FORMATION OF A STABLE CANAL CHANNEL M. M. Selyametov

UDC 627.133.4

Methods of calculating stable canal channels can be combined into three groups: method of permissible velocities, method of tractive force, and method of hydromorphometric relations, which abroad is called the "regime theory," The method of calculating stable canal channels with respect to the permissible velocity is used most widely in Soviet practice. The gist of this method is the assignment of a mean velocity of the cross section of the flow less than the permissible value for a given category of soils:

u
(i)

the mean and permissible velocity of the flow determined

An analysis of field and laboratory observations shows that canal channels undergo deformations on assigning a mean flow velocity even 25% less than the permissible, i.e., when U/Uo = 0.75. Cross sections of canals running in noncohesive alluvial soils are subjected to maximum reworking. To study the mechanism of formation of a stable section three experiments were set up [i] on an erodible model measuring 24 x 4 • i m composed of Amu Darya sands with dav ='0.2 mm (the control sites were located from the llth m to the 13th m). The hydraulic parameters of these experiments are given in Table i. A balance of sediments was provided during conduction of all experiments. The permissible noneroding velocity was visually determined experimentally. As the permissible velocity we took the value of velocity for which movement of the particles was completely absent. On the basis of the values obtained we plotted the relation uo = f(h, dav), shown in Fig. i. Experiments i and 2 were conducted on a model of trapezoidal cross section (with side slope m = 2) and experiment 3 on a model of cosinusoidal cross section. As we see from Table i, regardless of the initial ratio u/uo in all experiments there were considerable transformations of the cross section of the canals toward a decrease of the average depth and increase of the surface width. The experiments showed that initially not the bottom and not the near-edge part of the canal but the region of the underwater portion located at a certain distance from the water edge is subjected to deformations. Let us examine in more detail the character of formation of a stable cross section for the example of experiment 3 (Fig. 2). At the start of the experiment individual particles were set in motion at a distance of 15 cm from the water edge (vertical depth hv = 8 cm), moving at a certain angle to the water surface. The particles composing the bottom of the canal and base of the slope remained stationary. Dunes began to form at the site of the initial movement of the particles and the region occupied by them rapidly spread, occupying the entire surface of the slope. As the region and slope occupied by dunes increased, the rate of detachment of particles increased sharply. The surface width began to increase 2 h after the start of the experiment and during the 3.5 h of conducting the experiment it increased by I0 cm. The particles washed from the slope and shoulders of the canal moved along the troughs of the dunes to the base of the slope. The dynamics of the change in the cross section is shown in Table 2. Dunes are formed from the sand grains deposited at the base of the slope and rapidly spread from the base to the axis of the canal. The dunes formed on the canal bottom, just Translated from Gidrotekhnicheskoe Stroitel'stvo~ No. 7, pp. 27-30, July, 1981.

418

0018-8220/81/1507-0418507.50

9 1982 Plenum Publishing Corporation

TABLE 1 ITime [ | from Discharge Mean St~face Bottom ]Av.deptl~ Expt. start Q, velocity width B, width b. Haw cml em xpt. ]liters/see u, m/see cm | ,N

~

I

5o 114

2

50

114 ....

O_

78 217

65 65 65

32,0 35,6 25,9

143 223 362

44 44

26,2 24,9

170 193

--6;69 69 69

28,5 .... 32,9 29,8 26,0

65 65 65

14,2 8,2 6,9

Max. depth hmax em ] [

19,5 10,4 10,4

--67-- ,,- 7-i 19-7 65 65

9,9

9,2

I

I

14,0 13,1

2028 1824 2505

0,20 0,20 0,18

1676

1768

1) 7 ' 27---7-24 3

137 159 216 265

13,2 10,7 10,0

I I

27,6 16,0 14,4

TABLE 2 Time from Max. depth startof Surfacewidth expt. T, h B, em hma x, cm 6 9 26 40 47 78 89 115 159 187 217

