Three-dimensional finite-difference analysis of deformation and failure of weak porous sandstones subjected to uniaxial compression

The processes of deformation and fracture of porous sandstones are studied by a 3D finite-difference analysis coupled with a continuous damage mechanics approach. The statistics of more than 100 samples is analyzed. The structure of the pore space is considered explicitly with an assumption of spherical pores distributed in the computational domain. The sample represents a dual-phase material while other structural features are disregarded. In contrast to numerous works, the piecewise linear function based on the Drucker-Prager criterion is used as the yield/damage envelope. The modification is related to different slopes for positive and negative semispaces of a stress space similar to the two-dimensional Haigh-Westergaard space. This allows for a more flexible validation of the model parameters against the experimental data. The method applied is based on an explicit dynamic formulation. Coupled with MPI algorithm, it allows using more than 20 million mesh elements and yields a sufficiently more smooth description of phase boundaries. The scalar damage parameter, which controls the features of damage accumulation and degradation of strength, is also modified. Special attention is paid to the stages of deformation of the samples, which are matched with the points of the complete stress-strain curve. Based on the results of numerical modelling, the threshold stresses of crack initiation sigma(ci), damage sigma(cd), and peak sigma(p) are evaluated for samples with different porosities. The resulting values of the threshold stresses at different sample porosities and their failure patterns are in a satisfactory agreement with the experimental data and complement them.