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APPENDIX E EFFECTS OF AXLE WEIGHT ENFORCEMENT ON PAVEMENT LIFE 1.0 INTRODUCTION . One of the basic premises of truck weight enforcement is that there will be a net increase in pavement life (reduction in the rate of pavement deterioration). The following discussion summarizes two methods of determining the increase in pavement life one could expect from reduced axle loadings accrued through enforcement activities. The methods makes use of an AASHTO design procedure (~) providing for the traffic input to design to be in terms of accumulated (or projected) ~ 8,000 Ib. equivalent single axle loads (ESALs). In their approach, AASHTO uses the definition: "Load equivalency factors represent the ratio of the number of repetitions of any axle load and axle configuration (single, tandem, tridem) necessary to cause the same reduction in Present Serviceability Index (PSI) as one application of an ~ 8-km single axle load."(~. Thus, an axle load with an ~ 8-km equivalency of 2.5 could be considered to be 2.5 times more damaging than the ~ 8-km loading. The general approach, applied to both methods, is to determine the cumulative ESALs a given pavement is capable of sustaining before it's serviceability is reduced to an unacceptable level, ie, the design load capacity. Then, the traffic stream using that pavement is analyzed both before and after enforcement efforts are implemented to determine the effects of that enforcement on daily ESALs generated by the stream. Finally, the daily ESALs before and after enforcement are used to determine the estimated times (before and after enforcement) required to consume the load capacity. The first method discussed, an approximation method, probably is the most appropriate for We present NCHRP project as it is much easier to program and use and is in the spirit of the study where the goal, rather than focusing on the pavement design process, is to quantify what is accomplished by weight enforcement efforts. The method has a disadvantage in that it is unable to recognize the fact that most traffic streams have an inherent growth rate. Not dealing with that growth rate may result in significant errors with some traffic streams. ~ The contribution of Pavement Design Consultant, Ken McGhee, for this appendix is gratefully acknowledged. Appendix E
The second method, covered in Section 5 of this appendix, is theoretically more precise, but is much more difficult to apply as one needs a reasonably good grasp of the AASHTO pavement design process. The second method does deal with the expected growth rate of the Marc steam in question. 2.0 AN APPROXIMATION METHOD FOR DETERMINING THE EFFECTS OF AXLE WEIGHT ENFORCEMENT ON PAVEMENT LIFE 2.1 Introduction The method described here is designated as an approximation because it makes use of a means of approximating axle equivalencies. 2.2 Assumptions A. The analysis will be applied to a generic pavement that is defined as either a flexible pavement or a rigid! pavement. The user will have to specify which. It should be noted that, as shown below, for this approximation method the pavement thickness or structural number is not a factor. B. 2.3 Procedure Appendix E The fourth power rule will be used to calculate axle equivalency factors. (The rule states that the load equivalency factor increases approximately as a function of the ratio of any given axle load to the standard ~ 8-km single axle load raised to the fourth power.~(~) The approximation watt be reasonably accurate, but may be in error up to about 10% in estimated changes in pavement life expectancy as compared to the more precise method given in Section 5 of this appendix. One of the reasons the approximation method is likely to be somewhat in error is the inability of the method to account for growth in traffic volume throughout We life of the pavement. Estimate daily ESALs from axle weights measured or assumed prior to enforcement and after enforcement for the traffic stream in question. To do this, use the fourth power rule to calculate equivalencies. Then follow the procedure outlined in Section 4 of this appendix to calculate ESALs. This procedure will need to be gone through twice, once to determine the daily ESALs before enforcement (ESALb) and once for afterward (ESALa). Examples of using the 2
