cyclic loading of railway ballast under triaxial conditions and in arailway test facility

7/31/2019 Cyclic Loading of Railway Ballast Under Triaxial Conditions and in Arailway Test Facility

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Granular Matter (2009) 11:391401

DOI 10.1007/s10035-009-0144-4

Cyclic loading of railway ballast under triaxial conditionsand in a railway test facility

B. Aursudkij G. R. McDowell A. C. Collop

Received: 14 May 2008 / Published online: 19 May 2009

Springer-Verlag 2009

Abstract A recently developed large-scale triaxial test app-

aratus for railway ballast testing comprises a double-cellarrangement for measuring volume change by differential

pressure. Monotonic and cyclic tests were performed on

limestone ballast samples. Axial and volumetric strains and

breakage were determined from both types of test. Resilient

modulus and Poissons ratio were obtained only from the

cyclic tests. The permanent axial strain and breakage results

from the cyclic tests are compared with the simulated traffic

loading in the railway test facility (RTF) which comprises

three sleepers embedded in ballast over a subgrade. The traf-

fic loading in the RTF was applied by hydraulic actuators

with built-in displacement transducers. A column of painted

ballast was placed under a rail seat of the middle sleeper to

ease sample collection for sieve analysis at the end of the

test. The stress condition in the RTF is predicted by a simple

calculation based on findings of previous literature. It was

found that the results from the cyclic triaxial test with con-

ditions similar to the predicted conditions in the RTF were

comparable to those results from the RTF tests.

Keywords Railway ballast Cyclic loading

Laboratory testing

1 Introduction

The rail network is one of the most important transportation

systems in everyday life. It provides a fast means of transpor-

tation by a durable and economical system. In the past, the

train and track superstructure, such as rails andsleepers were

B. Aursudkij G. R. McDowell (B) A. C. Collop

University of Nottingham, Nottingham, UK

e-mail: [email protected]

thefocusof attentionof railway engineers. Less attentionwas

given to the substructure such as ballast, subballast and sub-grade even thoughthey areas importantas thesuperstructure.

While the superstructure provides the main function of the

railway, the substructure provides the foundation to support

the superstructure and to help the superstructure to reach its

optimum performance.

Track settlement occurs afterlong-termservice.Excessive

settlement can cause poor passenger comfort, speed restric-

tion, andpotentialderailment. According to Selig andWaters

[17], most of track settlement occurs in the ballast layer. It is

also important to study the degradation of ballast to increase

and predict ballast life on the track, reduce waste ballast,

minimise the frequency and cost of ballast replacement, and

lead to further developments in the railway industry.

Performing experiments on ballast in railway track is

desirable since results can be obtained for real site condi-

tions. However, it is very difficult to control test variables

and to collect data on site. Hence, the RTF introduced by

Brown et al. [4] was developed to simulate the conditions

in a real track in a proper controlled way. It is a full-scale

railway track model housed in a concrete pit filled with sub-

grade material and ballast. However, a test in the RTF takes

a long time to prepare and perform and a lot of labour and

effort is involved. Therefore, a large-scale triaxial test appa-

ratus, in which testing is less time-consuming and requires

less labour and effort, was also developed. The triaxial test is

performed on a large cylindrical ballast sample. Unlike the

conventional triaxial testing equipment, the test apparatus

measures samplevolume changeof a drysampleby differen-

tial pressure instead of measuring the volume of water enter-

ing or leaving a saturated sample or sample radial expansion

by conventional on-sample transducers. However, secondary

methods for volume change measurement were used when

the designed equipment for measuring volume change was

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392 B. Aursudkij et al.

Fig. 1 Vertical stress at sleeper base contact [18]

not available. The aims of this paper are to introduce the

newly developed triaxial test apparatus and to compare the

results from the triaxial tests with the results from the railway

test facility (RTF).

2 Typical loading on ballast

To perform ballast testing in a laboratory, the typical loading

conditions for ballast should be known so that the tests sim-

ulate the real site condition of ballast. According to Shenton

[18], the maximum vertical stress in the ballast at the sleeper

contact varied between 200 and 250kPa under a 100kN load

on the sleeper as shown in Fig.1. This is comparable to

Raymond and Bathurst [15] who reported that the average

vertical stress at the sleeper-ballast interface was 140kPa.

Key [9] varied thedeviatoric stressbetween 12.5 and250kPa

in his triaxial tests on ballast.

