CONCRETE LIBRARY OF JSCE NO. 36, DECEMBER 2000

AN INTEGRATED COMPUTATIONAL SYSTEM FORMASS/ENERGY GENERATION, TRANSPORT, ANDMECHANICS OF MATERIALS AND STRUCTURES

(Translation from Proceedings ofJSCE, No.627/V-44, August 1999)

Tetsuya ISHIDA Koichi MAEKAWA

The authors present an integrated computational system consisting of a 3D FE structural analysisprogram and a 3D FE thermo-hygro physical analysis system which can model the developmentand deterioration of concrete materials performance. The thermo-dynamic process providessolutions for temperature, pore pressure, pore distributions, and other material properties in both3D space and time. By passing this information to the structural mechanics process, the stress anddamage to RC members caused by temperature changes and shrinkage can be obtained. Thegeneration of cracks changes the material properties of mass transport, which are controlled bythermo-physics. This proposed integrated system can be used for the simultaneous evaluation ofoverall structural and material performances without distinguishing between structure anddurability.

Keywords: Durability, structural performance, parallel computation, crack, mass transport

Tetsuya Ishida is an assistant lecturer in the Department of Civil Engineering at University ofTokyo, Japan. He obtained his D.Eng from University of Tokyo in 1999. His research interestscover mass/energy transport phenomena in concrete and the mechanisms of shrinkage and creepof concrete. He is a member of the JSCE and the JCI.

Koichi Maekawaserves as professor in the Department of Civil Engineering at the University ofTokyo, Japan. He obtained his D.Eng. from University of Tokyo in 1985. He specializes innonlinear mechanics and constitutive laws of reinforced concrete, seismic analysis of structures, andconcrete thermodynamics. He is a member of the JSCE and the JCI.

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1. INTRODUCTION

At an early age, cementitious materials change in volume as a result of material-related factorssuch as heat generation, autogenous shrinkage and drying shrinkage. These volume changes causeinternal stresses in a restrained RC member and sometimes induce cracking, which accelerates themigration of moisture and ions. This results in accelerated steel corrosion and hence reduceddurability performance of RC structures [16][17][18][19]. Consequently, in order to evaluatevarious measures of structure performance over time, it is necessary to quantify the magnitude ofthese volume changes, the amount of internal stress and damage that results in RC members, andthe characteristics of mass transport in the cracked concrete. It has to be also noted that there is astrong linkage between the mechanical behavior of structural concrete and material quality. Theauthors understand that a unified approach to the mechanics governing stress and strain fields andthe thermo-hygro physics ruling mass and energy transport associated with thermo-dynamicequilibrium would serve as a technique for ensuring overall concrete structure performance aswell as concrete performance over the life-span ofa concrete structure [1].

In most past design methodologies, structure serviceability and material performance have beentreated separately. In this paper, the unification of mechanics and thermo-dynamics of materialsand structures is tackled to demonstrate the potential and future direction of research anddevelopment.

The volume change of cementitious materials at an early age is dependent on the mix proportion,powder composition, curing, and environmental conditions. In the proposed system, the volumechange is modeled from material parameters related to hydration, moisture, and pore structuredevelopment using 3D FE code DuCOM [2]. The induced stress and damage to the RC membercaused by this volume change is influenced by the shape and the size of the target structure,restraint conditions, material stiffness, and strength. By providing solutions for materialproperties such as strength, elastic modulus, temperature, water content, and pore structure to thestructural analysis program COM3 [3][15] at each step, the stress and the damage can be obtained.The generation of cracks alters the material properties in mass transport characteristics controlledby the thermo-physics system. Though each component in this system is crudely simplified andfurther progress and development is still needed to accomplish a complete system, the authorsaim to show that it is possible to develop a system dynamics for micro-scale pore structureformation and macro-scale defects and structural deformation.

2. OUTLINE OF FE PROGRAMS

2. 1 Thermo-hygro physics for concrete performance - the DuCOMsub-system -

In order to trace the early-age development of cementitious materials, it is necessary to considerthe inter-relationships among the hydration, moisture transport, and pore-structure developmentprocesses. The authors have been developing a 3D FE analysis program code-named DuCOMthatsimulates these phenomena. This section simply summarizes the overall schemes of this program,since details are presented in a published book [2].

The overall computational scheme is shown in Fig.l. The constituent material models areformulated based on microphysical phenomena, and they take into account the inter-relationshipsin a natural way. The inputs required in this scheme are mix proportion, powder materialcharacteristics, casting temperature, geometry of the target structure, and the boundary conditionsto which the structure will be exposed during its life-cycle. Using the multi-component hydrationmodel, solutions for temperature, degree of hydration, and amount of chemically combined waterare obtained [4][5]. By applying the average level ofhydration and chemically combined water toa micro pore structure development model, the porosity distribution of hydrated and non-hydratedcompounds around reference cement particles is calculated and the surface area of themicro-pores is estimated mathematically [2]. The resulting porosity and pore distributions areused to evaluate moisture conductivity. Using the moisture transport model, which considers bothvapor and liquid transports, the pore pressures, relative humidity, and moisture distribution can beobtained [6][7][8]. Here, water consumption due to hydration is considered in solving the massbalance equation, thereby naturally tracing the inter-dependence between moisture transport and

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the hydration process.

