Simulation of multi-support (i.e. spatially variable) seismic underground motions in sea areas plays a significant role in the seismic analysis of cross-sea structures such as cross-sea bridges or subsea tunnels. However, existing approaches for predicting multi-support seismic motions mainly focus on the dry site soils without overlying surface water. This paper proposes an approach for predicting multi-support seismic underground motions in layered saturated half space under surface water, subjected to oblique incident P waves. The transfer function in saturated soil under surface water, as the theoretical basis of the subsequent numerical simulation, is first derived based on wave propagation theory and the calculated reflection coefficients of P wave–induced P1, P2, SV waves in saturated soils. The derived transfer function is further employed to deduce and obtain the underground (sub-seabed) power spectral density function and response spectrum function. The two obtained functions, combined with the additional cross-coherence function, are subsequently employed to construct the cross power spectral density matrix and thus to simulate multi-support seismic underground motions. The solutions are validated against the target power spectral density, target response spectrum and target cross-coherence functions. A parametric analysis is presented where the effects of the soil thickness, the incident angle and the overlying water depth are investigated. Results show that the soil thickness, incident angle and overlying water depth have significant influences on the amplitude of transfer functions, which further affect the ratios between seismic ground and underground motions.
Various components including wave scattering, wave passage, and site simplification effects cause the ground motion to vary spatially [1,10,12,21,39,9]. It has been observed that the spatial variation of seismic motions has significant influence on the dynamic response of engineering structures, especially for those structures such as long-span bridges, transmission tower-lines systems, tunnels and dams [2,41–44]. Therefore, the reasonable simulations and predictions of multi-support seismic motions are necessary for a reliable structural response analysis [21,23,3,33,46]. Generally, it is necessary for simulating the multi-support seismic motions to construct the cross power spectral density matrix, which need the target PSD (power spectral density) function, target response spectrum and coherence function [20,22,24,27,31,35]. Based on this research framework, a number of methods have been developed, proposed and employed. In particular, Deodatis  presented a method to simulate spatial ground motions with different power spectral densities at different locations and investigated the influence of the spatial variation of ground motions on the seismic response of large embankment dams. This method was then extended to generate spatially varying seismic ground motion time histories by Deodatis et al. . Considering the influence of layered irregular sites and random soil properties on coherence functions, [4,5] presented an approximate method to simulate the spatially varying ground motions on the surface of non-uniform sites. Their method was then paid close attention and was extensively developed by many researchers [26,28,45]. Furthermore, the impact of the spatially varying seismic motions on the seismic response of different types of structures, such as transmission towerlines, large dams and large-span bridges, were also investigated by [1,37,14,30,48,19,34].