Service life prediction of fly ash concrete using an artificial neural network

Abstract

Carbonation is one of the most aggressive phenomena affecting reinforced concrete structures and causing their degradation over time. Once reinforcement is altered by carbonation, the structure will no longer fulfill service requirements. For this purpose, the present work estimates the lifetime of fly ash concrete by developing a carbonation depth prediction model that uses an artificial neural network technique. A collection of 300 data points was made from experimental results available in the published literature. Backpropagation training of a three-layer perceptron was selected for the calculation of weights and biases of the network to reach the desired performance. Six parameters affecting carbonation were used as input neurons: binder content, fly ash substitution rate, water/binder ratio, CO₂ concentration, relative humidity, and concrete age. Moreover, experimental validation carried out for the developed model shows that the artificial neural network has strong potential as a feasible tool to accurately predict the carbonation depth of fly ash concrete. Finally, a mathematical formula is proposed that can be used to successfully estimate the service life of fly ash concrete.

Graphical abstract

Keywords

concrete / fly ash / carbonation / neural networks / experimental validation / service life

1 Introduction

The service life of reinforced concrete structures can be reduced by many factors, including factors related to design errors during sizing or during execution, shear, or flexural strength defects due to excessive loading, and aging of the structure. In addition, the degradation of materials, such as the corrosion of reinforcement steels, is often the main cause of the decrease in structural capacity. The corrosion of reinforcements due to the carbonation of concrete is by far the problem encountered most commonly. This is the result of the exposure of most buildings to the atmosphere, which can cause defects ranging from simple traces of rust on the siding to a significant loss of bearing capacity, because of the reduction of reinforcement sections and/or the loss of adhesion after the cracking and bursting of embedded concrete. The factors controlling the carbonation of concrete are diffusivity of CO₂ and its reactivity with concrete. Diffusion depends on the porous concrete system and the exposure conditions. The porous concrete system depends on the type and content of the mixture, the water/cement ratio, and the degree of hydration.

Corrosion related to steel carbonation occurs in two distinct stages: an initiation or priming phase (also called an incubation phase) and a propagation phase. The transition from one phase to another corresponds to the “depassivation” of steel. The priming phase corresponds to the penetration of aggressive agents (mainly carbon dioxide, air, and chlorides) through the coating layer until the start of reinforcement corrosion (destruction of a passive film). The priming or incubation period depends largely on the processes that transport the aggressive elements to the reinforcement and on the chemical reactions occurring in the concrete and electrochemical reactions at the interphase. The coating quality (i.e., permeability thickness) plays a fundamental role in the penetration of aggressive agents [1]. The rust propagation phase leads to cracking and then to the destruction of the coating [2]. To study the durability of structures undergoing carbonation, we must study the mechanism of corrosion induced by carbonation [3]. The time required for corrosion to reach the first reinforcement bed by the carbonation effect is much longer than the duration of corrosion propagation [4]. According to Tuutti [2], the most appropriate method to increase the lifetime of concrete structures is to increase the incubation phase. This is also the approach used in the French Association of Civil Engineering guide [5]. The initiation (or incubation) phase is relatively slow and the propagation phase is shorter and characterized by a rapid decrease in structure performance until failure. Therefore, the study of the first phase remains crucial in preventing carbonation damage risks that become expensive in the propagation phase.

There are many more models relating to the initiation phase than to the propagation phase in Ref. [3]. Fagerlund [6] developed a method for the service life prediction of structures using a relationship between serviceability and time, which can be applied in cases of carbonation, sulfate attack, and alkali reactions. Niu et al. [7] estimated the service life of reinforced concrete structures using the degree of reliability of carbonation over time by applying the limit state equation. Liang et al. [8] established a relationship between carbonation and the age of concrete, inspired from Fick’s second law of diffusion, to predict the lifetime of a bridge under corrosion induced by carbonation. Although the expected life of a reinforced concrete structure differs according to its use, size, it is often estimated to be 50–65 years, which can be extended to 100–120 years for special or important buildings [9].

