Cam Clay Research Articles

Finite strain elastoplastic solutions for the undrained ground response curve in tunnelling

SummaryThe instantaneous response of saturated low permeability grounds to tunnel excavation is important for deformations and stability close to the tunnel face. It is characterized by zero volume change in combination with the development of excess pore pressures. In tunnelling through poor quality ground under great depth of cover and high in situ pore pressure, heavily squeezing conditions (characterized by very large convergences) may occur soon after excavation. This paper presents exact finite strain analytical solutions for the undrained ground response around cylindrical and spherical openings that are unloaded from uniform and isotropic initial stress states, on the basis of the Modified Cam Clay (MCC) model and the Mohr–Coulomb (MC) model. The solution for a Drucker–Prager material is also given as it requires only a very small modification to the MC solution. The so‐called ground response curve, that is, the relationship between the support pressure and the cavity wall displacement, is derived in closed form for the MC model. The solution for the MCC problem is semi‐analytical in that it uses the trapezium rule for the computation of a definite integral. The influence of the significant parameters of the problem on the predicted deformation behaviour is shown by means of dimensionless charts. Finally, the practical usefulness of the solutions presented is illustrated by applying them to the breccia zones of the planned Gibraltar Strait tunnel – an extreme case of weak, low permeability ground under high pore pressure. The solutions can serve as a trustworthy benchmark for numerical procedures that incorporate material and geometric nonlinearities. Copyright © 2014 John Wiley & Sons, Ltd.

Mechanical behaviour of gas-charged fine sediments: model formulation and calibration

Multi-phase fluid conditions encountered in geotechnical and geo-environmental problems have led to the development of models that account for the influence of gas solubility and compressibility on the behaviour of soils of various grain sizes. Yet, no consideration has been given to damages related to the nucleation and growth of gas bubbles in fine-grained soils. The purpose of this paper is to present a Cam Clay based constitutive model extended to incorporate such detrimental effects on gassy soils. This is achieved by deriving an analytical expression relating the preconsolidation pressure to a damage parameter dependent on the gas content. That expression is coupled to a deviatoric yield surface accounting for inherent and stress-induced anisotropy. Comparisons of simulations and experimental results attest that introducing a single additional parameter to a conventional Cam Clay type model allows key behavioural features of gas-charged fine sediments to be reproduced.

Deformation characteristics of a clayey interbed during fluid injection

Surface deformation due to fluid withdrawal has long been observed at the surface above aquifers and oil reservoirs. Uplift associated with fluid injection has also been observed. Although the processes of subsidence and uplift are reversible in a poroelastic setting, the presence of clayey interbeds can result in ground deformation behavior non-reversible because of their low permeability and nonlinear behavior. In this investigation a Cam clay model is used in conjunction with a poroelastic model to simulate the presence of a laterally extensive lens-shaped clayey interbed in a sandstone aquifer during fluid injection. Spatial and temporal changes associated with this interbed during aquifer pressurization are captured and can be clearly differentiated from the deformation of the surrounding poroelastic aquifer formation. Results for pore pressures and ground surface deformation patterns can be categorized into three distinct time intervals: an early time interval where the aquifer is pressurized but not the interbed leading to a lower region above the interbed; an intermediate time interval in which the interbed pressures slowly increase, approaching the pressure of the adjacent aquifer, leading to a potentially large surface uplift above the interbed; and a late time interval in which pressure equilibration is achieved between the interbed and aquifer and a highly non-symmetrical irregular surface deformation pattern results, which may be higher or lower than the background depending on the interbed characteristics. Reservoir configuration is found to be an important factor influencing ground deformation behavior, with more obvious deformation always occurring in a laterally confined aquifer as opposed to a laterally infinite aquifer.