fourth power rule and of calculating daily ESALs for both rigid and flexible pavements are given in Sections 3 and 4, respectively. B. Estimate the effects on pavement life brought about by weight enforcement. A given pavement will have a design load capacity of We ESAL`s and many designers use a 30 year design life. However, real ESALs typically far exceed those used in the design. So, the concept, assuming a zero annual growth rate in traffic, is: I. Calculate the life expectancy before enforcement Cubs from: L`b = W~/(ESALb*365), . Equation (~) 2. Calculate the life expectancy after enforcement (L`a) from: L`a = W,~/(ESAL`a*365), . Equation (2) 3. Calculate the percentage increase ~ = 1 Anti ~ ~n . In life (it;) from: TV `~a - Abel fib. . Equation (3) Note, however, that Wl8 cancels out of Equation (3) so that the percentage increase in pavement life is also the percentage decrease in daily ESAL,s brought about by enforcement and cart be expressed as In = lOO*(ESALb - ESALa)/ESALb. Because the design was does cancel out of the equations to estimate the benefit of enforcement the only real chore when using the approximation method is in calculating We ~ 8- kip equivalencies and the average daily ESALs. It is important to recognize, however, that only relative increases in pavement life can be determined using the approx~nation method. Absolute values of pavement life and changes therein can be determined only through using the method outlined In Section 5 of this appendix.. 3.0 FOURTH POWER RULE OF CALCULATING AXLE EQUIVALENCIES The formidable equations and calculations (Section 5 of this appendix) used to develop theoretically correct 1 8 Kip axle equivalency factors have led to much interest in handy methods of estimating those factors given a minimum of information. Fortunately, there is a generally applicable rule of thumb: "The load equivalency factor increases approximately as a function of Me ratio of any given axle load to the standard ~ 8-km single axle load raised to the fourth 3 Appendix E
power.". For example, calculations and AASHTO tabulations show that a 28 Lip single axle load on a flexible pavement has ~ ~ Lip equivalency factors ranging from 3.93 to 7.54 depending upon the structural number and terminal serviceability of the pavement being analyzed. On the over hand, the estimated factor from the 4th power rule, independent of pavement structure and terminal serviceability, would be en = e~*~28/! 8~4 = ~ *5.86 = 5.86 where en is the ~ 8-km equivalency for a 28-kin single axle load on a flexible pavement. and el8 is the 18-km equivalency for an 18-km single axle load on a flexible pavement, i.e. el8= 1.0. In order to make full use of the fourth power rule in calculating equivalencies it is necessary to establish some bases for those calculations for tandem and truism loads and to reflect differences in ~ 8-km equivalencies relating to pavement type (rigid or flexible). Table E] below has been determined from AASHTO calculations and tabulations (~) to provide reasonable starting points for each axle configuration and pavement type. TABLE E - ~ BASES FOR ESTIMATION OF 1 8-km EQUIVALENCY FACTORS Flexible Rigid Axle Basic Equivalency Equiv. Configuration Load~kips! Factor Factor Single ~ ~ .00 ~ .00 Tandem 34 1.09 1.95 Traded 48 1.03 2.55 Using Table E! the ~ 8-km equivalency for any axle loading can be estimated through use of We fourth power rule. For example, a 50 Lip tandem axle on a flexible pavement would have an estimated ~ 8-km equivalency of e50 = e34*~50/3414 = 1.09*4.68 - 5. 10. Appendix E 4
