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40 This chapter presents the methodology for developing vehi- cle repair and maintenance cost models using the two most promising models identified in this project: HDM 4 model and the model identified in the Texas Research and Develop- ment Foundation (TRDF) study (Zaniewski et al., 1982). This chapter also presents a new mechanisticâempirical approach to estimate the effect of pavement roughness on repair and maintenance costs. Repair and Maintenance Models HDM 4 Model HDM 3 allowed users to predict vehicle operating costs using relationships derived from road user cost studies in Brazil, India, Kenya, and the Caribbean (Watanatada et al., 1987). For HDM 4, the parts model was simplified over that used in HDM 3 (Bennett and Greenwood, 2003b). Equa- tions 5.1 through 5.4 show the final model. The HDM 4 model suggested parameters for parts and labor for all the vehicle classes are listed in Table 5-1. PARTS K CKM a a RI K CPCON dF pc kp pc= +( )[ ]+( ) + Ã 0 1 1 0 1 UEL( ) ( . )5 1 RI IRI IRI a a IRI a= + â( )( )max , , ( . )min 0 5 22 3 4 a IRI a a a IRI a IRI a a I IRI a 2 5 3 5 0 5 4 5 5 0 0 5 3 0 = â = = = ( . ) RI0 3â LH K PARTS Klh a lh= Ã( )+0 1 5 46 7a ( . ) where: PARTS = Standardized parts consumption as a fraction of the replacement vehicle price per 1000 km K0pc = Rotational calibration factor (default = 1.0) CKM = Vehicle cumulative kilometer (Table 5-1) a0, a1, kp = Model constants (Table 5-1) RI = Adjusted roughness IRI = Roughness in IRI (m/km) IRI0 = Limiting roughness for parts consumption in IRI (3 m/km) a2 to a5 = Model parameters K1pc = Translational calibration factor (default = 0.0) CPCON = Congestion elasticity factor (default = 0.1) dFUEL = Additional fuel consumption due to congestion as a decimal LH = Number of labor hours per 1,000 km K0lh = Rotation calibration factor (default = 1) K1lh = Translation calibration factor (default = 0) a6, a7 = Model constants (Table 5-1) The model suggests eliminating the effects of roughness on parts consumption at low IRI. This is achieved by using Equations 5.2 and 5.3. TRDF Study Winfrey (1969) presented repair and maintenance costs based on the results of surveys. These costs were updated by Claffey (1971). Zaniewski et al. (1982) further updated costs for maintenance and repair at constant speed at level terrain in good condition by multiplying Winfreyâs costs by a factor to reflect the current overall repair and maintenance costs and listing the costs in tables. The results from the TRDF study were generated for a Pavement Serviceability Index (PSI) of 3.5 (IRI was not the accepted standard roughness index at that time). To include the effect of pavement condi- tion, Zaniewski et al. (1982) compiled the two different rela- C h a p t e r 5 Repair and Maintenance Costs Model
41 extracted from Texas DOT and Michigan DOT databases (these data are presented in Appendix C). To correlate pavement condition and repair and maintenance, rough- ness data from the pavement management systems of Texas and Michigan DOTs were used. The content of the data obtained for all vehicle types appears adequate for making statistical inferences. Although the Mich- igan DOT fleet does not include heavy and articulated trucks (for normal operations), these data were available from the Texas DOT and the NCHRP 1-33 (Papagiannakis, 2000) data. The quality of the data depends on whether repair and maintenance costs could be related to pavement conditions (i.e., roughness) and the availability of sufficient variance in roughness condition between different regions/districts. tionships that were established as part of the Brazilian study (Watanatada, 1987) to estimate parts and labor expenses as a function of surface roughness and calculated adjustment factors (Table 5-2). Collection and Assessment of Data Applicability Repair and maintenance costs data (i.e., parts and labor costs) and vehicle