prediction of corrosion-free service life of concrete...

Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

-533-

PAPER REF: 6217

PREDICTION OF CORROSION-FREE SERVICE LIFE OF CONCRETE

STRUCTURES ALONG COASTAL REGIONS: A NUMERICAL

FRAMEWORK

S. Muthulingam1, B. N. Rao

2(*)

1Department of Civil Engineering, SSN College of Engineering, Kalavakkam 603 110, INDIA 2Structural Engineering Division, Indian Institute of Technology Madras, Chennai 600 036, INDIA (*)Email: [email protected]

ABSTRACT

Chloride-induced rebar corrosion in concrete along coastal regions is currently a serious

problem in the world. To estimate the corrosion-free service life of concrete structures, this

study proposes an effective numerical framework through a combination of finite element and

finite difference scheme. By considering the presence of rebars in concrete and by

incorporating enhanced parameter prediction models, this framework solves the associated

mass transport partial differential equations representing the process of chloride ingress in

concrete. It is observed that, in addition to water-binder ratio and cover depth, the sustenance

of corrosion-free service life of concrete under chloride environment is significantly governed

by rebar size and its locations. Moreover, estimated time-variant reductions in cross-sectional

area of longitudinal rebar and flexural capacity of the reinforced concrete beam show a clear

change in slope, when the middle bars start corroding.

Keywords: Chloride, concrete, corrosion, finite element method

INTRODUCTION

Chloride-induced rebar corrosion in concrete is currently a serious problem in the world.

Based on conservative estimates, one-half of highway bridges are deteriorating due to rebar

corrosion in the developed countries, and billions of dollars are required to repair or

rehabilitate the damaged structures. Reinforced concrete (RC) structures fail to perform their

intended functions, and their service lives are much shorter than what they were designed for.

Rebar corrosion is widely accepted as a reasonable explanation for such premature

deterioration incurred by RC structures. Moreover, a majority of the world’s population

inhabit marine atmosphere (coastal) zones, the interface between the land and seawater. In

such zones, salinity is the main source of built infrastructure deterioration; predominantly due

to the chloride-induced rebar corrosion of the embedded steel. Chloride ions present in coastal

zones, while being assisted by the prevailing wind, temperature and humidity, intrude into the

porous concrete. Chloride ingress into the concrete induces rebar corrosion, which is a

complex interaction between many physical and chemical processes.

Rebars embedded in concrete are: (i) chemically protected by the highly alkaline passive layer

(pH ~ 13−14); and (ii) physically protected by the concrete cover acting as a barrier against the intrusion of aggressive species. However, chloride-induced corrosion begins when the

concentration of chloride at the steel bar level reaches a critical chloride content or a chloride

threshold value thereby destroying the protective layer. Critical chloride content or chloride

Topic_J: Civil Engineering Applications

-534-

threshold value of rebar in concrete can be defined as the concentration of chloride at the

depth of the rebar that is necessary to sustain localized breakdown of its passive protection

layer and hence initiate its active corrosion. The time taken by chloride ions from external

sources (such as marine environments) to reach a threshold value at the rebar depth is defined

as time-to-corrosion initiation (TCI). When corrosion occurs, the nature of the attack can

result in an extreme loss of rebar cross-sectional thereby affecting significantly the tensile

capacity of the corroded component. In addition, damage associated with corrosion is

manifested in the form of cracking and spalling of the concrete cover.

In many countries, including India, coastal zones are not only thickly populated but are also

industrialized to a great extent. In such zones, in addition to sea-salt spray, industrial effluents

could contribute to the presence of chloride ions (Costa and Vilarrasa, 1993). Industrial

atmospheres have been reported to contain considerable amount of chloride (Cl−), sulphur

dioxide (SO2) and oxides of nitrogen (Natesan et al., 2006). The major part of India is

generally subjected to moderate climatic conditions; hence, early deterioration of concrete

structures is not a big area of concern. However, concrete structures in coastal and industrial

belts and certain extreme climatic zones are subjected to aggressive environment, and hence

the problems of early deterioration of concrete are a cause of concern in India. In addition,

poor quality of construction and environmental pollution in major cities has also lead to early

deterioration of concrete structures located in moderate climate zones and cities, respectively

(Kulkarni, 2009). Hence, civil engineering structures like buildings, bridges, docks, harbors

located in these zones are highly vulnerable to earlier deterioration due to atmospheric

chlorides attack.

Vast majority of existing works in the literature assume a uniform corrosion pattern around

the rebar circumference (e.g. Ahmed et al., 2007; Bhargava et al., 2003; Chen and

Mahadevan, 2008; Li et al., 2006; Liu and Weyers, 1998; Pantazopoulou and Papoulia, 2001;

Val et al., 2009). This is rarely the case in practice as chloride ions generally take a long time

to transport to the steel-concrete interface that is facing the interior of concrete because of the

impermeability of steel bars. Therefore, steel surface facing the outside environment is

usually subjected to a higher-level concentration of chloride ions, and so gets depassivated

and starts to corrode earlier than the other side of steel surface does. While on the surface

facing the interior of concrete, the amount of chloride ions is maintained at a very low-level

because of the impermeable nature of steel bars. Hence, breakdown of surface passive film

and corrosion of steel could hardly happen in this area before the cracking of concrete cover.

