Cam Clay Research Articles

Three-Dimensional Numerical Modeling of a Piled Embankment

This paper proposes a three-dimensional numerical modeling of an embankment over a soft ground mass improved by vertical stiff piles, using a finite-difference continuum approach (FLAC3D). Arching occurs in the embankment granular material, leading to load transfer onto the piles and surface settlement reduction and homogenization. The embankment, the piles, and the soft ground are explicitly taken into account in the proposed numerical model. First, a unit cell from the pile grid is considered. Two sorts of soft clay deposits and two embankment materials are successively modeled. The soft soil behavior is simulated by the modified Cam Clay model and the embankment material behavior is successively simulated by an elastic perfectly plastic model with a Mohr–Coulomb failure criterion and then by an isotropic hardening elastoplastic model, the CJS2 model, in order to approach the real system behavior. The calculations are performed in drained conditions, simulating the long-term behavior. The impact of the ...

Prediction of stresses and strains around model tunnels with adjacent embedded walls in overconsolidated clay

This paper presents the results of finite element analyses carried out using different constitutive models for overconsolidated clay: the Modified Cam clay model and the Three-Surface Kinematic Hardening (3-SKH) model. These analyses are evaluated against data from an extensive series of physical model tests examining the influence of an embedded wall placed near a tunnel on ground movements and tunnel stability. It is shown that for heavily overconsolidated soils reasonable predictions of both deformations and failure can be obtained from kinematic hardening models such as the 3-SKH model, which allow plastic deformation inside a Modified Cam clay state boundary surface.

Simulation of the progressive failure of an embankment on soft soil

A pragmatic strain-softening constitutive model, which is based on Modified Cam Clay, was applied to the simulation of the progressive failure of an embankment constructed on a deposit of sensitive (strain-softening) clay in Saga, Japan. A comparison of the predictions for this case indicates that if softening is ignored, only relatively small deflections and consolidation settlements are predicted, especially after construction. In contrast, for the case where softening is included in the analysis, progressive failure within the clay induces large shear deformations and finally failure of the embankment is predicted. This comparison suggests that softening-induced progressive failure should be considered in the design of embankments on such soils, and the residual strength of the deposit may have an important influence on the overall factor of safety of the construction. Detailed analyses of predicted excess pore water pressures, shear strains and shear stress levels in the ground indicate that considering the strain-softening process: (a) is associated with the buildup of excess pore water pressure; (b) promotes strain localization; and (c) results generally in a larger zone of soil involved in the failure.

Effect of flow rules and elastic strains on pressuremeter test results in dense sand

Simple numerical methods that allow to obtain stress and strain paths in sand during self-boring pressuremeter tests are presented in this paper. The material is considered to undergo deformation in drained and plane-strain conditions. The flow rules of Rowe, Cambridge-type (Cam clay and Nova) model, and the sawtooth model are used in the analysis. Elastic strains are also considered in relation with the flow rule of Rowe. The proposed approach has been evaluated using a reference pressuremeter test performed on Ticino sand in a calibration chamber. The results indicate that the stress–strain–volume change responses of the sand predicted by the various models are quite similar, with and without consideration of the elastic strain components.

Automatic substepping integration of the subloading tij model with stress path dependent hardening

This paper discusses the numerical integration of the subloading tij model. This is an elastoplastic model with stress path dependent hardening, which can predict the behaviour of normally consolidated clays or loose sands, as well as of over-consolidated clays or dense sands, with a small number of material parameters. Three features distinguish the subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor t ij ; (b) the split of the plastic strain increments in two components leading to a stress path dependent hardening; and (c) the use of two yield surfaces (subloading yield surface and normal yield surface). This last feature is based on the concept of sub-yielding stress states and adds an extra internal strain-like hardening variable, related to the relative density state, which demands its own evolution law. The three characteristics above greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam clay model, at the cost of only two additional parameters. Nonetheless, the numerical integration of the constitutive equations of subloading tij model is a bit challenging, mainly due to the stress path dependent hardening. In order to integrate the equations of subloading tij model in the same way as for any conventional model, the authors reformulated its equations in a simpler and direct manner. Here, these equations are integrated using multi-step explicit schemes, such as modified-Euler and Runge–Kutta–Dormand–Price, with automatic error control. Simple forward-Euler scheme is also used for the sake of comparison. The results show that the modified-Euler scheme is more accurate as well as faster than the other schemes analysed over a wide range of error tolerance. Besides, the automatic feature of these schemes is a great convenience for the users of numerical codes.

