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RESEARCH REPORT AALTO‐R‐001‐11

DuraInt Report – Task 4 - Deterioration Models with Interaction Olli‐Pekka Kari

RESEARCH REPORT AALTO‐R‐001‐11 2 / 40

1 Introduction ............................................................................................................................................... 4

2 Deterioration Processes of Reinforced Concrete ....................................................................................... 4

2.1 Carbonation .......................................................................................................................................... 4

2.2 Moisture Ingress ................................................................................................................................... 5

2.3 Chloride Ingress ................................................................................................................................... 5

2.4 External and Internal Frost Damage in Reinforced Concrete ............................................................... 6

3 Numerical Models for the Estimation of Deterioration of Reinforced Concrete ...................................... 6

3.1 Carbonation .......................................................................................................................................... 6

3.1.1 Diffusion of Carbon Dioxide ....................................................................................................... 6

3.1.2 Carbonation Rate ......................................................................................................................... 8

3.2 Moisture Ingress ................................................................................................................................... 9

3.3 Chloride Ingress ................................................................................................................................. 14

3.3.1 The Effect of Silica Fume on the Diffusivity of Chlorides ........................................................ 16

3.3.2 The Effect of Blast Furnace Slag or Fly Ash on the Diffusivity of Chlorides ........................... 17

3.3.3 Chloride Binding ....................................................................................................................... 17

3.4 External and Internal Frost Damage in Reinforced Concrete ............................................................. 18

3.5 Microstructural Calculation of Cement Paste ..................................................................................... 18

3.5.1 The Contents of Ca(OH)2 and C-S-H in Cement Paste ............................................................. 18

3.5.2 The Porosity of Cement Paste .................................................................................................... 19

3.6 Heat Diffusion .................................................................................................................................... 19

3.7 The Combined Effects of the Deterioration Mechanisms .................................................................. 20

3.7.1 The Effect of Carbonation ......................................................................................................... 20

3.7.2 The Effect of Chloride Diffusion ............................................................................................... 20

3.7.3 The Effect of External and Internal Frost Damage .................................................................... 20

4 Computer Simulations ............................................................................................................................. 22

4.1 Materials ............................................................................................................................................. 22

4.2 Basic Assumptions in the Calculations .............................................................................................. 22

4.2.1 Environmental Conditions ......................................................................................................... 23


4.2.2 Frost-Salt-Scaling ...................................................................................................................... 23

4.2.3 Chloride Ingress and Carbonation During Summer and Winter times ...................................... 24

4.2.4 Analysis of the Penetration of Chlorides through Concrete Cracks .......................................... 25

5 Results and Discussion ............................................................................................................................ 26

5.1 Frost-Salt, and Carbonation, and Chloride Penetration ...................................................................... 26

5.2 Carbonation and Chloride Penetration ............................................................................................... 27

5.3 Penetration of Chlorides through Concrete Cracks ............................................................................ 29

6 Error Estimation ...................................................................................................................................... 29

7 Conclusions ............................................................................................................................................. 30

References ....................................................................................................................................................... 31


1 Introduction One aim in the Duraint project is to combine different damage models to one service life calculation model and apply this model in wide geographical area. The main deterioration types in the project are: chloride diffusion, external and internal frost damage in concrete, cracking of concrete, and carbonation of concrete.

This part of the project is concentrated on the interaction between chlorides, carbonation and freezing effects on concrete. A developed numerical model (Kari, 2009) has been utilised as a basis for reaching the solution to the problem.

The main objective in the modelling is thus to determine the interactive effects between the penetrating chlorides and the carbonation of the concrete and freezing of concrete. A challenge in the modelling is to combine the mechanisms of varying humidity and temperature to the model, taking into account the freezing of the concrete. In addition to that, the external concentrations of the chlorides are not constant during the exposure period. The durability impacts of the cracks of the concrete need to be also investigate when developing the model.

2 Deterioration Processes of Reinforced Concrete

2.1 Carbonation There exist several factors affecting the carbonation rate and carbon dioxide diffusivity. The controlling parameters reflect the surrounding environment and characteristics of the concrete. The environmental factors are relative humidity, temperature, and external CO2 concentration. The water-to-binder ratio and types of cement and mineral admixtures can be attached to the characteristics of the concrete.

When concrete carbonation is being modelled, besides the factors presented above, both the effect of the concentration of free carbon dioxide in the pore solution at any given time and the degree of carbonation should be taken into account. The rate of carbon dioxide diffusion increases with an increase in the concentration of carbon dioxide in the pore solution. On the other hand, the degree of carbonation retards the carbonation process as a whole, i.e. both the carbon dioxide diffusion and reaction velocity are reduced as a result of the progressive carbonation.

To simplify the problem, additions of silica fume or blast furnace slag or fly ash are assumed not to have an effect on the carbonation rate, except through the maximum obtainable content of calcium carbonate. The formation of calcium carbonate is proportional to the cement and CaO contents in the concrete. As a result, all the cement types are handled similarly.

The net effect of the carbonation process is the retarded diffusion of species when ordinary Portland cement is used. Therefore, in the model, the carbonation process is assumed directly to affect the reduction of the diffusivities of the chlorides and moisture in OPC concrete. If blast furnace slag or fly ash cement is used as a cement replacement, the beneficial effect of carbonation is not taken into account because of the possible harmful effects on chloride diffusion. Silica fume replacements are treated in the same way because of a lack of data concerning the benefits of carbonation. The other possible chemical and physical effects and interaction with other ions are not included in the model.