Variation in the onset of corrosion reaction over the entire rebar surface, results in non-

uniform distribution of steel corrosion. Hence, the morphology of steel corrosion in concrete

is quite different from the widely employed assumption of uniform corrosion, and it will

undoubtedly propel the evolution of corrosion-induced damage in a different way than

uniform corrosion does (Liu and Li, 2004; Oh and Jang, 2003). In addition, it was reported

that the chloride accumulates in front of a rebar, which is much more pronounced for larger-

size bars (Oh and Jang, 2003). The higher accumulation of chlorides at bar location causes

faster corrosion of rebars. Hence the real state of corrosion is not uniform around a rebar. The

importance of considering the real state of corrosion in rebar is also supported by the fact that

the effect of non-uniform corrosion induced stresses in RC are more conducive to cover

cracking than uniform corrosion (Xia et al., 2012).

This study presents a numerical framework that can efficiently quantify time-variant

degradation in the flexural capacity of a corroding RC beam based on non-uniform corrosion.

This framework considers the effects of rebar size and location on the process of chloride

ingress into concrete and focuses on rebar corrosion due to atmospheric chlorides by

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

-535-

considering diffusion as the dominant mode of chlorides ingress. This work is presented in

two parts. The time to first onset of corrosion reaction for the corner and middle bars

embedded in a RC beam are presented in the first part of the study for 11 atmospheric

exposure stations in India by incorporating various parameters such as water/binder ratio

( )/w b , concrete cover thickness and rebars size. The second part of the work presents the

quantitative estimations of non-uniform reductions in the net cross-sectional areas of the

rebars in the RC beam. This part also presents an assessment of the time-variant degradation

in the flexural capacity of a corroding RC beam based on non-uniform corrosion.

CHLORIDE INGRESS MODEL

The problem of chloride ingress into concrete can effectively be studied as the interaction

between three phenomena, namely: heat transport; moisture transport; and chloride transport.

Each of these phenomena is represented by a partial differential equation (PDE) and their

interaction is considered by solving them simultaneously. The governing PDEs representing

the process of chloride ingress into concrete can be expressed in the following general form:

( ) 0+∇ ∇ =� r r

�ϒ Φ Θ Φ (1)

The correspondence between ϒ , Θ , Φ and the terms for the transport quantity is presented

in Table 1.

Table 1 - Correspondence between Eq. (1) and PDEs

Transport

Quantity

Φ ϒϒϒϒ ΘΘΘΘ

Chloride fC

1 a

cD

Moisture h ∂

∂

we

h

hD

Heat T pcρ TD

For chloride transport, fC is the free chloride content dissolved in the pore solution (kg/m

3),

a

cD and a

hD represent apparent chloride and humidity diffusion coefficients (m2/s),

respectively:

( ) ( ) ( ),

11

= ∂

+ ∂

c ref c c ca

c

b

e f

D f T f t f hD

C

w C

(2)

( ) ( ) ( ),

11

= ∂

+ ∂

h ref h h h ea

h

b

e f

D f T f h f tD

C

w C

(3)


-536-

where ,c refD and ,h refD are reference chloride and humidity diffusion coefficients (m2/s)

measured under standard conditions (Saetta et al., 1993), ew is evaporable water content (m3

of water/m3 of concrete), cf and hf are modification factors to account for the effects of

temperature, relative humidity, ageing and the level of hydration in concrete. These factors

are detailed in Muthulingam and Rao, 2014. The term b fC C∂ ∂ represents the binding

capacity of the cementitious system which is the slope of either Langmuir or Freundlich

binding isotherm. The binding isotherm relates the free and bound chloride content at

equilibrium and is characteristic of each cementitious system (Tang and Nilsson, 1993).

For moisture transport, hD represents humidity diffusion coefficient (m2/s) and the derivative

of water content with respect to pore relative humidity (i.e. ew h∂ ∂ ) is defined as moisture

capacity (m3 of water/m

3 of concrete). At standard temperature and pressure, adsorption

isotherm relates evaporable water content and pore relative humidity. Based on

thermodynamic principle of adsorption, Braunauer-Skalny-Bodor model considers this

relationship to depend on temperature, water-to-binder ratio (a ratio by mass) and level of

hydration in concrete, et in days (Xi et al., 1994). From the adsorption isotherm, moisture

capacity can be obtained by taking its derivative with respect to h :

( )

( ) ( )

2 2 2 2

2 2

1

1 1

meCkV Ch k h kw

h hk Chk hk

− +∂=

∂ − − + [m

3 of water/m

3 of concrete] (4)

where C is a constant that takes into account the influence of change in temperature on the

adsorption isotherm, k is a constant resulted from the assumption that the number of

adsorbed layers is a finite small number and mV represents the monolayer capacity. These

parameters are detailed in Muthulingam and Rao, 2014.

For heat transport, T is temperature (K), ρ is the density of concrete (or) rebar (kg/m3),

pc

is the specific heat capacity of concrete (or) rebar (J/kg K), and TD is the thermal

conductivity of concrete (or) rebar (W/m K).

RATE OF CORROSION

The corrosion rate ( corri ) of rebars in concrete structures is one of the most important

parameters for making reasonable service life prediction (Li et al., 2006; Otieno et al., 2012).