CrossSlope I, sectional ~ea ~, % cruz

137 150 159 172 182 188 216 218 238 26l 264 265

27,2 27,1 27,6 25,3 22,1 21,6 16,0 16,0 15,1 15,2 14,2 14,4

2096 2312 2655

Permis- Permissible ve- sible llocitg, v0' Froude Iera/see number Fro 26,8

23, 1 22,3

0,052 0,066 0,0.75

[ 0,10

24,0

0,051 0,059 0,062

I

28,5 36,5

0,045

Io--57 0,10 0,06 0,07 0,08

23,8

26,3 26,2

0,054 0,065 0,070

Angleof side slope ~~ 30 23 23 22 20 17 16 16 16 15 13 12

as the dunes on the slope, are parallel to one another. As a consequence of the fact that the traveling speed of the dunes on the slope considerably exceeds the traveling speed of the dunes on the canal bottom, this type of dune formation is quickly disrupted. As the arrival of sand material washed from the slopes to the bottom increases, the bed levels increase. A further increase of the surface width continues. The angle of the side slope decreases from ~ = 30 ~ in the initial section to ~ = 12 ~ in the formed stable section. As the concrete is eroded in the stretch of the initial formation of dunes the overlying near-edge of the slope and shoulders of the canal collapse. The graph of the traveling speed of the dunes over the width of the channel, shown in Fig. 3 (y is the vertical distance from the water edge), is a clear illustration of visual observations of the initial course of deformations of the cross sections. It is seen from Fig. 3 that at the initial instant the traveling speed of the dunes (curve I) at distance 0.12B from the water edge is four times greater than along the canal axis (B is the surface width). As a stable cross section forms the traveling speed of the dunes equalizes and reaches its maximum value on the channel line, i.e., along the axis of the channel. Within 185 h after the start of the experiment a dynamically stable channel was formed, the parameters of which, just as those of the flow, during the next 32 h remained practically unchanged (curve 3 in Fig. 3), i.e., a dynamically stable channel formed in which the average channel parameters do not change with time despite the longitudinal transport of sediments and migration of the bed forms. At the start of experiment 2 with a large margin of the mean velocity before the permissible (u/uo = 0.80) the cross section of the canal should not have been deformed, but the surface width during 114 h of conducting the experiment increased by 50 cm and the average depth hav decreased from 13.3 to 9.2 cm (Table i). The cause of deformation lies in the fact that the assignment of the mean velocity of the flow by the method of permissible velocities does not provide fulfillment of condition (i) on all verticals of the canal cross section. It was established that channel stability is determined most completely by the character of distribution of the Froude number F r v = f(y/B) over the width of the channel (Figs. 4, 5, and 6), where Fry = u~/yh v is the local value of the Froude number; uv is the mean velocity on the vertical; hv is the depth on the vertical; g is the acceleration of gravity. 419

h,

I

I

o/

m3Z

PI

r

I Fig. I. Relation uo = f(h) for d a v = 0.2 mm.

8 J c/

I

i

01 Z0

Zq

i

Z8 SZa0,cm/sec

~, c m / ~ c

,0 ~,.,'~ qo { 8u 70

7[

x

~I !

,6u

]~oo gq~\.u, cm

:

3Q L

h,CM Fig. 2. Cross sections of canal in experiment 3. I) Initial section; 2) 187 h after start of experiment. It was found on analyzing the investigations that the local value of the Froude number measured in the flow of a dynamically stable channel is always less than its permissible value for the entire flow, i.e.,

F~Fro,

(2)

where Fro = u~/gHav is the permissible value of the Froude number for the entire flow. It is seen from Figs. 4, 5, and 6 that regardless of the initial ratio u/uo at the initial instant the distribution of Frv in all experiments has the same character with a maximum value in the near-edge zone and a minimum value along the canal axis. By the time when a dynamically stable cross section is finally formed the maximum value of Frv occurs on the axis of the flow and condition (2) is fulfilled. If we compare the measured value of Frv with the permissible value of Fro at different times of conducting the experiment, then we can propose a detailed description of the process of formation of a dynamically stable channel. In Fig. 6 (experiment 3) the solid line shows the initial permissible value Fr~ = 0.045 (Table i). At the initial instant (curve i) in the interval y/B = 0.04-0.15 the value of F r v > Fr~, i.e., condition (2) is not fulfilled. If we compare the position of the zone of instability in Fig. 6 with Fig. 3, then we see that it coincides with the region of maximum traveling speeds of the dunes, where their initial formation occurs. In experiment 2 (Fig. 5) the zone of instability is located in the interval y/B = 0.02-0.22, and in experiment 1 the entire cross section is unstable (Fig. 4). The character of the distribution of Fry in the cross section changed 78 h after the start of experiment 3 (Fig, 6, curve 2). The value of the Froude number corresponding to this intermediate time, Fr~ n, is less than Frv already in the interval y/B = 0.13-0.87, i.e., due to the deformations that occurred practically the entire cross section becomes unstable. Since it is easier for the flow to deform the canal slopes than its bottom, a further increase of the surface width occurs. This state of the flow and channel (curve 2, Figs. 4-6) is characteristic for all experiments, from which follows that the deformed section of the canal during a certain time between the initial and final deformations becomes more unstable than the original section. During subsequent conduction of the experiment a further alteration of the channel occurs, which ends when there is a correspondence between the formed cross section and the velocity field of the f!ov in it and condition (2) will be fulfilled. 420

