Critical State Soil Mechanics Research Articles

A simple critical state approach to predicting the cyclic and monotonic response of sands with different fines contents using the equivalent intergranular void ratio

This paper focuses on developing a simple approach to describing the monotonic and cyclic behavior of sands with fines by employing the concept of equivalent intergranular void ratio, e , in the critical state soil mechanics framework. To establish and evaluate this approach, which facilitates the process of predicting the soils behavior and minimizes the experimental work required, a large number of datasets published in the literature for 10 different types of soils are processed and analyzed. The proposed approach makes it possible to predict the behavior and resistance of sands in a unique way for all the fines contents, stress levels and densities, without the need for performing tests at different fines contents. The issue of determining the b value, used as a physical constant in the definition of e , and the factors affecting it is studied. In this context, a recently established b-predicting equation is evaluated and its empirical parameters are calibrated with various datasets. Examining the influence of grading parameters on the b value resulted in a strong relationship between b and the particle size ratio. The results also show that the b value can be reliably estimated using the experimental data available at only two fines contents of 0 and 23 %.

UNDRAINED SHEAR STRENGTH OF K0CONSOLIDATED SOFT CLAYS UNDER TRIAXIAL AND PLANE STRAIN CONDITIONS

Theoretical formulas for predicting the undrained shear strength of K0consolidated soft clays under the stress path related to triaxial and plane strain tests are presented within the framework of critical state soil mechanics. An inclined elliptical yield surface is adopted to take account of the initial anisotropic stress state. The undrained strength is determined by combining the undrained stress path in the volumetric stress–strain space and the initial yield surface in the deviator-mean stress space. The derived mathematical expressions are functions of the critical state frictional angle, the plastic volumetric strain ratio and the overconsolidation ratio, which can be simplified into the solutions for isotropically consolidated clays under triaxial tests or under plane strain tests. The results calculated by using the theoretical formulas obtained in this paper are in good agreement with the available collected test results. It indicates that these new formulas are applicable to triaxial and plane strain tests on normally and lightly to moderately overconsolidated soft clays.

Bounding Surface Plasticity Model Incorporating the State Pressure Index for Rockfill Materials

AbstractThe critical state line of Tacheng rockfill material (TRM) was described by a pressure-power function. A simple bounding-surface plasticity model, combining the dilatancy stress ratio and peak-failure stress ratio pertaining to the state pressure index, was developed for TRM within the framework of critical-state soil mechanics and the bounding surface plasticity. Detailed investigations of influences of design parameters on the model predictions were carried out. The developed model, using a set of model constants, captured well behaviors such as strain hardening and volumetric contraction for TRM in a loose state (e.g., at a large initial void ratio or a high initial confining pressure) and strain softening and volumetric expansion in a dense state (e.g., at a small initial void ratio or a low initial confining pressure).

Undrained Behavior of Sand-Fines Mixtures and Their State Parameter

AbstractThe influence of fines on the undrained behavior of sand was investigated experimentally over a range of fines content and effective mean stress. The role of fines on compressibility and formation of meta-stable soil fabric was analyzed. For a fines content in the range of 5–30%, most of the specimens manifested reverse behavior opposed to the normal behavior of clean sand. The addition of fines led to shifting of both the isotropic consolidation line and the steady-state line, increased compressibility, and occurrence of reverse behavior. All these behavior attributes are linked when the test results are interpreted in the context of the critical-state soil mechanics framework. In particular, reverse behavior is associated with an isotropic consolidation line that locates above the steady-state line. Several quantitative measures for characterizing the undrained deviator stress-strain responses were proposed, and these measures manifested correlation with the state parameter at the start of undra...

Thermomechanical Constitutive Model for Saturated Clays Based on Critical State Theory

AbstractA thermomechanical constitutive model for predicting the isothermal behavior of saturated clays in different temperatures is presented in this paper. This model is developed based on the general framework of critical state soil mechanics and modified Cam-clay formulation. Most of the characteristics of saturated clays in temperatures lower than water’s boiling temperature have been taken into account. An attempt has been made to use the lowest possible number of extra parameters compared with the original Cam-clay model and to ensure that these new parameters have clear physical interpretations. An important feature in the model is thermal dependency of the critical state line in the deviatoric stress plane. The predictions have been compared with five sets of laboratory data available in the literature.

