A Feasibility Analysis of the Infrared Thermography Technique in Surface Crack Detection for High-Speed Rail Slab Track

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Introduction
Slab tracks have been widely used in a number of newly built high-speed rail (HSR) lines. However, due to the joint efect of train load and environmental factors, the structural defects of track structure occur with the increase in operation time [1,2]. Among the defects, the surface crack is a critical one which can cause structural deterioration and reduce the service safety of the track system [3]. To solve the problem, the maintenance-of-way department has formulated a crack management code by defning the width and length threshold of the surface crack and carrying out the manual inspection during the window time for track maintenance [4]. However, the manual inspection for track defects is a time-consuming and labor-intensive task, which is not suitable to be adopted on the busy HSR lines.
For the busy HSR lines, track inspection always faces great challenges such as the window time is narrow, the ambient light during the window time is dim, and the mileage of lines that need inspection is long [5,6]. It is therefore urgent to develop an efcient crack detection method for the surface crack on HSR slab track. Several previous studies focused on the development of online monitoring techniques for slab tracks based on advanced sensing and communication technologies [7,8] as well as the datadriven defect detection methods [9]. However, the problem of surface crack detection has rarely been reported. Under this background, the noncontact nondestructive testing (NDT) technology has been experimentally applied to the inspection of slab tracks, such as machine vision [10][11][12], ground penetrating radar (GPR) [13], and infrared thermography (IRT) [14,15]. Among these methods, the machine vision measurement can be afected by the dim light during window time at night, and the GPR detection can be interfered by the internal reinforcing rods of the track slab. Furthermore, the crack width on the slab surface can be as small as 0.1 mm, which undoubtedly poses higher requirements for the detection accuracy. In terms of minor crack detection, the IRT-based detection method with good adaptability and high precision has been widely used in bridge decks [16,17], building sidewalls [18,19], etc., but its feasibility in slab track detection has not yet been verifed. Tis research aims to analyze the feasibility of the potential application of IRT in crack detection for the slab track, which has signifcant practical value for the maintenance of the HSR line.
According to the thermal excitation mode, IRT can be carried out using two diferent approaches such as active detection and passive detection, [20]. For civil structures such as slab track, the existing research mainly adopts the passive excitation method for detection, in which the sunlight is used as the thermal excitation source. Te detection of potential crack is realized based on the analysis of temperature feld distribution on the surface of the structure. Te previous research related to the IRT-based crack detection mainly focuses on the following three aspects: the accuracy of detection, the environmental factors, and the detection performance in specifc engineering applications. For the detection accuracy, as limited by the structure size and the layout of the sensing unit, IRT is applicable to the damage within 10 mm of the near-surface depth [21], and the detection width can reach 1/16 inch [22], but the crack depth cannot be reported precisely [23]. In terms of environmental factors, considering the uncertainties caused by the microenvironment on the structural surface, the previous studies mainly conduct qualitative analysis on the efect of solar radiation, ambient temperature, and wind speed [21]. According to the previous research on the application of IRT, this technique has been adopted in the detection and development analysis for civil structural defects such as bridge cracks and building interlayer damage [24,25], but there are still few detailed research studies on the rail track. Due to the large size of the slab track, it can hardly be heated to meet the requirement of IRT-based crack detection. Furthermore, considering that the window time for inspection is at night, the efect of environmental factors on the performance of the thermal imagers should be studied prior to practical application on actual HSR lines.
Te rest of this study is organized as follows: Section 2 analyzes the characteristic of the temperature feld of the track slab and the principle of IRT-based concrete slab crack detection; in Section 3, the fnite element (FE) model of track slab with surface crack is established and verifed by the in situ measurement data of slab temperature feld; in Section 4, the efect of the factors including detection time, atmospheric temperature, and thermal sensitivity parameters of the thermal imager on the performance of crack detection are discussed, and the relative suggestions on IRTbased slab crack detection are given; fnally, in Section 5, some concluding remarks are presented.

