Acta Geotechnica DOI 10.1007/s11440-014-0327-y
REVIEW PAPER
Simulating train moving loads in physical model testing of railway infrastructure and its numerical calibration Hongguang Jiang • Xuecheng Bian • Chong Cheng • Yunmin Chen • Renpeng Chen
Received: 9 July 2013 / Accepted: 20 April 2014 Ó Springer-Verlag Berlin Heidelberg 2014
Abstract Ballastless high-speed railways have dynamic performances that are quite different from those of conventional ballasted railways. The essential dynamic characteristics of high-speed railways due to passing train wheels, such as the cyclic effect, moving effect, and speed effect, were put forward and discussed. A full-scale accelerated railway testing platform for ballastless highspeed railways was proposed in this study. The feasibility of the sequential loading method in simulating train moving loads, and the boundary effect of the proposed physical model of ballastless railways, was investigated using threedimensional finite element models. A full-scale physical model, 5 m long, 15 m wide, and 6 m high, was then
Invited Paper from the International Symposium on Geotechnical Engineering for High-speed Transportation Infrastructure (ISGeoTrans 2012), October 26 to 28 2012, Hangzhou, China. CoEditors Prof. Xiong (Bill) Yu, Case Western Reserve University, USA and Prof. Renpeng Chen, Zhejiang University, China.
established according to practical engineering design methods. Using a sequential loading system composed of eight high-performance hydraulic actuators, loads of a moving train with highest speed of 360 km/h were simulated. Preliminary experimental results of vibration velocities were presented and compared with field measurements of the Wuguang high-speed railway in China. Results showed that the experimental results coincided with the field measurements, demonstrating that the full-scale accelerated railway testing platform can simulate the process of a moving train and realistically reproduce the dynamic behaviors of ballastless high-speed railways. Keywords Field measurements Full-scale accelerated railway testing High-speed railway Sequential loading system Vibration velocity
H. Jiang Department of Civil Engineering, Key Laboratory of Soft Soils and Geoenvironmental Engineering, MOE, Zhejiang University, Room B507, Anzhong Building of Civil Engineering and Architecture, Zijingang Campus, Hangzhou 310058, China e-mail:
[email protected]
Y. Chen Department of Civil Engineering, Key Laboratory of Soft Soils and Geoenvironmental Engineering, MOE, Zhejiang University, Room A425, Anzhong Building of Civil Engineering and Architecture, Zijingang Campus, Hangzhou 310058, China e-mail:
[email protected]
X. Bian (&) Department of Civil Engineering, Key Laboratory of Soft Soils and Geoenvironmental Engineering, MOE, Zhejiang University, Room B406, Anzhong Building of Civil Engineering and Architecture, Zijingang Campus, Hangzhou 310058, China e-mail:
[email protected]
R. Chen Department of Civil Engineering, Key Laboratory of Soft Soils and Geoenvironmental Engineering, MOE, Zhejiang University, Room A428, Anzhong Building of Civil Engineering and Architecture, Zijingang Campus, Hangzhou 310058, China e-mail:
[email protected]
C. Cheng Institute of Hydraulic Structure and Water Environment, Zhejiang University, Hangzhou 310058, China e-mail:
[email protected]
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1 Introduction Ballastless slab tracks, which are taking the place of conventional ballasted tracks, are widely used in high-speed railways to meet the demands of increasing train speeds. Ballastless tracks have been in service for more than 30 years on the Shinkansen lines in Japan and have provided excellent performance in terms of maintaining track geometry and reducing maintenance costs. In China, ballastless tracks are extensively used for newly built highspeed railways such as the Jinghu and Wuguang high-speed railways. It is planned that the length of the Chinese railway network will increase to 16,000 km by 2020. Ballastless tracks adopt rigid concrete structures to replace traditional ballast layers used for ballasted tracks. Because of the different track structures and much higher train speeds, ballastless railways have dynamic performances that are quite different from those of ballasted railways, such as transient responses and permanent deformation. To understand the dynamic behaviors of ballastless railways, theoretical models have been used in investigating the train-induced vibrations of the track structure and ground. Steenbergen et al. [31] employed a model of a beam on viscoelastic half-space subjected to a moving load to assess the ability of several engineering solutions, such as soil improvements and increased track stiffness, to reduce vertical vibrations of the track structure. Song et al. [30] proposed a coupled train–slab track analysis model and verified it with field test data. Effects of uneven settlement of the subgrade on vibrations of the track structure and dynamic soil stress of the subgrade were discussed. Galvin et al. [8] used a three-dimensional (3D) multibody finite element–boundary element model to study vibrations due to train passage on ballast and nonballast tracks, and concluded that the soil vibration behavior was significantly different for the different track systems. Results