In order to investigate the dynamic response characteristics of composite rock with different joint angles, static compression test and dynamic impact test are carried out using WDW-300E servo pressure-testing machine and split Hopkinson pressure bar (SHPB) test system. The dynamic compressive strength, energy dissipation, and failure modes are compared between rock coal (R-C) and coal rock (C-R). Furthermore, a 3D SHPB simulation system is constructed using coupling finite difference method and discrete element method (FDM-DEM) to reproduce the energy evolution and failure modes of composite rock with different joint angles, and the fabric tensor is obtained based on secondary development. Finally, a constitutive model of composite rock is established considering joint angles. The results of experiment, simulation, and theoretical analysis show that for the case of uniaxial compression test, with the increase of joint angle, the peak stress of composite rock shows obvious U-shaped change, and the elastic modulus increases gradually while the peak strain decreases gradually. For the case of dynamic impact test, the peak stress, strain, and energy dissipation values of composite rock decrease first and then increase with the increase of angle, and the elastic modulus of composite rock increases monotonically after a slight fluctuation of 30°. The stress, energy dissipation and elastic modulus of composite rock R-C are larger than that of composite rock C-R. However, the strain value of composite rock R-C is generally less than of composite rock C-R. The failure mode of composite rock with small and large angle is mainly splitting under dynamic impact, and the fracture fragmentation is relatively small with high energy absorption rate, while the fracture fragmentation is mainly shear and splitting mixed failure with low energy absorption rate. The energy accumulation and transformation process inside the composite rock are analyzed by 3D simulation system, and the damage of the composite rock under impact is mainly concentrated on the coal side, and peak values of contact number and contact force with different joint angles are calculated by using fabric tensor. Based on Weibull distribution, a constitutive model of composite rock is constructed considering initial damage and dynamic failure effect, which is in good agreement with experimental and simulation results, verifying the correctness of the constructed model.

An increasing number of coal mines are being developed in deep and complicated geological environments due to the increased demand for underground coals [1, 2]. Layer structures such as composite coal rock columns or composite surrounding rocks are formed and undergo a more complicated stress state owing to the natural occurrences of coal bodies, which result in dynamic impact hazards and seriously influence the safe production in coal mines [3, 4]. In general, the composite rock body can be simplified into two composite modes of coal rock (C-R) and rock coal (R-C), and it shows different dynamic characteristics compared with a single coal or rock body [5]. Due to geological structure, obvious joint angles are obtained in the composite rock body. Therefore, a good understanding of these dynamic behaviors of composite rock body with different joint dips is critical to the stability of deep coal mines [6, 7].

Mechanical analysis was conducted to evaluate the stress distribution in composite rock with horizontal [8] and inclined direction [9] and explored the effect of different coal-rock height ratio [1012] under confining pressures. In addition, evolution patterns and distribution characteristics are obtained [13] and predicted the potential failure modes [8]. The existence of contact surface constraint resulted in an increase in the axial peak stress and peak strain compared with that without the contact surface [14], and permeability under true triaxial stress conditions was taken into considerations [15]. The strength in both impact direction and axial direction increased linearly with the loading strain rate [16]. The effects of loading rate on the dynamic compressive strength [17], dynamic tensile strength [18], and crack propagation characteristics are studied.

There are several studies on influence of preexisting holes on the properties of the rock specimen. There were five types of cracks at or near the tips depending on four preexisting flaws [19]. Samples containing the cross-fissured displayed obvious X-shaped shear failure mode regardless of fissure subjected to dynamic strain rate [20]. The crack evolution and failure modes mainly depended on cavity number and layout [21]. With the increase of cavity radius, the dissipated energy density accordingly showed a grow tendency, which results in smaller and smaller rock fragments [22, 23]. Joint played an important role in dynamic uniaxial compression tests including stress field and wave propagation [24, 25]. Rock failure is not only related to structure but also to the geological environment. A series of experimental studies have been conducted to explore the influence of external conditions. It was observed that the development of microcracks after cyclic wetting-drying treatments led to the reduction in dynamic compressive strength [26]. It is widely recognized that water-weakening on rock strength gradually decreased with increasing of the strain rate [2729]. Cold shock treatment of Brazilian splitting tests was conducted on the mechanical properties [30]. And dynamic compressive strength increased with the confining pressure but decreases with the pore pressure [31]. It was known that internal initiation and propagation of microcracks might result in macroscopic fragmentation [3236]. Under static and dynamic compression, wing cracks can continuously extend to a limited distance and ends, respectively [37]. The cracking processes of the single-flawed and multiflawed rock specimens were also found to be rate-dependent [38, 39]. A phase-field model for dynamic crack propagation is proposed [40].

