Optimization of a composite trapezoidal channel cross section with non-uniform lining material

Subject Areas : Analysis, design and construction of water structures

Farinaz Sadat Mirlohi ^{1 *}

1 - Master's degree in Civil-Water and Hydraulic Structures, Expert at Tarh Afra Consulting Engineers Company, Isfahan, Iran.

Received: 2025-04-10 Accepted : 2025-07-17 Published : 2025-02-09

Keywords: Optimization, Freeboard, Composite channel, Construction cost, Design variable,

Abstract :

In any engineering system, such as water conveyance channels, the primary objectives in design are minimizing costs and maximizing efficiency. Additionally, reducing the risk of overtopping is a critical consideration in channel design. Open channels typically feature either simple or compound cross-sections. Compound sections are characterized by varying side slopes on either side or different roughness coefficients across their surfaces. This study aims to reduce construction costs—including excavation and lining expenses—while minimizing overtopping risk by incorporating a freeboard allowance for a compound channel with identical side slopes but varying roughness coefficients on different surfaces. The problem formulation, constrained by Manning’s equation, leads to a nonlinear optimization problem solved using Wolfram Mathematica. The results demonstrate that when different roughness coefficients are applied to the channel walls and bed—and when lining costs also vary between these surfaces—the optimal side slopes differ compared to the uniform-cost scenario. However, the optimized hydraulic parameters (e.g., depth, velocity) remain similar to those of a simple trapezoidal section.

References:

Adarsh, S., Sahana, A.S. (2013). Minimum Cost Design of Irrigation Canals Using Probabilistic Global Search Lausanne. Arabian Journal for Science and Engineering. 38, 2631-2637. https://doi.org/10.1007/s13369-012-0493-x
Anwar A. A., Clarke D. (2005). Design of hydraulically efficient power-law channels with free board Journal of Irrigation and Drainage Engineering. 131:560-563. Applications (IJERA). 1:1317-1322.
Bhattacccharjya R. K. and Satish M. G. (2007). Optimal design of stable trapezoidal channel section using hybrid optimization techniques Journal of Irrigation and Drainage Engineering .133:323329.
Das A. (2000). Optimal channel cross secttion with composite roughness. Journal of Irrigation andDrainage Engineering. 126:68-71. https://doi.org/10.1061/(ASCE)0733-9437(2000)126:1(68)
Das A. (2007). Flooding probability constrained optimal design of trapezoidal channels. Journal of Irrigation and Drainage Engineering. 133:53-60. https://doi.org/10.1061/(ASCE)0733-9437(2007)133:1(53)
Ghasemi Khiadani, M., Khoshfetrat, A., & Maleki, M. (2024). Optimization of the cross-section and free board of trapezoidal channels based on the minimum probability of overflow and excavation and covering costs. Technical Strategies in Water Systems, 2(4), 304-314. https://doi.org/10.30486/TSWS.2024.783405
Ghazaw Y. M. (2011). Design and analysis of a canal section for minimum water loss. Alexandria Engineering Journal. 50:337-344
Guo C.Y. and Hughes C. (1984). Optimal channel cross section with freeboard. Journal of Irrigation and Drainage Engineering. 110:304-314. https://doi.org/10.1061/(ASCE)0733-9437(1984)110:3(304)
Han Y. C., Easa S. M. (2018). Exact Solution of optimum hydraulic power-law section with general exponent parameter [J]. Journal of Irrigation and Drainage Engineer.
Hussein A. (2008). Simplified Design of hydraulically efficient power-law channels with freeboard. Journal of Irrigation and Drainage Engineering. 134:380-386.
Kentli, A., & Mercan, O. (2014). Application of Different Algorithms to Optimal Design of Canal Sections. Journal of Applied Research and Technology, 12(4). https://doi.org/10.1016/S1665-6423(14)70092-6
Lavasani.E. (2020). Trapezoidal open channel cross section optimization by considering the total free height as a design variable and in terms of excavation, coating, evaporation, infiltration and acquisition costs. Master Thesis, Faculty of Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University. (In Persian)
Loganathan G.V. (1991). Optimal design of parabolic canals. Journal of Irrigation and Drainage Engineering. 117:716-735.
Roshanghar, K., Talat-Ahari, S., & Noori, A. (2014). Influence of Restricted Hydraulic Parameters on Optimal Design of open Channels Sections. Water and Soil Science, 24(2), 171-182.
Swamee, P. K., Mishra, G. C., & Chahar, B. R. (2000a). Design of minimum seepage loss canal sections. Journal of Irrigation and Drainage Engineering, 126(1), 28-32.
Swamee, P. K., Mishra, G. C., & Chahar, B. R. (2000b). Comprehensive Design of Minimum Cost IrrigationCanal Sections. Journal of irrigation and drainage engineering, 126(5), 322-327.