The chloride distribution in the cementitiousmaterials is calculated using the followingformulation [10]. Considering advective transportdue to bulk movementof the pore solution phase aswell as ionic diffusion due to concentrationdifferences, the flux of chloride ions in the porousmedium can be described as,

$sj =_i^0,VCr, +<bSuCrln (1)

M ix proportions,

temperature andboundary conditions

INP UT

Temperature, hydrationTHydration L _ ievei of each mineral

model~1

component

Bi-m odel p orositydistribution, in terlayer

p oro sity

M icros

cornp

truct u re

utati on~1

Pore pressure [ f ore-pressures, RH and

Go raputation moisture distribution<0E

C 3<D iS�" Chloride ion Dissolved & bound

｣ ｣01~

�" ch loride con cen tra tion0 -E｣ Q- I

I All conservationNo lawssatisfied? Yes

* YesSTOP OUTPU Tallresults

where, Jc/ - \Jx Jy Jz~] 'à" flux vector of chloride ions[mol/m2.sj; (j>: porosity of the porous media; 5":degree of saturation of the porous medium;Q=(7i/2)2 accounts for the tortuosity of the 3D porenetwork, which is uniformly and randomlyconnected; VT = [d/8x d/dy d/dz] : the gradientoperator; u = [ux uy uz]: advective velocity of ionsdue to the bulk movement of pore solution phase[m/s]; and Cci : concentration of ions in the poresolution phase [mol/1]. In the case of chloride iontransport in concrete, S represents the degree ofsaturation in terms of free water only, as adsorbedand interlayer components of water are also present. Here, it has to be noted that the diffusioncoefficient DCI is a function of ion concentration, since ionic interaction effects will be significantin the fine micro structures at increased concentrations, thereby reducing the apparent diffusivemovementdriven by the ion concentration gradient [22]. This mechanism, however, is not clearlyunderstood, so we neglect the dependence of ionic concentration on the diffusion processJin themodel. From several numerical sensitivity analysis, aadopted for DCI-

Fig.l Framework of DuCOM thermo-hygrophysics

constant value of 3.0x10" I'm/si is

The first term on the right-hand side ofEq. (1) expresses the diffusion of ions, whereas the secondterm describes advective transport due to the bulk movement of condensed pore water. Theadvective velocity of chloride ions might also be dependent on the ion concentration, as with thediffusion coefficient. In this paper, however, weassumethat the velocity vector of ions is equal tothat of liquid pore water, since there is not enough experimental data to establish a model for thisaspect.

u=u. (2)

where, u: advective velocity of chloride ions; and u,v: advective velocity of condensed water inpores, which is dependent on relative humidity and moisture content in pore structures.

It is well-known that chlorides in cementitious materials have free and bound components. Thebound components exist in the form of chloro aluminates and adsorbed phases on the pore walls,making them unavailable for free transport. It has been reported that the amount of boundchlorides would depends on the binder, the electric potential of the pore wall, and the pH of thepore solution. However, the exact mechanism is still not clear. In this paper, the free and boundcomponents of chlorides under equilibrium conditions are tentatively expressed by the followingempirical equations proposed by Maruya, et al. as [1 1],

1

a^ -1-0.35(^ -0.1)°

0.543

c,0, <o.i

0.1<C/0/ <3.0

3.0< C,,,,

(3)

131 -

where, Ctot: total chloride content [wt% of cement] (=Cfree+ Cbound,amount of free chloride andbound chloride, respectively); a.fixeci=Cfree+ Cbound'-equilibrium ratio of fixed chloride componentto total chloride ion component.

By solving the mass balance equation in terms of free chloride ions with the above formulations,the distribution of bound and free chloride ions in cementitious materials can be obtained at anyarbitrary stage.

2.2 Continuum mechanics of materials and structures - the COM3 sub system -

On the basis that structures are exposed to low level of stress under normal conditions, we assumethat linear creep constitutive equations including temperature/shrinkage strain and creep straincan be written as,

SK =-J(l+9)^K +Er +s,/,

e, =-f(l+9)dSL2G^

(4)

(5)

where, sv: average volumetric strain; av: average volumetric stress; £//: deviatoric stress; e\f.deviatoric strain; K: bulk modulus; G: shear modulus; cp: creep coefficient; 87-: unrestrained straindue to temperature; esh' unrestrained shrinkage strain due to pore pressure.

