The basic equation for flexible-pavement design given in the 1993 AASHTO design guide permits engineers to determine a structural number necessary to carry a designated traffic loading. The AASHTO equation is
> @
10 18 o 10
10
5.19
10
log = 9.36 log SN 1 0.20
log PSI / 2.7 0.40 1094 SN 1 2.32 log 8.07
R
R
W Z S
M
ª º
¬ ¼
'
ª º
¬ ¼
(4.1)
where
W18 = 18-kip–equivalent single-axle load (1 kip = 1,000 lb), ZR = reliability (z-statistic from the standard normal curve),
So = overall standard deviation of traffic, SN = structural number,
¨PSI = loss in serviceability from the time the pavement is new until it reaches its TSI, and MR = soil resilient modulus of the subgrade in lb/in2.
A graphical solution to Eq. 4.1 is shown in Fig. 4.5. Details on the variables that serve as inputs to Eq. 4.1 and Fig. 4.5 are as follows:
W18 Automobiles and truck traffic provide a wide range of vehicle axle types and axle loads. If one were to attempt to account for the variety of traffic loadings encountered on a pavement, this input variable would require a significant amount of data collection and design evaluation. Instead, the problem of handling mixed traffic loading is solved with the adoption of a standard 18- thousand-pound–equivalent single-axle load or (with 1 kip = 1000 lb) an 18- kip–equivalent single-axle load: (ESAL). The idea is to determine the impact of any axle load on the pavement in terms of the equivalent amount of pavement impact that an 18-kip single-axle load would have. For example, if a 44-kip tandem-axle (double-axle) load has 2.88 times the impact on pavement structure as an 18-kip single-axle load, 2.88 would be the W18 value assigned to this tandem-axle load. The AASHO Road Test also found that the 18-kip–
equivalent axle load is a function of the terminal serviceability index of the pavement structure. The axle-load equivalency factors for flexible pavement design, with a TSI of 2.5, are presented in Tables 4.1 (for single axles), 4.2 (for tandem axles), and 4.3 (for triple axles).
ZR Represents the probability that serviceability will be maintained at adequate levels from a user’s point of view throughout the design life of the facility.
This factor estimates the likelihood that the pavement will perform at or above the TSI level during the design period, and takes into account the inherent uncertainty in design. Equation 4.1 uses the z-statistic, which is obtained from the cumulative probabilities of the standard normal distribution (a normal distribution with mean equal to 0 and variance equal to 1). The z-statistics corresponding to various probability levels are given in Table 4.4. In the flexible-pavement-design nomograph (Fig. 4.5), the probabilities (in percent) are used directly (instead of ZR as in the case of Eq. 4.1), and these percent probabilities are denoted R, the reliability (see Table 4.4).
103
Figure 4.5 Design chart for flexible pavementsbasedon the use of mean values for each input. Redrawn from AASHTO Guide for Design of Pavement Structures, Washington, DC, The American Association of State Highwayand Transportation Officials, 1993. Used by permission.
Highways such as interstates and major arterials, which are costly to reconstruct (have their pavements rehabilitated) because of resulting traffic delay and disruption, require a high reliability level, whereas local roads, which will have lower impacts on users in the event of pavement rehabilitation, do not. Typical reliability values for interstate highways are 90% or higher, whereas local roads can have a reliability as low as 50%.
So The overall standard deviation, So, takes into account the designers’ inability to accurately estimate the variation in future 18-kip–equivalent axle loads, and the statistical error in the equations resulting from variability in materials and construction practices. Typical values of So are on the order of 0.30 to 0.50.
SN The structural number, SN, represents the overall structural requirement needed to sustain the design’s traffic loadings. The structural number is discussed further in Section 4.4.3.
¨PSI The amount of serviceability loss over the life of the pavement, ¨PSI, is determined during the pavement design process. The engineer must decide on the final PSI level for a particular pavement. Loss of serviceability is caused by pavement roughness, cracking, patching, and rutting. As pavement distress increases, serviceability decreases. If the design is for a pavement with heavy traffic loads, such as an interstate highway, then the serviceability loss may only be 1.2 (an initial PSI of 4.2 and a TSI of 3.0), whereas a low-volume road can be allowed to deteriorate further, with a possible total serviceability loss of 2.7 or more.
MR The soil resilient modulus, MR, is used to reflect the engineering properties of the subgrade (the soil). Each time a vehicle passes over pavement, stresses are developed in the subgrade. After the load passes, the subgrade soil relaxes and the stress is relieved. The resilient modulus test is used to determine the properties of the soil under this repeated load. The resilient modulus can be determined by AASHTO test method T274. Measurement of the resilient modulus is not performed by all transportation agencies; therefore, a relationship between MR and the California bearing ratio (CBR) has been determined. The CBR has been widely used to determine the supporting characteristics of soils since the mid-1930s, and a significant amount of historical information is available. The CBR is the ratio of the load-bearing capacity of the soil to the load-bearing capacity of a high-quality aggregate, multiplied by 100. The relationship, used to provide a very basic approximation of MR (in lb/in2) from a known CBR, is
MR = 1500 u CBR (4.2)
The coefficient of 1500 in Eq. 4.2 is used for CBR values less than 10. Caution must be exercised in applying this equation to higher CBRs because the coefficient (the value 1500 shown in Eq. 4.2) has a range of 750 to 3000.
