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Shock and Vibration
Volume 18, Issue 5, Pages 671-682

Shapes of Obstacles in the Longitudinal Road Profile

Oldřich Kropáč1 and Peter Múčka2

1Scientific Consultant, Kaňkovského 1241/2, CZ-182 00 Prague 8, Czech Republic
2Research worker, Institute of Materials and Machine Mechanics, Slovak Academy of Sciences, Račianska 75, SK-831 02 Bratislava 3, Slovakia

Received 22 December 2009; Revised 11 May 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A voluminous set of longitudinal road profiles gathered from the Long Term Pavement Performance (LTPP) program was processed using median filtering to separate individual large obstacles from the basic quasi-homogeneous random road unevenness. The shapes of 16590 obstacles were analysed partitioned into four sub-groups according to the asphalt-concrete vs. cement-concrete road surfaces, and positive (bumps) vs. negative (potholes) vertical elevations. The empirical obstacle shapes were fitted using seven symmetric and two asymmetric analytical shapes. Based on the root mean square error (RMSE) criterion and accounting for some practical aspects connected with the possible use for the simulation of road profiles with obstacles generalized parabolic shapes (power function) and half-sine shapes seem to be recommendable as adequate approximation functions. Asymmetric obstacle shapes of cosine and parabolic shapes were also briefly discussed and their impact on the vibration transient response of a quarter-car model outlined.