A COMPUTATIONAL METHOD FOR PERFORMANCE EVALUATION OF CEMENTITIOUS MATERIALS AND STRUCTURES

UNDER VARIOUS ENVIRONMENTAL ACTIONS

Tetsuya ISHlDA and Koichi MAEKAWA

ABSTRACT The objective of this study is to establish a computational system that can evaluate structural petformances exposed to various environmentaVweather actions. In this study, equilibriurn, adsorption/desorption, and transport phenomena of gas and ion, and corrosion of reinforcing bars in concrete are formulated based on thermodynamics and electrochemistry. The core of these formulations is based on thermodynamic couplings of moisture transport, powder material hydration and the microstructure formation phenomenon's with very few assumed funciional relationships. Preliminary simulation studies related to chloride transport, carbonation and corrosion show the versatility and extensibility of the proposed schemes.

1. INTRODUCTION

For the sustainable developrnent in the corning century, it is required that infrastructures retain the required performances over the long terrn. In order to construct a durable and reliable structure, it is necessary to evaluate a life cycle cost and its benefit as well as an initial const of construction. On the other hand, for an already deteriorated structure, a rational maintenance and repair should be conducted in accordance with the condition of the structure. Considering these rnatters, it is indispensable to grasp the structural performances under the expected environmental and load conditions during the service life.

In this study, equilibriurn, adsorption/desorption, and transport phenornena of gas and ion, and corrosion of reinforcing bars in concrete are forrnulated based on therrnodynarnics and electrochernistry. These rnaterial rnodels are installed into a therrno-hygro systern narned DuCOM, which originally covered the developrnent of cernentitious rnaterials at early age [Maekawagg]. By the proposed rnodels and their coupling systern, the authors airn to evaluate deterioration phenornena of rnaterials and structures for under long-term environrnental actions.

2. GENERAL OUTLINE OF THERMO-HYGRO SYSTEM

Fig.1 shows an outline of the overall cornputational scherne of therrno-hygro systern DuCOM, which can give the solutions of the material properties frorn birth to death. Developrnent of cernentitious rnaterials at early age is traced by considering the rnutual linkage of hydration, rnoisture transport and pore structure formation. The detailed discussions of these rnaterial rnodeling and their coupling systern are ornitted here, since the details were already presented in other literatures [Maekawagg]. In this study, the authors have extended the siope of this systern in order to cover the deterioration and degradation of cernentitious rnaterials and steel corrosion under long-terrn environrnental actions. For that purpose, concentrations of chloride ion, oxide, and carbon dioxide were added to the therrno-hygro systern as additional degrees of freedorn to be solved. The inputs required in this scherne are rnix proportion, powder rnaterial characteristic, casting ternperature, the geornetry of the target structure, and the boundary conditions to which the structure will be exposed during its life cycle. In analysis, each degree of freedom i (pore pressure, ternperature, concentration of chloride ions, carbon dioxide and oxygen) should satisfy rnass and energy conservation law with sirnultaneous therrno-dynarnic equilibriurn conditions. Potential terrn S(0), flux terrn J(0), and sink terrn Q(0) constituting the governing equations, are forrnulated as a nonlinear function of variables 0; based on thermodynarnic theory. The obtained rnaterial properties are shared through cornrnon variables beyond each sub-systern, therefore interactive problern, such as corrosion due to sirnultaneous attack of chloride ions and carbon dioxide, can be sirnulated in a natural way. Coupling these rnaterials rnodeling, an early age developrnent process and deterioration phenornenon during the service period can be evaluated for arbitrary rnaterials, curing and environrnental conditions in a unified rnanner. In the following sections, the authors will briefly introduce the general ideas of each rnaterial rnodeling and its coupling systern

iWandbomcWy -+diwJ,(û,,~û,)-Q(~,)=o Twics in this DaDer

Fig.1 Framework of DuCOM thermo-hygro physics

3. MODELING OF CHLORIDE ION TRANSPORT

Chloride transport in cementitious materials under usual condition 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 difference of concentration. The mass balance condition for free (movable) ion can be expressed as,

where, $; porosity of the porous media, S; degree of saturation of the porous medium, Co: concentration of ions in the pore solution phase [molll], Jc,; flux vector of the ions [mol/m2.s], ~ = ( d 2 ) ~ accounts for the tortuosity for a 3-D pore network which is uniformly and randomly connected, uT = [u, u,, u,] is the advective velocity of ions due to the bulk movement of pore solution phase [mls]. Material parameters shown in Eq. (l), such as porosity, saturation and advective velocity, are obtained directly by the thermo-hygro physics. Therefore, the flux of chloride ions can be obtained without any empirical equations andlor intentional fittings, once mix proportions, powder materials, curing and environmental conditions are given to the analytical system. Here, it is a well-known fact that chlorides in ce.mentitious materials have free and bound components. The bound components exist in the form of chloro aluminates and adsorbed phase on the pore walls, In this study, the relationship between free and bound components of chlorides under equilibrium conditions are expressed by the empirical formulation proposed by Maruya [Maruya98]. Qo, which accounts for the rate of binding or the change of free chloride to bound chloride per unit volume of concrete, can be obtained by Maruya's model. From the above discussions and formulations, distribution of bounded and free chloride ions can be obtained at arbitrary stage.

