Fault detection methods for 2D and 3D geomechanical numerical models

We develop automated methods for fault detection utilizing static stress and deformation fields at the onset of failure derived from numerical analysis. We calculate combinations and normalization of the distance from the Mohr circle to the Coulomb envelope, and of the second deviatoric strain invariant. A variation of the Cauchy distribution of these fields allows us to focus on the low values indicating rupture, with the help of the scale parameter delta. A threshold is then applied to decide at each spatial node of the mesh whether the material has reached failure or not. We then determine fault lines and planes from these isolated failure zones using image processing techniques, such as the Hough and the Radon transforms, or through a combined approach involving automated sorting of the nodes reaching failure through the k-means clustering technique followed by polynomial fitting to retrieve analytic expressions of the fault curves (in 2D) or fault surfaces (in 3D). The methods are efficient except when the stress field results in diffuse rupture zones that do not localize onto fault surfaces despite tuning delta. We also highlight the advantages of using the combined clustering/poly-fitting approach for 3D models compared to the image processing techniques. These automated fault detection methods should be useful in the interpretation of diverse failure mechanisms obtained through parametric sensitivity analyses requiring hundreds of simulations. The stress and strain fields used were derived from a numerical implementation of limit analysis, but classical finite-difference or finite-element techniques could have been used.