Quantifying the cross-correlation between effective cohesion and friction angle of soil from limited site-specific data

The effective cohesion (c′) and effective friction angle (ϕ′) of soil are important soil parameters required for evaluating stability and deformation of geotechnical structures. It is well known that there is cross-correlation between c′ and ϕ′ of soil and that this cross-correlation affects reliability analysis of geotechnical structures. Ignoring the cross-correlation between c′ and ϕ′ may lead to a biased estimation of failure probability. It is therefore important to properly quantify the cross-correlation between c′ and ϕ′ of soil for geotechnical analysis and design. However, the c′ and ϕ′ data obtained from field and/or laboratory tests for a project are usually limited and insufficient to provide a meaningful joint probability distribution of c′ and ϕ′ or quantify their cross-correlation. This poses a significant challenge in engineering practice. To address this challenge, this paper develops a Bayesian approach for characterizing the site-specific joint probability distribution of c′ and ϕ′ and quantifying the cross-correlation between c′ and ϕ′ from a limited number of c′ and ϕ′ data obtained from a project. Under a Bayesian framework, the proposed approach probabilistically integrates the limited site-specific c′ and ϕ′ data pairs with prior knowledge, and the integrated knowledge is transformed into a large number of c′ and ϕ′ sample pairs using Markov Chain Monte Carlo (MCMC) simulation. Using the generated c′ and ϕ′ sample pairs, the correlation coefficient of c′ and ϕ′ is estimated, and the marginal and joint distributions of c′ and ϕ′ are evaluated. The proposed approach is illustrated and validated using real c′ and ϕ′ data pairs obtained from direct shear tests of alluvial fine-grained soils at Paglia River alluvial plain in Central Italy.