Yield and shear of rough interlocked faults: analytical solution and experimental observations

Natural fault surfaces are interlocked, partly cohesive, and display multiscale geometric irregularities. Here we examine the nucleation of deformation and the evolution of shear in such interlocked surfaces using a closed-form analytical solution and a series of laboratory experiments.  The analytical model considers an interlocked interface with multiscale roughness between two linear elastic half-space blocks. The interface geometry is based on three-dimensional fault surfaces imaging. It is represented by a Fourier series and the plane strain solution for the elastic stress distribution is represented as a sum of the constant background stress generated by a uniform far-field loading and perturbations associated with the interface roughness. The model predicts the critical stress necessary for failure and the location of failure nucleation sites across the surface, as function of the initial surface geometry.

A similar configuration is adopted in laboratory experiments as carbonate blocks with rough interlocked surfaces generated by tensional fracturing are sheared in a servo-controlled direct shear apparatus. Resistance to shear and surface roughness evolution are measured under variable normal stresses, slip distances and slip rates.  We find that the evolution of surface morphology with shear is closely related to the loading configuration. Initially rough, interlocked, surfaces become rougher when normal stress and displacement rate are increased. Under a fixed, relatively low normal stress and fixed displacement rate however, the surfaces become smoother with increasing displacement distance.  

The shear of the interlocked slip surfaces is associated with volumetric deformation, wear and frictional slip, all of which are typically observed across natural fault zones. We suggest that their intensities and partitioning are strongly affected by the initial surface roughness characteristics, the background stress, and the rate and magnitude of shear displacement.