The experimental and numerical results indicate that joints have a great influence on crack dynamic propagation direction. And the crack propagation is positively associated with the loading rate [4146]. The quantitative relationships of dissipated energy density associated with different strain rates were explored [47]. The failure pattern of the rock changes with strain rates in the dynamic loading experiments [48].

At present, research on deformation of composite rock masses with different joint angles mainly focus on dynamic loading failure modes and its mechanisms. However, there is little research on the progressive evolution under dynamic loading and the coupling analysis of numerical simulation. In this paper, uniaxial compression test and SHPB test of composite rock mass were carried out. The crack development process was observed by high-speed camera, and the strength, failure mode, and energy dissipation of composite rock mass under impact were analyzed. Meanwhile, a coupled SHPB simulation system was established to reproduce the energy evolution and failure modes of composite rock mass under dynamic impact, and the internal contact was quantified by using the fabric tensor. Finally, based on Weibull distribution, the constitutive model considering joint angle of composite rock mass was constructed and compared with the experimental and numerical simulation results, and it provided some reference for the stability analysis of composite rock mass under dynamic action.

2.1. Materials and Preparation

The materials for this test were taken from Huozhou Coal Mining Company. The raw coal was taken from the on-site working face, and the sandstone mainly came from the roof and floor. The raw coal and sandstone were processed into samples with different joint angles and subjected to secondary smoothing treatment. Then, they were bonded into composite rock mass (50mm×50mm) using epoxy resin. The nonparallel and nonperpendicular end faces were reduced to less than 0.02 mm, to ensure good contact between the specimen and the bar [49]. As shown in Figure 1, the coal and sandstone are denoted as C and R, respectively. And they are divided into two groups (R-C and C-R), according to the order of the impact action of the incident bar.

2.2. Experimental Apparatus and Procedure

The static loading of the composite rock mass was carried out using WDW-300E servo pressure-testing machine (Figure 2(a)), the measurement accuracy was less than ±0.5% and its resolution was 0.001 mm, and the loading was applied on the composite rock mass in pressure-controlled conditions with a loading rate of 0.5 MPa/s until it failed. SHPB test system is shown in Figure 2(b). The incident bar, transmission bar, and punch of the test system are all made of high-strength alloy steel with a density of 7800 kg/m3, an elastic modulus of 200 GPa, and a bar diameter of 50 mm. Before the test, the composite rock mass was placed between the impact bar and the transmission bar, and Vaseline was evenly spread on both ends of the composite rock mass to ensure better contact. In order to compare the effects of different joint angles, the loading was controlled to be the same strain rate, and the loading signals were mainly collected by the strain gauges distributed in the incident bar, the composite rock mass, and the transmission bar. During the test, ultrahigh speed [18] was used to capture the whole process, and supplementary light was used to meet the light intensity requirements of the test.

2.3. Stress Uniformity under SHPB Test

According to the dynamic compressive strength test scheme recommended by International Society for Rock Mechanics and Rock Engineering (ISRM) [50], the dynamic stress balance is shown in Figure 3. It can be seen that the sum of the incident stress and the reflected stress was basically consistent with the transmission stress, indicating that the loading process satisfied the stress balance condition.

3.1. Stress-Strain Curve under Static Condition

In order to compare the result of stress-strain curve under static and dynamic conditions, the stress-strain curve of the composite rock mass with different joint angles under uniaxial compression is shown in Figure 4(a). When the joint angle was 0°, the peak stress of uniaxial compression was 30 MPa. The compressive strength gradually decreased and reached a minimum value of 18 MPa at 45°. Then, it began to increase significantly and reached a maximum value of 43 MPa at 90°, showing an obvious inverted U-shaped change [51]. Moreover, its peak strain (Figure 4(b)) gradually decreased with the increase of the angle. This was because the coal body was the main bearing structure under the compression condition, and the strain was mainly generated in the coal body part. With the increase of the angle, the proportion of the rock mass increased in the loading direction, which results in an increase in obvious supporting effect but decrease in the overall strain [52]. The elastic modulus (Figure 4(c)) was mainly determined by the stress-strain relationship. It can be obtained that the overall elastic modulus increased with the increase of the angle from Figure 4(a).