showed that vibrations of ballastless tracks were much smaller than those of ballasted tracks. However, the 3D finite element models require higher computational effort and storage. As an alternative method, 2.5-dimensional (2.5D) finite element models were proposed for the prediction of train-induced dynamic stresses and vibrations with lower computational cost [3, 9, 36]. Bian et al. [4] developed a train–slab track–subgrade dynamic interaction analysis model based on the 2.5-dimensional finite element method taking account of vertical track irregularities and studied the effect of the train speed on the dynamic responses of the track structure and ground. Besides the use of theoretical models, physical model tests have been carried out to investigate the dynamic responses and accelerate permanent settlement of railways under traffic loadings. Sekine et al. [29] built a 1:5 scale
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model of ballasted track and studied the effect of moving loadings on the permanent deformation of railway ballast. Al Shaer et al. [1] constructed a 1:3 scale ballasted track to study settlement under the loadings of moving bogies. They simulated different train speeds by adjusting the loading frequencies. Feng et al. [6] used a 1:2 scale model of ballastless track to study the dynamic performance of the subgrade under the loading of a single wheelset. Ishikawa et al. [12] examined the mechanical behavior of railway ballast subjected to repeated train passages using a 1:5 scale model of ballasted track. Test results of soil stresses and deformations obtained in the experiments for movingwheel loading and fixed-point loading were compared and discussed. The above-mentioned studies indicate that the dynamic performances of the track structure and subgrade in ballastless railways are quite different from those of conventional ballasted railways. To reproduce the realistic responses of high-speed railways in model tests, three crucial aspects of high-speed train loads—the cyclic effect, moving effect, and speed effect—should be taken into consideration.
2 Characteristics of high-speed traffic loads 2.1 Cyclic effect of train moving loads The geometry of railway tracks needs to reach a high alignment to meet the safety and comfort requirements of trains. The performance of railway tracks strongly depends on the mechanical characteristics of the subgrade, filled with various geomaterials, such as ballast, granular soil, and cohesive soil. During the service period of railways, the subgrade undergoes millions of loading cycles and soils deform nonelastically in response. When the train load is applied, the total deformation comprises resilient deformation and residual deformation. The rapidly fluctuating resilient deformation vanishes as the train wheel moves far from the observation point, and the residual deformation develops in the subgrade of railways as a result of the cyclic loading. When the load is removed, the initial geometry is not exactly recovered and small residual deformations remain. These residual settlements accumulate at the end of each cycle of traffic loading, and they represent one aspect of the cyclic effect that must be added to the effect of previous settlements [7, 17, 20, 21, 28]. The other aspect of the cyclic effect is that the elastic deformations do not always keep consistent during the loading cycles, which may result in an increase in stiffness [2, 11, 15, 33] or a decrease in stiffness [15, 16, 24, 35]. The cyclic effect on the residual settlement and soil stiffness largely depends on the
Acta Geotechnica
2.2 Moving effect of train loads Soil elements below the railway tracks are subjected to complex stress paths that involve a rotation of the principal stress directions as the train approaches and passes a given location. The vertical stress follows a path that is quite different from that of the lateral stress, mainly in terms of the sign (positive or negative) of the dynamic stress and the correspondence between the wheel position and the maximum or minimum dynamic stress. When the train wheel moves toward the observation point, both vertical and lateral stresses gradually increase. The lateral stress then decreases to zero when the train wheel is just above the observation point, while the vertical stress reaches a peak. The lateral stress then changes its sign owing to the position of the wheel and reaches the opposite peak before decreasing. However, the vertical stress remains as compression and decreases gradually after the peak. This process results in the rotation of the principal stress axis, which has been reported in both experimental tests [23] and theoretical models [25]. Cyclic loading with rotation of the principal stress axis can affect both the soil stiffness [18] and the rate of accumulation of the residual settlement [19]. Ishikawa et al. [12] examined the mechanical behavior of railway ballast subjected to repeated train passages using a 1:5 scale model of ballasted track. They concluded that loading methods had a considerable effect not only on the resilient deformation but also on the residual settlement. The resilient deformation and the rate of accumulation of residual settlement were much greater when soils were subjected to a moving load than when cycling the axial stress alone.