2.2 Moisture Ingress When the diffusion of moisture is being determined, the moisture content in the concrete can be defined by either the gradient of free water content or the gradient of pore relative humidity. The problem with the water content is that, even if the total water content is fixed, the free water content is a function of time. This is because a part of the water is consumed by the hydration reaction and thus becomes chemically combined water, which is immobile. Therefore, a more practical way is to use the gradient of pore relative humidity to represent the moisture content, which is a combined indicator for liquid water and water vapour (Suwito et al. 2006). Therefore, the pore relative humidity is controlling parameter for drying and wetting of concrete in the modelling. Consequently, the moisture capacity is the main parameter that has to be defined when solving the problem in terms of pore relative humidity.

The factors affecting the diffusion of moisture are pore relative humidity, temperature, hydration time, and material properties such as pore sizes and hydration. Because these factors, except the hydration time, are based on the same elements as within the carbonation process, there is no need to discuss them again. In the case of the hydration time, the required hydration degree is estimated through the calculation of the equivalent hydration period (Bazant and Najjar 1972). The liberated water resulting from carbonation is not taken into account and nor is the self-desiccation because of the insignificance of these effects in this case.

2.3 Chloride Ingress There are several different transport mechanisms for chloride ions into concrete, which can be divided into the following groups (Poulsen and Mejlbro 2006): diffusion, permeation, migration, and convection. Inside the concrete, chloride ions can be present in three different forms, according to Neville (1995):

chemically bound to the hydration products of cement

physically sorbed on the surfaces of the gel pores

dissolved in the pore solution.

Thus, some of the chlorides will be bound and the total amount of chlorides in the concrete is the sum of the free and bound chlorides. It is generally accepted that steel corrosion is caused by the free chlorides. Therefore, the differential equations are based on the concentration of free chlorides.

The factors that can be related to the chloride ingress are: temperature, pore relative humidity, curing time, chloride concentration, time of exposure, and material properties (diffusivity of aggregates, cement type, water-to-binder ratio). Basically, some of the factors, such as temperature, pore relative humidity, curing time, and specified material properties, affect chloride diffusion in a similar way than with both the carbonation process and moisture diffusion.

In order for the chloride penetration to be modelled, the factors presented above are taken into account in the calculations, as is chloride convection by moisture transport in unsaturated conditions (in saturated conditions the term vanishes). The effects of mineral admixtures are included in the model as follows: with silica fume by assuming that it directly affects the diffusion coefficient through reduction factors, and with blast furnace slag or fly ash by the age reduction factor. The age reduction factors of OPC concrete and OPC concrete with the addition of 10% silica fume (replacement level in this study) are assumed to be dependent on the water-to-binder ratio, according to the findings of Mangat and Molloy (1994). The use of blast furnace slag or fly ash to replace cement is assumed to affect the age reduction factor through the reduced factor that depends on the replacement level of blast furnace slag or fly ash in concrete. In order to prevent a limitless reduction of diffusivity with time, it is assumed that the decrease in the diffusivity, regardless of the cement type, takes place up to the age of 25 years and after that it remains constant, getting a 25-year value (Life-365 program manual 2008).


The other processes are assumed to affect the diffusivity of chlorides directly through the porosity changes caused by either frost damage or carbonation. It is not clear, however, how the progress of chloride diffusion affects the permeability of the concrete (Puatatsananon 2002), not to mention the other effects. Because of their indistinct effect on durability, these factors can be considered to be negligible. Therefore, the other possible chemical and physical effects and interaction with other ions are not included in the model.

2.4 External and Internal Frost Damage in Reinforced Concrete A completely or partially saturated porous medium exposed to temperatures below the freezing point is subjected to a purely thermal stress at the same time as the stress related to ice formation within its porosity. In addition to that, salt scaling is defined as superficial damage caused by freezing a saline solution on the surface of a concrete body. The damage is progressive and consists of the removal of small chips or flakes of material (Valenza et al. 2006). Frost salt scaling can be explained basically as a combination of internal microcracking and external action such as Glue-Spall theory due to freezing. In spite of the extent research on salt scaling, the proposed mechanisms cannot account for all of the phenomenology that is happening here. The modelling of internal and external frost action in this research has been done by studying the changes diffusivity properties of concrete, and taking into account the effect of subzero temperatures as a delaying effect of chemical processes.

3 Numerical Models for the Estimation of Deterioration of Reinforced Concrete

This chapter will present all the governing equations incorporated into the model for the estimation of concrete deterioration. The equations are based on the previous chapter, where the theory behind the numerical models was discussed.

3.1 Carbonation

3.1.1 Diffusion of Carbon Dioxide The diffusion of carbon dioxide is described by the following equation, based on Fick’s law (Saetta et al. 1993 and 1995, Brieger and Wittmann 1986, Puatatsananon 2002):

(3.1)

where Dg is the carbon dioxide diffusion coefficient [m2/s], g is the carbon dioxide concentration [kg/m3],

4 is the material parameter which reflects the characteristics of the concrete [-], and c is the concentration of CaCO3 [kg/m3]. The carbon dioxide diffusion coefficient is described as follows:

(3.2)

where Dg28 is the carbon dioxide reference diffusivity at an age of 28days [m2/s], F1(H) is the effect of the pore relative humidity [-],

F2(T) is the influence of the temperature [-], F3(te) is the effect of the curing time [-], and

,)]([ 4 t

cggradDdiv

t

gg

),()()()( 432128 cFtFTFHFDD egg


F4(c) is the decrease in CO2 diffusion as a result of carbonation [-].

