Influences of railway ballast sand contamination on loading pattern of pre-stressed concrete sleeper

Prévia do material em texto

Construction and Building Materials 233 (2020) 117324
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Construction and Building Materials
journal homepage: www.elsevier .com/locate /conbui ldmat
Influences of railway ballast sand contamination on loading pattern of
pre-stressed concrete sleeper
https://doi.org/10.1016/j.conbuildmat.2019.117324
0950-0618/� 2019 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.
E-mail addresses: ar_tkian@alumni.iust.ac.ir (A.R. Tolou Kian), javad_sade-
ghi@iust.ac.ir (J. Sadeghi), zakeri@iust.ac.ir (J.-A. Zakeri).
Ali Reza Tolou Kian, Javad Sadeghi ⇑, Jabbar-Ali Zakeri
School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran
h i g h l i g h t s
� Mechanical properties of sand-contaminated ballasts were experimentally obtained.
� Sleeper loading pattern in sand contamination condition of ballast was derived.
� New pattern for stresses under sleeper was developed for sand fouling condition.
� The values of stresses under sleeper were derived as a function of track condition.
� Current codes for design of sleeper were extended to include sand fouling condition.
a r t i c l e i n f o
Article history:
Received 26 January 2019
Received in revised form 12 October 2019
Accepted 17 October 2019
Keywords:
Ballast
Dry sand contamination
Concrete sleeper
Strain modulus
Direct shear test
Railway track
Design approach
a b s t r a c t
Effects of sand contamination of railways on the loading pattern of pre-stressed concrete sleepers were
investigated, using a FE model of railway track developed and validated in this research. To derive prop-
erties of contaminated ballasts, various laboratory tests were conducted. For the investigation, paramet-
ric analyses of the model were conducted in which the tests results were taken into the model as the
input data. A threshold for ballast sand-contamination level, beyond which sleeper responses were con-
siderably influenced with the contamination, was obtained. New mathematical expressions were derived
for the sleeper loading pattern by considering the effects of ballast sand contamination.
� 2019 Elsevier Ltd. All rights reserved.
1. Introduction
Sleepers and ballast are important components of a ballasted
railway track. The key functions of sleepers are to maintain track
geometry, provide lateral stability of the track, sustain the rail
forces and transfer the load to the ballast layer [57,56,55,18,19].
Ballast transmits the loads from sleepers to the sub-ballast layer,
maintains the track superstructure against lateral and longitudinal
loads, and damps the track-induced vibrations [60,25,46,71,72].
Supporting conditions and stability of sleeper are strongly depen-
dent on the ballast layer conditions. The main sleeper and ballast
design criteria are the sleeper bending moments and the level of
stresses imposed on the ballast layer. In other words, sleeper rail
seat loads and pressure distribution beneath the sleeper are the
sleeper main design parameters AREMA [3]. These are dependent
on the interaction between sleepers and ballast which is consider-
ably influenced by ballast conditions [85,27,37,79]. For instance,
after tamping process, ballast pressures are mostly concentrated
underneath the rail seat positions as indicated in Fig. 1(a).
Following accumulation of train passages, distribution of contact
pressures changes and the pattern of compressive stresses distri-
bution beneath the sleeper becomes more uniform (Fig. 1(b))
[55,79].
A review of the literature indicates that various patterns of
stress distributions beneath the sleeper have been suggested
(Table 1). The contact pressures pattern under the sleeper
influences the amounts and location of maximum and minimum
sleeper bending moments (i.e., sleeper design criterion).
A ballast layer gets contaminated due to mainly breakage of
ballast aggregates and/or infiltration of fine materials from the
subgrade layer and ballast surface to the ballast layer
[60,68,71,72,67]. For instance, sometimes, railways face frequent
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mailto:javad_sadeghi@iust.ac.ir
mailto:javad_sadeghi@iust.ac.ir
mailto:zakeri@iust.ac.ir
https://doi.org/10.1016/j.conbuildmat.2019.117324
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Table 1
Various patterns of sleeper-ballast contact pressure distribution suggested in the
literature.
Distribution of sleeper-
ballast contact pressure
Developers Comments
Talbot [65] Maximum pressure
at ends
AREMA [3], AS 1085.14
[4], Talbot [65]
Uniform contact
pressure
ORE [49], Talbot [65] Well-tamped rail
seat and sides
UIC [74] Maximum pressure
under rail seat
Talbot [65] Maximum pressure
at mid-span
UIC [74], Talbot [65],
Kerr [34]
Perfectly-tamped
sides
Sadeghi [54] Modified pressure
distribution
gnidaolevitalumuccaretfA)b(gnipmatretfathgiR)a(
Fig. 1. Pattern of ballast contact pressures beneath the sleeper.
2 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
sand storms, causing contamination of the railways with sand. This
phenomenon has been often reported in China, India and the Mid-
dle East and North African countries [77,58,71,72,16]. Some views
of ballasted tracks contaminated with sands in Yazd province of
Iran are shown in Fig. 2.
When the ballast gets contaminated with sand, it fails to play its
roles, and consequently the track safety is jeopardized [32,71,72].