2.3 Speed effect of train moving loads With the development of high-speed railways, train speeds have reached more than 300 km/h. The dynamic responses such as vibrations and dynamic soil stresses are largely dependent on the relationships between the train speed and the wave velocity of the subgrade. At lower speeds, the railway responses to a moving load can be explained by quasi-static solutions. However, as the train speed increases, dynamic phenomena gradually take over and dominate the response. It is known that resonance will result in excessive ground movements if the train speed approaches the Rayleigh wave velocity of the soil [14], which has been observed in soils such as peats and soft clays with a low Rayleigh wave velocity of 40–50 m/s [22]. The increase in train speeds raises concerns about degradation of the subgrade, fatigue failure of rails, and running safety of trains [13]. Field measurements taken by Priest and Powrie [26] showed that track displacement increased with train speeds, and the effective soil stiffness for fast trains was about 20 % less than that for slow trains. Yang et al. [37] built a two-dimensional dynamic finite element model to study the effect of train speeds on the dynamic soil stress. Results indicated that dynamic effects started to become apparent when the train speed was greater than 10 % of the Rayleigh wave velocity of the subgrade. The shear stress was underestimated by 30 % in a static analysis at a train speed of 50 % of the Rayleigh wave velocity. Therefore, accelerated railway testing should represent these three characteristics of high-speed trains. However, few experiments have considered these effects, and most have been conducted at reduced scales. To reveal the realistic dynamic interaction between the track structure and the subgrade and the permanent performance of
Steel-test box Actuator Track slab
Rail Fastener
Concrete base
Roadbed
6m
physical state of the soil (such as the dry density and moisture content) and stress characteristics (such as the dynamic stress level, confining pressure, and loading frequency). According to the results obtained in many cyclic triaxial tests, Suiker and Borst [32] divided the stress–strain relation into four response regimes. At low levels of stress, the cyclic response of the granular materials is fully elastic and the stiffness does not change, which is usually called the shakedown regime. As the stress increases, soils enter into the cyclic densification regime, in which the cyclic loads submit the granular materials to progressive plastic deformations, and the stiffness of soils gradually increases. When the level of the cyclic load exceeds the threshold strength of granular materials, frictional collapse occurs. In this frictional failure regime, the residual settlement develops more quickly and the stiffness tends to decrease. The final regime is the tensile failure regime, where the soils readily disintegrate, as they cannot sustain tensile stresses.
Subgrade
Subsoil
5m
15 m
Fig. 1 Diagrammatic sketch of the proposed full-scale model
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ballastless railways under high-speed trains, full-scale accelerated railway testing was developed in a steel test box with dimensions of 15 m 9 5 m 9 6 m deep at Zhejiang University, China. A sequential loading method based on the three-dimensional finite element models was proposed, and a set of sequential loading equipment was constructed in the laboratory. Verification tests were carried out first to demonstrate the reliability of the full-scale testing platform. Experimental results of vibration velocities were obtained and compared with field measurements of the Wuguang high-speed railway in China. Fig. 3 3D finite element model
3 Concept of the proposed accelerated full-scale model testing Figure 1 is the diagrammatic sketch of the proposed fullscale accelerated railway testing platform in a steel test box with dimensions of 5 m in length, 15 m in width, and 6 m in height. A sequential loading method was proposed to simulate train motion. The feasibility of the sequential loading method, and the boundary effect of the proposed full-scale physical model of ballastless railways, was investigated using three-dimensional finite element models. 3.1 Verification of the proposed sequential loading method
Rail A B
4.0
C D
Subsoil
30 Cross section
100 Longitudinal section
Fig. 2 Sections of the finite element model (unit: m)
