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Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part II: Shrinkage and creep of concrete
Abstract
In Part I of this paper (Int. J. Numer. Meth. Eng., in print) a mechanistic model of hygro-thermo-chemical performance of concrete at early ages has been introduced. Additionally, as compared to the existing models (e.g. J. Eng. Mech. (ASCE) 1995; 121(7):785–794; 1999; 125(9):1018–1027), an effect of relative humidity on cement hydration rate and associated hygro-thermal phenomena have been taken into account. Here we deal with mechanical performance of concrete at early ages and beyond, and in particular, evolution of its strength properties (aging) and deformations (shrinkage and creep strains), described by using the effective stress concept. This allow us for explanation and modelling of phenomena known from experiments, like drying creep (e.g. Mathematical Modeling of Creep and Shrinkage of Concrete. Wiley: Chichester, 1988), or some additional strains, as compared to pure shrinkage, which appear during autogenous deformations of a maturing, sealed concrete sample (e.g. Cement Concrete Res. 2003; 33:223–232). Creep is described by means of the modified microprestress-solidification theory by Bazant et al. (J. Eng. Mech. (ASCE) 1997; 123(11):1188–1194; 1195–1201), with some modifications to take into account the effects of temperature (Comput. Struct. 2002; 80:1511–1521) and relative humidity (Int. J. Numer. Meth. Eng., in print; Proceedings of the 5th World Congress for Computational Mechanics (WCCM), Vienna, Austria, 7–12 July 2002), on concrete aging. Shrinkage strains are modelled by using the effective stress principle in the form introduced by Gray and Schrefler (Eur. J. Mech. A/Solids 2001; 20:521–538; Appl. Mech. Rev. (ASME) 2002; 55(4):351–388), giving a good agreement with experimental data also for lower values of relative humidity.
... This exothermic process, caused from chemical reactions, leads to heat production inside of the material, which can be up to 50 • C in case of massive structures. Due to temperature evolution in the material, the kinetics of the hydration process is triggered and with the temperature increase the time of reaction increases as well [1][2][3]. ...
... The intent is to consider full coupling and interactions between these various phenomena. The properties of the materials are highly dependent on the degree of hydration [1]. The balance equations of the porous material will consider the effects hydration-dehydration and evaporation-condensation, which play main roles in material's phase changes. ...
... The permeability tensor in Equation (9) is reduced to = because it is assumed that concrete is an isotropic material. and denote the dynamic viscosity and relative permeability of the gas and liquid [1,14]. ...
The aim of this paper is to model the behavior of concrete during the initial stage of maturing. Most models consider only thermo‐mechanical phenomena assuming the hygral phenomena of less importance due to high liquid saturation. In order to grasp those effects, the proposed model is an extension of Gawin's model (D. Gawin, F. Pesavento, and B. A. Schrefler, Int J Numer Methods Eng 67(3), 299–331, 2006). The fresh concrete, modeled as porous material, is described within the well‐founded framework of the Theory of Porous Media. The multiphase material consists of a solid phase representing, for example, cement, gravel, etc., and a fluid and gas phase representing the pores filled with water and dry air. Compared to Gawin's model, here, beside the effect of hydration‐dehydration, the effect of evaporation‐condensation will be taken into account. A new formulation for the evaporation process in the fresh concrete is proposed and validated by an experimental study. The presented model is implemented in the research code PANDAS. The proposed model investigates and proves the assumption of Gawin's model to have a linear connection between porosity and hydration degree.
... The water sorption isotherm of cement pastes is a key constitutive parameter in hygro-thermo-chemo-mechanical models of concrete [1][2][3][4]. The isotherms link relative humidity RH (or partial pressure) with saturation degree, both of which determine the effective pressure that causes humidity-induced deformations [5]. ...
... The current models commonly consider that changes on desorption are due to microstructural changes caused by the increase in temperature [2,3,[18][19][20][21][22][23][24][25]. This is conceptually akin to how other properties, e.g. ...
... As a result, evaporation also becomes independent of pore size and the ink-bottle effect is overridden. 3 The isotherms computed at various temperatures, between 20 • C and 70 • C, are shown in Fig. 7.b. The adsorption isotherms from the simulations are qualitatively and quantitatively similar to the experimental ones. ...
The constitutive models of concrete often consider water desorption isotherms to be near-equilibrium and significantly affected by moderately high temperature, 40–80°C, typically through microstructural changes. However literature data suggest that adsorption, not desorption, is near-equilibrium and moderate temperatures do not cause microstructural changes. This work supports the latter theory, through dynamic vapor sorption experiments on cement paste at 20–80°C. Samples were pre-conditioned at 60% relative humidity and 20°C, and isotherms were measured for several humidity ranges and testing rates. The results, corroborated by classical DFT simulations, indicate that adsorption is near-equilibrium and mostly unaffected by temperature, whereas desorption is out-of-equilibrium due to the ink-bottle effect at high humidity, and interlayer water at low humidity. Starting from the second cycle, desorption at higher temperatures features a shift of the cavitation pressure and overall a smaller hysteresis. A conceptual model of pore-specific temperature-dependent hysteresis is proposed to qualitatively explain the results.
... Lackner and Mang (2004) adopted Rankine fracture criterion to build a chemo-plastic material model for EAC analysis, based on the data profiles of temperature and hydration degree of a dam. Gawin et al. (2006aGawin et al. ( , 2006b) developed a hygro-TCM model to simulate the early-age and long-term concrete behaviors. Based on a solidification-type model, they expressed concrete properties as a function of hydration degree. ...
... The exact stoichiometry of the hydration reactions and the influence of the environment still cannot be precisely quantified. In this paper, the hydration reaction is simulated as an overall hydration process, similar to many other multifield models (Cervera et al., 1999a(Cervera et al., , 1999bdi Luzio & Cusatis, 2009a, 2009bGawin et al., 2006aGawin et al., , 2006b. Assuming that the hydration kinetics can be described by postulating the existence of a Gibb's free energy dependent on temperature and hydration extent, the hydration reaction can be described by the following Arrhenius-type equation (Cervera et al., 1999a;di Luzio & Cusatis, 2009a;Ulm & Coussy, 1995): ...
... Therefore, they are considered valid theoretical approaches. Interested readers are referred to the benchmark studies (Cervera et al., 1999a(Cervera et al., , 1999bdi Luzio & Cusatis, 2009a, 2009bGawin et al., 2006aGawin et al., , 2006b. ...
Early‐age stress (EAS) is an important index for evaluating the early‐age cracking risk of concrete. This paper encompasses a thermo‐chemo‐mechanical (TCM) model and active ensemble learning (AEL) for predicting the EAS evolution. The TCM model provides the data for the AEL model. First, based on Fourier's law, Arrhenius’ equation, and rate‐type creep law, a TCM model is built to simulate the heat transfer, cement hydration, and viscoelasticity, which together determine the EAS evolution. Then, a material model composed of an eXtreme Gradient Boosting model and adjusted Model Code 2010 is built to allow for parametric study and database construction. Finally, an AEL framework is built, which incorporates principal component analysis (PCA), Gaussian process, and light gradient boosting machine (LGBM). This study resulted in the following findings: (1) The dimensionality of the 672‐by‐1 EAS vector can be effectively reduced by PCA, and the first principal component (PC) is a global index representing the magnitude of the EAS; (2) the mechanical field of the TCM model is validated by testing data. Correlation analysis on the first PC quantifies the influence of various input parameters of the TCM model, which is in accordance with common understandings of the EAS evolution process. (3) The AEL and one‐shot ensemble learning (OSEL) both achieve high prediction performance in the testing set, whose R2 reaches 0.961 and 0.948, respectively. Thanks to the uncertainty‐based query procedure, comparing with OSEL, AEL shows advantages in prediction performance over the whole training history. (4) AEL can significantly reduce the number of samples required for training, which can be a major improvement in efficiency considering the computational cost of the TCM model.
... Multiphase modeling of concrete, as originally introduced by [17,18], allows a physics-based description of the material behavior of concrete accounting for thermo-hygro-chemo-mechanical phenomena. In this context, the evolution of the material properties due to maturing is described in terms of the hydration degree. ...
... In multiphase modeling, coupling effects can be accounted for on the level of balance equations, or on the level of multiphase constitutive models. In the original multiphase model introduced by [17,18], the deformation-induced effect of the mechanical model on the hygral model was considered by accounting for the volumetric strain rate in the mass balance equations. This is an example for coupling on the level of balance equations. ...
... To the best knowledge of the authors, multiphase models currently used, including the ones from [9,10,17,18,22,23,25], do not capture the experimentally observed instantaneous change in internal relative humidity upon loading [11,12]. Even consideration of full coupling on the level of the mass balance equations, as done in the original work of [17,18], provides no remedy. ...
Multiphase modeling is a powerful framework for the simulation of the early-age and long-term behavior of concrete. Nevertheless, state-of-the-art multiphase models do not capture the experimentally observed instantaneous change in internal relative humidity upon external loading, which also manifests in the lack of predicting load-induced shrinkage. The approach presented in this publication is a step to overcome this deficiency. It is based on a poromechanical multiphase model for coupled creep and shrinkage of concrete, which is enhanced by a strong hygro-mechanical coupling, introduced via a load-dependent desorption isotherm. The enhanced model is evaluated for sealed and drying uniaxial compressive and tensile creep tests. Instantaneous changes in internal relative humidity upon loading are recovered by the enhanced model. In compression, the influence on the mechanical response is small. In contrast, the representation of tensile creep is significantly improved by considering load-induced shrinkage.
... the water degree of saturation S w . This postulation was expansively examined by Gawin et al. (2006) ;Gawin et al. (2006) and Pereira et al. (2010) . ...
... the water degree of saturation S w . This postulation was expansively examined by Gawin et al. (2006) ;Gawin et al. (2006) and Pereira et al. (2010) . ...
... In the two previously introduced approaches (Biot-Bishop ( Biot, 1941 ) and ( Coussy et al., 2003 )), the capillary pressure is considered to be the driving mechanism of the drying/wetting of the partially saturated porous materials. Similar approaches based on capillary mechanisms have been introduced by ( Gawin et al., 2006 ), ( Vlahini ć et al., 2009 ), and ( Rougelot et al., 2009 ). Nevertheless, the driving mechanisms of the drying/wetting of porous materials have been frequently debated in the literature. ...
