## 3 Results and Analysis
### Effect of Freeze-thaw Cycles on Mechanical Properties of Soil-Rock Mixtures
Based on the simulation results, it can be observed that the numerical simulation results are in close agreement with the laboratory test results. The errors between the fracture modulus and unconfined compressive strength are both less than 0.0000666996 GPa and 0.00621 MPa, respectively. Figure 14: Fitting and calculation results of mechanical characteristic parameters of soil–rock mixture with the number of freeze–thaw cycles. (**a**) Relationships between freeze–thaw cycles and peak strain as well as secant modulus. (**b**) Numerical simulation results in uniaxial compression under different freeze–thaw cycles. Figure 15 shows the crack propagation law of soil-rock mixtures under different freeze-thaw cycles. Combined with the crack increase curve in Figure 13a, it can be observed that with an increase in the number of freeze-thaw cycles, there is a significant increase in the strain occurring during the initiation of cracks within the soil-rock mixture. Furthermore, by analyzing the crack heat maps and crack propagation time-step diagrams of the soil-rock mixture under different freeze-thaw cycles, it can be observed that when the specimen is damaged by pressure, the failure started from the corner, then gradually extended to the middle and lower parts of the specimen, ultimately leading to final failure. In addition, when the crack extended to the middle, it also followed the pattern of spreading from the middle section toward both ends. Figure 16 shows the crack classification results of different soil-rock mixtures. According to the diagram, it can be observed that under different freeze-thaw cycles, the cracks generated in the compressive failure of the soil-rock mixture were mainly tensile cracks, followed by tension-shear cracks, and the least were compression-shear cracks. As the number of freeze-thaw cycles increased from 0 to 15, the occurrence of compressive shear cracks showed a decreasing trend, with the proportion of cracks decreasing from 1.37% to 0.76%. Additionally, tension-shear cracks and tensile cracks show an increasing and decreasing trend, respectively, from 0 to 10 freeze-thaw cycles. However, the pattern was not clearly observed from 10 to 15 cycles. The mesoscopic pore structure of porous materials has a significant influence on the macroscopic mechanical properties [27, 28]. To investigate the inherent relationship between the microporosity of soil-rock mixtures and their uniaxial compressive strength, the characteristic angular similarity and uniaxial strength were fitted and calculated. The fitting results are shown in Figure 17. It can be seen from the figure that the angular similarity of the distribution characteristics and uniaxial compressive strength under different freeze-thaw cycles have a good linear relationship, and the fitting correlation coefficient is 0.9928. The uniaxial compressive strength increased exponentially with the increase in similarity. As the freeze-thaw cycle increased from 0 to 15, the similarity coefficient of the electrochemical test for the soil-rock mixture gradually increased, which indicated that the microscopic porosity increased gradually. The repeated freezing and thawing processes generated frost heaving forces, which caused the expansion of the size of micropores or microdefects between soil and soil, soil and rock, and rock withen the soil-rock mixture. Exactly, the interconnection of pores and defects with different radii weakened the bonding strength within the soil-rock mixture, leading to a decrease in its uniaxial compressive strength.