Title: Systematic Investigation of Wavy Surface Roughness Profiles Using Common Roughness Algorithms
Program: Master of Science in Civil Engineering
Advisor: Dr. Nick Hudyma, Civil Engineering
Committee Members: Dr. Bhaskar Chittoori, Civil Engineering; and Dr. Mary MacLaughlin, Civil Engineering
Roughness is an important parameter in rock engineering. Sine wave-based simulated wavy profiles were used to investigate systematic changes of amplitude and frequency on roughness indices. Profiles were 1000 mm in length with amplitude ranging from 0-10 mm and frequency ranging from 0-10 Hz. The roughness algorithms used were Root Mean Square (RMS), Energy, Sinuosity, Z2, Mean Absolute Angle (MAA), and Modified Divider a Value. Roughness indices were visualized as contour plots. Similarities of the shapes and spacing of the contours as well as the magnitude of the roughness indices, prompted the pairing of RMS and Energy algorithms, Z2 and MAA algorithms, and Modified Divider a Value and Sinuosity algorithms.
Equations were developed to relate the paired roughness algorithms. The process for developing the equations began with producing best-fit surfaces of the roughness indices contour plots and assessing their validity using a tolerable percentage difference of 5% between roughness indices and best-fit surface-derived roughness indices. A translation equation using the roughness indices of the paired algorithms and a best-fit surface to the translation equation data was developed. The roughness indices of one of the paired algorithms multiplied by the translation factor yielded the computed roughness indices of the other paired algorithm. The computed roughness indices were compared to the roughness indices using a tolerable percentage of 5%. The equation linking Energy and RMS was successful at estimating the true roughness indices 83.3% of the time for a 5% tolerable difference. The equation linking Z2 and MAA was successful at estimating the true roughness indices 73.8% of the time for a 5% tolerable difference. The equation linking Sinuosity and Modified Divider a Value was successful at estimating the true roughness indices 86.1% of the time for a 1% tolerable difference.