4.4 Traditional AASHTO Flexible-Pavement Design Procedure
105
Table 4.1 Axle-Load Equivalency Factors for Flexible Pavements, Single Axles, and TSI = 2.5 Axle
load (kips)
Pavement structural number (SN)
1 2 3 4 5 6
2 0.0004 0.0004 0.0003 0.0002 0.0002 0.0002 4 0.003 0.004 0.004 0.003 0.002 0.002 6 0.011 0.017 0.017 0.013 0.010 0.009 8 0.032 0.047 0.051 0.041 0.034 0.031 10 0.078 0.102 0.118 0.102 0.088 0.080 12 0.168 0.198 0.229 0.213 0.189 0.176 14 0.328 0.358 0.399 0.388 0.360 0.342 16 0.591 0.613 0.646 0.645 0.623 0.606
18 1.00 1.00 1.00 1.00 1.00 1.00
20 1.61 1.57 1.49 1.47 1.51 1.55
22 2.48 2.38 2.17 2.09 2.18 2.30
24 3.69 3.49 3.09 2.89 3.03 3.27
26 5.33 4.99 4.31 3.91 4.09 4.48
28 7.49 6.98 5.90 5.21 5.39 5.98
30 10.3 9.5 7.9 6.8 7.0 7.8
32 13.9 12.8 10.5 8.8 8.9 10.0
34 18.4 16.9 13.7 11.3 11.2 12.5 36 24.0 22.0 17.7 14.4 13.9 15.5 38 30.9 28.3 22.6 18.1 17.2 19.0 40 39.3 35.9 28.5 22.5 21.1 23.0 42 49.3 45.0 35.6 27.8 25.6 27.7 44 61.3 55.9 44.0 34.0 31.0 33.1 46 75.5 68.8 54.0 41.4 37.2 39.3 48 92.2 83.9 65.7 50.1 44.5 46.5 50 112.0 102.0 79.0 60.0 53.0 55.0 Source:AASHTO Guide for Design of Pavement Structures, The American Association of State Highway and Transportation Officials, Washington, DC, 1993. Used by permission.
Table 4.2 Axle-Load Equivalency Factors for Flexible Pavements, Tandem Axles, and TSI = 2.5 Axleload
(kips)
Pavement structural number (SN)
1 2 3 4 5 6
2 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 4 0.0005 0.0005 0.0004 0.0003 0.0003 0.0002 6 0.002 0.002 0.002 0.001 0.001 0.001 8 0.004 0.006 0.005 0.004 0.003 0.003 10 0.008 0.013 0.011 0.009 0.007 0.006 12 0.015 0.024 0.023 0.018 0.014 0.013 14 0.026 0.041 0.042 0.033 0.027 0.024 16 0.044 0.065 0.070 0.057 0.047 0.043 18 0.070 0.097 0.109 0.092 0.077 0.070 20 0.107 0.141 0.162 0.141 0.121 0.110 22 0.160 0.198 0.229 0.207 0.180 0.166 24 0.231 0.273 0.315 0.292 0.260 0.242 26 0.327 0.370 0.420 0.401 0.364 0.342 28 0.451 0.493 0.548 0.534 0.495 0.470 30 0.611 0.648 0.703 0.695 0.658 0.633 32 0.813 0.843 0.889 0.887 0.857 0.834 34 1.06 1.08 1.11 1.11 1.09 1.08 36 1.38 1.38 1.38 1.38 1.38 1.38 38 1.75 1.73 1.69 1.68 1.70 1.73 40 2.21 2.16 2.06 2.03 2.08 2.14 42 2.76 2.67 2.49 2.43 2.51 2.61 44 3.41 3.27 2.99 2.88 3.00 3.16 46 4.18 3.98 3.58 3.40 3.55 3.79 48 5.08 4.80 4.25 3.98 4.17 4.49 50 6.12 5.76 5.03 4.64 4.86 5.28 52 7.33 6.87 5.93 5.38 5.63 6.17 54 8.72 8.14 6.95 6.22 6.47 7.15
56 10.3 9.6 8.1 7.2 7.4 8.2
58 12.1 11.3 9.4 8.2 8.4 9.4
60 14.2 13.1 10.9 9.4 9.6 10.7 62 16.5 15.3 12.6 10.7 10.8 12.1 64 19.1 17.6 14.5 12.2 12.2 13.7 66 22.1 20.3 16.6 13.8 13.7 15.4 68 25.3 23.3 18.9 15.6 15.4 17.2 70 29.0 26.6 21.5 17.6 17.2 19.2 72 33.0 30.3 24.4 19.8 19.2 21.3 74 37.5 34.4 27.6 22.2 21.3 23.6 76 42.5 38.9 31.1 24.8 23.7 26.1 78 48.0 43.9 35.0 27.8 26.2 28.8 80 54.0 49.4 39.2 30.9 29.0 31.7 82 60.6 55.4 43.9 34.4 32.0 34.8 84 67.8 61.9 49.0 38.2 35.3 38.1 86 75.7 69.1 54.5 42.3 38.8 41.7 88 84.3 76.9 60.6 46.8 42.6 45.6 90 93.7 85.4 67.1 51.7 46.8 49.7 Source:AASHTO Guide for Design of Pavement Structures, The American Association of State Highway and
Transportation Officials, Washington, DC, 1993. Used by permission.