AASHTO tabulations show a 50 Lip tandem axle load on a flexible pavement to have equivalencies ranging from 3.74 to 6.15. While most designers watt use the tabulated ~ 8-km equivalencies for pavement designs, it is well recognized that the fourth power rule may be close enough for many practical purposes given the uncertainties in estimating traffic characteristics including axle loads. Even when using the fourth power rule, however, pavement type (rigid or flexible) is important. Again, as an example a 50 kip tandem axle on a ngid pavement would have an equivalency much higher than above for a flexible pavement of approximately e50 = e34*~50/34)A4 = ~ .95*4.68 = 9. ~ 3. AASHTO tabulations show Mat the actual equivalency for a 50 kip tandem on a rigid pavement ranges from 7. ~ 7 to ~ 0.73 depending upon pavement thickness and terminal serviceability. Estimated equivalencies for other single, tandem, or tridem loads on both rigid and flexible pavements would be determined similarly using the factors given in Table E] as the bases for those estimates. REAPPLICATION OF THE FOURTH POWER RULE TO DETERMINATION OF DAILY 18-KIP EQUIVALENCIES (ESALs) FOR A TYPICAL TRAFFIC STREAM Table E-2 provides an example of determining the average daily ESALs for a typical traffic stream both before and after weight enforcement. In the procedure, single and tandem (tridem if present) axle load ranges for all axles in the traffic stream are provided. The fourth power rule is used to calculate the ~ 8-km equivalency for the m~-po~nt of each axle load range. For example, the ~2,000 - ~5,999 range has a mid-po~nt at 14-kips so the -Skip equivalency of the 14-km load is needed. As given in Section 3 of this appendix, the equivalency is calculated en = e~14/] 8~4 = ~ *.366 = 0.366. All other equivalencies in Table E-2 are calculated using the procedures given in Section 2 which follows and using the base values given in Table Eel. To calculate the daily ESAL contribution of each load class the number of axles in each class is multiplied by the ~ 8-km equivalency for that class. The sum of the contributions of all classes is the average daily ESAL`s for the traffic stream. Note in the example, that the daily ESALs before enforcement (ESALb) was 917 while after enforcement (ESALa) the total was 653. ~,, 5 Appendix E
Table E-2 FLEXIBLE PAVEMENT, 4th Power Rule ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM Single Axles | BEFORE ENFORCEMENT | AFTER ENFORCEMENT l Eqivalency No. Daity No. Daily Factor Axles ESALs Axles ESALs 0.006 18 0.108 18 0.108 0.03 12 0.36 10 0 3 0.095 370 35.15 260 24.7 0.366 40 14.64 30 10.98 1 300 300 320 320 2.23 42 93.66 6 13.38 O O 0.005 18 0.09 16 0.08 0.042 24 1.008 23 0.966 0.16 50 8 40 6.4 0.76 48 36.48 36 27.36 0.976 25 24.4 123 120.048 1.38 43 59.34 52 71.76 2.11 163 343.93 27 56.97 ~7 ~653.052 Axle Load Ranges 3000 - 6999 7000 - 7999 8000 - 1 1999 12,000- 15,999 16,000- 19,999 20,000 - 23,999 Tandem 6000 - 11 ,999 Axles 12,000- 17,999 18,000 - 23,999 30,000 - 31,999 32,000 - 33,999 34,000 - 37,999 38,000 - 41,999