Selig and Waters [17] performed a box test which was a

test that simulated ballast behaviour and performance under

field conditions. Ballast is placed in a box with a sleeper

segment shown in Fig. 2. The test can apply cyclic loading

to simulate traffic loading on the rail section as illustrated

by Lim [11] and shown in Fig. 3. Horizontal stress sensors

were installedon thewallof thebox to measure thehorizontal

stressin ballast.Theresults from oneof thesensorsare shown

in Fig.4. It can be seen from the figure that horizontal stress

in the ballast in the loaded and unloaded state (at maximum

and minimum load of the cyclic loading, respectively) fluc-

tuates between 20 and 60kPa and eventually reaches 30kPa.

Furthermore, according to Selig and Alva-Hurtado [16], the

in-situ confining pressure of self standing ballast perpendic-

ular to the rail was approximately 540kPa.

Thetypical loading frequency oftrafficloadingin thetrack

is normally around 810Hz for a normal train (by assuming

axle wheel spacing of 2.6m and train speed of 7594km/h)

and may reach 30Hz for a high speed train. However, load-

ing frequencies for different laboratory ballast testing vary

Fig. 2 Diagram of a box test [17]

300mm 700mm

Sleeper

Rail

Simulation Area

Fig. 3 Plan of rail and sleepers showing section representedby thebox

test [11]

depending on the capacity and constraint of each apparatus.

Compared to the magnitudes of vertical and horizontal load-

ing, the range of variation of loading frequency in laboratory

testing is significantly wider. This is because in real track,

high loading frequency increases the magnitude of dynamic

loading to the track caused by defects such as wheel flats or

welded joints on the track. Since the defects are not present

in laboratory testing, the loading frequency does not play an

important role. Key [9] applied 0.16Hz for the first 50 cycles

and then used 0.5Hz for the rest of the test. Shenton [18]

varied the loading frequency from 0.1 to 30Hz. However, he

used 0.1Hz for the first eight cycles in all of his tests. The

reason for applying low frequency during the beginning of

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Cyclic loading of railway ballast under triaxial conditions and in a RTF 393

Fig. 4 Effect of repeated load on horizontal stress in box test [17]

Fig. 5 Schematic diagram of the triaxial apparatus [1]

the test is that the deformations during the first few cycles

are generally large and they might exceed the capacity of a

testing machine in terms of the hydraulic oil flow required to

give the required deformation rate.

3 Large-scale triaxial test

3.1 Loading capacity

Figure5 [1] shows a schematic diagram of the triaxial test

apparatus. It can apply a constant confining stress of up to

1 MPa via pressurised air and water. This will be explained

in more detail in the later section which also involves the

volume change measurement system of this apparatus. The

apparatus is also capable of applying both monotonic and

cyclic loadings toa sample. Themaximumapplicable force is

100kN which is equivalent to a deviatoric stress of 1,415 kPa

on the designed sample (with 300mm diameter). The axial

load is applied to the sample by the movement of the bottom

ram against the stationary load cell at the top of the sample.

The maximum loading frequency of the apparatus is 10Hz.

However, the loading frequency in the performed cyclic tests

is limited to 4Hz due to the rate of oil flow that drives the

machine.

3.2 Volume change measurement

The principle of volume change measurement of this appara-

tus is based on the HKUST system presented in [13].It usesa

differential pressuremeasurement for volume change instead

of on-sample axial and radial displacement measurements.

This method was preferred due to the irregular outer surface

profile of the sample caused by the large size and angular

shape of the ballast. A conventional on-sample measuring

system such as strain collars would measure the localised

grain movement rather than the overall change in diameter

of the sample and would be difficult to attach to the irregular

surface of the sample such as the samples of [9,19].

The system uses water which is in direct contact with thesample membrane in an inner cell as shown in Fig. 5. Air at

a specified pressure is directed to the outer cell so that the

water in theneck is pressurised and consequently a confining

pressure is applied to thesample.As thepressuresin theinner

and outer cells are equal, the inner cell volume remains con-

stant so any change in the volume of the sample will displace

an equal volume of water in the inner cell.