Mineral additions are used more often by concrete producers. As these are generally industrial by-products, their consideration in the formulation of concrete in respect to the minimum cement dosage is of interest in terms of economy (reduction of raw material cost) and ecology (reduction of CO₂ emissions and consumption of nonrenewable resources). Cement additions affect the carbonation of concrete by two phenomena [10–16]. (1) Portlandite consumption due to the pozzolanic reaction implies that a small amount of CO₂ is sufficient to carbonate the remaining hydrates. The carbonation depth has been observed to be high when the amount of Ca(OH)₂ is low [17]. As a result, the presence of a cementitious addition causes an increase in the carbonation rate. (2) The modification of concrete porosity and permeability leads to an improvement in the properties of pozzolanic concrete transport under certain conditions (active pozzolan, long cure time, etc.).

Fly ash is a by-product of pulverized coal combustion, with or without fuel, and has been used widely as a cementitious additive in normal and high-performance concrete. Fly ash improves the performance and quality of fresh and hardened concrete. For fresh concrete, it affects the plastic properties by improving workability, reducing water demand and segregation, and decreasing the heat of hydration. For hardened concrete, fly ash increases the compressive strength, reduces permeability and corrosion of reinforcement, increases sulfate resistance, and reduces alkali–aggregate reactions [18].

There is no general agreement among researchers on how the use of fly ash in concrete tends to decrease the rate of carbonation [19]. Ogha and Nagataki [20] and Marques et al. [21] concluded that the carbonation coefficient increases with the increasing fly ash substitution rate. This increase is less appreciable for low water-binder (W/B) ratios and moderate substitution rates (30%) [22,23]. Burden [13] observed that increasing the fly ash substitution rate and W/B ratio while decreasing the wet cure time increases the carbonation depth.

The starting point in material modeling is always a set of experimental results. In a traditional analytical modeling technique, the behavior of a material is observed to identify its characteristics. Once the observation is performed, a mathematical model is developed to simulate the observed behavior. This process consists of coding behavioral knowledge into a set of mathematical rules. The important progress made in recent years in the field of artificial intelligence has made it possible to reduce the difficulties and overcome the limitations of linear models; artificial neural networks (ANNs) and deep learning are part of this progress [24,25]. These techniques can be used to provide models of treatment processes with two main objectives: better treatment efficiency and reduced operating costs. Indeed, neural networks do not require explicit knowledge of the process to be modeled as the neural network (NN) will develop its own knowledge from examples presented to it. It is therefore necessary to go through a learning phase to adjust various parameters of the network, after which the network can analyze new cases. The prediction of concrete carbonation by neural networks has been of interest for some time [26–33], but no one has yet estimated the lifetime of concrete containing cementitious additions by the ANN technique.

With the ever-increasing deterioration of infrastructure, all current major construction projects must include a lifetime requirement in their design. In addition, the prediction of service life must consider exposure conditions and the most influential parameters. Recently, Benítez et al. [34] chose the optimum mathematical model for the prediction of concrete structure service life subjected to carbonation-induced corrosion.

This paper estimates the lifetime of concrete containing different substitution rates of fly ash by predicting the carbonation depth using ANNs. Equations to calculate the carbonation depth of fly ash concrete using the parameters considered in the ANN model are also proposed. These equations could be used to estimate the carbonation depth and lifetime of fly ash concrete without conducting laboratory tests, which are costly and time consuming.

2 Artificial neural network model

2.1 Artificial neural network

ANNs are highly connected networks of elementary processors operating in parallel. Each elementary processor calculates a single output based on the information it receives. A multilayer NN is the most widely used type of neural network model, consisting of an input layer, one or multiple hidden layers, and one output layer [35]. Each layer contains several neurons, as shown in Fig. 1. The NN is trained by presenting it with a set of associated input–output data based on a training rule. The training process uses an algorithm, in which the NN develops a function between inputs and outputs. Generally, during a training process, the neurons receive input data from an external environment (x₁,x₂,...,x_n) and transmit them to neurons in a hidden layer, which are responsible for simple calculations of useful mathematics involving weights of connections (w₁₁,w₁₂,...,w_1n), biases (b₁,b₂,...,b_n), and input values. The result of these hidden neurons is transferred through a threshold or activation function (f), at which each neuron (processing element) limits the output with the allowed minimum and maximum [36]. The choice of function type proves to be an essential element of an ANN, and often nonlinear and more advanced functions are needed. Once this function is applied, the results are produced. Subsequently, these results become the inputs to all neurons in the adjacent layer (either the second hidden layer or the output layer) and the calculation process is repeated through the layers to the output layer. The output values are produced at the output neurons (noted y₁,y₂,...) as