4. MODELING OF CARBONATION

For simulating 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,

where, pgco2; density of CO2 gas [kgIrni, pdcy; density of dissolved CO2 in pore water [kglm3], Jmz; total flux of dissolved and gaseous CO2 [kglm .SI. For representing local equilibrium between gaseous and dissolved CO2, we use Henry's law, which states the relationship between the solubility of gas in pore water and the partial pressure of the gas. The transfer of the carbon dioxide is considered in both phases of dissolved and gaseous carbon dioxide. The flux of carbon dioxide can be formulated based on Fick's first law of diffusion, considering the effect of Knudsen diffusion, tortuosity, and connectivity of pores on diffusivity. QCO2 in the above equation is a sink term that represents the rate of CO2 consumption due to carbonation [kglm3.s]. The rate of CO2 consumption can be expressed by the

following differential equation, assuming that the reaction is of the first order with respect to ca2' and ~ 0 3 ~ - concentrations as,

Ca2+ + CO:- + CaCO,

where, Ccac03;concentration of calcium carbonate, k is a reaction rate coefficient. In order to calculate the rate of reaction with Eq. (3), 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.

H20 H H' +OH- c~(oH), ++ ca2+ + 20H- , .. H2C03 H H+ + HC0; w 2H' +CO:- CaCO, w Ca2' +CO:-

(4)

As shown in Eq. (4), carbonation is an acid-base reaction, where cation and anion act as Bronsted acid and base respectively. Furthermore, the solubility of precipitations is dependent on pH in pore solutions. Therefore, in order to calculate the ionic concentration in the pore solutions, the authors formulated an equation with respect to proton [H'], according to the basic principles on ion equilibrium; laws of mass action, mass conservation, and proton balance in the system [lshida99]. Using this equation, the concentration of proton in pore solutions can be calculated at arbitrary stage, once the concentration of calcium hydroxide and that of carbonic acid before dissociation are given.

5. MODELING OF CORROSION IN CONCRETE

In this section, we introduce the general scheme of micro-cell corrosion model based on thermodynamics and electro-chemistry. In Our modeling, it has been assumed that the corrosion would occur uniformly over

Cornputation of Evaluation of the condition _ the surface areas of the reinforcing bars in a finite electric potential -b of the passivity volume, whereas the formation of pits due to localized of corrosion attack of chlorides and the corrosion with macro cell , remains for future study. Fig.2 shows the flow of the output computation of corrosion rate. First of all, electric in pore water

potential of corrosion cell is obtained from the ambient ~h-iount of steel

temperature, pH in pore solution and partial pressure of oxide. which are calculated by other subroutine in the JE'':: Cornputation of the

corrosion rate - system. Next, based on the thermo-dynamical conditions, the condition of passive layers is evaluated Fig.2 Overall scheme of corroçion computation by the Pourbaix diagram, depending upon the 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. When the amount of oxygen supplied to the reaction is not enough, the rate of corrosion would be controlled by the diffusion process of oxygen. In this research, coupling with oxygen transport model, this phenomenon can be simulated. Finally, using the Faraday's law, electric current of corrosion is converted to the rate of steel corrosion. The detailed discussions on the formulations of the oxygen and steel corrosion are omitted for lack of space [lshida99].

Using the proposed method, transport of chloride ion under alternate drying wetting conditions were simulated. For verification, the experimental data by Maruya et al. were used. The size of mortar specimens were 5x5~10 [cm] and the water to powder ratio was 50%. After 28 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 20.. In the FEM analysis, mix proportions and the chemical composition of the cements (&A, C4AF, C3S, CpS, and gypsum) 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.3 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.

nictanre frnm the C I I ~ ~ C P Iml Depth of carbonation[mm]

401 WICSO% WIC60% WlC7OX - --- - - -.

Secondly, computations were performed to predicchIoride [*% Of

Chloride content [wt% of cernent]

Depth of carbonation[mm]