Railway industries face critical challenges in sandy areas since
track components get damaged. For instance, sleeper breakage
has been frequently reported in these areas [80,58]. Review of
the literature indicates that although the responses of sleeper with
unsupported conditions (i.e., hanging sleeper) or with insufficient
ballast stiffness have been investigated in the available literature
[41,33,32,82,63,30,76,36–38,3,58,2,78], there is no trace of any
investigation into the effects of ballast contamination on the sleep-
ers mechanical behavior. Because of the important role of sleepers
in the track support system, there is a need to investigate the slee-
per behavior in the sandy areas. This study is a response to this
need. The effects of various dosages of sand-contamination of bal-
last on the main sleeper design parameters including rail seat load
and sleeper-ballast loading pattern were investigated in this
research. For this purpose, a three-dimensional finite element
model of ballasted tracks was developed. The model consisted of
track superstructures as well as substructures. The model validated
(a) Highly contaminated tarck
Fig. 2. Views of ballasted tracks with different levels of sa
with the results of a comprehensive field test carried out in this
study. The mechanical properties of ballast contaminated with dif-
ferent dosages of dry windblown sand, were obtained from direct
shear tests and plate load tests (PLTs) in the laboratory of the
School of Railway Engineering. The test results were imported into
the model and thereafter, through parametric analyses of the
model, the effects of ballast sand contamination on the sleeper
response (loading pattern) were investigated. The loading pattern
includes the rail seat load, the wheel loads distribution on the con-
secutive sleepers, and the sleeper-ballast loading pattern. Using
the results obtained, the current sleeper loading patterns were
extended by developing new expressions for the sleeper response
as a function of ballast level of contamination. This research pre-
sents new mathematical expressions for design of railway concrete
sleepers which extend application of the current codes of practice
including windblown sand-contamination conditions.
2. Vehicle-track interaction model
Various models have been developed to investigate vehicle-
track interaction. For instance, railway critical velocity and vibra-
tion propagation inrailway track systems have been studied by
Sheng et al. [62] and Mazher et al. [45]. In this study, a three-
dimensional finite element model of ballasted railway track for
evaluation of effects of sand contamination on mechanical behav-
ior of sleepers was developed in the ABAQUS software. It comprises
track superstructure (i.e., rail, rail pad, pre-stressed sleeper) and
track substructure (i.e., ballast, sub-ballast and subgrade layer).
Two views of the model are presented in Fig. 3. The properties of
the track components (except ballast) were considered linear elas-
tic (as suggested in the literature [56,7,63,41,36,37,23]). Ballast
behavior was modeled using the Mohr-Coulomb plasticity model.
This model has been proposed and frequently used in the literature
for modeling of mechanical behavior of ballast materials [17,61].
For instance, ballast settlement under cyclic loading [61], stress
distribution in ballast [13,12,26], and stress distribution in
sleeper-ballast interface [24] have been investigated using the
Mohr-Coulomb plasticity model. Using the Mohr-Coulomb model,
the friction angle of ballast materials was taken into account in
the FE simulation. According to the literature [52,66,47,44,51],
the input parameters of the Mohr-Coulomb model can be derived,
using results of direct shear test and PLT. Some of the literature
(b) Moderatly conatminated track
nd-contamination in Iranian eastern railway network.
b) Spring-dashpot used as rail pad in the modela) General view of the model
Fig. 3. Views of the model developed in present study.
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 3
indicates that the Mohr-Coulomb failure envelope for the ballast
and other rock-fill materials is non-linear in practice although its
mathematical expression is presented in a linear form
[40,31,75,72]. In fact, the failure envelopes of the shear stress are
curved and cross the zero intercept [31,72]. Therefore, the cohesion
for the clean and sand-contaminated ballast samples was consid-
ered zero in the model. Properties of the ballast with various
dosages of dry windblown sands were obtained from the tests
(i.e., direct shear tests and repeated plate load tests) conducted
in this study. The tests results were used as model inputs. Rails,
sleepers, ballast, sub-ballast and subgrade layers were simulated
with the brick (eight-node) solid elements. The spring-damper ele-
ments were used to simulate the rail pad underneath the rail. Truss
elements with initial pre-stressing forces were used to simulate
the pre-stressed tendons of the sleeper. Geometry and material
properties of the rail and the sleeper were taken from the proper-
ties of the UIC60 rail and B70 pre-stressed concrete sleeper (used
in the Europe and the Middle East countries). The depth of the bal-
last was assumed 300 mm (as in the field). Also, sub-ballast and
subgrade layers thicknesses were considered 200 and 4700 mm,
respectively. The length of the model was 12.6 m which includes
21 sleepers with 600 mm spacing. It has been shown in the litera-
ture [56,27,37,36] that the dimensions of the model are sufficient.
Through parametric analyses, it was also shown that any increase
in the depth, length or width of the model makes less than 1%
change in the results.
