Issues on concepts of effective stress and seepage force arising from anatomizing Swedish slice method

The Swedish slice method has played an important role in the teaching of soil mechanics and the design of slope engineering. Its two expressions for effective stress analysis are investigated by anatomizing the derivation process of the normal effective stress on the bottom of a soil slice and by analyzing their calculated results comparatively. It is found that theoretically both expressions are not applicable to the slope stability analysis under the seepage condition in a general sense, and practically their calculation errors are obvious and scattered. The reason for this is due, respectively, to the neglect of the boundary water forces on the sides of soil slices when soil mass element is analyzed and the neglect of the seepage forces when soil skeleton element is analyzed. Further investigations on the differential equations of force equilibrium of a soil element reveal that the two equivalent approaches proposed by Taylor for treating the influence of seepage on the effective stress of soil skeleton, namely, the approach considering saturated weight and boundary water force when soil mass is analyzed and the approach considering effective weight and seepage force when soil skeleton is analyzed, can be used in the limit equilibrium analysis methods for a rigid body such as the slice method. However, in the analytical and numerical methods for seepage-deformation coupling analysis for problems like slope seepage stability and consolidation, only the soil mass element can be considered. Under this circumstance, the soil skeleton element cannot be considered and the seepage force concept cannot be applied. The reason for this is that under the seepage condition the effective stress is, physically, not a stress variable. The effective stress and pore water pressure determining the seepage force are interdependent and non-independent stress state variables controlling correspondingly the deformation and strength of soil skeleton and the flow net field.