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. Popular approach is to employ transformation models for its 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 (278×5) for parameters liquid limit (LL), plasticity index (PI), clay fraction (CF), CEC and SSA (labelled as CLAY/C-S/5/278) is developed. Thereafter, multivariate
distribution for the five parameters in the database is constructed using vine copula approach.
Implementation of the proposed approach is demonstrated by updating prior/unconditional probability density function (PDFs) of CEC and SSA given single/ multiple clay parameters using
Bayes’ rule. The posterior/conditional PDFs of CEC and SSA are also summarized as practitioner friendly analytical expressions. Two geotechnical application examples are also shown. In the proposed approach, CEC and SSA are characterized by their complete joint distribution, and is, therefore, superior to the popular deterministic transformation approach in literature.
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