The fourth power law (also known as the fourth power rule) states that the stress on the road caused by a motor vehicle increases in proportion to the
fourth power
In arithmetic and algebra, the fourth power of a number ''n'' is the result of multiplying four instances of ''n'' together. So:
:''n''4 = ''n'' × ''n'' × ''n'' × ''n''
Fourth powers are also formed by multiplying a number by its cube. Furth ...
of its
axle load
The axle load of a wheeled vehicle is the total weight bearing on the roadway for all wheels connected to a given axle. Axle load is an important design consideration in the engineering of roadways and railways, as both are designed to tolerate a m ...
. This law was discovered in the course of a series of scientific experiments in the United States in the late 1950s and was decisive for the development of standard construction methods in road construction.
Background
At the beginning of the 1950s, the
American Association of State Highway Officials
The American Association of State Highway and Transportation Officials (AASHTO) is a standards setting body which publishes specifications, test protocols, and guidelines that are used in highway design and construction throughout the United St ...
(AASHO) dealt with the question of how the size of the axle load affects the service life of a road pavement. For this purpose, a test track was built in
Ottawa, Illinois
Ottawa is a city in LaSalle County, Illinois, United States, and its county seat. It is located at the confluence of the navigable Fox River (Illinois River tributary), Fox River and Illinois River, the latter being a conduit for river barges and ...
, which consisted of six loops, each with two lanes. The lanes were paved with both asphalt and concrete of varying thicknesses. In the two-year test, trucks with different axle loads then drove the roads almost continuously. The test was called the
AASHO Road Test
The AASHO Road Test was a series of experiments carried out by the American Association of State Highway and Transportation Officials (AASHTO), to determine how traffic contributed to the deterioration of highway pavements.
Methodology
The ...
.
When evaluating the series of tests, it was found that there is a connection between the thickness of the pavement, the number of load transfers and the axle load, and that these have a direct effect on the service life and condition of a road. The service life of the road is thereby reduced with approximately the fourth power of the axle load.
The accuracy of the law of the fourth power is disputed among experts, since the test results depend on many other factors, such as climatic conditions, in addition to the factors mentioned above.
Calculation examples
This example illustrates how a car and a truck affect the surface of a road differently according to the fourth power law.
* Car (total weight 2
tonne
The tonne ( or ; symbol: t) is a unit of mass equal to 1,000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton in the United States to distinguish it from the non-metric units of the s ...
s, 2 axles): load per axle: 1 tonnes
* Truck (total weight 30 tonnes, 3 axles): load per axle: 10 tonnes
times as large
The ''load'' on the road from one axle (2 wheels) is 10 times greater for a truck than for a car. However, the fourth power law says that the ''stress'' on (damage to) the road is this ratio raised to the fourth power. Since the truck has three axles, this value is tripled, but since the car has two axles, the comparison value is reduced by half. Therefore, the resulting stress difference between truck and car is 15,000 to 1.
See also
*
Pavement engineering
Pavement engineering is a branch of civil engineering that uses engineering techniques to design and maintain flexible (asphalt) and rigid (concrete) pavements. This includes streets and highways and involves knowledge of soils, hydraulics, and mat ...
*
Pavement performance modeling
Pavement performance modeling or pavement deterioration modeling is the study of Road surface, pavement Deterioration modeling, deterioration throughout its life-cycle. The health of pavement is assessed using different performance indicators. S ...
References
External links
AASHO Road Testat Federal Highway Administration website
*{{cite book , author = Highway Research Board , year = 1962 , title = The AASHO Road Test: Report 7, Summary Report , url = https://onlinepubs.trb.org/Onlinepubs/sr/sr61g/61g.pdf , location = Washington, DC , publisher = National Academy of Sciences—National Research Council , via = Transportation Research Board
Pavement engineering
Tests