characteristics (i.e., vehicle type, odom- eter readings, model year, vehicle age, etc.) have been collected from different sources, including commercial truck fleet data collected as part of NCHRP Project 1-33 ( Papagiannakis, 2000) and state DOT vehicle fleet data Vehicle Type Parts Consumption Model Labor Model CKM (km) kp a0*1E 6 a1*1E 6 a6 a7 Motorcycle 50,000 0.308 9.23 6.2 1161.42 0.584 Small car 150,000 0.308 36.94 6.2 1161.42 0.584 Medium car 150,000 0.308 36.94 6.2 1161.42 0.584 Large car 150,000 0.308 36.94 6.2 1161.42 0.584 Light delivery car 200,000 0.308 36.94 6.2 611.75 0.445 Light goods vehicle 200,000 0.308 36.94 6.2 611.75 0.445 Four-wheel drive 200,000 0.371 7.29 2.96 611.75 0.445 Light truck 200,000 0.371 7.29 2.96 2462.22 0.654 Medium truck 240,000 0.371 11.58 2.96 2462.22 0.654 Heavy truck 602,000 0.371 11.58 2.96 2462.22 0.654 Articulated truck 602,000 0.371 13.58 2.96 2462.22 0.654 Mini bus 120,000 0.308 36.76 6.2 611.75 0.445 Light bus 136,000 0.371 10.14 1.97 637.12 0.473 Medium bus 245,000 0.483 0.57 0.49 637.12 0.473 Heavy bus 420,000 0.483 0.65 0.46 637.12 0.473 Coach 420,000 0.483 0.64 0.46 637.12 0.473 1 km = 0.62 mi Table 5-1. HDM 4 repair and maintenance model parameters and vehicle characteristics. Pavement Serviceability Index IRI (m/km) Passenger Cars and Pickup Trucks Single-Unit Trucks 2-S2 and 3-S2 Semi Trucks 1 8.94 2.3 1.73 2.35 1.5 6.69 1.98 1.48 1.82 2 5.09 1.71 1.30 1.5 2.5 3.85 1.37 1.17 1.27 3 2.84 1.15 1.07 1.11 3.5 1.98 1.00 1.00 1.00 4 1.24 0.90 0.94 0.92 4.5 0.59 0.83 0.90 0.86 1 m/km = 63.4 in./mi Source: Zaniewski et al. (1982) Table 5-2. Repair and maintenance costs adjustment factors.
42 â¢ Group A: roughness > 2.1 m/km (133.1 in./mi) â¢ Group B: 1.9 m/km (120.5 in./mi) < roughness < 2.1 m/km (133.1 in./mi) â¢ Group C: 1.7 m/km (107.8 in./mi) < roughness < 1.9 m/km (120.5 in./mi) â¢ Group D: 1.5 m/km (95.1 in./mi) < roughness < 1.7 m/km (107.8 in./mi) â¢ Group E: roughness < 1.5 m/km (95.1 in./mi) This classification was obtained using the average rough- ness of 1.9 m/km (120.5 in./mi) and a standard deviation of 0.2 m/km (12.7 in./mi). Repair and maintenance data for vehicle fleets reported in NCHRP 1-33 (Papagiannakis, 2000) were correlated with pavement condition (IRI) and compared with HDM 4 pre- dictions (Figure 5-3). Figure 5-3 indicates the following regarding the data reported in NCHRP 1-33: â¢ The range of IRI is limited. â¢ The parts costs are lower than those predicted by HDM 4. â¢ The labor costs are much lower than those predicted by HDM 4. The HDM 4 model was calibrated using data from developing countries (e.g., Brazil, India) that tend to overestimate the labor hours expended for repair and maintenance compared to US conditions. Also, there is a difference between parts consump- tion in the United States and those predicted from HDM 4 because of the different market places and inflation in parts and vehicle prices. In light of this situation, the research team decided to update the results of the TRDF study and develop a new mechanisticâempirical model. Preliminary analysis of pavement roughness data in Michigan and Texas suggests that there is enough variability in rough- ness conditions among different regions, districts, and counties. The regions of Michigan were divided into three categories (Figure 5-1): â¢ University and metro regions (~50% of sections with IRI > 2.4 m/km) â¢ Bay and Southwest regions (~30% of sections with IRI > 2.4 m/km) â¢ Superior, North, and Grand regions (~20% of sections with IRI > 2.4 m/km) Similarly, the road network for the state of Texas was divided into five groups (Figure 5-2): Source: Michigan DOT 0% 10% 20% 30% 40% 50% 60% Superior North Grand Bay Southwest Univ. Metro % o f se ct io ns w it h IR I > 2. 4 m /k m Region Figure 5-1. Percentage of Michigan sections with IRI > 2.4 m/km by region. 1 m/km = 63.4 in./mi Source: Texas DOT Figure 5-2. Categories of roughness for Texas DOT districts.
