Hypoplastic Model Predictions for Ennore Sand Under Monotonic and Cyclic Loading Conditions
Authors: Wani S. , Rehman M. U. , Rao M. S. , Kadasami R. K. , Banerjee S. 
Published: August 2024

ABSTRACT:
The hypoplastic constitutive model is widely utilized for simulating soil behaviour. This study investigates the applicability of the hypoplastic model in predicting the mechanical behaviour of sand under both monotonic and cyclic loading conditions. Monotonic loading conditions are explored to comprehend the soil's strength and deformation characteristics, while cyclic loading conditions are crucial for understanding the soil's response under repeated loading, particularly its behaviour during the unloading and reloading phases. In this research, monotonic and cyclic triaxial drained tests were conducted on Ennore sand under various confining pressures. It is observed that with an increase in confining pressure, there is an increase in stiffness and a decrease in the dilative response. The advanced hypoplastic model is calibrated for Ennore sand, and model predictions are compared with the experimental results. It is noticed that the hypoplastic model, integrated with the memory surface and intergranular strain (MS-IS), performs more effectively under cyclic conditions compared to the basic hypoplastic model. However, the most advanced MS-IS hypoplastic model still falls short in predicting a realistic volumetric response during the unloading and reloading phases.

1 INTRODUCTION
Sand, a common and widely used granular material, is subjected to cyclic loading in various situations, such as during earthquakes, offshore structures, and foundation systems (Kumar and Kandasami, 2023). Understanding and accurately modelling the behaviour of sand under cyclic loading will allow engineers to predict the response of sandy soils, which is crucial for designing structures that can withstand dynamic forces and avoid potential failures. Moreover, modelling the sand behaviour also plays a pivotal role in optimizing construction techniques and materials, ensuring the durability and stability of structures over time. The cyclic behaviour of sand depends on the effective confining pressure, void ratio, density, and initial/boundary conditions.
Typically, the constitutive modelling of sand is "stress-based", where one or more yield surfaces exist inside the stress space (Fuentes and Triantafyllidis, 2015). These stress-based models include traditional plasticity theory based models (Pastor et al., 1990; Heidarzadeh and Oliaei, 2018), bounding surface models (Dafalias and Hermann, 1982; Dafalias, 1986), multisurface plasticity models (Mroz, 1967, 1969; Mroz and Norris, 1978), subloading plasticity (Hashiguchi, 1980, 1989, 2023), hypoplastic models (Wu and Bauer, 1994; Wu and Niemunis, 1996; Wu and Kolymbas, 2000; Bauer and Wu, 1993; He et al., 2022) and neohypoplasticity models (Loges and Niemunis, 2015; Niemunis et al., 2016; Niemunis and Grandas Tavera, 2019; Mugele et al., 2024) combined with the critical state framework to predict the behaviour of sand under diverse loading conditions. Over a period of time, these models have been modified and enhanced to include the dependency of stiffness on the void ratio and Lode angle, the small strain effect on loading reversal, and cyclic mobility. Among these models, the adoption of the hypoplastic model to predict the sand response under complex loading conditions has gained momentum due to its simplicity. Wu and Bauer (1994) developed the hypoplastic model specifically for granular materials based on tensor polynomial and representation theory, offering a unique framework distinct from classical elastic-plastic theories, which were initially designed for metals. Subsequent modifications to the hypoplastic model included the integration of density and stiffness functions to account for the void ratio's impact on the strength (Bauer and Wu, 1993; Wu et al., 1996; Wu and Kolymbas, 2000). However, limitations such as unrealistic stress-strain/volume change behaviour during drained cyclic loading, as well as inaccuracies in predicting stiffness, stress path, and pore pressure during undrained cyclic loading, restrict its usage in a wide range of applications. The rationale behind this limitation is that the model fails to capture the material's stress history, as demonstrated by the experiments. Variations in the behaviour of granular materials during the unloading phase of cyclic loading were observed in experimental experiments. These variations may have been caused by changes in the force chain, fabric, or density, which resulted in anisotropic features and stiffness change (Kandasami and Murthy, 2017). Thus, it is essential to capture the loading history of sand during the cyclic loading. Recently in 2023, the memory surface model and intergranular strain concepts were incorporated in the hypoplastic model by Alipour and Wu (2023) to predict the cyclic response of granular materials.