Abstract
High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks. Once the concrete block falling occurs, serious consequences follow, and traffic safety may be endangered. The aerodynamic shockwave evolves from the initial compression wave may be an important inducement causing the tunnel lining cracks to grow and form falling concrete blocks. A joint calculation framework is established based on ANSYS Fluent, ABAQUS, and FRANC3D for calculating the crack tip field under the aerodynamic shockwave. The intensification effect of aerodynamic shockwaves in the crack is revealed, and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor (SIF) are analyzed. Results show that (1) the aerodynamic shockwave intensifies after entering the crack, resulting in more significant pressure in the crack than the input pressure. The maximum pressure of the inclined and longitudinal cracks is higher than the corresponding values of the circumferential crack, respectively. (2) The maximum SIF of the circumferential, inclined, and longitudinal crack appears at 0.5, 0.68, and 0.78 times the crack front length. The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack. The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves. (3) The influence of train speed on the SIF of the circumferential crack is more than 40%. When the train speed, crack depth, and crack length change, the change of pressure in the crack is the direct cause of the change of SIF.
Keywords: Falling concrete blocks; Tunnel lining cracks; Aerodynamic shockwave; Intensification effect; Crack tip field; Stress intensity factor
(ProQuest: ... denotes formulae omitted.)
1 Introduction
Since the Shinkansen railway in Japan first opened to the public in 1964, high-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks (Zhou et al., 2023). For example, in Fukuoka Tunnel on the Sanyo Shinkansen railway, a vault concrete block suddenly fell as the train was approaching the tunnel exit and hit the roof of train carriages 9, 10, and 12 successively, damaging the pantographs of several train carriages and causing a groove with a length of 10 m on the top of carriage 9. The line was suspended for 5 h (Du et al., 2021). On January 12, 2016, a vault concrete block of a construction joint of the Pingshan Tunnel in China fell off, resulting in a limiting speed of 120 km/h to the train and affecting the train operation for more than 2 h (Shi et al., 2022). On July 29, 2018, at the entrance of a tunnel on the Hokkaido Shinkansen in Hamana, one concrete block fell from the tunnel vault, with a weight of 5.8 kg, as shown in Fig. 1(a). More field photos of such accidents can be found in Fig. 1(b) (Shi et al., 2022). As we can learn from the above accidents, once the concrete block falling occurs in high-speed railway tunnels, serious consequences follow, and traffic safety may be endangered.
As investigated and reported by the Japanese Railway Comprehensive Technology Research Institute, the aerodynamic pressure caused by high-speed trains is one inducement of concrete block spalling of tunnel lining (Asakura & Kojima, 2003). Duc to the combination of construction defects, environmental corrosion, and concrete shrinkage, the lining surface of high-speed railway tunnels in operation is randomly distributed with many cracks. When a high-speed train enters the tunnel, the air at the tunnel entrance is compressed to produce an initial compression wave. The longitudinal propagation of the initial compression wave is affected by the inertial effect (Stenfan & Kaltenbach, 2008; Wang et al., 2018). The pressure, temperature, and sound velocity of the compressed air increase when the initial compression wave propagates longitudinally at the sound velocity. As the propagation distance increases, the inertia effect makes the wavefront gradually steeper, and the gradient becomes larger. When traveling beyond the critical distance, the initial compression wave evolves into a shockwave with its gradient close to infinity (Chen et al., 2022; Stenfan & Kaltenbach, 2008; Wang et al., 2018). When the shockwave transmits into the crack, due to the restriction of the crack surface, a violent reflection and superposition may occur. The superposed shockwave causes stress concentration at the crack tip, resulting in crack growth and connection with other cracks, forming a falling concrete block. Noting the increasing speed of high-speed trains, the aerodynamic impact of shockwaves on tunnel lining cracks cannot be ignored.
Researchers have conducted a series of studies against harmful influences of train-induced aerodynamic pressure, including the micro-pressure wave at tunnel entrance (Zhang et al., 2017, 2019), dynamic response of the train (Liu et al., 2017), and fatigue performance of the train (Zhou et al., 2019). For example, Zhang et al. (2017) conducted dynamic model experiments to study the micropressure waves generated by high-speed trains while passing through the tunnels of five different portals. They found that the oblique portals have a noticeable alleviating effect on the micro-pressure waves. Kim et al. (2021) designed a buffer structure based on the biological characteristics of shark gills, which can reduce the micro-pressure wave by 78% and the gradient of the compression wave by 56%. Liu et al. (2017) adopted numerical simulation methods to study the dynamic response characteristics of highspeed trains when passing through tunnels. They found that the lateral force and overturning moment change drastically when the train enters and exits the tunnel. Zhou et al. (2019) calculated the fatigue properties of the metal and weld of high-speed trains based on the rainflow counting method and the Miner and Cartcn-Dolan criteria. The fatigue performance of the weld is significantly lower than that of the metal, and the fatigue damage caused by the train passing through the tunnel accounts for approximately 25 % of the total damage. The above research reveals that the aerodynamic impact generated by highspeed trains passing through the tunnel not only causes environmental pollution and the reduction of passenger comfort, but even causes damage to the train body with high strength.
Therefore, researchers have also paid attention to the influence of the train-induced aerodynamic impact on the secondary lining of tunnels. Gong and Zhu (2018) explored the response mechanism of the secondary lining under aerodynamic pressure and made cyclic statistics of stress time history at vulnerable locations based on the rainflow counting method. By integrating the concrete S-N curve and Miner linear cumulative damage theory, the fatigue life of the secondary lining was also estimated. Du et al. (2021) proposed a concrete dual fatigue damage model to study the fatigue behaviour of secondary linings under nonlinear, time-varying aerodynamic loads. They demonstrated that the damage accumulation of the secondary lining rises monotonically as the consumed life fraction increases, whereas the residual life declines monotonically. Chen et al. (2022) studied the temporal and spatial characteristics of compression waves in secondary lining cracks by establishing a 2D computational fluid dynamics (CFD) crack model and found that the pressure in the crack increases with the increase in train speed and crack width.
