PASSAGE OF FLOODS OVER RIVER FLOODPLAINS M. M. Gendel'man

UDC 627.152.153

The problem of determining the part of the flood runoff passing over the floodplain and the kinematics of the floodplain flow is known in connection with water-balance investigations of river basins and the design of low-head run-of-river dams for the needs of reclamation, water supply and hydropower. The factual information about the river runoff, particularly when implementing designs for the passage of floods over the floodplain in the case of lowhead dams, revealed that the methods of hydraulic calculations of the characteristics of the floodplain flow being used are not sufficiently reliable [i]. An incorrect estimation of the hydraulic resistances of the channel and especially the flood plain leads to substantial calculation errors in the majority of cases. Furthermore, the effect of the interaction of the channel and floodplain flows is not, as a rule, reflected in the calculations, and the flow is artificially divided into adjacent but, in essence, isolated parts. An estimation of the resistance of river channels and floodplains on the basis of their verbal characterization with respect to the calculated site is most often inadmissible. Consideration of a qualitative description of the channel and floodplain relief and vegetation on the stretch of investigation does not introduce sufficient refinements when determining the sought quantity. We can hardly consider it advisable, having confined ourselves just to prototype data, to attempt to relate the roughness coefficient of the stretch to a criterion characterizing only the floodplain vegetation and not taking into account the morphology of the floodplain [2]. In this respect special experimental investigations are more justified [3]. The development of numerical parameters determining the floodplain relief

Fig. i.

General view of the model of the investigated stretch.

Translated from Gidrotekhnicheskoe

692

0018-8220/81/1511-0692507.50

Stroitel'stvo, No. ii, pp. 32-36, November~ 1981. 9 1982 Plenum Publishing Corporatio n

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Fig. 2. Schematic diagram of the investigated stretch and plan of currents during a flood of 1% probability (according to the data of the experiment with a forest). i) In the numerator is the number of the point gauge, in the denominator the water level, m; 2) boundary of inundation of the floodplain; 3, 4) velocity distribution in the experiment respectively without and with the forest; 5) transverse section of floodplain flow; 6) residual hills. TABLE i. Characteristics of the Discharges and Velocities of the Floodplain Flow at the Investigated Sites under Natural Conditions (according to the experimental data)

vf, max,m/sec

i

~r

Meas.

site

wfthout zore.st

with forest

Series I, flood of 0.01% prob. I[ [ 0,30 0,19 I 0,80 0,74 0,73 1,30 III 0,66 0,71 0,90 Series II, flood of 0.1% prob.

0,45 0,80 0,70

~oithout with rest forest

0,61 0,56 IlI 0,54 0,55 Series III, flood of 1.0% prob. II 0,09 [ 0,14 0,39 0,38 III O,41 0,29

1,35 1,00

0,40 1,10 0,75

0,10 0,85 0,70

0,I0 0,80 0,60

and vegetation and especially the obtainment of relationships between these parameters and roughness coefficients, are a quite complex problem. Therefore, the method of physical modeling was selected for investigating the passage of floods over the floodplain of a large meandering river.

693

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Fig. 3. Rating curves at site Ii!. i) Experimental curve with forest; 2) same without forest; 3) calculated curve; 4) prototype measurements; c) total curve; p) main channel.

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Fig. 4. Ratio of the floodplain discharge to the total Qf/Q as a function of contraction of the main channel ~c/~. a) Site I; b) site II; c) site III. i, 2, and 3) Respectively, for floods of 0.01, 0.I, and 1.0% probability.

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c

The model method used [4] is based on the premise that the flows in the prototype and model obey a power-function relationship between the Chezy coefficient C and the Reynolds number Re in such a form C=A

Rel:.

