Mohr space and its application to the activation prediction of pre-existing weakness

Abstract

The activation coefficient equations in the “activation criterion of pre-existing weakness” are relatively complex and not easy to apply to specific applications. The relative activity of pre-existing weaknesses is often critical in geological analysis. The Mohr circle can be used only in two-dimensional stress analysis. By applying the “activation criterion of pre-existing weakness” and combining it with numerical analysis, we establish the correspondence between the pole (σn, τn) of a pre-existing weakness plane and its orientation in “Mohr space”. As a result, the normal stress (σn) and shear stress (τn) of a pre-existing weakness plane can be readily expressed in Mohr space. Furthermore, we introduce the method and procedures for predicting the activation and relative activation of pre-existing weaknesses in Mohr space. Finally, we apply the Mohr space method and compare the predictions to sandbox modeling results and 3D seismic data. The results show that Mohr space can be used in stress analysis to estimate the activation of a pre-existing weakness in any triaxial stress state.