As shown earlier, the percentage increase in pavement life is estimated to be Li = lOO*(ESALb - ESALa)/ESALb = 28.8%. Table E-3 is an example of the ESAL calculations for a rigid pavement assumed to be in the same traffic stream as above. Note the substantially higher values for both before and after enforcement ESALs as compared to the flexible case. The estimated increase in pavement life due to enforcement is not greatly different for the two pavement types as the rigid Li is L`j = 100*~1283-872~/1283 = 32.0%. 5.0 MORE PRECISE METHOD OF CALCULATING INCREASED PAVEMENT LIFE DUE TO WEIGHT ENFORCEMENT AASHTO design procedures provide for the traffic input to design to be in terms of accumulated (or projected) 18,000 lb. equivalent single axle loads (ESALs). In their approach, AASHTO uses the definition: "Load equivalency factors represent the ratio of the number of repetitions of any axle load and axle configuration (single, tandem, tridem3 necessary to cause the same reduction in Present Serviceability Index (PST) as one application of an ~ 8-km single axle load."~]). Because of that definition, many designers view the equivalency factor of a given axle load to be a relative measure of pavement damage inflicted by that load. The serviceability index (PS! or p) is a subjective measure of pavement condition on a O to 5 scale with 0 defined as unusable and 5 defined as perfect. While there are many variations, a typical new road will have an initial serviceability (pa or PS! at time 0) of about 4.4 while the terminal or no longer acceptable serviceability (p') generally ranges from 2.0 to 3.0. Unfortunately, the analysis of traffic data from a pavement design standpoint is greatly complicated by the fact that the relationship between axle loads and ESALs (equivalency factor) is geometric rather than linear and the relationship is a fimction of pavement structural capacity as well the level~f-service at which the pavement is considered to have failed (the terminal PSI). Furler, the relationships differ for flexible and rigid pavements. ESAL equations for both types Of pavements and for single and tandem axle loads were derived Tom the AASHO Road Test Hi. Relationships for tridem axles have been developed through other research to extend the Road Test results Hi. 7 Appendix E
Table E - 3 RIGID PAVEMENT, 4th Power Rule ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM BEFORE ENFORCEMENT T AFTER ENFORCEMENT Eqivalency No. Daily No. Daily Factor Axles ESALs Axles ESALs 0.006 18 0.108 18 0.108 0.03 12 0.36 10 0 3 0.095 370 35.15 260 24.7 0.366 40 14.64 30 10.98 1 300 300 320 320 2.23 42 93.66 6 13.38 O O 0.01 18 0.18 16 0.16 0.074 24 1.776 23 1.702 0.284 50 14.2 40 11.36 1.35 48 64.8 36 48.6 1.73 25 43.25 123 212.79 2.45 43 105.35 52 127.4 3.74 163 609.62 27 100.98 Total 1283.094 872.46 Axle Load Ranges Single 3000 - 6999 Axles 7000 - 7999 8000 - 11999 12,000- 15,999 16,000- 19,999 20,000 - 23,999 Tandem 6000- 11,999 Axles 12,000 - 17,999 18,000 - 23,999 3O,000 - 31,999 32,000 - 33,999 34,000 - 37,999 38,000 - 41,999
The ESAL equivalency factor equations for flexible pavements are: log~O(wX/w~) = 4.79*Iog~0~ ~+~ ~-4.79*Iog~0~Ex+L,2) Go = Tog,0~4.2 -p~/2.7] bX = 0.40 + [O O81*~Ex + L2)'`3.233/~(SN + I)^5.19*~2^3.23] where Go - log~0~4.5 - p~/3.0] + 4.33*Iog~0~2 + GtIbx - Gt/b~ . Equation (4) . Equation (5) . Equation (6) WX = number of loads of magnitude Ex required to reduce the PS} to pi, wig= number of {8 kip loads required to reduce the PS] to p', Ex = load on one single axle or one tandem axle set (kips), ~2 = axle code (! for single axle and 2 for tandem axIe), SN = pavement structural number (see Section 6 for examples of SN determination), pi = terminal serviceability (on a O to 5 scale typical p' values are 2.0, 2.5, and 3.0), and big= value of bx when Ex = ~ ~ and ~2 = i' For rigid pavements, the equations are: log,O(wX/w~) = 4.62*Iog,0~+~-4.62*Iog,0(L`x+~2) + 3.28*Iog~0~2 + G/bx - Gab 9 . Equation (7) . Equation (~) Appendix E