EDF is currently working on multiple projects concerning the durability of concrete structures. Among these projects, a research program focuses in particular on the drying behavior of a high performance concrete used as a shell for nuclear waste packages. The package of interest noted as C1PGSP, will be at first conserved in a storage facility and then disposed of at Cigéo, i.e. the future underground disposal facility for long term radioactive waste in France.During the storage phase, the “F44Adj” concrete shells will be submitted to relative humidity that could be lower than 50% and a relatively high ambient temperature (attaining 50°C). Under these conditions, the impact of drying has to be evaluated and EDF is required to verify the package against the risk of cracking of the concrete shell due to structural restraining of strains.The overall objective of this thesis is to provide a new valid poromechanical model that can be used to study the risk of cracking of the concrete shell caused by the restriction of drying shrinkage.Previous modelling works based on a classical Thermo-Hydro-Mechanical (THM) formalism have shown the need of a better understanding of the drying behavior of concrete, in particular to what concerns the hydromechanical coupling. As a matter of fact, the THM models based on the poromechanical works of Biot, Terzaghi and then Coussy et al. (2003), are proven to be only valid for a relative humidity higher than 50% (Wyrzykowski et al., 2017). In this thesis, we propose a new poromechanical model that extends and adapts those models to a lower relative humidity. This result is obtained by introducing the mechanism of adsorption of water molecules on the pores surface and its effect on the hydro-mechanical coupling.Apart from the hydromechanical coupling, the drying kinetics of the concrete impacts the kinetics of shrinkage. The existing models of water transfer are examined and discussed with respect to their applicability to high performance concretes (such as the F44Adj). Hence, two chapters of this thesis are devoted to the water retention phenomenon and to the transfer properties of the concrete.Finally, material properties are necessary to correctly model the drying behavior of the F44Adj concrete. For this reason, EDF has established an experimental program in order to obtain the data necessary to calibrate the transfer parameters as well as to validate the proposed poromechanical model. Hence, a large section of each chapter is dedicated to the description and analysis of experimental results, then to calibration of the model parameters.The proposed model is finally applied to simulate the drying of the C1PGSP package under storage conditions; results are compared with those obtained in older simulations performed at EDF.
... Gawin et al. [21] proposed a mathematical calculation method for creep of concrete, which decomposed the total creep strain rate tensor into two parts: viscoelastic strain rate and viscous flow strain rate. Li et al. [11] analyzed the early creep performance of concrete by using the ring restraint experiment, which showed that this method can not only ensure the accuracy of the early creep of concrete measured by the experiment but also be simpler than the calculation method of concrete early creep proposed by Gawin et al. [21]. ...
... Gawin et al. [21] proposed a mathematical calculation method for creep of concrete, which decomposed the total creep strain rate tensor into two parts: viscoelastic strain rate and viscous flow strain rate. Li et al. [11] analyzed the early creep performance of concrete by using the ring restraint experiment, which showed that this method can not only ensure the accuracy of the early creep of concrete measured by the experiment but also be simpler than the calculation method of concrete early creep proposed by Gawin et al. [21]. erefore, the ring restraint experiment was also adopted in this study, and the early creep experiment of concrete was carried out according to the concrete mix proportion shown in Table 2. ...
... where E is the static elastic modulus of the concrete, GPa; μ is Poisson's ratio of the concrete, taking 0.2 [33]; σ x , σ y , and σ z represent the capillary water tension of the concrete element in the X-axis, Y-axis, and Z-axis directions. e higher-order terms of equation (21) were ignored, equations (22)-(24) were substituted into (21), and the volume strain of concrete was obtained as follows: ...
Through the adiabatic temperature rise experiment, the adiabatic temperature rise of concrete with hydration time was recorded. Based on the maturity degree theory, the relationship between the hydration degree of the concrete and the equivalent age was determined. Then, the hydration degree prediction model of the concrete's early elastic modulus and tensile strength was established. The local temperature and humidity of the concrete were measured by the shrinkage experiment, and based on the capillary water tension theory, a temperature-humidity prediction model for the early shrinkage of the concrete was designed. According to the ratio of the creep deformation and elastic deformation of concrete which were obtained through the restraint ring experiment, a model for predicting the early creep coefficient of concrete was proposed. Based on the coupling effect of “hydration-temperature-humidity,” a prediction model of early cracking risk coefficient of concrete under multifield coupling was proposed. Finally, several groups of slab cracking frame experiments were carried out, and the cracking risk prediction results of concrete were consistent with the actual situation, which indicated the correctness of the early cracking risk prediction model of concrete.
... This method entails defining appropriate constitutive equations for the solid, liquid, and gaseous phases within the medium, which are then averaged for a multi-phase environment. Several studies have developed multi-phase models for early-age concrete, notable among them are the works of Gawin et al. [31,63] and Di Luzio and Cusatis [27,28], alongside numerous other references, including recent contributions [44,45,58,64]. Typically, the impact of temperature on moisture diffusion is accounted for, enabling a more realistic modeling of moisture transfer within the analyzed element. ...
... Analogous to the functions of hydration heat development based on equivalent time, analytical formulations for affinity have also been proposed. Notably, the proposal of Cervera et al. [91], refined by Gawin et al. [63], and further developed by Leal da Silva and Šmilauer [122] stands out. They suggested empirical laws for determining the model coefficients B 1 , B 2 , and η instead of relying solely on experimental fitting: ...
Cement-based materials encompass a broad spectrum of construction materials that utilize cement as the primary binding agent. Among these materials, concrete stands out as the most commonly employed. The cement, which is the principal constituent of these materials, undergoes a hydration reaction with water, playing a crucial role in the formation of the hardened composite. However, the exothermic nature of this reaction leads to significant temperature rise within the concrete elements, particularly during the early stages of hardening and in structures of substantial thickness. This temperature rise underscores the critical importance of predictive modeling in this domain. This paper presents a review of modeling approaches designed to predict temperature and accompanying moisture fields during concrete hardening, examining different levels of modeling accuracy and essential input parameters. While modern commercial finite element method (FEM) software programs are available for simulating thermal and moisture fields in concrete, they are accompanied by inherent limitations that engineers must know. The authors further evaluate effective commercial software tools tailored for predicting these effects, intending to provide construction engineers and stakeholders with guidance on managing temperature and moisture impacts in early-age concrete.
... Lastly, a potentially attractive modeling category for describing the time-dependent material behavior of the hardening 3D printed concrete throughout the complete construction process could be offered by multiphase models, e.g., by extending respective models for conventionally cast concrete [27][28][29][30][31]. They enable the time-dependent modeling of the hydration process incorporating the evolution of material strength and stiffness, temperature or creep and shrinkage by considering physical processes on the microstructure. ...
... The additional parameters for the over-nonlocal implicit gradient-enhanced regularization of the softening behavior in (26), (27) and (28) are chosen as ε * f = 3 · 10 −2 , m = 1.05 and l = 1.25 mm, preserving the specific mode I fracture energy G * fI ≈ 0.11 N/mm. The latter is estimated for the concrete used for 3D printing of the ...
3D printing of concrete is a promising construction technology, offering the potential to build geometrically complex structures without the use of cost-intensive formwork. The layer-wise deposit of filaments during the 3D printing process results in an intrinsic orthotropic mechanical behavior in the hardened state. Beyond that, the material behavior of 3D printed concrete (3DPC) is governed by a highly nonlinear behavior, characterized by irreversible deformations, strain hardening, strain softening and a degradation of the material stiffness. In this contribution, a new constitutive model for describing the orthotropic and highly nonlinear material behavior of 3DPC will be presented. It is formulated by the extension of a well-established isotropic damage plasticity model for concrete to orthotropic material behavior by linear mapping of the stress tensor into a fictitious isotropic configuration. The performance of the new model will be evaluated by finite element simulations of three-point bending tests of 3DPC samples, performed for different orientations of the loading direction relative to the printing direction and comparison with experimental results. In addition, the applicability of the model to replicate the mechanical behavior of 3DPC, manufactured by the alternative 3D printing process of binder jetting of cementitious powders, will be demonstrated by 3D finite element simulations of an arch structure with varying orientations of the loading direction relative to the layering. Overall, the proposed model provides a computationally efficient modeling approach for large-scale finite element simulations of 3DPC structures, being a promising alternative to complex and computationally expensive finite element models considering distinct interfacial planes.
... With the application of z damage and fracture mechanics in concrete, some researchers have proposed damage mechanics models for early age concrete [7,8], including: Cervera et al. [9] used a viscoelastic damage model considering the aging effects can be simulated to the early aging of concrete, creep phenomena. Gawin et al. [10] investigated the mechanical properties such as strength characteristics of early age concrete, considering the effect of relative humidity on the hydration reaction of cement. A part of researchers considered the influence of fine structure such as aggregates on the crack resistance performance of early age concrete structures and developed corresponding fine mechanics models, for example, Grassl et al. [11] analyzed the effect of aggregate size on concrete microcracks using a nonlinear finite element based on the two-dimensional lattice approach. ...
... is a history-dependent scalarω(ξ, t) valued function of the bond between two material points and [31] as: ω( , ) = { 0, the bond is intact 1, the bond is broken (10) The further detail of the history-dependent scalar-valued function is ω( , ) described in Sect. 2.2.4. ...
In this study, a coupled chemo-thermo-mechanical bond-based Cosserat peridynamic model is proposed for early-age concrete. The model can consider effect of cement particle size and relieve Poisson's ratio limitation, which is suitable to simulate the initiation and propagation of crack in early-age concrete structures. Numerical simulations mainly focus on the temperature evolution, variation of hydration degree, and mechanical behavior for early-age concrete. And they verify the importance of value of Poisson's ratio and effect of cement particle size on mechanical properties and crack evolution of early-age concrete structures. Numerical results show the great potential of the proposed model in modeling fracture behaviors of early-age concrete.
