Temperature Correction for FWD Deflection in Cement Pavement Void Detection

The use of the falling weight deﬂectometer (FWD) for detecting pavement voids is based on the principle that, under the same impact load, the deﬂection of pavements with voids increases signiﬁcantly. Under the eﬀect of temperature, the cement pavement becomes warped, which aﬀects the deﬂection detection accuracy. In order to improve the accuracy of FWD detection of cement pavement voids, a three-dimensional numerical model of cement pavement on a multilayered elastic foundation under the coupled action of temperature and load is established in this paper. In addition, under diﬀerent pavement void, climatic, and load conditions, the inﬂuence of temperature diﬀerence between top and bottom of the plate on the deﬂection of the center point of plate angle load is studied. Considering the temperature diﬀerence between top and bottom, the temperature correction coeﬃcient is established and experimentally veriﬁed the accuracy of the temperature correction coeﬃcient. The results showed that, within the ranges of positive and negative temperature diﬀerences, the ﬁtting degree of the temperature correction coeﬃcient for the cement pavement exceeded 0.99, which was consistent with the variation trend of the temperature correction coeﬃcient obtained through ﬁeld tests. The error was lower than 7%, which veriﬁed the applicability of the temperature correction coeﬃcient for the dynamic deﬂection of cement pavements based on FWD. The accuracy of the FWD method in detecting cement pavement voids was improved, and this study demonstrated theoretical reference value and practical engineering signiﬁcance.


Introduction
Cement concrete pavement structures have advantages of extended service life, strong load diffusion capacity, easy constructability, accessibility of constituent materials, and low cost, and they are widely used for all types of highways [1]. However, during the service life of cement pavement, the pavement is prone to experience cracks, disconnections, voids, and other problems, owing to the combined action of the driving load and external environment. ese problems have a significant impact on driving comfort and human safety [2]; the most significant impact on traffic is attributed to the voids in the cement concrete pavement [3,4]. After concrete pavement voids are formed, the accurate and rapid detection of void damage in the concrete pavement is the focus of several studies.
Scholars have investigated the detection of voids in cement pavements, among which the most widely used technique is the void determination method based on the deflection. e void determination method is mainly divided into two types: falling weight deflectometer detection and Benkelman beam test [5,6]. e FWD detection is used more widely because of its established technique and easy implementation. FWD detection is based on the principle that, under the same impact load, the deflection of the void area increases significantly [7][8][9][10][11][12]. Because of the influence of climatic factors, such as solar radiation and ambient temperature, cement pavement panels experience temperature warping at different degrees [13][14][15], which affect the accuracy of actual pavement detection results. Wen et al. systematically analyzed the impact of pavement voids under the coupled action of environment and load, described the formation process of voids, and highlighted the significant causes of cement concrete bottom voids [16]. Zeng et al. used ANSYS and the FWD method to measure the deflection data of the panel center and panel angle of cement pavement and developed a method of estimating the scope of the panel angle void of cement pavements [17]. Chen et al. established a three-dimensional model of cement concrete pavement voids, verified the accuracy of the model by comparing its results with theoretical solutions and measured values, and proposed an analytical method for identifying cement concrete pavement voids [18]. Toth et al. evaluated the fouryear meteorological data and deflection measurements of a section in Hungary, analyzed the variation of deflection parameters at different periods, and formulated correction factors based on the assessment results [19]. rough field observations, theoretical analysis, and relevant calculations, Jing et al. developed a method to determine the pavement temperature gradient using local meteorological data of several years [20]. Duan et al. performed simulation calculations on cement concrete pavement, analyzed the variation trend of the temperature stress of the plate angle under the conditions of complete contact with the pavement and plate angle void, and determined the main factors that influenced the temperature stress of the plate angle [21]. Based on a systematic analysis of the warping deformation of the sidewalk panel under a positive temperature gradient, Zhao et al. determined the modifiable temperature gradient of the internal deflection of a sidewalk panel. ey established the correction method and the corresponding regression expression of the FWD test panel internal deflection [22]. Sheng et al. proposed improvement measures for the deflection test on old cement concrete pavements, evaluated the deflection of the solid engineering plate angle, plate center, and joint edge, and determined the reasonable temperature of the deflection test [23]. Dou et al. adopted the stress intensity factor as the evaluation criterion to perform three-dimensional finite element simulation of early pavement fracture expansion based on the theory of linear-elastic fracture mechanics. ey analyzed the effects of fracture depth, overload, and temperature on fracture expansion [24]. Currently, studies on cement pavement temperature fields and FWD on pavement void detection have been conducted, but research on FWD pavement void detection under the coupled action of temperature and load have not been conducted in detail. erefore, through the establishment of a threedimensional numerical model for cement pavements under temperature and load coupling and the pavement plate deflection under the temperature and load coupling under different climatic and void conditions, the temperature difference between the top and bottom was analyzed. e correlation of deflection temperature correction coefficient was established, and the temperature correction coefficient was developed by considering the temperature difference between the top and bottom. Furthermore, the accuracy of the temperature correction coefficient was verified experimentally. e research results are useful for improving the accuracy of the FWD method for detecting cement pavement voids in different climates.  Table 1 lists the size setting of the void condition, and Figure 1 shows the plate angle and plate edge of the void model.

