Abstract
A ballastless track is susceptible to damage and even failure of structural components under the long-term effects of extremely high temperatures. In this paper, considering the influence of different constraint boundaries, a 1 : 4 scaled model of a ballastless track-bridge structural system was produced and placed in a large-sized environmental chamber. The thermal performance of the track structure was studied by carrying out temperature loading tests at extreme temperatures. In combination with the scaled-down model test data, a 3D nonlinear finite element model was established to investigate the damage evolution of broad-narrow joints under temperature gradient loading. The results are shown as follows: (1) the cement asphalt (CA) mortar layer has a hysteretic effect on the vertical temperature transfer. The most unfavorable structural part is between the track slab and the CA mortar layer of the track structure. (2) The constraint conditions accelerate the rate of temperature transfer, creating disturbances to the internal stresses of the track structure and amplifying the internal stresses induced by the environmental temperature increase. (3) Temperature and longitudinal stresses in the track’s structural layers are highly correlated. There is a significant quadratic regression between internal temperature and structural stresses in different extreme high-temperature environments. (4) As the temperature gradient load increases, the damage occurs at the junction of the broad-narrow joint and tends to expand towards the ends, which has little effect on the compression damage of the broad-narrow joint but significantly increases the tension damage. The research could provide useful guidance for the scientific operation and maintenance of the ballastless track in extreme high-temperature environments.
1. Introduction
Ballastless tracks have a long service life, low maintenance requirements, and high reliability, and, hence, a more extensive application in high-speed railways [1, 2]. The China Railway Track System (CRTS) II slab track is widely applied in high-speed railways in China, such as the Beijing-Shanghai and Beijing-Tianjin High-Speed Railways [3, 4]. To ensure the smoothness and continuity of the line, the high-speed railway has adopted a large number of “bridge instead of road” construction solutions, with the Beijing-Shanghai high-speed railway bridge accounting for 80.47% of the line. The bridge-track structure is composed of rails, fasteners, prestressed track slabs, CA mortar layer, concrete base, sliding layer, and box girder, with broad-narrow joints between adjacent track slabs. The track structure is shown in Figure 1.
In the ballastless track service process, the environmental temperature has a nonnegligible role in structural deterioration, causing structural warpage and deformation [5], longitudinal buckling [6], and interface damage [7, 8]. It is worth noting that the broad-narrow joints are relatively weak, showing extrusion damage, cracks, and falling off. An example is shown in Figure 1. The damage to the broad-narrow joints is a serious threat to the structural stability and operational safety of the track. In recent years, extreme high-temperature climates have been frequent, and extremely high temperatures in southern and south-western China have exceeded the historical extreme of 41°C [9]. Track structural diseases are becoming more and more serious. To avoid such serious defects and propose effective maintenance strategies to improve the serviceability of the CRTS II slab track, it is necessary to investigate the thermal performance under extremely high-temperature conditions and to reveal the evolution of damage to broad-narrow joints.
At present, a series of studies have been carried out on the temperature field and thermal-induced effects of the ballastless track. Based on the field test data, Sun et al. [10] analyzed the temperature distribution characteristics of the ballastless track by mathematical and statistical methods and proposed an empirical formula for the surface temperature of the track slab. In addition, Lou et al. [11] proposed a statistical method of virtual distribution in response to the lack of accuracy of existing statistical analysis methods of temperature, using the high moment theory of reliability to investigate the temperature action of bridge-track structures of high-speed rail in China. Zhao et al. [12] carried out routine high-temperature tests in summer to study the temperature distribution pattern of the track on high-speed rail bridges and proposed the longitudinal and transverse temperature distribution trends of the track. Considering the track structure direction and geographical location, Yang et al. [7] determined the bottom boundary conditions of the ballastless track temperature field by theoretical derivation and established a three-dimensional calculation model of the track temperature field to analyze the temperature characteristics of the ballastless track under continuous high-temperature weather. At the same time, You et al. [13–15] used numerical simulation software to establish a three-dimensional thermal conduction numerical model to investigate the temperature field distribution of the track structure and establish the mapping relationship between the track structure and the ambient temperature.
