An updated reference configuration formulation for large-deformation problems

This paper examines difficulties encountered when using the Green-Nagdi rate and presents an updated configuration formulation for problems dealing with large deformations. It is shown that a natural link can be established between the updated reference configuration and linearized updated Lagrangian formulations, if Truesdell's objective stress rate is used. Owing to this connection, any limitations associated with the described formulation would be expected to also apply to an updated Lagrangian formulation and vice versa. It is pointed out that, if second-order effects are induced, the Truesdell rate appears in the rate equation for equilibrium even when strains are infinitesimal. By examining a simple-shear problem, where hypoelastic material behaviour with ‘Hooke's law’ is assumed, it is shown that the spherical state of stress is coupled with the shear stress when using the Truesdell or Green-Nagdi stress rate. It is suggested that objective stress rates, introduced in large-deformation formulations, may contribute to erroneous predictions if a constitutive law is developed independent of the adopted stress rate.     

Determination of the Effective Stress Law for Deformation in Coalbed Methane Reservoirs

Effective stress laws and their application are not new, but are often overlooked or applied inappropriately. The complexity of using a proper effective stress law increases when analyzing stress variation in coal as a result of gas production or mining. In this paper, an effective stress law is derived analytically for coalbed methane reservoirs, combining the concepts of matrix shrinkage/swelling and external stress by including the effect of sorbing gas pressure on the elastic response of the reservoir. The proposed law reduces to that of Terzaghi when the compressibility of bulk material is sufficiently greater than the compressibility of the solid grain, and without the strain associated with matrix shrinkage/swelling effect. Moreover, it is shown that the Biot coefficient (α) can have a value larger than unity for self-swelling/dilation materials, such as coal. The proposed stress–strain relationship was validated using experimental results. Overall, the effective stress law for deformation was extended for sorptive materials, providing a new and unique technique to analyze the elastic behavior of coal by reducing three variables, namely, external stress, pore pressure and matrix shrinkage/swelling along with the associated stress, down to one variable, “effective stress”.     

Coupled finite‐element simulation of injection well testing in unconsolidated oil sands reservoir

This paper presents a finite‐element (FE) model for simulating injection well testing in unconsolidated oil sands reservoir. In injection well testing, the bottom‐hole pressure (BHP) is monitored during the injection and shut‐in period. The flow characteristics of a reservoir can be determined from transient BHP data using conventional reservoir or well‐testing analysis. However, conventional reservoir or well‐testing analysis does not consider geomechanics coupling effects. This simplified assumption has limitations when applied to unconsolidated (uncemented) oil sands reservoirs because oil sands deform and dilate subjected to pressure variation. In addition, hydraulic fracturing may occur in unconsolidated oil sands when high water injection rate is used. This research is motivated in numerical modeling of injection well testing in unconsolidated oil sands reservoir considering the geomechanics coupling effects including hydraulic fracturing. To simulate the strong anisotropy in mechanical and hydraulic behaviour of unconsolidated oil sands induced by fluid injection in injection well testing, a nonlinear stress‐dependent poro‐elasto‐plastic constitutive model together with a strain‐induced anisotropic permeability model are formulated and implemented into a 3D FE simulator. The 3D FE model is used to history match the BHP response measured from an injection well in an oil sands reservoir. Copyright © 2013 John Wiley & Sons, Ltd.     

An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.     

Anisotropic viscoplastic modeling of rate‐dependent behavior of clay

The objective of this study is to derive an effective stress‐based constitutive law capable of predicting rate‐dependent stress–strain, stress path and undrained shear strength and creep behavior. The flow rule used in the MIT‐E3 model and viscoplasticity theory is employed in the derivation. The model adopts the yield surface capable of representing the yield behavior of the Taipei silty clay and assumes that it is initially symmetric about the K₀‐line. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress rotation after shear. There are 11 parameters required for the model to describe the soil behavior and six of them are exactly the same as those used in the Modified Cam‐clay model. The five additional parameters can be obtained by parametric studies or conventional soil tests, such as consolidation tests, triaxial compression and extension tests. Finally, verification of the model for the anisotropic behavior, creep behavior and the rate‐dependent undrained stress–strain and shear strength of the Taipei silty clay is conducted. Copyright © 2010 John Wiley & Sons, Ltd.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

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The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

Arbitrary Lagrangian–Eulerian method for large‐strain consolidation problems

In this paper, an arbitrary Lagrangian–Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore‐water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated‐Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd.     