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30
Subgrade
Fastener
1.2 1.3 0.2
Observation points Track slab CAM layer Concrete base Roadbed
2.3 0.4 0.3 0.2
The sequential loading method is expected to apply loads directly at positions of fasteners on a track slab with a certain phase lag to simulate the running of train wheels along the continuous rails. The applied loads were obtained from the fastener forces under the loading of a moving train. The concept of the sequential loading method was proposed and validated by Takemiya and Bian with the substructure method [34]. Two 3D finite element models (FEMs) were used, one in which wheels moved along the rails (called the moving-wheel model) and the other in which fixed-point loads were applied sequentially to fasteners (called the sequential loading model). The moving-
wheel model represented the realistic train motion. Both the finite element analyses were performed in the time domain using direct time integration with implicit schemes. The time step of the analyses was fixed at 0.001 s. The 3D FEMs for ballastless high-speed railways, with dimensions of 100 m 9 30 m 9 33 m deep, were established according to the Chinese high-speed railway design code. The slab track–subgrade system consisted of rails, fasteners, a 0.19-m-thick track slab, a layer of cement asphalt mortar (CAM) over a 0.3-m-thick concrete base, a 0.4-m-thick roadbed, a 2.3-m-thick subgrade, and a 30-mdeep subsoil, as shown in Fig. 2. Figure 3 shows the 3D FEM of the moving-wheel model, consisting of 345,612 elements and 377,244 nodes. According to the symmetry of the cross section, only half the railway was modeled. Bernoulli–Euler beam elements were used to simulate the CHN60 rail. The rail was connected to the track slab by fasteners that were simulated by spring-damper elements. Elements of the track structure and substructure were simulated with eight-node linear brick elements. The nodes at the bottom boundary were fixed in all directions. Vertical and horizontal springs were applied at both ends of the rail to keep the rail in place at the ends of the finite element model. The physical parameters of the track structure and substructure are given in Table 1, which are in agreement with the Chinese highspeed railway design code. The loading method for the moving-wheel model was different from that for the sequential loading model. In the moving-wheel model, the rail was built from nodes and beam elements, and the nodes of the rail were considered as the loading nodes. Every third loading node was connected to the track slab by spring-damper elements. As the spacing S between the fasteners was 0.63 m, the spacing between the loading nodes was s1 = 0.21 m (=0.63/3 m). As illustrated in Fig. 4, the loads can be deemed as triangular pulses distributed among three nodes. These triangular pulses moved from one node to another in a time step equal to the node spacing of the loading nodes, s1, divided
Acta Geotechnica Table 1 Material properties of the ballastless railways Rail
Track slab
CAM
Concrete base
Roadbed
Subgrade
Subsoil
Elastic modulus (MPa)
2.1e5
3.5e4
92
3.0e4
400
180
60
Poisson ratio
0.3
0.16
0.4
0.16
0.3
0.3
0.42
Wheel
90
Node1 Node2
s1=0.63/3 m
Node3
80
Load (kN)
70
S=0.63 m Node Beam element
Rail Fastener
S=0.63m
Loading curves of nodes
50 40 30 20
Node 1
Node 4 Node 3
Node 2
Result of the moving wheel model Input load of the sequential loading model
Track slab
Node1 Node2 Node3
60
80
Fastener force (kN)
100
Rail segment Fastener Track slab
t
60 Node 1 Node 2
40
20
10 0
0
t1=s1/v
Time
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Time (s)
Fig. 4 Loading method of the moving-wheel model Fig. 5 Loading method of the sequential loading model
by the train speed, v, of the moving loads, t1 = s1/v [10]. A carriage of CRH2-type trains was used. The distance between two wheels of one bogie was about 2.5 m, and the spacing between two bogies of one carriage was about 17.5 m. Each rail was subjected to the axle load of 70 kN. In this case, the fastener force for the passage of one carriage was calculated and is shown in Fig. 5, where the time evolution of the fastener force has the shape of the letter M. In the sequential loading model, the rail was cut off between fasteners and each fastener was connected to one rail segment. The fastener force was then applied directly to the node that connected the rail segment to the springdamper element. These M-type