The unrestrained strain due to temperature and that due to pore pressure at each time and eachpoint are obtained by calculation from material parameters in DuCOM, such as temperature, porepressure, water content, and pore structure [9]. This calculated strain is passed to COM3. As aresult, the thermal stress due to temperature gradient, the shrinkage stress due toself-desiccation/moisture loss, and combinations of these are implicitly considered by this system.The strain tensor can be described as,

where, [£>']=,

｣ **

8 ｻ >

- [ｻ

0 ^

O yy

[D -

f<p d c

fa d e

+

e T + 6 .

e T + E .

^ 0 y d o t 8 T + 8 .

E _ , 0 0 >IW c 0

s .ｫ O y, U c/c 0

E z* 0 J q x fc 0

(6)

if-i.3{3K

.ll If-L-Ll if_L__L'G) 3{3K 2Gj 3{3K 20

iu+ri L(±.±3{3K Gj 3{3K 2G

if-L+l]3{3X Gj

Sym m.

0 0 0

0 0 0

0 0 0

1- i - O O2G

1- 02G

1

2G

(7).

Solving the equation (6) for stress {CT} gives the basic equation in matrix form as,

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{a}=[D]{£}-{Jqxfo}-[D]{er+£J (8)

where, [D]: stress-strain matrix. Before cracking, theelastic modulus in matrix D is obtained from thecalculated hydration level at each gauss point in eachelement. As for the judgment of cracking in the stressfield, if the principal tensile stress at any gauss pointexceeds the tensile strength, we assume that a crackwould occur at that point. A tensile model of crackedconcrete with tension softening as proposed byOkamura [14] is introduced in this study.

Normalized tensile stress

r| SBa,(6,;c)=/,| ^-£

(9)1 ,000 2,000 3,000

Tensile strain [micro]4,000

Fig.2 Tension softening model for crackedconcrete

where, CT/:mean tensile stress normal to cracks; ft:tensile strength of concrete; E/: tensile strain normal tocracks; s^: cracking strain of concrete; c: stiffeningfactor. The softening behavior of the cracked concrete is modeled by changing the parameter c, whichexpresses the sharpness of the tension-softening curve. Parameter c can be set at 0.4 for RC concretewith ordinary deformed bars, whereas the value for plain concrete can be obtained from the concrete'sfracture energy and the element size [14] (Fig.2).

Crack propagation due to drying shrinkage involves the generation and growth of smeared microcracking over the surface, and stress relaxation occurs as a result of micro cracking. It has to alsobe considered that local cracking between the paste matrix and aggregate will occur [24]. In pastresearch, the generation and propagation of micro cracking was evaluated in terms of localfracture energy [23], but no established theory exists for this behavior. Therefore, in thisinvestigation, we use the above tension-softening model as applied to macroscopic RC membersin order to evaluate the stress relaxation after shrinkage cracking [14].

As for the creep coefficient in equations (4) and (5), we adopt the Bazant-Panula formulation [20].

9fcO= 9rk~" +a)('--0'lr (10)

where, t: time [day]; to: loading period [day]; cpr: coefficient representing the effect of mixproportion and temperature, te; r\ : coefficient representing the effect of temperature history; m:coefficient representing the effect of compressive strength; and a: coefficient representing theeffect of water-to-cement ratio.

Strictly speaking, the above model is not well suited to stress analysis under drying conditions,since this creep function represents only basic creep. Still, in this paper, creep function given byeq. (10) is tentatively adopted for the calculations that follow, since we focus mainly on thevalidity of the proposed method from the viewpoint of numerical analysis.

The authors have been working on another constitutive law that is able to describetime-dependent behavior in terms of deformation and internal stress, as well as the fracturephenomena of restrained structures, for arbitrary thermo-dynamical states. For a detaileddiscussion of this, see the published paper [21].

3. DUAL PARALLEL PROCESSING OF THERMO-PHYSICS AND STRUCTURALMECHANICS

For numerical evaluation of overall structural and material performance, we propose parallelprocessing of two coupled sub-systems as shown in Fig.3. The main feature of this system is thatperfect two-way communication is available between the structural mechanics and materialcharacteristics, whereas in conventional thermal stress analysis, material parameters such astemperature rise are passed to the structural analysis in only a one-waytransfer.

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Mix F

Md;: 1

iI �"

m s e I c ditim m

I tatioCom m on

storage areaStrength ,stiffness,temperature.water

�"�"m felm �"I�" If 1�"1

y

content.and porepressure. etc..

I �"�"Ii �"�"II ill n

i 1 a il1 Imn m m 0m m �"Iro I1 ac PC

R

dam age

epeat until final st

s B 1 1 �"�"

g

｣

ta y

Fig.3 Coupled 3D-FEM scheme of solution forhydration, moisture transport, and structureformation problem in concrete

This system can be embodied in a multitaskingoperating system such as UNIX or Windows. Inthis framework, constituent sub-systems withdifferent schemes for solving the variousgoverning equations, do not have to becombined into a single process. The operatingsystem manages the tasks of each system, andthe two sub-systems are connected by ahigh-speed signal bus or network so as to sharethe commondata.