(1)y_i=f\left({\displaystyle \sum w_{ij}{X}_j+b_j}\right),

where f is the activation function. The three activation functions used most commonly are the “threshold”, “linear”, and “sigmoid” functions.

An output error (e) value is deducted from the predicted outputs (y_j) and the target outputs (t_k):

(2)e={\displaystyle \sum _{k=\mathrm{1}}^m{\left(t_k-y_k\right)}^{\mathrm{2}}}.

Generally, the training process is iterative and stops when an acceptable error is reached. At the end of the learning process, the network should be able to give the output solution (s) for any data set based on the developed generalized architecture.

The reliability of any model can be measured by statistical performance factors, including the mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and the determination coefficient (R²) calculated by Eqs. (3)–(6), respectively:

(3)MAE={\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^n\left|x_i-y_i\right|}}{n}},

(4)RMSE=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^n{\left(x_i-y_i\right)}^{\mathrm{2}}}}{n}}},

(5)MAPE={\displaystyle \frac{\mathrm{1}}{n}}\left({\displaystyle \sum _{i=\mathrm{1}}^n\left|{\displaystyle \frac{x_i-y_i}{x_i}}\right|\times \mathrm{100}}\right),

(6)R^{\mathrm{2}}={\left(\frac{{\displaystyle \sum _{i=\mathrm{1}}^n\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}}{\sqrt{{\displaystyle \sum _{i=\mathrm{1}}^n{\left(x_i-\overline{x}\right)}^{\mathrm{2}}{\displaystyle \sum _{i=\mathrm{1}}^n{\left(y_i-\overline{y}\right)}^{\mathrm{2}}}}}}\right)}^{\mathrm{2}},

where x_i and y_i are the experimental and predicted values of the ith sample, respectively; \overline{x} and \overline{y} are the mean values of experimental and predicted data, respectively; and n is the number of samples. Typically, lower values of the error terms and a higher value of R² indicate good prediction performance of the model.

As the phenomenon is complex, self-validation of a developed ANN model based on minimizing the error and maximizing the correlation is insufficient. In this case, parametric study analysis, further comparison with other existing models, and experimental validation are carried out to evaluate the performance of the prediction model.

2.2 Data collection and analyses

Carbonation depth data of fly ash concrete were extracted and compiled from research to build a database with 300 data points [13,14,19,23,37–45]. Many attempts were made to reach the most influential parameters on the service life of fly ash concrete regarding the carbonation depth. Six parameters were considered as inputs to the ANN model: binder content (B), fly ash percentage (FA), W/B, CO₂ concentration, relative humidity (RH), and time of exposure (t). The output was the carbonation depth (d) measured after 28 d of wet cure. The number, distribution, and origin of the collected data are summarized in Table 1 and their statistical properties are summarized in Table 2.

After dividing the data, each input and output value must be limited before processing in a NN, so the data were normalized between −1 and 1 to be compatible with the limits of the sigmoidal transfer function tangent chosen for our proposed model. The following equation was used for the standardization of data:

(7)X_n=aX+b,

where X are the current values of the input or output parameters, X_n are the normalized values of the input or output parameters, and a and b are coefficients of the normalized equation calculated by Eqs. (8) and (9), respectively:

(8)a={\displaystyle \frac{X}{X_{\max }-X_{\min }}},

and

(9)b={\displaystyle \frac{X_{\max }+X_{\min }}{X_{\max }-X_{\min }}},

where X_min and X_max are the minimum and maximum of the input or output parameters, respectively.