Experimental characterization of ceramic pebble beds

Several materials have been developed in Europe and Japan for the DEMO reactor that will be tested in ITER. The paper describes a solid breeder for nuclear fusion reactor exploiting ceramic pebbles made of Lithium Orthosilicate (Li 4SiO 4) and Lithium metatinate (Li 2TiO 3), with a diameter ranging between 0.5 mm and 1 mm. The main advantages of the pebbles are resistance to thermal stresses and the possibility to easily fill the complex geometries of the blanket. The results of experimental tests are presented, which enable the determination of the behaviour of single pebbles under compression and the parameters of the pebble beds needed to define their constitutive equations. Several standard tests on samples of pebble beds were performed: triaxial, direct shear and compression. The parameters of the Cam–Clay model were obtained from these tests. This model is normally used to describe soil materials (clay, sand) but in our case was used to simulate the triaxial tests with a finite elements computer code. The numerical results show a good agreement with the theoretical ones. Therefore this model could be used to determine the mechanical behaviour of the solid breeding blanket under normal and accidental conditions.

Capability of constitutive models to simulate soils with different OCR using a single set of parameters

Incorporation of void ratio as a state variable into constitutive models allows, in principle, to use a single set of parameters for soils with different OCRs. Two sets of experimental data on reconstituted clays are used for evaluation of three constitutive models of different complexity (Modified Cam clay model, 3SKH model, hypoplastic model for clays). Although all the models predict the influence of OCR correctly from the qualitative point of view, quantitative comparison using a suitable scalar error measure reveals merits and shortcomings of different models.

A volume–stress model for sands under isotropic and critical stress states

A simple volume–stress model for granular soils under isotropic and critical stress states is presented. The model is formulated in the double logarithmic space of void ratio versus mean stress. It has the same number of parameters as used in the Cam Clay models to describe isotropic compression, with one additional parameter to define the critical state curve. The model can qualitatively describe a number of unique features of sand behaviour. Comparison with experimental data indicates that the model is able to predict well the volume change of a range of different sands subjected to isotropic and triaxial compression.

A combined neural network/gradient‐based approach for the identification of constitutive model parameters using self‐boring pressuremeter tests

AbstractThis paper presents a numerical procedure of material parameter identification for the coupled hydro‐mechanical boundary value problem (BVP) of the self‐boring pressuremeter test (SBPT) in clay. First, the neural network (NN) technique is applied to obtain an initial estimate of model parameters, taking into account the possible drainage conditions during the expansion test. This technique is used to avoid potential pitfalls related to the conventional gradient‐based optimization techniques, considered here as a corrector that improves predicted parameters. Parameter identification based on measurements obtained through the pressuremeter expansion test and two types of holding tests is illustrated on the Modified Cam clay model. NNs are trained using a set of test samples, which are generated by means of finite element simulations of SBPT. The measurements obtained through expansion and consolidation tests are normalized so that NN predictors operate independently of the testing depth. Examples of parameter determination are demonstrated on both numerical and field data. The efficiency of the combined parameter identification in terms of accuracy, effectiveness and computational effort is also discussed. Copyright © 2008 John Wiley & Sons, Ltd.

A variational principle of elastoplasticity and its application to the modeling of frictional materials

Starting from a thermomechanical description of elastoplasticity, a stress-based variational principle is derived. The principle, which generalizes von Mises’s principle of maximum plastic dissipation, reproduces the conventional elastic/hardening-plastic framework applicable to metals as a special case and further proves to be suitable for developing constitutive models for frictional materials. Application of the principle to the isotropic and triaxal compression behaviour of sands is considered by means of a non-conventional extension of the modified Cam clay model. The new model allows for the specification of arbitrary stress-dilatancy relations without altering the yield potential or introducing a separate flow potential. Moreover, the elastoplastic tangent modulus is always symmetric, regardless of the degree of apparent nonassociativity.

Maldistribution of fluids in extrudates

Solid–liquid pastes featuring high volume fractions of particulates are frequently used in ceramic forming operations. When pastes are used it is important that the particulate distribution remains uniform throughout the body. The stresses imposed during extrusion processing can, however, promote differential flow between the solid and liquid phases giving rise to product and processing problems. Reliable models for predicting phase distribution changes in these multi-phase systems are in their infancy. This paper reports progress towards developing simulation techniques and practical systems to verify the numerical approaches. Pastes containing glass spheres suspended in a highly viscous Newtonian fluid have been extruded at various speeds and solids loadings. Load and liquid content data are presented which form the basis for model verification. Soil mechanics approaches are used here to encapsulate the inherently multi-phase nature of these systems. The modified Cam–Clay model has been implemented in a finite element analysis simulation of ram extrusion using the ABAQUS platform. The simulation requires regular and extensive remeshing and monitoring of the conservation of mass. Predictions of extrusion pressures and deformation behaviour are compared with the experimental data for a series of square-ended and conical dies.

