HBRC Journal (2014) xxx, xxx–xxx

Housing and Building National Research Center

HBRC Journal

http://ees.elsevier.com/hbrcj

Modeling the corrosion initiation time of slag concrete

using the artificial neural network

O.A. Hodhoda, H.I. Ahmed

b,*

a Professor of Properties and Strength of Materials, Struct. Eng. Dept., Faculty of Engineering, Cairo University, Egyptb Civil Eng. Dept., Faculty of Engineering, Cairo University, Egypt

Received 31 July 2013; revised 16 December 2013; accepted 22 December 2013

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KEYWORDS

Artificial neural network;

Slag;

Chloride;

Corrosion;

Diffusion;

Steel reinforcement

Corresponding author. Tel.:mail address: hany281@yaho

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esearch Center.

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Abstract This paper focuses on the Artificial Neural Network (ANN) as an alternative approach

to simulate the corrosion initiation time of slag concrete obtained from the error function solution

to Fick’s second law of diffusion. The adopted network architecture consists of four neurons in the

input layer, which represents the values of concrete cover depth, apparent chloride diffusion coef-

ficient, chloride threshold value and surface chloride concentration, and one neuron in the output

layer, which represents the value of the corresponding corrosion initiation time. Back Propagation

(BP) algorithm was employed for the ANN training in which a Tansig function was used as the non-

linear transfer function. The research results obtained from both ANN model and the error func-

tion solution to Fick’s second law of diffusion demonstrate that the corrosion initiation time of slag

concrete increases with increasing both the concrete cover and the chloride threshold value and

decreases with increasing both the surface chloride concentration and the chloride diffusion coeffi-

cient. Through the comparison of the estimated results from ANN model and the error function

solution to Fick’s second law of diffusion, it was clear that there was a high correlation between

the corrosion initiation time obtained from the error function solution to Fick’s second law of dif-

fusion and the corresponding corrosion initiation time predicted by the ANN model.ª 2014 Production and hosting by Elsevier B.V. on behalf of Housing and Building National Research

Center.

Introduction

Chloride-induced corrosion of the steel reinforcement is iden-tified as the main cause of deterioration of different types of

2815364..I. Ahmed).

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.A. Hodhod, H.I. Ahmed, Moournal (2014), http://dx.doi.or

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Reinforced Concrete (RC) structures (e.g. bridges, parkinggarages, off-shore platforms, etc.). The main sources of chlo-rides include seawater and deicing salts used during winter.Corrosion of the steel reinforcement leads to concrete fracture

through cracking, delamination and spalling of the concretecover, reduction of concrete and reinforcement cross sections,loss of bond between reinforcement and concrete, and reduc-

tion in strength and ductility [1]. As a result, the safety and ser-viceability of RC structures are reduced.

A reliable prediction of the time to corrosion initiation of

RC structures exposed to chlorides is critical for the selectionof a durable and cost-efficient design and for the optimization

deling the corrosion initiation time of slag concrete using theg/10.1016/j.hbrcj.2013.12.002

ousing and Building National Research Center.

2 O.A. Hodhod, H.I. Ahmed

of the inspection and maintenance of built structures, which isessential to minimize the life cycle costs. Existing models aremostly based on the assumption of a Fickian process of diffu-

sion for predicting the time and space variations of chloridecontent in concrete and on the concept of chloride thresholdto define the corrosion resistance of reinforcing steel to chloride

attack [1]. Therefore, the governing parameters of this diffu-sion-based corrosion initiation time include the concrete coverdepth, chloride diffusion coefficient in concrete, surface chlo-

ride concentration, and chloride threshold level assuming thepresence of moisture and oxygen for the corrosion to proceed.

The corrosion of RC structures can be described as a two-stage process: (i) corrosion initiation stage; and (ii) corrosion

propagation stage [2]. For chloride-induced corrosion, the ini-tiation stage corresponds to the period of time during whichchlorides penetrate the concrete without observed damage.

The corrosion initiation time is defined as the time at whichthe concentration of chlorides at the steel surface reaches acritical or threshold value.