~8 X

2z O

~t 4~ gs~g~/a

Fig. 3. Traveling speed of the dunes over the width of the channel in experiment 3. Time from start of experiment: i) 2 h; 2) 78 h; 3) 217 h.

o,qo o, a o

,

9

o,az

. ~ o,z8 ~

Fig. 4. Distribution of the Froude number Frv over the width of the channel in experiment i. Time from start of experiment: i) 0; 2) 59; 3) 114 h.

o

&~

o,2 o,36'~/8

In the formed dynamically stable cross section the angle of side slopes in the nearedge zone is equal to ~ = ii-14 ~ (Fig. 2). Precisely for such gentle side slopes the mean velocity is distributed such that condition (2) is fulfilled and the section is equally stable over the width. Any change in the regime of the velocities toward their increase leads to loss of stability of such a section and to the formation of a new equally stable section. Thus, for each soil category a certain permissible Froude number corresponds to each selected average depth for the entire section. The distribution of Frv in the canal is characterized by gradients of the mean velocity over the width of the flow. For such velocity gradients we can introduce the concept of permissible gradients, i.e., values for which movements of particles in the near-edge region are completely absent, into the solution of the two-dimensional problem of hydraulics. However, to make a check with respect to permissible gradients it is necessary to know the distribution of local velocities on verticals in the planned channel. The dynamically stable section of a canal can be obtained by the trial-and-error method: on the basis of the known distribution of the mean velocities over the width in the section taken we construct the corresponding distribution of Fr~ and compare it with the permissible value of Fr v, as shown in Fig. 6. In solving the two-dimensional problem we can calculate the distribution of the mean velocity over the channel width by Skrebkov's equation [2]

~@P (y) a@q (y) a=[ (y). Equation (3) is solved by the numerical factorization method and in it a = ~ , (i/hv)(dhv/dp),

(3) P(y) =

421

~zq o,zo

r '-

a,18

O,12

"~~

o

r----

,f

g

oj

r

3i

Z

i /Z

>0,08

--

IV//

.v'/ / A ;o J~,'o

I

"+--x----x

: [ o,z o,3 o,~/~

0

Fig. 5

'ljl I

,

"t---x---J---• I

o,~ I o,e

] i

a,s

-X

o,~/8

Fig. 6

Fig. 5. Distribution of the Froude number Frv over the width of the channel in experiment 2. Time from start of experiment: i) 0; 2) 52; 3) 114 h. Fig. 6. Distribution of the Froude number Frv over the width of the channel in experiment 3. Time from start of experiment: i) 0; 2) 78; 3) 187 h. g V F+

(ah~v/d~.

q(y)=AW c, f(Y)=--(g/h)I,

--,

where I is the bottom slope; C, Chezy coefficient; A, a coefficient characterizing turbulence of the flow, which with consideration of A. V. Karaushev's formula for the eddy viscosity coefficient is equal to

A=ghv/2MC, where M = 48 for C ~ 60 and M = 0.7C + 6 for i0 < C < 60. For a symmetric trapezoidal section of the canal, the boundary conditions will be

