Load Equivalency

Plate theory: solutions limited to a single tire print Prickett & Ray (1951) – provided a graphical extension of Westergaard theory to multiple-wheel loads (pattened after Newmark’s extension of Boussinesq soln.) - resulted in PCA code “Airport”-  int. - dimensionless ratios a=loaded radius, s=tire spacing Load Equivalency

Kreger (1967) – H51 program - Dense liquid edge stress Peutz et al (1968) – Burmister linear-elastic theory - BISAR code allowed for multiple-wheel loads Yoder & Witczak (1975) Used dimensional analysis in a graphical summary of Pickett & Ray charts d L x Edge Interior Single, dual, or dual tandem wheel loads

Asphalt Institute - used s/a FAA based on tire configuration) Effort has always been to transform the actual multiple-wheel load into an equivalent loading system consisting of a single wheel. ESWL: Equivalent Single Wheel Load ESAL: Equivalent Single Axle Load ESAR: Equivalent Single Axle Radius

COE (1940); CBR Design Method (B-29 Aircraft Loading) Load & wheel spacings combinations that yield a LEF of 1 when compared to any “given” single axle. LEF depended on: - wheel spacing and dual spacing - mechanistic response - layer thickness & moduli Boussineq soln ESWL

Equal Vertical Stress (Boyd & Foster )

Maximum Vertical Stress or Deflections

Equal Vertical Deflection (Boyd & Ahlvin ) As long as S d /a and h 1 /a remain the same, the load factor will be the same. Dimensional analysis - s/a - r/a - z/a

Equal Tensile Strain

Equal Contact Pressure

used all responses. - used super positioning - abandoned constant pressure assumption - equated the contact area of the ESWL to that of one wheel of the assembly Gerrand & Harrison – 1970

AASHTO (AASHO) Rd Test - ESAL concept developed in 1940 – adopted by the Calif. Div of Highways - AASHO based it on PSI; mainly roughness (but intended originally for fatigue induced distress) Nonetheless, AASHO’s entirely statistical-empirical ESAL concept is based on the assumption that the destructive effect of a number of applications of a given axle group (defined in terms of load magnitude and configuration) can be expressed in terms of a different number of applications of a standard or base load. (Ioannides et al 1993) Linear cumulative damage (Miner’s fatigue hypothesis) - been used for everything from rutting to erosion & pumping. ESAL

Irick & Hudson (1964) - Stated 4 th power law applied to a ratio of deflections - Scala (1970): LEF based on load induced deflection but is not independent of pavement structure. ESAL Approach was less mechanistic; more statistical - Decon (1969): attempted to ‘prove’ the ESAL, i.e. EALF = W t18 /W tx =(ε x /ε 18 ) γ ; γ=4 - Suggested using γ = Proof of ESWL concept never done

 = 4 Rutting & Fatigue  = 11 to 33 for semi-rigid  is sensitive to infrequent heavy loads  varies from 1.2 to 8 if the standard load is well chosen Every country has a different  for the same design ! OECD (1988) Refuted 4 th power law concluded that not possible to prove the existence of a law of equivalence between loads in terms of their damaging effects on pavements. the power (  ) is different for each pvmt type.

The radius of an equivalent single wheel that gives the same response as a dual assembly for the same load. - governed by For interior loading (Tayabji et al 1987) Max bending stress (superposition) (Ioannioes et al 1993) ESAR

Equate(For equal P)

Traffic Analysis n i = (n 0 ) i (G)(D)(L)365(Y) (n 0 ) i = initial number or reps/day (G)= growth factor (D)= directional distribution factor (L)= lane distribution factor (Y)= design period - yrs

Traffic Analysis p i = % of total reps for the i th load group F i = EALF for the ith load group (ADT) 0 = initial avg daily truck traffic T= % of trucks A= avg axles per truck T f = truck factor = # of 18k SAL applications per truck