Modelling and back-analysing failures in steep limestone cliffs

The observation of 12 rock fall scars in steep limestone cliffs has shown that the fallen masses were stable as a result of relatively small rock bridges. These results demonstrate that consideration of rock bridges is necessary for a realistic evaluation of stability. Limit equilibrium methods of analysis are presented for sliding and toppling, for both isostatic and hyperstatic conditions. These methods are illustrated with four case histories. The results of nine back-analyses of rock falls with volumes between 24 and 3500 m3 are presented. The rock cohesion obtained from back-analysis appears to be significantly lower than the cohesion obtained from classical laboratory tests. This discrepancy can be attributed to several factors including: a spatial and temporal scale effect, the oversimplified modelling (two-dimensional limit equilibrium) and some uncertainties affecting the geometrical data. When analysing the stability of a cliff with a limit equilibrium method, the authors suggest dividing the cohesion by a “scale and method” factor of 3.