MODELLING OF CHLORIDE TRANSPORT COUPLED WITH MOISTURE MIGRATION IN CONCRETE WITH APPLICATION TO CRACKED CONCRETE STRUCTURES

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1 International RILEM Symposium on Conete Modelling CONMOD May 2008, Delft, The Netherlands MODELLING OF CHLORIDE TRANSPORT COUPLED WITH MOISTURE MIGRATION IN CONCRETE WITH APPLICATION TO CRACKED CONCRETE STRUCTURES Prince O Neill Iqbal (1) and Tetsuya Ishida (2) (1) PhD, Department of Civil Engineering, The University of Tokyo, Japan. (2) Associate Professor, Department of Civil Engineering, The University of Tokyo, Japan Abstract Conete is a wonderful invention of construction industry as a simple manageable composite material, but its perfection of construction is fraught with inhibited disabilities of conete of multifarious nature and extent, thus the ingress of deleterious materials, like chloride is facilitated to troublesome extent. In this research the chloride penetration in conete is modeled under marine environment loadings. The strong sorption flux generated as a result of wetting and drying cyic exposure is modeled by simulating completely saturated environment at the exposed surface. Coupling the moisture conductivity model with chloride transport model then simulates chloride profiles. In reality conete is never ackfree, therefore chloride transport in acked conete is also modeled by introducing large air spaces (void elements) in the acked zone, by introducing a separate chloride diffusion coefficient for ack. Chloride diffusivity along the ack length is enhanced by considering, constrictivity parameter independent of bound chlorides. Numerical verifications were found in good agreement with past experimental studies. 1. INTRODUCTION In this research real time marine environment phases are modeled in laboratory controlled conditions, with a unique approach to simulate completely saturated environment. The environmental modeling for saturated condition has been carried out by applying positive pore pressure at the exposed surface elements and numerical analysis is performed by the direct coupling of the enhanced moisture migration model, with chloride transport model. However, in the real environment, conete structures are not always ack-free, and therefore chloride diffusion model is extended for acked conete. The formation of acks ineases the transport properties of conete so that moisture along with chloride ions and, oxygen, easily penetrate and reach the reinforcing steel and speed up the initiation of steel corrosion in conete. To simulate the chloride movement in the acked path, the chloride diffusion, is separately defined for acked and sound conete.the above models were implemented into a finite-element computational program DuCOM which simulates the early-age development process of cementitious materials. The calculated concentration profiles of total chloride ions are verified through a comparison with experiment results. 455

2 2. DuCOM- A THERMODYNAMIC DURABILITY CONCRETE MODEL In this research DuCOM model is used, which is the durability computation model developed by Conete Laboratory-The University of Tokyo, Japan. The originality of this model comes from the fact that DuCOM is a composite multipurpose model, which predicts the state of the conete from its birth, to its entire life. It comprises several sub-models, which work together and are interlinked. The development of multi-scale mio-pore structures at early age is obtained for average degree of cement hydration in the mixture. For any arbitrary initial and boundary conditions, the vapor pressure in pores, relative humidity (RH), and moisture distribution are mathematically simulated according to a moisture transport model that considers both vapor and liquid phases of mass transport. The moisture distribution, RH, and mio-pore structure characteristics in turn control the Cl -1, CO 2 and O 2 diffusion and rate of carbonation under arbitrary environmental conditions. In this study the chloride transport in sound and acked conete is the primary focal point. [1]. Association map of the whole model is summarized as Fig. 1 1: Cement hydration 2: Mio-pore structure 3: Moisture transport 6: Ion equilibrium 5:CO 2 transport 4: Cl -1 transport 7: O 2 transport 8: Reinforcement