The direct mechanical effects of seepage force on the behavior of hydrate-bearing porous media (HBPM) have often been neglected in previous studies, which may lead to inaccurate predictions of the mechanical behavior of HBPM under seepage conditions. Here, we propose an extended three-phase physical model for unsaturated HBPM, including gas, capillary water, and generalized solid skeleton (GSS). Based on the model, the force balance equations for the three phases are formulated. Performing a force analysis of generalized solid particles under seepage conditions, we find that the tangential force acting on the generalized solid particle is the seepage force in HBPM. By combining this finding with the formulated balance equations, we derive the expression for the seepage force, which can distinguish the mechanical effects between the tangential force and normal force. The stresses, induced by the tangential force (i.e., seepage force), are divided into two types: one acts on the cross sections of generalized solid particles and the other on the contacts between particles. Neither of them is transmitted through the GSS. The former mainly causes the particles themselves to compress, whereas the latter primarily influences the sliding of the particles at contacts. Based on the mechanisms of these two stresses, their effects on the mechanical behavior of HBPM are quantified, which provides a new insight to evaluate the direct mechanical effects of seepage force.

Soil is prone to structural degradation under water infiltration, and the combined effects of dry density and salinity further complicate its hydraulic conductivity and drying shrinkage behavior. However, previous studies have primarily focused on single factors, and the interactive mechanisms between compaction state and salinity remain poorly understood. To investigate the hydraulic conductivity and drying shrinkage behavior of soil under different dry densities and salinity levels, this study examined three dry densities (1.30, 1.35, 1.45 g/cm³) and four NaCl contents (0, 0.5%, 2%, 6%). Saturated hydraulic conductivity (ks) and drying shrinkage were systematically measured. The results indicate that dry density is the primary factor controlling pore structure evolution, ks and drying shrinkage behavior. Increasing dry density markedly reduced porosity (up to 15.95%), ks (by 57.14–92.91%), and drying shrinkage. In contrast, salinity exhibited non-monotonic, density-dependent effects. Salts increased porosity through electrochemical interactions and crystallization-induced pore support, but their effects on ks and drying shrinkage displayed threshold and reversal behavior. These coupled effects demonstrate strong nonlinearity and density dependence, providing a mechanistic basis for compaction optimization and the stability assessment of soil under saline conditions.

The effective stress equation for unsaturated soil is the most important equation in unsaturated soil mechanics. It has been derived by many scholars using different methods. However, none of them considered the gradient of the pore water content, which results in unreasonable force balance equations for different constituent phases in unsaturated soil. To introduce the gradient, we propose an extended three-phase physical model that includes capillary water, air, and generalized soil skeletons. Based on this model, three balance equations for these three constituent phases are separately formulated by considering the gradient of the pore water content. Comparing the result of the superposition of these three balance equations with the total balance equation, we derive a generalized Terzaghi’s effective stress equation. This equation states that the effective stress is equal to the total stress minus the neutral stress. In comparison with the classical Bishop’s equation, the generalized Terzaghi’s equation ensures a smooth and continuous transition from unsaturated to saturated conditions not only in mathematical expression but also in physical meaning. Furthermore, the different pressure effects of capillary water and adsorbed water, their volumetric (or areal) effects, and the transformation between them can be considered by adopting the effective saturation of the capillary water as the effective stress parameter. Therefore, the generalized Terzaghi’s equation can provide a better choice for estimating the effective stress in unsaturated soils.