Using viscous boundaries, it was ensured that the wave reflec-
tion at the model boundaries was eliminated [42,28,41,56]. To sim-
ulate the in-field condition of the ballast-sleepers interaction, any
transfer of tensile stress between the sleeper and the ballast was
not allowed. To this end, a contact between the sleeper and the
underlying ballast was defined by the use of the penalty method
in which the contact force at each node in the sleeper-ballast inter-
face is proportional to the sleeper vertical deflections respect to the
underlying ballast. Any relative displacement between the sleeper
and the ballast layer was not allowed in the lateral and longitudi-
nal directions by defining tangential contact between the sleeper
and the ballast as suggested in the literature [28,56]. Through sur-
vey of the literature [81,6,56,83,5] method of loading of the model
was adopted. That is, in order to load the track model, a single
wheel-set with no lateral and longitudinal forces is considered
(i.e., there is no displacement of the sleeper in the lateral and lon-
gitudinal directions). According to the literature, this is an appro-
priate approach for investigation of short-term response of track
[39,56]. The wheel-set included two wheels only (i.e., loading of
the track model comes from one axle of a vehicle). To model
wheels of the wheel-set, rigid plates (i.e., plates with a high bend-
ing stiffness) were used. Surface of the plate was similar to inter-
face area of the wheel and the rail. Half of axle load of the
vehicle was applied to the plates [41,56]. Only the normal forces
of the wheels were considered in the simulation. Frictionless con-
tact was used for the wheel-rail interface in the tangential direc-
tion. In order to define load transfer mechanism in vertical
direction between the plates (i.e., the wheels) and the rail,
surface-to-surface contact was considered for the wheel-rail inter-
face in normal direction. For the simulation of the normal contact
between the wheel and the rail, penalty method was used
[28,41,56]. The penalty method was used to define the interaction
between the wheel and the rail such that the wheel-rail contact
force was proportional to the wheel vertical deflection respect to
the rail. The wheels were run with a constant speed on the top
of the rails head in longitudinal direction of the track. This method
of modeling the wheels simulates constant vertical forces moving
along the rails.
3. Model validation
In order to validate the model, a comprehensive field investiga-
tion was carried out in the Iranian railway network and the results
obtained were compared with those of the model (i.e., the rail and
sleeper vertical displacements, measured in the field test, were
compared with those obtained from analysis of the model). The
details are presented hereunder.
3.1. Field test
Field test was made in the eastern Iranian railway network
called Bafgh-Mashhad railway line in Khorasan province (Fig. 4).
This line is considerably contaminated with sands due to frequent
sand storms. The section of the line considered in the test is
straight with no gradient. Track components included UIC60 rails,
B70 pre-stressed concrete sleeper (with 0.6 m spacing), and ballast
made of basalt aggregates. Three LVDTs were used in the test, one
mounted on the rail foot between the sleepers, the second one on
the sleeper end, and the third one on the rail web. The in-situ test
setup is presented in Fig. 5. As indicated in this figure, the LVDTs
were set on the concrete sleepers and connected to the steel frame
(Fig. 5a). This frame was fixed to the ground (the benchmark) two
meters away from the rail (Fig. 5b).
Track responses were recorded with TMR-211 data recording
system and the sampling rate was set to 1000 (Hz). Track responses
due to the passages of a freight train weremeasured. The train com-
posed of one GE locomotive and twenty five wagons (Fig. 6a and b).
The GE locomotive and wagons have two bogies with three and two
axles, respectively. The train axle load was 225 (kN). The configura-
tion of the train is indicated in Fig. 7. The rail and sleeper displace-
ments measured in the tests are presented in Fig. 8. There were six
consecutive empty wagons (i.e., without goods) within the train;
this can be depicted in Fig. 8 where the track deflections under the
empty wagons were smaller than the others.
For the validation of the model, properties of the track compo-
nents were measured and imported into the model as the model
input. For this purpose, plate load tests (PLTs) were conducted on
Fig. 4. Map and view of the field test location in Iran railway network.
(a) Position of LVDTs conneted to the steel fame (b) Steel framefirmly fixed to the ground
Fig. 5. In-situ test setup.
nogawthgierF)b(evitomocoL)a(
Fig. 6. Train passage during the field test using TMR-211 data logger and laptop computer.
Fig. 7. Distance between axles of the train (in m).
4 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
the ballast and subgrade layers in the field. The tests were made in
two steps. First, the sleeper (on which the LVTD was connected)
was removed from the track (right after the completion of the dis-
placement measurement) (Fig. 9a) and then, the PLT was carried
out on the ballast beneath the left rail seat of the sleeper. The tests
were carried out in accordance with DIN 18134 [86]. In the second
step, the ballast was dug and the PLT was made on the subgrade.
The results of the plate tests are presented in Fig. 10. This figure
indicates the settlements versus the pressures obtained from the
PLTs performed on the ballast and subgrade layers.
To measure density of the ballast, the method suggested by
Selig and Waters [60] was adopted. Measurement of the ballast
repeelsnoliarfotnemecalpsiD)b(repeelsfotnemecalpsiD)a(
(c) Displacement of rail between sleepers 
Fig. 8. Results of In-situ measurement of track displacements.
tsallabnoTLP)b(TLPgnitcudnocrofrepeelsafolavomeR)a(
(c) PLT on subgrade 
Fig. 9. PLT setup in the track.
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 5
Fig. 11. In-situ density measurement of ballast.
Table 2
Strain modulus obtained from PLTs (MPa).
Layer on which test was conducted EV1 EV2
Ballast layer 22.9 61.2
Subgrade 27.3 75.2
(a) size distribution of sand material
Fig. 12. Particle size distribution of b
edargbusnoTLP)b(tsallabnoTLP)a(
Fig. 10. . Pressures versus settlements obtained from PLTs.
6 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
density was made for the ballast beneath the right rail seat of the
sleeper (Fig. 11). Test result indicates that the density of contami-
nated ballast is 1885 kg/m3. From analyses of the results obtained,
the strain modulus of the ballast and subgrade in the first and sec-
ond cycle of the loading were derived. They are presented in
Table 2.