pulses, obtained from the moving-wheel model, were applied sequentially to the rail segments with a time interval t = S/v (S = 0.63 m), as shown in Fig. 5. It should be noted that fasteners experienced a tensile force when the wheel moved near the fasteners. However, the tensile force cannot be simulated in the sequential loading system established in the following section. Therefore, the treatment of the actual input load in the sequential loading model was an approximation, with the tensile force being neglected. Results of the dynamic stress–time history curves and stress paths are given and compared between the movingwheel model and the sequential loading model. Four observation points at depths of 0.2, 1.5, 2.7, and 6.7 m from the roadbed surface are selected in the middle cross section of the models; these are named points A, B, C, and D, respectively. Figure 6 compares the calculated dynamic
soil stress–time history curves under the loading of one moving carriage, consisting of vertical stress syy and shear stress syz at four different depths. Points M, N, O, P, and Q denote the positions of the moving carriage relative to the observation points when the carriage is far away, when the first bogie arrives, when the center of the carriage arrives, when the second bogie arrives, and when the carriage is far away in the other direction, respectively. The dynamic soil stresses at the four observation points are zero when the carriage moves from the far point M. As the carriage approaches, both vertical stresses and shear stresses increase. The shear stresses reach a peak first, when the carriage is 3.0 m away, before the first bogie of the carriage arrives at point N. The vertical stresses then continue to increase until reaching a peak, while the shear stresses decrease to zero as the first bogie arrives at point N. As the first bogie moves far away, the vertical stresses decrease to a minimum value, while the shear stresses increase to the opposite peak first, and then decrease to zero. When the second bogie arrives, soil elements experience the same loading process. However, as the depth increases, stress superposition resulting from the two bogies of the carriage becomes increasingly significant. Therefore, distributions of dynamic soil stresses will be more uniform at deeper soil depths. It is also found that dynamic soil stresses are dominated by bogies of the carriage, and no axles are visible within the subgrade depths. Results obtained from the sequential loading model agree well with those
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Moving wheel model A B Location C D
Vertical stress (kPa)
18 16
N
2.5m
P
Sequential loading model Location A B C D
14 12 10 8 6 4 2
O
6
Location
4
Shear stress (kPa)
20
Stage IV
2
Stage III
The second bogie
0
The first bogie
-2
-4 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Stage I
Time (s) 0
Moving wheel model A B Location C D
6 4
Sequential loading model A B Location C D Q
2
M
N
O P
-2 -4 -6 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (s)
(b) Fig. 6 Dynamic soil stress–time history curves. a Vertical stress, b shear stress
obtained from the moving-wheel model, which indicates that the proposed sequential loading method can reproduce the soil stress state under the loads of a moving train. Figure 7 shows the stress paths followed, on a graph of deviatoric stress s (=(syy - szz)/(syy - szz)2.2) against shear stress s (=syz), by the soil elements at the four observation points during the passage of one carriage. The stress paths are divided into four stages according to the reference locations between the soil elements and the carriage. In stage I, both the deviatoric stresses and the shear stresses increase as the carriage approaches. In stage II, the shear stresses decrease, while the deviatoric stresses continue to increase and reach a peak when the first bogie arrives at position N. Afterward, the deviatoric stresses start to decrease, while the shear stresses reach the opposite peak in stage III. Finally, both the deviatoric stresses and shear stresses decrease as the carriage arrives at position O. As the second bogie approaches, soil elements experience the second loading cycle. However, the stress paths will be different because of the stress superposition at deeper
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Stage II
-6
(a)
Shear stress (kPa)
Sequential loading model A B C D
Q
M
0
0
Moving wheel model A B C D
2
4
