Hypoplastic Model Research Articles

Numerical Analysis of Stone Columns for the Reduction of the Risk of Soil Liquefaction

Although stone columns have been frequently used for the prevention of soil liquefaction in the last few years, their mechanical performance is still not fully understood. Both numerical calculations with conventional constitutive models and small-scale laboratory experiments do not explain the improving mechanisms satisfactorily. Under seismic effects, the interaction between the soil and the columns, especially between the pore water and the soil skeleton, makes the understanding of this method even more difficult. In this paper, an application of stone columns for the prevention of soil liquefaction is numerically investigated by means of 2D and 3D simulations. A hypoplastic model was used for the soil description. The drainage effect of the columns and their contribution to the stiffening of the ground were considered separately. Furthermore, the impact of the columns installation method was investigated by increasing soil density and stress ratio. Finally, the role of the intensity of the dynamic load was studied.

Calibration of a Hypoplastic Constitutive Model with Elastic Strain Range for Firoozkuh Sand

A series of laboratory experiments on Firoozkuh sand were conducted followed by a set of numerical simulations to determine the parameters of a general hypoplastic constitutive model for sand. This model describes inelastic and incrementally nonlinear material properties without a yield surface and detached strain increments in the elastic and plastic portions that is used to accurately simulate soil behavior for small and large strains and unloading–reloading paths. The general models are salient and the model requires unique constitutive constant values for all densities of a particular soil at all pressures. The 13 hypoplastic parameters used were calibrated through standard laboratory monotonic and cyclic triaxial and oedometer tests. Additional undrained triaxial and cyclic triaxial testing data that had not been used in the calibration process were used to validate the parameters.

Extension of a basic hypoplastic model for overconsolidated clays

Abstract This paper presents a new rate-dependent hypoplastic constitutive model for overconsolidated clays. The model is developed based on a basic hypoplastic model proposed recently for sand. New density and stiffness factors are introduced to account for history dependence. The Matsuoka-Nakai failure surface is incorporated for the limit stress criterion. With six constitutive parameters, the model is capable of predicting the hardening/softening, shear dilation/contraction, and asymptotic state for overconsolidated clays. Comparison between numerical predictions and experimental results shows this model can properly describe the main features of both reconstituted and undisturbed clays with different overconsolidation ratios.

Performance-based analysis of tunnels under seismic events with nonlinear features of soil mass and lining

Accurate prediction of tunnel behavior and damage states under seismic loading remains a challenge. This study carried out tunnel behavior and risk assessment using numerical dynamic analysis on a NATM tunnel. A hypoplastic model that considers intergranular strain was calibrated for a particular sand using experimental tests and numerical simulations. It then was used in numerical simulations for the surrounding soil to allow precise prediction of soil dynamic behavior at all ranges of strain. The elastic perfectly plastic model was used for the tunnel lining to detect plastic hinges under seismic motion. Similar trends for all drift-PGA curves at different surcharges and soil densities indicate that all models experienced the same phenomena at similar time intervals and represent different performance levels. The serviceability level of the tunnel is the point at which the first plastic hinge forms. The collapse prevention level produces failure mechanisms that cause instability and collapse.

Hypoplastic and viscohypoplastic models for soft clays with strength anisotropy

SummaryThis paper presents a new viscohypoplastic model for soft clays accounting for their typical features—strength anisotropy and rate dependency. The model is based on the hypoplastic model for clays enhanced by the anisotropic shape of the asymptotic state boundary surface. It has been shown that if the surface is skewed, the model predicts different ultimate strength in compression and in extension. Additional enhancement makes the tensor L bilinear in the strain rate, which more realistically predicts the stress paths ofK0consolidated samples. The new model has been evaluated by simulating laboratory experiments on soft marine clays (Singapore and Bangkok clays). The model can be easily calibrated using only undrained triaxial and odometer tests. The model is subsequently enhanced by the rate effects. The resulting viscohypoplastic model has been evaluated using experiments of remolded kaolin clay and St. Herblain clay. It is shown that the enhanced model can predict important features of soil viscous behavior, such as rate dependency of strength and preconsolidation pressure, relaxation, and creep.

