according to ASTM (1995):

D4767-95.

Calibration of the pore pressure transducers and the LVDTs was carried out prior to every

test in order to ensure accuracy.

3. Results and Discussion

The pore pressure transducer and the linear variable differential transformer (LVDT) were

calibrated before every test to capture correct readings for every test. The response of the

pore pressure transducer and the LVDT at the two extreme tested frequencies (i.e. 1.0 Hz and

5.0 Hz) is shown in Fig. 5. For better clarity, only selected initial cycles are plotted but the

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same trend continues over the accumulated number of cycles. The peaks and the troughs

coincide with the applied loading, indicating that the transducers measure the reading without

any phase difference.

3.1 Factors governing the fluidization of subgrade

The build-up of excess pore pressure accompanied by the development of axial strain due to

undrained cyclic loads is influenced by factors such as the soil properties and loading

characteristics. In this study, the role of soil dry density (or relative compaction) is addressed,

along with the influence of both frequency and CSR of cyclic loads given that other physical

parameters such as initial PSD and plasticity remain unchanged.

Cyclic behaviour of subgrade

Typical examples of stress paths of soil (d = 1790 kg/m3) induced by the cyclic load at

different cyclic stress ratios (CSR) are shown in Fig. 6a. In this set of data, 1.0 Hz frequency

is chosen to demonstrate how the stress path response varies with value of CSR. Where the

CSR < 0.5, the cyclic axial strain (ac) of specimens gradually increases to a stable level as N

increases; for example, ac only changes slightly after it reaches 0.6% at N = 1000 cycles,

despite a continuous increase of N up to 50,000 cycles. However, where the CSR 0.5 there

is a rapid increase in cyclic axial strain which indicates soil failure at an early stage. For

example, where the CSR = 0.5, ac increases dramatically from 0.5% at N = 10 to 2.6% at N =

50, resulting in critical number of cycles, Nc ≈ 32. A steeper increment of axial strain with

N > 50 ceases at ac = 5%. Corresponding to this excessive deformation there is a drop in the

deviatoric stress in the stress path, when the CSR 0.5 (Fig. 7). It occurs in conjunction with

the large cyclic axial strains occurring when CSR 0.5. This indicates that the soil loses its

shear strength due to fluidization which tends to occur before the stress path reaches the

conventional undrained failure line. On the other hand, for the stable specimens (CSR <

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CSRc), the stress path does not reach the failure envelope (Fig. 7).

It is interesting to note that the undrained failure line represents a relatively high value

of the angle of shearing resistance, and this may be attributed to the specimen being

compacted to a very high Relative Compaction (RC ≈ 99%), as well as containing a

substantial amount (> 30%) of fine to medium sand (see Fig. 2). Such unusually high values

for the undrained friction angles have also been reported in the past for certain fine grained

clayey soils (e.g. Lo 1962; Dìaz‐Rodrìguez et al. 1992; Cola and Cortellazzo 2005). For

different densities, i.e., d = 1680 and 1600 kg/m3, the same behaviour is observed but

showing a distinct influence of CSR and frequency, as explained later in the paper.

The build-up of excess pore pressure under cyclic loads

This section describes the evolution of excess pore pressure which is the key driving factor in

the failure of soil by cyclic undrained loading. As the CSR is increased, the cyclic excess

pore pressure (EPP) also increases (Fig. 6b) however the incremental rate of EPP varies with

different values of CSR. Fig. 8a shows the rate of EPP build-up which is defined as the

incremental ratio between EPP and log(N), plotted against the logarithm of N, for f =1.0 Hz

and d = 1790 kg/m3. The results show that the rate of increment in EPP is almost identical

(i.e., the same slope of the curves) for CSR = 0.2, 0.3 and 0.4 despite them having different

initial EPP (i.e., at N = 1). All these curves become stable and with an insignificant change as

N > 2000, which indicates no further increment in EPP. Increasing CSR to 0.5 leads to a rapid

and continuous rise in EPP, especially when N > 10. For CSR = 1.0, the EPP turns into a

highly unstable state (i.e., sharp increase) just after 3 cycles.

