Abstract: In current engineering and research, the indices of cross-sectional deformation extracted from point clouds are primarily convergent deformation, which can hardly reflect the deformation characteristics of sectionally continuous deformation properties of shield tunnel linings under the action of a joint. To fully extract the cross-sectional deformation characteristics from point clouds, a deformation characterization method, which takes joints as boundary to fit each segment separately in a polar coordinate system using Fourier functions, is proposed. The fitted curves of each segment are then meshed based on the same density, and the node coordinates are tracked to derive the displacement field of each segment. Full-scale experiments and numerical models are used to validate the reliability of this method. In addition, theoretical analysis and numerical experiments are conducted to examine the influence of key factors (such as the types of fitting functions, influence of measurement errors, and selection of reference system) on deformation extraction results. The findings reveal the following: (1) The higher the order of the Fourier function used for fitting, the more detailed the fitting of the segment lining profile. (2) Under the effect of measurement errors, the application of high-order Fourier functions is susceptible to overfitting, which results in an increase in the deformation extraction error. (3) The proposed method shows its effect and feasibility in actual shield tunnel engineering.

Key words: shield tunnel, laser scanning, point clouds, Fourier function, cross-sectional deformation