A Study on the Design Depth of Permeable Road Pavement through Dynamic Load Experiment

This study investigated vertical strain and stress through a dynamic load experiment at the testing area of Ke-Da Road, Pingtung, Taiwan. A thirty-five-ton truck was moved at constant speeds of 40, 60, and 80 km/h to simulate heavy load conditions to study the mechanical variations. From the results, it was found that the strain and stress curves of the permeable road pavement showed asymmetry due to the viscoelastic property of the open-grade friction course. The results showed that vertical strains and vertical stresses of permeable road pavement were greatly affected by the axle configuration and the change in traffic speed. Furthermore, to propose the design thickness of a permeable road pavement, the pavement strain and stress were modelled with respect to depth using regression based on these collected data. According to the stress regression models and considering the construction uncertainty, the recommend design depth of a permeable pavement is 30 cm. The findings of this study would be helpful in determining the permeable road pavement depth when subjected to heavy traffic load, and the material combination of open-graded friction concrete, porous asphalt concrete, and permeable cement concrete was proposed in this study during the design period.


Introduction
Due to the connected pores, the strength and the life-cycle of permeable road pavements are mostly lower than those of conventional pavement under repeated moving loads of traffic [1][2][3][4]. Under this dynamic load condition, the pavement can face failure from serious rutting and fatigue cracking. Thus, the thickness of the permeable road pavement design must be sized to support the moving traffic loads to ensure a longer life. In the past, permeable road pavements were mostly applied in light-traffic areas rather than heavytraffic areas [3,5,6]. In other words, the application scope of permeable road pavements is limited [4,6].
Many researchers have investigated pavements' mechanical responses with several methods, such as field tests [7][8][9][10][11][12][13][14], theoretical analysis [15][16][17], and finite-element method simulations [4,9,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Firstly, some research has studied the pavement responses through field testing. In El-Hakim's study [7], the tensile strain in asphalt layers, vertical pressure on the subgrade surface, moisture in the subgrade material, and the temperature profile of three different pavements were monitored by researchers to evaluate the performance of the pavements. The three different pavements were perpetual pavement design with rich bottom mix (RBM) layer, perpetual pavement design without RBM, and a conventional pavement design. The results show that two perpetual pavements are subjected to lower stresses and corresponding strain values in the lowest and highest asphalt layers compared cal responses of asphalt pavement, few of the literature have documented the mechanical responses of permeable road pavements. To understand and expand on the applications of permeable pavement, the vertical strains and stresses of permeable road pavement under heavy vehicle loadings with three different designed speeds were investigated and studied without consideration of temperature, pore water pressure, and moisture.

Materials and Methods
A series of dynamic load experiments were conducted in this study to investigate the permeable road pavement responses. The dynamic load experiments were conducted in the study area of the permeable road pavements in Ke-Da road, Pingtung, Taiwan. A 35-ton truck was used in this study and moved at constant speeds of 40, 60, and 80 km/h to model heavy load conditions.

Study Area
The study area (N 22 • 39 44.6268", E 120 • 33 38.376") is located at Section III of Ke-Da Road, between 15k + 125 and 15k + 225, route 187 of Pingtung County, Taiwan. Ke-Da Road is a dual carriageway with a 3-m rapid-vehicle lane and a 5.5-m mixed-vehicle lane, in both north and south driving directions. This road is the main route between National Pingtung University of Science and Technology and Pingtung City. The permeable road pavement test area of Ke-Da Road was constructed in June 2018. The pavement consists of three layers: 3 cm-thick open-graded friction concrete (OGFC), 10 cm-thick porous asphalt concrete (PAC) at surface course, and 40 cm-thick permeable cement concrete (PC) at base course.
Air void content is the basic property of permeable road pavement. The OGFC content was 16.4% by volume. Due to the high void content of the OGFC, water can quickly be removed and a rough surface structure can be formed. The OGFC has good skid resistance and high permeability. With the same benefits, the air void content of PAC was 17.1% in volume under the wearing course. The maximum nominal aggregate size of OGFC was 3/8" (9.5 mm). However, the surface course used PAC mixed with the modified Type III asphalt, with a maximum nominal aggregate size of 3/4". The gradations of each material are presented in Table 1. The basic physical properties of surface course materials are listed in Table 2. The applications of permeable PC have great potential environmental benefits. The stormy rainfall can be well-managed and the groundwater quality can be improved via the water infiltration process. At a 0.44 water-cement ratio, the proportion of PC on the site was 261 kg cement, 135 kg water, 980 kg aggregate of 3/4", 653 kg aggregate of 3/8". The average compressive strength after 7 and 28 days of PC was 112.8 and 142.2 kg/cm 2 , respectively, as shown in Table 3. However, voids in the PAC and PC pavement were easily clogged within three years after construction due to sediment and dust, etc. [31].