Effect of cyclic stress ratio (CSR)

The effect of CSR on the cyclic response of the soil specimen has been partly shown in the

previous section, which indicates that there is a certain critical stress ratio (CSRc), where the

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excess pore pressure (EPP) begins to increase rapidly with a substantial drop in the deviatoric

stress q, indicating the inception of fluidization. The following section aims to demonstrate

how CSR can affect cyclic behaviour of the subgrade soil by plotting the largest incremental

rate of EPP over varying values of CSR. Fig. 8b shows the range of CSR where there is a

sudden jump in the incremental rate of EPP. It is evident that this abrupt change indicates a

critical or unstable state where the subgrade soil turns into slurry. This threshold value CSRc

varies with the dry density of soil and its loading frequency. For example, when CSRc is

between 0.4 and 0.5 for f =1.0 Hz and d = 1790 kg/m3, reducing the dry density to 1680 and

1600 kg/m3 results in a lower range of CSRc, i.e., between 0.3 to 0.4 and between 0.2 to 0.3,

respectively. However, despite these findings in the current study, a larger number of tests

with a wider array of CSR are still needed to accurately establish values at which subgrade

soil is fluidized.

Effect of frequency (f) on fluidization

The loading frequency has a significant effect on the development of cyclic axial strains (Fig.

9). For CSR < CSRc where the sample does not fluidize, a CSR of 0.3 which is smaller than

the critical level, there is some difference in the cyclic axial strain; basically, the larger the

frequency the greater the cyclic axial strain. For f = 1.0 Hz, ac gradually increases to 0.25%

at the end, i.e., N = 50,000 cycles but it increases faster to a larger level, i.e., 0.9 % for f = 5.0

Hz at the same N. Note that this cyclic axial strain represents the recoverable and the residual

component. The permanent deformation of the subgrade under undrained cyclic load is the

residual component that usually accumulates over a large number of cycles (Li and Selig

1996; Duong et al. 2014).

For CSR = 0.5 that is larger than the critical value CSRc, it is seen that the larger the

frequency (i.e., the faster the train speed), the later will be the inception of soil fluidization

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(Fig. 9). For example, a rapid growth of EPP and ar is triggered at N of about 32 cycles for f

= 1.0 Hz (i.e., after t = 20 s), but it takes nearly 3200 cycles (after 240 s) to reach the same

state when f increases to 5.0 Hz. A similar frequency dependent behaviour can also be found

in previous studies (Voznesensky and Nordal 1999; Zhou and Gong 2001; Andersen 2009;

Dash and Sitharam 2016) despite having different soils and cyclic properties; albeit the

influence of CSR on this fN relationship is sometimes missing with a small frequency level,

i.e., 1.0 Hz commonly used.

A smaller frequency implies a longer time period for the load to be acting on the soil

prior to unloading within a given cycle, leading to the development of larger residual excess

pore pressure (EPP) and axial strain of the test specimens. Referring to Fig. 5, which

indicates the evolution in EPP and axial strain corresponding to the applied cyclic loading at

different frequencies. It is observed that the residual EPP at f = 1.0 Hz is significantly larger

over the same time period compared to f = 5.0 Hz, leading to the larger total accumulated

EPP over N. Interestingly, this also corresponds to a greater accumulation of the residual

axial strain when f = 1.0 Hz compared to the larger frequency of 5.0 Hz. The above

observations lend support to the fact why a smaller frequency can at times initiate fluidization

earlier considering CSR > CSRc. However, it is noteworthy that smaller frequencies (e.g., 0.1

Hz) used in liquefaction research may not capture the same experimental observations; e.g.

Yasuhara et al. (1982) when compared to the relatively high frequencies typically applied to

soft subgrade beneath heavy haul tracks (Indraratna et al. 2011).

Stable and fluidized subgrade due to cyclic loads

For stable samples, increasing the number of cycles N leads to build-up of excess pore

pressure (EPP) and accumulation of cyclic axial strain (ac), but this trend gradually stabilizes

at larger values of N with respect to the limit of 50,000 cycles set in the current study (Fig.

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10a). In the case of fluidization, there is a rapid increase in EPP and ac after a certain number

of cycles, which is associated with a sharp drop in the deviator stress (q) and mean effective

stress (p’) (as seen from Fig. 7). While these observations corroborate with some past studies

of undrained instability of soft subgrade (e.g. Selig and Waters 1994; Hendry et al. 2012), it

is anticipated that the overall mechanism of subgrade fluidization and mud pumping should

be further addressed through the role of other governing factors too as discussed in the later

section.

The results indicate that the sample fluidizes when N reaches a critical value, Nc

corresponding to a rapid growth in excess pore pressure and axial strain. To identify Nc, the

rate of increment in axial strain over N is used, as shown in Fig. 10b. In general, the axial

strain evolution in those specimens is such that the fluidized and stable forms are represented

in convex and concave plots, respectively. A sharp rise in the incremental rate of axial strain

indicates the critical number Nc associated with the inception of fluidization of the specimens.

