Modeling of structural performances under coupled environmental and weather actions

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00, pp Modeling of structural performances under coupled environmental and weather actions K. Maekawa and T. Ishida University of Tokyo, Department of Civil Engineering, Hongo, Bunkyo-ku, Tokyo, Japan A B S T R A C T The authors propose a so-called life-span simulator that can predict concrete structural behaviors under arbitrary external forces and environmental conditions. In order to realize this kind of technology, two computational systems have been developed; one is a thermohygro system that covers microscopic phenomena in C-S- H gel and capillary pores, and the other one is a structural analysis system, which deals with macroscopic stress and deformational field. In this paper, the unification of mechanics and thermo-dynamics of materials and structures has been made with the ion transport of chloride, CO and O dissolution. This proposed integrated system can be used for simultaneous overall evaluation of structural and material performances without distinguishing between structure and durability. R É S U M É Les auteurs proposent un simulateur qui peut prévoir les comportements structuraux d un béton (sur toute sa longueur de vie), soumis à des forces extérieures arbitraires et sous un environnement quelconque. Ce simulateur est basé sur le couplage de deux modèles analytiques : un modèle thermohydraulique qui simule les phénomènes microscopiques dans le gel C-S-H et les pores capillaires, et un modèle de structures qui intègre les contraintes macroscopiques et les déformations du béton. Dans cet article, l association de la mécanique et thermodynamique des matériaux avec l analyse des structures est réalisée par le transport des ions chlorhydriques, et la dissolution du CO et O. Ce modèle intégré, que nous proposons, peut être utilisé simultanément pour l évaluation complète des structures et pour l évaluation des performances des matériaux, sans distinction entre structure et durabilité. 1. INTRODUCTION For sustainable development in the coming century, it is necessary that the infrastructures retain their required performances over the long term. In order to construct a durable and reliable structure, it is necessary to evaluate the life cycle cost and its benefits as well as the initial cost of construction. On the other hand, for an already deteriorated structure, a rational maintenance and repair plan should be implemented in accordance with the condition of the structure. Considering these points, it is indispensable to grasp the structural performances under the expected environmental and load conditions during the service life. The objective of our research is to develop a so-called lifespan simulator capable of predicting structural behaviors for arbitrary conditions. Fig. 1 shows the schematic representation of the lifespan simulator of material science and mechanics of structures. Our research group has been developing two numerical simulation tools. One is a thermo-hygro system named DuCOM [1], which covers the microscale phenomena governed by thermodynamics. This computational system can evaluate an early age development of cementitious materials and deterioration processes of hydrated products under long-term environmental actions. In the following section, the overall scheme of this system and each material modeling will be introduced. The other one is a nonlinear path-dependent structural analytical system named COM3 [, 3]. For arbitrary mechanical actions including temperature and shrinkage effects, the structural response as well as mechanical states of constituent elements can be predicted. The solidification model of hardening concrete composite has been also installed in this system for predicting timedependent behavior depending on temperature, moisture profile, and micropore structure of materials [4, 5] /0 RILEM 591

2 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 Fig. 1 Life-span simulation for materials and structures. Fig. Framework of DuCOM thermohygro physics. In most past design methodologies, structure serviceability and material performance have been treated separately. However, it has to be noted that structural deformations and capacity are really linked with both micropore based deterioration and large-scale mechanical defects represented by cracking, yielding and damaging of materials with respect to control volume. In turn, the progress in macro-scale material damage and defects are also dependent on both the structural deformation and environmental boundary conditions. Here, nonlinearly accelerated change of material and structural performances takes place simultaneously. For example, corrosion and associated volume expansion induces additional cracks and defects that accelerate the migration of moisture and