6
8
Deviatoric stress (kPa) Fig. 7 Stress paths for soil elements at different depths
depths caused by the two bogies. At lower depths below the track structure, stress paths induced by the two bogies closely resemble each other and one bogie corresponds to one loading cycle. As the soil depth increases, the deviatoric stresses at the end of stage IV move toward the maximum value, which may result in two bogies corresponding to one loading cycle. It seems that soil elements near the track experience more and larger stress cycles than soil elements at greater depths. The increase in the number of cycles and magnitudes of train loads is likely to result in larger permanent deformation; thus, soil elements at shallower depths are more likely to experience increased displacements and possible shear failure than those in the deeper ground [27]. Results of the sequential loading model are in good agreement with those of the movingwheel model, which demonstrates that the proposed sequential loading method can simulate the process of train motion. 3.2 Boundary effect of the proposed physical model of high-speed railways It is difficult and unrealistic to build a real railway with infinite length in the laboratory. Instead, it is planned to build a full-scale model that is 5 m long, 15 m wide, and 6 m high according to the dimensions of the steel test box at Zhejiang University. Therefore, it is necessary to evaluate the boundary effect of the reduced dimensions in the model testing on the static and dynamic responses of the track structure and substructure. A reduced 3D finite element model was thus built with the same component and physical parameters of the moving loading model as shown in Fig. 3. The only difference was that the dimensions of the subsoil were reduced from 100 m in length, 30 m in
Acta Geotechnica
Resilient deformation (mm)
0.4
FEM-100 m Reduced FEM-5 m
0.3
0.2
0.1
Fig. 9 Established model of a slab track–subgrade system
0.0 1
10
100
Frequency (Hz)
(a) 30
Table 2 Physical parameters of silty soil and coarse sand Specific gravity
FEM-100 m Reduced FEM-5 m
Dynamic soil stress (kPa)
25
Maximum dry density (g/cm3)
Cu
Cc
Silty soil
2.67
1.62
2.51
1.32
Coarse sand
2.66
2.11
4.80
0.62
20
15
10
5
0 1
10
100
Frequency (Hz)
(b) Fig. 8 Comparisons of the numerical results obtained with two 3D FEMs. a Resilient deformation, b dynamic soil stress
width, and 30 m in thickness to 5 m in length, 15 m in width, and 2.5 m in thickness. Sinusoidal loads with frequency varying 1–100 Hz were applied to the rails in the FEM with length of 100 m and the reduced FEM with length of 5 m. Dynamic loads with amplitude of 140 kN were exerted above the fasteners in the middle cross section. Figure 8 shows the numerical results of the resilient deformation and dynamic soil stress obtained from these two FEMs. Figure 8 (a) shows the resilient deformation at the subgrade surface varying with loading frequency. The resilient deformation increases very slowly when the loading frequency is lower than 10 Hz. It then develops rapidly until reaching a maximum value of around 0.38 mm at the first natural frequency of 16 Hz. As the loading frequency increases, the resilient deformation decreases with a sharp drop and then followed by some minor fluctuations. The maximum resilient deformation is about 10 times that in the quasi-static state. A similar
relationship of the dynamic soil stress with the loading frequency is found in Fig. 8 (b). The maximum dynamic soil stress at the first natural frequency of 16 Hz is about 6.3 times that at 1 Hz. Results obtained from the reduced FEM with length of 5 m agree well with those obtained using the FEM with length of 100 m, especially at low frequencies (B20 Hz). Since the train-induced loading frequency for the subgrade soil is low, it is reasonable to carry out experimental tests to study the performance of ballastless high-speed railways under moving-train loads using the full-scale model with dimensions of 5 m in length, 15 m in width, and 6 m in height.
4 Construction of the full-scale testing platform for ballastless high-speed railways 4.1 Full-scale physical model of a ballastless highspeed railway The full-scale physical model of a ballastless high-speed railway was established according to the practical engineering design methods. The physical model of a slab track–subgrade system comprises, from the bottom–up, a 2.5-m-deep subsoil, a 2.3-m-thick subgrade, a 0.4-m-thick roadbed, a 0.3-m-thick concrete base, a 0.05 m layer of CAM, a 0.19-m-thick track slab, fasteners, and rails, as shown in Fig. 9. Materials in the three layers of the substructure—the subsoil, subgrade, and roadbed—were Qiantang River silty soil, coarse sand, and gravel. The physical parameters of
