Thermo-Chemo-Mechanical Model for Concrete. I: Hydration and Aging

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.     

Three-Dimensional Damage Model for Concrete. II: Verification

A three-dimensional damage model for concrete has been proposed in the preceding paper, Part I: Theory. This paper focuses on the application of the damage model for quasi-brittle materials such as concrete. The determination of model parameters for the evolution rule of damage is discussed. The model parameters to consider the frictional stress and the stiffness reduction under hydrostatic compression are also studied. For verification, the proposed model is applied to concrete subjected to confined compression, triaxial, loading, and cyclic loading. Consistent results, as compared with other researchers’ experimental data, were obtained, and the proposed model is considered worthy of further research work.     

Nonlinear Creep Damage Model for Concrete under Uniaxial Compression

An isotropic model for creep damage of concrete under uniaxial compression is proposed, where the combined effect of nonlinear viscous strain evolution and crack nucleation and propagation at high stress levels is considered. Strain splitting assumption is used for creep and damage contributions. Creep is modeled by a modified version of solidification theory. As usual in the modeling of damage of concrete, a damage index based on positive strains is introduced. As particular cases, the proposed model reduces to linear viscoelasticity for long time low stress levels whereas, for very high stresses, tertiary creep causing failure at a finite time can be described. The effect of strength variation with time is also included. The model is numerically implemented to perform time integration of nonlinear equations by means of a modified version of exponential algorithm. The model is validated through comparison with experimental results. Some numerical examples are also presented, where the roles of concrete ageing and strength variation with time are investigated.     

Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: II. Computation and Validation

The concrete material model developed in the preceding Part I of this study is formulated numerically. The new model is then verified by comparisons with experimental data for compressive and tensile uniaxial tests, biaxial tests, and triaxial tests, as well as notched tests of mode I fracture and size effect.     

Anisotropic Damage Model for Concrete

In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.     

Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: I. Theory

The mechanical behavior of the mesostructure of concrete is simulated by a three-dimensional lattice connecting the centers of aggregate particles. The model can describe not only tensile cracking and continuous fracture but also the nonlinear uniaxial, biaxial, and triaxial response in compression, including the postpeak softening and strain localization. The particle centers representing the lattice nodes are generated randomly, according to the given grain size distribution, and Delaunay triangulation is used to determine the lattice connections and their effective cross-section areas. The deformations are characterized by the displacement and rotation vectors at the centers of the particles (lattice nodes). The lattice struts connecting the particles transmit not only axial forces but also shear forces, with the shear stiffness exhibiting friction and cohesion. The connection stiffness in tension and shear also depends on the transversal confining stress. The transmission of shear forces between particles is effected without postulating any flexural resistance of the struts. The shear transmission and the confinement sensitivity of lattice connections are the most distinctive features greatly enhancing the modeling capability. The interfacial transition zone of the matrix (cement mortar or paste) is assumed to act approximately in series coupling with the bulk of the matrix. The formulation of a numerical algorithm, verification by test data, and parameter calibration are postponed for the subsequent companion paper.     

Microplane Model M4 for Concrete. II: Algorithm and Calibration

This paper represents Part II of a two-part study in which a new improved version of the microplane constitutive model for damage-plastic behavior of concrete in 3D is developed. In Part II, an explicit numerical algorithm for model M4 is formulated, the material parameters of model M4 are calibrated by optimum fitting of the basic test data available in the literature, and the model is verified by comparisons with these data. The data in which strain localization must have occurred are delocalized, and the size effect is filtered out from the data where necessary. Although model M4 contains many material parameters, all but four have fixed values for all types of concretes. Thus the user needs to adjust only four free material parameters to the data for a given concrete, for which a simple sequential identification procedure is developed. If the user's data consist only of the standard compression strength and the strain at uniaxial stress peak, the adjustment is explicit and immediate. Good agreement with an unusually broad range of material test data is achieved.     

Continuum Microviscoelasticity Model for Aging Basic Creep of Early-Age Concrete

We propose a micromechanics model for aging basic creep of early-age concrete. Therefore, we formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste (composed of cement, water, hydrates, and air), and one related to concrete (composed of cement paste and aggregates). Homogenization of the “nonaging” elastic and viscoelastic properties of the material’s contituents involves the transformation of the aforementioned viscoelastic boundary value problems to the Laplace-Carson (LC) domain. There, formally elastic, classical self-consistent and Mori-Tanaka solutions are employed, leading to pointwisely defined LC-transformed tensorial creep and relaxation functions. Subsequently, the latter are back-transformed, by means of the Gaver-Wynn-Rho algorithm, into the time domain. Temporal derivatives of corresponding homogenized creep and relaxation tensors, evaluated for the current maturation state of the material (in terms of current volume fractions of cement, water, air, hydrates, and aggregates; being dependent on the hydration degree, as well as on the water-cement and aggregate-cement ratios) and for the current time period since loading of the hydrating composite material, allow for micromechanical prediction of the aging basic creep properties of early-age concrete.     

