Data for figures 3–5.

This paper proposes a physics-informed extreme learning machine (PIELM) for analyzing consolidation immediately after cavity expansion. The deep neural networks in traditional physics-informed neural network (PINN) framework are substituted by the extreme learning machine (ELM) network with only one hidden layer. By using exact definition of stress invarients, the distribution of excess water pressure after cavity expansion is rigorously incorporated into PIELM framework as initial conditions. Then, a loss vector is obtained by combining governing equation, initial conditions and boundary conditions, and the ELM network can be directly trained by optimising the loss vector via the least squares method. It is found that: (i) the PIELM approach can provide accurate prediction for consolidation analysis after cavity expansion; and (ii) the dissipation of excess water pressure heavily relies on its initial distribution that is related to soil mechanical behaviour. This proposed approach can serve as an efficient tool to interpret consolidation coefficient from piezocone penetration tests (CPTU) with measured data.

本文提出了一种用于圆孔扩张后即刻固结分析的物理信息极限学习机（physics-informed extreme learning machine, PIELM）。传统物理信息神经网络（physics-informed neural network, PINN）框架中的深度神经网络，被仅含单隐藏层的极限学习机（extreme learning machine, ELM）网络所替代。通过采用应力不变量的精准定义，将圆孔扩张后的超孔隙水压力分布作为初始条件，严格融入PIELM框架之中。随后，通过结合控制方程、初始条件与边界条件得到损失向量，并借助最小二乘法对损失向量进行优化，即可直接训练ELM网络。研究结果表明：（i）PIELM方法可对圆孔扩张后的固结分析实现精准预测；（ii）超孔隙水压力的消散过程极大程度依赖于其与土体力学行为相关的初始分布。所提方法可作为一种高效工具，基于实测数据从孔压静力触探试验（piezocone penetration tests, CPTU）中反演固结系数。