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Density (g/cm3 ) 1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.5
5.0
Depth from the bottom (m)
Depth from the bottom (m)
3.0
Density (g/cm3)
2.0
1.5
1.0
0.5
Desired value 1.8 g/cm3
0.0
1.9
2.0
3.5
3.0
Desired value 2.1 g/cm3
2.5
(a) Moisture content (%) 21
24
2.5
2.0
1.5
1.0
0.5
0.0
5.0
Depth from the bottom (m)
Depth from the bottom (m)
3.0
18
2.3
4.0
Moisture content (%) 15
2.2
4.5
(a)
12
2.1
Desired value 18%
(b)
2
3
4
5
6
4.5
4.0
3.5
3.0
2.5
Desired value 4%
(b)
Fig. 10 Test results of the compacted subsoil. a Density, b moisture content
Fig. 11 Test results of the compacted subgrade. a Density, b moisture content
the silty soil and coarse sand are given in Table 2. The liquid limit and plastic limit of silty soil are 35 and 24 %, and the plastic index is equal to 9. These three structures were compacted by layers to the individual desired densities at their optimum moisture contents. The subsoil was compacted every 25 cm, a layer to a desired density of 1.8 g/cm3 at a moisture content of 18 %. The subgrade was compacted every 25 cm, a layer to a desired density of 2.1 g/cm3 at a moisture content of 4 %. The tested density and moisture content of compacted soils are shown in Fig. 10 for the subsoil and Fig. 11 for the subgrade. After the three structures were filled and compacted, the compactness and stiffness of the subgrade and roadbed were examined; these properties were represented by the compaction coefficient K, foundation coefficient k30, and deformation modulus Ev2, Ev2/Ev1. For the subgrade, test values of compaction coefficient K, foundation coefficient
k30, and the second deformation modulus Ev2, Ev2/Ev1 are 0.95–0.97, 306–402 MPa/m, 143–157 MPa, and 1.7–2.3, all of which satisfy the specification limits of 0.95, 130 MPa/m, 80 MPa, and 2.5, respectively. For the roadbed, test values of compaction coefficient K, foundation coefficient k30, and the second deformation modulus Ev2, Ev2/Ev1 are 0.97–0.98, 272–309 MPa/m, 134–160 MPa, and 1.8–2.1, all of which satisfy the specification limits of 0.97, 190 MPa/m, 120 MPa, and 2.5, respectively. The track structure (also called the superstructure) mainly consisted of a concrete base, a CAM layer, a track slab, fasteners, and rails. The concrete base, with dimensions of 5 m 9 3 m 9 0.3 m, was poured with concrete in situ. The track slab of the China Railway Track System I (CRTS I) with dimensions of 4.962 m 9 2.4 m 9 0.19 m was used in the experiment. The CHN60-type rails were connected to the track slab by WJ–7 fasteners with static stiffness of 2.85 9 107 N/m.
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(a)
(b) Fig. 12 Sequential loading system. a Sequential loading equipment, b loading control software
4.2 Sequential loading system The sequential loading system was implemented according to the proposed sequential loading method mentioned above. Figure 12 (a) is the photograph of the established sequential loading equipment for simulating the load of the
moving train; the equipment consists of reaction frames, eight hydraulic actuators, and eight loading distribution girders. The original continuous rails were cut into eight 30-cm segments. The connection of rail segments and the track slab via fasteners remained the same. Eight hydraulic actuators were placed corresponding to the positions of
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25
Track slab
Dynamic soil stress (kPa)
Vibration velocity (mm/s)
8
4
0
-4
Roadbed surface
20
15
10
5
-8
0
-12 0
1
2
3
(a)
Vibration velocity (mm/s)
6
4
2
0
-2
-4 2
3
Time (s)
(b) Fig. 13 Recorded experimental results of vibration velocity versus time at train speed of 270 km/h. a Track slab, b roadbed surface
fasteners, and distribution girders were installed on each fastener to transfer loads applied by the actuators to the track structure. Loading control software was developed to manage the behaviors of the eight actuators. The numerical results of fastener forces obtained from the 3D FEM were integrated into the software, and adjacent actuators acted with a time interval t. The highest train speed simulated in the experiment was 360 km/h.
