Soil Constitutive Modelling Using Neural Networks

Abstract

Constitutive models are one of the main building blocks of the Finite Element Analysis that nowadays is used in almost every geotechnical engineering project. Thus, finding realistic stress-strain behaviour models has been one of the main fields of research in Geotechnical Engineering. However, constitutive equations have become increasingly complex featuring 10 or more parameters as inputs with sometimes small correlations to physical properties (Beaty & Byrne, 1998; Bauer, 1996). Thus, a more data driven approach can be determined to account for that issue. In this thesis, that data driven approach will be attempted by using Neural Networks. The main goal of the thesis is to access if Neural Networks can be used to model constitutive soil behaviour. Specifically, two approaches are used to model stress-strain behaviour of soils.
The first approach is classified as a generic approach because the investigation is mostly focused on which techniques of the Neural Network can help with the modelling of stress and strain behaviour. In that way the Network can be thought of as a “black box”. The prediction after the training of the Neural Network is achieved by dataset retrieved inputs and from inputs that are retrieved from the last step of the prediction. The latter has the objective of replicating the prediction as it is achieved from a typical constitutive model. The aim is the minimisation of errors after training. The feedback and the non-feedback predictions do not produce the same results which imply that the network is sensitive towards a certain input. This is further validated by conducting a sensitivity analysis and by looking into the activation of each node for certain loading cases. Dropout and reassessing the inputs and outputs are attempted to resolve this issue but the results remain erroneous.
The second approach is to create a component based Neural Network. In this case a link is created between the function of the neural Network and typical soil behaviour. The linear elastic model is modelled with a linear activation function. In this case the network is successful in reproducing the full linear-elastic matrix. The linear elastic perfectly plastic model is modelled by connected the linear elastic matrix with a ReLU layer as it is seen in continuum mechanics. The Neural Network accurately predicts the stress-strain relationship. And it can be used to also predict the stress path of “noisy” datasets. However, when trained with noise the signal added to the training dataset is recognised as a pattern from the Neural Network. Finally, the work hardening model does not successfully model the stress-strain relationship as it tends to exaggerate the contribution of the stress input versus the strain input. All in all, this is an effort towards the development of a Neural Network constitutive model with the final aim of producing data driven constitutive models.