In order to measure the degree of ballast sand contamination in
the field, samples of the ballast were obtained in accordance with
ASTM D75/D75M [11]. Sieve analyses of the ballast and sand sam-
ples were conducted in accordance with ASTM C136 [9]. The
results obtained are presented in Fig. 12. To determine the level
of ballast contamination, the percentage of fouling (contamination)
was used as a contamination index, which is defined as the ratio of
the dry weight of the particles smaller than the 9.5 mm to the dry
weight of the sample [60]. Sieve analysis of ballast samples indi-
cates that the percentages of contamination of ballast layer were
approximately 25%. Water content of the ballast and sand samples
was determined in accordance with ASTM D4643 [8]. The results
indicate that moisture of the ballast and sand samples was approx-
imately 0% (less than 1.5%).
The track in the field test has UIC60 rails with a moment of iner-
tia of 30.55 � 106 mm4 and elastic modulus of 210 GPa. The flexi-
ble rail pads were from high density polyethylene (HDPE) with
200 kN/mm stiffness. Sleepers of the track were B70 pre-stressed
concrete sleeper with length of 2.6 m, mass of 300 kg, and elastic
modulus of 37 GPa. B70 sleeper has eight steel pre-stressed ten-
dons with diameter of 7 mm and elastic modulus of 210 GPa. To
obtain Mohr-Coulomb model parameters of the ballast, laboratory
large-scale direct shear tests were made on the ballast samples
(b) size distribution of ballast material
allast and sand in the field test.
sexobraehsfohtdiW)b(sexobraehsfothgiehdnahtgneL)a(
Fig. 13. Large-scale direct shear testing machine.
Table 3
Cohesion and angle of shearing resistance of ballast
samples.
Percentage of contamination (%) 25
Angle of shearing resistance (Degree) 44.2
Cohesion (kPa) 17.3
(a) Displacement of sleeper
(c) Displacement of
Fig. 14. Comparison between results o
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 7
taken from the field. The shear tests on the ballast samples were
conducted in accordance with ASTM D3080 [10], using a large-
scale direct shear testing machine. The machine comprises of top
and bottom shear boxes [72]. The bottom shear box has the inside
length, width, and depth of 540, 440 and 180 mm, respectively. The
top square shear box has the inside length of 440 (mm) and depth
of 180 (mm) [72]. The front and side views of the direct shear
(b) Displacement of rail on sleeper
 rail between sleepers 
f field measurements and model.
(a) For positive rail seat bending moment (b) For negative center bending moment
Fig. 15. Pattern of ballast pressure distribution beneath the sleeper suggested in AS 1085.14 [4].
Fig. 16. Particle size distribution of ballast used for parametric studies.
8 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
testing machine are presented in Fig. 13. The preparation proce-
dure of sand-contaminated ballast samples was adapted from the
method suggested in the literature [29,31,53,71,72,21,73]. That
is, the ballast was placed in the boxes in four layers. On the top
of each layer, a certain amount of sands were spread. After adding
the sand to each layer, the ballast was compacted using a hand
tamper [53,71,72]. To reproduce field track condition, ballast sam-
ples in boxes was compacted to achieve the in situ density of con-
taminated ballast (i.e., 1885 kg/m3). To perform the test, the top
box was clamped in place and the bottom shear box was pushed
in the horizontal direction [72]. The ballast samples were sheared
under four normal stresses of 50, 100, 150 and 200 (kPa). All the
experiments were conducted under the dry conditions. From the
diagram of the maximum shear stress versus the normal pressures,
the cohesion and the angle of shearing resistance of samples were
obtained, using the Mohr-Coulomb failure model. The results are
presented in Table 3.
3.2. Comparison of results
The properties of the track components in the site (as presented
in Tables 2 and 3) were imported into the model. The results mea-
sured from the in-situ test and those obtained from the model are
compared in Fig. 14. The train speed was 47 km/h as it was
obtained from the time history of the wheel loads (Fig. 8). That
is, the speed was computed from the distance between two con-
secutive wheels divided by the time interval between the two
wheels. The displacement obtained from the in-situ experiment
due to the passage of three wheels of a locomotive bogie is pre-
sented in Fig. 14. Three peaks in Fig. 14 indicate the wheels loads
of the bogie. Results indicate that the differences between the
model prediction and the measurement are 8.5% (at the most).
As presented in Fig. 14, a good agreement was observed between
the results obtained from the model and the field test. The differ-
ences can be due to some possible imperfections in the track and
the vehicle omitted in the model.
4. Effects of sand contamination on sleeper design parameters
According to the current codes of practice, design of sleepers is
based on the bending moment capacity at the rail seat and mid-
span sections of the sleeperAREMA [3,4], UIC 713 [84]. Therefore,
the sleeper design approach is mainly dependent on the sleeper
loading pattern which includes rail seat load and sleeper-ballast
contact pressure as they constitute the bases for the computation
of sleeper bending moment.
In accordance with AS 1085.14 [4], a uniform sleeper-ballast
contact pressure is assumed in a certain length of the sleeper
beneath the rail seat positions in order to derive the positive slee-
per bending moment at the rail seat. It is illustrated in Fig. 15(a).
Also, the negative bending moment at the center of the sleeper is
derived based on an assumption of a uniformballast pressure
beneath the total length of the sleeper (Fig. 15(b)). The rail seat
load and the intensity of the uniform pressure underneath the slee-
per are denoted as Qr and Wi (W1 and W2) in Fig. 15.
