Environmental variables in the concrete saturation degree modelling

Com o objetivo de facilitar o calculo do grau de saturacao do concreto, visto que e um fator influente no coeficiente de difusao de ions cloreto no interior do concreto, foram elaborados modelos matematicos que dispensam medicoes locais. Pesquisas concluidas comprovam a influencia do grau de saturacao no coeficiente de difusao, e um modelo proposto viabiliza o calculo do coeficiente de difusao de ions, considerando as variacoes do grau de saturacao para cada tipo de concreto. Os modelos foram elaborados atraves de analises estatisticas de variaveis ambientais que influenciam na variacao do grau de saturacao. Como conclusao da pesquisa elaborou-se quinze modelos obtidos pela regressao linear multipla, que estimam o grau de saturacao medio sazonal de cada tipo de concreto, gerando um erro percentual maximo, inferior a 5%.


1.Introduction
Many studies have been undertaken to improve the techniques and materials used in concrete buildings.Few centuries ago, it was believed that concrete would have an infinite service life, and that a concrete building would never fail or suffer from environmental influences.However, this idea ended when the first corrosion-related problems started to appear, which led to cracks and deterioration problems in need for repairs or even led to partial or total failure of large structures.Since then, engineers are engaged in understanding this concrete deterioration process.Based on past researches, it is possible to calculate, based on a model derived from the Fick's second Law, Crank [2], the time at which the reinforcement of a concrete structure will start to be attacked by chloride ions and, hence, to be able to use prevention measures to make this attack more difficult.This study dealt with concretes located in a mist region and, for this reason, they were considerably attacked by chloride ions present in the water droplets.To obtain better results from the model described above, there is a need to measure the seasonal variations of the saturation degree (SD) to correlate them with the diffusion coefficient used in the model (Guimarães [3], Climent et al. [1], Nielsen e Geiker [10]).Two previous works allowed these measurements and provided data that allowed the studies on the factors influencing the SD variation.Guimarães [3] developed a method to measure the degree of saturation in concrete structures and Souza [11] determined, statistically, the minimum periodicity of the measurements.SD is one of the most decisive factors in the intensity of the ingress of chloride ions in concrete structures.Recent studies proved the importance of taking into account the SD influence on the chloride diffusion in concrete structures located in maritime environments.According to Guimarães and Helene [6] and Guimarães [9], there is a large difference between the chloride ingress depth assumed by deterministic models and the real value found in structures located in the south of Brazil, when the SD was not accounted for.Aiming to find models that allow obtaining approximations for the values of SD, without the need for periodical measurements, the influence of the environmental variables in the estimative of SD was studied and a group of mathematical models that allowed these approximations was obtained.Hence, after Souza [11] conclusions, weekly measurements of SD had been carried out in the specimens used in his research for four more years, which led to the development of models capable of duplicating the SD values, with no need to measure them.SD is a measurement related with the humidity degree of the concrete.This humidity starts in its outer layer, continuing towards its interior.As climate changes occur, the wet and dry process of the concrete starts.The aggressive agents that attack concrete (e.g.chlorides) penetrate through the outer layer of the concrete.Once inside the concrete, chlorides tend to dissipate until they reach and depassivate the steel bars.This triggers the deterioration process of the concrete.By definition, SD is the percentage of the pore solution volume by the total volume of pores.SD is defined by the percentage of the humidity degree of the specimen's mass in relation to the water absorption after immersion and boiling.(Guimarães [7]) Previous studies proved the direct influence of the concrete SD in the diffusion of chloride ions in the interior of the concrete.Some researchers that developed their studies on topics that contributed for the maintenance and durability of concrete, examining factors that stimulate the penetration of chloride ions into concrete and  Since SD calculations are difficult, the models that estimate the service life of concrete (Crank [2]) and that do not take into account the SD influence on the ion diffusion coefficient calculations, tend to lose their accuracy.This is another factor that this study aimed for: to be able to calculate with a better accuracy the service life of concrete structures or the cover depth necessary for a certain service life to be achieved for a specific structure.

Materials
The materials used in this study are presented as follows.The characterisation of the materials is shown in tables 1, 2, 3 and 4.These parameters were obtained from a previous study undertaken by Souza [11], where they were compared with the values of SD.

