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Khikmatov Bekzod Fazliddinovich, applicant of the Chair of Hydrology and Hydrogeology of the M. Ulugbek's National University of the Republic of Uzbekistan E-mail: nauka@fvv.uz Pirnazarov Ravshan Topvoldievich, associate professor, of the Fergana State University E-mail: pirnazarov.r@mail.ru
CALCULATION OF THE OUTBREAK DISCHARGES THROUGH A CLOSURE CHANNEL WITH TRAPEZOID SHAPE OF CROSS-SECTION
Abstract: The technique for calculation of the outbreak discharges flowing through the closure channel of trapezoid shape is considered. With few limitatios this technique was tested on the example of the blocked-up dam of Kurbankul lake.
Keywords: blocked-up dam, outbreak lake, water level, rise of the level, discharge, closure channel, cross-section, trapezoid shape, outbreak discharges, calculation techniques.
Introduction. In the mountains of Central Asia and in Uzbekistan, as well, outbreak lakes of different genetic origin are observed rather often. Under influence of different factors such as meteorological, hydrological, geological, hydrogeological and others, they are filled with flood water, and then overflow over the blocked-up dam begins. With such conditions the closure channels with different shape of cross-section are formed over the top of dam. In some cases such closure channels are formed on the dam body. Often this is facilitated with a high hydrostatic hydraulic head before the dam.
From the published literary sources [1-10] it is known that many researches made calculations of the maximum outbreak discharges for the conditions when the block-ups or dams are were washed out immediately. As it was noted by Yu. M. Denisov [1; 2], this condition made it possible to be constrained with application of relevant calculation formula without taking the temporal dynamics of the studied phenomenon into account. More comprehensive analysis of this process has shown that the duration of the natural washout always has its end and can continue from several minutes to several days. Besides, the duration of the washout of the closure channel is one of the main factoros which influence the value of the maximum break-out discharge [1].
Data. In this work the technique elaborated by Yu. M. Denisov for calculation of the outbreak discharges flowing through the closure channel with the cross-section of trapezoid shape is interpreted for the conditions of the blocked-up dam of Kurbankul lake. This lake is related to the blocked-up type of tectonic group according to the genetic classification of A. M. Nikitin [4]. It is located on the northern slopes of the Alay ridge, at the height of1725 m above sea level
in the basin of Koksu river of the right tributary of Shakhi-mardansai river (Syrdarya river basin). In the calculations the full-size data obtained in the result of conduction of special topographic-and-geodesic, hydrological and hydrogeologial works carried out during the field studies performed in the region of the investigated territory [7] were used.
Results and discussion. It is known that the closure channels in most cases are of optional shape. For the step-by-step solution of this task we assumed the following succession of the shapes of the closure channel cross-section: rectangular, trapezoid and parabolic shapes. We have considered the issues of the calculations of the outbreak discharges flowing through the closure channel with the rectangular cross-section in the previous work [10]. This work is related to consideration and testing of the techniques designed for calculation of the outbreak discharges flowing through the closure channel with the trapezoid cross-section applying the method developed by Yu. M. Denisov [1] on the example of the blocked-up dam of Kurbankul lake.
For the solution of this task according to the method of Yu. M. Denisov, let's introduce the following symbols:
P(Z, t) - area of the closure channel below Z horizontal at t time;
Z - height of the horizontal at t time;
Z (t) - mark of the low border of the closure channel at t time;
Z (t) - mark of the upper (for the hidden on the top) border of the closure channel at t time;
Хp(Z, t) - length of the perimeter of the closure channel below Z horizontal at t time;
BP (Z, t) - width of the closure channel below Z horizontal at t time. Proceeding from all mentioned above, it equals to:
Section 2. Geography
dP
BP(z,t) = —, dZ
(1)
On base of the mentioned above it is worth to note that that the following two cases of formation of the closure channel are observed:
1) with the condition if Z (t) > Z (t) - then the closure channel is open;
2) with the condition if Z2P (t) < Z (t) - then the closure channel is closed on the top, i.e. the closure channel is formed on the dam body.
Let'consider the first case, i.e. when the closure channel is open and the first condition is fulfilled. Then the discharge through the closure channel at t time is calculated according
to the following determined integral:
ZB (t)
Qp(t) = J Bp(Z,t)•[(ZB(t)-Z)]0,5 • dZ, (2)
Zip(t)
Taking the expression (l) into account, it is possible to write the following equation for the outbreak discharge as folows:
Zb (t)
QP (t) = \ [2g(Zb (t) - Z)]0,5 • dZ (3)
Zip(t)
After integration of equation (3) by parts, we obtain the following equation:
Zb (t)
QP (t) = J
Zip(t)
g _ P(Z,t) 2 JZB(t) - Z
dZ
(4)
The second case, i.e., the condition Z2P (t) < ZB (t) is fulfilled, and the closure channel will be closed on the top. In this case for calculation of the outbreak discharge Q(t) it is necessary to change ZB(t) variable in the upper threshold of integration to Z (t) in formulas (2), (3) and (4). With this, the outbreak discharge Q^(t) can be estimated with the available values of the following morphometric characteristics of the closure channel at t time:
1) P(Z, t) - area of the closure channel below Z horizontal at t time;
2) ZB(t) - mark, i.e., the height of the width of the closure channel at t time;
3) Z (t) - mark of the low border of the closure channel at t time;
4) Z (t) - mark of the upper border of the closure channel hidden on the top at t time;
We would like to knote that expression (4) is the most general formula derived for the calculation of the outbreak discharges QP(t). As it was noted above, in the majority of cases of the dam outbreaks, the closure channels are open.