... where the material function av ws s S w ð Þ is determined experimentally, see e.g. Gawin et al. (2006). ...
... This issue needs some additional studies which are planned in future. The creep itself might be numerically modelled by means of effective stresses in a similar way as done for concrete at early ages by Gawin et al. (2006). ...
The paper presents a novel mathematical model of coupled hygro-thermo-mechanical processes in a porous material, partially saturated with liquid water and exposed to temperatures below the freezing point of pore water. Water – ice phase change is modelled by means of a non-equilibrium approach considering both water supercooling and a hysteresis of ice content during freezing and thawing of moist porous materials. The hysteresis results in different crystallization pressure and material strains during freezing and thawing processes at a given temperature. The latter effect is modelled by means of the effective stress principle, considering crystallization pressure of ice in the material pores. Methods used for discretization of the model equations and their numerical solution are described.
The model is applied for solving the numerical example dealing with laboratory Dynamic Mechanical Analysis test of two different cement mortars saturated with water and exposed to temperatures below the freezing point of water (down to −15 °C) where hysteresis of strains was observed. The results are used for experimental validation of the proposed model. Then, for a 1-D case concerning water freezing-thawing of a wall, the effects on the simulation results of the phase-change model parameters, of the material hygro-thermal state, of the supercooling phenomenon and finally of the rate of temperature variation, are analyzed and discussed.
... Hence, it can be said that the mechanical behaviour of a concrete structures depends on several physical and 167 chemical processes that occurs within the concrete constituents at multiple length scales (Dariusz Gawin et al., 168 2006a, 2006bMaekawa et al., 2009;Nguyen et al., 2012). Moreover, the behaviour of the two major constituents 169 of concrete (cement paste and aggregate) are quite contrasting in nature. ...
Prediction of time-dependent deformation such as shrinkage and creep are of utmost interest in terms of long-term
13 serviceability of a concrete structure. However, owing to highly heterogeneous nature of concrete, existing
14 macroscopic prediction models lack in terms of its general applicability. Hence, in this study, a multi-scale
15 description is used to simulate the shrinkage and creep of concrete where the heterogeneity and associated
16 physical-chemical processes are modelled in a mathematical framework. A hierarchical homogenisation technique
17 is used to link across different scales. Model predicated shrinkage and creep are then validated with the
18 corresponding experimental data. Model prediction is also compared with few national codes and popular
19 macroscopic models to highlights the associated gaps in these models that can be overcome with the present
20 developed multi-scale approach
... A multi-rate explicit integration strategy is proposed, which allows this complex multi-field fully coupled governing equation to be well solved. Numerical simulations mainly focus on the terms of temperature, water vapour pressure and damage level to verify the validity of the model [5][6][7][8][9]. And they additionally demonstrate the effect of cement particle size and importance of value of critical fracture energy on mechanical properties and crack propagation of heated concrete. ...
... Due to a coupled nature of the problem, a staggered solution strategy offers more accurate analysis [13], solving moisture and heat transport and passing the obtained fields to a mechanical model. Fully coupled problems with chemical submodels were proposed as well [14][15][16]. ...
Concrete pavements are subjected to the combination of moisture transport, heat transport and traffic loading. A hygro-mechanical 3D finite element model was created in OOFEM software in order to analyse the stress field and deformed shape from a long-term non-uniform drying. The model uses a staggered approach, solving moisture transfer weakly coupled with MPS viscoelastic model for ageing concrete creep and shrinkage. Moisture transport and mechanical sub-models are calibrated with lab experiments, long-term monitoring on D1 highway and data from 40 year old highway pavement. The slab geometry is 3.5×5.0×0.29 m, resting on elastic Winkler-Pasternak foundation. The validation covers autogenous and drying strain on the slab. The models predict drying-induced tensile stress up to 3.3 MPa, inducing additional loading on the slab, uncaptured by current design methods.
... Afterward, they extended the framework to model the evolution of deformations, caused by creep and shrinkage. The microprestress-solidification theory developed by Bažant [13,14] is used to model the creep component [15]. Based on the model of Gawin et al., Gamnitzer et al. [16,17] modeled coupled shrinkage and creep in a multiphase formulation. ...
To assure high safety levels and functionality over the lifespan of concrete structures (50–100 years), it is important to understand the material’s behavior. As widely known, concrete changes its performance over time typically leading to enhanced material properties if deterioration mechanisms are neglected (e.g. Alkali-Silica Reaction). This contribution considers merely the former aspect of enhanced material properties. The source of the so-called concrete aging is the ongoing hydration of the cement paste, which depends on the environmental conditions and the mix design. Consequently, it is crucial to understand the evolution of concrete properties as a function of the reaction degree. In this contribution, the previous established age-dependent lattice discrete particle model developed by Wan et al. for UHPC is applied to normal and high strength concretes. This model consists of a multi-physics model solving the relevant heat and moisture transport mechanisms as well as the chemical reactions and a discrete particle model which simulates concrete at the meso-scale. These two components are coupled by a set of aging functions, mapping the reaction degree to the meso-scale parameters. The framework is applied to an extensive data-set, including test data of concretes with various compositions and ages between 1 day and 155 days. The experimental data include calorimetric and shrinkage tests, measurements of internal humidity and temperature as well as different kinds of mechanical tests. The framework captures the experimental data well with minor changes in the aging laws. Furthermore, the results indicate a strong dependence of the aging parameters on the cement type.
... Concrete have the feature that properties are time-dependence [12,13], because the hydration process of cement increases first and then slows down with time. For example, the elastic modulus value increases rapidly in 1-7 d and can reach more than 85 % of the final value, profoundly affecting long-term properties [14,15]. Before formwork was removed, the contact between the maximum water loss surface of sidewall and air was blocked by formwork, humidity change due to water loss was negligible. ...
Formwork type (FT) and demolding time (DT) profoundly affect sidewall concrete's thermal deformation and stress. However, FT and DT are mostly based on subjective judgments, and lack of quantitative research data. Therefore, this paper proposes a method combining laboratory experiments, computer simulation, and engineering practice to study the effects of ambient temperature, different FTs, and DT on the sidewall's temperature change with time, temperature distribution in space, displacement change with time, thermal deformation, temperature stress for the first time. Results show that: the hydration heat release of cementitious material is the driving force for thermal deformation; in the height and depth directions, sidewall temperature is high in the middle and low on both sides; the use of steel formwork produces less thermal deformation and lower temperature stress than the use of wood formwork; when using steel formwork, it is recommended that the DT be 9 d in winter and 7 d in summer; for wood formwork, the DT be 12 d in winter and 10 d in summer. The recommended DT for the specific FT in different ambient temperature can be calculated by applying the research method in this paper. The research results can provide helpful thinking for decision-making on the engineering site.
... This difference between simulation and experiment was probably due to the time-dependent behaviour of the cement paste (i.e., creep) not being included in the poromechanical models [3,[6][7][8]. The quantification of the creep part of autogenous shrinkage has thus become an important research topic in recent years [6][7][8]11,12]. Hu et al. [6], for example, used the Kelvin-Voigt model to predict the visco-elastic component of cement paste. ...
A structure-based modelling framework was established to simulate the three-dimensional autogenous shrinkage of cement paste. A cement hydration model, HYMOSTRUC3D-E, was used to obtain the microstructures and ionic concentrations of the cement paste. A lattice fracture model based on the effective stress and effective modulus was used to consider the elastic and creep parts of autogenous shrinkage. For Portland cement pastes with water-to-cement ratios of 0.3 and 0.4 (where the time zero of autogenous shrinkage was set as the time of the drop in internal relative humidity), the simulated linear elastic autogenous shrinkage was respectively −188 and −79 μm/m at 160 h. The obtained linear total autogenous shrinkage including elastic and creep deformations was respectively −501 and −236 μm/m at 160 h. These values of the elastic autogenous shrinkage and total autogenous shrinkage are close to the predications of poromechanical models and experimental data obtained using a corrugated tube.
... Reasonable consensus results were found (comparable to analytical solution when provided) and the accuracy of existing HAM-softwares (Heat, Air and Moisture) which participated was controlled. [Gawin et al., 2006a] [Gawin et al., 2006b] proposed a fully coupled hygro-thermo-chemo-mechanical model that describes the different physical processes at the macro scale and explore their implications on the material state. [Thiery et al., 2007] introduced new laws for gas transfers regarding the diffusion coefficient of vapor in function of saturation and porosity and regarding regarding the relative permeability to gas. ...
The drying of cement-based materials affects directly their durability, which has a major economic, societal, and environmental impact.The conventional experimental techniques such as gravimetric and sensor-based measurements, which are employed to study the drying-driven processes, provide only bulk-averaged or point-wise measurements which are not sufficient to characterize these processes. However, the significant advances in full-field techniques have allowed unprecedented insight into these local processes. Notably, for cement-based materials, x-ray and neutron tomography lend themselves as highly complementary tools for the study of their THM behavior. In fact, the high sensitivity to density variations of x-ray imaging gives access to the developments of fractures, in 4D (3D+time). On the other hand, neutron tomography allows the study of the evolution of the moisture field in 4D, thanks to its high hydrogen sensitivity.This Ph.D. takes advantage of these two highly complementary techniques, which, together with advanced numerical modeling tools, allowed for a novel experimental/numerical insight to study the drying-driven physical processes in cement-based materials.In this work, two experimental campaigns were performed at the NeXT instrument located at the ILL. In the first campaign, neutron tomography was employed to characterize the moisture distribution of a set of cylindrical mortar samples which were set to dry sequentially in a TH controlled environment (T = 20℃ et RH = 35%) to represent different hydric states. The main phases of the mortar (aggregates, cement paste, and voids were separated, and saturation profiles were deduced and validated against the weight loss measurements. In the second experimental campaign, more complexity was added to the experimental drying conditions by heating concrete and cement paste samples up to moderate temperature which has led to the appearance of cracks in the later sample. The analysis of the acquired simultaneous neutron/x-ray data-set (once aligned in time and across modalities) allowed for the quantification of the 4D moisture profiles which were found to predict an overall water loss at hydric equilibrium coherent with the corresponding analytical analysis. In the cement paste sample, the x-ray dataset captures the evolution of an extensive cracking network, opening, and propagation toward the core of the sample. Then, a novel analysis procedure was proposed which allowed the extraction of these fractures and the analysis of their interplay with local drying as captured through neutron imaging.On the other hand, the numerical approach employed in this study consisted of improving the numerical model predictive capacity by assessing the implications of common simplifications on the modeling response. These common simplifications can be divided in three main categories which regard the consideration of gaseous transport modes, the TH and HM couplings, and the morphological description of the material. Quantification of these simplifications effects regarding the used model and the choice of TH coupling laws was done by comparing mass loss response surfaces in relative humidity and temperature space for multiple configurations. The results show relative error maps at early, mid, and late drying stages for every compared case. On the other hand, the simplification regarding the HM coupling was evaluated in a 2D mesoscopic simulation framework where an artificial concrete mesostructure had to be generated for cracking localization purposes. The cracking impact was then assessed both locally on the saturation fields and on the global mass loss response. Finally, a CT-FE mapping scheme was proposed which consisted of extracting the mesoscale morphology of concrete (aggregates and pores) from x-ray/neutron attenuation fields and presenting it explicitly on a FE mesh. This has permitted to perform 3D multiphase THM simulation of concrete at the mesoscale.
