The results of one of the inserted delamination are presented to perform the comparison between the experimental and numerical surface temperatures and thermal gradients. Other studies showed that different internal defect characteristics (size, thickness, and depth) have distinct thermal responses through the day [24
], affecting the favorable period to detect the damages using IRT. In the present study, both experimental and simulated results for the upper-right (2 cm deep) delamination will be shown next, followed by the yearly analysis performed using the finite element method.
4.1. Comparison of Experimental and Simulated Results
shows four pairs of thermograms obtained from the experiment and FEM simulation. The temperature range of the thermograms was unified to facilitate the surface temperature comparison, and the color pallet was adjusted to improve the visualization of the damages in each experiment. The chosen palette has one scale where the red color represents the highest surface temperatures, and the blue color is associated with the lowest surface temperatures. The presented thermograms are from 12:00 (noon) and 9:00 p.m., representing heating up and cooling down phases registered in the passive IRT inspection, respectively.
In Figure 4
it is possible to observe non-uniform heating in the experiment, where the heating and cooling processes follow the solar movement, which varies through the day and the months. Figure 4
b confirms the work of Hiasa et al. [23
] by showing that the numerical model can reproduce the heating of the sample edge according to the solar orientation. In general, the surface temperatures are convergent. However, the experimental thermograms present a high level of non-uniform heating when compared to the FEM simulations, which were possibly caused by the environmental conditions on the field. Relative humidity, presence of clouds, and surroundings elements were not considered in the numerical simulation, which could have led to the inconsistencies observed between the actual temperature measurements and simulation [23
]. A higher discrepancy exists between Figure 4
g and Figure 4
h, where the difference in the surface temperature reached 7 °C. One possible explanation for this difference could be the presence of humidity and fog in the experiment environment, which is a common situation during the winter mornings and nights, causing a lower temperature in the concrete surface in the experimental sample. However, the comparison of the thermograms illustrates the applicability of the FEM model in predicting the IRT images with reasonable accordance with the field inspection using the actual information about the structure and environmental conditions [32
]. A complete quantitative temperature comparison for the surface temperature values for the upper-right (2 cm deep) delamination is provided in Figure 5
The differences between simulated and experimental surface temperatures were observed mainly during the morning and evening times. As reported in the thermograms analysis, these differences are probably due to the boundary conditions assumed in the model, which only considered the sample orientation related to the Sun, solar radiation, coefficient of convection based on the wind speed, and ambient temperature at the study site. In addition, several susceptible errors in the technique could have contributed to the observed differences, including errors in the accuracy of the thermal camera, in the instrumentation used to measure the environmental conditions, or by the local weather station. However, the purpose of this study was to verify the competence of the proposed computer-based technique to detect subsurface damages and identify a convergence with the thermal gradients’ detections in the IRT practical application under different boundary conditions. Further works will address the FEM updating to optimize the parameters used in the proposed model.
The thermal gradient between the healthy and damaged surface temperatures is the main parameter for detecting subsurface damages in infrared thermographic inspections. In this context, Figure 6
shows the difference between the measured and simulated contrast values during the days of experimentation, calculated using the surface temperatures from Figure 5
. The contrast values obtained by the numerical simulation are aligned to those calculated from the measurements performed by the IRT thermal camera, even with the temperature differences reported in the previous figure.
The amplitude of the simulated contrast followed the periodic variation of the gradients through the days that the experiments were carried out, where gradients were small for the autumn and winter months (April, June, and July) compared to the spring and summer months (November and February). The Pearson Correlation (R), the Mean Bias Error (MBE), and the Mean Absolute Error (MAE) were calculated to assess the covariability and the deviation among the simulated results from the FEM model and the observed results from the IRT experiments (Table 3
The MBE measures the overall bias of the model, and MAE measures the absolute extent of the errors without considering their directions [45
]. Table 3
shows that in most cases, the MBE produced positive values for the surface temperatures and thermal gradient, indicating that the model has a trend to overestimate the experimental results. An exception is seen in April, where MBE showed that the model underestimates the surface temperatures. However, thermal gradients were constantly overestimated. These trends can be confirmed by looking at the curves in Figure 5
and Figure 6
. The MAE is greater for the surface temperatures simulations, with averages differences ranging from 2.17 °C to 4.38 °C. However, the absolute error is under 0.6 °C in all thermal gradient tests, which indicates that the contrast between healthy and damaged areas is convergent, despite the surface temperature differences. Therefore, these results are aligned with the findings of previous studies [23
], where the numerical simulation presented the capability of reproducing the thermal gradients measured in the thermographic inspections using passive heating. Rumbayan and Washer [32
] reported the deviation measurements for the thermal contrast between their model and the experimental results. The correlation indices (R) were between 0.70 and 0.92, and the contrast differences (MBE) and absolute error (MAE) were below 1 °C. Hiasa et al. [24
] also calculated the correlation coefficient (R) between FEM simulation results and IRT measurements of the concrete surface temperature using three different thermal cameras, obtaining results above 0.97 in all cases. In this sense, we confirm the authors’ conclusion that the FEM can represent a tool to predict the concrete surface temperatures and support practical IRT inspections.
