Numerical Model for Time-Dependent Fracturing of Concrete

A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.     

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.     

Temperature Effect on Concrete Creep Modeled by Microprestress-Solidification Theory

The previously developed microprestress-solidification theory for concrete creep and shrinkage is generalized for the effect of temperature (not exceeding 100°C). The solidification model separates the viscoelasticity of the solid constituent, the cement gel, from the chemical aging of material caused by solidification of cement and characterized by the growth of volume fraction of hydration products. This permits considering the viscoelastic constituent as non-aging. The temperature dependence of the rates of creep and of volume growth is characterized by two transformed time variables based on the activation energies of hydration and creep. The concept of microprestress achieves a grand unification of theory in which the long-term aging and all transient hygrothermal effects simply become different consequences of one and the same physical phenomenon. The microprestress, which is independent of the applied load, is initially produced by incompatible volume changes in the microstructure during hydration, and later builds up when changes of moisture content and temperature create a thermodynamic imbalance between the chemical potentials of vapor and adsorbed water in the nanopores of cement gel. As recently shown, this simultaneously captures two basic effects: First, the creep decreases with increasing age at loading after the growth of the volume fraction of hydrated cement has ceased; and, second, the drying creep, i.e., the transient creep increases due to drying (Pickett effect) which overpowers the effect of steady-state moisture content (i.e., less moisture—less creep). Now it is demonstrated that the microprestress buildup and relaxation also captures a third effect: The transitional thermal creep, i.e., the transient creep increase due to temperature change. For computations, an efficient (exponential-type) integration algorithm is developed. Finite element simulations, in which the apparent creep due to microcracking is taken into account separately, are used to identify the constitutive parameters and a satisfactory agreement with typical test data is achieved.     

Time-Dependent Behavior of Concrete-Filled Steel Tubular Arch Bridge

This paper develops a simplified method using a summation procedure and a related computer program to calculate the time-dependent behavior of a concrete filled steel tubular (CFST) arch bridge based on the geometric compatibility principle, a step-by-step time incremental process, and self-equilibrium equations. An experimental test on a scaled (1:5) segmental model of the main arch ribs of the Maocaojie Bridge was used to confirm the effectiveness of the proposed calculation method for evaluating the long-term behavior of CFST arch bridge under sustained load. It is concluded that: (1) the numerical results were in good agreement with the experimental results, demonstrating that the proposed analytical model is capable of predicting long-term effects for CFST arch bridges; (2) the stresses in the steel tubes increased, and the compressive stresses in the concrete decreased due to the effects of concrete creep and shrinkage. The maximum relaxation of the compressive stress in concrete due to concrete creep was 52.7% of the initial concrete stress, and the maximum increase of stress in the steel tubes was 27.3%; and (3) more than 90% of the total creep of the concrete took place in the first year. Subsequent creep of the concrete was limited because of the lack of water exchange between the structure and atmosphere and the reduction of compressive stress in the concrete.     

Nonlinear Quasi-Viscoelastic Behavior of Composite Beams Curved In-Plan

A numerical formulation for the nonlinear quasi-viscoelastic (creep and shrinkage) analysis of steel-concrete composite beams that are curved in their plan is developed. The creep behavior of the concrete is considered by using the viscoelastic Maxwell-Weichert?model, in which the aging effect of the concrete is taken into account. Geometric nonlinearities and the partial shear interaction that exist at the deck-girder interface in the tangential (or longitudinal) direction and in the radial (or horizontal) direction owing to the flexibility of the shear connectors are considered in the strain-displacement relationship. The modeling based on the developed formulation is validated by comparisons with available results reported in the literature. The effects of initial curvature, partial interaction, and geometric nonlinearity on the time-dependent behavior of curved composite beams are illustrated in selected examples.     

Creep Deformation of Fiber Reinforced Plastics-Plated Reinforced Concrete Tensile Members

The problem of long-term creep deformation of reinforced concrete tensile elements strengthened by external fiber reinforced plastic (FRP) plates is studied. Formation of discrete cracks in concrete under tension is taken into account. A kinematic model is used, where relative slips between concrete, steel bars, and FRP plates are considered, governed by viscous interface shear stress–slip laws. Bazant’ solidification theory and exponential algorithm are used to obtain incremental constitutive equations for concrete as well as for steel-concrete and FRP-concrete interface laws. Moreover, cohesive normal stresses across transverse cracks in concrete are considered. The incremental differential system of equations is transformed into a nonlinear algebraic system by a finite difference discretization with respect to axial coordinate. Several numerical examples are presented, concerning both short-term and long-term loadings. It is shown that reinforcing by means of FRP plates or sheets has significant beneficial effects on the behavior of reinforced concrete elements under service loadings because (1) it increases concrete tension stiffening effect and (2) it strongly reduces crack width. The present study shows that these beneficial effects are preserved also in the case of long-term loadings.     