Three-Dimensional Electromechanical Impedance Model. II: Damage Analysis and PZT Characterization

Piezoceramic transducers (PZTs) are extensively used in the nondestructive evaluation of damages in various engineering structures. This paper, the second of a two-part paper, focuses on the application of a PZT using three-dimensional (3D) directional sum impedance (DSI). The semianalytical 3D admittance has been formulated and experimentally validated in the first paper. This part deals with the application of the 3D DSI model in damage analysis where by damages were numerically simulated for various types of specimens and the DSI admittance signatures were predicted and compared. The deviations of the signature from that of the undamaged state provide an indicator for the health of the structure. This technique is nondestructive in nature, and the damages were quantified using root-mean-square deviation in signatures with respect to the undamaged state signature. In Part I, the properties of the PZT and their influences on admittance signatures were briefly presented. In this part, a thorough investigation was made and the importance of all the PZT properties in damage analysis was presented.     

Model for Reinforced Concrete Members under Torsion, Bending, and Shear. II: Model Application and Validation

A model was recently proposed for predicting the load-deformation response of a reinforced concrete member under torsion combined with bending and shear to spalling or ultimate. This paper shows the application of the model to create interaction surfaces to predict the failure of a member subjected to different ratios of applied torsion, bending, and shear. The model was validated by comparing the predicted and experimental behavior of 28 members from three experimental studies available in the literature. The members were loaded under torsion combined with different ratios of bending, and shear. The torque-twist behavior, reinforcement stress, and concrete surface strain predicted by the model were in close agreement with the experiments. This paper also describes how the model can be applied to create interaction surfaces. The interaction curves predicted by the model were validated by comparing the predicted and experimental capacities of 17 specimens available in the literature.     

Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4

Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Ba?ant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.     

Damage Analysis of Hanshin Expressway Viaducts during 1995 Kobe Earthquake. II: Damage Mode of Single Reinforced Concrete Piers

The damage mode that single reinforced concrete (RC) piers of the Hanshin Expressway Kobe Route suffered during the 1995 Kobe earthquake is discussed. On the Kobe Route, many single RC piers suffered from flexural mode damage; however, some suffered from shear failure, and most shear failure occurred in piers with rectangular cross sections. The flexural and shear capacity of each pier are calculated based on the design documents, and the ratio of flexure to shear capacity, r, is calculated by taking into account the mass of the pier column. It is found that the damage mode (flexure or shear) in the severely damaged single RC piers from P1 to P350 can be explained by the value of r, either >1.0 (flexural mode) or <1.0 (shear mode).     

The “Chunnel” Fire.?II: Analysis of Concrete Damage

In Part I of this study, a material model for the in-situ behavior of rapidly heated concrete was developed that accounts explicitly for the dehydration of concrete and its cross-effects with deformation (chemomechanical couplings) and temperature (chemothermal couplings). In this part of the study, the model is used in finite-element analysis of the tunnel rings of the Channel Tunnel (the “Chunnel”) exposed to fire. An analysis of the finite-element results—i.e., the profiles of temperature, dehydration, stresses, and plastic strains—clearly shows that the thermal spalling that occured during the Chunnel fire is initiated by an in-plane biaxial compressive stress clog closed to the heated surface. The compressive stresses are caused by restrained thermal dilatation and are bounded by chemoplastic softening due to dehydration. They provoke permanent radial deformation, which can be attributed to spalling. The role of thermal damage and thermal decohesion is discussed by comparing elastic, chemoelastic, and chemoplastic stress developments during the 10 h fire exposure. It is found that the salient feature to capture the initiation of thermal spalling at a structural level is the chemoplastic softening behavior at a constitutive material level. It is also shown that a reinforcement on the cold-side, as well as steel fiber reinforcement of concrete, in tunnel rings may significantly increase the risk of thermal spalling.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. II: Computation

Following the formulation of the constitutive model in the preceding Part I in this issue, the present Part II addresses the problems of computational algorithm and convergence of iterations. Typical numerical responses are demonstrated and the parameters of the model are calibrated by test data from the literature.     

Modeling of Early-Age Creep of Shotcrete. I: Model and Model Parameters

In this paper, creep and viscous flow are revisited from the standpoint of constitutive modeling of thermo-chemo-mechanical couplings in early-age concrete. Within the framework of closed reactive porous media, creep is modeled by means of two mechanisms: a stress-induced water movement within the macropores and a relaxation mechanism in the micropores of cement gel, both of which lead to aging effects on creep and viscous flow of concrete. Regarding the first creep mechanism, aging results from chemomechanical couplings. Concerning the second mechanism, long-term aging is attributed to the relaxation of microprestresses in the micropores. Following the formulation of the model, it is shown how the material parameters can be identified from creep tests performed at different ages of loading. Finally, the model is applied to shotcrete, for which proper experimental data are missing.     