bx = 1.00 + [3.63*(LX + L2)^5.20]/[(D + 1)^8.46*L2^3.52] where D is the slab thickness in inches. 5.1 Flexible Pavement Examples Equation (9) Equations 6 and 7 above solve for the loge of the inverse of the equivalency factors. For the flexible pavement example used in the ~ 993 AASHTO Design Guide A the SN = 5, and pi = 2.5. Assuming that on that pavement we want to determine the ~ g kip equivalency for a 22 kip single axle load Ex = 22 hips, ~2 = l, and Equation ~ reduces to log,O(w22/w,~) = -0.34 w22/w~ = 0.457 and the equivalency factor e22 = /0.457) = 2. ~ 8. Similar calculations produce the tabulation of flexible pavement single axle Toad equivalency factors for pi = 2.5 and structural numbers ~ through 6 given in Table E-4. Again, for the flexible pavement example one can calculate equivalency factors for +~_1~~ ret 1~1.~ l_~r art;_;_ ~ 1 - - at, __ _ _ ~llklt;lIl Wilt; lUdLlb fly ~18111118 ~ 42 = 2 in Equations 4 and 5. went using a 34 kip tandem axle load Equation 4 reduces to log~O(wX/w,') = -0.03 7 wow = 0.918 and the equivalency factor e34 = I/~0.918) = 1.09. The last calculation shows that for a flexible pavement a 34 hip tandem load is approximately equivalent to an ~ ~ kip single axle load. Similar calculations produce the tabulation of flexible pavement tandem axle load equivalency factors for pi = 2.5 and structural numbers ~ through 6 given In Table D.5 of Me ~ 986 AASHTO Guide for the Design o/Pavement Structures. Studies by Treybig, et.al.~ have extended the AASHO Road Test results to trident axles. While He analysis of tndem axle equivalencies is well beyond the scope of the present study, Table D.6 of the 1986 AASHTO Guide for the Design of Pavement Structures is a tabulation of flexible pavement trident equivalency factors for structural numbers 1 through 6 and pi = 2.5. It should be noted in that Table that a 48 kip trident load has an ~ g kip equivalency of approximately one. Appendix E 10
5.2 Rigid Pavement Examples For the rigid pavement example used in the ~ 993 AASHTO Design Guide (~) the slab thickness D = 1 0, and pi = 2.5. Assuming that on that pavement we want to determine the ~ ~ kip equivalency for a 22 kip single axle load Ex = 22 Lips, ~2 = it, and Equation 7 reduces to log,O(w22/w~) = -0.3 76 w22/w~ = 0.421 and the equivalency factor e22 = I/~0.421) = 2.38. Similar calculations produce the tabulation of rigid pavement single axle load equivalency factors for pi = 2.5 and slab thicknesses of 6 through ~ 4 given in Table D. ~ 3 of the ~ 986 AASHTO Guide for the Design of Pavement Structures. Again, for the rigid pavement example one can calculate equivalency factors for tandem axle loads by assigning ~2 = 2 in Equations 7 and 9. Then, using a 34 kip tandem axle load Equation 7 reduces to log,O(w34/w~)- -0.289 W34/W,8 = 0.514 and the equivalency factor e34 = I/~0.514) = 1.95. The last calculation shows that for a rigid pavement a 34 hip tandem load has an equivalency nearly double that for an ~ ~ kip single axle load. Similar calculations produce the tabulation of rigid pavement tandem axle load equivalency factors for pi = 2.5 and slab thicknesses of 6 through 14 inches given in Table D.14 in the 1986 AASHTO Guide for the Design of Pavement Structures. Again, while the analysis of tridem axle equivalencies is well beyond the scope of the present study, Table D.15 in the 1986 AASHTO Guide for the Design of Pavement Structures is a tabulation of rigid pavement tandem equivalency factors for slab thicknesses of 6 Trough 14 inches and p' = 2.5. 5.3 Calculating ESAL Applications for Mixecl Traffic Table E-4 is an example of total daily ESAL calculation for trucks (in most such analyses buses are included with trucks while passenger cars and pickup trucks are ignored as the ESAL contributions of those classes are insignificant) in a traffic stream for a flexible pavement where SN = 5 and Pt = 2.5. Note that the table summarizes single and tandem axles separately as the equivalency factors are quite different. 11 Appendix E
