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Effect of train vibration on settlement of soil: A numerical analysis
Kah-Yong Tiong, Felix Ngee-Leh Ling, and Zaihasra Abu Talib
Citation: AIP Conference Proceedings 1892, 030013 (2017);
View online: https://doi.org/10.1063/1.5005679
View Table of Contents: http://aip.scitation.org/toc/apc/1892/1
Published by the American Institute of Physics
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AIP Conference Proceedings 1892, 030014 (2017); 10.1063/1.5005680
Effect of Train Vibration on Settlement of Soil: A Numerical
Analysis
Kah-Yong Tiong1, a), Felix Ngee-Leh Ling1,2,b) and Zaihasra Abu Talib1, c)
1
Universiti Tun Hussein Onn Malaysia, Faculty of Civil & Environmental Engineering,
86400 Parit Raja, Johor, Malaysia
2
Universiti Tun Hussein Onn Malaysia, Research Centre for Soft Soil (RECESS),
86400 Parit Raja, Johor, Malaysia
b)
a)
kahyong93@hotmail.com
Corresponding author: felix@uthm.edu.my
c)
zaihasra@uthm.edu.my
Abstract. The drastic development of transit system caused the influence of ground-borne vibrations induced by train on
ground settlement became concern problem nowadays. The purpose of this study is to investigate soil settlement caused
by train vibration. To facilitate this study, computer simulation of soil dynamic response using commercial finite element
package – PLAXIS 2D was performed to simulate track-subgrade system together with dynamic train load under three
different conditions. The results of simulation analysis established the facts that the soil deformation increased with
raising in water level. This phenomenon happens because the increasing water level not only induced greater excess pore
water pressure but also reduced stiffness of soil. Furthermore, the simulation analysis also deduced that the soil
settlement was reduced by placing material with high stiffness between the subgrade and the ballast layer since material
with high stiffness was able to dissipate energy efficiently due to its high bearing capacity, thus protecting the subgrade
from deteriorating. The simulation analysis result also showed that the soil dynamic response increased with the increase
in the speed of train and a noticeable amplification in soil deformation occurred as the train speed approaches the
Rayleigh wave velocity of the track subgrade system. This is due to the fact that dynamic train load depend on both the
self-weight of the train and the dynamic component due to inertial effects associated with the train speed. Thus,
controlling the train speeds under critical velocity of track-subgrade system is able to ensure the safety of train operation
as it prevents track-ground resonance and dramatic ground.
INTRODUCTION
The drastic economic expansion and the demand of high speed and high-passenger-load cause train to become
one of the important transport system. However, the elevated ground-borne vibration level generated by train is now
a growing engineering challenge nowadays. The ground vibration with frequency ranging from 5 to 150 Hz can
cause vertical resonance and destruction to structures in close proximity [1]. Furthermore, the impact of water on the
performance of railways cannot be neglected as increasing water table lead to degradation of railway, jeopardizing
running safety. Therefore, it is crucial to ensure that the railway system not only adequate performance under
loadings but also resilient enough to survive under high water table.
The stiffness of protective layer placing between the subgrade and the ballast layer plays an important role in
studying track deterioration. Evaluation on its dynamic benefits is essential to investigate proper track improvement
solutions and optimizing the design so as to reduce track vibrations and track degradation rate. Besides that, the
thickness of subgrade plays an important role in studying track deterioration so as to ensure it is able to distribute the
dynamic soil stress. While most analysis and design methods developed so far seldom take into consideration of
wheel-rail dynamic interaction and only used constant axle weight as wheel-rail force and this may lead to
Proceedings of the International Conference of Global Network for Innovative Technology and AWAM International Conference in Civil Engineering (IGNITE-AICCE’17)
AIP Conf. Proc. 1892, 030013-1–030013-8; https://doi.org/10.1063/1.5005679
Published by AIP Publishing. 978-0-7354-1574-4/$30.00
030013-1
underestimation of high frequency train vibration [2]. The property of waves generated by high-speed train when
approaching critical speed is not well known as field measurements are still not feasible, they therefore deserve
more research attention.
This study aimed to model settlement of soil caused by train vibration using 2D finite element program, PLAXIS
2D 2015 and suggest some practicable solutions to mitigate the settlement of soil. This paper demonstrated some
results of the model application to simulate numerically track-subgrade system together with dynamic train load and
analyze soil dynamic performance under different situations. Firstly, the impact of soil responses of different design
solutions by introducing different type of protective layers with different stiffness was evaluated. This was
essentially trying to confirm the track vibrations reduction in an enhanced dynamic behavior for the track. Then, the
soil dynamic responses including soil stresses, pore water pressure and soil displacement at the design condition
with water table at different layers of soil were modeled and compared. Determination of the critical zone of
influence due to dynamic load due to train vibration was discussed considering the relationship between the distance
from the source of vibration and attenuation of the dynamic soil stresses along subgrade depth. Lastly, track
settlement progression along with train speed was also numerically investigated especially when the speed of train
approaches critical velocity of the soil.
