SERVICE-LIFE EVALUATION OF REINFORCED CONCRETE UNDER COUPLED FORCES AND ENVIRONMENTAL ACTIONS

Transcription

1 SERVICE-LIFE EVALUATION OF REINFORCED CONCRETE UNDER COUPLED FORCES AND ENVIRONMENTAL ACTIONS Koichi MAEKAWA nd Tetsuy ISHIDA University of Tokyo 7-- Hongo, Bunkyo-ku, Tokyo, Jpn ABSTRACT The uthors propose so-clled life-spn simultor tht cn predict concrete structurl behviors under rbitrry externl forces nd environmentl conditions. In order to relize this kind of technology, two computtionl systems hve been developed; one is thermo-hygro system tht covers microscopic phenomen in C-S-H gel nd cpillry pores, nd the other is structurl nlysis system, which del with mcroscopic stress nd deformtionl field. In this pper, the unifiction of mechnics nd thermo-dynmics of mterils nd structures hs been mde with the ion trnsport of chloride, CO nd O dissolution. This proposed integrted system cn be used for the simultneous overll evlution of structurl nd mteril performnces without distinguishing between structure nd durbility. INTRODUCTION For sustinble development in the coming century, it is necessry tht the infrstructures retin their required performnces over the long term. In order to construct durble nd relible structure, it is necessry to evlute the life cycle cost nd its benefits s well s the initil cost of construction. On the other hnd, for n lredy deteriorted structure, rtionl mintennce nd repir pln should be implemented in ccordnce with the condition of the structure. Considering these points, it is therefore indispensble to grsp the structurl performnces under the expected environmentl nd lod conditions during the service life. The objective of our reserch is to develop so-clled lifespn simultor tht enbles us to predict the structurl behvior for rbitrry conditions. Fig. shows the schemtic representtion of the lifespn simultor of mteril science nd mechnics of structures. Our reserch group hs been developing two numericl simultion tools. One is thermo-hygro system nmed DuCOM [, which covers the micro-scle phenomen governed by thermodynmics. This computtionl system is cpble of evluting the erly ge development of cementitious mterils nd deteriortion processes of hydrted products under long-term environmentl ctions. In the following section, the overll scheme of this system nd ech mteril modeling will be introduced. The other one is nonliner pth-dependent structurl nlyticl system nmed COM [[. For rbitrry mechnicl ctions including temperture nd shrinkge effect, the structurl response s well s mechnicl sttes of constituent elements cn be predicted. The solidifiction model of hrdening concrete composite hs been lso instlled in this system for

2 Environmentl Actions Drying-wetting. Wind. Sunlight. ions/slts etc. Scle [m Output: Hydrtion degree, Microstructure, Distributions of Moisture /Slt /Oxygen /CO, ph in pore wter, corrosion rte etc. Thermo-hygro system Stte lws Mss/energy blnce - Hydrtion strts 4 Het. Initil defects Oxidtion, Crbontion, deteriortion Time (Dys) Unified evlution Scle - [m Mcroscopic crcking Output: Stress, Strin, Accelertions, Degree of dmge, Plsticity, Crck density etc. Mechnicl Actions Ground ccelertion Grvity Temperture nd shrinkge effects Fig. Lifespn simultion for mterils nd structures Continuum Mechnics Deformtionl comptibility Momentum conservtion predicting time-dependent behvior depending on the temperture, moisture profile, nd micropore structure of mterils [4. It hs to be lso noted tht the structurl deformtion nd cpcity re relly linked with both micro-pore bsed deteriortion nd lrge-scle mechnicl defects represented by crcking, yielding nd dmging of mterils with respect to control volume. In turn, the progress in mcro-scle mteril dmge nd defects re lso dependent on both the structurl deformtion nd environmentl boundry conditions. Here, nonlinerly ccelerted chnge of mteril nd structurl performnces tkes plce simultneously. For exmple, corrosion nd ssocited volume expnsion induces dditionl crcks nd defects which lso ccelerte the migrtion of moisture nd ions. In this pper, the unifiction of mechnics nd thermo-dynmics of mterils nd structures will be tckled for showing the possibility nd future direction of reserch nd development. The uthors understnd tht the unified pproch of mechnics which governs stress nd strin fields nd thermo-hygro physics ruling mss nd energy trnsport ssocited with thermo-dynmic stte equilibrium would serve s techniclity of ensuring totl performnces of concrete structures s well s structurl concrete performnce over the life spn of concrete structures. THERMO-HYGRO PHYSICS FOR CONCRETE PERFORMANCE --DuCOM -- The development of young ged concrete is intimtely ssocited with the thermodynmic processes, such s hydrtion of powders, moisture trnsport nd micro structure development, which show dynmic progress from - to [dys. It hs to be noted tht these phenomen exhibit strong mutul link. For exmple, the development of micro structures cn be chieved by the precipittion of hydrted products, nd the moisture profile in cementitious mterils influences the rte of hydrtion. Furthermore, properties of pore structure determine the moisture conductivity. Our reserch group hs been developing D finite element nlysis progrm,

3 C C SG C C4AF FA CA CS CS dsorption of Sp C SiO 4 4 C slt with Sp C C γ Sp C Hydrtion Het Rte Time Consumption of C ion Delying of C(OH) nucletion E i H i = γ βi λ µ si H i, T ( Qi ) exp R T T Fig. Modeling of the hydrtion of cement nd pozzolns gel Liquid trnsport Vpor trnsport Knudsen fctor History dependent liquid viscosity MOISTURE CONDUCTIVITY Liquid vpor Computed from pore structure directly Rndom pore model PORE STRUCTURE DEVELOPMENT Bsed on cement prticle expnsion Growth dependent on the verge degree of hydrtion Prticle growth Si P f i b r f i - div( K P) r Si - Wp = Ł P ł t t t MOISTURECAPACITY Obtined from the pore structures (B.E.T theory) Hysteresis isotherm model considering inkbottle effect sturtion RH slope MOISTURE LOSS DUE TO HYDRATION Obtined directly from hydrtion model. Bsed on rection pttern of ech clinker component Cement composition dependent Fig. Schemtic representtion of moisture trnsport modeling in concrete llowing to simulte these interctive processes (Fig.) [[5. This section simply summrizes the overll schemes nd the core points, since the detils were lredy resented in other litertures. The hydrtion of both constituent minerls of cement nd pozzolns is trced by simultneous differentil equtions bsed on the Arrhenius lw of chemicl rection [6[7. The rte of hydrtion is mthemticlly specified in terms of temperture, free wter content in cpillry pores, degree of hydrtion nd ssocited cluster thickness of C-S-H gel lyers precipitted round non-rected cement prticles (Fig.). Then, the chemicl process nd its