... The vapor produced at the drying front that moves ahead and condensates in the colder region of the dense ceramic structure (so-called "moisture clog") is pointed out as one of the main causes for the pressure build-up in such materials during heating. While some numerical simulations [107] corroborate this effect, limited experimental observations and quantification have been carried out so far. Therefore, the neutron tomography technique might be an important tool to be applied in the study of such a phenomenon. ...
Despite the continuous evolution on the performance of refractory ceramic products, monolithic materials still require special attention during their processing steps as various phase transformations may take place during the curing, drying and firing stages. Drying is usually the longest and the most critical process observed during the first heating cycle of refractory linings, as the enhanced particle packing and reduced permeability of the resulting microstructure may lead to recurrent explosive spalling and mechanical damage associated with dewatering and the development of high steam pressure at the inner regions of such dense materials. In this context, this review article mainly addresses (i) the theoretical aspects related to the drying process of dense refractories, (ii) the influence of the phase transformations derived from the binder additives, and (iii) the usual and advanced experimental techniques to assess the water removal from consolidated castable pieces. Many studies have pointed out that due to the complex nature of this phenomenon (i.e., considering combined thermal stresses and pore pressure, heterogeneous microstructure, evolving pore structure with temperature, etc.), the mechanisms behind the water withdrawal and castables explosive spalling are lacking further understanding and, consequently, it has been difficult to save time and energy during the first heating of industrial equipment lined with ceramic materials. On the other hand, different methods are used for refractory spalling assessment and many efforts have been carried out in applying in situ imaging techniques (such as NMR and neutron tomography) to follow the moisture evolution during such thermal treatments.
... Various approaches to early-age cracking calculations can be found in the literature [21,[25][26][27][28][29][30][31][32][33]. Some design approaches are merely an estimation of whether the concrete will crack or not, while other and more complex approaches, chemo-mechanical [34] thermo-chemo-mechanical [35] or hygro-thermo-chemo-mechanical approaches [36], also provide a prediction of the crack development and the size and rate of occurring crack widths [37]. For all such early-age crack assessments, the accuracy of the outcome is very dependent on the quality and correctness of the models and material parameters used as input [23,[38][39][40][41][42]. ...
Ultra-High Performance Concrete (UHPC) exhibits high autogenous shrinkage (AS) which significantly increases the risk of early age cracking. To predict the risks of early age shrinkage cracking of environmentally friendly CEM III-based UHPC, a numerical model originally developed for early age crack assessment of ordinary concrete, has been further developed and applied on a demonstration wall with high risk of cracking, cast on a non-deforming slab. The design of the wall was determined through numerical simulation using different parameters, resulting from specific experiments performed on the desired concrete mixture. Early age crack assessment parameters for the model were obtained through different tests performed using the Temperature-Stress Testing Machine (TSTM). Finally, this UHPC wall was built, and occurring strain deformations were recorded in real time using fiber optic (SOFO) sensors embedded in the wall, and measurements taken from demountable mechanical strain gauges (DEMEC). Restrained shrinkage measurements were obtained for the same mixture through ring tests. A comparison between the numerical simulation results and the measurements proved that the proposed model is suitable for UHPC, and the model predicts well the time of crack appearance. Finally, it has been shown that shrinkage values along the wall height are influenced by the degree of restraint.
... (2) 弥散裂缝模型 ： 这方面的代表性研究工作包 括 [6][7][8] 等提出的早龄期混凝土弥散裂缝模型； (3) 损伤力学模型： 随着混凝土损伤力学的兴起， 若 干学者 [9][10][11][12][13][14] 将部分经典的损伤模型推广至早龄 期混凝土； (4) 微细观力学模型：为了考虑混凝土细观结构特 别是粗骨料对早龄期混凝土抗裂性能的影响， 部分学者发展了相应的微细观力学模型 [15][16][17] 。 上述工作为研究早龄期混凝土力学性能奠定了良好 的基础。然而，这些研究大多采用较为简单的裂缝 模型， 也未能考虑裂缝演化与水化反应、 热量传输等 过程之间的相互耦合，自然也很难描述早龄期混凝 土裂缝的演化过程并量化开裂后材料的力学性能。 近年来，法国学者Nguyen等 [18][19][20] 采用脆性断裂 相场模型描述开裂混凝土的力学行为，并考虑裂缝 与水化反应、热量传输之间的耦合效应，能够较好 地描述早龄期的裂缝演化过程。脆性断裂相场模型 根植于Francfort-Marigo [21] 提出的线弹性断裂能量变 分原理，解决了Griffith能量方法需要预设裂缝路径 的难题；由于将尖锐裂缝正则化为具有一定尺度的 裂缝带，并引入在[0, 1]之间连续分布的裂缝相场及 其梯度描述裂缝状态，脆性断裂相场模型非常便于 通过有限元、无网格、物质点等多种数值方法加以 实现。 可以严格证明 [22] ： 当裂缝尺度趋近于零时， 脆 ...
During curing of concrete, hydration and thermal transfer inevitably result in expansion and shrinkage and hence, large tensile stresses in early-age concrete structures. As the mechanical properties of young concrete are still very low, structures are vulnerable in the construction stage to defects induced by crack nucleation, propagation and evolution, severely threatening the integrity, durability and safety of concrete structures and infrastructures like nuclear containment vessels, bridges and tunnel linings, hydraulic and off-shore structures. In order to predict the fracture property of earlyage concrete and quantify its adverse effects on structural performances, it is pressing to investigate the computational modeling of early-age cracking in concrete structures under the chemo-thermo-mechanically coupled environment. To the above end, in this work we propose a multi-physically coupled phase-field cohesive zone model within our previously established framework of the unified phase-field theory. The interactions between the crack phase-field with the hydration reaction and thermal transfer are accounted for, and the dependence of the characteristics of crack phase-field evolution, e.g., the strength-based nucleation criterion, the energy-based propagation criterion and the variational principle based crack path chooser, etc., on the hydration degree and/or temperature, are quantified. Moreover, the numerical implementation of the proposed model in the context of the multi-field finite element method is also addressed. Representative numerical examples indicate that, with the couplings among hydration, thermal transfer, mechanical deformations and cracking as well as the competition between thermal expansion and autogenous shrinkage both properly accounted for, the proposed multiphysical phase-field cohesive zone model is able to reproduce the overall cracking process and fracture property quantitatively. Remarkably, the numerical predictions are affected by neither the phase-field length scale nor the mesh discretization, ensuing its promising prospective in fracture control of early-age concrete structures. © 2021, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.
... The vapor produced at the drying front that moves ahead and condensates in the colder region of the dense ceramic structure (so-called "moisture clog") is pointed out as one of the main causes for the pressure build-up in such materials during heating. While some numerical simulations [107] corroborate this effect, limited experimental observations and quantification have been carried out so far. Therefore, the neutron tomography technique might be an important tool to be applied in the study of such a phenomenon. ...
Despite the continuous evolution on the performance of refractory ceramic products, monolithic materials still require special attention during their processing steps as various phase transformations may take place during the curing, drying and firing stages. Drying is usually the longest and the most critical process observed during the first heating cycle of refractory linings, as the enhanced particle packing and reduced permeability of the resulting microstructure may lead to recurrent explosive spalling and mechanical damage associated with dewatering and the development of high steam pressure at the inner regions of such dense materials. In this context, this review article mainly addresses (i) the theoretical aspects related to the drying process of dense refractories, (ii) the influence of the phase transformations derived from the binder additives, and (iii) the usual and advanced experimental techniques to assess the water removal from consolidated castable pieces. Many studies have pointed out that due to the complex nature of this phenomenon (i.e., considering combined thermal stresses and pore pressure, heterogeneous microstructure, evolving pore structure with temperature, etc.), the mechanisms behind the water withdrawal and castables’ explosive spalling are lacking further understanding and, consequently, it has been difficult to save time and energy during the first heating of industrial equipment lined with ceramic materials. On the other hand, different methods are used for refractory spalling assessment and many efforts have been carried out in applying in situ imaging techniques (such as NMR and neutron tomography) to follow the moisture evolution during such thermal treatments. These novel techniques, also addressed in this review, might be of particular importance to provide more accurate data for the validation of many state-of-the-art numerical models, which can be used to predict the steam pressure developed in refractory systems and help in the design of proper heating schedules for such products.
