Abstract
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.
Highlights
A soil–rock mixture (SRM) is a heterogeneous geomaterial that is composed of rock blocks with different particle sizes and a soil matrix
The fractal theory was invoked to explore the fractal characteristics of the particle of SRM; the particle gradation of SRM
Indistribution this study, the fractal theory wascurves invoked to at explore fractal predicted by using the fractal dimension and relative threshold; the numerical large-scale the particle distribution of SRM; the particle gradation curves of SRM at diffe direct shear tests were simulated by using PFC2D, and the variations in shear strength were predicted by different using the fractal dimension and relative threshold; the parameters of SRM with particle sizes were studied
Summary
As fractal theory is widely used [15,16,17,18,19,20,21,22,23], many researchers [24,25,26,27,28,29,30,31] have found that geomaterials exhibit fractal characteristics, and the rock joints, particle distribution, and pores at different scales have self-similarity, which is consistent with the evolution of geomaterials under natural conditions. Xiao et al [37] investigated the crushing characteristics of single particles and assemblies of rockfill materials with different nominal diameters and discussed the effects of the particle size on the Weibull modulus, compressibility index, and ultimate fractal dimension He et al [38] obtained the pore size distribution of the calcareous sand, quartz sand, and glass beads by using nuclear magnetic resonance tests, and fractal theory was introduced to describe the fractal properties of the pore size distribution. The fractal theory was invoked to analyze the fractal characteristics of the particle distribution of SRM, numerical simulations of direct shear tests of SRM samples at different scales were conducted by using the discrete element method (DEM), and the variations in shear strength parameters of SRM at different scales were studied
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