3.2. Stress-Strain Curve under Dynamic Condition

Figure 5 showed the dynamic response of the composite rock mass R-C with different joint angles. The stress peak value was 45 MPa when the joint angle was 0°, and it gradually decreased with the increase of the angle, it reached a minimum value of 22 MPa at 45°. Then, it began to gradually increase to a maximum value of about 60 MPa at 90°, which was consistent with variation under static condition [53]. The peak strain decreased first and then increased with the increase of the angle, and it reached the minimum value of 0.001 at 45°. The reason for this was composite rock mass with 45° was prone to failure along the joint surface under the dynamic impact. In addition, there were rock mass distributing at both ends in the composite rock mass with 60° and 90°, and it can also be observed that existence of rock mass limited the overall deformation [54]. The elastic modulus first decreased slightly and then gradually increased to about 9 GPa with small joint angle, and it reached to 10 GPa and 11 GPa with the joint angle greater than 45°.

Figure 6 showed the dynamic response of composite rock mass C-R with different joint angles. The variation of peak stress and strain with respect to angle was similar to that of the composite rock mass R-C. However, the peak stress of composite rock mass C-R was smaller than that of composite rock mass R-C, and this was mainly due to the fact that the coal body had a certain buffering effect when it was directly subjected to the impact, resulting in a smaller peak strength of the composite rock mass C-R. The peak strain of composite rock mass C-R was greater than that of the composite rock mass R-C. This implied that deformation was more obvious in the coal body, and deformation was more likely to occur when coal body was directly impacted [55]. As a whole, the elastic modulus was slightly smaller than that of the composite rock mass R-C, indicating that its ability to resist deformation was relatively weak [56].

3.3. Failure Mode

Based on the photos obtained with the ultrahigh-speed camera, the crack images were extracted through Python program [57, 58], and the obtained images were processed by python-compiled programs including gray, adaptive mean, and adaptive Gaussian, and then, cracks were identified. Figure 7 showed the failure forms of composite rock masses with different joint angles under static loading and dynamic impact. Under static loading conditions, tensile cracks appeared in the composite rock masses of 0° and 90°, but shear cracks along the joint were generated in the composite rock masses of 30°, 45°, and 60°. Under dynamic loading conditions, tensile failure was also recognized in the composite rock masses of 0° and 90°. It was worth mentioning that mixed shear and tensile failures occurred in the composite rock masses of 30°, 45°, and 60°, in which shear cracks were along the joint plane and tensile cracks were mainly generated on the side of the coal body. Therefore, the failure modes of composite rock masses with small and large angles were mainly tensile failure, and it was mixed shear and tensile failures for the angle of 30°, 45°, and 60° [59, 60].

3.4. Analysis of DIF

The dynamic increasing factor (DIF) is the ratio of dynamic compressive strength to static compressive strength [61], and it reflects the increase degree of compressive strength, which can be expressed as follows:
(1)DIF=fdf,
where fd and f are dynamic compressive strength and static compressive strength, respectively.

It can be seen from Figure 8 that DIF of the composite rock mass was between 1.2 and 1.6. When the joint angle was 0° and 90°, the DIF value of R-C of the composite rock mass was greater than that of the composite rock mass C-R, and the former was smaller than later for other angles. It could be attributed to failure mode of the composite rock mass. The tensile failure was dominant when the joint angle was 0° and 90°, and the higher strength was easy to appear in the composite rock mass R-C, while for the joint angles were 30°, 45°, and 60°. The composite rock mass C-R was relatively difficult to slip, and there were more cracks appearing in the coal body, resulting in a higher increase in strength [62].

3.5. Dissipated Energy Analysis

According to the principle of energy conservation [63], the energy in the test mainly includes input energy, reflected energy, transmission energy, and dissipated energy. Dissipated energy mainly reflects the process of initiation, development, and failure of internal defects in rock mass, which is the fundamental reason of instability of composite rock mass. The expressions of each part are as follows:
(2)Wi=A0ρ0C00tσi2tdt,Wr=A0ρ0C00tσr2tdt,Wt=A0ρ0C00tσt2tdt,Wd=WiWrWt,β=WdWi,
where Wi, Wr, Wt, and Wd are input energy, reflected energy, transmission energy, and dissipated energy, respectively. β is energy dissipation per unit volume, and it is an index of the absorption capacity of the composite rock mass to external energy. The fragmentation is the direct manifestation of the absorption capacity.