43 Updating Results of TRDF Study Texas and Michigan DOT data were first sorted by car make, model, and year. Then, only repair costs related to damage from vibrations were extracted (e.g., underbody inspection, axle repair and replacement, and shock absorber replacement). In spite of the adequacy of data quality, it was not possible to fit a relationship between roughness and repair and maintenance cost for the following reasons: â¢ The data showed wide scatter and high variability. â¢ The range of roughness was narrow (IRI between 1.4 and 2.4 m/km) and does not cover the full range encountered in the United States (IRI ~ 1 to 5 m/km). â¢ The maximum roughness (IRI) was less than 3 m/km (190.2 in./mi); earlier studies (Bennett and Greenwood, 2003b; Poelman and Weir, 1992) reported no effect on repair and maintenance costs at such a low level of roughness. To deal with these limitations, the latest comprehensive research conducted in the United States (Zaniewski et al., 1982) was used and updated to current conditions. The models were updated using macro-economic model cor- rections for overall (average) economic data (e.g., average labor hours for typical vehicles and average parts cost com- parisons). This update was done by multiplying the costs from the TRDF study (which take into account all the rel- evant factors such as roughness, grade, and speed) by the ratio of current overall repair and maintenance costs to those used in the TRDF study. Current overall repair and maintenance costs were estimated using Michigan and Texas DOT databases. The inflation rate between 1982 and 2007 was calculated as the ratio of current overall average repair and maintenance costs to those reported in the TRDF study. Table 5-3 shows the costs from the TRDF study, current repair and maintenance costs, and the inflation rate for dif- ferent vehicle classes. The 1982 database collected by Zaniewski et al. (1982) does not include medium trucks (6.350 to 11.793 metric tons or (a) Parts Consumption (b) Labor Hours 1 m/km = 63.4 in./mi 0 0.01 0.02 0.03 0.04 0.05 0 1 2 3 4 5 6 P ar ts C os t ($ /k m ) IRI (m/km) 0 0.25 0.5 0.75 1 0 1 2 3 4 5 6 L ab or C os t ($ /k m ) IRI (m/km) NCHRP 1-33 HDM 4 Figure 5-3. Parts consumption and labor hours estimates. Vehicle Class Average Cost ($/km) x 10 3 Average Cost ($/mi) x 10 3 Inflation Ratio (1982 to 2007) Average Vehicle Ageâ (years) Average Vehicle Odometer Readingâ (km) Data Pointsâ Zaniewski et al. (1982) Current Costâ (2007) Zaniewski et al. (1982) Current Costâ (2007) Small car 21.44 40.23 34.3 64.37 1.56 9.23 96,215 680 Medium car 26 41.6 Large car 30.03 48.05 Pickup truck 33.01 51.78 52.82 82.85 1.57 7.31 92,038 2764 Light truck 61.88 92.13 99 147.4 1.49 7.80 86,963 1536 Medium truck 87.50* 118.6 140* 189.76 1.36 7.40 87,449 1831 Heavy truck 87.50 119.27 140 190.83 1.36 12.50 196,378 1735 Articulated truck 90.63 124.28 145 198.85 1.37 14.64 352,633 181 Buses 87.50* 119.12 140* 190.59 1.36 22.75 323,174 8 1 km = 0.62 mi * Assumed equal to heavy truck cost â Estimated using both Texas and Michigan DOT data Table 5-3. Repair and maintenance costs.
44 14,000 to 26,000 lb) based on the US DOT Vehicle Inventory and Use Survey classification. However, the data collected as part of this study (especially the data collected from Texas DOT) included all truck classes (light, medium, heavy, and articulated trucks) and buses. Therefore, the average repair and maintenance costs for medium trucks and buses were assumed to be equal to those for heavy trucks. Table 5-3 also presents the number of data points for the data collected from Michigan and Texas DOTs. Enough data points that are representative of current vehicle and commercial truck fleets in the United States were available for statistical inferences. The effect of roughness was accounted for using an approach similar to that used in Zaniewski et al. (1982). First, the HDM 4 repair and maintenance equations were compiled for all vehicle classes for different roughness levels (from 1 to 6 m/km in increments of 0.5 m/km). Then, these values were compared to the baseline condition, which is assumed to be 2 m/km (PSI â 3.5). The proportionate change from this baseline condition to the respective roughness level is the adjustment factor applied to the updated costs. Adjustment factors for each vehicle class and IRI value were calculated using Equations 5.5 and 5.6 and are summarized in Table 5-4. The HDM 4 model assumes no effect of roughness on parts consumption at low IRI (less than 3 m/km), which is achieved by using the smoothing relationship given in Equations 5.4 and 5.5. This assumption was also reported in