Table E - 4 FLEXIBLE PAVEMENT SN =5, psubt = 2.5 ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM BEFORE ENFORCEMENT AFTER ENFORCEMENT Eqivalency No. Daily No. Daily Factor Axles ESALs Axles ESALs 0.005 18 0.09 18 0.09 0.032 12 0.384 10 0.32 0.088 370 32.56 260 22.88 0.36 40 14.4 30 10.8 1 300 300 320 320 2.18 42 91.56 6 13.08 O O 0.005 18 0.09 16 0.08 0.037 24 0.888 23 0.851 0.151 50 7.55 40 6.04 0.758 48 36.384 36 27.288 0.974 25 24.35 123 119.802 1.38 43 59.34 52 71.76 2.08 163 339.04 27 56.16 Total 906.636 649.151 Axle Load Ranges Single 3000 - 6999 Axles 7000 - 7999 8000 - 11999 12,000- 15,999 16,000- 19,999 20,000 - 23,999 Tandem Axles 6000 - 11,999 12,000 - 17,999 18,000 - 23,999 30,000 - 31,999 32,000 - 33,999 34,000 - 37,999 38,000 - 41,999
In the tabulation, axle loadings are grouped as convenient. Then, the equivalency factors are determined from Equations 4 through 9. Alternatively, the equivalencies could be interpolated from the appropriate tables (Tables D.4, D.5, D.6, D.13, D.14, or D.15 ofthe 1986 AASHTO Guide for the Design of Pavement Structures as appropnate) in order to estimate the ESAL contribution from each axle grouping. For example, note that the heaviest single axle class in the stream is 26,000 - 29,999. The equivalency factor applied to that group is 5.39 as given in Table D.4 of the 1 986 AASHTO Guide for the Design of Pavement Structures for a 28 hip single axle load. There was only one axle in that group so the total ESAL contribution from the group is 1*5.39 = 5.39 ESALs. Similarly, the total ESAL contribution from all groups is the estimated ESALs for the traffic stream. For the example, daily ESALs are determined for both the before arid after enforcement conditions. The total daily ESALs before enforcement (ESALb) is 907 while the total after enforcement RESALE is 649. The estimated increase in pavement life is then L`j = lOO*(ESAL`b - ESAL`a)/ESALb = 100*~907 - 6491/907 = 28.4%. Note that this value is very close to that determined in Section 4 through the fourth power rule for the same traffic stream on a generic flexible pavement. A similar analysis has been applied to the above traffic stream assuming the pavement in question is rigid with a slab thickness (D) of ~ O in. and a terminal serviceability index Spit of 2.5. This analysis is summarized in Table E-5 where it may be noted that the major difference is in the equivalency factors for tandem axles which are much higher than for the flexible pavement case. For the rigid case, the total dally ESALs before enforcement (ESALb) is 1303 while the total after enforcement RESALE is 871. The estimated increase in pavement life for this case is then Li = 100*~1301-871~/1301 = 33.~%. Again, the estimated increase in pavement life for this method is very close to that determined in Section 4 through Me fourth power rule for We same traffic stream on a generic ngid pavement. If, instead of estimating the increase in pavement life, it is desired to determine an estimate of absolute pavement life before and after enforcement activities it is necessary to apply the AASHTO design equations as given in Section 6 of this appendix. 13 Appendix E
Table E - 5 RIGID PAVEMENT, D = 10, psubt = 2.5 ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM BEFORE ENFORCEMENT | AFTER ENFORCEMENT Eqivalency No. Daily No. Daily Factor Axles ESALs Axles ESALs 0.006 18 0.108 1 18 0.108 0.03 12 0.36 10 0.3 0.081 370 29.97 260 21.06 0.338 40 13.52 30 10.14 1 300 300 320 320 2.38 42 99.96 6 14.28 O O 0.085 18 1.53 16 1.36. 0.064 24 1.536 23 1.472 0.254 50 12.7 40 10.16 1.32 48 63.36 36 47.52 1.72 25 43 123 211.56 2.48 43 106.64 52 128.96 3.87 163 630.81 27 104.49 Total 1303.494 871.41 Axle Load Ranges Single Axles 3000 - 6999 7000 - 7999 8000 - 11999 12,000 - 15,999 16,000- 19,999 20,000 - 23,999 Tandem 6000- 11,999 Axles 12,000 - 17,999 18,000 - 23,999 30,000 - 31,999 32,000 - 33,999 34,000 - 37,999 38,000 - 41,999