The computational modeling proposed in this study showed the possibility of identifying subsurface damages in reinforced concrete bridge slabs at different times of the year and under different environmental conditions, including temperature, wind speed, and solar radiation. Although the simulated thermal gradient results present an average difference of 0.39 °C compared to the experimental inspection, the correlation between the model results and the experimental study was equal or above 0.96 in all the thermographic tests. Consequently, the reasonable accuracy of the simulation supports the extrapolation of the model analyses to a long period.
4.2. Discussion on Appropriate Periods for IRT Inspection of Concrete Bridge Slabs Based on Long-Term Fem Analysis
Numerical simulation of 1 year of the inspection was performed using the FEM model of the concrete slab with fabricated delaminations and the weather conditions data available in the Brazilian meteorological database [41
] near the study site. All the information about the environmental conditions used in the long-term simulation is available anytime in the referred database, for open consultation or download. In addition, all the modeling data are available for interested readers through email requests.
The results of the long-term simulation are presented in Figure 7
. The period of simulations started on 1 November 2018, the same month that the experimental program started, and ended on 31 October 2019. The analysis was performed 24 h per day, with hourly time steps. Each daily simulation took an average time of 152 s, which reduced an entire year’s analysis to approximately 16 h. The simulations were performed using a desktop computer with 16 GB RAM, 2.3 GHz Intel Core i7 CPU, and an NVIDIA GeForce MX250 GPU. The daily varying input parameters of the model were presented in Table 1
. Conventionally, the year was divided into the local seasons: Autumn (March, April, and May), winter (June, July, and August), spring (September, October, and November), and summer (December, January, and February).
The incidence of the rain was plotted in Figure 7
, and the numerical model correctly simulated the low thermal gradients values in these events, mainly between the ±0.5 °C thresholds. The solar radiation parameter allows this prediction, as rainy days usually have low solar radiation levels, generating a model outcome that correctly shows these days as not favorable for inspections. ASTM D 4788-03 [46
], which is the American standard that regulates the thermographic inspections in bridge decks, recommends that the bridge deck should remain dry for at least 24 h hours before an IRT inspection. In addition, the regulation prescribes a minimum thermal gradient of 0.5 °C between healthy areas and areas with suspected delamination to identify subsurface damage.
The direct observation from Figure 7
allows us to percept the difference in the thermal gradient behavior along the seasons, where months with warmer weather have greater thermal gradient values and a larger number of simulations with reliable thermal gradients (out of the ASTM D4788-03 boundaries). The greater thermal gradient between damaged and undamaged areas facilitates subsurface damage identification [9
] because the contrast in the thermogram colors becomes more noticeable with the increase of the temperature difference. Table 4
presents the number and percentage of IRT simulations that exceed the ASTM D4788-03 recommendation of a minimum thermal gradient, according to the different seasons considered in the simulation. The detection percentage was calculated by dividing the number of hourly detections by the number of hourly simulations. The damage was considered as detected by the IRT technique if, after the hourly simulation, the temperature difference between the concrete surface on top of the delaminated area and the concrete surface without delamination was equal or greater than 0.5 °C.