Aggressive agents such as chlorides, water, and oxygen pen-etrate into concrete through the pore spaces in the cement pastematrix and micro-cracks. The rate of penetration is dependent

primarily on the quality of concrete and more particularly onthe water/cement (w/c) ratio of the concrete mix and the pres-ence of supplementary cementing materials (e.g. silica fume,fly ash, or slag) and/or protective systems that delay or slow

down chloride ingress. In porous solids, such as concrete, mois-ture may flow via the diffusion of water vapor, and via non-sat-urated or even saturated capillary flow in finer pores [3].

Chloride ingress into concrete from external sources istherefore due to multiple transport mechanisms, such as diffu-sion and adsorption. However, adsorption occurs in concrete

surface layers that are subjected to wetting and drying cycles,and it only affects the exposed concrete surface down to 10–20 mm [4,5]. Beyond this adsorption zone, the diffusion pro-

cess will be dominated [5].Chloride diffusivity is one of the important properties of

concrete affecting durability of RC structures, especially whenthe structure is built in a marine environment. The ingress of

chloride ions into concrete is a complicated process which in-volves many different transport mechanisms. The most domi-nant process is diffusion, governed by Fick’s second law.

Diffusion is the mechanism that is capable of bringing chlo-rides to the level of the reinforcing steel, thereby acceleratingthe corrosion of the rebar. Diffusion occurs when saturated

concrete is exposed to a chloride solution at normal pressure,a chloride concentration gradient is created between the sur-face and the interior pore solution. The driving force behindthis process is the difference in chloride concentration.

Collepardi et al. [6] demonstrated that chloride diffusioninto concrete can usefully be modeled by the error functionsolution to Fick’s second law of diffusion by Crank [7]. Eq.

(1) mathematically expresses Fick’s second law of diffusionfor the non-steady state condition, where the concentrationC of the medium is changing with time t, as follows:

dc

dt¼ Dca

d2c

d2xð1Þ

Eq. (1) is applicable only to one-dimensional flow with thespace co-ordinate x, measured normal to the section. Theparameter Dca is the apparent diffusion coefficient. The

Please cite this article in press as: O.A. Hodhod, H.I. Ahmed, Moartificial neural network, HBRC Journal (2014), http://dx.doi.or

equation may be solved for a semi-infinite medium using theLaplace transformation, assuming that the surface concentra-tion is constant (C0), the initial concentration in the concrete

is zero and the infinite point condition C(x =1, t > 0) is alsozero since it is far enough away from the surface. The errorfunction solution as applied by Crank is based on these

assumptions, and may be stated as Eq. (2), as follows:

C ¼ C0 1� erfx

2ffiffiffiffiffiffiffiffiffiDcatp

� �� �ð2Þ

where, C(x,t) = chloride concentration at depth and time,Co = surface chloride concentration, Dca = apparent diffu-sion coefficient, t = time for diffusion, x = concrete coverdepth, and erf = statistical error function.

When C(x,t) is set equal to the chloride corrosion initiationconcentration (chloride threshold value), and Eq. (2) is solvedfor t, the time for diffusion of chloride ions to the chloride cor-

rosion initiation concentration can be determined.Recently, some researches on the artificial neural network

(ANN) in data processing are introduced in the field of dura-

bility and they are very efficient compared with the simpleregression method obtained from available experimental data[8].

The main objective of this paper was to study the corrosioninitiation time of slag concrete exposed to chlorides, also, thepossibility of using ANN to simulate the corrosion initiationtime obtained from the error function solution to Fick’s sec-

ond law of diffusion.Therefore, the present study was undertaken with the fol-

lowing main objectives:

(1) To investigate impacts of concrete cover, chloridethreshold value, surface chloride concentration and

chloride diffusion coefficient; on the corrosion initiationtime of slag concrete.

(2) To simulate the error function solution to Fick’s secondlaw of diffusion using ANN model approximating the

relationship between the corrosion initiation time of rein-forcing steel in concrete and its governing parameters.

Network architecture

In this study, an ANN model was used to simulate the corro-sion initiation time of slag concrete obtained from the errorfunction solution to Fick’s second law of diffusion approxi-

mating the relationship between the corrosion initiation timeof the top layer of reinforcing steel in concrete and its govern-ing parameters.