Thermo-Chemo-Mechanical Model for Concrete. II: Damage and Creep

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.     

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.     

Fracturing Rate Effect and Creep in Microplane Model for Dynamics

The formulation of microplane model M4 in Parts I and II is extended to rate dependence. Two types of rate effect in the nonlinear triaxial behavior of concrete are distinguished: (1) Rate dependence of fracturing (microcrack growth) associated with the activation energy of bond ruptures, and (2) creep (or viscoelasticity). Short-time linear creep (viscoelasticity) is approximated by a nonaging Maxwell spring-dashpot model calibrated so that its response at constant stress would be tangent to the compliance function of model B3 for a time delay characteristic of the problem at hand. An effective explicit algorithm for step-by-step finite-element analysis is formulated. The main reason that the rate dependence of fracturing must be taken into account is to simulate the sudden reversal of postpeak strain softening into hardening revealed by recent tests. The main reason that short-time creep (viscoelasticity) must be taken into account is to simulate the rate dependence of the initial and unloading stiffness. Good approximations of the rate effects observed in material testing are achieved. The model is suitable for finite-element analysis of impact, blast, earthquake, and short-time loads up to several hours duration.     

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.     

Creep-Effect on Mechanical Behavior of Concrete Confined by FRP under Axial Compression

Despite many successes in concrete creep studies, its effect on the mechanical behavior of concrete members is far from a thorough case-specific understanding. For the members that have been subjected to a long-term load, the classical stress-strain models describing the short-term behavior of either confined or unconfined concrete are unsuitable. In order to investigate this creep-effect, an experiment on eight concrete cylindrical columns confined by fiber-reinforced polymer (FRP) is carried out. Based on the theory of plasticity for concrete, a constitutive model that takes into account the effect of creep on mechanical behavior of concrete confined by FRP is presented. In the model, the creep law inspired in the microprestress-solidification theory is generalized to triaxial stress condition for the calculation of the creep of the concrete columns confined by FRP. The predictions of the model agree well with the experimental results. The present study indicates that the creep increases the elastic modulus, slightly decreases the compressive strength, and degrades the deformation capability of the concrete confined by FRP.     

Creep Modeling in Excavation Analysis of a High Rock Slope

Based on the distinct element method, a numerical procedure is presented for simulation of creep behavior of jointed rock slopes due to excavation unloading. The Kelvin model is used to simulate viscous deformation of joints. A numerical scheme is introduced to create incremental contact forces, which are equivalent to producing creep deformation of a rock-joint system. The corresponding displacement of discrete blocks due to creep deformation of contact joints can be calculated by equilibrium iteration. Comparisons of results between the numerical model and theoretical solutions of a benchmark example show that the presented model has excellent accuracy for analysis of creep deformation of rock-joint structures. As an application of the model, residual deformations of the high rock slopes of the Three Gorges shiplock due to excavation unloading and creep behavior are investigated. By simulating the actual excavation process, the deformation history of a shiplock slope is studied. Good agreement has been achieved between numerical prediction and field measurements. It demonstrates the effectiveness of the presented model in analysis of the creep deformation due to excavation unloading of high rock slopes.     

Uncertainty Analysis of Creep and Shrinkage Effects in Long-Span Continuous Rigid Frame of Sutong Bridge

The long-term behavior of long-span prestressed concrete continuous rigid-frame bridges is significantly sensitive to creep and shrinkage. Therefore, it is important to accurately estimate creep and shrinkage effects. This paper presents modified prediction models that are based on the creep and shrinkage models in the existing bridge code. These modified prediction models match well with the test results of the high-strength concrete used in the continuous rigid frame of the Sutong Bridge in China. Results indicate that the accuracy in predicting creep and shrinkage can be enhanced greatly by measuring short-term creep and shrinkage on the given concrete and by modifying the prediction model parameters accordingly. Subsequently, the probabilistic analysis method of structural creep and shrinkage effects was studied. Uncertainty analysis of time-dependent effects in the given bridge was performed using the modified model, and results were compared with field-test data. Two approaches for mitigating deflections that were used in the continuous rigid frame of the Sutong Bridge are introduced. Finally, the time-dependent deflection at the midspan attributable to creep and shrinkage was analyzed.     

