CHAPTER 7: INTEGRATING SKID RESISTANCE AND TIRE/ROAD NOISE
7.3 Application of the Proposed Analysis Framework
The above developed analysis framework is next further elaborated through a hypothetical case study. The assumptions and problem definition are first presented.
The mixture design procedures introduced in the previous section are then performed to incorporate functional performance into the porous mixture selection process. The resulting mixture design is considered to be the optimum solution.
7.3.1 Description of the Hypothetical Problem
An in-service highway section is suffering from two problems: high accident- tendency caused by insufficient wet skid resistance and over-irritating traffic noise emitted from high-speed vehicles. A porous surface layer is to be installed in the rehabilitation of this highway section in order to solve both problems. The following information is made available at the time of mixture design.
The design rainfall intensity is 100 mm/h. Considering road geometry and drainage capacity, the critical water film thickness for safety evaluation is computed to be 1.2 mm.
The temperature variation in a year is from 5 °C (in winter) to 35 °C (in summer) at the project location.
The design speed for road geometry is 90 km/h. This is also applicable in the frictional and acoustical performance design.
The design service life is 10 years, within which regular maintenance will be performed to prevent porous surface failure from clogging.
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According to the local pavement agency's recommendation, the terminal skid number acting on a worn tire at the design speed should be at least 31.
According to the environmental agency's requirement, the average noise level in the nearby residential should be lower than 65 dB(A). This can be converted to a 97 dB(A) CPX noise level at the design speed, taking into account the traffic composition on roadway and the distance from roadway to residence.
The linear crash-friction relationship proposed by the Organization for Economic Cooperation and Development (OECD, 1984) is adopted in this case study, with a decreasing rate of 0.045 acc/mvm per unit increase in skid number. Geometric relationship is assumed between noise level variation and its quantified worth. The relative importance of frictional and acoustical performances is set to be 0.6 : 0.4.
Six mixture designs with variations in nominal max aggregate size and porosity value (see Table 7.7) are produced in the laboratory. All these mixtures satisfy the requirements in structural strength, drainage capacity, moisture susceptibility and durability. Two levels of porous layer thickness is under consideration, namely 40 mm and 60 mm.
Only the material cost is taken into consideration. The other costs are assumed identical for all the candidate mixtures. The cost of material does not only differ with thickness, but also increases with porosity due to high-viscosity asphalt or additives used. The relative cost ratio for each mixture is shown in Table 7.7.
7.3.2 Framework Application
The developed analysis framework is next performed step by step on the illustrative hypothetical case study. The derivation follows the workflow shown in Figure 7.4, and the artificial neural network technology is applied to facilitate the performance prediction.
Step 1: Design Criterion Determination
283 The most unfavorable skid number occurs on a smooth tire traveling on the flooded pavement (with a 1.2 mm water film) at the design speed (i.e. 90 km/h). This value on an old pavement after 10 years of service is required to be 31. The numerical simulation could be directly conducted at this most-unfavorable condition, but for the generalization of the approach, simulations are performed according to the standard condition specified in ASTM E274 (ASTM, 2011a) at 80 km/h. Therefore, speed and water thickness corrections should be made on the terminal SN. This can be achieved through a parametric analysis as in Chapter 4. Although the corrections may not be identical for every mixtures, to unify the standard, the worst case values are used here.