4 Next Itertion Hydrtion Degree of Mtrix The prticle growth Volume nd weight of inter nd outer products inner product unhydrted core Bulk porosity of Cpillries, gel nd interlyer. porosi ty. outer product Totl surfce re (/m ) Cpillries, gel, nd interlyer r ro prticle rdius dr Outer products density t r ρ ρ ( φ ) δ m δ mx = ζ r r r Representtive Men CSH grin seprtion Mtrix micro pore structure START Increment time, continue yes no Size, shpe, mix proportions, initil nd boundry conditions Conservtion lws stisfied? Fig.4 Outline of the pore structure development computtion Hydrtion computtion Temperture, hydrtion level of ech component Corrosion model Corrosion rte, mount of O consumption Governing equtions Microstructure computtion Bi-modl porosity distribution, interlyer porosity Crbon dioxide trnsport nd equilibrium Gs nd dissolved O concentrtion S t Pore pressure computtion Ion equilibrium model Fig.5 Frmework of DuCOM thermo-hygro physics Chloride trnsport nd equilibrium interction mong minerls nd dditive pozzolns re considered by shring common vribles ssocited with pore solution, wter nd temperture. During the hydrtion process, mss nd het energy conservtions hve to be stisfied with respect to moisture nd temperture. At the sme time, moisture migrtion in terms of vpor nd liquid wter nd het flux re incorported in the conservtion conditions of the second lw of thermo-dynmics. The equilibrium conditions re simultneously to be solved together, nd the mss nd energy trnsport resistnce denoted by permebility nd conductivity hs to be formulted. The permebility of vpor nd liquid wter is mthemticlly formulted bsed on the micro-pore size distribution s demonstrted in Fig. [8[9. The pth of moisture in cement pste is thought to be ssembly of smll sized fictitious pipes nd its integrtion results in the mcroscopic permebility. Tortuosity on percoltion nd the thermo-dynmic ctivtion of surfce energy onto the micro-scle viscosity of pore wter re tken into ccount. It is to be noted tht the simple micro-mechnicl modeling is pplied without ny vrible fitting. As nturl wy, the pore structure formtion model, s illustrted in Fig.4, is dded in the system dynmics of trnsient concrete performnce modeling [. The sttisticl pproch to the ( θ ) i divj Pore pressures, RH nd moisture distribution ph in pore wter i ( θ, θ ) Q ( θ ) = i i i i Dissolved nd bound chloride concentrtion Crbon dioxide trnsport nd equilibrium Gs nd dissolved CO concentrtion

5 micro pore structurl geometry of hrdened cement pste hving interlyer, C-S-H gel nd cpillry pores is used. The porosity distribution of hydrted nd non-hydrted compounds round referentil cement prticles is clculted nd the surfce re of micro-pores is estimted mthemticlly. By ssuming sttisticl distribution function with regrd to the pore sizes, the uthors extend the geometricl description of micro pores. The connective mode of ech pore volume is lso defined with simple probbility on the bsis of which the pth-dependency of isotherm of moisture is successfully described [. Recently, in ddition to the bove modeling relted to erly ge development phenomenon, the uthors hve been extending the scope of DuCOM in order to cover the deteriortion nd resolution of cementitious mterils nd steel corrosion. Here, concentrtions of chloride ion, oxide, nd crbon dioxide were dded to the thermo-hygro system, s dditionl degrees of freedom to be solved (Fig.5). Ech physicl vrible should stisfy the lw of mss conservtion shown in Fig.5, sme s the story in terms of the temperture nd moisture profile computtion in the previous discussions. Potentil term S(θ), flux term J(θ), nd sink term Q(θ) constituting the governing equtions, re formulted s nonliner function of vribles θ i bsed on thermodynmic theory. The obtined mteril properties re shred through common vribles beyond ech sub-system, therefore interctive problem, such s corrosion due to simultneous ttck of chloride ions nd crbon dioxide, cn be simulted in nturl wy. Coupling these mterils modeling, n erly ge development process nd deteriortion phenomenon during the service period cn be evluted for rbitrry mterils, curing nd environmentl conditions in unified mnner. In the following sections, the uthors will introduce the generl ides of ech mteril modeling nd its coupling system. Formultion of Chloride Ion Trnsport It is well-known fct tht chlorides in cementitious mterils hve free nd bound components. The bound components exist in the form of chloro lumintes nd dsorbed phse on the pore wlls, mking them unvilble for free trnsport. It hs been reported tht the mount of bounded chlorides would be dependent on the binders, electric potentil of pore wll, nd ph in pore solutions. However, their exct mechnisms re still not cler. In this pper, the free nd bound components of chlorides under equilibrium conditions re tenttively expressed by the following empiricl equtions proposed by Mruy et l. s [, C. α fixed =.5.54 ( C.) tot.5 tot. C tot. C. tot () where, C tot ; totl mount of chloride [wt% of cement (=C free C bound, mount of free chloride nd bound chloride, respectively), α fixed = C free C bound ; equilibrium rtio of fixed chloride component to the totl chloride ion component. Considering the dvective trnsport due to the bulk movement of pore solution phse s well s the ionic diffusion due to concentrtion difference, the flux of free chlorides in pore wter cn be expressed s,

