Critical State Concept Research Articles

Ice rubble frictional resistance by critical state theories

To describe the ice rubble shear strength, the Mohr–Coulomb criterion is often recommended. However, its inconsistency with some shear strength measurements was reported in the literature. The paper argues that a main source of this inconsistency is the ice rubble tendency towards volumetric changes which are ignored in the Mohr–Coulomb criterion. This argument is supported by the available data on bi-axial compression of ice rubble. The influence of volumetric changes on the ice rubble shear strength can be included by the means of the critical state concept. Several models based on this concept were reviewed; one of which, the Cam clay model, showed the best consistency with the bi-axial compression data and reported friction angles (presumably close to the critical state).

A generalized plasticity constitutive model for sand-gravel mixtures

This paper presents a model for prediction of the mechanical behavior of sand-gravel mixtures using generalized plasticity and critical state concepts. Proposed model is based on the difference between critical state lines of sand and sand-gravel mixture in e-Lnp' plane. A generalized plasticity model is considered as the base model for sandy soil. Its state parameter, dilation rate and hardening function are modified to involve the effects of gravel particles on the behavior of mixture. Gravel content is considered as a physical parameter for determination of four new added parameters of the model. Verification of the proposed model performed considering four sets of experiments conducted by different researchers on poorly graded sandgravel mixtures. According to the results, proposed model provides satisfactory qualitative and quantitative predictions of the behavior of sand-gravel mixture. Stress- strain behavior besides volumetric strains in drained condition and induced pore pressure during undrained loading are satisfactory predicted which indicates the possibility of its application in boundary value problems of geotechnical engineering.

A visco‐elasto‐plastic model for granular materials under simple shear conditions

SummaryThe numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre‐collapse and post‐collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi‐static to dynamic conditions, in particular when the material experiences a sort of solid‐to‐fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi‐static one and the collisional one. The former is determined by using a perfect elasto‐plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated. Copyright © 2015 John Wiley & Sons, Ltd.

Thermal-Hydro-Mechanical Analysis of Frost Heave and Thaw Settlement

AbstractFrost heave and thaw settlement are the cause of substantial damage to infrastructure in regions of seasonal freezing as well as seasonal thawing (permafrost). While frost heaving of soils has been researched for decades, less attention has been paid to quantitative estimates of settlement and loss of strength of soils due to thawing. A constitutive model is developed, capable of simulating freezing and thawing of soils, and associated changes in the soil strength. While the porosity growth parameters describing frost heaving have been calibrated and validated for a specific soil, the description of the thawing phase has not been validated due to a lack of experimental data. The yielding of the frozen soil is described using the critical state concept, with the pore ice content being an important parameter affecting the yield function. The model was calibrated using available laboratory test data and used in the simulation of a freezing–thawing cycle in the soil with embedded footing.

Thermo-mechanical constitutive modeling of unsaturated clays based on the critical state concepts

A thermo-mechanical constitutive model for unsaturated clays is constructed based on the existing model for saturated clays originally proposed by the authors. The saturated clays model was formulated in the framework of critical state soil mechanics and modified Cam-clay model. The existing model has been generalized to simulate the experimentally observed behavior of unsaturated clays by introducing Bishop's stress and suction as independent stress parameters and modifying the hardening rule and yield criterion to take into account the role of suction. Also, according to previous studies, an increase in temperature causes a reduction in specific volume. A reduction in suction (wetting) for a given confining stress may induce an irreversible volumetric compression (collapse). Thus an increase in suction (drying) raises a specific volume i.e. the movement of normal consolidation line (NCL) to higher values of void ratio. However, some experimental data confirm the assumption that this reduction is dependent on the stress level of soil element. A generalized approach considering the effect of stress level on the magnitude of clays thermal dependency in compression plane is proposed in this study. The number of modeling parameters is kept to a minimum, and they all have clear physical interpretations, to facilitate the usefulness of model for practical applications. A step-by-step procedure used for parameter calibration is also described. The model is finally evaluated using a comprehensive set of experimental data for the thermo-mechanical behavior of unsaturated soils.

