Probabilistic approaches to assessing variability in mechanical properties of rock masses by applying theory of extremes and Monte Carlo simulation

Rock mass, as a naturally formed material, shows great inherent variation on its mechanical properties which significantly influences its deformation and failure behaviors. Rock engineers deal with this variation from the initial stage of site characterization to the final design of the rock structures. Designers have been attempting to cope with this variation by using safety factors which do not consider the inherent variability of rock mass properties.; A probabilistic approach is proposed to assess the variability of rock mass mechanical properties which employs Monte Carlo simulation and theory of extremes. This method treats rock mass properties as random variables. The mechanical properties of intact rocks, as the input data for the simulation, are analyzed first by using theory of extremes to estimate their probability distributions. Then, Monte Carlo simulation is carried out. The results from the simulation are analyzed by applying theory of extremes. Finally, as application examples, the scale effect on rock mass mechanical properties and the calculation of an underground opening deformation are analyzed by using the proposed method.; The analyses indicate that the simulated mechanical properties of rock masses follow the third type asymptotic distribution of the smallest values as the data obtained from the laboratory and field borehole jacking tests show the same type of probability distribution. This proposed approach helps describe the nature of the inherent variability of mechanical properties of rock masses. It provides a means of assessing the variability of the rock mass properties which is difficult to be accomplished by experimental means. This extremal distribution is proposed as a probabilistic model to describe the behavior of mechanical properties of rock mass. Monte Carlo simulation is proposed as a general approach to estimate probability distributions of rock mass properties. The probability distribution characteristics of rock mass properties will help rock engineers to arrive at more rational designs for some critical underground structures, such as high-level nuclear waste repositories, compared to design methods based on the safety factor concept.