A novel and general form of effective stress in a partially saturated porous material: The influence of microstructure

A recently published constitutive model for drying of a partially saturated porous material is extended to take into account finite air (gas) pressure as well as finite external load, variables that are absent during simple drying under atmospheric conditions. We further use the result to derive a general form of effective stress in a partially saturated material. The proposed framework overcomes a primary shortcoming of the classic Bishop effective stress expression and offers a novel way to incorporate important morphological features. In addition, we show how existing micromechanical homogenization techniques aided by basic descriptions of material morphology may be used to inform the study of elastic deformations in the partially saturated media. We further show that for two very specific schemes, and thus for two particular morphologies of porous materials, the proposed effective stress framework remarkably reduces to a volumetric average pressure form which is commonly encountered in literature. In this work, we also provide an extensive discussion and critique of the classic Bishop effective stress approach.