Modified Cam Clay Research Articles

Performance of mixed formulations for the particle finite element method in soil mechanics problems

This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy’s law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule

The paper presents a critical state bounding surface constitutive model for describing the behaviour of overconsolidated clays for a wide range of overconsolidation ratios, called the Hardening State Parameter – HASP model. Keeping the simplicity and the same set of the parameters as Modified Cam Clay, the HASP model provides a more realistic description of numerous elements of clay behaviour. With the new state parameter formulation of the hardening rule, elasto-plastic behaviour is enabled from early stages of loading. In undrained conditions, general shape of effective stress paths for various overconsolidation ratios and negative pore pressure is well predicted. In drained conditions, strain hardening, strain softening, as well as smooth transition from contractive to dilatant behaviour before the peak strength is reached are described. Verification is done against published results of drained and undrained tests in triaxial compression and extension, on the samples with various overconsolidation ratios.

Dilatancy Relation for Overconsolidated Clay

Abstract A distinct feature of overconsolidated (OC) clays is that their dilatancy behavior is dependent on the degree of overconsolidation. Typically, a heavily OC clay shows volume expansion, whereas a lightly OC clay exhibits volume contraction when subjected to shear. Proper characterization of the stress-dilatancy behavior proves to be important for constitutive modeling of OC clays. This paper presents a dilatancy relation in conjunction with a bounding surface or subloading surface model to simulate the behavior of OC clays. At the same stress ratio, the proposed relation can reasonably capture the relatively more dilative response for clay with a higher overconsolidation ratio (OCR). It may recover to the dilatancy relation of a modified Cam-clay (MCC) model when the soil becomes normally consolidated (NC). A demonstrative example is shown by integrating the dilatancy relation into a bounding surface model. With only three extra parameters in addition to those in the MCC model, the new model and t...

Influence of vertical loads on lateral response of pile foundations in sands and clays

Although the load applied to pile foundations is usually a combination of vertical and lateral components, there have been few investigations on the behavior of piles subjected to combined loadings. Those few studies led to inconsistent results with regard to the effects of vertical loads on the lateral response of piles. A series of three-dimensional (3D) finite differences analyses is conducted to evaluate the influence of vertical loads on the lateral performance of pile foundations. Three idealized sandy and clayey soil profiles are considered: a homogeneous soil layer, a layer with modulus proportional to depth, and two-layered strata. The pile material is modeled as linearly elastic, while the soil is idealized using the Mohr–Coulomb constitutive model with a non-associated flow rule. In order to confirm the findings of this study, soils in some cases are further modeled using more sophisticated models (i.e. CYsoil model for sandy soils and modified Cam-Clay (MCC) model for clayey soils). Numerical results showed that the lateral resistance of the piles does not appear to vary considerably with the vertical load in sandy soil especially at the loosest state. However, the presence of a vertical load on a pile embedded in homogeneous or inhomogeneous clay is detrimental to its lateral capacity, and it is unconservative to design piles in clays assuming that there is no interaction between vertical and lateral loads. Moreover, the current results indicate that the effect of vertical loads on the lateral response of piles embedded in two-layered strata depends on the characteristics of soil not only surrounding the piles but also located beneath their tips.

Numerical modelling of mechanical behaviour of partially saturated soils using coupled FEA

The effects of degree of saturation and water table depth on settlement and pore water dissipation behaviour of partially saturated soils has been analysed using coupled finite element analysis in the present study. The fundamental equations governing the fully coupled constitutive behaviour of partially saturated soils are presented. To obtain the numerical solution, a FORTRAN program has been developed. Modified cam clay model has also been implemented into a finite element code. The results are validated with available results in the literature. The behaviour of partially saturated soil under strip footing is considered as an example. Results indicate that under surface loading, consolidation behaviour of the partially saturated soils is governed by the initial degree of saturation and depth of water table.

The modified Cam-Clay (MCC) model: cyclic kinematic deviatoric loading

Different realizations of the modified Cam-Clay (MCC) models are reviewed. Several extensions of the MCC model are discussed, including models with kinematic hardening and bounding surface, the general plasticity model, extension of the MCC model to include finite strain, and different variants of the pressure hardening rules, including bi-modulus extension, hypoplastic, and the hyperelastic potential extensions. The associated flow rules coupled with different hardening equations are considered. The main attention is paid to the case of the infinitesimal strains. Numerical examples of kinematic deviatoric loadings for the considered model with linear elastic initial response are presented and analyzed.