6 φs K P J Cl = DCl CCl φsuccl u = () Ω ρφs where, J Cl T = [J x J y J z ; flux vector of the ions [mol/m.s, φ; porosity of the porous medi, S; degree of sturtion of the porous medium, D Cl ; diffusion coefficient of the chloride ions in pore solution phse [m /s, Ω=(π/) ccounts for the verge tortuosity of single pore s fictitious pipe for mss trnsfer, nd this prmeter considers the tortuosity of hrdened cement pste mtrix, which is uniformly nd rndomly connected in -D system [[9, T = [ / x / y / z : the grdient opertor, C Cl : concentrtion of ions in the pore solution phse [mol/l, ρ : density of wter, nd u T = [u x u y u z is the dvective velocity of ions due to the bulk movement of pore solution phse [m/s. The dvective velocity u is directly obtined from the pore pressure grdient P nd moisture conductivity K, which depends on wter content, micro pore structures, nd moisture history s shown in Fig.. In the cse of chloride ion trnsport in concrete, S represents the degree of sturtion in terms of the free wter only, s dsorbed nd interlyer components of wter re lso present. Here, it hs to be noted tht diffusion coefficient D Cl would be function of ion concentrtion, since ionic interction effects will be significnt in the fine micro structures t incresed concentrtions, thereby reducing the pprent diffusive movement driven by the grdient of ion concentrtion [. This mechnism, however, is not clerly understood, therefore we neglect the dependency of the ionic concentrtion on the diffusion process in the modeling. From the severl numericl sensitivity nlysis, constnt vlue of. - [m /s is given for D Cl. The first term on the right-hnd side of Eq. () expresses the diffusion of ions, wheres the second term describes the dvective trnsport due to the bulk movement of condensed pore wter. The dvective velocity of free chloride ions might be lso dependent on the ion concentrtion, similrly to the diffusion coefficient. In this pper, however, we ssumed tht the velocity vector of ions would be equl to tht of pore liquid wter, since there is not enough experimentl dt to estblish model for this spect. Mteril prmeters shown in the Eq.(), such s porosity, sturtion nd dvective velocity, re obtined directly by the thermo-hygro physics. Therefore, the flux of chloride ions cn be obtined without ny empiricl equtions nd/or intentionl fittings, once mix proportions, powder mterils, curing nd environmentl conditions re given to the nlyticl system. Sme story cn be pplied for other modeling, sy, formultion of CO nd O trnsport, steel corrosion nd ion equilibrium. The mss blnce condition for free chloride cn be expressed s, t ( φsc ) divj Q = cl Cl Cl () where, Q Cl ; the rte of binding or the chnge of free chloride to bound chloride per unit volume of concrete [mol/m.s, which cn be computed by ssuming locl equilibrium conditions shown in the eq.(). From the bove discussions nd formultions, distribution of bounded nd free chloride ions cn be obtined t rbitrry stge. Modeling of Crbontion For simulting crbontion phenomen in concrete, equilibrium of gs nd dissolved crbon

7 dioxide, their trnsport, ionic equilibriums, nd crbontion rection process re formulted bsed on thermodynmics nd chemicl equilibrium theory. Mss blnce condition for dissolved nd gseous crbon dioxide in porous medium cn be expressed s, { φ[ t ( S) ρ S ρ } divj Q = gco dco CO CO (4) where, ρ gco ; density of CO gs [kg/m, ρ dco ; density of dissolved CO in pore wter [kg/m, J CO ; totl flux of dissolved nd gseous CO [kg/m.s, Q CO ; sink term tht represents the rte of CO consumption due to crbontion [kg/m.s. For representing locl equilibrium between gseous nd dissolved CO, we use Henry s lw, which sttes the reltionship between the solubility of gs in pore wter nd the prtil pressure of the gs [. The trnsfer of the crbon dioxide is considered in both phses of dissolved nd gseous crbon dioxide. The flux of crbon dioxide cn be formulted bsed on Fick s first lw of diffusion. However, fctors such s complicted pore network, Knudsen diffusion etc, reduce the pprent diffusivity of crbon dioxide. Considering the effect of Knudsen diffusion, tortuosity, nd connectivity of pores on diffusivity, the flux of CO J CO cn be expressed s, J CO = d c g φd φ D ( DdCO ρdco DgCO ρgco ) DdCO = dv DgCO = Ω r Ω rc dv N where, D gco ; diffusion coefficient of gseous CO in porous medium[m /s, D dco ; diffusion coefficient of dissolved CO in porous medium[m /s, D g ; diffusivity of CO gs in free tmosphere[m /s, D d ; diffusivity of dissolved CO in pore wter [m /s, V; pore volume, r c ; pore rdius in which the equilibrted interfce of liquid nd vpor is creted, which is determined by thermodynmic conditions, N k ; Knudsen number, which is the rtio of the men free pth length of molecule of CO gs to the pore dimeter. Knudsen effect on the gseous CO trnsport is not negligible in low RH condition, since porous medium for gs trnsport becomes finer s reltive humidity decreses. As shown in eq.(5), diffusion coefficient D dco is obtined by integrting the diffusivity of sturted pores over the entire porosity distribution, wheres D dco is obtined by summing up the diffusivity of gseous CO through unsturted pores. The crbontion rection in cementitious mterils is simply described by the following chemicl rection. C CO - CCO The clcium ion decomposed from the dissolution of clcium hydroxide is ssumed to rect with crbonte ion, wheres the rection of silicic cid clcium hydrte (C-S-H) is not considered, since its solubility is quite low compred with clcium hydroxide. The rte of the rection cn be expressed by the following differentil eqution, ssuming tht the rection is of the first order with respect to C nd CO - concentrtions s, ( C ) CCO Q CO = = k[c [CO (7) t where, C CCO ; concentrtion of clcium crbonte, k is rection rte coefficient, which shows the temperture dependence. In the current stge, we focus on the crbontion phenomenon under k (5) (6)

