Undrained volume and stress change behavior of unsaturated very dense sands

The one-dimensional form of Skempton's B equation is inadequate to describe the behavior of cohesionless materials with pore fluids that contain large quantities of free and dissolved gas. Fredlund derived the compressibility of an air–water pore fluid in terms of the ideal gas laws, gas solubilities, and saturations. This paper extends the derivation of the compressibility of pore fluids, and couples the compressibility with that of the soil skeleton (e – σ′ relationship) to extend Skempton's equation to the most general one-dimensional undrained case. The differential equation derived is studied for the specific case of unloading behavior of oil sands: a very dense relatively incompressible quartzose sand, which contains sufficient volumes of interstitial bitumen to result in undrained behavior. The behavior of these materials, which have stiffnesses approaching that of water, can be qualitatively understood by means of a spring model: the stiffest spring (either pore fluid or soil skeleton) absorbs most of the stress change, and the stiffness of the springs change with changing total stress level.Practical application of the concepts herein should not be difficult for soils having very compressible skeletons, but for very dense sands, the derivation of the appropriate e – σ′ relationship is very difficult. Other system parameters that have a great effect on the behavior are the gas saturation, the gas solubility coefficients, and the initial stress conditions.