Three-dimensional back-analysis of saturated rock slopes in discontinuous rock—a case study

Two historic block failures on the left abutment of Pacoima Dam, California, are back-analysed using three-dimensional limit equilibrium analysis. Water pressures within the boundary joints are introduced by parametric addition of vectors using enhanced stereographic projection. The magnitude and orientation of the resultant necessary to cause failure are established, as a function of the available friction angle. The influence of joint friction on the joint water pressure required to initiate block sliding and on the failure mode is discussed. It is shown that with increasing joint water pressure the orientation of the resultant dictates a changing failure mode, in the cases studied, from double plane to single plane sliding. The actual failure mode depends on the available friction angle of the joints. The influence of increasing joint water pressure on the factor of safety is also discussed. It is shown that the rotation of the resultant force by the addition of joint water forces rapidly reduces the factor of safety. The rate of change of the factor of safety with respect to joint water pressure in the base joints is shown to be higher for double plane sliding and lower for single plane sliding for the same block, when both failure modes are investigated. Block theory analysis is used to assess the stability of the right abutment of Pacoima Dam, presently concealed by a thick layer of gunite, and the critical blocks in the abutment are found using the procedure of Hatzor. It is demonstrated that in contrast to the unstable left abutment, the right abutment is perfectly safe, by virtue of kinematics alone. This theoretical result is strongly validated by the field performance of the right abutment, which experienced several episodes of strong ground motions in the past.