On the importance of 3D stress state in 2D earthquake rupture simulations with off-fault deformation

During the last decades, many numerical models have been developed to explore the conditions for seismic and aseismic slip. Those models explore the behavior of frictional faults, embedded in either elastic or inelastic mediums, and submitted to a far field loading (seismic cycle models), or initial stresses (single dynamic rupture models). Those initial conditions impact both fault and off-fault dynamics. Because of the sparsity of direct measurements of fault stresses, modelers have to make assumptions about the initial conditions. To these days, Anderson theory is the only framework that can be used to link fault generation and reactivation to the three-dimensional stress field.  In this study, we focus on the initial stresses in 2D plane strain models developed to compute off-fault deformation. It has been demonstrated that initial conditions, in particular the angle between fault and the greatest compressive stress, is of crucial importance for the localization and intensity of off-fault inelastic deformation. However, because those models are performed on a 2D plane, the importance of the out-of-plane stress have never been investigated. We show that it can lead to set up a stress field that is not in agreement with Anderson theory (i.e., modelling a strike-slip fault in a three-dimensional stress field appropriate for reverse faulting). We investigate the influence of initial stresses by comparing equivalent models with “correct” and “incorrect” initial stress fields, keeping constant rupture-related parameters (stress drop, seismic ratio), angle between fault and greatest principal stress, and depth. We first use purely elastic models to study the influence of initial stresses on the assessment of two plastic criteria (Drucker-Prager and Coulomb stress change). We show that setting up the incorrect initial stress field can lead to underestimating the different yield criteria. The error is of the order of magnitude of the dynamic stress drop. Moreover, setting up the incorrect pre-stresses leads to errors in the estimation of potential off-fault failure modes. Then, we explore the influence of pre-stresses conditions on off-fault inelastic deformation. Using two different modelling strategies (a plastic deformation model and a micromechanics model computing dynamic damage), we show that setting up the incorrect stress field can lead to underestimate the size of the damage zone by a factor of 3 to 6 for the studied cases.  Moreover, because of the interactions between fault slip and off-fault deformation, we show that initial stress field influences the rupture propagation. Setting up the correct stress field can significantly slow the rupture, because of the more important quantity of damage induced.