Geomechanical characterization of an anisotropic fractured rock mass using fuzzy system and Monte Carlo simulation

Characterizing fractured rock masses is a major challenge in geotechnical and mining engineering because of uncertainties in both intact rock properties and fracture behavior. These uncertainties reduce confidence in the estimation of geomechanical parameters, which are critical for reliable design. Deterministic approaches often rely on mean values and therefore underestimate or overestimate variability, leading to unsafe or overly conservative outcomes. This study proposes an integrated framework that combines fuzzy logic with Monte Carlo simulation to quantify uncertainty in fractured rock mass properties. Seven key parameters—Poisson’s ratio, Young’s modulus, uniaxial compressive strength (UCS), cohesion, friction angle, and the Hoek–Brown constants m and s—were modeled as fuzzy variables using triangular membership functions. Degrees of membership (DoM) from ۰.۲ to ۰.۸ were applied to define parameter ranges, and Monte Carlo simulation with ۲۵۰۰۰ iterations was conducted for each DoM level to derive ۹۵% confidence intervals. Results show that confidence intervals consistently narrow as DoM increases, indicating reduced uncertainty. Two quantitative indices—confidence interval width (CIW) and relative uncertainty (RU)—were introduced, confirming that higher DoM levels correspond to lower uncertainty. A sensitivity analysis further demonstrated that while normal distributions yield narrower intervals due to small standard deviations, log-normal and uniform distributions capture broader variability. Additional tests with intermediate DoM values confirmed the stability and robustness of the framework. Overall, the fuzzy–Monte Carlo approach offers a systematic and practical tool for uncertainty quantification in rock engineering. By incorporating variability into parameter estimation, the method enhances the reliability of numerical modeling and provides stronger support for reliability-based geotechnical design.

کلیدواژه ها:

Uncertainty ، Geomechanical characterization ، Fractured Rock Mass ، Fuzzy ، Monte Carlo simulation