The reference diffusivity of carbon dioxide at an age of 28 days (at a temperature of 25°C) can be determined using the compressive strength of concrete as (Saetta and Vitaliani 2005):

(3.3)

where fck is the compressive strength (cylindrical) of the concrete at an age of 28 days [MPa]

The effect of the pore relative humidity H on the diffusivity of carbon dioxide, i.e. the decrease in CO2 diffusivity as the relative humidity increases, is defined using the following formula for F1(H):

(3.4)

A function F2(T) takes into account the influence of temperature by means of the formula, based on Arrhenius’ law:

(3.5)

where Q is the activation energy of the carbonation process [kJ/mol], Rgas is the gas constant [kJ/mol·K], T0 is the reference temperature at which the Dg28 is measured [K] and T is the actual absolute temperature in the concrete [K].

The influencing factor of the curing time of the concrete F3(te) takes the form

(3.6)

where is the ratio of diffusivity at time ∞ to 28d, i.e. = Dg∞/Dg28 [-] and te is the equivalent curing time of the concrete [days]. The equivalent curing time (or hydration period) te can be defined as follows (Bazant and Najjar 1972):

(3.7)

where t0 is the time of the first exposure of the concrete [s], t determines the dependence of te on the temperatures T and T0 [-], and h determines the dependence of te on the pore relative humidity h [-]. t and h are given by

,101021

025.07

28

s

mD MPa

f

g

ck

.)1()( 5.21 HHF

,exp)(0

2

TR

Q

TR

QTF

gasgas

,28

)1()(3e

e ttF

,0

0 t

t

hte dttt


(3.8)

(3.9)

where Uh is the activation energy of hydration [kJ/mol].

The ratio Uh/R in Equation

(3.8) is determined as (Saetta et al. 1993):

(3.10)

The last function F4(c) reflects the decrease in CO2 diffusion caused by carbonation:

(3.11)

where is a material-dependent coefficient [-] and R is the degree of carbonation [-]. The degree of carbonation can be determined as follows:

(3.12)

where CaCO3max is the total obtainable amount of CaCO3 in the pore solution [kg/m3].

The value of CaCO3max can be derived from the following equation (Steffens et al. 2002):

(3.13)

where z is the cement content of the concrete [kg/m3] and C is the calcium oxide concentration in the cement [%].

The carbonation reaction front can be defined as the point where the carbonation degree R is equal to 0.9, according to Meier et al. (2005) and Steffens et al. (2002).

3.1.2 Carbonation Rate The carbonation rate can be written as follows (Saetta et al. 1993 and 1995, Brieger and Wittmann 1986, Puatatsananon 2002):

andTTR

U

gas

ht

11exp

0

,)5.75.7(114

Hh

39.0

][263

][30][4600

KT

KK

R

U

gas

h

,1)(4 RcF

,max3

3

CaCO

CaCOR

),2.3(0052.0max3 CzCaCO


(3.14)

where f1(H) is the effect of the pore relative humidity [-],

f2(g) is the carbon dioxide concentration [kg/m3], f3(R) is the degree of carbonation [-], f4(T) is the influence of the temperature [1/s], and 1 is the material parameter reflecting the characteristics of the concrete [-].

The pore relative humidity H also has an essential effect on the reaction rate. In dry concrete (H < 0.5) the process will come to a halt, while above that level the value of f1(H) will range between 0 and 1. This is given by

(3.15)

The f2(g) function reflects the effect of the free carbon dioxide concentration g in the pores. It will take a value of 0 in the zones where the carbon dioxide has not penetrated, and a value of 1 in the zones where the carbon dioxide concentration is equal to the atmospheric concentration gmax. The function is given by

(3.16)

The degree of carbonation R will affect the carbonation rate as follows:

(3.17)

The last equation takes into account the effect of the surrounding temperature by using Arrhenius’ equation:

(3.18)

where A is the Arrhenius constant [1/s], and T is the actual absolute temperature in the concrete [K].

3.2 Moisture Ingress The moisture diffusion is expressed through the formulation (Xi et al. 1994, Ababneh et al. 2003, Puatatsananon 2002):

),()()()(][

432113 TfRfgfHf

t

c

t

CaCOv

.19.01

9.05.0)5.0(2

5

5.000

)(1

H

HH

H

Hf

.)(3

max2

m

kg

g

ggf

.1)(3 RRf

,)(4TRQ gaseATf


(3.19)

where W is the total water content for the unit volume of material [g/g], H is the pore relative humidity [-], and Dh is the humidity diffusion coefficient [m2/s]. The humidity diffusion coefficient can be calculated according to (Martin-Perez 1999):

(3.20)

where Dh28 is the moisture reference diffusivity at an age of 28 days [m2/s], F1(H) is the effect of the pore relative humidity [-],

F2(T) is the influence of the temperature [-], and F3(te) is the effect of the hydration time [-].

Dh28 can be evaluated from the concrete water-to-binder ratio (w/c) by the following equation, which is based on experimental results (Persson 1997):

(3.21)

F1(H) takes into account the effect of the pore relative humidity on the moisture diffusivity and is given by

(3.22)

where 0 is the ratio between the minimum and maximum diffusivities of moisture [-],

Hc is the humidity at which Dh drops to halfway between its minimum and maximum values [-], and n is the parameter characterising the spread of the drop in Dh [-].

Figure 1 illustrates the above parameters in Equation (3.22), which are based on the experimental results (Martin-Perez 1999).

