Stochastic tunnel convergence in spatially variable medium using rotated and non-rotated anisotropic random fields with adaptive surrogate model

Deterministic analysis of tunnel convergence completely neglects the uncertainties present in geotechnical parameters, while conventional probabilistic approaches treat inputs as random variables but often ignore the spatial variability of soil. Traditional methods, such as Monte Carlo simulations (MCS), become impractical for computationally expensive numerical models. Previous studies have primarily considered isotropic or non-rotated anisotropic variability, with limited attention to rotated anisotropic correlation structures. Although surrogate models improve MCS efficiency, their capability to address high-dimensional problems of rotated random fields remains very limited. This study presents a probabilistic framework for tunnel convergence analysis that incorporates spatial soil variability via an adaptive sparse polynomial chaos expansion (SPCE) surrogate model, further enhanced by global sensitivity analysis (GSA) to improve computational efficiency. The spatial variability of Young’s modulus is modelled as a two-dimensional (2D) random field using the Karhunen-Loève (K-L) expansion. The influence of isotropic and rotated anisotropic random fields on tunnel convergence is investigated. Results show that the rotation angle significantly affects vertical displacement under anisotropic conditions, whereas its impact is less pronounced under isotropic conditions. Additionally, an increase in correlation length leads to greater tunnel displacement. Both surrogate models (adaptive SPCE and GSA-based SPCE) demonstrate high computational efficiency without compromising accuracy. Compared to MCS, adaptive SPCE reduces the number of simulations by 75%, while GSA-based SPCE achieves computational cost reductions of 92.5% and 97.5% for anisotropic and isotropic cases, respectively.