Rigid Pavement ESAL Equation

At first glance, this equation looks quite complex – it is.

 
Where: W = axle applications inverse of equivalency factors (where W18 = number of 18,000 lb (80 kN) single axle loads)
Lx = axle load being evaluated (kips)
L18 = 18 (standard axle load in kips)
L2 = code for axle configuration
1 = single axle
2 = tandem axle
3 = triple axle (added in the 1986 AASHTO Guide)
x = axle load equivalency factor being evaluated
s = code for standard axle = 1 (single axle)
G = a function of the ratio of loss in serviceability at time, t, to the potential loss taken at a point where pt = 1.5
pt = “terminal” serviceability index (point at which the pavement is considered to be at the end of its useful life)
b = function which determines the relationship between serviceability and axle load applications
D = Slab Depth in inches

Example Calculation

  • Assumptions: Single axle, 30,000 lb (133 kN), D = 7 in., pt = 2.5
  • Answer: (Table D.13, p. D-15, 1993 AASHTO Guide) = 7.7
  • Calculations

 
where : W18  = predicted number of 18,000 lb (80 kN) single axle load applications
W30 = predicted number of 30,000 lb (133 kN) single axle load applications
Lx = L30 = 30
L2x = 1 (single axle)
G = serviceability loss factor
=
b30 = curve slope factor
=
and G/b30 = -0.1761/5.7298 = -0.03073
b18 =
G/b18 = -0.1761/1.3709 = -0.12845
Thus,
and of W18 loads allowable with a 30,000 lb. single axle
Finally, LEF = (same as contained in 1993 AASHTO Guide âcol Appendix D)