HYDROLOGIC

COMPUTATIONS

STRUCTURES

ON

RIVERS

FOR

THE

SUBJECT

TO

DESIGN MUD

OF

HYDRAULIC

FLOWS

I. P . S m i r n o v

UDC 627.141.i.627.133.001.24

Hydrologic computations for the design of structures for mud-flow control and other purposes on sedimentladen rivers has a specific particularity. This is caused primarily by the large concentration of sediment in the stream and by the complexity of the causes generating a mud flow. Many methods of computation adopted in river hydrology are not applicable to mud flows. Thus, the determination of the maximum silt loads in rivers by processing the hydrometric observations is not applicable in the case of mud flows because of the lack of a sufficiently long series of observations. In the best case there are only isolated data on the discharges determined after the passage of the mud flow. The water component cannot be determined in the usual way, even in the case where a sufficiently long series of observations on floods is available. For example, the maximum flow with a 1~/c exceedance probability on the Little Almatinka River at Medeo was determined on the basis of a 28-year series of observations to be 29 mS/see, while the maximum discharge of the 1921 mud flow, having approximately the same exceedance probability, was several rimes larger than this figure. How, then, can this discrepancy between the maximum discharge of the water flood and the water component of the mud flow be explained ? First, during the indicated 28-year period of observation maximum flows of various origins were recorded: from snow melt and rain, from glacier melt, and from glacier melt and rain. ExceptionaI floods produced by rain only, that is by storms, were not observed during this period, since intensive storms of long duration did not occur in this time interval. If such storms had occurred, they would have generated mud flows and not water floods. Second, mud streams are generated usually when the softs in the basin are saturated due to preceding precipitation. Such soils may contain up to 50%water. when a mud flow is generated in such soils its water component increases significantly [ 1 , 2 ] . At first sight it would appear that the pore water can represent only an insignificant portion of the flood water, particularly in the case of an exceptional flood. Actually this is not correct. Let us assume that in a given basin there was a mud flow having a volumetric weight of the mud mass 7c = 1.7 ton/m~; the soils which generated the mud flow had a volumetric weight yp and a specific weight gn of 1.4 and 2.65 t o n / m s respectively; the soils were 100% saturated with water (8 = 1); the porosity of the softs is n=l

"(p

I .4

- - ,(---~= I - - ~

= 0.47.

Then, by I. P. Smirnov's formula [1, 2] ~c =

1 +~w(?p-4-n) 1 -kgw

(1) '

where w-

QQ_pp "re--1 1,7--I Qw-- 7 p - j - n _ _ ? c "1.4-}- 0.47__ 1,7 = 4 . 1 ,

i.e ., for each cubic meter of water there is an inflow of 4.1 m s of water saturated soil. Let us assume that Qw = 10 mS/sec, in which case a volume of 41 mS/sec of water-saturated soil enter the stream. This soil will contain a quantity of pore water equal to Qp = 41 - 0.47 = 19.3 mS/sec, a quantity of sediments measured as a compact volume (the solid component of the mud flow) Qs = 41 9 0.53 = 21.7 ma/sec, while the discharge of the mud flow represents Qm = 19.3 + 21.7 + 10 = 51 mS/sec).

Translated from Gidrotekhnichesko Stritel'stvo No. 11, pp. 29-31, November 1969.

1033

(2)

I. P. S MIRNOV

1034 TABLE 1

Category of mudflow potential o f the basin Very high High Average Low

J

Forest area

FcT

~0,25 0,25--0,15 0,15--0,05

d0

05

ratio f/ Fct

>0,65--0,70 0,65--0,45 0,45--0,25 <0,25

>0,30--0,35 O,35 -0,20 0,20--0,10

<0,io

d0, I0 0,10--0,25 0,25--0,35 >0,35

Volur~ Freq. of Basin of mu( mud Fct flow flOWS from i oncemoJ shape V km 2, of years

tons/rr >20 20--10 10-- 5

<5

t

I0--I5 30--15 40--30

>40

>0,3 0,30--0,15 0,15--0, 10 <0, 10

Density of river and ravine network kin/kin 2 > 8 ~, 8--5, 5--2,


From the above data it can be seen that discharge of the mud flow becomes more than five Exceedance Volumetric wt. of the times larger than the water discharge, while the Category of mud-] mud-flow mass for the robabiUty in corresponding water component increases approximately three exceed, prob. in % to 7 c = 1 times. Consequently, for the determination of one 0.01 1,0 of the basic characteristics of the mud stream, the Very high 1 High maximum discharge and v o l u m e , it is necessary to 70 I ,65--I ,70 I ,55--I ,60 Average determine beforehand the m a x i m u m discharge( volI, 50--I, 55 50 I ,60--I ,65 Low 30 I, 50--I, 55 I ,35--I ,40 ume) of the water runoff which can be generated by 20 I ,30--I ,35 I, 15--I ,20 the precipitation Hpl and also the volumetric weight of the mud-flow mass Y c , the volumetric weight y p , and the specific weight Yn of t h e soils, and their degree of saturation 6 . TABLE 2

1

flo_2pote__mial /

An analysis of the existing literature and available basic data on observations and investigations on water and mud streams indicated that, under the conditions prevailing in Kazatdastan, the following methods are the most suitable for the determination of the basic characteristics: 1. For the determination of the maximum discharges of rain-generated floods it is possible to use the formula of D. L. Sokolovski in a slightly modified form: 0.28H.~aF ct

Ow=

"t.

