NorSand4AI: a comprehensive triaxial test simulation database for NorSand constitutive model materials
Authors: Ozelim Luan Carlos de Sena Monteiro , Casagrande Michéle Dal Toé , Cavalcante André Luís Brasil 
Published: April 2024

Abstract. In soil sciences, parametric models known as constitutive models (e.g., the Modified Cam Clay and the NorSand) are used to represent the behavior of natural and artificial materials. In contexts where liquefaction may occur, the NorSand constitutive model has been extensively applied by both industry and academia due to its relatively simple critical state formulation and low number of input parameters. Despite its suitability as a good modeling framework to assess static liquefaction, the NorSand model still is based on premises which may not perfectly represent the behavior of all soil types. In this context, the creation of data-driven and physically informed metamodels emerges. The literature suggests that data-driven models should initially be developed using synthetic datasets to establish a general framework, which can later be applied to experimental datasets to enhance the model's robustness and aid in discovering potential mechanisms of soil behavior. Therefore, creating large and reliable synthetic datasets is a crucial step in constructing data-driven constitutive models. In this context, the NorSand model comes in handy: by using NorSand simulations as the training dataset, data-driven constitutive metamodels can then be fine-tuned using real test results. The models created that way will combine the power of NorSand with the flexibility provided by data-driven approaches, enhancing the modeling capabilities for liquefaction. Therefore, for a material following the NorSand model, the present paper presents a first-of-its-kind database that addresses the size and complexity issues of creating synthetic datasets for nonlinear constitutive modeling of soils by simulating both drained and undrained triaxial tests. Two datasets are provided: the first one considers a nested Latin hypercube sampling of input parameters encompassing 2000 soil types, each subjected to 40 initial test configurations, resulting in a total of 160 000 triaxial test results. The second one considers nested quasi-Monte Carlo sampling techniques (Sobol and Halton) of input parameters encompassing 2048 soil types, each subjected to 42 initial test configurations, resulting in a total of 172 032 triaxial test results. By using the quasi-Monte Carlo dataset and 49 of its subsamples, it is shown that the dataset of 2000 soil types and 40 initial test configurations is sufficient to represent the general behavior of the NorSand model. In this process, four machine learning algorithms (Ridge Regressor, KNeighbors Regressor and two variants of the Ridge Regressor which incorporate nonlinear Nystroem kernel mappings of the input and output values) were trained to predict the constitutive and test parameters based solely on the triaxial test results. These algorithms achieved 13.91 % and 16.18 % mean absolute percentage errors among all 14 predicted parameters for undrained and drained triaxial test inputs, respectively. As a secondary outcome, this work introduces a Python script that links the established Visual Basic implementation of NorSand to the Python environment. This enables researchers to leverage the comprehensive capabilities of Python packages in their analyses related to this constitutive model.