Predicting carbonation coefficient using Artificial neural networks and genetic programming

Highlights

• This study focuses on the modeling of the concrete carbonation phenomenon.

• For that purpose, 827 case studies are analysed, collected in the literature.

• Soft Computing techniques were used to predict the carbonation coefficient.

• Artificial Neural Networks and Genetic Programming were the techniques applied.

• The significant variables to explain the carbonation phenomenon were identified.

Abstract

Concrete carbonation is considered an important problem in both the Civil Engineering and Materials Science fields. Over time, the properties of concrete change because of the interaction between the material and the environment and, consequently, its durability is affected. Conventionally, concrete carbonation depth at a given time under steady-state conditions can reasonably be estimated using Fick's second law of diffusion. This study addresses the statistical modelling of the concrete carbonation phenomenon, using a large number of results (827 specimens or samples, i.e. 827 is the number of data concerning the measurement of the carbonation coefficient in concrete test specimens), collected in the literature. Artificial Neural Networks (ANNs) and Genetic Programming (GP) were the Soft Computing techniques used to predict the carbonation coefficient, as a function of a set of conditioning factors. These models allow the estimation of the carbonation coefficient and, accordingly, carbonation as a function of the variables considered statistically significant in explaining this phenomenon. The results obtained through Artificial Neural Networks and Genetic Programming were compared with those obtained through Multiple Linear Regression (MLR) (which has been previously used to model the carbonation coefficient of concrete). The results reveal that ANNs and GP models present a better performance when compared with MLR, being able to deal with the nonlinear influence of relative humidity on concrete carbonation, which was the main limitation of MLR in modelling the carbonation coefficient in previous study. ANNs are commonly seen as a black box; in this study, an attempt is made to address this issue through Knowledge Extraction (KE) from trained weights and biases. KE helps to understand the influence of each input on the output and the influences identified by the KE technique are in accordance with general knowledge.

Introduction

Carbonation-induced corrosion and chloride-induced corrosion are considered the major causes of deterioration in reinforced concrete structures [1]. Therefore, concrete carbonation is a subject of great concern. Carbonation is a natural physicochemical process caused by the penetration of carbon dioxide from the surrounding environment into concrete through pores in the matrix, where the carbon dioxide reacts with hydrated cement. Calcium hydroxide (Ca (OH)2) in contact with carbon dioxide (CO2) forms calcium carbonate (CaCO3). This reaction neutralizes the natural protection of reinforcement steel provided by concrete, which in turn promotes the initiation of corrosion of the steel bars [2]; Sistonen et al., 2009; [3,4]. Conventionally, concrete carbonation depth at a given time under steady-state conditions can be reasonably estimated using Eq. (1). This well-known equation is based on Fick's second law of diffusion [1,3,5,6].

$$x_c\left(t\right)=k\sqrt{t}$$

where x_c(t) is the carbonation depth at the time t [mm], k is coefficient of carbonation [mm/day^0.5] and t is the duration of carbonation [days].

In this equation, the carbonation coefficient encompasses concrete quality (e.g. water/cement (w/c) ratio, binder type, and binder content) and the environmental conditions (e.g. temperature, relative humidity and concentration of carbon dioxide) [1].

It is generally agreed that carbonation does not occur in the same way in all mixes, nor does it occur in all circumstances. Different mixes, as well as the same mix exposed to different environments, will lead to distinct carbonation rates [7,[8], [49]]. The carbonation coefficient may significantly vary from one concrete element to another depending on the environmental exposure conditions and micro structural parameters, which are linked with the concrete composition and the type of materials used. The main factors affecting concrete carbonation are: the porous system of hardened concrete, which in turn depends on the w/c ratio, the type of binder, the amount of Ca(OH)₂ and the degree of hydration; the relative humidity (for dissolution of Ca(OH)₂); and the concentration of CO₂ [5,9].