Methodology
With the material, five mix proportions were used: three mixes with same consistency and different w/c ratio; three mixes with the same w/c ratio and different consistencies, being one of the mixes common to both families of mixes.All mixes have the same mortar ratio of 52%.Table 3 shows the mix proportions, the slump test results and the specific mass of the fresh concrete.Table 4 presents the compressive strength at 28 and 60 days of the mixes.Thirty concrete specimens were cast, leading to fifteen families of concrete with two specimens each.These specimens were cut (see figure 1) from 2 different cylinders of 10 cm in diameter.A disc saw was used to cut the specimens, which is usually found in concrete laboratories.The specimens were extracted from two directions (vertical and horizontal), of concrete blocks, as shown in figure 1.These slices originated thirty cylinders measuring 10 cm in diameter and 4 cm in height, which is approximately the same as the cover of steel bars.The specimens were covered with two layers of silicon, except in one of surfaces, according to the casting surface of the specimen.The dry mass of the specimens was measured prior and after to the application of the silicon layers.Once the exposure environment for the specimens was chosen, a frame made of timber and polystyrene was constructed aiming to hold the specimens, and allowing the non-covered surfaces to be partially exposed to the natural environment.The exposure surfaces were chosen by the researchers at the beginning of the study, and are shown in figure 2. Each pair of specimens was installed together in the frame (made with timber to expose specimens), being one specimen with a humidity degree considerably low and the other considerably high.The SD measurements were only taken into account when both specimens had a similar SD value, in equilibrium with the environment.From the thirty specimens, they were extracted in pairs from the same direction, to calculate their average variations of SD.In total, 15 families of specimens were examined, varying the extraction position, the mix proportion and the exposure in natural environ-  Environmental variables in the concrete saturation degree modelling ment.The measurements were carried out in pre-set dates and times, even in rainy days.Table 5 summarizes the identification of specimens per family.Once a week, the daily mass of each specimen was measured by a digital scale, as shown in figure 3. The dry initial mass of each specimen was also measured.Guimarães [7] established a methodology to measure SD of concrete, as shown in equations 1 and 2. (1)

daily mass M dry = dry mass
It is important to calculate SD due to the fact that it influences on the variation of the diffusion coefficient of chloride ions in the interior of the concrete.The diffusion coefficient of ions, however, is a variable in the equation that estimates the ser-vice life of concrete structures.Crank [2] presents the following solution for the Fick's second Law, which estimates the service of concrete, for a constant diffusion coefficient. (3)

service life, in years z = Gaussian error function
The fact that the Crank [2] model does not take into account some factors influencing the diffusion coefficient, leads to an error in its result and to a lack of accuracy in the estimative.The SD factor is not commonly used in service life models.Since it is already known the importance of SD, this work aims to make easier its calculation for further consideration in the Crank's [2] model.For that, the diffusion coefficient proposed by Guimarães [3] is used, which considers the influence of the type of cement (R c ), mean temperature per season (R T ), saturation degree (R SD ) and the position of the attack surface in relation to the casting surface (R CS ) on the diffusion coefficient of the concrete.(4)

diffusion coefficient considering the exposure conditions in the micro environment D const.Cl -(lab) = diffusion coefficient obtained in laboratory in saturated concrete condition (SD = 100%)
The objective of this study is to investigate SD through environmental variables.For that, it was considered as a hypothesis that each environmental variable influences in a more or less significant way the SD of concrete.Aiming to not take into account the less significant variables, a statistical study was undertaken by measuring the linear correlation coefficients between the analysed variables and the SD.The analysed variables were: atmospheric pressure, dry air temperature, maximum temperature, minimum temperature, relative humidity, precipitation rate, internal evaporation rate (Pichê), humid air temperature, insolation hours, cloudiness, visibility and external evaporation rate.In the first statistical analysis, it could be verified that the variable showing the highest correlation was the maximum temperature (MT), except for the family 2122 (family of specimens 21 and 22), even though MT was the second highest correlation.Table 6 shows the results for this analysis for all families of concrete.A seasonal average of SD for each family of concrete is considered in the model proposed by Guimarães [3] to calculate the diffusion coefficient of chloride ions.Therefore, since the linear correlation is high for the MT variable, simple linear regression models were developed for all these families, as a function of the average MT for each season.The model returns the average seasonal SD for each family of concrete.Table 7 presents the models developed by simple linear regressions and their correlation coefficients (R).To investigate the behaviour of the model regarding the SD response, it was examined the measurements of a new sample of SD (seasonal average of measurements) with the values obtained in the models.For the research to continue, it was investigated the significance of other environmental variables for the development of models obtained through multiple linear regression.It is important to note that a variable is taken as significant in the model if the p value (significance test) is lower than 5% (0.05).The modelling was elaborated by mathematical computational programmes that calculate the coefficients of the independent variables, the intercept coefficient and the significances of the used variables in relation to SD.The results are matrix models including sum and multiplication of matrixes.

