Constraints from fault roughness on the scale-dependent strength of rocks

Emily E Brodsky,Thibault Candela,James D Kirkpatrick

doi:10.1130/g37206.1

Abstract

Principal slip surfaces in faults have measurable roughness generated during slip. The roughness both records previous events and poses the boundary conditions for future rupture. Digital, high-precision roughness data are now available at the field scale (tens of centimeters to tens of meters) for at least 22 faults, and at the laboratory scale (millimeters to tens of centimeters) for a subset of these. We quantify the slip surface roughness by measuring the aspect ratio, which is the average asperity height divided by the profile length. Higher aspect ratios indicate rougher surfaces. From the field studies, two major trends have emerged: (1) fault surface roughness lies in a restricted range with aspect ratios in the slip-parallel direction of 0.07%–0.5% for profiles of 1 m length, and (2) fault surfaces are rougher at small scales than large ones. These features can both be interpreted as fingerprints of scale-dependent strength, which sets a limit to the aspect ratio of the surface. The measurements imply that shear strength scales with the observation scale, L , as L –0.4 . The new understanding of the physical controls on roughness allows generalization of the extant measurements of a wide array of faults.

Highlights

Principal slip surfaces in faults have measurable roughness generated during slip
Two major trends have emerged: (1) fault Given an observation scale, L, the mean asperity surface roughness lies in a restricted range with aspect ratios in the slip-parallel direction of height is an integral of the power up to that scale
The scaling of strength proposed here poses a problem at small scales where H/L appears to increase without bound, and at large scales where the implication is that faults become infinitely weak (Fig. 4)

Summary

INTRODUCTION

Fault zones contain well-defined slip sur- based lidar on an exposure of the exhumed fault where H is the average height of asperities faces. In this paper we review the major features of fault roughness that have been observed to date with a focus on the aspect ratio H/L and its scale dependence to interpret the data. Fault slip surfaces are shear cracks (mode II or III) and the observed Hurst exponent here is 0.6 in the slip direction This difference is not surprising as the stress field locally is different than in the crack tip region of a tensile fracture. In the case of the Corona Heights fault (California, USA), the observed Hurst exponent is 0.63 over scales of 10-3 to 101 m, which implies that the yield strain, and strength, is proportional to L–0.47 (Fig. 4). This case study where both the roughness data and geological information are available highlights the direct manifestation of failure at multiple scales

CONCLUSIONS AND IMPLICATIONS

Findings

Part 2: Nonplanar faults