## 3 Results and Analysis
### Effect of Freeze-thaw Cycles on Mechanical Properties of Soil-Rock Mixtures  
Figure 13a shows the stress-strain curve of the soil-rock mixture under different freeze-thaw cycles. From the graph, it can be observed that the stress-strain curve also exhibits stages of pore compaction (OA stage), elastic deformation (AB stage), unstable development (BC stage), and the post-failure stage (after point C). Meanwhile, as the number of freeze-thaw cycles increased from 0 to 15, there was a noticeable decrease in peak intensity and peak secant modulus. However, the peak strain and pore compaction stages showed an increasing trend. Figure 13b shows the fitting results of the relationship between the number of freeze-thaw cycles and various mechanical parameters of the soil-rock mixture. From the figure, it can be observed that as the number of freeze-thaw cycles increased from 0 to 15, the uniaxial compressive strength decreased from 0.37095 MPa to 0.19431 MPa, representing a decrease of 47.62%. Furthermore, there is a strong exponential relationship between the compressive strength and freeze-thaw cycles, with a high fitting correlation coefficient of up to 0.99752. With the gradual increase in the number of freeze-thaw cycles, the uniaxial compressive strength showed an exponential decrease. In the fitting calculations of the relationship between the number of freeze-thaw cycles and peak strain and peak secant modulus (Figure 14a), as freeze-thaw cycles gradually increased, the peak strain increased  
Figure 12: Fitting results in similarity of soil–rock mixtures to the number of freeze–thaw cycles. Figure 13: Stress–strain curve and crack number curve of soil–rock mixture under different freeze–thaw cycles. (**a**) Stress–strain curves under different freeze–thaw cycles. (**b**) The fitting relationship between freeze–thaw cycles and uniaxial compressive strength. from 2.115% to 4.608%, and the modulus decreased from 0.16492 GPa to 0.0398 GPa. In addition, both the peak strain and the peak secant modulus exhibit a strong exponential relationship with freeze-thaw cycles, with fitting correlation coefficients of 0.99179 and 0.99873, respectively. When the number of freeze-thaw cycles gradually increased, the peak strain and the peak secant modulus showed exponential increasing and exponential decreasing trends, respectively. In the discrete element simulation of uniaxial compression tests on soil-rock mixtures, the stress-strain curves exhibit similar deformation stages as those of rock stress-strain curves. Therefore, the parallel cementation model, which is the most widely used in the numerical calculation of discrete elements in geotechnical engineering, is selected to carry out the numerical simulation of the uniaxial compression tests. In the numerical simulation of uniaxial compression tests on soil-rock mixtures with different freeze-thaw cycles, microstructural parameters such as density, stiffness ratio (Kratio), porosity, friction coefficient (Fric), and internal friction angle (pb_fa) remained unchanged. The paper only focused on varying the effective modulus (emod)/bond effective modulus (pb_emod) and cohesive force (pb_coh)/tensile strength (pb_ten), which are factors influencing the modulus and compressive strength. In the selection of a simulated modulus for the specimens, the elastic deformation of soil-rock mixtures under different freeze-thaw cycles was relatively short and difficult to calculate accurately. Therefore, the peak secant modulus was chosen for numerical simulation as an alternative. Table 2 shows the numerical calculation of the mesoparameters of soil-rock mixtures under different freeze-thaw cycles. It can be seen from the table that with the increase in the number of freeze-thaw cycles, the emod/pb-emod and pb_coh/pb_ten both show a decreasing law. Table 3 and Figure 14b are numerical simulation results of uniaxial compression tests of soil-rock mixtures at different freeze-thaw cycles.