Improvement of a Hypoplastic Model for Granular Materials Under High-Confining Pressures

The behavior of granular materials during loading depends on the level of stresses. When confining pressure increases, the peak shear strength, the residual shear strength and the stiffness gradually decrease; besides, the volumetric behavior is shown to be influenced by the stress level. In this paper, such effects, due to changes in stress levels, have been incorporated into a modified von Wolffersdorff hypoplastic model. For this purpose, reference void ratios and exponent α and β, the parameters of the original hypoplastic model are modified using experimental data. The performance of the proposed model is demonstrated by using simulated triaxial tests on Hostun sand with cell pressures up to 15 MPa. The study shows the ability of the improved model to highlight the behavior characteristics of granular materials in dilatancy and (peak) resistance under high stress better than the original model.

Centrifuge and numerical modelling of stress transfer mechanisms and settlement of pile group due to twin stacked tunnelling with different construction sequences

Abstract This study reports a series of centrifuge model tests, aiming at investigating the effects of construction sequence of twin stacked tunnels advancement on an existing pile group under working load in dry sand. Twin stacked tunnelling was simulated after the other with the first tunnel excavated near the mid-depth of the pile shaft and the second either next to the toe of the pile (test ST) or below the pile (test SB). In addition, two tests were performed with change of construction sequence of twin stacked tunnels (i.e. tests TS and BS). The first tunnel was excavated either near the pile toe (test TS) or below the pile (test BS) and second tunnel near the mid-depth of the pile shaft. The centrifuge tests were back-analysed by three-dimensional finite element analyses using a hypoplastic model, which takes strain-dependent and path-dependent soil stiffness into account. The measured and computed results have revealed that change of twin stacked tunnels construction sequence had substantial effects on pile group settlement, pile cap tilting and lateral movement in the pile group. In contrast, no significant effect was found on induced bending moment and load transfer mechanism in the piles.

An intergranular strain concept for material models formulated as rate equations.

SummaryThe intergranular strain concept was originally developed to capture the small‐strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic models are presented in this article. These approaches differ in the determination of the elastic stress response, which is used for reversible deformations. The first approach determines an elastic response from the original material model, and the second one uses an additional elastic model. Both approaches are applied on barodesy. The simulations are compared with experimental results and with simulations using hypoplastic models with the original intergranular strain concept.

On proportional deformation paths in hypoplasticity

We investigate rate-independent stress paths under constant rate of strain within the hypoplasticity theory of Kolymbas type. For a particular simplified hypoplastic constitutive model, the exact solution of the corresponding system of nonlinear ordinary differential equations is obtained in analytical form. On its basis, the behaviour of stress paths is examined in dependence of the direction of the proportional strain paths and material parameters of the model.

A hypoplastic model for granular soils incorporating anisotropic critical state theory

SummaryIt is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress‐strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus‐Bauer hypoplastic model, and a scalar‐valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.

Finite element modelling of an energy-geomembrane underground pumped hydroelectric energy storage system

The increasing need for energy storage technology has led to a massive interest in novel energy storage methods. The energy geomembrane system is such a novel energy storage method. The concept of the system is briefly introduced, and a holistic numerical model of the system is presented. The model uses advanced finite-element techniques to model the energy storage system using fluid cavity elements. The developed geomembrane energy system is modelled with different constitutive models to represent the soil behaviour: a linear elastic model, a nonlinear Mohr-Coulomb model, and a hypoplastic constitutive model. The consequences of these different models on the results are studied. Hereby, the focus is the first inflation and deflation cycle of the system.

Fully-coupled analysis for the behaviour of flexible retaining structures under seismic conditions

The study concerns the analysis of the behaviour of two propped reinforced-concrete diaphragm walls in coarse sand under seismic conditions. Fully-coupled dynamic equilibrium and pore water flow under unsaturated conditions for the soil have been taken into account, in order to assess the effects that the development of excess pore water pressures can have on the performance of such structures when dynamic conditions occur. The von Wolffersdorff hypoplastic model and the van Genuchten soil-water retention model have been used to describe the mechanical and retention behaviour of the sand. The Finite Element predictions of the soil and retaining structure behaviour show a significant dependence of the seismic performance of the structure – evaluated in terms of permanent displacements and structural loads, in view of the modern performance-based design criteria – on the excess pore pressures developed in the soil during the seismic shaking, even when dynamic liquefaction does not occur.

