# Physics-informed extreme learning machine (PIELM) for consolidation around an expanded cylindrical cavity

## TL;DR

This paper introduces a physics-informed machine learning method to analyze soil consolidation after cavity expansion, offering accurate predictions and insights into water pressure dissipation.

## Contribution

The novel approach replaces deep neural networks in PINNs with a single-layer ELM network, improving efficiency while maintaining accuracy.

## Key findings

- The PIELM approach provides accurate predictions for consolidation analysis after cavity expansion.
- Excess water pressure dissipation depends heavily on its initial distribution, which is influenced by soil mechanical behavior.

## Abstract

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.