A note on the stability analysis of earth dams

Abstract

All methods of stability analysis of earth dams presently available for design are based on the principle of limiting equilibrium. According to this principle, the available shear strength along a potential sliding surface is reduced by a factor of safety so that the mass contained within the sliding surface and the free surface is in a state of limiting equilibrium. It is well known that the solution to the problem of determining the available shear strength is statically indeterminate. However, an acceptable solution is one that would describe the state of stress along the surface with reasonable assumptions. For the static analysis of dams, where only the value of the factor of safety is needed, any of the existing methods may be used (Bishop, 1952). But when designing for earthquake conditions by the displacement methods, both the factor of safety as well as the resultant shear force vector are needed. At present there are methods which give both of these (Bishop, 1952; Morgenstern and Price, 1965), but these methods need a high speed computer. A graphical method of circular arc analysis which finds both the factor of safety and the resultant shear force vector with surprisingly good agreement with computer results is presented in this Note. As mentioned earlier, the stability analysis is based on limiting equilibrium. Under the circumstances, when the force vectors representing the external forces, the total shearing resistance along the base of the entire sliding surface and the total normal force are drawn, a closed polygon should be produced. At the same time the forces should satisfy the moment equilibrium condition.