Effect of 1-D Non-Planar Surface Topography on Rocking Ground Motion Induced by Incident Plane P-Wave

Abstract

The kinematics of any point on the ground undergoing seismic motion can be described by translations along and rotations about three orthogonal axes. The three rotational components include the rocking components (i.e., rotations about two horizontal axes) and the torsional component (i.e., rotation about the vertical axis). The rotational components of ground motion have been receiving attention of earthquake engineers because of their ability to cause damage over and above that posed by the translational components. Despite this, most earthquake-prone regions of the world are not instrumented with rotational seismometers and, as a result of the dearth of recorded rotational ground motion data, techniques to estimate rotational motions from the relatively abundant translational ground motion data offer an attractive alternative to estimate the additional seismic loads due to the rotational motions. Such techniques, referred to as ‘single-station’ techniques, involve many simplistic assumptions concerning the geometry of seismic wave fronts and composition of the medium in which the seismic waves travel. One of these assumptions concerns modelling the ground as a flat surface. Because this assumption may not always hold and because little research has been conducted to estimate the effect of a non-planar surface topography on the synthesized rotations, this study addresses this research gap by considering the case of a plane P-wave incident at the non-planar surface of a homogeneous elastic half-space. A perturbation-based method is used to analytically solve for the resulting surface rocking motion and this solution is compared with that corresponding to flat-topography case.