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 (LTACs) 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 crosscorrelated random field modelling method is employed to investigate the surface settlement caused by shield tunnel construction. The effects of different LT-ACs of (c, f), (c, E), and (f, E) on the surface deformation of shield tunnel excavation are revealed.