Rate-Dependent and Long-Term Yield Stress and Strength of Soft Wenzhou Marine Clay: Experiments and Modeling

This paper focuses on the rate-dependent yield stress, undrained strength, and long-term undrained strength of clay. Various oedometer and triaxial tests were performed on Wenzhou marine clay. The uniqueness of rate-dependent and long-term yield stress and strength is discussed. A new anisotropic elastic viscoplastic model is proposed by adopting the concept of anisotropy and isotropy processes. The determination of model parameters is discussed, demonstrating how all model parameters can be determined in a straightforward way requiring the same basic tests as for the Modified Cam Clay model. Experimental verifications are carried out using the constant strain-rate and creep tests on the Wenzhou marine clay.

Finite Element Analysis of Clay Shear Band under Plane Strain Condition

The clay shear band analysis under plane strain condition were based on modified cam clay model in finite element software ABAQUS. Normally Consolidated Clay and lightly overconsolidated clay were analyzed in the article. Loading speed, size of soil specimen, different consolidation state (Normally Consolidated Clay and lightly overconsolidated clay) are considered. These factors have effect on the distribution of Pore water pressure, the effective stress path of nodes in shear band and out of shear band and the angle between the shear band and horizontal line. All the differentia and effects were used to analyze the production conditions and formation mechanism of shear band. The results show that size of clay specimen can influence the number of shear band. When the height-width ratio is large, the number of shear band will increase.

An elastoplastic model with combined isotropic–kinematic hardening to predict the cyclic behavior of stiff clays

This paper presents a kinematic hardening model for describing some important features of natural stiff clays under cyclic loading conditions, such as closed hysteretic loops, smooth transition from the elastic behavior to the elastoplastic one and changes of the compression slope with loading/unloading loops. The model includes two yield surfaces, an inner surface and a bounding surface. A non-associated flow rule and a kinematic hardening law are proposed for the inner surface. The adopted hardening law enables the plastic modulus to vary smoothly when the kinematic yield surface approaches the bounding surface and ensures at the same time the non-intersection of the two yield surfaces. Furthermore, the first loading, unloading, and reloading stages are treated differently by applying distinct hardening parameters. The main feature of the model is that its constitutive equations can be simply formulated based on the consistency condition for the inner yield surface based on the proposed kinematic hardening law; thereby, this model can be easily implemented in a finite element code using a classic stress integration scheme as for the modified Cam Clay model. The simulation results on the Boom Clay, natural stiff clay, have revealed the relevance of the model: a good agreement has been obtained between simulations and the experimental results from the tests with different stress paths under cyclic loading conditions. In particular, the model can satisfactorily describe the complex case of oedometric conditions where the deviator stress is positive upon loading (compression) but can become negative upon unloading (extension).

Undrained Cylindrical Cavity Expansion in Critical State Soils Considering Soil Structure

A closed form method of analysis is proposed to predict the stresses and pore water pressure developed in soil mass due to the expansion of cylindrical cavity in undrained condition. Often Modified Cam Clay model (MCC) has been used to describe soil behavior, but unfortunately MCC formulation does not include soil structure. To study the effect of soil structure during cylindrical cavity expansion Structured Cam Clay model has used to describe yield surface and flow rule. It is assumed that the expansion of cavity occurs under condition of plane strain. The evaluation of present method illustrates a good comparison with observations made from field. It is also observed that soil structure affect significantly to the distribution of stresses and pore water pressure during expansion of cylindrical cavity.

