# Integrated Neural Network and Finite Element Analysis for constitutive modelling of soil

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## Abstract

Finite Element Analysis is an application used in many engineering fields, including geotechnical engineering. With increasing complexities of structures and material behavior, classical approach for non-linear finite element analysis has become computationally expensive (Gulikers, 2018). In order to improve the efficiency and accuracy of the model, Machine Learning (ML) is introduced. The ever-increasing accessibility and magnitude of computational power has made machine learning gained popularity since 1990s. Artificial Neural Networks have especially been proven to be a versatile machine learning framework, capable of solving complex tasks such as voice recognition to solving failure analysis of structures. This thesis aims at implementing soil constitutive models such as Linear Elastic and Elasto-plastic models and integrating them into a Finite Element Engine. Two different approaches have been attempted to implement the ANN into the constitutive models. The first approach involves the implementation of a "Generic" Neural network to simulate the natural anisotropic behavior of soils. Datasets have been generated with the help of theoretical soil tests classified as ‘Standard’ and ‘Non-standard’ tests. The standard tests depict an isotropic behavior, where the strains and stresses in different directions are proportionate. Non-standard tests consist of data representing anisotropic behavior where the strain increments in every direction are randomized. The neural network has first been implemented for a linear elastic soil model. Itis observed that when the network is trained and tested with similar kind of data, predictions are accurate. However, when the neural network is trained with a certain type of data (such as standard test), it is unable to predict the response for the other data (non-standard test). When the neural network (trained with standard data) is subsequently implemented in Finite Element analysis by deriving and substituting the material stiffness matrix from the neural network in a constitutive model, the difference between the isotropic linear elastic matrix (for linear elastic model) and the matrix derived from the neural network lead to significant errors, despite the accurate predictions of the neural network. The second approach is a component based approach in which the neural network is modeled to learn the typical behaviors of soil such as linear elasticity and plasticity. The data for training and testing the neural network are generated using standardized laboratory tests (CRS, DSS, Biaxial etc.). The neural network is modeled for linear elastic soil, by applying certain weight constraints. It is observed that the neural network has accurate predictions. Further implementation in constitutive model shows that the neural network is able to mimic the behavior of Linear elastic soil model. The neural network model, is subsequently implemented to predict Mohr-Coulomb behavior, and the predictions are significantly accurate. Further the generalization ability of the network is analyzed to evaluate the practical applicability of the network, followed by a sensitivity analysis to get an understanding about the influencing parameters in the network. The devised neural network, when implemented in a constitutive model displays a behavior similar to the theoretical constitutive model of Mohr-Coulomb soil. Finally, this thesis concludes with the implementation of the neural network constitutive model in Finite Element Analysis where it leads to convergence errors in the model.