Plastic Volumetric Strain Research Articles

Evolution of the soil water retention curve based on plastic volumetric strain

The water retention behaviour of soil can be defined as the relationship between the degree of saturation (or water content) and suction at a constant temperature, which characterises the hydraulic behaviour of unsaturated soils, normally represented as the soil water retention curve (SWRC). The SWRC is commonly measured at nominal net stress by initially saturating a soil specimen and then subjecting it to drying and wetting paths, resulting in major drying and wetting curves. However, there is evidence that during these major drying and wetting paths and initial saturation, soil can undergo volumetric deformation with changes in void ratio, sometimes plastically. Therefore, for coupling the SWRC with mechanical behaviour, the dependency of SWRC on other state variables such as void ratio has been proposed. In this paper, an approach to defining SWRC for a particular plastic volumetric strain is presented within the generalised MPK model. The SWRC evolves as soil is subjected to wet/dry cycles, eventually approaching drying and wetting curves relevant to an environmentally-stabilised state. The performance of this model is demonstrated by the simulation of the loading/unloading/drying/wetting paths followed in a laboratory experiment. In addition, the evolution of the commonly-considered major drying and wetting curves is simulated, highlighting key features of the environmentally-stabilised line..

Effect of plastic volumetric strains on shakedown of hardening granular soils

The granular soils are pressure dependent materials and substantial volume change occurs during loading. Some granular soils contract (volume decrease) when sheared and some dilate (volume increase), depending on their initial state. Owing to the plastic volume change that accompanied plastic deformation, the lack of normality rule arises and the granular soil exhibits a non-associated flow rule. As known the non normality has destabilizing effect on the soil behavior in the hardening regime (loss of positive definiteness of the second order work). The unstable behavior usually develops in association with dilation. A contracting soil displaying hardening and stable material behavior under drained conditions, may succumb to unstable flow type when its behavior becomes dilating. This paper deals with the extension of the static shakedown theorem to dilative granular soils in drained conditions, exhibiting pre-failure instability in the hardening regime, in the framework of non associated plasticity.

Modeling cyclic shearing of sands in the semifluidized state

SummaryLiquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress‐strain response in earthquake‐induced liquefaction and post‐liquefaction is complex and yet very important for stress‐deformation and performance‐based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre‐liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post‐liquefaction response.

Quantifying “transitional” soil behaviour

The last decade has seen an increasing amount of research on so called “transitional” soils that are characterised by incomplete convergence to unique normal compression lines and/or critical state lines in simple laboratory tests. This topic has often provoked reaction, perhaps because some have seen it as a challenge to critical state frameworks of soil behaviour. A particular issue is whether incomplete testing or other test defects might cause such an apparent behaviour. Confusion around the topic has not been helped by the wide range of degrees of convergence seen for different materials and differences seen between convergence in compression and shearing. This paper proposes a unifying means of plotting laboratory test data from such soils that will hopefully provide a rational framework for such discussions, since it makes explicit the degree of convergence towards unique volumetric states for different forms of loading. Data are examined for three “transitional” soils. The results show that bringing about convergence for these soils would require strains beyond those that may easily be applied and that the lack of convergence cannot solely be an artefact of test defects. Plastic volumetric strain was found to cause much faster convergence than plastic shear strain.

Analysis of Factors Affecting the Direction of Plastic Strain Increment in Sand

Taking the standard sand of Fujian as the test material, this paper concentrates on studying the influence of different stress increment directions on the direction of plastic strain increment of sand materials under different stress states and the underlying mechanism. The test results show that the plastic strain increment angle rotates counterclockwise with the increase of stress increment direction angle, but the two angles do not coincide; the higher the stress state parameters is, the larger the stress increment direction angle range corresponding to sand dilatation is, the smaller the plastic strain increment direction angle range is, and the plastic volumetric strain still increases in critical state.The plastic flow mechanism of sand is explained from the average stress increment, generalized shear stress increment and stress state, which may provide theoretical reference and numerical support for the related research of plastic strain increment direction of sand.