Corrosion rate of rebars in concrete structures is affected by various factors, namely,

supplementary cementitious materials, moisture content, cyclic wetting and drying, sustained

loading, loading history, concrete resistivity, concrete quality, cover depth, temperature,

cracking, dissolved oxygen content and exposure conditions (Otieno et al., 2012). By

considering few or more of the above-mentioned factors, various corrosion rate prediction

models were proposed in literature. Corrosion level of the rebar is generally determined in

terms of depth of the attack penetration (e.g. Val et al., 2009). The corrosion penetration

depth, dp (mm) at an exposure time, t (years) after corrosion initiation, ct can be estimated

based on Faraday’s law (Rodriguez et al., 1996):


-537-

( ) ( )corr0.0116 d= ⌠⌡

c

t

d

t

p t i t t (5)

Vu and Stewart (2000) expressed the corrosion rate up to one year (corr(0) ,i µA/cm2

) after the

end of the corrosion initiation phase for an ambient relative humidity of 75% and a

temperature of 20 oC as given in Eq. (6).

1.64

corr(0)

37.8 1

c

w

bi

C

− − = [µA/cm2

] (6)

where cC represent concrete cover thickness (cm) and w b represents water-to-binder ratio.

During the corrosion propagation phase corri can be expressed as follows:

( ) 0.29

corr corr(0)0.85

ci i t t

−= − [µA/cm2

] (7)

where t is the time to which corri is to be predicted (years) and ct is time-to-corrosion

initiation (years). For the corrosion rate model of Vu and Stewart (2000), ( )dp t can be

expresses as:

( ) ( )

1.64

0.71

1

0.5249d c

c

w

bp t t t

C

− − = − (8)

Further, BS 6349−1 suggested the mean and upper limit values of corrosion rate for various

exposure zones that apply to each face exposed to the environment of the zone.

FLEXURAL CAPACITY OF RC BEAM

The time-variant flexural capacity of the corroding RC beam ( )uRM due to the net reduction

in the cross-sectional areas of the longitudinal rebars can be given by Eq. (9).

( ) ( ) ( )2

1 3

1 s s

uR s s e

c e

f A tM t f A t z d

z z f b d

= −

(9)

where sA is the area of the longitudinal tensile rebar, s

f is the yield strength of the steel, ed is

the effective depth of the rebar, cf is the compressive strength of concrete and b is the width

of the section. The value of 1z (conversion factor for compressive stress block of concrete)

for a parabolic-rectangular stress block is 0.81. The value of 2z (ratio of the depth of centroid

of the stress block to the depth of neutral axis) for a parabolic-rectangular stress block is 0.42.

The value of 3z (ratio of the compressive strength of concrete in the girder to that of the

design cube compressive strength of concrete) was taken as 0.67, which is based on the size

factor equal to 0.85 while using cylinder compressive strength, and the conversion of

cylinder strength to cube strength (Pillai and Menon, 2009).


-538-

When RC beams undergo severe corrosion, other structural damage mechanisms, namely,

concrete cracking, delamination and spalling of the concrete cover, reduction of concrete

cross-section and loss of bond between the rebar and concrete are also observed (Bhargava et

al., 2011). However, robust prediction models that can estimate the flexural capacity of RC

beams by incorporating the damage mechanisms are hardly found in the literature (Stewart

and Suo, 2009). Therefore, in the current study, flexural capacity of the corroding RC beam is

evaluated without considering the related structural damage mechanisms.

ATMOSPHERIC CHLORIDES−−−−INDIAN SCENARIO

The chloride deposition rate is a very important parameter for evaluating the corrosion of

metals. Estimating the amount of chlorides present in the atmosphere through deposition

measurements by using either wet or lead peroxide candle, is a part of standardized

procedures to measure the amount of chloride salts that are captured from the atmosphere on

the exposed area of the apparatus. Recently, the chloride deposition rate (mg/m2/day) values

have been reported for 11 exposure stations in India by a study conducted to evaluate

atmospheric corrosion of metals at these stations (Natesan and Palaniswamy, 2009; Natesan et

al., 2008). These stations have different temperature, humidity and pollutant (both liquid and

gas) concentrations. Fig. 1 shows the location of 11 stations.

Fig. 1 - Atmospheric exposure stations in India

Furthermore, 11 atmospheric exposure stations are categorized into five types based on the

type of atmosphere prevailing at a particular station, viz. marine, industrial, marine-industrial,

rural and urban stations (Natesan and Palaniswamy, 2009; Natesan et al., 2008). The stations

2, 3, 4, 7, 8 and 9 are categorized as marine stations while station 10 is categorized as the

industrial station. Further, the stations 1 and 5 are categorized as marine-industrial and hill

stations respectively. The stations 6 and 11 are categorized as rural and urban station

respectively.

Although chloride deposition rate is a very important parameter for evaluating the corrosion

of metals, in the case of RC structure, it is not directly related to corrosion of the rebar

(Tanaka et al., 2001). The cumulative chloride deposition on the surface of the measuring


-539-

apparatus is correlated to the chlorides accumulation on the surface of the concrete through

empirical relationships. One such empirical relationship proposed for correlation is proposed by

Tanaka et al. (2001), and the same is given in Eq. (10).

0.4

1.5=s dC C (kg/m3) (10)

where, dC represents chloride deposition rate (mg/dm2/day). The chloride deposition rate and

the equivalent surface chloride content ( sC ) for 11 atmospheric exposure stations along with

their annual mean temperature and relative humidity are listed in Table 2. It can be observed

from Table 2 that among 11 atmospheric exposure stations, two of the stations, namely,

Chennai and MPT have relatively higher surface chloride contents.

Table 2 - Data for 11 atmospheric exposure stations in India

Station name Mean temperature

(oK)

†

Mean relative

humidity†

Cd

(mg/m2/day)

Cs

(kg/m3)

Min. Max. Min. Max.

