Fourth-Power Load Equivalency

Damage rises with the fourth power of load

The AASHO Road Test established empirically that pavement damage scales roughly with the fourth power of axle load relative to a standard eighteen-thousand-pound axle. The exponent is what makes this counter-intuitive: doubling an axle load does not double the damage, it multiplies it by sixteen.

Run the arithmetic on a passenger car and the result is startling. A car axle of around two thousand pounds is about one-ninth of the standard axle, and one-ninth to the fourth power is roughly one ten-thousandth. Ten thousand cars do the structural damage of one truck axle.

What this means for a design

A road can carry a hundred thousand vehicles a day and be designed almost entirely around the two or three thousand trucks among them. This is why the truck percentage and the truck factor are the inputs worth spending effort on, and why a traffic count that does not classify vehicles is close to useless for structural design.

It also explains a familiar observation: a residential street with almost no traffic can fail early if it is on a refuse collection route or a bus route. A handful of heavy axles per week outweighs all the cars.

An approximation, and an old one

The fourth-power rule comes from a single road test conducted in the late 1950s on specific materials in a specific climate. It remains standard practice and it remains an empirical approximation. Mechanistic-empirical design methods model stress and strain directly rather than through an equivalency factor, and give different — often better — answers for materials the original test never covered.

Calculators that use this method

• Pavement Design ESAL CalculatorConvert a traffic stream into equivalent single axle loads over the design life — the number pavement thickness is designed against.