A nonlinear criterion for triaxial strength of inherently anisotropic rocks

Rocks encountered at many underground construction sites are laminated and exhibit direction-dependent strength behavior. It is also a well-established fact that the strength varies in a nonlinear manner with confining pressure. There is a need of strength criterion which could capture the nonlinearity as well as the anisotropy in the triaxial strength behavior of the rocks. It is essential that the criterion should be simple and must involve minimum testing to the extent possible. Further, the parameters of the criterion should have wide acceptability among the geotechnical fraternity. In the present study, a nonlinear strength criterion for transversely isotropic rocks is presented. Critical state concept Barton (Int J Rock Mech Mining Sci Geomech Abstr 13(9):255–279, 1976) has been used to define the curvature of the criterion. With a correctly defined curvature and starting from a reference point (UCS), it is possible to accurately assess the triaxial strength for given confining pressure. An experimental study conducted on triaxial strength behavior of three types of anisotropic rocks namely phyllite, slate and orthoquartzite has been discussed. A data base comprising more than 1140 triaxial tests conducted worldwide on anisotropic rocks has been compiled. Statistical evaluation of goodness of fit of the proposed criterion to the data base has been carried out. Further, the predictive capabilities of the proposed criterion have been evaluated by determining the error in estimation of triaxial strength if only few triaxial test data are available for determining the criterion parameters. The data base has also been back analyzed to assess the critical confining pressure for anisotropic rocks. Statistically, the critical confining pressure for anisotropic rocks can be taken nearly equal to 1.25 times the maximum UCS (obtained by applying load either parallel or perpendicular to planes of anisotropy). It is concluded that reasonable estimates of the triaxial strength of anisotropic rock can be made through the proposed criterion using minimum amount of triaxial test data available.

Evaluation of crushing stress at critical state of granulated coal ash in triaxial test

A series of triaxial compression tests was performed on three types of granulated coal ash (GCA) to investigate their shear and crushing behaviour. The experimental results show that GCA displays different dilatancy characteristics to other natural granular materials due to excessive breakage even at low stresses. A simple constitutive model for crushable soils with the ability to predict the mechanical and deformation behaviour of GCA is introduced. This constitutive model uses a new strength parameter, the so-called reference crushing stress, which affects the evolution of the failure state curve. The mean stress when the peak stress ratio reduces to the critical state stress ratio and the mean stress when the peak friction angle reduces to the critical state friction angle were employed to determine the peak strength of GCA in combination with relative density and confining pressure. These three parameters, defined using the critical state concept within the framework of triaxial testing, are examined and their linear correlations are shown. It is also noted that the reference crushing stress strongly correlates with the single particle strength for a given type of GCA and, as such, has some specific mechanical meaning.

Predictive Modeling of the Evolution of Fault Structure: 3-D Modeling and Coupled Geomechanical/Flow Simulation

Reconstruction of geological structures has the potential to provide additional insight into the effect of the depositional history on the current-day geomechanical and hydro-geologic state. Accurate modeling of the reconstruction process is, however, complex, necessitating advanced procedures for the prediction of fault formation and evolution within fully coupled geomechanical, fluid flow and temperature fields. In this paper, a 3-D computational approach is presented that is able to forward model complex structural evolution with multiple intersecting faults that exhibit large relative movement within a coupled geomechanical/flow environment. The approach adopts the Lagrangian method, complemented by robust and efficient automated adaptive meshing techniques, an elasto-plastic constitutive model based on critical state concepts, and global energy dissipation regularized by inclusion of fracture energy in the equations governing state variable evolution. The proposed model is validated by comparison of 2-D plane strain and 3-D thin-slice predictions of a bench-scale experiment, and then applied to two conceptual coupled geomechanical/fluid flow field-scale benchmarks.

Elastoplastic model with loading memory surfaces (LMS) for monotonic and cyclic behaviour of geomaterials

SUMMARYA new elastoplastic model called loading memory surface based on the critical state concept and the multi‐surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three‐dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three‐dimensional generalization of the well‐known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.

A constitutive model for cemented clays capturing cementation degradation

Laboratory experiments show that the effect of cementation on clays gradually diminishes as the confining pressure increases (particularly at high confining pressures) due to the degradation of cementation bonds. The main aim of this paper is to propose a constitutive model for cemented clays, referred to as the Cemented Cam Clay model (CCC), to simulate the cementation degradation during loading. The failure envelope of the proposed model is formulated to describe the behaviour of the cemented clay at a low pressure range similar to over-consolidated soils, while it merges with the Critical State Line of reconstituted sample gradually as the confining pressure continues to increase. In order to examine the stress–strain behaviour of cemented clays, an energy dissipation equation is developed inspired by the Modified Cam Clay model. The characteristics of the proposed model, including a non-associated plastic potential function and elasto-plastic stress–strain relationship, are presented in light of the Critical State concept. Validity of the proposed constitutive model derived from the modified energy equation is evaluated against triaxial test results for cemented clays available in literature.