According to the literature [34,37,32], ballast conditions have
considerable effects on the sleeper design parameters (i.e., rail seat
load and ballast-sleeper pressure). It means that the conditions of
the ballast should be considered in the design of sleepers. In
response to this need, the influences of different percentages of
the ballast sand contamination on the sleeper main design param-
eters were investigated in this research. To this end, first, labora-
tory tests were made to draw angle of shearing resistance,
cohesion, and strain modulus of ballasts as a function of sand con-
taminations levels; and then, parametric analyses were made,
using the model developed here, to derive the influence level of
ballast contamination on the sleeper loading pattern (i.e., sleeper
design parameters).
4.1. Laboratory tests: correlation between contamination and ballast
mechanical properties
In order to draw the properties of the ballast contaminated with
dry windblown sand, seven samples with 0, 5, 15, 20, 25 30 and 35
percentages of contamination were prepared by adding assigned
amounts of sands to the clean ballast samples. The gradation curve
of the clean dolomite limestone ballast tested in the laboratory is
shown in Fig. 16. The preparation of the samples was similar to
that described in Section 3.1. It was made in the laboratory of
the School of Railway Engineering at Iran University of Science
and Technology. All the laboratory tests were performed under
dry conditions (i.e., dry ballast and dry sand).
The large-scale direct shear testing machine (Fig. 13) described
in Section 3.1 was used to obtain the fiction angle, and the cohe-
sion of the samples (ballast with various percentages of sand con-
taminations). The procedure of the direct shear tests on the
samples was similar to that described in Section 3.1 and detained
in [72].
To derive the strain modulus (EV) of the ballast, repeated plate
load tests were conducted in accordance with DIN 18134 [86]
described in [71]. To this end, the ballast samples were placed in
120(cm) 120(cm)
100(cm)
Reaction frame 
(a) steel chamber and rigid reaction frame (b) arrangements of loading 
and measurement devices
(c) fouled ballast samples in 
the chamber
Fig. 17. Repeated plate load test set-up.
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 9
three layers in a large steel chamber. Sand was spread on the top of
each layer. The ballast samples were compacted similar to that of
the shear box samples [71]. The ballast depth in the chamber
was 30 (cm) which is similar to that in the railway fields. The
length, width and depth of chamber were 120 (cm), 120 (cm)
and 100 (cm), respectively as indicated in Fig. 17a. The center of
chamber was under the steel rigid frame. The frame was clamped
securely to the laboratory floor. To conduct the test, a steel rigid
circular plate with 200 mm diameter and 30 mm thickness was
used as the loading plate [71]. Cement mortar with thin thickness
was made beneath the loading plate to make a smooth surface on
the top of the ballast samples. The load was applied on the rigid
plate through hydraulic jack and measured by a load cell [71].
The jack was attached to the beam of a steel rigid frame. The load
cell was placed under the jack. In order to fill the gap between the
load cell and the loading plate, steel solid plates and cylinders were
installed between the plate and the load sensor as shown in
Fig. 17b. To present the inside of the steel chamber (Fig. 17c), the
front wall of the chamber was temporary removed.
To perform the test, the load was applied in six stages with
equal increments [86]. The load was increased until the maximum
pressure (i.e., 0.5 MPa) was obtained. The ballast settlements dur-
ing the test were measured using an LVDT which was attached to
the loading plate [71]. The ballast settlement versus normal stress
of the samples was obtained, and consequently EV2 was obtained
based on DIN 18134 [86] The large-scale direct shear test and
repeated plate load tests were conducted on each sample. The
results of the large shear box tests on the samples (i.e., the fiction
angle, and the cohesion) and those obtained from PLTs (i.e., stain
modulus) are presented in Table 4.
Table 4
Test results for clean and sand-contaminated ballast samples.
Percentage of contamination (%) 0 5 15
Contamination condition Clean Moderately
clean
Moderately
contaminated
Angle of shearing resistance
(Degree)
53 51 48
Cohesion (kPa) 12 17 21
EV2 (MPa) 73 71 69
Table 5
Elastic modulus of clean and sand-contaminated ballast samples.
Percentage of contamination (%) 0 5
Elastic modulus (MPa) 69 67
The relationship between EV2 and elastic modulus (E) for ballast
was derived by Paderno [49,50] as under:
E ¼ p
3
ð1� m2ÞEV2 ð1Þ
in which m is Poisson’s ratio. Eq. (1) was derived based on the theory
of elasticity [70,15,69]. Using Eq. (1), the elastic modulus of ballast
samples was computed and the results are presented in Table 5.
Comparison was made between results obtained (in this study)
for the clean ballast samples and those derived from direct shear
tests available in the literature. The results are presented in Table 6.
As indicated in Table 6, the angle of shearing resistance reported in
the literature for the clean ballast ranges from 43 to 57 degree. This
is in good agreement with that obtained in this research (i.e., 53
degree). The clean ballast cohesion reported in the literature
ranges from 12 to 72 kPa. This wide range is due to the boundary
condition of shear box which varies from one research to another
[64,53,72]. That is, when shear box dimensions are large enough,
the influences of the shear box boundary on the test results are
minimized, and in turn, the cohesion obtained are small (varies
from 12 to 15 kPa) [64,72]. However, when the box dimensions
(its width and depth) are not large enough (compared to the parti-
cle size), noticeable confinement is imposed on the ballast aggre-
gates and therefore, unexpectedly significant cohesion is
obtained for the cohesion-less ballast material [64,53,72]. This is
worthwhile to mention that the cohesion values obtained for the
clean and sand-contaminated samples (indicated in Table 4) have
only mathematical meanings. In fact, the Mohr-Coulomb failure
envelope for the ballast and other rock-fill materials is non-linear
in practice and the failure envelopes of the shear stress cross the
20 25 30 35
Contaminated Contaminated Contaminated Highly
contaminated
47 46 43 40
22 26 18 14
66 64 43 33
15 20 25 30 35
66 64 61 38 28
Table 7
Correlation between ballast percentages of sand contamination and track modulus (u).