2.3 Model development

There are no precise methods to choose the number of hidden layers and neurons in each layer; this can be done in an iterative way [46]. In the network-development process, weights of the fully interconnected layers are adjusted and finally, neurons of the output layer produce the network-predicted result. The network architecture for the proposed model is shown in Fig. 2.

The data were divided into 60% (180 data points) for training, 20% (60 data points) for testing, and 20% (60 data points) for validation [31,46]. The training method used most commonly is backpropagation, in which, after entering the values of the input cells and according to the error obtained at the output, we correct the weights. Backpropagation calculates the gradient of the error for each neuron, from the last layer to the first. This cycle is repeated until the error curve of the network increases (we must be careful not to over-drive a NN that will become less efficient). The method used to improve network generalization and avoid overfitting in the present model is the retraining NN. It is a good idea to train several networks to ensure that a network with good generalization is found. A MATLAB (R2014a) program was developed to train the model using the Levenberg–Marquardt algorithm, which is known for its accuracy and speed of convergence, until the desired performance is obtained. The training process is controlled by checking the plots of train, test, and validation errors simultaneously, and is stopped automatically when any of the following conditions occurs [46]: the maximum number of epochs (cycles) is reached; the maximum duration of time is exceeded; the performance goal is reached; the performance gradient falls below the minimum specified; the Marquardt adjustment parameter (momentum) exceeds the maximum specified; or validation performance has increased more than the maximum fail time since the last time it decreased (early stopping). The ANN model parameters are given in Table 3.

Figure 3 illustrates the correlation between the predicted values of the three learning phases and the experimental values. From the correlation coefficients obtained (0.99, 0.95, and 0.98 for training, testing, and validation, respectively), we can see that the proposed model has good performance.

2.4 Comparison of the ANN model and other models in the literature

A comparison was made between the ANN-predicted values and experimental results collected from four papers not included in the database [47–50], as well as values obtained by applying the models of Papadakis [51] and Burden [13]. The latter models are the only reported models developed for the prediction of the carbonation depth of fly ash concrete that consider almost the same parameters chosen in this study. The carbonation depth evolution X_c (m) with time t (s) is calculated using the following equation [51]:

(10)X_{\mathrm{c}}=\sqrt{{\displaystyle \frac{\mathrm{2}{D}_{{\mathrm{e,CO}}_{\mathrm{2}}}\left({\mathrm{CO}}_{\mathrm{2}}/\mathrm{100}\right)t}{\mathrm{0.33}CH+\mathrm{0.214}CSH}}},

where CO₂ is the concentration of carbon dioxide (%) and D_{{\mathrm{e,CO}}_{\mathrm{2}}} is the diffusivity of CO₂ (m²/s). CH and CSH in Eq. (10) are the hydrate quantities in concrete (kg/m³). On the other hand, Burden [13] estimated the carbonation depth by the following equation:

(11)X=\left[\left(\mathrm{13.8}\times W/B\right)\left(\mathrm{1}+{\displaystyle \frac{FA}{\mathrm{45}}}\right)cur{e}^{\mathrm{0.25}}-\mathrm{2}\right]\sqrt{t},

where W/B is the water/binder ratio, FA is the fly ash percentage (%), cure is the cure time (d), and \sqrt{t} is the square root of exposure time (\sqrt{\mathrm{d}}).

The comparison was made in terms of different performance indicators. Figure 4 shows the different values of these indicators in accordance with the comparison of experimental research results and results obtained by the abovementioned models. According to Fig. 4, the ANN model has low MAPE, MAE, and RMSE indicators, and a high coefficient of determination, R², compared to the other two models. This indicates the robustness and reliability of the proposed ANN model. Papadakis [51] developed a model for limited W/B ratios (0.35 ˂ W/B ˂ 0.85) and Burden [13] worked on concretes containing high fly ash substitution rates (50%). In addition, the latter did not consider all the parameters used in our proposed model. This proves that the ANN model can generalize new data in well-specified ranges of variation.