)],([)]([ HgradDdivW

H

t

HHgradDdiv

t

H

H

W

t

Whh

),()()( 32128 ehh tFTFHFDD

.10081.0)/(41.0/1.72

10228

s

mcwcwDh

,

11

1

1)( 0

01 n

cHH

HF


Function F2(T) is determined in the same way as with the diffusion of carbon dioxide (Equation (3.5)), except the activation energy Q is for the moisture diffusion process.

The parameter F3(te) that takes into account the effect of the hydration time te (calculated from Equation (3.7)), is determined as

(3.23)

The moisture capacity of concrete HW can be defined considering concrete as a two-phase composite

material, the aggregate being one phase and the cement phase being the other (Xi et al. 1999). It is expressed by

(3.24)

where fagg is the weight percentage of the aggregate [-], fcp is the weight percentage of the cement paste [-],

aggagg H

Wf

is the moisture capacity of the aggregate [-], and

cpcp H

Wf

is the moisture capacity of the cement paste [-].

The total water content at a constant temperature, i.e. the absorption isotherm, needs to be determined for both the cement paste and aggregates. It is based on the BSB model (Brunauer et al. 1969) and can be evaluated by (Xi et al. 1994):

Figure 1 Dependence of F1(H) on pore relative humidity, 0 = 0.05, Hc = 0.75, and n = 6-16 (Martin-Perez 1999).

.13

3.0)(3e

e ttF

,cp

cpagg

agg H

Wf

H

Wf

H

W


(3.25)

where C is a constant parameter [-], k is a constant parameter [-], and Vm is the monolayer capacity [-].

The above parameters are determined from the following expressions for the cement paste and aggregates (Martin-Perez 1999):

(3.26)

(3.27)

The parameters n and Vm above for cement paste are (denoted as ncp and Vmcp):

(3.28)

(3.29)

,])1(1[)1( HkCHk

HVkCW m

,][855

exp

T

KC

,1

11

1

C

Cn

k

,6.015

5.265.1

3.015

5.299.0

,52.233.05.5

,6.03.052.233.015

5.2

c

wif

t

andc

wif

t

daystifc

w

c

wanddaystif

c

w

t

n

e

e

e

ee

cp

.6.022.0

068.012.1

3.022.0

068.0985.0

,545.085.0024.0

,6.03.0545.085.022.0

068.0

c

wif

t

andc

wif

t

daystifc

w

c

wanddaystif

c

w

t

V

e

e

e

ee

mcp


The parameters for aggregates are (denoted as nagg and Vmagg) (Puatatsananon 2002):

(3.30)

where npsagg describes the pore structure of the aggregates.

npsagg is given as presented in Table 1.

The monolayer capacity for aggregates, Vmagg, can be expressed by

(3.31)

where Vpsagg describes the pore structure of the aggregates. Vpsagg can be determined in the way shown in Table 2.

As a result, the moisture capacity of concrete in the general case is obtained as a derivative of an absorption isotherm of concrete (Equation (3.25)) with respect to the pore relative humidity.

(3.32)

Table 1 The values of npsagg depending on the pore structure of aggregates (Puatatsananon 2002).

Table 2 The values of Vpsagg depending on the pore structure of aggregates (Puatatsananon 2002).

,063.4 psaggagg nn

,00647.0 psaggmagg VV

aggcp

i ii

imii

ii ffff

kHCkH

VkHCkCf

H

W

21

2

122

,222

1

,,111

11


3.3 Chloride Ingress Chloride diffusion in unsaturated concrete in the form of free chlorides is expressed as (Ababneh et al. 2003, Xi et al. 1999, Oh et al. 2001, Martin-Perez 1999, Puatatsananon 2002):

(3.33)

where Ct is the total chloride concentration [gchloride/gconcrete], Cf is the free chloride concentration [gchloride/gconcrete],

tf CC is the binding capacity of the concrete,

DCl is the chloride diffusivity of the concrete [m2/s],

is the unit converter [-], and W is the total water content for the unit volume of material [g/g] given by Equation (3.25).

In saturated concrete the term tW vanishes.

The chloride diffusivity DCl is determined as follows

(3.34)

where f1(gi) is the effect of the aggregates on the diffusivity [m2/s], f2(w/c,t0) is the influence of the water-to-binder ratio and curing time [-], f3(T) is the effect of the temperature [-],

f4(H) is the effect of the pore relative humidity [-], f5(Cf) is the effect of the chloride concentration [-] f6(t) is the effect of the time of exposure [-], and F4(c) is the effect of carbonation as defined before [-].

The effect of the aggregates on the effective diffusivity of the concrete f1(gi) at reference age is given by

(3.35)

where Di is the diffusivity of the aggregates [m2/s], Dm is the diffusivity of the cement paste [m2/s] and gi is the volume fraction of the aggregates [-].

The diffusivity of the cement paste can be evaluated by using the following equation:

,)(

ffCl

t

ff Ct

WCgradDdiv

C

C

t

C

),()()()()(),/()( 46543021 cFtfCfHfTftcwfgfD fiCl

,

31

1)(1

mi

mi

imi

DDDg

gDgf

,12 2

2.4

2 s

mVV

S

VVD c

pp

cpp

m


(3.36)

where Vp is the porosity of the cement paste [%], Vp

c is the critical porosity of the cement paste [%], and S is the specific surface area [-]. The porosity of the cement paste is calculated in this case by using the absorption isotherm of saturated concrete (H = 1). The absorption isotherm must be converted to a volume fraction, which is done by multiplying it by the bulk specific gravity of the cement paste (estimated value 2.5). The value of the critical porosity of the cement paste is assumed to be 3%.

The specific surface area can be estimated through the monolayer capacity Vm (Equations (3.29) and (3.31)). It is assumed that S = Vm.

