Bem2d.jl: A quadratic co-location two-dimensional boundary element approach to quasi-static faulting problems with gravity and non-planar topography

Linear elastic boundary element models are commonly used tools to understand the mechanics of earthquake cycle processes and their contribution to the growth of tectonic structures. Here we describe a two-dimensional plane strain linear elastic boundary element approach to earthquake cycle and tectonic processes based on the displacement discontinuity method. This approach integrates an analytic solution for coincident interactions using three node quadratic elements and the classic particular integral approach to uni-directional gravity. Three node quadratic elements are more accurate than classical constant displacement elements and enable the exact representation displacements, stresses and tractions on elements subject to slip gradients. We demonstrate the recovery of analytic solutions and illustrate the combined effects of faulting and gravitational body forces in the presence of topographic relief.

Automated summary

The linear elastic boundary element model is a common tool for understanding the mechanics of earthquake cycle processes and their impact on tectonic structure growth. This study introduces a two-dimensional plane strain linear elastic boundary element approach based on the displacement discontinuity method, incorporating three node quadratic elements and the classic particular integral approach. The accuracy of three node quadratic elements provides a more exact representation of displacements, stresses, and tractions on elements with slip gradients, demonstrating the recovery of analytic solutions and the combined effects of faulting and gravitational body forces in the presence of topographic relief.