3.1 Model Development

We based our model on the Multilayer Perceptron model trained by Backpropagation Momentum algorithm. The methodology used to obtain the model is presented in flowchart of Figure 2.

Figure 2 Flowchart of the prediction model of depth of carbonation in concrete 

In the first stage, the database is set up to cover all input variables (relative humidity, CO₂ concentration, concrete compressive strength, cement type, exposure conditions, use and mix design of admixtures, and age of concrete). The database is composed by experimental results from ^{Meira et al. (2006)} and Vieira et al. (2009), and by ^{Possan (2010)} focus group, using respectively 179 and 100 data points. Some input variables were converted to numbers in order to be properly associated to the AAN, such as cement type (CP II-E, CP II-F, CP II-Z, CP III, CP IV and CP V ARI), numbered from 1 to 6. Exposure conditions was also represented by 1.30, 1.00 and 0.65 when exposed to indoor environment, external environment yet protected from rain and unprotected from rain, respectively, as established by ^{Possan (2010)}. This process defined the model applicability and boundaries for input variables, as presented in Table 1.

The boundaries or domain defines limits to use the model, since AAN are unable to extrapolate results, and it is only possible to map and to train an ANN within its domain (^{Braga et al., 2000}). AAN requires splitting the entire database in three smaller databases, one for training, other to validate, and the last to evaluation. Figure 3 shows the amount of data allocated in each database.

Figure 3 Amount of data allocated in each database. 

Each database (training, validation and evaluation) are used in a step of the process of modelling with AAN. The first database is responsible to train the network, through each pair of input/output. The second database is responsible to validate and to certify the trained network. The third and last database is responsible to test and to check the model capabilities.

AAN trained was then classified by topology, activation function and learning rate of the train algorithm, as described by ^{Félix (2016)}.

We created 1200 ANN’s with different learning rates (0.1, 0.2, 0.3 and 0.4), input entries (4, 5 and 7 perceptron’s), number of hidden layers (one or two), and number of perceptron’s in the hidden layer (from 0 to 9). With all possible combinations, resulted in 1200 ANN’s (4*3*10*10). See Figure 4 for details.

Figure 4 Tested topologies and input entries. 

We adopted the root mean square error (RMSE) between depths of carbonation measured and depths of carbonation evaluated by the trained network as convergence criteria, according to Equation (1).

(1)

where n is the number of outputs, x _i is the value provided by the network for the i-th output, and x_m is the average of the values from all outputs.

ANN training is made by the package Project-Yapy (^{Konzen et al., 2011}), provided in C++.

ANN performance was evaluated by the following parameters: correlation coefficient (R²), root mean square error (RMSE), maximum error (E_max, largest error provided), and minimum error (E_mim, smallest error provided). These parameters were evaluated both in the training stage and in the validation stage. In the test stage, these parameters were also used to access the performance of the network.

After ordering by their performance, it was possible to select the network that could better represent the carbonation of concrete. Figure 5 shows the selected network, containing three layers of perceptrons. The first layer has seven neurons, responsible for input. The second (or hidden) layer has four neurons, which are responsible to processing information, and the last layer has a single neuron, responsible for output - depth of carbonation in concrete.

Figure 5 Chosen topologies and input entries. 

Correlation charts between the carbonation depths modeled by the program (modeled depth) and the natural carbonation depths (observed depth, provided by ^{Possan (2010)}) are shown in Figures 6 (a) and 6(b).

Figure 6(a) Training correlation. 

Figure 6(b) Validation correlation. 

A complete description of the training process of the networks and the parameters used in the modeling can be found in ^{Felix (2016)}.

3.2 Parametric analysis of carbonation

We decided to perform a parametric analysis of the influence of the input variables on the evaluation of the carbonation depth in concrete. The analysis was divided into four, evaluating the influence of a single or two input variables, as shown in Figure 7.

Figure 7 Input parameters evaluated in each parametric analysis. 

4.1 Validation with reference

Initially, in order to certificate the performance of the developed model, we compared our results with others proposed models and degradation values provided by ^{Possan (2010)}. Equation (2)-(6) introduces carbonation models provided by Smolczyk (1976), ^{Vesikari (1988)}, ^{Bob & Afana (1993)}), ^{EHE (2008)} and ^{Possan (2010)}, respectively.

