Hypoplastic Constitutive Model Research Articles

Numerical study on the lateral behavior of pile groups in Toyoura sand using the hypoplastic constitutive model

A pile group under lateral loading is a complex pile‒soil-pile interaction problem. In this study, numerical analysis was used to investigate the lateral behavior of pile groups arranged in a 3 × 3 configuration with varying piles spacings. The hypoplastic constitutive model embedded into ABAQUS software through the UMAT subroutine was used to characterize the stress‒strain relationship of Toyoura sand. The effects of the pile spacing on the load‒displacement relationship of the pile group, the bending moment-depth relationship of each pile in the pile group, the deflection-depth relationship, and the soil resistance distribution were investigated. The results indicate that the lateral bearing capacity of the pile group decreases by more than 50% when the pile spacing is reduced from 7D to 3D. When the pile spacing is greater than 5D, the “edge effect” of the laterally loaded pile group gradually decreases, and when the pile spacing is greater than 7D, the “shadowing effect” can be negligible, and the wedge-shaped failure zone of the pile group occurs within a depth of 5D below the mud surface.

Probabilistic back analysis of reservoir landslide considering hydro-mechanical coupled observations

Precisely assessing statistical parameters to characterize spatial soil variability presents a significant challenge in probabilistic slope stability analysis, primarily due to inherent soil uncertainties and limited field-specific data. Probabilistic back analysis, recognized as an effective and reliable technique, offers a rational method for utilizing observational data to invert parameters. Nevertheless, previous investigations into parameter inversion for slope stability analysis have seldom considered the coupling of hydro-mechanical characteristics in reservoir landslides. This study proposes a novel integrated Bayesian framework to perform back analysis of reservoir landslides, incorporating the spatial variability of hydro-mechanical parameters. Within this framework, a hypoplastic constitutive model is developed to characterize the step-like deformation of the reservoir slope. The posterior knowledge of the saturated permeability coefficient and shear strength parameters is obtained by collecting field monitoring data of the underground water level and ground displacement. The Maliulin landslide, located in the Three Gorges Reservoir area of China, is used as an illustrative example to validate the proposed framework through back analysis of spatially variable soil parameters and probabilistic stability analysis. The results demonstrate that the proposed Bayesian updating framework significantly reduces the uncertainties associated with statistical values of soil parameters, providing more accurate and reasonable updated soil parameters for probabilistic slope stability analysis.

On anisotropic local bifurcation based on hypoplastic model

The incipience of shear band in homogeneous granular materials is well captured by the bifurcation analysis. Most bifurcation analyses are based on isotropic plastic constitutive models. In this paper, a hypoplastic constitutive model is presented by considering a fabric tensor for inherent anisotropy. Based on this model, we carry out bifurcation analysis for the plane strain case, and then extend the analysis to consider general three-dimensional stress state. The theoretical results are compared with experiments on sand conducted using a plane strain device and a true triaxial device. It's indicated the salient features of stress-strain behaviour and shear band formation are well captured by our analyses.

Hypoplastic predictions of changes in undrained shear strength during episodic loading

Episodic loading patterns of undrained loading and consolidation are relevant to offshore foundation whole-life applications from variable metocean and operational conditions. In related finite-element simulations of foundation–soil interactions, the selected constitutive model then has to capture general trends of the soil response due to episodic loading, including changes in shear strength which affects the foundation's capacity. In this study, element test simulations using clay hypoplasticity were conducted to investigate the model's capability to capture general trends in the evolution of void ratio and undrained strength, which have been observed in direct simple shear (DSS) experiments on normally consolidated clay. Episodic loading in these DSS tests consisted of periods of undrained shear interspersed with consolidation and was applied to samples of normally consolidated kaolin clay. The clay hypoplastic constitutive model with the intergranular strain extension can be used to capture the response of normally consolidated clay subjected to episodic loading.

Hypoplastic constitutive model of inherently anisotropic sand

The modeling of anisotropic sand has always been a challenging and prominent issue in geotechnical constitutive research. This paper presents a hypoplastic constitutive model for inherently anisotropic sand. An anisotropic state variable A, which is defined by the joint invariants of the stress and fabric tensor, is introduced to account for the fabric anisotropy. This form of A can be referred to as a re-arrangement that allows for easier calibration. And this modification leads to the anisotropic contraction of the failure surface. The softening parameter in the critical state line is revised from a fixed to a state-dependent type, for achieving unified simulations of monotonic sand mechanical behaviour under different drainage conditions and within a wide range of stress levels and densities. Simulations of various monotonic element tests show that the salient features of inherently anisotropic sand, including barotropy, pyknotropy, strain softening, and dilatancy, can be well captured. Particularly, we make the first attempt to simulate pure stress-controlled true triaxial tests using hypoplastic constitutive under both drained and undrained conditions. Moreover, we provide a method to further optimize the flow direction by introducing an exponential formula.

