Approximate plastic yield criteria of geomaterials with pores and grains embedded in a porous matrix

Abstract

Mineral grains and porosity are two common properties of geomaterials. This study focuses on establishing a macroscopic yield criterion for geomaterials having pores and mineral grains at the mesoscale which is embedded in a porous matrix. At the microscale, the solid phase is pressure-sensitive and obeys to the Drucker–Prager criterion which considers the asymmetric property between tension and compression. Based on a two-step homogenization procedure and the modified secant method, a macroscopic yield criterion is firstly derived which takes into account the effects of microstructure on the macroscopic mechanical behaviors of the studied material, such as the meso-porosity and mineral grains content at the mesoscale, the micro-porosity and the pressure-sensitive of the solid phase at the microscale. However, it overestimates the material strength in compressive loading by comparing with the Fast Fourier Transform (FFT) based numerical results. Then, this criterion is improved by considering the exact solution in pure hydrostatic loading of a porous medium with a Drucker–Prager matrix. By comparing to the numerical results with different microstructures and to experimental data, the new macroscopic yield criterion is estimated and validated. The main features of the studied geomaterial are well captured by this criterion.