First, material properties are calculated byDuCOM. After one step of execution, thecalculated results for temperature, water content,pore pressure, pore structure, stiffness, andstrength are stored in the commondata area. Asignal to begin execution is then sent to thesleeping process (COM3). COM3 becomesactive and reads the information from thecommondata area, using it to perform the stresscomputation. In this analysis, the damage levelof the RC member is obtained, and thecalculated results are written to the commonarea after execution. These steps are continuedtill one of the processes completes itscomputation. Following this procedure, each FE program can share computational results betweenthe two systems at each gauss point in each finite element.

The chief advantage of unifying the material and structural analysis processes in this manner isthe numerical stability of an explicit scheme. Furthermore, this multi-tasking coupled methodenables engineers to easily link independently developed computer codes, even if they are indifferent computer languages and based on different algorithms. As a matter of fact, only slightmodification is required for data exchange with the commonmemoryspace through high-speedbus, and a short system management program alone is needed.

4. Numerical Simulations

4. 1 Moisture distribution in cracked concrete

Using the proposed computational system, numerical simulations of moisture loss in crackedconcrete were carried out. It has been reported that there should be a close relationship betweenmoisture conductivity and the damage level of cracked concrete; that is, moisture conductivityshould be dependent on the crack width or the continuity of each crack [16][17][18][19]. Theproposed system, in which information is shared between the thermo-hygro and structuralmechanics processes, is able to describe this behavior quantitatively by considering theinter-relationships between moisture conductivity and cracking properties. However, to check thevalidity of the proposed system itself, three rough assumptions of moisture conductivity aftercracking were made as shown in Fig.5: conductivity after cracking rises by ten times (Case I) andfifty times (Case III) compared with that before cracking, and it increases proportionally to thetensile strain of the cracking elements (Case II). Creep behavior after cracking is not considered,since deformation due to cracking would be large enough to make creep negligible. The analysiscan, however, consider the time-dependent behavior of average strain, including the width ofcracking as shrinkage increases.

The target structure in this analysis was a concrete slab, which has a 30% water-to-powder ratiousing medium heat cement. The volume of aggregate was 70%. After 3 days of sealed curing, thespecimen was exposed to 50%RH. Figure 4 shows the mesh layout and the restraint conditionsused for this analysis.

Figure 6 shows the cracked elements, the distribution of moisture, and the normalized tensile

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Restrained inall directions

Mass/energy à"-à"transfer from 1.0surface element

Restrained x andy displacements

Fig.4 Mesh layout used for FE analysis

Water content [kg/m3]0 .1 0

0 .0 9

S in g le c a lc u la t io n C a s e I

P a ra lle l c a lc u la tio n

0 .0 8

0 .0 7

D ry in g tim e : 8 .5 2 d a y s

; - L * - , ' o T ¥ i i i

1 .0

0 .0 6 (S o ften in g z on e ) ｰ ,Ai

0 .0 5

0 .0 4

3 0 [c m ]

1 0 1 5 2 0 2 5

Distance from surface[cm]

Water content [kg/m3]0 .1 0

0 .0 9

S in g le c a lc u la t io n C a s e

P a ra lle l c a lc u la tio n

0 .0 8

0 .0 7

0 .0 6

D ry in g t im e : 8 .5 2 d a y s

/ (S ofte n in g zo n e)_1 .0/

/ ｰ ,A

0 .0 5

0 .0 4

I I //

/ -,-'/

3 0 [c m ]

1 0 1 5 2 0 2 5

Distance from surface[cm]

Water content [kg/m3]U .1 U

0 .0 9

S in g le c a lc u la t io n C a s e

P a ra lle l c a lc u la tio n

0 .0 8

0 .0 7

0 .0 6

0 .0 5

0 .0 4

D ry in g tim e : 8 .5 2 d a y s

/C rac ke d e le m e nt/ t rac ke d e le m e nt(S o fte ning z o ne ) 0 , / f,

// _3 0 [c m ]

1 0 1 5 2 0 2 5

Ratio of moisture conductivity after crackingto that before cracking

50

10

Case III: Fifty times large (Constant)

Case II: Increasesproportionally totensile strain

I Case I: Ten times larger (Constant)

Cracking strainTensile strain

1 000[micro]

Fig.5 Moisture loss behavior for different dryingconditions

Water content [kg/m3]U .1 U

0 .0 9

S in g le c a lc u la tio n C a s e I

P a ra lle l c a lc u la t io n

0 .0 8

0 .0 7

0 .0 6

0 .0 5

0 .0 4

c ra ck e d e le m e n t D ry in g tim e : 3 1 .1 d a y s

(S ofte n i n g zo n e)

�" - - f f i �"�" �"�"^ �"�" ^ ^ ^ �" ^ �" 1

/

X 1 .0

/

a , / f,

3 0 [c m ]

. // . 0

1 0 1 5 2 0 2 5

Distance from surface[cm]

