The emergence of crack-like behavior of frictional rupture: Edge singularity and energy balance

Abstract

The failure of frictional interfaces -the process of frictional rupture -is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake physics. A necessary condition for the emergence of a crack-like behavior is the existence of stress drops in frictional rupture, whose basic physical origin has been recently elucidated. Here we show that for generic and realistic frictional constitutive relations, and once the necessary conditions for the emergence of an effective crack-like behavior are met, frictional rupture dynamics are approximately described by a crack-like, fracture mechanics energy balance equation. This is achieved by independently calculating the intensity of the crack-like singularity along with its associated elastic energy flux into the rupture edge region, and the frictional dissipation in the edge region. We further show that while the fracture mechanics energy balance equation provides an approximate, yet quantitative, description of frictional rupture dynamics, interesting deviations from the ordinary crack-like framework -associated with non-edge-localized dissipation -exist. Together with the recent results about the emergence of stress drops in frictional rupture, this work offers a comprehensive and basic understanding of why, how and to what extent frictional rupture might be viewed as an ordinary fracture process. Various implications are discussed.

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

“…This observation enables us to map frictional rupture fronts to cracks by employing the linearity of the governing equations and subtracting τ r . Interestingly, however, recent work [55,56] demonstrated the emergence of crack-like behavior of frictional rupture fronts for more realistic rate dependent friction. The simplicity of the adopted model (slip-weakening) enables us to highlight the importance of non-steady propagation (section 3.2) and geometrical effects (section 3.3) present during propagation of supershear rupture fronts.…”

Variation of Hydraulic Properties Due to Dynamic Fracture Damage: Implications for Fault Zones

“…From quasi‐static shear failure experiments in intact rock (Aben et al, ; Lockner et al, ; Wong, , ), it is known that Γ is dissipated prior to a sharp change in slope as further weakening of the fault commences (Figure c). The existence of such a break in slope “separating” dissipation of Γ and W b has also been shown for dynamic shear rupture following a rate‐and‐state weakening law rupture simulation (Barras et al, ). The advantage of Scenario 2 is that an a priori knowledge on further slip‐weakening processes is not needed—after all, the effect of rupture‐induced dynamic off‐fault damage on these slip‐weakening processes is yet unclear.…”

Geomaterials Evaluation: A New Application of Ashby Plots

“…Faults commonly initiate and grow in weak planes such as rock joints, bedding planes, veins, and interfaces between different sedimentary rocks in the upper crust [35,43]. The frictional ruptures in the geological faults are found to experience significant stress drops (as shown in Figure 5b) and show crack-like behaviors in the initiation and propagation processes [44][45][46]. The Dugdale-Barenblatt model is used to describe and analyze these quasi-static shear cracks with friction [47], in which the maximum half-opening of the crack in the process zone is given as follows:…”