Modeling the unsaturated soil zone in slope stability analysis

The linear form of the extended Mohr-Coulomb shear strength equation uses a [φ.sup.b] parameter to quantify the rate of increase in shear strength relative to matric suction. When the [φ.sup.b] value is unknown, a [φ.sup.b] equal to 15° is sometimes used in the slope stability study to assess the influence of matric suction on the stability of a slope. In many cases, however, a [φ.sup.b] value of zero is used, signifying that the effect of matric suction is ignored. Experiment results have shown that the relationship between the shear strength of an unsaturated soil and matric suction is nonlinear. Several semi-empirical estimation equations have been proposed relating the unsaturated shear strength to the soil-water characteristic curve. In this paper, the results of a study using two-dimensional slope stability analysis along with an estimated nonlinear shear strength equations is presented. The effects of using an estimated nonlinear shear strength equation for the unsaturated soils are illustrated using three example problems. Several recommendations are made for engineering practice based on the results of the example problems. If the air- entry value (AEV) of a soil is smaller than 1 kPa, the effect of matric suction on the calculated factor of safety is trivial and the [φ.sup.b] value can be assumed to be zero. If the AEV of a soil is between 1 and 20 kPa, the nonlinear equations of unsaturated shear strength should be adopted. For soils with an AEV value between 20 and 200 kPa, an assumed [φ.sup.b] value of 15° provides a reasonable estimation of the effects of unsaturated shear strength in most cases. For soils with an AEV greater than 200 kPa, [φ.sup.b] can generally be assumed to be equal to the effective angle of internal friction, $', in applications where geotechnical structures have matric suctions around 100 kPa.