The diffusivity of the aggregates can be determined in the same way as with cement paste, or may be taken as being a constant equal to 1·10-16 m2/s (Ababneh et al. 2003). The constant value was used in this study.

The effect of the water-to-binder ratio and curing time can be evaluated by

(3.37)

where t0 is the curing time [days].

Equation (3.37) is valid for concrete with a curing time of less than 28 days. If the curing time is longer, the value of t0 takes the 28-day value.

Function f3(T) is determined in the same way as with the diffusion of carbon dioxide (Equation (3.5)), except that the activation energy Q is for the chloride diffusion process, depending on the water-to-binder ratio and possible additions (Table 3).

The influence of the pore relative humidity on the diffusivity of chlorides f4(H) can be determined as follows:

Table 3 Activation energies for OPC and OPC with additions (Puatatsananon 2002).

,280,

62500

28

300

28

4

1),/( 0

0

55.6

002

tt

c

wttcwf


(3.38)

where Hc is the critical pore relative humidity [-].

The critical pore relative humidity Hc takes the same value as in the case of the moisture diffusion, i.e. Hc = 0.75.

The effect of the free chloride concentration on diffusivity is expressed by

(3.39)

where kion is a constant [-] and m is a constant [-].

The effect of the time of exposure is defined as (Martin-Perez 1999, Mangat and Molloy 1994, Maage et al. 1996, Bamforth 1998):

(3.40)

where t is the actual time of exposure [a], tref is the reference time [a], and

ma is the age reduction factor [-] . The age reduction factor ma is determined in the case of OPC as (Mangat and Molloy 1994):

(3.41)

Since it is not realistic to define the reduction of diffusivity as continuing indefinitely, the age reduction factor ma is assumed to be valid up to 25 years. After the concrete has reached that age the value of ma remains constant, getting a 25-year value (Life-365 program manual 2008). According to personal communication with E. Bentz (2009), the assumption of 25 years was added primarily because of a lack of experimental data for older concretes with high proportions of supplementary cementing materials and is not based on empirical observations of performance.

3.3.1 The Effect of Silica Fume on the Diffusivity of Chlorides The addition of silica fume reduces the permeability and diffusivity of concrete. The following equation is used for the diffusivity of concrete with silica fume additions, based on diffusion data (Life-365 program manual 2008):

(3.42)

where DSF is the diffusion coefficient of concrete with silica fume additions [m2/s], DOPC is the diffusion coefficient of OPC concrete [m2/s], and SF is the replacement level of silica fume in concrete [%].

,

11

1

1)( 44

cHH

Hf

,)(1)(5m

fionf CkCf

,)(6

am

ref

t

ttf

,150,165.0 SFeDD SFOPCSF

.7.03.0,6.05.2

c

w

c

wma


Equation (3.42) is valid for silica fume replacement levels lower than or equal to 15%. It is also assumed that the addition of silica fume has no direct influence on the value of ma, and thus ma is determined in a similar way as with OPC (Equation (3.41)).

3.3.2 The Effect of Blast Furnace Slag or Fly Ash on the Diffusivity of Chlorides The replacement of cement by blast furnace slag or fly ash affects the rate of reduction in diffusivity and, hence, the value of ma (Equation (3.41)). The effect of blast furnace slag on the value of ma is defined as (Life-365 program manual 2008):

(3.43)

where SG is the replacement level of blast furnace slag in concrete [%] and

FA is the replacement level of fly ash in concrete [%].

Equation (3.43) is valid for a replacement level of blast furnace slag lower than or equal to 70% and for fly ash the same with 50%. The water-to-binder ratio is assumed to have no effect on the reduction of diffusivity in this case.

3.3.3 Chloride Binding The total chloride concentration is given by

(3.44)

where Cf is the free chloride concentration [gchloride/gconcrete] and

Cb is the bound chloride concentration [gchloride/gconcrete].

Therefore, the binding capacity of concrete may be rewritten as

(3.45)

The term fb CC is called the chloride isotherm. In this study, the Freundlich isotherm model is chosen

because of the high external chloride concentration (Tang and Nilsson 1993). It is given by (Martín-Pérez, B. 1999)

(3.46)

where is the binding constant [m3 of pore solution/m3 of concrete], is the binding constant [m3 of pore solution/m3 of concrete],

500,700,5070

4.02.0,,

FASG

FASGm flyashslaga

,bft CCC

,1

1

f

bt

f

CCC

C

1 f

f

b CC

C


The binding constants and are dependent on the cement system used and on the units employed for Cb and Cf . The constants that were used in the simulations were based on the values that can be found in literature general and by (Martín-Pérez, B. 1999) for the similar cement types.

3.4 External and Internal Frost Damage in Reinforced Concrete Due to the lack of well-established and validated model for the external and internal frost damage in concrete and the complexity of the modelling, the internal and external damage have been assumed to affect directly

on the diffusivities of all the species in question as

(3.47)

where Dfd is the diffusivity of the frost-damaged concrete [m2/s], Di is the diffusivity of the species in question [m2/s],

is the increased porosity of the concrete after frost damage [m3/m3] and

is the initial porosity of the concrete [m3/m3].

Measured internal damage (RDM%) and scaling values can be therefore utilised directly as inputting values of Dfd through changes in porosity if available.

