Abstract: A novel method for calculating lining flatness based on multiparameter fusion is proposed to address challenges in the refined characterization of the surface flatness of the initial shotcrete layer of sprayed anchor linings. The proposed method integrates the fractal dimension （D） and the root mean square of the first derivative （Z₂） to establish a quantitative functional relationship with a flatness coefficient (n_JRC) (correlation coefficient R² = 99.8%). The validity and accuracy of the developed formula are verified through comparisons with results obtained using the joint roughness coefficient (m_JRC) formula from classical literature. The method is applied to three-dimensional (3D) point cloud data collected from an on-site tunnel test section, in which tunnel contour lines are extracted and segmented to calculate flatness values at different positions of the initial shotcrete layer. The proposed method is further compared with traditional approaches, and the key findings include the following: (1) The proposed method enables a more comprehensive characterization of the microscopic roughness and macroscopic geometric features of tunnel lining surfaces by integrating the power parameters of fractal dimension and the root mean square of the first derivative to calculate the flatness coefficient. (2) To achieve omnidirectional flatness detection without blind spots, the proposed method effectively captures 3D irregular surface features that are difficult for traditional methods to identify by computing the weighted average of adjacent two-dimensional contour lines. (3) The proposed method outperforms conventional methods in terms of detection sensitivity and 3D irregular feature capture, thereby more accurately reflecting the complex spatial variability characteristics of the tunnel lining surfaces.

Key words: tunnel engineering, shotcrete lining, flatness, multiparameter fusion, three-dimensional laser scanning