Water content [kg/m3]0.10

0.09

0.08

0.07

0.06

0.05

0.04

Single calculation Case IIParallel calculation

cracked element Drying time: 31."Idays(Softening zone)

1 0 1 5 2 0 25

Distance from surface[cm]

Water content [kg/m3]0.10

30

0.09

0.08

0.07

0.06

0.05

0.04

Single calculationParallel calculation

Case 111

Cracked element(Softening zone)

Drying time: 31.1days

1.0

°,A

Distance from surface[cm]

Fig.6 Moisture and internal stress distribution

1 0 1 5 2 0 25

Distance from surface[cm]

in concrete exposed to drying conditions

30

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Chloride content [Wt% of cement]3.5

Single calculationParallel calculation

After 365 days

Cracked element(Softening zone)

"Uà""à" \£f

Chloride content [Wt% of cement]3.5

10 15 20 25

Distance from surfacefcm]30

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Single calculationParallel calculation

After 900 days

Cracked element(Softening zone)

1 0 1 5 2 0 25

Distance from surface[cm]30

Fig.7 Chloride content in concrete exposed to drying conditions

stress at each point from the boundary surface exposed to drying conditions. The moisturedistribution calculated without stress analysis is also shown in Fig.6. As these results show,cracking begins from an element near the surface and the crack progresses internally as dryingprogresses. It is also clear that the moisture loss rises due to cracking.

4.2 Chloride content in cracked concrete

Next, the migration behavior of chloride ions in cracked concrete was simulated. The size andshape of the target specimen, restraint conditions, and mix proportion are same as in the previousanalysis. The specimen was exposed to 0.5 1 [mpl/1] chloride ions under alternating dry (7 days) andwet (7 days) cycles. The distribution of chloride ions inside the concrete after 365 days and 900 dayswasas shown in Fig.7.

In this analysis, we assumethat the liquid conductivity of concrete after cracking is ten times that ofnon-damagedconcrete. Whena structure is exposed to wetting conditions, there is a flux of liquidwater from outside to inside, and the chloride ions are transported by this flux. The analyticalresults indicate that chlorides move deep inside the concrete when cracking is considered. It shouldbe noted, however, that the ratio of conductivity after cracking to that before cracking does not haveany physical meaning. To check the validity of the proposed system, the simplest assumption wasadopted in the analysis.

4.3 Ingress of chloride ions into RC beam damaged by external loading

The final test case was a numerical simulation of the ingress of chloride ions into an RC beamdamaged by external loading. Figure 8 shows the size of the beam, the layout of the FE mesh, andthe loading conditions used in this analysis. The reinforcement ratio was 0.96%. For the FEanalysis of RC structures with a concentrated arrangement of reinforcement, An et al. propose ananalytical method to differentiate the RC control volume (RC zone) and the plain concretevolume (PL zone), which have different softening/hardening characteristics. The RC zone isspecified for concrete confined by reinforcement, whereas the PL zone is applied to areas faraway from the steel bars [14]. In this analysis also, we consider two different zones in RC beamsto take into account the difference in concrete mechanics near or far from the reinforcing bars(Fig.8). The tension stiffening model is shown in Fig.2. Stiffening factors c for the RC zone andthe PL zone were given as 0.4 and 2.0, respectively [14]. As for the mix proportion adopted inDuCOM, the water-to-cement ratio was 45% and the volume of aggregate was 65%. After 7 daysof sealed curing, loading was applied with displacement control until a deflection of 0.42[mm]was reached. Figure 9 shows the relationship between load and deflection at the center section,and the cracked element caused by loading.

After loading, the characteristics of behaviors of chloride transport into the damaged RC beam weresimulated. The bottom surface of the beam was exposed to a concentration of chloride ions (0.51[mol/1]) under alternating dry (7 days) and wet (7 days) cycles. Wetting was simulated by anenvironmental relative humidity of 99%, whereas drying was given as 50%RH. The characteristics

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Unit [cm ] 20 Load M O nn HH T

131

P L Zone I151

iB nn R 6; K

90 _| p=0.96%

Load [tf]3.0

Fig.8 Mesh layout and load conditions used in FE analysis

Chloride content [Wt% of cement]3.5

Cracked elementsdue to bending

Load , /7_

t tIngress of chloride ions

After 365 days

Deflection at center section fmm]

Chloride content [Wt% of cement]3.5

Cracked elementsdue to bending

t \ t t tIngress of chloride ions

After 365 days

8 10 12

Distance from bottom [cm]

Chloride content [Wt% of cement]3.5

14 16

4 6 8 10 12

Distance from bottom [cm]14 16

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Lo adrs B i

1= 1�"HIm m== ii IIis

C r a c k e d e l e m e n t sd u e t o b e n d i n g

t II n g r e s s o f c h l o r i d e i o n s

W i t h o u t c o n s i d e r a t i o n o f c r a c k sa n d m a s st r a n s p o r t c o u p j i n g

A f t e r3 6 5 d a y s

4 6 8 1 0 1 2

Distance from bottom [cml1 4 1 6

Fig.9 Distr ibution of chloride ion in damaged RC beamdue to external load

of masstransport after cracking can be expected to differ in the RC zone and the PL zone as a resultof the different crack density, and weunderstandthat a detailed discussion of this is needed in future.In this analysis, however,the moisture conductivity of the cracked area is roughly assumedto be 10times that before cracking for the sake of simplicity.

