Discharge capacity of shaft spillway with a polygonal section: a case study of Djedra dam (East Algeria)

This paper proposes a new design for the shaft spillway of the Djedra dam (East Algeria). The procedure consists of replacing the circular section with a polygonal configuration of twelve (12) sections. The study of the model was divided into five different versions according to the variants of technical modifications of the water intake funnel; this configuration was tested on a hydraulic model in the laboratory of hydroelectric power plants of the Moscow State University of Environmental Engineering. The use of the polygonal section weir can greatly simplify the formwork of the structure, also the free entry funnel increases the discharge coefficient by 20%, without exposing the head of the weir to the risk of cavitation. In the event of submersion, the adopted design can ensure the crossing of an estimated relative flow with a probability of P1⁄4 0.01%, which means reducing the height of the dam by 0.68 m, and thus making the hydraulic structure more efficient economically and more reliable. The experimental model was produced on a 1:60 scale of the prototype, which guarantees self-simulation of the hydraulic phenomena of the Djedra dam, and its final design is judged to be hydraulically satisfactory and recommended for construction.


INTRODUCTION
In order to specify the parameters of the shaft spillway with a polygonal configuration, hydraulic researches were carried out in two stages, a theoretical analysis, and hydraulic tests on the physical model in the laboratory of hydroelectric power station of Moscow State University of Environmental Engineering.
The first stage consists of the theoretical analysis to specify the technical solutions and the parameters of the spillway and shows that the hydraulic calculation of the weir in a well is determined according to a given flow rate of the contours of the structural elements which ensure the normal system operation. It is necessary to design the structure in such a way that under normal conditions of their operation, a stable flow regime was provided (pressure or non-pressure) within the water supply part (tunnel) (Sun et al. ). Transient, partial-pressure hydraulic modes are allowed only when ensuring the transition from a pressureless regime to a pressure regime and conversely, without the occurrence of significant ripple effects, which should be justified by special calculations and laboratory data hydraulic studies (Slissky ; Rozanov et al. ).

Study area
The Djedra dam is located in the East of Algeria and is intended for long-term regulation of the river flow. The coordinates of its location are 7 54 0 17.305″E 36 16 0 44.064″N.
Its geographical location is presented in Figure 1.

Site rainfall data
Average annual precipitation for the watershed of wadi Djedra is adopted from the Souk-Ahras meteorological station. The distribution within the year is irregular; in the wet season from September to April it falls to on average 87-90% of the annual sum and in the period from November to Marchalmost 80%. During certain years, in dry periods, the precipitation is less than 1% of the annual sum.
The average annual precipitation in the study area for the period 1920-2007 is presented in Table 1.
The structure of the dam includes a reinforced concrete dam about 60.0 m high with a crest level of 560.0 m, a weir in a well with a head in polygonal section, a tunnel and a water channel. The detail is presented in Figure 2.
The main hydraulic parameters of the Djedra dam are summarized in Table 2.

Experimental setup
The test installation was placed in the organic glass pane in the laboratory of the laboratory of hydroelectric power stations of the Moscow State University of Environmental Engineering (Russia); this channel has a bottom with zero slope, a width of 100 cm and a length of 950 cm and is joined to a feeding tank whose dimensions in area are 1.64 × 2.0 m. The structure of this channel is shown in   The shape of the funnel for receiving the water from the spillway into a well is designed in polygonal section, and its dimensions in area are shown in Figure 5.

Instrumentation and measurement techniques
The Unit and total flows were calculated in accordance with the depths and velocities measured.   In accordance with formula (1) we have:  Thus, if we examine the movement of water in the water pipe, the determining force there will be the force of friction at the borders of the flow (White ): The similarity of the phenomena (according to the Equation (1)) must be ensured in the event of satisfaction of the relationship: where, μ -dynamic viscosity; ν -kinematic viscosity.
From (3) we get: That is to say during the simulation of the friction forces at the border of the flow, the Reynolds numbers for nature and the model must be identical. Reynolds numbers are equal for the full-scale structure and the reduced model can be determined using Table 3 in the case of using water as a test liquid (Chanson ).
In accordance with Table 3, the scale coefficients for converting the main characteristics of the model spillway into full-scale work are:  -Velocity scale m V : time scale m t : -flow conversion m Q : The  Table 4.
The flow rate of the flow through the weir in a well is determined by the next equation (Akan ):

RESULTS AND DISCUSSION
The hydraulic structure depends on several hydrological, geological, and geotechnical conditions which differ from one case to another, but the good thing is that the same approach can be applied for other cases, the same hydraulic approach and the same equations can be applied too, to improve the functioning of the structure and reduce the costs as well, it is for this reason that all design parameters are given in dimensionless values, which allows them to be used in accordance with the theory of hydraulic similarity.
All parameters of the proposed structure of the mine spillway can be used regardless of the climatic and other characteristics of a particular region, therefore a limitation in the use of such works, is conditioned by another more efficient spillway structure, which will be solved by an economic comparison of these variants.
The paper is of course a case study, but this case can be similar to others in terms of the manner of treating the hydraulics structures, so we have written this paper in such a way, that it can be considered as a protocol, The discharge capacity of a mine spillway is determined by the discharge of two structural elements: a water intake funnel and the output section of the shaft spillway (Akan

).
As can be seen in the graphs in Figure 8 which show the discharge characteristics of the water intake funnel when operating with the flow free mode Q int. funnel ¼ f (Z NWL ) depending on the water level of the upstream level and the discharge characteristics of the output section of the shaft Q output. Section ¼ f (Z WL output. Section , а) depending on the water level in the trunk mine and the height of its output section a: where: σ 1: submerging coefficient; m: Flow coefficient of the ridge of the intake funnel; L: Distance of the crest of the intake funnel; H: Head on the crest of the intake funnel; g ¼ 9.81 m/s 2 -acceleration of gravity.
The flow rate Q of the output section of the shaft is calculated by the equation (Akan ): where μ is the generalized flow coefficient, determined by the equation (Moise ): where: The analysis in Figure 9 shows a graph of the maximum discharge pressure of the free flow mode on the crest of the intake funnel over the relative height of the outlet section of the mine shaft. This dependence is well approximated by the Equation (14), is the result of a mathematical treatment of the experimental curve of Figure 9:  for the transition point from the free and submerged operation is shown in Figure 10.
Equations (15) and (16)     resistance. In this section, the change in the flow coefficients is well described by the equation: Flood routing is often the most important hydraulic problem posed by the construction of large dams. This study is a unique case in Algeria, its configuration was tested on a hydraulic model in the laboratory, and proposes a new design for the well spillway of the Djedra dam (eastern Algeria). The procedure consists of replacing the circular shape with a polygonal configuration of twelve (12)

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.