As discussed above, researchers have tried to understand the adverse effects of train aerodynamic effects on the service performance of secondary lining. However, the aerodynamic impact of shockwaves on tunnel lining cracks has not been reported before. Although the design, construction, and management departments of high-speed railways have proposed a number of specific measures, including improving design standards and construction technology, to prevent tunnel lining diseases, the problems of falling concrete blocks in high-speed railway tunnels have not been fundamentally solved. To achieve the longterm effectiveness of tunnel lining disease control, the significance of studying the crack tip field of tunnel lining under the action of aerodynamic shockwaves can be best understood.
Aiming at the characteristic and influence law of the crack tip field in high-speed railway tunnel linings under train-induced aerodynamic shockwaves, a joint calculation framework based on ANSYS Fluent, ABAQUS, and FRANC3D is established. Section 2 introduces the specific process and modelling details of the joint calculation framework. Section 3 analyzes the temporal and spatial variation characteristics and intensification effects of shockwaves inside cracks. Section 4 investigates the evolution characteristics of the stress field at crack front and the influencing factors of the stress intensity factor (SIF).
2 Calculation of the crack tip field
2.1 Joint calculation framework
Figure 2 shows the joint calculation framework of the crack tip field in high-speed railway tunnel linings under train-induced aerodynamic shockwaves based on ANSYS Fluent, ABAQUS, and FRANC3D. As shown in Fig. 2, the calculation has the following steps:
(1) ANSYS Fluent is used to establish the crack geometry model, set boundary conditions, mesh, set the solution scheme, and solve the aerodynamic pressure acting on the crack surfaces.
(2) Establish tunnel-soil models based on ABAQUS and perform preliminary meshing. Then, FRANC3D is adopted to insert cracks and generate fine meshes near the crack tip. Subsequently, ABAQUS is applied to set the boundary conditions, material properties, element types, crack tips, and virtual crack propagation directions.
(3) Apply the aerodynamic pressure calculated in ANSYS Fluent onto the crack surfaces of the ABAQUS model and solve the crack tip field.
More details of the calculation method can be found in Sections 2.2 and 2.3.
2.2 Calculation of the aerodynamic pressure
The orientation of lining cracks in high-speed railway tunnels is highly random and can be roughly divided into three categories: circumferential, inclined, and longitudinal. Hence, circumferential, 45° inclined, and longitudinal cracks on the tunnel vault are selected as typical cases in this research. The shape of the crack front is assumed to be half elliptic for simplification (Huang et al., 2022; Khadcmi-Zahedi & Shishcsa, 2019). According to previous research and accident reports shown in Fig. 1, tunnel lining cracks with a depth of 10-50 mm are the most common, and the size of falling concrete blocks is usually more than 10 cm (Chen et al., 2022). Consequently, the crack depth and length range from 10 to 50 mm and 100 to 500 mm, respectively. A certain width must be assigned to the crack in the computational fluid dynamics (CFD) calculation. By comparing the standards in various countries, as summarized by Teng (2015), a critical width of 3 mm has been identified as the threshold for determining the probability of concrete spalling, as indicated in Table 1. Therefore, the crack width is set as 3 mm in the CFD calculation. The crack width is the maximum distance between two surfaces of the crack, as shown in Fig. 3.
Considering that the crack size is much smaller than the tunnel size, and a time step of less than a microsecond is needed to calculate the pressure propagation inside the crack, unacceptable computational resources must be paid when using a full-sized tunnel model. Therefore, a cuboid space of 3.0 m × 2.0 m × 2.0 m outside the crack is used to replace the full-sized tunnel model, as shown in Fig. 4. In the cuboid model, the first plane perpendicular to the X-axis is set as the Pressure-inlet boundary to apply the aerodynamic shockwave caused by the train. The second plane perpendicular to the X-axis is set as the Pressureoutlet boundary. The top plane of the cuboid, which is connected with the crack, is set as No-slip Wall to simulate the tunnel vault surface. The two crack surfaces arc also designated as No-slip Walls to achieve the reflection of the aerodynamic shockwave. The finite volume method (FVM) and the Pressure-based solver are adopted for calculating. The air compressibility is considered, and the aerodynamic pressure inside the crack is simulated by the unsteady viscous к-г turbulence model. The gradient is solved by the least squares cell-based method. The pressure-velocity coupling equation is processed using the semi-implicit algorithm (SIMPLE). The bounded central difference and the second-order upwind difference schemes are adopted to solve the momentum equation and time integral, respectively. The discretized equation is calculated by the unsteady method with double-time step.
Because of the inertial effect, the pressure gradient of the initial compression wave increases with the propagation distance, but the peak pressure of the compression wave tends to be stable (Chen et al., 2022). For this reason, a compression wave with an infinite gradient is applied on the Pressure-inlet boundary, and the peak pressure of the compression wave can be calculated using Eq. (1) (Howe et al., 2000):
... (1)
where ρa is the air density and ρa = 1.29 kg/m3; Vt is the train speed; Ma denotes the Mach number; Atr and Atu represent the train and tunnel cross-sectional area, respectively. The current research mainly focuses on the CRH380B train (Atr = 11.29 m2) and the tunnel with the standard cross-section of horseshoe shape (Atu = 100 m2), the most frequently used high-speed train type and tunnel cross-section in China, respectively. According to Eq. (1), the peak pressure of the compression wave is 2087 Pa when the train speed is 350 km/h. Figure 5 presents the corresponding shockwave input in the Pressure-inlet boundary.