ions. In this paper, the unification of mechanics and thermo-dynamics of materials and structures is tackled to demonstrate the potential and future direction of research and development. When the computational methods are utilized for structural performance evaluation, the actual quality achieved in the structure should be taken into account. This is due to the fact that the qualities of materials are different at each location owing to the material segregation. In the latter part of this paper, we briefly introduce the experimental works, which were carried out in order to evaluate the non-uniform quality of concrete in RC members.. THERMO-HYGRO PHYSICS FOR CON- CRETE PERFORMANCE DUCOM In order to trace the early-age development of cementitious materials, it is necessary to consider the inter-relationships among the hydration, moisture transport, and pore-structure development processes. For example, microstructure development can be achieved by the precipitation of hydrated products, and moisture profile in cementitious materials influences the rate of hydration. Furthermore, properties of pore structure determine the moisture conductivity. Our research group have been developing a 3D FE analysis program code-named DuCOM that simulates these phenomena. This section simply summarizes the overall schemes of this program, since details are presented in a published book [1]. The overall computational scheme is shown in Fig.. The constituent material models are formulated based on microphysical phenomena, and they take into account the inter-relationships in a natural way. The inputs required in this scheme are mix proportion, powder material characteristics, casting temperature, geometry of the target structure, and the boundary conditions to which the structure will be exposed during its life-cycle. Using the multi-component hydration model, solutions 59

3 Maekawa, Ishida Fig. 3 Governing equation and constitutive models for chloride ion. for temperature, degree of hydration, and amount of chemically combined water are obtained [6, 7]. The hydration of both constituent minerals of cement and pozzolans is traced by simultaneous differential equations based on the Arrhenius law of chemical reaction. The rate of hydration is mathematically specified in terms of temperature, free water content in capillary pores, degree of hydration and associated cluster thickness of C-S-H gel layers precipitated around non-reacted cement particles. Then, the chemical process and its interaction among minerals and additive pozzolans are considered by sharing common variables associated with pore solution, water and temperature. By applying the average level of hydration and chemically combined water to a micro pore structure development model, the porosity distribution of hydrated and non-hydrated compounds around reference cement particles is calculated and the surface area of the micropores is estimated mathematically [1]. The resulting porosity and pore distributions are used to evaluate moisture conductivity. Using the moisture transport model, which considers both vapor and liquid transports, the pore pressures, relative humidity, and moisture distribution can be obtained [8, 9]. Here, water consumption due to hydration is considered in solving the mass balance equation, thereby naturally tracing the inter-dependence between moisture transport and the hydration process. Recently, in addition to the above modeling related to early age development phenomenon, the authors have been widening the application of DuCOM in order to cover the deterioration and resolution of cementitious materials and steel corrosion under long-term environmental actions [10, 11]. For that purpose, concentrations of chloride ion, oxide, and carbon dioxide were added to the thermo-hygro system, as the additional degrees of freedom to be solved (Fig. ). Each physical variable should satisfy the law of mass conservation shown in Fig.. Potential term S(θ), flux term J(θ), and sink term Q(θ) constituting the governing equations, are formulated as 593 the nonlinear functions of variables θ i based on thermodynamic theory. The obtained material properties are shared through the common variables beyond each sub-system, therefore an interactive problem, such as corrosion due to the simultaneous attack of chloride ions and carbon dioxide, can be simulated in a natural way. Coupling these materials modeling, an early age development process and deterioration phenomenon during the service period can be evaluated for arbitrary materials, curing and environmental conditions in a unified manner. In the following sections, the authors will introduce the general ideas of each material modeling and their coupling system..1 Formulation of chloride ion transport and equilibrium Chloride transport in cementitious materials under usual conditions is an advective-diffusive