On generalization of constitutive models from two dimensions to three dimensions

AbstractIn this paper, a study is made of the generalization of constitutive models for geomaterials from two‐dimensional stress and strain states to three‐dimensional stress and strain states. Existing methods of model generalization are reviewed and their deficiencies are highlighted. A new method is proposed based on geometries of the model imprints on two normal planes. Using the proposed method, various three‐dimensional failure criterions suitable for geomaterials are implemented directly into a two‐dimensional model and the generalized model is identical to its original form for the axially symmetric condition. To demonstrate the application of the proposed method, the Modified Cam Clay model is extended using the Matsuoka–Nakai failure criterion. Simulations of soil behaviour for loading in the principal stress space are presented and analysed. Copyright © 2008 John Wiley & Sons, Ltd.

Stress update algorithm for elastoplastic models with nonconvex yield surfaces

AbstractA stress update algorithm for elastoplastic models with nonconvex yield surfaces is presented. An explicit algorithm based on the Runge–Kutta embedded method of second‐order accuracy is developed. The crossing of the yield surface is properly taken into account by means of a robust intersection‐finding algorithm. This algorithm is based on a simple multiple‐root‐finding technique, which requires the yield function, evaluated along a given secant stress path, to be continuously differentiable to the second order. The accuracy of the intersection‐finding algorithm is illustrated through examples using simple yield functions similar to the ones adopted in models for unsaturated soils and the modified Cam clay model yield surface with a nonconvex Argyris et al. failure criterion. Isoerror surfaces and finite element simulations are used to investigate the accuracy and efficiency of the stress update algorithm. It is observed that although the algorithm for nonconvex surfaces is slower than its equivalent for convex surfaces, the accuracy can be controlled locally by means of specified tolerances. Copyright © 2008 John Wiley & Sons, Ltd.

Drained bearing response of shallow foundations on structured soils

This paper examines the drained bearing response of circular footings resting on structured soil deposits. Numerical simulations have been carried out using a finite element formulation of the Structured Cam Clay model. A parametric study was conducted by varying the parameters that govern the behaviour of structured soils and guidelines are given for designers to identify when effects of the soil structure are important. Under fully drained conditions, deformation within the structured soil supporting the footing usually occurs as a local or punching shear failure due to high compressibility of the structured soil and the mobilised bearing pressure increases with the footing movement, without reaching an ultimate value. A novel approximate method is presented to obtain the load–displacement response of a rigid circular footing resting on the surface of a structured soil deposit. This requires the properties of the soil in the reconstituted state and two additional parameters, which govern the natural structure of the soil. The proposed method has been applied to a published case study, where plate load test results are given for rigid circular steel plates resting on structured soil deposits. Fair agreement is observed between the computed and experimental results, suggesting the approximate method may be useful in design studies of foundations on structured soil deposits.

Optimization framework for calibration of constitutive models enhanced by neural networks

AbstractA two‐level procedure designed for the estimation of constitutive model parameters is presented in this paper. The neural network (NN) approach at the first level is applied to achieve the first approximation of parameters. This technique is used to avoid potential pitfalls related to the conventional gradient‐based optimization techniques, considered here as a corrector that improves predicted parameters. The feed‐forward NN (FFNN) and the modified Gauss–Newton algorithms are briefly presented. The proposed framework is verified for the elasto‐plastic modified Cam Clay model that can be calibrated based on standard triaxial laboratory tests, i.e. the isotropic consolidation test and the drained compression test. Two different formulations of the input data to the NN, enhanced by a dimensional reduction of experimental data using principal component analysis, are presented. The determination of model characteristics is demonstrated, first on numerical pseudo‐experiments and then on the experimental data. The efficiency of the proposed approach by means of accuracy and computational effort is also discussed. Copyright © 2008 John Wiley & Sons, Ltd.

