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.

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.

This paper develops a new time-dependent hypoplastic model for normally consolidated and overconsolidated clays. A novel viscous strain rate formulation is derived from the isotach concept and incorporated into the total strain rate of the hypoplastic framework, allowing for viscous deformation at the onset of loading. The hypoplastic flow rule is defined for the direction of the viscous strain rate and its intensity directly linked to the overconsolidation ratio (OCR) and secondary compression coefficient. The Matsuoka-Nakai criterion is further introduced into the strength parameter through the transformed stress technique, enabling the model to describe the stress-strain-time behaviour of clays in general stress space. In addition, a new scalar function is proposed and implemented into the model to consider the OCR effect on the initial stiffness. The model predictive ability is finally examined by simulating laboratory tests on three different clays with various OCRs and stress paths, demonstrating that the model can capture the rate dependency, stress relaxation, and creep behaviours for both normally consolidated and overconsolidated clays under various loading conditions.

We propose a constitutive model for both the solid-like and fluid-like behavior of granular materials by decomposing the stress tensor into quasi-static and collisional components. A hypoplastic model is adopted for the solid-like behavior in the quasi-static regime, while the viscous and dilatant behavior in the fluid-like regime is represented by a modified mu(I)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu (I)$$\end{document} rheology model. This model effectively captures the transition between solid-like and fluid-like flows. Performance and validation of the proposed model are demonstrated through numerical simulations of element tests.

This paper discusses the finite element analysis of assemblage of clay lumps placed in clay slurry and undergoing compression using a structured hypoplastic soil model. The stress state of the fill was treated as that of a structural clay, which ignores the micromechanics of the complex double-porosity fill. Sensitivity of the fill was used as a numerical parameter to quantify the structure of the fill based on its initial specific volume. In the absence of any strong anisotropy, the above sensitivity was equal to the ratio of the size of the structured state boundary surface and the Roscoe surface. In addition to the five basic parameters used in the modified Cam clay model, this hypoplastic model with its own metastable structure used three more variables to account for the structural degradation. These variables considered the rate of structural degradation, relative importance of shear and volumetric strains, and the soil's ultimate sensitivity, respectively. The findings were validated by comparing the numerical results to the experimental data of two different clay fills which had undergone isotropic and one-dimensional (1-D) loading. These two stress states are applicable to near surface and thick double-porosity clay fills, respectively. The complete analysis was controlled by the initial specific volume of the fill. Its reconstituted behaviour was achieved only when the imposed normal stress surpassed the preconsolidation pressure of the clay lumps. The controlling variables ranged between 0.37 and 0.75 for the two different clays to model their structure degradation. A parametric study was used to further elaborate on this behaviour. Some discussion on the initialisation of the soil sensitivity is also presented.

The presence of fines can significantly influence the mechanical behavior of soils. In this study, a hypoplastic model is extended to simulate the stress-strain relationship of sand-fines mixtures. Firstly, three modifications are incorporated into the model to accurately simulate the effective stress path, hardening rate, and limited flow type response of sand during undrained loading. Additionally, a novel formulation is proposed to capture the critical state line of soil mixtures across a wide range of fines content. This formulation is then integrated into the characteristic void ratios of the hypoplastic model, enabling it to effectively consider the combined influence of void ratio, confining pressure, and fines content on the density state of the sand-fines mixtures. The predictive capability of the model is demonstrated through a comparison of simulation results and experimental data for undrained triaxial tests conducted under various conditions.

Monopiles serve as the foundational support for offshore wind turbines and are constructed as large, hollow, and rigid steel pipes. Given their offshore installation, these foundations experience cyclic lateral forces from wind and waves. This paper focuses on investigating the cyclic lateral capacity of monopiles through experimental and numerical analysis. The study examines varying factors such as slenderness (L/D) ratios of 2, 4, and 6, load amplitudes (xi b) of 40%, 30%, and 20%, and different densities of sand (RD) at 35%, 55%, and 75%. One-way cyclic loading at a frequency of 0.25 Hz was applied during the experiments using a pneumatic cylinder setup to the model piles. Numerical analysis was conducted on the prototype piles using PLAXIS 3D finite element software. The analysis utilised a hypoplastic model with an intergranular strain concept as the constitutive model. The model was validated against the experimental results of MLD2/LA40/RD55 and exhibited similar behaviour. The experimental findings indicate an initial 40% increase in stiffness during the first 10 cycles, leading to a higher accumulation of displacement. However, as the number of cycles increased, the rate of stiffness increase decreased due to soil getting dispersed around the pile, resulting in an increased rate of accumulated displacement. This behaviour was observed across various L/D ratios, load amplitudes, and soil densities. Additionally, an increase in load amplitude and L/D ratio, as well as a decrease in soil density, resulted in higher accumulated displacement and reduced stiffness.