Ratios of Pavement Damage to User Fees

Transcription

1 TRANSPORTATON RESEARCH RECORD Ratios of Pavement Damage to User Fees ROBERT NCHOLLS An important decision that state legi latres are charged with i the apporlionment of highway ser fees among the varios weight classes of vehicles. Departments of transportation m t provide spporting and convincing data for these legislative decisions. Crrently, the most rational basis for setting ser fees is the prediction of pavement damage by sing the AASHTO 1986 pavement design eqations. Axle load eqivalency charts are prepared from the AASHTO 1986 De ign Manal eqations for determining the damage to rigid and flexible pavement by single-, tandem-, and triple-axle load from 2 to 90 kip. Tables present the ratios of pavement damage (according to 1 hese eqations) to road ser charges for different classes of vehicles in two states having among the lower and higher road ser fee in the contry. The method for compting ratio of pavement damage to ser fees for these two states provides a fa. t and convenient means for all states to evalate and adjst their road ser fees for each class of vehicle. Heavy axle loads shorten pavement life. n order to allocate ser fees, load effects mst be qantified. This paper addresses the qestion: "Are road ser revenes proportioned eqitably among varios weights of vehicles according to the pavement damage which they case?" Axle load eqivalency charts are prepared from the AASHTO 1986 Design Manal (1) eqations that relate the damage to rigid and flexible pavements by single-, tandem-, and triple-axle loads from 2 to 90 kips. Tables compare the ratios of pavement damage, according to these eqations, to road ser charges for different classes of vehicles in two states having among the lower and higher road ser fees in the contry. AASHO ROAD TEST EQUVALENCY FACTOR EQUATONS The AASHO Road Test eqivalency factor eqations (2) were extended by the AASHTO 1986 Design Manal, Appendix MM (J), to inclde the following: 1. Single-axle, maximm load to 50 kips; 2. Tandem-axle, maximm load to 90 kips; 3. Triple-axle, maximm load to 0 kips; 4. Eqivalency factors for terminal serviceability index (p,) between 2 and 3; and 5. Rigid pavements-eqivalency factors for slabs p to 14 in. thick. For flexible pavements, these eqations are log (W:) = log (Lx + L1) w,18 G, log L 2 + f3x (1) Civil Engineering Department, University of Delaware, Newark, Del _ l p, G, - og (L.. + L.J 3 't3 f3x = (SN + 1) s. 1 9L.23 where w,x = total nmber of applications of a given axle load x; w, 18 = eqivalent nmber of applications of the standard 18-kip axle load; Lx = load on one single, tandem, or triple axle (kips); L 2 = axle code (1, 2, or 3 for single, tandem, or triple axle, respectively); SN = strctral nmber; p, = terminal serviceability index, which relates varios indicators of pavement distress to overall srface qality; and f3 18 = vale of f3x when Lx is eqal to 18 and L 2 is eqal to 1. For rigid pavements, the eqations are w log ---E... = log (Lx + L 2 ) w,18 = p, G ' og 2.7 where Dis the slab thickness (in.). For both flexible and rigid pavements, the eqation for translating w,x into w, 18 is w2 lx w,18 = ---1 w,x - According to AASHTO (2), there is considerably more ncertainty in extending the eqations to triple axles than in extending them to higher loads on single and tandem axles. AXLE LOAD EQUVALENCY CHARTS n order to permit rapid estimates of pavement damage by different vehicle classes, Eqations 1-7 were programmed in Fortran for preparing the load eqivalency charts shown in Figres la-lf. The program sorce code is given in the ap- (2) (3) (4) (5) (6) (7)

