Stress Path Dependency Research Articles

Continuous hyperplastic models for overconsolidated clays

This paper presents four constitutive models for prediction of the behaviour of overconsolidated clays under triaxial loading conditions. Their formulations are based on a new continuous hyperplastic framework. Continuous hyperplasticity allows the derivation of plasticity models which simulate smooth stress-strain behaviour, have continuous memory, and are guaranteed to obey the laws of thermodynamics. All four models are capable of simulating the triaxial stress-strain behaviour of overconsolidated clays in a wide strain range. The ability of the models to predict the stress path dependency of the clay behaviour is evaluated against experimental data obtained on undisturbed Laval samples of Bothkennar clay.

Suction effects on a compacted clay under non-isothermal conditions

The paper presents the results of an experimental study on the effects of suction and temperature on the volumetric behaviour of an unsaturated soil. Statically compacted Boom clay samples have been used in the testing programme, which has been performed using an oedometer apparatus with simultaneous control of suction and temperature. Suctions up to 0·45 MPa and temperatures up to 80°C have been applied. Special measures have been taken to control and minimise the problems associated with phase changes and vapour migration at high temperatures. A comprehensive experimental programme has been carried out, including isothermal tests with control of vertical stress, suction and temperature, non-isothermal tests under constant suction, and isothermal swelling pressure tests. Testing samples at two compacted soil densities provides observations concerning a wide scope of behaviour ranging from collapse to swelling behaviour on wetting. Test results obtained at 80°C have been compared with those of tests performed at room temperature (22°C). Based on these comparisons, thermal effects on a variety of features of behaviour such as swelling potential, swelling pressure, collapsibility, shrinkage strains, compressibility, stress path dependence and degree of strain reversibility are presented and discussed. Although the basic behaviour is similar at high and low temperatures, various significant differences are identified concerning mainly swelling strains developed during wetting and compressibility with respect to loading. Swelling pressure test results indicate that the high-temperature samples yield at a lower stress than that observed in room-temperature samples, suggesting that the stress domain bounded by the main yield surface reduces as temperature increases—a behaviour feature shared with saturated soils.

Suction effects on a compacted clay under non-isothermal conditions

The paper presents the results of an experimental study on the effects of suction and temperature on the volumetric behaviour of an unsaturated soil. Statically compacted Boom clay samples have been used in the testing programme, which has been performed using an oedometer apparatus with simultaneous control of suction and temperature. Suctions up to 0·45 MPa and temperatures up to 80°C have been applied. Special measures have been taken to control and minimise the problems associated with phase changes and vapour migration at high temperatures. A comprehensive experimental programme has been carried out, including isothermal tests with control of vertical stress, suction and temperature, non-isothermal tests under constant suction, and isothermal swelling pressure tests. Testing samples at two compacted soil densities provides observations concerning a wide scope of behaviour ranging from collapse to swelling behaviour on wetting. Test results obtained at 80°C have been compared with those of tests performed at room temperature (22°C). Based on these comparisons, thermal effects on a variety of features of behaviour such as swelling potential, swelling pressure, collapsibility, shrinkage strains, compressibility, stress path dependence and degree of strain reversibility are presented and discussed. Although the basic behaviour is similar at high and low temperatures, various significant differences are identified concerning mainly swelling strains developed during wetting and compressibility with respect to loading. Swelling pressure test results indicate that the high-temperature samples yield at a lower stress than that observed in room-temperature samples, suggesting that the stress domain bounded by the main yield surface reduces as temperature increases—a behaviour feature shared with saturated soils.

A stress vector-based constitutive model for cohesionless soil (II)—Application

The stress vector-based constitutive model for cohesionless soil, proposed by SHI Hong-yan et al., was applied to analyze the deformation behaviors of materials subjected to various stress paths. The result of analysis shows that the constitutive model can capture well the main deformation behavior of cohesionless soil, such as stress-strain nonlinearity, hardening property, dilatancy, stress path dependency, non-coaxiality between the principal stress and the principal strain increment directions, and the coupling of mean effective and deviatoric stress with deformation. In addition, the model can also take into account the rotation of principal stress axes and the influence of intermediate principal stress on deformation and strength of soil simultaneously. The excellent agreement between the predicted and measured behavior indicates the comprehensive applicability of the model.