Percentage of contamination (%) 0 5 15 20 25 30 35
Track modulus (N/mm2) 40.1 35.4 34.1 32.4 31 24.7 19.8
Fig. 18. Maximum rail seat loads for different percentages of contamination.
Table 6
Comparison of test results for clean ballast obtained from direct shear test.
Researcher Specific gravity Ballast material d50 (mm) Cc Cu Angle of shearing resistance (Degree) Cohesion (kPa)
Present study 2.7 Limestone 27 1.2 2.1 53 12
Indraratna et al. [31] 2.7 – 15 1.2 2.5 54 15
Rahman [53] 2.72 – 33 0.9 2 51 13
Huang et al. [29] 2.62 Granite 45 1.1 1.4 47 72
Boler [14] – Limestone 35 1.0 1.6 43 67
Dissanayake et al. [20] 2.68 Biotite gneiss 44 1.0 2 57 13
Cc: coefficient of curvature; Cu: coefficient of uniformity.
10 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
zero intercept [40,31,75,72]. Therefore, the cohesion for the clean
and sand-contaminated ballast samples was considered zero in
the model.
The ballast pyramid model was used to derive stiffness of bal-
last layer [22], Ahlbeck and Kerr [1,43]. Based on the pyramid
model, the ballast stiffness is as under:
kB ¼ bðbþ 2htanuÞhEB ð2Þ
in which EB is the elastic modulus of ballast materials, kB and h are
the stiffness and depth of ballast layer, respectively; b is the diam-
eter of ballast loaded area, and ø is the friction angle of the ballast.
Track modulus is the main parameter used in the Winkler
model for analysis and design of railway track [59]. It is a function
of mainly ballast stiffness, sub-ballast stiffness, subgrade stiffness,
rail pad stiffness and sleeper spacing and computed based on the
pyramid model and the spring series model [22], Ahlbeck and Kerr
[1,43,80]. The track modulus (u) of the samples for various contam-
ination levels was derived based on the laboratory and field tests
results. The results are presented in Table 7.
4.2. Parametric analyses: windblown sand-contamination effects
Properties of the clean and sand-contaminated ballast samples
(Table 4) were taken into the model. That is, the results of the
direct shear test and the PLT were used as the input parameters
of the Mohr-Coulomb model. Properties of the other track compo-
nents including rail, rail pad, sleepers and subgrade were consid-
ered similar to those of the track in the field test as described in
Section 3.1. The loading pattern of the pre-stressed concrete slee-
per (rail seat loads and pressure distribution beneath the sleeper)
as the main sleeper design parameters for various levels of sand
contaminations was obtained from dynamic analyses of the model.
Since the stiffness of subgrade (i.e., strain modulus of subgrade)
has an influence on the load distribution factor, the effect of sub-
grade stiffness on the results was investigated in the parametric
analyses of the model. For this purpose, values of EV2 of subgrade
were varied from 27 MPa to 170 MPa in the parametric analyses.
This range was obtained from the literature [36,37,24].
4.2.1. Sleeper-rail contact load
Fig. 18 indicates the influences of ballast sand contamination on
the rail seat loads. As illustrated in this figure, when the wind-
blown sand contamination percentage is lower than 25%, the sand
contamination of the ballast has negligible influences on the rail
seat load (the differences of the responses are less than 5%). There-
fore, distribution of the wheel load on the consecutive sleepers for
the contamination of less than 25% is approximately similar to the
clean condition. It is indicated in Fig. 18. However, as the degree of
contamination becomes higher than 25%, there is a sharp decrease
in the rail seat load.
Through measurements of the ballast voids, it was found that
the percentage of sand contamination of 25% corresponds to the
conditions in which the sand materials entirely fill up the voids
in the ballast aggregates. Important changes in ballast mechanical
properties (presented in Table 4) as well as sleeper responses for
degree of sand contamination greater than 25% indicates that
25% of sand contamination is the threshold of the fines content
[35]. With sand contaminations of 30% and 35%, the rail seat load
decreases are 7% and 12%, respectively. As the stiffness of ballast
reduces (due to increase in sand contamination), the track modulus
decreases. This causes a more uniform distribution of the wheel
load on the underneath sleepers and therefore, the maximum rail
seat load is reduced.
According to AS 1085.14 [4], the rail seat load (Qr) is derived
from Eq. (3), where ‘‘j” is the dynamic amplification factor (the
ratio of the dynamic load to the static load) provided in the avail-
able codes of practice [4,84], and DF is the load distribution factor
(the percentage of load transferred from the wheel load to the
underneath sleeper). Q is the static wheel load. ‘‘j” takes one when
the load is static.
