# 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)