Development of a generalized plasticity constitutive model for cemented sands using critical state concepts

This paper presents a model for the prediction of the mechanical behavior of cemented soils in saturated state using generalized plasticity and critical state concepts. The proposed model is based on the difference between isotropic compression curves of cemented and uncemented soils in e-Lnp' space. Generalized plasticity model proposed by is considered as the base model for the uncemented soil and its flow rule and hardening functions besides the elastic parameters are modified to consider cementation effects adding six new parameters. Cement content is considered as a physical parameter for the determination of model parameters. Model evaluation was conducted for three different sets of triaxial tests on cemented sands. Based on the results, the proposed model provides satisfactory qualitative and quantitative predictions. Deviatoric stress–shear strain and volumetric strain–shear strain curves are predicted fairly well. It shows the possibility of model application in boundary value problems of geotechnical engineering.

Unique critical state characteristics in granular media considering fabric anisotropy

The concept of the critical state in granular soils needs to make proper reference to the fabric structure that develops at critical state. This study identifies a unique property associated with the fabric structure relative to the stresses at critical state. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found at critical state, and is path-independent. Numerical simulations using the discrete-element method under different loading conditions and intermediate principal stress ratios identify a unique power law for this relationship. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the conditions of constant stress and unique void ratio required by the conventional critical state concept, the new definition imposes the additional constraint that K reaches a unique value at critical state. A unique spatial critical state curve in the three-dimensional space K–e–p′ is found for a granular medium, the projection of which onto the e–p′ plane turns out to be the conventional critical state line. The new critical state concept provides an important reference state for a soil to reach, based on which the key concepts in the constitutive modelling of granular media, including the choice of state parameters, dilatancy relation and non-coaxiality, are reassessed, and future exploratory topics are discussed.

An Efficient Model for Numerical Simulation of the Mechanical Behavior of Soils. Part 1: Theory and Numerical Algorithm

A numerical model to simulate the mechanical behavior of soils is presented in this first part of the present work. This paper reports some advances obtained in the first stage of an ongoing research, which aims to develop a robust and efficient algorithm for consolidation analyses of saturated/unsaturated soils. Hence, the present work is mainly concerned with basic issues, such as efficiency of the finite element formulation and accuracy of the constitutive formulation. Since geotechnical materials exhibit elastoplastic characteristics, the theory of plasticity is applied here by means of the critical state concept using the Cam-Clay formulation. The constitutive equation is integrated using an explicit algorithm where the strain increment is divided into a number of sub-steps defined automatically by the numerical scheme. Eight-node hexahedral finite elements with one-point quadrature are employed in the spatial discretization of the geometrical domain. In order to avoid excitation of spurious modes, an efficient hourglass control is utilized in conjunction with a corotational formulation, which also contributes to the treatment of geometrical and physical nonlinearities.

Analytical Methods and Formulas for Modeling High Temperature Superconductors

The electrodynamics of type-II superconductors is considered in the quasi-static limit when the concept of the so-called critical state is well applicable to the superconductors. We review analytical techniques and formulas used to describe the critical states in the superconductors of the various shapes characteristic of high-temperature superconducting materials. In particular, it is explained how 3-D critical-state problems for thin planar superconductors can be reduced to more simple 2-D problems. Within this approach, the critical states in a thin infinitely long superconducting strip are analytically described not only in the simplest case of a constant critical current density jc but also in the case of anisotropic flux-line pinning and for simple model dependence of jc on the magnetic-field magnitude. We also present the analytical solutions of the critical-state problem for superconducting strips with ferromagnetic substrates and for various arrays of superconducting strips with a transport current or in an external magnetic field. In particular, one of the discussed configurations of the strips can model superconducting power transmission cables. We also describe some analytical solutions of the electrodynamic equations for type-II superconductors with power-law voltage-current characteristics.

A simple critical-state-based double-yield-surface model for clay behavior under complex loading

The critical state concept has been widely used in soil mechanics. The purpose of this study is to apply this concept in the framework of multi-mechanism elastoplasticity. The developed model has two yield surfaces: one for shear sliding and one for compression. In this model, the location of the critical state line is explicitly considered and related to the actual material density to control the peak strength and the phase transformation characteristics. The stress reversal technique is incorporated into the model for describing clay behavior under complex loading including changes of stress direction. The determination of the model parameters is discussed; it requires only one drained or undrained triaxial test up to failure with an initial isotropic consolidation stage. The model is used to simulate drained and undrained tests under monotonic loading with different over-consolidation ratios on various remolded and natural clays, including true triaxial tests with different Lode’s angles. Drained and undrained tests under cyclic loadings are also simulated by using the set of parameters determined from monotonic tests. The comparison between experimental results and numerical simulations demonstrate a good predictive ability of this new simple model.

From solid to granular gases: the steady state for granular materials

SUMMARYThis paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.

