Construction and Building Materials 270 (2021) 121370
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Construction and Building Materials
journal homepage: www.elsevier.com/locate/conbuildmat
Dynamic response of stabilized cinder subgrade during train passage
Tengfei Wang a,b, Qiang Luo a,b,⇑, Liang Zhang a,b, Shiguo Xiao a,b, Hang Fu a,b
a
b
MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong Univ., Chengdu 610031, China
School of Civil Engineering, Southwest Jiaotong Univ., Chengdu 610031, China
h i g h l i g h t s
Comparative study of SC and traditional fill was made for subgrade serviceability.
Vertical stress, displacement, velocity, and acceleration over subgrade surface were recorded during train passages.
Longitudinal distribution of measured stress was captured by a combination of Gaussian functions.
Impact of train speeds on subgrade vibrations was statistically analyzed.
SC outperforms traditional fill in earth structure with higher dynamic stability.
a r t i c l e
i n f o
Article history:
Received 20 July 2020
Received in revised form 9 September 2020
Accepted 16 October 2020
Available online 5 November 2020
Keywords:
Cinder
Dynamic properties
Field monitoring
Railway
Subgrade
a b s t r a c t
Cinder (scoria) is a promising and low-cost fill material for ballasted track substructures with soil stabilization techniques. However, the comprehensive dynamic assessment of its suitability as railway aggregate is insufficient. In this paper, natural cinder and local fine-grained soil as its stabilizer were first
tested for their basic properties. Permeability and consolidated drained dynamic triaxial tests were conducted on their mixtures at two blend ratios (2:1 and 3:1). Then, a field monitoring program was performed at two test sections in the Addis Ababa–Djibouti Railway, Ethiopia, using embedded pressure
cells and integrated vibration sensors over the subgrade surface. Signals of dynamic stress, displacement,
velocity, and acceleration were recorded during train passages at speeds between 5 and 100 km/h. A comparison was made between the dynamic responses of the earth structures constructed using stabilized
cinders and traditional geomaterials. The longitudinal distribution of measured vertical stress was captured by an empirical formula incorporating normalized Gaussian functions, which was employed for
a rough estimation of rail seat loads. Impact of train speed on subgrade vibrations in terms of four
recorded signals was ultimately revealed with statistical analyses. Results from laboratory tests and field
monitoring demonstrated that stabilized cinder generally outperforms the baseline fill due to better
dynamic stability of the constructed facilities.
Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction
Rail transportation of commodities has advantages over road
transportation in terms of transportation costs, safety, volume,
and speed. In 2010, the Ethiopian Government proposed the new
National Railway Network of Ethiopia, setting a strategic goal to
allow Ethiopia a stable and sustainable economic development.
Currently, there are three electrified standard gauge railway lines
in Ethiopia, including Addis Ababa–Djibouti Railway (operational),
⇑ Corresponding author at: 111 1st N Section, 2nd Ring Rd, Chengdu 610031,
China.
E-mail addresses: w@swjtu.edu.cn (T. Wang), lqrock@swjtu.edu.cn (Q. Luo),
Lzhang@swjtu.edu.cn (L. Zhang), xiaoshiguo@swjtu.cn (S. Xiao), FuHang99@my.
swjtu.edu.cn (H. Fu).
https://doi.org/10.1016/j.conbuildmat.2020.121370
0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
Awash–Weldiya Railway (under construction), and Weldiya–
Mekelle Railway (under construction). Since other lines are in the
planning stage, the expansion of the railway network continues
for decades, along with the proposal of the East African Railway
Master Plan. Ethiopia’s geological outcrop pattern is characterized
by a broad range of sedimentary, igneous, and metamorphic rocks
[1]. A sub-tropical, humid climate contributes to a wide distribution of deep residual soils, while naturally occurring granular soils
are quite limited for railway earthwork construction. The haulage
of suitable fill materials over a long distance is not realistic due
to the expensive operations.
The Great Rift Valley of Ethiopia extends for>1,000 km from the
Afar Depression to the Turkana Depression in a NE-SW to N-S direction. Pyroclastic materials have been extruded and ejected from
vents and fissures in this area during volcanic eruptions and
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
Railway Line (Fig. 1). Particle size analysis was conducted for both
soil samples following ASTM D6913 04, and their grain size distributions are shown in Fig. 1d. Table 1 shows the physical and
mechanical properties of the tested samples. Note that Modified
Proctor tests were performed on the cinder as per ASTM D1557
07. It is imperative to evaluate the strength of the porous particles of cinder because the particles were crushable under moderate
dynamic/impact loads. Hence, the L.A. abrasion tests were also
employed. The L.A. abrasion loss was 43.0% on average for the collected samples, satisfying the aggregate specifications in TB 2897–
1998. By further applying the mechanical stabilization techniques,
its suitability as fill material in the railway subgrade can be secured
appropriately [13]. Due to the high vesicularity characteristics of
cinder, the apparent relative density and oven-dry relative density
were used instead of specific gravity as follows:
formed cones principally consisting of basaltic (scoriaceous) cinder, boulders, and cobbles. Cinder (scoria) has enormous potential
for railway infrastructure construction due to local abundance and
environmental benefits. However, high vesicularity of its particles
limits its use in earth structure construction because it usually fails
to comply with railway specifications in terms of soil compaction
and modulus of subgrade reaction. Its practical utility is also challenged by grain breakage potential and the variability [1] of engineering parameters.
Cinder has been applied to road and railway construction in
Ethiopia and other engineering projects. Newill et al. [2], Newill
and Aklilu [3], and Newill et al. [4] assessed its suitability as the base
and sub-base course material in low-volume roads by laboratory
testing, field compaction trials, and full-scale construction trials.
The results showed that stabilizing natural cinders with quarry fines
and volcanic ash substantially improve its engineering properties.
Other researchers [5–8] also examined the options of using finegrained soils and volcanic ash, and lime stabilization technique in
enhancing the mechanical performance of modified cinder as coarse
aggregate. Rocher [9] has summarized the particle size range of cinder for a variety of applications, including drainage of the pavement
structures, road pavement seats, and lightweight embankments
[10]. Hearn et al. [1] analyzed the considerable variations of cinder
from different cones in terms of CBR strength and gradation, concluding that maars and steep-sided well-defined cones appear to
generate higher quality geomaterials in roadwork applications.