8 constnt temperture, nd coefficient k is ssumed to be constnt (k=.8 [l/mol.sec) determined from severl sensitivity nlyses. The uthors understnd tht the formultion bsed on the Arrhenius lw of chemicl rection should be considered for more generic tretment. In order to clculte the rte of rection with eq.(7), it is necessry to obtin the concentrtion of clcium ion nd crbonic cid in the pore wter t rbitrry stge. In this study, we consider the following ion equilibriums; the dissocition of wter nd crbonic cid, nd the dissolution nd the dissocition of clcium hydroxide nd clcium crbonte. Here, the presence of chlorides is not considered, lthough we understnd tht chloride ions re likely to ffect the equilibrium conditions. The formultion including chlorides remins for future study. H O H OH C( OH) H CO H HCO H CO CCO C C OH CO - (8) Although the hydronium ion H O is present in wter nd confers cidic properties upon queous solutions, it is customry to use the symbol H in plce of H O. As shown in eq.(8), crbontion is n cid-bse rection, where ction nd nion ct s Brönsted cid nd bse respectively. Furthermore, the solubility of precipittions is dependent on ph in pore solutions. Therefore, ccording to the bsic principles on ion equilibrium, the uthors im to formulte the crbonte rection in concrete [4. First of ll, let us consider the equilibrium rection of crbonic cid. From the lw of mss ction, the corresponding equilibrium expression is, K w = [H [OH [H [HCO [H [CO K = K b = (9) [H CO [HCO where, K i is the equilibrium constnt of concentrtion for ech dissocition, we give these vlues s, K w =. -4, K =. -4, K b = t 5 respectively [. Next, the mss conservtion lw is pplied for the ions from dissolution of crbon dioxide nd re-dissolution of clcium crbonte. - - [ H CO [ HCO [ S = CO C () where, C is the concentrtion of dissolved crbon dioxide [mol/l, which cn be obtined from ρ dco in eq.(4). S is the solubility of clcium crbonte, which cn be clculted by the solubility-product constnt. Using eq.(9) nd (), concentrtions of H CO, HCO - nd CO - cn be obtined s, [H CO = α [HCO [CO - - = α = α ( C S ) ( C S ) ( C S ) α α = [H α = [H = [H K K K [H K K [H K K [H K b [H K K b [H K K b b () The solubility of clcium crbonte cn be obtined by the following reltionship s,

9 K = [C [CO () sp where, K sp is the solubility-product constnt of the clcium crbonte (=4.7-9, t 5 ). Similrly, the solubility of clcium hydroxide cn be clculted s, - K sp = [C [OH () where, K sp is the solubility-product constnt of the clcium hydroxide (=5.5-6, t 5 ) [. Considering the common ion effect on the ech solubility, eq. () nd eq. () cn be replced with the solubility of clcium crbonte S nd tht of clcium hydroxide S s, - ( S S ) α ( C S ) K = ( S ) [ OH K sp = sp S (4) From the mss conservtion conditions, concentrtion of ions should stisfy the following reltionships. - d d - C = [H CO [HCO [CO (5) S - - = [H CO s [HCO s [CO s = [C s c d S = [C (6) where, [i d, [i s, nd [i c re the concentrtion of ion from the dissolution of CO gs, clcium crbonte nd clcium hydroxide, respectively. For exmple, the totl concentrtion of crbonic cid [H CO shown in eq. (9) becomes the summtion of [H CO d from CO gs nd [H CO s from CCO. In ddition, the bove ions should stisfy the lw of proton blnce, in which the mount of donor is equl to tht of ccepter in terms of proton in the Brönsted-Lowry theory. The eqution deduced by the lw of proton blnce is obtined s, [H [C - - c [H CO s [HCO s = [OH [HCO c [CO c From the bove equtions describing the conditions of ion equilibrium, finlly we obtin s, [ H αc [ H S w α C Sα Sα = K (7) (8) Using eq.(8), the concentrtion of proton in pore solutions cn be clculted t rbitrry stge, once the concentrtion of clcium hydroxide nd tht of crbonic cid before dissocition re given. It hs been reported tht micro-pore structure in cementitious mterils would be chnged due to crbontion. In this pper, the uthors use n empiricl set of equtions tht re proposed by Seki et l. s [5, φ = φ φ = ( R ).5 φ C(OH).6 < R R C(OH) C(OH) <..6 where, φ ; porosity fter crbontion, R C(OH) ; the rtio of the mount of consumed C(OH) for the totl mount of C(OH). (9) Micro-Cell Bsed Corrosion Model

10 Temperture ph in pore solution Prtil pressure of O ph in pore solution Concentrtion of Cl - ions [V E O Logi of O Computtion of electric potentil of corrosion cell Evlution of the condition of the pssivity logi corr Output Amount of steel corrosion Amount of consumed O Amount of dissolved O in pore wter Temperture Computtion of the corrosion rte E Fe E corr Logi of Fe.RT αzf Tfel grdient logi log i c Fig.6 Overll scheme of corrosion computtion Fig.7 The reltionship between electric current nd voltge for node nd cthode In this section, we introduce the generl scheme of micro-cell corrosion model bsed on thermodynmics nd electro-chemistry. In our modeling, it hs been ssumed tht the steel corrosion would occur uniformly over the surfce res of the reinforcing brs in finite volume, wheres the formtion of pits due to loclized ttck of chlorides nd the corrosion with mcro cell remins for future study. For mking it possible to tret the formtion of mcro cell, we understnd tht it is necessry to consider mgneto-electricl field governed by Mxwell s principle s well s the mss, momentum nd energy conservtions. Fig.6 shows the flow of the computtion of corrosion rte. When we consider the micro-cell bsed corrosion, it cn be ssumed tht the re of node is equl to tht of cthode nd they re not seprted from ech other. Therefore, we do not tret the electricl conductivity of concrete, which governs the mcroscopic trnsfer of ions in pore wter. First of ll, electric potentil of corrosion cell is obtined from the mbient temperture, ph in pore solution nd prtil pressure of oxide, which re clculted by other subroutine in the system. The potentil of hlf-cell cn be expressed with the Nernst eqution s [6, Fe E - ( s) Fe ( q) e ( Pt) O ( g) H O( l) 4e( Pt) = 4OH ( q) Fe = E Θ Fe ( RT z F) ln h Fe Fe E O Θ ( RT z F ) ln( P P ).6pH () Θ = E where, E Fe ; stndrd cell potentil of Fe, node (V, SHE), E O ; stndrd cell potentil of O, cthode (V, SHE), E Θ Fe; stndrd cell potentil of Fe t 5 (=-.44V,SHE), E Θ O; stndrd cell potentil of O t 5 (=.4V,SHE), z Fe ; the number of chrge of Fe ions (=), z O ; the number of chrge of O (=), P Θ ; tmospheric pressure. Strictly speking, the solution of other ions in pore wter might ffect the electric potentil of cell. However, it is difficult to consider the effect of ion solutions on the hlf-cell potentils, therefore we dopt the bove equtions, ssuming the idel conditions. Next, bsed on the thermo-dynmicl conditions, the condition of pssive lyers is evluted by the Pourbix digrm, which shows tht there re conditions where steel corrodes, res where protective oxides form, nd n re of immunity to corrosion depending upon the ph nd the potentil of the steel. From the electric potentil nd the formtion of pssive lyers, electric current tht involves chemicl rection cn be clculted so tht conservtion lw of electric O O O

