Abstract
The finite deformation of an unsaturated porous medium is analysed from first principles of mixture theory. An expression for Bishop’s effective stress is derived from (1) the deformation-dependent Brooks and Corey’s water retention curve and (2) the restrictions on the constitutive relationships of an unsaturated medium subject to finite deformation. The resulting expression for the effective stress parameter chi is reasonably consistent with experimental data from the literature. Hence, it is shown that Bishop’s equation is constitutively linked to water retention curves in deforming media.
Highlights
Unsaturated soil mechanics is of utmost importance in many applications
The merit of the proposed equation is that it is based on a rigorous thermodynamic framework, and it results in formulating the effective stress parameter based on the physically meaningful parameters
The parameters that are required in order to estimate the effective stress parameter at different net stress and capillary pressure levels are basically the parameters which describe the equation of the soil water retention curve at different net stress levels
Summary
Unsaturated soil mechanics is of utmost importance in many applications. Examples are rainfall-induced landslides and slope failures, the settlement of foundations on (and bearing capacity of) the unsaturated soils, and wetting- and drying-induced volume changes in the expansive and collapsible soils. By means of an empirical equation for the effective stress, Masin (2010) formulated and investigated the void ratio dependency of degree of saturation for various capillary pressure values All these studies point to the fact that soil water retention curve changes as a result of a change in void ratio. We expect to observe the stress-level dependency of the amount of different phases in unsaturated soils and the stress measures have to be dependent on the amount of different phases Such dependency has commonly been introduced to the current hydromechanical modelling frameworks using soil water retention (capillary pressure–saturation) curves. The effective stress parameter is expressed alternatively as a function of capillary pressure and air entry pressure as previously discussed (Khalili and Khabbaz 1998) From this brief review, we can conclude that the stress measures in unsaturated soils are closely connected to SWRC equation. Concluding remarks and some suggestions for future studies are provided
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