Manali 292 312 0.61 0.86 75.21 1.35

Chennai 293 312 0.59 0.95 304.60 2.35

Cuddalore 293 308 0.64 0.90 39.49 1.05

Nagapattinam 295 307 0.61 0.80 18.18 0.75

Tuticorin 293 307 0.58 0.95 47.65 1.12

Mahendragiri 292 310 0.50 0.95 Nil Nil

Mangalore 292 307 0.63 0.92 69.00 1.30

MPT 290 306 0.61 0.86 266.40 2.22

NIO, Goa 289 304 0.63 0.89 Nil Nil

Mumbai 292 306 0.56 0.94 30.00 0.93

Surat 288 313 0.62 0.89 13.80 0.68

PROBLEM STATEMENT

For further study, a RC beam section of size 350 × 700 mm shown in Fig. 8.4(a), reported in

the literature (Pillai and Menon, 2009) is considered. In the considered cross-section; (i) cC ,

d and ed represent cover thickness, rebar diameter size and effective depth, respectively; and

(ii) four rebars are present, of which two bars of interest in future discussion are named B1

(middle bar) and B2 (corner bar). Moreover, to consider the effects of rebar sizes and locations

on the spatial and temporal evolution of total chloride content (TCC) and TCI around the steel-

concrete interface, various bar diameter (12, 16, 20, and 25 mm), cover thickness (25−75 mm

in multiples of 5 mm) and /w b ratios (0.4, 0.5, and 0.6) are also considered. The adopted RC cross-section is discretized using four noded isoparametric quadrilateral elements as shown in

Fig. 2. Care is taken to ensure that sufficient number of nodes is present along the

circumference of the rebar (40 nodes) to capture the smooth spatial progress of TCC and TCI.


-540-

a b

Fig. 2 - RC beam: (a) Cross-section and (b) Finite element discretization

The external environmental conditions that are specific to each of the atmospheric station

need to be imposed on the exposed boundaries of the numerical model. The current study

considers that, all the four sides of the RC beam are exposed to atmospheric chlorides. Using

the mean temperature and relative humidity distribution data listed in Table 8.1, and assuming

a sinusoidal variation similar to that reported in the literature (Bastidas-Arteaga et al., 2011),

the monthly variations of temperature and humidity are obtained by curve fitting techniques

as a function of time expressed in years:

( ) ( )max min max min sin 22 2

π+ −

= +env

T T T TT t t (11)

( ) ( )( )max min max min sin 2 0.52 2

env

h h h hh t tπ

+ −= + − (12)

In FE analysis, the material properties of rebar, namely, density, specific heat capacity and

thermal conductivity of rebar are taken as 7850 kg/m3, 620 J/kg.°K and 50 W/m.°K,

respectively. Moreover, ,h refD values of 1 × 10-12, 5 × 10

-12 and 2.5 × 10

-11 m

2/s are considered

(Saetta et al., 1993) for /w b ratios of 0.4, 0.5, and 0.6, respectively. In addition, 0.8 kg/m3 (AS

1379:2007) of TCC is considered as critical chloride content.

SOLUTION PROCEDURE

a.1. Determine actual temperature profile throughout the FE mesh (including rebar) from

by taking into account the initial temperature profile,

a.2. Determine humidity profile throughout the FE mesh (excluding rebar) by taking into

account the temperature profile estimated in the previous step and the initial humidity

profile,

Cc d

de

B1 B1 B2 B2


-541-

a.3. Perform iterative procedure to obtain the actual profile of h by using the profile of h obtained from the previous iteration until a given convergence criterion is reached,

a.4. Evaluate the amount of evaporable water from adsorption isotherm,

a.5. Evaluate free chloride profile throughout the FE mesh (excluding rebar) by taking into

account the temperature and humidity profiles estimated in the previous step and the

initial free chloride profile,

a.6. Perform iterative procedure to obtain the actual profile of fC by using the profile of

fC obtained from the previous iteration until a given convergence criterion is reached,

a.7. Determine TCC values, by using the chloride binding relationship and the adsorption

isotherm,

a.8. If TCC values at the level of the rebar have reached the critical value, corrosion is

assumed to have initiated,

a.9. Determine time-dependent corrosion penetration depth ( )dp t at depassivated region

along the perimeter of the rebar,

a.10. Evaluate non-uniform corrosion states of rebar based on the estimated spatial

distributions of ( )dp t ,

a.11. Numerically calculate the time-variant net reduction in the cross-sectional area of rebar

based on the estimated corrosion penetration depth.

RESULTS AND DISCUSION

TIME-TO-CORROSION INITIATION

From the numerical analysis, it is observed that the rebars in RC beam that are located in two of

the 11 stations, namely, Chennai and MPT experience corrosion over the simulation period of

100 years. This is because; the surface chloride content values reported at these stations are

relatively higher. Higher humidity and temperature values at the Chennai station could also be a

reason for the corrosion. Table 3 shows the time to first onset of corrosion reaction for B1 and B2

bars at the Chennai station, for various combinations of rebar size, cover thickness and /w b ratio.

Similarly, Table 4 shows the time to first onset of corrosion reaction for B1 and B2 bars at MPT

station, for various combinations of cover thickness, rebar size and /w b ratio.

