Improvements to solutions for normal depth in multiple sections of tunnels. (June 2020) - Shang, Haixin
Abstract: The normal depth is an essential parameter for the design, operation, and maintenance of open channels. The circular, city-gate crossing and egg-shaped sections are often used in non-pressure tunnels in hydraulic engineering, agricultural irrigation, and sewerage works. However, the equations governing the normal depth in various sections are complicated implicit transcendental equations. In order to improvements the solutions for normal depth in multiple sections of tunnels, a function model is first established for the geometric features of various sections using the mathematical transform method and while considering non-dimensional parameters. Then implement the revised PSO algorithms in MATLAB, and establish three right solution's formulas for the normal depths in different non-pressure tunnel sections through optimization. The error analysis results and project cases show that the established formula has broad applicability. The maximum relative errors of the formula for normal depths are less than 0.07%, 0.04%, and 0.07% in circular, city-gate crossing, and egg-shaped sections, respectively, which are more accurate than the existing formulas. The results of this research may be useful in design, operation, and maintenance in tunnel engineering. Highlights: The formula for the normal depths in various tunnel has broad applicability and more accurate than the existing formulas.