Three-dimensional site response and dynamic stress concentration around a spherical cavity in an unsaturated porous half-space under SV-wave incidence

A three-dimensional semi-analytical solution is developed to investigate seismic site response and dynamic stress concentration around a spherical cavity embedded in an unsaturated porous half-space under SV-wave incidence. The formulation combines wave-function expansions with Hankel integral transforms and employs a stable truncation–quadrature scheme to satisfy both the free-surface condition and the cavity boundary conditions in a unified manner. In contrast to conventional two-dimensional or quasi-three-dimensional analyses, the proposed framework is able to capture the intrinsically three-dimensional redistribution of the wavefield around a compact spherical cavity, including section-dependent stress concentration and migration of critical response directions. Convergence with respect to truncation order and integration discretization is examined, and the solution is validated against limiting cases and independent numerical simulations. Using the proposed framework, the effects of relative frequency, burial depth, incident angle, saturation, porosity, and the SWCC parameter α on ground-surface displacement and cavity-surface dynamic stress concentration factor (DSCF) are systematically analyzed. The three-dimensional characteristics of the stress field are further examined, and a systematic sensitivity analysis is performed to identify the dominant factors controlling site amplification and local stress concentration. The results show that buried depth and frequency govern the dynamic response, whereas saturation and porosity mainly play secondary modifying roles. The present study provides a fully three-dimensional benchmark for wave scattering and seismic response in unsaturated porous media and offers new insight into the seismic assessment of shallow underground cavities in partially saturated ground.