The volume change is measured by recording the differ-

ential pressure between the water in the neck of the inner

cell and the water inside a reference tube using a differential

pressure transducer. At the beginning of each test, the water

levels in both the inner cell and reference tube are equal. If

the sample in the inner cell expands, the water level in the

inner cell rises while the water level in the reference tube

remains at the same level. The differential pressure trans-

ducer reading is converted to a volume change based on the

known cross-sectional areas of the inner cell neck and the

reference tube. However, the volume change from the dif-

ferential pressure transducer reading is the combination of

the sample volume change and the volume change due to the

displacement of the bottom ram movement. Therefore, the

volume change from the bottom ram must be subtracted to

obtain the sample volume change.

The differential pressure transducer cannot register the

volume change instantaneously. Therefore, the loading speed

must be sufficiently low. A loading rate of 1 mm/min and fre-

quency of 0.2Hz was used in the monotonic and cyclic tests

(for measuring resilient properties), respectively. The origi-

nal HKUST system was originally developed for a smaller

and more uniform sample and would probably measure

dynamic volume change at a higher frequency. A scale was

attached to the neck of the inner cell to double check the

accuracy of the volume change measurement. For the large

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y = 0.9895x

R2

= 0.9999

0

10,000

20,000

30,000

40,000

50,000

60,000

0 10,000 20,000 30,000 40,000 50,000 60,000

Volume change by bottom ram (mm3)

Volum

echangereading(mm

3)

Fig. 6 Calibration results of the differential pressure transducer

triaxial system used here, although the resilient volumetric

strain may not be accurate over one cycle at 0.2Hz, it is con-

sidered that the accuracy is sufficient to measure permanent

volumetric strain over many such cycles.

The differential pressure transducer can be calibrated by

displacing a known volume in the system by moving thebottom ram upward in increments. However, this has to be

done without a sample to ensure that the only volume change

that the transducer reads is from the bottom ram movement.

Figure6 shows the average calibration results from ten cal-

ibrations. It can be seen from the figure that the differential

pressure transducer is satisfactory.

However, the differential pressure transducer was not

available during some tests. Therefore, some other second-

aryvolumechangemeasurement methods that didnot require

a major modification to the existing system were used. For

monotonic tests, the scale, attached to the neck of the inner

cell, whose main purpose is to double check the accuracy

of the differential pressure transducer was used to measure

sample volume change instead. But this cannot be used with

cyclic tests as the movement of the water level was too fast to

be read with the scale. For a cyclic test, the ultrasonic prox-

imity transducer was used to measure volume change. The

ultrasonic proximity transducer shown in Fig. 7 uses sound

waves above the audible limit, to measure the distance from

a transmitter to a surface. It measures the time lag between

the transmitted sound waves and the return sound waves and

converts this to voltage. It is ideally suited to provide a non-

contact switching device or an analogue device to measure

fluid level. The only way of fitting it without a significant

modification was to carry out a test with the outer cell

removed. The transducer was clamped to a shaft support-

ing the load cell so that it could look directly down to the

water in the inner cell.

A test was then carried out with a sample under vacuum

in the inner cell as the external pressure could not be applied

with theoutercellremoved.Thissystem appearedtobework-

ing well for the low frequency up to 1 cycle per minute. How-

ever, at 4 Hz the upper shaft supporting the load cell could be

140mm long

Wave transmitter

located at the tip

of the transducer

Fig. 7 Ultrasonic proximity transducer (UPT) [1]

seen to be moving laterally, because the top platen was tilted

due to uneven settlement of the ballast. This would not hap-pen when the outer cell is in place as it acts as a support for

the upper shaft and keeps the top platen level. The test was

stopped at this stage and only test results up to 2,000 cycles

were obtained. However, the differential pressure transducer

had now been returned from the manufacturer and was used

in the remaining part of this test and the other cyclic tests.

3.3 Test sample

According to Skoglund [19], the diameter of a cylindrical tri-

axial test sample shouldbe approximately five to seven times

the maximum particle size of the sample for meaningful test

results. Since a typical maximum particle size of ballast is

50mm, the apparatus was designed for a sample of 300mm

diameter, i.e. six times the maximum ballast particle.

The height of the sample is 1.5 times the diameter, i.e.