From Tables 3 and 4, it can be observed that, for the given values of cover thickness and water-

to-binder ratio, TCI for B2 bar is faster than that for B1 bar. Additionally, the ratio between

TCI of B1 and B2 bar falls within the range of 1.3−1.6, indicating TCI for B2 bar is 30−60%

faster than that for B1 bar. The direct implication of this observation is that the subsequent

onset of cracking, as corrosion level increases over time would be much more serious in

concrete cover around the corner bars than that in concrete cover around the middle bars.

Therefore, corner bars need more protection from external chloride environment. Between

these two stations, TCI values for both B1 and B2 bars of the RC beam at Chennai station is

higher than that at MPT station. This differences in TCI values between them are observed to

range between 2−45 years for various combinations of cover thickness, rebar size and /w b ratio.


-542-

Table 3 - TCI values for Chennai station

d

Cc

B1 bar B2 bar d

Cc

B1 bar B2 bar

w/b ratio w/b ratio w/b ratio w/b ratio

0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6

12

25 22.3 8.5 5.4 7.4 3.1 1.9

20

25 15.2 6.1 3.8 6.6 2.9 1.8

30 35.6 14.4 9.1 11.6 5.1 3.1 30 26.3 10.4 6.5 10.5 4.5 2.8

35 53.6 21.7 13.6 17.5 7.4 4.5 35 40.5 16.4 10.3 15.5 6.6 4.2

40 74.7 30.7 19.4 24.5 10.4 6.4 40 58.7 24.3 15.3 22.0 9.3 5.8

45 98.6 41.5 25.8 33.3 14.0 8.6 45 80.7 33.4 20.7 29.6 12.5 7.8

50 * 52.4 32.6 43.4 18.2 11.3 50 * 43.5 27.4 38.6 16.4 10.3

55 * 62.7 39.5 54.6 22.9 14.4 55 * 53.7 33.7 48.8 20.6 13.1

60 * 73.6 46.4 67.4 28.4 17.6 60 * 64.5 40.5 60.6 25.6 16.2

65 * 83.6 52.5 81.6 34.4 21.5 65 * 75.5 47.4 74.7 31.5 19.7

70 * 91.5 57.4 97.6 41.3 25.6 70 * 85.5 53.5 89.6 37.7 23.6

75 * * 64.7 * 48.5 30.4 75 * 94.7 59.5 * 44.7 28.3

16

25 18.2 7.1 4.5 7.0 3.0 1.8

25

25 13.1 5.3 3.4 6.5 2.9 1.8

30 30.3 12.2 7.6 11.0 4.6 3.0 30 22.3 9.1 5.6 10.3 4.4 2.8

35 46.5 18.7 11.8 16.3 7.0 4.3 35 34.7 14.3 8.9 15.2 6.4 4.1

40 66.6 27.4 17.3 23.2 9.7 6.2 40 50.7 20.7 13.3 21.0 9.1 5.6

45 88.8 37.4 23.4 31.3 13.2 8.3 45 70.7 29.4 18.4 28.3 12.2 7.5

50 * 47.6 30.3 40.6 17.3 10.7 50 94.6 38.7 24.4 37.3 15.6 9.8

55 * 58.6 36.6 51.7 21.7 13.6 55 * 49.4 30.6 47.3 20.1 12.4

60 * 69.5 43.5 64.4 27.2 17.0 60 * 59.5 37.4 58.4 24.6 15.4

65 * 79.5 49.6 77.7 32.7 20.5 65 * 69.7 43.7 71.4 30.3 18.9

70 * 89.6 56.4 93.5 39.4 24.6 70 * 79.7 50.4 86.6 36.4 22.6

75 * 98.6 61.7 * 46.4 29.3 75 * 89.7 56.5 * 43.2 27.0

Table 4 - TCI values for MPT station

d

Cc

B1 bar B2 bar d

Cc

B1 bar B2 bar

w/b ratio w/b ratio w/b ratio w/b ratio

0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6 0.4 0.5 0.6

12

25 67.5 28.4 15.7 19.6 8.4 4.8

20

25 44.5 18.7 10.6 17.3 7.5 4.3

30 * 47.6 26.6 31.6 13.6 7.6 30 78.7 33.5 18.6 27.7 12.2 6.8

35 * 72.6 40.5 47.6 20.4 11.4 35 * 53.6 29.8 41.5 18.0 10.2

40 * * 56.5 67.5 28.7 16.3 40 * 79.5 44.4 58.7 25.4 14.3

45 * * 73.5 91.5 39.3 21.8 45 * * 59.7 80.5 34.5 19.4

50 * * 89.6 * 50.7 28.5 50 * * 76.5 * 45.4 25.4

55 * * * * 64.5 36.3 55 * * 92.6 * 57.6 32.5

60 * * * * 79.7 44.7 60 * * * * 71.8 40.5

65 * * * * 97.5 54.6 65 * * * * 88.6 49.6

70 * * * * * 65.5 70 * * * * * 59.7

75 * * * * * 77.5 75 * * * * * 71.5

25 53.8 22.6 12.7 18.3 8.0 4.4

25 36.7 15.7 9.0 17.1 7.5 4.2

30 92.6 39.6 22.4 29.3 12.6 7.2 30 64.8 27.7 15.5 26.6 11.7 6.6

35 * 62.6 34.7 44.3 19.0 10.6 35 * 45.4 25.4 39.6 17.3 9.7


-543-

16

40 * 89.7 49.7 62.6 26.7 15.2

25

40 * 67.6 37.6 55.5 24.3 13.5

45 * * 66.6 85.5 36.5 20.5 45 * 94.6 52.6 75.6 32.5 18.4

50 * * 83.6 * 47.8 26.8 50 * * 68.5 99.8 42.6 24.1

55 * * 99.6 * 61.4 34.4 55 * * 84.6 * 54.6 30.6

60 * * * * 76.4 42.6 60 * * * * 68.5 38.4

65 * * * * 92.6 51.7 65 * * * * 83.7 47.3

70 * * * * * 62.6 70 * * * * * 56.6

75 * * * * * 73.7 75 * * * * * 67.6 *No corrosion for the numerical simulation of 100 years

