A flexible pavement has a 4in hotmix asphalt wearing surface

A flexible pavement has a 4-in hot-mix asphalt wearing surface, a 7-in dense-graded crushed Stone base, and a 10-in crushed stone sub-base. The pavement is on a soil with a resilient modulus of 5000 psi. The pavement was designed with 90% reliability, an overall standard deviation of 0.4, and a APSI of 2.0 (a TSI of 2.5). The drainage coefficients are 0.9 and 0.8 for the base and sub-base, respectively. How many 25-kip single axle loads can be carried before the pavement reaches its TSI?

Solution

Solution:
Given Data:
   D1 = 4 inch D2 = 8 inch           D3 = 8 inch
   Mr = 10,000 psi           M2 = M3 = 1.0 So = 0.5
   PSI = 4.5 PSI = 2.0           TSI = 2.5

Loads:
   Single Axle = 1080 20 kip
   Single Axle = 400 24 kip
   Tandem Axle = 680 40-kip

Design Size =?
   R = 90 %       (b).   99%
   SN = a1D1 + a2D2M2 + a3D3M3    ------------ (1)
   Putting values in Equ. (1)
   SN = (0.44)(4) + (0.30)(8)(1) + (0.11)(8)(1) = 5.039 = 5
   Equivalency facor From Tables

20 kip single axle equivalent = 1.51
   24 kip single axle equivalent = 3.03
   40 kip tandem axle equivalent = 2.08
Thus;   total daily 18 kip ESAL

Daily W18= Equivalence Factor x Number of passes
   Daily W18 = 1.51(1080) + 3.03(400) + 2.08(680) = 4257.2       18-kip ESAL
We have a general formula

Design ESALS (w18)=Daily ESAL x Years x 365

(a)   At R = 90%,       Zr = -1.282
Now,    By using AASHTO Design Equation:
   W18 = 26,128,077
   So; year = (26128077)/(365*4257.2)
       Year = = 16.82 years

(b)   At R = 99%,       Zr = -2.362
   After solving equation, W18 comes and to be:
   W18 = 7,854,299
   So; Year = (7854299)/(365*4257.2)
       Year = = 5.05 years