Tunnel Water Inflow Prediction and Uncertainty Quantification Using Vine Copula-Coupled Sparse Polynomial Chaos Expansion

Abstract

Accurate prediction and uncertainty quantification of tunnel water inflow are critical for construction safety, risk mitigation, and groundwater-control planning. However, conventional analytical and numerical methods are often limited by simplified assumptions and high computational cost, while many machine learning models lack reliable uncertainty quantification. To address these limitations, this study proposes a framework by coupling vine copula dependence modeling with sparse polynomial chaos expansion (SPCE). The framework utilizes a vine copula to characterize the asymmetric dependence among input parameters. Two distinct approaches are used to construct the SPCE models: the arbitrary polynomial chaos expansion (aPCE) method, assuming independence in the original space, and the Rosenblatt transform-based polynomial chaos expansion (Rt-PCE) method, which maps correlated inputs into an independent space via the Rosenblatt transform to establish rigorous orthogonal polynomials. Validation using a database of 600 cases shows that SPCE models achieve point accuracy comparable to artificial neural network (ANN) and Gaussian process regression (GPR) with superior numerical stability. Notably, Rt-PCE yields the best predictive robustness and outperforms both benchmarks in probability density fitting, particularly in capturing extreme tail behavior. Furthermore, the study confirms that neglecting input dependence biases probability estimations, whereas vine copula-based modeling effectively captures both the central tendency and tail features of inflow distributions. The proposed framework provides decision support for resource-efficient intervention planning under uncertain hydrogeological conditions.