A bounding surface model of gas-hydrate-bearing sediments

Gas hydrates are a very promising energy source, but its exploitation also faces some challenges in marine geotechnics. The dissociation and formation of hydrates can significantly change the mechanical properties of sediment layers. Large-scale extraction of natural gas hydrate may trigger submarine landslides; therefore, an appropriate constitutive model is necessary for the safe exploitation of natural gas hydrates. In this paper, a bounding surface model of gas-hydrate-bearing sediments (GHBSs) is developed based on the modified Cam-clay model. The size of the bounding surface is related to hydrate saturation by introducing an additional hardening parameter. It is assumed that the additional hardening parameter is related to the hydrate saturation level and plastic volumetric strain. The method for determining the model parameters is given. The model is used to simulate the triaxial compression drainage test of GHBS under different test conditions. It is demonstrated that the model can adequately capture the main deformation characteristics of GHBS. The proposed model is implemented into a finite-element method software program, and finite-element modelling of the plane strain test is carried out. The comparison of results shows the validity of the model.

Simplification of the Gurson model for large-scale plane stress problems

This paper discusses formulation of the constitutive model for ductile fracture prediction in large-scale metal structures that can be approximated using shell mechanics. One of the primary considerations is the issue of bridging the length scales between micromechanical phenomena governing ductile fracture (i.e. void nucleation, growth and coalescence), which occurs on the scale of several micrometers, and large scale industrial applications. A micromechanics-based shear-modified Gurson model is used as a reference for the proposed formulation. The model is simplified and implemented in generalized plane stress state, with only the most relevant phenomena considered. Bridging of the length scales is achieved through the calibration function that approximates exponential damage growth after the onset of localized neck that cannot be explicitly represented with shell elements. The resulting formulation is a phenomenological three invariant plasticity model with a scalar damage variable dependent on the volumetric plastic strain and deviatoric plastic work. The latter term is dependent on the Nahshon-Hutchinson omega function, which is based on a normalized Lode angle. The model is used to simulate a response of a hat-shaped high strength steel automotive component under three-point bending. Calibration of the model parameters is performed based on uniaxial and plane-strain tensile tests. Close correlation between experimental and analysis results are achieved validating the assumptions and proposed formulation.

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand. This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand. Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment (i.e. dilatancy rate). Lack of an article that gathers these formulas is clear in the literature. Thus, this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands. Stress-dilatancy relation is usually not the same under compression and extension conditions. Furthermore, it may also be different under loading and unloading conditions. Therefore, the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading. Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship, more weight is allocated to stress-dilatancy relationship in this research.

Non-orthogonal elastoplastic constitutive model with the critical state for clay

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept, and the model framework is presented from the perspective of the magnitude and direction of the plastic strain increment. The magnitude is obtained based on the improved elliptical yield function and the plastic volumetric strain dependent hardening parameter. The direction is determined by applying the non-orthogonal plastic flow rule with the Riemann-Liouville fractional derivative to the yield function without the necessity of additional plastic potential function. The presented approach gives rise to a simple model for soil with five parameters. All parameters have clear physical meaning and can be easily identified by triaxial tests. The model performance is shown by analyzing the evolution process of the yield surface, the hardening rule and the plastic flow direction. The capability of the proposed model to capture the mechanical behaviours of clay with different stiffness is also confirmed by predicting test results from the literature.

A unified elasto-plastic constitutive model for sandy and clayey soils accounting for at-rest condition

ABSTRACT Taking advantages of some existing two-surface soil constitutive models in a critical state framework, a unified two-surface constitutive model was developed for rigorous simulation of elasto-plastic deformation of different soils such as loose and dense sands, normally and over-consolidated clayey soils subjected to any type of monotonic loadings. Employing the dilatancy parameter, the strain-softening and stress-dilatancy were described using non-associated flow rule to generalise the application of the model to different soils under various stress states. The applicability of the proposed model was validated comparing the numerical simulations with the existing experimental data for variety of soils subjected to different phases of monotonic loadings. The model was found to be capable of simulating drained and undrained behaviour of clayey and sandy soils under triaxial stress conditions as accurate as the constant stress-ratio loading state. The results also demonstrated the ability of the model to determine the at-rest earth pressure coefficient (K0 ) for variety of soils suitable to be applied to the geotechnical problems affected by this parameter such as piles groups and retaining earth structures. While the formulation of hardening parameter in the integration scheme is based on volumetric and deviatoric plastic strains, the simulation of dilatancy response especially in dense sands showed an excellent agreement with the experimental data.