corrosion Figure 1 Basic Frame work of DuCom 3. GOVERNING EQUATION FOR CHLORIDE TRANSPORT COUPLED WITH MOISTURE MIGRATION Chloride transport in cementitious materials under usual conditions is an advectivediffusive phenomenon. In modeling, the advective transport due to bulk movement or pore solution phase is considered, as well as ionic diffusion due to concentration gradients. Mass balance for free (moveable) chlorides can be expressed as shown in Eq. 1 [1, 2, 3] ( SC ) + divj Q = 0, t φ (1) Where φ: porosity, S: degree of saturation of porous media, and CCl: concentration of free chlorides in pore solution, and JCl: total flux of chloride ion. The first term in equation (1) represents the rate of change in total amount of chloride ion per unit time and volume, the second term is the flux of chloride ion, and the third term QCl is a sink term. Only capillary and gel pores, which can act as transport paths for chloride ions, are considered (the porosity φ of equation (1) is the sum of the capillary pores and the gel pores). The flux of chloride ions through a porous body, taking both the diffusion and convection, is expressed by Eq. 2 φs J = δd C + φs. u. C (2) Ω Where: J: chloride flux (mol/m2.s), Ω :tortuosity (reduction factor in terms of complex mio-pore structure) δ :constrictivity (a reduction factor due to interaction between pore 456

3 structure and ion transport) D : Diffusion coefficient of chloride ion in the pore solution (m 2 /s), C : concentration of chloride ions in the pore solution phase (mol/l), u T =[ux uy uz]: the velocity vector of ions due to the bulk movement of pore solution phase (m/s), φ : Porosity of the porous media (m 3 /m 3 ).[1] At the boundary level, the surface flux of chloride ions has been modeled taking into account the diffusion and quasi-adsorption flux (Maruya et-al [4].) The second term in Eq. 2 represents the convection transport of chloride ions due to bulk movement of liquid water in the porous media. It is here the chloride transport model and moisture migration model are coupled to simulate the interlinked phenomenon of chloride advection with moisture currents. Therefore the moisture movement into and out of the system directly affects the chloride distribution in the same way as is happening in the real diffusion-convection marine environment. 4. MODELING OF SUBMERGED ENVIRONMENT IN DuCOM Since convection (transport of chloride ions with moisture flow in conete) is one of the major causes of chloride transport in wetting and drying environments, hence in this research, the emphasis is laid on the transport of moisture from the exposed surface towards inner core. For moisture movement dominant in vapour form, the surface mass flux is given by Eq. 3 q s = E b ( h h ) s where, -E b is the emissivity coefficient and a value of is given to the constant. h is the relative humidity of the interior and h s is the relative humidity of the surrounding environment. This equation is valid for the case where moisture transport takes place mainly in vapor form such as exposure to drying or moisture adsorption [5,6]. In the above equation, the environmental relative humidity h s as well as that of the interior can be correlated to the pore pressure head. The relationship between the pore pressure P l and the relative humidity h is desibed by the following Kelvin s equation as. P l ρrt = ln h M where, is the density of liquid, M is the molecular mass of liquid, R is the universal gas constant, T is the absolute temperature. Relative humidity in Eq. 4 h has a domain from 0 to 1.0, i.e., the surrounding humidity value ranges from 0% (completely dry air) to 100% (fully saturated air). As found in the formulation, from a theoretical viewpoint, both these extremes are singularity points for Kelvin s equation. Another important aspect of this equation is that it always gives negative value of pore pressure for any value of relative humidity. In water submerged environment, however, hydraulic pressure acts on the exposed surface, and moisture moves under the positive pore pressure head. This condition cannot be reproduced by Kelvin s equation, even though a value sufficiently ose to 100% is given. In other words, the completely saturated conditions can never be simulated, which always ends up in suction pressure (negative pore pressure). To distinguish the water submerged conditions from un-saturated humid environment, there are two options to define the boundary conditions in the analytical system. For water submergence, positive pore pressure equal to the hydraulic head of water is applied to the exposed surface, whereas for un-saturated environment, the negative pore pressure computed (3) (4) 457