Plq~P

(3)

where H r is the computed precipitation depth of the given exceedance probability determined from the empirical probability curves of the annual maximum depths of 24-hour precipitation recorded within various time intervals; within various time intervals; ~f is a coefficient which characterizes the decrease of the average amount of precipitation as a function of the size of the river-basin area; the value of this coefficient is determined according to the recommendation given in [4]; a is the runoff coefficient; Fct is the runoff-generating portion of the river basin in km2; t n is the time to peak of the rising limb of the flood hydrograph in hours; f is the shape coefficient of the hydrograph; 6rr is a coefficient which accounts for the effect of forests. The volume of the rain-generated runoff is determined by the formula IlZw=1000Hp 9a - Fct" qJ~..

(4)

2. The volumetric weight of the mud-flow mass and other characteristics of the mud stream are determined from a detailed investigation of data for the individual basins. One of the basic computational parameters of the mud streams is the volumetric weight of the mud- flow mass Yc" It characterizes the degree of saturation of the stream with sediment, which is a function of the physical-geographical and morphological characteristics of the basins. For practical computations it appeared useful to classify the basins according to their potential of experiencing mud flows in the following categories: a) very high mud-flow potential; b)high mud-flow potential; c) average mud-flow potential; and d) low mud-flow potential. Determination of the mud-flow potential must be based on the following main factors: a) the degree of erodibility of the basin (the ratioof mud-flow generating area to the total runoff generating portion of the basin

COMPUTATIONS FOR THE DESIGN OF HYDRAULIC STRUCTURES

1035

fr

TABLE 3

=--~--); b) the steepness of the slopes (the general relief of lc. Q I ,70 1,65 1,60 I, 55 I, 50

"fc, W 1,55 1,50 1,45 1,40 1,35

~'c, Q 1,40 I ,35 1,30 i ,20 1,15

lc, !17 1,30 1,25 1,20 1,15 1,10

the basin) I; c) the river channel slopes i; c) the amount and distribution of vegetation (coniferous and deciduous forest, bush); d) the frequency and duration of the mud flows; e) the volume from an area of one square kilometer contributed by one mud flow; the density of the river and ravine network; f) the shape of the basin (ect). Lz

Tentative quantitative indices determining the category of mud stream potential of a basin are given in Table 1. Obviously, the above listed factors do not represent all those determining the complex phenomenon of mudflow generation, and for this reason the indices given in Table 1 should be considered as tentative only. When classifying the basins i n categories according to quantitative indices it is necessary to take into account fc also their qualitative aspects. Thus, for a single value g = - - the mud-flow potential of the basin will be different Fct (for otherwise equal conditions) if the location of the mud-flow generating ravines on the slopes and the cohesion and grain-size distribution curves of the softs supplying the sediments are different~ For otherwise identical conditions,inflow of sediments to the stream wftl depend on the grain size distribution of the soils which make up the river charmel and banks and on the shape of the channel, i . e . , the steepness of the banks and their erodibility. It must be assumed that the higher the mud-flow potential of a basin the higher the volumetric weight of the mud-flow mass during generation of the mud flow. Theoretical and experimental investigations [5 to 7] showed that the turbulent flow regime of streams saturated 9 Wn with sediments is maintained up to a volumetric saturation of about 40% that is, up to S = = 0.4. In this case Wc the movement of the sediments is determined by the liquid phase. The maximum volumetric weight of the mudflow mass can then be determined according to the following relationship: ~c=l~-S fin--I) = I + 0,4 (2.65--1) = 1.66_~_I.7 t o n / m s

(5)

This value of the volumetric weight can be adopted for basins with very high mud-flow potential as a maximum for conditions very favorable for the formation of turbulent mud flows. For basins with low mud-flow potential the value of 7c will obviously have intermediate values. In addition, this value obviously depends also on the computational exceedance probability of the precipitation and maximum discharge, on the basis of the following considerations: With a decrease of the computed exceedance probability the computed amount of precipitation and the maximum discharge of equal exceedance probability will increase, the flow velocity of the slopes and in the river channels will increase, the slope and channel erosion will also increase, and as a result the amount of sediment in the river and the volumetric weight of the mud-flow mass will also go up. With the increase of the computed exceedance probability, there will be a decrease of the amount of precipitation, maximum discharge, flow velocity, and of the sediment concentration, and for a certain value of these factors the generation of mud flows will become impossible, the flood will consist of water only ( Yc = 1) for any category of mud-flow potential. For example, on the basis of the observations and operational experience accumulated by the Mud-Flow Warning Service, precipitations of 30 mm and less, corresponding to exceedance probabilities of 70 % and more, are considered unable to produce mud flows in the Little Almatinka River Basin, which has a high mud-flow potential.