Developing an advanced carbonation prediction model that encompasses all the governing parameters for the carbonation coefficient is a difficult task, mainly because several parameters are complex to describe mathematically. Various theoretical and experimental studies have been carried out to estimate the concrete carbonation depth [[10], [11], [12], [13], [14], [15], [16]]. Most carbonation models are semi-empirical, i.e. their development starts from a theoretical basis, which is completed by fitting the required parameters to experimental results. In this sense, new models must be defined in order to describe the complex behaviour of the carbonation coefficient, which in turn will focus on structural health monitoring. The recent data driven modelling techniques of Artificial Neural Networks (ANNs) and Genetic Programming (GP) can be the most suitable way for this task owing to their learning ability from the available data and model free structure.

Earlier attempts were made to predict carbonation depth with relevant input parameters (Lu et al., 2014; [6,17]. For example, in Kwon and Song [18]; CO₂ diffusion coefficients were estimated through a neural network algorithm, with three components in OPC mix design and relative humidity as inputs neurons. The results show a reasonable decrease in the diffusion coefficient with higher relative humidity and lower w/c ratio, with maximum differences of 6.3% between estimated and experimental data. A two-phase model was developed by Seung and Wang (2016) [45], in which the strength of slag concrete was predicted in phase 1 while, in phase 2, the results from the hydration model were used as input parameters for the carbonation reaction model with different curing conditions and slag contents. Further studies in this area suggest that ANNs can be an effective tool to predict the carbonation depth in concrete since they can capture the complex relationship amongst the parameters to predict the output (Luo et al., 2016; [19,20]. Several studies were conducted for determining the strength of concrete with different materials, testing methods, displaying good performance of the models [[21], [22], [43]]. Another technique that has been widely used to determine the strength of concrete is Genetic Programming [23]; Kulkarni and Londhe, 2018). Genetic algorithms were used to obtain the optimum concrete mix proportions, considering the exposure conditions of carbonation and design parameters and determining the intended diffusion coefficients [24].

In previous studies, there seems to be no consensus on the way the carbonation coefficient should be determined. This coefficient is fundamentally a durability indicator that comprises all the variables relating to the environmental severity and the characteristics of concrete itself [[12], [42]]. Artificial Neural Networks (ANNs) were usually used to predict the carbonation depth, but few works are available in the literature related with the use of Genetic Programming (GP) to predict the carbonation coefficient even though GP has been successfully used as a prediction/forecasting tool in many works [25]. The output in ANNs is in terms of weights and biases while that of GP in the form of equations, which can be easily used for replicating the study or to apply the results obtained in other contexts. The current research intends to develop models to predict the carbonation coefficient and compressive strength of concrete using Artificial neural networks (ANNs) and Genetic programming (GP) and compare their results. Additionally, a knowledge extraction exercise is carried out using the trained weights and biases of the ANNs, which serves two-fold purposes. First, the influence of each parameter on the carbonation coefficient can be determined, which allows evaluating the coherence of the models obtained. Secondly, the mathematical complexity of ANNs can be simplified, as a modelling tool, if the first purpose is accomplished. The influence of the various parameters adopted in the GP model is also discussed in the present study.

Some of the authors of this study developed multiple linear regression (MLR) models, as a first approach, to predict the carbonation coefficient and compressive strength of concrete [26]. In the previous study, the authors acknowledged the influence of the relative humidity of the exposure environment in the carbonation phenomenon; however, the MLR model proposed, due to its linear nature, was unable to model the nonlinear effect of the relative humidity in the concrete carbonation rate, and the sample analysed was divided into two samples, leading to two different models, one for cases in which the relative humidity is 70% or less, and the other for cases where the relative humidity is higher than 70%. In this sense, it was mentioned that a nonlinear model could also have been used, based on a polynomial or even an exponential function, among other options, to overcome the limitation of a linear model as MLR. The current work is thus an extension of the mentioned work, in which the carbonation coefficient and strength of concrete are predicted using Artificial Neural Networks (ANNs) and Genetic Programming (GP). The performance of the models developed using ANNs and GP are compared with models developed using MLR. The 28-day compressive strength of concrete was further predicted using the water-binder ratio, clinker ratio in the binder (%) and curing time (days) as input parameters [26].