The application of cinder in low-volume roads in Ethiopia proves
successful with soil stabilization techniques. A general guideline
for the extensive use of cinder in road construction and rehabilitation programs has been proposed by Hearn et al. [1]. However, few
works were available on its applications in the railway.
Liao et al. [11] have performed unconfined compression tests on
clay-modified cinder to evaluate its breakage potential. They concluded that after experiencing particle breakage under dynamic
loads, the stabilized cinder still meets the railway requirement
for aggregate in the upper portion of the subgrade. Luo et al. [12]
developed a guideline for the use of mechanically stabilized cinder
(SC) in railway layered earth structure primarily based on laboratory testing and field compaction trials. Although the potential of
SCs as railway aggregate was evidenced, the dynamic responses
of track substructure constructed using SCs during train operation
remains elusive. As a novel geomaterial, SC should also be assessed
based on performance against standard (baseline) fill in practical
applications.
To this end, two test sections in the Addis Ababa–Djibouti Railway, where earth structures were constructed by SC and traditional fill (conforming to the Chinese National Railway Class 2
Standard), were selected for a field monitoring program in cooperation with China Railway Group Limited (CREC). This paper is organized as follows. Natural cinder sample and its stabilizer (local
fine-grained soil) were first tested for their physical and mechanical properties. Dynamic triaxial tests are conducted on SCs at two
mixing ratios to obtain their ultimate shear strength. Then, sensors
were installed on the subgrade surface in two experimental sites to
record vertical stress, displacement, velocity, and acceleration signals of a train passing at six different speeds. The performance of
two types of subgrades (SC and standard) were compared based
on data interpretation. Finally, the train-induced stress distribution
characteristics and speed impact on subgrade vibration were
discussed.
Sd ¼ ma =ðmb mc Þ
ð1Þ
Sa ¼ ma =ðma mc Þ
ð2Þ
where Sd is the oven-dry relative density, and Sa denotes the
apparent relative density following ASTM C127 – 15; ma is the
mass (in gram) of the oven-dry test sample in air, mb is the mass
(in gram) of the saturated-surface-dry test sample in air, and mc
is the apparent mass (in gram) of the saturated test sample in
water. Given the Atterberg limits and the grain size distribution,
the potential stabilizer can be classified as silty sand, conforming
to the Unified soil classification system (USCS).
The cinder mechanically stabilized by local clayey soil has been
proven suitable for constructing the road base course under heavy
traffic loads [6]. In this study, the selection of stabilizer (silty sand)
was based on its availability and transportation costs. Field application trials, including field construction tests, indicated that mixing ratios of 3:1 and 2:1 by mass (cinder/stabilizer) can achieve the
best compaction performance [12]. Hence, the mechanical properties of SCs at two blend ratios of 3:1 and 2:1 were examined by laboratory tests. From the perspective of Ethiopia’s climatic conditions
(wet season from June to September), it is necessary to evaluate
the drainage performance of railway earth structure. Fig. 2 presents the results of typical soil permeability tests. The coefficients
of permeability decreased with the degree of compaction for two
mixed soils in a predictable manner. They were classified as moderately permeable fill materials at relative compactions of 85, 90,
and 93% as per GB 50487–2008.
The dynamic properties of stabilized aggregate under cyclic
loading were assessed with dynamic triaxial tests [14,15]. Specimens (100 mm in height and 50 mm in diameter) were prepared
at 93% compaction under two hydraulic conditions (optimum
moisture content and fully saturated) to represent the working
condition and the worst-case scenario. Two confining pressures
0
(r3 , 20 and 70 kPa) were applied to the specimens to reproduce
the in-situ principal stress at the surface of the subgrade or the
interface between subgrade and embankment (2.5 m in depth from
the surface of the subgrade). Given the target train speed (80 km/h
for freight and 120 km/h for passenger) and the geometric characteristics of wagons, an input load in the form of a sinusoidal wave
with 5 Hz frequency was used in the stress-controlled tests (Fig. 3).
Specimens were exposed to a consolidation process before cyclic
loading, and drainage was allowed during the shear phase.
Fig. 3a shows a typical time-history of the imposed axial loads.
Upon the completion of specimen consolidation, the dynamic
stress amplitude gradually increased following the normalized
stress a ¼ rd =rs ¼ 0:05; 0:1; 0:2; , where rs is the shear strength
of mixed soil under monotonic loading. Particle size analysis was
performed to assess the impact of cyclic loading on aggregate
degradation. Fig. 3b shows that the breakage phenomenon was
2. Properties of stabilized cinder
Natural cinder and fine-grained soil as its potential stabilizer
were collected from the vicinity of the Addis Ababa-Djibouti
2
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
Fig. 1. Fill material availability and grain size distribution: (a) cinder cone tephra in pit excavations, (b) a typical porous cinder particle, (c) borrow area of silty sand, and (d)
grading curves of cinder and the stabilizer.
Table 1
Test results for natural cinder and its stabilizer.
Sample
qmax (g/cm3)
wOPT (%)
Gs
Sa
Sd
LL (%)
PL (%)
L.A. abrasion loss (%)
Cinder
Stabilizer
1.46
1.48
10.3
20.9
–
2.54
2.36
–
1.89
–
–
41.6
–
33.4
43.0
–
Note: qmax = maximum dry density; wOPT = optimum moisture content; Gs = specific gravity; Sa = apparent relative density; Sd = oven-dry relative density; LL = liquid limit;
PL = plastic limit.
(20 kPa), and saturated (70 kPa) conditions, respectively. Likewise,
those values were 171, 287, 97, and 153 kPa for the 3:1 stabilized
aggregate. It is worth noting that when the train-induced dynamic
soil stress was less than the critical values, no failure occurred in
the soil mass. At the same time, significant permanent volume
changes were expected as the dynamic stress levels approached
the threshold value. Thus, SC meets the dynamic strength requirements of earth structure fill materials in accordance with the Chinese National Railway Class 2 Standard. Based on laboratory test
results, SC is recognized as a promising abundant aggregate with
environmental benefits. Nevertheless, as laboratory conditions
may differ from field studies, its suitability requires further validation against on-site dynamic response.
Coefficient of permeability (cm/s)
10-1
Highly permeable
GB 50487 - 2008
10-2
Moderately permeable
10-3
2:1 SC
3:1 SC
10-4
78
3. Field assessment of vibrations in railway stabilized subgrade
81
84
87
90
93
96
3.1. Site description and field monitoring
Compaction (%)
Fig. 2. Evolution of stabilized cinder permeability vs. relative compaction.
