In order to solve the problem that the calculation formulas of critical depth in arched-section tunnel aren′t expressed by explicit function, a new direct method for calculating critical depth of a arched-section tunnel, which follows from an analysis of the value calculation on the relationship between the relative critical depth and the introduced dimensionless parameter, was derived from transforming the critical flow equation based on improved particle swarm optimization. Error analysis and a computed illustration using the direct formula indicated that the maximum relative error is 0.37 percent in the utility range (ratio of critical depth to arch radius in 1.00～1.85), and the formula has definite conception and brief form.