MODELLING
Commercial Finite Element Package-PLAXIS 2D was used to simulate the track-subgrade system together with
dynamic train load. Plain strain model with 15-node triangular elements instead of axisymmetric model was chosen
in PLAXIS since this study involved geometries with a uniform cross section and the corresponding stress state and
loading involved travelled in z-direction perpendicular to the cross section. The material models adopted in this
study were the Linear Elastic model and Mohr Coulomb model. The behavior of all the materials was considered to
be undrained as the changes in dynamic train load took place faster than the flow of water whereas underneath the
bottom layer was assumed to be bedrock, which disallowed penetration of groundwater.
According to the tutorial manual of PLAXIS 3D [3], in order to consider the maximum shear forces in the
middle of the spans, the dynamic point loads were located at sleeper distance which is 30cm giving a total of 117
dynamic point loads for this study. The data used to simulate the dynamic train load was based on study carried out
previously [1] with the wheel–rail load amplitude at different train speeds summarized in Fig. 1. However, the
frequency was determined by using following formula:
࢜
ࢌൌ
(1)
ࣅ
Where: f = frequency; v = velocity; ࣅ=wavelength
Since the point loads in PLAXIS 2D had the unit kN/m, this meant that the loads were in essence line loads
which are continuous in third unseen dimension causing the magnitude of the point loads obtained from Fig. 1 was
required to be divided by two so as to represent the full axle load was distributed over an effective width of
approximately 2 m.
FIGURE 1. The wheel–rail load amplitude at different train speeds [1]
030013-2
The dynamic time interval for the dynamic point loads played a vital role in representing the speed of train in
PLAXIS 2D. The time interval was chosen to cover the time needed for all axles of the train to pass the 35 m of
modelled geometry. The time step was constant because the train speed and the distance between dynamic point
loads were constant which 0.3m for this study. For example, a train with speed 180 km/h passes every 30 cm in
0.006 sec, hence, the time interval must be chosen 0.006 sec for the fixed dynamic point loads.
Model Description for Parametric Study
The track-subgrade systems was assumed to consist of two layers of soil which were sand and semi-dense
backfill soil with ballast and protective layer on the upper face. Dynamic analysis with harmonic loads was utilized
in this study. In order to simulate the dynamic train load, data from the Fig. 1 was adopted in which the speed of the
train was assumed to be 200 km/h with the amplitude and wavelength of 0.005 and 15.5m. By using the equation
(1), frequency of 3.58 Hz is obtained. From Fig. 1, the wheel rail loads were 70.14kN. However, in order to
represent the full axle load was distributed over an effective width of approximately 2m, the obtained wheel rail
loads need to be divided by two. Therefore, the loading acted on the track-subgrade systems was set to be 35.07kN.
The dynamic time interval of 0.0054s was set to represent the dynamic motion of the train. Geometric and material
parameters for the parametric study are summarized in Fig. 2(a) and Table 1.
Dynamic analysis with three different modelling schemes was carried out for parametric study. Firstly, the
influence of water table on the dynamic performance of soil under high-speed train was studied by changing the
water level in the model. The following test sequence was used in parametric study: water table at protective layer
(0.5m from ground surface), water table at semi-dense backfill layer (1.0m from ground surface), water table at top
surface of sand layer (2.5m from ground surface) and water table at middle of sand layer (7.25m from ground
surface).
Secondly, the effectiveness of the fibre composite with various stiffness used in protecting the subgrade from
deterioration due to high speed train vibration was investigated in which the protective layer was modelled using
Linear Elastic as material models with Young Modulus of 14040MPa, 18560MPa, 23080MPa and 27600MPa for
the four different cases respectively in this modelling scheme.
Lastly, the impact of train speed on the settlement of ground especially when the speed of train approached
critical velocity of the soil was studied and ground settlement due to train speed before and after approaching critical
velocity was compared. The data from Fig. 1 was adopted so as to simulate train speed of 200 km/h, 250 km/h, 300
km/h and 350 km/h with dynamic load and dynamic time interval of 35.07 kN/m and 0.0054s, 40 kN/m and 0.0043s,
55 kN/m and 0.0036s, 60 kN/m and 0.0031s respectively. The amplitude multiplier and frequency used in these
four cases are 0.005 and 3.58 Hz respectively.