Large-size rebars proneness to higher chloride build-up lead to faster corrosion. The corrosion

reaction sets in first at locations along the perimeters of rebars, where the chloride build-up is

faster and higher. From tables 3 and 4 it can be observed that, for the given values of cover

thickness and water-to-binder ratio, with the increase in the rebar size, TCI for B1 bar is faster

by about 4−6% between any two intermediate sizes (i.e. 12 and 16 mm, 16 and 20 mm, and 20

and 25 mm) and about 10−15% between the extreme sizes (i.e. 12 and 25 mm).

Furthermore, from the numerical analysis it is also observed that, neither the corner bar nor the

middle bar experiences corrosion in the other nine stations. This can again be attributed to the

lower values of surface chloride content at these stations. For example, zero surface chloride

content values are reported for two of the nine stations, namely, Mahendragiri and NIO; hence,

rebars at these stations could hardly experience any corrosion.

The minimum cover thickness required to sustain a corrosion free service life of 50 years to the

RC beam at Chennai and MPT stations for various parameters (rebar size and location, /w b ratio) are listed in Table 5 based on the estimated TCI values (Tables 3 and 4).

Table 5 - Minimum cover thickness for corrosion free service life of 50 years

.

Station

w/b = 0.4 w/b = 0.5 w/b = 0.6

B1 Bar B2 Bar B1 Bar B2 Bar B1 Bar B2 Bar

Chennai 35 – 40 55 – 60 55 – 60 >75 >70 >75

MPT 25 – 30 35 – 40 35 – 40 50 – 55 40 – 45 65 – 70

It can be observed from Table 5 that the minimum cover thickness requirements are functions

of both /w b ratio, and, rebar size and location. It can also be observed from Table 5 that,

cover thickness requirements for Chennai station are higher than that for MPT station. As a

part of the durability requirements, IS 456:2000 has classified coastal environment under

severe exposure class and hence recommends a minimum cover thickness value of 40 mm and

the maximum /w b ratio of 0.45 for RC components exposed to these environments. From the

numerical analysis, it is observed that, IS 456:2000 cover thickness recommendations are

sufficient to sustain a corrosion free service life of 50 years for the middle bars of the RC

beam, however, are found to be inadequate for the corner bars. For example, minimum cover

thickness for Chennai station ranges between 55−60 mm for the w/b ratio of 0.4, which are

higher than the value recommended by IS 456:2000. Inadequate cover thickness can have

serious implications on the durability requirements of RC components exposed to coastal

environments. Moreover, insufficient cover thickness can result in premature deterioration

resulting in early reconstruction or major repairs involving huge expenditures. In addition,

premature deterioration may also lead to sudden failure of structures leading to loss of life and

property (Ramalingam and Santhanam, 2012).


-544-

TIME-VARIANT CROSS-SECTIONAL AREA OF REBAR

To estimate the time-variant degradation of flexural capacity in the RC beam caused by rebar

corrosion, the time-variant reduction in the net section of the rebar needs to be quantified. In the

current study, the corrosion penetration depths around steel-concrete interfaces of rebars are

estimated based on two of the corrosion rate models, namely, Vu and Stewart (2000) and BS

6349−1. The former is a time-variant corrosion rate model, whereas the latter is a constant

corrosion rate model. Figs. 3(a) and (b) show the time-variant cross-sectional area of the

longitudinal rebars of the RC beam, for various combinations of cover thickness (25 and 30 mm)

and rebar diameter (12 and 16 mm), and having a /w b ratio of 0.4.

Fig. 3 - Time-variant cross-sectional area of the longitudinal rebars for Cc = 25 and 30mm:

(a) d = 12 mm and (b) d = 16 mm

Similarly, Figs. 4(a) and (b) show the time-variant cross-sectional area of the longitudinal rebars

of the RC beam, for various combinations of cover thickness (25 ,30 and 35 mm) and rebar

diameter (20 and 25 mm), and having a /w b ratio of 0.5.

The following observations can be made from Figs. 3 and 4:

(i) In general, the estimated values of ( )sA t based on Vu and Stewart (2000) model is

much higher than that based on BS 6349−1. This can be attributed to relatively higher corrosion rate estimation by the former.

(ii) After the onset of corrosion reaction in the middle bars (B2), the estimated values of

( )sA t based on Vu and Stewart (2000) model has a diverging trend from BS 6349−1 model. This is because the former is built based on time-variant corrosion rate,

whereas the latter is a constant corrosion rate model.

(iii) The corrosion reaction sets in first around the steel-concrete interfaces of corner bars

than the middle bars. The values of ( )sA t show a clear change in slope, when the

middle bars (B1) start corroding. This change in slope indicates increased reduction in

the values of ( )sA t .

(iv) The effects of cover thickness on the values of ( )sA t are more evident from the

model of Vu and Stewart (2000), due to this model incorporating cC as one of the

parameter.