(2)

(3)

(4)

(5)

(6)

where is y is the carbonated depth (mm), a is the rate of carbonation, f _c is the concrete compressive strength (Mpa), f _clim is a limiting value for the carbonated concrete compressive strength (MPa), t is the age of concrete (years) and ac is water/cement ratio. The input parameters that are function of the type of binder and exposure conditions are defined using tables provided by each author in their work. More details can be found in ^{Félix (2016)}.

Some scenarios are provided in Table 2 and compared in Figure 8 (a)-(d)(8(b), 8(c)), showing the depth of carbonation vs time.

Figure 8(a) Test Stage - Scenario I. 

Figure 8(b) Test Stage - Scenario II. 

Figure 8(c) Test Stage - Scenario III. 

Figure 8 (d) Test Stage - Scenario IV. 

Em todos os cenários o teor de adição (no concreto) é zero e o tempo de análise é de 60 anos.

The results show the applicability of the model and that the proposed model is an efficient tool for estimating the depth of carbonation in concrete.

4.2 Parametric Analysis

Figure 9 shows depth of carbonation in concrete after 50 years obtained in the proposed model varying only the type of binder and the compressive strength. In this simulation, we considered an environment protected from rain, with 65% of relative humidity, 0.04% CO₂, and no additions in the concrete production.

Figure 9 Depth of carbonation as a function of type of binder and compressive strength. 

One may notice in Figure 9 that concretes produced with CP III and CP IV present greater depth of carbonation, notably with low compressive strength concretes. ^{Jiang et al. (2000)} and ^{Possan (2010)} noticed a negative influence of additions on the depth of carbonation, due to the reduction of the alkali reserve when the concrete is produced with CP III and CP IV, which have high levels of slag (from 35 to 70%) and pozzolan (from 15 to 50%) in their compositions, respectively. CP II-E and CP II-Z are also composed cements (with slag and pozzolan, respecively), however with lower levels of admixtures. That would explain the lower depth of carbonation in concrete produced with CP II-E and CP II-Z than CP III and CP IV.

One may notice in Figure 10 the influence of additions content (silica fume) on the depth of carbonation. It is observed that the depth of carbonation is barely affected by the addition in concretes with higher compressive strength (40, 50 and 60 MPa). Is also noted that the higher the addition content, greater is the depth of carbonation for concretes with lower compressive strength than 40 MPa. ^{Kulakowski et al. (2009)} report that, in concrete with higher compressive strengths (greater than 30 MPa), the CO₂ intake is smaller due to porosity, even for concretes with low alkaline reserves. The authors point out that, for concrete with compressive strength greater than 40 MPa, the depth of carbonation is independent of additions and type of cement. In the case of lower compressive strength, the presence of additions increases the depth of carbonation, and the alkali reserve effect predominates (^{Kulakowski et al., 2009}).

Figure 10 Depth of carbonation as a function of levels of additions and compressive strength. 

Figure 11 shows the depth of carbonation in a 50 years old concrete obtained in the proposed model when relative humidity and the environment exposure conditions are modified. In this simulation, we considered a concrete structure with compressive strength of 30 MPa, CP III, 0.04 % CO₂, and no additions in the concrete production.

Figure 11 Depth of carbonation as a function of relative humidity and exposure conditions. 

One may notice in Figure 11 that the depth of carbonation reach maximum when relative humidity is close to 60%. ^{Parrot (1987)}, ^{Neville (1997)} and ^{Possan (2010)} point out that depth of carbonation reaches its maximum value when the relative humidity is between 50 and 80%. They also mention that the relative humidity can be considered as the environmental factor with the greatest influence on carbonation. ^{Possan et al. (2017)} observed in a 35 years old concrete dam that the larger the internal humidity, the lower the depth of carbonation depth. The authors also notice that no carbonation was observed when moisture was about 100%.

Figure 12 shows the depth of carbonation as a function of the exposure conditions to different CO₂ concentrations. In this simulation, we considered a concrete structure with compressive strength of 30 MPa, CP III, relative humidity of 65%, no additions in the concrete production, and in an unprotected outdoor environment.

Figure 12 Depth of carbonation as a function of CO₂ concentrations. 

One may notice that higher degree of exposure to CO₂, greater the depth of carbonation in concrete over time. An increase of 0.1% of CO₂ concentrations leads to an increase of carbonated depth in 2.15%.