1036

I.P. SMIRNOV

In other basins the value of the precipitation incapable of producing mud flows will obviously have other values related basically to their mud-flow potential. From the above it follows that the saturation of the stream with sediment and the volumetric weight of the mud-flow mass have to be selected as a function of the computed exceedance probability of the maximum mudflow-generating runoff and of the category of mud-flow potential of the basin. Table 2 gives tentative values of the volumetric weight of the mud-flow mass as a function of the category of mud-flow potential of the basin and of the computed exceedance probability. Table 2 gives the maximum values of the volumetric weight Yc, Q of the mud-flow mass corresponding to the maximum mud-flow discharges. The average values of the volumetric weight of the mud-flow mass for the whole volume of the mud-flow runoff will be somewhat lower than the maximum values. I. I. Kherkheulidze suggested an equation expressing the relationship between the maximum and average sediment concentration in the stream [9]. Table 3 gives the maximum values Yc,Q and the corresponding average values 7c, W, computed according to the equation suggested by I. I. Kherkheulidze in tons/m 3 (the values are rounded off). The ratios -we - = ~W and QC = r

Ww

which indicate how many times the volume or the discharge of the mud-

Qw

flow will increase in comparison to its liquid phase can be designated as mud-flow coefficients. Their value can be found as a function of the volumetric weight of the mud-flow mass 7c, and of the soils 7 - , and of the water saturation 5 . On the basis of adopted values for Yc' 7p' and 5 it is possible to compile tabffes giving the values of ~Q, and OW. The specific weight of the soils is taken to be equal to 2.65 tons/m 3. From the detailed equation of I. P. Smirnov it is possible to determine the mud-flow coefficients: %w= 1 +gw[l + n ( 1 - - a ) ] ,

(6)

where Wp

Yc,w'-- 1

~w=-~w- ('fp + "G.wn+ an) -- ('fc,Wan + "~,w) q~Q= t +gw[1 + n ( 1 - - ~ ) l , he re Qp 7c,Q- 1 ~w= Qw --(~p ~- ~c,q n + an) -- (7r qan+~c Q) " The values #W and ~0Q can be determined from the equations of I. I. Kherkheulidze and M. V. Tsovyan [9,

1%

In this manner the equations for the determination of the maximum discharges and volumes of mud-flowrunoff occurrences, applicable in the case of turbulent mud flows, assume the following general form:

LIT E R A T URg- C I T E D 1. 2. 3. 4. 5. 6.

I . P . Smirnov, "On the generation and dynamics of sediment-laden streams," Trudy KazNIGMI, 1__~1(1959). I . P . Smirnov, "Effect of initial moisturizarion of river basins on the generation of mud flows, their maximun discharges, and sediment volumes," Tmdy SANIGMI, Tashkent (1963). Methodological Recommendation for the Compilation of a Water Resources Handbook [in Russian], VoL 7, Part III (1963). G . A . Alekseev,"Objective statistical methods for the determination of storm precipitatXon,"Meteorologia i Gidrologia, No. 7 (1966). M . A . Velikanov, Land Hydrology [in Russian], Gidrometeoizdat (1948). M . A . Mostkov, "Hydrologic relationships in mountainuous streams," Proceedings of the Third All- Union Conference on Mud Flows, in: Mud Flows and Measures to Control Them [in Russian], Izd. AN SSSR (1957).

COMPUTATIONS

7. 8. 9. 10.

FOR THE DESIGN OF H Y D R A U L I C S T R U C T U R E S

1037

V.S. Knoroz, "Displacement of sand by a stream under pressure," Izvestiya VNIIG, 40 (1949). S.B. Kavetskii, V. R. Gulina, I. O. Raushenbakh, and M. P. Rybkina, "Some conclusions on the possibility of further investigation of catastrophic rain-generated floods," Trudy KazNIGMI, 1_22(1959). I . I . Kherkheulidze, Hydrologic and Hydraulic Problems of Bridge Crossings [in Russian], Tbilisi (1958). M.V. Tsovyan, Storm-Generated Mud Floods in the Territory of the Armenian SSR and the Methodology of their Computation [in Russian], Summary presentation of a thesis for obtaining the degree of Candidate in Science, Erevan (1965).