Application of deep learning in geotechnical engineering with a focus on constitutive models

Abstract

Constitutive models, which provide a relationship between stress and strain to predict the response of a material to external stimuli, are essential to solving boundary value problems. Constitutive models were traditionally developed by selecting analytical relationships whose parameters were obtained from experimental observations. Due to the limitations of traditional experimental setups, the constitutive models were initially limited to certain loading and boundary conditions. With the advent of new experimental setups such as digital image correlation, X-ray computed tomography, digital volume correlation, and computational methods, the potential to obtain large stress-strain databases that account for complex loading and boundary conditions, has significantly increased. Moreover, the advances in statistical modeling, specifically deep learning methods, along with computing capabilities have provided new tools for predicting insights and patterns from datasets. As such, deep learning methods have yielded improved accuracy of traditional constitutive models by either replacing or complementing classical constitutive models. Although deep learning-derived constitutive models have been shown to yield cohesive and complete frameworks, the reliability of their predictions is linked to the quality of the training dataset. Accordingly, the objectives of this study are to identify methods and test their effectiveness in evaluating the quality, completeness, and consistency, of databases for developing stress-strain relationships via deep learning. The study includes elastic linear and nonlinear constitutive models, domain heterogeneity, and load path dependency, along with different machine learning techniques. Complete, biased, and distorted stress-strain datasets were constructed to evaluate the effectiveness of various methods in determining the quality of the dataset. Lastly, deep learning constitutive model predictions were assessed using simulations for well-documented geotechnical engineering problems.