Probabilistic transformation models for preconsolidation stress based on clay index properties

- A transformation model for preconsolidation stress based on clay index properties is developed.
- The model is probabilistic because it predicts the PDF of preconsolidation stress.
- Validation shows that the model outperforms previous models proposed in the literature.
- Analytical forms for the model are available. Engineers do not need to derive Bayesian equations.

This paper develops probabilistic transformation models that predict the probability density function (PDF) of the preconsolidation stress (σ′p) of a clay based on its index properties. These probabilistic transformation models are more versatile than traditional transformation models that only provide point estimates, because the PDF can quantify the transformation uncertainty in σ′p and also can be further used to develop median and confidence interval estimates for σ′p. The confidence interval is especially useful because the transformation uncertainty in σ′p is fairly significant. Three probabilistic transformation models are developed: one is a generic model and the other two are models specialized for contractive and dilative clays. The generic model is applicable to both contractive and dilative clays, but its transformation uncertainty is larger. The two specialized models require the prior knowledge about the contractive/dilative behavior for the clay of interest, but their transformation uncertainties are smaller. The performances of the three probabilistic transformation models are verified by statistical cross-validation and independent validation database. The analytical forms for the median and confidence interval estimates are presented in this paper so that engineers do not need to derive the Bayesian equations.