Strain aging and load relaxation behavior of type 316 stainless steel at room temperature

The strain aging and load relaxation behavior of type 316 stainless steel (SS) at room temperature were studied. It is shown that rapid aging occurs in 316 SS at room temperature to an extent that affects the load relaxation behavior of the material. Qualitatively, the aging behavior was found to agree with those reported earlier for Fe-Ni-C-alloys, and the observed aging characteristics could be explained by using an earlier proposed vacancy-interstitial mechanism. The load relaxation behavior is analyzed in terms of Hart’s state variable model. Effects of strain aging and strain hardening on the load relaxation behavior and the scaling of the relaxation curves are determined. It is shown that aging can be accounted for by a time-dependent change in a model parameter, which is dependent on the mobile dislocation density and the dislocation mobility. In addition, a dependency on plastic state of the same parameter previously held constant was found. It is concluded that this phenomenon, which in 316 SS could be rationalized in terms of increasing forest dislocation density, is likely to be more general, and a provision for it should be made in the state variable theory. S. P. Hannula formerly Research Associate in the Department of Materials Science and Engineering, Cornell University, Ithaca, NY M. A. Korhonen, formerly Visiting Assistant Professor in the Department of Materials Science and Engineering, Cornell University, Ithaca, NY     

Indentation creep behaviors of Mg61Cu28Gd11 and （Mg61Cu28Gd11）99.5Sb0.5 bulk metallic glasses at room temperature

The room temperature creep behaviors of Mg61Cu28Gd11 and(Mg61Cu28Gd11)99.5Sb0.5 bulk metallic glasses(BMGs) were revealed by means of nanoindentation technique.The creep mechanism was explored by characterization of creep rate sensitivity,creep compliance and retardation spectra.The results showed that the experimental creep curves could be well described by a generalized Kelvin model.The low creep rate sensitivity of both Mg-based BMGs indicated that their room temperature creep was dominated by localized shear flow.In addition,the(Mg61Cu28Gd11)99.5Sb0.5 glassy alloy exhibited lower creep rate sensitivity,creep compliance and milder retardation peak,indicating its higher creep-resistance and less relaxed state.Furthermore,the creep retardation spectrum consisted of two relatively separated peaks with the well defined characteristic relaxation times.     

Theoretical Study on Short-Term and Long-Term Deflections of Fiber Reinforced Polymer Prestressed Concrete Beams

This paper presents the methods for predicting the short-term and time-dependent deflections of fully or partially prestressed concrete beams with fiber reinforced polymer (FRP) tendons under sustained bending moment and axial force. The age-adjusted effective modulus method is used to model the creep behavior in the concrete and the relaxation in the FRP prestressing tendons. A tension-stiffening model is proposed to evaluate the stiffness of the section after cracking. The analytical values are compared to the test results and it is found that the analytical values are in good agreement with the experimental results.     

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.     

High-temperature creep in an Al-8.5Fe-1.3V-1.7Si alloy processed by rapid solidification

The creep behavior of an Al-8.5Fe-1.3V-1.7Si alloy processed by rapid solidification is investigated at three temperatures ranging from 623 to 723 K. The measured minimum creep strain rates cover seven orders of magnitude. The creep behavior is associated with the true threshold stress, decreasing with increasing temperature more strongly than the shear modulus of aluminum. The minimum creep strain rate is controlled by the lattice diffusion in the alloy matrix, and the true stress exponent is close to 5. The apparent activation energy of creep depends strongly on both applied stress and temperature and is generally much higher than the activation enthalpy of lattice self-diffusion in aluminum. Also, the apparent stress exponent of minimum creep strain rate depends on applied stress as well as on temperature and is generally much higher than the true stress exponent. This behavior of both the apparent activation energy and apparent stress exponent is accounted for by the strong temperature dependence of the threshold stress-to-shear modulus ratio. The true threshold creep behavior of the alloy is interpreted in terms of athermal detachment of dislocations from fine incoherent Al₁₂(Fe, V)₃Si phase particles, admitting a temperature dependence of the relaxation factor characterizing the strength of the attractive dislocation/particle interaction.     

Block FEM for Time-Dependent Shear-Lag Behavior in Two I-Girder Composite Bridges

This paper presents a time-dependent finite-element analysis of a two I-girder composite bridge with a concrete slab. The creep and shrinkage of the concrete slab are considered as sources of time-dependent behavior. This analysis, unlike others, includes the shear-lag effect of the concrete slab on the time-dependent behavior of two I-girder bridges. An example calculation is given for a two-span continuous composite bridge with a cracking region in the concrete deck near the interior support. It is shown that the shear-lag effect becomes significant at the edge of the cracking region and at the bridge ends.     

Thermomechanical Framework for the Constitutive Modeling of Asphalt Concrete

This study is concerned with the constitutive modeling of asphalt concrete. Unlike most constitutive models for asphalt concrete that do not take into account the evolution of the microstructure of the material, this study incorporates the evolution of the microstructure by using a framework that recognizes that a body’s natural configurations can evolve as the microstructure changes. The general framework, on which this study is based, is cast within a full thermomechanical setting. In this paper, we develop models within the context of a mechanical framework that stems from the general framework for models based on the full thermodynamic framework and the resulting equations represent a nonlinear rate type viscoelastic model. The creep and stress relaxation experiments of Monismith and Secor are used for validating the efficacy of the model, and it is found that the predictions of the theory agree very well with the available experimental results. The advantages of using such a framework are many, especially when one wants to model the diverse mechanical and thermodynamic response characteristics of asphalt and asphalt concrete.