This section provides the results of the dynamic assessment of
two subgrades constructed by SCs and traditional fills following
China’s railway specification TB 10001–2016 under train passages.
The suitability of SC as subgrade fill was evaluated based on field
evidence and their mechanical properties obtained from laboratory
tests. As shown in Fig. 5, a comprehensive field monitoring program was executed at two test sections (DK 71 + 215 and DK
81 + 550) close to Bishoftu, Ethiopia. Fig. 6 displays the crosssection of two types of earth structures with their geometry and fill
materials. The total width of the subgrade surface (between the
two shoulders) of the double-track ballasted railway was 11.7 m,
with a slope gradient of 1.75 (H): 1(V). The thickness of the granular layer (ballast + sub-ballast), top subgrade, and bottom subgrade was 0.45, 0.6, and 1.9 m. The embankment height varied
according to the foundation (subsoil) conditions. During the earthwork construction, a 20-t smooth single-drum vibratory roller was
used for subgrade compaction at a constant speed of 5 km/h given
nominal during the tests. Hence, the particles showed considerable
resistance to degradation under working conditions.
Fig. 4 shows the accumulation of plastic axial strain against the
number of loading cycles. During each test, the dynamic stress
above the threshold can be determined as the cumulative axial
strain continues to increase with load cycles and soil failure above
that threshold. It can be seen that the plastic strain practically
tends to be constant at normalized stress of 0.4 (or less) in the
2:1 mixed soil subjected to a confining pressure of 20 kPa. In contrast, the threshold stress was much lower in the 3:1 mixed soil.
Based on the monotonic consolidated drained (CD) triaxial test
results, the critical dynamic stress level was obtained. In the case
of the 2:1 stabilized aggregate, 253, 358, 85, 120 kPa were obtained
for OMC (20 kPa confining pressure), OMC (70 kPa), saturated
3
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
Fig. 3. Loading pattern (a) and changes in the particle size of SCs at optimum moisture content before and after the cyclic loading (b).
8
8
(a)
6
4
2
0
0
2
4
6
8
Number of loading cycles, N ( 104)
d / s
(b)
4
0
10
0
2
4
6
8
Number of loading cycles, N ( 104)
10
6
4
=
(c)
2
0
Normalized stress level,
0.05
0.1
0.2
0.3
0.4
0.5
0.6
d / s
p (%)
Normalized stress level,
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Plastic strain,
p (%)
Plastic strain,
=
2
6
0
Normalized stress level,
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
d / s
Plastic strain,
Plastic strain,
p (%)
6
=
p (%)
Normalized stress level,
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2
4
6
8
Number of loading cycles, N ( 104)
d / s
(d)
4
2
0
10
=
0
2
4
6
8
Number of loading cycles, N ( 104)
10
Fig. 4. Variations in plastic strain (ep ) vs. load cycle numbers (N) at a confining pressure of 20 kPa (red lines indicate specimen failure); (a) 2:1 stabilized soil at optimal
moisture content, (b) 2:1 fully-saturated stabilized soil, (c) 3:1 stabilized soil at optimal moisture content, and (d) 3:1 fully- saturated stabilized soil. (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of this article.)
4
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
Fig. 5. Trajectory of the Addis Ababa-Djibouti Railway Line with the location of the field monitoring program (a) and overview of stabilized cinder subgrade (b).
Fig. 6. Geological profile of the ballasted track superstructure and underlying structures constructed by SC (DK 71 + 215) and traditional fill material (DK 81 + 550).
it was selected as the fill material for constructing the top subgrade. The fills were classified into Groups B and C as per China’s
railway classification standard TB 10001–2016, depending primarily on their particle size distribution characteristics. From the perspective of K 30 values and grain size distribution, these structures
meet the aggregate requirements and are comparable, allowing
comparison of their dynamic performance under traffic load.
the engineering properties of coarse fills. The maximum thickness
of the compacted layer was controlled at 35–40 cm. The operation
in the field was generally based on the following standard: one
pass of static compaction (beginning) + one pass of low-vibration
compaction + two to four passes of intense-vibration compaction + one pass of low-vibration compaction + one pass of static
compaction (final step).
Table 2 provides the basic properties of earth structure fills used
in each structural layer based on field measurements upon the
completion of subgrade construction. K 30 values indicate the modulus of subgrade reaction. It is defined as the reaction pressure
maintained by the foundation soil per unit settlement measured
at a 1.25 mm settlement under a 300-mm diameter bearing plate.
It should be noted that different blend ratios were adopted from
laboratory tests and field application trials for three layers of the
SC subgrade as per their mechanical performance [12]. The 2:1
mixed soil outperforms the aggregate at other blend ratios. Hence,
3.2. Geotechnical instrumentation and the vehicle
Field instruments primarily consisted of integrated vibration
sensors, a signal amplifier, earth pressure cells, and data acquisition devices. The integrated vibration sensors (physical dimensions
of 56 mm 56 mm 77 mm; weight: 0.75 kg) were developed
and manufactured by the Institute of Engineering Mechanics,
China Earthquake Administration. Table 3 presents the technical
specifications for the integrated vibration sensors. The main role
Table 2
Physical and mechanical properties of fill materials with field measurements.
Test section
Layer
Fill *
Classification *
Cu
Cc
Gs (g/cm3)
K 30 * (MPa/m)
SC
Top subgrade
Bottom subgrade
Embankment
Top subgrade
Bottom subgrade
Embankment
Stabilized soil (2:1)
Stabilized soil (3:1)
Stabilized soil (3.5:1)
Coarse-grained soil
Coarse-grained soil
Silty sand
B
B
B
B
B
C
139.58
110.34
77.00
62.5
102.0
–
0.78
8.73
11.69
5.33
2.53
–
2.55
2.56
2.52
2.53
2.53
–
169.5
158.0
159.0
162.5
157.5
154.5
Baseline
*Note: 1. 2:1, 3:1, and 3.5:1 indicate the mixing ratios of stabilized soil; 2. It is determined based on the China’s code TB 10001–2016; 3. It is the modulus of subgrade reaction
obtained from rigid plate load tests.
5
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
Table 3
Technical specifications of geotechnical instrumentation.
