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.     

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.     

Viscoplastic Cap Model for Soils under High Strain Rate Loading

A viscoplastic cap model of the Perzyna type was developed for simulating high strain rate behaviors of soils. An associative viscous flow rule was used to represent time-dependent soil behaviors. The viscoplastic cap model was validated against experimental data from static and dynamic soil tests. The model was also compared with soil behaviors under creep and stress relaxation with good agreement. However, the model was unable to represent tertiary creep where strain softening became significant. The model was subsequently integrated into LS-DYNA for finite-element simulations of high strain rate behaviors of sandy and clayey soils in explosive tests. The significance of strain rate effect on the soil responses is presented herein. It is concluded that the viscoplastic cap model is adequate for simulations of soil behaviors under high strain rate loading, creep, and stress relaxation, covering a wide range of time-dependent problems.     

Transitional Thermal Creep of Early Age Concrete

Couplings between creep of hardened concrete and temperature∕water effects are well-known. Both the level and the gradients in time of temperature or water content influence the creep properties. In early age concrete the internal drying and the heat development due to hydration increase the effect of these couplings. The purpose of this work is to set up a mathematical model for creep of concrete that includes the transitional thermal effect. The model governs both early age concrete and hardened concrete. The development of the material properties in the model is assumed to depend on the hydration process and the thermal activation of water in the microstructure. The thermal activation is assumed to be governed by the Arrhenius principle, and the activation energy of the viscosity of water is found applicable in the analysis of the experimental data. Changes in temperature create an imbalance in the microstructure termed the microprestresses, which reduce the stiffness of the concrete and increase the creep rate. The aging material is modeled in an incremental way reflecting the hydration process in which new layers of cement gel solidify in a stress free state and add stiffness to the material. Analysis of experimental results for creep of early age and hardened concrete either at different constant temperature levels or for varying temperature histories illustrate the model.     

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.     

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.     

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.     

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.     

The viscoelastic nature of chorioamniotic membranes

This study establishes the viscoelastic nature of the human chorioamniotic membrane. Membrane tissue taken from term pregnancies was placed in a state of biaxial stress consistent with the condition in which membranes rupture in normal healthy patients. The phenomena of creep, stress relaxation, elastic recovery, and time-dependent load deformation relations were demonstrated. The experiments needed to produce these phenomena are described. The results are graphically reported. The experiments were performed using samples of fetal membranes and compared to gum rubber which is a known elastic material. From the results, one can conclude that fetal membranes are viscoelastic. The flow freely under applied stress, and they have elastic and viscous properties which are time dependent.     

Creep Analysis of Axially Loaded Fiber Reinforced Polymer-Confined Concrete Columns

An analytical model is developed to study the time-dependent behavior of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) and fiber-wrapped concrete columns (FWCC) under sustained axial loads. The model utilizes the double power law creep function for concrete in the framework of rate of flow method, and the linear viscoelastic creep model for FRP. It follows geometric compatibility and static equilibrium, and considers the effects of sealed concrete, multiaxial state of stresses, creep Poisson’s ratio, stress redistribution, variable creep stress history, and creep rupture. The model is verified against previous creep tests by the writers on FWCC and CFFT columns. It is then used to study the practical design parameters that may affect creep of FRP-confined concrete under service loads, or lead to creep rupture at high levels of sustained load. Creep of FWCC is shown to be close to that of sealed concrete of the same mix, as the effect of confinement on creep of concrete is not very significant. CFFT columns, on the other hand, creep much less than FWCC, mainly due to axial stress redistribution. As the stiffness of the tube increases relative to the concrete core, larger stress redistributions take place further reducing the creep. However, there is a threshold, beyond which, stiffer tubes would not significantly lower the creep of concrete. Creep rupture life expectancy of CFFT columns is shown to be quite acceptable.     