Figure 9 showed the energy dissipation values of the composite rock mass with different joint angles under dynamic loading. The energy dissipation value first decreased and then increased as the angle increased, which was similar to the dynamic strength curve. However, it can be seen that the energy dissipation value was the smallest at 60°, while its dynamic strength was the smallest at 45°, indicating that the energy dissipation was not only related to the dynamic strength but also affected by its failure mechanisms. From Figures 7(b) and 7(c), it can be seen that the shear along the joint plane was mainly obtained in the composite rock mass with 60°, and the tensile failure was less compared with that at 45°, so its energy dissipation value was smaller. Keeping the same joint angle, energy dissipation value of composite rock mass R-C was larger than that of composite rock mass C-R, which results from that the dynamic strength of composite rock mass R-C was higher, contributing indirectly to larger energy dissipation value.

Figure 10 showed the energy absorption rate under different joint angles. The energy absorption rate of composite rock mass with 0° was the highest about 0.51~0.56, corresponding to the smallest fragment size after failure. The minimum energy absorption rate was 0.43~0.47, and its size was the largest after failure [64]. The energy absorption rate can be divided into three categories according to the angle, which can provide a better reference for the rock-breaking of the composite rock mass.

4.1. Establish of Numerical Model

The SHPB simulation system [6567] was established by coupling the continuous medium constructed by FLAC3D and the discrete medium constructed by PFC3D (Figure 11). The geometry of the sample was 50mmdia×50mmheight, which consisted of 56265 particles. The length of incident bar and transmitted bar was 2000 mm, which was divided into 108967 units. The calibration parameters of the bar and composite rock mass are shown in Table 1. The incident bar, composite rock mass, and transmission bar were all equipped with measuring balls to monitor the stress state.

In order to verify the validity of the model [68], monitoring points were set at the position of the coupling wall to record the stress from the incident bar to the sample and the sample to the transmission bar. It can be seen from Figure 12(a) that the forces at both ends of the sample were balanced, and the dynamic stress was in balance on the incident bar and the transmission bar (Figure 12(b)), suggesting the correctness of the established model.

4.2. Dynamic Impact Process

Figure 13 showed the different stages of dynamic loading process of the composite rock masses under the dynamic impact. It can be seen that the peak strength of the numerical simulation and the test results tend to be consistent. However, the numerical simulation results did not show an obvious compaction stage, which can be attributed to a precompression process before the calculation, contributing to an accelerated trend with the strain.

In order to better describe the dynamic impact process [69], five characteristic points were selected here to obtain the propagation process of the stress wave in the progressive failure process of the fragment field, which can be divided into the following stages (Figure 14):

  • (1)

    Stage A (F): the incident wave propagated from left was reaching to right of the composite rock mass

  • (2)

    Stage B (G): the wave passed through the composite rock mass, resulting in stress concentration, and no clear deform appeared in the composite rock mass

  • (3)

    Stage C (H): part of the stress wave was reflected, the stress at both ends of the composite rock mass continued to increase, and the macroscopic deformation area began to appear

  • (4)

    Stage D (I): the stress of the composite rock mass reached to peak value, and obvious fragments were obtained

  • (5)

    Stage E (J): the stress-strain curve stayed in postpeak stage, and the macroscopic failure was finally formed

4.3. Evolution of Cracks

As shown in Figures 15(a) and 15(b), taking the joint angle of 0° as an example to show the crack evolution process of the composite rock mass. For the composite rock mass R-C, the internal microcracks started to initiate on both sides, and the number of microcracks increased rapidly near the peak stress. Moreover, the number of microcracks of the coal body was significantly larger than that of the rock body, and macroscopic damage was finally formed. For the composite rock mass C-R, the internal microcracks mainly started directly on the coal body and expanded until the deformation became unstable. Figures 15(c) and 15(d) showed the failure modes of composite rock mass under different joint angles. For composite rock mass R-C and C-R, the composite rock mass of 0° and 90° formed tensile failure, and the composite rock mass of 30°, 45°, and 60° underwent shear deformation until macroscopic failure [70]. It can be seen that the coal body was easy to form stress concentration and was more prone to failure. The failure mode was basically consistent with the experimental observation phenomenon [71, 72].