Item
Type
Measurement
Capacity
Accuracy
Sensitivity
Earth pressure cell
Integrated vibration sensor
DYB-5
891–2
Dynamic earth pressure
Displacement
Velocity
Acceleration
200 kPa
15 mm
50 mm/s
20 mm/s2
2 kPa
N/A
1 mm/s
0.2 mm/s2
0.1 kPa
N/A
0.5 mm/s
0.1 mm/s2
granular layer and the top subgrade right beneath two adjacent
concrete crossties. The observed dynamic stress intensity and
train-induced vibration on the top of the subgrade provided useful
information for the dynamic or transient characteristics of soil
structures. It was expected that additional sensors mounted at deeper levels in the subgrade could help explore the attenuation law
of dynamic stress in soil structure under ballasted tracks [16].
However, it was not easy to implement it in practice due to extensive excavations, which disturbed the constructed facilities. Given
that the data quality and accuracy can be significantly affected by
sensor sensitivity [17], a laboratory calibration method similar to
an existing methodology [18] was implemented for all the manufactured earth pressure cells (EPCs). As a result, the actual stress
conditions of the sensors in the full-scale subgrade were adequately captured and reproduced.
Fig. 8 shows an overview of the established procedure of
geotechnical instrumentation. The first step was to locate the monitoring sites and excavate the ballast and sub-ballast materials
between the track components and upper subgrade in a few adja-
of the sensors was to measure vibration acceleration (Mode 1),
velocity (Mode 2), and displacement (Mode 3) at once during each
pass of the locomotive. These modes should be set up by a mini
controller before the field measurements. The signal amplifier
was used in conjunction with integrated vibration sensors because
of some essential data processing applications such as filtering,
integration, signal amplification, and impedance conversion. If
the signal received by the integrated vibration sensor becomes
weaker, the signal amplifier is activated to improve the accuracy
of the collected data. At the same time, the amplification factor is
adjusted, making it easy to use in practice. Earth pressure cells
(model DYB-5, Dandong Three of Instrument, Co., Ltd, China, specifications in Table 3) were mounted to collect the train-induced
dynamic stress at the structural interface between the granular
layer and the earth structure.
As shown in Fig. 7, in each experimental site, there were 12
integrated vibration sensors (total 24 for two sections) and four
earth pressure cells (total eight for two sections). They were
mounted close to each other at the interface level between the
Fig. 7. Instrument configuration for field monitoring at each test section: top view (a) and cross-section view (b). ‘(3)’ indicates three different measurement modes.
Fig. 8. Field instrumentation procedure: (a) ballast and sub-ballast excavation, (b) smoothing surface, (c) installing pressure cells, (d) leveling, (e) installing integrated
vibration sensors, and (f) backfilling and manual compaction.
6
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
also useful for field investigations. The train was run at six different
speeds, including 5, 20, 40, 60, 80, and 100 km/h. The detailed test
scheme is summarized in Table 5.
cent crossties. The soil surface was smoothened and leveled off
(Fig. 8d) to allow the embedded EPCs to receive upward pressures
from the track superstructure. Following this, a standard sand layer
(poorly graded with the grain size range of 0.25–0.5 cm) with a
thickness of 5 cm was placed beneath the location of horizontal
EPCs to prevent stress concentration phenomenon and associated
transducer damage. Another layer of sand of the same thickness
was laid on top of the EPCs to complete the installation of sensors.
Cell wires were protected by rubber bushings or aluminum alloy
from possible damage during the final backfill compaction. The
installation of the integrated vibration sensors followed a similar
pattern.
In contrast, three sensors were mounted next to the EPCs and
maintained in displacement, velocity, and acceleration modes. A
steel protective shield was used around the measurement units
instead of the sand layer. The granular material was then backfilled
and compacted in the original positions. Then, it was necessary to
inspect field compaction quality against the railway specifications
to complete the entire installation process of instruments.
Before the beginning of the monitoring program, an advanced
automatic level was used to determine the relative height levels
of the rail, from which the rail height difference can be obtained
as an indication of track geometry. It was understood that regular
track maintenance is required to keep the track in good order. Nevertheless, the serviceability of the underlying track substructure
can be inferred to some extent from these measurements. The
study area extended 100 m longitudinal in two test sections and
included both left and right rails.
Fig. 9a shows an overview of the train used for the field experiment. It was powered by two connected ERF (Ethiopian Railways
Freight) locomotives (Ethiopian variant of HXD1C, CRRC Corporation Limited, China). An ERF locomotive of the Addis AbabaDjibouti Railway was selected because of its distinct advantages
of energy-saving, economic benefits, and comprehensive environmental protection. Table 4 shows some technical specifications
for the selected locomotive. As shown in Fig. 9b, the data acquisition unit (imc Test & Measurement GmbH, Germany) was able to
handle up to 100 kHz per channel, which was compatible with
the signal sources and sensors considered in this study (i.e., pressure and vibration). The spectrum of the data acquisition system
merged integrated real-time calculations of the data, which was
3.3. Data collection and processing
Fig. 10 shows the track geometry conditions of the instrumentation structure for track level deviations against sampling length
intervals. Fig. 10b shows a diagram of the measurement method.
In this diagram, the curve ABC denotes the real track level variations lengthwise. The level difference at midpoint B reflects the
irregularity of the track. The track level deviation is similar for
the left and right rails of both test sections, but the magnitude of
the level difference is smaller for the SC subgrade, mainly in the
5 mm range. The track level deviation is positively correlated
with the length interval, reaching up to 20 mm with a sampling
interval of 100 m. This indicates that the serviceability of conventional subgrade during track maintenance requires improvements
to mitigate the track substructure settlement under routine traffic
loads. In practice, track irregularities directly affect the dynamic
response of railway subgrade during train passages and can be
used as a useful indicator of field performance assessment.
Table 5
Test cases for field dynamic assessment of two earth structures.
Test section
Train
speed
(km/h)
Operation
Annotation
SC subgrade (DK 71 + 215)
and standard subgrade
(DK81 + 550)
5
1 round
trip
5 round
trips
5 round
trips
5 round
trips
5 round
trips
1 round
trip
Recorded data serve
as calibration
20
40
60
80
100
Reduced operations
due to safety
considerations
Fig. 9. The ERF electric locomotive used in the field test (a) and the data acquisition system (b).
Table 4
Mass and geometric characteristics of ERF locomotive used in field testing of subgrade vibrations.
