Development of a probabilistic block theory analysis procedure and its application to a rock slope at a hydropower station in China

The paper deals with a development of a new procedure to perform probabilistic block theory analysis using the vector method. The procedure includes the following three main features: (a) the joint orientation is considered as a bivariate distribution including the correlation that exists between the joint dip angle and dip direction angle; (b) the variability of discontinuity shear strength is incorporated in the analysis; (c) it performs deterministic and probabilistic block theory analysis including the mode of failure (MOF), maximum safe slope angle (MSSA), factor of safety (FS) and the instability probabilities for different cut slope dip angles (CSDA) and different MOFs. A rock slope at a hydropower station in China is used as a case study to illustrate the use of the developed procedure. The slope has six sets of discontinuities. Therefore, both deterministic and probabilistic block theory analyses were conducted for 4-plane, 5-plane, 6-plane and 7-plane blocks to study the stability of the rock slope under different MOFs and CSDA. For most MOFs, the MSSA obtained through deterministic analysis were found to be significantly higher than the CSDA obtained corresponding to zero instability cumulative probability. The differences obtained between the deterministic and probabilistic analyses resulted mainly due to the variability of discontinuity orientation. The case study illustrated the importance and superiority of the probabilistic analysis over the deterministic analysis. For the investigated rock slope by selecting the CSDA of 40° and 50°, the total instability cumulative probability can be limited to less than 5% and 10%, respectively.