450mm.However,BishopandGreen [3] suggested theheight

should be twice the diameter to eliminate the effect of fric-

tion at both ends of the sample. Nevertheless, the ratio of 1.5

enabled easier and more economical design of the cells in

this project. The governing factor was the rate of oil flow;

for typical resilient strains in ballast, the required displace-

ment rate at a maximum desirablefrequency of 10Hzwas not

feasiblehence a shorter sample was required. Duncan and

Dunlop [5] concluded that end friction caused an insignif-

icant increase in the angle of shearing resistance in their

drained triaxial tests on sand. Furthermore, they added that

lubricationat bothends wasnecessary whenvolumetric strain

neededto becalculated.This was because endfrictionusually

caused the triaxial sample to bulge into a barrel shape. This

means the diameter of the sample was not uniform through

the whole height of the sample which affects the calculation

of volumetric strain. However, this is not a problem in this

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0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70

Particle size (mm)

%P

assing Limestone

Specification

Fig. 8 Grading of limestone ballast sample and ballast grading

specification according to RT/CE/S/006 Issue 3 [14]

case with the double-cell arrangement since the volumetric

strain can be measured directly. Even though the overall vol-

umetric strain is measured by the differential pressure trans-

ducer, thevolumetric strain is stillnon-uniform. Additionally,an attempt wasmade to reducesample endfrictionby placing

a pair of 300 mm diameter circular latex sheets sandwiching

a film of silicone grease at each end of the sample.

Ballast whichfollows the UK ballast grading specification

RT/CE/S/006 Issue 3 [14] shown in Fig.8 is used to make

up a sample. The sample is prepared in a split aluminium

mould on a vibrating table. The bottom latex sheets, used

to reduce sample end friction, are placed at the bottom of

the sample. It should be noted that they had 20mm diam-

eter holes at their centres for drainage purposes. Ballast is

then filled in three layers with equal height. Each layer is

vibrated for thirty seconds with a 20kg surcharge on top ofeach layer. The sample mass ranges between 48 and 52kg,

corresponding to a bulk density of 1,5001,630kg/m3 and

void ratio of 0.6 to 0.7. The sample is covered by two layers

of latex membrane. The thicknesses of the inner and outer

membranes are 2 and 1mm, respectively. It was found that a

bicycle repair kit could be used to fix the holes in the mem-

branesif there were any. Another pair of latexsheetsis placed

at the top of the sample. This pair has no hole because drain-

age is not possible through the top of the sample. After that,

the silicone grease is applied in the top and bottom grooves

located at both sample ends. An o-ring is used to seal the

membranes into the groove at each end. Also, insulating tapeis put around both o-rings and two jubilee clips are used to

cover the o-rings. The jubilee clips hold the position of the

o-rings during a test while the tape helps to maintain an even

pressure on the o-rings.

3.4 Test procedure and programme

Both monotonic and cyclic tests were performed on lime-

stone samples. After each test, the sample is sieved to obtain

theparticle size distribution. Fora monotonic test, thesample

is initially put under a seating load of 1kN and then loaded at

1 mm/minuntil theaxialstrainreachesapproximately 12%to

ensure that the sample does not expand radially so much that

it touches and might damage the inner cell. Since the value

of axial strain is used as a finishing point of each test, the

maximum deviatoric stress for each test is unknown before

the test. However, the peak strength of the material shouldbe obtained by doing so. It should be noted that the differ-

ential pressure transducer was not yet available when con-

ducting the monotonic tests. The sample volume change was

obtained by reading the scale on the inner cell neck instead

as explained in Sect.3.2.

For the cyclic tests, one hundred thousand cycles of sinu-

soidal loading are applied to the sample. The sample is also

put under a seating load of 1 kN at the beginning of the test.

Then, the load is slowly increased to the mean load, i.e. the

midpoint between the maximum and minimum load of the

cyclic loading, at approximately 0.5kN per minute to avoid

a sudden dilation which might damage the inner cell andmake the water in the neck overflow. Subsequently, cycles

1 to 5 and 6 to 30 are loaded with durations of 5minutes

per cycle and 1minute per cycle, respectively. Then, most

parts of the test are performed with a frequency of 4Hz

untilcycle 100,000. However, cycles 31100, 181200, 481

500, 9811,000, 1,9812,000, 4,9815,000, 9,98410,000,

19,98120,000, 49,98150,000, and 99,981100,000 are

loaded at 0.2Hz to obtain the sample volume change. It

should be noted that during cyclic loading, the seating load

of 1 kN is always kept to ensure that the sample was always

in contact with the load cell. Unlike the monotonic tests, the

differential pressure transducer was used in the cyclic tests.

However, for one cyclic test, the volume change during the

first 2,000 cycles was measured by the ultrasonic proxim-

ity transducer. After that, the differential pressure transducer

was used instead as explained in Sect.3.2.

