Nonlinear Rheology at Shallow Depths with Reference to the 2016 Kumamoto Earthquakes

Abstract

Abstract Strong S waves produce dynamic stresses, which bring the shallow subsurface into nonlinear inelastic failure. We examine implications of nonlinear viscous flow, which may be appropriate for shallow muddy soil, and contrast them with those of Coulomb friction within a shallow reverberating uppermost layer with low‐seismic velocities. Waves refract into essentially vertical paths at the shallow layers and produce tractions on horizontal planes. The Coulomb ratio of shear traction to lithostatic stress for S waves equals the resolved horizontal acceleration normalized to the acceleration of gravity. The ratio of dynamic vertical normal traction to lithostatic stresses is the vertical normalized acceleration from P waves. The predicted viscous inelastic strain rate in muddy soil begins at low normalized accelerations and then increases mildly and nonlinearly with increasing normalized acceleration. Failure is unaffected when P waves decrease the vertical normal traction. Seismic waves recorded at KiK‐net station KMMH16 for the 2016 Kumamoto mainshock and strong foreshock show these effects. Inelastic deformation commences at a normalized horizontal acceleration of ∼0.25 and reduces S‐ and P‐wave velocities within the uppermost ∼15 m reverberating layer. Normalized horizontal accelerations and the Coulomb stress ratio reach ∼1.25. Strong S waves arrived even when strong P waves produced vertical tension on horizontal planes. In contrast, inelastic Coulomb failure commences at a normalized horizontal acceleration equal to the effective coefficient of friction; rapid inelastic strain precludes even higher accelerations. Furthermore, horizontal planes should fail from the stresses of strong S waves during the tensional cycle of strong P waves.