A soil–rock mixture (SRM) is a type of heterogeneous geomaterial, and the particle distribution of SRM can be described by fractal theory. At present, it is difficult to quantify the fractal dimension of a particle size distribution and understand the scale effect in SRMs. In this study, the fractal theory and discrete element method (DEM) were introduced to solve this problem. First, the particle gradation of SRM was dealt with by using fractal theory. The fractal structure of particle distribution was studied, and a method of calculation of the fractal dimension is presented in this paper. Second, based on the fractal dimension and relative threshold, the particle gradations of SRMs at different scales were predicted. Third, numerical direct shear tests of SRM at different scales were simulated by using the DEM. The scale effects of shear displacement, shear zone, and shear strength parameters were revealed. Last, taking the maximum particle size of 60 mm as the standard value, the piece-wise functional relationship between shear strength parameters and particle size was established. The results are as follows: for SRM in a representative engineering area, by plotting the relationship between particle cumulative mass percentage and particle size, we can judge whether the SRM has a fractal structure; in Southwest China, the frequency of the fractal dimension of the SRM is in the normal distribution, and the median fractal dimension is 2.62; the particle gradations of SRMs at different scales calculated by fractal dimension and relative threshold can expand the study scope of particle size analysis; when the particle size is less than 70 mm, the strength parameters show a parabolic trend with the particle size increases, and if not, a nearly linear trend is found. The proposed method can describe the fractal characteristics of SRM in a representative engineering area and provides a quantitative estimation of shear strength parameters of SRM at different scales.

As the typical multi-phase geotechnical material, the particle size distribution of the natural soil–rock mixture (S–RM) has a significant impact on the structural and mechanical properties. The coarse grain content used in the laboratory and simulation tests falls short of accurately describing the particle size distribution feature of the entire material. The main subject of this article is the influence of the fractal dimension on mechanical behaviors based on the fractal theory. The double fractal characteristics were principally discussed along with the typical particle size distribution characteristics of the S–RM in the Three Gorges Reservoir and southwest China. The influence of the various fractal dimensions on the mechanical behaviors of S–RM was then investigated using three groups of large–scale triaxial tests, and the responses of the linear and nonlinear strength indexes were analyzed. The results show that the stress–strain curves of S–RM in the hyperbolic shape are visible under various confining pressure, and the nonlinear strength characteristics can be observed. The coarse grain content exhibits a negative correlation to the average fraction dimension. The difference between the coarse and fine grain fraction dimensions becomes considerably more obvious as the coarse grain content increases, which also increases the error when using the average fractal dimension. The voids between the coarse grains cannot be filled with the fine grains as the grain coarseness grows, resulting in a loose structure and a contact frictional effect, which lowers cohesion and raises the peak friction angle.

Soil–rock mixture is a common geo-material found in natural deposit slopes and various constructions, such as tunnels, hydropower stations, and subgrades. The complex mechanical characteristics of soil–rock mixture arise from its multi-phase compositions and cooperative interactions. This paper investigated the mechanical properties of soil–rock mixture, focusing on the influence of rock content, and soil–rock interface strength was discussed. Specimens with varying rock contents were subjected to uniaxial compression tests. The results indicated that rock content, as a key structural parameter, significantly controls the crack propagation trends. As rock content increases, the initial structure of the soil matrix is damaged, leading to the formation of a weak-strength soil–rock interface. The failure mode transitions from longitudinal cracking to multiple shear fractures. To analyze the strength of the soil–rock interface from a mesoscopic perspective, simulations of soil–rock mixture specimens with irregular rock blocks were conducted using the particle discrete element method (PDEM). At the meso-scale, the specimen with 30% rock content exhibited a complex particle displacement distribution, with differences in the direction and magnitude of displacement between soil and rock particles being critical to the failure modes of the specimen. As the soil–rock interface strength increased from 0.1 to 0.9, the distribution of force chains within the specimen shifted from a centralized to a more uniform distribution, and the thickness of force chains became increasingly uniform. The strength responses of the soil–rock mixture under uniaxial compression condition were discussed, revealing that the uniaxial compression strength (UCS) of soil–rock mixture decreases exponentially with increasing rock content. An estimation formula was developed to characterize the UCS of soil–rock mixture in relation to rock content and interface strength. The findings from both the experiments and simulations can provide valuable insights for evaluating the stability of deposit slopes and other constructions involving soil–rock mixture.