Three monotonic tests and four cyclic triaxial tests were

performed on limestone samples with constant confining

stresses of 10, 30, and 60kPa. The parameters of each test

can be found in Table 1. It should be noted that the names of

the monotonic tests indicate the confining stresses while the

names of the cyclic tests indicate both confining stresses and

maximum (q/p)max ratios.

3.5 Monotonic test results

Figure9 shows the plot of deviatoric stress against axial

strain. It can be seen that the deviatoric stress eventually

becomes stable and does not drop significantly. Figure 10

shows the plot of volumetric against axial strain. It can be

seen from the figure that after a short period of volumetric

compression, thesamplebegan to dilate. The test with 10kPa

has the largest dilation corresponding to its largest (q/p)max.

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Table 1 List of triaxial tests

Test type Test Confining Max (q/p)max Density

name stress deviatoric (kg/m3)

(kPa) stress (kPa)

Monotonica M10 10 N/A N/A 1,511

M30 30 N/A N/A 1,539

M60 60 N/A N/A 1,545

Cyclic C10/2.0 10 60 2.0 1,539

C30/2.0b 30 180 2.0 1,559

C60/1.5 60 180 1.5 1,600

C60/2.0 60 360 2.0 1,592

aAll three monotonic tests were performed without the differential

pressure transducerbThe ultrasonic proximity transducer was used only during the first

2,000 cycles. The differential pressure transducer was used afterwards

0

50

100

150

200

250

300

350

400

0 5 10 15

Axial strain (%)

Deviatoricstress(kPa)

M10 (10 kPa),q/p'max = 2.3

M30 (30 kPa),q/p'max = 2.2

M60 (60 kPa),q/p'max = 2.0

Fig. 9 Deviatoric stress versus axial strain from monotonic tests

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.00 5 10 15

Axial strain (%)

Volumetricstrain(%)

M10 (10 kPa),q/p'max = 2.3

M30 (30 kPa),q/p'max = 2.2

M60 (60 kPa),q/p'max = 2.0

Compression

Dilation

Fig. 10 Volumetric strain versus axial strain from monotonic tests

The volumetric straindata shows that thesamples were more

or less dilating at a constant rate after about 12% strain, sug-

gesting that a critical state was not imminent, but rather that

each sample hadreached andsustained its peak strength over

quite a large range of strain.

Figure11 shows the particle size distributions of the sam-

ples after the monotonic tests. It should be noted that only

particle sizes smaller than 22.4mm are shown in the figure

because thenumber ofparticleslarger than 22.4mmremained

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25

Size (mm)

%p

assing

M10 (10 kPa)

M30 (30 kPa)

M60 (60 kPa)

Fig. 11 Particle size distributions after monotonic triaxial tests

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 20,000 40,000 60,000 80,000 100,000

Permanent

axialstrain(%)

No. of cycles

C10/2.0, qmax = 60kPa

C30/2.0, qmax = 180kPa

C60/1.5, qmax = 180kPa

C60/2.0, qmax = 360kPa

Fig. 12 Permanent axial strains from cyclic triaxial tests

approximately the same after each test and no particles sma-

ller than 22.4mm were put in the sample before the test. It

can be seen from the figure that even though the breakage is

small, it increases with the decreasing level of dilation. This

findingagreeswith [7] whostated that thebreakageincreased

when dilation was suppressed.

3.6 Cyclic triaxial test results

According to Fair [6], thepermanentaxial strains from cyclic

triaxial tests on ballast from similarly prepared tests are not

consistent.Thecauseof this discrepancyis thebeddingerrors

occurring during the first cycle. Following that, the perma-

nent axial strains of the first cycles from all cyclic tests were

removed.

The permanent axial strains from the tests are shown in

Fig.12. It can be seen from the figure that with the same con-

fining stress, permanent axial strain increases with increas-

ing deviatoric stress or increasing (q/p)max. With the same

(q/p)max, the sample contracts more with increasing confin-

ing stress. Also, with the same maximum deviatoric stress,

permanent axial strain increases with increasing (q/p)max.

The permanent volumetric strains are shown in Fig. 13.

According to the figure, only the test with 10kPa shows

dilative behaviour (negative permanent volumetric strain).