Material Parameters.
e model size and material parameter setting of each structure layer were determined ( Table 2) to simulate the actual cement concrete pavement structure better.

Temperature and Load Applications.
e temperature stress was applied to input the corresponding value directly into the plate top and bottom of the cement concrete pavement during the initial step of the load setting. Based on the data for the measured temperature and temperature difference between the top and bottom of the plate in each season listed in Table 3, 25°C and −25°C were selected as the upper and lower limits of the temperature difference between the top and bottom, and the temperature gradient was set as 5°C.
e temperatures of the cement concrete pavement slab for a monitoring period of one year in four seasons were analyzed. ere was a significant linear relationship between the top temperature of the plate and the bottom temperature difference of the plate [25,26]. e correlation equations between the top temperature of the plate and the bottom temperature difference of the plate for the cement concrete pavement in each season are listed in Table 4.      e load was simplified to that on a square area with a side length of 26.6 cm at the top of the panel and 25 cm from the corner edge of the panel under static loads. e thirdgrade loads were 50, 70, and 90 kN.

Boundary Conditions.
In the initial analysis step, the panel boundary conditions were set as follows: where U 1 and U 2 are the translational displacements in the directions of Models 1 and 2, respectively, and U R 1 , U R 2 , and U R 3 are the rotation angles centered on axes 1, 2, and 3, respectively.
In this model, the soil base was not set. Instead, an elastic modulus of 50 MPa was directly set at the bottom of the subbase as the boundary condition.

Model Meshing.
Nonuniform grid technology is applied in this model, considering that this paper is mainly to study the variation law of deflection at the center point of plate angle load under the coupled action of temperature and load. erefore, the mesh division of cement concrete pavement slab is more intensive than that of the base layer. Considering the particularity of the loading area, the cement concrete pavement slab was split several times, and the three-dimensional finite element overall model of the cement concrete pavement and the partition effect of the pavement slab mesh were obtained as shown in Figure 2