The design of the ANN model requires identifying the net-work architecture (i.e. number of input neurons, output neu-rons, hidden layers, and neurons in each hidden layer) andthe network settings (activation function and learning rate).

For the corrosion imitation time, the adopted network architec-ture consists of four neurons in the input layer, which representthe values of concrete cover, chloride diffusion coefficient, chlo-

ride threshold value and surface chloride concentration, andone neuron in the output layer, which represents the value ofthe corresponding corrosion initiation time (Ti).

The optimal number of hidden layers was determined byconsidering the trade off between generalization and mappingcapabilities of the neural network. Basically, the choice is

deling the corrosion initiation time of slag concrete using theg/10.1016/j.hbrcj.2013.12.002

Modeling the corrosion initiation time of slag concrete 3

limited to one or two hidden layers because of the ability ofthese networks to approximate any nonlinear function andmap any unknown relationships between the input and output

variables [9]. Four-layer ANNs (i.e. two hidden layers) havesuperior fitting capabilities over three-layer ANNs (i.e. onehidden layer), however, three-layer ANNs are computationally

faster and have better generalization capabilities [10]. Also, itwas reported that 95% of the working applications were basedon three-layer networks with only few exceptions [11]. That is

why a three-layer ANN was selected for the presentapplication.

For the network settings, activation functions are applied tobind the network input and output of the different layers to a

specific range that the network can efficiently handle. Thisrange is usually scaled between 0 and 1 or �1 and 1. Differentactivation functions are provided by the used simulator, such as

sigmoid, threshold, step, linear, and Gaussian functions. Theselection of the most appropriate function is also a matter oftrial-and-error. A scaling range between 0 and 1 with the logis-

tic sigmoid activation function was found to be the best settingsfor the present application. The learning rate, which identifiesthe amount of adjustments to connection weights during train-

ing, was determined based on the network performance.The learning rate was set to change from 1.0 to 0.1 accord-

ing to the percentage of correct predictions (from 100% to 0%)in each training cycle. This set up is efficient since it results in

high learning rates in the early training cycles, and low learn-ing rates in advanced training cycles, which is required to finetune network weights and achieve network stability.

Results and discussion

Time to corrosion initiation of slag concrete

Effect of chloride threshold value

The results of corrosion initiation time obtained from theANN model and the error function solution to Fick’s second

law of diffusion for slag concrete of various chloride thresholdvalues of (0.1%, 0.2%, 0.3%, 0.4% and 0.5%), a constant con-crete cover of 0.05 m, a constant chloride diffusion coefficient(1 · 10�11 m2/s), and exposed to a constant surface chloride

concentration of 5% are shown in Fig. 1.It is generally clear from the results obtained from both

ANN model and the error function solution to Fick’s second

law of diffusion that the corrosion initiation time is increasedwith increasing the chloride threshold value. Where, the values

Fig. 1 Effect of chloride threshold on corrosion initiation time

of slag concrete.

Please cite this article in press as: O.A. Hodhod, H.I. Ahmed, Moartificial neural network, HBRC Journal (2014), http://dx.doi.or

of corrosion initiation time obtained from ANNmodel for slagconcrete of various chloride threshold values of 0.1%, 0.2%,0.3%, 0.4% and 0.5% were about 17, 22, 27, 30 and 33 years,

respectively. While, the values of corrosion initiation time ob-tained from the error function solution to Fick’s second law ofdiffusion were about 17, 22, 27, 31 and 35 years, respectively.

Effect of concrete cover depth

The results of corrosion initiation time obtained from the ANNmodel and the error function solution to Fick’s second law of

diffusion for different slag concrete mixes of various concretecover depths (0.03, 0.04, 0.05, 0.06 and 0.07 m), a constantchloride diffusion coefficient (0.6 · 10�11 m2/s), a constant

chloride threshold value of 0.3% and exposed to a constant sur-face chloride concentration of 1% are shown in Fig. 2.

It is generally obvious from the results obtained from both

ANN model and the error function solution to Fick’s secondlaw of diffusion that the corrosion initiation time is increasedwith increasing the concrete cover depth. Where, the values ofcorrosion initiation time obtained from ANN model for slag

concretes made with various concrete cover depths of 0.03,0.04, 0.05, 0.06 and 0.08 m were about 53, 95, 148, 209 and264 years, respectively. While, the values of corrosion initia-

tion time obtained from the error function solution to Fick’ssecond law of diffusion were about 53, 95, 148, 213 and290 years, respectively.