Similar trends for the stable and unstable sand specimens under cyclic loading were noted in

the past by various researchers (Youd 1973; Selig and Chang 1981; Katzenbach et al. 2004).

Effect of dry density

The frequency-dependent behaviour is also found in soils with different densities, as

shown in Fig. 11. For CSR > CSRc in which the sample is fluidized after the number of cycles

reaches the critical level Nc, almost a linear relationship between Nc (logarithm scale) and

frequency is observed, despite the difference in dry densities. The effect of frequency

becomes more apparent (i.e., the greater slope of the log (Nc)-f curve) when the soil has a

larger dry density. This is because, for a given loading frequency, the greater the dry density,

the greater the critical value of Nc. In stable cases (i.e. CSR < CSRc), the largest cyclic axial

strain (ac) after N = 50,000 cycles was considered to evaluate the influence of frequency. The

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soil with a higher dry density apparently results in less permanent deformation. Hence, one

may conclude that for CSR < CSRc, a train moving at a higher speed (larger frequency) can

cause more permanent deformation to the subgrade beneath the track. However, when CSR >

CSRc where the subgrade is susceptible to fluidization, the greater the train speed, the later

the inception of subgrade fluidization under undrained condition.

The samples with a greater dry density or relative compaction tend to resist cyclic

loads better under the same loading conditions. This results in a greater threshold for the

critical stress ratio CSRc (Fig. 12a). For example, samples with d = 1790 kg/m3 fluidize

when CSR 0.5, but at lower densities (1600 and 1680 kg/m3) the test specimens fluidize at a

lower CSR (0.3 and 0.4, respectively). Although specimens with a lower density can fail at a

smaller CSR, it takes more number of cycles to initiate fluidization at the corresponding

critical CSRc. As shown in Fig. 11, increasing the magnitude of CSR decreases the value of

Nc, which further clarifies how significantly the CSR can affect Nc in relation to a given soil

density.

For subgrade soils subject to a CSR < CSRc, the influence of varying dry density on

residual axial strain is of some concern. The axial strain of subgrade soil with a different

densities is compared under the same loading conditions, i.e., f = 1.0 Hz and CSR = 0.2 and

0.3 (only considering cases with CSR < CSRc) is compared. The results shown in Fig. 12

reveal the considerable influence that dry density can have on the permanent (residual) axial

strain (ar) of soil, such that the larger the density, the smaller the permanent strain. For

example, ar increases from 0.08 to almost 0.4 when d decreases from 1790 to 1600 kg/m3 at

the same CSR of 0.2; apparently the higher value of CSR results in a larger axial strain.

These findings also complement some previous studies (Georgiannou et al. 1991; Hyodo et

al. 1991) which indicate that reducing the void ratio by increasing the dry density or RC helps

to mitigate residual deformations as well as increasing the cyclic shear strength of subgrade

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soil.

3.2 Fluidization of subgrade soil due to cyclic load

Fig. 13a shows an example of a test specimen fluidizing under cyclic load (f =1.0 Hz, CSR =

0.5), where the upper part of the specimen forms a slurry (i.e. thick suspension of fine

particles). As the specimen is subjected to repeated loading with the help of the dynamic

actuator, the load acts on the top of the specimen. Here, under a combination of threshold

cyclic loading and frequency, excess pore water released by some densification of the middle

to the lower region of the specimen seemed to have migrated upwards carrying very fine

particles. The above type of instability could be conveniently examined by measuring the

change in water content over the specimen height after testing. For example, for a selected

specimen (d = 1790 kg/m3, CSR = 0.5, f = 1.0 Hz), the post-fluidization water content at its

uppermost part was measured to be 23.1%, in relation to the average water content of 20.1%

of the back-saturated specimen prior to applying the cyclic loading (see Table 2). The above

observations are further supported by large-scale testing conducted by Chawla and Shahu

(2016), where mud pumping under railway loading was simulated using physical modelling

of a track element, and a substantial increase in the water content was measured just beneath

the sleeper after instability.

