Site response to multi-directional earthquake loading: A practical procedure

Site response to earthquake loading is one of the fundamental problems in geotechnical earthquake engineering. Most site response analyses assume vertically propagating shear waves in a horizontally layered soil–rock system and simply ignore the effect of site response to vertical earthquake motion, although actual ground motions are comprised of both horizontal and vertical components. In several recent earthquakes very strong vertical ground motions have been recorded, raising great concern over the potential effect of vertical motion on engineering structures. Being a step toward addressing this concern, this paper presents a simple and practical procedure for analysis of site response to both horizontal and vertical earthquake motions. The procedure involves the use of the dynamic stiffness matrix method and equivalent-linear approach, and is built in the modern MATLAB environment to take full advantages of the matrix operations in MATLAB. The input motions can be specified at the soil–bedrock interface or at a rock outcropping. A detailed assessment of the procedure is given, which shows that the procedure is able to produce acceptable predictions of both vertical and horizontal site responses.