Parameter
Symbol
Unit
Concrete
Sleeper
Ballast
Protective
layer
Backfill –
semi-dense
soil
Sand
TABLE 1. Material property of idealised track-subgrade systems [3]
Material
Saturated
Bulk
Poison Effective Effective Angle of
Model
unit
unit
ratio
Friction Cohesion dilatancy
weight of
weight
angle
soil
of soil
ϕ'
ܿ’
ߛ௦௔௧
ߛ௨௡௦௔௧
ߥ
߰
ι
ι
݇ܰ/݉ଷ ݇ܰȀ݉ଷ
݇ܰȀ݉ଶ
Young
Modulus
Ƞ
݇ܰȀ݉ଶ
Linear
Elastic
MohrCoulomb
Linear
Elastic
MohrCoulomb
-
24
0.15
-
-
-
-
21
19
0.30
35
30
5
30000
23
22
0.25
40
30
15
55000
-
9.71
0.36
-
-
-
35000
MohrCoulomb
20
19
0.35
40
5
10
8000
030013-3
(b) Case study
(a) Parametric study
FIGURE 2. The idealized model along the track-subgrade systems in z-direction
Model Description for Case StudyThe data used for the case study to calibrate the models was obtained from an
example in tutorial manual of PLAXIS 3D 3D [3] with material parameters summarized in Table 2. The geometric is
shown in Fig. 2(b).
Parameter
Symbol
Unit
Concrete
Sleeper
Ballast
Protective
layer
Backfill –
loose soil
Backfill –
dense soil
Organic
silt
Peat
Sand
TABLE 2. Material property of idealised track-subgrade systems [3]
Saturated
Bulk unit
Poison Effective Effective
Angle of
unit
weight of
ratio
Friction
Cohesion
dilatancy
weight of
soil
angle
soil
ϕ
ߛ௦௔௧
ߛ௨௡௦௔௧
ߥ
ܿ
߰
ι
ι
݇ܰȀ݉ଷ
݇ܰȀ݉ଷ
݇ܰȀ݉ଶ
Linear
24
0.15
Elastic
Mohr21
19
0.30
35
30
5
Coulomb
Mohr23
22
0.25
40
30
15
Coulomb
Mohr19
18
0.35
28
10
0
Coulomb
Mohr20
19.5
0.35
28
10
0
Coulomb
Mohr11
11
0.35
26
15
0
Coulomb
Mohr13
13
0.35
25
10
0
Coulomb
Mohr20
19
0.35
40
5
10
Coulomb
Material
Model
Young
Modulus
Ƞ
݇ܰȀ݉ଶ
30000
55000
25000
43000
2000
4000
8000
In order to investigate the impact of train speed on the settlement of ground and the influence zone of train
especially when the speed of train approached critical velocity of the soil, seven cases were simulated with
amplitude multiplier and frequency of 0.005 and 3.58 Hz. Dynamic parameters used in case study are shown in
Table 3.
030013-4
TABLE 3. Dynamic parameters for different train speed
Case
1
2
3
4
5
6
7
Speed
Dynamic load
Dynamic time interval
km/h
200
250
300
350
400
450
500
kN/m
35.07
40.00
55.00
60.00
70.00
75.00
80.00
s
0.00540
0.00430
0.00360
0.00310
0.00270
0.00240
0.00217
RESULTS AND DISCUSSION
The results of the study were discussed separately in the following subtopics based on the pre-determined
influence factors.
The Effect of Water Level from Ground Surface
The results obtained from the dynamic analysis clearly showed that when the ground water was at the lowest
level which is at middle of sand layer, at 7.25m from ground surface, the smallest excess pore water pressure of 71.8
km/m2 obtained, and consequently leading to the smallest vertical soil displacement of 0.2912m. Plot of excess pore
water pressure over vertical displacement presented linear increased trend with rising water level. Figure 3 shows
that increasing water table resulted in the building up of excess pore water causing lower effective stress in the soil,
thus larger dynamic responses of the soil when the soil is subjected to dynamic train load as shown in Fig. 4. It is
important to note that the excess pore water pressure would increase rapidly because the pore water inside soil had
insufficient time to drain out under the impact loading from train's passages at high speeds. Furthermore, the
increase in water table results in the decrease in stiffness enabling the Rayleigh wave velocity of the soil to be
reached more easily, causing large deformation of soil to occur [4].