Investigating the release and flow of snow avalanches at the slope-scale using a unified model based on the material point method

Snow slab avalanches start with a failure in a weak snow layer buried below a cohesive snow slab. After failure, the very porous character of the weak layer leads to its volumetric collapse and thus closing of crack faces due to the weight of the overlaying slab. This complex process, generally referred to as anticrack, explains why avalanches that release on steep slopes can be triggered from flat terrain. On the basis of a new elastoplastic model for porous cohesive materials and the Material Point Method, we investigate the dynamics of mixed-mode anticracks, the subsequent detachment of the slab and the flow of the avalanche. In particular, we performed two and three dimensional slope scale simulations of both the release and flow of slab avalanches triggered either directly or remotely. We describe the fracture and flow dynamics on a realistic topography and focus on the volumetric plastic strain, stress invariants, propagation speed and flow velocity. Our simulations reproduce typical observations of “en-echelon” fractures and the propagation speed reached up to three times that measured in field experiments. In addition, slab fracture always started from the top in the Propagation Saw Test while it systematically initiated at the interface with the weak layer at the crown of slope-scale simulations in agreement with limited field observations. During the avalanche flow, snow granulation, erosion and deposition processes were naturally simulated and do not need additional implementations. Our unified model represents a significant step forward as it allows simulating the entire avalanche process, from failure initiation to crack propagation and to solid-fluid phase transitions, which is of paramount importance to forecast and mitigate snow avalanches.

Hardening–Softening Constitutive Model of Hard Brittle Rocks Considering Dilatant Effects and Safety Evaluation Index

The damage and even failure of hard brittle rocks has been the most important challenge facing the safety of construction of deep engineering works, so the key to solving this problem is the recognition of the strength characteristics and description of the mechanical behavior of hard brittle rocks. Therefore, in view of this problem, in this study, we first analyzed the strength and mechanical response characteristics revealed in tests of, and site excavation in, hard brittle rocks. Second, by analyzing rock-strength envelopes on meridional and deviatoric planes, the generalized polyaxial strain energy (GPSE) strength criterion was applied. This allows description of the effects of the minimum principal stress, intermediate principal stress, hydrostatic pressure, and Lode’s angle of stress on the strength of hard rocks. By establishing evolutionary relationships of strength parameters and dilation parameters with plastic volumetric strain in rock failure, we established an elasto-plastic mechanical constitutive model for hard brittle rocks based on the GPSE criterion. In addition, through use of the failure approach index theory and the dilatancy safety factor, an evaluation index for degree of damage considering dilatant effects of rocks was proposed. Finally, the constitutive model established in this study and the proposed evaluation index were integrated into the numerical simulation method to simulate triaxial tests on rocks and numerical simulation of deformation and fracture of the rocks surrounding the deep-buried auxiliary tunnels in China’s Jinping II Hydropower Station. In this way, the reasonableness of the model and the index was verified. The strength theory and the constitutive model established in this research are applicable to the analysis of high-stress deformation and fracture of hard brittle rock masses, which supports the theoretical work related to deep engineering operations.

The compression and collapse behaviour of intact loess in suction-monitored triaxial apparatus

Loess is susceptible to large and sudden volume reduction induced by loading or wetting. The work in this paper focused on compression and collapse behaviour of the intact loess under isotropic stress condition. To this purpose, an improved technique was introduced for the unsaturated triaxial apparatus that was capable of precise injecting know the amounts of water into the specimen, while continuously monitoring the suction. Tests were performed under two separate hydro-mechanical paths: isotropic compression at various suctions and wetting in steps at various net isotropic stresses. Experimental measurements indicated that the compression behaviour of the intact loess was highly affected by the extent of the level of the suction. The wetting-induced collapse behaviour depended on both the extent of applied net isotropic stress and the hydro-mechanical path. The collapse potential reached a maximum when the specimen was wetted at the initial yield stress. No unique of yield curve was identified from loading and wetting paths in a suction–net mean stress plane. For the same plastic volumetric strain, the suction decrease yield curve identified from wetting path appeared under the loading–collapse yield curve identified from loading path. Interestingly, the uniqueness of the yield curve was identified from loading and wetting paths in a suction–mean effective stress plane. An elastoplastic model of the intact loess under isotropic stress condition incorporating soil water retention behaviour was proposed, using the mean effective stress as constitutive stress. This model is able to reproduce the volumetric behaviour of the intact loess along constant suction paths and wetting paths quite well, using a single-valued compressibility index.

