Evaluation of instability of quasi-saturated sand with entrapped gas due to decreasing total confining stress

The collapse of quasi-saturated sand with entrapped air due to decreasing total confining stress under undrained conditions has been widely reported in engineering practice. This material instability can fundamentally be related to dual effect of occluded gas bubbles: (1) altering undrained shear characteristics and (2) changing the relative compressibility between pore fluid and solid skeleton. Existing studies, however, have mainly treated these two effects independently. This work presents a theoretical framework to interpret the aforementioned instability that allows accounting for the interactions between the dual effect of gas. For this purpose, a state-dependent constitutive relation for gassy sand is employed that can well represent the gas effects of enhancing shear resistance and transferring unloading to soil skeleton. This soil model further enables evaluating the stability of quasi-saturated soils during constant deviatoric stress undrained shear with decreasing total mean stress, based on second-order work, the singularity of the symmetric part of the constitutive matrix, and test controllability. The experimentally observed collapse of loose gassy sand during the aforementioned stress path is analyzed by combining the constitutive model and stability criteria. This analysis finds that the reduction in effective stresses is initially driven by transferring unloading to soil skeleton, but becomes dominated by shear-induced contraction of soil matrix as failure is approached. Observed soil collapse can be well anticipated by probing the loss of controllability, yet lagging vanishing second-order work. The latter condition corresponds to the reversal in pore pressure and soil volume rate and represents a precursor for instability. Lastly, this work shows that the competition between the dual effect of the gas is key to understanding the non-monotonic dependence of instability potential on the properties of pore fluid and its compressibility.