Temperature Field in Track Slab.
Due to the actual operation condition of HSR, the surface temperature feld of the track slab is determined by the surrounding environment. An energy balance mode is then formed between the track slab and the surrounding air [26]. It includes the following three typical forms of heat transfer in thermodynamics: (1) heat conduction, i.e., heat transfer and heat storage between solid structures such as concrete slab, CA mortar, and concrete basement in the slab track structure; (2) thermal radiation, i.e., direct solar radiation, difuse solar radiation, and ground-refected radiation absorbed by the surface of slab track structure; (3) thermal convection, which refers to the heat transfer between the solid materials (mostly the concrete) near the surface of the track structure and air. Te interaction of the three abovementioned heat transfer modes is shown in Figure 1. When calculating the internal temperature feld of the slab track structure, a clear understanding of thermophysical properties of diferent materials in the slab track structure, the airfow state in the fuid region, and the solar radiation on each side of the slab track is needed. So, the formation of the track slab temperature feld mainly involves the following three aspects: solar radiation (including direct and difuse solar radiation), convective heat transfer between track slab surface and air, and the heat conduction in the slab track.

Principle of Crack Detection by IRT.
When the surface of the concrete slab receives direct sunlight, the slab temperature increases gradually through the heat transfer between the concrete materials. If there is a crack on the slab surface, the crack part is flled with air, so that the air in the crack plays the role of heat insulation and hinders the heat transfer in the concrete near the crack area. Note that the thermal conductivity of air is only 0.0241 w/m•°C at 25°C, while the thermal conductivity of concrete is 1.67 w/m•°C. Terefore, during the daytime, when the heat is transferred inside the track slab, it will accumulate in the crack area, and the temperature in the crack area is higher than that in the surrounding noncrack area. During the night time, the heat absorbed by the track slab in the daytime continues to dissipate into the atmosphere. Due to the low thermal conductivity of the air in the crack area, the heat consumption rate at the crack is slow, and the temperature in the crack area is higher than that in the noncrack area. Consequently, the infrared radiation from the slab surface can be read by an infrared thermometer which converts the infrared radiation into temperature so that the temperature diference at the slab surface can be obtained and the surface crack can be detected. Te relationship between the temperature at the slab surface and the radiation emitted from the slab surface can be determined by the Stefan Boltzmann law, as expressed by [27] W � εσT 4 object , where W represents the amount of radiation emitted per unit time of the slab surface (W/m 2 ), ε represents the infrared emissivity of the slab surface, σ is Stefan's constant which equals to 5.67 × 10 − 8 W/(m 2 •K 4 ), and T object represents the absolute temperature of the slab surface (K). Te temperature diference used to detect the surface crack can be expressed by the following equation [27]: where T(crack) is the temperature at the crack on the slab surface and T(sound) represents the temperature at noncrack (sound) area on the surface. Figure 2 illustrates the principle of IRT detection of the surface cracks on concrete slabs [26]. On this basis, the temperature diference between the crack and noncrack area on the slab surface can be described as the color diference between these areas on the thermal images. So, the problem of crack detection becomes the development of an infrared image processing algorithm to extract the crack area from the thermal image. With such an algorithm, the length and width of the surface crack can be identifed.

Key Factors.
As mentioned before, the key factors infuencing the performance of IRT crack detection systems mainly include the detection time, ambient temperature, and thermal sensitivity of the device.
(1) Detection time: Since the track slab undergoes an endothermic process during the daytime and an exothermic process at night, diferent detection times will lead to obvious diferences in the diference of temperatures between crack areas and noncrack areas. Terefore, it is necessary to consider the efect of detection time on the performance of IRT. (2) Ambient temperature: Asa poor conductor of heat, the energy absorbed and refected by fne cracks on the concrete surface varies greatly under diferent ambient temperatures [28]. Furthermore, the thermal sensitivity parameters of the equipment are also signifcantly afected by the ambient temperature, and the resolution of the thermal imager (i.e., the minimum temperature diference that the thermal imager can detect) under the low air temperature will be greater than that under the high air temperature. (3) Termal sensitivity of the imager: In most cases, the thermal imager detects the infrared radiation energy distribution on the slab surface through the built-in IR radiation detector and lens. Te thermal sensitivity is usually referred to as the noise equivalent temperature diference (NETD) value refecting the minimum resolvable temperature diference, which is one of the key parameters of the thermal imager to characterize the efectiveness in identifying the surface crack.