A new double hardening constitutive model for frozen mixed soils

In this paper, a new double hardening constitutive model for frozen mixed soils is proposed, in which a new yield function is formulated based on the strength data of frozen soils. The associated flow rule is adopted, and the position, shape and size of the plastic potential surface are determined by four hardening parameters, two of which are considered to be functions of plastic volumetric strain and plastic shear strain, respectively. By this method, the plastic potential surface can change in shape during the process of loading. Furthermore, the constitutive model can be used to simulate both strain hardening–softening and volume contraction–dilatancy. In addition, the suggested range of constitutive parameters and the sensitivity analysis of the parameters are also provided. Finally, by verifying the experimental data of frozen mixed soils under different confining pressures, temperatures and mass ratios, it is found that the constitutive model proposed here can accurately predict the mechanical properties of frozen mixed soils well.

Modelling effects of recent suction history on small-strain stiffness of unsaturated soil

Recent suction history has been found to affect shear modulus of unsaturated soil at small strains (i.e., from 0.001% to 1%). In this study, a bubble model for unsaturated soil is developed within the framework of kinematic hardening and bounding surface plasticity. An elliptical elastic bubble is defined inside a modified Cam-clay bounding surface. Being a key feature of the proposed model, the size of the elastic bubble is modelled as a function of suction, degree of saturation, and plastic volumetric strain. Translation of the elastic bubble is governed by suction, degree of saturation, and stress increments. Moreover, hardening modulus depends on not only stress and void ratio, but also suction, degree of saturation, and relative position of the elastic bubble and the bounding surface. The proposed model is evaluated using suction-controlled constant-p shear tests on completely decomposed tuff (silt). It is evident that the new model is capable of capturing well the effects of recent suction history on nonlinear stress–strain relation and shear modulus degradation at small strains.

A non-associative orthotropic plasticity model for paperboard under in-plane loading

In this paper, we present an in-plane yield criterion using sub-surfaces that are related to the orthotropic material axes of paperboard. A non-associative flow rule is proposed to decouple the plastic volumetric strain response from the yield surface’s shape. This offers adaptability of both, the yielding under biaxial tension and the plastic Poisson’s ratios under tension and compression. Anisotropic hardening is introduced by making use of the sub-surface structure of the yield surface formulation. In addition, a scaling function for shear hardening is introduced in order to describe the material behaviour under compressive loading with superimposed shear. Off-axis tensile and compression tests were performed to determine the necessary material parameters. Hereby, significant differences were found between the plastic Poisson’s ratios under tension and compression. To account for local variations in paperboard density, a homogenization on basis of transmitted light images is suggested and applied to strain measurements by digital image correlation.

Interpretation of piezocone penetration and dissipation tests in sensitive Leda clay at Gloucester test site

A modified piezocone penetration test (CPTu) analytical solution based on spherical cavity expansion and critical state soil mechanics (SCE–CSSM) is employed for assessing yield stress, undrained shear strength, and flow parameters in sensitive Leda clay at the Gloucester test site. For sensitive and structured clays, the formulation relies on the mobilized effective stress friction angle ([Formula: see text]) defined at two parts of the stress–strain curve: (i) peak stress ([Formula: see text]) and (ii) maximum obliquity ([Formula: see text]). Input parameters for assessing the overconsolidation ratio ([Formula: see text], where [Formula: see text] is preconsolidation stress and [Formula: see text] is current effective vertical stress) from CPTu results include: undrained rigidity index (IR= G/su, where G is shear modulus and suis undrained shear strength), plastic volumetric strain potential (Λ = 1 – (Cs/Cc), where Csis swelling index and Ccis virgin compression index), and effective friction angles ([Formula: see text] and [Formula: see text]). A direct CPTu means of assessing the undrained rigidity index in a reliable manner is also developed that gives the Nktcone factor and matches profiles of undrained shear strength from triaxial compression tests (suTC). The modified solution is also implemented on two additional sites: a sensitive-quick clay in Norway and structured varved clay from New England. Interpretations of the coefficient of consolidation and permeability from pore-water pressure dissipation tests at Gloucester are evaluated using the SCE–CSSM formulation and shown to be comparable with independent laboratory and field tests.