To investigate the thermal-induced effects of the ballastless track, Cho et al. [16] conducted field tests on the continuous reinforced concrete track (CRCT) to investigate the effect of temperature changes on the CRCT crack width and proposed various methods to improve the performance of the CRCT. Cai et al. [17] investigated the force mechanism of broad-narrow joints based on numerical simulations and pointed out that the poorer the quality of the concrete in the joint, the smaller the temperature rise leading to the joint damage and the larger the damaged area. Chen et al. [18] established an analytical expression for the displacement field during the warping of a track slab based on the equilibrium differential equation and analyzed the warping deformation law of the track plate under multiple factors. Song et al. [19] established a refined finite element model of the CRTS II slab ballastless track structure based on meteorological data and the characteristics of the track multistory structure and proposed an analysis method for thermal deformation. Wang et al. [20] analyzed the stresses and deformations of the track under different temperature loads through numerical simulations, pointing out that the increase in structural stresses caused by extreme weather led to the decay of the tensile strength of the CA mortar. Chen et al. [21] explored the interface damage evolution under temperature loading through full-scale transverse shear experiments and numerical simulations. Zhou et al. [22] carried out indoor cyclic temperature and static load tests to investigate the effect of interstory clearance on the displacement, strain, and stiffness of the track structure.
In summary, previous researchers have mainly investigated the internal temperature distribution of track structures through long-term simultaneous monitoring of ambient and structural temperatures, while few studies have been carried out on the effects of various environmental temperatures on the structural deformation and stresses of the CRTS II slab track under different boundary conditions, especially in extremely high-temperature environments. In addition, several results have been obtained using different research methods to investigate the thermo-induced effects of ballastless tracks, and they indicate that the broad-narrow joint damage causes the track slab to arch. Nevertheless, the damage evolution of joints in extreme high-temperature environments needs further investigation. Based on this, a 1 : 4 scaled model of the CRTS II ballast track on the bridge with two different boundary conditions is produced to study the temperature distribution, stress, and longitudinal displacement of the track structure under extreme high-temperature conditions; a finite element numerical model is established based on the reduced scale model, and the validity of the numerical model is verified by test results to reveal the evolution of the broad-narrow joint damage under different temperature gradient loads.
2. Experiment Program
2.1. Design and Production of the Specimen
The CRTS II ballastless track-bridge system consists of a simply supported girder and a CRTS II slab ballastless track. To ensure the continuity of the structure, a 32 m prestressed simply supported concrete box-beam was selected as the prototype bridge in this paper. Due to the large size of the prototype structure and the limitations of the test site, a commonly used 1 : 4 scaled model was used for the indoor tests to accurately simulate the mechanical characteristics of the CRTS II slab tracks. In addition, to consider the influence of different boundary conditions on the structural performance, two 1 : 4 scaled models of the prototype track-bridge structure with two boundary conditions (restrained end specimen and free end specimen) were made, as shown in Figure 2.
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The similarity ratio of structural parameters in the scaled model is listed in Table 1. The structural materials used in the dimensional reduction model are consistent with those of the prototype structure. The strength grade of concrete for the precast track slab and broad-narrow joints is C55, and the strength grades of concrete for the concrete base and simple beam are C40 and C50. The mix ratios for the concrete are listed in Table 2. The mechanical properties of the CA mortar layer meet the requirements, and the mix ratios are listed in Table 3. An HRB400 is used for the ordinary reinforcement of the box beam and track structure, and the track slab is connected longitudinally with a 20 mm diameter refined rebar to ensure its continuity. The specific material parameters are listed in Table 4.
2.2. Experimental Apparatus
The extreme high-temperature loading tests were conducted in a large environmental chamber in the State Key Laboratory of Chongqing Jiaotong University. The environmental chamber consists of five environmental chambers (A, B, C, D, and E) and has a complex environmental system that enables artificial acceleration tests of structures of different scales under complex environmental effects, such as high-temperature drying, low-temperature freezing, and thawing. The environment device is illustrated in Figure 3.
2.3. Measuring Point Arrangement and Data Collection
An extensive array of mechanical sensors was deployed during mockup construction, including (1) temperature sensors (TSs) for measuring the temperature distribution of the track structure (track slab, the CA mortar layer, and the base plate); (2) strain gauges (SGs) for measuring the strain of the track slab and concrete base; and (3) displacement gauges (DGs) for measuring the horizontal displacement at the end section of the track slab for the freedom specimen. As shown in Figure 4(a), the longitudinal direction is set as the Y-axis, the horizontal direction as the X-axis, and the vertical direction as the Z-axis. The sensor names and their positions are shown in Figure 4(a) with reference to a 3D Cartesian coordinate system. The specific arrangement of the sensors is shown in Figures 4(b) and 4(c).
