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

Abstract

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.

Hydraulic conductivity variation in compacted bentonite–fly ash mixes under constant-volume and free-swelling flow conditions

“…Bentonite (B) was used to construct a liner layer adhering to both the permeability and strength criterion (Marcial et al 2002;Meier and Shackelford 2017). Due to high specific surface area, B is also an ideal retention medium there by limiting the migration of contaminants to groundwater (Sharma et al 2021). However, the compacted clay liner constructed with only B is susceptible to high swelling, shrinkage cracks, poor compressive strength, high compressibility and uneconomical for mass utilization (Daniel and Benson 1990;Gilbert et al 1996;Komine and Ogata, 2003;Budihardjo et al 2021).…”