Experimental investigation on dilatancy behavior of frozen silty clay subjected to long-term cyclic loading

An interesting and common feature of frozen silty clay cyclic behavior is that the accumulation of shear strain is not significant after a critical number of loading cycles, whereas the volumetric strain accumulates continuously in cyclic triaxial tests of frozen soils. Under cyclic triaxial conditions, the deformation mechanism of a frozen soil is often considered as a combination of frictional sliding and volumetric compaction, and hence the accumulated plastic volumetric strain can be divided into a dilation component due to shearing and a compaction component due to mean stress. A series of cyclic triaxial tests are carried out on a frozen silty clay. The evolution of volumetric dilation in each test is investigated against the accumulation of plastic shear strain. Volumetric dilation in these tests is shown to start right from the beginning, without a clear initial compression phase that is typically observed in testing unfrozen dense sand or stiff clay. The dependence of volumetric dilation on stress measures including cyclic stress amplitude, confining pressure or initial stress ratio is not pronounced, whereas the nonlinearity between the volumetric dilation and accumulated plastic shear strain is apparent. The plastic shear strain is then employed as a state variable, and a state-dependent dilation law is proposed to explain the experimental results. The experimental data and the proposed dilation law can potentially be incorporated into some cyclic constitutive models, leading to new insights of the behavior of frozen soils.

Behavior of steel fiber-reinforced concrete-filled FRP tube columns: Experimental results and a finite element model

This paper presents the results of an experimental study together with the first finite element (FE) model for the compressive behavior of fiber-reinforced polymer (FRP)-confined steel fiber-reinforced concrete (SFRC). 73 existing experimental test results of FRP-confined and actively confined SFRC specimens tested under axial compression were initially assembled. Additional axial compression tests were conducted on 16 actively confined SFRC specimens to address the gaps in the existing test database to compile a reliable database for the FE modeling of FRP-confined SFRCs. The analysis of experimental test results revealed that the compressive behavior of FRP-confined SFRCs is influenced by the steel fiber volume fraction and aspect ratio. New expressions were developed for the hoop rupture strain of the FRP jacket, axial strain-lateral strain relationship of FRP-confined and actively confined SFRC, and relationship between the confining pressure and the compressive strength of actively confined SFRC by considering the influences of the volume fraction and aspect ratio of internal steel fibers. A recently developed concrete damage-plasticity model, which was shown to be the most accurate currently available model for confined plain concrete, was adopted for the prediction of the compressive behavior of FRP-confined SFRC. The failure surface and flow rule of the model were modified based on the results from actively and FRP-confined SFRC. The results show that model predictions of the axial stress-axial strain, lateral strain-axial strain, axial stress-volumetric strain, plastic volumetric strain-axial plastic strain, and plastic dilation angle-axial plastic strain relationships are in good agreement with the experimental results of FRP-confined SFRC. The new model provides improved accuracy over the best performing existing models of FRP-confined plain concrete in predicting the behavior of FRP-confined SFRC.

The Stress Triaxiality Effect under Large Plastic Deformation of a Polybutylene Terephthalate (PBT)

In this work, we focus on a new generation of polymer named Polybutylene terephthalate (PBT). In order to analyse and determine true behaviour of this polymer, a special experimental method was used. Hence, the true stress/strain responses are investigated under a large plastic deformation in different stress triaxiality frameworks with a particular attention on the volumetric strain evolution, with their decomposition to an elastic volumetric strain, plastic volumetric strain and the pure shear. Moreover, the effect of stress triaxiality on the plastic instability and the fracture strain is also examined. With the plastic instability analysis, it was found that plastic strain hardening increases gradually with the triaxiality. Finally, in order to evaluate the damage of this polymer, a theoretical damage formula is proposed.