Constitutive and numerical modeling of hydro-mechanically coupled behavior of unsaturated soils

Abstract

This dissertation presents a comprehensive theoretical and numerical investigation into the complex hydro-mechanically coupled behavior of unsaturated soils. Geotechnical materials existing above the groundwater table are characterized by a three-phase composition of solid particles, pore water, and pore air, giving rise to matric suction. This suction fundamentally alters the soil's mechanical properties, typically increasing its stiffness and shear strength, but also introducing complex phenomena such as collapse upon wetting. Accurate prediction of the behavior of these soils is critical for the safe and economical design of a wide range of geotechnical structures, including foundations, slopes, embankments, and earth-retaining systems. However, the intricate interplay between the hydraulic and mechanical responses presents significant challenges for constitutive modeling and numerical analysis. This research addresses these challenges by developing an advanced elasto-plastic constitutive model and implementing it within a robust finite element framework capable of solving complex boundary value problems under various loading conditions. The investigation begins with a thorough review of the foundational principles of unsaturated soil mechanics, establishing the context and identifying the limitations of existing approaches. A central issue in the field is the definition of an appropriate stress state. While single effective stress concepts, such as Bishop's effective stress, offer a convenient extension from saturated soil mechanics, they have been shown to have significant limitations in universally capturing the distinct effects of net stress and suction on both volumetric and deviatoric behavior. Consequently, this work adopts the more versatile independent stress variable framework, utilizing net stress and matric suction to separately yet concurrently govern the unsaturated soil's response. This approach provides a more rigorous foundation for modeling the independent mechanisms of deformation induced by mechanical loading and changes in moisture content. The literature review further examines established elasto-plastic models, with a particular focus on the Barcelona Basic Model (BBM), which pioneered the application of critical state concepts to unsaturated soils. While transformative, BBM and its derivatives have certain significant limitations, particularly concerning the interaction of different yield mechanisms and the formulation of hardening laws. This dissertation aims to build upon this foundational work by proposing a new model that addresses these specific issues. The primary theoretical contribution of this research is the formulation of a novel, fully coupled hydro-mechanical constitutive model for unsaturated soils. The model is developed within an elasto-plastic framework and is designed to capture the key features of unsaturated soil behavior with enhanced accuracy. A significant innovation lies in the improved formulation of the yield surfaces. The model incorporates a Loading-Collapse (LC) yield surface, which governs plastic yielding due to changes in net stress, and a Suction Increase (SI) yield surface, which controls plastic deformation resulting from drying. The formulation addresses the issue of the intersection between these surfaces in stress space by adopting a smooth, rounded shape, which overcomes numerical difficulties and provides a more realistic representation of yielding under combined loading paths involving simultaneous changes in net stress and suction. One of the cornerstones of the proposed model is a novel combined volumetric-deviatoric hardening rule. In many existing models, hardening is driven solely by plastic volumetric strain, which can be insufficient for capturing the full spectrum of soil behavior, especially under shear stress. The new rule makes the pre-consolidation pressure, which defines the size of the yield surface, dependent on both the accumulated plastic volumetric strain and the accumulated plastic deviatoric strain. This allows the model to more accurately simulate phenomena such as stiffness degradation and strength evolution under complex, non-isotropic stress paths, providing a more robust prediction of soil response from initial loading through failure. The coupling between hydraulic and mechanical behavior is a central theme of the model's formulation, reflecting the physical reality that these two processes are inseparable in unsaturated soils. This two-way coupling is explicitly integrated into the framework. The influence of the mechanical state on the hydraulic response is captured by making the Water Retention Curve (WRC), which defines the relationship between suction and water content, dependent on void ratio of the soil. As the soil compresses or swells under mechanical load, its pore structure changes, and this formulation ensures that its water retention properties are updated accordingly. Conversely, the influence of the hydraulic state on the mechanical response is fundamentally embedded in the core of the proposed model. Changes in matric suction and degree of saturation directly affect the size and shape of the yield surface through the hardening laws. This allows the model to naturally capture critical behaviors such as the increase in soil stiffness and strength upon drying and the potential for sudden volume reduction, or collapse, upon wetting under a constant applied load. To enable the analysis of practical engineering problems, the developed constitutive model is implemented into a sophisticated numerical framework based on the finite element method. The foundation of this framework is a rigorous derivation of the governing equations for multi-phase porous media, derived from the fundamental principles of mass and momentum balance for the solid, liquid, and gas phases. This leads to a fully coupled system of equations that simultaneously solves for the displacement of the solid skeleton and the pore pressures of the fluid phases. Recognizing that geotechnical problems span a wide range of loading rates, three distinct numerical formulations were developed to provide both accuracy and computational efficiency: a Fully Dynamic Unsaturated (FDU) formulation, which includes all inertial terms associated with both the solid and fluid phases, making it suitable for high-frequency events like blast loading; a Partly Dynamic Unsaturated (PDU) formulation, which retains the solid skeleton inertia while neglecting fluid inertia, ideal for many seismic and dynamic analyses; and a Quasi-Static Unsaturated (QSU) formulation, which neglects all inertial terms for the analysis of relatively slow processes such as consolidation and infiltration. The validity and robustness of the coupled theoretical and numerical framework are demonstrated through a series of comprehensive application problems in one-dimensional soil setting. The simulations begin by verifying the model's ability to reproduce the behavior of a fully saturated soil column, showing that its predictions for consolidation and settlement match classical theories and results from an established commercial software. The framework is then applied to the benchmark problem of one-dimensional (1-D) infiltration into an unsaturated soil column, with the numerical results showing fairly good agreement with well-known experimental data, thus validating the model's capacity to capture coupled flow-deformation processes. Further simulations of quasi-static loading on unsaturated soil columns under various suction and permeability conditions demonstrate the model's ability to accurately predict settlements and highlight the critical role of suction in controlling soil deformability. Finally, the model is subjected to cyclic loading conditions to showcase the capabilities of the combined hardening rule and the dynamic formulations, effectively capturing the evolution of deformation, saturation, and pore pressure under time-varying loads. In conclusion, this dissertation successfully develops and validates a comprehensive framework for the analysis of unsaturated soils. The proposed constitutive model advances the state-of-the-art by introducing an improved yield surface formulation and a combined volumetric-deviatoric hardening law, leading to a more accurate representation of complex soil behavior. Its implementation within a versatile, multi-phase finite element framework provides a powerful tool for analyzing a wide spectrum of practical geotechnical engineering problems. While this research significantly enhances the modeling capabilities, avenues for future work include the incorporation of thermal effects, anisotropy, and extension to more complex, three-dimensional (3-D) boundary value problems. Ultimately, this work contributes to a deeper understanding of unsaturated soil mechanics and provides improved tools for engineering practice.