Hexahedral meshes are used to discretize the geometry model based on mosaic technology. To determine the reasonable mesh size, the circumferential crack with length, width, and depth of 100, 3, and 50 mm, respectively, is taken as an example here (the train speed is 350 km/h). Five mesh sizes, namely, 0.02, 0.04, 0.06, 0.08, and 0.1 mm, are used to discretize the geometry model. Figure 5 (a) shows the time history of the deepest location inside the crack under different mesh sizes. As shown in Fig. 5(a), as the mesh size decreases, the pressure results gradually converge. The pressure results are lower for larger mesh sizes. When the mesh size is 0.04 mm, the pressure result is very close to the 0.02 mm result, with a maximum difference of only 2.1 %. To balance the computational efficiency and accuracy, 0.04 mm mesh is finally chosen for all CFD models with a total element number of 2-3 million. In addition, determining a reasonable time step is crucial for the accuracy of the calculation results. Figure 5(b) compares the results for five different time-step scenarios. Like the mesh-independent results, the pressure results stabilize as the time step shortens. According to Fig. 5(b), the time step in the CFD simulation is determined as 1 × 10-7 s.
2.3 Calculation of the crack tip field
2.3.1 Theoretical background
In concrete fracture mechanics, SIF, usually represented by If can be used to describe the stress state near the crack tip and is widely used in crack stability evaluation (Panian & Yazdani, 2020; Tong et al., 2017). According to the double-X fracture criterion of concrete, stable crack propagation occurs when the SIF exceeds the initial fracture toughness Kinilc, and unstable fracture happens when the SIF exceeds the unstable fracture toughness Kuctc (Xu & Reinhardt, 1999). J-integral is another important fracture mechanics parameter applicable to clastic or clastic-plastic materials. Considering the concrete is a typical clastic-plastic material, the J-integral is solved before the SIF is calculated. As shown in Fig. 6(a), Γ represents a random clockwise integration path around the crack tip. The Jintcgral can be expressed as a closed line integral of the path Γ (Miao et al., 2022):
... (2)
where ds denotes the length increment along the integration path; T represents the tension vector acting on ds and T = σ.n; α is the displacement; a is the stress of ds; n is the normal unit vector of ds; W is the strain energy density under clastoplastic conditions. According to the theory of plastic deformation, W can be written as follows:
... (3)
As shown in Fig. 6(b), when a rectangular integration path surrounding the crack tip is defined, Eq. (2) can be expressed in an explicit form as follows:
... (4)
Under the three-dimensional condition, assuming that the concrete along the integration path is in an elastic state, the SIF can be calculated by Eqs. (5) and (6) (Shih & Asaro, 1988):
... (5)
... (6)
where KI, KII and KIII represent the SIF for mode I, mode II, and mode III crack; E and v are the elastic modulus and Poisson's ratio of the material, respectively. Under the action of aerodynamic shockwaves, the lining cracks are typical mode I crack and and are zero. Consequently, under plane strain conditions, Ky can be solved according to Eq. (5).
2.3.2 F E model
As shown in Fig. 7(a) and (b), the tunnel-soil model is established by ABAQUS. Comprehensively considering the boundary effect and computational efficiency, the height and width of the model are both set as 100 m, and the tunnel is located in the middle. Generally, the tunnel length is generally more than ten times the size of the area of interest (Wang et al., 2019). The tunnel length in this research is 20 times the length of the longest crack, namely, 10 m. The tunnel is composed of an initial support, secondary lining, and tunnel invert. The clearance height and width of the tunnel are 9.1 and 13.3 m, respectively; the clearance area of the tunnel is 100 m2, and the thickness of the secondary lining is 0.45 m. The tunnel model is discretized using hexahedral meshes using the ABAQUS default meshing tool, and the preliminary finite element (FE) model is presented in Fig. 7(c). The grade level of the reinforcement of the tunnel is HRB335 with a yield strength of 335 MPa. The clastic modulus and Poisson's ratio are 200 GPa and 0.3, respectively.
To accurately calculate the SIF in ABAQUS, fine meshes need to be locally assigned near the crack. However, it is extremely difficult to mesh in ABAQUS when considering the crack. The adaptive remeshing technical of FRANC3D can perfectly solve this problem (Fracture Analysis Consultants, Inc (FAC)). Therefore, FRANC3D is adopted to generate a locally fine mesh within the range of 1.0 m x 1.0 m near the crack. At the same time, considering the singularity of the stress at the crack tip, n (n = 3, 4, 5, 6) circles of contour element are generated near the crack front to obtain a high-precision crack tip field. The other areas within the range of 1.0 m x 1.0 m is divided into tetrahedral meshes. The local FE model after remeshing is shown in Fig. 7(d). The local FE model is then merged into the preliminary FE model of ABAQUS, and the hexahedral and tetrahedral elements in the model are set as 3D solid C3D20R. The high-stress gradient at the crack tip area is captured by second-order singular elements with quarter-points. A tangentially continuous crack tip is defined in ABAQUS, and the direction perpendicular to the crack front in the crack plane is defined as the virtual crack growth direction, as shown in Fig. 7(d).
We have investigated the influence of crack widths on the crack tip filed before calculating the crack tip field. As shown in Fig. 8, we have established a new circumferential crack model with a crack width of 3 mm. The aerodynamic pressure caused by a train running at 350 km/h is acted on two crack surfaces. Fig. 9 compares the maximum SIF at the crack front of the two model. S denotes the path of the crack front. The shape of two SIF curves of the crack front is identital. The maxumum differenc is only 1.1%, indicating that the crack width has limited influence on the crack tip field. Hence, the crack width is not considered in the calculation of the crack tip field for convenience.
In the tunnel-soil model, the mechanical behaviour of the soil is described by the elastic perfectly-plastic constitutive relation based on the Mohr-Coulomb criterion with a non-associative flow rule. The concrete damage plasticity (CDP) performs well in simulating the mechanical behavior of concrete in tunnel engineering, for it well describes the plastic and damage of concrete (Liu et al., 2021). Hence, the CDP model is more appropriate to describe the nonlinear behavior of concrete compared with elastic models for concrete. Considering the high degree of nonlinearity at the crack tip, we adopted the CDP model in our research. The concrete grades of the initial support, secondary lining and invert are C25, C30 and C40, namely the compressive strengths arc 25, 30 and 40 MPa measured from 150 mm × 150 mm × 150 mm concrete cubes in China, respectively (Ministry of Housing and UrbanRural Development of the People's Republic of China, 2015). Table 2 summarises the main mechanical parameters of each material. Taking C30 concrete as an example, the density, elastic modulus, and Poisson's ratio are 25.0 kN/ m3, 27 800 kPa, and 0.20, respectively. The strcss-strain curve of C30 concrete is listed in Tables 3 and 4. A nodesurface contact is created between the soil and concrete. The tangential and normal contact behaviors are controlled by a penalty-based Coulomb friction model and a hard contact prcssurc-ovcrclosurc relationship model, as given in Eqs. (7) and (8), respectively.