phenomenon. In the modeling, the advective transport due to the bulk movement of pore solution phase is considered, as well as the ionic diffusion due to the concentration differences. The mass balance condition for free (movable) chlorides can be expressed as (Fig. 3), ( φsc ) cl + divjcl QCl = 0 t φs (1) JCl = D Cl C Cl + φ S u C Cl Ω K = P u ρφs where, φ: porosity of the porous media, S: degree of saturation of the porous medium, C Cl : concentration of ions in the pore solution phase [mol/l], J Cl : flux vector of the ions [mol/m.s], u T = [u x u y u z ] is the advective velocity of ions due to the bulk movement of pore solution phase [m/s], and Ω: tortuosity of pore-structures for a 3-D pore network which is uniformly and randomly connected. The tortuosity is a parameter that expresses a reduction factor in terms of chlorides penetration rate due to the complex micropore structure. In the current model, this parameter is determined by considering the geometric characteristics of the pore structure based on the experimental data for various water-to-cement ratios [1]. Material parameters shown in Equation (1), such as porosity, saturation and advective velocity, are directly obtained based on the thermo-hygro physics. For example, the advective velocity u is obtained from the pore

4 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 pressure gradient P and liquid water conductivity K which are calculated by moisture equilibrium and transport model, according to water content, micro pore structures, and moisture history. In the case of chloride ion transport in cementitious materials, S represents the degree of saturation in terms of the free water only, as adsorbed and interlayer components of water are also present. Here, it has to be noted that the diffusion coefficient D Cl in the pore solution may be a function of ion concentration, since ionic interaction effects will be significant in the fine microstructures at increased concentrations, thereby reducing the apparent diffusive movement driven by the ion concentration gradient [14]. This mechanism, however, is not clearly understood, so we neglect the dependence of ionic concentration on the diffusion process in the model. From several numerical sensitivity analyses, a constant value of [m /s] is adopted for D Cl. From the above discussions, the total diffusivity of concrete is described as the product of D Cl and φs/ω, which depends on the achieved microstructures (the initial mix and curing condition dependent variables) and moisture history. It is a well-known that chlorides in cementitious materials have free and bound components. The bound components exist in the form of chloroaluminates and adsorbed phases on the pore walls, making them unavailable for free transport. In this study, the relationship between free and bound components of chlorides is expressed by the equilibrium model proposed by Takeda and Takegami, as shown in Fig. 3 [1, 13]. In the model, the bound chlorides are classified into two phases: adsorbed and chemically combined components. Through these studies [1, 13], it can be assumed that the amount of the combined phases is approximately constant in terms of weight percent of hydrated gel products, whereas that of adsorbed phase is strongly dependent on the constituent powder materials. For example, in the case of using BFS, the amount of adsorbed phases becomes larger compared with the case of OPC, which leads to higher binding capacity of BFS concrete and mortar. This means that the adsorbed component plays a major role in the chloride binding capacity of concrete. Assuming local equilibrium conditions based on this relationship, the rate of binding or the change of free chloride to bound chloride per unit volume Q Cl can be obtained. From the above discussions and formulations, the distribution of bounded and free chloride ions can be obtained without any empirical equations and/or intentional fittings, once mix proportions, powder materials, curing and environmental conditions are given to the analytical system.. Modeling of carbonation For simulating the carbonation phenomena in concrete, equilibrium of gas and dissolved carbon dioxide, their transport, ionic equilibriums, and carbonation reaction process are formulated based on thermodynamics and chemical equilibrium theory. Mass balance condition for dissolved and gaseous carbon dioxide in porous medium can be expressed as, t where, ρ gco : density of CO gas [kg/m 3 ], ρ dco : density of dissolved CO in pore water [kg/m 3 ], J CO : total flux of dissolved and gaseous CO [kg/m.s]. The local equilibrium between gaseous and dissolved carbon dioxide is represented here by Henry s law, which states the relationship between gas solubility in pore water and the partial gas pressure. The CO transport is considered in both phases of dissolved and gaseous carbon