泥质粉砂岩蠕变特性及非线性蠕变模型研究

为揭示地下岩体非线性蠕变力学特性,对中风化泥质粉砂岩开展分级单轴加载蠕变试验。泥质粉砂岩典型蠕变曲线可划分为减速蠕变、稳态蠕变和加速蠕变阶段,使用给定蠕变速率阈值法求得的岩石长期强度为14.3 MPa。为了描述岩石非线性蠕变特性,引入了一个与时间应力水平相关的非线性黏塑性元件,将其与广义Kelvin体和带开关的黏性体串联,得到了改进的非线性黏弹塑性蠕变模型。使用Origin平台的Levenberg-Marquardt非线性最小二乘法反演得到模型的蠕变力学参数,通过将广义Kelvin蠕变模型、伯格斯蠕变模型和改进黏弹塑性蠕变模型与试验曲线进行比较,分析了各自的适用特点。结果表明：本研究提出的改进黏弹塑性蠕变模型可以较好地描述中风化泥质粉砂岩加速蠕变阶段特征,揭示了泥质粉砂岩的非线性蠕变力学特性。     

Model for Shear Response of Asphaltic Concrete at Different Shear Rates and Temperatures

This paper presents a model for shear response of asphaltic concrete, taking into account of strain-rate and temperature effects. The model employs rate-dependent hyperplasticity theory, which is based on a thermomechanical framework. A principle of the theory is that the entire constitutive behavior can be defined by two scalar potentials: an energy potential and a flow potential. The viscous behavior of the model corresponds to the results of rate process theory and defines the strain-rate and time dependent behavior. The initial modulus and shear strength are each assumed to be exponential functions of the inverse of temperature. The model is verified and calibrated against the unconfined compression test data for asphaltic concrete at different strain rates and temperatures. A viscoelastic damage model is also addressed to make a comparison with the model developed here. Comparison between the test data, the predictions of the new model, and the predictions of the viscoelastic damage model are discussed.     

A model for anelastic relaxation controlled cyclic creep

In the paper we derive an expression for the cyclic minimum strain rate of cyclic creep in systems where anelastic relaxation is a controlling mechanism. The cyclic creep behavior is modeled by assuming that the anelastic strain recovered during the off-load periods must first be stored during the on-load periods before nonrecoverable creep results. To perform the derivation, the time dependence of the anelastic relaxation is reported for two oxide dispersion strengthened alloys and shown to be adequately described by a double exponential function. The time dependence of the anelastic relaxation is then incorporated into an expression, generally used to describe static minimum strain rate data, to obtain the frequency dependence of the cyclic minimum strain rate. The predicted values of the derived expression using results from static creep and strain relaxation tests are in excellent agreement with the experimentally observed cyclic creep results with the use of no adjustable parameters. The proposed model of anelastic strain storage delaying nonrecoverable creep is also shown to be consistent with the observed effects of temperature and maximum load on the cyclic minimum strain rate.     

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.     

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.     

An analysis of the transient stage in low stress viscous creep

Transient creep data recorded during low stress viscous creep of α-Ti, α-Zr, β-Co and zircaloy-2 are presented. The data are analysed in terms of the effect of stress, temperature and grain size on transient time as well as transient strain. Transient time is seen to be independent of stress in all four materials. Transient time decreases with increasing temperature and the variation can be described by an Arrhenius relation. Upto a grain size of nearly 100 μm, the transient time increases with increasing grain size. In the case of α-Ti and β-Co, beyond 100 μm and under conditions that facilitate Harper-Dorn creep to dominate flow, transient time exhibits grain size independent behaviour. Transient strain, normalised with elastic strain, appears generally to be independent of stress, temperature and grain size. Transient viscous creep data presented here, excluding those pertaining to coarse grained α-Ti and β-Co, can be satisfactorily rationalised following the grain boundary diffusion based model proposed by Raj. In regard to materials with grain size coarser than 100 μm, the data for α-Ti were more comprehensive and have been explained by a model proposed here, which is based on mutual annihilation of preexisting dislocations by volume diffusion controlled climb.     

Constitutive Model for Time-Dependent Behavior of FRP–Concrete Interface

A fundamental understanding of fiber-reinforced polymer (FRP) laminate bonding behavior, including bond strength and effective bonding length, is of primary importance for the development of design guidelines and codes for concrete structures strengthened with externally bonded FRP reinforcement as a bond-critical application. However, the long-term serviceability of such FRP-strengthened structures is still a concern due to a lack of both long-term performance data and a suitable model to represent these performances. This study aims at presenting a viscoelastic model describing the time-dependent behavior of the FRP–concrete interface. The proposed model has been calibrated using strain measurements of the designed specimen for the experimental investigation of the time-dependent behavior of the FRP–concrete interface, including the development of the effective bonding length. Afterward, the proposed model satisfactorily predicts the time-dependent bonding length of the FRP sheet in comparison with the experimental results. The effects, both of creep of the adhesive layer and of creep and shrinkage of the concrete, on the changes in the effective bonding length of the PFRP sheet are also discussed.     

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.     

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.     

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.