Monitoring Instruments
The layout of the instruments used in this study is shown in Figure 1. Each layer was equipped with eight vertical strain transducers (KM-100 B), also from Tokyo Sokki Kenkyujo Co., Ltd. (Tokyo, Japan) to measure the dynamic strains. Ten earth pressure cells (Model 3500 Series) from Geokon, Inc. (Lebanon, NH, USA) were installed to measure the vertical stress at the PAC of upper, middle, and lower layers. All gauges were installed in the mixed-vehicle lane and in the right wheel path, and evenly distributed between the two areas (area A and area B). During the tests, two data acquisition systems DSPL-24 from Geomaster were used to acquire the data from strain transducers and pressure cells in the permeable road pavement. DSPL-24 can measure the velocity and acceleration at a high resolution. The sampling rate of DSPL-24 was 50 samples per second. Equations (1) and (2) are used to calculate the strains and the applied pressures in the field tests.
where P is the applied pressure, kPa; R 1 . and R 0 . are the current and initial output reading in millivolts, volts or milliamps; G is the gage factor, as shown in Table 5. (Note that gage factor is for an excitation of 10 volts. For any other excitation voltage, V, the gage factor shown must be multiplied by 10/V.)

Dynamic Load Experiment
The dynamic load experiment was carried out on 25 October 2019. During the experiment, the average atmosphere temperature was 27.5 • C, and there was no rainfall. The 35-ton semitrailer truck from the Seven Seas Company (see Figure 2a) was used. The weight of the semitrailer truck was determined according to the limited total weight of the semitrailer of Road Traffic Safety Rules of the Ministry of Justice of the Republic of China (Taiwan) [32]. Figure 2b shows the configuration of the truck axles, and individual static wheel load was calculated using the lumped mass method. There were fourteen 315/80 R22.5 wheels in the experiment truck. The static loads for each wheel and the standard pressure of the wheels are listed in Table 6.  Table 6.
In addition, the limited speed of vehicles on Ke-Da road is 60 km/h, according to the Road Traffic Safety Rules. The 40 km/h and 80 km/h truck speeds also were performed to study the difference between strain and stress responses. The truck moved along the prmarked path for the right wheel in the mixed-vehicle lane and with constant speeds of 40, 60, and 80 km/h during tests. A video recorder was placed on the field to ensure the truck wheels' passage on the positions.   In addition, the limited speed of vehicles on Ke-Da road is 60 km/h, according to the Road Traffic Safety Rules. The 40 km/h and 80 km/h truck speeds also were performed to study the difference between strain and stress responses. The truck moved along the pr-marked path for the right wheel in the mixed-vehicle lane and with constant speeds of 40, 60, and 80 km/h during tests. A video recorder was placed on the field to ensure the truck wheels' passage on the positions.

Data Process
Through dynamic load experiments, the data of various depths of permeable pavement were obtained. During the experiment, it was difficult for the outer wheels of the truck to accurately press the sensor position, and hard to produce meaningful strain and stress data in every trial. Therefore, it is necessary to process data after field experiments. The acceptable raw data were extracted through the following procedures.

1.
Four peaks in the strain and stress of the permeable road pavement must be detected by the instrument. The four peaks indicate that the wheel pressed against the instrument; 2.
The detected values have to have positive pressure and positive tension; 3.
The stress and strain responses of the surface layer have to be larger than those of the base layer; 4.
The faster the vehicle speed, the smaller the stress and strain responses in the pavement, which is consistent with the literature [10,19,27]; 5.
The time difference between the two truck axles should be calculated to determine if the trial is acceptable for the consideration of speed.