Type
no. of wagons
no. of axles
inter-bogie spacing (m)
inter-axle spacing (m)
axle spacing* (m)
axle load (t)
HXD1C
2
12
11.76
2 + 2.25
6.4
25
Note: * refers to the adjacent axle spacing between two wagons.
7
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
Fig. 10. Track level deviation varying with the length interval (a) and a graph of the track geometry measurement (b).
lected on the top of subgrade (presence of granular layer mitigated
the vibrations), instead of the tracks; Second, by comparison with
coaches (passenger car), the locomotives used in this study possess
higher axle loads (25 t) and smaller inter-axle spacing (2 m + 2.2
5 m). The amplitude of resilient deformation is mainly below
0.6 mm at 60 km/h and below 1.0 mm at 100 km/h. The trough that
reaches the center of the two axles of the bogie can be captured at
low-speed levels but becomes less noticeable as the train speeds
up.
The velocity and acceleration time history curves show consistency with the passage of locomotive. Supposing that the axles are
directly acting on the overlying track structure, considerable velocity and acceleration fluctuations can be observed. At the same time,
their amplitudes drop rapidly to near zero between the approach of
the two bogies. Train-induced earthwork vibrations in terms of
maximum displacement, velocity, and acceleration are higher in
conventional subgrade than in the SC subgrade. This phenomenon
is also related to the diversified stiffness of track foundation constructed by two types of fills over time. The critical difference
between the on-site dynamic performance of the two subgrades
further confirms that SC outperforms baseline fill (classified as
Groups B and C).
The power spectrum of a time series describes the distribution
of power into the frequency components that comprise the signal.
Based on Fourier analysis, the received physical signal can be
decomposed into a spectrum of continuous range frequencies,
which contains essential information about the nature of the time
series. Fig. 12 shows the frequency contents of train-induced velocities at speeds of 60 and 100 km/h. Standard and SC subgrades present approximately the same dominant frequencies under the
same train speed conditions. Information on the frequency spectrum peaks at about 1.50 Hz and 3.83 Hz at an operational speed
of 60 km/h. When evaluating railway vibrations, a distinction is
made between dynamic and quasi-static excitations [19]. The former is related to the dynamic train-track interaction, while the latter is affected by both wheel combination and train speed. During
the passage of a train, the dynamic loading feature can be regarded
as a combination of axles that continuously act on one fixed point
of the rail, characterized by the load frequency of a mobile unit.
Based on the geometry of the ERF locomotive and a train speed
of 60 km/h, a load frequency of 1.5 Hz corresponds to a representative length of 11.76 m, which is the center-to-center distance of
The time-domain characteristics of train-induced subgrade
vibrations with respect to dynamic soil stress, vertical displacement, velocity, and acceleration are shown in Fig. 11 for two specific operating speeds of 60 and 100 km/h. Since two connected
locomotives were used for field measurements, time-domain signals were recorded and presented concurrently for the passage of
one train. The time history curve of mobilized soil stress on the
top of the subgrade is comparable to the Mshaped curve within
the range of a three-axle bogie during train passage. The local maximum dynamic stress occurred directly beneath each axle load of
the bogie and decreased to the first trough when it reached the
center of two adjacent axles. The dynamic stress reached another
peak due to the approaching axle of the second train. Then, the second trough occurred and rose to the third peak as the third axle
approached. This indicates that the mobilized soil stress during
the passage of each bogie featured a typical and similar threeaxle load characteristic. Besides, the dynamic stress was nominal
between the approaches of the two locomotive bogies, and their
peak values were substantially larger in the SC subgrade than in
the standard subgrade. This was primarily attributed to the fact
that SC tends to harden by chemical processes comparable to Pozzolanic reactions and hydration into a stronger and more rigid
mass. As a result, SC subgrades become stiffer in the presence of
chemical reactions over time and promote greater dynamic soil
stress peak than standard subgrades during vehicle operation.
Positive displacements are predefined to indicate upward
movements from the equilibrium position. Dynamic displacements
are not directly measured. Instead, they are obtained by integrating the velocity signal with a bass-cut filter to avoid the baseline
drift and DC bias. Since the integration process was involved,
potential errors may arise for the calculated displacements. Unfortunately, the accuracy of displacement measurement was not provided by the manufacturer for the integrated vibration sensor,
which renders the displacement items questionable. It is emphasized that the displacement data presented here were unavoidably
affected; however, the tendency generally reveals the subgrade
vibration characteristics due to train passage. Negative displacement occurs as the bogie passes by, and vertical displacement
becomes positive between the two bogies approaching. It is convenient to identify each axle for dynamic stress, but this identification becomes difficult for vibration displacement. This can be
attributed to two primary reasons: First, the displacement was col8
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
two bogies in the same vehicle. A load frequency of 3.83 Hz corresponds to the inter-axle spacing in one bogie (i.e., 4.25 m). The
peak velocity corresponding to the frequency of 1.50 Hz is the
maximum, indicating that the subgrade dynamic response is
strongly affected by the cyclic loading of two adjacent bogies of
the same vehicle. This serves as the basis for reproducing the
train-induced dynamic loads in numerical simulations and fullscale model tests. Spectral analysis of the two-track substructures
at a speed of 100 km/h shows a similar pattern with predictably
higher amplitudes at the two dominant frequencies (2.36 and
6.27 Hz). Several other dynamic excitation mechanisms underlying
railway vibrations have been discussed in the literature [20,21],
and the related frequency ranges must only be considered in
high-speed railways. The dominant frequencies observed in heavy
haul railways where total weight is relatively high have been summarized in the literature [22].Fig. 13.
4. Discussion
4.1. Dynamic vertical stress distribution
There are several established theoretical models for determining the effects of traffic load-induced stress on the foundation of
a track. The Boussinesq elastic model-based approach has previously calculated vertical soil stress distributions in track substructures, assuming that both granular and subgrade layers are treated
as integrated elastic, isotropic, and homogeneous materials [23–
25]. Two typical load types are considered: uniformly distributed
loads acting on a surface (crosstie base) and point loads. Nevertheless, this approach using these types of loads is not practical for
predicting substructure soil stress distributions under ballasted
tracks [26]. The load spread model is another frequently used
method [27–29], assuming that soil stress is uniformly distributed
in the area under a crosstie and is confined by boundaries that are
inclined at a specific angle to the vertical. This approach is not satisfactory, but it provides better measurement matching than
Boussinesq’s solution [26].