Fabric and connectivity as field descriptors for deformations in granular media

Granular materials involve microphysics across the various scales giving rise to distinct behaviours of geomaterials, such as steady states, plastic limit states, non-associativity of plastic and yield flow, as well as instability of homogeneous deformations through strain localization. Incorporating such micro-scale characteristics is one of the biggest challenges in the constitutive modelling of granular materials, especially when micro-variables may be interdependent. With this motivation, we use two micro-variables such as coordination number and fabric anisotropy computed from tessellation of the granular material to describe its state at the macroscopic level. In order to capture functional dependencies between micro-variables, the correlation between coordination number and fabric anisotropy limits is herein formulated at the particle level rather than on an average sense. This is the essence of the proposed work which investigates the evolutions of coordination number distribution (connectivity) and anisotropy (contact normal) distribution curves with deformation history and their inter-dependencies through discrete element modelling in two dimensions. These results enter as probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model using tessellation as an abstract representation of the granular system. The end product is a micro-mechanically inspired continuum model with both coordination number and fabric anisotropy as underlying micro-variables incorporated into a plasticity flow rule. The derived plastic potential bears striking resemblance to cam–clay or stress–dilatancy-type yield surfaces used in soil mechanics.

Cyclic consolidation and axial friction for seabed pipelines

Finite-element analyses of the axial sliding resistance of a seabed pipeline embedded in soft normally consolidated modified Cam clay are presented. The study demonstrates the rise in axial resistance associated with episodes of movement with intervening periods of consolidation. It is shown that the excess pore pressures generated during undrained axial movements lead to significant consolidation and strength gain in the surrounding soil. For modified Cam clay, using properties representative of kaolin, the resistance rises exponentially with cycles and reaches the drained limit within approximately 10–20 episodes of movement and consolidation. The rate of gain in resistance is shown to be controlled by the volumetric stiffness ratio, κ/λ, for soil that is initially normally consolidated. Simple relationships are proposed that will assist in utilising this beneficial phenomenon in design practice. The increase in axial sliding resistance due to consolidation may mean that mitigation requirements against cyclic axial pipe walking, caused by thermal expansion, may be reduced or eliminated.

APPLICATION OF CONSTITUTIVE MODELS IN THE VOLCANIC TEPHRA “TIERRA BLANCA JOVEN”

The volcanic tephra Tierra Blanca Joven (TBJ) covers most of the Metropolitan Area of San Salvador where problems of mass wasting problems occur. To understand its behavior the Mohr-Coulomb, Modified Cam Clay and Hypoplasticity constitutive models were used to simulate consolidation and triaxial tests; looking for the one closer to real laboratory results. The constitutive models are used into finite element software to simulate the behavior of a soil mass (slope stability, bearing capacity etc.). Shear box, drained triaxial and consolidation tests were made in order to obtain the parameters for the models. The soil must be either saturated or dry, otherwise unsaturated properties are needed. After comparing the results of the constitutive model it was observed that none of them display exactly the real behavior observed in the laboratory. Mohr-Coulomb is the model that is used in all the geotechnical studies in El Salvador and it was the model that showed more deficiencies. Hypoplasticity showed good results in the triaxial tests but deviated from reality in the consolidation results. The results indicate that a different constitutive model and lab equipment are necessary (as TBJ is an unsaturated soil) to characterize the behavior of the soils in El Salvador.

The subloading isotropic plasticity as a variable modulus model

The subloading concept is an extension of mathematical plasticity which defines an internal surface to the conventional yield surface. It is indeed a versatile approach, especially for the modelling of soils under quasi-static cycles with smooth transitions from pure elastic to elastoplastic behaviour. For the case of isotropic hardening models, this paper demonstrates that the subloading isotropic plasticity is equivalent to a variable modulus approach and therefore a simpler and equivalent methodology can be adopted instead. In addition to demonstrating this equivalence, an alternative formulation that was presented elsewhere and that uses only one surface is briefly discussed. The alternative formulation can then be easily applied to popular models for soils such as the Cam clay model. Finally, some numerical predictions are presented in order to illustrate the capabilities of the subloading isotropic plasticity and the corresponding variable modulus approach.

The verification of subsoil parameters based on back analysis of a bridge

The paper presents the analysis of foundation of the road bridge. The numerical calculation of the bridge abutment was made in FEM Software with subsoil modelled as solid defined by Cam Clay model. Number of calculations was made by using variable parameters of soil. Results were compared with geodetic measurements. Soil properties designated by lab test and geological boreholes, were verified with computer back analysis results.