3.5 Microstructural Calculation of Cement Paste

3.5.1 The Contents of Ca(OH)2 and C-S-H in Cement Paste There is a need for the microstructural calculation of the cement paste in some equations. In that case, the contents of Ca(OH)2 (denoted as CH, [kg/m3]) and C-S-H [kg/m3] in the cement paste have to be determined. The calculation is performed through the expressions for the estimation of the chemical composition of Portland cement and Portland cement with silica fume proposed by Papadakis (1999). The values were approximated from the values that can be found general in literature for the cases where blast furnace slag or fly ash is used as a replacement.

OPC and OPC with silica fume are analysed in terms of oxides: total CaO (C), SiO2 (S), Al2O3 (A), FeO3 (F),

and SO3 ( S ). The weight fractions of the oxides (C, S, A, F, and S ) in the cement (c) and pozzolans (p) are denoted as fi,c and fi,p.

Even if the chemical reactions of hydration do not proceed to completion, the simplified equations for hydration can be used, as follows:

(3.48)

These reactions are valid when there is an excess of gypsum, i.e.

.102

10

42

362

1264

12423

3232

3233

AFHCHCHAFC

HSACHHSCAC

CHHSCHSC

CHHSCHSC

).501.0786.0( ,,, cFcAcSfff

,10

ifd DD


(3.49)

Using the stoichiometry of the reactions and the molar weights of the reactants and products, the produced components needed in this work can be determined and are given for Portland cement by

(3.50)

(3.51)

In the presence of silica fume, the pozzolanic reaction takes place and is given by

(3.52)

(3.53)

where s is the active (glass) part of SF [-].

For the completion of pozzolanic activity, the value of CH in Equation (3.52) must be positive. If CH = 0, the maximum obtainable pozzolan content Pmax [kg/m3] that can react with all the Ca(OH)2 produced during the hydration can be obtained as

(3.54)

3.5.2 The Porosity of Cement Paste

The porosity of cement paste before leaching, i.e. the initial porosity , is defined as (Ljungkrantz et al. 1994):

(3.55)

where is the degree of hydration [-].

It is assumed that hydration proceeds to completion in this work if no data available. Thus, the degree of

hydration is the maximum obtainable value that is calculated simply by the expression (Taylor 1997):

(3.56)

Note that the air pores are not included in Equation (3.55) and, if necessary, need to be added there.

3.6 Heat Diffusion Temperature variations can be modelled by using the following equation (Puatatsananon 2002):

andCfffffCH cFcAcScScC ,,,,, 392.1182.2851.17.0321.1

.85.2 , CfCSH cS

andPf

CfffffCH

pSs

cFcAcScScC

,

,,,,,

851.1

392.1182.2851.17.0321.1

,85.2 ,, PfCfCSH pSscS

.

851.1

392.1182.2851.17.0321.1

,

,,,,,

maxpSs

cFcAcScScC

f

CfffffP

,32.0)/(

19.0)/(0

cw

cw

.10,38.0

)/( cw


(3.57)

where is the density [kg/m3], C is the specific heat of concrete [J/kgK], k is the thermal conductivity of concrete [W/mK], and Q is the rate of heat per unit volume generated within the body [W/m3].

3.7 The Combined Effects of the Deterioration Mechanisms The following assumptions are applied to the combined effect of the deterioration mechanisms. All the effects are directed to the diffusion coefficients of the substances. The bases of these assumptions have been described earlier. Figure 2 presents the equations used in the calculations.

3.7.1 The Effect of Carbonation It has been shown that the net effect of carbonation is to retard the diffusion of both moisture and chloride into OPC concrete. These effects can be described by multiplying the chloride and moisture diffusion coefficients by the function F4(c) (Equation (3.11)), which reflects the decrease in CO2 diffusion as a result of carbonation. The retarded diffusion of chlorides as a result of carbonation is not valid when silica fume or blast furnace slag is used as a cement replacement.

3.7.2 The Effect of Chloride Diffusion It is assumed that chloride diffusion itself has no implication for the other deterioration mechanisms.

3.7.3 The Effect of External and Internal Frost Damage The increased diffusivity of concrete relating to the effect of internal and external frost damage is assumed to affect directly to the other mechanisms. On the other hand, following from the temperature dependency of the chemical processes, sub-zero temperatures may delay or halt the progression of the process, such us in the case of carbonation.

QTgradkdivt

TC

)]([


Figure 2 The equations used in the calculations.


4 Computer Simulations

4.1 Materials Seven different kind of concrete mixes were chosen for the simulations. The water to cement ratio varied between 0.42 and 0.50. Mixes were normal or rapid type (R) or contained blast furnace slag (type KJ400) or fly ash (FA). Air entrainment was either 2% or 5% in all the mixes. The concrete specimens that were used in the simulations are presented in Table 4. The other specific data from the concrete mixes needed for the simulations, e.g. chemical composition of cements, aggregate properties and mechanical properties of the specimens, can be found in Table 4.

Table 4 Concrete specimens used in the simulations.

4.2 Basic Assumptions in the Calculations The calculations were performed as follows. The dimensions of the rectangle under study, which describes the structure on the field, were 100x100 mm2. The 1D mesh was used to describe the rectangle. The mesh

was denser at the external edges towards exposure solutions. The time stepping in the calculations was one day. This length was finally chosen after the testing of various time steps. Boundary values and the environmental concentrations Cen of the species used in the calculations were as

CO2 = 400 ppm (average concentration in atmosphere)

Cl- = 0.06 % wt of conc. (according to the exposure tests)

T and RH varied according to the graph of environmental conditions

The diffusivities of the simulated concrete mixes for chlorides were determined in laboratory (Table 5). Those values were used as input values in the calculations, that is the modelling parameters were adjusted for the values in the simulations.

Table 5 Experimentally determined chloride diffusivities for simulated concrete mixes.


