A physics knowledge-based surrogate model framework for time-dependent slope deformation: Considering water effect and sliding states

The surrogate model serves as an efficient simulation tool during the slope parameter inversion process. However, the creep constitutive model integrated with dynamic damage evolution poses challenges in development of the required surrogate model. In this study, a novel physics knowledge-based surrogate model framework is proposed. In this framework, a Transformer module is employed to capture strain-driven softening-hardening physical mechanisms. Positional encoding and self-attention are utilized to transform the constitutive parameters associated with shear strain, which are not directly time-related, into intermediate latent features for physical loss calculation. Next, a multi-layer stacked GRU (gated recurrent unit) network is built to provide input interfaces for time-dependent intermediate latent features, hydraulic boundary conditions, and water-rock interaction degradation equations, with static parameters introduced via external fully-connected layers. Finally, a combined loss function is constructed to facilitate the collaborative training of physical and data loss, introducing time-dependent weight adjustments to focus the surrogate model on accurate deformation predictions during critical phases. Based on the deformation of a reservoir bank landslide triggered by impoundment and subsequent restabilization, an elasto-viscoplastic constitutive model that considers water effect and sliding state dependencies is developed to validate the proposed surrogate model framework. The results indicate that the framework exhibits good performance in capturing physical mechanisms and predicting creep behavior, reducing errors by about 30 times compared to baseline models such as GRU and LSTM (long short-term memory), meeting the precision requirements for parameter inversion. Ablation experiments also confirmed the effectiveness of the framework. This framework can also serve as a reference for constructing other creep surrogate models that involve non-time-related across dimensions.