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-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 20,000 40,000 60,000 80,000 100,000

No. of cycles

Permane

ntvolumetricstrain(%)

C10/2.0

C30/2.0

C60/1.5

C60/2.0

Compression

Dilation

Fig. 13 Permanent volumetric strains from cyclic triaxial tests

0

50

100

150

200

250

300

0 20,000 40,000 60,000 80,000 100,000

No. of cycles

Resilientmo

dulus(MPa)

C10/2.0

C30/2.0

C60/1.5

C60/2.0

Fig. 14 Resilient moduli from cyclic triaxial tests

However, test C60/2.0 dilates at the beginning of the tests

and then contracts after a few cycles. This might be because

themaximumdeviatoric stressin this test (360 kPa)was equal

to the peak strength of the sample under the same confining

stress in the monotonic test as shown in Fig. 9. Furthermore,

with thesame (q/p)max, onemightexpect thepermanentvol-

umetric strain to increase with increasing confining stress.

However, the strain from C60/2.0 is less than C30/2.0 prob-

ably because of the dilation at the beginning of C60/2.0.

The plot of resilient modulus (Mr) against number of

cycles is shown in Fig. 14. It was found that the final resilient

moduli followed the K model (Mr = k1k2, where

is the sum of principle stresses and k1 and k2 are empirical

constants; [10]) as shown in Fig.15. According to the figure,

k1 and k2 were found to be 6.7 and 0.6, respectively. The

Poissons ratios are shown in Fig. 16. It was found from the

figure that definite trend of Poissons ratio cannot be found

from the tests with the same (q/p)max. The fluctuations in

the resilient modulus and Poissons ratio results may be due

to the electrical drift that can affect the differential pressure

transducer as it is very sensitive.

Figure17 shows the particle size distribution of the fines

after each cyclic test. The breakage behaviour matches the

findings of [8]. According to them, the behaviour of ballast

Mr = 6.70.6

0

50

100

150

200

250

300

0 100 200 300 400 500 600

Sum of principle stresses (kPa)

Resilientmodulus(MPa)

C10/2.0

C30/2.0 C60/2.0

C60/1.5

Fig. 15 Resilient moduli versus sum of principal stresses

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 20,000 40,000 60,000 80,000 100,000

No. of cycles

Poisson'sratio

C10/2.0

C30/2.0

C60/1.5

C60/2.0

Fig. 16 Poissons ratios from cyclic triaxial tests

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25

Size (mm)

%p

assing

C10/2.0,max q =60 kPa

C30/2.0,max q =180 kPa

C60/1.5,max q =180 kPa

C60/2.0,max q =360 kPa

Fig. 17 Particle size distributions from cyclic triaxial tests

breakage resulting from cyclic triaxial tests with the same

maximum deviatoric stress can be divided into three zones

as shown in Fig. 18. The ballast breakage index in the fig-

ure indicates the breakage level based on calculation of area

under the particle size distribution before and after each test

as shown in Fig.19. The first zone is called the dilatant unsta-

ble degradation zone (DUDZ). In this zone, excessive radial

expansion occurs due to low confining stress (about 10

30kPa) and results in shearing and attrition of particle which

causes degradation. The second zone is called the optimum

degradation zone (ODZ) where the degree of degradation

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Fig. 18 Effect of confining pressure on particle degradation [8]

Fig. 19 Ballast breakage index in [8]

is smallest among the three zones and the confining stress

is about 3075kPa. This level of confining stress is able

to help the sample achieving the optimum particle arrange-

ment where the average number of contact per particle is

maximised and hence the probability of particle breakage

is reduced [12]. The confining stress in the third zone or

the Compressive stable degradation zone (CSDZ) is larger

than 75 kPa. In this zone, the breakage index increases with

increasing confining stress. Even though the maximum aver-

agenumber of contact perparticle canalso beachieved in this

Subgrade

Concrete slabs

Ballast

Geogrid(optional)

Sleepers

Loadactuators

Loadingframe

I-beam

I-beam

2.10 m

0.90 m

0.30 m

0.20 m

0.15 m

123

Fig. 20 End-view diagram of the facility [1]

zone, increasing confining stress level increases the stress atparticle contact and thus increases the breakage level.

Similar to the findings of [8], the breakages from C30/2.0

andC60/1.5 which have thesame maximum deviatoric stress

are similar as theybothare in the ODZ (thesecondzone).The

breakage from C60/2.0 is larger than C60/1.5 due to larger

deviatoric stress. Furthermore, the breakage from C10/2.0 is

comparable to C30/2.0 and C60/1.5. If the test with 10kPa

confiningstress hadthesamemaximumdeviatoricstresswith

C30/2.0 and C60/1.5, i.e. 180kPa, the breakage from that

test would have been larger than the two. However, the test

with 10kPa confiningstresspresentedhere hadthe maximum

deviatoric stress of 60kPa. Therefore, the level of breakagewas reduced so that it was comparable with C30/2.0 and

C60/1.5.

