Simulation of Spatially Variable Seismic Underground Motions in U-Shaped Canyons

This paper focuses on the study of simulations for spatially variable seismic underground motions in U-shaped canyons. First, a canyon ground cross-coherence function based on commonly used coherence function models of flat terrain, is deduced and presented. To further obtain the underground cross-coherence function, a mathematical expression, including its specific deduction process for describing the relationship between coherence functions of multi-support ground and underground motions, is also given in detail and adopted. Then, the key factors (i.e. canyon underground power spectrum density and canyon underground coherence function) for simulating the spatially variable seismic underground motions are obtained by a two-step transferring method from flat-ground to underground soil. Furthermore, a program is coded for generating the spatially variable seismic underground motions. The effectiveness of the generated seismic motions is further verified. Finally, two numerical examples are taken to validate the proposed simulation approach, illustrating the specific characteristics of canyon coherence function. The analysis results show the apparent differences of the simulated seismic motions using the canyon coherence function from those using conventional coherence function models of flat terrain. The proposed approach provides some insights for anti-earthquake analysis of soil-structure interaction or underground structures in canyon topography.