11 chrge should be stisfied in locl re (Fig.7). The reltionship between electric current nd voltge for node nd cthode cn be expressed by the following Nernst eqution s, c (. RT.5 z F ) log ( i i ) η = (. RT.5 z F ) log ( i i ) η = Fe O c () where, η ; overvoltge t node [V, η c ; overvoltge t cthode [V, F; Frdy s constnt, i ; electric current density t node [A/m, i c ; electric current density t cthode [A/m. Corrosion current I corr cn be obtined s the point of intersection of two lines. The existence of pssive lyer reduces the corrosion progress. In this model, this phenomen is described by chnging the Tfel grdient. When the mount of oxygen supplied to the rection is not enough, the rte of corrosion would be controlled by the diffusion process of oxygen. In this pper, coupling with oxygen trnsport model, this phenomenon cn be simulted. The detiled discussion on the formultions of the oxygen is omitted for lck of spce, since they re lmost sme s those of crbon dioxide [7. Finlly, using the Frdy s lw, electric current of corrosion is converted to the rte of steel corrosion. It hs to be noted tht these models re only derived from the thermodynmics nd electrochemistry, nd the uthors understnd tht further development nd improvement re still needed thorough vrious verifiction of corrosion phenomen in rel concrete structures. CONTINUUM MECHANICS OF MATERIALS AND STRUCTURES -- COM -- For simulting structurl behviors Service Strts Time (dys) expressed by displcement, deformtion, stresses nd mcro-defects of mterils in view of continuum plsticity, frcturing nd Externl Environment (wether) Lods crcking, well estblished continuum effects mechnics cn be used s illustrted in Fig.8. The comptibility condition, equilibrium nd constitutive modeling of mteril mechnics re the bsis nd the sptil verging of -6 overll defects in control volume of finite -,- Mcro Crcks Reinforcements element is incorported into the constitutive Stress Crck Tension model of qusi-continuum. The uthors Strin dopted D finite element computer code nmed COM for structurl dynmics, Stress of steel Yield which hs been lso developed t the Comp. University of Tokyo for sttic s well s dynmic ultimte limit sttes [[. Strin of steel This frme of structurl mechnics hs n inter-link with thermo-hygro physics in Sher stress trnsfer terms of mechnicl performnces of cross crck mterils through the constitutive modeling in both spce nd time. In this study, the Fig.8 Mcro-scle defects nd micro-scle pore structures instntneous stiffness, short-term strengths

12 of concrete in tension nd compression, free volumetric contrction rooted in coupled wter loss nd self-desicction cused by vrying pore sizes re considered in the creep constitutive modeling of liner convolution integrl (Fig.8). The volumetric chnge provoked by the hydrtion in progress nd wter loss is physiclly tied with surfce tension force developing inside the micro-cpillry pores. Of course, the micro-pore size distribution nd moisture blnce of thermo-dynmic equilibrium re given from the code DuCOM t ech time step. The crcking is the most importnt dmge index ssocited with mss trnsport inside the trgeted structures. Crcks re ssumed to be induced norml to the mximum principl stress direction in D extent when the tensile principl stress exceeds the tensile strength of concrete. As stted before, the strength is numericlly evluted from the degree of micro structurl formtion. In relity, the explicit reltion of the specific strength nd formed porosity with intrinsic sizes is dopted in this study. After crck initition, the tension softening on progressive crck plnes is tken into ccount in the form of frcture mechnics. In the reinforced concrete zone, in which bond stress trnsfer is expected being effective, the tension stiffness model is brought together. Since the externl lod level, with which the environmentl ction be coupled in design, is rther lower thn the ultimte limit sttes, compression induced dmge ccompnying dispersed micro-crcking is disregrded in this study. UNIFICATION OF THERMO-PHYSICS OF MATERIALS AND MECHANICS OF STRUCTURES For numericl evlution of the totl structurl nd mteril performnces, we propose the dul prllel processing of coupling two sub-systems shown in Fig. 9 [7. This system cn be embodied on the multitsk opertion system. In this frmework, constituent sub-systems, which hve different schemes to solve the different governing equtions, don t need to be combined into single process. The opertion system mnges the job of ech system, nd two sub-systems re connected by high-speed signl bus or networks so s to mutully shre the common dt informtion. First, mteril properties re clculted by DuCOM. After one step of execution, clculted results, such s temperture, wter content, pore pressure, pore structure, stiffness, nd strength, re stored in the common dt re. After tht, signl is sent to the sleeping process (COM) to DuCOM Initil nd boundry conditions Clcultion Stndby strt execution. COM tht becomes ctive reds the informtion from the common dt re nd performs the stress computtion. In this nlysis, the dmge level of RC member is obtined, nd clculted results re written in the common re fter its execution. These steps re continued till Write Red Clcultion considering crck dmge Common storge re Strength,stiffness, temperture,wter content,nd pore pressure,etc.. Degree of dmge Repet until finl step COM Shpe, size restrint condition Stndby Red Clcultion considering different properties Write Stndby Fig. 9 Prllel processing of DuCOM nd COM