dioxide. Considering the effect of Knudsen diffusion, tortuosity, and connectivity of pores on the diffusivity, the flux of CO can be formulated based on the Fick s first law of diffusion as, J = D ρ + D ρ D where, D gco : diffusion coefficient of gaseous CO in porous medium[m /s], D dco : diffusion coefficient of dissolved CO in porous medium[m /s], D 0 g : diffusivity of CO gas in a free atmosphere[m /s], D 0 d : diffusivity of dissolved CO in pore water [m /s], V: pore volume, r c : pore radius in which the equilibrated interface of liquid and vapor is created, N k : Knudsen number, which is the ratio of the mean free path length of a molecule of CO gas to the pore diameter. Knudsen effect on the gaseous CO transport is not negligible in low RH condition, since the porous medium for gas transport becomes finer as relative humidity decreases. As shown in Equation (3), the diffusion coefficient D dco is obtained by integrating the diffusivity of saturated pores over the entire porosity distribution, whereas D gco is obtained by summing up the diffusivity of gaseous CO through unsaturated pores. The substitution of porosity saturation S for the integrals in the above equation in order to generalize the expression for an arbitrary moisture history gives, D D { } φ[ ( 1 S) ρgco + S ρ dco] + divj Q = 0 CO dco dco gco gco d r dco gco ( ) c g φd0 φ D dv dv D 0 = gco = Ω Ω 1 + N dco 0 n φs = D Ω d 0 CO CO n ( ) m ( m m) g φ D 1 S 0 = Ω 1+ l r t where, n is a parameter representing the connectivity of the pore structure, and might vary with the geometrical characteristics of the pores [11]. In the model, through sensitivity analysis, n is tentatively assumed to be 4.0, which is the most appropriate value for expressing the reduction of CO diffusivity with the decrease of relative humidity (Fig. 4). In Equation (4), the integral of the rc k () (3) (4) 594

5 Maekawa, Ishida Fig. 4 Relationship between CO diffusivity and relative humidity. Knudsen number is simplified so that it can be easily put into practical computational use; r m is the average radius of unsaturated pores, and t m is the thickness of the adsorbed water layer in the pore whose radius is r m. Q CO in Equation () is a sink term that represents the rate of CO consumption due to carbonation [kg/m 3.s]. The rate of CO consumption can be expressed by the following differential equation, assuming that the reaction is of the first order with respect to Ca + and CO 3 - concentrations as, + - Ca + CO3 CaCO3 (5) CaCO 3 + = ( C ) Q Ca CO - CO = k[ ][ 3 ] t where, C CaCO3 : concentration of calcium carbonate, k is a reaction rate coefficient. In this paper, a unique coefficient is applied (k =.08 [l/mol.sec]), although the reaction rate coefficient involves temperature dependency. In order to calculate the rate of reaction with Equation (5), it is necessary to obtain the concentration of calcium ion and carbonic acid in the pore water at arbitrary stage. In this study, we consider the following ion equilibriums; dissociation of water and carbonic acid, and dissolution and dissociation of calcium hydroxide and calcium carbonate. + HO H + OH H CO H + HCO H + CO + Ca OH Ca OH ( ) + + CaCO Ca + CO 3-3 Here, the presence of chlorides is not considered, although chloride ions are likely to affect the above equilibrium conditions. The formulation including chlorides remains for future study. As shown in Equation (6), carbonation is an acidbase reaction, in which cations and anions act as a Brönsted acid and base, respectively. Furthermore, the solubility of precipitations is dependent on the ph of the pore solutions. Therefore, in order to calculate the ionic (6) concentration in the pore solutions, the authors formulated an equation with respect to protons [H+], according to the basic principles on ion equilibrium; laws of mass action, mass conservation, and proton balance in the system [11, 16]. Using the equation, the concentration of protons in pore solutions can be calculated at arbitrary stage, once the concentration of calcium hydroxide and that of carbonic acid before dissociation are given. It has been reported that micropore structure is changed due to the carbonation. In this paper, the authors use the empirical equations that are proposed by Saeki et al. as [17], ( ) φ = φ( RCa(OH) ) 0.6 < RCa(OH) < 10. φ = 0.5 φ (7) ( RCa(OH) 06. ) where, φ : porosity after carbonation, R Ca(OH) : the ratio of the amount of consumed Ca(OH) for the total amount of Ca(OH)..3 Microcell-based corrosion model In this section, we introduce the general scheme of microcell corrosion model based on thermodynamics and electro-chemistry. In our modeling, it is assumed that the corrosion will occur uniformly over the surface areas of the reinforcing bars in a finite volume, whereas the formation of pits due to localized attack of chlorides and the corrosion with macro cell remains for future study. Fig. 5 shows the flow of the corrosion computation. When we consider the microcell based corrosion, it can be assumed that the area of anode is equal to that of cathode and they are not separated from each other. Therefore, we do not treat the electrical conductivity of concrete, which governs the macroscopic transfer of ions in pore water. Fig. 5 Overall scheme of corrosion computation. First of all, the electric potential of corrosion cell is obtained from the ambient temperature, ph in pore solution and the partial pressure of oxide, which are calculated by other subroutine in the system. The potential of halfcell can be expressed with the Nernst equation as [18], 595