... (7)
... (8)
where τeq and τcr are equivalent frictional shear stress and critical shear stress; µ is the frictional coefficient and д = 0.5 according to the suggestion of Cao et al. (2012); pc denotes the normal contact pressure; ti and t2 are two orthogonal component components of the shear stress on the contact surface.
Subsequently, 52 general static steps are created in ABAQUS. Only one soil layer (clay) is taken into account in the model for simplification. The mechanical parameters are also listed in Table 2. In the first simulation step, we achieve a ground stress equilibrium based on the Geostatic procedure provided by ABAQUS. In the following step, tunnel linings are activated. Fifty sets of aerodynamic pressure data calculated in ANSYS Fluent are loaded onto two crack surfaces by mapped fields from point cloud data in the remaining 50 steps. It is worth mentioning that that no common node exists between the two cracked surfaces. The two crack surfaces can open and close when surface loads acting on them, even though the crack width is 0 mm.
The contour elements near the crack front significantly influence the SIF, and the meshing in this area should be carefully done. As shown in Fig. 10, the main characteristics of the contour elements can be expressed by three parameters, the contour diameter d, number of contours гц and partition angle 00. An independent analysis of the above three parameters is conducted to guarantee the accuracy of SIF. The ranges of each parameter are that d is from 0.37) to 0.67), n from 2 to 5, and 00 from 22.5° to 90°. Taking the circumferential crack with a length and depth of 100 and 50 mm, respectively, as an example (the train speed is 350 km/h), Fig. 11 shows the distribution of Ky along the crack front 5 under different parameters. As shown in Fig. 11, the SIF results gradually converge when d is in the range of 0.37)-0.47), n of 4-5, and 00 of 22.5°-45°. Therefore, d = 0.47), n = 4, and 00 = 45° are adopted by all models in this paper.
2.4 Verification
2.4.1 Verification of the cuboid model
We have performed an independence test on the geometric size of the cuboid space before performing all simulations. As shown in Fig. 12, four models with four increasing sizes are involved in the independence test. The sizes of the first three models are 1.0 m x 1.0 m x 1. 0 m, 2.0 m x 1.5 m x 1.5 m, and 3.0 m x 2.0 m x 2.0 m, and the fourth model is a full-scale model. The full-scale tunnel model is 1000 m in length. The cross-section is established according to the geometry of the most popular tunnel type in China, namely, the horseshoe-shaped tunnel with an area of 100 m2. The crack is located at the middle length of the tunnel on the vault. The boundary conditions of the two models arc similar. The pressure monitoring pointes are at the crack tip. The pressure caused by an 8carriagc CRH380B train with a speed of 300 km/h is taken as the input pressure. Figure 13(a) compares the pressure results obtained from the four models. To better compare the pressure results, it is assumed that the pressure wave arrives the crack at the same time in the four models. As shown in Fig. 13(a), when inputting an aerodynamic pressure curve into the four models, the pressures collected from the model with sizes of 2.0 m x 1.5 m x 1.5 m and 3.0 m x 2.0 m x 2.0 m are close to that from the full- scale model. The result obtained from the 1.0 m x 1.0 m × 1.0 m model largely deviates from the full-scale model. This deviation may be caused by the wall effect. Hence, we finally choose the 3.0 m × 2.0 m × 2.0 m model in this research to achieve a high-efficiency and -accuracy calculation.
In our previous research, we have also validated the reliability of the full-scale tunnel model based on field measurement results (Liu et al., 2023). Figure 13(b) presents a comparison between the field measurements and simulation results. As depicted in the figure, the simulated aerodynamic pressure corresponds well with the measured values at the field site. Although the field measurements capture more fluctuations in the aerodynamic pressure, there is only a 5.4% deviation between the two sets of results. This deviation can be attributed to differences in surface smoothness and air temperature between the simulation and field conditions. Therefore, the reliability of the fullscale tunnel model has been confirmed. Further details regarding this verification process can be found in Liu et al. (2023).
2.4.2 Varification of the FE model
We have adopted a field measurement study to verify the accuracy of ABAQUS model (Liu et al., 2023). The SIF of crack tips is hard to measure in a field measurement, whereas the strain data of concrete is easier to obtain. In the field measurement, the tunnel has a length of 5900 m. The tunnel cross-section type is similar with that introduced in Section 2.3.2. A circumferential crack is located at the tunnel vault with a length of 43 mm. Its maximum depth and width and are approximately 55 and 3 mm, respectively. As illustrated in Fig. 14(c), four strain gauges numbered from SI to S4 arc adopted to collect the tensile strain of the crack tip. A total of 12 sets of strain data caused by the aerodynamic pressure of trains are collected. The speed of 12 trains is 300 km/h approximately. Much information about the field measurement can be found in the reference (Liu et al., 2023).
The FE model is established based on the methods introduced in Section 2. The strain monitoring points of the FE model is the same as the field measurement. Maximum strains are used to verify the FE methods here. As indicated in Fig. 15, the maximum tensile strain recorded in the field measurement is different when different trains passing by because of the randomness of concrete. The average values of the maximum tensile strain recorded by SI, S2, S3, and S4 are 48.0, 54.9, 54.0, and 41.3 ps, respectively. The maximum strain results of the FE model are also plotted in Fig. 15. At the position of SI and S2, the maximum tensile strain calculated by the FE model is 45.6 and 51.4 ps, respectively, which are close to the mean value measured in the field study. This phenomenon indicates that the FE method adopted in this research is reliable.