Numerical simulations of deep penetration problems using the material point method

Penetration problems in geomechanics are common. Usually the soil is heavily disturbed around the penetrating bodies and large deformations and distortions can occur. The simulation of the installation of displacement piles is a good example of the interest of these types of problems for geomechanics. In this paper the Material Point Method is used to overcome the difficulties associated with the simulations of problems involving large deformation and full displacement type penetration. Recent modifications of the Material Point Method known as Generalized Interpolation Material Point and the Convected Particle Domain Interpolation are also used and evaluated in some of the examples. Herein a footing submitted to large settlements is presented and simulated, together with the processes associated to a driven pile under undrained conditions. The displacements of the soil surrounding the pile are compared with those obtained by the Small Strain Path Method. In addition, the Modified Cam Clay model is implemented in a code of MPM and used to simulate the process of driving a pile in dry sand. Good and rather encouraging agreement is found between compared data.

Analysis of Piezocone Penetration under Different Drainage Conditions with the Two-Phase Material Point Method

The piezocone penetration test (CPTU) is commonly used to identify a soil’s profile and estimate its material properties. Depending on the soil type, ranging from clay to sand, undrained, partially drained, or drained conditions may occur during cone penetration. In silt and sand–clay mixtures, the CPTU penetration is characterized by partially drained conditions, which are often neglected in data interpretation. The effect of drainage on CPTU measurements has been mainly studied experimentally. Numerical analyses are rare because taking into account large soil deformations, soil–water and soil–structure interactions, and nonlinear soil behavior is still a challenging task. This paper presents and discusses numerical simulations of CPTU in saturated soils with the two-phase material point method. Soil behavior is described with the modified cam clay model. This study investigates the effects of pore pressure dissipation during penetration, cone roughness, and horizontal stress state, comparing the results with experimental data. The paper discusses the effect of neglecting partial drainage in deriving the shear strength parameters for silty soils and suggests a procedure to estimate the consolidation coefficient for performing CPTU at different penetration rates.

A strength criterion for frozen sodium sulfate saline soil

Salt content has been proven to be an important influencing factor on the mechanical properties of frozen saline soils, whose strength criterion is different from that of unfrozen saline soils or frozen soils without salts. In this paper, a series of conventional triaxial tests are carried out for frozen saline soils with sodium sulfate at a temperature of –6 °C. A strength criterion of the frozen saline soils, including the influence of salt content, is established by using the generalized nonlinear strength theory. Based on conventional triaxial test results, a modified hydrostatic pressure expression is proposed according to the critical strength function of the modified Cam clay model in the meridian plane. The influence of salt content on the shear strength of the frozen saline soils is investigated according to their freezing temperature curves as well as the formation of salt and ice crystals. The relationship between salt content and friction angle is analyzed. The proposed strength criterion of frozen saline soil is proved to be reliable by extrusion elongation triaxial tests. This criterion can reasonably reflect the major nonlinear strength characteristics of frozen saline soils, including the influences of change in salt content, pressure melting, and ice crushing.

A New Elasto-Plastic Critical State Model RU+MCC for Overconsolidated Soil

The paper presents a reasonably advanced constitutive law for soil – a hybrid of the Modified Cam Clay and a new RU development. The Modified Cam Clay model is an isotropic hardening elasto – plastic model originated by Burland in 1967 [1] within the critical state soil mechanics. This model describes realistically mechanical soil behaviour in normal consolidation states. The other one is designed to ensure more adequate soil responses to reloading paths, particularly in the range of small strains. The RU+MCC model has been implemented in the FEM computer code Z_SOIL.pc. To test the influence of the small strain nonlinearity on soil – structure interaction as well as to exhibit the ability of the proposed model to simulate realistically this effect, a comparative study based on the FEM solution has been carried out. As a benchmark a trial loading test of strip footing was used.

A new hydro-mechanical model for bentonite resaturation applied to the SEALEX experiments

Bentonite barriers perform safety critical functions in many radioactive waste disposal concepts, but it is challenging to accurately predict bentonite resaturation behaviour in repository settings. Coupled models of the hydro-mechanical response of bentonite are used to demonstrate understanding of bentonite behaviour in experiments and to predict the response of bentonite in a repository environment. Following trials of a range of numerical approaches, a new model is presented, referred to as the Internal Limit Model, which makes use of key observations on limiting stresses supported in bentonite samples in experimental data. This model is based on the Modified Cam Clay model, and uses the observation that for a given dry density of bentonite, there is a limiting stress that the sample can support, be that stress due to swelling, compaction or suction, to explicitly couple the hydraulic and mechanical models. The model is applied to experimental data from the SEALEX experiments, involving a 70/30 by mass mixture of MX80 bentonite and sand. The model is able to reproduce the experimental data using a single set of parameters for all the experiments considered. This builds confidence that the model will be useful in the future for predictive modelling given appropriate data to characterise the bentonite material being used.

Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

SummaryGeomaterials such as soils and rocks are inherently anisotropic and sensitive to temperature changes caused by various internal and external processes. They are also susceptible to strain localization in the form of shear bands when subjected to critical loads. We present a thermoplastic framework for modeling coupled thermomechanical response and for predicting the inception of a shear band in a transversely isotropic material using the general framework of critical state plasticity and the specific framework of an anisotropic modified Cam–Clay model. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Subsequently, stress‐point simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermomechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling of Laboratory Tests on Saint-Roch-de-l’Achigan Clay with S-CLAY1S Model

This technical note presents some results of numerical simulations performed to evaluate the influence of anisotropy and destructuration on the stress-strain response of Saint-Roch-de-l'Achigan clay. The oedometer and triaxial tests were simulated with the finite-element method using two different constitutive models to represent the soil: the S-CLAY1S model, which accounted for anisotropy and destructuration, and the isotropic modified Cam clay model (MCC), which was used for comparison. In contrast to the MCC model, the S-CLAY1S model was able to simulate the compression curve for the whole range of stresses with one parameter set and, hence, represented soil behavior in the triaxial test in a more realistic way than the MCC. The results of this study confirm that when using recommended procedures for the determination and calibration of the input parameters, the S-CLAY1S model represents well the overall behavior of Saint-Roch-de-l'Achigan clay in the specific cases analyzed.

Some general remarks on hyperplasticity modelling and its extension to partially saturated soils

The essential ideas and equations of classic plasticity and hyperplasticity are successively recalled and compared, in order to highlight their differences and complementarities. The former is based on the mathematical framework proposed by Hill (The mathematical theory of plasticity. Oxford University Press, Oxford, 1950), whereas the latter is founded on the orthogonality hypothesis of Ziegler (An introduction to thermomechanics. Elsevier, North-Holland, 1983). The main drawback of classic plasticity is the possibility of violating the second principle of thermodynamics, while the relative ease to conjecture the yield function in order to approach experimental results is its main advantage. By opposition, the a priori satisfaction of thermodynamic principles constitutes the chief advantage of hyperplasticity theory. Noteworthy is also the fact that this latter approach allows a finer energy partition; in particular, the existence of frozen energy emerges as a natural consequence from its theoretical formulation. On the other hand, the relative difficulty to conjecture an efficient dissipation function to produce accurate predictions is its main drawback. The two theories are thus better viewed as two complementary approaches. Following this comparative study, a methodology to extend the hyperplasticity approach initially developed for dry or saturated materials to the case of partially saturated materials, accounting for interface energies and suction effects, is developed. A particular example based on the yield function of modified Cam–Clay model is then presented. It is shown that the approach developed leads to a model consistent with other existing works.

Coupled analysis of dynamically penetrating anchors

The development of a numerical procedure for the finite element analysis of anchors dynamically penetrating into saturated soils is outlined, highlighting its unique features and capabilities. The mechanical behaviour of saturated porous media is predicted using mixture theory. An algorithm is developed for frictional contact in terms of effective normal stress. The contact formulation is based on a mortar segment-to-segment scheme, which considers the interpolation functions of the contact elements to be of order N, thus overcoming a numerical deficiency of the so-called node-to-segment (NTS) contact algorithm. The nonlinear behaviour of the solid constituent is captured by the Modified Cam Clay soil model. The soil constitutive model is also adapted so as to incorporate the dependence of clay strength on strain rate. An appropriate energy-absorbing boundary is used to eliminate possible wave reflections from the artificial mesh boundaries. To illustrate the use of the proposed computational scheme, simulations of dynamically penetrating anchors are conducted. Results are presented and discussed for the installation phase followed by ‘setup’, i.e., pore pressure dissipation and soil consolidation. The results, in particular, reveal the effects of strain rate on the generation of excess pore pressure, bearing resistance and frictional forces. The setup analyses also illustrate the pattern in which pore pressures are dissipated within the soil domain after installation. Hole closure behind a dynamic projectile is also illustrated by an example.