4 by Kelvin s equation (Eq. 4) is used. In the following verifications, submerged environments (completely saturated condition) is reproduced by applying positive pore pressure at the surface node of the elements so that the sorption flux of liquid water can be simulated by more realistic manner. 5. APPLICATION TO ALTERNATE WETTING AND DRYING (MARINE) ENVIRONMENTS Alternate wetting and drying is a typical marine environment. To model moisture migration in marine environment, three weekly alternate wetting and drying cyes are designed in laboratory-controlled environment as (33hr wet in 3days + 33hr in 4days), (9hr wet in 3days + 9hr wet in 4days) and (1hr wet in 3days + 1hr wet in 4days). 5.1 Material and specimen preparation Ordinary Portland cement, regular tap water, coarse sand and a w/c of 50% was provided to all specimens. The mix proportion of cement to sand was kept at 1:2.25. Cement content 580Kg/m 3, water 290Kg/m 3 and sand 1305Kg/m 3 were used. Specimens consist of cylinders 50mm diameter and 100mm height. Curing was done for 28days in sealed condition at 20 o C. After curing, the top 4mm slice from the surface of all the specimens was removed to minimize the surface disturbances. Dry cutting was done for slicing of the specimens. 5.2 Specimen preparation for chloride testing For the determination of chloride profiles, specimens were tested after 1, 7 and 12 months exposure by potentiometer titration technique. In this experiment, slicing method was used for the determination of chloride contents. Thickness of each slice was measured and specimen loss due to the blade thickness of the cutter was accounted for in measuring the depth of each slice from the surface. After this, the slices of respective specimens were grounded and tested for the chloride contents according to the relevant ASTM standard C1152/C1152M-04 (for acid soluble chloride). [7] 5.2 Analytical boundary conditions In the modeling, only one surface was exposed to the environment to simulate the sealed specimen with one face exposed. For the initial curing period the moisture flux in and out of the specimen was restricted, whereas the heat flux was allowed during curing and environment exposure conditions. The submerged wetting cye was modeled by applying saturated pore pressure at the surface element and drying environment corresponds to 60% RH. 5.3 by saturated pore pressure The method of application of saturated pore pressure is applied to model alternate wetting and drying for 33hr, 9hr and 1hr wetting cyes. Fig. 2, 4 and 6 show chloride penetration results for 33hr, 9hr, and 1hr wetting at 20 0 C, 6%NaCl case. Fig.3, 5 and 7 are the corresponding moisture gain and loss results. The experimental and analysis in all the cases are in good agreement. 458

5 Cl % by wt of cemen Cl % by wt of cemen C l % by w t of cemen Experimental results- 20oC-6%-33hr Depth mm Experimental results-20oc-6%-9hr Depth mm Experimental results- 20oC-6%-1hr Exerimental results-1month Experiment results- 7month 1 year exp 1month 7month 1year Experiment results-1month Experiment results- 7month Experiment results- 12month 1month 7month 12month moisture gain/loss gm Moisture gain/loss gm hr wet 20 o C Saturated pore pressure analysis Time hrs Exp Figure 2 Chloride profiles for 33hr wetting Figure 3 Moisture migration for 33hr wetting Figure 4 Chloride profiles for 9hr wetting Depth mm Experiment result-1month Experiment result-7month Experiment result- 12month 1month 7month 12month Moisture gain/loss gm hr wet -20 o C Saturated pore pressure analysis Time hr Exp Figure 5 Moisture migration for 9hr wetting 1hr wet 20 o C Saturated pore pressure analysis Time hrs Experiment Figure 7 Moisture migration for 1hr wetting Figure 6 Chloride profiles for 1hr wetting The analysis results for chloride transport and corresponding moisture migration show strong coupling in the experimental as well as analytical results. An inease in moisture gain and loss significantly amplify the chloride penetration depths and concentration. This is due to the strong convection flux of chloride ions generated by wetting and drying cyes. The physical phenomena of convection transport of chloride ions is early simulated by coupled modeling of chloride transport and moisture migration results. 