Post-peak behavior and flexural ductility of doubly reinforced normal- and high-strength concrete beams

The complete moment-curvature curves of doubly reinforced concrete beams made of normal- or high-strength concrete have been evaluated using a newly developed analytical method that takes into account the stress-path dependence of the constitutive properties of the materials. From the moment-curvature curves and the strain distribution results obtained, the post-peak behavior and flexural ductility of doubly reinforced normal- and high-strength concrete beam sections are studied. It is found that the major factors affecting the flexural ductility of reinforced concrete beam sections are the tension steel ratio, compression steel ratio and concrete grade. Generally, the flexural ductility decreases as the amount of tension reinforcement increases, but increases as the amount of compression reinforcement increases. However, the effect of the concrete grade on flexural ductility is fairly complicated, as will be explained in the paper. Quantitative analysis of such effects has been carried out and a formula for direct evaluation of the flexural ductility of doubly reinforced concrete sections developed. The formula should be useful for the ductility design of doubly reinforced normal- and high-strength concrete beams.

Petroleum Reservoir Simulation Coupling Fluid Flow and Geomechanics

Summary This paper presents a discussion of the issues related to the interaction between rock deformation and multiphase fluid flow behavior in hydrocarbon reservoirs. Pore-pressure and temperature changes resulting from production and fluid injection can induce rock deformations, which should be accounted for in reservoir modeling. Deformation can affect the permeability and pore compressibility of the reservoir rock. In turn, the pore pressures will vary owing to changes in the pore volume. This paper presents the formulation of Biot's equations for multiphase fluid flow in deformable porous media. Based on this formulation, it is argued that rock deformation and multiphase fluid flow are fully coupled processes that should be accounted for simultaneously, and can only be decoupled for predefined simple loading conditions. In general, it is shown that reservoir simulators neglect or simplify important geomechanical aspects that can impact reservoir productivity. This is attributed to the fact that the only rock mechanical parameter involved in reservoir simulations is pore compressibility. This parameter is shown to be insufficient in representing aspects of rock behavior such as stress-path dependency and dilatancy, which require a full tensorial constitutive relation. Furthermore, the pore-pressure changes caused by the applied loads from nonpay rock and the influence of nonpay rock on reservoir deformability cannot be accounted for simply by adjusting the pore compressibility.

Stress Path Testing for Proper Characterization of Unbound Aggregate Base Behavior

Realistic pavement stresses induced by moving wheel loads were examined in granular base layers, and the significant effects of rotation of principal stress axes were addressed for a proper characterization of unbound aggregate behavior. Granular material resilient moduli are commonly determined at the centerline of wheel loading without taking into account the effects of moving wheel loads and the constantly rotating field principal stress states. Differences that exist between field- and laboratory-applied stress states were identified by comparing the field stresses simulated using a nonlinear axisymmetric finite element program, GT-PAVE, with the stress states commonly used in the standard resilient modulus test procedure, AASHTO T294-94. Three sets of complete triaxial test data obtained from testing aggregates under various realistic in situ stress paths caused by moving wheel loading were analyzed. Eight different granular material modulus models were developed from the experimental test data to include the applied mean stress, the applied shear stress, and the slope of stress path loading. Because of the complex loading regimes followed in the laboratory tests, characterization models that simultaneously analyzed the static and dynamic components of the applied mean and deviator stresses produced a high degree of accuracy. Models that consider the stress path slope variations predict the best stress path dependency of aggregate behavior caused by moving wheel loads. Such advanced models that allow for the effects of principal stress rotation better describe the granular material behavior under the actual field loading conditions.