Bourdeau and Harr [30] used the stochastic stress diffusion theory to describe the load transfer imposed on granular media. The
resulting load transfer modes in the ballast layer are plausible as
they explain the patterns of heterogeneity and variability. Zhang
et al. [26] developed a modified spreading model by combining
stochastic stress diffusion theory with the original load spread
model. In this approach, the solution for stress propagation when
a uniform pressure (p) acts on a strip with a width of 2a (schematically displayed in Fig 0.13) is as follows:
Fig. 11. Time histories of train-induced dynamic soil stress, vertical displacement,
velocity, and acceleration at speeds of 60 km/h (a) and 100 km/h (b).
2.5
1.50 Hz
2.0
Amplitude (mm/s)
1.5
SC
Traditional fill
3.83 Hz
1.0
Speed: 60 km/h
0.5
0.0
3
2.36 Hz
2
6.27 Hz
Speed: 100 km/h
1
0
0
2
4
6
8
10
12
14
16
Frequency (Hz)
Fig. 13. Schematic of the modified load spread model in layered substructure
applications: B is sleeper width; h is load spreading angle (Modified from Zhang
et al. [26]).
Fig. 12. Power spectrum of train-induced velocities in two test sections at speeds of
60 km/h and 100 km/h.
9
T. Wang, Q. Luo, L. Zhang et al.
rz ðx; zÞ
p
Construction and Building Materials 270 (2021) 121370
xþa
xa
¼ Uð pffiffiffi Þ Uð pffiffiffi Þ
z m
z m
empirical model agrees somewhat in terms of shape and magnitude with the observed values with an R-squared (coefficient of
determination) equal to 0.982 for conventional subgrades and
0.961 for SC subgrades. The symbol S refers to the crosstie spacing
(0.6 m in this study). Therefore, the difference in the standard deviations of the two fitted curves is notable. Since the parameter r
reflects the influence area of a single axle on the subgrade surface,
the higher value (i.e., 0.94 S) in Fig. 14a indicates that a larger portion of the standard subgrade surface is substantially affected by a
single wheel load. This observation is consistent with lower peak
values recorded in the standard subgrade than those in the SC subgrade. This confirms that the synergistic effect of the three axles of
one bogie can be successfully decoupled and captured using the
three Gaussian functions.
Rail seat load is a fundamental parameter for track structure
design (Fig. 15a). As shown in Fig. 15b, several studies [23,31,32]
have focused on the determination of it by assimilating rail components into beam resting on continuous linear elastic foundations
(Winkler model). The deflection on continuous rails is first converted to discrete deflections (Fig. 15c). Hence, the maximum rail
seat load can be calculated with three parameters: crosstie spacing,
maximum rail deflection, and track foundation modulus. In contrast to this theoretical approach, the normalized rail seat load
can also be inferred indirectly from the distance-domain vertical
stress distribution curve (Fig. 14) combined with the following
empirical formula:
ð3Þ
where rz ðx; zÞ is vertical stress in gravel material, t is coefficient
of diffusivity associated with soil compaction, and coefficient of
earth pressure, UðxÞ is cumulative normal distribution function, x
and z are coordinates of longitudinal (horizontal) and vertical axis.
It is worth noting that uniform pressure (p) is obtained from the
load spread model.
The modified spread model can quantify the mobilized vertical
stress distribution. However, it essentially requires several physical parameters that may be difficult to obtain, such as rail seat load,
foundation modulus, and coefficient of earth pressure. Inspired by
this approach, the study used the Gaussian function to measure
vertical soil stress distributions on the subgrade surface. Since
axles can be readily identified in the subgrade (Fig. 11), an empirical model combining three Gaussian functions is considered to
superimpose the three-axle loads of one bogie given by:
rs ðxÞ ¼ ½
P3
w g ðxÞ
i¼1 i i
P
rmax
3
max
i¼1
wi g i ðxÞ
xl 2
12ð r i Þ
g i ðxÞ ¼ rp1ffiffiffiffi
e
2p
i
ð4Þ
i ¼ 1; 2; 3;
rp ¼ ð1 þ av Þ r0 ;
ð5Þ
where rs is mobilized dynamic soil stress, x is the horizontal
position, g i ðxÞ denotes Gaussian function where li is the position
of bogie axle (in this case, l1 ¼ 0, l2 ¼ 2:25, and l3 ¼ 4:25 conforming to geometric characteristics of bogie),ri (i = 1, 2, 3) is standard deviation; wi denotes weight factor of axle load in case of
non-negligible differences among three axles (otherwise wi ¼ 1),
rmax is maximum value of dynamic soil stress as a function of r0
(observed soil stress value at a speed of 5 km/h) and train velocity,
v (>5 km/h), a is velocity coefficient [(km/h)-1] accounting for
speed effect on mobilized dynamic soil stress. If r0 is unavailable,
it can be calculated using an empirical formula [16].
Fig. 14 shows a comparison of the measured and predicted
dynamic stresses of two vehicles passing by curve fitting at a speed
of 60 km/h using Eqs. (4) and (5). In this scenario, the distancedomain signals were converted from the time-domain signals after
multiplying time by train speed. It should be noted that the initial
point (distance = 0 m) on the horizontal axis corresponds to the
first axle load of the bogie, and the inter-axle spacing equals
4.25 m. Although there are some minor discrepancies, the
q ¼ Uðx þ 0:5SÞ Uðx 0:5SÞ
where q ¼ q=Q is normalized rail seat load; UðxÞ is the cumulative distribution function of the Gaussian function used in the fitting of the recoded data (Fig. 14). The calculated results for the
two subgrades are compared with the track design practice and
available data from literature [26,33,34] in Fig. 15d. The predicted
values generally fall within the range of design standards and
research results, and the characteristics of the subgrade fill (e.g.,
soil foundation modulus) appear to have little effect on the rail seat
load. Although estimations yielded reasonable values, it is worth
noting that this prediction only depends on the standard deviation
of the fitted Gaussian function. At the same time, the status of track
components, granular layer, subgrade layer, and load transmission
in the ballast layer is entirely ignored, which may cause accuracy
issues. In light of this, the accuracy of the indirect evaluation of rail
60
60
Measured, Locomotive #1
Measured, Locomotive#2
Empirical model R2 = 0.982
Measured, Locomotive #1
Measured, Locomotive #2
Empirical model R2= 0.961
(a) Traditional fill
0.94S
w1 p=50.63
40
Dynamic soil stress (kPa)
Dynamic soil stress (kPa)
ð6Þ
w2 p=56.71
w3 p=61.29
20
w2 p=60.85
w3 p=65.98
20
inter-axle spacing
0
0
2
4
0.82S
w1 p=62.09
40
inter-axle spacing
-2
(b) SC
6
0
8
-2
Position (m)
0
2
4
6
8
Position (m)
Fig. 14. Longitudinal distribution of observed train-induced dynamic soil stress compared to empirical model at a speed of 60 km/h; (a) traditional fill, (b) SC.
