A multi-dimensional cloud-model-based fuzzy evaluation method for grading nonlinear tunnel large deformation

Abstract Tunnel large deformation is governed by coupled effects of rock mass strength, groundwater, and discontinuity conditions. In practice, blurred grade boundaries and inconsistent indicator definitions often undermine the stability and interpretability of conventional threshold-based grading and single-weighting methods, especially in cross-project applications. This study develops a multi-dimensional cloud-model-based fuzzy grading framework for nonlinear large deformation. Under predefined grading intervals, asymmetric cloud models are established to derive membership (association) intervals of each indicator across grades; the upper–lower envelope bandwidth of these intervals is further extracted to quantify sample dispersion and variability, thereby mitigating boundary sensitivity. A subjective–objective integrated weighting strategy is adopted: subjective weights are obtained from an expert scoring matrix, while objective weights are computed using EWM, CRITIC, PCA, and TOPSIS. The representative objective scheme is selected based on grading accuracy and then fused with the subjective weights to form comprehensive weights. Moreover, a same-grade coupling mechanism is introduced to construct pairwise coupling cloud models, which quantify the joint support of indicator combinations for grade discrimination and provide interpretable explanations for misclassifications with actionable optimization directions. Validation on Telmo, Huangjiagou, and Muzhailing datasets yields accuracies of 88%, 90%, and 85%, outperforming single-weighting schemes. Aggregating the three projects produces a global ranking of 13 indicators, offering a unified, robust, and interpretable basis for grading, early-warning prioritization, and mitigation optimization.