Kinematic hardening model for overconsolidated clays

Abstract The proposed model puts a particular emphasis on accurate simulation of stress-strain behaviour of overconsolidated clays both within the small strain region of high stiffness and during the large-scale yielding. To achieve this, the model utilizes existing formulations which proved to be successful in description of clay behaviour in these regions, and makes an attempt to bridge between them. The model utilizes the principles of the multiple surface kinematic hardening plasticity and is constituted by three elliptical yield surfaces in triaxial stress space. Two of the surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third one is the rotating elliptical MIT-E3 large-scale yield surface with a non-associated flow rule. All three surfaces are subject to both kinematic and isotropic hardening with corresponding hardening rules. The model requires 17 parameters, out of them eight are small strain and nine are large strain parameters. Performance of the model in prediction of the stress path dependency of clay behaviour was evaluated against experimental data obtained on undisturbed Laval samples of Bothkennar clay.

Influence of Reservoir Stress Path on Deformation and Permeability of Weakly Cemented Sandstone Reservoirs

Summary The influence of production-induced changes in reservoir pore pressure on compressibility and permeability of weakly cemented sandstones has been analyzed. Laboratory experiments simulating reservoir depletion have been conducted over a range of stress paths that a reservoir may follow. The results suggest that compressibility of weakly cemented sandstones is stress path dependent. Compressibility measured under uniaxial strain conditions, or a stress path defined by a lower ratio of the rate at which the effective horizontal to effective vertical stress were increased than the one associated with uniaxial strain, is more than twice the corresponding value found from the hydrostatic loading experiment. In contrast, matrix permeability measured in the maximum stress direction show no significant stress path dependence. Experimental results suggest that a better understanding of the stress-sensitive behavior of weakly cemented sandstones can only be gained by dealing more directly with the microstructure of the rock. The stress-path-dependent nonlinear behavior of weakly cemented sandstones is related to effects of shear-enhanced compaction. Increasing cementation has been experimentally shown to reduce stress sensitivity. The observed nonlinearity is attributed to dilatancy rather than shear-enhanced compaction, also reflected by permeability measurements made in the maximum stress direction.

Non-linear model of small-strain behaviour of soils

The paper describes a general approach to the development of a constitutive model for predict-ing the generalized small-strain behaviour of soils. The model incorporates non-linear stress— strain behaviour, stress-path dependence and a consistent definition of the small-strain region (SSR). Based on this general approach, a simple model is proposed which incorporates crossanisotropic elasticity within the linear elastic region (LER) and elliptical boundaries for the LER and SSR. The model leads to unique normalized stress—strain behaviour of undisturbed Bothkennar clay for the complete range of stress probe directions in triaxial stress space. The comparison confirms the uniqueness of the normalized volumetric and deviatoric stress— strain behaviour. The model can easily be incor-porated into numerical procedures for solving two- and three-dimensional boundary value problems. ĺarticle décrit une conception générale de la mise au point ´un modéle constitutif pour prédlre le comportement général des sols soumis à de petites contraintes. Le modèle regroupe la réaction aux tensions/déformations non liné aires, la variabilité en function du parcours de déformation et une définition cohérente du domaine des petites contraintes. A partir de cette conception générale, les auteurs proposent un modéle simple qui incorpore ĺléasticité transanisotrope dans le domain é1astique linéaire et les limites elliptiques du domaine élastique lin&aci\ute;aire et du domaine des petites contraintes. Le modèle produit un comportement spécifique de ĺargile Bothkennar non remaniée face à des tensions/déformations normalisées dans toute la gamme de directions de la sonde de tension, dans ĺespace de contrainte triaxiale. La comparaison confirme la spécificité de la réacdon à des tensions/déformations hydrostatiques et dé viatrices normalisées. Il est facile ´incorporer le modéle dans des formules numériques pour résoudre les problèmes de valeurs limites à deux ou trois dimensions.

