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.

This study, proposes the use of a novel rubber-sand concrete (RSC) material, which comprises rubber particles, sand, and cement, as an aseismic material in practical engineering construction. The uniaxial compressive strength (UCS) of damping materials is an important factor that directly affects the seismic activity in underground structures. To predict the UCS of RSC, artificial intelligence model back propagation neural network (BPNN), which is optimized through four swarm intelligence optimization (SIO) algorithms: particle swarm optimization algorithm (PSO), fruit fly optimization algorithm (FOA), lion swarm optimization algorithm (LSO), and sparrow search algorithm (SSA), is used. The dataset for the prediction models was obtained from uniaxial compression tests in the RSC laboratory. The performances of the four hybrid intelligence models were evaluated using six performance indicators: the root mean square error (RMSE), correlation coefficient (R), determination coefficient (R²), mean absolute error (MAE), mean square error (MSE), and sum of square error (SSE).The prediction capability of these models was graded based on these indicators using a ranking system. The results show that the prediction ability of the LSO-BPNN hybrid model is better than that of the three other hybrid models, with RMSE of (1.0635, 1.2352), R of (0.9887, 0.9713), R² of (0.9776, 0.9165), MAE of (0.7257, 0.8243), MSE of (1.1352, 1.5256), SSE of (64.7074, 36.6151), and ranking score of (24, 24) in the training and testing phases, respectively. Therefore, the LSO-BPNN hybrid model is an efficient and accurate method for predicting the UCS of RSCs. Sensitivity analysis showed that rubber and sand were the most important elements that affected UCS prediction, followed by cement, with the lowest relative importance being RPZ. This study provides guidance for the extension and application of RSC materials to underground seismic engineering.

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.