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2.4. Test Condition
According to the 2021 China Climate Bulletin, the temperature in South China has exceeded the historical temperature extreme value of 41°C [9]. Based on this, the ballastless track temperature loading tests were conducted in different extreme high-temperature environments (40°C, 43°C, and 46°C). At the same time, the environmental chamber temperature rise rate was kept consistent, and the test duration was 24 h.
3. Experimental Results
The temperature distribution, stresses, and deformation of the scaled-down model, with different constraints, are compared under three extreme high-temperature conditions to investigate the effect of extremely high temperatures on the thermal performance of the CRTS II track structure.
3.1. Vertical Temperature Distribution
The temperature-time curves for the model with two different constraints for three extreme high-temperature conditions are given in Figure 5. As observed from Figure 5, the temperature of the structural layer of the ballastless track rises gradually over time under different extreme high-temperature conditions, with the structural temperature rising faster in the early stages of warming, but the internal temperature rises more slowly in the middle and late stages. Additionally, the temperature of the track slab rises faster than other structural layers, and there are differences in temperature between the different structural layers. The temperature distribution curves of the top surface of the track slab, the bottom surface of the track slab, and the CA mortar layer are widely spaced. Meanwhile, the temperature distribution curves of the CA mortar layer and the concrete base are less spaced, and the more pronounced the temperature hysteresis is further away from the top surface of the track. It indicates that the CA mortar layer has a hysteretic effect on the vertical temperature transfer.
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From Figures 6 and 7, it is clear that the temperature of the track slab of the constraint specimen is always slightly higher than the temperature of the freedom specimen during the test under the three extreme high-temperature conditions for both boundary conditions. In addition, as the extremely high-temperature increases, the rate of heat transfer increases, and the specimens take less time to reach the same temperature in the constraint specimens compared to the freedom specimens. In summary, the constraint specimens had an amplifying effect on the temperature, accelerating the rate of temperature conduction.
3.2. Vertical Temperature Gradient Distribution
To obtain the most unfavorable structural layers of the track structure subject to temperature under different constraints, a comparative analysis of the interstory and intrastory temperature gradients of the track structure system was carried out, as shown in Figure 8. According to Figure 8(a), the maximum positive temperature gradient between the upper track slab and the lower track slab for the constraint specimens is around 90°C/m at 40°C and 43°C. The maximum temperature at 46°C is 120°C/m, an increase of 33.3% compared to earlier. Moreover, the higher temperature gradients between the track slab and the CA mortar layer of the constraint specimen are 120°C/m, 140°C/m, and 160°C/m under the extreme temperatures of 40°C, 43°C, and 46°C, respectively. It can be found that the temperature gradient between the most unfavorable structural layers tends to increase gradually with the increase of the test environment temperature, which intensifies the possibility of the creation of separation joints between the structural layers.
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According to Figure 8(b), the maximum positive temperature gradients between the track slab and the CA mortar layer of the constraint specimen are 88°C/m, 92.45°C/m, and 100.5°C/m under the extreme temperature of 40°C, 43°C, and 46°C, respectively. The temperature gradients in the freedom specimens all rose somewhat at increasing temperature extremes, but to a lesser extent compared to the constraint specimens.
In summary, the most unfavorable structural layer of the track structure was found between the track slab and the CA mortar layer, and the temperature gradient between the layers tends to increase gradually with the increase of extreme temperatures. It can be assumed that peeling, slippage, and separation are most likely to occur between the track slab and the CA mortar layer. In subsequent studies, scholars should pay attention to the effect of the CA mortar layers on the temperature effect of ballastless tracks.
3.3. The Stress of Track Structure
The stress-time curves for the specimens at each measured point of the span track structure for the two scaled models under different extreme high-temperature conditions are shown in Figure 9. As a whole, the longitudinal stresses in the track slab and concrete base of the scaled-down model increase sharply and then slowly with increasing duration under different extreme high-temperature environments. In addition, the longitudinal stresses in both the track slab and the concrete base increase to varying degrees as the extreme heat environment increases. It should be noted that the sequence of stresses in the track slab is altered from that in the concrete base.
