Seismic Response of Squat Rigid Bodies on Inclined Planes with Rigid Boundaries

A planar rigid-body dynamics formulation describing the seismic behavior of a squat rectangular rigid body initially resting on an inclined rigid plane is presented. The downslope motion of the body is limited by a rigid boundary perpendicular to the inclined plane. This type of problem appears in several practical applications. Coulomb and hysteretic friction with velocity- and pressure-dependent properties are considered at the body-to-ground interface. The weaknesses of hysteretic friction models incorporating static and kinetic velocity-dependent components are identified and remedied. Impact models for collision of the body with the rigid boundary and the inclined plane are also derived. The formulation is embodied in a numerical model through a dedicated computer code. A comparative study is conducted to demonstrate the effects on the body response of major model characteristics, including the rigid boundary; inclination angle; Coulomb, hysteretic, and combined Coulomb-hysteretic friction; and velocity dependence of the frictional properties. It is shown that the presence of the rigid boundary considerably affects the body response, and that small inclination angles can significantly limit the outward body displacement.