Dilatancy equation for coarse-grained soils incorporating particle breakage energy

The internal relationship between particle breakage and stress deformation of coarse-grained soils can be reflected by the particle breakage energy. The change law of particle breakage of coarse-grained soils during triaxial tests is studied. According to this law, the fraction coefficient M in the energy balance equation proposed by Ueng and Chen is modified to solve the problem that the particle breakage energy calculated by the energy balance equation violates the thermodynamic law. On this basis, a simple dilatancy equation for coarse-grained soils is developed. The main conclusions are as follows: (1) The proposed mathematical relationship among particle breakage index, confining pressure and axial strain can describe the change law of particle breakage well. (2) The reasonable calculation of particle breakage energy is realized by modifying the fraction coefficient in the energy balance equation, which satisfies the thermodynamic law. (3) The test results show that the ratio of the dilatancy energy to the total input work is very small, so it can be ignored in the energy balance equation. (4) There is an obvious linear relationship between \textdE_\textb / \textd\varepsilon _\texts and M, and a dilatancy equation can be developed by substituting this linear relationship into the energy balance equation, and this dilatancy equation can well simulate the dilatancy behaviors of coarse-grained soils, and its mathematical form is simple enough, so that its plastic potential function can be derived, which provides conditions for the subsequent studies on the fraction-order constitutive model considering particle breakage.