## 4 Conclusions  
This research paper conducted laboratory freeze-thaw cycling, uniaxial compression tests, and electrochemical impedance spectroscopy (EIS) on soil-rock mixtures. Additionally, it utilized discrete element method (DEM) simulation software (PFC2D) to simulate and calculate the uniaxial compression tests under different freeze-thaw cycles. The similarity of the distribution characteristic angle and pure resistance of the soil-rock mixture under different freeze-thaw cycles were introduced to indirectly characterize the microscopic pores, and the influence on the distribution characteristic points, distribution characteristic angles, and similarity was analyzed. In addition, the effects of freeze-thaw cycling on macroscopic physical parameters such as uniaxial compressive strength, crack initiation, and crack propagation were discussed. The intrinsic relationship between similarity and uniaxial compressive strength was established. The main conclusions of the paper are as follows:  
1. Under different freeze-thaw cycle conditions, the similarity of distribution characteristic angles in soil-rock mixtures can indirectly represent the microporosity. The similarity and the tangent values of the distribution characteristic angles in the soil-rock mixture exhibit a good exponential relationship with the number of freeze-thaw cycles. As the freeze-thaw cycles increased, the number of microscopic pores within the soil-rock mixture gradually increased, and the tangent values of the distribution characteristics decreased while the similarity increased.
2. The uniaxial compressive strength, peak secant modulus, and peak strain of the soil-rock mixture had good exponential relationships with the number of freeze-thaw cycles. The uniaxial compressive strength and peak secant modulus both exhibited exponential decay with an increasing number of freeze-thaw cycles. However, the peak strain showed an exponential increase trend. In addition, the stage of pore compaction also shows an increasing trend with an increasing cycle.
3. With an increasing number of freeze-thaw cycles, the effective modulus (emod)/bonded effective modulus (pb_emod) and the cohesion (pb_coh)/tensile strength (pb_ten) both exhibited decreasing trends. The strain of the soil and rock mixture when cracks begin to germinate also increased significantly. Under different freeze-thaw cycles, the failure modes and crack propagation patterns of the soil-rock mixture were generally similar. The crack propagation extended from the edges and corners toward the middle-lower part, with partial expansion toward both ends in the central region. The  
Figure 17: Fitting relationship between similarity of soil–rock mixture and macroscopic mechanical properties.  
failure crack type was mainly tensile failure, followed by tensile-shear failure, and the compression-shear failure occurred the least.
* Under different freeze-thaw cycles, there was a good linear relationship between the similarity of the soil-rock mixture and uniaxial compressive strength. The uniaxial compressive strength exhibited a linear decrease with an increasing similarity.  
Conceptualization, H.D.; Methodology, B.Z. and G.T.; Software, B.Z.; Formal analysis, H.D.; Investigation, B.Z. and G.T.; Data curation, Y.X.; Writing--original draft, B.Z. and G.T.; Writing--review and editing, H.D. and Y.X.; Supervision Y.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the school-enterprise joint project of Central South University, China (Grant No.2021 XQLH153), China National Key R&D Program during the 14 th Five-year Plan Period, China (Grant No.2021 YFC2900400), National Natural Science Foundation of China Youth Science Foundation, China (Grant No.52004327).  
Not applicable.  
All the data analyzed in this study are included in this published article.  
The author would like to thank the anonymous reviewers and sponsors.  
The authors declare no conflict of interest.