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.