Pavement Plate Angle Deflection under Coupled Effect of Temperature and Load under Different Climatic Conditions.
In Table 3, data for each season cement pavement, the measured top plate temperature, bottom plate temperature, and temperature difference indicated that the average temperature of the season's plate for the top and bottom temperature difference was significant. However, the difference between the average temperature of the plate bottom for each season was not significant. Hence, the coupled effects of the pavement void deflection in four seasons at the same temperature difference and load were analyzed. e deformation of the plate angle load center point in the finite element model of cement concrete pavement under the temperature stress and the coupled temperature-load effect was determined. Equation (2) was then introduced to calculate the corresponding deflection of the plate angle load center point at various temperature differences: In equation (2), D 1 is the deflection value of the center point of the plate corner load, considering the effect of the temperature stress field (μm). L 1 is the deformation of the center point of the plate corner load, considering the combined action of the temperature and load stress field (μm). L 2 is the deflection value of the center point of the plate corner load, considering only the temperature stress (μm).
Equation (2) was used to compute the load center point for each season and the values of the corresponding deflection at the temperature difference ( Figure 3). e following observations were made.
(1) e deflection under the coupled action of the temperature stress and the tertiary load at the negative and positive temperature differences at the center point of the plate angle load in each season was significant. (2) At the same temperature difference, there was no significant difference in deflection between the four seasons, and the deflection fluctuated slightly above and below the mean value in each season. e variation trend of deflection at the center point of the plate angle load under the coupled action of temperature and three-stage loading was analyzed (Figure 4). e following was found: (1) At the same temperature difference and under the same load, the effect of the void depth on the deflection could be ignored. e void depth increased with the void radius, and the deflection variation range between different void radii was broad. (2) At the same temperature difference, the deflection under each void condition decreased with increasing temperature difference when the temperature difference was negative but increased with increasing temperature difference when the temperature difference was positive.   Advances in Civil Engineering increased with the void width; and the deflections among the different void widths exhibited significant variations (2) At the same temperature difference, the deflection under each void condition decreased with increasing temperature difference when the temperature difference was negative but increased with increasing temperature difference when the temperature difference was positive (3) Under the same void condition, the deflection increased with the load at the same temperature difference e comparison between Figures 4 and 5 shows that, at the same temperature difference and under the same load, the deflection under the plate edge void condition is larger than that under the plate angle void condition.

Correlation Analysis between Pavement Temperature
Difference and Correction Coefficient. In this study, the modification coefficient of the influence degree of temperature difference on the deflection of the center point of the plate angle load was introduced and denoted as φ. e coefficient is calculated using where φ is the correction coefficient of the temperature difference to the deflection value of the center point of the plate angle load and D 2 is the deflection value of the center point of the plate corner load, ignoring the effect of the temperature stress field (μm). e deflection values for the center point of the plate angle loads of 50, 70, and 90 kN (without considering the temperature effect) obtained through numerical simulation are listed in Table 5. e correction coefficient distributions and the corresponding fitting curves for the deflections at the center point of the plate angle loads of 50, 70, and 90 kN were calculated and plotted ( Figure 6). e following results were obtained.
(1) Within the negative temperature range, the correction coefficient decreased with an increase in the  temperature difference; in the positive temperature range, however, the correction coefficient increased with increasing temperature difference, and finally tended to be stable (2) At the same temperature difference, the correction coefficient did not change significantly with an increase in the load e relative error between the correction coefficients that corresponded to different temperature differences and their mean values under the three-stage load was not more than 5%. erefore, the average correction coefficient under the three-stage load represented the temperature correction coefficient under different loads, the calculated average temperature correction coefficient was sorted out, and the fitting curves were plotted, as shown in Figure 7.
When the positive and negative temperature differences were obtained, the correlation between the temperature difference and the correction coefficient could be expressed as follows.
Negative temperature range:

(5)
Based on the plate angle deflection values of the cement concrete pavement plate that corresponds to the difference in temperature obtained during the temperature field variation tests, equations (4) and (5) were used to calculate the corresponding plate angle center deflections. e comparison is depicted in Figure 8. It was found that the actually detected deflection value fluctuates up and down the  calculated value, the entire variation trend of the plate with the calculated data was fitted, and the finite element model was validated using equations (4) and (5). e accuracy of the simulated results was consistent with the test results. e average temperature correction coefficients under different plate edge void conditions were analyzed (Figure 9). e fitting analytical equations are expressed as follows.

