Physics‐constrained hierarchical data‐driven modelling framework for complex path‐dependent behaviour of soils

Abstract There is considerable potential for data‐driven modelling to describe path‐dependent soil response. However, the complexity of soil behaviour imposes significant challenges on the training efficiency and the ability to generalise. This study proposes a novel physics‐constrained hierarchical (PCH) training strategy to deal with existing challenges in using data‐driven models to capture soil behaviour. Different from previous strategies, the proposed hierarchical training involves ‘low‐level’ and ‘high‐level’ neural networks, and linear regression, in which the loss function of the neural network is constructed using physical laws to constrain the solution domain. Feedforward and long short‐term memory (LSTM) neural networks are adopted as baseline algorithms to further enhance the present method. The data‐driven model is then trained on random strain loading paths and subsequently integrated within a custom finite element (FE) analysis to solve boundary value problems by way of validation. The results indicate that the proposed PCH‐LSTM approach improves prediction accuracy, requires much less training data and has a lower performance sensitivity to the exact network architecture compared to traditional LSTM. When coupled with FE analysis, the PCH‐LSTM model is also shown to be a reliable means of modelling soil behaviour under loading‐unloading‐reloading and proportional strain loading paths. In addition, strain localisation and instability failure mechanisms can be accurately identified. PCH‐LSTM modelling overcomes the need for ad‐hoc network architectures thereby facilitating fast and robust model development to capture complex soil behaviours in engineering practice with less experimental and computational cost.