Distribution of suspended sediment concentration in wide sediment‐laden streams: A novel power‐law theory

The diffusion equation of suspended sediment concentration in a wide sediment‐laden stream flow is dependent on the vertical gradient of streamwise velocity and the sediment diffusivity. This study aims at investigating the influence of the streamwise velocity laws on the suspended sediment concentration distributions, resulting from the solution of the diffusion equation. Firstly, the sediment concentration distributions are obtained numerically from the solution of the diffusion equation using different velocity laws and compared with the experimental data. It is found that the power‐law approximation produces good computational results for the concentration distributions. The accuracy of using a power‐law velocity model is comparable with the results obtained from other classical velocity laws, namely log‐law, log wake‐law and stratified log‐law. Secondly, a novel analytical solution is proposed for the determination of sediment concentration distribution, where a power‐law, wall‐concentration profile is coupled with a concentration wake function. The power‐law model (for velocity and concentration) is calibrated using the experimental data, and then a generalized wake function is obtained by choosing a suitable law. The developed power‐law model involving the wake function adjusted by an exponent predicts the sediment concentration distributions quite satisfactorily. Finally, a new explicit formula for the suspended‐load transport rate is derived from the proposed theory, where numerical computation of integrals, as needed in the Einstein theory, is avoided.     

Borehole failure analysis in a sandstone under anisotropic stresses

Borehole failure under anisotropic stresses in a sandstone is analyze numerically for various borehole sizes using a nonlinear elastic–plastic constitutive model for a Cosserat continuum. Borehole failure is identified as macroscopic failure of the borehole through the development of shear bands and breakouts. The results compare well both qualitatively and quantitatively with experimental results from polyaxial tests on Red Wildmoor sandstone. They show that the hole size effect of the borehole failure strength is independent of the far‐field stress anisotropy and follows a ? power law of the hole size. A similar scale effect equation with a ? power law is proposed for the scale effect of the maximum plastic shear strain at failure. This equation can be useful for better predicting hole‐size‐dependent failure with standard codes based on classical continua. The effect of stress anisotropy on the borehole failure stress is found to be independent of the hole size. The failure stress decreases linearly to 40% as the stress anisotropy increases. However, the maximum plastic shear strain at failure is stress anisotropy independent and therefore the critical plastic shear strain for failure is only hole‐size dependent. Copyright © 2009 John Wiley & Sons, Ltd.     

A constitutive model for crushed salt

A constitutive model for crushed salt is presented in this paper. A creep constitutive model is developed first and compared with test results. The constitutive model presented here concentrates on creep deformation because saline media behave basically in a ductile and time‐dependent way. An idealized geometry is used as a common framework to obtain stress–strain macroscopic laws based on two deformation mechanisms: fluid‐assisted diffusional transfer creep and dislocation creep. The model is able to predict strain rates that compare well with results from laboratory tests under isotropic and oedometric conditions. Macroscopic laws are written using a non‐linear viscous approach, which incorporates also a viscoplastic component, based on critical state theory. The viscoplastic term is intended for non‐creep deformation mechanisms such as grain reorganization and crushing. Copyright © 2002 John Wiley & Sons, Ltd.     

Interpretation of unsaturated soil behaviour in the stress – Saturation space,I: Volume change and water retention behaviour

Unsaturated soil behaviour, such as volume change, shear strength and yield stress, is usually interpreted and modelled in terms of stress and suction. This approach is consistent with laboratory tests where suction is a controllable variable. However, it also suffers some limitations. This paper (Parts I and II) presents an alternative approach for interpreting unsaturated soil behaviour, which is built in the space of stress versus degree of saturation. In Part I, a new volume change equation is proposed in terms of stress and degree of saturation, to give a better explanation to the non-linear change of soil compressibility under constant suctions. The soil compression index is assumed to be a function of the effective degree of saturation and is interpolated from the known compressibility at the fully saturated state and that at a dry state. An alternative approach to simulate hydraulic hysteresis and hydro-mechanical interaction is then introduced, which enables the calculation of the effective degree of saturation under complex stress and suction paths. The proposed volume change equation and the approach to describe saturation variation, which are two fundamental aspects to establish constitutive laws for unsaturated soils, are validated against a variety of experimental data in literature.     