Temperature Correction Factor.
e temperature difference-mean temperature correction coefficient relationship for the plate angle void (Figure 9) and plate edge void ( Figure 10) conditions were compared and analyzed, as depicted in Figure 11. e variation trends of the temperature differenceaverage temperature correction coefficients obtained analytically and through the calculation of the two types of cement concrete pavement void conditions were consistent (Figure 11), and the relative error was lower than 1%. erefore, considering the temperature difference-temperature correction factor obtained using equations (6) and (8), the mean value was adopted as the temperature correction factor under the void conditions at negative temperatures. Similarly, by considering the temperature difference-temperature correction factor obtained using equations (7) and (9), the mean value was selected as the temperature correction factor under the void condition at positive temperatures.
Negative temperature range: φ � −0.0003 · ∇T 3 − 0.0216 · ∇T 2 − 0.4888 · ∇T + 1.0002, Positive temperature range: φ � 2 · 10 − 5 · ∇T 3 − 0.0011 · ∇T 2 + 0.0229 · ∇T + 1.0092,  detector, crane, FWD, hand-held grinding machine, and two cement concrete pavement plates with stable foundations. One plate was used to simulate the conditions of the plate corner voids, and the other plate was used to simulate the conditions of the plate edge voids. e field test process is shown in Figure 13, and the specific experimental steps were as follows:

Field Test Verification
(1) e temperature sensor was embedded in the specific location of the predrilled cement concrete pavement slab, and the buried depth was the thickness of the pavement slab. After the sensor was embedded, it was sealed with premixed cement concrete and compacted with force.
(2) e intact cement concrete pavement slab without voids was lifted using a crane, and the panel corner void was set at the corner of the top panel of the base course with the plate angle fixed as the circle center; the void radius and void depth were 1 m and 2 cm, respectively. e panel edge void was set at the edge of the top slab of the base course with 0.5 m as the void width and 2 cm as the void depth.   (3) In addition, an infrared temperature detector was used to collect temperature data for the top and bottom of the slab, and an FWD was used to collect deflection data for the center point of the plate corner load. e interval for the above data collection was once every 1 h.

Analysis of Test Results.
After the above test data were sorted, the deflection value corresponding to a zero temperature difference during daily tests was selected as the standard value of all the deflection tests for that day, and the ratios of all deflection values (including zero temperature difference) to the above standard value was counted, in other words, the temperature correction coefficient (Figure 14).
A comparison between the model results and test results showed that when the pavement slab had a negative temperature difference, the actual temperature correction coefficient of the panel corner and edge voids fluctuated up and down within a narrow fluctuation range, and the average fluctuation was not higher than 7%. When the pavement slab had a positive temperature difference, the actual temperature correction coefficients of the panel corner and edge void fluctuated within a narrow fluctuation range of less than 5% on the average. ese results show that, in practice, the temperature correction coefficient can be used for correcting the measured deflection precisely.

Conclusion
In this study, through the establishment of coupled temperature and load finite element model of cement pavement, the effect of temperature difference at the bottom and top of the slab and deflection of the center point of the plate corner load under different void, climatic, and load conditions was investigated. In addition, the temperature difference between the top and bottom and the correlation of deflection temperature correction coefficient was analyzed. Furthermore, the temperature correction coefficient was developed considering the temperature difference between the top and bottom, and the accuracy of the temperature correction coefficient was verified experimentally.
(1) Based on the monitoring and analysis of the temperature field of a cement concrete pavement through full-size outdoor tests for up to one year, the relationship between the plate top temperature of the cement concrete pavement and the temperature difference at plate top and bottom of the cement concrete pavement in each season was established. (2) e deflection of the plate angle load center point under the coupled action of temperature and load in each season was calculated, and its variation was evaluated. It was found that, considering the effect of the temperature difference, the deflection decreased with increasing negative temperature difference but decreased with increasing positive temperature difference under each void condition. different void conditions. In the case of a negative temperature difference, the correction coefficient decreased with an increase in temperature difference; at a positive temperature difference, the correction coefficient increased with an increase in temperature difference. (5) Two specific conditions of plate corner and plate edge voids were selected for the tests. It was found that the error between the measured and calculated values of the temperature correction coefficients for these two conditions was not higher than 7%, which demonstrated the accuracy of the temperature correction coefficient.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.