Abstract: Rapid prediction of soft soil foundation consolidation is essential for embankment stability assessment and post- construction settlement evaluation. Existing data-driven models often rely on large-scale labeled samples and neglect the governing physical mechanisms, which limits their accuracy and generalization under complex drainage boundaries and stratigraphic conditions. To address this issue, a physics-informed deep operator model, termed TDC-PI-DeepONet (time-dependent consolidation- physics-informed DeepONet), is proposed by incorporating Terzaghi’s consolidation theory into the DeepONet (deep operator network) framework. In the proposed model, the branch network encodes the consolidation coefficient field, while the trunk network takes the time-depth coordinates as input. Their feature representations are combined to learn the nonlinear operator mapping from the consolidation coefficient field to the spatiotemporal evolution of excess pore water pressure. Considering the spatial variability of soil properties, lognormal Gaussian random fields are used to generate consolidation coefficient samples, and the governing equation, initial condition, and boundary conditions are embedded into the loss function as physical residuals. The model is validated using single-layer and double-layer consolidation cases under different drainage boundaries and is compared with analytical solutions, PINNs (physics-informed neural networks), and standard DeepONet. The results indicate that, compared to the PINNs, the TDC-PI-DeepONet model exhibits more accurate prediction for pore pressure dissipation under various stratigraphic and drainage conditions. The error level is overall lower and the distribution is more concentrated. Based on the statistical results of the test set EL2, the average error of the model is reduced by approximately 26%, and the deduction time for new cases is reduced from hundreds of seconds to tens of milliseconds. When compared to the DeepONet model, the TDC-PI-DeepONet model achieves lower errors and more stable predictions in multilayer heterogeneous cases. The TDC-PI-DeepONet model provides an efficient and physically consistent approach for rapid consolidation prediction of complex soft soil foundations.

Key words: soft soil foundation, consolidation coefficient, operator model, Gaussian random field, rapid prediction