Rock Plasticity from Microtomography and Upscaling

We present a workflow for upscaling of rock properties using microtomography and percolation theory. In this paper we focus on a pilot study for assessing the plastic strength of rocks from a digital rock image. Firstly, we determine the size of mechanical representative volume element (RVE) by using upper/lower bound dissipation computations in accordance with thermodynamics. Then the mechanical RVE is used to simulate the rock failure at micro-scale using FEM. Two cases of different pressures of linear Drucker-Prager plasticity of rocks are computed to compute the macroscopic cohesion and the angle of internal friction of the rock. We also detect the critical exponents of yield stress for scaling laws from a series of derivative models that are created by a shrinking/expanding algorithm. We use microtomographic data sets of two carbonate samples and compare the results with previous results. The results show that natural rock samples with irregular structures may have the critical exponent of yield stress different from random models. This unexpected result could have significant ramifications for assessing the stability of solid materials with internal structure. Therefore our pilot study needs to be extended to investigate the scaling laws of strength of many more natural rocks with irregular microstructure.