... (2) 弥散裂缝模型 ： 这方面的代表性研究工作包 括 [6][7][8] 等提出的早龄期混凝土弥散裂缝模型； (3) 损伤力学模型： 随着混凝土损伤力学的兴起， 若 干学者 [9][10][11][12][13][14] 将部分经典的损伤模型推广至早龄 期混凝土； (4) 微细观力学模型：为了考虑混凝土细观结构特 别是粗骨料对早龄期混凝土抗裂性能的影响， 部分学者发展了相应的微细观力学模型 [15][16][17] 。 上述工作为研究早龄期混凝土力学性能奠定了良好 的基础。然而，这些研究大多采用较为简单的裂缝 模型， 也未能考虑裂缝演化与水化反应、 热量传输等 过程之间的相互耦合，自然也很难描述早龄期混凝 土裂缝的演化过程并量化开裂后材料的力学性能。 近年来，法国学者Nguyen等 [18][19][20] 采用脆性断裂 相场模型描述开裂混凝土的力学行为，并考虑裂缝 与水化反应、热量传输之间的耦合效应，能够较好 地描述早龄期的裂缝演化过程。脆性断裂相场模型 根植于Francfort-Marigo [21] 提出的线弹性断裂能量变 分原理，解决了Griffith能量方法需要预设裂缝路径 的难题；由于将尖锐裂缝正则化为具有一定尺度的 裂缝带，并引入在[0, 1]之间连续分布的裂缝相场及 其梯度描述裂缝状态，脆性断裂相场模型非常便于 通过有限元、无网格、物质点等多种数值方法加以 实现。 可以严格证明 [22] ： 当裂缝尺度趋近于零时， 脆 ...
During curing of concrete, hydration and thermal transfer inevitably result in expansion and shrinkage and hence, large tensile stresses in early-age concrete structures. As the mechanical properties of young concrete are still very low, structures are vulnerable in the construction stage to defects induced by crack nucleation, propagation and evolution, severely threatening the integrity, durability and safety of concrete structures and infrastructures like nuclear containment vessels, bridges and tunnel linings, hydraulic and off-shore structures. In order to predict the fracture property of early-age concrete and quantify its adverse effects on structural performances, it is pressing to investigate the computational modeling of early-age cracking in concrete structures under the chemo-thermo-mechanically coupled environment. To the above end, in this work we propose a multi-physically coupled phase-field cohesive zone model within our previously established framework of the unified phase-field theory. The interactions between the crack phase-field with the hydration reaction and thermal transfer are accounted for, and the dependence of the characteristics of crack phase-field evolution, e.g., the strength-based nucleation criterion, the energy-based propagation criterion and the variational principle based crack path chooser, etc., on the hydration degree and/or temperature, are quantified. Moreover, the numerical implementation of the proposed model in the context of the multi-field finite element method is also addressed. Representative numerical examples indicate that, with the couplings among hydration, thermal transfer, mechanical deformations and cracking as well as the competition between thermal expansion and autogenous shrinkage both properly accounted for, the proposed multiphysical phase-field cohesive zone model is able to reproduce the overall cracking process and fracture property quantitatively. Remarkably, the numerical predictions are affected by neither the phase-field length scale nor the mesh discretization, ensuing its promising prospective in fracture control of early-age concrete structures.
... However, the results obtained under a standard environment cannot be directly applied to concrete structures, in which, interior humidity and temperature strongly depend on the structure sizes, external environment conditions, and concrete hydration. Shrinkage models [11] are also recommended to account for the coupling impact of different environmental factors and the interaction of different types of shrinkage. ...
The complex compositions and large shrinkage of concrete, as well as the strong constraints of the structures, often lead to prominent shrinkage cracking problems in modern concrete structures. This paper first introduces a multi-field (hydro–thermo–hygro–constraint) coupling model with the hydration degree of cementitious materials as the basic state parameter to estimate the shrinkage cracking risk of hardening concrete under coupling effects. Second, three new key technologies are illustrated: temperature rise inhibition, full-stage shrinkage compensation, and shrinkage-reducing technologies. These technologies can efficiently reduce the thermal, autogenous, and drying shrinkages of concrete. Thereafter, a design process based on the theoretical model and key technologies is proposed to control the cracking risk index below the threshold value. Finally, two engineering application examples are provided that demonstrate that concrete shrinkage cracking can be significantly mitigated by adopting the proposed methods and technologies.
... A two-dimensional simulation of a concrete slab under the condition of moisture thermal-mechanical coupling was carried out. D. Gawin et al. [64,65] regarded concrete as a multiphase porous material and proposed a mathematical model for analyzing the hygro-thermal behavior of high-temperature concrete. Jaroslav Kruis et al. [66] studied and analyzed the effective computer implementation of the coupled analysis of prestressed concrete nuclear reactor based on the hygro-thermal-mechanical coupled analysis. ...
The deformation and cracking of concrete will lead to various deterioration processes, which will greatly reduce the durability and service life of the concrete pavement. The relating previous studies and analysis revealed that the coupling action of environmental temperature, moisture, and wheel load will cause cracking and seriously affect the normal service and durability of pavement concrete. This paper presents theoretical and numerical state-of-the-art information in the field of deformation and failure of pavement concrete under coupling action of moisture, temperature, and wheel load and draws some conclusions. (a) Concrete is a typical porous material, moisture and heat transfer theory has obtained enough data to simulate the hygro-thermo properties of concrete, and the relationship between moisture and heat is very clear. (b) There are few studies on concrete pavement or airport pavement considering the coupling action of moisture, temperature, and wheel load. (c) Concrete pavement is subjected to hygro-thermal-mechanical coupling action in service, which has the characteristics of a similar period and its possible fatigue effect. (d) COMSOL software has certain advantages for solving the coupled hygro-thermal-mechanical of concrete.
... The elastic modulus of the porous materials such as the mortar can be simply concluded by the method of generalized mixture rule (GMR) [63], which has a strict mathematical derivation. The GMR can be expressed as Equations (21) and (22): where E is the elastic modulus, V is the volume fraction of the component, the subscript i represents the ith phase, and c represents the composite consisting of N phases. The effects of microstructures are expressed by a scaling fractal parameter J. ...
The composited cementitious materials usually have superior performance; for example, using limestone powder (LP) and fly ash (FA) as the admixtures of cement in concrete/mortar is a popular way of improving the properties of concrete/mortar structures. In this work, we performed experimental tests to study the hydration process and pore distribution in mortar containing different ratios of LP and FA. Based on the results of mercury intrusion porosimetry (MIP), a numerical mortar model with random pore is built. The model can reflect the synergistic hydration interaction and filling effect caused by the admixtures of LP and FA. After analyzing the hydration process, the coupled chemical-thermal-mechanical method was used to simulate the characteristics of mortar containing LP and FA. The coupling model can simulate the "hump-type" hydration acceleration stage of the mortar at early age, which is specifically caused by the LP, proved in the experimental test. Additionally, the special, "hump-type" stage is important to enhance the early strength of the mortar. At different levels of admixture content, the random pore model and coupled method can predict the evolution process of the mechanical properties well, at early age and for long-term strength. Both experimental and numerical results suggest that the mortar containing admixtures of the proper ratio of LP to FA have good mechanical properties, which can be applied to engineering structures.
... Lackner and Mang [15] proposed a chemo-mechanical model for early-age cracking of concrete in which the effect of relative humidity is also neglected. Gawin et al. [16,17] developed a hydro-thermalchemo-mechanical model of concrete at early ages which comprehensively accounts for the aging and hydrothermal coupling but lacks a comprehensive constitutive law for early-age concrete. Di Luzio and Cusatis [18] proposed the solidification-microprestress-microplane (SMM) model describing the mechanical behavior of concrete at early age under variable hydrothermal conditions. ...
The early cracking of concrete beam bridges remains a concern in civil engineering. An analytical model considering the combined effect of thermo-hydro-mechanical processes forms the basis for assessing the cracking risk of girders during construction. Based on the equivalent hydration theory, the temperature and moisture conduction processes and the evolution of the mechanical properties of concrete were modeled as a function of the equivalent age. A coupling model for the temperature and moisture fields was established, and a theoretical framework for analyzing the thermo-hydro-mechanical combined effect was presented. Based on this, a numerical analysis method was proposed and implemented into ABAQUS; the results were validated with some typical tests. Finally, a long-span prestressed concrete (PC) box girder bridge with balanced cantilever construction was taken as an example, and the causes of web cracking and its impact degree were analyzed. The results show that the rate of moisture conduction is significantly lower than the rate of temperature conduction; even for thin-walled components, there exists a significant humidity gradient on the surface layer. The humidity-induced shrinkage and restraint of the precast members are the main causes of web cracking.
... This observation leads authors such as [68] to implement models that rely on the state of stresses to determine this parameter. Furthermore, in the proposed formulation, the equivalent pore pressure (π in part 2.3) does not consider the effects associated to disjoining pressure and surface tension which are predominant in fine pore [6,38]. ...
Cement based material structures have to be managed over long periods. However, they are exposed to numerous loadings and present time-dependent deformations. In addition, the material is a porous medium in which pore pressure has an impact on macroscopic behaviour. The goal of this study is to better forecast the long term behaviour of cement based materials taking into account interactions between loads, time-dependent deformations and pore pressure. To do so, a previous model developed by the authors is extended to implement the impact of pore pressure on mechanical behaviour. Two applications are run on a mature ordinary concrete. The damage state is clearly dependent of the mechanisms involved in the modelling. Considering pore pressure allows to find damage depth more accurate regarding experimental evidences. After a calibration of one test (at hr = 45%), we were able to predict the behaviour of other tests, with an underestimation of 10% on one sample where hr changed. Interestingly, it was not manageable to use the same Biot parameter for the drying shrinkage and the mechanical modelling. As a result, by changing drastically the mechanical behaviour, the modelling of pore pressure is important to accurately assess the cracking state.
... However, the multi-physics modeling is out of the scope of the manuscript and also the dimensions of this type of structures prevent its use for now. For general constitutive formulations that starts from early-ages, an interested reader can also refer to the formulations presented in [17][18][19][20][21]. ...
This paper presents a general procedure for a rate-type creep analysis (based on the use of the continuous retardation spectrum) which avoids the need of recalculating the Kelvin chain stiffness elements at each time step. In this procedure are incorporated three different creep constitutive relations, two recommended by national codes such as the ACI (North-American) and EC2 (European) building codes and one by the RILEM research association. The approximate expressions of the different creep functions with the corresponding Dirichlet series are generated using the continuous retardation spectrum approach based on the Post–Widder formula. The proposed rate-type formulation is implemented into a 3D finite element code and applied to study the long-term deflections of a prestressed concrete bridge built in Romania, which crosses a wide artificial channel that connects the Danube river to the port of Constanta in the Black Sea.
