Surface tortuosity and its application to analyzing cracks in concrete

Previous studies of tortuosity were restricted to a curve in 2D or 3D. We propose several measures of surface tortuosity based on surface normals and principal curvatures, and apply these measures to analyze the tortuosity of three-dimensional crack surfaces of concrete. We show that all crack surfaces are similar in tortuosity despite their different sizes and locations, while distinctive from various geometric surfaces.