Results and discussions
The highest absolute error found in the simple linear regression model was 2.73 units, which corresponds to a percentage error of 4.24% in relation to the local measurement, for the family 1920 (family of specimens 19 and 20).The results of a second analysis with the multiple linear regression model indicate that a second variable, in the majority of the cases the relative humidity -RH, increases the correlation coefficient of the models, helping to explain the SD values obtained in the models.Table 8 shows the models obtained by the multiple linear regression, the values of the correlation coefficient (R) and the results of the significance test (p) for each variable used in the model.It is important to note that, for the family 1516 (family of specimens 15 and 16), the independent variables used were MT and internal evaporation rate (IER), for the family 2930 (family of specimens 29 and 30) were MT and the humid air temperature (HAT) and for the other families were MT and RH.The same analysis of the model behaviour undertaken for the simple linear regression was carried out for the models of multiple linear regression analysis.The highest calculated absolute error was of 2.47 units, which corresponds to a percentage error of 3.83% for the family 1920 (family of specimens 19 and 20).The fact that a second variable have increased the correlation coefficient of the model, what can be observed by comparing tables 7 and 8, indicates that the multiple linear regression is better adjusted to the proposed objective, leading to a maximum percentage error lower than 5%.The lowest correlation coefficients calculated are referent to the specimens with the surface turned up, lateral or down or to the specimens exposed to laboratory conditions.Notwithstanding, the multiple linear regression model generated better results.To develop the models, it was investigated a possible time shift of SD in response to the environmental variables.Once verified that there was not a shift higher than 24 hours, it was not necessary to adjust time in the models.Since the multiple linear regression model adjusted better to the proposed objective, this model was utilised as a standard for a guide that can be consulted in the design of SD for each type of concrete structure.Table 9 shows this guide.It was not possible to compare the results obtained with other studies, since it was not found references of models for the calculation of SD through environmental variables.New mod- Environmental variables in the concrete saturation degree modelling els are being studied for high initial strength concretes, thus allowing a future comparison of results.

Conclusions
The main conclusion of this research was the possibility to adjust two models, one originated from a simple linear regression and another from a multiple linear regression, to obtain with good accuracy the values of mean SD in the seasonal periods, for concrete with pozzolanic cement for structures located in maritime zone, in the south of Brazil.
There is an indication that the use of the models may reduce per-sonnel and material costs spent for the local measurements of SD.
Once defined the type of concrete used in a structure as well as its position in relation to the exposure surface, the most appropriate model to calculate the mean SD for the four seasons can be chosen.After this calculation is performed, the result obtained from the model proposed by Guimarães [3] is used to determine the corresponding diffusion coefficient.This coefficient as well as the values of other variables are input data for Crank's [2] model based on the second Fick's Law to estimate the service life of concrete structures.Moreover, it can be concluded that there is no time shift higher than 24 hours in the response of SD to the maximum temperature, relative humidity, internal evaporation rate and humid air temperature.Finally, table 9 can be used as a guide of models that can be consulted for the calculation of SD in each type of concrete structure, in the analysed region.This study has its limits in the South of Brazil, in a mist zone, ensuring local results only, and a new study is necessary to use the models in other regions.

Table 1 -
Grading of fine aggregate

Table 2 -
Grading of coarse aggregate

Table 3 -
Mix proportions, slump test results and specific mass of fresh concrete * c: cement, fa: fine aggregate, ca: coarse aggregate, w/c: water to cement ratio M. G. T. PERAÇA | A. T. C. GUIMARÃES | H. C. PICCOLI Cement -Type CP IV 32 from Votorantin Fine aggregate -quartz origin sand with grading according to table 1 Coarse aggregate -granite origin crushed aggregate with grading according to table 2 Potable water

Table 4 -
Compressive strength (MPa) * Not accounted due to the 60 days results

Table 5 -
Identification of specimens

Table 6 -
Correlations of concrete families with environmental variables

Table 7 -
Models obtained by simple linear regression

Table 8 -
Models obtained by multiple linear regression