a(B/2)=/=O, a(B)----0; ~i(B/2)=0, (i(B) :i&0. If as a result of calculations by Eq. (3) it turns out that Fro < F r v , then the assigned mean velocity in the canal must be reduced and all calculations repeated. On the basis of the aforesaid we can propose various methods of creating a stable canal channel. We will examine them for the example of experiment 3. i. For the canal cross section taken the mean velocity in it is assigned from condition (2). The initial mean velocity of the flow when the average depth H a v = 17.7 cm is equal to u = 28.5 cm/sec (see Table i), and to fulfill the condition Fr~ ~ Frv the mean velocity must be taken equal to u = 22 cm/sec. With such a decrease in the mean velocity the capacity of the canal will be reduced by 23% and this same cross section will be able to conduct a discharge Q = 58 liters/sec. 2. In the zone of the canal cross section where Fr~ < Frv (in the interval y/B = 00.15) the depth is increased (dashed line in Fig. 2). However, in this case there exists a limitation, since the angle of repose for saturated Amu Darya sand with d a v = 0.2 mm, determined experimentally, is ~ = 29 ~ and the design angle of the side slopes f~' = 36 ~ . Thus this method of fulfilling inequality (2) cannot be used in the near-edge zone for the given soil conditions. 3. The flow is given the opportunity to form a channel with an equally stable profile (Fig. 2). We see from Table 1 that the relative width of such a channel is B/Hay = 26.5. 4. The canal section is isolated from the direct effect of the flow in those places where FrY < Fry, i.e., the slope is protected in the zone from the water edge to 0oI5B (Fig. 6). 422

The most preferred is method 4, but for a final choice in each particular case it is necessary to perform technicoeconomic calculations and compare variants. CONCLUSIONS i. Deformation of the canal cross section occurs where Fro < F r v . 2. A stable canal section can be obtained by two methods: take cross-sectlonal shapes and a velocity regime such that the inequality Fro ~ Frv is fulfilled at all points of the wetted perimeter; partially reinforce the canal side slopes in the region where Fro < Frv. LITERATURE CITED .

2.

N. A. Mikhailova, M. M. Selyametov, and O. B. Shevchenko, "Laboratory investigation of the formation of stable canal channels," Gidrotekh. Stroit., No. 7 (1980). G. P. Skrebkov, "Calculation of the vertical velocity distribution over the width in open channels," in: New Methods of Calculation and Construction of Hydraulic Structures [in Russian], Vysshaya Shkola, Moscow (1972).

IINVESTIGATIONS OF CATASTROPHIC MAXIMUM DISCHARGES OF THE ARAKS RIVER G. T. Trembovel'skii

UDC 627.512

Observations of the maximum discharges of the Araks River at the Karakala streamgauging station were carried out from 1934 to 1978, at the Kyzyl-Vank station ("Araks" hydrostation) from 1965 to 1978, at the Gyz-Galasy station (Khudaferin hydrostation) from 1965 to 1971, from 1973 to 1974, and in 1978, and at the Karadonly station from 1912 to 1917 and from 1926 to 1978. During the period from 1912 to 1968 the maximum discharges at the basin outlet at Karadonly varied from 240 m3/sec (1961) to 1700 m3/sec (1968), and an exceptionally high flood passed on May 7, 1969 with a maximum discharge Qmax = 2700 m3/sec exceeding the average value by 2.7 times and the highest during the 60 years by 1.7 times. At the Karakala station a flood peak with Qmax = 1700 m3/sec passed on May i, 1969, at the "Araks" hydrostation (Kyzyl-Vank) with Qmax = 2370 m3/sec on May 5, and at the GyzGalasy station at the peak of the flood Qmax = 2700 m3/sec on May 6. The value of the maximum discharge of the Araks River that passed in 1969 against the background of the long-term series of observations characterizes this flood as catastrophic, of quite rare frequency. According to the archival and literature data, large floodings from overflowing of the Kura and Araks rivers occurred in 1828, 1850, 1868, 1895, 1986, and 1915. During the floods more than i00,000 ha were inundated. The 1850 flood inundated the Dzhavad district and northern part of the Lenkoran district, and in 1896 a large break occurred on the right bank of the Araks River near Saatly village and the flood water rushed across the entire Mugan steppe to the Kyzyl-Agach Bay of the Caspian Sea. Traces of the break remained in the form of a deep channel, called the New Araks. The overflows and break of the Araks were due to three causes: the passage of high floods, deposition of a large amount of sediments in the lower course of the river, and the absence in the 19th century of protective levees on the river banks. Before construction of the levees the Araks was freer than now to change its channel and flooded vast areas of land in the Mugan and Mil'skaya steppes, depositing sediments there. Originally embanking was carried out by the population itself, and only since 1896, after the break of the Araks, did government agencies begin to participate in protection works. Translated from Gidrotekhnicheskoe Stroitel'stvo, No. 7, pp. 30-32, July, 1981. 0018-8220/81/1507-0423507.50

9 1982 Plenum Publishing Corporation

423