4.4. Fabric Tensor

The contact between particles is generally regarded as an important index to determine the mechanical properties of particles, including normal contact force perpendicular to the contact plane and tangential contact force parallel to the contact. It is normal contact force that influence the force between particles under general conditions, so normal contact force should be focused on. Here, the fabric tensor proposed by Oda [73] was used to analyze contact force, which can be directly characterized through secondary development. The expression is as follows:
(3)ϕij=1Ncc=1Ncnicnjc,
where ϕij is the contact normal fabric tensor, nic is the unit vector along the normal line of contact, and Nc is the total contact number of particle system.

Figure 16 showed the peak values of contact number and contact force of composite rock mass with different joint angles. With the increase of joint angles, both contact number and contact force decreased first and then increased, reaching the minimum value at 60°. The maximum values of contact number and contact force of composite rock mass R-C were 244 N and 810 N, respectively, while the maximum values of composite rock mass C-R were 182 N and 504 N, respectively, which were smaller than composite rock mass R-C. This is because the stress entering the composite rock mass C-R was relatively small due to different wave impedances, resulting in correspondingly smaller contact number and contact force. The peak values of contact force and contact number for the two composite rock masses both appeared in the coal body, indicating that stress concentration was formed, and thus instability failure was more likely to occur [74, 75]. It can be used as an important reference index to improve the accuracy of disaster warning.

4.5. Analysis of Energy

The function of obtaining the contact energy between particles was compiled using the FISH language, including kinetic energy, strain energy, cementation energy, damping energy, and cementation failure energy [76]. During the impact process, the cementation energy and strain energy accumulated and reached the peak value. Shear displacement occurred between the particles of the composite rock mass, and the microcracks expanded, penetrated, and released energy. Then, the damping energy and cementation failure energy began to increase and became stable, and instability and failure occurred.

Taking the composite rock mass R-C with 0° (Figure 17) as an example, the kinetic energy reached the maximum value of 20 kJ at the initial stage and then gradually decreased, while the cementation energy and strain energy gradually accumulated, reaching to the maximum values of 320 kJ and 150 kJ, respectively. The microcracks in the composite rock mass expanded after the peak stress, and the cementation energy and strain energy decreased significantly. Some energy was converted into the damping energy and cementation failure energy, reached to 100 kJ and 50 kJ, respectively. With the increase of the joint angle (30°, 45°, 60°, and 90°), the energy peaks first decreased and then increased. The bonding energy and strain energy reached a minimum of 150 kJ and 75 kJ when the joint angle was 60°, while the damping energy and the bonding failure energy were 75 kJ and 50 kJ, respectively.

As shown in Figure 18, with the increase of the joint angle, the energy variation of the composite rock mass C-R was also similar to that of the composite rock mass R-C. The energy peaks displayed a trend of decreasing first and then increasing, which indicated that the change of the energy of the composite rock mass was closely related to the joint angle. Therefore, the bearing capacity of the composite rock mass maintained a corresponding relationship with the energy accumulation and release characteristics, indicating that the failure process of the sample was essentially energy adjustment.

5.1. Establish of Damage Constitutive Model

It is assumed that the composite rock mass is composed of a large number of units, and the strength of the units conform to Weibull statistical distribution [77]. Under constant strain rate dynamic loading, its probability density function is as follows:
(4)P=mε0εε0m1expεε0m=mε0ε̇tε0m1expε̇tε0m,
where ε̇ is strain rate, t is loading time, and m and ε0 are Weibull statistical distribution parameters. The unit is gradually destroyed in the process of dynamic impact. Damage variable [78] of composite rock mass is as follows:
(5)Dd=NdN=0εNPdεN=1expε̇tε0m,
where Dd is damage variable of composite rock mass, Nd is failure units, and N is total number of units.
(6)Dδ=1EδE0,
where Dθ is initial damage variable, Eθ is initial elastic modulus of composite rock mass with angle, and E0 is initial elastic modulus of composite rock mass.
Then,
(7)σ=1DE0ε=1Dd1DδE0ε=1DdEδε,σ=expε̇tε0mEδε.
In the process of dynamic loading [79], the stress peak point σmax,tm satisfies as follows:
(8)σt=tm=σmax,σtt=tm=0.
The expressions are as follows:
(9)σt=Eδε̇expε̇tε0m1ε̇tmε0ε̇tε0m1,lnσmaxEδε̇t=ε̇tε0m,ε̇tε0m=1m.
The parameters can be obtained,
(10)m=1lnσmaxlnEδε̇t,ε0=ε̇tm1/m=ε̇t1lnσmaxlnEδε̇tlnEδε̇t/σmax.