Relationship between Permeable Road Pavement Strain and Stress with Respect to Pavement Depths
Based on attenuation pattern results at 40, 60, and 80 km/h, a logarithmic regression analysis was conducted with the regression reference methods used in previous studies [33][34][35][36]. The peak values of maximum vertical strains and vertical stresses caused by the fourth wheel were selected and plotted on the logarithmic regression. A logarithmic regression analysis was performed on the plot, showing the maximum vertical strains and vertical stresses versus the depth. The following equations were derived, as shown in Equations (3) and (4). To avoid obtaining negative values for the logarithmic plot, 0 cm depths were omitted and the regression analysis was performed from 1 cm depths onwards.
where y vs,speed is the peak vertical strain of pavement for the specific speed of the truck; y vs, speed is the peak vertical stress of pavement for the specific speed of the truck, kPa; x is the specified pavement depth cm; α vs and α vp is the coefficient of the depth; β vs is the regression slope of the y vs,speed −ln(x) plot; β vp is the regression slope of the y vp,speed −ln(x) plot; γ vs is the regression intercept of the y vs,speed −ln(x) plot; γ vp is the regression intercept of the y vp,speed −ln(x) plot.
Based on the results of the Analysis of Variance (ANOVA) in the regression models, a series of tests were performed. Firstly, the test to determine the overall model adequacy was conducted using the F-test. If the model is deemed adequate, the β. coefficients in models were inferred using t-test. As observed in the figures, the stresses and strains did not return to 0 after the truck wheel moved away the instrumented position, and the single-curve response shows asymmetry due to the viscoelastic property of the OGFC. The surface layer (3 cm and 8 cm) of the permeable road pavement is subjected to obvious tensile vertical strains under moving loads. Four peaks occurred at 3 cm and 8 cm pavement depths. The vertical strains caused by the third and fourth wheel axles dominate in the loading period at each truck speed. Table 7 shows that, under the truck speeds of 40, 60 and 80 km/h, the maximum vertical strains of 3 cm depth in permeable pavement at the fourth peak were 1099.85, 979.46 and 742.13, respectively. The fourth peak vertical strain at the 8 cm depth was 9.54, 9.29 and 5.42, respectively, under 40, 60 and 80 km/h. Compared with the depth of 3 cm, the vertical strain value of 8 cm in the permeable road pavement was much lower. In addition, the increase in truck speed caused a vertical strain at the 3 cm pavement depth that was greater than that with the 8 cm pavement depth. The results show that increasing the speed has more influence on the vertical strain of the 3 cm pavement depth, as presented in the previous research [9].

Results and Discussion
in the previous research [9].
According to Lu et al. [26], with the increase in truck speed, the reaction time of a certain point on the road surface is reduced, thus reducing the strain on the road. The results of practical observations indicate that it is possible to extend permeable road pavement service life at higher traffic speeds over the long term. Moreover, the axle configuration and the truck speed have no effect on the vertical strain at the depths of 33 cm and 53 cm in the permeable road pavement, as shown in Figure 5.        According to Lu et al. [26], with the increase in truck speed, the reaction time of a certain point on the road surface is reduced, thus reducing the strain on the road. The results of practical observations indicate that it is possible to extend permeable road pavement service life at higher traffic speeds over the long term. Moreover, the axle configuration and the truck speed have no effect on the vertical strain at the depths of 33 cm and 53 cm in the permeable road pavement, as shown in Figure 5.      Figures 6 and 7 show four peaks in stress responses at 3 cm, 8 cm, and 13 cm pavement depths as the wheel axles passed pressure cells. The maximum stress response was recorded at the rear wheel axle of the truck. An accumulating stress effect was found from the third to the fourth peaks. This indicated that the axle configuration of the truck significantly influenced the vertical stresses of the upper layer of permeable road pavement. As expected, the lower layers of the permeable road pavement were less influenced by the wheel axles of the truck, as shown in Figure 8. The maximum values of stress responses at each depth are summarized in Table 8 to compare the dynamic stresses and traffic speeds. The results showed that maximum vertical stress values occurred at 3 cm and 8 cm depths at a 40 km/h test round. Conversely, the maximum vertical stress values at 3 cm and 8 cm depths at an 80 km/h traffic speed are the lowest of all of the truck speeds. For example, maximum vertical stress response values for the fourth peak at a 3 cm pavement depth were 30.76, 22.9, and 8.36 kPa, respectively, under traffic speeds of 40, 60, and 80 km/h. At an 8 cm depth, the vertical stress responses for the fourth peak were lowered to 17.34, 9.93, and 1.63 kPa, respectively, under traffic speeds of 40, 60, and 80 km/h.  Figures 6 and 7 show four peaks in stress responses at 3 cm, 8 cm, and 13 cm pavement depths as the wheel axles passed pressure cells. The maximum stress response was recorded at the rear wheel axle of the truck. An accumulating stress effect was found from the third to the fourth peaks. This indicated that the axle configuration of the truck significantly influenced the vertical stresses of the upper layer of permeable road pavement. As expected, the lower layers of the permeable road pavement were less influenced by the wheel axles of the truck, as shown in Figure 8. The maximum values of stress responses at each depth are summarized in Table 8

Relationship of Permeable Road Pavement Strain and Stress with Respect to Pavement Depths
The aforementioned results were used to evaluate the relationship between maximum vertical strains and stress with respect to pavement depth, as shown in Figure 9. The trends show that the maximum vertical strain decreases while the depth increases. The figure clearly shows that the response at the 3 cm pavement depth is the largest, and the response rapidly decreases at the 8 cm depth; as the depth increases, the strain response approaches zero.