4 Railway test facility

4.1 Apparatus

A detailed presentation of the RTF has been given by Brown

et al. [4]. The RTF is housed in a concrete pit with dimen-

sions of 2.1 m(width) 4.1 m(length) 1.9 m(depth). A

schematic end-view of the facility and a photo are shown in

Figs.20 and 21 [1], respectively. Figure 20 [1] shows that a

geogrid can be placed at the bottom or at any point in the

ballast layer but it was not used in the test presented here.

The pit was filled with subgrade material and railway ballast.

Silt was chosen as the subgrade material because of its

availability and ease of placing and compaction. It was com-

pacted in 180-mm layers using a plate vibrator to a depth of

900mm. After compaction, it had a density of 1,770kg/m3,

surface stiffness of approximately 18.42MPa, anda moisture

content of 15.5%. The ballast used in the RTF is the same

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Fig. 21 The railway test

facility [1]

12

3

Sleeper

number

LVDT

(front end)

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Time (s)

Load(kN)

Actuator 1

Actuator 2

Actuator 3

Fig. 22 Loading pattern in the railway test facility [1]

type of ballast used in the triaxial tests, i.e. limestone. Theballast was placed and compacted in 100-mm layers by the

same plate vibrator to a depth of 300mm.

Three concrete sleepers were embedded in the ballast.

Loading is transmitted from three servo hydraulic actuators

to the sleepers by means of the spreader beams (three steel

beams on top of the sleepers in Fig. 21 [1]) located on rollers

on the rail seatings. Each actuator has a built-in vertical dis-

placement transducer for recording the settlement. In addi-

tion to the vertical displacement transducer in the middle

actuator, the settlement of the middle sleeper was also mea-

sured from two LVDTs: one at each end of the middle sleeper

(as shown in Fig.21 [1]) to double check the settlement read-ing from the middle actuator.

4.2 Test procedure

Simulated traffic loading is achieved by applying sinusoidal

loading with maximum magnitude of 94kN and 90 degree

phase lag between each actuator as shown in Fig.22 [1]. This

loading pattern was suggested by Awoleye [2]. It is intended

to simulate a train running over three sleepers with 50% of

the wheel load on the middle sleeper and 25% of the wheel

load on the outer sleepers. With this loading pattern, the RTF

simulates an axle load of approximately 20tonnes which is

comparable to a typical heavy axle load on top of the middlesleeper. Due to the pressure and flow capacity of the hydrau-

lic pump in the laboratory, the loading frequency in the RTF

was limited to 3Hz.

Simulated traffic loading of one million cycles is applied

to the ballast in the RTF. Before a test, a 300-mm diameter

column of painted ballast is placed under the front-end rail

seat of the middle sleeper to aid sample collection after the

test. To obtain the settlement, the position readings from the

three actuators and two LVDTs located at both front and rear

ends of the middle sleeper are recorded when all sleepers are

held at 1kN load to ensure that they are in contact with the

actuator. The readings are manually taken before the cyclicloading begins and after cycles 100, 1,000, 2,000, 5,000,

10,000, 20,000, 50,000, 100,000,150,000,200,000,250,000,

300,000,400,000,500,000, . . ., and1,000,000.After the test,

the painted ballast column is collected for sieve analysis.

5 Result comparison: triaxial and railway test facility

tests

A simple analysis can be performed to estimate the stress

conditions under the loading area of the RTF and to compare

the results with the triaxial tests. This analysis is based on the

findings from [17,18]. From Fig. 1, Shenton [18] found that

the maximum contact pressure at sleeper base was approxi-

mately200250 kPa. According to Selig andWaters [17], the

observed horizontal stress in ballast fluctuated but eventually

reached 30kPa as shown in Fig. 4. In other words, this is a

typical residual horizontal stress in ballasted tracks.