6 MODELING OF CHLORIDE DIFFUSIVITY IN CRACKED CONCRETE Since real conete structures are never ack-free, therefore in this research, chloride diffusion in acked conete is also modelled. The authors proposed the transport of chloride ions in acked conete by introducing large void spaces [8] in a control volume to represent ack and proposing a model for chloride diffusivity through acked region. 459

6 6.1 Crack modelling by voids The distribution of multi-scale pores inuding acks is represented by the following function. () r = φv () r + φcpvcp () r + φglvgl () r φlr φ + Where, φ is the volume fraction of acks [m 3 /m 3 ], V (r) is a function that specifies the average size of acks, as given by the following equation V () r = 1 exp( B r) Where, B is a porosity distribution parameter for acks [1/m]. Chloride diffusivity in the acked part is formulated as a function of two predominant factors, i.e., volume fraction of acks φ and the parameter B representing ack width. 6.2 Proposed void diffusivity of chloride ions The authors proposed the void diffusivity of chloride ions. To simulate chloride transport through acked conete in a comprehensive way, the diffusivity of chloride ions is formulated separately for hardened conete (sound part) and acks. For saturated condition, the convective term in chloride flux equation 2 is negligible, thus the chloride flux can be formulated as shown in Eq. 6 J φs φ S = δd + ξ δ Ω Ω D C Where, S : degree of saturation of acks, δ cp and δ : constrictivity parameters for cement paste and ack, respectively, Ω cp and Ω : tortuosity parameters for cement paste and ack, respectively. The parameter δ cp and Ω cp in Eq 6 corresponds to δ and Ω in the original Eq 2. When the width of ack is large enough (mm scale), it is assumed that there is no effect of electrical interaction between chloride ions and the ack. As the width of ack deeases, however, such interaction will become dominant, which leads to apparent reduction of diffusive movement of chloride ions. As a first approximation, the relation between δ cp and ack width is given as 4 δ = 0.99 tanh{ r (log( r ) + 5.5)} + 1 On the other hand, tortuosity parameter is assumed to be unity for acks, because acks can be simplified as straight transport path and be not as complex as mio-pore structure of hardened cement paste. In modelling, this enhanced void diffusivity of chloride ions is applied only to the direction of propagation of ack. When D Cl, diffusion coefficient of chloride ion in solution (in free space), was used for acked part, it was found that the apparent movement of chloride ions in acking was much underestimated. This is because mass transport in such bulk spaces is driven not only by concentration gradient, but also by convection current due to even small temperature gradient and/or small hydraulic pressure gradient, which are negligible in the case of mass transport in cementitous materials. To take into account the transport of chloride ions due to these convection currents the diffusion coefficient of the chloride ions in the void is set to a value of fifty times larger than the value in free water by introducing the convection current parameter ζ = 50 as shown in Eq 6. (4) (5) (6) (7) 460

7 6.3 Experimental verification of ack model for chloride diffusivity In this section, verification has been made for the chloride penetration model in acked conete by using experimental data from Pa Pa Win [9]. In this experiment, specimens were prepared as Beam (Prism) specimens of 100 x 100 x 400 mm in size and were reinforced with two 10 mm diameter plain bars for single ack at the tension side. The specimens were sealed in plastic bag for the first 28 days at 20 C. A three point bending test was applied for single ack. Visible ack lengths ranged from 60 to 90 mm. After all preparations, the specimens were kept in the control room of 20 C and RH of 60% waiting for