To further verify the correctness of the calculation method of the crack tip field under 3D conditions, a 3D cuboid model with an edge crack is established using the method introduced in Section 2.3. As shown in Fig. 16 (a), the thickness of the cuboid is L the height is 2 hļ t = 1.75, the width is wit = 1.5, and the crack depth is a! t = 0.5. The mechanical behavior of the cuboid is described by an ideal elastic model with corresponding elastic modulus and Poisson's ratio of E = 1.0 and d = 1/3, respectively. Uniform tensile stresses are loaded on the upper and lower ends of the cuboid. Li et al. (1998) solved the SIF of the edge crack using the boundary clement (BE) method and FE method, respectively. Figure 16(b) presents the comparison between the FE results in this paper and the above two groups of results. Duc to the symmetry of the crack, only half the length of the crack front (Vw = 0.5) is shown in the figure. As shown in Fig. 16(b), Ky at the crack front presents an arch distribution, namely, large in the middle and small at the ends. The three groups of results capture a similar distribution. The FE results in this paper agree well with those of Li et al. (1998), with a maximum error of only 3.4%.
The above verifications demonstrate that the calculation method of the crack tip field developed in this paper is reliable.
3 Intensification effect of aerodynamic shockwaves
Figure 17 shows the pressure distribution on the crack surface of circumferential, inclined, and longitudinal cracks with time when the train speed is 350 km/h. As shown in Fig. 17, the aerodynamic shockwave intensifies after entering the crack, resulting in more significant pressure in the crack cavity than the input pressure. The main reasons arc as follows. First, the energy brought by the compression wave rapidly gathers because the pressure continues to enter the crack. Second, the propagation space narrows sharply when the pressure propagates into the crack cavity. Under the restriction of crack surfaces, the compression waves are reflected and superposed repeatedly in the narrow space, leading to a further increase of the pressure inside the crack.
As shown in Fig. 17(a), for the circumferential crack, the entering of pressure wave into the crack is an instantaneous process. Specifically, the pressure wave enters the crack through the crack opening at an instant (approximately t = 0.16 ms). After entering the crack from the crack opening, the compression wave propagates along the depth direction and reaches the deepest location of the crack cavity at approximately 0.32 ms. Subsequently, the compression wave propagates back to the crack opening, and the pressure in the crack decreases (/ = 0.48 ms). The compression waves in the circumferential crack arc symmetrically distributed along the crack length, and the compression wave peaks appear at the crack tip. As shown in Fig. 17 (b) and (c), the pressure distribution characteristics in the inclined and longitudinal cracks are similar. The compression wave is asymmetrically distributed in the crack.
A series of measuring points are used to analyze further the spatial and temporal characteristics of the aerodynamic pressure in the crack along the depth and length directions. The measuring points are arranged between the two crack surfaces on the axial plane. Figures 18-20 show the pressure time histories of measuring points in the circumferential, inclined and longitudinal cracks, respectively. As shown in Figs. 18-20:
(1) For the circumferential crack, the shockwave enters the crack opening at approximately 0.11 ms in the depth direction. Then the pressure of measuring points 1# to 5# rises successively, and the peak pressure of each measuring point increases with the increase in depth. The peak pressure of measuring point 1# is 3693 Pa, 1.85 times the input pressure. For measuring point 5#, the peak pressure rises to 10 655 Pa, 5.32 times the input pressure. It is worth noting that the deeper the location of the measuring point, the earlier the pressure will reach the peak. The reason is that the pressure value is small before it arrives at the deepest location. The pressure at the other measuring point rises to the peak only after the superposition of the pressure wave at the crack tip. In the length direction, the pressure distribution on the crack surface presents apparent symmetry. In addition, the peak pressure of the measuring point located on the symmetry axis is the highest. Specifically, the peak pressure of measuring point 3# is 1.52 and 1.30 times the corresponding value of measuring points 6# and 7#, respectively.
(2) The pressure variation in the longitudinal and inclined cracks is similar. Taking the inclined crack as an example, in the depth direction, the pressure at the measuring point increases with the increase in depth. The peak pressure at the measuring point 5# is 6043 Pa, 3.02 times the input pressure. The peak pressure of measuring points increases monotonously along the crack length direction. Unlike the circumferential crack, because the angle between the shockwave propagation direction and the crack length direction is less than 90°, the highest pressure peak occurs at measuring point 9# instead of the deepest position of the crack (measuring point 5#). The maximum pressure of the inclined and longitudinal cracks is 8466 and 6910 Pa, 79.5% and 64.9% of the corresponding values of the circumferential crack, respectively. The reason is that the pressure wave enters the circumferential crack instantaneously, and the input energy of the circumferential crack is the highest within the same time duration compared with inclined and longitudinal cracks.
4 Characteristics of the crack tip field
4.1 Evolution characteristics of the crack tip field
After the CFD calculation, aerodynamic pressure data are loaded onto two crack surfaces by mapped fields from point cloud data in ABAQUS. Figure 21 illustrates the loading method of aerodynamic pressure on crack surfaces.
Figure 22 shows the evolution of the maximum principal stress at the crack tip of circumferential, inclined, and longitudinal cracks with time when the train speed is 350 km/ h. As illustrated in Fig. 22, the stress at the three crack tips increases first and then decreases, similar to the aerodynamic pressure on crack surfaces (Fig. 17). For the circumferential crack, the stress at the crack tip is always symmetrical. Before 0.08 ms, the pressure wave docs not enter the crack, and the stress at the crack tip is zero. At approximately 0.14 ms, the stress on both sides of the crack tip began to rise. With the continuous input of compression waves into the crack cavity, the high-stress zone at the crack tip gradually transfers from the two ends to the crack depths. The highest stress occurs in the deepest location at approximately 0.32 ms. When the pressure wave begins to propagate outward from the deepest location of the crack, the stress at the crack tip decreases. For inclined and longitudinal cracks, the crack tip stress is asymmetrical. The stress at the crack tip near the incident side of the compression wave increases first and then transfers to the other side. The highest stress appears at the second half of the crack tip, and the occurrence time is approximately 0.32 ms. The highest stress of the two cracks is slightly lower than that of the circumferential crack.
