Analytical and numerical investigation of site response due to vertical ground motion

Owing to the repeatedly observed strong vertical ground motions and compressional damage of engineering structures in recent earthquakes, the multi-directional site response analysis is increasingly critical for the seismic design of important structures, such as nuclear power plants and high earth dams. However, the site response to the vertical component of the ground motion has not been the subject of detailed investigation in the literature. Therefore, in this paper, the vertical site response due to vertical ground motion is investigated by employing both analytical and numerical methods. First, a one-dimensional frequency domain analytical solution, which can be employed for vertical site response analysis in practice, is studied and compared against time domain finite-element (FE) analyses for the two extreme soil state conditions (i.e. undrained and drained conditions). The vertical site response is further investigated with hydro-mechanically (HM) coupled FE analysis, considering solid–fluid interaction. The parametric studies undertaken show that the predicted vertical site response is strongly affected by the parameters characterising the hydraulic phase, namely, soil permeability and soil state conditions, both in terms of frequency content and amplification. The subsequent corresponding quantitative investigation, of the frequency content and amplification function of the vertical site response, shows that depending on the soil permeability the response is dominated by the two types of compressional waves (fast and slow waves). Notably, the parametric studies identify a range of permeability that significantly affects dynamic soil properties in terms of P-wave velocities, damping ratios and vertical site response, and this range is relevant for geotechnical earthquake engineering applications. It is therefore recommended that coupled consolidation analysis is necessary to simulate this effect accurately at such permeability-dependent intermediate transient states between fully undrained and drained conditions. Finally, this work suggests a simple modification of standard total-stress site response analysis to account for vertical ground motion and solid–pore fluid interaction. In order to simulate the attenuation of the response due to solid–pore fluid interaction effects, it is suggested to employ additional HM viscous damping in total-stress analysis, further to the one used to account for hysteretic material damping. This additional viscous damping can be quantified based on the empirical curves proposed in the paper.