Modelling and simulation of spatially varying earthquake ground motions at sites with varying conditions

In a flat and uniform site, it is reasonable to assume that the spatially varying earthquake ground motions at various locations have the same power spectral density or response spectrum. If an engineering site with varying soil conditions at different structural supports is considered, this assumption is no longer valid because of different local site amplification effect. This paper presents an approximate method to model and simulate spatially varying ground motions on the surface of an uneven site with non-uniform conditions at different locations in two steps. In the first step, the base rock motions at different locations are assumed to have the same intensity, and are modelled by a filtered Tajimi–Kanai power spectral density function or other stochastic ground motion attenuation models. The base rock ground motion spatial variation is modelled by an empirical coherency loss function. The power spectral density functions of the surface motions on the site with multiple soil layers are derived based on the deterministic 1D wave propagation theory, neglecting the wave scattering on the uneven canyon surface, and assuming that the base rock motions consist of out-of-plane SH   wave or in-plane combined PP and SVwaves propagating into the site with an assumed incident angle. In the second step, a stochastic method to generate spatially varying time histories compatible with non-uniform spectral densities and a coherency loss function is developed to generate ground motion time histories on an uneven site. Two numerical examples are presented to demonstrate the proposed method. Each generated ground motion time history is compatible with the derived power spectral density at a particular point on the site or response spectrum corresponding to the respective site conditions, and any two of them are compatible with a model coherency loss function.

► A method to simulate spatially varying earthquake ground motions is introduced.
► Wave passage, incoherence and local site effects are considered.
► 1D wave propagation theory is involved.
► Different response spectra at different locations can be considered.