Three-dimensional numerical analysis of twin tunnelling in two-layered soil strata

Tunnelling induces stress change and displacement in the ground. The excavation of a new tunnel in stratified soil can trigger different patterns of stress redistribution, which may adversely influence nearby tunnels. Research on multi-tunnel interaction has mainly been performed on the assumption of a uniform ground. The effects of different soil stratifications on tunnelling interaction remain poorly understood. In this paper, three-dimensional numerical parametric studies verified by previous centrifuge tests were carried out to analyse the twin tunnelling effects in two-layered soil. An advanced hypoplastic constitutive model that can capture stress-, path-, and strain-dependency of soil behaviour is adopted. Numerical cases investigated include perpendicular twin tunnelling in two sand layers with different relative densities and the location of the interface between the two sand layers. It is revealed that larger settlements and a wider surface settlement trough occur when tunnelling in two-layered soil strata than in a uniform ground. This is because of the wider and larger soil arch induced in two-layered soil strata. The structural response including tunnel deformation, induced bending moment, and induced hoop stress of the existing tunnel can be greater when tunnelling in layered soil strata than in a uniform ground owing to larger stress relief. Moreover, the combination of bending moment and hoop stress can exceed the M−N failure envelope of the structure in layered soil. A conventional simplified assumption of a uniform ground can underestimate of the influence of new tunnel excavation on existing tunnels, resulting in unsafe designs.

Influence of drainage conditions on piezocone penetration mechanism in offshore clays

ABSTRACT CPTu (piezocone penetration test) is widely used in engineering practice to determine various parameters of clays under partially drained conditions. However, most existing research is based on undrained or fully drained conditions for clays, leading to underestimation or overestimation of soil strength. By applying the Eulerian-Lagrangian large deformation finite element method to analyse the water-soil interaction, the CPTu driving mechanism in offshore saturated soft clays under different drainage conditions is revealed. An advanced hypoplastic constitutive model for clays is used to simulate the nonlinear behaviour of kaolin under different drainage conditions. The generation, accumulation, and dissipation of excess pore water pressure under different drainage conditions are analysed, as well as the influence of excess pore water pressure on cone tip resistance and the effective stress of the soil during the CPTu penetration process.

Influence of soil and pile properties on the critical length of laterally loaded piles

Piles could undergo various deformation and failure modes which were depended on their classification. Previous research primarily utilized the equation proposed by Poulos and Hull to classify the pile. While the Poulos and Hull method offers advantages in terms of its simplicity, it is not entirely suitable for contemporary applications involving large-diameter piles and complex soil profiles. In this study, a three-dimensional pile-soil coupling finite element model is proposed using the hypoplastic constitutive model. The main goal of this paper was to present extensive three-dimensional finite element analyses to examine the lateral response of a monopile embedded in sand. This research reevaluates five existing methods for determining the critical length of laterally loaded piles. The evaluation considers both directly assigned and indirectly calculated methods for determining the soil's elastic modulus. The findings reveal that Dobry's equation offers superior prediction for the critical length across various soil conditions. However, for low relative density soils, the Poulos and Hull method demonstrates better suitability. The numerical results presented in this study are expected to provide design references for further practical applications of the monopiles.

Hypoplastic modeling post-failure behavior of sandy slope with porosity spatial variability

Recent probabilistic studies have thoroughly examined how uncertainties in soil shear strength affect slope stability, while the impact of spatial variability in soil porosity on post-failure behaviors of slopes has received less attention. Overlooking the influence of porosity may lead to inaccurate assessments of slope post-failure behaviors. This study presents a random smoothed particle hydrodynamics (RSPH) framework for probabilistic analysis of slope failure with large deformation using a critical state-based hypoplastic constitutive model. The results indicate that the proposed RSPH method provides reasonable estimates for slope post-failure behaviors. Increases in both the coefficient of variation (COV) and the scale of fluctuation (SOF) of porosity give rise to underestimations of the run-out distance and sliding volume. Additionally, slope failure modes are affected by increasing uncertainty of porosity, which may contribute to the occurrence of deep-seated failures.