3 Experimentation

3.1 Test procedures

The experimental program included three sets of concrete mixtures at w/cm ratios of 0.4, 0.5, and 0.6, prepared by the partial replacement of cement by equal weights of fly ash. Each set had mixtures at four fly ash replacement percentages: 0% (control mix), 20%, 30%, and 50% of the total binder content. The Portland cement used is general-purpose cement (GU) marketed in Quebec, Canada; its Blaine surface area is 444.1 m²/kg. Class F fly ash, with a Blaine surface area of 387 m²/kg and density of 2360 kg/m³, was used. The chemical compositions of the materials used are shown in Table 4. Crushed aggregates (5–10 and 10–20), with densities of 2.71–2.73, and quarry sand, with a density of 2650 kg/m³, were used. A superplasticizer (Eucon 37) and an air entraining were used as additives to improve the mixture properties.

The mixtures were placed in 100 mm × 100 mm × 400 mm prisms, covered with a plastic film to avoid evaporation of water, and stored for 24 h. After demolding, the mixtures were placed in a humid chamber (RH>95%) for 28 d. The mixture proportions are summarized in Table 5. C00FA refers to the control concrete, and C20FA, C30FA, and C50FA concretes contained 20%, 30%, and 50% fly ash replacement, respectively.

After curing, samples were placed in an ambient medium (RH = 55% and t = 23°C) for 14 d to stabilize the internal RH of the microstructure. Then, each prism was covered with aluminum foil to ensure one-dimensional carbonation. The samples were then transferred to the carbonation chamber under controlled environmental conditions (CO₂ = 4%, RH = 65%, t = 20°C) for 7, 28, 90, and 180 d, as shown in Fig. 5.

Three samples were used for each carbonation test, and the carbonation depth is given by the mean of these three results.

3.2 Results and discussion

Figures 6(a)–6(d) show that for each fly ash substitution rate (0%, 20%, 30%, and 50%), the carbonation depths increase by increasing the W/B ratio and age. The porosity of the microstructure increases with the increase of the W/B ratio, which facilitates the penetration of CO₂ through the concrete pores. This has been observed in several previous studies [23,52,53]. On the other hand, for each W/B ratio, the carbonation depth increases with the substitution rate of fly ash at all ages. For the control concrete, there is almost no difference between the different W/B ratios at an early age, but differences begin to appear at an age of 28 d with the progression of hydration reactions and the formation of CH likely to carbonate. The highest carbonation depths are marked for W/B = 0.6 because of the high porosity that facilitates the penetration of carbon dioxide.

By substituting cement with 20% fly ash, a slight increase in carbonation depth is observed compared to that of the control concrete at an early age for different W/B ratios. At a later age, this difference remains low for low W/B ratios (0.4 and 0.5), whereas it is 100% for W/B = 0.6 at 180 days. The pozzolanic effect of fly ash by the formation of CSH tends to clog the pores and slow down the diffusion of CO₂. However, the remaining amount of CH will be carbonated and create a difference in the carbonation depth for the two types of concrete. By increasing the W/B ratio (0.6), the high concrete porosity facilitates CO₂ penetration into the cement matrix. For 30% FA concrete, the difference between the carbonation depth compared to the control concrete is much greater for high W/B ratios (0.5 and 0.6). A slight increase is noted for low W/B ratios (0.4) at all ages. For 50% FA concrete, a large difference between carbonation depths, compared to control concrete, is observed for different W/B ratios, especially at a later age. The amount of CH is low because of the substitution of cement by fly ash, which accelerates the carbonation process. On the other hand, a concrete containing 20%–30% fly ash with a 0.4 W/B ratio has lower carbonation depths than those of a concrete with 0.5 and 0.6 W/B ratios without additions. A 30% FA concrete with 0.5 W/B ratio has a lower carbonation depth than those of a control concrete with 0.6 W/B ratio at all ages. A concrete containing 50% fly ash with 0.4 W/B ratio has a lower carbonation depth than those of a control concrete with 0.5 and 0.6 W/B ratios at all ages.

