Three-dimensional characterization method of pile–rock interface roughness based on fractal geometry

Abstract

Shaft friction is an important component of the pile foundation bearing capacity in construction projects, whereas the roughness of a pile–rock interface is one of the key components affecting shaft friction. An accurate characterization of the roughness of a pile–rock interface can help in determining the lateral friction of the pile–rock interface. In the present study, a new fractal geometry characterization parameter was proposed based on traditional roughness characterization methods and the structural function of a fractional Brownian field, namely, the three-dimensional (3D) characteristic roughness parameter l∗. Its definition, geometric meaning, and calculation method are described herein. In addition, photogrammetry was used to obtain grayscale images of pile–rock interfaces from an actual construction project. The results verified through a 3D reconstruction method reveal that the grayscale values can be used to represent the changes in the interface profile. Consequently, the 3D fractal dimension D, the surface root mean square deviation Sq, and the 3D characteristic roughness l∗ were calculated based on the grayscale values of the processed images. A comparison and verification of the results demonstrate that the 3D characteristic roughness parameter is more objective and advantageous than the other parameters. The 3D characteristic roughness is not only suitable for characterizing the roughness of pile–rock interfaces, but also applicable to characterize the roughness of other surface types, including rock discontinuities, rock joints, and concrete and road surfaces.