6 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 () ( )+ ( ) + Fe s Fe aq e Pt E E RT z F lnh Θ = +( Fe Fe Fe ) + Fe ()+ ()+ ( )= ( ) - O g H O l 4e Pt 4OH aq Θ = +( ) ln( ) E E RT z F P P Θ O O O O 006. ph where, E Fe : standard cell potential of Fe, anode (V, SHE), E O : standard cell potential of O, cathode (V, SHE), E Θ Fe: standard cell potential of Fe at 5 C (=- 0.44V,SHE), E Θ O : standard cell potential of O at 5 C (=0.40V,SHE), z Fe : the number of charge of Fe ions (=), z O : the number of charge of O (=), P Θ : atmospheric pressure. Strictly speaking, the solution of other ions in pore water might affect the electric potential of cell. However, it is difficult to consider the effect of ion solutions on the half-cell potentials, therefore we adopt the above equations, assuming the ideal conditions. Next, based on the thermo-dynamical conditions, the condition of passive layers is evaluated by the Pourbaix diagram, where steel corrodes, areas where protective oxides from, and an area of immunity to corrosion depending on ph and the potential of the steel. From the electric potential and the formation of passive layers, electric current that involves chemical reaction can be calculated so that conservation law of electric charge should be satisfied in a local area (Fig. 6). The relationship between electric current and voltage for anode and cathode can be expressed by the following Nernst equation as, ( ) ( ) a η =. 303RT 0. 5 zfef log ia i0 c (9) η = (. 303RT 0. 5 zo F) log( i ) c i0 where, η a : overvoltage at anode [V], η c : overvoltage at cathode [V], F: Faraday s constant, i a : electric current density at anode [A/m ], i c : electric current density at cathode [A/m ]. Corrosion current I corr can be obtained as the point of intersection of two lines. The existence of passive layer reduces the corrosion progress. In this model, this phenomenon is described by changing the Tafel gradient. When the amount of oxygen supplied to the reaction is not enough, the rate of corrosion would be controlled (8) by the diffusion process of oxygen. In this paper, coupling with oxygen transport model, this phenomenon can be simulated. The detailed discussion on the formulations of the oxygen is omitted for lack of space, since they are almost same as those of carbon dioxide [10]. Finally, using the Faraday s law, electric current of corrosion is converted to the rate of steel corrosion. It has to be noted that these models are only derived from the thermodynamics and electrochemistry, and the authors understand that further development and improvement are still needed thorough various verification of corrosion phenomena in real concrete structures. 3. CONTINUUM MECHANICS OF MATERI- ALS AND STRUCTURES COM3 For simulating structural behaviors expressed by displacement, deformation, stresses and macro-defects of materials in view of continuum plasticity, fracturing and cracking, well established continuum mechanics can be used as illustrated in Fig. 7. The compatibility condition, equilibrium and constitutive modeling of material mechanics are the basis and the spatial averaging of overall defects in control volume of finite element is incorporated into the constitutive model of quasi-continuum. The authors adopted a 3D finite element computer code named COM3 for structural dynamics, which has been also developed at the University of Tokyo for static as well as dynamic ultimate limit states [, 3]. This frame of structural mechanics has an inter-link with thermo-hygro physics in terms of mechanical performances of materials through the constitutive model- Fig. 6 The relationship between electric current and voltage for anode and cathode. Fig. 7 Macro-scale defects and microscale pore structures. 596