FIGURE 3. Excess pore water pressure for different water level
030013-5
FIGURE 4. Vertical soil displacement for different water level
The Effect of Protective Layer’s Stiffness
The analysis compared the effectiveness of protectively layer which consisted of fibre composite with four
different Young Modulus. Figure 5 shows that the settlement behaviour of soil decreased when stiffer material was
used as the protector layer. Fibre composite with largest Young Modulus of 27600MPa, which was the stiffest
material gave the least soil deformation of 0.3827x10 -3m whereas fibre composite with Young Modulus of
14040MPa which was the least stiff material gave the greatest soil deformation of 0.3859 x10 -3m. Therefore, it was
affirmed that placing stiffer and more durable materials between the subgrade and the ballast layer was effective in
reducing the train vibration levels, consequently reducing the impact of dynamic train load acting on the subgrade,
thus protecting the deformation of subgrade. Besides that, usage of stiffer and more durable materials serve to
increase the underlying Rayleigh wave speed of the track subgrade system, reducing the possibility of train speed
approaching the critical speed, thus preventing large soil deformation to occur [5].
FIGURE 5. Vertical displacement for different stiffness of protective layer
The Effect of Train Speed
Figure 6 and Fig. 7 show that when the speed of the train increased, the vertical displacement of soil also
increased. When the train running at high speeds, larger energy is transferred to the subgrade causing the subgrade
to withstand greater dynamic stress leading to increased soil deformation. The soil displacement response showed a
noticeable amplification at train speed of 300km/h for both graph, suggesting that this speed was approaching the
critical velocity. Figure 7 shows that the vertical soil displacement reached the peak at train speed of 390km/h,
suggesting that this speed is the critical velocity in this case. Critical speed is the speed on which train movement
cause track-ground resonance and dramatic ground vibration amplification [6]. When train speed was exceeded the
critical velocity (390km/h in this case), the soil displacement showed a progressive decrement as the train speed was
away from the Rayleigh wave velocity of the track-subgrade system [2].
030013-6
Vertical displacement
(x10-3m)
5
4.5
4
3.5
3
2.5
150
200
250
300
350
400
Speed (km/h)
FIGURE 6. Vertical soil displacement results for different train speeds in parametric study
Critical velocity
FIGURE 7. Vertical soil displacement results for different train speeds in case stu dy
CONCLUSIONS
The results proved that deformation of soil increased with the increase in water level which would induce higher
pore water pressure in soil. Therefore, when considering the optimal design of infrastructure components in building
resilient and sustainable railway system, designer need to consider not only capability of the components to perform
adequately under service loads but also resilient enough to survive under high water table.
Besides that, the results of simulation analysis of parametric study for protective layer consisting of fibre
composite with different stiffness which was placed between the subgrade and the ballast layer proved that the
settlement and vibrations of the soil is able to be reduced with the use of material with high stiffness. The result
deduced that usage of stiffer material can reduce impact load and protect the subgrade from deteriorating and
demonstrated to be a good solution in improving the track dynamic behaviour and to extend its lifetime.
Lastly, the analyses also showed that the vibration response of the underlying soil was magnified with train
speed which meant the increment in train speed is accompanied by the increase track and soil displacement. The
result also proved that when train speed approaches the critical speed, the track-subgrade system vibration
maximally amplified as a consequence of “resonance-like“ phenomenon.Thus, controlling the train speeds below the
critical velocity of the track-subgrade system is considered as one of the way to ensure the safety of train operation
and reduce the environmental vibration produced by the running trains.
ACKNOWLEDGMENT
The authors wish to express grateful and thankful appreciate to the financial support from University Tun
Hussein Onn Malaysia through the Centre for Graduate Studies and Office for Research, Innovation,
Commercialization and Consultancy Management (ORICC).
030013-7
REFERENCES
1.
2.
3.
4.
5.
6.
G. Gao, J. Song, G. Chen, & J. Yang, Soil Dynamics and Earthquake Engineering 77, 274-278 (2015).
P. N. Thach, H. L. Liu, & G. Q. Kong, Soil Dynamics and Earthquake Engineering 55, 92–99 (2013).
M. Shahraki, M.R.S. Sadaghian, K.J. Witt, & T. Meier, Plaxis Bulletin 36 (Autumn 2014).
H. Jiang, X. Bian, J. Jiang, & Y. Chen, Engineering Geology 206, 18–32 (2016).
D. P. Connolly, G. Kouroussis, O. Laghrouche, C. L. Ho, M. C. Forde, Construction and Building
Materials 92, 64–81(2014).
X. Bian, H. Jiang, & Y. Chen, Procedia Engineering 143, 769–781 (2016).
030013-8
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