Evaluating the Applicability of a Hypoplastic Constitutive Model for Double-Porosity Fills Undergoing Isotropic and 1-D Consolidation

Evaluating the Applicability of a Hypoplastic Constitutive Model for Double-Porosity Fills Undergoing Isotropic and 1-D Consolidation

An improved hypoplastic model incorporating intergranular strain for overconsolidated clay

Hypoplastic constitutive models are able to describe overconsolidated behaviors of clay with a single nonlinear tensor function using a set of parameters. For instance, an advanced hypoplastic model by Wang and Wu (2020) has successfully reproduced overconsolidated history by incorporating a structure tensor. To simulate the recent stress history effects and the stiffness variations at small strains of clay, the intergranular strain tensor is introduced by Niemunis and Herle (1997) to reproduce stress-path dependent stiffness of clay. The improved hypoplastic model is examined against experiments on overconsolidated Chicago clay. It is evidently concluded that the improved model is capable of replicating stress-path dependency on the small-strain behavior of overconsolidated clay.

3D SPH implementation to large deformation of granular mass using an advanced hypoplastic constitutive model

In this study, an advanced hypoplastic model incorporating the critical state is integrated into smoothed particle hydrodynamics (SPH) for the numerical investigation of geotechnical large-deformation problems. Moreover, a return mapping strategy is proposed to regulate the stress state to avoid calculation failure. Furthermore, a closed-form solution to predicting the failure surface implicitly incorporated in the hypoplastic model is derived. The proposed SPH method is examined with element tests such as the oedometer test and biaxial compression test to observe a good performance of the SPH model. Finally, the SPH model is applied to numerically reproducing sand column collapse to investigate the effect of the initial void ratio on the behavior of soil.

Experimental determination of hypoplastic parameters and cyclic numerical analysis for railway bridge backfills

AbstractLong integral bridges experience an enhanced cyclic soil structure interaction with their granular backfills, especially due to seasonal thermal loading. For numerical modelling of this interaction behaviour under cyclic loading, it is important to employ a suitable constitutive model and calibrate it thoroughly. However, up to the present, experimental data and calibrated soil models for this purpose with focus on typical well-graded coarse-grained bridge backfill materials are rarely available in the literature. Therefore, one aim of this paper is to present results of a comprehensive cyclic laboratory testing programme on highly compacted gravel backfill material. Based on this, a hypoplastic constitutive model with intergranular strain extension for small strain and cyclic behaviour is calibrated and evaluated against the experimental test data. The soil model’s abilities and limitations are discussed at element test level. In addition, cyclic FE analyses of an integral bridge are conducted with several hypoplastic parameter sets from the literature and compared to the calibrated gravel backfill material. The investigation highlights that poorly-graded sands show significantly smaller cyclic earth pressures compared to well-graded gravels intended for the backfilling of a bridge. The soil structure interaction behaviour is clearly governed by the general soil model stiffness, including the small strain stiffness.

Numerical Study of the Piezocone Test in Sandy Soil under Different Drainage Conditions Using a Hypoplastic Constitutive Model

Numerical Study of the Piezocone Test in Sandy Soil under Different Drainage Conditions Using a Hypoplastic Constitutive Model

Calibration of Hypoplastic Parameters for Danube Sand

Abstract The relationship between stress and strain tensors in soil is described by the soil constitutive equation, which depends on the soil type and deformation conditions. The development of various constitutive models has enabled a better understanding of the macromechanical properties of soil. One such model is hypoplasticity, which was discovered more than three decades ago. The purpose of this study is to determine whether hypoplasticity could accurately represent the behavior of Danube sand, a specific type of sand. The researchers conducted laboratory measurements to obtain the eight basic hypoplastic parameters of Danube sand and employed the intergranular strain concept as an extension of hypoplasticity to achieve a more precise material behavior. All the parameters were then utilized to simulate the cyclic triaxial test using the SoilTest Module of PLAXIS. The results showed that the hypoplastic constitutive simulation model for Danube sand was capable of making relatively accurate predictions for accumulative settlement.

Slope stability analysis with a hypoplastic constitutive model: Investigating a stochastic anisotropy model and a hydro‐mechanical coupled simulation

AbstractA reliable constitutive model is essential for accurately predicting slope deformation in numerical analysis, which includes assessing slope stability as an integral component. However, calculating slope stability in numerical models can be challenging due to complex boundary conditions and advanced constitutive models, especially when probabilistic and hydro‐mechanical coupled simulations are required. In this paper, we use a vector‐sum method‐based framework for slope stability analysis that incorporates a critical state hypoplastic constitutive model. The rationality and accuracy of the stability results are initially verified through critical slip surface analysis and a factor of safety evaluation. Subsequently, we investigate the probability‐based slope stability and failure characteristics by incorporating the spatial variability of strength parameters into the hypoplastic model. Finally, the Baishuihe landslide in the Three Gorges Reservoir Region is examined as a case study, where hydro‐mechanical coupled simulations are conducted under actual water level and rainfall conditions. The time‐varying stability and deformation characteristics of the landslide are analyzed and compared with the results obtained from the Mohr‐Coulomb model. The analysis results demonstrate the practicality and efficiency of using a hypoplastic model for probabilistic and time‐varying slope stability calculations. Furthermore, it highlights the superior ability of the hypoplastic model to accurately describe reservoir landslide deformation processes.

