American Society of Civil Engineers

Improved Channel Cross-Section with Two-Segment Parabolic Sides and Horizontal Bottom

by Said M. Easa, M.ASCE, (Prof., Dept. of Civ. Engrg., Ryerson Univ., Toronto, ON, Canada M5B 2K3. E-mail:

Journal of Irrigation and Drainage Engineering, Vol. 135, No. 3, May/June 2009, pp. 357-365, (doi:

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Document type: Journal Paper
Discussion: by Sarat Kumar Das E-mail: and et al.    (See full record)
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Discussion: by Ali R. Vatankhah E-mail:    (See full record)
Abstract: A channel cross-section with parabolic sides and horizontal bottom has been recently published and proved to be more economical (provide lesser construction cost per unit length) than the trapezoidal cross-section. This paper presents a new and improved cross section with two-segment parabolic sides and horizontal bottom. Each side of the cross- section consists of two parabolic segments smoothly connected. Closed-form relationships for the cross-sectional area and perimeter are developed. For specific parameter conditions, the new cross-section produces most of the common cross-sections, including the parabolic sides — horizontal bottom and trapezoidal cross-sections, as well as new cross-sectional shapes. It provides an additional degree of freedom in determining the optimal cross-sectional design. A spreadsheet-based optimization model for the new cross-section that minimizes the total construction cost (excavation and composite linings) is developed. The constraints of the model include channel discharge and physical requirements, such as flow depth, top width, and side slope with fixed or depth-dependent freeboard. The model was validated and the cross-sectional performance was evaluated using different design scenarios. The optimization results show that the new cross-section is more economical and more flexible than a cross-section with (one-segment) parabolic sides. As such, it should be of interest to the irrigation and drainage engineers.

ASCE Subject Headings:
Cross sections
Optimization models
Construction costs