Improvement of Bivariate Cross-Correlated Random Field Modeling Based on Archimedean Copulas

In this study, the bivariate random field modelling method considering different dependent structures between soil parameters based on Laplace-transformed Archimedean copulas (LT-ACs) is improved and employed to investigate the soil deformation performance caused by shield tunnelling. Firstly, based on copula theory and the two-step idea, a bivariate joint cumulative distribution function (CDF) is constructed by combining marginal distributions and LT-ACs. The marginal distributions are used to characterize the randomness of a single geotechnical parameter, and the LT-ACs are used to characterize the dependences between geotechnical parameters. Next, to improve the sampling efficiency, the Marshall-Olkin (M-O) algorithm based on the inverse Laplace transform is employed to sample the LT-ACs. Combined with the covariance matrix decomposition method, the improved approach is utilized to generate a bivariate cross-correlated random field. The modelling feasibility and efficiency superiority of the proposed approach is verified through comparative analysis. Finally, the improved cross-correlated random field modelling method is employed to investigate the surface settlement caused by shield tunnel construction. The effects of different LT-ACs of (c, ϕ), (c, E), and (ϕ, E) on the surface deformation of shield tunnel excavation are revealed.