... Shrinkage of concrete can certainly have several causes and can occur in different forms [10,11,12] namely Plastic-shrinkage, drying-shrinkage, thermal-shrinkage and endogenous-shrinkage, these phenomenon are directly related to the aging of the concrete [13,14,15], they are especially due to the water gradient between concrete and its environment [16,17], resulting in a decrease in relative humidity and an evolution in the porous structure of cementitious material [18,19,20]. ...
This manuscript aims to describe the different elements involved in the phenomenon of concrete cracking, and to discover the impact of the addition of plastic grains of type (PVC) coming from industrial waste and polypropylene fibers (PP) on the kinetics and final differential shrinkage magnitude of cementitious materials, the experimental results show that the shrinkage is mainly driven by the drying depth. Results also show that the addition of PVC granulates and Polypropylene fibers lead to a significant reduction of the final differential shrinkage for all the mortar mixtures formulated. Based on that results, the generated opening crack developed evolves with differential shrinkage, it is also affected positively by the addition of polypropylene fibers and PVC waste.
Basic creep plays an important role in assessing the risk of early-age cracking in massive structures. In recent decades, several models have been developed to characterize how the hydration process impacts the development of basic creep. This study investigates the basic creep of various concrete mixes across different ages at loading. The analysis focuses on the very early stages (less than 24 hours) and early stages (less than 28 days) of concrete development. It is shown that a logarithmic expression that contains two parameters describing the material can accurately model basic creep from a very early age. One parameter relates to the creep amplitude and depends solely on the composition of the concrete. The other relates to the kinetics of creep and depends on the age of the material at loading and the nature of the concrete mixture. The logarithmic expression corresponds to a rheological model consisting of a single dashpot wherein viscosity exhibits a linear evolution over time. The model offers the advantage of eliminating the need to store the entire stress history for computing the stress resulting from the restriction of the free deformation. This approach significantly reduces computation time. A power-law correlation is also observed between the material aging parameter and the degree of hydration. This relationship depends on the composition. At least two compressive creep tests performed at two different degrees of hydration are needed to calibrate the material parameters and consider the effect of aging on basic creep compliance.
Biaxially prestressed large concrete structures of the confinement building in nuclear power plants (NPPs) should meet the safety requirement for the extension of the service time. Long‐term delayed strains of concrete are one of the key factors determining the safety factor in these structures. This article presents 30‐year long in situ measurement results of strain evolution of confinement buildings in four different NPPs. The delayed strains are predicted at a material level using the next‐generation Eurocode‐2, and the influence of temperature as proposed by the fib model code 2010, making use of delayed strain characteristics of the corresponding concrete from a previous study. We found that the default law given in Eurocode underestimates the delayed strain. However, with the possibility of adjusting the shrinkage and creep laws, the prediction results fit with a good accuracy for the in situ measurement.
This study presents the formulation and validation of a three-dimensional Flow Lattice Model (FLM) with application to the Hygro-Thermo-Chemical (HTC) model for analysis of moisture transport and heat transfer in cementitious materials. The FLM is a discrete transport model formulated in association with meso-mechanical models, such as the Lattice Discrete Particle Model. This enables the simulation of transport phenomena at the length scale at which the material exhibits intrinsic heterogeneity. The HTC theoretical formulation is based on mass and energy conservation laws, written using humidity and temperature as primary variables, and considering explicitly various chemical reactions, for example, cement hydration and silica fume reaction, as internal variables. In this work, the HTC formulation was extended to include the effect of temperature on the sorption isotherm. The FLM solutions were compared with those of a continuum finite element implementation of the HTC model and experimental data available from the literature; the overall agreement demonstrates the reliability of the proposed approach in reproducing phenomena such as cement hydration, self-desiccation and temperature-dependent moisture drying.
Concrete is a heterogeneous material whose constituents (e.g., hydrated cement paste, aggregate etc.) ranges from a characteristic length-scale of a few nanometres to metre. Hence, prediction of its realistic mechanical properties needs a deeper study at different length-scale. In this paper, multiple physical and chemical processes that occurs within concrete constituents at different length-scale are considered and a combined multi-scale and multi-physics-based analysis method to characterise the behaviour of concrete has been proposed. Firstly, concrete is described at three different length-scale, micro, meso and macro level based on the information of the constituents at different scale. Thereafter, based on the constituents (e.g., C3S, C2S etc.) hydration at micro-level, cement paste RVE (representative volume element) is formed and analyzed to obtain the homogenized properties of the cement paste. Such homogenized properties are then used as an input for the matrix properties in the next higher scale i.e., at meso-level where aggregates are randomly placed inside the cement matrix. Like micro-scale, homogenisation is performed at meso-level to obtain macro-scale properties of concrete. It is the meso-level of description where coupling of the hygro-thermal-mechanical phenomena is considered. By using such a progressive homogenisation approach at different scale and including coupled hygro-thermal-mechanical phenomena makes the strength prediction model of concrete both multi-physics and multi-scale dependent. A wide range of simulations are afterwards performed, and the proposed model is then validated with the corresponding available experimental results that highlights the robustness of the model. Such an approach of studying concrete would give the designer the flexibility through which an optimum and targeted design of a cementitious material like concrete can be achieved numerically that would otherwise require several time-consuming and costly experiments.
The intense UV irradiation factor in the plateau area is easy to ignore, but it may have adverse effects on the microstructure and properties of concrete. Theredore, to clarify the evolution characteristics and the corresponding mechanism of the drying shrinkage of cement-based materials under intense UV irradiation environments at high altitudes cement mortars incorporating three types of mineral admixture were prepared to investigate the drying shrinkage, mass loss and microstructure, respectively. The hydration process and microstructure of samples were discussed in detail by microscopic experiments including TG-DTG, MIP, XRD, and IR patterns analysis. The results show that the mass loss and drying shrinkage of the cement-mineral admixture mortar exposed to intense UV irradiation were higher than those under the standard environment. Under intense UV radiation environment, the total porosity, mesoporosity (<50 nm), and carbonization degree of each group of samples increased. However, UV irradiation did not change the phase composition, chemical bond type, and polymerization degree of the CSH gel of the cement-based material. The incorporation of fly ash and slag resulted in the reduction of drying shrinkage of mortars, an increase in carbonation degree, and decreasing the hydration degree.
Part II of the study of a wet mix shotcrete focuses on creep and shrinkage as well as on the thermal and hygral behavior. It deals with the time-dependent mechanical behavior due autogenous shrinkage, combined autogenous and drying shrinkage, and basic creep and combined basic and drying creep for moderate and high levels of sustained compressive stress, applied at different shotcrete ages. Furthermore, the evolution of the temperature due to hydration and the degree of hydration, the evolution of the porosity and the water content of sealed specimens, and the desorption isotherm are determined, providing additional material data for shotcrete models.
For high stress levels, the dependence of the creep strain rate of concrete on the acting stress is nonlinear. Furthermore, very high stress levels may lead to a critical growth of microcracks resulting in material failure. For the lifetime assessment of creep sensitive concrete structures by means of numerical simulations, the realistic description of nonlinear creep is crucial. However, many concrete models are formulated for either nonlinear time-independent material behavior, or time-dependent material behavior, restricted to linear creep. This is the motivation for extending a damage-plasticity model, aiming at a unified and computationally efficient approach for representing the highly nonlinear time-dependent material behavior of concrete. Well established approaches for modeling the evolution of material properties, inelastic deformation, damage, creep and shrinkage serve as basis for considering nonlinear creep and material failure due to high sustained acting stress. The extended material model for concrete is validated by comprehensive experimental results from the literature.
This study aims to provide an efficient and accurate machine learning (ML) approach for predicting the creep behavior of concrete. Three EML models are selected in this study: Random Forest (RF), Extreme Gradient Boosting Machine (XGBoost) and Light Gradient Boosting Machine (LGBM). Firstly, the creep data in Northwestern University (NU) database is preprocessed by a prebuilt XGBoost model and then split into a training set and a testing set. Then, by Bayesian Optimization and 5-fold cross validation, the 3 EML models are tuned to achieve high accuracy (R² = 0.953, 0.947 and 0.946 for LGBM, XGBoost and RF, respectively). In the testing set, the EML models show significantly higher accuracy than the equation proposed by the fib Model Code 2010 (R² = 0.377). Finally, the SHapley Additive exPlanations (SHAP), based on the cooperative game theories, are calculated to interpretate the predictions of the EML model. Five most influential parameters for concrete creep compliance are identified by the SHAP values of EML models as follows: time since loading, compressive strength, age when loads are applied, relative humidity during the test and temperature during the test. The patterns captured by the three EML models are consistent with theoretical understanding of factors that influence concrete creep, which proves that the proposed EML models show reasonable predictions.
Alkali-activated binder (AAB) concrete is regarded as a green building material due to its high strength, chemical corrosion resistance, and low carbon emission. However, the shrinkage of AAB is more significant than that of ordinary Portland cement (OPC) and hinders the engineering applications of AAB. Current studies related to AAB shrinkage focus on the mechanisms and influencing factors of shrinkage. There are few shrinkage prediction models to guide the structural design. Compared with cement hydration, the hydration and polymerization of AAB are more complex and have many influencing factors. In addition to the factors affecting OPC shrinkage, the types, modulus, and alkali content of the activator can also affect AAB shrinkage. By comparing the results obtained by the existing shrinkage prediction models for OPC concrete and the shrinkage tests of AAB concrete, it is found that the empirical prediction model for OPC concrete cannot predict AAB concrete shrinkage well. Moreover, the theoretical method based on the capillary pressure mechanism also has challenges with predicting AAB concrete shrinkage due to the lack of statistical models related to microscopic parameters such as pore saturation, internal relative humidity, and creep coefficient of gels. According to the Kelvin-Laplace equation and viscoelastic analysis theory, a semi-theoretical prediction model could be established by studying the correlation between the mixed proportion of raw materials and the microscopic parameters of AAB concrete. The model may be one of the most rapid and efficient methods for predicting AAB concrete shrinkage.