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According to Figures 9(a) and 9(b), in the comparison of five positions of the track slab for the constraint in the specimen, the left position of F-X3Y2Z2 at the midspan is the largest, with the values of 4.05 MPa, 5.97 MPa, and 7.58 MPa under the extreme temperatures of 40°C, 43°C, and 46°C, respectively. The longitudinal stress at the extreme temperature of 46°C is 87% higher than the longitudinal stress at 40°C. Moreover, the middle point at the first end (F-X2Y1Z2) is the smallest, with the values of 1.86 MPa, 2.98 MPa, and 3.98 MPa under the extreme temperatures of 40°C, 43°C, and 46°C, respectively. Unlike the track slab, the largest stress in the concrete base of the constraint specimen is the middle point at the midspan (F-X2Y2Z2) and the smallest stress is the middle point at the second end (F-X2Y3Z2).
According to Figures 9(c) and 9(d), in the comparison of five positions of the track slab for freedom in the specimen, the middle position of F-X2Y1Z2 at the second end is the largest, with the values of 4.33 MPa, 5.98 MPa, and 7.10 MPa under extreme temperatures of 40°C, 43°C, and 46°C, respectively. The longitudinal stress at the extreme temperature of 46°C is 64% higher than the longitudinal stress at 40°C. Moreover, the middle point at the second end (F-X2Y3Z2) is the smallest, with the values of 1.46 MPa, 2.77 MPa, and 3.86 MPa under the extreme temperatures of 40°C, 43°C, and 46°C, respectively. It can be seen that the longitudinal stresses in the base plate and the track plate vary in a similar pattern.
The above analysis indicates that the longitudinal stress increases are proportional to the environmental temperature, and the constraint conditions have a positive effect on the stress in the track slab, which is induced by the rise in environmental temperature.
3.4. Structure Temperature-Stress Correlation Analysis
To investigate the correlation between temperature and longitudinal stress, Pearson’s correlation coefficient [24], Spearman’s rank correlation coefficient, and Kendall’s rank correlation coefficient [25] are used for the correlation analysis, which are listed in Table 5. The three correlations reflect the direction and extent of the trend between the two variables, with values ranging from −1 to 1, with 0 indicating no correlation, positive values indicating positive correlation, and negative values indicating a negative correlation.
According to the above equation, the correlation test results between the temperature of the structural layer of the ballastless track and the longitudinal stress for two scaled models under different extreme high-temperature environments are listed in Table 6. From Table 6, all the three correlation coefficients are in the range of 0.8–1.0, indicating that the correlation between structural layer temperature and longitudinal stress is extremely high. Therefore, to ensure the safety of train operation, the focus should be on the ballastless track operating temperature environment to prevent the external temperature from being too high, causing defects within the ballastless track.
In addition, the relationship between the internal temperature and the longitudinal stress of the track structure is also investigated in this paper. The temperature-stress relationship for the ballastless track slabs and the concrete base were regressed using a quadratic polynomial nonlinear regression, with the test points uniformly distributed on both sides of the mean of the polynomial fit curve and within the 95% confidence interval, as shown in Figure 10. Therefore, there is a significant quadratic regression relationship between the internal temperature and the structural stresses for two scaled models under different extreme high-temperature environments. As can also be seen from Figure 10, the curve fitting results of the constraint track slab (a) are completely different from (b), (c), and (d). It was indicated that the temperature-stress curves of the track slab at the extremely high temperatures of the constrained condition are less different. This may be because the temperature effect on the track slab was magnified by the restraint conditions. Hence, the higher the temperature was, the lower the magnification was, resulting in a smaller difference in the temperature-stress curve of the track slab at each temperature extreme.
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3.5. The Displacement of Track Structure
The longitudinal displacement of the track slab and the concrete base of the track structure gradually increases over time and as the temperature increases, as shown in Figure 11. From Figure 11, the relative displacement between the track slab and concrete base of the scaled specimen is about 0.503 mm and 0.548 mm under the extremely high temperatures of 40°C and 43°C, respectively. There is a significant degradation of the mechanical properties of the CA mortar layer under high temperatures, which reduces the interlayer bonding properties [19]. At the extremely high temperature of 46°C, the rate of increase in the longitudinal displacement of the track slab and the concrete base of the track structure increased significantly compared to the former. Meanwhile, the longitudinal displacement of the concrete base of the track structure is smaller than that of the track slab, which leads to a rapid increase of 0.667 mm in terms of the relative displacement between the track slab and the concrete base of the track structure. This illustrates that the interface forces and restraints between the track slab and concrete base are closely related to the CA mortar layer at high temperatures.
