Expanded pore-emanated cracking model for brittle failure of sedimentary rocks under triaxial compression

Abstract

Brittle fracture and its relationship to deformation and strength have been a fundamental area of research in rock mechanics. This paper presents an expanded pore-emanated cracking model to better understand the fracture behaviors and predict the compressive strength of sedimentary rocks. This proposed model is developed to account for a triaxial compression condition using the triaxial compression test results on sandstone, limestone and siltstone samples from Wyoming, USA and experimental data on sedimentary rocks collected from published literature. The normalized critical crack length is determined from the proposed model through which the peak compressive strength is estimated when the stress intensity at the crack tip reaches a critical value called the fracture toughness. Results indicate that the rock porosity and pore radius have an inverse relationship with the compressive strength. Adopting the porosity-permeability relationship, the pore radius is calculated in terms of porosity and grain size. Next, the effect of grain size is implicitly included in the model and negatively correlated with the compressive strength. Moreover, a new approach is proposed for the estimation of fracture toughness based on the pore radius and confining pressure. The predicted compressive strengths from the proposed model show a good agreement with the measured strengths with a mean bias (i.e. average ratio of the measured to predicted strengths) of 1.014. The influence of ϕ and KIC on σ1 was thoroughly studied using parametric study. The study concludes that the effect of ϕ is more prominent than KIC on σ1. At a constant porosity of 0.1, the stress ratio decreases from 0.0082 to 0.0078 when KIC increases from 0.1 to 0.2, indicating a 5% decrease in stress ratio. Whereas, at a constant KIC of 0.1, the stress ratio increases from 0.0082 to 0.014 when the porosity increases from 0.1 to 0.2, indicating 71% increases in stress ratio and therefore compressive strength.