High-performance concrete easily generates early-age cracks due to its sharp and large temperature and relative humidity (RH) changes. The temperature and RH with and without axial compressive stress were experimentally examined in this study. The test results show that the temperature and RH have an obvious coupled effect at an early age. The RH quickly decreases when the temperature sharply and substantially increases and sharply increases when the temperature steeply and substantially decreases. When the stress is applied, a clear abrupt increase in the RH appears, and when the compressive stress is unloaded, a clear abrupt decrease in the RH appears. During the loading, the decrease rate of RH smaller compared with its development tendency without load. The compressive stress has no significant effect on the temperature. Additionally, based on the previous studies and theoretical derivations, the coupled hygro-thermo-chemo-mechanical model of early-age concrete is proposed. The predicted results calculated by the proposed model are in good agreement with the test data in this study and the open literature.
Early-age cement-based materials undergo significant physical and chemical changes and have a complex mutual relationship among their temperature, humidity and mechanical behavior. As the second part of this study, this paper builds a multi-field coupling equation model taking into account the staged characteristics of the deformation for early-age cement-based materials based on the Hybrid Mixture Theory, and the accuracy of calculation results are verified with the test results obtained in the first part of this study. Moreover, the multi-field coupling model has been adopted to simulate the evolution of the different types of deformation for early-age cement-based materials. The results show that the multi-field coupling model established in this paper and the staged deformation calculation model established for early-age cement-based materials in the first part of this study can be used to better describe the development of their early-age temperature, humidity and deformation. Moreover, thermal strain is the earliest deformation that may cause cracking of cement-based materials, and chemical shrinkage has a certain compensation effect on thermal strain. In addition, the coefficient of thermal expansion (CTE) and the coefficient of stiffness influence (CSI) as well as their effects on thermal and chemical deformations have been analyzed. The results of this study can provide an important reference for analyzing the performance evolution of early-age cement-based materials.
This paper presents a method to numerically investigate the microstructural effect on the creep behavior of cement paste at the microscale. The lattice fracture model is extended to consider local time‐dependent deformations of calcium‐silicate‐hydrate phases in the cement paste by imposing local forces. The term “experimentally informed model” is used herein as the heterogeneous microstructures of hardened cement pastes were obtained by using the X‐ray computed microtomography and directly implemented into the model. The mechanical and creep properties of different constituents at the resolution of 5 µm were inversely identified from the fracture and creep bending tests on cementitious microcantilever beams at the microscale. The model is then validated through the comparison with the testing results of cement pastes with different w/c ratios and microstructures. It is found that the developed model can successfully reproduce experimentally observed behaviors and be applied to explain the experimental results in detail. With the method presented in this paper, the relationship between the volume fractions of different components and the global creep behavior of cement paste can be established. The validation of the model performed at the microscale forms a basis for the multiscale analysis of concrete creep.
The authors start with an introduction to the concepts involved in physics giving the equations of flow through porous media and the deformation characteristics of soils and rocks. Succeeding chapters deal with the practical implications of these phenomena and explain the application of theory in both experimental and field work. Details are given of actual incidents, such as the subsidence experienced in Venice and Ravenna. The authors have also formulated a consolidation code, which is detailed at the end of the book, and provide instructions on how to modify the given program.
Models for thermo-hydro-mechanical behavior of saturated/unsaturated porous media are reviewed. The necessary balance equations are derived using averaging theories. Constitutive equations are obtained using the Coleman-Noll procedure and thermodynamic equations for the model closure are introduced. A particular form of the governing equations is then solved numerically and the numerical properties are discussed. Application examples conclude the paper. There are 165 references in this review article.
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.
For the evaluation of the risk of thermal cracking in hardening massive concrete elements, knowledge of the development of
strength and deformability of early-age concrete is extremely important. Based on an extensive experimental research program
on hardening concrete elements, a degree of hydration-based description for the compressive strength, Young's modulus, the
uniaxial tensile strength, the splitting tensile strength, the flexural tensile strength, Poisson's ratio and the peak strain
are all worked out. An extension of the formulation of Sargin for the stress-strain relation for short-term compressive loading
leads to a degree of hydration-based stress-strain relation for hardening concrete. Good agreement with experimental results
is reported.
Pour bien évaluer le risque de fissuration thermique dans un béton jeune, il est très important de pouvoir en déterminer d'une
manière fiable les caractéristiques mécaniques. Sur la base de plusieurs essais mécaniques effectués sur le béton pendant
sa phase d'hydratation, on a pu établir une expression qui relie au degré d'hydratation la résistance à la compression, le
module d'élasticité, la résistance à la traction, la résistance à la flexion, la résistance à la traction par fendage, le
coefficient de Poisson et la déformation à la contrainte maximale. Une extension de la relation “contrainte-déformation” établie
par Sargin pour un béton durci, mène à une expression basée elle aussi sur le degré d'hydration. Pour l'ensemble des caractéristiques
étudiées, on peut constater une bonne concordance entre les résultats et les relations proposées.
A numerical model that accounts for the hydration and aging phenomena during the early ages of concrete curing is presented in a format suitable for a finite element implementation. Assuming the percolation of water through the hydrates already formed as the dominant mechanism of cement hydration, the model adopts an internal variable called hydration degree, whose evolution law is easily calibrated and allows an accurate prediction of the hydration heat production. Compressive strength evolution is related to the aging degree, a concept that accounts for the influences of the hydration and curing temperature on the final mechanical properties of concrete. The model capabilities are illustrated by means of a wide set of experimental tests involving ordinary and high performance concretes, and through the simulation of the concrete curing on a viaduct deck of the Öresund Link.
Creep and shrinkage testing of two sets of specimens is described. For the size and shape tests, the specimens modeled 100 to 400 mm section square columns, 100 to 400 mm thick slabs, and sealed specimens. For the age at loading tests the specimens modeled 150 mm square columns, 150 mm thick slabs, and sealed specimens that were loaded at concrete ages ranging from 8 to 182 days. Strains were monitored while the specimens were kept in a constant environment room. The experimental results form an extensive and consistent series that can be used to calibrate or validify creep and shrinkage prediction methods. The experimental results are compared with predictions based on the method recommended by ACI Committee 209 and a simple method for an improvement of predictions is presented.
Different expressions of the effective stress principle can be found in the literature, in particular some are written in finite form and others in incremental form. For the purpose of the paper we take for granted that stress–strain relationships exist or can be obtained for the effective stress coming from both formulations. We investigate the consequences of the choice of particular finite or differential forms when they are introduced in a weak form of the linear momentum balance equation of two- of three-phase porous media for its numerical solution. For partially saturated geomaterials the importance of the capillary pressure–saturation relationship is pointed out.
This paper explores the theory of reactive porous media in the modeling of thermochemomechanical couplings of concrete at early ages. The formulation is based upon thermodynamics of open porous media composed of a skeleton and several fluid phases saturating the porous space. It accounts explicitly for the hydration of cement by considering the thermodynamic imbalance between the chemical constituents in the constitutive modeling at the macrolevel of material description. In particular, the diffusion of water through the layers of hydrates is considered as the dominant mechanism of the hydration with respect to the kinetics of two apparent phenomena: aging and autogeneous shrinkage-the first related to the formation of hardened cement gel, the latter induced by capillary effects related to the formation of menisci due to water consumption through hydration. The intrinsic relations concerning heat generation, aging, and autogeneous shrinkage are so derived. Furthermore, it allows to make precise the decoupling hypothesis in order to clarify the linkages between different aging models: solidification theory and maturity models. In particular, it is shown that hydration degree, autogeneous shrinkage, and maturity are equivalent state variables, provided that stress and temperature evolutions do not effect the thermodynamic imbalance of hydration.
The basic creep of concrete is the time-dependent strain caused by a sustained stress in absence of moisture movements. It is the strain observed on sealed specimens. Similar to other properties of concrete, it is dependent on the age of concrete, as a consequence of long-time chemical reactions associated with the hydration of cement. This paper formulates the solidification theory with a continuous retardation spectrum, and shows how this spectrum can be readily and unambiguously identified from arbitrary measured creep curves and how it then can be easily converted to a discrete spectrum for numerical purposes. The identification of the continuous spectrum is based on Tschoegl’s work on viscoelasticity of polymers. Attention is limited to basic creep.
The classical viscoelastic models for aging materials such as concrete, which consist of Volterra history-integral equations, found only limited applications since they required storing the entire stress or strain history. Although the subsequent introduction of the Dirichlet series expansion of the creep or relaxation function reduces these requirements by leading to a set of linear differential equations equivalent to aging Kelvin or Maxwell chain models, problems arose in the identification of the aging moduli of these models. This paper refines and extends a recent formulation that remedies these problems by considering the aging to result from the progressive solidification of a basic constituent that behaves as a nonaging viscoelastic material. The new possibilities explored involve the alternative use of the relaxation function for characterizing the nonaging constituent, and the expansion of both the compliance and relaxation functions of the constituent into Dirichlet series. In this way, one recovers the rate-type equations of an aging Kelvin or Maxwell chain in which all the moduli vary proportionally to a single aging function v(t). Some convenient advantages are the well-posedness of the problem of moduli identification, with always positive values, and the nonexistence of creep or relaxation reversal upon load removal.
The theory that was formulated in the preceding paper is verified and calibrated by comparison with important test data from the literature pertaining to constant as well as variable stress at no (or negligible) simultaneous drying. Excellent agreement is achieved. The formulation describing both elastic and creep deformations contains only four free material parameters, which can be identified from test data by linear regression, thus simplifying the task of data fitting. For numerical structural analysis, the creep law is approximated in a rate-type form, which corresponds to describing the solidified matter by a Kelvin chain with nonaging elastic moduli and viscosities. This age-independence on the microlevel makes it possible to develop for the present model a simple version of the exponential algorithm.
