Shape characterization methods of irregular cavity using Fourier analysis in tunnel.

The erosion of soluble rock and transformation of groundwater result in the high geometrical irregularity of cavities in nature. The purpose of this paper is to quantitatively describe the shape of irregular cavities using Fourier transform analysis. Firstly, multi-level characterization indexes of the 2D section of cavities have been proposed, considering the high shape irregularity of cavities. The first level indexes include Shape Factor (SF), Aspect Ratio (AR) and Sphere Like (SL). The second level indexes consist of Angularity Factor (AF) and Convexity Factor (CF). The third level indexes are Roundness Factor (RF). Then, the geometric contour of cavity was transformed into a 2D waveform, with an equal-angle points sampling of the cavity boundary. The geometric boundary of irregular cavity was segmented and transformed from discrete time domain to frequency domain based on discrete Fourier transform (DFT). Furthermore, we proposed Fourier shape descriptor, which was found to control the cavity shape. The relationship between Fourier shape descriptors in different sequences and multi-level characterization indexes was determined using designed and irregular nature cavities as sample data. The results demonstrated that the Fourier shape descriptors​ D2, D3 and D8 mainly control multi-level characterization indexes including the overall shape, the irregularity and the roughness of the cavity boundary, respectively. Finally, the 3D characterization method of cavity shape was further proposed based on averaging the 2D sections, which hence offers a possible way to further quantitatively study the mechanical properties of surrounding rockmass effected by the irregular shape of cavities.