An Improved Optimal Cloud Entropy Extension Cloud Model for the Risk Assessment of Soft Rock Tunnels in Fault Fracture Zones

Abstract

Existing risk assessment approaches for soft rock tunnels in fault-fractured zones typically employ single weighting schemes, inadequately integrate subjective and objective weights, and fail to define clear risk. This study proposes a risk-grading methodology that integrates an enhanced game theoretic weight-balancing algorithm with an optimized cloud entropy extension cloud model. Initially, a comprehensive indicator system encompassing geological (surrounding rock grade, groundwater conditions, fault thickness, dip, and strike), design (excavation cross-section shape, excavation span, and tunnel cross-sectional area), and support (support stiffness, support installation timing, and construction step length) parameters is established. Subjective weights obtained via the analytic hierarchy process (AHP) are combined with objective weights calculated using the entropy, coefficient of variation, and CRITIC methods and subsequently balanced through a game theoretic approach to mitigate bias and reconcile expert judgment with data objectivity. Subsequently, the optimized cloud entropy extension cloud algorithm quantifies the fuzzy relationships between indicators and risk levels, yielding a cloud association evaluation matrix for precise classification. A case study of a representative soft rock tunnel in a fault-fractured zone validates this method’s enhanced accuracy, stability, and rationality, offering a robust tool for risk management and design decision making in complex geological settings.