The Effective Stress Equation

Abstract

Based on the analysis of the equilibrium of solid particles of an unsaturated sample subject to a certain suction, it is possible to establish an analytical expression for Bishop´s parameter X. With this parameter, the effective stress can be evaluated and used to predict the shear strength and volumetric behavior of unsaturated soils. For the determination of parameter X, three elements are required: the saturated fraction, the unsaturated fraction, and the degree of saturation of the unsaturated fraction of the sample. The equation established for parameter X clarifies some features of the strength of unsaturated soils that, up to now, had no apparent explanation. A drawback to this expression is that the three required parameters for the determination of X cannot be obtained from current experimental procedures.

Keywords: Equilibrium, Total stress, Effective stress, Suction, Volumetric behavior, Shear strength, Effective stress parameter, Saturated fraction, Unsaturated fraction, Dry fraction, Degree of saturation of the unsaturated fraction, Microstructure, Macrostructure, Water menisci, Homogeneous material.