2 1oor (&) loor 1 _- (b) SN SN io r SN l SN 6..: 0...,..... = g o.1)- FLEXBLE PAVEMENT SNGLE AXE LOAD..: < "',..... = g... "'.... o. l f- FLEXBLE PAVEMENT TANDEM AXE LOAD - Terminal serviceability = 2, Strctral nmber 1 to 6 Terminal serviceability =- 3, Strctral nmber =- 1 to Terminal serviceability = 2, Strctral nmber = 1 to 6 Terminal serviceability = 3, Strctral nmber... 1 to 6. O Ol'--.._1"0'2oc_-3040so'--.ool... 20:----:40-60:----;::80!---, 0 0, (C) p t p t 3, SN 1 01 (d) 1 pt 2, D = p m 2, D = 3, D = 14 1 ' t - 3, D = 6" 3, SN 6..: ;:: t;... g "'... "' J o.r FLEXBLE PAVEMENT TRPLE AXE LOAD..: < "',..... = g... "' RGD PAVEMENT SNGLE AXE LOAD Terminal serviceability = 2, Strctral nmber = l to 6 Terminal serviceability = 3, Strctral nmber = l to 6,01 Terminal serviceability.,. 2, Thickness = 6 to 14 inches Terminal serviceability = 3, Thickness = 6 to 14 inches O Ol_.,, BOlOO.001 " "2b30--,4050 FGURE 1 (contined on next page)

3 Nicholls 1,., fl... "' RGD PAVEMENT TANDEM AXLE LOAD Terminal serviceability 2, Thickness 6 to 14 inches Teripinal serviceability 3, Thickness 6 to 14 inches ooi ' :--- iol _.'--, ' , FGURE 1 Axle load eqivalency factors: (a) single-, (b) tandem-, and (c) triple-axle loads on flexible pavements; and (d) single-, (e) tandem-, and (f) triple-axle loads on rigid pavements. pendix. Figres la-le show the ratio between the nmber of axle loads and the nmber of 18-kip single-axle loads that do eqivalent damage to a flexible pavement as a fnction of axle load for single, tandem, and triple loadings for pavements having SN between 1 and 6. Figres ld-lf show the ratio between nmber of axle loads and nmber of 18-kip singleaxle loads that do eqivalent damage to a rigid pavement as a fnction of axle load for single, tandem, and triple loadings for D between 6 and 14 in. The following examples illstrate se of the eqivalency charts. Example 1 How many passes of a 30-kip single-axle load case the same damage as 1,000 passes of an 18-kip single-axle load on a flexible pavement having SN of 4 and p, of 2? Soltion nterpolating Figre la for single-axle loads on a flexible pavement with Lx = 30 kips, SN = 4, and p, = 2, yields w,)w, 18 =.1. 1,000/.1 = 99 passes. Example 2 How many passes of a 50-kip tandem-axle load case the same damage as 1,000 passes of an 18-kip single-axle load on a - in. rigid (concrete) pavement having a terminal serviceability of 2.5? Soltion nterpolating Figre le for tandem-axle loads on rigid pavements with Lx = 50 kips, D = in., and p, = 2.5, yields w,)w, 18 = ,000/9.5 = 5 passes. The AASHTO (1) measre of pavement qality is the present serviceability index (PS), a composite nmber that relates varios indicators of pavement distress to overall srface qality. Pavement distress appears as roghness, rtting, cracking, falting, blowps, potholes, etc. The distress indicators possess a degree of objectivity, bt the overall rating is necessarily sbjective. For simplicity, the AASHTO 86 design method assmes that an eqivalent single-axle load (ESAL) of 18 kips cases a nit damage to pavement and a nit redction in srface qality, both of which are constant over the pavement life (J).