Numerical analysis of time dependent settlements and pore water pressures by example of the plate loading test

Possibilities of modelling the deformation behaviour of water-saturated cohesive soils are discussed. it is concluded that a non-linear constitutive lawa should be used in connection with Biot's consolation theory. A hypoelastic law is considered in detail following a brief introduction to the theory and the numerical solution scheme. Starting from an “incremental Hookien” model extension is made by a dilatancy term in order to obtain pore pressure distribution in line with experimental results. The well known Skempton approach is included as a special case. Results of an earlier research project run in the Stuttgart University Insitute, namely stress and strain controlled plate loading tests, are chosen to compare calculation and measurements. Satisfactory results could be achieved to a large extent after the variation of two significant parameters - the cohesiion and the permeability - within their range of scatter. The importance of a time dependent coupled analysis is shown by comparison to an uncoupled analysis for the limiting cases “undrainded” and “ideally drained”.     

Three-dimensional finite element modelling of stress relaxation tests in anisotropic clayey medium: direct problem and back analysis

This paper deals with a new strategy for initial stress identification by stress relaxation methods, coupled with finite element calculation, and applied to the overcoring test. The back-analysis of such a test uses an inversion method which consists in the minimisation, with a gradient-based algorithm, of a cost functional of least-squares type, which quantizes the difference between measured and computed strains. The computed strains are assessed by three-dimensional finite element modellings of the overcoring test. The inversion methodology is applied to a recent in situ overcoring test performed at Mont Terri laboratory, Switzerland. The inversion gave good results and allows us to validate the inversion methodology. The constitutive law considered for this application is transverse isotropic elasticity but the inversion method developed is applicable to most constitutive laws and every kind of in situ test.     

Finite element consolidation analysis of soils with vertical drain

This paper presents a finite element procedure for the analysis of consolidation of layered soils with vertical drain using general one‐dimensional (1‐D) constitutive models. In formulating the finite element procedure, a Newton–Cotes‐type integration formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (Modified Newton) iteration scheme. The proposed procedure is then applied for the consolidation analysis of a number of typical problems using both linear and non‐linear soil models. Results from this simplified method are compared with those from a fully coupled consolidation analysis using a well‐known finite element package. The average degree of consolidation, excess porewater pressure and average vertical effective stress are almost the same as those from the fully coupled analysis for both the linear and non‐linear cases studied. The differences in vertical effective stresses are tolerable except for the values near the vertical drain boundaries. The consolidation behaviour of soils below a certain depth of the bottom of vertical drain is actually one‐dimensional for the partially penetrating case. Therefore, there are not much differences in whether one uses a one‐dimensional model or a three‐dimensional model in this region. The average degree of consolidation has good normalized feature with respect to the ratio of well radius to external drainage boundary for the cases of fully penetrating vertical drain using a normalized time even in the non‐linear case. Numerical results clearly demonstrate that the proposed simplified finite element procedure is efficient for the consolidation analysis of soils with vertical drain and it has better numerical stability characteristics. This simplified method can easily account for layered systems, time‐dependent loading, well‐resistance, smear effects and inelastic stress–strain behaviour. This method is also very suitable for the design of vertical drain, since it greatly reduces the unknown variables in the calculation and the 1‐D soil model parameters can be more easily determined. Copyright © 2000 John Wiley & Sons, Ltd.     

杭州西湖疏浚底泥工程性质试验研究

针对西湖疏浚底泥的沉积规律、颗粒分布、渗透特性、压缩特性等工程性质进行了室内试验,并分别对室内沉积土样和库区沉积土样的工程性质做了比较,得到了渗透系数、压缩系数等指标沿深度和距离上的变化规律。试验结果对进一步了解疏浚底泥的工程特性具有参考意义,也有利于指导蓄泥库疏浚底泥的后期处理措施的制定。     

A general basis for yield,failure and potential functions in plasticity

A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.