A Method for General Analyzing Nonlinear Weirs Discharge (Case Study: Millsite Dam Spillway)

Document Type : Research Article


1 Civil Engineering Dept., Engineering Faculty, Urmia University, Urmia, Iran

2 Civil Engineering Dept., Engineering Faculty,, Urmia University, Urmia, Iran.


Introduction: The safety of dams is directly related to the sufficiency of spillway capacity. Most dam failure occurs due to overtopping when the discharge capacity of the spillway was not sufficient. The safe operation of the spillway, under abnormal conditions, is an essential factor in the safety of dams. According to reports released by the International Committee on Large Dams, about one-third of dam failures stem from inadequate spillways. Owing to this sensitivity, the spillway must be designed and constructed as a strong, reliable, and highly productive structure that can be ready for operation at any time. Nonlinear weirs which can be seen in various forms in the plan are economical structures to increase the discharge capacity in a limited width. These weirs have a higher discharge capacity in the same hydraulic head and width. Due to the hydrodynamic complexities of the flow in nonlinear weirs, a general analytical method has not been developed yet in the literature to estimate the discharge capacity of this type of weirs. Usually, the discharge capacity of any nonlinear weir is obtained through various experimental investigations. In this research, a general method is presented for estimating the discharge capacity of nonlinear spillways.
Methodology: The EDA method is based on nonlinear weir discharge analysis using energy and discharge equations for discrete elements of the solution domain (weir crest in the plan). On the other hand, due to the specific behaviors that occurred in nonlinear weirs (disturbed zone) which have a tangible effect on their discharge capacity, these effects have been taken into account. The geometry of the weir in the plan is the desired solution domain, which is divided into small elements and the corresponding equations in each element have been analyzed. The disturbed zone may also form at the junction of the weir crest to the sidewalls. This phenomenon reduces the discharge capacity, especially at high hydraulic heads. To apply the impact of this phenomenon on the discharge capacity of the affected elements, the relationships and results of the past works could be used. The system of differential equations for each element is solved following the discretization of the solution domain. Thus, the flow discharge past each element is found. Thereafter, the disturbed zones are identified and their reduction effects on the flow discharge of the elements are considered estimating the reduction factors of elements. Finally, the total discharge of non-linear weir will be obtained by integrating over the entire solution domain. To achieve this goal, a computer program is developed using the MATLAB programming language to code the above-mentioned steps.
Results and Discussion: This method is based on elementary analysis of nonlinear weirs, which calculates the discharge capacity of these weirs by solving energy and discharge equations for each element and correcting the effects of disturbed zones. For evaluating the performance of the proposed method, laboratory results performed on oblique and trapezoidal labyrinth weir have been used. Results show that the accuracy of the EDA model for calculating the discharge capacity has been in the error range of 12% and 20%, respectively. Also, the results of the laboratory model of the rehabilitation project of the Millsite dam spillway (arc labyrinth weir) have been used to investigate the performance of the proposed method in complex geometries. The EDA model with a maximum error of 15% had a satisfactory prediction of the discharge capacity of the Millsite dam weir.
Conclusion: Due to the unique characteristics and increasing application of nonlinear spillways in dams and other hydraulic structures, a general method for analyzing the discharge capacity of these structures can play an important role in design phases. One of the most important applications of nonlinear weirs is in dams where they are revised as rehabilitation projects to increase the capacity of the spillway overpass or increase the volume of the dam reservoir. Due to the hydrodynamic complexity of the flow in nonlinear weirs, no general method has been proposed for their discharge analyses and has often been investigated by laboratory models. In this research, a general method for analyzing nonlinear weirs discharge is presented. To ensure the performance of the EDA method, the laboratory model of oblique and trapezoidal labyrinth weir (at different scales) that studied has been used. The results show that the proposed method has good accuracy in estimating the discharge capacity of oblique and trapezoidal labyrinth weirs. The Millsite Dam spillway, which has one of the notable rehabilitation projects, was also investigated. The results show that the proposed method is relatively better in estimating the discharge capacity of the Millsite Dam spillway over other methods.