A constitutive model for unsaturated soils with consideration of inter-particle bonding

The paper presents a physically-based constitutive model for unsaturated soils that considers the bonding effect of water menisci at inter-particle contacts. A bonding factor has been used to represent the magnitude of the equivalent bonding stress, defined as the bonding force per unit cross-sectional area. The average skeleton stress is employed to represent the effect of average fluid pressures within soil pores. Based on an empirical relationship between the bonding factor ζ and the ratio e/es (where e and es are void ratios at unsaturated and saturated states, respectively, at the same average skeleton stress), we propose an elasto-plastic constitutive model for isotropic stress states, and then extend this model to triaxial stress states within the framework of critical state soil mechanics. Because only one yield surface is needed in the proposed model, a relatively small number of parameters are required. Comparisons between experimental data and model results show that, in most cases, the proposed model can reasonably capture the important features of unsaturated soil behavior.

A unified plasticity model for large post-liquefaction shear deformation of sand

Based on previous experimental findings and theoretical developments, this paper presents the formulation and numerical algorithms of a novel constitutive model for sand with special considerations for cyclic behaviour and accumulation of large post-liquefaction shear deformation. Appropriate formulation for three volumetric strain components enables the model to accurately predict loading and load reversal behaviour of sand, fully capturing the features of cyclic mobility. Compliance with the volumetric compatibility condition, along with reversible and irreversible dilatancy, allows for physically based simulation of the generation and accumulation of shear strain at zero effective stress after initial liquefaction. A state parameter was incorporated for compatibility with critical state soil mechanics, enabling the unified simulation of sand at various densities and confining pressures with a same set of parameters. The determination methods for the 14 model parameters are outlined in the paper. The model was implemented into the open source finite-element framework OpenSees using a cutting-plane stress integration scheme with substepping. The potentials of the model and its numerical implementation were explored via simulations of classical drained and undrained triaxial experiments, undrained cyclic torsional experiments, and a dynamic centrifuge experiment on a single pile in liquefiable soil. The results showed the model’s great capabilities in simulating small to large deformation in the pre- to post-liquefaction regime of sand.

Constitutive modeling of dense gravelly soils subjected to cyclic loading

SUMMARYA constitutive model for dense gravelly soils was developed to reproduce their responses under cyclic loadings. Its application aims at nonlinear dynamic analyses of earth structures involving gravelly soils, such as rockfill dams and railroad ballasts. The framework of generalized plasticity was modified to incorporate the concept of stress distance for better simulation of unloading and reloading responses. It was then combined with the theory of critical state soil mechanics to develop the constitutive model. The model has the following important features: unified simulation of particle breakage through translating critical state line, smooth transition from unloading to reloading in the stress space, and proper modeling of cyclic hysteresis, cyclic densification, and cyclic hardening of dense gravelly soils. Most of the model parameters can be obtained through simple calculation using conventional triaxial test results, and their calibration process was discussed. The model was used to simulate the cyclic responses of three gravelly soils with satisfactory accuracy. Copyright © 2014 John Wiley & Sons, Ltd.

Evaluation of coefficient of consolidation for dilatory dissipation in piezocone test in overconsolidated cohesive soils

The interpretation method for dilatory dissipation, showing an initial temporary increase in pore pressure, in piezocone tests in overconsolidated clayey soils was investigated in this study. Finite difference analyses on the dissipation after cone penetration were performed with various ground conditions. The spatial distribution of initial excess pore pressure induced by cone penetration was determined from experimental estimations through in-situ tests and laboratory physical model tests and theoretical predictions by the cavity expansion theory and critical state soil mechanics. A method to evaluate the coefficient of consolidation from dilatory dissipation results was developed through the assessment of numerical simulation results. Comparing the application results with the laboratory-determined values, it was verified that the proposed approach provided a reliable and consistent evaluation of the coefficient of consolidation.

Guidelines for Calibration and Use of the Severn-Trent Sand Model in Modeling Cantilevered Wall-Supported Excavations

AbstractThe Severn-Trent sand model is an advanced elastoplastic constitutive model that accurately reproduces the nonlinear mechanical response of coarse-grained soils at small to relatively high strain levels under monotonic loading. The model, formulated within the framework of critical state soil mechanics, includes advanced plasticity modeling concepts such as kinematic hardening, multisurface plasticity, and bounding surface plasticity. This paper shows how the use of Severn-Trent can be extended in modeling cantilevered wall-supported excavations. Following a brief description of the approach taken to introduce the constitutive model into a finite-difference commercial code, guidelines for the model calibration are discussed. Accounting for the approximation, which affects the evaluations of some variables, several plane-strain numerical analyses are performed. The parametric study aims to evaluate to what extent the response of a cantilevered retaining structure in a dry, normally consolidated Toy...

