Modelling dependency of multivariate soil parameters using various vine copula models

Abstract

Copula-based approaches have been increasingly employed to model the dependency among soil parameters. Nevertheless, existing applications are predominantly confined to conventional low-order bivariate copulas, which limits their capability to capture complex multivariate dependency structures. To overcome this limitation, this study introduces the use of vine copula models for advanced dependency modelling in geotechnical engineering. To demonstrate the applicability of various vine copula structures, a slope reliability analysis framework was developed by integrating Monte Carlo simulation with a Multilayer Perceptron regression model. The influence of different vine copula configurations on the estimated probability of failure was systematically examined, and their performance was rigorously evaluated. The results reveal that the choice of vine copula structure has a significant impact on the predicted failure probability. Moreover, the proposed vine copula models exhibit closer agreement with the observed statistical characteristics of soil parameters compared to the traditional multivariate normal distribution approach. Overall, this study provides practical insights into the selection and construction of appropriate vine copula models for high-dimensional dependency modelling, particularly in geotechnical applications. The proposed framework enables more reliable estimation of slope failure probabilities.

 Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 213-230.