Azimi, A.H., Rajaratnam, N. and Zhu, D.Z. (2014). Submerged flows over rectangular weirs of finite crest length. Journal of irrigation and drainage Engineering, 140(5), 06014001.
Borghei, S.M., Vatannia, Z., Ghodsian, M. and Jalili, M.R. (2003). Oblique rectangular sharp-crested weir. In: Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering, 156(2), 185-191.
Carrillo, J.M., Matos, J. and Lopes, R. (2020). Numerical modeling of free and submerged labyrinth weir flow for a large sidewall angle. Environmental Fluid Mechanics, 20(2), 357-374.
Christensen, N.A. (2012). Flow characteristics of arced labyrinth weirs, MSc Thesis, Utah State University, Utah, 107p.
Crookston, B.M. (2010). Labyrinth weirs, PhD Thesis, Utah State University, Utah, 223p.
Crookston, B.M. and Tullis, B. P. (2012). Arced labyrinth weirs. Journal of Hydraulic Eng., 138(6), 555-562.
Crookston, B.M. and Tullis, B.P. (2012). Labyrinth weirs: Nappe interference and local submergence. Journal of Irrigation and Drainage Engineering, 138(8), 757-765.
Crookston, B.M. and Tullis, B. P. (2013). Hydraulic design and analysis of labyrinth weirs. I: Discharge relationships. Journal of Irrigation and Drainage Engineering, 139(5), 363-370.
Crookston, B.M., Mortensen, D., Stanard, T., Tullis, B.P. and Vasquez, V. (2015, April). Debris and maintenance of labyrinth spillways. In: Proceedings of the 35th Annual USSD Conference, Louisville, KY, USA, 13-17.
Erpicum, S., Laugier, F., Boillat, J.L., Pirotton, M., Reverchon, B. and Schleiss, A.J. (2011). Labyrinth and piano key weirs. CRC Press.
Erpicum, S., Tullis, B.P., Lodomez, M., Archambeau, P., Dewals, B.J. and Pirotton, M. (2016). Scale effects in physical piano key weirs models. Journal of Hydraulic Research, 54(6), 692-698.
Hay, N. and Taylor, G. (1970). Performance and design of labyrinth weirs. Journal of the Hydraulics Division, 96(11), 2337-2357.
ICOLD. (1999). Bulletin on Risk Assessment: Risk Assessment as an Aid to Dam Safety Management, Draft, International Commission of Large Dams, Draft 24.08.99, 102 p.
Khode, B.V., Tembhurkar, A.R., Porey, P.D. and Ingle, R.N. (2012). Experimental studies on flow over labyrinth weir. Journal of Irrigation and Drainage Engineering, 138(6), 548-552.
Lopes, R., Melo, J.F. and Matos, J. (2008). Characteristic Depths and Energy Dissipation Downstream of a Labyrinth Weir, 51-58.
Magalhães, A. and Lorena, M. (1989) Hydraulic design of labyrinth weirs, Rep. No. 736, Lisbon, Portugal: National Laboratory of Civil Engineering.
Majedi Asl, M., Fuladipanah, M., Daneshfaraz, R. and Jannat, K. (2021). Modeling and assessment of discharge coefficient of arc labyrinth weir using experimental and meta-model methods. Iranian Journal of Soil and Water Research, 52(7), 1987-2000. (in Persian)
Ohadi, S. and Jafari-Asl, J. (2021). Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs. Flow Measurement and Instrumentation, 77, 101787.
Pfister, M., Battisacco, E., De Cesare, G. and Schleiss, A.J. (2013). Scale effects related to the rating curve of cylindrically crested Piano Key weirs, Intl. Conf. on Labyrinth and Piano Key Weirs II, 73–82, CRC Press, London.
Pfister, M., Capobianco, D., Tullis, B. and Schleiss, A.J. (2013). Debris-blocking sensitivity of piano key weirs under reservoir-type approach flow. Journal of Hydraulic Engineering, 139(11), 1134-1141.
Safarzadeh, A. and Noroozi, B. (2017). 3D hydrodynamics of trapezoidal piano key spillways. International Journal of Civil Engineering, 15(1), 89-101.
Sangsefidi, Y., Mehraein, M., Ghodsian, M. and Motalebizadeh, M.R. (2017). Evaluation and analysis of flow over arced weirs using traditional and response surface methodologies. Journal of Hydraulic Engineering, 143(11), 04017048.
Shafiei, S., Najarchi, M. and Shabanlou, S. (2020). A novel approach using CFD and neuro-fuzzy-firefly algorithm in predicting labyrinth weir discharge coefficient. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(1), 1-19.
Spencer, A.C. and Tullis, B. (2017).  Millsite dam arced labyrinth weir design, United States Department of Agriculture Natural Resources Conservation Service.
Swamee, P.K., Ojha, C.S.P. and Mansoor, T. (2011). Discharge characteristics of skew weirs. Journal of hydraulic research, 49(6), 818-820.
Taylor, G. (1968). The performance of labyrinth weirs, PhD Thesis, University of Nottingham, Nottingham, 410p.
Thompson, E.A., Cox, N.C., Ebner, L. and Tullis, B. (2016). The hydraulic design of an arced labyrinth weir at Isabella Dam, 6th International Symposium on Hydraulic Structures, Hydraulic Structures and Water System Management, Utah State University, Portland, Oregon, USA, 27-30 June 2016.
Torres, C., Borman, D., Sleigh, A. and Neeve, D. (2021). Application of Three-Dimensional CFD VOF to Characterize Free-Surface Flow over Trapezoidal Labyrinth Weir and Spillway. Journal of Hydraulic Engineering, 147(3), 04021002.
Tullis, J.P., Amanian, N. and Waldron, D. (1995). Design of labyrinth spillways. Journal of hydraulic engineering, 121(3), 247-255.
Zounemat-Kermani, M., Kermani, S.G., Kiyaninejad, M. and Kisi, O. (2019). Evaluating the application of data-driven intelligent methods to estimate discharge over triangular arced labyrinth weir. Flow Measurement and Instrumentation, 68, 101573.