13 Chloride content [wt% of cement 5. After 8 Mrkers : Test dt (Mruy et l.) Lines : Computtion 4. Drying 7dys... Totl chloride Free chloride Wetting 7dys Cl ion:.5[mol/l Diffusion only Distnce from the surfce [m Chloride content [wt% of cement 5. After 8dys Mrkers : Test dt (Mruy et l.) Lines : Computtion Totl chloride Free chloride Drying 7dys Wetting 7dys Cl ion:.5[mol/l Diffusion only Distnce from the surfce [m Chloride content [wt% of cement 5. After 8 Mrkers : Test dt (Mruy et l.) Lines : Computtion 4. Diffusion Advective trnsport... Totl chloride Free chloride Drying 7dys Wetting 7dys Cl ion:.5[mol/l Distnce from the surfce [m Chloride content [wt% of cement 5. After 8dys Mrkers : Test dt (Mruy et l.) Lines : Computtion 4. Diffusion Advective trnsport... Totl chloride Free chloride Drying 7dys Wetting 7dys Cl ion:.5[mol/l Distnce from the surfce [m Fig. Chloride content profile in concrete exposed to cyclic wetting nd drying one of the processes completes its computtion. Following these procedures, ech FE progrm cn shre the computtionl results between two systems t ech guss point in ech finite element. The chief dvntge of unifying mteril nd structurl nlysis in this mnner is numericl stbility of explicit scheme. Furthermore, this coupling method under multi-tsk opertion enbles engineers to esily link independently developed computer codes even if being written by different computer lnguges nd lgorithms. As mtter of fct, slight modifiction for dt exchnge with the common memory spce through high-speed bus is needed with short system mnger progrm lone. NUMERICAL SIMULATIONS Chloride Trnsport into Concrete Under Cyclic Drying-Wetting Condition Using the proposed method, trnsport of chloride ion under lternte drying wetting conditions were simulted. It hs been confirmed in the pst reserch tht the concentrtion of chloride ner the surfce lyer is higher thn tht of the solution when concrete specimen is submerged in it. This phenomenon cnnot be explined by the diffusion theory lone. In order to consider this behvior, we use the ion dsorption model in the surfce lyer proposed by Mruy et l. This model expresses the flux of chloride ions driven by the grdient of electricl force; the positive chrge t the pore surfce drws chloride ions tht hve negtive electric chrges.

14 Depth of crbontion[mm 4 W/C5% W/C6% W/C7% CO=% RH=55% Computtion Experiment [9 Mrkers Lines 4 Time[Dys Depth of crbontion[mm W/C5% W/C6% W/C7% Computtion CO=% RH=55% Experiment [9 Mrkers Lines 4 Time[dys 5 5 Fig. Crbontion phenomen for different CO concentrtions nd W/C Depth of crbontion[mm Computtion Experiment Mrkers Lines RH :8% CO:% W/C65% W/C55% Time[dys Depth of crbontion[mm Computtion Experiment Mrkers Lines 5 5 RH :5% CO:% Time[dys Fig. Crbontion phenomen for different CO concentrtions nd W/C For verifiction, the experimentl dt by Mruy et l. were used [. The size of mortr specimens were 5 5 [cm nd the wter to powder rtio ws 5%. After 8 dys of seled curing, the specimens were exposed to cyclic lternte drying (7 dys) nd wetting (7 dys) cycles. The drying condition ws 6%RH, wheres the wetting ws exposed to chloride solution of.5 [mol/l t. In the FEM nlysis, mix proportions nd the chemicl composition of the cements (C A, C 4 AF, C S, C S, nd gypsum) were given. The curing conditions nd exposure conditions were lso given s boundry conditions for the trget structures. All of these input vlues corresponded to the experimentl conditions. Fig. shows the distribution of free nd bound chlorides from the boundry surfce. For comprison, we nlyzed two cses; one considering only diffusive movement nd the other including the dvective trnsport due to the bulk movement of pore wter s well s the diffusion process. As shown in the nlyticl results, the distribution of bound nd free chlorides cn be resonbly simulted with dvective trnsport due to the rpid suction of pore wter under wetting phse. W/C65% W/C55%

15 ph CO [mol/l C(OH) [kg/m CCO [mol/l 4. 6 C(OH). 4. ph.5 CCO W/C=5%.8 W/C=55%. 8 W/C=5%.6 6 W/C=55% After 8dys 8 CO After 8dys Distnce from the surfce [cm Distnce from the surfce [cm Fig. Distribution of ph, clcium hydroxide nd clcium crbonte under the ction of crbonic cid. Crbontion Phenomen in concrete In this section, computtions were performed to predict the progress of crbontion for different CO concentrtions, reltive humidity, nd wter to cement rtio. The mount of C(OH) existing in cementitious mterils cn be obtined by multi-component hydrtion model s [6[7, C S 6H 4 C AF C CSH C( OH) CS 4H CSH C( OH) ( OH) H CAH 6 When blst furnce slg nd fly sh re used, C(OH) will be consumed during hydrtion. The consumption rtios of slg nd fly sh rections re ssumed to be % nd % of rected mss, respectively, in this nlysis [6[7. First, the ccelerted crbontion tests were studied. For verifiction, the experimentl dt done by Uomoto et l were used [8. Fig. shows the comprison of nlyticl results nd empiricl formul tht ws regressed with the squre root t eqution. Similr to the previous cse, ll of the input vlues in the nlysis corresponded to the experimentl conditions. Anlyticl results show the reltionship between the depth of concrete in which ph in pore wter becomes less thn. nd exposed time. The simultions cn roughly predict the progress of crbontion for different CO concentrtion nd wter to powder rtio. Next, we studied the influence of the mbient reltive humidity on the progress of crbontion. In the ccelertion test, Structurl ge until crcking due to corrosion [yer CO:% Cl ion:.5[mol/l 6%RH dys 99%RH dys W/C4% W/C5% W/C6% () Cover depth [mm specimens were exposed to 5%RH nd Fig.4 Time till first signs of crcking due to corrosion for concrete