-545-

Fig. 4 - Time-variant cross-sectional area of the longitudinal rebars for Cc = 25, 30 and 35 mm:

(a) d = 20 mm and (b) d = 25 mm

TIME-VARIANT FLEXURAL CAPACITY

Eq. (9) relates the time-variant flexural capacity of the corroding RC beam with the time-variant

cross-sectional area of the longitudinal rebars (Figs. 3 and 4). Figs. 5(a)−(c) show the time-

variant flexural capacity of the RC beam, for various combinations of cover thickness (25 and 30

mm) and rebar diameter (16, 20 and 25 mm), and having a /w b ratio of 0.4.

The following observations can be made from Fig. 5:

(i) In general, the estimated values of ( )uRM t based on Vu and Stewart (2000) model is

much higher than that based on BS 6349−1. This can be attributed to relatively higher estimations of ( )sA t values by the former.

(ii) The differences between the values of ( )uRM t estimated based on Vu and Stewart

(2000) and BS 6349−1 models decreases with the increase in cover thickness. This is

because the corrosion rate and hence ( )sA t values estimated by the former decreases

with increase in cover thickness.

(iii) Similar to the patterns of ( )sA t observed in Figs.8.5 and 8.6, the values of ( )uRM t

also show a clear change in slope, when the middle bars (B1) start corroding. This

change in slope indicates increased reduction in the values of ( )uRM t .


-546-

Fig. 5 - Time-variant flexural capacity of the RC beam with w/b ratio of 0.4 and Cc of 25 and 30 mm:

(a) d=16 mm, (b) d=20 mm and (c) d=25 mm

Similarly, Figs. 6(a)−(d) show the time-variant flexural capacity of the RC beam, for various

combinations of cover thickness (35 and 40 mm) and rebar diameter (12, 16, 20 and 25 mm), and

having a /w b ratio of 0.5. The distributions of the values of ( )uRM t illustrated in Figs 6(a)−(d) indicate almost identical behavior similar to the observations made in Fig. 5. In addition, as

expected ( )uRM t reduction is relatively higher, which can be attributed to the effects of

corrosion accompanying the higher /w b ratio (=0.5).

Finally, Figs. 7(a)−(d) show the time-variant flexural capacity of the RC beam, for various

combinations of cover thickness (45 and 50 mm) and rebar diameter (12, 16, 20 and 25 mm), and

having a /w b ratio of 0.6. The distributions of the values of ( )uRM t illustrated in Figs 7(a)−(d) indicate almost identical behavior similar to the observations made in Figs. 5 and 6. In addition,

as expected ( )uRM t reduction is relatively highest, which can be attributed to the effects of

corrosion accompanying the highest /w b ratio (=0.6).


-547-



SUMMARY AND CONCLUSIONS

In this study a numerical framework that can efficiently quantify time-variant degradation in

the flexural capacity of a corroding RC beam based on non-uniform corrosion presented. This

framework considered the effects of rebar size and location on the process of chloride ingress

into concrete and focused on rebar corrosion due to atmospheric chlorides by considering

diffusion as the dominant mode of chlorides ingress. Further, time to first onset of corrosion

reaction for the corner and middle bars embedded in a RC beam are presented for 11

atmospheric exposure stations in India by incorporating various parameters such as /w b ratio, concrete cover thickness and rebars size. Moreover, quantitative estimations of non-uniform

reductions in the net cross-sectional areas and an assessment of the time-variant degradation

in the flexural capacity of a corroding RC beam are evaluated based on non-uniform

corrosion.


-548-



For the given values of cover thickness and water-to-binder ratio, TCI for B2 bar is faster than

that for B1 bar. In addition, the ratio between TCI of B1 and B2 bar is observed to fall within

the range of 1.3−1.6, indicating TCI for B2 bar is 30−60% faster than that for B1 bar. The

larger the rebar, in general, the bigger the obstruction, and therefore, the higher the chloride

build-up. The minimum cover thickness required to guarantee a certain number of corrosion-

free service life is observed to increase not only with the increase in water-to-binder ratio but

also with the rebar locations and sizes.

It is observed from the numerical analysis that the rebars in RC beam that are located in two of

the 11 stations, namely, Chennai and MPT experience corrosion over the simulation period of

100 years. This is because, the surface chloride content values reported at these stations are

relatively higher. In addition, it is also observed from the numerical analysis that neither the

corner bar nor the middle bar experiences corrosion in the other nine stations. This can again be

attributed to the lower values of surface chloride content at these stations. Moreover, estimated

time-variant reductions in cross-sectional area of longitudinal rebar and flexural capacity of

the RC beam show a clear change in slope, when the middle bars start corroding.


-549-

REFERENCES

[1]-Ahmed SFU, Maalej M, Mihashi H. Cover cracking of reinforced concrete beams due to

corrosion of steel. ACI Materials J, 2007, 104, p. 153–161.

[2]-AS 1379 2007. Specification and Supply of Concrete. Sydney: Standards Australia.

[3]-Bastidas-Arteaga E, Chateauneuf A, Sanchez-Silva M, Bressolette P, Schoefs F. A

comprehensive probabilistic model of chloride ingress in unsaturated concrete. Engineering

Structures, 2011, 33, p. 720–730.

[4]-Bhargava K, Ghosh AK, Mori Y, Ramanujam S. Analytical model of corrosion-induced

cracking of concrete considering the stiffness of reinforcement. Structural Engineering &

Mechanics, 2003, 16, p. 749–769.

