CHAPTER 3: DEVELOPMENT OF NUMERICAL MODEL FOR SKID
3.4 Validation of Skid Resistance Simulation Model
The proposed skid resistance simulation model is next validated against published experimental results for both conventional dense-graded pavements and porous pavements. Although previous models developed for dense-graded pavements have been validated in past research studies (Ong and Fwa, 2006; Ong and Fwa, 2008), neither of them involves coupled VOF-FSI simulation. Therefore, it is necessary to validate the proposed model for dense-graded pavements first to ensure its capability in simulating skid resistance on conventional surfaces. The model is then validated for porous pavements using past experiments.
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3.4.1 Derivation of Skid Number from Numerical Simulation Model
The skid number at speed v (denoted as SNv), based on the lock-wheel skid resistance test (ASTM, 2011a), can be determined from the simulation. Skid number is defined as the ratio between horizontal resistance force and vertical loading force acting on the same test tire, normalized by a scale of 100. A higher skid number indicates a better skid resistance performance. Skid number can be calculated as:
100 )
(
x z
v F F
SN (3.44)
where Fx is the horizontal backwards resistance force acting on tire model, and Fz is the vertical downwards load applied on the tire. Both these two variables could be obtained from the numerical simulation model. Horizontal resistance force Fx and vertical load Fz are further explained by:
drag traction
x F F
F (3.45)
uplift contact
z F F
F (3.46)
where Ftraction is the traction force developing at tire-pavement interface, Fdrag is the fluid drag force developing at tire-fluid interface, Fcontact is the contact force between tire and pavement surface, and Fuplift is the fluid uplift force acting on tire surface. In these variables, Fdrag and Fuplift are direct outputs from the fluid model, Fz is an input parameter, and Ftraction is derived from Fcontact:
z uplift
contact
traction F F F
F (3.47)
where μ is the coefficient of friction between tire tread and pavement surface at wet condition. It is usually determined through experiments in laboratory or field, and varies with the surface properties of contact materials. Combining Equations (3.44) to (3.47), the skid number SNv could be expressed as:
100
z
drag uplift
z
v F
F F
SN F
(3.48)
The friction coefficient μ is commonly represented by the skid number at an extremely low speed SN0, and it is assumed that the wet friction coefficient maintains
125 constant with the increase of speed. In the case that experimental SN0 values are unavailable, an iterative back calculation approach developed by Fwa and Ong (2006) can be used to derive the friction coefficients from field skid resistance tests, using the simulation model. The detailed procedures are shown in Figure 3.12 and described below.
Step 1: For each set of experimental results with the same pavement and tire, a measurement of skid resistance at a speed v is randomly selected. The measured skid number is SNv;
Step 2: Assume a reasonable initial SN0 value (normally 50) as the friction coefficient used in the proposed model and run the model at sliding speed v to derive a numerical skid number SNv* from the model outputs;
Step 3: Adjust the value of SN0 based on the difference between numerical SNv* and measured SNv, according to the equation (new trial SN0) = (last trial SN0) + 0.5(SNv* - SNv);
Step 4: Perform the simulation again using the new trial SN0 as the friction coefficient to get a new numerical skid number SNv*;
Step 5: Repeat steps 3 and 4 until the error between numerical and measured results (i.e. ε = SNv* - SNv) is sufficiently small; and
Step 6: The resulted SN0 value is taken as the wet friction coefficient at tire- pavement interface and all the skid numbers at other sliding speeds are predicted by the proposed model with the back-calculated SN0.
3.4.2 Validation of the Model for Conventional Pavement
Numerous experimental studies were performaed on wet-pavement skid resistance using in-field measurements under different operation conditions defined by various parameters, such as sliding speed, water film thickness and wheel load.
Many of such studies were conducted according to the ASTM E274 standard (ASTM, 2011a) with standard smooth tires as specified in the ASTM E524 standard (ASTM,
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2008b). The experiments conducted by Horne (1969) and Agrawal and Henry (1977) were used to validate the proposed model on conventional dense-graded pavements.
The experimental data are shown in Table 3.5.