16 Unit [cm Mss/energy trnsfer from. surfce element cm 8. x z y. Restrined in ll directions Restrined x nd y displcements Wter content[kg/m Single clcultion Prllel clcultion Crcked element(softening zone). σ t f t. dys dried [cm Distnce from the surfce[cm Wter content[kg/m. Single clcultion.9 dys dried.9 Prllel clcultion.8 Crcked element(softening zone) Wter content[kg/m. Single clcultion 5. dys dried.9 Prllel clcultion.8 Crcked element(softening zone).7..6 σ t f t.5 [cm Distnce from the surfce[cm.7..6 σ t f t.5 [cm Distnce from the surfce[cm Fig.5 Moisture nd internl stress distribution in concrete exposed to drying condition 8%RH with CO concentrtions of %. As shown in Fig., nlysis cn resonbly follow the experimentl dt for different W/C nd environmentl conditions. Fig. shows the distribution of ph in pore wter, CO, clcium hydroxide, nd clcium crbonte inside concrete, exposed to the CO concentrtion of %. Two different wter to powder rtio, W/C=5% nd 5%, were nlyzed. It cn be shown tht higher resistnce for the crbonic cid ction is chieved in the cse of low W/C. Numericl Simultion of Coupled Crbontion nd Chloride Induced Corrosion Corrosion of steel in concrete due to simultneous ttck of chloride ions nd crbon dioxide were simulted. One-dimensionl concrete members tht hve three different wter to powder rtio, W/C=4, 5, 6%, with only one fce exposed to the environment were considered. In this nlysis, the stge where concrete crcking occurs ws defined s limit stte with respect to the steel corrosion. The progressive period until the initition of longitudinl crcking were estimted by the eqution proposed by Yokozeki et l [9. which is function of cover depth. Fig.4 shows the reltionships between cover depth nd structurl ge until crcking due to corrosion obtined by the proposed thermo-hygro system. It cn be seen tht the concrete nerer to the exposure surfce would show erly sign of corrosion induced crcking, nd low W/C concrete hs higher

17 resistnce ginst corrosion. Moisture Distribution in Crcked Concrete In the following sections, in order to show the possibility of the unifiction of structure nd durbility design, severl primitive simultions were conducted by using the proposed prllel computtionl system. First cse study is moisture loss behvior in crcked concrete. It hs been reported tht there would be close reltionship between the moisture conductivity nd the dmge level of crcked concrete, tht is, moisture conductivity would be dependent on the crck width, or the continuity of ech crcking. The proposed system, in which the informtion cn be shred between thermo-hygro nd structurl mechnics system, cn describe this spect quntittively by considering the inter-reltionship between the moisture conductivity nd properties of crcking. For representing the ccelertion of drying out of concrete due to crcking, the following model proposed by Shimomur were used in this nlysis [. JV J L before crcking J w = () cr cr JV J L JV J L fter crcking where, J w is the totl mss flux of wter in concrete, J V nd J L re mss flux of vpor nd liquid in non-dmged concrete respectively, nd J V cr nd J L cr re mss flux of the vpor nd liquid wter through crcks. In this simultion, only J V cr is tken into ccount for the first pproximtion, since diffusion of vpor would be predominnt when concrete re exposed to drying conditions. From the experimentl study done by Shimomur et l., it hs been confirmed tht the flux J V cr cn be expressed s [, J cr V = ερ D h (4) where, ε ; verge strin of crcked concrete, which cn be computed by COM, ρ V ; density of vpor, D ; vpor diffusivity in free tmosphere, h; reltive humidity. This formultion ssumes elstic deformtion of uncrcked region in tension to be smll compred with crck opening. The trget structure in this nlysis is concrete slb, which hs % wter to powder rtio using medium het cement. The volume of ggregte ws 7%. After dys of seled curing, the specimen ws exposed to 5%RH. Fig. 5 shows the mesh lyout nd the restrint condition used in this nlysis. Fig.5 shows the crcked elements, the distribution of moisture, nd normlized tensile stress t ech point from the boundry surfce exposed to drying condition. Moisture distribution clculted without stress nlysis is lso shown in Fig.5. As shown in the results, the crck occurs from the element ner the surfce, nd the crck progresses internlly with the progress of drying. It is lso shown tht the mount of moisture loss becomes lrge due to crcking. Ingress of Chloride Ion in RC Bem Dmged by Externl Lod The second cse is the numericl simultion bout the ingress of chloride ion in RC bem dmged by externl lod. Fig 6 shows the size of the bem, lyout of FE mesh nd lod condition used in this nlysis. The reinforcement rtio is.96%. For FE nlysis of RC structures, AN proposed the model which combines the nonlinerity of crcked concrete in RC zone nd plin concrete zone (PL zone) [. In this nlysis lso, we considered two different zones in RC V

18 Unit [cm Lod 5 PL Zone RC Zone 9 p=.96% Fig.6 Mesh lyout nd lod condition used in FE nlysis Lod [tf Crck occurs t the bottom b c Crcked elements due to bending Deflection t the center section [mm Chloride content [Wt% of cement Crcked elements due to bending Lod Ingress of chloride ion.4 Without considertion. of crcks nd mss trnsport coupling Distnce from the bottom [cm Chloride content [Wt% of cement Crcked elements due to bending Lod Ingress of chloride ion.4 Without considertion. of crcks nd mss trnsport coupling Distnce from the bottom [cm b Chloride content [Wt% of cement Lod c Crcked elements due to bending Ingress of chloride ion.4 Without considertion of crcks nd mss. trnsport coupling Distnce from the bottom [cm Fig.7 Distribution of chloride ion in dmged RC bem due to externl lod bems to tke into ccount the difference of concrete mechnics ner or fr from reinforcing brs (Fig.6). As for the mix proportion given to DuCOM, wter to cement rtio is 45%, nd the volume of ggregte is 65%. After 7 dys of seled curing, lod is pplied with displcement control. Fig.7 shows the lod-deflection reltionship nd crcked elements due to bending. After loding, behviors of chloride trnsport into dmged RC bem were simulted. The bottom surfce of the bem is exposed to the concentrtion of chloride ion.4 [mol/l under

