The Direct Solution on Normal Depth of an Egg-Shaped Section Tunnel

Abstract

An egg-shaped is consisted of four parts: One arc bottom, two side circular arc arch and one circular arc roof umbrella arch. It is complex shape. Aiming at traditional methods there are complicated and the defects of inaccurate. on the basis of summarizing the predecessors' research, Based on the normal water depth basic equation mathematical transformation of egg-shaped sections, the interrelation between dimensionless water depth and the dimensionless parameter were analyzed, We use the power function as the formula form, with minimum residual standard deviation as the goal, the coefficients of the formula can be calculated based on the theory of optimization and regression. Then, we get calculation formula for normal water depth. This formula is not a piecewise function, and need not to choose the suitable formula according to the dividing flow. The results can be directly calculated. Results of the example calculation and error analysis showed that the maximum relative error of normal water depth was 0.675% respectively in the utility range (The ratio of water depth divided by height of tunnel is from 0.05 to 0.85). Using this algorithm, above 92 % of the computation error on normal water depth was less than 0.25%. The average error of the formulas was not more than 0.118% .The hydraulic calculation formula will be widely used in engineering design and project management due to its high accuracy and simple form.