4 280 Example 3 This example (3) illstrates how changes in gross vehicle weight (GVW), weight distribtion, and axle arrangement affect pavement life. A 60-kip tractor-semitrailer is sed for the base case. This vehicle is a type that can be replaced by a twin-trailer trck. Assmed design vales for the AASHTO load-eqivalency factors are p, = 2.5, D = 9 in., and SN = Base Case of 60-kip Tractor-Semitrailer (Figre 2a). Pavement Type Flexible Rigid ESALs by Axle or Axle Grop 1 Single Tandem Tandem Total Base pls 6 kips, with weight distribtion between front and rear tandem axles nchanged, adjsted for 9 percent fewer trips (Figre 2b ). Becase of the higher payload, the vehicle will reqire 0.91 as many vehicle-miles to deliver the same load as the lighter trck. ESALs by Axle or Axle Grop Pavement 2 3 Total Above Type Single Tandem Tandem x 91% Base Flexible Rigid Base case with twin-trailer trck axle arrangement, GVW and weight distribtion nchanged (Figre 2c). Assme that the axle arrangement is changed to five single axles, the sal twin-trailer trck arrangement. ESALs by A r/p nr A rlp r.rnp Pavement Above Type Single Single Single Single Single Total Base Flexible Rigid om Effect of combination of higher weight, less niform weight distribtion, and different axle arrangement, adjsted for 9 percent fewer trips (Figre 2d). ESALs by Axle or Axle Grop Pavement Total Above Type Single Single Single Single Single x 91% Base Flexible Rigid , n this case, the cmlative effect of higher weight, less niform weight distribtion, and a different axle arrangement is greater than the sm of the individal changes. This reslt occrs becase changes to weight distribtion and axle arrangement alter the incremental impact of the added 6 kips of weight as well as the impact of the original 60 kips. Also, dividing a tandem axle nevenly between the two single axles to match typical weight distribtions of twins increases the effect on pavement wear. Table 1 presents the for-axle loading effects. (a} (b) (c) 01 (d) 6J TRANSPORTATON RESEARCH RECORD 1311 bj 1 -:op kips bj -oo.o.o ' t kips 11 o-o o-o 0, t kips -o o-o 0 ' ' kips FGURE 2 Axle arrangements and weights (3). OBSERVATONS REGARDNG LOAD EQUV ALENCES Effects of Axle Weight, Pavement Thickness, and Terminal Serviceability ndex The AASHTO 86 (1) eqations indicate that load eqivalency factors increase approximately with the forth power of axle load. For example, the load eqivalency on rigid pavement fr a 12-kip la is 0.19, wht:rt:as fr a 20-kip axle it is 1.51 (Figre ld). Ths the 20-kip load is 8 times as damaging as the 12-kip load, i.e. (20/12)4, and shold argably pay approximately 8 times as mch per vehicle-mile in highway revene. The power term varies only slightly with strctral nmber (SN), pavement thickness (D), and terminal serviceability index (p,) (Figres la to lf). State Revenes State road-ser taxes are of three major types, the most important being fel taxes and fees incidental to fel taxes. The second type, motor vehicle revenes, consists of motor vehicle registration and related fees, some of which are not paid annally, e.g., title fees and drivers' license fees. The third type incldes vehicle-mile, ton-mile, and axle-mile taxes. The assignment of pavement costs has a major effect on the overall cost assignments to different vehicle classes. Not only is pavement cost the largest component of highway dollars, there is a greater variation in the relative cost responsibilities of vehicles of different weights than for any other component of highway costs. FHW A ( 4) gives 1987 road ser taxes and property taxes levied on vehicles of varios weights by each state to provide a planning tool for highway administrators and legislators concerned with highway ser fees. A

5 Nicholls 281 TABLE 1 SUMMARY OF FOUR-AXLE LOADNG EFFECTS (3) Case kip tractor-semitrailer kip semi, 9% fewer trips kip twin kip twin, 9% fewer trips Flexible Pavement Total ESALs ncrease Over Base Rigid Pavement Total ESALs ncrease Over Base total of 14 vehicles were sed to illstrate the range and magnitde of state taxes (Figre 3): 3 passenger cars, 5 singlenit trcks, 5 vehicle combinations, and 1 motorcycle ( 4). The federal taxes on gasoline, vehicles, and tires were exclded, as was the annal se tax on vehicles over 55,000 lb gross weight. These are niform throghot the nation and wold not affect comparisons among states. Local taxes other than property taxes were also exclded; the registration fees and motor fel taxes imposed by conties and cities were beyond the scope of the stdy ( 4). n order to avoid the complex sitations that wold be encontered in compting taxes on vehicles in nterstate op- Lightweight PaB&enger Car 4 s A 2 3 Medimweight Paeeengar Car 6 7 Gl Heavyweight Passenger Car vs 5000-Pond 14,000-Pond Gasoline- 24,000-Pond Gesolina- 24,000-Pond Diesel- Piclr.p Trck Powered Stake Trck Powered Van Trck Powered Van Trck ,000-Pond Diesel-Powered 40,000-Pond Diesel-Powered 3-Axle Dmp Trck 3-All:le Tractor-Semitrailer 60,000-Pond Diesel-Powered 4-Axle Tractor-Semitrailer 11 80,000-Pond Diesel-Powered 5-Axle Tractor-Semitrailer 12 80,000-Pond Diesel-Powered 5-Axle Tractor-Semitrailer and Fll Trailer 13 80,000-Pond Diesel-Powered 5-Axla Trck and Fll Trailer -14!lotorcycle FGURE 3 Vehicle classifications for a state revene stdy (4).

