Stress Heterogeneity and the Onset of Faulting Along Geometrically Irregular Faults

Abstract

Faulting in rocks occurs when accumulated elastic stress is released along weak discontinuities. The event characteristics depend on the loading conditions, the mechanical properties of the rocks, and the geometry of the fault. Quantifying the effect of geometrical irregularities on stress accumulation and material yielding is therefore fundamental for evaluating fault stability at a wide range of scales and in various tectonic and geoengineering settings. For example, laboratory experiments demonstrate that surface roughness amplitude strongly influences slip dynamics during shear (Harbord et al., 2017;Ohnaka, 1973), while numerical simulations predict that geometrical irregularity of large natural faults affects magnitudes, nucleation, and distribution of earthquakes (

Simulated Rupture Dynamics and Radiated Energy on Heterogeneously Damaged Faults

“…The mathematical similarity of the stress field allows for "translating" the geometrical interface irregularity (i.e., two-body) into damage heterogeneity (i.e., three-body). It can be shown (Morad et al, 2022;Sagy & Lyakhovsky, 2019) that the solution, as demonstrated here for the simple sinusoidal damage heterogeneity (Equation 6), is valid for a stochastic damage distribution (Figure 2b) and for stress around a homogenous damage layer with thickness heterogeneity (Figure 2c). The thickening of the damage zone leads to the same stress variations as the reduction of the shear modulus.…”

“…Following previous works (F. M. Chester & Chester, 2000;Morad et al, 2022), the perturbation of the shear stress component, 𝐴𝐴 𝐴𝐴 (1) 𝑥𝑥𝑥𝑥 , for the static stress distribution near such interface, is proportional to the remote stress, 𝐴𝐴 𝐴𝐴 (0) 𝑥𝑥𝑥𝑥 , and decays exponentially with the distance, z, from the interface:…”

“…Following previous works (F. M. Chester & Chester, 2000; Morad et al., 2022), the perturbation of the shear stress component, $${\sigma }_{xz}^{(1)}$$, for the static stress distribution near such interface, is proportional to the remote stress, $${\sigma }_{xz}^{(0)}$$, and decays exponentially with the distance, z , from the interface: $$${\sigma }_{xz}^{(1)}=2{\mu }_{f}\,{\sigma }_{xz}^{(0)}{e}^{-kz}k\,{A}_{\zeta }\,(1-kz)\,\mathrm{Sin}(kx)$$$ …”

“…We search for the solution of the stress perturbation, 𝐴𝐴 𝐴𝐴 (1) 𝑖𝑖𝑖𝑖 , using the same form of the Airy stress function originally suggested by Johnson and Fletcher (1994) and utilized for calculating stress distribution around faults (F. M. Chester & Chester, 2000;J. S. Chester & Fletcher, 1997;Morad et al, 2022;Sagy & Lyakhovsky, 2019). For Sin-like undulations of the damage zone properties with the same wave number, k, as in Equation 1,…”

“…Since the thickness of the zone is small and we search for the first order perturbation of the background homogeneous solution, the condition (Equation 4) should be applied at z = 0 together with zero normal displacement, due to the symmetry between the upper and lower blocks. We search for the solution of the stress perturbation, $${\sigma }_{ij}^{(1)}$$, using the same form of the Airy stress function originally suggested by Johnson and Fletcher (1994) and utilized for calculating stress distribution around faults (F. M. Chester & Chester, 2000; J. S. Chester & Fletcher, 1997; Morad et al., 2022; Sagy & Lyakhovsky, 2019). For Sin‐like undulations of the damage zone properties with the same wave number, k , as in Equation 1, $$$\left[\frac{{\mu }_{1}(x)}{{\mu }_{0}}-\frac{{h}_{1}(x)}{{h}_{0}}\right]={A}_{d}\,\mathrm{Sin}(kx)$$$ the stress solution in the outer elastic blocks exhibits the same exponential decay as predicted by (Equation 2), and leads to explicit relation between the undulation amplitudes A d and A ζ ( ν —Poisson ratio): $$${A}_{d}=2{\mu }_{f}(1-2\nu )\frac{{A}_{\zeta }}{{h}_{0}}$$$ …”