Qr ¼ j:DF:Q ð3Þ
From analyses of the model, the DFs for various degrees of
contamination were obtained when a single static wheel load
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 11
was considered. Using the test and model results, mathematical
expressions were derived for the correlation between the load dis-
tribution factor and ballast contamination (Eqs. (4) and (5)).
DF %ð Þ ¼ �0:001EV2;S MPað Þ � 0:2651ð ÞBPC %ð Þ þ 0:0301EV2;S MPað Þ
þ 35:781 BPC < 25% ð4Þ
DF %ð Þ ¼ ð7� 10�5EV2;S MPað Þ � 0:0369ÞBPC %ð Þ þ 0:057EV2;S MPað Þ
þ 41:493 BPC � 25% ð5Þ
where BPC is ballast percentage of dry windblown sand contamina-
tion (BPC) and EV2,S stands for the subgrade strain modulus (in the
second cycle of loading). Since track modulus is more frequently
used in the current code of practice for design of sleepers, the load
distribution factor (DF) was derived as a function of track modulus
which takes into account the sleeper supporting conditions (i.e.,
condition of contaminated ballast, sub ballast, and subgrade)
described earlier. It is presented in Eq. (6) in which u stands for
the track modulus in MPa.
Fig. 19. Comparison of DF: current study, Australian standard [4], AREMA [3] and
UIC 713 [84].
Fig. 20. Distribution of contact p
DF %ð Þ ¼ �0:0034u2 MPað Þ þ 0:3772u MPað Þ þ 29:768 10
< u MPað Þ < 60 ð6Þ
The main railway codes of practice for the design of sleepers
assume that the wheel load is distributed on three consecutive
sleepers and the sleeper under the wheel receives 50% of the wheel
load as long as the sleeper spacing is 60 cm and the rail is heavier
than 47 kg/mAREMA [3], AS 1085.14, 2003 [4], UIC 713 [84]. It
means that DF is 50% (constant) in the current codes of practice.
The main limitation of the majority of the current codes of practice
is the lack of consideration of track supporting conditions in the
computation of rail seat load. Among the current codes, only the
Australian standard [4] presents the rail seat load as a function of
track modulus (based on the Winkler theory); this is indicated in
Eq. (7).
DF ¼
ffiffiffiffiffiffiffi
u
4EI
4
r
s
2
ð7Þ
where s and EI are the sleeper spacing and the rail flexural rigidity,
respectively. A comparison of the DFs obtained from the numerical
analysis, and those proposed by the current codes of practice (i.e.,
AREMA [3], UIC 713, and AS 1085.14 2003 [4]) is presented in
Fig. 19. As indicated in Fig. 19, Australian Standard (i.e., Winkler
theory) underestimates loads transmitted from the wheel to the
sleeper while the European and American standards AREMA [3]
overestimate it. As sand contamination increases, the underestima-
tion made by theWinkler theory is intensified. In high levels of sand
contamination, DFs proposed by AREMA[3] and UIC [84] are 76%
more than those of the Winkler theory (Australian Standard [4]).
Fig. 19 indicates a large discrepancy among the DFs proposed by
the current codes of practice. To overcome this problem/confusion,
Eqs. (4) to (6) can be used to derive DF for the design of sleepers
when supported by sand-contaminated ballast.
4.2.2. Sleeper-ballast contact pressure
Distribution pattern of contact pressure beneath the sleeper
obtained from the analyses of the model (when the subgrade stiff-
ness was the same as that in the field test) is presented in Fig. 20.
As shown in this figure, when the percentage of sand contamina-
ressure beneath the sleeper.
Fig. 21. Distribution of average of contact pressures beneath sleeper.
12 A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324
tion is less than 25%, the influences of the ballast sand contamina-
tion on the contact stress distribution underneath the sleeper is
negligible. However, there is a significant distinction between the
results of the contact stress distribution obtained from the model
with clean ballast and those of the model with 35% sand contami-
nation. In order to make a more clear comparison of the results, the
average of the stresses is presented in Fig. 21. In this figure, contact
stresses are averaged in three evenly divided parts of the sleepers.
Note that, the effective sleeper length is one-third of the sleeper
length in the AREMA standard [3]. According to Fig. 21, as the bal-
last gets contaminated withdry windblown sand, the average of
the contact stresses at the corners and mid-span zones of the bal-
last length decrease 11% and 14%, respectively. The obtained
results, indicate that plastic strain and permanent settlement of
Fig. 22. Sleeper loading pattern: the ratios of the magnitudes of the uniform pressures un
contamination conditions.
ballast is negligible (less than 0.04 mm) even when increasing
the level of sand contamination.
Based on the results obtained, the magnitude of the uniform
contact pressure under the center of the sleeper and under the rail
seat were derived. They are mathematically presented in Eqs. (8)
and (9).
a1ð1=m2Þ ¼ ð2� 10�5EV2;SðMPaÞ � 0:0046ÞBPCð%Þ
� 0:001� EV2;SðMPaÞ þ 0:9116 ð8Þ
a2ð1=m2Þ ¼ ð�3� 10�7EV2;SðMPaÞ � 0:0038ÞBPCð%Þ
� 0:0015� EV2;SðMPaÞ þ 1:0855 ð9Þ
where a1 and a2 are the ratios of the magnitudes of the uniform
ballast-sleeper contact pressure in one third of the sleeper length
at the center and at the corner of the sleeper to the static wheel
load, respectively. These expressions present the pressure distribu-
tion as a function of ballast percentage of windblown sand contam-
ination (BPC) and subgrade strain modulus.