Micro mechanics of isotropic normal compression

Discrete element modelling has been used to investigate the micro mechanics of isotropic normal compression. One-dimensional (1D) normal compression has previously been modelled in three dimensions using an oedometer and a large number of particles and without the use of agglomerates, and it was shown that the compression index was solely related to the strengths of the particles as a function of size. The same procedure is used here to model isotropic normal compression. The fracture of a particle is governed by the octahedral shear stress within the particle (due to the multiple contacts) and a Weibull distribution of strengths. The octahedral shear stresses, due to local anisotropic stresses within a sample with isotropic boundary stresses, are shown to give rise to a normal compression line (NCL) and the evolution of a distribution of particle sizes. The compression line is parallel to the 1D NCL in log e–log p space, in agreement with traditional critical state soil mechanics and confirming that the compression index is solely a function of the size effect on average particle strength, which determines the hardening law for the material. The paper shows, for the first time, how local octahedral shear stresses induced in the particles within the sample generate an isotropic normal (clastic) compression line.

Influence of fines content on liquefied strength of silty sands

Critical state soil mechanics is a useful framework to understand sand behavior. In this paper, a relationship is developed for estimating undrained critical shear strength of sands based on the critical state framework. The relationship is validated by comparison with laboratory test results and sand liquefied strength from field liquefaction failure case histories. Using this relationship, the influence of fines content on undrained critical shear strength is studied for different combinations of effective stress and density. The parametric study indicates that depending on soil void ratio, effective stress, and the shape and mineralogy of the fine particles, undrained critical strength may increase, remain the same, or decrease as the amount of fines content increases. Both the susceptibility to liquefaction and the severity of strain-softening are affected by adding fines. It is suggested that the critical state parameter is inadequate for describing the behavior of liquefiable sands and sand shearing-compressibility should be taken into account in liquefaction analysis.

Influence of state and compressibility on liquefied strength of sands

Critical-state soil mechanics is a useful framework to understand sand behavior. In this paper, a relationship is developed for estimating undrained critical shear strength of sands based on the critical-state framework. The application of this relationship is demonstrated by comparison with laboratory test results and sand liquefied strength from field liquefaction flow failure case histories. Using this relationship, the effects of effective stress variation and density on undrained critical shear strength are studied for different combinations of critical-state line parameters corresponding to several reference sands. The parametric study indicates that depending on sand void ratio, undrained critical shear strength may increase, remain the same or decrease as sand shearing–compressibility (represented by the slope of the critical-state line) increases. The underlying mechanisms of field failures in dense sands and reverse behavior of compressible sands are explained through this relationship. It is suggested that the critical-state parameter alone is insufficient for describing the behavior of liquefiable sands and sand shearing–compressibility should be also taken into account for estimating undrained shear strength corresponding to the changes in density and effective confining stress.

Constitutive Model for Strength Characteristics of Municipal Solid Waste

This paper presents modification of the derivation of a previously proposed constitutive model for the prediction of stress-strain behavior of municipal solid waste (MSW) incorporating different mechanisms, such as immediate compression under loading, mechanical creep, and time-dependent biodegradation effect. The model is based on critical state soil mechanics incorporating increments in volumetric strains because of elastic, plastic, creep, and biodegradation effects. The improvement introduced in this paper is the modified critical state surface and considers five variable parameters for the estimation of stress-strain behavior of MSW under different loading conditions. In addition, an expression for the strain hardening rule is derived, with considerations of time-dependent mechanical creep and biodegradation effects. The model is validated using results from experimental studies and data from published literature. The results are also compared with the predictions of the stress-strain response obtained from a well-established hyperbolic model. (c) 2014 American Society of Civil Engineers.

Quantifying the evolution of soil fabric during shearing using scalar parameters

The packing density of a soil is typically described in terms of the scalar parameters void ratio, specific volume or porosity. Within a critical-state soil mechanics framework, the response of a sand is considered to depend on its ‘state', that is, the combination of void ratio and effective stress. When soil is considered from a particle-scale perspective, the packing density is often described using the coordination number (CN), that is, the average number of contacts per particle. Using particles with simple geometries, discrete-element method (DEM) simulations, photoelastic tests and experiments on analogue soils (e.g. glass ballotini) have all demonstrated a correlation between CN and mechanical response. This study investigates whether these correlations apply to real soils using direct measurement of the fabric via micro-computed tomography (micro-CT). A variety of scalar fabric descriptors was measured during the triaxial compression of both intact and reconstituted Reigate sand samples. While each of the parameters considered provides useful information, the contact index (CI), a parameter that takes the contact area into account, was found to be a more sensitive metric in assessing the effects of fabric than coordination number, branch vector length or void size.