6 (a)!iew YORK NEW JERSEY OREGON FLORDA NEW MEXCO OHJO DELAWARE MARYLAND L-OU1SANA SOUTH DAKOTA VERMONt TENNESSEE DAHO AL\Sl<.A HAllA LLNOS llsconsn P E'NSYLV ANA :>ORTH DAKOTA DST. OF COL. MCHGAN ALABAMA TEXAS MSSOUR MASSACHUSETTS KENl'UCKY OKLAHOMA ARKANSAS l<yohwc e... CALEORNA Ol 'A :::::::: NORTit CAROLNA NEVADA GEORGA WEST MNhSOTA VRGNA MONANA SOUTl: CAROLNA COLORADO MANE UTA!! NEBRASKA NDA. NEW HAMPSHRE ARlZONA llashlngton MSS SSPP VRGNA KANSAS CONNECTCUT RHODE ls.l\nd DOLLARS LEGEND: - REGSTRATON ETC GASOLNE TAX OlJPROPERTY TAX LEGEND: - REGSTRATON ETC GASOLNE TAX lj)property TAX (b) ALABAMA ALASKA HAWA DELAWARE E, OKLAHOMA WYOMNG NEW JERSEY MCHGAN FLORDA NEW YORK MARYLAND LOUSANA TEXAS NORTH DAKOTA GEORGA DST. OF COL. MASSACHUSETTS TENNESSEE VERMONT MSSOUR SOUTH DAKOTA CALFORNA MNNESOTA NORTH CAROLNA ARKANSAS PENNSYLVANA UTA!! SOUTH CAROLNA KENTUCKY WEST VRGNA MANE NEW HAMPSHRE NEW MEXCO WSCONSN OWA OHO NEBRASKA KANSAS VRGNA LLNOS MSSSSPP WASHNGTON ONTANA NEVADA DAHO RHODE SLAND NDANA CONNECTCUT COLORADO OREGON ARZONA FGURE 4 State road-ser and property taxes: (a) on a medim passenger car (No. 2), (b) on an 80,000-lb diesel five-axle tractor-semitrailer and fll trailer combination (No. 12) in private se (4) THOUSANDS OF DOLLARS

7 Nicholls 283 eration, intrastate operation was specified. Withot this stiplation, the stdy wold have needed to (a) inclde the additional taxes and fees applicable only to nterstate carriers, and (b) consider an almost infinite variety of circmstances, inclding varios state reciprocity and proration agreements. Althogh property taxes on motor vehicles have no direct relation to the amont of highway se and in most states are not available for highways, they are closely related to registration fees and make p sch a large portion of the total taxes on motor vehicles in some states that they were inclded in Figre 4 to obtain eqitable comparisons ( 4). Examples of Road-User Revene Assessments This section explores the qestion: "How eqitably are road ser revenes in two states, Delaware and Ariona, representing low and high total road-ser fees, proportioned among the varios weights of vehicles according to the pavement damage which they case?" By dividing Delaware's and Ariona's total ser revenes provided by FHWA (4), for each class of vehicle by the vehicle-miles per year from Table 1, sed for estimating this revene, then dividing the reslt by the ESAL for that vehicle class, the ratios of pavement damage cost to serfee presented in the right-hand colmns of Tables 2 and 3, for Delaware and Ariona, respectively, are obtained. Tables 2 and 3 relate to only pavement damage cost, throgh the ESAL ratings. They do not inclde other highway costs, sch as ser costs, congestion delay, air polltion, noise, highway administration, etc. Notice that the interpretation of the right colmn of Table 2, for Vehicle