The paper presents a new general constitutive law for creep in which the aging due to continuing hydration of cement is taken into account in a manner that is both simpler and physically better justified than in existing theories. Micromechanical analysis of the solidification process is used to show that the aging may be modeled as a growth of the volume fraction of load-bearing solidified matter (hydrated cement), which itself is treated as nonaging and thus is describable as a nonaging viscoelastic material. The analysis shows that a history integral should be used to express the rate, rather than the total value, of the viscoelastic strain component. Material functions can be chosen in a way that yields previously established simple laws, i.e., the double power law, logarithmic law and log-double power law, as special asymptotic cases. The creep strain is obtained as a sum of aging and nonaging viscoelastic strains and an aging viscous strain (flow). Nonlinearity is introduced by modifying the current creep rate as a function of the current stress. Verification by test results and numerical application is left to Part II, which follows.
This paper presents a numerical algorithm for the microprestress-solidification theory developed in a companion paper and verifies this theory by comparisons with typical test data from the literature. A model for cracking is incorporated in the algorithm.
A new physical theory and constitutive model for the effects of long-term aging and drying on concrete creep are proposed. The previously proposed solidification theory, in which the aging is explained and modeled by the volume growth (into the pores of hardened portland cement paste) of a nonaging viscoelastic constituent (cement gel), cannot explain long-term aging because the volume growth of the hydration products is too short-lived. The paper presents an improvement of the solidification theory in which the viscosity of the flow term of the compliance function is a function of a tensile microprestress carried by the bonds and bridges crossing the micropores (gel pores) in the hardened cement gel. The microprestress is generated by the disjoining pressure of the hindered adsorbed water in the micropores and by very large and highly localized volume changes caused by hydration or drying. The long-term creep, deviatoric as well as volumetric, is assumed to originate from viscous shear slips between the opposite walls of the micropores in which the bonds or bridges that cross the micropores (and transmit the microprestress) break and reform. The long-term aging exhibited by the flow term in the creep model is caused by relaxation of the tensile microprestress transverse to the slip plane. The Pickett effect (drying creep) is caused by changes of the microprestress balancing the changes in the disjoining pressure, which in turn are engendered by changes of the relative humidity in the capillary pores. Numerical implementation, application, and comparison with test data is relegated to a companion paper that follows in this issue.
Part 1 of the paper presents a new numerical model of hygro-thermal and hydration phenomena in concrete at early ages and beyond. This is a solidification-type model where all changes of material properties are expressed as functions of hydration degree, and neither as maturity nor as equivalent hydration period as in maturity-type models. A mechanistic approach has been used to obtain the governing equations, by means of an averaging theory of Hassanizadeh and Gray, also called hybrid mixture theory. The developments start at the micro-scale and balance equations for phases and interfaces are introduced at this level and then averaged for obtaining macroscopic balance equations. Constitutive laws are directly introduced at macroscopic level. The final equations, mass (water species and dry air), energy and momentum balance equations, have been written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacements. An evolution equation for the internal variable, hydration degree, describes hydration rate as a function of chemical affinity, considering in addition to the existing models, an effect of the relative humidity on the process. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by hydration process, i.e. porosity, density, permeability, and strength properties. Phase changes and chemical phenomena, as well as the related heat and mass sources are considered. Two examples showing possibilities of the model for analysis of autogenous self-heating and self-desiccation phenomena, as well as influence of the ambient relative humidity and the concrete element dimensions upon hygro-thermal performance and shrinkage of the elements, are presented and discussed. Copyright © 2006 John Wiley & Sons, Ltd.
Non-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials. Copyright © 2001 John Wiley & Sons, Ltd.
Solving fully coupled non-linear hygro-thermo-mechanical problems relative to the behaviour of concrete at high temperatures using monolithic models is nowadays a very interesting and challenging computational problem. These models require an extensive use of computational resources, such as main memory and computational time, due to the great number of variables and the numerical characteristics of the coefficients of the linear systems involved. In this paper, a number of different variants of a frontal solver used within HITECOSP, an application developed within the BRITE Euram III ‘HITECO’ EU project, to solve multiphase porous media problems, are presented and evaluated with respect to their numerical accuracy and performance. When developing the variants, several optimization techniques have been adopted, such as data structure, cache and branches optimizations. Specifically, numerical accuracy has been evaluated using a modified componentwise backward error analysis. The main result of this work is a new solver which is both much faster and more accurate than the original one. Specifically, the code runs over five times faster and numerical errors are reduced by up to three orders of magnitude. Copyright © 2003 John Wiley & Sons, Ltd.
Model B3 for creep and shrinkage prediction in the design of concrete structures, presented as a RILEM Recommendation inMater Struct.28 (1995) 357–365, is calibrated by a computerized data bank comprising practically all the relevant test data obtained in various
laboratories throughout the world. The coefficients of variation of deviations of the model from the data are distinctly smaller
than for the latest CEB model, and much smaller than for the previous ACI model (which was developed in the mid-1960's). The
effect of concrete composition and design strength on the model parameters is identified as the main source of error. The
model is simpler than the previous models (BP and BP-KX) developed at Northwestern University, yet it has comparable accuracy
and is more rational.
The form of the equilibrium effective stress acting on the solid phase of a porous medium containing two immiscible fluid phases is derived. The derivation makes use of the postulation of the thermodynamics of the system at the macroscale, a scale on the order of tens of pore diameters. The postulation at this scale facilitates the identification of the fraction of the solid surface in contact with each fluid phase as being the appropriate coefficient weighting each of the fluid phase pressures analogous to the Bishop parameter. In addition, the curvature of the surface of the solid phases is shown to impact the pressure exerted on the solid phase by the fluid. For the special case of low saturations when the wetting phase may be considered to be present only as a film on the solid phase, the macroscale disjoining pressure is found to modify the equilibrium form of the effective stress. In addition to the equilibrium effective stress, which is related to the forces acting on the interface between the solid phase and the fluids, the appropriate relation between the fluid pressures at the fluid–fluid interface is obtained. This analysis leads to the expression for the capillary pressure as a function of the phase pressures and the disjoining pressure.
In this paper some aspects of equilibrium and transfer moisture properties of high-performance materials are presented and compared with ordinary cement pastes and concretes. First, the equilibrium moisture properties of the hardened materials are described by means of water vapour sorption isotherms, which illustrate the hysteretical behaviour of the materials. Experimental results of drying shrinkage versus relative humidity (RH) are also reported here. These experimental data are in good agreement with the numerical results provided by a thermodynamic modelling based on capillary stresses and hygromechanical couplings. In particular the linearity of the strains-RH curve over a wide range is pointed out in both cases. Isothermal drying process at RH = 50% has experimentally and numerically been studied. After identification of the intrinsic permeability of the materials from experimental weight losses, numerical moisture profiles were compared with gamma-ray attenuation measurements. The influence of the initial moisture state of the materials that results from self-desiccation in particular was pointed out on the evolution of the moisture profiles as a function of time.
This paper describes a new concept for the prevention of self-desiccation in hardening cement-based materials. The concept consists of using fine, superabsorbent polymer (SAP) particles as a concrete admixture. This leads to water entrainment, i.e. the formation of water-filled macropore inclusions in the fresh concrete. Consequently, the pore structure is actively designed to control self-desiccation. In the paper, self-desiccation and water entrainment are described and discussed. The description is based on a reinterpretation of Powers' model for the phase distribution of a hydrating cement paste. The paper forms the first part of a series. In the second part, experimental observations will be presented.
In this paper, various mechanisms suggested to cause autogenous shrinkage are presented. The mechanisms are evaluated from the point of view of their soundness and applicability to quantitative modeling of autogenous shrinkage. The capillary tension approach is advantageous, because it has a sound mechanical and thermodynamical basis. Furthermore, this mechanism is easily applicable in a numerical model when dealing with a continuously changing microstructure. In order to test the numerical model, autogenous deformation and internal relative humidity (RH) of a Portland cement paste were measured during the first week of hardening. The isothermal heat evolution was also recorded to monitor the progress of hydration and the elastic modulus in compression was measured. RH change, degree of hydration and elastic modulus were used as input data for the calculation of autogenous deformation based on the capillary tension approach. Because a part of the RH drop in the cement paste is due to dissolved salts in the pore solution, a method is suggested to separate this effect from self-desiccation and to calculate the actual stress in the pore fluid associated with menisci formation.
Mechanics and thermodynamics of saturated–unsaturated porous materials and quantitative solutions SHRINKAGE AND CREEP OF CONCRETE 363 10. Carol I, Bazant ZP. Viscoelasticity with aging caused by solidification of nonaging constituent
- Ba Schrefler
Schrefler BA. Mechanics and thermodynamics of saturated–unsaturated porous materials and quantitative solutions. Applied Mechanics Review (ASME) 2002; 55(4):351–388. Copyright 2006 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2006; 67:332–363 SHRINKAGE AND CREEP OF CONCRETE 363 10. Carol I, Bazant ZP. Viscoelasticity with aging caused by solidification of nonaging constituent. Journal of Engineering Mechanics (ASCE) 1993; 119:2252–2269.
The effective stress principle: incremental or finite form? International Journal for Numerical and Analytical Methods in
- Ba Schrefler
- Gawin
Schrefler BA, Gawin D. The effective stress principle: incremental or finite form? International Journal for Numerical and Analytical Methods in Geomechanics 1996; 20(11):785 – 815. Copyright 2006 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2006; 67:332–363
A multiphase approach in the analysis of behavior of concrete as porous-viscous material
- D Gawin
- F Pesavento
- Schrefler
- Ba
Gawin D, Pesavento F, Schrefler BA. A multiphase approach in the analysis of behavior of concrete as porous-viscous material. Proceedings of the 5th World Congress for Computational Mechanics (WCCM), 7–12 July 2002, Vienna, Austria.
Modelling of coupled hygro-thermal phenomena in building materials and building components (in Polish) Scientific Bulletin of Łód´ University No 853
- D Gawin
Gawin D. Modelling of coupled hygro-thermal phenomena in building materials and building components (in Polish). Scientific Bulletin of Łód´ University No 853. Editions of Łód´ University: Łód´.
Properties of Concrete Longman House: Harlow
- Am Neville
Neville AM. Properties of Concrete (4th edn). Longman House: Harlow, 1995.
Longman House: Harlow
- Properties Of Concrete
- Neville
- Schrefler