4.4 Traditional AASHTO Flexible-Pavement Design Procedure
107
Table 4.3 Axle-Load Equivalency Factors for Flexible Pavements, Triple Axles, and TSI = 2.5 Axleload
(kips)
Pavement structural number (SN)
1 2 3 4 5 6
2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 6 0.0006 0.0007 0.0005 0.0004 0.0003 0.0003 8 0.001 0.002 0.001 0.001 0.001 0.001 10 0.003 0.004 0.003 0.002 0.002 0.002 12 0.005 0.007 0.006 0.004 0.003 0.003 14 0.008 0.012 0.010 0.008 0.006 0.006 16 0.012 0.019 0.018 0.013 0.011 0.010 18 0.018 0.029 0.028 0.021 0.017 0.016 20 0.027 0.042 0.042 0.032 0.027 0.024 22 0.038 0.058 0.060 0.048 0.040 0.036 24 0.053 0.078 0.084 0.068 0.057 0.051 26 0.072 0.103 0.114 0.095 0.080 0.072 28 0.098 0.133 0.151 0.128 0.109 0.099 30 0.129 0.169 0.195 0.170 0.145 0.133 32 0.169 0.213 0.247 0.220 0.191 0.175 34 0.219 0.266 0.308 0.281 0.246 0.228 36 0.279 0.329 0.379 0.352 0.313 0.292 38 0.352 0.403 0.461 0.436 0.393 0.368 40 0.439 0.491 0.554 0.533 0.487 0.459 42 0.543 0.594 0.661 0.644 0.597 0.567 44 0.666 0.714 0.781 0.769 0.723 0.692 46 0.811 0.854 0.918 0.911 0.868 0.838 48 0.979 1.015 1.072 1.069 1.033 1.005 50 1.17 1.20 1.24 1.25 1.22 1.20 52 1.40 1.41 1.44 1.44 1.43 1.41 54 1.66 1.66 1.66 1.66 1.66 1.66 56 1.95 1.93 1.90 1.90 1.91 1.93 58 2.29 2.25 2.17 2.16 2.20 2.24 60 2.67 2.60 2.48 2.44 2.51 2.58 62 3.09 3.00 2.82 2.76 2.85 2.95 64 3.57 3.44 3.19 3.10 3.22 3.36 66 4.11 3.94 3.61 3.47 3.62 3.81 68 4.71 4.49 4.06 3.88 4.05 4.30 70 5.38 5.11 4.57 4.32 4.52 4.84 72 6.12 5.79 5.13 4.80 5.03 5.41 74 6.93 6.54 5.74 5.32 5.57 6.04 76 7.84 7.37 6.41 5.88 6.15 6.71 78 8.83 8.28 7.14 6.49 6.78 7.43 80 9.92 9.28 7.95 7.15 7.45 8.21 82 11.1 10.4 8.8 7.9 8.2 9.0 84 12.4 11.6 9.8 8.6 8.9 9.9 86 13.8 12.9 10.8 9.5 9.8 10.9 88 15.4 14.3 11.9 10.4 10.6 11.9 90 17.1 15.8 13.2 11.3 11.6 12.9 Source:AASHTO Guide for Design of Pavement Structures, The American Association of State Highway and
Transportation Officials, Washington, DC, 1993. Used by permission.
Table 4.4 Cumulative Percent Probabilities of Reliability, R, of the Standard Normal Distribution, and Corresponding ZR
R 0 1 2 3 4 5 6 7 8 9 9.5 9.9 90 –1.282 –1.341 –1.405 –1.476 –1.555 –1.645 –1.751 –1.881 –2.054 –2.326 –2.576 –3.080 80 –0.842 –0.878 –0.915 –0.954 –0.994 –1.036 –1.080 –1.126 –1.175 –1.227 –1.253 –1.272 70 –0.524 –0.553 –0.583 –0.613 –0.643 –0.675 –0.706 –0.739 –0.772 –0.806 –0.824 –0.838 60 –0.253 –0.279 –0.305 –0.332 –0.358 –0.385 –0.412 –0.440 –0.468 –0.496 –0.510 –0.522 50 0 –0.025 –0.050 –0.075 –0.100 –0.125 –0.151 –0.176 –0.202 –0.228 –0.241 –0.251 Example: To be 95% confident that the pavement will remain at or above its TSI (R = 95 for use in Fig. 4.7), a ZR value of –1.645 would be used in Eq. 4.1 (and in Eq. 4.4).