Let's consider the example of calculation of the values of the outbreak discharges QP(t) using formula (4) with the prescribed shapes of the open closure channels. Proceeding from
the task of the work, let's assume that the shape of the closure channel is of trapezoid type. Then the area of the closure channel below Z horizontal at t is estimated with the expression:
P(Z,t) = Bp (Z1P (t),t)(Z - Zip (t)) + (Z - Z1P (t^ (5)
tga
where a - is the angle of slide of the closure channel wall.
In this case, with substituting the values of P(Z, t), i.e., of the area of the closure channel with trapezoid shape of the cross-section to the formula (4) and with integrating it, we get the formula for the calculation of the outbreak discharge in the following form:
Qp (t) = -J fBP (Zp (t ),t )(Zr (t) - Z1P (t ))2 +
(6)
+ ^ • i6 • g(Zb(t) - Zip(t))2, tga i5 2
After a number of simplifications and transformations, the calculation formula (6) derived by Yu. M. Denisov for calculation of the discharge flowing through the closure channel with trapezoid shape of the cross-section is as follows:
QP (t) = e- m ■ bfig -Ah(7) where: e - is lateral compression coefficient. In our case it can be assumed that e = 1.0, as the angle of slide of the closure channel wall a = 6 o30/; m - discharge coefficient, for the closure channel similarily as for the spillway with a thick wall of trapezoid shape m = 0.35 [3]; b - width along the closure channel; in our case - the width along the bottom of the closure channel, i.e., dry channel b = 11 m; g - free fall acceleration, 9.81 m/s2; Ah - flow depth in the closure channel.
The last formula is applied for calculation of possible discharge flowing through the dry channel located over the top of the blocked-up dam of Kurbankul lake. The cross-section of the dry channel is of trapezoid shape (table 1).
In the table it is shown that with the inflow ofwater to the basin of Kurbankul lake (which is 115 m3/s), after 5 minutes its level will rise to 14 cm. Consequently, the depth of the flow in the former dry channel will be also 0.14 m. In the result, the value of discharge in the closure channel will be Q = 0.89 m3/s. In the end of the next 5 minute period its value rises three times and reaches 2.66 m3/s.
It is necessary to note that because of the absence of the clearly manifested channel over the dam top, this quantity can be taken as the channel-forming discharge. Actually saying, this quantity of discharge after intensive washing out of the mountain rocks over the dam with a big slope, begins to form an appropriate channel. During the subsequent calculation periods the value of discharge flowing through the dry channel over the dam rises intensively, and reaches up to 13.37 m3/s after 30 minutes.
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Table 1. - Calculation of possible outbreak discharges flowing through the closure channel with the trapezoid cross-section
№ in order Time, t, mill. s ■ m ■ byflg Ah, m 3 Ah, * Qp(t), m3/s
1 0 0 0 0
2 5 0.14 0.052 0.89
3 10 0.29 0.156 2.66
4 15 0.43 0.282 4.81
5 20 0.57 0.430 7.34
6 25 0.71 0.598 10.21
7 30 17.06 0.85 0.784 13.37
8 35 0.98 0.970 16.55
9 40 1.12 1.185 20.22
10 45 1.25 1.398 23.84
11 50 1.38 1.621 27.66
12 55 1.50 1.837 31.34
13 60 1.63 2.081 35.50
14 90 2.39 3.695 63.03
Conclusions. On the base of the obtained results, the affects negatively the stability of the blocked-up dam, and this
following conclusions can be made: can facilitate the origination of the mudflows in Koksu river
1) in the calculations it is assumed that the shape and sizes channel down the blocked-up dam which is undesirable;
of the cross-section of channel over the dam are constant. In 2) in perspective, with taking the recommendations and
our case only the flow depth (Dit is necessary to take to ac- proposals given in the former studies [7] into account, it is
count that the above mentioned discharge values will wash necessary to take relevant measures directed to the provision
out the channel, and consequently, its deepening takes place of stability of the blocked-up dam and for the prevention of
and discharge values will be much greater. Such circumstance the overflow of water over the top of the blocked-up dam.
References:
1. Denisov V. M. On the average velocity of the uniform motion of the free-flow turbulent flows // Proceed. of SANII of Goskogidromet. 1982.- Issue 94(175).- P. 56-74.
2. Denisov Yu. M. Calculation of the outbreak discharge values and washing-out of the closure channel // Proceed. Of NIGMI. 2010.- Issue 12(257).- P. 3-18.
3. Kiselev P. G. Reference book on hydraulic calculations.- M.-L.: Gosenergoizdat, 1961.- 352 p.
4. Nikitin A. M. Lakes of Central Asia.- L.: Gidrometeoizdat, 1987.- 106 p.
5. Nikitin A. M. Investigation of the outbreak lakes of Central Asia // Survey information.- Series 37.27. Land hydrology.-Obninsk, 1990.- Issue 1.- 35 p.
6. Pirnazarov R. T. Outbreak lakes and factors determining their stability // Transactions of HS of Uzbekistan.- Tashkent, 2007. - Volume 29.- P. 146-149.
7. Pirnazarov R. T., Khikmatov F. Kh. Hydrometeorological regime of the outbreak lakes and the issues of their risk reduction.- Tashkent: "Fan va texnologiya", 2013.- 176 p.
8. Fleishman S. M. Mudflows.- L.: Gidrometeoizdat, 1978.- 312 p.
9. Herget Yu., Glazyrin G. E. Preliminary results of geomorphological investigation of the Verkhnee Ikhnach lake (Pskem river basin, Western Tien-Shan) in summer 2003 // Proceed. of NIGMI.- Tashkent, 2005.- Issue 5 (250).- P. 96-105.
10. Khikmatov B. F. On the techniques of calculation of the outbreak discharges with rectangular shape of the closure channel // Materials of the republican scientific-and-practical conference.- Tashkent, 2018.- P. 239-240.
