Accurately modeling soil-fluid coupling under large deformations is critical for understanding and predicting phenomena such as slope failures, embankment collapses, and other geotechnical hazards. This topic has been studied for decades and remains challenging due to the nonlinear responses of geotechnical structures, which typically result from plastic yielding and finite deformation of the soil skeleton. In this work, we comprehensively summarize the theory involved in the soil-fluid coupling problem. Within a finite strain framework, we employ an elasto-plastic constitutive model with linear hardening to represent the solid skeleton and a nearly incompressible model for water. The water content influences the behavior of the solid skeleton by affecting its cohesion. The governing equations are discretized by material point method and two sets of material points are employed to independently represent solid skeleton and fluid, respectively. The proposed method is validated by comparing simulation results with experimental results for the impact of water on dry soil and wet soil. The capability of the method is further demonstrated through two cases: (1) the impact of a rigid body on saturated soil, causing water seepage, and (2) the filling of a ditch, which considers the erosion of the foundation. This work may provide a versatile tool for analyzing the dynamic responses of fluid and solid interactions, considering both mixing and separation phenomena.

Constitutive models of sands play an essential role in analysing the foundation responses to cyclic loads, such as seismic, traffic and wave loads. In general, sands exhibit distinctly different mechanical behaviours under monotonic, regular and irregular cyclic loads. To describe these complex mechanical behaviours of sands, it is necessary to establish appropriate constitutive models. This study first analyses the features of hysteretic stressstrain relation of sands in some detail. It is found that there exists a largest hysteretic loop when sands are sufficiently sheared in two opposite directions, and the shear stiffness at a stress-reversal point primarily depends on the degree of stiffness degradation in the last loading or unloading process. Secondly, a stress-reversal method is proposed to effectively reproduce these features. This method provides a new formulation of the hysteretic stress-strain curves, and employs a newly defined scalar quantity, called the small strain stiffness factor, to determine the shear stiffness at an arbitrary stress-reversal state. Thirdly, within the frameworks of elastoplastic theory and the critical state soil mechanics, an elastoplastic stress-reversal surface model is developed for sands. For a monotonic loading process, a double-parameter hardening rule is proposed to account for the coupled compression-shear hardening mechanism. For a cyclic loading process, a new kinematic hardening rule of the loading surface is elaborately designed in stress space, which can be conveniently incorporated with the stressreversal method. Finally, the stress-reversal surface model is used to simulate some laboratory triaxial tests on two sands, including monotonic loading tests along conventional and special stress paths, as well as drained cyclic tests with regular and irregular shearing amplitudes. A more systematic comparison between the model simulations and relevant test data validates the rationality and capability of the model, demonstrating its distinctive performance under irregular cyclic loading condition.

The majority of existing effective stress-based constitutive models approach thermal effects through the temperature dependency of surface tension and its effects on the soil-water retention curve (SWRC) and effective stress. Experimental tests and theoretical studies, however, suggest that the temperature effect on surface tension alone is not sufficient to properly explain thermal-induced changes in the effective stress and SWRC. This study focuses on the temperature-dependent elastoplastic behavior of low plasticity unsaturated soils by developing a set of constitutive-level relations that incorporate temperature-dependent SWRC and effective stress models. These models account for the effect of temperature on the enthalpy, contact angle, and surface tension. The application of the presented constitutive relations was demonstrated and validated for low plasticity soils, specifically incorporating temperature effects into the hardening modulus, specific volume change, yield stress of the modified Cam-Clay model, and stress-strain relationships. The proposed relationships are incorporated in any effective stress-based constitutive model for modeling temperature dependency of elastoplastic response in low plasticity unsaturated soils. Employing these relationships can enhance the numerical simulation of low plasticity unsaturated soils under thermo-mechanical or other coupled processes involving temperature-dependent conditions.

The hypoplastic theory has gained significant attraction in the geomechanics community for constitutive modeling and numerical simulation. However, the absence of an analytical benchmark for numerical simulations incorporating the hypoplastic model remains a notable gap. This study revisits the basic hypoplastic model for normally consolidated soil, as proposed by Wu et al., by providing explicit formulations of the failure criterion and material parameters. Furthermore, closed-form hypoplastic solutions are derived for normally consolidated soil in three elemental tests: oedometer, simple shear and true triaxial tests. The solutions are assessed by comparing the analytical results with numerical integration and geotechnical test data. Additionally, a novel formula for estimating the at-rest earth pressure coefficient is derived, and compared to the widely adopted Jaky equation. Our solutions not only provide insights into hypoplastic model enhancement but also serve as robust benchmarks for numerical implementations.

