Of course!
But it is a good approximation. Under some circumstances the exponent can be as low as 2 and in others as high as 11.
"Finding 4. An increase in axle weight generally causes a more than proportional increase in pavement damage. The relationship appears to approximate an exponential function, and various studies have assumed the power of the exponent to be about 4 as a rule. Estimates of the exponent’s power vary substantially, however.
The “fourth-power” rule emerged from in-situ pavement tests conducted in the 1950s by the organization now known as AASHTO, the American Association of State Highway and Transportation Officials. The tests involved subjecting a large number of pavement structures to alternative axle loads and configurations, and then measuring the resulting damage (see Highway Research Board 1962). For each type of pavement, AASHTO subsequently derived a load equivalence factor that varies by axle configuration and axle weight. The load equivalence factor expresses the pavement damage relative to that from an 18,000 lb single axle. Analysis of the variation in these factors by axle weight led to the fourth-power “rule,” which is actually a rough generalization. Subsequent studies of pavement damage from traffic have used a variety of methods. In addition to full-scale road tests like those conducted by AASHTO—which are time-consuming and expensive—studies have used accelerated pavement testing devices and computer simulations. By passing a vehicle over a short stretch of pavement in rapid succession, an accelerated device enables 20 years of serviceability loss to be obtained in several weeks or months. The results from these various studies are, in combination, messier than those from the AASHTO study. Even when the measure of pavement condition was the same as in the AASHTO tests (the present serviceability index), some of the findings have diverged substantially from the fourth-power rule. For example, the accelerated pavement tests conducted by Chen and Shiah (2000) indicated an exponential power of about eight versus AASHTO’s four. The authors speculated that the difference may have resulted partly from the use of heavier axles in their tests than in the AASHTO tests. Another contributing factor was that the vehicles in their tests traveled at slower speed (21 km/hr) than in the AASHTO tests."
For the truly curious, the above came from this publication:
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ctr.utexas.edu]