Figure 9 shows the distribution of chloride ions at points a, b, and c. The parallel simulations clearlyshowdeeper ingress of chloride ions up to 100 days as comparedto the results when cracking andmasstransport coupling are not considered. It can also be seen that the ingress of chloride ionsincreases near the center section, since in a cracked element the bulk movementof chloride ions inpore watercan easily take place.

5. CONCLUSIONS

An integrated computational system for thermo-physics and structural mechanics is proposed.Based on coupling under a multi-tasking operating system, it enables engineers to easily linkindependently developed computer codes even if different languages and algorithms are used,since each system is managed by the operating system and the calculated results are shared

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through a commondata area. Though each component in this system is crudely simplified andfurther development is required to achieve a finished system, the dynamics of micro-scale porestructure formation and macro-scale structural defects and deformations as calculated by thissystem indicate its potential.

Appendix

The governing equations solved by the proposed system are shown in Figs, a, b, and c. Figure ashows the mass and energy conservation laws which govern the thermo-physics of materials, aswell as the balance equations which govern the mechanics of structures. These conservation lawsmust be satisfied in all material systems and so they apply to the field of concrete materials.Figure a also shows the mass, energy, and momentumtransport terms, and sink term, for theabove equations. These governing equations are derived from the specific characteristics ofconcrete materials. In this system, we neglect momentumtransport with mass transport andmomentumgeneration by product and/or loss of mass and energy, since their magnitude would bequite small. Figures b and c show the state, compatibility, and constitutive laws of mass, energy,and solid concrete. These equations are also modeled by considering the specific characteristics ofconcrete.

Table I shows input values needed for the calculation. In addition to the list in Table I, the x, y,and z-coordinates of each node and the element type/shape of the analytical target are required forthe analysis. These input values determine the initial value at time=0, and also determine some ofthe material constants shown in Table II. Other material constants are taken from experimentalresults. By solving the above governing equations under given material constants and initialconditions, the variables shown in Table III are obtained in 3D space and the time domain.

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Conservation laws (mass, energy, and momentum conservation)Conservation of mass and energy

:~L0r-\a0+divJx -£x =ot [__&!

^0-\^0 ^^0r.hlnririfi 3 r/ \ i 37"

ions [10]: &. 0[(*«' +*cf)Sc,Ca] Heat energy[13]: PC-

Balance equation3a,

a*£+JT, =0

Mass, energy, and momentumtransport terms

Moisture [6][7]JW=-DWVP, Dw=K,+Kr

. =MLfrv^Y^=£A^.r^L. Nt=-^1 SOTlU" J " J'-l+tft 2(r-O

/ , ^ WJ1+ii'lw-^n=n..cxolG. RT) G.=G_^, ^+l~TT~ F'-TT

à"à" ' à"à" -"à"à"à" v à"'à" ; à"'à"

|5 J,_0 0r.

Mass, energy, and momentum sink terms

Moisture [2]a. 0a*+af.f.&£l0P-2>.-£-i

Chloride ion [10]f

0 _dCbouml

Qa ~~dT

Heat energy [4][5]QH = wmy.PlH,

H . =v. -6.-u. à"//.- exo[ £,(g,)fl 1

L * I T Tn

Ma-JP,=/(«WI,) ii--=1"| 1~f: a

v -~/Momentumgeneration by product/loss of massis neglected

n,-4^-) «=[..59(^-)+o,]!

wier cracKing

A,=10-(K,+KV) ,or =50-(K,+KV)

Chloride ion [10] Heat energy [13]T -(*. _I_A ^e .l_^cv_\7/" a.,, r I , � ^m

JH =-x,,vy

Fig.a Conservation laws, mass/energy transport, and sink term

State, compatibility, and constitutive law of mass, energy, and solid

Strength, elastic modulus, and Unrestrained straindeformability against pore pressure[9][12] due to temperature [13]

//=aexp(-bà"V ) a,b:constant^=V«p(-VrJ '-5o=50xlO^[m] £r =«cAr

£=8.5-103/;*3 f, =0.27f^

Unrestrained shrinkage straindue to pore pressure [9]

£,* = $<o,s,o,fpow -+-

^sl,

Esh = E/3

Compatibility equation Constitutive law of solid concrete [13][20] K= G=-

a«d x

_ dv 9uE0~~;b+lh

, (0= rl±4#%^J o 3tf(f') A'+£T+e.,

3v 9w 3ve =- e =--+-^--"." 3, , 'à"' 3, , 3,

u/ u/ u^

E x Ejle- +£�À +£, 0y =-(0a +0)r +at

*H*0?%03u dw3 z d z+dx e0=*9-*90v Sij=0iJ-SiJ-Gl,

3(1-2v) " 2(1+v)