10
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
Single axle load = Q
Rail
0.6
Normalized rail seat load, q/Q
Crosstie
Estimated, Standard
Estimated, SC
China's design practice
Recommended in literature
0.5
0.4
0.3
0.2
0.1
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Position (m)
Fig. 15. Modeling of rail track deflection for obtaining rail seat load based on Winkler model (a–c, after [26]) and comparison of normalized rail seat loads obtained from
different methods (d, data from literature [26,33,34]).
and ending times of data extraction are initially defined with the
threshold stress of the time-history curves of dynamic soil stress.
The time range is then classified from the dynamic stress variations
into three domains with two troughs. The peak values are
extracted from each colored domain in sequence and combined
to compile a dataset for statistical analysis. Signals of different
observations adopted the same point in the time of sampling.
Descriptive statistics of the extracted peak values of the four
recorded items are presented in Figs. 17–20. A train speed of
5 km/h is first defined as the quasi-static speed so that the effect
of operating speed on subgrade vibrations can be evaluated against
benchmarks. Fig. 17 shows the maximum dynamic soil stress
above of the subgrade as the train speed increases from 5 to
100 km/h. The induced dynamic stress of the two structures grows
almost linearly with increasing train speed, and the stresses at
100 km/h increase by 26% (for SC) and 31% (for traditional fill) over
the quasi-static conditions.
The French National Railway Company (SNCF), International
Union of Railways Office for Research and Experiments, and the
German Federal Railway have employed an empirical method
[23,44,45] for assessing the dynamic amplification of axle loads
using observed rail stress data:
seat loads can be improved if the vertical stress distribution is collected at shallower depth beneath the crossties (most accurate if
stress sensors are mounted beneath the base of sleeper).
4.2. Effect of train speed on subgrade vibrations
The effect of train speed on the vibration characteristics of track
structure, including track components and foundations, has been
extensively investigated by field measurements [16,17,22,35,36],
full-scale model testing [37–39], and numerical simulations [40–
42]. As widely accepted, stress amplitudes, displacement, velocity,
and acceleration are significantly amplified with speed upgrading.
The critical velocity effect [16,43] can occur on high-speed rails,
imposing a serious threat to safe operation. Given the target speed
of 80 km/h for freight, a speed range of 5–100 km/h was considered
for evaluating train speed impact on the dynamic performance of
two-track foundations. Focus is placed on the statistical analysis
of the peak values in all measured items. To clearly observe the
data extraction process, the first portion of Mshaped stress signals and the corresponding displacement, velocity, and acceleration signals in Fig. 11a were expanded in Fig. 16. The beginning
60
kPa
Sampling area
t = tb
t = te
/ ¼ Ps =P ¼ 1 þ kð
40
Soil stress
20
0
Axle 1
0.4
0.0
-0.4
10
Displacement
mm
mm/s
Velocity
0
-10
4
m/s2
Acceleration
0
-4
5.1
5.2
5.3
5.4
5.5
5.6
3
ð7Þ
where / denotes velocity impact factor, P s is static wheel load
(kN), P is operational wheel load (kN), k denotes a parameter determined from track elements, track geometry, and the age of vehicles, v is train speed (km/h). This equation is similar to Eq. (5)
that can be used to calculate the velocity coefficient (a) as
0.0026 for the SC subgrade and 0.0031 for the standard subgrade,
meeting the specification requirements [< 0.005 (km/h)-1]
described as the critical lines in Fig. 17. The maximum dynamic
stress of the two structures at 100 km/h also statistically meet
the pressure requirements (<100 kPa, China’s design code TG/GW
120–2015) taking the axle loads into account. The threshold stress
(i.e., 85 kPa) in extreme conditions obtained from the dynamic triaxial tests performed on the immersed specimens (Fig. 4) is also
presented for SC. This indicates that the immersed SC fills during
the rainy season can maintain dynamic stability under long-term
traffic impacts. The structural stability of SC subgrades is generally
superior to conventional subgrades in terms of velocity
coefficients.
Axle 3
Axle 2
v
Þ
100
5.7
Elapsed time (s)
Fig. 16. Diagram of sampling method in the statistical analysis of extremum of
dynamic soil stress, vertical displacement, velocity, and acceleration (tb and te are
the beginning and ending times of sampling, respectively).
11
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
100
100
(a) SC
(b) Traditional fill
Dynamic soil stress (kPa)
Threshold stress (immersion)
80
80
Critical line
= 0.0026
60
Critical line
60
Quasi-static reference
40
40
20
20
0
Quasi-static reference
= 0.0031
25%~75%
Range within 1.5IQR
Median Line
Mean
Outliers
0
5
20
40
60
80
100
5
20
40
60
80
100
Train speed (km/h)
Train speed (km/h)
Fig. 17. Boxplot of train-induced peak dynamic soil stress vs. train speeds at two test sections (IQR denotes the interquartile range).
(a) SC
(b) Traditional fill
1.0
1.0
Vertical displacement (mm)
Specification requirement
Specification requirement
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
25%~75%
Range within 1.5IQR
Median Line
Mean
Outliers
0.0
5
20
40
60
80
100
5
20
40
60
80
100
Train speed (km/h)
Train speed (km/h)
Fig. 18. Boxplot of train-induced peak vertical displacements vs. train speeds at two test sections.
20
20
Vertical velocity (mm/s)
(a) SC
(b) Traditional fill
15
15
10
10
5
5
0
25%~75%
Range within 1.5IQR
Median Line
Mean
Outliers
0
5
20
40
60
80
100
5
20
40
60
80
Train speed (km/h)
Train speed (km/h)
Fig. 19. Boxplot of train-induced peak vertical velocity vs. train speeds at two test sections.
