A Singularity-Free Crack Model Inferred from Contained
Laboratory-Generated Earthquakes
Abstract
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.