<pM= <pr(C' +x)(' -'Tr

<pr = /(rmx proportion, T)

t, =/(Temp.history)m=/(Comp.strength)X =/(W/P)

r\T = /(Temp,history)

Fig.b State and compatibility law of mass, energy, and solid (No.l)

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State, compatibility, and constitutive law of mass, energy, and solid

Pore structure formation [2]r , _a*W (l,1 P

i-<Llp, 'P* w^

Before contact<b =1.0

<j)/r = \twstpg )/ 2 After contact0ou =}-(X+Y}/2

� _V_(70/70 \ J . _I/A J k* k2Z.Pi '\^i/^-,=0; Vgl = "sVch ~M»fr A =-«U-0,,, J| -7 Tx + r+-

,w.

>c,=l-K, -(l-ap=-

r p $* =$*à" +bgi +bcp

pf =p,pw&+p/^XMj/(p,, +pp,)

Adl, +B50m +C5m +D=0^= (4-U+3(l-O/{3(«+3)}5= Ml -<t>J+2(l-<t,0J}r0/(W+ 2)

c= Mi-O+(i-+JKV("+i)2D = -(a/-03/3)[<t./,1 + Pp/>/pJ

3(/7+3) 77+2 W+l

0^2

y=-l<b,_+B^I z=-^-+-j I pu. I «-t-j H-t-z «-t-i

Sl =5]0fpc +1500f0 +3100fj.

C=19.0/^ +1.5/, +1.0//l

0-0d*+*-+c]

SA, =2$, |°B,exp(-5,r)rfInr 5^ =P^ à"Mg

*W=*fr+^'^+<l»«J,-^ l^-l-exp(-5,r)

TTiermodynamic equilibrium of massMoisture[6][7][8] <, _=A? + r(0}^v=^ ri_in* 1 S.=S^+S^

Hr/S/r =RH0

0.525 x1Q- - RH (Drying stage)

/j=P^hJW=-2T

M, rc Slot =<i>,A + (<lv + <f>c,X

(l-RH/RHm\l -RH/RHm +15RH)

-jM,##,,, =exp p,Rf(r - ta)

s ^=s,.+ \dV=S -S, In5, >fceW,,MJ

w...

(Diying to wetting stage)_rfi-f^*~1P I r/ ' J 0«i=0+ fm"-dV=Sc[\+]nSr -hiSe]

=re^=i_.vnr_R,u.v cnrf c i, v cL r» cj"end-Jj "" -* ""fV "'cJ-"0

S,r = RH

(Wetting stage)

S lr =l+ (RH-l{-0^}V \RHn0a-l)

(Wetting to drying stage)

1 C,0, <0.5C,_, =Cr, +C,

Chlorideion[11] a^ri-l-0.5(C/0,-0.5)039 0.5<C/0,<4.5 "" _ """0.141 4.5<C,0/ a^-C-10

Fig.c State and compatibility law of mass, energy, and solid (No.2)

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Appendix Table. I List ofinputvalues

PI Initial pore pressure [Pa] WpowCci Initial concentration ofCl ions[mol/l] VgT Initial temperature [K] fpc

Mass ratio of chemical component ofc ement (C2S, C3S, C4AF, C3A, gypsum)

/«

pp Densityofpowdermaterials [kg/m ]W/P Water-to-powder ratio

Table. II List of material constant

ffap*p

p/Pv

pcD0

Dc,

0

TI/

l,n

*-7in cu

^

Pi

W,

Q,ra

PFpo

T0

R

PP

Pw

Density of liquid [kg/m3]

Density of saturated vapor [kg/m3]

Heat capacity [kcal/K.m3]

0ch

<(>/«

eg

Vapor diffusivity in free atmosphere [m2/s] s/

Chloride ion diffusivity in pore solution phase[m2/s] "

Parameter representing tortuosity of pore(=(*/2)2)

Viscosity under ideal conditions [Pa.s]

Mean free path ofa water molecule [m]Maximumadditional Gibbs energy for theactivation of flow(=3 500kcal/mol)Heat conductivity [kcal/K.m.sec]Mass ratio of chemical component z of r.

cementAmount of water consumed by chemicalcomponent / due to hydration [mol/mol]Maximum theoretical specific heat ofcomponent / [Real] "Powder weight per unit volume [kg/m3] M

Reduction factor representing theretardation effect on hydration of fly ash yand organic admixtureCoefficient representing the effect ofmineral composition (C^S, à¬28) on Vthydration rateReference temperature (=293 K)Gas constant [J/mol.K]Density of powder materials [kg/m3]Density of chemically hydrated products[kg/m3]

Table. Ill List ofvariables

Time [s]