A Two-Surface Model with Anisotropic Hardening and Nonassociated Flow Rule for Geomaterials

A two-surface model is proposed to describe various volumetric behavior with change in the direction of a stress-controlled path. The model is formulated using the following concept of the isotropic-kinematic hardening. For overconsolidated soils, the nonassociated flow rule is used because of the occurrence of volumetric change, which is beyond the descriptive capabilities of the associated flow rule, during the loading with an abrupt change of stress path. The proposed model consists of nine material parameters that can be determined with a few triaxial tests. The model is verified by comparing model predictions with experimental results. In addition, the shear strength increases for the material that has the characteristic of stress path dependency are evaluated. Experimentally stabilized behavior which contradicts the theoretical condition for material stability by Drucker is discussed.

Stress path dependence of matrix permeability of North Sea sandstone reservoir rock : Rhett, D W; Teufel, L W Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P345–353. Publ Rotterdam: A A Balkema, 1992

Stress path dependence of matrix permeability of North Sea sandstone reservoir rock : Rhett, D W; Teufel, L W Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P345–353. Publ Rotterdam: A A Balkema, 1992

Analysis of rail track structures (ARTS)

The computer program ARTS for the static non-linear analysis (with or without allowing any element to take tension) of track structures is presented. The finite element method is used and a choice of hexahedronal, pentahedronal and beam elements is provided which can model non-homogeneous isotropic elastic material properties. The program allows the calculation of contact forces between two structures (i.e. the ground and the tie/rail system). There are two techniques for describing the material non-linearity. Triaxial test data for ballast or granular material may be processed in a cubical spline form to allow for variable Young's modulus and Poisson's ratio, or a hyperbolic model may be employed. This permits the program to take into account the ballasts' stress path dependence. Elements can be selected as permitted, or not, to take tension. If permitted to take tension then the stress-strain or Poisson's ratio-strain characteristics are identical in tension and compression. Initial elastic properties may be imposed or body and surcharge conditions may be input allowing the program to calculate initial stresses and thus properties. A sample analysis has been selected to demonstrate the general problem solving procedure and the input and output descriptions.

Generalized stress-path-dependent soil behaviour with a new hollow cylinder torsional apparatus

A new hollow cylinder torsional shear apparatus is described. The apparatus is suitable for investigating soil behaviour under generalized stress paths, including principal stress rotations, characteristic of earthquake and offshore-wave loadings. A new, more rational assessment of stress nonuniformity across the wall of the hollow cylinder specimen is made, and the "no go" regions of the stress space are delineated that limit stress nonuniformity to acceptable levels. Operation of the apparatus and experimental procedures for tests on reconstituted specimens of sand are described. Typical results of drained tests on loose and dense sand are presented to illustrate the capabilities of the apparatus as a general stress-path loading device and to highlight the stress-path dependence of soil behaviour, in particular, the deformation response to principal stress rotations. Key words: hollow cylinder apparatus, generalized stress paths, principal stress rotation, sand, deformations.

A Constitutive Model for Soils Evaluating Principal Stress Rotation and Its Application to Some Deformation Problems

A constitutive model for soils by which the strain increments ( dɛ x , dɛ y and dγ xy ) are directly related to the stress increments (dσ x , dσ y and dτ xy ) is proposed. The stress-strain matrix between the strain increments and the stress increments is expressed in xy -coordinates fixed arbitrarily. In order to evaluate the influence of rotation of the principal stress axes on strains, “principal stress rotation tests” with several rotation times, in which the stress path circles several times along the circumference of a Mohr’s stress circle, are carried out by a “two-dimensional arbitrary stress apparatus” using a stack of aluminium rods. The “arbitrary” stress path dependency of strains is also examined by the same apparatus, and analyzed by the proposed model. The finite element analysis of soil foundation under a uniform strip load is performed using the proposed model, and the influence of rotation of the principal stress axes on settlements and lateral displacements is checked by comparing the computed results under different contribution factors (5% to 100%) of strains due to rotation of the principal stress axes. It is seen from the computed results that the settlements and lateral displacements are influenced significantly by the principal stress rotation.