Depths
The aforementioned results were used to evaluate the relationship between maximum vertical strains and stress with respect to pavement depth, as shown in Figure 9. The trends show that the maximum vertical strain decreases while the depth increases. The figure clearly shows that the response at the 3 cm pavement depth is the largest, and the response rapidly decreases at the 8 cm depth; as the depth increases, the strain response approaches zero.
Meanwhile, multiple regression models were developed to estimate vertical strains at different pavement depths, as presented in Figure 9. These models all performed well, with R 2 coefficients of 0.97. Table 9 shows the results of an ANOVA F test analysis for the vertical strain models. The F value for each model was compared to the critical F value (Fcrit). The F values were 15.815, 16.345, and 15.772 for models of 40, 60, and 80 km/h, respectively. These F values are lower than the Fcrit (18.513), indicating that H0 is acceptable. The effect of truck-driving speed on the depth in terms of maximum vertical strains and maximum vertical stresses was insignificant.  Meanwhile, multiple regression models were developed to estimate vertical strains at different pavement depths, as presented in Figure 9. These models all performed well, with R 2 coefficients of 0.97. Table 9 shows the results of an ANOVA F test analysis for the vertical strain models. The F value for each model was compared to the critical F value (F crit ). The F values were 15.815, 16.345, and 15.772 for models of 40, 60, and 80 km/h, respectively. These F values are lower than the F crit (18.513), indicating that H 0 is acceptable. The effect of truck-driving speed on the depth in terms of maximum vertical strains and maximum vertical stresses was insignificant. On the other hand, permeable road pavement stresses with respect to pavement depths at traffic speeds of 40, 60, and 80 km/h of traffic are shown in Figure 10a-c. It can be observed that the internal permeable road pavement stresses obviously decreased as depths increased. However, the influence under the lower traffic speeds for porous asphalt pavement (from 3 to 8 cm) was smaller than that under higher traffic speeds. Moreover, regardless of traffic speeds, the stresses were close to zero below the 30 cm depth layers. As shown in Figure 10, the R 2 coefficients of regression for the models of 40, 60, and 80 km/h were 0.943, 0.973, and 0.940, respectively.   After confirming that the multiple regression model is significant through the F test, a test of the individual coefficients in the multiple regression model was performed. The calculated t-values were 2.0315, 3.3775, and 2.5805 for the models of 40, 60, and 80 km/h, respectively, which are larger than t 0.1 (1.886), as shown in Table 11. p-values for these models were larger than 0.05. Thus, the null hypothesis is rejected, indicating that the independent variables for the 40, 60, and 80 km/h models are meaningful. Moreover, the regression formulas estimated that, when the vertical stress of the pavement is 0 KPa, the pavement depths will be 22, 19, and 18 cm at speeds of 40, 60, and 80 km/h, respectively. To widely apply the permeable road pavement in heavy traffic loading areas, the depths estimated by the stress regression model are used to suggest the design depth value of the permeable road pavement for heavy-load traffic designs. Considering the condition of pavement overload, it is necessary to introduce a specified safety factor in the design. Therefore, the theoretical results obtained through these models are multiplied by a safety factor of 1.2 to 1.5 according to the suggestion of highway-graded classification. Thus, the recommended design depth of the permeable road pavement is 30 cm, and this result is the same as the study of Yang et al. [37].

Conclusions
This paper presents the mechanical responses of the permeable road pavement and the design thickness of the pavement through the established models of depth-vs.-stress and depth-vs.-strain. The main findings of this field investigation and regression model led to the following conclusions:

•
The result of vertical strains and vertical stresses in permeable road pavement indicated that the stresses and strains did not return to 0 after the truck wheel moved away from the instrumented position, and the single-curve response performs asymmetrically due to the viscoelastic property of the OGFC.

•
The vertical strains and vertical stresses at the OGFC and the PAC showed an accumulating effect from the third to fourth axle from the collected data. Thus, the axle configuration significantly influences the strain and stress values of the permeable road pavement.
• Vertical strains and stresses of the permeable road pavement were strongly influenced by the truck driving speeds. An increase in truck speed decreases the reaction time of a point on the pavement, which reduces the pavement strain. This indicates that it is possible to extend the service life of a permeable road pavement at reasonably higher traffic speeds. • By using the ANOVA F-test and t-test, from these models, the multiple logarithmic regression models of vertical stresses vs. vehicle speeds of 40, 60, and 80 km/h are meaningful. The estimated depths of the permeable road pavements are 22, 19, and 18 cm at speeds of 40, 60 and 80 km/h, respectively. Considering the results and the construction uncertainty, the recommended design thickness of the permeable pavement is 30 cm under the OGFC, PAC, and PC combination reported in Tables 1 and 2, while the dynamic impacting force is not under consideration. Funding: This study was received partly funding from Pingtung county government, Taiwan, R.O.C.

Conflicts of Interest:
The authors declare no conflict of interest.