4.2.1 Environmental Conditions Temperature variations as well as the moisture conditions were determined by the following graph (Figure 3) which is based on the measured test data on the field (note the possible updating of the data). Green line in the graph describes temperature T and blue line is relative humidity RH. The both values are assumed to obey a sine function.

Figure 3 Environmental conditions on the field that were used in the modelling.

4.2.2 Frost-Salt-Scaling The effect of frost-salt-scaling on the carbonation and chloride ingress and, basically, on the ingresses of the other species, was taken into account by investigating the scaled surface, marked here as XFS in Figure 4. XFS is based on the test results of each concrete mix after 56 freeze-thaw cycles in the laboratory which has been converted to response the scaling on the field. A front of the scaled surface and, further, cracked surface has been determined by multiplying XFS by the time of exposure tn. The diffusivity is assumed to be infinite in the scaled area as all the material has been vanished there, i.e. D1/D2 → ∞.

Figure 4 The effect of scaling on the ingresses of the other species in the calculations.


The P-rate method (Finnish Road Administration 2005) can be utilized here as the relation that can be found between the P-rates and the scaling on the field. Firstly, the P-rates for the concrete mixes which were based directly on the test results after 56 freeze-thaw cycles were calculated by using the equation as

(4.1)

where ksid is the cement factor [-] and m56 is the test result of scaling after 56 cycles [g/m2].

After calculations of the P-rates the scaling after 5 years’ exposure on the field can be read from the following graph (Matala, S.) presented in Figure 5 (P-rate given as P-luku, 5 year’s exposure as

Kenttärapauma). The scaling on the field (V) was assumed to take place as 1-dimensional and the values were converted directly to XFS as a 5 year value.

Figure 5 The relation between P-rates and the scaling on the field after 5 years' exposure.

4.2.3 Chloride Ingress and Carbonation During Summer and Winter times The chloride profiles vary a lot during the wetting and drying periods of concrete. During the wetting period chlorides, originated here from de-icing salt, move inside the structure with, basically, the penetrating moisture. When the concrete is under drying state the evaporating moisture carries the chlorides out from the structure near the drying surface. As a result, the chlorides will accumulate near the concrete surface where the drying action is not effective anymore. The phenomenon is described in the schematic Figure 6.

Sub-zero temperatures may delay or halt the progression of the chemical processes and the moisture movement, especially when the de-icing is not effective. Therefore, the prerequisite for proceeding carbonation process cannot be always found during the winter time and the process is delayed at least then. The carbonation process has been assumed to halt on sub-zero temperatures in the simulations of this study.


Figure 6 Schematic picture of chloride concentration under wetting and drying and the described accumulation peak of chlorides after 5, 10 and 15 years of exposure.

4.2.4 Analysis of the Penetration of Chlorides through Concrete Cracks

The objective of this part of the research was to find parameters significance for chloride migration in cracked concrete by the means of computer simulation. The main focus was the crack size. The principles for the measurements, and the results for the crack width and length, and chloride migration measurements trough the crack zone of the specimens are presented in Figure 7. Preparation of the specimens and the other specific data can be found from (Sillanpää 2010).

Figure 7 Chloride penetration through the crack zone.


The experimental test results were used as input values for the numerical simulations. The diffusion coefficient was defined to be the main parameter in the simulations. It was calculated from the average chloride migration depth of the intact edges of the specimens when pure diffusion was assumed. A diffusion of chlorides into the specimens was simulated for four crack types with different widths and lengths. The fitted crack lengths were estimated from the results of the crack width and length measurements shown in the Figure 7. The cracks were assumed to be as wedge-shaped as it can be assumed to be more realistic. The mesh used in the calculations and the example of the comparisons between the experimental and simulated chloride migrations are presented in Figure 8.

Figure 8 Mesh used in the calculations and a comparison between the calculated and experimental chloride migrations.

5 Results and Discussion

5.1 Frost-Salt, and Carbonation, and Chloride Penetration The calculated penetration profiles of chlorides for the concrete mixes 3C, 5C, 7A and 8A exposed to either carbonation + chlorides (Carb) or just chlorides (No carb) under the deterioration caused by freezing and thawing are presented in Figure 9. Frost-scaling was biggest for the mix 5C (Rapid Portland Cement), and lowest for the mix 7A (50% BFS). The calculated values for the depth of the scaled surface varied between approximately 4 mm and 48 mm (Table 6). The scaled surface depth of mix 3C was, however, approximately, less than half from the same of mix 5C. The mix that contained 24% FA (8A) performed better, but was not as good as mix 7A concerning the FSS.

As a result of the scaling, chloride penetration depths as well as the peak of the accumulated chlorides were deeper in the concrete. The difference between mixes 7A and 5C is therefore obvious. On the other hand, the highest chloride concentrations can be reached with mix 7A. The peak is located about in the depth of 10 mm though. The concentration drops quite rapid after that being near 0% in the depth of 50 mm. The situation and the shape of the chloride penetration curve are almost same for mix 8A, even though slightly inferior, but far away from the performance of mix 5C. A rapid proceeding of scaling may cause the high surface chloride concentration in the mix 5C. As a conclusion, it seems that the using of BFS or FA as a cement replacement may improve the concrete properties against FSS.


The influence of carbonation when comparing the results of cases “no carb” and “carb” seems to be biggest for the mix 3C and lowest for mix 7A. The result is not consistent with the theory as the situation should be exactly opposite way when BFS has been used as cement replacement. This observation can be considered to be, however, less meaningful in the case as it seems that frost scaling is dominating the whole process.

