Modeling the static liquefaction of unsaturated sand containing gas bubbles

As a modification of the deviatoric hardening plasticity model, a material state-dependent model was proposed to simulate the response of unsaturated sand containing gas bubbles under undrained triaxial conditions. Affected by the compressibility of gas, the stress paths under undrained conditions approach the drained response of sand when the initial degree of saturation is low. Upon an increase in the degree of saturation, the stress path gradually approaches the saturated undrained response. According to the prediction based on the second-order work criterion, static liquefaction occurs in loose sand, but not in dense sand. Increases in the degree of saturation and the initial gas pressure reduce the stress ratio at the instability points. The instability line obtained by connecting those instability points in the p-q space is nonlinear, and its slope depends on the initial void ratio, the initial degree of saturation, the initial gas pressure, and the confining stress. After comparing the experimental results in the literature with the theoretical prediction, the proposed model was shown to precisely predict the onset of the static liquefaction of unsaturated sand containing gas bubbles.