On the Deterministic Description of Earthquakes

Abstract

[1] The quantitative estimate of earthquake damage due to ground shaking is of pivotal importance in geosciences, and its knowledge should hopefully lead to the formulation of improved strategies for seismic hazard assessment. Numerical models of the processes occurring during seismogenic faulting represent a powerful tool to explore realistic scenarios that are often far from being fully reproduced in laboratory experiments because of intrinsic, technical limitations. In this paper we discuss the prominent role of the fault governing model, which describes the behavior of the fault traction during a dynamic slip failure and accounts for the different, and potentially competing, chemical and physical dissipative mechanisms. We show in a comprehensive sketch the large number of constitutive models adopted in dynamic modeling of seismic events, and we emphasize their prominent features, limitations, and specific advantages. In a quantitative comparison, we show through numerical simulations that spontaneous dynamic ruptures obeying the idealized, linear slip-weakening (SW) equation and a more elaborated rate-and state-dependent friction law produce very similar results (in terms of rupture times, peaks slip velocity, developed slip, and stress drops), provided that the frictional parameters are adequately comparable and, more importantly, that the fracture energy density is the same. Our numerical experiments also illustrate that the different models predict fault slip velocity time histories characterized by a similar frequency content; a feeble predominance of high frequencies in the SW case emerges in the frequency ranges [0.3, 1] and [11, 50] Hz. These simulations clearly indicate that, even forgiving the frequency band limitation, it would be very difficult (virtually impossible) to discriminate between two different, but energetically identical, constitutive models, on the basis of the seismograms recorded after a natural earthquake.

The mechanics of lubricated faults: Insights from 3‐D numerical models

“…[63] In the framework of the classical linear slip-weakening model [Ida, 1972], it is well-known that the occurrence of the supershear transition is basically controlled by the value of the strength parameter, which represents the ratio between the strength excess and the dynamic stress drop (see equation (15) in Bizzarri [2011b] and references cited therein). As a consequence, the supershear transition also depends on the initial level of stress on the fault.…”

“…(see Bizzarri [2011b] for a compendious review), which represents in an average, macroscopic sense, the behavior at the microscopic asperity contacts level.…”

Rapid Estimation of Damage to Tall Buildings Using Near Real-Time Earthquake and Archived Structural Simulations

“…The rupture process is then allowed to evolve dynamically as dictated by an assumed fault friction law. The development of dynamic source models is an active area of research in earthquake source physics (e.g., Guatteri et al, 2003;Harris et al, 2009;Lapusta and Liu 2009;Schmedes et al, 2010;Bizzarri, 2011;DeDontney et al, 2011). While dynamic source models may better characterize earthquake source physics, the theory is more complex and less mature when compared with kinematic source modeling (e.g., the state of stress in the earth and the fault friction law are not known; they are not as well-constrained as kinematic source parameters such as slip).…”

Dynamic modelling of a mining-induced fault slip

“…As mentioned by Bizzarri (2011), slip-weakening friction laws are a widely employed friction law to simulate dynamic behaviour of fault-slip as a source for earthquakes (Bizzarri, 2012;Bizzarri, Cocco, Andrews, & Boschi, 2001;Oglesby & Mai, 2012;Tinti et al, 2004). A linear slip-weakening friction law is generally expressed as (Bizzarri, 2011):…”