Figure 9 Effect of frost-scaling on carbonation and chloride penetration - validated with test results. Concrete mixes 3C, 5C, 7A and 8A. Exposure period 25 years.

Table 6 Calculated P-rates and FS for the concrete mixes.

5.2 Carbonation and Chloride Penetration The calculated penetration profiles of chlorides for the concrete mixes Y05A2, BFS05A2 and FA05A2 exposed to either carbonation + chlorides (Carb) or just chlorides (No carb) are presented in Figure 10. As can


be seen from the graphs, the using of BFS or FA slowed down the chloride ingress compared to the case where only OPC where used. Chlorides penetrated least into the BFS-mix which is consistent with the theory. However, the measured values which were used as input values for the simulation did not seem to be according to the theory, i.e. chloride diffusion increased with carbonation. In spite of the extent work that were done for clarifying the issue, the reason for that was not found. On the other hand, in few studies (Ngala and Page 1997) chloride penetration has been observed to increase in the carbonated concrete when BFS or FA was used. Obviously, this does not explain the increased diffusion in carbonated OPC-concrete. The major result, which is the observed difference between the behaviour of the mixes, can be still read from the graphs though.

The carbonation depths were calculated to the mixes of this part as presented in Table 7. These values based only on theory. The calculated carbonation depth was clearly biggest for the BFS-mix whereas the depth was in the other two mixes was close to each other. The calculated carbonation depth for the BFS-mix was 21 mm. This value is actually very close to the possible minimum reinforcement depth used (25 mm) leading to possible initiation of corrosion on that depth in the long-term because of the carbonation.

Figure 10 Effect of carbonation on chloride penetration - validated with test results. Concrete mixes Y05A2, BFS05A2 and FA05A2. Exposure period 25 years


Table 7 Calculated carbonation depths [mm] after 25 years' exposure.

5.3 Penetration of Chlorides through Concrete Cracks The penetrations of chlorides through the simulated concrete crack with various sizes are presented in Figure 11. As can be seen from the figures, the penetration depth increases with the increasing crack size as expected. The simulated result can be characterized to be consistent with the results achieved in the experiments when crack size and shape is close to the ideal crack as assumed in the simulation. The detailed analyses about the issue can be found in (Sillanpää 2010).

Figure 11 Chloride penetration through simulated crack widths and lengths.

6 Error Estimation Various potential sources of inaccuracies may exist in relation to the theory behind the modelling, structure, and calculation of the model, and the experiments used for validation. These have to be taken into account when the reliability of the model is being evaluated. The key factors which may cause dispersion in the results are discussed below:

Modelling assumptions and limitations The necessary modelling assumptions and limitations determined before have a direct impact on the reliability of the model for describing a problem in a real environment. However, a major part of the effects on the long-term durability of reinforced concrete can be considered to be negligible over the whole service life of the structures that are of concern here. The focus of this study is


material-based ageing. In overall lifetime estimations the strength and properties and cracking of the concrete are also important aspects. The cracks, combined with load variations, affect structural ageing.

Material-dependent constants The values used for material-dependent constants and references were taken partly from the literature when case-specific data were not available. Naturally, this kind of procedure increases the uncertainty of the results as the experimental arrangements and materials differ from case-specific values.

Chemical interaction mechanisms The couplings of different ageing mechanisms were performed through their diffusivities. Naturally, not all the possible chemical compositions formed in the defined environment can be taken into account. These impacts of missed compositions can be evaluated as being minor, because the dominant mechanisms were taken into account in the construction of the model.

Carbonation The effects of the carbonation of concrete on the other ageing mechanisms presented were not taken into account, excluding the direct interaction with chloride and moisture ingresses on OPC concrete. These impacts can, however, be assumed to be minor.

Chloride ingress The effect of the time of exposure, i.e. the age reduction factor of the diffusivity of chlorides, has a significant impact on the results of a calculation performed with the FEM model. The assumption that the age reduction factor is constant after an exposure period of 25 years (Chapter 3.3) can be considered to be conservative. It is, however, obvious that this presumption causes distortion in the results. The conversion of the modelling results to the units as weight of concrete without the relevant data from concrete porosity includes a potential source of error.

7 Conclusions The results received emphasize importance to consider interaction between different deterioration mechanisms of reinforced concrete. The deterioration caused by the combined mechanisms is significantly more harmful than the ageing induced by a single mechanism. The mathematical methods based on a group of differential equations can be used to simulate the interaction of different deterioration mechanisms. The mechanisms recognised and included in the mathematical model were: the carbonation of concrete; moisture ingress; chloride penetration and internal and external frost damage. However, the model can also be used to describe deterioration due to a single deterioration mechanism.

The carbonation depths received did not exceed the depth of 25 mm during the 25 years’ exposure. The calculations predicted that plain cements would perform best, whereas cements with blast furnace slag ingredients led to greater carbonation depths.

The computed chloride ingresses were relatively high in concrete mixes at ordinary reinforcement depths (25-75 millimetres) when they were suffering frost damage probably exceeding or close to the general estimated critical corrosion threshold values (0.05% wt of concrete) in the long run. The penetration depths were clearly smaller with the mixes containing BFS or FA than with plain mix. It should be noted that actual threshold values should be determined case by case.

There was some indication of consistency between the measured length and telltale width of a crack and also with the length of a crack and chloride migration depth at the crack. But then the chloride migration depth below the end point of a crack was independent from the telltale width of a crack.

The main uncertainty of the model relates to the lack of the controlling of both the aleatory and epistemic uncertainties which will make the evaluation of the accuracy of the model more complicated.


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