Powder weight per unit volume [kg/m3]Aggregate volume per unit volume [kg/m3]

Weight fraction of Portland cement

Weight fraction of blast furnace slag

Weight fraction of fly ashAmountof organic admixture

Specific porosity of gel products (=0.28)Specific porosity of inner products (=0.28)Th ickness of interl ayer porosity(=2.8x1 0-10[m])

Specific surface area of interlayer porosity[m2/kg]Parameter representing a generic pattern ofdeposition of products around particle

Radius of powder particle [m]

Ratio of volume to the external surface area ofa typical hydrate products[nm]Weight fraction of portland cement

Weight fraction of blast furnace slag

Weight fraction offly ash

Equivalent spherical cell radius [m]

sag Specific surface area of hydrates [m2/kg]

rm Minimumradiusofpores [m]

Molecular mass of liquid [kg/mol]

Surface tension of liquid [N/m]

Volume of aggregate per unit volume [m /m ]

Coefficient of linear expansion of concrete [1 /K]Fractional volume of powder materialsKronecker delta

v Poisson's ratio

r\i Non-dimensional thickness of cluster

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Pore pressure [Pa] Vs

Concentration of chloride ions [mol/1] WsTemperature [K] aFlux of moisture [kg/m2.sj pg

Flux of chloride ions [mol/m2.s] §cpFlux of heat [kcal/m2.s] (j)g/

Moisture conductivity [kg/Pa.m.s]Liquid conductivity [kg/Pa.m.s]

Vapor conductivity [kg/Pa.m.s]

Viscosity of fluid under non-ideal conditions[N -s/m2]

Effective non-ideal viscosity of the porefluid [N-s/m2]

Additional energy for activation of flowFictitious humidity parameter

Pore radius [m]Pore radius in which the equilibrated interfaceof liquid and vapor is created [m] °Normalized pore volume [m3/m3]

Knudsen number

Velocity vector of pore solution phase

Flux of liquid [kg/m2.s]

Qp Sinkterm for moisture balance rmax

n Term representing bulk porosity change �^pd effects *rmax

� Termrepresenting water consumption due^hyd to hydration r"'in

Amount of chemical combined water perP unit weight of hydrated powder materials S,-min

n ,~i\,~-\[kg/kg]

-Accumulated heat generation of chemical' component / [kcal]

";HO

� Termrepresenting the reduction of free^ chlorides ""'"

CboundAmount of bound chlorides [mol/1] RHmin

QH Heat generation term S0j r Heat generation rate of clinker component

1 /[kcal/kg.s] ^lr

,, Reference heat rate of/-th component at �00 temperature T0 [kcal/kg.s] lot

fa\ Activation energy of component /Em [kcal.K/kg.s] 0ix0d

P, Reduction of probability of contact C,ot

Volume of hydrated products [m3/m3]Weight of hydrated products [kg/m3]

Average degree of hydrationDry density of gel products [kg/m3]

Capillary porosityGel porosityInterlayer porosityTotal porosityPorosity at outermost boundary of theexpanding cluster

Cluster thickness

Specific surface area of capillary porosity[m2/m3 ]

Specific surface area of gel porosity [m2/m3]

Porosity distribution parameterRelative humidiry

Thickness of adsorbed layer [m]

Humidity required to fully saturate a poreDegree of saturation due to adsorbed waterDegree of saturation due to condensed waterDegree of saturation due to condensed waterin virgin wetting pathPore radius of the largest pores thatexperienced a complete saturation in thewetting history [m]Highest saturation experienced by the porousmedia in its wetting historyPore radius of the smallest pores thatexperience emptying out in the drying history[m]

Lowest saturation of porous media in itswet-dry history

Highest saturation experienced by interlayerporosity in its wetting historyLowest saturation experienced by interlayerporosity in its drying historyMinimum RH experienced in its dryinghistoryDegree of saturation of gel and capillary pores

Degree of saturation of interlayer porosity

Degree of saturation of total pores

Equilibrium ratio of fixed chloride componentto total ion componentTotal amount of chloride ions [mol/1]

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between unhydrated compounds and freepore water

K>f,.ee Amount offree water sr

Unrestrained shrinkage strain due to porepres sureDeformability against capillary stress [Pa] aj/

0i

£,/0h

Esh

fc' Compressivestrength [Pa]Vpore Volume of capillary pores above 50nm

Elastic module [Pa]Tensile strength [Pa]External force in /-direction

u Displacement in x-direction

v Displacement in y-direction

w Displacement in z-direction

t Loading period [s]

e,y Straintensor

0,j Stresstensor

References

Unrestrained strain due to temperature

Average volumetric stress

Average volumetric strainDeviatoric stressDeviatoric strainBulk modulusShear modulusCreep coefficientCoefficient representing effect of mixproportion and temperatureCoefficient representing effect of temperaturehistoryCoefficient representing effect of compressivestrengthCoefficient representing effect of W/CCoefficient representing effect of temperaturehi story

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