5 Comparison of the results of preliminary experiments with field measurements Field measurements were taken on a testing section of the Wuguang high-speed railway before it was officially put into service in China [5]. The track structure was almost identical to the full-scale physical model presented in this
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2
3
Fig. 14 Recorded experimental results of dynamic soil stress versus time at train speed of 270 km/h
Roadbed surface
1
1
Time (s)
Time (s)
0
0
study. During the field tests, a CRH2-type high-speed train with axle load of 140 kN was used, and its travelling speed varied from 180 to 360 km/h. Dynamic responses such as vibration velocities of the track structure and dynamic soil stresses of the subgrade were measured during the passage of the high-speed train. To verify the reliability of the proposed full-scale accelerated railway testing to simulate train moving loads, experimental results of vibration velocities were compared with the field measurements of the Wuguang high-speed railway. Figure 13 shows the typical time histories of vibration velocity at train speed of 270 km/h recorded in the fullscale accelerated railway testing. The positive sign indicates the downward vibrations. The amplitude of vibration velocity at track slab is about 6.81 mm/s at the train speed of 270 km/h and is nearly twice that at roadbed surface. From Fig. 13 (a), it can be found that the locations of the train axles can be identified easily from the peaks, while they are invisible in the dynamic responses at roadbed surface. It indicates that vibration velocity responses gradually become to be dominated by train bogies from wheel axles with transmission of the vibrations from the track slab to the roadbed. Similar phenomenon is also found in the recorded experimental results of the dynamic soil stress versus time, which is plotted in Fig. 14. Each peak in the responses of the dynamic soil stress corresponds to one bogie. The amplitude of the dynamic soil stress is a superposition of adjacent bogies in two carriages, and it values 19.5 kPa at the train speed of 270 km/h. Table 3 shows the experimental results and field measurements of vibration velocities at the track slab and roadbed surface varying with train speeds for the comparison purpose. The train speed in the laboratory testing was determined according to the field measurement
Acta Geotechnica Table 3 Comparisons of vibration velocity between the experimental results and field measurements at track slab and roadbed surface Structures
Train speed (km/h)
Track slab (mm/s) Roadbed surface (mm/s)
180
216
270
288
360
Field
5.14
6.17
7.13
7.33
9.52
Experiment
4.53
5.87
6.81
7.23
9.55
Field Experiment
1.24 1.37
2.21 2.21
3.66 3.38
3.75 3.76
5.22 4.64
Field measurements (mm/s)
12
Track slab Concrete base Roadbed surface
10
8
6
4
Line y=x
2
0 0
2
4
6
8
10
12
Experimental results (mm/s) Fig. 15 Correlation between the experimental results and field measurements
conditions to ensure the same train speed. The vibration velocities of the track slab and roadbed increase with the train speed. The maximum vibration velocity of the roadbed surface is about 5 mm/s, which is only half that of the track slab. It is found that the experimental results of vibration velocities are in good agreement with the field measurements, although the vibration velocities of the field measurements are a little larger than those of the experimental results, which may be caused by the dynamic interaction between train wheels and rails due to the slight track irregularity for these new rails. In general, the comparisons validate the reliability of the full-scale testing platform in simulating the passage of high-speed trains. Figure 15 shows the correlation of vibration velocity between the experimental results and field measurements selected at the same train speeds varying from 180 to 360 km/h, where vibration velocities of the track slab, concrete base, and roadbed are presented. The data points of the field measurements and experimental results are mostly located close to the line y = x that represents the perfect positive correlation, indicating that the experimental results are closely approximate to the field measurements. These comparisons further demonstrate that the
full-scale railway testing platform can simulate the process of train motion and reproduce the dynamic behaviors of ballastless railways as a feasible alternative to field measurements.
6 Conclusions Ballastless high-speed railways exhibit dynamic performances that are quite different from those of traditional ballasted railways. In this study, the cyclic effect, moving effect, and speed effect of high-speed trains on the dynamic performance of railway infrastructure were discussed. Consequently, a new sequential loading method for the load of a moving train was then proposed and calibrated using 3D FEMs. Distributions of dynamic soil stresses and stress paths at deeper soils were quite different from those at shallower soils owing to the stress superposition with the increase in soil depth. Soil elements at shallower layers experienced more stress cycles with higher loading intensities than those at deeper depths. A full-scale railway testing platform of a ballastless track–subgrade system was established according to the practical engineering design methods. With the help of a sequential loading system composed of eight high-performance hydraulic actuators, loads of a moving train with highest speed of 360 km/h were simulated. Preliminary experimental results of vibration velocities were presented and compared with field measurements of the Wuguang high-speed railway. Vibration velocities of the track structure and roadbed increased monotonically with the train speed varying from 180 to 360 km/h, and the experimental results coincided with field measurements. The full-scale railway testing thus demonstrated its ability to simulate the process of a moving train and realistically reproduce the dynamic behaviors of ballastless railways. More dynamic responses of the track and infrastructure under the load of a moving train, as well as the permanent deformation in the subgrade soil, will be studied on the full-scale railway testing platform in the future work. Acknowledgments Financial support from the Natural Science Foundation of China (Grant Nos. 51178418, 51222803 and 51225804) is gratefully acknowledged. The authors are grateful to Mr. Xiang Xu for his assistance in the model testing.
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