4 Proposal of analytical formula

Based on Fick’s first law, X (t) = A\sqrt{t}, Saetta et al. [54–56] proposed the following formula according to parameters influencing carbonation:

(12)A=f_{\mathrm{ma}\mathrm{t}}\left(B\times W/B\times FA\right)·f_{\mathrm{e}\mathrm{n}\mathrm{v}}·\left(\mathrm{C}{\mathrm{O}}_{\mathrm{2}}\times RH\times T\right)·f_{\mathrm{cure}},

with f_mat being the material parameters’ function (with B, W/B, % FA); f_env, the environmental parameters’ function (with CO₂, RH, T), and f_cure, the cure conditions’ function. In our case, we consider only the parameters introduced as input neurons in the ANN model (B, W/B, FA, RH, CO₂, and t) to develop the formula.

Based on existing models and the behavior of the carbonation depth as a function of each parameter studied, it was possible to propose a mathematical formula. For this purpose, the following expression was chosen [57]:

(13)A={\displaystyle \frac{{\left(W/B\right)}^{\alpha }\times {\left(\mathrm{C}{\mathrm{O}}_{\mathrm{2}}\right)}^{\beta }}{{\left(B\right)}^{\gamma }\times {\left(\mathrm{1}-RH\right)}^{\delta }\times {\left(\mathrm{1}-FA\right)}^{\theta }}}.

A nonlinear estimation was used to find best-fit values of α, β, γ, δ, and θ coefficients by using Statistica 12 software, which facilitates the identification of statistical model coefficients. To assess how the equations fit to the experimental data, the coefficient of correlation was used. The best correlation obtained was:

(14)X_{\mathrm{c}}={\displaystyle \frac{{\left(W/B\right)}^{\mathrm{1.93}}\times {\left(\mathrm{C}{\mathrm{O}}_{\mathrm{2}}\right)}^{\mathrm{0.43}}}{{\left(B\right)}^{\mathrm{0.08}}\times {\left(\mathrm{1}-RH\right)}^{\mathrm{1.76}}\times {\left(\mathrm{1}-FA\right)}^{\mathrm{1.94}}}}\sqrt{t}.

Figure 7 compares the proposed formula results, ANN results, and those of Papadakis [51] with the experimental results of this work, as summarized in Table 6.

The Papadakis model gave the lowest determination coefficient (75%), whereas the proposed formula and ANN model had almost the highest coefficients of 86% and 85%, respectively. According to Table 6, all errors of the ANN model and the proposed formula were lower than those of the Papadakis model. This result confirms that the ANN model and the proposed formula are more efficient than the semi-empirical model proposed by Papadakis [51], which overestimated the results. According to Sabet and Jong [58], this overestimation is due to the steaming of samples at 105°C during preconditioning, which led to accelerated carbonation and much higher results.

The proposed formula, as well as the ANN model, can be used to predict the fly ash concrete carbonation depth in the same variation range of parameters affecting the carbonation of fly concrete, as mentioned above. Although the objective of the paper is not to test different ANN types, the proposed ANN model can effectively learn and predict fly ash concrete carbonation and can better address this complicated physicochemical phenomenon while considering the absence of well-validated models in the field of concrete technology.

5 Service life prediction of fly ash concrete

Carbonation is manifested in concrete in two successive phases [2]: in the first phase, called the incubation phase, the carbon dioxide diffuses through the concrete pores until it reaches the first reinforcement bed after a time of incubation for a carbonation depth X_c = e, where e is the concrete coating. In the second phase, called the propagation phase, the carbonation propagates by going beyond the reinforcements with the decrease in pH up to values lower than 9. This carbonation process tells us that the most important phase we must consider when estimating the service life of concrete is the incubation phase.

The ANN model proposed in this study has been applied to accelerated carbonation results, but to estimate the lifetime (incubation), it is necessary to convert the accelerated carbonation depth to the natural carbonation depth. Researchers have found good correlations between accelerated carbonation and natural carbonation [23]. However, the relationships derived from these studies are applicable only to their own results. Recently, Czarnecki and Woyciechowski [59] found that the accelerated carbonation depth for CO₂ = 1% is identical to that of natural carbonation. From Eq. (11), if X_c = e and the deduction of Czarnecki and Woyciechowski [59] are considered, the duration of the incubation phase can be estimated by the following relationship:

(15)t_{\mathrm{incubation}}={\left({\displaystyle \frac{B^{\mathrm{0.08}}\times {\left(\mathrm{1}-RH\right)}^{\mathrm{1.76}}\times {\left(\mathrm{1}-FA\right)}^{\mathrm{1.94}}}{{\left(W/B\right)}^{\mathrm{1.93}}\times {\left(\mathrm{C}{\mathrm{O}}_{\mathrm{2}}\right)}^{\mathrm{0.43}}}}\times e\right)}^{\mathrm{2}},

when assuming a fly ash concrete exposed to natural carbonation (CO₂ = 1%) and a RH of 65%.