Figure 23 shows the time histories of SIF at the crack front of circumferential, inclined, and longitudinal cracks when the train speed is 350 km/h. Figure 24 further shows the SIF distribution along the crack front of the three cracks with time.
As shown in Fig. 23, the SIF of the three cracks presents a variation rule of first increasing and then decreasing. For the circumferential crack, the SIF of seven measuring points at the crack front increases successively with the compression wave entering the crack. With the increase in the depth, the occurrence time of peak SIF at each measuring point delays, and the peak value increases. The maximum SIF of the circumferential crack appears in the deepest location, indicating that the deepest location of the circumferential crack is the most likely place for crack growth. For inclined and longitudinal cracks, the SIF of all measuring points in the clockwise direction increases successively, corresponding to the propagation direction of the compression wave. The maximum SIF of the two cracks appears in the second half of the crack front.
As shown in Fig. 24, when the pressure wave enters the circumferential crack, the distribution of SIF evolves from a U shape to an M shape and then to an inverted U shape along the crack front. The maximum SIF at the deepest location reaches 2.29 kPa-m1/2. For inclined and longitudinal cracks, the SIF at the crack front rises at the incident side and reaches its peak at the other side. The maximum SIF of the inclined crack appears at 0.68 times the crack front Ingth, and the corresponding Ky is 1.98 kPa-m1/2; The maximum SIF of the longitudinal crack appears at 0.78 times the crack front length, and the corresponding Ky is 1.71 kPa-m1/2. The maximum SIF of the circumferential crack is 15.7 % and 13.4 % higher than that of the inclined and longitudinal crack. The above results indicate that the possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves.
4.2 Influence factors of the SIF
To investigate the influences of train speed, crack length, crack depth, and shockwave incidence angle on the SIF of the circumferential crack, Fig. 25 shows the SIF distribution curve at the moment when Ky reaches the maximum value under different factors. In Fig. 25(di), the black lines on the secondary lining correspond to the crack depth direction. The red area represents the covering layer of the crack when G = 150°. The figure also applies linear or power functions to fit the maximum Ky. In train aerodynamics, the relationship between the train speed and train-induced aerodynamic effect is usually described by power functions (Yang et al., 2022). Therefore, the relationship between maximum Ky and train speed is fitted by a power function, and the linear function is applied to fit other factors. The coefficient of variation CV is adopted to quantify the sensitivity of SIF to different factors:
..., (9)
where σ and µ are the standard deviation and mean of the data, respectively.
As shown in Fig. 25, the distribution characteristic of SIF at the crack tip is the same under different factors, and only the maximum value varies with different factors. The maximum SIF at the crack tip is proportional to the 2.3 power of the train speed, proportional to the crack depth and shockwave incidence angle, and inversely proportional to the crack length. It is worth noting that according to Eq. (1), the compression wave peak caused by the train entering the tunnel is proportional to the quadratic power of the train speed. In addition, previous studies have shown that when a train passes the trackside facilities of the open-air railway, the amplitude of aerodynamic pressure generated is proportional to the square of the speed (Xiong et al., 2018; Yang et al., 2022). This phenomenon indicates that the influence of train speed on the crack tip field may be greater than that on the trackside structure of the open-air railway and the tunnel lining surface. According to the CV values in the figure, the sensitivity of SIF to different factors is as follows: train speed > crack depth > shockwave incidence angle > crack length. Specifically, when the train speed changes, the CV value is as high as 44.0%. When the crack depth and the shockwave incidence angle change, CV values are 17.9% and 16.1%, respectively. When the crack length changes, the CV value is only 3.81%.
Figure 26 shows the maximum pressure in the circumferential crack under different factors. As shown in Figs. 25 and 26, the influence rules of different factors on the maximum pressure and the SIF are consistent. The maximum pressure inside the crack is also proportional to the 2.3 power of the train speed, proportional to the crack depth and the shockwave incidence angle, and inversely proportional to the crack length. According to Fig. 26(a)-(c), when the train speed, crack length, and crack depth change, the CV value of the maximum pressure and the maximum SIF is close, indicating that the change of pressure is the direct cause of the change of SIF. However, it can be seen from Fig. 26(d) that, compared with the maximum pressure, the shockwave incidence angle significantly influences the maximum SIF. When the shockwave incidence angle changes, the CV value of the pressure peak is only 5.51 %, while the corresponding value of SIF is 16.1%. With the increase in the shockwave incidence angle, the covering concrete of the crack diminishes. Namely, the volume of concrete participating in the resistance to aerodynamic pressure becomes less. This is the main reason accounting for the increasing of crack tip SIF.
5 Conclusions
The train-induced aerodynamic shockwave significantly induces the tunnel lining cracks to grow and form falling concrete blocks. A joint calculation framework is established based on ANSYS Fluent, ABAQUS, and FRANC3D for calculating the crack tip field under the aerodynamic shockwave. The intensification effect of aerodynamic shockwaves in the crack is revealed, and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor (SIF) are analyzed. The main conclusions arc as follows:
(1) The aerodynamic shockwave intensifies after entering the crack, resulting in more significant pressure in the crack cavity than the input pressure. The main reasons include the continuous entry of compression waves, the narrowing space for propagation, and the reflection and superposition under the restriction of crack surfaces. The pressure on the circumferential crack surface is symmetrically distributed along the crack length, and the maximum pressure appears at the crack tip and is more than five times the input pressure. The maximum pressure of the inclined and longitudinal cracks is lower than the corresponding values of the circumferential crack, respectively.