Implementation of an elasto‐plastic constitutive model for cement stabilized clay in a non‐linear finite element analysis

Purpose – Several constitutive models are available in the literature to describe the mechanical behaviour of cement stabilized soils. However, difficulties in implementing such models within commercial finite element programs have hindered their application to solve related boundary value problems. Therefore, the aim of this study is to implement a constitutive model, which has the capability to simulate cement stabilized soil behaviour, into the finite element program ABAQUS through the user material subroutine UMAT.Design/methodology/approach – After a detailed review of existing constitutive models for cement stabilized soils, a model based on the elasto‐plastic theory and the extended critical state concept with an associated flow rule is selected for the finite element implementation. A semi‐implicit integration method (cutting plane algorithm) with a continuum elasto‐plastic modulus and path dependent stress prediction strategy has been used in the implementation. The performance of the new finite ...

Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks

Rocks encountered in civil and mining engineering fields are invariably jointed and act under triaxial or polyaxial stress conditions. The Mohr–Coulomb shear strength criterion is the most widely used criterion for jointed rocks. In its present form there are two major limitations of this criterion; firstly it considers the strength response to be linear, and, secondly the effect of the intermediate principal stress on the strength behaviour is ignored. A modified non-linear form of Mohr–Coulomb strength criterion has been suggested in this study to overcome these limitations. Barton's concept of critical state for rocks has been imbibed in the linear Mohr–Coulomb criterion to deduce a semi-empirical expression for non-linear criterion. However, the shear strength parameters of the conventional Mohr–Coulomb criterion are used in the proposed criterion. The proposed criterion is a simple and rational nonlinear polyaxial strength criterion for anisotropic jointed rocks. In an earlier publication [1] the applicability of the criterion was evaluated for intact rocks. In present paper the criterion is extended to jointed rocks, which are anisotropic in nature. The applicability of the proposed criterion has been verified by applying it to extensive experimental data on triaxial and polyaxial test results on jointed rocks available from literature. Applicability of the criterion, to explain rock burst conditions for some Indian rocks, is also demonstrated.

Physical and mechanical properties of decomposed granite soils sampled in Cheongju, Korea

Decomposed granite soils are in a wide range of conditions depending on the degrees of weathering. This paper is intended to examine laboratory tests, such as consolidation tests and conventional triaxial compression (CTC) tests conducted in order to find out the mechanical properties of Cheongju granite soil. Along with the foregoing, the results of basic physical tests conducted in order to grasp the physical properties of Cheongju granite soil were described and based on the results, methods to calculate the mechanical parameters of numerical approaches using Lade’s single and double surface work-hardening constitutive model were examined. Finally, this study is intended to explain the stress properties of Cheongju granite soil used as a geotechnical material based on its shear behavior and critical state concept using the results of isotropic consolidation tests and triaxial compression tests. As a conclusion, it can be seen that in the relationship between confining stress and maximum deviator stress, the slope is maintained at a constant value of 2.95. In the drained CTC test, maximum deviator stress generally existed in a range of axial strain of 6 to 8% and larger dilatancy phenomena appeared when confining stress was smaller. Finally, based on the results of the CTC tests on Cheongju granite soil, although axial strain, deviator stress and pore water pressure showed mechanical properties similar to those of over consolidated soil, Cheongju granite soil showed behavior similar to that of normally consolidated soil in terms of volumetric strain. Key words: Granite soil, stress-strain relation, single and double surface work-hardening model, soil parameter.

The Effect of Dilation and Particle Breakage on the Volumetric Behavior of Carbonate Sands (Technical Note)

In this paper the volumetric behavior of four carbonate sands having different physical properties and crushable grains are investigated using isotropically consolidated-drained triaxial tests. Three sands were obtained from the north shores of the Persian Gulf, south of Iran, called Hormoz, Kish and Tonbak sands, and one was obtained from the south beaches of England and called Rock beach sand. The studied sands have different particle size distribution, shapes and physical properties. Shapes of the grains in these soils are as platy, needle, bulky, angular, subangular and porous, in which show the different sources and deposition environments of them. Tests results conducted on the studied carbonate sands show that different properties of them result in different particle breakage ratio during loading, so that it increases with confining pressure, axial strain, slenderness and area to thickness ratio of the soil grains. Volumetric response of these soils is complex due to interaction of dilation and contraction resulted from particle breakage during shear loading. Therefore, regarding the unknown values of void ratios changes from dilation and particle breakage, the critical state concept become complex. In fact, there is not a real critical state in these soils at least up to axial strain of %20. It is also impossible to reach the critical sate concept using the common triaxial tests apparatus considering of its axial strain limitation. The randomly observed deformation under constant volume is apparent and not real. Such a situation is the volumetric balance between dilation and contraction due to particle breakage. Considering the relative values of these two parameters, the location of the apparently critical state is variable and curve shape, and it is depend on the initial void ratio, dilation, particle breakage and confining pressure. It is expected that the dilation ends up fast, however, particle breakage occurs as the shear strains are applied.