The service life varies according to the fly ash substitution rate, the W/B ratio, and the coating thickness, e, as shown in Figs. 8(a)–8(c). The W/B ratio plays an important role in the service life of concrete, with and without fly ash; the lower it is, the longer the concrete life because of the densification of the microstructure, which prevents penetration of aggressive agents, such as CO₂. For different W/B ratios (0.4, 0.5, and 0.6), the service life increases with increasing coating thickness, which represents a reinforcement protection envelope. For a coating thickness ranging from 20 to 60 mm, the lifetime of a concrete without additions varies from 150 to 1200 years, 100 to 450 years, and 25 to 220 years for W/B ratios of 0.4, 0.5, and 0.6, respectively. The substitution of cement by fly ash decreases the lifetime of fly ash concrete. This decrease is much more appreciable for higher substitution rates (40% and 60%). From Fig. 8(a), it can be deduced that the substitution of cement with 20% FA and a coating of 30 mm can give a concrete the same lifetime as a control concrete with a coating of 20 mm. Beyond 30 mm of coating, the lifetime of the concrete with 20% FA substitution exceeds 200 years. Comparing Figs. 8(a) and 8(b), it is noted that the lifetime of the concrete with 20% FA replacement and 0.4 W/B ratio is the same as that of a concrete without additions and with 0.5 W/B ratio for the different coating thicknesses.

6 Conclusions

Based on the results of this study, the following conclusions can be drawn.

1) From correlation coefficients obtained for training, testing, and validation, the proposed ANN model has good performance.

2) By applying the ANN model developed in this study and two empirical models on experimental results of other researchers, the ANN model gave the best correlations. This proves its performance and generalization capacity for new data not included in the database.

3) The experimental results found in this study indicate the validity of the ANN model and its ability to predict the carbonation depth of fly ash concrete better than the physicochemical model proposed by Papadakis.

4) Carbonation depths increase by increasing the W/B ratios and age for each fly ash substitution rate (0%, 20%, 30%, and 50%). This is because the porosity of the microstructure increases with the increasing W/B ratio, which facilitates CO₂ penetration through the concrete pores.

5) By substituting cement with 20%, 30%, and 50% fly ash, an increase in the carbonation depth is observed compared to that of plain concrete at an early age for different W/B ratios. At a later age, this difference remains low for low W/B ratios (0.4 and 0.5), whereas it is higher for W/B = 0.6. The pozzolanic effect of fly ash by the formation of CSH tends to clog pores and slow down the diffusion of CO₂. However, the remaining amount of CH will be carbonated and create a difference in the carbonation depth between these two types of concrete.

6) Concrete containing up to 50% fly ash with a low W/B ratio (0.4) gives low carbonation depths compared to a control concrete with high W/B ratios (0.5 or 0.6).

7) Applying the formula proposed in this work to experimental results for the validation of the ANN model proves that this formula can be used to predict fly ash concrete service life.

8) Assuming a fly ash concrete exposed to natural carbonation and a RH of 65%, the service life varies according to the fly ash substitution rate, the W/B ratio, and the coating thickness, e; the lower the W/B ratio and the higher the e, the longer the concrete lifespan for all fly ash substitution rates.

9) The substitution of cement by fly ash decreases the lifetime of fly ash concrete. This decrease is much more appreciable for higher substitution rates (40% and 60%).

10) The concrete lifespan containing 20% FA replacement with 0.4 W/B ratio is the same as that of plain concrete with 0.5 W/B ratio for different coating thicknesses.

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