A stress dilatancy relationship for coarse-grained soils incorporating particle breakage

The energy consumption of particle breakage is added to the Cambridge energy balance equation so that the energy balance equation for coarse-grained soil is obtained. To reasonably measure the energy consumption of particle breakage, a function of friction coefficient relating to the axial strain is proposed to replace the friction coefficient as a constant in the energy balance equation based on the evolution rule of particle breakage. Then, according to the energy balance equation of coarse-grained soil, the energy consumption of particle breakage is calculated, and the particle breakage energy increases with axial strain increasing, which satisfies the thermodynamic law. Based on this energy balance equation, a simple stress dilatancy relationship is developed. In this stress dilatancy relationship, the relationship between dEb/pdεs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{d}}E_{{\text{b}}} /p{\text{d}}\varepsilon_{{\text{s}}}$$\end{document} and M/Mf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M/\sqrt {M_{{\text{f}}} }$$\end{document} can be described by a simple function with acceptable accuracy. This stress dilatancy relationship is validated with the satisfactory capability to predict the dilatancy behavior of coarse-grained soils, which can be the effective choice to build the constitutive model.