In addition to measuring the change in water content along the failed specimen height,

its upper and central regions were examined in the Malvern particle size analyser

(Mastersizer). From Fig. 13b, it is clearly evident that a considerable amount of fines (< 75

m) has been accumulated in the upper part of the test specimen (≈ 36%) compared to that of

the middle region (≈ 24%), which previously had a fines content of as much as 30%, as

shown in Fig. 2b. This clarifies that during the application of cyclic loading, an upward

migration of fines transported by the displaced water can occur, thereby facilitating the

formation of a slurry or suspension in the near vicinity of the specimen surface. The changes

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in the water content and the particle size distribution were measured to be marginal at the

bottom quarter of the specimen, hence not plotted in Fig. 13b. A complementary study by

Takatoshi (1997) postulated that during heavy haul train passage, the cyclic nature of closing

and opening of a gap at the sleeper-ballast interface would generate a dynamic suction with

the effect of drawing up the moisture from the subgrade towards the sleeper. In a field

scenario, this suggests that the shallow part of the subgrade soil with substantially increased

water content (over-saturation) during continual cyclic loading, can become vulnerable to

fluidization upon heavy haul train passage.

4. Practical implications and future research

The results of this study reflect the relative roles of different causative factors contributing to

soil fluidization under cyclic loading. They are listed as follows:

Relatively high water content (close to the liquid limit)

Vulnerable fine-grained soil

Initial dry density (i.e., initial void ratio)

Magnitude of the applied cyclic stress

Confining pressure

Loading frequency

Duration of the loading (Number of cycles)

The effect of principal stress rotation due to the moving wheel loads is not considered in this

study, however, it is expected that the stress rotation will aggravate the pore pressure build-up

associated with residual strains (Gräbe and Clayton 2009; Mamou et al. 2017; Cai et al.

2018).

In order to predict whether mud pumping may or may not occur in contrast to quasi-

static undrained failure (i.e. rapid post-peak strain softening without fluidization) has been a

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dilemma for rail practitioners, given the significant increase in axle loads of long heavy haul

trains in recent times. Although some previous studies have reported conventional undrained

failure of soft soil foundations under cyclic loading (Hyde et al. 2006; Guo et al. 2017), it is

believed that these clayey soils would have been able to resist fluidization due to adequate

cohesion, compared to the low-plasticity soil tested in the current study.

In order to rationalise the current observations within a practical framework, all test

data have been plotted with an apparent fluidization representation, viz. cyclic resistance

chart, as illustrated in Fig. 14. For a known magnitude of CSR, the corresponding critical

number of cycles Nc can then be evaluated from Fig. 14. For example, a quasi-exponential

relationship between Nc and CSR is plausible for f = 1.0 Hz (R2 > 0.95). Nevertheless, this

simplified approach would not necessarily provide a credible prediction of the laboratory

behaviour when f reaches up to 5.0 Hz, given the larger scatter over the different soil

densities (R2 < 0.80). This suggests that more detailed investigation for quantifying the role

of subgrade dry density is required in relation to various critical combinations of CSR and

frequency, to accurately quantify the critical number of cycles Nc for initiating potential

fluidization.

While the current study provides some insight to better understanding of loading

conditions that may contribute to the inception of pumping (fluidization) of a low-plasticity

soil , further testing encompassing a broader array of cyclic loads applied to different types of

fine-grained subgrade (both cohesive and low-plastic soils) will need to be conducted in the

future. Additionally, the tests would to distinctly demarcate a slurry-state instability line from

that of a conventional undrained failure. In this regard, a few key questions remain to be

answered: (i) the exact role of the initial water content on the vulnerability of a given soil to

fluidization, (ii) quantifying the demarcation between a traditional undrained failure envelope

(no fluidization) and a potential state boundary for initiating mud pumping under different

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cyclic loading conditions, and (iii) the beneficial effect of internal ‘free draining’ due to the

presence of a significant sand/gravel fraction.

5. Conclusions

A series of undrained cyclic triaxial tests with varying CSR (0.1 to 1.0) and loading

frequency (f = 1.0 to 5.0 Hz) was carried out to investigate the cyclic loading response of test

specimens (N ≤ 50000 cycles) with varying compacted densities. The following salient

findings are highlighted:

The laboratory observations suggest that the mud pumping phenomenon under cyclic

loading can be explained by the internal redistribution of moisture to the upper regions of

the soil together with the upward migration of the finest particles (< 75 m). Naturally,

when the increased water content approaches the liquid limit of the soil, then a slurry-like

state is formed towards the top of specimen. In this regard, fluidization of low-plastic

fines can be considered as a special case of cyclic mobility that can occur in any type of

soil, as stated by Castro and Poulos (1977).

At relatively high water content, fluidization is triggered if the cyclic stress ratio (CSR)

exceeds a critical level, and this threshold varies depending on the dry density of the soil.