Class 9, for example, is not that it shold pay 846 times as mch per mile as Vehicle Class 1 pays, to eqalie fees for pavement damages, bt that it shold pay 846 times what it presently pays if fees for Vehicle Class 1 remained the same. The effect of overload provisions in state laws may also be of interest. Althogh Table 2 presents three-axle trcks (Vehicle Class 8) carrying 50 kips, a provision in Delaware law, for example, permits p to 70 kips for three-axle trcks carrying constrction or agricltral prodcts, for an additional fee of $0 per year. This allowance for added weight at the added cost increases the ratio presented in the right-hand colmn of Table 2 for Vehicle Class 8 from 2,035 to 2,035(.0 ESAL/3.7)($806/$906) = 4,893. CONCLUSONS The right-hand colmns of Tables 2 and 3 present the large disparities between ratios of vehicle ESALs to ser fees per vehicle-mile among the 14 vehicle weight classes in the two states, ranging from 0.24 to 3,078 in Delaware and from 0.15 to 1, 713 in Ariona. On the basis of the AASHTO design eqations, Vehicle Class 7 in Table 3, for example, shold pay 408 times what it now pays in road ser fees in order to pay its share of pavement damage cost eqivalent to that of Vehicle Class 1. This method of pavement damage costing, together with the other components of highway costing (congestion, polltion, etc.) and jdgments regarding the val- es of services provided by the varios classes of vehicles, can be sed by state legislatres to assess highway ser fees. ACKNOWLEDGMENT This stdy was condcted for the Delaware Department of Transportation. David Matsen was the project coordinator. REFERENCES 1. AASHTO Gide for Design of Pavement Strctres, Vol. 2. AASHTO, Washington, D.C., AASHTO nterim Gide for Design of Pavement Strctres. AASHTO, Washington, D.C., 1972 (Chapter revised, 1981). 3. Special Report 211: Twin Trailer Trcks: Effects on Highways and Highway Safety. TRB, National Research Concil, Washington, D.C., Road User and Property Taxes on Selected Motor Vehicles. FHW A, U.S. Department of Transportation, APPENDX FORTRAN SOURCE CODE FOR EQUATONS 1-7 REM Axle load eqivalency factors REM Program in two parts. Fnctl is the first three graphs, REM sing Eq. 1. Fnct2 is the second three REM graphs, sing Eq. 2. REM LlO - log base fnction DEF FNLlO(nmber) = LOG(nmber)/LOG(lO) REM NV - inverse log base DEF FNNV(nmber) = lo'nmber REM Wl,W2,W3 dmmy variables (simplify steps) M = 19 :REM part of Wl. Made it easier to keep track. Fnctl: For L2 = 1 to 3 : REM cycle graphs 1 to 3 Lprint"Eq. 1 Graph L2 =";L2:LPRNT REM loop for reading three PT and SN vales for each graph (Eq 1) FOR = 1 to 3 READ PT() NEXT FOR = 1 to 3 READ SN() NEXT REM loop for six LX vales (each line) FOR - 1 to 6 READ LX() NEXT REM begin data analysis FORK = 1 to 3 :REM loop for PT GTl = (4.2-PT(K))/( ) GT = FNLlO(GT) FOR J = 1 to 3 :REM Loop for SN

