Soil-water-air coupled finite deformation analysis considering trapped air and continuous air phases

Since the soil–water characteristic model relates the matric suction and the water content, it cannot describe changes in the water content when the suction is zero and constant, i.e., all the pore air is trapped air. To reasonably describe changes in the water content due to air entrapment and the compressibility of trapped air, this paper presents a deformation analysis method based on the mixture theory for a four-phase mixture consisting of the soil skeleton, capillary water, trapped air, and continuous air, in which the pore air phase is divided into trapped air and continuous air phases. Specifically, considering the mass conservation equation and the equation of motion for each phase of trapped air and continuous air, and considering the mass exchange between the trapped air and continuous air phases, governing equations were derived for the initial and boundary value problems of the four-phase mixture in a finite deformation field using a rate-type equation of motion.

Two examples are provided to validate the new method. Firstly, experiments and analyses of soil water retention tests were conducted under multiple drying-wetting cycles. A comparison shows that, even if hysteresis is not considered in the relationship between the effective degree of saturation and suction, the new method can successfully describe the gradual decrease in the degree of saturation at a suction of 0 kPa with multiple drying-wetting cycles, indicating that the pore air gradually becomes trapped in the pore water, by modelling the mass exchange between the trapped air and continuous air phases. Secondly, analyses of an unexhausted and undrained triaxial compression test under zero suction were conducted, comparing the new and previous soil–water-air coupling methods. The results show that the new method, unlike the previous method, can successfully simulate the experimental result. This is because the new method is able to describe the compressibility of trapped air as the change in the capillary water degree of saturation, which is a novel state variable defined as the ratio of the volume of capillary water to the total volume of capillary water and trapped air.

The new method contributes to the simplification of the soil–water characteristic model and enables evaluations of the soil deformation behavior due to the compressibility of trapped air, such as a countermeasure against liquefaction caused by unsaturation.