Development and Verification of the Numerical Model
During HSR operation, the track slab exchanges energy with the external environment all the time [29,30], so the temperature distribution on the track slab is highly correlated with the environmental factors. Te diference in thermal parameters between the air in the crack area and the concrete leads to the diference in the energy exchange between crack areas and noncrack areas with the environment. Consequently, the temperature diference between the two is generated. Tus, by establishing an FE model of the temperature feld of concrete slab with surface cracks considering the energy exchange with the external environment, the distribution of temperature at the crack and noncrack surface areas can be calculated by simulating the change of the external environment.

FE Model.
In this study, the longitudinally coupled slab track with surface cracks is chosen in the FE modeling. Te model is established by using computational fuid dynamics (CFD), in which the three-dimensional (3D) solid element is adopted to simulate the track concrete slab, CA mortar (cushion) layer, and the concrete basement, respectively. Te crack is simulated as a small rectangular groove on the upper surface of the track slab, as shown in Figure 3.
Considering that the width of the surface crack is much smaller than the length of the track slab (6.45 m), the distortion of slab temperature feld would be limited to the Mathematical Problems in Engineering crack areas. Terefore, it is feasible to include only part of the track structure in numerical simulation. Table 1 shows the key dimensional parameters of the 3D track model in the numerical simulation.
According to the previous research [29,30] and some trial calculations, the track section considered in numerical simulation is determined as follows: the edge of track structure is 5 Lrail from the inlet of air fuid, 15 Lrail from the outlet of air fuid (Lrail is the width of concrete base), the height of the whole fuid region is 6 Hrail (Hrail is the sum of the thickness of track slab, CA mortar layer and concrete base), and the width of the whole fuid region equals to the length of track structure, i.e., 1.272 m. Figure 4 shows the air fuid region of the track structure considered in the calculation.
Te calculation results of the slab temperature feld and the temperature diference between crack areas and noncrack areas are determined by the input thermal parameters of slab track materials. Tese materials mainly include the concrete, CA mortar layer, and air in the track structure. Table 2 lists the thermal parameters of these materials.

Environmental Factors.
As proved by previous research, the change of slab surface temperature is determined by the change in airfow, solar radiation, and ambient temperature [28]. So, the key to the success of the numerical simulation is to model these environmental factors. Tis section presents the modeling of airfow, solar radiation, and ambient temperature.
(1) Airfow: Te air fuid region around the track slab is characterized by constant viscosity, incompressibility, and isotropy. It should be noted that, due to the airfow, there will be convective heat transfer between the air fuid and the slab surface. For the problem of airfow and the corresponding convective heat transfer phenomenon, the dynamic renormalization group (RNG) method [31] can be used to simulate the airfow condition on the surface of concrete slab.   (2) Solar radiation: Te track slab absorbs the solar radiation energy through radiation heat transfer to form the temperature feld on the slab surface. It should be noted that the length of the computational fuid region in the FE model exceeds 20 m, and the scattering of the solar radiation caused by the air medium and particles on the slab surface should be taken into account. In this regard, the P-1 radiation model is used to simulate the radiation transfer on the slab surface. In this model, the parameters related to solar radiation are obtained through the monitoring device installed on an HSR line (as shown in Figure 5); for the ground-refected radiation, the refection coefcient is defned by where G R is ground-refected radiation, G ND is direct solar radiation, G Dθ is difuse solar radiation, ρ g is the refection coefcient of the ground to solar radiation, and α surf is the inclination angle of slab surface relative to the horizontal plane. Terefore, for the track slab, the solar radiation energy absorbed by its surface can be expressed as where G t is the solar radiation absorption coefcient of the slab surface. (3) Ambient temperature: the change in ambient temperature with time can be expressed by the following equation [32]: where T air is the average of maximum and minimum value of daily temperature, T air is the average of the diference between the maximum and minimum daily temperature, and τ is the time (in h) and it is defned that τ � 0 at 6 a.m, ω � 2π/24, and τ 0 � 3.
Another important step is to determine the initial temperature feld of the slab track. It is also based on feld measurement, and the temperature distribution of track slab is obtained by installing resistance temperature sensors at diferent depths inside the slab (the distance between each temperature sensor and the upper surface of the track slab is 0 mm, 50 mm, 100 mm, 150 mm, 200 mm, and 230 mm [4]). Subsequently, the measurement data can be used to ft a temperature distribution curve which will then be input into the FE model.

