Equivalent Stress Equation for Unsaturated Soils. I: Equivalent Stress

In 1959 Bishop stated his effective stress equation for unsaturated soils. However, the difficulties in estimating the value of its main parameter χ, made this equation useless and it was abandoned for some time. Only recently, it has been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. However, up to now the most successful equations to quantify the value of parameter χ are empirical and not satisfactory for most soils. Based on the analysis of the equilibrium of the solid particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for Bishop’s parameter χ. The resulting stress has been called equivalent stress (in contrast with effective stress) and can be used to predict the shear strength of unsaturated soils. The equivalent stress is written as a function of the net stress and suction and requires two parameters: the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. This equivalent stress clarifies some features of the strength of unsaturated soils that up to now had no apparent explanation. However, the determination of its two parameters cannot be made from current experimental procedures. A method for the determination of these parameters and a comparison between experimental and theoretical results for the shear strength of unsaturated soils are presented in a companion paper.