exposure to 8% NaCl solution. The experimental set up was started at 3 months of conete age in the control environment of 20 C and RH of 60% room. The specimens were laid in the NaCl solution trays of specified concentration for exposure time of 7 days and 1 month. The concentration values in this section were calculated as the average of values obtained at 2 mm depth intervals in X-direction on a fixed area of 76 x 76 mm. In the analysis, exposed nodes were restrained at the saturated pore pressure, and the values of ack volume and ack width were provided. Y-axis 0.2mm ack width X-axis Exposed surface (mm) Figure 8 2D chloride profiles for 0.2mm ack-1month Y-axis 0.3mm ack width X-axis Exposed surface (mm) Fig. 10 2D chloride profiles for 0.3mm ack-7days Cl% by cement Cl% by cement mm ack 0.45w/c Experiment Depth from exposed surface mm Figure 9 Average chloride profiles in ack for 0.2mm ack-1month 0.3mm ack- 0.45w/c Experiment Depth from exposed surface mm Fig. 11 Average chloride profiles in ack for 0.3mm ack-7days 461

8 Fig. 8 shows the 2D profile of the chloride penetration along and aoss the ack for 1 month. Fig. 9 shows the average chloride penetration depth along Y-axis (vertical direction) for 1 month exposure periods for the same 0.2 mm ack width. Similarly Fig. 10 and 11 corresponds to 0.3mm ack width. Analytical results are in very good agreement with the experiment for all these cases. 7. CONCLUSIONS In this research a unique approach is adopted to simulate completely saturated conditions in a typical marine environment, for alternate wetting and drying. To model continuous alternate wetting and drying marine environments, analysis was made by taking positive pore pressure as a degree of freedom at the surface element. This kind of analytical approach is highly advantageous for tidal and splash zones. Since conete structures are never ack-free, therefore in this research, an attempt has been made to extend the modeling of chloride transport in acked conete. From 2D chloride penetration profiles along ack, it is ear that chloride transport is very rapid along and aoss the ack boundaries. To treat this phenomenon, the ack was modeled at the mio-scale level by void element methodology, originally proposed for cemented soils. In this research, the chloride diffusivity along the ack length is proposed by considering the effect of chloride transport through the ack with a constrictivity parameter independent of bound chlorides. The analytical results by this method give very good agreement with the experiment. 8. REFERENCES [1] Maekawa K., Ishida T., and Kishi T. Multi-scale Modeling of Conete performance- Integrated Materials and Structural Mechanics, Journal of Advanced Conete Technology, JCI, Vol. 1, No. 2, , pp July 2003 [2] Ishida T., and Maekawa K., An Integrated Computational System for Mass/Energy Generation, Transport, and Mechanics of Materials and Structures, Journal of JSCE, No.627/V-44, August [3] Maekawa K., Chaube R., and Kishi T., Coupled Mass Transport, Hydration and Structure Formation- Theory for Durability Design of Conete Structures, Printed in book, entitled, Integrated Design and Environmental Issues in Conete Technology, edited by K. Sakai, E & FN Spon. [4] Maruya, T., Matsuoka, Y., and Tangtermsirikul, S. Simulation of Chloride Movement in Hardened Conete, Conete Library of JSCE, No.20, pp , 1992 [5] Prince O Neill Iqbal, and Tetsuya Ishida, Chloride Transport in Conete Exposed to Marine Environment, JCI Annual Convention, Vol. 29, No. 1, pp , Sendai, Japan, 2007 [6] Prince O'Neill Iqbal, and Tetsuya Ishida, Modeling of chloride transport in conete coupled with moisture migration in marine environment based on thermodynamic approach. The International Symposium on Social Management Systems, Yichan, China, March [7] ASTM standard designation C1152/C 1152M-04 Standard Test Method for Acid Soluble Chloride in Motor and Conete [8] Nakarai K., Ishida T., and Maekawa K., Multi-Scale Physicochemical Modeling of Soil- Cementitious Material Interaction, Soils and Foundations, Vol. 46, No.5, , October [9] Win Pa Pa, Evaluation of Effect of Crack on Chloride Ions Penetration in Reinforced Conete Structures, PhD Thesis, Graduate School of Science and Engineering, Saitama University, Saitama, Japan, September,