We present a constitutive model for the mechanical behavior of granular flow for both solid-like and fluid-like regimes. The stress rate tensor is decomposed into rate-independent and rate-dependent parts. The hypoplastic model is used for the rate-independent part, while the mu(I)$\mu (I)$-type rheological model is employed for the rate-dependent part. The Stokes number is introduced to capture the influence of interstitial fluid viscosity within the rate-dependent part of the model. The model performance is demonstrated through numerical simulations of element tests, encompassing both granular materials and granular-fluid mixtures.

Numerical challenges, incorporating non-uniqueness, non-convexity, undefined gradients, and high curvature, of the positive level sets of yield function F > 0 are encountered in stress integration when utilizing the return-mapping algorithm family. These phenomena are illustrated by an assessment of four typical yield functions: modified spatially mobilized plane criterion, Lade criterion, Bigoni-Piccolroaz criterion, and micromechanics-based upscaled Drucker-Prager criterion. One remedy to these issues, named the Hop-to-Hug (H2H) algorithm, is proposed via a convexification enhancement upon the classical cutting-plane algorithm (CPA). The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point. Furthermore, a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform. Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence. All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation, in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

The behavior of soft soils distributed in coastal areas usually exhibits obvious time-dependent behavior after loading. To reasonably describe the stress-strain relationship of soft soils, this paper establishes a viscoelastic-viscoplastic small-strain constitutive model based on the component model and the hardening soil model with small-strain stiffness (HSS model). First, the Perzyna's viscoplastic flow rule and the modified Hardin-Drnevich model are introduced to derive a one-dimensional incremental Nishihara constitutive equation. Next, the flexibility coefficient matrix is utilized to extend the one-dimensional model to three-dimensional conditions. Then, by combining the HSS elastoplastic theory with the component model, the viscoelastic-viscoplastic small-strain constitutive model is subsequently established. To implement the proposed model for numerical analysis, the corresponding UMAT subroutine is developed using Fortran. After comparing the results of numerical simulations with those of existing literature, the reliability of the constitutive model and the program written in this paper is verified. Finally, numerical examples are designed to further analyze the effects of small-strain parameters and viscoelastic-viscoplastic parameters on the time-dependent behavior of soft soils.

Modelling the cyclic response of granular materials is key in the design of several geostructures. Over the years, numerous constitutive models have been proposed to predict the cyclic behaviour of granular materials. However, pertaining to the hypoplastic constitutive models, one of the significant limitations is their inability to accurately predict the geomechanical response during the unloading and reloading phases. This study introduces an extension of the MS-IS hypoplastic model designed to enhance the predictions during non-monotonic loading conditions. Addressing the limitations observed in the hypoplastic models during the unloading and reloading phases, the proposed model incorporates an additional stiffness feature. This new stiffness function is integrated into the foundational framework to enhance the model's overall stiffness response. For the unloading phase, the introduction of a stiffness degradation factor aims to modify the volumetric response and account for the realistic stiffness degradation. Additionally, for the reloading phase, stiffness is now a function of the mean effective stress. The novel model's performance is validated against experimental data, encompassing diverse loading and boundary conditions.

Damping plays an important role in the design of offshore wind turbine structures. The hysteretic damping of the seabed soil represents the energy dissipation caused by the soil-particle interaction and the nonlinear behavior of the soil under cyclic loading. However, the effect of sand damping on the lateral response of the monopile foundation of an offshore wind turbine is still unclear. In this paper, the effect of soil hysteretic damping on the lateral dynamic response of a monopile foundation in a sandy seabed is investigated using a subplastic soil constitutive model. The constitutive model response at the foundation level is verified by comparing the monotonic and cyclic responses of the monopile with the results of the 1g model test. The results show that when soil hysteretic damping is present in the monopile-soil system, the energy dissipation in the soil reduces the stress accumulation in the soil, resulting in a reduction in the bending moment and horizontal displacement of the monopile, compared with the case without soil hysteretic damping. The results are crucial for optimizing the monolithic design of offshore wind turbine structures.

An important drawback of the hypoplastic model is the inaccurate prediction of the sand behavior under undrained monotonic loading conditions. The model is not able to reproduce the limited liquefaction type response widely observed in undrained tests on loose sand, and it often underestimates the initial stiffness and hardening rate of sand during the shearing. To address these issues, three novel modifications are introduced into a basic hypoplastic model to enhance its undrained predictive capability. Firstly, a new factor is added to the nonlinear term of the model, allowing the simulation of a purely elastic response at the beginning of loading. By doing so, the model can accurately capture the initial stiffness and undrained effective stress path of sand. Secondly, the characterized void ratios are related to an evolving state variable, enabling the model to reasonably reproduce the limited flow response and quasi-steady state. Furthermore, a new term is incorporated into the deviatoric part of the strain rate to adjust the hardening rate of the model. The model performance for undrained loading is significantly improved through the above modifications, as evidenced by the good agreement between simulation results and experimental data for tests with varying densities and confining pressures.