Particle shape and local breakage significantly affect the deformation characteristics of crushable granular materials. However, in the existing constitutive model research, there is less introduction of particle shape on particle breakage. A quantitative parameter for the three-dimensional particle shape (Average spherical modulus GM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{G_{M}}$$\end{document}) is proposed in this study. Combined with GM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{G_{M}}$$\end{document}, the triaxial compression test of granular materials with different particle shapes was carried out, and the particle size distribution before and after the test was determined. The results indicate that the local damage mechanism governs the macroscopic deformation behavior of granular materials, as influenced by the particle gradation of the samples before and after the triaxial compression test. Based on these findings, a binary medium model with a friction element weakening factor is proposed. This model incorporates the effects of particle shape and breakage behavior, significantly enhancing its calculation accuracy. Experimental results demonstrate that the model effectively predicts the deformation of crushable granular materials, accounting for particle shape.

To investigate the mechanical properties of frozen peat soil derived from Dianchi Lake's lacustrine deposits, a low-temperature triaxial shear test was conducted under various influencing factors, utilizing an improved TSZ-2 fully automatic strain control instrument. This study aimed to examine the mechanical behavior of frozen peat soil at different temperatures, confining pressures and moisture levels. Additionally, the binary medium model theory was introduced to analyze the deviatoric stress-strain relationship in frozen soil. The test results indicate that as strain increases, the deviatoric stress-strain curve divides into three stages: linear-elastic, elastic-plastic and stable stages. The volume deformation primarily involves bulk expansion, and the deformation characteristics of frozen peat soil can be explained using a binary medium model. The peak strength of frozen peat soil is positively correlated with confining pressure and moisture content, but negatively correlated with temperature. In the experimental setup, the impact of confining pressure on strength initially rises and then declines, while moisture content exhibits higher sensitivity to strength. Cohesion increases as temperature decreases, and the internal friction angle fluctuates between 20.56 degrees and 24.89 degrees. Based on the simplified binary medium model, the equations suitable for frozen peat soil are constructed and the results are verified with good applicability.

In order to eliminate the undesirable characteristics of carbonaceous mudstone roadbed fillers, cement and fly ash are used to modify the pre-disintegrated carbonaceous mudstone, and the stress-strain relationship of pre-disintegrated carbonaceous mudstone before and after modification are analyzed by a series of conventional unconsolidated undrained triaxial compression tests at different confining pressures and different ages. Based on the microscopic modification mechanism of carbonaceous mudstone and the concept of binary medium model, the products from hydration reaction of pre-disintegrated carbonaceous mudstone, cement, and fly ash are regarded as bonded elements, and the pre-disintegrated carbonaceous mudstones without hydration reaction are regarded as frictional elements, and the binary medium model of modified pre-disintegrated carbonaceous mudstone is established. The results show that the stress-strain curve of pre-disintegrated carbonaceous mudstone is strain-hardening type, and the stress-strain of pre-disintegrated carbonaceous mudstone modified by fly ash and cement is strain-softening type, and the mechanical properties of modified pre-disintegrated carbonaceous mudstone are significantly improved. The deformation and damage mechanism of modified carbonaceous mudstone is investigated by applying the concept of binary medium model from a mesoscopic perspective, and the stress-bearing mechanism of bonded elements and frictional elements in external loading and stressing processes are analyzed. Finally, the measured data reveals that the binary medium model can simulate both the stress-strain softening characteristics of modified pre-disintegrated carbonaceous mudstone and the stress-strain hardening characteristics of organic material-modified expansive soils reasonably well.