Development of a discrete roughness index for longitudinal road profiles

Engineers of off-road equipment, on-road vehicles, pavement and tyres must assess the roughness of a terrain surface for the design of their products. A ubiquitous roughness index is the International Roughness Index (IRI), which quantifies the roughness of a section of road based on the average suspension travel for a particular vehicle at a prescribed speed. The Discrete Roughness Index (DRI) developed in this work addresses a fundamental limitation of the IRI. Specifically, the DRI is calculated for each discretely measured location along a terrain surface; furthermore, the DRI is applicable to vehicles travelling at varying speeds and parameters other than the Golden Quarter-Car on which the IRI is based. The development begins with a consistent discretisation of the terrain surface, vehicle response and the IRI. The Fractional Response Coefficient is then developed which serves a fundamental role in the development of the DRI. Finally, the DRI is developed and its properties are discussed through theory and simulation of the ASTM E1926-08 Profile. One important property of the average DRI is that it converges to the IRI as the distance between sampled points becomes smaller, for the particular case when the Golden Quarter-Car model is simulated at 80 kph. The DRI is a more general solution of the roughness estimation problem than the IRI; therefore, the IRI is a proper subset of the DRI in which the DRI is averaged over a section of road.