Boundary Condition.
Te boundary condition considered in the model mainly includes the following: structural surface boundary condition, interlayer contact surface boundary condition, and fuid region boundary condition.
(1) Structural surface boundary condition: Since the solar radiation on the surface of the slab and the surrounding ambient temperature are known, the structural surface boundary condition can be regarded as the 3 rd kind of boundary condition, as described by Newton's law of cooling for concrete slab surfaces exposed to solar radiation as whilst for the surfaces not exposed to solar radiation, it can be expressed as where λ crack is the thermal conductivity of the track slab, T railway is the surface temperature feld of the concrete slab, n ⇀ denotes the unit vector in the normal direction of the slab surface, α crack is the absorption coefcient of solar radiation on slab surface, Q solar is the solar radiation received by slab surface, σ is the Boltzman constant, ε crack is the long-wave emissivity of the surface material of slab track, T crack and T atmos are surface temperature of slab and the ambient temperature, respectively, and T kcra and T katmos are the absolute temperatures at the slab surface and the absolute air temperature, i.e., T kcra � T crack + 273. 15 and T katmos � T atmos + 273.15. (2) Interlayer contact surface boundary condition: In this study, we assume that the slab track has no interlayer damage so that it can be regarded as the 4 th type of boundary condition, as expressed by the following equation: where T solid1 and T solid2 are surface temperature values of track slab and concrete basement at the contact surface, λ solid1 and λ solid2 are the thermal conductivity of two diferent parts in contact with each other in the slab track structure, and n ⇀ denotes the unit vector in the normal direction of slab surface. It is seen that when the track slab, CA mortar layer, and the concrete basement are in good contact, the temperature on both sides of the contact surface is equal, and the heat can be smoothly transferred to the adjacent layers through the contact surface. (3) Fluid region boundary condition: Tis study regards the fuid region as the velocity-inlet type. Considering the airfow in the fuid region [31], the fuid outlet boundary is defned as the pressure-outlet type, and the pressure value at the outlet is set as 1 atm. Te left and right sides of the fuid region and the concrete slab in contact with the fuid region sides are set as the translational periodic boundary.
To eliminate the efect of track structure on the airfow at the top of the computational fuid region, the height of the fuid region is set to six times the height of the slab track structure, including the track slab and concrete basement, and the length of the fuid region is set to more than 10 times the width of the track structure. Besides, the top of the computational fuid region is set as a symmetrical boundary, and the bottom surface of the fuid region is regarded as the ground and set as the adiabatic wall boundary.

Parameter Setting in Calculation.
In numerical calculation, the P-1 model is chosen as the radiation model and the RNG k-ε model is chosen as the turbulence model to simulate airfow. In the radiation model, the ground radiation refection coefcient is set to 0.2, and in the RNG k-ε turbulence model, the standard wall function is used as the near-wall treatment method of the turbulence model. In the transient analysis, the starting time is 0:00 am, and the size of each time step is set to 3600s. To reduce the residual errors, the number of time steps is set to 48. Te large errors in the frst few time steps can be compensated by calculating the change in the temperature feld of the track within 48 hours.