Numerical simulation of piezocone dissipation test in clays

The piezocone is one of the most widely used in-situ tools with which to characterise the soil profile, distinguishing different types of sediment, and to provide quantitative data on the soil strength and consolidation characteristics. For fine-grained soils where penetration occurs under nominally undrained conditions, consolidation characteristics are obtained from dissipation tests conducted with the piezocone brought to rest. Dissipation testing is interpreted to yield a coefficient of consolidation, by comparison of the excess pore pressure decay with theoretical solutions. It is generally acknowledged that the coefficient of consolidation derived from in-situ dissipation tests will be greater, by a factor of perhaps 2 to 10, than values derived from oedometer tests on samples recovered from the corresponding depth. Apart from potential differences in horizontal and vertical permeability, differences arise from the influence of the rigidity index on the initial excess pore pressure field and the more complex stress paths undergone by soil elements surrounding the piezocone by comparison with an oedometer test. In order to advance the science underlying interpretation of dissipation testing, a careful parametric study has been undertaken using finite-element analysis, with the soil modelled as modified Cam Clay. The aim has been to derive an ‘operative' coefficient of consolidation, linked to the consolidation and swelling parameters of the soil model, thus allowing quantitative treatment of the difference in coefficients of consolidation derived from laboratory oedometer or in-situ dissipation testing. The effect of partial consolidation during the penetration phase is also considered.

Experimental Study of Isotropic and Anisotropic Constitutive Models

AbstractThis paper analyzes the validity of the yield surface and flow rule of several isotropic and anisotropic constitutive models. These aspects are studied based on drained triaxial tests, with a number of different stress paths in a computer-controlled stress path cell. The Cam clay, modified Cam clay, and p-q-θ models are used to study the isotropic behavior, whereas the anisotropic conditions are analyzed using the Melanie, MIT-E3, and S-CLAY1 models. Both under the isotropic and anisotropic conditions, the results indicate that the surface described by the undrained effective stress path is suitable for simulating the yield and plastic potential surfaces. In terms of isotropic behavior, the p-q-θ model is the most suitable for predicting the yield, whereas the plastic potential function is closely simulated by the yield function of the modified Cam clay model. For the anisotropic models studied, the MIT-E3 model provides a better approximation of the anisotropic behavior of the Santa Clara clay.

Chemo-mechanical modelling of lime treated soils

Lime treatment has been widely used to improve mechanical properties of soils. However, less has been done to account for the effect of the treatment on constitutive relationships. In this study, a comprehensive programme of isotropic consolidation tests and drained triaxial experiments were designed and carried out on saturated specimens of a silt treated with quicklime. The chemical composition in hydrates, portlandite, and carbonates was determined using thermogravimetric analysis and differential thermal analysis. The modifications to the mechanical parameters of the soil were evaluated in the framework of the Cam Clay elastoplastic model. The experimental results revealed that the addition of lime leads to the modification of the critical state. For concentrations in lime higher than 1%, the treated specimens displayed a different normal compression line compared to the untreated state. Chemical analysis revealed the production of cementitious compounds for every concentration tested. A constitutive model was proposed to describe the observed behaviour of lime treated soils in the framework of the Structured Cam Clay. The model accounts for the modifications on the mechanical parameters of the soil. A chemo-mechanical coupling was established between the yield stress and the mass concentration in cementitious compounds.

A Thermodynamic Approach to Effective Stresses in Unsaturated Soils Incorporating the Concept of Partial Pore Deformations

The thermodynamical analysis presented here follows from the work of Coussy et al., who proposed a thermodynamically consistent model for unsaturated soils that is based on a Bishop‐like effective stress to describe the stress–strain relationship while the water saturation (or the capillary pressure) is involved in a saturation‐induced hardening in addition to the mechanical hardening. We extended this model to include the effect of interfaces in the mechanical behavior and we showed that the Bishop‐like stresses involved in the elastic and plastic responses respectively can take different expressions. The Modified Cam–Clay model used for saturated soils is extended to unsaturated soils through the use of these Bishop‐like stresses. This model is compared to some experimental results reported from the literature.

