Construction of Quasi-Site-Specific Geotechnical Transformation Models Using Bayesian Sparse Dictionary Learning

Transformation models commonly are used in geotechnical practice to estimate design parameters (e.g., friction angle ϕ) required for geotechnical design and analysis from measurement data obtained from laboratory or in situ tests [e.g., N values obtained from standard penetration tests (SPTs)]. Because many transformation models have been developed in the literature and site investigation data obtained from a specific site often are limited, it is challenging to select a suitable transformation model or develop a site-specific transformation model. To address this challenge, this study proposes a novel data-driven method called Bayesian sparse dictionary learning (SDL) for constructing a quasi-site-specific transformation model using existing transformation models from the literature and limited site-specific measurements. From a signal processing perspective, the proposed approach utilizes existing transformation models as basis functions, or atoms in SDL, and employs limited site-specific data to select nontrivial atoms for construction of a quasi-site-specific model and prediction. Existing transformation models and limited site-specific data are leveraged effectively in a systematic and coherent manner. Prediction uncertainty arising from limited site data is quantified under a Bayesian framework. Illustrative examples showed that the proposed approach efficaciously constructs a quasi-site-specific transformation model (e.g., a ϕ versus SPT-N model) and outperforms existing transformation models and traditional methods in terms of greatly reduced prediction uncertainty and significantly improved model fidelity, e.g., both interpolation and extrapolation of design parameters (e.g., ϕ) from measurement data (e.g., SPT N₆₀).