[5]-Bhargava K, Mori Y, Ghosh AK. Time-dependent reliability of corrosion-affected RC

beams—Part 1: Estimation of time-dependent strengths and associated variability. Nuclear

Engineering and Design, 2011, 241, p. 1371–1384.

[6]-Chen D, Mahadevan S. Chloride-induced reinforcement corrosion and concrete cracking

simulation. Cement Concrete Composites, 2009, 30, p. 227–238.

[7]-Costa JM, Vilarrasa M. Effect of air pollution on atmospheric corrosion of zinc. British

Corrosion J, 1993, 28, p. 117–120.

[8]-IS 456: 2000. Plain and Reinforced Concrete. Code of Practice (4th revision). New Delhi:

Bureau of Indian Standards.

[9]-Kodur VKR, Sultan MA. Effect of temperature on thermal properties of high-strength

concrete. J of Materials in Civil Engineering, 2003, 15, p. 101–107.

[10]-Kulkarni VR. Exposure classes for designing durable concrete. Indian Concrete J, 2009,

83, p. 23–43.

[11]-Li CQ, Melchers RE, Zheng JJ. Analytical model for corrosion-induced crack width in

reinforced concrete structures. ACI Structural J, 2003, 103, p. 479–487.

[12]-Liu YD, Li YH. Mechanistic model and numerical analysis for corrosion damage of

reinforced concrete structure. International J of Fracture, 2004, 126, p. 71–78.

[13]-Liu YP, Weyers RE. Modeling the time-to-corrosion cracking in chloride contaminated

reinforced concrete structures. ACI Materials J, 1998, 95, p. 675–681.

[14]-Muthulingam S, Rao BN. Non-uniform time-to-corrosion initiation in steel reinforced

concrete under chloride environment. Corrosion Science, 2014, 82, p. 304–315.

[15]-Natesan M, Palaniswamy N. Atmospheric corrosivity and durability maps of India.

Corrosion Reviews, 2009, 27, p. 61–112.

[16]-Natesan M, Selvaraj S, Manickam T, Venkatachari G. Corrosion behavior of metals and

alloys in marine-industrial environment. Science and technology of advanced materials, 2008,

9, p. 1–7.

[17]-Natesan M, Venkatachari G, Palaniswamy N. Kinetics of atmospheric corrosion of mild

steel, zinc, galvanized iron and aluminium at 10 exposure stations in India. Corrosion

Science, 2006, 48, p. 3584–3608.

[18]-Neville AM. Properties of concrete. 1993, 4th ed. Pearson Education.


-550-

[19]-Oh BH, Jang BS. Chloride diffusion analysis of concrete structures considering effects of

reinforcements. ACI Materials J, 2003, 100, p. 143–149.

[20]-Otieno M, Beushausen H, Alexander M. Prediction of corrosion rate in reinforced

concrete structures – a critical review and preliminary results. Materials and Corrosion, 2012,

63, p. 777–790.

[21]-Pantazopoulou SJ, Papoulia KD. Modeling cover-cracking due to reinforcement

corrosion in RC structures. J of Engineering Mechanics, 2001, 127, p. 342–351.

[22]-Pillai SU, Menon D. Reinforced concrete design. 2009, 3rd ed. Tata McGraw-Hill

Education.

[23]-Ramalingam S, Santhanam M. Environmental exposure classifications for concrete

construction–A relook. Indian Concrete J, 2012, 86, p. 18–28.

[24]-Rodriguez J, Ortega LM, Casal J, Diez JM. Corrosion of reinforcement and service life

of concrete structures, Durability of Building Materials and Components, 1996, 7, Stockholm,

p. 117–126.

[25]-Saetta AV, Scotta RV, Vitaliani RV. Analysis of chloride diffusion into partially

saturated concrete. ACI Structural J, 1993, 90, p. 441–451.

[26]-BS 6349–1:2000. Maritime structures. Part 1: code of practice for general criteria.

British Standard.

[27]-Stewart MG, Suo QH. Extent of spatially variable corrosion damage as an indicator of

strength and time-dependent reliability of RC beams. Engineering Structures, 2009, 31,

p. 198–207.

[28]-Tanaka Y, Kawano H, Watanabe H, Nakajo T. Study on required cover depth of concrete

highway bridges in coastal environment, Proceedings of the 17th US–Japan Bridge

Engineering Workshop, Tsukuba, Japan. Department of Civil Engineering, 2009, Seoul

National University.

[29]-Tang LP, Nilsson LO. Chloride binding-capacity and binding isotherms of opc pastes

and mortars. Cement and Concrete Research, 1993, 23, p. 247–253.

[30]-Val DV, Chemin L, Stewart MG. Experimental and numerical investigation of corrosion-

induced cover cracking in reinforced concrete structures. Journal of Structural Engineering,

2009, 135, p. 376–385.

[31]-Vu KAT, Stewart MG. Structural reliability of concrete bridges including improved

chloride-induced corrosion models. Structural Safety, 2000, 22, p. 313–333.

[32]-Xi YP, Bazant ZP, Jennings HM. Moisture diffusion in cementitious materials –

Adsorption-isotherms. Advanced Cement Based Materials, 1994, 1, p. 248–257.

[33]-Xia N, Ren QW, Liang RY, Payer J, Patnaik A. Nonuniform Corrosion-Induced Stresses

in Steel-Reinforced Concrete. Journal of Engineering Mechanics, 2012, 138, p. 338–346.

prediction of corrosion-free service life of concrete...

Documents