On feasibility of rate-independent stress paths under proportional deformations within hypoplastic constitutive model for granular materials

We study stress paths that are obtained under proportional deformations within the rate-independent hypoplasticity theory of Kolymbas type describing granular materials like soil and broken rock. For a particular simplified hypoplastic constitutive model by Bauer, a closed-form solution of the corresponding system of non-linear ordinary differential equations is available. Since only negative principal stresses are relevant for the granular body, the feasibility of the solution consistent with physics is investigated in dependence of the direction of a proportional strain path and constitutive parameters of the model.

Применение стационарной гипопластической модели для моделирования движения сыпучей среды

Для моделирования движения гранулированной среды предложен вариант стационарной гипопластической модели. С целью решения задачи выбран метод сглаженных частиц, особенностью реализации которого является использование в расчетах комбинированного ядра, с малым параметром сглаживания. Выполнен расчет процесса обрушения песчаного столба и проведено сравнение полученных численных результатов моделирования с известными экспериментальными данными. Purpose. The aim of this study is а development of mathematical models that describe the complex motion of a granular medium in the process of its disintegration that allows evaluating the possibility of using a simplified stationary hypoplastic model to describe this process. Methodology. To describe the motion of a granular medium, the classical equations of motion and mass conservation were used. The calculation of the deviator of the stress tensor is performed within the framework of a simplified hypoplastic model. The work uses the hypothesis of a linear relationship between the pressure function and the density of the granular medium. This hypothesis is typical for smoothed particle methods, one of the variants of which is proposed for the numerical implementation of the problem. Results. A new mathematical model of the problem of the motion of a granular medium in the process of its disintegration is formulated. An algorithm for solving the problem based on the method of smoothed particles is proposed. The problem of disintegration of a sand pillar is solved numerically. A comparative analysis of the obtained solutions with experimental data is accomplished. Findings. Using the assumption that the propagation velocity of elastic waves that determine the stress-strain state in sand particles is much higher than the velocities of particles arising from sand shedding, an approximate model for calculating the stress state of a moving granular medium based on a stationary hypoplastic model is presented. To solve the problem, the method of smoothed particles with a small smoothing parameter was implemented with the help of a new combined interpolation core in the calculations. To verify the mathematical model and the selected method, the implementation of the smoothed particle method was performed and the problem of disintegration of the sand column was solved. The obtained solution of the problem shows satisfactory agreement with the experimental data.

Intergranular-strain elastic model for recent stress history effects on clay

An elastic model is proposed to enhance elastoplastic models for the non-linear stiffness variations at small strains and the recent stress history effects of clay. This model relies on the intergranular strain concept that is introduced by Niemunis and Herle (1997). The intergranular strain model achieves great success in modeling the recent stress history effects, but its application has mainly be restricted in augmenting hypoplastic models. This work proposes a new interpolation rule for directional stiffness to facilitate the incorporation of the intergranular strain model into the framework of elastoplasticity. The correlations between intergranular strain parameters and the reference strain of well-established modulus degradation curves are obtained to ease the model calibration. The intergranular strain elastic model is used to enhance a bounding surface plasticity model, and the performance of the augmented model is examined against experimental observations on compressible, lightly-overconsolidated Chicago clay. The comparison of the model against experimental evidence shows that the proposed elastic model is capable of enhancing existing elastoplastic models for replicating the effects of recent stress history on the small-strain behavior of clay.

Extended hypoplastic model incorporating the coordination number for the simulation of granular flow

AbstractIn this contribution, a hypoplastic viscous soil model incorporating viscous and grain‐inertia rate effects observed in granular flows is enhanced by means of the coordination number, which allows to characterize the evolution of the microstructure of the granular material. Near a critical solid volume fraction and critical coordination number there exists a transition from a solid‐like (rate‐independent) to a flow‐like (rate‐dependent) behavior of granular materials. This information is used to calibrate a so‐linear concentration factor, which controls viscous and grain‐inertial rate effects in terms of the rate dependent evolution of the coordination number. The influence of this proposed hypoplastic model considering the coordination number is investigated in this paper by means of a simple undrained shear test .

