Excavation responses and reliability of soft rock tunnels considering spatial variability based on Copula theory

Purpose The purpose of this study is to investigate the effects of spatial variability and parameter correlation on the structural responses and reliability of moderately buried tunnels during excavation. The study aims to clarify how cross-correlated random fields (CRF) and stratigraphic anisotropy influence tunnel failure mechanisms and to provide quantitative insights for reliability-based tunnel design. Design/methodology/approach A stochastic numerical framework was developed based on Copula theory to generate CRF for the cohesion and internal friction angle of surrounding rocks. The random fields were incorporated into a two-dimensional numerical model, and 65,100 Monte Carlo simulations were performed to evaluate tunnel responses under various stratigraphic dip angles and Kendall correlation coefficients. The probability of tunnel failure was quantified using two indicators: crown settlement and the proportion of the plastic zone. Findings The results show that parameter correlation strongly affects tunnel reliability. As the Kendall correlation coefficient increases from negative to positive, the dominant failure mode shifts from crown-settlement-controlled to plastic-zone-dominated behaviour. The smaller of the horizontal and vertical scales of fluctuation (SOF) governs the lower bound of tunnel failure probability. Although the stratigraphic dip has limited influence on settlement, it significantly affects plastic zone development, revealing the anisotropic nature of spatial variability in rock masses. Originality/value This study provides a quantitative framework for integrating parameter correlation and spatial variability into tunnel reliability analysis. The findings enhance the understanding of anisotropic effects in red-bed rock masses and offer practical guidance for the design and risk assessment of tunnels in heterogeneous geological environments.