# Flexible 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 SN = structural number

#### Example Calculation for a Single Axle

• Assumptions:    Single axle, 30,000 lb (133 kN), SN = 3, pt = 2.5
• Answer: (Table D.4, p. D-6, 1993 AASHTO Guide) = 7.9
• 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 = -0.2009/4.388 = -0.04578 b18 = G/b18 = -0.2009/1.2204 = -0.1646 Thus, and of W18 loads allowable with a 30,000 lb.  single axle Finally, LEF = (same as contained in 1993 AASHTO Guide ?nbsp;Appendix D)

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#### Example Calculation for a Tandem Axle

• Assumptions:    Tandem axle, 40,000 lb (133 kN), SN = 5, pt = 2.5
• Answer: (Table D.5, p. D-7, 1993 AASHTO Guide) = 2.08
• Calculations

 where : L40 = 40 (tandem axle) L18 = 18 (single axle) L2x = 2 (tandem axle) L2s = 1 (single axle) G = serviceability loss factor = b40 = curve slope factor = and G/b40 = -0.2009/0.53824 = -0.37325 b18 = G/b18 = -0.2009/0.50006 = -0.40175 Thus, Finally, LEF = (same as contained in 1993 AASHTO Guide nbsp;Appendix D)