Frictional Stability at High Pressure vs. Fault Angle: A Derivation for Experimental Applications Including Confining Resistance and Its Implications for Natural Seismicity

Abstract:

Friction is an important tectonic control relevant for crustal strength, faulting, and earthquakes. Real faults have complex geometries that can often be represented in a cylindrical triaxial stress testing machine with a pre-defined saw-cut sample between axial pistons. However, results from this inclined sawcut geometry can be difficult to analyze because both normal and shear stress are coupled to applied axial stress. Specifically, determining shear stress and fault stability are challenging. Dieterich and Linker 1992 address the problem of general fault stability vs. fault angle from the perspective of rate and state friction; we add to their approach to provide a direct application to triaxial experiments.

This work addresses the analysis gap by re-deriving stability in terms of measurable triaxial machine parameters (axial stiffness and positive fault angle) and also addresses several common sources of experimental error. Our analysis reveals unstable regions at angles <15 degrees not predicted by Dieterich and Linker 1992. This is due to the transformation of axial stiffness to shear stiffness which has a sine relationship for triaxial geometry that approaches zero effective shear stiffness at small angles. Surprisingly, viscous confining resistance (forces resisting pistons pushing radially into confining media) has little to no effect on stability because it increases normal stress. Also surprising is the 2-3x decrease in stability that can be provided by frictional forces between shearing and axial driving pistons with a friction coefficient of 0.1. Area change of sample contact with slip can have unintuitive effects and lead to rapidly changing effective stiffness during a single experiment. These effects can also be thought of in a general way and applied to understand seismicity on natural very low/high angle faults such as the anomalous number of high angle earthquakes noted by Sibson and Xie 1998.