Computing track modulus (u) for various sleeper supporting
conditions and ballast contamination, the expressions for a1 and
a2 were obtained as a function of track modulus which can be
directly used in the analysis and design of sleepers.
a1ð1=m2Þ ¼ �0:0015� uðMPaÞ þ 0:8095 ð10Þ
a2ð1=m2Þ ¼ 0:0068� uðMPaÞ þ 0:9384 ð11Þ
Using Eqs. 3, 6, 10 and 11, the rail seat load and the ballast slee-
per contact pressure (as the main sleeper deign parameters) are
obtained as a function of track modulus (which is influenced by
track sand contamination level).
der the sleeper (at the rail-seat and sleeper center position) and DF values in railway
A.R. Tolou Kian et al. / Construction and Building Materials 233 (2020) 117324 13
Based on the current railway codes of practice ([3,4,84]), the
main criterion in the design of concrete sleepers is the bending
moment capacity of the sleepers. That is, the bending moments
at the rail-seat load and at the sleeper mid-span sections are com-
puted (bending moment demand) and the results are compared
with the moment capacities provided in the current codes. It
means that for the design of sleeper, one has to only derive the
bending moment at the rail seat position and at the center of the
sleeper. Therefore, to simplify application of this research results,
sleeper bending moments are presented as a function of parame-
ters derived here (a1, a2, and DF):
Mc ¼ L
2
9
a1 � bc
8
þ a2 � br
� �
� DF � g
2
 !
� Q � j ð12Þ
Mr ¼ a2 � br � L� gð Þ
2
8
� Q � j ð13Þ
whereMc and bc are thebendingmoment and the sleeperwidthat the
center of the sleeper, respectively;Mr and br are the bendingmoment
and the sleeper width at the rail seat position, respectively; L and g
are the sleeper length and the track gage, respectively; Q is the static
wheel load; DF, a1 and a2 are as defined earlier. DF and a1, a2 are
obtained from Eqs. (6), 10 and 11 or Fig. 22a and b.
Because mechanical properties of ballast contaminated with the
other materials/fines (i.e., crushed ballast, silt, coal dust, clay and
etc.) differ from those of ballast sand contaminated, application
of the obtained results is limited to dry sand-contaminated ballast
condition.
5. Conclusions
Influences of ballast windblown sand contamination (as a main
factor in reduction of ballast stiffness) on the sleeper design
parameters were investigated in this study. For this purpose, a
three-dimensional finite element model of ballasted railway track
(consisting of rails, rail pads, sleepers, pre-stressed tendons, bal-
last, sub-ballast and subgrade) was developed. To validate the
model, a thorough in-situ test was conducted in a sandy area.
The input data of the model were obtained from the tests in a rail-
way field and in a laboratory. Comparisons of the results obtained
from the model with those of the in-situ measurements indicate
that there was a good agreement between the model results and
those of the tests (there was at the most 8.5% difference).
The influences of different percentages of the ballast sand con-
tamination (and in turn ballast stiffness reductions due to sand
contamination) on the sleeper main design parameters were inves-
tigated in two steps; first, laboratory tests were made to draw fic-
tion angle, cohesion, and strain modulus of the ballast as a function
of sand contaminations levels; and then, parametric analyses were
made, using the model developed here. Several ballast samples
with different percentages of sands were prepared in a laboratory.
PLTs and large-scale direct shear tests were conducted on the bal-
last samples and the results were implemented as the input for the
model. The model results obtained indicate that when the percent-
age of the sand contamination is less than 25%, the ballast sand
contamination has negligible influences on the sleeper responses;
however, as the sand contamination exceeds 25%, the rail seat load
and contact pressure under the sleeper decrease. That is, 25% of
sand contamination is an important limit and the threshold of
the fines content. When the degree of sand contamination becomes
more than the threshold of sand content, decreases in the angle of
shearing resistance and the stiffness of the ballast occur noticeably.
Despite the considerable effect of ballast stiffness (ballast con-
tamination) on the sleeper mechanical behavior, it has been omit-
ted in the current codes of practice. In this research, the
formulation of the sleeper design parameters in the current codes
was extended by incorporating the effect of ballast degree of sand
contamination (and ballast stiffness). New mathematical expres-
sions were developed for the sleeper design parameters (the rail
seat load and ballast-sleeper contact pressure). They presents the
sleeper design parameters as a function of track modulus which
is influenced by ballast mechanical conditions (such as ballast level
of sand contamination). To simplify the application of the results in
the real world of practice, a new approach for the design of con-
crete sleepers was developed, offering new expressions for the
sleeper design criterions/parameters. That is, the new approach
extends the application of the current sleeper design approach by
including the condition in which sleeper is supported with dry
sand-contaminated ballast layer.
Declaration of Competing Interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
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	Influences of railway ballast sand contamination on loading pattern of pre-stressed concrete sleeper
	1 Introduction
	2 Vehicle-track interaction model
	3 Model validation
	3.1 Field test
	3.2 Comparison of results
	4 Effects of sand contamination on sleeper design parameters
	4.1 Laboratory tests: correlation between contamination and ballast mechanical properties
	4.2 Parametric analyses: windblown sand-contamination effects
	4.2.1 Sleeper-rail contact load
	4.2.2 Sleeper-ballast contact pressure
	5 Conclusions
	Declaration of Competing Interest
	References