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.

中文翻译：

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土壤复杂路径依赖行为的物理约束分层数据驱动建模框架

数据驱动的建模在描述路径相关的土壤响应方面具有相当大的潜力。然而，土壤行为的复杂性对训练效率和泛化能力提出了重大挑战。本研究提出了一种新的物理约束分层 (PCH) 训练策略，以应对使用数据驱动模型捕捉土壤行为的现有挑战。与以前的策略不同，所提出的分层训练涉及“低级”和“高级”神经网络，以及线性回归，其中神经网络的损失函数是使用物理定律构建的，以约束解决方案域。采用前馈和长短期记忆 (LSTM) 神经网络作为基线算法，以进一步增强本方法。然后，数据驱动模型在随机应变加载路径上进行训练，随后集成到自定义有限元 (FE) 分析中，以通过验证来解决边界值问题。结果表明，与传统的 LSTM 相比，所提出的 PCH-LSTM 方法提高了预测精度，需要的训练数据少得多，并且对精确网络架构的性能敏感性较低。当与有限元分析相结合时，PCH-LSTM 模型也被证明是在加载-卸载-再加载和比例应变加载路径下模拟土壤行为的可靠方法。此外，可以准确识别应变局部化和不稳定失效机制。