5.2. Validation of Damage Constitutive Model

In order to verify the correctness of the model, the model fitting parameters of composite rock mass with different joint angles were analyzed and calculated, as shown in Table 2. The established model was compared with the test results and simulation results, as shown in Figures 19 and 20.

It can be seen from Figures 19 and 20 that the simulation results reached the peak fastest, and the values before the peak were generally larger than the experimental and theoretical analysis results. It was denoted that the preloading process of the simulated test leaded to numerical model being in the compaction stage, then the stress increased directly, and the difference in the postpeak stage was relatively large under dynamic loading. However, the theoretical analysis results were in good agreement with the experimental results, and the main reason was that the initial damage and dynamic loading of the composite rock mass were taken into account. On the whole, the theoretical analysis results, experimental results, and simulation results were within the scope of errors (0.7~1) [80], indicating the correctness of the composite rock mass constitutive model, and it can provide a theoretical basis for stability analysis [77, 81, 82].

Dynamic failure effect of composite rock mass with different joint angles was systematically studied using electrohydraulic servo pressure-testing machine and SHPB impact device and compared with the results of 3D coupling simulation system and constitutive model. The main conclusions are as follows:

  • (1)

    Under static loading, with the increase of joint angle, the stress peak of composite rock mass decreased firstly and then increased and reaching the minimum value of 18 MPa at 45°. The elastic modulus increased monotonically to 5.6 GPa, while the peak strain decreased gradually to 0.012. Under dynamic loading, the peak stress and strain of composite rock mass R-C and C-R displayed a U shape with the increase of angle, and the elastic modulus increased monotonically after a slight fluctuation of 30°. The stress and elastic modulus of composite rock mass R-C were larger than that of composite rock mass C-R, while the strain value of composite rock mass R-C was generally smaller than that of composite rock mass C-R

  • (2)

    The energy dissipation values of composite rock mass of R-C and C-R under dynamic loading firstly decreased and then increased with the increase of joint angle, and reached the minimum values of 70 J and 66 J at 60°, respectively. Composite rock with small and large joint angle was mainly tensile failure, and it was mainly shear and tensile mixed failure for intermediate joint angle. The failure of the two composite rock masses mainly concentrated on the coal side

  • (3)

    Internal energy accumulation and transformation process in composite rock mass under the dynamic loading were obtained by 3D simulation, contact number and contact force were characterized by fabric tensor, and peak value of contact number and contact force first decreased and then increased with increase of joint angle. Both of the peak values were mainly distributed in coal side, and it was easier to form stress concentration, which completely agreed with experimental observations

  • (4)

    Based on Weibull distribution, the dynamic constitutive model under dynamic loading was constructed, which not only considered the initial damage of composite rock mass but also comprehensively described the failure effect of dynamic loading. The comparison among the analysis results, experimental results, and numerical simulation showed that the model can predict the stress-strain relationship of composite rock mass with different joint angles. It can provide reference for analysis of joint effect of composite rock mass

The research presented in this study can be useful for predicting rock failure subjected to impact loading, which plays an important role in mining and civil engineering. The effect of other factors such as the amplitude and type of impact loading will be taken into account in the next step. In future, other scenarios may be considered, for example, impact take place under creep conditions. Accurate prediction of the failure in real rock mass is important, and there is currently no ideal method for predicting the destruction, which should be further researched in the future.

The data presented in this study are available on request from the corresponding author.

The authors declare no conflict of interest.

Financial support for this work was provided by the Outstanding Scholar of Sun Yuezaki (800015Z1179), Hebei Province Ecological Wisdom Mine Joint Fund Project (E2020402036), the Fundamental Research Funds for the Central Universities (2009QZ03), and Open Fund of State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (KF2020-06).

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