Effect of surface chloride concentration

The results of corrosion initiation time obtained from theANN model and the error function solution to Fick’s second

law of diffusion for different slag concrete mixes of a constantchloride threshold value of 0.3%, a constant concrete coverdepth of 0.05 m, a constant chloride diffusion coefficient

(0.8 · 10�11 m2/s), and exposed to different surface chlorideconcentrations (1%, 2%, 3%, 4% and 5%) are shown in Fig. 3.

It is generally apparent from the results obtained from bothANN model and the error function solution to Fick’s second

law of diffusion that the corrosion initiation time is decreasedwith increasing the surface chloride concentrations. Where, thevalues of corrosion initiation time obtained from ANN model

for slag concrete exposed to various surface chloride concen-trations (1%, 2%, 3%, 4% and 5%) were about 116, 65, 43,36 and 33 years, respectively. While, the values of corrosion

initiation time obtained from the error function solution toFick’s second law of diffusion were about 111, 57, 44, 37and 33 years, respectively.

Fig. 2 Effect of concrete cover on corrosion initiation time of

slag concrete.

deling the corrosion initiation time of slag concrete using theg/10.1016/j.hbrcj.2013.12.002

Fig. 3 Effect of surface chloride on corrosion initiation time of

slag concrete.

Fig. 4 Effect of chloride diffusion on corrosion initiation time of

slag concrete.

4 O.A. Hodhod, H.I. Ahmed

Effect of chloride diffusion coefficient

The results of corrosion initiation time obtained from the ANNmodel and the error function solution to Fick’s second law of

diffusion for different slag concrete mixes of varied chloridediffusion coefficients (from 0.4 · 10�11 to 0.8 · 10�11 m2/s), aconstant concrete cover depth of 0.05 m, a constant chloride

threshold value of 0.3% and exposed to a constant surface chlo-ride concentration of 1% are shown in Fig. 4.

It is generally apparent from the results obtained from both

ANN model and the error function solution to Fick’s secondlaw of diffusion that the corrosion initiation time is decreasedwith increasing the chloride diffusion coefficient. Where, thevalues of corrosion initiation time obtained from ANN model

for slag concrete of various chloride diffusion coefficients of0.4 · 10�11, 0.5 · 10�11, 0.6 · 10�11, 0.7 · 10�11 and 0.8 ·10�11 m2/s were about 205, 170, 148, 131 and 116 years, respec-

tively. While, the values of corrosion initiation time obtainedfrom the error function solution to Fick’s second law of diffu-sion were about 222, 177, 148, 127 and 111 years, respectively.

Moreover, it can be generally stated from the results shownin Figs. 1–4 that there was a high correlation between the cor-rosion initiation time obtained from the error function solu-

tion to Fick’s second law of diffusion and the correspondingcorrosion initiation time predicted by ANN model and it givesvery close estimates of corrosion initiation time of slag con-cretes and it was successfully learned the complex relationship

between input and output parameters.

Please cite this article in press as: O.A. Hodhod, H.I. Ahmed, Moartificial neural network, HBRC Journal (2014), http://dx.doi.or

Conclusions

The main conclusions of this study can be summarized asfollows:

(1) The research results obtained from both ANN modeland the error function solution to Fick’s second law of

diffusion demonstrate that the corrosion initiation timeof slag concrete increases with increasing both concretecover and chloride threshold value and decreases withincreasing both surface chloride concentration and chlo-

ride diffusion coefficient.(2) Comparison between the error function solution to Fick’s

second law of diffusion and ANN model predictions has

proven that there was a high correlation between the cor-rosion initiation times obtained from the error functionsolution to Fick’s second law of diffusion and those pre-

dicted by ANNmodel, where, the prediction ANNmodelgives very close estimates of corrosion initiation time ofslag concrete mixes. Moreover, the ANN model success-

fully learned the complex relationship between inputand output parameters and has efficiently characterizedthe corrosion initiation time of slag concrete.

Conflict of interest

None declared.

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