Computation of the seismic stability of rock wedges

Summary Newmark's concept of computing the permanent displacement under seismic loads has been combined with the conventional limit equilibrium analysis to compute the displacements of a rock wedge. The rock wedge formed by the intersecting planes may or may not have a tension crack in the upper slope surface. As the static analysis of a rock wedge is available from the literature, only the seismic problem is treated theoretically in more details.A computer program has been developed to compute the displacements from the digitised input data of the acceleration-time-history. The program can take into account the water pressure on the intersecting planes and on the planes of the tension crack. The effect of rock anchors if present is also taken care of in addition to static surcharge loads. The program calculates the conventional static factor of safety, remaining resistance against sliding, the critical acceleration, exciting force, relative velocity with time and the cumulative displacements.Two model examples are presented: one with simple sinusoidal acceleration and the other one with actual earthquake data considering the different systems of forces acting on the wedge. The results are critically discussed with respect to the different parameters e. g. anchor forces, water pressure and cohesion influencing the magnitude of displacements under seismic loads. It is shown that the critical acceleration is a better index for the seismic stability than the conventional factor of safety.The critical acceleration presented in this paper serves as a very handy tool for a site engineer to get the first hand information about the stability of the wedge for a given acceleration-time-history without going into the details of dynamic analysis.Notations A, B Inclined intersecting planes - C, D Geometric points on the intersection ofA andB - a _cr Critical acceleration - a _h Horizontal acceleration - a _v Vertical acceleration - a _r Relative acceleration of the wedge - DF Driving force - DF _dyn Dynamic driving force - DF _st Static driving force - FS Factor of safety - g Acceleration due to gravity - m Mass of the wedge - RF Resisting force - RF _dyn Dynamic resisting force - RF _st Static resisting force - RS Remaining resisting force against sliding - RS _dyn Total seismic induced force - RS _st Remaining static resisting force against sliding - s _r Cumulative relative displacement of the wedge - TRS Total remaining resisting force against sliding - v _r Relative velocity of the wedge - W Weight of the wedge - W _A ,W _B Weight of the wedge in the planeA andB - Dip of line of intersection of the planesA andB - Average friction angle - _A , _B Friction angle of planeA andB - I, II, III, IV Points in the curve shown in Fig. 6