12
100
Construction and Building Materials 270 (2021) 121370
T. Wang, Q. Luo, L. Zhang et al.
Vertical acceleration (m/s2)
(a) SC
(b) Traditional fill
6
6
4
4
2
2
0
25%~75%
Range within 1.5IQR
Median Line
Mean
Outliers
0
5
20
40
60
80
100
5
20
40
60
80
100
Train speed (km/h)
Train speed (km/h)
Fig. 20. Boxplot of train-induced peak vertical acceleration vs. train speeds at two test sections.
Laboratory tests were performed primarily on natural cinder, local
stabilizer, and their mixtures at two blend ratios (2:1 and 3:1) to
obtain appropriate physical and mechanical properties. A field
monitoring program was conducted at two experimental sites with
two fill materials (SC and Group B/C soil) used in track substructures. Vertical stress, displacement, velocity, and acceleration on
the subgrade surface beneath crossties were recorded under a train
traveling at six speeds. Time-domain and frequency-domain characteristics of collected data, dynamic stress distribution, rail seat
load, and train speed effects were revealed for two earth
structures.
Laboratory test results showed that cinder mixed with local
silty sand at blend ratios of 2:1 and 3:1 is classified as a moderately
permeable soil within a relative compaction range of 85–93%. The
breakage potential of SC particles is nominal under the imposed
cyclic loading. In the worst-case scenario (immersion at confining
pressure of 20 kPa), the 2:1 and 3:1 stabilized aggregates yielded
dynamic stress thresholds of 85 kPa and 97 kPa, respectively. They
satisfied the strength requirements for the subgrade aggregates of
ballasted tracks at a maximum speed of 80 km/h (freight).
Based on field records, the axles can be easily identified for
dynamic soil stress, while only bogies can be recognized for vertical displacement, velocity, and acceleration in both substructures.
Frequency-domain signals suggest that the cyclic loading of two
adjacent bogies of the same vehicle has the greatest impacts on
the vibrations of two subgrades. An empirical model incorporating
three Gaussian functions can be used to capture the measured longitudinal distribution of vertical stress on the subgrade surface.
The rail seat loads predicted by a simplified approach using the
stress distribution model are reasonably consistent with design
practice and literature recommendations [26,33,34].
Track irregularities are more pronounced in the baseline section
than in the SC section, partially reflecting a smaller settlement in
the SC subgrade. Train passages induced higher amplitudes of
dynamic soil stress, and lower amplitudes of vibration displacement, velocity, and acceleration in the SC subgrade than those of
the standard subgrade. The maximum vertical displacement at
100 km/h is 0.25 mm and 0.62 mm for SC and baseline sites, both
below the tolerance of 1 mm according to TB 10001–2016. The
evolution of dynamic stress amplitudes with train speeds demonstrates that the impact of speed is more significant on conventional
subgrade than on SC subgrade. A linear correlation was established
between stress and train speed for SC (velocity coefficient = 0.00
26) and baseline (velocity coefficient = 0.0031) sites. Finally, it
In the SC subgrade, the resilient deformation (vertical displacement) grows almost linearly with train speed at a rate of 0.024 mm
per 10 km/h. In contrast, the increasing rate reaches a maximum of
0.06 mm per 10 km/h for the standard subgrade, suggesting that
the resilient deformation of the standard subgrade is more susceptible to train speed. Both rates tend to be attenuated as train speed
increase. Resilient deformations are relatively small under quasistatic conditions for both structures (0.014 and 0.025 mm) and
improve significantly as the train speed increases. The calculated
mean value of the peak vertical displacement at 100 km/h is
0.25 mm for SC subgrades and 0.62 mm for standard subgrades,
both below the tolerance of 1.00 mm for the ballasted track
roadbed stability as per TB 10001–2016. It has been further verified that the dynamic performance of SC subgrades is superior to
conventional subgrades.
More outliers can be seen in Figs. 19–20 based on the statistical
analysis of vibration velocity and acceleration compared to
Figs. 17–18. The vibration velocity of the SC structure increases
almost linearly with the train speed at a rate of 1.3 mm/s per
10 km/h and reaches a peak of 13.94 mm/s at 100 km/h. In contrast, the growth rate and peak value at 100 km/h are 1.12 mm/s
per 10 km/h and 14.60 mm/s for the conventional substructure.
The biggest difference lies in the quasi-static conditions. This
means that a vibration velocity of 0.98 mm/s is recorded in the
SC section and 3.29 mm/s in the baseline section. The vibration
acceleration of the SC subgrade increases substantially from 0.58
m=s2 (quasi-static) to 2.51 m=s2 as train speeds reaches the maximum of 20 km/h. Similarly, vibration acceleration increases from
1.01 m=s2 to 2.94 m=s2 in the conventional subgrade. After this
(>20 km/h), the growth rates are nearly constant for two structures. The measured acceleration of the SC subgrade increases at
a rate of 0.27 m=s2 per 10 km/h. The rate decreases to 0.24 m=s2
per 10 km/h for the conventional subgrade. The maximum acceleration obtained at 100 km/h is 4.64 m=s2 for SC and 4.86 m=s2 for
standard fill material. Vibration acceleration follows a similar pattern for both structures. However, the SC subgrade has a much
broader interquartile range than the conventional subgrade and
is positively correlated with train speed.
5. Concluding remarks
The dynamic performance of ballasted track subgrade
constructed by mechanically stabilized cinder (SC) was evaluated.
13
T. Wang, Q. Luo, L. Zhang et al.
Construction and Building Materials 270 (2021) 121370
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terms of dynamic behaviors for railway applications. In addition,
its suitability as a subgrade fill under ballasted tracks is well
documented.
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CRediT authorship contribution statement
Tengfei Wang: Conceptualization, Methodology, Formal analysis, Writing - original draft, Funding acquisition. Qiang Luo: Conceptualization, Methodology, Supervision, Project administration,
Funding acquisition. Liang Zhang: Validation, Investigation. Shiguo Xiao: Resources, Writing - review & editing. Hang Fu:
Software.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China [Grant Nos. 41901073 and 51878560], the Shanghai Key Laboratory of Rail Infrastructure Durability and System
Safety [Grant No. R202003], the China Postdoctoral Science Foundation [Grant No. 2019 M663556], and the Fundamental Research
Funds for the Central Universities [Grant No. 2682020CX66].
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