Earthquake-Induced Shear Stresses in Soils

Closed-form expressions for the earthquake-induced shear stress magnitude in soils and its phase shift with respect to the ground acceleration are presented. They are expressed as functions of the depth, the damping ratio of the soil, and the thickness of the resonant layer. In the development of these expressions the soil was treated as a viscoelastic material with a horizontal surface and harmonic surface displacement. The natural frequency is determined by assuming that a known depth of soil is in resonance. The shear stress induced in the soil by the earthquake is then evaluated from the governing equation of motion and expressed in complex form. As in the simplified method of evaluating soil liquefaction potential, the magnitude of the shear stress is presented as the product of the rigid-body shear stress and a stress-reduction coefficient. By doing this an analytic expression for the stress-reduction coefficient is derived.