Overall, the results represented two distinct trends when a subgrade soil of low plasticity

was subjected to undrained cyclic loads over a significant number of cycles (N ≤ 50000

in current tests). While the stable samples experienced a decreasing incremental rate of

strain and excess pore pressure (EPP) build up, the fluidized samples experienced a rapid

increase in axial strain and EPP over the number of applied loading cycles N.

For those soil specimens which were susceptible to fluidization, the higher the

frequency, the greater the corresponding critical number of cycles Nc. When CSR <

CSRc the test specimens did not fluidize, irrespective of the compacted dry density,

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applied frequency and the number of loading cycles.

Acknowledgements

This research was supported by the Australian Government through the Australian

Research Council's Linkage Projects funding scheme (project LP160101254) and the

Industrial Transformation Training Centre for Advanced Technologies in Rail Track

Infrastructure (ITTC), University of Wollongong. The financial and technical support from

SMEC-Australia and ARTC (Australian Rail Track Corporation) is acknowledged.

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Tables

Table 1 Properties of subgrade soil collected from the mud pumping site after remediation

(Wollongong, Australia)

Characteristics of sub-soil Values

Liquid limit, LL 26%

Plasticity index, PI 11%

In situ moisture content1 14.6 %

Specific Gravity, Gs 2.63

Maximum Dry density (kg/m3) 1814

1Note: It is the water content of the subgrade after frequent occurrence of mud pumping

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Table 2 Summary of the specimen properties and loading conditions prior to the testing

Loading propertiesInitial dry

density(d,

kg/m3)2

Relative compaction

(RC)

Initialvoid ratio(e0)

Volume change during

saturation (cm3)

Averagewater

content upon back-

saturation Frequency(f, Hz)

Initial deviator

stress(kPa)

Constant confining pressure,

(kPa)𝜎′𝑐

Applied CSR

(Eq. 1)

1600 88% 0.644 30 24.62% 1, 2 and 5 10 15 0.1-0.4

1680 93% 0.556 24 22.27% 1, 2 and 5 10 15 0.2-0.5

1790 99% 0.469 18 20.12% 1, 2 and 5 10 15 0.2-1.0

2 Note: The specimens were compacted to an initial water content of 15%.

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Fig. 1 (a) Stress path during liquefaction and flow deformation of sands

(b) Axial strain evolution for different modes of failures

(c) Presumed stress path during the fluidization of soil under triaxial loading

Devia

tor

str

ess, q

Mean effective stress, p'

Failure line

Flow

deformation

Phase

transformation

line

Liquefaction

Axia

l str

ain

Number of cycles, N

Flow

deformation

Liquefaction

Shear

failure

(a) (b)

(c)

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a)

Fig. 2 (a) Severe mud pumping reported at a site near Wollongong, NSW

(b) Selected particle size distributions (PSD) in relation to various mud pumping studies

(a)

(b)

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Fig. 3 Mud pumping sites and corresponding soil properties related to plasticity

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Fig. 4 Specimen preparation using the nonlinear undercompaction method

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Fig. 5 Soil response at different frequencies over time: (a) excess pore pressure (EPP) and (b)

axial strain

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Fig. 6 Development of (a) cyclic axial strain and (b) Mean excess pore

pressure with varying CSR (d = 1790 kg/m3; f =1.0 Hz)

(a)

(b)

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Fig. 7 Stress paths for fluidized and stable specimens (d = 1790 kg/m3)

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Fig. 8 (a) Incremental rate of excess pore pressure (EPP) over increasing N (b) Peak

incremental rate of mean excess pore pressure vs CSR (d = 1790 kg/m3, f = 1.0 Hz)

(a)

(b)

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Fig. 9 Evolution of cyclic axial strain at different values of CSR and loading frequency

(d = 1790 kg/m3)

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Fig. 10 (a) Development of axial strain in stable and fluidized test specimens (b) Incremental

rate of mean EPP over increasing number of cycles

(a)

(b)

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Fig. 11 Effect of frequency on the (a) critical number of cycles (b) residual axial strain

(CSR < CSRc)

(a)

(b)

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Fig. 12 Effect of dry density on the (a) CSRc and Nc (b) residual axial strain (f = 1.0 Hz)

(a)

(b)

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Fig. 13 Post-fluidization analysis (a) Fluidized specimen subjected to CSR > CSRc

(b) Migration of fines within the fluidized specimen (1790 kg/m3, CSR 0.5, f = 1.0 Hz)

Very fine fraction < 75 m

Original PSD

(same as Fig. 2)

(a)

(b)

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Fig. 14 Cyclic resistance chart for different frequencies (fluidized specimens)

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A LABORATORY STUDY ON FLUIDIZATION OF SUBGRADE …