7 Maekawa, Ishida ing in both space and time. The instantaneous stiffness, short-term strengths of concrete in tension and compression, free volumetric contraction rooted in coupled water loss and self-desiccation caused by varying pore sizes are considered in the creep constitutive modeling of liner convolution integral (Figs. 7 and 8). In the unified solidification modeling for shrinkage and creep [4, 5], aggregates are idealized as suspended continuum media of perfect elasticity, whereas cement paste is treated as the solidified nonaging clusters having individual creep properties (Fig. 8). The aging process itself is represented by the solidification of these clusters. The combined effect of external loads and pore water pressure is treated as the driving force for the concrete deformation. The volumetric change provoked by the hydration in progress and water loss is physically tied with surface tension force developing inside the microcapillary pores. Of course, the micropore size distribution and moisture balance of thermo-dynamic equilibrium are given from the code DuCOM at each time step. The cracking is the most important damage index associated with mass transport inside the targeted structures. Cracks are assumed to be induced normal to the maximum principal stress direction in 3D extent when the tensile principal stress exceeds the tensile strength of concrete. After crack initiation, the tension softening on progressive crack planes is taken into account in the form of fracture mechanics. In the reinforced concrete zone, in which bond stress transfer is expected being effective, the tension stiffness model is brought together. Since the external load level, with which the environmental action be coupled in design, is rather lower than the ultimate limit states, compression induced damage accompanying dispersed microcracking is disregarded in this study. Fig. 8 Unified solidification model of hardening concrete composite. one-way transfer. This system can be embodied in a multitasking operating system such as UNIX or Windows. In this framework, constituent sub-systems with different schemes for solving the various governing equations do not have to be combined into a single process. The operating system manages the tasks of each system, and the two sub-systems are connected by a high-speed signal bus or network so as to share the common data. First, material properties are calculated by DuCOM. After one step of execution, the calculated results for temperature, water content, pore pressure, pore structure, stiffness, and strength are stored in the common data area. A signal to begin execution is then sent to the sleeping process (COM3). COM3 becomes active and reads the information from the common data area, using it to perform the stress computation. In this analysis, the 4. UNIFICATION OF THERMO-HYGRO PHYSICS OF MATERIALS AND MECHANICS OF STRUCTURES For numerical evaluation of overall structural and material performance, we propose parallel processing of two coupled sub-systems as shown in Fig. 9 [19]. The main feature of this system is that perfect two-way communication is available between the structural mechanics and material characteristics, whereas in conventional thermal stress analysis, material parameters such as temperature rise are passed to the structural analysis in only a Fig. 9 Parallel processing of DuCOM and COM3. 597

8 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 Fig.10 Chloride content profile in concrete exposed to cyclic drying wetting and drying. Fig. 11 Carbonation phenomena for different CO concentrations and water-to-cement ratios. damage level of the RC member is obtained, and the calculated results are written to the common area after execution. These steps are continued till one of the processes completes its computation. Following this procedure, each FE program can share computational results between the two systems at each gauss point in each finite element. 5. NUMERICAL SIMULATIONS 5.1 Chloride transport into concrete under cyclic drying-wetting conditions Using the proposed method, the transport of chloride ion under alternate drying wetting conditions was simulated. For verification, the experimental data by Maruya et al. were used [0]. The size of mortar specimens was [cm] and the water to powder ratio was 50%. After 8 days of sealed curing, the specimens were exposed to cyclic alternate drying (7 days) and wetting (7 days) cycles. The drying condition was 60%RH, whereas the wetting was exposed to a chloride solution of 0.51 [mol/l] at 0 C. In the FEM analysis, mix proportions and the chemical composition of the cements were given. The curing conditions and exposure conditions were also given as boundary conditions for the target structures. All of these input values corresponded to the experimental conditions. Fig. 10 shows the distribution of free and bound chlorides from the boundary surface. For comparison, we analyzed two cases; one considering only diffusive movement and the other including the advective transport due to the bulk movement of pore water as well as the diffusion process. As shown in the analytical results, the distribution of bound and free chlorides can be reasonably simulated with advective transport due to the rapid suction of pore water under wetting phase. 5. Carbonation phenomena in concrete In this section, computations were performed to predict the progress of carbonation for different CO concentrations and water to cement ratio. The amount of Ca(OH) existing in cementitious materials can be obtained by multi-component hydration model as [6, 7], C S 6H C S H 3Ca OH C S 4H C S H Ca OH C AF Ca OH 10H C AH ( ) + + ( ) ( ) + (10) For verification, the experimental data done by