Determination of hypoplastic parameters for a typical gravel backfill material of railway bridges

Laboratory test programs on gravel are rare due to the maximum grain size of the material. In this paper an experimental program with triaxial tests under cyclic loading and oedometric tests on highly compacted gravel specimens, representative for bridge backfills materials, is summarized. It is used to calibrate a hypoplastic constitutive model, which includes an extension for intergranular strain to account for the cyclic loading behaviour. So far calibrated parameter sets of this soil model are scarce in literature, especially for coarse grained materials. The calibrated parameter set can be used in numerical studies, e. g. on the cyclic soil structure interaction of integral railway bridges.

Generalized hydro-mechanically coupled hypoplastic constitutive model for unsaturated collapsible soils

In this paper, a generalized hypoplastic constitutive model for unsaturated soils based on the work of Fuentes and Triantafyllidis [2013] is presented. The constitutive model is formulated in terms of effective stresses, degree of saturation and suction. The main feature of the model is a Limiting Surface (LS) which describes the maximum achievable void ratio as a function of mean effective stress and degree of saturation. The LS allows to capture the wetting-induced collapse of initially unsaturated soils. The performance of the proposed model is demonstrated by backcalculation of a well-documented experimental study on over 30 samples of compacted Pearl clay by Sun et al. [2004] under isotropic as well as triaxial loading conditions. For this purpose, the proposed model is coupled with a hypoplastic model for the soil-water retention curve, which interrelates the effective degree of saturation with the suction and the void ratio.

Formulation and implementation of a hypoplastic constitutive model for interface behavior of mechanical joints

The effects of the contact interface must be considered during the design process of the assembly structures connected by mechanical joints. An advanced three-dimensional (3D) constitutive model is needed to describe the complex behavior of the contact interface in a detailed finite element (FE) model. However, the simplified Coulomb friction law, which is a bilinear model without considering the microslip behavior and stiffness degradation, is often applied to the surface-surface contact element for modeling the interface in commercial FE programs. In this paper, a new 3D hypoplastic constitutive model for the nonlinear interface behavior is presented. This model is built on the framework of hypoplasticity developed by Kolymbas and the hypothesis of continuous media. First, the general hypoplastic model is derived based on the kernel formula and several restrictions and simplified according to the characteristics of the contact interface. Then, the coefficients of the model are associated with the widely used physical parameters by combining the model with the initial stiffness ratio, normal contact law and Coulomb law. Benefiting from the hypoplastic theorem, the deduced constitutive model has a simple mathematical formulation in which only five parameters are contained. Simulations of several monotonic and cyclic shear tests show that the model can represent the salient characteristics of the joint interface (e.g. stick/microslip/macroslip behaviors, motion coupling and pressure-dependency). Thus, it can be used to predict the response of the joint interface from arbitrary multi-axial load histories more precisely. The constitutive model is then implemented in a commercial FE program via analysis of a double-beam structure subjected to harmonic excitation. And vibration experiments on several preload levels are performed to validate the effectiveness and the applicability of the proposed model to the real joints. The results calculated from the FE model with the improved reduction techniques are in good agreement with the experimental data.

The Hypoplastic Constitutive Model for Sandy Soil Considering the Rotation of the Principal Stress Axis

Considering the influence of fabric on the critical state of sandy soil, an anisotropic hypoplastic constitutive model is developed by introducing the anisotropic critical state line that takes into account the rotation of the principal stress axes. With the introduction of new anisotropic state variables defined by the joint invariants of the stress tensor and fabric tensor, the critical state equation of sandy soil is established to describe the effects of three factors, namely, anisotropic parameters, stress states, and the relationship between principal stresses and fabric directions, on the critical state. The mechanical response of sandy soil under different deposition angles can be described by considering the rotation of principal stresses relative to the fabric. The application range of Wu et al.’s isotropic hypoplastic model (2017) is extended by incorporating the effect of principal stress rotation on the stress–strain relationship of sandy soil. Based on a series of Toyoura sand plane strain tests, the effects of void ratio, confining pressure, and principal stress axis rotation angle on anisotropic strength and deformation characteristics are simulated under low confining pressure. Furthermore, a comparison with Wu’s transversely isotropic hypoplastic model (1998) is made regarding their simulation performances. The proposed model exhibits a balanced performance when simulating the variation of anisotropy in both strength and deformation with respect to the rotation angle, without being overestimated within a certain range of rotation angles. The prediction results demonstrate, to a certain degree, the validity and effectiveness of the proposed model.