The numerically simulated results of skid resistance experiments conducted by Horne (1969) and Agrawal and Henry (1977) are presented in Table 3.6. Further comparisons on simulated curves against measured values are shown in Figure 3.13.
As indicated by the ASTM E274 standard, the acceptable standard deviation of this test is ±2 SN units. Therefore, the 95% confidence interval of this test has a range of
±3.92 SN units. As seen in Table 3.6, only one simulation got a result out of this range (with an error of +4.8 SN units from the measured value), and all the percentage errors are below 12% except this case. It is seen that most high percentage errors correspond to lower skid numbers.
3.4.3 Validation of the Model for Porous Pavement
Although the amount of skid resistance tests on porous pavements is not as extensive as that on conventional pavements, there are still some measured experimental results that can be used to validate the proposed model on porous pavements. In an experimental study conducted by the Oregon Department of Transportation and Oregon State University in the early 1990s, skid resistance performances of several porous asphalt pavement sections were evaluated using the lock-wheel trailer test (Younger et al., 1994). Different road sections were selected to provide a mix of traffic conditions and pavement ages. All the tested sections were constructed with the same porous asphalt mixture named ODOT F-mix, but the porosities of different sections differed a lot due to the different service and traffic histories. Variations in porous layer thickness were also available among these projects. The same water application mechanism was adopted in all the tests, providing a water film thickness of 0.55 mm (ASTM, 2011a).
127 The porosities of selected porous pavement sections were measured using core samples (inner and outer wheel paths) in the laboratory, while the permeability was measured in the field using a specially designed falling-head outflow device. The skid numbers of each section at different skidding speeds were measured according to the ASTM E274 standard (ASTM, 2011a). The pavement properties and skid resistance performance of each tested section are listed in Table 3.7.
The proposed model is next validated against this experimental study by Younger et al. (1994). The average measured porosity and permeability values are input to the model to predict the skid numbers. There is no permeability measurement available for the Jumpoff Joe section in the experiment report. However, its porosity is very similar to that of the Grants Pass section and the locations of these two sections are quite near to each other. Therefore it is reasonable to assume the same permeability range as Grants Pass for Jumpoff Joe. Numerical results derived from the proposed model are shown in Table 3.8 and Figure 3.14.
It can be seen from Table 3.8 that most numerical prediction errors are less than 2 SN units and all the percentage errors are less than 8%. This indicates that the proposed model can simulate skid resistance on porous and non-porous pavements.
However, the simulation results of Jumpoff Joe seems to be less satisfactory, with two errors near 3 SN units. This may be a result of the incomplete information for Jumpoff Joe in the experimental measurements, demonstrating the importance of proper permeability evaluation for an accurate skid resistance prediction.
Besides the estimation of the average performance trends, the range bounds for skid numbers of Murphy Road-Lava Butte and Hayesville-Battle Creek are predicted based on the extreme porosity and permeability values. The skid numbers at a zero speed, SN0, used in the prediction of skid resistance range are back calculated from the average curves shown in Figure 3.14. The range of SN0 thus reflects the prediction error of SN0 due to the measurement errors in lock-wheel skidding tests, while the difference in curve shapes reflects the different decreasing trends of skid
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number with increasing skidding speed due to the errors or variances in porosity and permeability measurements. Therefore, this approach considers both experimental errors and pavement property inconsistency. Figure 3.15 shows the simulation results.
This approach is not applied to Grants Pass and Jumpoff Joe because of their narrow porosity range (i.e. 1.1% porosity variation).
From Figure 3.15, all the measured data points fall into the predicted SN ranges, demonstrating the capacity of the model to predict a range of skid resistance performance that vehicles may experience on the road. The prediction range depends on the quality of input data, as well as the sliding speed as seen in Figure 3.15 where prediction ranges are larger at higher speeds. The decrease in skid number with sliding speed is steeper on a surface with lower porosity compared to that on a surface with higher porosity. Therefore, the decreasing rate of the upper bound, which is derived from the maximum porosity, is less than that of the lower bound, which is derived from the minimum porosity. The practical meaning of this phenomenon is that the actual skid resistance a vehicle experiences on a porous pavement may not be identical spatially, especially at high speed, because of the porosity/permeability variation.