Numerical investigations of the installation process of giant deep-buried circular open caissons in undrained clay

Numerical investigations of the whole installation process of giant deep-buried circular open (GDCO) caissons in undrained clay were conducted using 3D large deformation finite-element (LDFE) method performed by the Coupled Eulerian-Lagrangian (CEL) approach. This study was focused on the installation mechanism and soil deformation characteristics of GDCO caissons. A kinematic and continuous numerical technique based on the CEL approach accounting for the synchronous coupling between the penetration and excavation was first introduced to simulate real installation process of GDCO caissons. An advanced user-defined hypoplastic (HP) constitutive model was applied to match the clay behaviors realistically. The measured values of penetration resistance and ground surface settlement were compiled from centrifuge tests available to validate the proposed numerical technique and show the superiorities of HP model. The plastic zone, deformed soil flow, stress distribution and penetration resistance developed in clay were effectively captured to investigate the installation mechanism. Furthermore, the soil deformation including ground surface settlement and radial displacement around the caisson were examined. The simplified semi-empirical equations were then proposed to predict the ground surface settlement pattern and maximum value.

Liquefaction susceptibility of non-plastic silty sands using hypoplastic model simulations

ABSTRACT A detailed numerical analysis was performed on sands and non-plastic silty sands to examine the soil behaviour under triaxial loading conditions. An advanced hypoplastic soil element model has been used for the numerical simulations. The model parameters are constant for the given soil material and are determined easily by using mathematical formulations after conducting the basic experiments in the laboratory. The numerical model is validated with experimental data of triaxial tests before performing the numerical investigations. It is aimed to study the liquefaction resistance of sand and silty sands based on the critical state line (CSL), steady state line (SSL) and stress ratio at 20% failure strain under static loading. Results indicate that as the fines content increases, the CSL or SSL shifts to downwards, i.e., dilation decreases within the given range of pressures which indicate that the liquefaction susceptibility of sand increases with the addition of the fines content.

A 3D particle finite element model for the simulation of soft soil excavation using hypoplasticity

A numerical model based on the particle finite element method (PFEM) combined with a hypoplastic constitutive model is proposed for the analysis of soft soil excavations by means of single and multiple excavation tools. The PFEM allows to efficiently account for large deformations of the excavated soil material and free surfaces characterizing the simulation of tool–soil interaction during excavation. The utilization of a hypoplastic model, formulated in rate form, allows for a straightforward coupling with the standard velocity-based PFEM. Furthermore, effects such as pressure and density dependency of the soil stiffness are consistently incorporated into the formulation. The solution of the governing equations is performed implicitly, while an adaptive sub-stepping scheme is employed for the explicit time integration of the constitutive equation. Thus, the accuracy of the solution is improved at both global and local (constitutive) levels. The performance of the method is evaluated by means of the numerical re-analysis of selected geotechnical benchmark examples and soft soil excavations in 2D and 3D setups.

Small-strain shear moduli modeling of sand: a non-equilibrium thermodynamic approach, including an application to Leighton Buzzard sand

The shear stiffness of soil may decay with strain level by orders of magnitude. This feature of soil plays a critical role in different geotechnical constructions. The constitutive models of small-strain shear moduli used in elasto-plastic and hypoplastic models are mainly based on empirical formulas. In this paper, a constitutive model predicting the small-strain shear moduli of sand is established based on a non-equilibrium thermodynamic approach known as the granular solid hydrodynamics. Using a specific mathematical formulation for the off-diagonal transport coefficient of sand, the proposed model is able to characterize the shear stiffness variation of sand at different strain levels. A calibration procedure for all nine parameters of the model is derived, taking Leighton Buzzard sand as an example. The model predictions of shear moduli for this sand, at different confining pressures or along with different stress paths, are in good agreement with the testing data.