9 Maekawa, Ishida Fig. 1 Distribution of ph, calcium hydroxide, and calcium carbonate under the action of carbonic acid. that have three different water to powder ratio, W/C=40, 50, 60%, with only one face exposed to the environment were considered. In this analysis, the stage where concrete cracking occurs was defined as a limit state with respect to the steel corrosion. The progressive period until the initiation of longitudinal cracking were estimated by the equation proposed by Yokozeki et al. [], which is a function of cover depth. Fig. 13 shows the relationships between cover depth and structural age until cracking due to corrosion obtained by the proposed thermo-hygro system. It can be seen that the concrete nearer to the exposure surface will show an early sign of corrosion induced cracking, and low W/C concrete has the higher resistance against corrosion. Fig. 13 Time till first sings of cracking due to corrosion for concrete exposed to CO gas and salty water. Uomoto et al. were used [1]. Fig. 11 shows the comparison of analytical results and empirical formula that was regressed with the square root t equation. Similar to the previous case, all of the input values in the analysis corresponded to the experimental conditions. Analytical results show the relationship between the depth of concrete in which ph in pore water becomes less than 10.0 and exposed time. The simulations can roughly predict the progress of carbonation for different CO concentration and water to powder ratio. Fig. 1 shows the distribution of ph in pore water, CO, calcium hydroxide, and calcium carbonate inside concrete, exposed to the CO concentration of 3%. Two different water to powder ratio, W/C=5% and 50%, were analyzed. It can be shown that higher resistance for the carbonic acid action is achieved in the case of low W/C. 5.3 Numerical simulation of coupled carbonation and chloride induced corrosion The behaviors of steel corrosion in concrete due to simultaneous attack of chloride ions and carbon dioxide were simulated. One-dimensional concrete members 5.4 Moisture distribution in cracked concrete In this section, in order to show the possibility of a unification of structure and durability design, a simple simulation was conducted by using the proposed parallel computational system. It has been reported that there should be a close relationship between moisture conductivity and the damage level of cracked concrete; that is, moisture conductivity should be dependent on the crack width or the continuity of each crack. The proposed system, in which information is shared between the thermo-hygro and structural mechanics processes, is able to describe this behavior quantitatively by considering the inter-relationship between moisture conductivity and cracking properties. For representing the acceleration of drying out due to cracking, the following model proposed by Shimomura were used in this analysis [3]. JV + JL before cracking Jw = cr cr (11) JV + JL + JV + JL after cracking where, J w is the total mass flux of water in concrete, J V and J L are the mass flux of vapor and liquid in non-damaged concrete respectively, and J cr V and J cr L are the mass flux of vapor and liquid water through cracks. In this simulation, only J cr V is taken into account for the first approximation, since diffusion of vapor would be pre- 599

10 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 Fig. 14 Moisture and internal stress distribution in concrete exposed to drying condition. dominant when concrete are exposed to drying conditions. From the experimental study done by Shimomura et al., it has been confirmed that the flux J cr V can be expressed as [4], cr JV = ερvda h (1) where, ε : average strain of cracked concrete, which can be computed by COM3, ρ V : density of vapor, D a : vapor diffusivity in free atmosphere, h: relative humidity. The target structure in this analysis was a concrete slab, which has 30% water to powder ratio using medium heat cement. Mesh layout and the restraint conditions used in this analysis are shown in Fig. 14. The volume of aggregate was 70%. After 3 days of sealed curing, the specimen was exposed to 50%RH. Fig. 14 shows the cracked elements, the distribution of moisture, and normalized tensile stress at each point from the boundary surface exposed to drying condition. Moisture distribution calculated without stress analysis is also shown in Fig. 14. As shown in the results, the crack occurs from the element near the surface, and the crack progresses internally with the progress of drying. It is also shown that the amount of moisture loss becomes large due to cracking. 