others studies (Poelman and Weir, 1992) and was observed from the data collected as part of this study. AF COST IRI COST i i = ( ) ( )2 5 5( . ) COST IRI PARTS IRI LH IRIi i i( ) = ( )+ ( ) ( . )5 6 where: AFi(%) = Adjustment factor (percentage) COST (IRIi) = Total cost per 1,000 km evaluated at IRIi PARTS (IRIi) = Parts consumption per 1,000 km evaluated at IRIi using Equation 5.1 LH (IRIi) = Labor cost per 1,000 km evaluated at IRIi using Equation 5.4 IRIi = International Roughness Index (m/km) MechanisticâEmpirical Approach A mechanisticâempirical methodology was developed in this study to estimate the effect of roughness on repair and mainte- nance costs. The approach consists of conducting fatigue dam- age analysis using numerical modeling of vehicle response. Its main assumption is that damage to vehicle suspension com- ponents follows a Minerâs rule type of fatigue accumulation (Poelman and Weir, 1992; HammarstrÃ¶m and Henrikson, 1994). A sensitivity analysis was performed to quantify the relationship between roughness level and vehicle suspension damage. The analysis consists of the following steps: 1. Generate an artificial road surface profile for a given roughness (IRI); 2. Estimate the response of the vehicle using numerical modeling of the vehicle; 3. Compute the induced damage to the vehicle suspension using a rainflow counting algorithm and Minerâs rule; 4. Repeat Steps 1 through 3 for different roughness levels. Artificial Generation of Road Surface Profiles The road roughness profiles can be represented as stochastic processes, depending on the spatial road coordinate x of the traveling vehicle (ISO-8608:1995, âMechanical Vibrationâ Road Surface Profileâ). The one-sided power spectral density (PSD) is a simple and often used road roughness representation approach. A detailed description of the models currently in use is included in Appendix C. These models were used to generate road profiles for roughness prediction purposes. In Vehicle Class Adjustment Factors IRI (m/km) 1.0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Small car 1.0 1.0 1.0 1.0 1.01 1.03 1.12 1.26 1.40 1.55 1.71 Medium car 1.0 1.0 1.0 1.0 1.01 1.03 1.12 1.26 1.40 1.55 1.71 Large car 1.0 1.0 1.0 1.0 1.01 1.03 1.12 1.26 1.40 1.55 1.71 Pickup trucks 1.0 1.0 1.0 1.0 1.01 1.03 1.12 1.26 1.40 1.55 1.71 Light truck 1.0 1.0 1.0 1.0 1.01 1.05 1.20 1.41 1.65 1.91 2.18 Medium truck 1.0 1.0 1.0 1.0 1.01 1.04 1.15 1.32 1.50 1.69 1.90 Heavy truck 1.0 1.0 1.0 1.0 1.01 1.04 1.15 1.32 1.50 1.69 1.90 Articulated truck 1.0 1.0 1.0 1.0 1.01 1.03 1.14 1.29 1.45 1.62 1.80 Buses 1.0 1.0 1.0 1.0 1.02 1.06 1.24 1.52 1.83 2.17 2.53 1 m/km = 63.4 in./mi Table 5-4. Repair and maintenance costs adjustment factors.
45 1979, Robson suggested the following model to generate the pavement surface roughness profiles, which was included in ISO 8608:1995: S k c ku n( ) = â ( . )5 7 Where Su(k) = Displacement spectral density (m3/cycle) n = 2.5 K = n Nâ n = 0,1, . . . . (N - 1) = Wavenumber N = Number of samples in the profiles D = Distance interval between successive ordinates of the surface profile c = Characterizes the roughness level The constant c in Equation 5.7 was found to be correlated with the IRI (Robson, 1979) and could be estimated using Equation 5.8: c IRI m cycle= Ã ( ) ( )â1 69 10 5 88 2 1 2 3 2. ( . ) To generate a random road surface profile, a set of ran- dom phase angles uniformly distributed between 0 and 2p is applied to the desired spectral density. Then, the inverse discrete Fourier transform was applied to the spectral coef- ficients (Cebon, 1987). Dynamic Vehicle Simulation As reported by Prem (2000) and Cebon (1999), several numerical models have been developed to predict the behavior of vehicles when traveling on irregular pavement surfaces. The most basic models are based on quarter-vehicles represented by a second-order, two-degree-of-freedom, linear differen- tial equation (Equation 5.9), whereby the vehicle response is computed for the vertical orientation with the pavement sur- face profile as the excitation function (Figure 5-4). m x c x x k x x k x u tu u s s u s s u t u&& & &â â( )â â( )+ â ( )( ) = 0 (5 9 0 . ) m x c x x k x xs s s s u s s u&& & &+ â( )+ â( ) = ï£±ï£²ï£´ ï£³ï£´ Where, u (t) = Road profile (time) xu = Elevation of unsprung mass (axle) xs = Elevation of sprung mass (body) kt = Tire spring constant ks = Suspension spring constant mu = Unsprung mass ms = Sprung mass cs = Shock absorber constant To account for the more complex behavior of road vehicles, more sophisticated vehicle models have been developed to describe the dynamic behavior of half-vehicles (complete axle) and even