19 lternte drying (7dys) nd wetting (7dys) cycles. Wetting is simulted by n environmentl reltive humidity of 99.9%, wheres drying condition is given s 5%RH. During wetting stge, the moisture flux through crcked re cnnot be negligible, since crcks would cuse the rpid suction of pore wter. However, there hs not been enough knowledge to quntify this spect yet. Therefore, liquid conductivity fter crcking ws roughly ssumed becoming to times before crcking. Fig.7 shows ech distribution of chloride ion t point, b nd c. The prllel simultion clerly shows deeper ingress of chloride ion within dys, compred to the results without considering crcks nd mss trnsport coupling. It cn be lso seen tht the mount of ingress of chloride ion increses ner the center section, since in crcked element the bulk movement of chloride ion in pore wter cn esily tke plce. CONCLUSIONS The numericl simultion system tht cn evlute structurl behviors under coupled forces nd environmentl ctions ws proposed in this pper. This system consists of two computtionl system, tht is, one is thermo-hygro system tht covers microscopic phenomen in C-S-H gel nd cpillry pores, nd the other is structurl nlysis system, which del with mcroscopic stress nd deformtionl field. In thermo-hygro system, genertion nd trnsfer of het, moisture, gs nd ions in micro-pore structures were formulted bsed on thermodynmics nd electrochemistry. Coupling these mterils modeling, n erly ge development process nd deteriortion phenomenon during the service period cn be evluted for rbitrry mterils, curing nd environmentl conditions in unified mnner. Numericl verifictions show tht this method cn roughly predict ingress of ion, crbontion nd corrosion phenomen for different mterils, curing nd environmentl conditions. The mcroscopic structurl behviors were linked with both the microphysicl phenomenon nd externl lod nd restrint conditions. In this pper, the unifiction of mechnics nd thermo-dynmics of mterils nd structures hs been mde. Though ech component in this system re crudely simplified nd further progress nd development is still needed for ccomplishing entire system, the system dynmics of micro-scle pore structure formtion nd mcro-scle defects nd deformtion of structures cn be shown s possible pproch in this study. REFERENCES K. Mekw, R. P. Chube, nd T. Kishi, Modeling of Concrete Performnce, E&FN SPON, 999. K. Mekw, P. Irwn nd H. Okmur, Pth-dependent Three Dimensionl Constitutive Lws of Reinforced Concrete Formtion nd Experimentl Verifictions, Structurl Engineering nd Mechnics, Vol.5, No.6, pp , 997. H. Okmur nd K. Mekw, Nonliner Anlysis nd Constitutive Models of Reinforced Concrete, Gihodo, Tokyo R. Mbrouk, T. Ishid, nd K. Mekw, Solidifiction model of hrdening concrete composite for predicting creep nd shrinkge of concrete, Proceedings of the JCI, Vol., No.,

20 pp Concrete Lbortory, University of Tokyo, Kishi, T. nd Mekw, K. Multi-component model for hydrtion heting of portlnd cement, Concrete Librry of JSCE, No.8, pp. 97-5, Kishi, T. nd Mekw, K., Multi-component model for hydrtion heting of blended cement with blst furnce slg nd fly sh, Concrete Librry of JSCE, No., pp. 5-9, Chube, R.P. nd Mekw, K. A study of the moisture trnsport process in concrete s composite mteril, Proc. of the JCI, Vol. 6, No., pp.895-9, Chube, R.P. nd Mekw, K. A permebility model of concrete considering its microstructul chrcteristics, Proc. of the JCI, Vol. 8, No., pp. 97-9, 996. Ishid, T., Chube, R.P., Kishi, T. nd Mekw, K., Modeling of pore wter content in concrete under generic drying wetting conditions, Concrete Librry of JSCE, No., pp , 998. T. Mruy, S. Tngtermsirikul, nd Y. Mtsuok, Modeling of Chloride Ion Movement in the Surfce Lyer of Hrdened Concrete, Concrete Librry of JSCE, No., pp.69-84, 998. O. E. Gjørv nd K. Ski, Testing of Chloride Diffusivity for Concrete, Proceedings of the Interntionl Conference on Concrete under Severe Conditions, CONSEC95, pp , 995. J. R. Welty, C. E. Wicks nd R.E. Wilson, Fundmentls of Momentum, Het, nd Mss trnsfer, John Wiley & Sons, Inc., H. Freiser nd Q. Fernndo, Ionic Equilibri in Anlyticl Chemistry, John Wiley & Sons, Inc., (96). 5 T. Seki, H. Ohg nd S. Ngtki, Mechnism of Crbontion nd Prediction of Crbontion Process of Concrete, Concrete Librry of JSCE, No.7, pp.-6, West, J.M., Corrosion nd oxidtion, Sngyo-tosyo, Ishid, T., An integrted computtionl system of mss/energy genertion, trnsport nd mechnics of mterils nd structures, PhD thesis submitted to University of Tokyo, 999 (In Jpnese). 8 T. Uomoto nd Y. Tkd, Fctors Affecting Concrete Crbontion Rtio, Concrete Librry of JSCE, No., pp.-44, K. Yokozeki, K. Motohshi, K. Okd nd T. Tsutsumi, A Rtionl Model to Predict the Service Life of RC Structures in Mrine Environment, Forth CANMET/ACI Interntionl Conference on Durbility of Concrete, SP7-4, pp , 997. T. Shimomur, Modelling of Initil Defect of Concrete due to Drying Shrinkge, Concrete Under Severe Conditions, CONSEC 98, Vol., pp.74-8, 998. T. Nishi, T. Shimomur nd H. Sto, Modeling of Diffusion of Vpor Within Crcked Concrete, Proceedings of the JCI, Vol., No., pp , 999 (In Jpnese). X. An, K. Mekw nd H. Okmur, Numericl Simultion of Size Effect in Sher Strength of RC Bems, Proceedings of JSCE, No.564, V-5, pp.97-6, 997.