(2) The stress at the crack front of circumferential, inclined, and longitudinal cracks increases first and then decreases, similar to the aerodynamic pressure on crack surfaces. For the circumferential crack, the stress at the crack front is always symmetrical. With the continuous input of compression waves into the crack cavity, the high-stress zone at the crack front gradually transfers from the two ends to the crack depths. The highest stress occurred in the deepest location of the crack. For inclined and longitudinal cracks, the crack front stress is asymmetrical. The stress at the crack front near the incident side of the compression wave increases first and then transfers to the other side. The highest stress of the two cracks is slightly lower than that of the circumferential crack.
(3) For the circumferential crack, the distribution of SIF evolves from a U shape to an M shape and then to an inverted U shape along the crack front. For inclined and longitudinal cracks, the SIF at the crack front rises at the incident side and reaches its peak at the other side. The maximum SIF of the circumferential, inclined, and longitudinal crack appears at 0.5, 0.68, and 0.78 times the crack front length. The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack. The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves.
(4) The maximum SIF of the circumferential crack is proportional to the 2.3 power of the train speed, proportional to the crack depth and shockwave incidence angle, and inversely proportional to the crack length. The influence of train speed on the SIF of the circumferential crack is more than 40 %; the influence of crack depth and the shockwave incidence angle are more than 10 %, respectively. When the train speed, crack depth, and crack length change, the change of pressure in the crack is the direct cause of the change of SIF.
The current work is still limited despite a calculation framework for simulating the crack tip field under aerodynamic pressure is proposed in this research. For example, we can improve our analysis by comparing our method to other numerical techniques, such as extended finite element method, partition of unity finite element method, and other meshfree methods. Moreover, crescent crack near the construction joint is also a common type of crack in tunnels. Efforts should also be made to investigate the aerodynamic pressure and crack tip field of crescent cracks.
CRediT authorship contribution statement
Yi-Kang Liu: Investigation, Software, Validation, Writing - original draft. Yu-Ling Wang: Validation, Writing - review & editing. E Deng: Data curation, Funding acquisition, Methodology, Writing - review & editing. Yi-Qing Ni: Funding acquisition, Writing - review & editing. Wei-Chao Yang: Conceptualization, Funding acquisition, Project administration, Writing - review & editing. Wai-Kei Ao: Writing - review & editing.
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.
Acknowledgement
This work was funded by the National Natural Science Foundation of China (Grant Nos. 51978670 and 52308419), the Science and Technology Research and Development Program of China railway group limited (Grant Nos. 2021-Major-01 and 2022-Key-22), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2023ZZTS0369), the Guangdong Basic and Applied Basic Research Foundation Project (Grant No. 2021B1515130006), the Innovation and Technology Commission of Hong Kong, China (Grant No. K-BBY1), and the Hong Kong Polytechnic University's Postdoc Matching Fund Scheme (Grant No. 1-W21Q).
Received 7 February 2023; received in revised form 13 October 2023; accepted 6 January 2024 Available online 3 April 2024
Peer review under the responsibility of Tongji University
* Corresponding author at: National Rail Transit Electrification and Automation Engineering Technology Research Center (Hong Kong Branch), The Hong Kong Polytechnic University, Hong Kong 999077, China.
E-mail address: [email protected] (E Deng).
References
Asakura, T., & Kojima, Y. (2003). Tunnel maintenance in Japan. Tunnelling and Underground Space Technology, 18(2/3), 161-169.
Cao, Y., Wang, P. Y., Jin, X. L., Wang, J. W., & Yang, Y. Z. (2012). Tunnel structure analysis using the multi-scale modeling method. Tunnelling and Underground Space Technology, 28, 124-134.
Chen, Y. B., Gao, Y., Shi, S. H., Xu, F., & Zhao, W. G. (2022). Characteristics of transient pressure in lining cracks induced by highspeed trains. Journal of Wind Engineering and Industrial Aerodynamics, 228, 105120.
Du, J. M., Fang, Q., Wang, G., Zhang, D. L., & Chen, T. L. (2021). Fatigue damage and residual life of secondary lining of high-speed railway tunnel under aerodynamic pressure wave. Tunnelling and Underground Space Technology, 111, 103851.
Fracture Analysis Consultants, Inc (FAC). (2015). FRANC3D Theory Manual 2015, Version 7:51. https://franc3d.in/.
Gong, C., & Zhu, Z. D. (2018). Numerical Study for the Aerodynamic Effects of High-speed Trains on Secondary Lining. Henan Science, 36 (5), 721-727 (in Chinese).
Howe, M. S., Iida, M., Fukuda, T., & Maeda, T. (2000). Theoretical and experimental investigation of the compression wave generated by a train entering a tunnel with a flared portal. Journal of Fluid Mechanics, 425, 111-132.
Huang, C., Chen, T., Xia, Z., & Jiang, L. (2022). Numerical study of surface fatigue crack growth in steel plates repaired with CFRP. Engineering Structures, 268.
Khademi-Zahedi, R., & Shishesa, M. (2019). Application of a finite element method to stress distribution in buried patch repaired polyethylene gas pipes. Underground Space, 4(1), 48-58.
Kim, D. H., Cheol, S. Y., Iyer, R. S., & Kim, H. D. (2021). A newly designed entrance hood to reduce the micro pressure wave emitted from the exit of high-speed railway tunnel. Tunnelling and Underground Space Technology, 108, 103728.
Li, S., Mear, M. E., & Xiao, L. (1998). Symmetric weak-form integral equation method for three-dimensional fracture analysis. Computer Methods in Applied Mechanics and Engineering, 151(3/4), 435-459.
Liu, J. W., Shi, C. H., Lei, M. F., Wang, Z. X., Cao, C. Y., & Lin, Y. X. (2021). A study on damage mechanism modelling of shield tunnel under unloading based on damage-plasticity model of concrete. Engineering Failure Analysis, 123(3), 105261.
Liu, T. H., Chen, Z. W., Chen, X. D., Xie, T. Z., & Zhang, J. (2017). Transient loads and their influence on the dynamic responses of trains in a tunnel. Tunnelling and Underground Space Technology, 66, 121-133.