full-vehicle models (Gillespie, 1985). These have been aimed at predicting the roll and pitch response of vehicles, which have been found to be significant for some vehicle types. It was suggested, however, that in most cases, the vertical vibra- tion remains the dominant component of vibration induced by irregular pavement surfaces (Gillespie, 1985). A half- or quarter-car model cannot be expected to predict loads on a physical vehicle exactly, but it will highlight the most important road characteristics as far as fatigue damage accumulation is concerned; it might be viewed as a âfatigue-load filterâ (Cebon, 1999; Prem, 2000; BogsjÃ¶, 2006; Kouta, 1994; Rouillard, 2008). There have been several such models with various specific parameter values proposed to emulate the response of a wide variety of road vehicles ranging from small sedans to large trucks with air ride and more conventional steel suspension systems (Cebon, 1999). These models have also been used to predict the response of large vehicles with different axles in recogni- tion of the differing suspension elements used for the driverâs cabin and the trailer. Quarter-car parameters for a passenger car ( Sayers and Karamihas, 1998) and a full truck with typical air and steel suspensions (Cebon, 1999) are given in Figure 5-5. ms mu ks cs kt u(t) xu xs Figure 5-4. Schematic of two-degrees-of-freedom quarter-car vehicle model. 20 2 0.4 500 4500 Air CarTruckConstants 220KNs/m cs 0.1252MN/mkt 0.0281MN/mks 40500kgmu 2504500kgms -SteelUnitName Model Parameters ms mu ks cs kt u(t) xu xs Figure 5-5. Parameters for quarter-car vehicle model.
46 A simple generic linear numerical quarter-vehicle model was developed to compute the vertical vibration level of typi- cal vehicle types from different pavement profiles at constant speeds. This numerical model, developed with the Matlab/ SimulinkÂ® programming environment, effectively computes the solution to the two-degrees-of-freedom system using the fixed-point method. The inputs to the model are the longitu- dinal pavement profile and the velocity of the vehicle. Vehicle Fatigue Damage Analysis Minerâs linear accumulation hypothesis was used to esti- mate the total fatigue damage caused by a given load sequence: D Ni i = â 1 5 10( . ) where Ni is the number of cycles to failure at a given load level i. For a given sinusoidal load amplitude Ui, Ni can be obtained using Basquinâs relation: N C Ui i= â â1 5 11Î² ( . ) Usually, for vehicle components, the fatigue exponent b takes values between 3 and 8 (BogsjÃ¶, 2006). A typical b value for steel suspensions can be obtained using the âhalf- lifeâ rule. This rule states that the half life of a steel compo- nent will be approximated by a 10% to 12% increase in cyclic load amplitude (Fuchs and Stephens, 1980). Applying this to Basquinâs relation gives a b value for steel suspensions of 6.3 (Kouta, 1994; BogsjÃ¶, 2006; and Abdullah et al., 2004). Since loads caused by road roughness fluctuate randomly, it is necessary to extract cycles from the load sequence to assess the fatigue damage. The rainflow counting method introduced by Matsuishi and Endo (1968) was used for this purpose: The load sequence on the sprung mass of the vehicle model is rain- flow counted to extract the load cycles Ui. The definition of the rainflow counting method was given by Rychlik (1987) and adopted in ASTM E 1049-85R05, âStandard Practices for Cycle Counting in Fatigue Analysis.â Therefore, the total fatigue damage caused by the rainflow-counted load sequence is: D C Ui i = â Î² ( . )5 12 where Ui = Mi - miRFC. Suspension Failure Threshold Vehicle owners tend to replace their suspensions at about 160,000 km (100,000 mi) for cars and 400,000 km (250,000 mi) for trucks (Repair Pal, 2009). This value was also reported as the lifetime warranty for suspensions given by vehicle manufacturers in the United States. Consequently, in this study, the average life of car and truck suspensions for typical driving conditions was assumed to be about 160,000 km (100,000 mi) and 400,000 km (250,000 mi), respectively. Vehicle suspensions are generally replaced when certain signs of wear become evident to compromise the safety and comfort of drivers. The amount of service life used up to that point was estimated using the following procedure: 1. Estimate the roughness (IRI) distribution of US roads (Figure 5-6), in the range of 1 m/km (63.4 in./mi) for a smooth road to 6 m/km for a very rough road. The prob- ability density distribution presented in Figure 5-6 was generated using the data reported by the FHWA (2008); 2. Generate 30 road surface profiles for each of the IRI values; 3. Calculate the accumulated damage (DIRI ij ) induced by each of the road profiles generated in Step 2 for a length of 1.6 km (1 mi) and assuming a value of 6.3 for b in Equa- tion 5.12; 4. Take the average value of the accumulated damage calcu- lated for each profile set having the same IRI level. 