8 TABLE 2 ESTMATED RATOS OF PAVEMENT DAMAGE COSTS TO USER FEES ON THE BASS OF FHWA (4) VEHCLE USER FEES AND MLEAGE DATA FOR DELAWARE Ratio, (a) (b) with Vehicle DE total Vehicle cl.all \S!']'. foe milil 1 User fee Axle loads, Vehicle per vm k!p.i 2 Ratio Glass , , , ,T , ,17.14, T ,2T , ,T35.54, / n Vehicle miles (vm) in thosands T stands for tandem xle. For all 14 vehicle classes, gross weight is assmed to be carried eqally by all tires, i.e. single axles with for tires carry cwice the weight of single. axles with two tires, etc. This assmption nder-estimates the pavement damage done by vehicles with nbalanced loads. ESALs from Figs. serviceability of ld and le for in. rigid pavement with terminal ESALs will differ somewhat for flexible pavements. TABLE 3 ESTMATED RATOS OF PAVEMENT DAMAGE COSTS TO USER FEES ON THE BASS OF FHWA (4) VEHCLE USER FEES AND MLEAGE DATA FOR ARZONA (a) (b) Vehicle AR total Vehicle User fee Axle lo&ds, v ehicle Ratio ser fee mil.ll Ratio, with Glass , , , ,T , ,17.14, 2.96 T ,2T , ,T35.54, l

9 Nicholls B18 =.4 + (.081 *(19)'(3.23))/(SN(J) + 1)'(5.19) LPRNT'LinePT,SN : 11 ;PT(K) 11, 11 SN(J):LPRNT:LPRNT LPRNT LX Wtx/Wt18 11 :LPRNT FOR = 1to6 :REM loop for LX BX =.4 + (0.81 *(LX() + L2)'(3.23))/ ((SN(J) + 1Y(5.19)*L2'(3.23)) Wl =FNL(M)*4.79 W2=FNL(LX() + L2)*4.79 W3 + FNL(L2)*4.33 logdpoint = Wl-W2+ W3+GT/BX-GT/B18 Dpoint = FNNV(logDpoint) LPRNT ;LX() Dpoint NEXT :REM Cycle to next point LX LPRNT:LPRNT:LPRNT NEXT J:REM cycle to next SN NEXT K:REM Cycle to next PT NEXTL2 Fnct2: For L2 = 1 to 3 : REM Cycle graphs 4 to 6 LPRNT 11 Eq. 2 Graph L2 = 11 ;L2:LPRNT REM Loops for reading three PT and D vales for each graph (Eq 2) FOR = 1to3 READ PT() NEXT FOR = 1 to 3 READ D() NEXT REM Loop for six LX vales (each line) FOR = 1to6 READ LX() NEXT REM Begin data analysis FORK = 1 to 3 :REM Loop for PT GTl = (4.5-PT(K))/( ) GT = FNLlO(GTl) FOR J = 1 to 3 :REM Loop for D B18 = 1 + (3.63*(19)'(5.2))/(D(J) + 1)'(8.46) LPRNT'LinePT,D : 11 ;PT(K) 11 11, D(J):LPRNT:LPRNT LPRNT LX Wtx/Wt18 11 :LPRNT FOR = 1to6 :REM Loop for LX BX = 1 + (3.63*(LX() + L2Y(5.2))/((D(J) + 1Y(8.46)*L2'(3.52)) Wl = FNL(M)*4.62 W2 = FNLlO(LX() + L2)*4.62 W3 = FNL(L2)*3.28 logdpoint = Wl-W2+ W3+GT/BX-GT/B18 Dpoint = FNNV(logDpoint) LPRNT ;LX() Dpoint NEXT :REM Cycle to next point LX LPRNT:LPRNT:LPRNT NEXT J: REM Cycle to next D NEXT K:REM Cycle to next PT NEXTL2 REM PT(l,2,3),SN(l,2,3),LX(l,2,3,4,5,6) REM Graph 1, Eq. 1 DATA 2,2.5,3,2,4,6,2,5,l0,20,30,50 REM Graph 2, Eq. 1 DATA 2,2.5,3,2,4,6,,20,40,50,60,90 REM Graph 3, Eq. 1 DATA 2,2.5,3,2,4,6,20,40,50,60,80,0 REM PT(l,2,3),D(l,2,3),LX(l,2,3,4,5,6) REM Graph 4, Eq. 2 DATA 2,2.5,3,6,,14,2,5,,20,30,50 REM Graph 5, Eq. 2 DATA 2,2.5,3,6,,14,,20,40,50,60,90 REM Graph 6, Eq.2 DATA 2,2.5,3,6,,14,20,40,50,60,80,0 Pblication of this paper sponsored by Committee on Pavement Management Systems. 285