In a monthly analysis, December presented a larger percentage of contrast results exceeding the 0.5 °C thresholds. This month represents the beginning of the summer in Brazil and, together with January and February, compose the summer season in the southern hemisphere. This season had a higher quantity of simulations of thermal gradient values exceeding the ASTM D 4788-03 [46
] recommendation. The warmer weather in the summer facilitates the heating propagation by solar radiation, the main heating source for passive IRT inspection, which increases the heating of the concrete sample and, therefore, the identification of the damages [24
]. Winter and autumn months also present a high incidence of solar radiation; however, the air temperatures usually are lower than summer and spring, and the presence of humidity and fog are more frequent, which makes heat propagation difficult. In general, it can be observed that the summer and spring represent favorable periods to perform infrared thermographic inspections under passive heating in this case of study, with 17.42% more reliable detections than the autumn and winter period. These findings challenge the observation of Hiasa et al. [24
], which reported no significant effect of seasonal environment on the simulated thermal gradient in Orlando, Florida. One explanation could be the extent of the simulation, where they simulated one sunny day in each season, while this study performed an extended and continuous simulation of the entire seasons. Moreover, the study location probably has a different weather condition, which naturally produces different results. On the other hand, our data support the Al Gharawi et al. [47
] work by showing that the thermograms captured in warmer months tend to have higher contrast results compared to colder months.
The heatmap in Figure 8
displays the hourly contrast values resulted from the FEM long-term analysis. The black color indicates the higher negative thermal gradients values (where the delaminated concrete area had lower surface temperature than the surrounding concrete), and yellow means the higher positive thermal gradients values (where the delaminated area presented higher surface temperature than the healthy concrete area). The inappropriate periods for inspection are illustrated in the purple color, when the thermal gradients were between −0.5 °C and 0.5 °C, i.e., insufficient, according to the ASTM D 4788-03 recommendation. The values of the x-axis start in November following the experimental program. From the top to the bottom of the y-axis, the heatmap shows the daily hours of the simulated inspection.
The thermal gradient values had a pattern through the days, evolving from negative values at midnight, showing higher positive intensity during the day, and returning to negative values during the night. Although all the months present favorable periods for inspections, the heatmap shows that the valid thermal gradients were more frequent in the warmer months (summer and spring). Several days in October, November, December, January, and February presented temperature differences between the delaminated and healthy areas close to 3 °C. The colder seasons presented modest temperature differences through the months, probably because of the winter and autumn weather conditions, such as small days and lower air temperatures [37
]. Therefore, the heatmap in Figure 8
reasserts the conclusion that the warmer months appear to provide better conditions for inspections than colder months.
The results of this research imply that by having the geographic information of the location (coordinates and global zone), a reliable meteorological database, and the characteristics of the damaged structure, the inspector may simulate the daily thermal oscillation at the inspected structure. Thus, by evaluating the results of the finite element simulation, the inspector would be able to assess the most favorable time window to carry out the thermographic inspection of subsurface defects in reinforced concrete bridge slabs, avoiding excessive visits to the bridge field and/or experimental tests, as was previously introduced by previous studies [23
]. Furthermore, long-lasting thermographic inspections in real structures would provide information that can be processed using lock-in thermography based on passive thermography, and thermal modeling can help in understanding the data from the inspection, as was the case study of the Old Kingdom constructions of Egypt [48
]. An open research opportunity would also be the study of the relation between the concrete temperature strains and the concrete strength proprieties using FEM. Once the temperature variation can cause dangerous temperature strains in concrete elements, the strength of the concrete structure could be improved by varying the characteristics of concrete materials. As the analysis can consider a number of environmental and concrete material scenarios, the numerical simulation can reduce the intense labor work of visiting different structures or construct several concrete samples. Furthermore, the analysis of the steel reinforcement effect in the heat flow through reinforced concrete structures inspected by IRT can also be performed.
To the best knowledge of the authors, the studies present in the literature did not simulate a passive IRT numerical analysis of delamination detection in a concrete structure during an entire year. The complete simulation of a long period allows us to assess the effects of the seasonal variations in the IRT inspections without excessive tests, showing that spring and summer seasons are favorable periods to use the IRT technique. The use of numerical simulation to support the temperature-based inspections highlights an application for the finite element method in infrastructure health monitoring. The proposed simulation approach also meets the premises of sustainability since it intends to help the maintenance of the structures to allow their use by the next generations. Although the presented model was developed based on a static damage area and the results depend on the characteristics of the sample, and the study location, the general concept of the model can be considered for further analysis of other concrete structures and in other locations with different environmental conditions. Moreover, the model can be improved by adding a greater number of experimental tests and more precise physical parameters. In addition, an agenda of the practical tests must be maintained since the thermal proprieties of the structural materials may change along the lifetime of structures and the FEM model requires calibration [49