Based on the analysis of the equilibrium of solid particles of an unsaturated sample subject to certain suction it is possible to establish an analytical expression for Bishop´s parameter χ. The resulting stress can be used to predict the shear strength and volumetric behavior of unsaturated soils. The effective stress is written as a function of the net stress and suction and requires three parameters: the saturated fraction, the unsaturated fraction and the degree of saturation of the unsaturated fraction of the sample. This equation 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 determination of these three parameters cannot be made from current experimental procedures.
Keywords: Degree of saturation of the unsaturated fraction, Dry fraction, Effective stress parameter, Effective stress, Equilibrium, Homogeneous material, Macrostructure, Microstructure, Saturated fraction, Shear strength, Suction, Total stress, Unsaturated fraction, Volumetric behavior, Water menisci.