Developing a General Method for Analyzing Nonlinear Weirs Discharge (Case Study: Spillway of Millsite Dam)

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.

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.

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.

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.