A Case History on Underpinning for a Distressed Building on Hard Residual Soil Underneath Non-Uniform Loose Sand

ABSTRACT This paper presents a case history on the failure of Suranivet 9, a student dormitory in the campus of Suranaree University of Technology (SUT), Thailand. The dormitory encountered excessive differential settlement due to the variation in soil profile. Part of the building was underlain by very stiff to hard SUT silty clay and part by loose clayey sand. Underpinning to extend the foundations down to stable stratum was employed to strengthen bearing capacity and minimize settlement. The underpinning design and procedure were summarized. In practice, the static formula was used for the preliminary micro-pile design (selection of pile section and length for different loads and soil profiles). The undrained shear strength (Su) of SUT silty clay was approximated using the Stress History and Normalized Soil Engineering Properties (SHANSEP) technique and standard penetration number (N). The finite element method was employed to predict the load-settlement curve of the micro-pile. Modified cam clay model was proved as a suitable model for this prediction. The measured settlements of the underpinned foundations after one year service were less than 0.5 mm. This small settlement guarantees the stability of the underpinned structure. It is also found that the settlement ratio (ratio of the measured settlement of underpinned foundations to the predicted settlement of single micro-pile) varied from 0.7 to 3.0.

Anisotropic creep model for soft soils

In this paper a new anisotropic model for time-dependent behaviour of soft soils is presented. The formulation is based on a previously developed isotropic creep model, assuming rotated Modified Cam Clay ellipses as contours of volumetric creep strain rates. A rotational hardening law is adopted to account for changes in anisotropy due to viscous strains. Although this will introduce some new soil parameters, they do not need calibration as they can be expressed as functions of basic soil parameters through simple analytical expressions. To start with, the one-dimensional response of the model is discussed, making it possible to explore how the model is capable of capturing key features of viscous soft soil behaviour. Subsequently, the three-dimensional generalisation of the model is presented, followed by comparison with experimental data, showing good agreement in both triaxial undrained compression and extension. In the authors' opinion, the simple formulation of the model makes it attractive for use in engineering practice.

Identifying parameters controlling soil delayed behaviour from laboratory and in situ pressuremeter testing

AbstractThe aim of this paper is to present a methodology for identifying the soil parameters controlling the delayed behaviour from laboratory and in situ pressuremeter tests by using an elasto‐viscoplastic model (EVP‐MCC) based on Perzyna's overstress theory and on the elasto‐plastic Modified Cam Clay model. The influence of both the model parameters and the soil permeability was studied under the loading condition of pressuremeter tests by coupling the proposed model equations with Biot's consolidation theory. On the basis of the parametric study, a methodology for identifying model parameters and soil permeability by inverse analysis from three levels of constant strain rate pressuremeter tests was then proposed and applied on tests performed on natural Saint‐Herblain clay. The methodology was validated by comparing the optimized values of soil parameters and the values of the same parameters obtained from laboratory test results, and also by using the identified parameters to simulate other tests on the same samples. The analysis of the drainage condition and the strain rate effect during a pressuremeter test demonstrated the coupled influence of consolidation and viscous effects on the test results. The numerical results also showed that the inverse analysis procedure could successfully determine the parameters controlling the time‐dependent soil behaviour. Copyright © 2008 John Wiley & Sons, Ltd.

The modified cam clay model for constrained compression of human morsellised bone: Effects of porosity on the mechanical behaviour

Morsellised cortico-cancellous bone (MCB) is often used in revision surgery for filling skeletal defects. The MCB porosity is found to influence the degree of bone ingrowth. Thus expressing a material model in terms of porosity may be attractive from a clinical point of view. We analysed the moisture content and performed constrained compression testing of human impacted and unimpacted MCB, in order to determine material parameters for the common constitutive soil model: modified cam clay. The model seemed to be suitable for the unimpacted pellets with a logarithmic bulk modulus κ = 0.059 ± 0.0019 and a logarithmic hardening constant λ = 0.36 ± 0.014 . This model, relating the specific volume (and porosity) to the logarithm of stress, may be suited to find the best compromise of stiffness and porosity for MCB.

Plastic anisotropy of soft reconstituted clays

The aim of the paper is to extend the experimental validation of the S-CLAY1 model, which is a recently proposed elastoplastic constitutive model that accounts for initial and plastic strain-induced anisotropy. Drained stress path controlled tests were performed on reconstituted samples of four Finnish clays to study the effects of anisotropy in the absence of the complexities of structure present in natural undisturbed clays. Each test involved several loading, unloading, and reloading stages with different values of stress ratio and, hence, induced noticeable changes in the fabric anisotropy. Comparisons between test results and model predictions with the S-CLAY1 model and the modified Cam clay model demonstrate that despite its simplicity, the S-CLAY1 model can provide excellent predictions of the behaviour of unstructured soil.