A Methodology for Modeling a Multi-Dimensional Joint Distribution of Parameters Based on Small-Sample Data, and Its Application in High Rockfill Dams

The composition of high rockfill dam materials is complex, and the mechanical parameters are uncertain and correlated in unknown ways due to the influences of the environment and construction, leading to complex deformation mechanisms in the dam–foundation system. Statistical characteristics of material parameters are the basis for deformation and stress analysis of high core rockfill dams, and using an inaccurate distribution model may result in erroneous analysis results. Furthermore, empirically evaluated distribution types of parameters are susceptible to the influence of small sample sizes, which are common in the statistics of geotechnical engineering. Therefore, proposing a multi-dimensional joint distribution model for parameters based on small-sample data is of great importance. This study determined the interval estimation values of Duncan–Chang E-B model parameters—such as the mean value and coefficient of variation for the core wall, rockfill, and overburden materials—using parameter statistical analysis, bootstrap sampling methods, and Akaike information criterion (AIC) optimization. Additionally, the marginal distribution types of each parameter were identified. Subsequently, a multi-dimensional joint distribution model for Duncan–Chang model parameters was constructed based on the multi-dimensional nonlinear correlation analysis of parameters and the Copula function theory. The application results for the PB dam demonstrate that joint sampling can effectively reflect the inherent correlation laws of material parameters, and that the results for stress and deformation are reasonable, leading to a sound evaluation of the cracking risk in the core wall of high core rockfill dams.