5. Estimate the number of kilometers per IRI (LiIRI) value using the distribution obtained in Step 1 and assuming that these vehicles are driven for 160,000 km (100,000 mi) and 400,000 km (250,000 mi) for cars and trucks respectively. 6. Compute the total accumulated damage using Equa- tion 5.13: D D Lreplace IRI ij j IRI i i = Ã ï£« ï£ ï£¬ï£¬ï£¬ï£¬ ï£¶ ï£¸ ï£·ï£·ï£·ï£· = = â 1 30 301 5 13 N â ( . ) For example, using the above procedure, the value for Dreplace is about 87.3% at 112 km/h (70 mph) for cars and 62.2% at 96 km/h (60 mph) for trucks. 1 m/km = 63.4 in./mi Source: FHWA (2008) Probability Density Function Cumulative Distribution 13.6 20.2 29.1 14.5 8.7 4.3 3.1 2.5 2.3 1.7 0 20 40 60 80 100 0 10 20 30 40 1 1.5 2 2.5 3 3.5 4 4.5 5 >5 Pe rc en ta ge ( % ) IRI (m/km) C um ul at iv e Pe rc en ta ge ( % ) Figure 5-6. Road surface roughness distribution in the United States.
47 Suspension Damage in Cars Figure 5-7 shows the damage accumulated in car suspen- sions after 160,000 km (100,000 mi) on a road with a given (constant) IRI value. This damage is obtained by multiplying the damage calculated in Step 3 (for cars) by 160,000. The error bars show the error in accumulated damage caused by the variations in the profiles; i.e., different profiles will gen- erate different suspension vibrations (even though they may have the same IRI). Many car manufacturers design their vehicles for the 90th to 95th percentile road roughness (Poelman and Weir, 1992). Figure 5-6 shows that 3.9 m/km (247.3 in./mi) is the 93rd per- centile of the roughness distribution in the United States. Fig- ure 5-7 shows that a car driven for 160,000 km (100,000 mi) on a road with IRI = 3.9 m/km would accumulate suspen- sion damage of about 84.5%, which is very close to the value obtained from Equation 5.13 (87.3%). This confirms the rea- sonableness of the value for b used in the analysis. Road profiles from in-service pavements were used to check the accuracy of the approach for estimating car suspension damage. Table 5-5 summarizes the pavement conditions of the different sections used in this study. Figure 5-8 shows the accu- mulated suspension damage for cars induced by actual and artificially generated profiles at each roughness level. These data show that the results from actual profiles follow the gen- eral trend of the curve generated using artificial profiles (with limited scatter). This variance is caused by the actual content of the profiles. For example, the two profiles highlighted in Fig- ure 5-8 (Profiles 3 and 6) have an IRI of 2.4 m/km (152 in./mi); however, Profile 3 causes more damage than Profile 6. Accord- ing to Table 5-5, Profile 3 has deteriorated joints while Profile 6 has only low severity faulting and curling. The additional cost induced by roughness features when the accumulated damage reaches Dreplace was assumed to be equal to the price of a new suspension and the labor hours for replacement. This value is equal to $1,000 according to Repair Pal (2009). The repair and maintenance cost for 1 m/km = 63.4 in./mi 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.2 0.4 0.6 0.8 1 IRI (m/km) A cc um ul at ed d am ag e Figure 5-7. Accumulated damage in car suspensions after 160,000 km (100,000 mi) as a function of IRI at 112 km/h (70 mph) using the mechanisticâempirical approach. Road Summary Information I-69 I-69 I-69 I-69 LTPP 20-0201 I-69 M-99S M-99N Creyts Rd Waverly Rd LTPP 20-0101 Pavement type PCC PCC PCC PCC PCC PCC PCC AC AC AC AC Length (km) 0.64 0.93 0.93 1.4 0.15 4.8 6.4 9.4 2.5 1.3 0.15 IRI range (m/km) 1.7-3.2 1.3-1.8 1.6-2.8 2.7-4.1 1.9 1.1-2.5 1.5-2.6 0.8-4.6 1.3-8.5 3.3-6 1.5 Faulting Counts Low 199 124 57 150 33 56 205 â Not applicable Medium 16 4 12 48 1 0 1 â High 1 0 0 0 0 0 0 â Highest magnitude (mm) 25.4 14.2 9.7 13.7 14 2.2 4.1 â Lowest magnitude (mm) â3.4 â2.8 â3.8 â10.9 1 â3.5 â6.8 â Deteriorated joints Counts â â 1 2 â â â Height differential (mm) â â â5.3 â13.9 â â â Width (m) â â 0.14 0.5 â â â Curling Counts 57 57 â â â 260 â â Highest magnitude (mm) 4.5 2.3 â â â 4.5 â â Potholes* Counts N/A N/A N/A N/A N/A N/A N/A 3 13 6 0 Highest magnitude (mm) N/A N/A N/A N/A N/A N/A N/A â8.3 â22.4 â10.2 â 1 mi = 1.6km; 1 in./mi = 0.0157 m/km; 1 in = 25.4 mm; 1 ft = 0.3 m * AC pavement distresses Table 5-5. Summary surface conditions for in-service pavements used in the analysis.
