A novel consolidation analysis framework: universal function approximators regularized by physical principles

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Abstract
Analytical and numerical techniques are widely used to analyze and interpret soil consolidation problems. An important limitation is the requirement for significant geotechnical knowledge and expertise to derive “true” solutions. This study proposes an alternative: a universal function approximator regularized with known physical principles. The proposed approach here advances previous work to solve one-dimensional consolidation considering both self-weight and large strains, as well as two-dimensional consolidation by vertical drains. Initial and boundary conditions of the studied consolidation problems are first strongly and weakly enforced for comparison. A neural network is adopted here as the function approximator. To boost prediction accuracy, a novel strategy is proposed to adaptively sample data points for training. An estimate of epistemic uncertainty is achieved using the confidence interval of ensembled multiple outputs. The results show that the proposed approach accurately predicts the behaviors of complex consolidation processes. Results also indicate that regularization using weak physical constraints can alleviate the imbalance of back-propagated gradients of different loss terms and, in turn, achieve higher accuracy. The proposed method is generic, mesh-free, more robust, and can be applied to a wide range of geotechnical problems.

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