4. Numerical Model of the Reduce-Scale Tests
At present, several scholars have established ballastless track temperature field models that are mainly based on outdoor field tests to study the ballastless track temperature field distributions and temperature effects, while less research has been conducted on the temperature effects of track structures under extreme temperature loads. Additionally, in existing analytical models, the temperature load is normally considered to be a temperature rise or decrease. In reality, when the temperature of the track changes, there is a temperature gradient within it. Besides, the evolution of the damage between the slab joints has not been investigated at a sufficient depth. The refined numerical model based on the reduced scale model is established to analyze the simulation of the temperature gradient loading effects on the damage behavior of the broad-narrow joint.
4.1. Finite-Element Modeling
In this paper, considering the influence of the self-weight of the track structure, the finite element model was established for the indoor scaled model. The material parameters and dimensions of the finite element model are shown in Tables 1 and 4, respectively. This model contains 87,991 solid elements and 139,540 nodes, and in order to effectively consider the functional characteristics and correlations between the various layers of the track structure, the solid element C3D8R is adopted to simulate the components of the track slab, CA mortar layer, concrete base, simple box girder, and broad-narrow joint, as illustrated in Figure 12, and the steel rails were not considered for simplification. The mesh has proved to be convergent.
The two interfaces (i.e., broad-narrow joint-slab and CA mortar layer-slab) were simulated by the cohesive contact to study the behavior of adhesive mechanics. According to the theory of CZM, the main properties of the interface (stiffness, strength, and fracture energy) can be obtained from a previous experimental study [26]. The tie was adopted to simulate the bond force between the concrete base and the CA mortar layer and a simple supported beam. Due to the traditional theory of elasticity-plasticity having limitations in describing the material properties of concrete, the concrete damaged plasticity model for concrete (CDP) was introduced in this calculation [27, 28]. The CDP can be used to calculate the damage behavior of the broad-narrow joint. This paper aims to investigate the damage evolution of the broad-narrow joints and to improve the efficiency of the calculation. The CDP model was only defined at the broad-narrow joints, and the rest of the model was simplified to a linear elastic material. The bottom of a simple box girder and both ends of the whole structure were fixed. In addition, the results for the intermediate broad-narrow joints were selected for analysis, taking into account boundary effects.
4.2. The Model Verification
The predictions of the CRTS II slab track nonlinear finite element model were validated by using the temperature load tests on the indoor scaled model. As shown in Figure 13, at extreme temperatures of 40°C, the vertical temperature distribution results of the constraint specimen by a simulation model were validated by using the experimental results from temperature load tests. According to Figure 13, the measured data are similar and consistent with the values calculated by the finite element model, with a maximum error of 3.33% for the track slab, 1.65% for the CA mortar layer, and 1.56% for the base slab, all within 5% of the calculated values. The results show that numerical predictions agree reasonably well with the experimental measurements. Therefore, the nonlinear finite element model has the potential of simulating the structural performance of CRTS II slab tracks under various temperature conditions. This indicates that the finite element model can be used for subsequent analysis.
4.3. Temperature Gradient Load
In the actual service environment of the ballastless track, the upper surface of the track slab is directly exposed to air, and the lower surface is in contact with the CA mortar layer. Their heat absorption and dissipation are different. As a result, there is necessarily a temperature gradient in the vertical direction of the track structure. Referring to the field test research results of the ballastless track structure temperature field by domestic and foreign scholars and the Code of Design of High-Speed Railway (TB 10621–2014), the maximum positive and negative vertical temperature gradients of the track slab are taken as 90°C/m and −45°C/m, respectively, in this paper, and the specific working conditions are shown in Table 7. It varies linearly along the thickness direction.
4.4. Analysis of Finite Element Simulation Results
4.4.1. Effect of Positive Temperature Gradients
The broad-narrow joint damage parameters were calculated at 30°C/m, 60°C/m, and 90°C/m, respectively. The results are shown in Figure 14. It can be seen that the damage parameters of the broad-narrow joints gradually increase when the temperature gradient increases from 30°C/m to 90°C/m. At a temperature gradient of 30°C/m, the damage has started to occur in broad-narrow joints with a value of 0.2289. Meanwhile, the maximum damage parameters of the broad-narrow joints reached about 0.6 under 90°C/m. According to Figures 14(a)–14(c)), the tension damage is primarily distributed at the junction between the broad joint and narrow joint, and as the positive temperature gradient increases, the area of damage expands along with the vertical position of the broad-narrow joints towards the ends. The broad-narrow joints have a special-shaped structure and are less constrained, resulting in tension damage in the joint interface. In addition, it should be noted that narrow joints are more severely damaged than wide joints.
