Strong seismic shaking of randomly prestressed brittle rocks, rock damage, and nonlinear attenuation

Abstract

Strong seismic waves produce frequent episodes of transient oscillating dynamic stress in the shallow subsurface within seismically active areas. Dynamic stress drives slip on a network of preexisting small fracture planes and leaves residual stresses once shaking ceases. The residual stresses act as prestresses during the next strong earthquake. Local failure occurs on fractures at low dynamic stresses where the prestresses are favorably aligned, while most of the bulk rock remains intact. Hence nonlinear attenuation of strong seismic waves commences at dynamic stresses well below those for pervasive Coulomb failure. Consideration of the fractal distribution of prestresses indicates that nonlinear attenuation increases rapidly with dynamic stress. Vertically propagating shear waves provide simple scaling relationships for quick application: (1) Nonlinear attenuation is concentrated near the quarter wavelength depth. (2) The Coulomb stress ratio (dynamic/lithostatic stress) above the quarter wavelength depth scales with the sustained dynamic acceleration in g's. Rate and state friction thus provides estimates of the maximum sustained acceleration from Coulomb stress ratio at failure: ∼1 for regolith that has repeatedly failed, ∼1.5 for shallow intact sandstone, and ∼2 for shallow intact granite. A potentially observable effect occurs with shallow brittle regolith on hillslopes where gravity causes net downslope creep during strong shaking. Analogous crack network behavior with prestress occurs in the damage zone surrounding the rupture zone of major faults. Pulverized rock forms at shallow depths when rock is repeatedly deformed in strong shaking to just beyond the elastic limit, but strain does not localize into a crack network.