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This study focuses on the consolidation behavior and mathematical interpretation of partially-saturated ground improved by impervious column inclusion. The constitutive relations for soil skeleton, pore air and pore water for partially saturated soils are proposed in the context of partially-saturated ground improved by impervious column inclusion. Settlement equation and dissipation equations of excess pore air/water pressures for a partially saturated improved ground are then derived. The semi-analytical solutions for ground settlement and pore pressure dissipation are then obtained through the Laplace transform and validated by the existing solutions for two special cases in the literature and the numerical results obtained from the finite difference method. A series of parametric studies is finally conducted to investigate the influence of some key factors on consolidation of partially saturated ground improved by impervious column inclusion. Based on the parametric study, it can be found that a higher value of the area replacement ratio or modulus of the pile results in a longer dissipation time of excess pore air pressure (PAP), a shorter dissipation time of excess pore water pressure (PWP), and a lower normalized settlement.

Considered that the gas content of partially saturated soil would decrease under a shock load, which would cause volumetric plastic deformation, Lyakhov's constitutive model is improved. The P-α state equation is used to describe the volume compression relationship of partially saturated soil. Numerical and experimental results are compared to validate the material model. The peak stress and duration of shock wave are crucial to study the dynamic response of underground structures. Considered the saturation of partially saturated soils under natural conditions increases with depth and both peak stress and duration change when shock waves propagate in inhomogeneous media, several partially saturated soil models with linearly decreasing air content in the depth direction are developed. The propagation law of shock waves with various peak stresses and durations in partially saturated soils is studied. The results show that the peak stress caused by the incident load in partially saturated soil first decreases and then increases under incident loads with a shorter duration, and it increases monotonically under incident loads with a longer duration. The rate of change in the incident peak stress is proportional to the air content at the top of the partially saturated soil. The peak free-field stress reaches its maximum, which is 2.2 to 5.5 times the peak stress of the incident load, in fully saturated soil. Long-duration incident loads such as nuclear explosions are more threatening to underground structures than short-duration incident loads. Underground structures buried in fully saturated soil or below fully saturated soil with higher air contents above are more at risk than underground structures buried in partially saturated soil with smaller air contents.