Model Verifcation.
To verify the FE model, the measurement data obtained by the proposed system, including the ambient temperature, solar radiation, and wind speed, are input into the numerical model. Ten, the temperature at diferent depths inside the slab is calculated. Te simulation results can be compared with the monitoring data of temperature, which are measured by an online temperature monitoring system [4] (see Figure 6). Te measure points are located at the distances of 50, 100, 150, and 200 mm from the slab surface. Figure 7 shows the comparison of measured and simulated temperature values of the track slab at diferent depths within 24 hours. It can be seen that the variation of simulated temperature data at diferent depths with time is consistent with the measured temperature data. Te maximum diference between the two occurs between 11: 00 am and 2:00 pm at the slab surface (i.e., the depth is 0 mm). Te simulated temperature value at the slab surface is larger than the measured value, and the maximum diference appears at noon, which is 1.66°C. Besides, it is seen that the error rate gradually decreases with the depth. Te reason is that with the increase in the slab depth, the concrete is less afected by the change in external temperature and solar radiation and the heat transfer inside the concrete slab decreases.
It should be noted that the key to the detection of surface cracks lies in the temperature diference between the crack area and the noncrack area on the slab. Terefore, to further illustrate the efectiveness of the model, this study selects another two groups of measured data (in autumn and winter) to calculate the slab surface temperature. Figure 8 shows the calculation results.
As seen in Figure 8, the maximum diference between the simulation and measurement results is below 2°C and usually occurs in the period from 11:00 am to 2:00 pm. In other periods, the maximum error does not exceed 0.15°C. Considering the window time for track inspection and maintenance is 0:00-3:00 am and the simulated temperature in this period matches the measured temperature very well, we could conclude that the fnite element model can be used to analyze the feasibility of IRT detection of slab surface cracks (note that, for modern HSR lines, the track inspection is conducted during window time).

Analysis of Factors Influencing the Performance of Slab Crack Detection
It can be seen from Section 2.3 that the main factors afecting the feasibility of IRT in detecting slab surface cracks include detection time, ambient temperature, and thermal sensitivity. Terefore, this section uses the proposed numerical model to assess the infuence of these factors on the efectiveness of the IRT detection. According to the current maintenance code for slab track and the in situ investigation on the slab surface cracks of the operating HSR [31], in this study, the width and depth of slab surface crack are set to 0.2 mm and 20 mm, respectively ( Figure 9). Besides, to facilitate the comparative analysis, we take the temperature at the nodes along longitudinal centerline of track slab surface (shown in "temperature extraction line" in Figure 9).

Efect of Detection Time.
To analyze the efect of detection time on the detection performances, the measured ambient temperature, solar radiation, and wind speed are input into the FE model to calculate the surface temperature feld on track slab over time. Te calculation result of temperature values during window time (0:00-3:00 a.m.) along the aforementioned slab centerline is presented in Figure 10. It appears that the temperature values at the crack area are higher than that at the noncrack area. Tis is mainly because the thermal conductivity of the internal air at the crack is low, so the heat consumption at the crack is relatively slow. Consequently, a certain amount of heat is accumulated at the crack area, which leads to the higher temperature at crack area. Terefore, the temperature value at the crack is the maximum value in the range from the crack center to the concrete area near the crack edge, and the temperature begins to drop and reach a minimum value in the concrete area near the crack edge.

Mathematical Problems in Engineering
Trough a detailed analysis of the four curves in Figure 10, it is seen that when the cracks appear on the slab surface, the temperature on the slab surface near the crack will change considerably and the temperature gradient will be formed. Besides, during the window time, the temperature diference between the slab surface with and without crack gradually increases with time. Terefore, it is suggested that the crack detection should be conducted after the window time, i.e., around 3:00 am.