Coupled Finite Element Analysis of Partially Embedded Offshore Pipelines during Vertical Penetration

Diverse vertical embedment response is observed for partially embedded pipelines when experimentally tested under similar initial and boundary conditions. Although vertical resistance of pipelines is presented through simple analytical solutions, a number of factors contribute to complications in implementing these theories into practice. The objectives of this research is to provide a more detailed investigation on the vertical embedment for the partially-embedded pipelines (PEPs) using a coupled large deformation finite element (CLDFE) analysis with contact. A modified Cam Clay (MCC) model represents the elastoplastic response of the soil. The model of pipeline embedment investigates the effect of drainage condition on heave forming with respect to rate of penetration. Besides, effect of frictional contact on the heave development and wedging effect is investigated and design-related considerations are proposed. It is shown that depending on the rate of pipeline penetration and soil consolidation rate, the pipeline penetration response can be categorised as undrained, partially drained or fully drained.

Influence of stone column installation on settlement reduction

The paper presents numerical simulations investigating the settlement reduction caused by stone columns in a natural soft clay. The focus is on the influence of the soft soil alteration caused by column installation. A uniform mesh of end-bearing columns under a distributed load was considered. Therefore, the columns were modelled using the “unit cell” concept, i.e. only one column and the corresponding surrounding soil in axial symmetry. The properties of the soft clay correspond to Bothkennar clay, which is modelled using S-CLAY1 and S-CLAY1S, which are Cam clay type models that account for anisotropy and destructuration. The Modified Cam clay model is also used for comparison. Column installation was modelled independently to avoid mesh distortions, and soft soil alteration was directly considered in the initial input values. The results show that the changes in the stress field, such as the increase of radial stresses and mean stresses and the loss of overconsolidation, are beneficial for high loads and closely spaced columns but, on the contrary, may be negative for low loads, widely spaced columns and overconsolidated soils. Moreover, whilst the rotation of the soil fabric reduces the settlement, in contrast the soil destructuration during column installation reduces the improvement.

Thermo-poromechanics of a fluid-filled cavity in a fluid-saturated geomaterial

In this paper, we examine the coupled thermo-poromechanical behaviour of a fluid-saturated porous medium of infinite extent bounded internally by a fluid-filled cavity. The mechanical behaviour of the porous skeleton can either be Hookean elastic or elasto-plastic, with a constitutive response corresponding to a modified Cam Clay plasticity model. The fluid within the cavity can be subjected simultaneously to a temperature rise and a pressure pulse. The paper presents analytical results for the spherically symmetric thermo-poroelasticity problem and these are used to validate the thermo-poroelasticity module of a computational code. We proceed to examine the thermo-poroelasto-plasticity problem. Results presented in the paper illustrate the interaction between thermal and mechanical phenomena and their influence on the cavity fluid pressure and the skeletal stresses at the cavity boundary. The paper presents solutions that will be of value in benchmarking exercises.

An effective stress analysis of partially embedded offshore pipelines: Vertical penetration and axial walking

A study on quantifying offshore pipeline resistance during vertical penetration and axial walking is presented, based on coupled pore pressure and displacement finite element analysis with the Modified Cam Clay model. Following the validation of the numerical method against published centrifuge test results and limit analysis solutions, we present the findings of a detailed parametric study on the response of partially-embedded pipelines under vertical and axial movements, employing 2-D plain strain and full 3-D soil–pipeline models. Emphasis is put on practical findings, and on proposing simplified expressions for the estimation of the contact enhancement factor and of the equivalent friction factor, that can be used at least for preliminary design purposes.