Probabilistic estimation of specific surface area and cation exchange capacity: a global multivariate distribution

Specific surface area (SSA) and cation exchange capacity (CEC) are two fundamental clay properties. However, the determination of CEC and SSA is challenging due to inherent uncertainties and difficulty in experimental measurement. A popular approach is to employ transformation models for their estimation. However, most of the existing models were developed on limited sample sizes and quantification of uncertainty associated with the estimate is not possible. Therefore, this study proposes a multivariate probabilistic approach for estimation of CEC and SSA. First, a five-dimensional database (278 x 5) for the parameters liquid limit (LL), plasticity index (PI), clay fraction (CF), CEC, and SSA (labelled as CLAY/GS/5/278) is developed. Thereafter, multivariate distribution for the five parameters in the database is constructed using the vine copula approach. Implementation of the proposed approach is demonstrated by updating the prior-unconditional probability density functions (PDFs) of CEC and SSA given single or multiple clay parameters using Bayes' rule. The posterior or conditional PDFs of CEC and SSA are also summarized as practitioner-friendly analytical expressions. Two geotechnical application examples are shown as well. In the proposed approach, CEC and SSA are characterized by their complete joint distribution and therefore this approach is superior to the popular deterministic transformation approach in literature.