6. QUANTITATIVE EVALUATION OF NON- UNIFORM QUALITY OF CONCRETE IN RC MEMBERS In most past examinations, small-sized specimens have been used for checking durability performances of concrete structures. Here, it has to be remembered that material qualities specified by the small specimens cannot always be assured in all domains of a structure since actually achieved material qualities are dependent on construction methods and the property of the fresh concrete. This causes difficulty in forecasting structural performance. In the latest JSCE concrete specifications [5], quality differences between test-pieces and actual structural concrete can be taken into account by introducing a partial safety factor. For example, in case of a self-compacting concrete that is expected to overcome a number of uncertainties inherent in construction methods [6], the safety factor can be set as unity. On the other hand, for ordinary concrete, it has not been cleared how to determine the value of the safety factor for various cases. It really depends on the construction methods, concrete materials, and structural dimensions. From these backgrounds, we made RC column and beam specimens in order to evaluate the influence of the structural details, slump values, and construction methods 600

11 Maekawa, Ishida Fig. 15 Experimental conditions. Fig. 18 Results of multiple regression analysis for each core sampling location (column specimen). Fig. 16 Core sampling zones in column and beam specimens. Fig. 19 Variation of carbonation depth between standard specimen and core samples (column specimen). Fig. 17 Results of multiple regression analysis for each core sampling location (beam specimen). on the segregation phenomena (Fig. 15). After curing, test specimens were cored from the structures, and the specific gravity and porosity were measured (Fig. 16). The total number of core specimens was 78. By using a multiple regression analysis, we tried to evaluate an effect of each factor on the segregation. In the multiple regression analysis, the variation of porosity from the standard specimen was given as a dependent variable, whereas experimental parameters related to core sampling location, structural detail, slump values and construction method were defined as independent variables. Analytical results are shown in Figs. 17 and 18. The influences of each factor on the segregation are shown at each location. This means that the non-uniform qualities of concrete can be roughly evaluated if the structural detail, kinds of materials, and construction method are known. Fig. 19 shows the difference of carbonation progress due to non-uniform quality of structural concrete. As shown figure, at upper surface, the depth of carbonation is about 3% more than that of the small-sized 601

12 Materials and Structures/Matériaux et Constructions, Vol. 35, December 00 specimen. Therefore, it is not conservative to evaluate the structural durability performances by the test results of small specimens, unless the non-uniformity of materials is considered in design procedures. 7. CONCLUSIONS The numerical simulation system that can evaluate structural behaviors under coupled forces and environmental actions was proposed in this paper. This system consists of two computational system, that is, one is a thermo-hygro system that covers microscopic phenomena in C-S-H gel and capillary pores, and the other is structural analysis system, which deal with macroscopic stress and deformational field. In thermo-hygro system, generation and transfer of heat, moisture, gas and ions in micropore structures were formulated based on thermodynamics and electrochemistry. Coupling these materials modeling, an early age development process and deterioration phenomenon during the service period can be evaluated for arbitrary materials, curing and environmental conditions in a unified manner. Numerical verifications show that this method can roughly predict ingress of ion, carbonation and corrosion phenomena for different materials, curing and environmental conditions. The macroscopic structural behaviors were linked with both the microphysical phenomenon and external load and restraint conditions. In this paper, the unification of mechanics and thermo-dynamics of materials and structures has been made. Though each component in this system are crudely simplified and further progress and development is still needed for accomplishing entire system, the system dynamics of microscale pore structure formation and macro-scale defects and deformation of structures can be shown as a possible approach in this study. 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