Slip on wavy frictional faults: is the 3rd dimension a sticking point?

Abstract

The formulation for the 3D triangular displacement discontinuity boundary element method with frictional constraints is described in detail. Its accuracy in comparison to analytical solutions is then quantified. We show how this can be used to approximate stress intensity factors at the crack tips. Using this method, we go on to quantify how slip is reduced on fault surfaces with topography, where the asperities are approximated as a sinusoidal waveform, i.e. corrugations. We use stress boundary conditions (compressive) orientated such that frictional contacts shear. We show that slip reductions relative to planar faults for 2D line and 3D penny-shaped crack models are comparable within 10% when slip is perpendicular to the corrugations. Using the 3D model, we then show how slip is reduced more when corrugation wavelengths are doubled compared to the reduction due to corrugation misalignment with the slip direction. When slip is parallel with the corrugation alignment we show that reducing the out-of-plane stress, from the normal traction acting on the fault when planar to that resolved on a perpendicular plane, has the same effect as halving the length of the corrugation waveform in terms of slip reduction for a given amplitude.

Stress Inversion in a Gelatin Box: Testing Eruptive Vent Location Forecasts With Analog Models

“…To calculate the elastic stresses within the gelatin, we use the two‐dimensional (2D) BE code “ Cut&Displace ” (Crouch et al., 1983; Davis et al., 2017, 2019). We approximate the experiment's geometry as plane strain, as we observed no strain in the analog model's y ‐direction (Figure 1a).…”

Extreme curvature of shallow magma pathways controlled by competing stresses

“…Here we use a theoretically equivalent, but more flexible, approach based on the maximum stress intensity, K. In our analytical approach, we re-duce the sill geometry to that of a penny-shaped crack subject to stress gradients (Supplementary Information), with an opening that is compatible with the surface displacements observed along the short-axis of the sill (see Methods). At selected points along the sill's path, we calculate K, around the tip-line 9 , and assume the greatest tip-line advance occurs in the direction where K is largest (Paris fatigue law 10 ). In our numerical simulations, we discretise the sill into triangular elements 10,11 and update the tip-line at each step using the local value of K as compared to the critical rock strength, K c .…”

“…We include stresses due to gravitational loading and traction-free boundary conditions on the surface 9,17 . Using orientations of the crack in the 3D space obtained by inverting surface deformation (see Methods), our model explains the turning of the sill for snapshots along its path ( Fig.…”

“…Extended Data Fig. 5 is computed using a numerical scheme to evaluate how K I (equation (1)) decreases as the crack approaches the half-space surface 9 .…”

Extreme Curvature of Shallow Magma Pathways Controlled by Competing Stresses: Insights From the 2018 Sierra Negra Eruption

“…In our analytical approach, we reduce the sill geometry to that of a penny‐shaped crack subject to stress gradients, with an opening that is compatible with the surface displacements observed along the short‐axis of the sill. At selected points along the sill’s path, we calculate K around the tip‐line (Davis et al., 2019), and assume the greatest tip‐line advance occurs in the direction where K is largest (akin to Paris fatigue law [Davis et al., 2020]). In our numerical simulations, we discretize the sill into triangular elements (Davis et al., 2020; Nikkhoo & Walter, 2015) and update the tip‐line at each step using the local value of K as compared to the critical rock strength, K c .…”