Elasto-plastic constitutive modeling of plain concrete and an optimization procedure for parameter evaluation

An elasto-plastic constitutive model is developed to characterize the stress-strain behavior of plain concrete. The model utilizes a single yield surface to describe both yielding and failure behavior. An innovative approach is adopted to model volumetric behavior in compressive and dilative regimes. The transition between compression and dilation is identified by the point on the yield surface where the gradient tensor is deviatoric. The proposed approach provides a better control in predicting volumetric behavior of concrete. In addition, the model describes effectively other factors such as hardening, stress path dependency, and variation of shear strength with orientation of stress paths on the octahedral plane. Another unique feature of this model is its ability to account for the variation of the shape of the yield surface on the octahedral plane with confining pressure. An optimization procedure is developed to evaluate the material constants associated with the model. Stress-strain and volumetric responses for a number of tests are predicted and compared with experimental data. Overall, a good agreement between predictions and observations is obtained.

Isotropic hardening elastoplastic model for sand considering the stress path dependency in three-dimensional stresses : Nakai, T Soils FoundV29, N1, March 1989, P119–137

Isotropic hardening elastoplastic model for sand considering the stress path dependency in three-dimensional stresses : Nakai, T Soils FoundV29, N1, March 1989, P119–137

An Isotropic Hardening Elastoplastic Model for Sand Considering the Stress Path Dependency in Three-Dimensional Stresses

ABSTRACT An isotropic hardening elastoplastic constitutive model for sand is developed by extending the model for clay proposed before. This model for sand (named tij-sand model) can precisely take into consideration the influence of intermediate principal stress on the deformation and strength characteristics by using the concept of the mechanical quantity tij and the influence of stress path on the direction of plastic flow by dividing the plastic strain increment into two components, in the same way as the previous model for clay (tij -clay model). In the present paper, a new “plastic work based on tij” W*p is defined, and it is experimentally shown that W*p is proper as the quantity of state for sand. Then, the model for sand is formulated by employing W*p as the strain hardening parameter, in place of the plastic volumetric strain ɛvp in the model for clay. The validities of the model are confirmed by various shear and consolidation tests under triaxial compression, triaxial extension and three different principal stresse conditions and stress probe tests under triaxial compression and extension conditions. All of the soil parameters of the model can be determined by a conventional triaxial compression test after loading-unloading-reloading isotropic consolidation.

Mechanical Modeling of Material Damage

A systematic theory to describe the anisotropic damage states of materials and a consistent definition of effective stress tensors are developed within the framework of continuum damage mechanics. By introducing a fictitious undamaged configuration, mechanically equivalent to the real damaged configuration, the classical creep damage theory is extended to the general three-dimensional states of material damage; it is shown that the damage state can be described in terms of a symmetric second rank tensor. The physical implications, mathematical restrictions, and the limitations of this damage tensor, as well as the effects of finite deformation on the damage state, are discussed in some detail. The notion of the fictitious undamaged configuration is then applied also to the definition of effective stresses. Finally, the extension of the effective stresses incorporating the effects of crack closure is discussed. The resulting effective stress tensor is employed to analyze the stress-path dependence of the elastic behavior of a cracked elastic-brittle material.

Damage variables and related effective stresses in continuum damage mechanics.

A systematic theory to describe the anisotropic damage states of materials and a consistent definition of effective stress tensors are developed. By introducing a fictitious undamaged configuration mechanically equivalent to the real damaged configuration, the classical creep damage theory is extended to the general three-dimensional states of material damage. It is shown that the damage state can be described in terms of a symmetric second rank tensor. The physical implications, mathematical restrictions and the limitations of this damage tensor, as well as the effects of finite deformation on the damage state are discussed in some detail. The notion of the fictitious undamaged configuration is then applied to the definition of effective stresses. Finally, the extension of the effective stresses incorporating the effects of crack closure is discussed. The resulting effective stress tensor is employed to analyze the stress-path dependence of the elastic behavior of a cracked material.