Predicting the yield envelope of sandstones from mechanical and microstructural properties

The aim of this study is to investigate the possibility of predicting the yield curves of sandstones considering only a few key mechanical parameters, and more importantly microstructural properties. Porous rocks are modeled as a set of 2D circular grains subjected to radial and axial stresses that reflect the external forces applied on the material. The contact between individual grains define local planes. The sample is assumed to yield at the inception of nonlinear response on one of these planes, when local stresses reach either shear, tensile, or compressive limit values. A Mohr–Coulomb criterion is considered, with a tensile cutoff and a limitation on the maximum allowable shear stress. The parameters of the developed yield equations are then divided into two groups. The first category relates to the microstructure of the material: porosity, grain radius, intergranular contacts radius, and intensification factor. The second category contains a set of four mechanical properties: the cohesion, the friction angle, the maximum shear, and the compressive limit. While the first set differs from one sandstone to another, the second one is assumed to be the same for all sandstones showing similar mineral compositions. The experimental data for five sandstones, Berea, Boise, Darley Dale, Diemelstadt, and Rothbach, are gathered from the literature. The mechanical parameters are calculated based on Rothbach sandstone experimental data. Satisfactory predictions of the yield limits for the remaining sandstones are obtained from their microstructural characteristics.