6.0 DETERMINATION OF FLEXIBLE PAVEMENT STRUCTURAL NUMBER AND ESTIMATED PAVEMENT LIFE FROM AASHTO EQUATIONS 6.1 DETERMINATION OF FLEXIBLE PAVEMENT STRUCTURAL NUMBER The structural number (SN) is a measure of relative pavement strength and is defined as: SN = a,h, + a2h2 + - - - - + aj\ Equation (10) where: from the top down, h, is the thickness of layer one which has a layer coefficient of a,, h2 is the thickness of layer two which has a layer coefficient of al, etc. Table E-6 is a tabulation of layer coefficients for materials typically used in flexible pavement construction. As an example of SN determination, if a pavement is comprised of 6-in. of crushed stone base (a2 = 0. 14) and 4-in. of asphalt concrete (a, = 0.44) the pavement has a SN = 0.44*4 + 0.14*6 = 2.6. 6.2 DETERMINATION OF ESTIMATED PAVEMENT LIFE FROM AASHTO EQUATIONS 6.21 FLEXIBLE PAVEMENTS 6.211 AASHTO Design Equation The AASHTO Design equation for flexible pavements is: tog,OW~ = ZR*SO + 9.36*Iog~0(SN + 1) - 0.20 + (Iog~O(DPSI/2.711/~0.40 + 1094/(SN+115'9) + 2.32*Iog~0MR- 8.07 where: Wig Equation ~ ~ The predicted accumulated traffic on the design lane during the design period (typically 30 years) in equivalent ESALs, 15 Appendix E
Appendix E ZR = the starboard normal deviate corresponding to the desired design reliability (for 50% reliability ZR = 0 and I/2 of the pavement wart fail before the end of the design period, etc.) (a typical reliability for major highways is 95% with ZR = - ~ .64), SO = the overall standard deviation associated with pavement performance prediction (a typical value for flexible pavements is 0.35), SN = the pavement structural number defined earlier, DPSI= the change in pavement serviceability during the design period (a typical value is 1.9), and MR = the effective roadbed soil resilient modulus (AASHTO T 274) in psi. 6.212 Example of Design Equation Use For purposes of demonstrating the effects of chances in cumulative ESALs it may be best to simplify Equation ~ ~ above by using typical values for all variables except ESALs and SN. The 1993 AASHTO Design Guide (~) offers a convenient example where the following values are assigned: ZR= -~64 (reliability = 95°/O) SO = 0.35 DPSI= I.9 MR = 5000 psi. Then, the AASHTO flexible design equation reduces to: log~OW~ = -0.26 + 9.36*Iog,0(SN + I) - --c~ 0.15.3/~0.40 + 1094/(SN+~5 ~9) Equation ~12) It should be emphasized that Equation 12 is a gross simplification of the AASHTO flexible pavement design equation and should never be used for the design of specific pavements. The sole purpose of the simplified equation is to permit analysis of the ESAL vs. thickness relationship as a part of the study to assess the effects of weight enforcement on pavement performance. To examine the effects of various cumulative ESALs on pavement life it is convenient to assume a known existing pavement of say SN = 5. Equation ~ 2 then solves 16
TABLE E- 6 PAVING MATERIALS USED IN MSHTO DESIGNS RIGID PAVEMENTS Modulus of Material Typical Thicla~ (in.) Modulus of Rupture (psi) Subgrade Reaction (pci) (4 cl~aract'3rs) (3 characters) (3 characters) PCC (poplars! 6-15 in. carry Default = 650 Default = 200 As) FLEXIBLE PAVEMENTS Typical Material Thickness (h) (in.) (4 characters) Surface: high stab. asphalt 1 - 4 in. concrete four stability asphalt 1 - 4 in. concrete Base: high slate. 2- 16in. - asphalt coracle Shed 2- 12in. Strength Coethcient (a) (4 characters) Default = 0.44 DefauH = 0.20 Default =0.40 (1) Default = 0.14 sandy 2 - 12in. DefauH = 0.07 ~1 cerr~e'* by 4 - 8 in. Default = 0.20 sane aspect hid 4 - Sin. Default= 0.34 sane lime bmabrent 4 - 8 in. D^uR = 0.= Subbase: sandy gravel 2 - 18in. Default = 0.11 sand or sandy clay 2- 18in. Default = 0.~)8 Except as noted, default values are from the 1972 MSHTO Interim Guide for Design of Pavement Structures. (a) Recommendation of Me Project 2~34 research beam.
