[1] Energy loss in a fault damage zone, outside the slip zone, contributes to the fracture energy that determines rupture velocity of an earthquake. A nonelastic two-dimensional dynamic calculation is done in which the slip zone is modeled as a fault plane and material off the fault is subject to a Coulomb yield condition. In a mode 2 crack-like solution in which an abrupt uniform drop of shear traction on the fault spreads from a point, Coulomb yielding occurs on the extensional side of the fault. Plastic strain is distributed with uniform magnitude along the fault, and it has a thickness normal to the fault proportional to propagation distance. Energy loss off the fault is also proportional to propagation distance, and it can become much larger than energy loss on the fault specified by the fault constitutive relation. The slip velocity function could be produced in an equivalent elastic problem by a slip-weakening friction law with breakdown slip Dc increasing with distance. Fracture energy G and equivalent Dc will be different in ruptures with different initiation points and stress drops, so they are not constitutive properties; they are determined by the dynamic solution that arrives at a particular point. Peak slip velocity is, however, a property of a fault location. Nonelastic response can be mimicked by imposing a limit on slip velocity on a fault in an elastic medium.

Rupture Dynamics With Energy Loss Outside the Slip Zone

[1] We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgrb.50217

A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation

[1] We perform three-dimensional (3-D) numerical calculations of dynamic rupture along non-planar faults to study the effects of fault roughness on rupture propagation and resultant ground motion The fault roughness model follows a self-similar fractal distribution over length scales spanning three orders of magnitude, from ~102 to ~105 m The fault is governed by a strongly rate-weakening friction, and the bulk material is subject to Drucker-Prager viscoplasticity Fault roughness promotes the development of self-healing rupture pulses and a heterogeneous distribution of fault slip at the free surface and at depth The inelastic deformation, generated by the large dynamic stress near rupture fronts, occurs in a narrow volume around the fault with heterogeneous thickness correlated to local roughness slopes Inelastic deformation near the free surface, however, is induced by the stress waves originated from dynamic rupture at depth and spreads to large distances (>10 km) away from the fault The present simulations model seismic wave excitation up to ~10 Hz with rupture lengths of ~100 km, permitting comparisons with empirical studies of ground-motion intensity measures of engineering interest Characteristics of site-averaged synthetic response spectra, including the distance and period dependence of the median values, absolute level, and intra-event standard deviation, are comparable to appropriate empirical estimates throughout the period range 01–30 s This class of model may provide a viable representation of the ground-motion excitation process over a wide frequency range in a large spatial domain, with potential applications to the numerical prediction of source- and path-specific effects on earthquake ground motion

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgrb.50094

Rupture dynamics and ground motion from 3-D rough-fault simulations

強い速度弱化摩擦とオフフォールト塑性を持った地震破壊,その2:非平面断層

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

A Domain Decomposition Approach to Implementing Fault Slip in Finite-Element Models of Quasi-static and Dynamic Crustal Deformation

Observations demonstrate that faults are fractal surfaces with deviations from planarity at all scales. We study dynamic rupture propagation on self-similar faults having root mean square (rms) height fluctuations of order 10 -3 to 10 -2 times the profile length. Our 2D plane strain models feature strongly rate-weakening fault friction and off-fault Drucker–Prager viscoplasticity. The latter bounds otherwise unreasonably large stress concentrations in the vicinity of bends. Our choice of a cohesionless yield function prevents tensile stress states and thus fault opening. A consequence of strongly rate-weakening friction is the existence of a critical background stress level above which self-sustaining rupture propagation, in the form of self-healing slip pulses, first becomes possible. Around this level, at which natural faults are expected to operate, ruptures become extremely sensitive to fault roughness and exhibit substantial fluctuations in rupture velocity. Except for shallow inclinations of the maximum compressive stress to the fault (less than about 20°), the fluctuations are anticorrelated with the local fault slope. These accelerations and decelerations of the rupture, together with naturally emerging slip heterogeneity, excite waves of all wavelengths and result in ground acceleration spectra that are flat at high frequency, consistent with observed strong motion records.

/pdf/earthquake-ruptures-with-strongly-rate-weakening-friction-9reor30t9j.pdf

Earthquake Ruptures with Strongly Rate-Weakening Friction and Off-Fault Plasticity, Part 1: Planar Faults

Natural fault surfaces exhibit roughness at all scales, with root-mean-square height fluctuations of order 10− 3 to 10− 2 times the profile length. We study earthquake rupture propagation on such faults, using strongly rate-weakening fault friction and off-fault plasticity. Inelastic deformation bounds stresses to reasonable values and prevents fault opening. Stress perturbations induced by slip on rough faults cause irregular rupture propagation and the production of incoherent high-frequency ground motion.

/pdf/earthquake-ruptures-on-rough-faults-1h23z24muw.pdf

Lin Cong

Papers

Earthquake Ruptures with Strongly Rate-Weakening Friction and Off-Fault Plasticity, Part 1: Planar Faults

Earthquake ruptures on rough faults