Two-phase Material Point Method applied to the study of cone penetration

This paper presents numerical simulations of Cone Penetration Test (CPT) in water-saturated soft soils taking into account pore pressure dissipation during installation. Besides modelling interaction between soil skeleton and pore fluid, the problem involves large soil deformations in the vicinity of the penetrometer, soil–structure interaction, and complex non-linear response of soil. This makes such simulations challenging. Depending on the soil’s permeability and compressibility, undrained, partially drained or drained conditions might occur. Partially drained conditions are commonly encountered in soils such as silts and sand–clay mixtures. However, this is often neglected in CPT interpretation, which may lead to inaccurate estimates of soil properties. This paper aims at improving the understanding of the penetration process in different drainage conditions through advanced numerical analyses. A two-phase Material Point Method is applied to simulate large soil deformations and generation and dissipation of excess pore pressures during penetration. The constitutive behaviour of soil is modelled with the Modified Cam Clay model. Numerical results are compared with experimental data showing good agreement.

Modelling of anisotropy and consolidation effect on behaviour of sunshine embankment: Australia

This paper investigates the time-dependent behaviour of Sunshine embankment on soft clay deposit with and without prefabricated vertical drains. An elasto-viscoplastic model was used to investigate the influence of anisotropy and creep effect on the settlement behaviour of the embankment. The constitutive model, namely ACM accounts for combined effects of plastic anisotropy and creep. For comparison, the problem is also analysed with isotropic Modified Cam Clay model which does not consider creep effect. To analyse the PVD improved subsoil, axisymmetric vertical drains were converted into equivalent plane strain conditions using two different mapping approaches. The results of the numerical analyses are compared with the field measurements. The numerical simulations suggest that the anisotropic creep model is able to give a better representation of soft clay response under an embankment loading. The isotropic model which neglects the effects of anisotropy and creep may lead to inaccurate predictions of soft clay response. Additionally, the numerical results show that the mapping method used for PVD improved soft clays can accurately predict the consolidation behaviour of the embankment and provide a useful tool for engineering practice.

Numerical simulation of deep penetration of a Piezocone in a Strain-Softening clay

This paper presents a numerical model which has the ability to simulate Piezocone penetration starting from the ground surface in saturated soft clays. The constitutive behavior of the soil is modeled using the Modified Cam Clay model and the model has been verified using centrifuge model tests. The variation of cone resistance is examined with various parameters, which influence the penetration resistance of the cone, such as rigidity index of the soil, in situ stress anisotropy, roughness at the cone–soil interface and the overconsolidation ratio of the soil. A correlation has been developed incorporating the influence of above parameters on the Piezocone resistance and results are compared with previous correlations based on the finite element method. Finally, the strain-softening behavior of the soft clay on the penetration resistance is investigated. The brittleness or sensitivity of the soil increases with the increase in degree of strain-softening but the results do not show significant reductions in computed cone penetration resistance. The cyclic penetration tests simulated using the proposed model show that the Ball and T-bar penetration tests are better than Piezocone test in predicting the degree of soil sensitivity.

Finite Element Modelling of a Deep Excavation in Boston Blue Clay

The work investigates the behaviour of a deep excavation that forms part of a wide basement located in Boston, Massachusetts, USA. The glacial marine clay deposit is modelled with a kinematic hardening model for structured soils, its reduced bubble model version and the well-known Modified Cam Clay model. The aim of the work is to assess the effects of the added features of the advanced model, such as small-strain stiffness, structure degradation and anisotropy, on the numerical prediction of the overall behaviour of the excavation. The first part of the paper provides a brief description of the site conditions, ground profile and construction sequences for the case study under consideration. Then, the soil model calibration process using experimental undrained triaxial, self-boring pressuremeter and constant rate of strain consolidation tests is discussed. Finally, the comparison of the predicted wall deflection and ground settlements profiles with observed movements is presented.

A Constitutive Model for Unsaturated soils based on a Compressibility Framework dependent on Suction and Degree of Saturation

The Modified Cam Clay model is extended to account for the behaviour of unsaturated soils using Bishop’s stress. To describe the Loading – Collapse behaviour, the model incorporates a compressibility framework with suction and degree of saturation dependent compression lines. For simplicity, the present paper describes the model in the triaxial stress space with characteristic simulations of constant suction compression and triaxial tests, as well as wetting tests. The model reproduces an evolving post yield compressibility under constant suction compression, and thus, can adequately describe a maximum of collapse.