3D Analytical Solution for Stress and Elastic Energy Around Geometrically Irregular Interlocked Surfaces: Applications to Natural Faulting

The heterogeneity of shear resistance associated with surface roughness along fractures plays a crucial role in out-of-fault stress distribution, slip dynamics, and the energy dissipation during failure. We present a new 3-D analytical solution for the static stress field and elastic energy distribution near rough faults. The inputs for our calculations are the far-field stresses, the surface geometry, and the frictional strength of the fault. We then apply failure criteria to evaluate the likelihood of failure in the vicinity of the fault. Our scale-independent solution effectively captures stress heterogeneity in various contexts of nonplanar faults and shows that surface topography variations perpendicular to the slip direction significantly influence both the orientations and magnitudes of local stress as well as the likelihood of failure. Consistent with the previous 2-D solution, stress components decay exponentially with distance from the fault surface, with the decay factor corresponding to the wavelength of surface undulations. Our findings indicate that fault geometry and far-field stress conditions, which establish zones with both low failure likelihood and high energy density, promote the occurrence of the largest slip events. The solution has applications in seismological and geoengineering hazard assessments, offering valuable insights into stress distribution, energy dynamics, and failure conditions along geometrically complex fault systems.