From both findings, it is reasonable to simulate the con-

dition of ballast under traffic loading in the RTF by a cyclic

triaxial test with constantconfiningstressof 30kPa andmaxi-

mumaxial stress of 200250 kPa. Thevalues of theconfining

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0.0

0.20.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 20,000 40,000 60,000 80,000 100,000

No. of cycles

Perm

anentaxialstrain(%) C10/2.0

C30/2.0

C60/1.5

C60/2.0

RTF

Fig. 23 Permanent axial strains from cyclic triaxial tests and railway

test facility

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20 25

Size (mm)

%p

as

sing

C10/2.0

C30/2.0

C60/1.5

C60/2.0

RTF

Fig. 24 Particles smaller than 22.4mm from cyclic triaxial tests and

railway test facility

stress and maximum axial stresses result in (q/p)max from

1.96 to 2.13. This stress condition matches the condition oftest C30/2.0 (30kPa confining stress and (q/p)max of 2.0).

The permanent axial strains and particle size distribution

from the cyclic triaxial tests are compared to the permanent

axial strain of the middle sleeper and the particle size dis-

tribution of the painted ballast from the RTF as shown in

Figs.23 and 24. The permanent axial strain from the RTF

was obtained by dividing the settlement by the ballast height

prior to the test (300mm). It should be noted that since the

first data point of strain starts at cycle 100 in the RTF, the

strains of thefirst 100cycles from allcyclic triaxial tests were

removed to compare the results on the same basis. Also, the

strain from the RTF after cycle 100,000 is not included inthe plot as the triaxial tests were performed for only 100,000

cycles. It can be seen from both figures that the results from

test C30/2.0 are very close to the RTF results as expected.

6 Conclusions

A new large-scale triaxial test apparatus for testing a

cylindrical sample of railway ballast has been developed.

The apparatus records the sample volume change by mea-

suring the difference between the level of pressurised water

surrounding the sample and the fixed level of water under

the same pressure by the differential pressure transducer. As

the system cannot detect the volume change instantaneously,

the loading speed must be sufficiently low. However, when

thedifferential pressure transducer wasnotavailable, thevol-

ume change was measured by recording the change in level

of pressurised water surrounding the sample instead.Both monotonic and cyclic triaxial tests were performed

on limestone samples with grading within the standard spec-

ification. Three monotonic tests with constant confining stre-

sses of 10, 30, and 60kPa were performed. It was found that

the samples reached their peaks strength when they were

loadeduntilapproximately12%axialstrain.Thesample with

lowest confining stressgave thelargestamountof dilationbut

the smallest amount of breakage.

Four cyclic tests were performed. Three were performed

with (q/p)max of 2.0 and each with confining stresses of

10, 30, and 60kPa. The other test was performed under

confining stress of 60 kPa and (q/p)max of 1.5. It was foundin the cyclic tests with the same (q/p)max that the permanent

axial and volumetric strains increased with increasing con-

fining stress. However, in the test with 60kPa confining stress

and (q/p)max of 2.0, thesample dilated for thefirst few cycles

and then contracted. This might be because the maximum

axial stress equalled the peak strength of the sample under

monotonic loading, when large amounts of dilation occurred.

The resilient modulus was found to follow the K model.

Also, even with small deviatoric stress, the breakage from

the test with 10 kPa and (q/p)max of 2.0 was comparable to

the other tests with much larger deviatoric stress except for

the test with 60kPa and (q/p)max of 2.0. This is because

the test with 10kPa and (q/p)max of 2.0 showed dilative

behaviour.

A RTF has been built in a concrete pit and comprises sub-

grade material, ballast, and three sleepers. The sleepers are

loadedwith outof phasesinusoidal loading to simulate traffic

loading. The settlement can be recorded by the displacement

transducers in the loading hydraulic actuators. A column of

painted ballast with 300-mm diameter is placed under the

front-end rail seat of the middle sleeper to aid ballast collec-

tion for sieve analysis after the test.

A simple analysis based on typical observed residual hor-

izontal stresses and bearing stresses beneath sleepers gives

rise to a stress regime consistent with that used in the triaxial

tests. According to the analysis, the stress conditions under

the loading area of the RTF are similar to a triaxial test with

30kPa confining stress and (q/p)max ratio from 1.96 to 2.13.

Thepermanentaxial strainandparticle size distribution from

the triaxial test with confining stress of 30 kPa and (q/p)maxratio of 2.0 were found to be very close to the RTF. This

calculation gives some confidence that the stresses applied

in the triaxial tests were appropriate to in-situ conditions.

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cyclic loading of railway ballast under triaxial conditions and in arailway test facility

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