Estimation of Critical State Parameters from One-dimensional Consolidation and Triaxial Compression Tests

Determination of critical state parameters are essential, when critical state soil mechanics based soil models are used for the analysis. Isotropic consolidation test and triaxial tests with accurate measurements of volume change and pore pressure are essential for the direct measurement of critical state parameters. However, in the conventional geotechnical engineering practice, isotropic compression tests are usually not conducted but only one-dimensional consolidation test are performed. The usual parameters reported in most of the soil investigation reports are the shear strength parameters c′ and ϕ′ and the consolidation parameters such as compression index (C c ) and the recompression index (C r ) apart from, the overburden pressure σ 0′ and the corresponding void ratio e0. The critical state parameters are seldom reported in most of the soil investigation reports. This paper explains a procedure to estimate the critical state parameters, in the absence of isotropic compression test data, based on one-dimensional consolidation tests and triaxial compression tests, using the equations of Modified Cam clay state boundary surface. Comparison of the calculated values from the suggested method with the measured values, on three reconstituted soils and one undisturbed soil, lends support to the validity of the proposed procedure.

The plastic limit of clays

The plastic limit of soils was first described by Atterberg in 1911. The thread-rolling test was standardised at the US Public Roads Bureau in the 1920s and 1930s, and has subsequently become one of the standard tests of soil mechanics. This paper reviews the original definitions of plastic limit as proposed by Atterberg, and proposes that the brittle failure observed in the plastic limit test is caused by either air entry or cavitation in the clay. Critical state soil mechanics is used to show that the observed range of undrained shear strengths of soils at plastic limit is consistent with this hypothesis. The fallacy that strength at plastic limit is a constant is highlighted, and the implications for geotechnical practice are discussed.

Effects of Woody Vegetation on Seepage-Induced Deformation and Related Limit State Analysis of Levees

AbstractWork in this paper investigates the effects of woody vegetation on soil hydraulic conductivity and the related probability of exceeding deformation-based performance limit states. A summary of results obtained from laboratory and field hydraulic conductivity tests for four levee sites is presented. Limit states, as defined based on the framework of critical state soil mechanics, are developed and simple probability analyses are used to quantify the probability of exceedance under hydraulic loading. A case study of Elkhorn Levee near Sacramento, California, is presented to demonstrate the applicability of the limit states concept. The field and laboratory hydraulic conductivity data obtained from the four levee test sites show no clear trend to support the notion that woody vegetation leads to either high or low values of hydraulic conductivity; site-specific testing is needed to discern such an effect. Even though the levee case used in this study (Elkhorn) was in a marginal condition of stability...

Constitutive modeling of the destructuration and anisotropy of natural soft clay

The mechanical behavior of natural clays is affected by their inherent anisotropy and metastable soil structure. A simple hierarchical model that considers initial anisotropy and destructuration was formulated within the framework of critical state soil mechanics. In the proposed model, stress sensitivity and a destructuration index were introduced to account for the degree of bonding and the rate of destructuration, respectively. An inclined yield surface was used to incorporate the effect of the initial anisotropy. The proposed model can be degenerated to the Modified Cam Clay model by setting the initial stress sensitivity equal to unity and using a horizontal yield surface. Reasonable agreement between the model simulations and the experimental results on a variety of stress paths demonstrated that the proposed model can capture well the deformation behavior of natural clay and reconstituted soil. The model was implemented into the finite element program for the numerical analysis of an embankment on soft clay improved with prefabricated vertical drains. The numerical predictions were compared with the field-measured data in terms of embankment settlement. Additionally, the numerical simulations were analyzed in terms of horizontal displacements, excess pore water pressure, mean effective stress and volumetric strain. All of the simulations and comparisons indicate the importance of considering the effects of plastic anisotropy, interparticle bonding and destructuration caused by loading beyond yield stress and field disturbance in analyzing the behavior of an embankment on natural soft clay.

Applicability of Cam-Clay Models for Tropical Residual Soils

The development of a critical state framework for saturated soils provides a powerful conceptual model based on the generalized principles of the elasto-plastic behavior of frictional materials (Schofield and Wroth, Critical state soil mechanics, 1968]. The model has been modified to meet the requirements of more complex applications (Wheeler, Proceedings of XIV ICSMFE, 1997). An attempt has been made in the present paper to apply conventional Cam-clay models to capture the stress–strain–pore pressure response of tropical residual soils. For this purpose oedometer tests and consolidated undrained triaxial tests were conducted on undisturbed soil specimens and reconstituted soil specimens of five soils collected form the surrounding areas of Tirupati in Andhra Pradesh. Using the Cam-clay models the predictive capabilities of these models are brought out in comparison to the experimental results on tropical residual soils. It has been shown that the Cam-clay models can only capture the behavior of remolded soils devoid of cementation whereas the Wheeler model can effectively predict the behavior of natural soils considered in the present investigation which show strain softening associated with positive pore pressures.