P92钢的蠕变损伤容许量系数及蠕变断裂机理

利用P92钢在595、610、640、670℃的高应力试验条件下的蠕变试验数据,得出其Norton应力指数,依据Norton应力指数的大小判定其蠕变机理为位错蠕变。同时结合1种新的蠕变变形及断裂模型,引入将蠕变损伤看作1个内在的阶段变量的蠕变损伤容许量系数,根据蠕变损伤容许量λ=2.94,判断其蠕变变形和断裂是位错运动控制的。微观组织的观察也表明,蠕变后的试样中位错密度大大降低,高密度位错是P92钢持久强度高的原因,伴随着位错密度的下降,P92钢持久强度降低直至断裂。     

Creep of Polymer Matrix Composites. II: Monkman-Grant Failure Relationship for Transverse Isotropy

This research concerns polymer matrix composite (PMC) materials having long or continuous reinforcement fibers embedded in a polymer matrix. The objective is to develop comparatively simple, designer friendly constitutive equations intended to serve as the basis of a structural design methodology for this class of PMC. Here (Part II), the focus is on extending the damage/failure model of an anisotropic deformation/damage theory presented earlier. A companion paper (Part I) by the writers deals with creep deformation of the same class of PMC. The extension of the damage model leads to a generalization of the well known Monkman/Grant relationship to transverse isotropy. The usefulness of this relationship is that it permits estimates of (long term) creep rupture life on (short term) estimates of creep deformation rate. The current extension also allows estimates of failure time for various fiber orientations. Supporting exploratory experiments are defined and conducted on thin-walled specimens fabricated from a model PMC. A primary assumption in the damage model is that the stress dependence of damage evolution is on the transverse tensile and longitudinal shear traction acting at the fiber/matrix interface. We conjecture that a supplemental mechanism of failure is the extensional strain in the fiber itself. The two postulated mechanisms used in conjunction suggest that an optimal fiber angle may exist in this class of PMC, maximizing the time to creep failure.     

Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures

A computational constitutive model was developed to predict damage and fracture failure of asphalt concrete mixtures. Complex heterogeneity and inelastic mechanical behavior are addressed by the model by using finite-element methods and elastic–viscoelastic constitutive relations. Damage evolution due to progressive cracking is represented by randomly oriented interface fracture, which is governed by a newly developed nonlinear viscoelastic cohesive zone model. Computational simulations demonstrate that damage evolution and failure of asphalt concrete mixtures is dependent on the mechanical properties of the mixture. This approach is suitable for the relative evaluation of asphalt concrete mixtures by simply employing material properties and fracture properties of mixture components rather than by performing expensive laboratory tests recursively, which are typically required for continuum damage mechanics modeling.     

Coupled Creep and Seepage Model for Hybrid Media

The permeability coefficient of a rock mass depends mainly on the aperture of the joint and the porosity of the block, which may alter with time when creep of the rock mass is taken into account. Therefore, a coupled creep and seepage model for hybrid media is proposed in this paper. Large-scale and strongly permeable joints are simulated according to their spatial distributions, while other discontinuities are treated as equivalent continuum. Based on the fundamental mechanism of creep effects on the permeability of the rock mass, together with empirical equations for hydraulic conductivity, coupled creep and seepage equations for filled joints, rough joints, and equivalent continuum are proposed. By application of these equations, governing equations for the coupled creep and seepage model are deduced. A simplified numerical solution is proposed to solve the coupled creep and seepage model. The coupled model is shown to simulate the evolvement of seepage, deformation, and stress field in a gravity dam. By comparing the results derived by coupled and uncoupled models, it is concluded that the coupling between creep and seepage should be taken into account when performing engineering design of large dams.     

Thermomechanical fatigue,oxidation, and Creep: Part II. Life prediction

A life prediction model is developed for crack nucleation and early crack growth based on fatigue, environment (oxidation), and creep damage. The model handles different strain-temperature phasings(i.e., in-phase and out-of-phase thermomechanical fatigue, isothermal fatigue, and others, including nonproportional phasings). Fatigue life predictions compare favorably with experiments in 1070 steel for a wide range of test conditions and strain-temperature phasings. An oxide growth (oxide damage) model is based on the repeated microrupture process of oxide observed from microscopic measurements. A creep damage expression, which is stress-based, is coupled with a unified constitutive equation. A set of interrupted tests was performed to provide valuable damage progression information. Tests were performed in air and in helium atmospheres to isolate creep damage from oxidation damage.