48 a given IRI level is calculated by dividing the accumulated damage corresponding to that IRI value (see Figure 5-7) by Dreplace and multiplying the result by $1,000. Suspension Damage in Trucks Figure 5-9 shows the truck suspension damage resulting from driving 400,000 km (250,000 mi) on a road with a given (constant) IRI value. This damage is obtained by multiplying the damage induced by each of the road profiles generated for a given IRI value (for trucks) for a length of 1.6 km (1 mi) by 400,000. The error bars show the accumulated damage caused by the variations in the profiles (i.e., different profiles will generate different suspension vibrations although they may have the same IRI). Trucks are generally designed for the 80th to 95th per- centile road roughness. Figure 5-6 shows that 3.2 m/km (203 in./mi) is the 87th percentile of the roughness distribu- tion in the United States. Figure 5-9 shows that a truck driven on 400,000 km (250,000 mi) of road with IRI = 3.2 m/km will accumulate suspension damage of about 66%. This value is very close to the value obtained from Equation 5.16 (62.2%) confirming the reasonableness of the value for b used in the analysis. The additional cost caused by roughness features when the accumulated damage reaches Dreplace was assumed to be equal to the price of a new suspension plus the required labor hours for replacement. The total cost was estimated to be $3,000 and $1,800 for air and steel suspensions, respectively. The repair and maintenance cost for a given IRI level is calculated by dividing the accumulated damage corresponding to that IRI value (see Figure 5-9) by Dreplace and multiplying the result by the replacement cost. Actual road profiles were also used to check the accuracy of the approach for estimating truck suspension damage. Figure 5-10 shows the accumulated suspension damage for trucks caused by actual and artificially generated profiles at each roughness level. Similar observations can be made (i.e., the results from actual profiles follow the general trend of the curve generated using artificial profiles with limited scatter). Mechanistic versus Empirical Approach Figures 5-11 and 5-12 show the results from (1) the mechanisticâempirical (M-E) approach using actual profiles from the Michigan road network and the Long Term Pave- ment Performance (LTPP) database, (2) the mechanisticâ 1 m/km = 63.4 in./mi 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.2 0.4 0.6 0.8 1 IRI (m/km) A cc um ul at ed d am ag e Artificial profiles Actual profiles Profile 3 Profile 6 Figure 5-8. Accumulated car suspension damage from actual and artificial pavement surface profiles. 1 m/km = 63.4 in./mi 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 IRI (m/km) A cc um ul at ed d am ag e 96 km/h (60 mph) Figure 5-9. Effect of road surface roughness on truck suspension after 400,000 km (250,000 mi) using the mechanisticâempirical approach. 1 m/km = 63.4 in./mi 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 IRI (m/km) A cc um ul at ed d am ag e Artificial profiles Actual profiles Figure 5-10. Accumulated truck suspension damage from actual pavement surface profiles.
