Nearest Linear Failure Surface, a New Method to Determine the Reliability of Numerical Models in Geomechanics

In geomechanical systems, reliability analysis aims to determine the failure probability according to the uncertainties existing in rock mass properties and support materials, as well as diagnosing the significance of each uncertainty. Although there are very diverse methods to determine the reliability of geomechanical models, the employment of precise methods for determining the reliability of a numerical model is practically impossible due to computational difficulties. The only general solution to solve the reliability problem is to use Monte Carlo simulation. However, for most systems, with engineering accuracy, thousands of realizations are required to use Monte Carlo simulation. Although this number of realizations for analytical functions can be performed very quickly, running this number of realizations for a numerical code is practically impossible. In the proposed Nearest Linear Failure Surface method (NLFS), with the least number of runs, the reliability of rock space and its failure probability is investigated during a short period of time and with appropriate accuracy. The idea of the NLFS method is inspired by finding the design point (β-point in the well-known First Order Reliability Method) assuming that the performance function is linear. In this research, a computer code has been developed to implement the NLFS method and by combining this code with FLAC 2D software, reliability of an underground road tunnel with uncertain cohesion, friction angle, and tensile strength of surrounding rock was determined. The results indicate the high efficiency of the proposed method in determining the reliability of numerical models in a very short time and with high accuracy.