Liu, Y. K., Deng, E., Yang, W. C., Ni, Y. Q., Zhou, Z., & Zhang, J. J. (2023). Aerodynamic intensification effect and dynamic response of cracks on high-speed railway tunnel linings. Tunnelling and Underground Space Technology, 140, 105308.
Miao, S., Pan, P.-Z., Hou, W., He, B., & Yu, P. (2022). Stress intensity factor evolution considering fracture process zone development of granite under monotonic and stepwise cyclic loading. Engineering Fracture Mechanics, 273, 108727.
Ministry of Housing and Urban-Rural Development of the People's Republic of China. (2015). GB 50010-2015: Code for Design of Concrete Structures. China Architecture Publishing & Media Co., Ltd. (in Chinese).
Panian, R., & Yazdani, M. (2020). Estimation of the service load capacity of plain concrete arch bridges using a novel approach: Stress intensity factor. Structures, 27, 1521-1534.
Shi, C. H., Wang, A., Sun, X. H., & Yang, W. C. (2022). Research on the movement law and traffic safety zoning of spalled blocks in the linings of high-speed railway tunnels. Tunnelling and Underground Space Technology, 128(2/3), 104614.
Shih, C. F., & Asaro, R. J. (1988). Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I-Small Scale Yielding. International Journal of Solids and Structures, 55(2), 299-316.
Stenfan, A., & Kaltenbach, H.J. (2008). Sensitivity of the wave-steepening in railway tunnels with respect to the friction model. In Proceedings of the 6th International Colloquium on: Bluff Body Aerodynamics and Applications, Milano, Italy (pp. 1-16).
Teng, Z. N. (2015). Research on evaluation and treatment method of tunnel structural cracks disease [Master's thesis, Southwest Jiaotong University]. Chinese National Knowledge Infrastructure (in Chinese).
Tong, L. W., Liu, B., & Zhao, X. L. (2017). Numerical study of fatigue behaviour of steel reinforced concrete (SRC) beams. Engineering Fracture Mechanics, 178, 477-496.
Wang, F. Y., Zhou, M. L., Zhang, D. M., Huang, H. W., & Chapman, D. (2019). Random evolution of multiple cracks and associated mechanical behaviors of segmental tunnel linings using a multiscale modeling method. Tunnelling and Underground Space Technology, 90, 220-230.
Wang, H. L., Lei, B., Bi, H. Q., & Yu, T. (2018). Wavefront evolution of compression waves propagating in high speed railway tunnels. Journal of Sound and Vibration, 431, 105-121.
Xiong, X. H., Li, A. H., Liang, X. F., & Zhang, J. (2018). Field study on high-speed train induced fluctuating pressure on a bridge noise barrier. Journal of Wind Engineering and Industrial Aerodynamics, 177, 157-166.
Xu, S. L., & Reinhardt, H. W. (1999). Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part III: Compact tension specimens and wedge splitting specimens. International Journal of Fracture, 98(2), 179-193.
Yang, W. C., Liu, Y. K., Deng, E., Wang, Y. W., He, X. H., Huang, Y. M., & Zou, Y. F. (2022). Moving model test on the aerodynamic pressure of bilateral inverted-L-shaped noise barriers caused by highspeed trains. Journal of Wind Engineering and Industrial Aerodynamics, 228, 105083.
Zhang, L., Yang, M. Z., Liang, X. F., & Zhang, J. (2017). Oblique tunnel portal effects on train and tunnel aerodynamics based on moving model tests. Journal of Wind Engineering and Industrial Aerodynamics, 167, 128-139.
Zhang, L., Yang, M. Z., Niu, J. Q., Liang, X. F., & Zhang, J. (2019). Moving model tests on transient pressure and micro-pressure wave distribution induced by train passing through tunnel. Journal of Wind Engineering and Industrial Aerodynamics, 191, 1-21.
Zhou, W., Chen, L., Wang, Z. G., Ding, S. S., & Shan, Y. L. (2019). Aerodynamic load spectrum and fatigue behaviour of high-speed train's equipment cabin. Fatigue & Fracture of Engineering Materials & Structures, 42(\\), 2579-2595.
Zhou, Z., Zhang, J. J., Gong, C. J., & Wu, W. (2023). Automatic tunnel lining crack detection via deep learning with generative adversarial network-based data augmentation. Underground Space, 9, 140-154.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
© 2024. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Abstract
High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks. Once the concrete block falling occurs, serious consequences follow, and traffic safety may be endangered. The aerodynamic shockwave evolves from the initial compression wave may be an important inducement causing the tunnel lining cracks to grow and form falling concrete blocks. A joint calculation framework is established based on ANSYS Fluent, ABAQUS, and FRANC3D for calculating the crack tip field under the aerodynamic shockwave. The intensification effect of aerodynamic shockwaves in the crack is revealed, and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor (SIF) are analyzed. Results show that (1) the aerodynamic shockwave intensifies after entering the crack, resulting in more significant pressure in the crack than the input pressure. The maximum pressure of the inclined and longitudinal cracks is higher than the corresponding values of the circumferential crack, respectively. (2) The maximum SIF of the circumferential, inclined, and longitudinal crack appears at 0.5, 0.68, and 0.78 times the crack front length. The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack. The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves. (3) The influence of train speed on the SIF of the circumferential crack is more than 40%. When the train speed, crack depth, and crack length change, the change of pressure in the crack is the direct cause of the change of SIF.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
Details
1 School of Civil Engineering, Central South University, Changsha 410075, China; The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen 518057, China
2 National Rail Transit Electrification and Automation Engineering Technology Research Center (Hong Kong Branch), The Hong Kong Polytechnic University, Hong Kong 999077, China; Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China
3 National Rail Transit Electrification and Automation Engineering Technology Research Center (Hong Kong Branch), The Hong Kong Polytechnic University, Hong Kong 999077, China; Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China; The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen 518057, China
4 School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Research Center of High-speed Railway Construction Technology, Changsha 410075, China