49 empirical approach using artificially generated profiles, and (3) the empirical approach (i.e., updated TRDF study) for cars and trucks, respectively. The results show that the accumulated damage computed using actual profiles follows the curve generated for artificial profiles with limited scat- ter. The variance is caused by the difference in actual profile roughness contents. While roughness effects below 3 m/km are minimal, a constant repair and maintenance cost, which corresponds to other routine maintenance costs that are not related to roughness is still observed. Therefore, the curves were shifted upward from the mechanisticâempirical analysis to match the empirical curves in the IRI range below 3 m/km (190 in./mi). The results from the mechanisticâempirical approach compare very well with the empirical data up to an IRI of 5 m/km (317 in./mi), with a standard error of about 2%. Since the typical IRI range in the United States is 1 to 1 m/km = 63.4 in./mi; 1 mi = 1.6 km Figure 5-11. Car repair and maintenance costs. 1 m/km = 63.4 in./mi Figure 5-12. Truck repair and maintenance costs. 5 m/km, these results are appropriate for pavement manage- ment at the network level. However, at the project level, the effect of roughness features should be considered. Effect of Roughness on Repair and Maintenance Costs Figure 5-13 presents the change in repair and maintenance as a function of IRI. It should be noted that the mechanisticâ empirical approach only estimates the effect of roughness on passenger cars and articulated trucks. The updated TRDF study was used to estimate the effect for the other vehicle classes (i.e., SUV, van, and light truck). The figure indicates the following: â¢ The effect of roughness on repair and maintenance costs increases as speed increases. â¢ Roughness affects light trucks and SUVs more than articu- lated trucks and passenger cars. Summary In this chapter, two different approaches for estimating repair and maintenance costs induced by pavement rough- ness were proposed: (1) An empirical approach that uses the updated TRDF study (Zaniewski et al., 1982) and adjustment factors (Table 5-4) and (2) a mechanisticâempirical approach to conduct fatigue damage analysis using numerical model- ing of vehicle vibration response. The results from the mechanisticâempirical approach and the empirical results (i.e., updated Zaniewskiâs tables) were found to be very similar for up to an IRI of 5 m/km, with a standard error of about 2%. Because the typical IRI range in the United States is between 1 and 5 m/km, this approach 1 m/km = 63.4 in./mi 1 1.2 1.4 1.6 1.8 2 2.2 2.4 1 2 3 4 5 6 A d ju st m en t f ac to rs IRI (m/km) Medium car and Van SUV Light truck Articulated truck Figure 5-13. Effect of roughness on repair and maintenance costs.
50 seems applicable to US conditions. All the models currently in use are empirical in nature, except for the VETO model, which is reported to yield predictions that are much higher than the actual costs observed in Sweden. Table 5-6 summa- rizes the change in repair and maintenance costs per kilo- meter for all vehicle classes due to change in IRI from the baseline condition of IRI = 1 m/km (63.4 in./mi). The developed model is a combination of the mechanisticâ empirical approach and the updated TRDF study. The mechanisticâempirical approach to estimate the effect of Speed Vehicle Class Average Repair and Maintenance Cost * ($/km) Average Repair and Maintenance Cost * ($/mi) Baseline Conditions ($/km) Baseline Conditions ($/mi) Adjustment Factors from the Baseline Conditions IRI (m/km) 1 2 3 4 5 6 56 km/h (35 mph) Medium car 0.040 0.064 0.015 0.024 1.0 1.0 1.1 1.4 1.7 Van 0.052 0.083 0.020 0.032 1.0 1.0 1.1 1.4 1.7 SUV 0.052 0.083 0.020 0.032 1.0 1.0 1.2 1.7 2.3 Light truck 0.058 0.092 0.021 0.034 1.0 1.0 1.2 1.7 2.2 Articulated truck 0.124 0.199 0.046 0.074 1.0 1.0 1.1 1.5 1.8 88 km/h (55 mph) Medium car 0.040 0.064 0.019 0.030 1.0 1.0 1.1 1.4 1.7 Van 0.052 0.083 0.025 0.040 1.0 1.0 1.1 1.4 1.7 SUV 0.052 0.083 0.025 0.040 1.0 1.0 1.2 1.7 2.3 Light truck 0.058 0.092 0.029 0.046 1.0 1.0 1.2 1.7 2.2 Articulated truck 0.124 0.199 0.063 0.101 1.0 1.0 1.1 1.5 1.8 112 km/h (70 mph) Medium car 0.040 0.064 0.023 0.036 1.0 1.0 1.1 1.4 1.7 Van 0.052 0.083 0.030 0.047 1.0 1.0 1.1 1.4 1.7 SUV 0.052 0.083 0.030 0.047 1.0 1.0 1.2 1.7 2.3 Light truck 0.058 0.092 0.035 0.057 1.0 1.0 1.2 1.7 2.2 Articulated truck 0.124 0.199 0.077 0.123 1.0 1.0 1.1 1.5 1.8 1 m/km = 63.4 in./mi * These costs were obtained by converting the average costs in Table 5-4 to $/km and $/mi and are unit repair costs related only to damage from vibrations. Table 5-6. Effect of roughness on repair and maintenance costs. pavement conditions on repair and maintenance costs only involves passenger cars and articulated trucks. Then, it uses the results from the 1982 TRDF study by Zaniewski et al. to estimate the costs for the other vehicle classes. The model is expected to provide better estimates of repair and mainte- nance costs at the project and network levels. For project-level analysis, the actual road profile should be used to take into account the effect of roughness features. To facilitate use of the developed model, a computer program (provided on the accompanying CD-ROM) has been prepared.