Elastic Deformation due to Polygonal Dislocations in a Transversely Isotropic Half-Space

Abstract

Based upon the fundamental solution to a single straight dislocation segment, a complete set of exact closed‐form solutions is presented in a unified manner for elastic displacements and strains due to general polygonal dislocations in a transversely isotropic half‐space. These solutions are systematically composed of two parts: one representing the solution in an infinite transversely isotropic medium and the other accounting for the influence of the free surface of the half‐space. Numerical examples are provided to illustrate the effect of material anisotropy on the elastic displacement and strain fields associated with dislocations. It is shown that if the rock mass is strongly anisotropic, surface displacements calculated using an isotropic model may result in errors greater than 20%, and some of the strain components near the fault tip may vary by over 200% compared with the transversely isotropic model. Even for rocks with weak anisotropy, the strains based on the isotropic model can also result in significant errors. Our analytical solutions along with the corresponding MATLAB source codes can be used to predict the static displacement and strain fields due to earthquakes, particularly when the rock mass in the half‐space is best approximated as transversely isotropic, as is the case for most sedimentary basins. Online Material: MATLAB scripts to calculate rectangular and triangular dislocations in a transversely isotropic half‐space.