'''1 W/CSO% WlC6OX WIC7OI - - - C02=10% - -- - RH=%%

Cornputation Experirnent -zL?GJi

4.0

Advective transport

5.0

concentrations and water to cement ratio. The amount of Ca(OH)2 existing in cementitious materials can be obtained by multi-component hydration. First, the accelerated carbonation tests were studied. For verification, the experimental data done by Uomoto et al were used [Uomoto93]. Fig.4 shows the comparison of analytical results and empirical formula that was regressed with the square root t equation. 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 CO2 concentration and water to powder ratio. Fig.5 shows the distribution of pH in pore water, CO2, calcium hydroxide, and calcium carbonate inside concrete, exposed to the CO2 concentration of 3%. Two different water to powder ratio, W/C=25% and 50%, were analyzed. It can be shown that higher resistance for the carbonic acid action is achieved in the case of low WIC.

Wetting 7days

CI ion:0.5l[rnol/l] l.O

Diffusion only 0.01 0.02 0.03 0.04 0.05

Distance frorn the surface [rn] 0.01 0.02 0.03 0.04 O.O%te exposea to cyciic wetting ana arying

4.0

After 182days Markers : Test data (Mawya et al.) Lines : Cornputation

Drying 7days

Corrosion of steel in concrete due to sirnultaneous attack of chloride ions and carbon dioxide were

Ca(OH)2 [kglm31 CaC03 [molll] PH CO2 [molll] 160

After 1800days

I

8 ', CO2 After 1800days

7 '~ O 2 4 6 8 10 12

0.00

Distance from the surface [cm] Distance from the surface [cm]

Fig.5 Distribution of pH, calcium hydroxide and calcil lm carhnnate I inder the actinn nf carhnnir: acid

Structural age until cracking due to corrosion [year] 35

sirnulated. One-dirnensional concrete rnernbers c02:3%

that have three different water to powder ratio, 30

WlC=40, 50, 60%, with only one face exposed to ,, the environrnent were considered. In this analysis, the stage where concrete cracking 20 99%RH IOda~s

occurs was defined as a lirnit state with respect l5 to the steel corrosion. The progressive period

until the initiation of longitudinal cracking were IO estirnated by the equation proposed by Yokozeki et al. which is a function of cover depth 5 -

[Yokozeki97]. Fig.6 shows the relationships between cover depth and structural age until

O O 20 40 60 80 100 120

Cover depth [mm] cracking due to corrosion obtained by the proposed therrno-hygro systern. It cari be seen Fig.6 Tirne till first signs of cracking due to corrosion

that the concrete nearer to the exposure surface for concrete exposed to CO2 gas and salty

would show early sign of corrosion induced water

cracking, and low WIC concrete has a higher resistance against corrosion.

7. CONCLUSIONS

Therrno-dynarnical based rnodels for chloride transport, pH fluctuation, ions equilibriurn, transport and equilibriurn of oxide and carbon dioxide, and steel corrosion were presented in this paper. Material pararneters needed in the formulations were obtained by therrno-hygro systern, sirnulating an early age developrnent process. Coupling these rnaterials rnodeling, deterioration phenornenon during the service period can be evaluated for arbitrary rnaterials, curing and environrnental conditions in a unified rnanner. Nurnerical verifications show that this rnethod can roughly predict ingress of ion, carbonation and corrosion phenornena for different rnaterials, curing and environrnental conditions. Through further research and effort for generalization and upgrading of rnaterial rnodels, the authors understand that this frarnework can be served as so-called lifespan simulation in future.

REFERENCES [Maekawa991 Maekawa, K., Chaube, R.P. and Kishi, T. Modeling of Concrete Performance, E&FN SPON, 1999 [Maruya98] Maruya, T., Tangtemsirikul, S. and Matsuoka, Y. Modeling of chloride ion rnovernent in the surface layer of hardened concrete, Concrete Library of JSCE, No.32, pp.69-84, 1998 [Freiser63] Freiser, H. and Fernando, Q. lonic equilibria in analytical chemistry, John Wiley and Sons, Inc., 1963 [Uornoto93] Uornoto, T. and Takada, Y. Factors affecting concrete carbonation and prediction of carbonation process of concrete, Concrete Library of JSCE, No.21, pp.31-44, 1991 [Yoikozeki97] Yokozeki, K., Motohashi, K., Okada, K. and Tsutsurni, T. A rational rnodel to predict the service life of RC structures in marine environment, Forth CANMETIACI International Conference on Durability of Concrete, SP 170-40, pp.777-798, 1997 [Ishida99] Ishida, T. An integrated computational systern of masslenergy generation, transport and rnechanics of rnaterials and structures, PhD thesis submitted to University of Tokyo, 1999