Efect of Ambient Temperature.
To investigate the infuence of ambient temperature, this paper uses the temperature data samples measured on an HSR line in East China. Te data being collected in summer, autumn, and winter are chosen for the analysis (see Figure 11). Table 3 and Figure 12 show the temperature values at the crack (maximum point), the adjacent area of crack (minimum point), and noncrack area on the slab surface during the window time in three seasons, as well as the temperature diference between diferent areas. It is seen that from summer to winter, the temperature at the crack area and its adjacent area on the slab surface are continuously reduced due to the decrease in external ambient temperature, whilst the temperature diference between them (① and ② in Table 3) on the slab surface also decreases with the decrease in atmospheric temperature. In winter, the temperature diference between ① and ② at window time is only from 0.043°C to 0.079°C. In such a situation (temperature difference is less than 0.1°C), the thermal imaging equipment is unable to identify the surface crack without external heat source excitation.
It should be noted that for the HSR slab track, the slabs are much easier to crack in summer than in winter, due to the internal stress caused by high temperature. Terefore, it is suggested that the crack detection for slab track should be conducted in summer. If it needs to be implemented in winter, the external thermal excitation source should be introduced.

Efect of Termal Sensitivity.
Termal sensitivity is normally referred to as NETD, which represents the minimum temperature diference that can be identifed by an infrared thermal imager under certain environmental conditions. Considering that the detection of the surface crack depends on the identifcation of the temperature increase at crack areas, the efect of thermal sensitivity on the detection accuracy should be analyzed. In view of this, this research assesses the efects of thermal sensitivity by calculating the temperature diference under diferent surface crack widths.

Mathematical Problems in Engineering 9
Summer (20 August Figure 11: Ambient temperature measured on an HSR line in East China.  According to the maintenance rules for slab track of Chinese HSR [28], the surface cracks (depth: 20 mm) of track slab with three widths of 0.1 mm, 0.2 mm, and 0.3 mm are input in the model. Te temperature diference between crack and noncrack areas under diferent crack widths is analyzed.
Using the measured data at the window time (0:00-3:00 a.m.) in summer, the simulated temperature values along the centerline of the track slab under three diferent crack widths are obtained. Ten, the temperature diferences between the crack area (maximum point), the adjacent area of crack (minimum point), and noncrack area on slab surface are compared, as presented in Table 4 and Figure 13.
It can be seen from Table 4 and Figure 13 that when the crack width is smaller, the temperature diference between crack area and its adjacent area is smaller. Terefore, to realize IRT detection for track slab cracks, the NETD of the thermal imager should be high enough to identify the temperature diference when the crack width is no smaller than 0.1 mm, as required by maintenance rules. Terefore, during the window time for track maintenance in summer (the ambient temperature is higher than 25°C), the minimum limit of thermal sensitivity of the thermal imager should be lower than 108mk@25°C; that is, when the atmospheric temperature is 25°C, the minimum temperature diference that can be recognized by the thermal imager is less than 0.108°C.

Concluding Remarks
How to realize the rapid and accurate detection of the cracks becomes a key issue in the maintenance of today's HSR line. Tis study analyzes the key factors afecting the performance of IRT detection for slab track cracks. Te mechanism of the temperature feld distribution under diferent test conditions is revealed using the FE method. Te efect of the key factors, including the detection time, the ambient temperature in detection, and thermal sensitivity of the thermal imager are assessed. Te main fndings are summarized as follows: (i) Te proposed FE model can efectively calculate the temperature feld of slab track, and the maximum error of results at window time is only 0.15°C. (ii) During the window time at night, the temperature diference between crack and noncrack areas  gradually increases with time. In this regard, it is suggested to conduct crack detection after the window time, i.e., 2:00-3:00 a.m. (iii) Under the condition of no auxiliary heat source, the crack detection for slab track should better be conducted in summer with a high incidence of surface crack than in winter. (iv) To realize efective crack detection in summer as the atmospheric temperature being higher than 25°C, the minimum limit of NETD of the thermal imager in the crack detection should be smaller than 108mk@25°C.
Tese fndings provide evidence for the use of the IRT method in the track slab crack detection. However, it is also worth noting that due to the complex service condition of the actual HSR line, the efects of other environmental factors such as wind, rain, and lightning, as well as the skill of operators can also pose an existential impact on the detection accuracy. Terefore, it is highly desirable to conduct further research to reveal their efects on the detection accuracy of slab cracks.

Data Availability
All data, models, or code that support the fndings of this study are available from the corresponding author upon reasonable request.