1ogl0Wl8 = 6.72 and Wl8 = 5.2 x 106. If the traffic stream analyzed above for a flexible pavement with SN = 5 arid pi = 2.5 is used the before (ESALb) and after DESALT enforcement daily ESALs are 907 and 649, respectively. It can be shown that a pavement undergoing an annual growth rate in traffic volume will accumulate the design Was according to Me equation n = Bog* + r*W~/365*ESAL)~/Iog~O(! + r)....Equation (13) where n = the estimated pavement life in years, r = the annual growth rate expressed as a decimal, ESAL = the average daily ESALs at the beginning of the analysis period. Assuming a 5% annual rate of growth in traffic for the above example the pavement would have been predicted to last no = Fog* + 0.05*5.2 x 106/365*907~/Iog~0~.05) = 12.0 yrs. With the same growth rate after enforcement the pavement would be predicted to last A= [Iog~O*~] + 0.05*5.2 x 106/365*649~/Iog~0~.05) = 15.3 yrs. Then, We increase in expected pavement life due to enforcement is 15.3 - 12.0 = 3.3 years or 27.5%. Note that the percentage increase in pavement life compares well with that determined from Me approximation method used earlier. 6.22 RIGID PAVEMENTS 6.221 AASHTO Design Equation The AASHTO Design equation for ngid pavements is: log~OW~ = ZR*SO + 7.35*Iog~0(D + 1) - 0.06 + [Iog~O(DPSI/3.0~/~1 + (1.624*107~/(D+11846] ~ (4 22 - 0.32p~*Iog~o{tst*c~(Do.75 - Appendix E 1.132~/~215.63*~(D°75 - 18 42/(EJk)°25~] E ti (14) 18
where, in addition to that defined above: D= 1 _ s- J= E c the slab thickness (in.) estimated mean PCC modulus of rupture (AASHTO T97) in psi, a factor used to account for the ability of rigid slab to transfer loads across discontinuities such as cracks and joints (typical values range from 2.5 to 4.0, see AASHTO), PCC elastic modulus in psi (typically 4 to 5 * lob), and the modulus of subgrade reaction, the load in pounds per square inch on a loaded area of the roadbed soil or subbase divided by the deflection in inches of the soil or subbase (psi/in), (typical values are 50 to 3001. In addition, for rigid pavements the initial serviceability (PSIO or PS} at time O) is about 4.2 while the terminal or no longer acceptable serviceability (PSI') is about 2.5. Therefore, a typical DPST is about I.7. Now, it is possible to solve Equation 14 for local conditions and, and making the appropriate substitutions in EquationI3, go through the analysis of before and after enforcement traffic streams to assess the impact of that enforcement on pavement life. 7.0 CONCLUSION The foregoing discussion of pavement design pnociples has addressed the major issues underlying methods of determining Me increase In pavement life one could expect from reduced axle loadings accrued through enforcement activities. The application of these principles is seen In the software product of NCHRP 20-34, the Truck Weight Enforcement Evaluation Tool. 19 Appendix E
Appendix E 8.0 REFERENCES American Association of State Highway and Transportation Officials, "AASHTO Guide for Design of Pavement Structures", Washington, DC, ~ 993. American Association of State Highway and Transportation Officials, "AASHTO Interim Guide for Design of Pavement Structures ~ 972", (Chapter Ill Revised, ~ 98 ~ ), Washington, DC, ~ 972, ~ 98 i. Treybig, H. J. and H. L. Von Quintus, "Equivalency Factor Analysis and Prediction for Triple Axles", Report No. BR-2/l, Austin Research Engineers for Texas Research and Development Foundation, Austin, TX, 1976. 20
