loading page

A Singularity-Free Crack Model Inferred from Contained Laboratory-Generated Earthquakes
  • Chun-Yu Ke,
  • Gregory Mclaskey,
  • David Kammer
Chun-Yu Ke
Cornell University

Corresponding Author:ck659@cornell.edu

Author Profile
Gregory Mclaskey
Cornell University
Author Profile
David Kammer
ETH Zurich
Author Profile


Earthquakes are commonly modeled as shear cracks, where the slip profile of an earthquake rupture is the spatial distribution of relative displacement between fault surfaces. It is an accumulated result of all the processes during the earthquake: nucleation, propagation, and arrest. Understanding the characteristics of a slip profile gives insight into the associated stress changes, which is generally immeasurable on natural faults, and is useful for understanding the underlying friction law. Most models focus on simplicity for application purposes. For instance, the elastic crack model (Bilby & Eshelby, 1968) established that a perfect crack with uniform shear stress drop leads to an elliptical slip profile; Cowie and Scholz (1992) proposed a crack model with constant-stress cohesive zones at the crack tips, which results in “bell-shaped” slip profiles. However, the elliptical model results in unphysical stress singularities at crack tips, and the plateau in stress drop distribution near crack tips in the “bell-shaped” model is infeasible for friction dominated ruptures because it is commonly believed that slip is always accompanied by shear stress drop, e.g. slip-weakening friction law (Andrews, 1976). ­ We present results from recent large-scale laboratory experiments where all the rupture processes are contained in a 3-meter long saw-cut granite fault (Ke et al., 2018) and slip local fault slip and shear stress changes are measured at 16 locations along the fault. Guided by the laboratory experiments, we derived an analytical model to faithfully represent measured slip profiles δ(x), and shear stress changes Δτ(x), resulting from laboratory earthquakes. Field measurements of slip profiles revealed that slip profiles are commonly tapering roughly linearly toward the tips. The proposed model includes this feature, and thus fits slip profiles measured from natural earthquakes on isolated faults better than other idealized analytical models. For more complex natural earthquakes, our model can be used as a basis function. Our results suggest that inelastic earthquake processes can be solely originated from friction, and the shape of an earthquake rupture is likely between the elliptical and bell-shaped idealized models.