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According to Figures 14(d)–14(f), the maximum compressive damage of the broad-narrow joints under a temperature gradient of 30°C/m and 30°C/m is 0.143 and 0.37, respectively. In addition, it can be noted that the extent of compression damage to wide joints is less obvious mainly because the narrow joints are smaller in size and are prone to stress concentration, with the area of compression damage extending to the narrow joints.
4.4.2. Effect of Negative Temperature Gradients
The broad-narrow joint damage parameters were calculated at −15°C/m, −30°C/m, and −45°C/m, respectively. The results are shown in Figure 15. From Figure 15, under negative temperature gradient loading, the degree of damage to the broad-narrow joints is small and increases more slowly as the negative temperature gradient increases. The damage is mainly distributed at the ends of the junction between the broad joint and the narrow joint, but there are differences in the location of tensile and tension damage. According to Figures 15(a)–15(c), tensile damage occurs mainly at the junction between the broad joint and narrow joint, which is the same as the location of the tensile damage under positive temperature gradient loading. However, the cause of the damage is different. As the negative temperature gradient increases, the corner of the track slab will warp deformation, creating a vertical force on the broad joints and causing tensile damage to the broad-narrow joint joints.
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Similarly, the compressive damage occurs at the transverse end areas of the wide joints and continues to extend to both sides as the negative temperature gradient increases. The stress concentration at the wide and narrow joints of the track structure and the excessive tensile stresses at the joints will lead to localized cracking of the nearby CA mortar and concrete, affecting the longitudinal continuity of the track structure.
In summary, temperature gradients have a significant impact on the broad-narrow joint damage, with tensile damage being particularly significant. At present, although ballastless track reaches −45°C/m and 90°C/m less frequently in actual service, there has been no widespread deterioration. However, the increasing frequency of extreme weather in recent years may exacerbate the damage to broad-narrow joints.
5. Conclusions
In this study, the temperature loading tests with different extreme high-temperatures were conducted with respect to two constraint conditions on a quarter-scale specimen of the ballastless track-bridge system in the large environmental testing chamber. The influence of different extreme high-temperature environments on the thermal performance (e.g., temperature distribution, stresses, and longitudinal displacements) of the track structure was analyzed. Based on the reduced scale model tests, a three-dimensional finite element model was established to investigate the damage evolution of the broad-narrow joints between the plates. The following conclusions can be drawn from this study:(1)The most unfavorable structural area is the track slab-CA mortar layer interface, which is susceptible to peeling, slippage, and interlayer separation. The constraint conditions accelerate the rate of temperature transfer, creating disturbances to the internal stresses in the track structure and amplifying the internal stresses induced by the environmental temperature rise.(2)The three correlation coefficients between the structural layer temperature and longitudinal stress in the ballastless track under differing constraints ranged from 0.8 to 1.0, with a high correlation. There is a significant quadratic regression relationship between internal temperature and structural stress under different extreme high-temperature environments.(3)At extremely high temperatures, the longitudinal displacement between the track plate and the base plate increases significantly, with the longitudinal displacement of the base plate being less than the longitudinal displacement of the track plate and the relative displacement increasing to 0.667 mm. It is noticed that the mortar layer plays an important role in the interface forces and restraint between the track slab and the concrete base at high temperatures.(4)With a positive temperature gradient loading, compression damage to the narrow joints is more severe. Tensile damage is located at the junction of the wide and narrow joints and extends along the vertical direction of the broad-narrow joints towards both ends as the positive temperature gradient increases. In addition, under negative temperature gradient loading, the compression damage occurs at the transverse ends of the wide joints, and with increasing negative temperature gradients, the area of compression damage continues to extend to the transverse sides.
Data Availability
All data, models, and code generated or used during the study are included in the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant no. 52178273), the Natural Science Foundation of Chongqing (Grant no. cstc2021jcyj-msxmX1159), the Chongqing Talent Plan Project (Grant no. CQYC20210302391), the Chongqing Project of Joint Training Base Construction for Postgraduates (Grant no. JDLHPYJD2020004), and the Chongqing Postgraduate Research and Innovation Project (Grant no. CYB22230).