The speed correction in the specific condition is -1.0 SN units from 90 to 80 km/h, and that for water film thickness is 1.8 from 1.2 to 0.5 mm. The deterioration of skid number with pavement age is assumed to be 15 SN units within its first 10 years' life according to Rezaei et al.'s model (2011), and the seasonal fluctuation of skid number in the project area is taken as 4.2 SN units. Combining the terminal SN value with the long-term effects, the design criterion on skid number is determined as
51 2 . 4 15 8 . 1 0 . 1
31
r
SN (7.3)
The acceptable maximum tire/road noise should be corrected by the vehicle speed as well. This can be achieved through a parametric analysis similar with that in Chapter 6. Again, the worst case is adopted in this study. The speed correction for the given condition is found to be -1.0 dB(A) from 90 to 80 km/h. The increase of CFX noise level with pavement age is assumed to be 8 dB(A) in the first 10 years' service life, and the seasonal effect on tire/road noise due to temperature variation is derived to be -0.9 dB(A) based on Bueno et al.'s work (2011) . Combining the terminal CFX sound pressure level with the long-term effects, the design criterion on tire/road noise is determined as
1 . 87 9 . 0 8 0 . 1
97
r
SPL dB(A) (7.4)
Step 2: Functional Performance Prediction
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An artificial neural network was developed based on numerical simulation results to enhance the efficiency of performance predictions. The network training data cover the whole variation ranges of design parameters used in this case study. It is considered adequately accurate to generate fluid forces and noise reductions from this network. Tables 7.8 and 7.9 show the predictions of functional performance, with the wet-pavement friction coefficients measured in the laboratory on compacted specimens of each mixture design. The "generated noise" in Table 7.9 is obtained from the tire/road noise simulation performed on an ideal surface with the texture of examined porous specimen but without any acoustic absorption ability. It is observed that the predicted skid number for Mixtures A-40 and F-40 is lower than the design criterion (SN = 51) and the predicted noise level for Mixtures B-40, D-40 and F-40 is higher than the 87.1 dB(A) noise criterion. Therefore, these four mixtures do not satisfy the functional requirements and should be removed from the candidates. The extreme cases within the practicable ranges are also extracted from the ANN technique. The upper and lower bounds of tire/road noise can be directly obtained from the network outputs, while those for safety benefit should account for material cost difference, which is a best estimation from the information available.
Step 3: Functional Performance Valuation
The approach of safety benefit quantification was presented in Section 7.2.2.1.
The lowest skid number obtained from the neural network is adopted as the baseline of safety valuation. The differences between predicted skid number and the baseline are used to calculate the potential accident reduction for each mixture design, taking the decreasing rate of 0.045 acc/mvm per unit increase in skid number. The variation of skid number with pavement age is assumed the same for all the mixtures, therefore, the SN differences maintain identical with time. The reduction in monetary loss is proportional to the reduction in accident count. The coefficient is taken as L, which could be derived based on the proportions of accidents with various severities. The
285 present value of monetary benefit is derived with the present value factor at a given interest rate r. It is then divided by the material cost to estimate the benefit-cost ratio:
Cost Z AR Cost
r r L r AR C
B
10 10
1 1 1
/ (7.5)
where AR is the accident reduction per million of vehicle-mile. Z is a constant for various mixtures, provided constant L and r. Therefore, the benefit-cost ratio could be presented by accident reduction rate and the relative cost. The same procedures are also performed on the extreme cases of mixtures with regards to safety benefits. The calculation results are shown in Table 7.10.
The quantification of acoustic benefit was introduced in Section 7.2.2.2.
Since there is no reliable approach available to date in the valuation of overall benefit of tire/road noise reduction, simple relationships observed in previous studies may be adopted in practice. Geometric growth is assumed in this study to describe the relationship between tire/road noise reduction and its value. The parameters in this relationship can be defined by the extreme noise levels.
Step 4: Performance Index Calculation
Skid resistance performance index (SPI) is defined on a linear scale of 0 to 10, with the extreme cases serving as upper and lower bounds. Acoustical performance index (API) is defined on a geometric scale with the same range. The values of these two indices are listed in Table 7.11. The indices for each candidate mixture design are then easily read from the table based on its safety benefit-cost ratio or tire/road noise level. The functional performance index (FPI) is then derived by linear superposition of SPI and API, letting the weighting factor α and β take the values of 0.6 and 0.4, respectively. The performance indices of each mixture are shown in Table 7.12.
Step 5: Optimal Design Selection
Comparing FPI among candidate mixture designs, it is obvious that Mixture E-40 possesses the highest FPI value. Therefore, in this particular project, Mixture E-
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40 (produced from 12.5 mm aggregates with a 24.4% porosity and 40 mm porous layer thickness) should be selected as the final design considering the optimization of functional performance.