(i)

For morphologically homogeneous channels the factor A, having dimension C, is apparently a constant. In particular, in a similar relationship obtained from the data of prototype and laboratory investigations on meandering stretches of rivers at water levels close to the lip of the main channel, this factor was equal to 5 m~ [5]. In conformity with the initial premise the interrelations between the scale coefficients of velocities Mv, water discharge MQ, slopes Mi, and linear dimensions in plan M l and with respect to height M h have the following form A/I__ ~A517~417 v --

~wh

~w i

(2)

and ,~Q

~ 3AI2JT,]~4/7

(3)

The modeled stretch with a length along the channel of about 80 km encompasses three successive narrowings of the floodplain (Figs. 1 and 2). The horizontal scale of the model was taken equal to 2000 and the vertical i00. For the conditions of the problem being solved, which reduces to an investigation of the hydraulic characteristics of the floodplain flow of a large meandering river, the adopted 20-fold distortion of the linear scales of the model is apparently admissible. The model was formed from sand along contour lines which were laid out by a tape. The upper layer of the model, 2-3 cm thick, was made of concrete. A coordinate grid with a l-m side of the squares was plotted on the ooncrete surface of the model. The model was equipped with: a weir for measuring the flow of water delivered to the model; a baffle wall dissipating the excess energy of mixing of the flow coming directly to the model; point gauges for measuring the water level; settling basin; gate for regulating the depth and an outlet. The velocity field of the flow was measured by photographing luminescent floats. A small current

694

a

b

c

Fig. 5. Maximum velocity of the floodplain flow vf max as a function of contraction of the main chSnnel Wc/m. a) Site I; b) site !I; c) site III. i, 2, and 3) Respectively, for floods of 0.01, 0.I, and 1.0% probability.

Ah, m I

~ A h ,

a

m

Ah, m

c

Fig. 6. Backwater in the upper pool of the structure Ah as a function of contraction of the main channel mc/~. a) Site I; b) site ii; c) site II!. i, 2, and 3) Respectively, for floods of 0.01, 0.i, and 1.0% probability. meter, heat-resistance current meter, and Rehbock tube with a mechanotron differential manometer designed by the State Hydrological Institute (GGI), were used as needed~ The absence of initial information about floods of rare occurrence in the investigated stretch needed for calculation and calibration of the model required making new assumptions. In particular, the difference of the levels of the free water surface at the initial and end sections of the model stretch was assumed constant in all floods and equal to the low-water level. This assumption is sufficiently justified by the considerable length of the stretch and, primarily, by the results of measurements of the slopes in the low-water period, during low floods, and high-water marks. According to these data, the difference of levels of the water surface between points to which point gauges I and 7 correspond on the model is 1.5 m. Furthermore, investigations were conducted on the model for different, but each time steady, regimes. The assumptions made permitted obtaining the rating curves at the investigated sites (Fig. 3). In this case the method of conducting the experiments consisted of the following. A certain water discharge was admitted to the model. By means of a gate the required water level was maintained at the control section (point gauge 2) and the difference of levels between point gauges 1 and 7 was measured. That discharge for which the slope corresponded to the prototype data was taken as the sought discharge. The discrepancy of up to 20% between the discharge values obtained thus on the model and the prototype values is probably due to the substantial effect of the distortion of the linear scales of the model, especially on the flow in the main channel. The results of the prototype measurements of the velocities and calculations of the discharge can also contain a considerable error, since they were performed within morphologically complex stretches of the channel. According to the adopted method of modeling, the ratio of the prototype value of the Froude number to its value on the model is equal to MFr = MvMh-~ = 0.5, and the corresponding ratio of the Reynolds numbers MRe = MvM h = 500. According to the data of the prototype measurements, during a low flood at site I, e.g., the Froude number calculated from the average values of the hydraulic characteristics was equal to 0.i and the Reynolds number to 7 x 106. For the indicated scale factors such a comparatively low value of Fr and rather larger value of Re provide at least a quantitative similarity of the model flow to the prototype 695

TABLE 2. Flood

probability 0,01 0,1 1,0

Data of Hydraulic Calculations

Of/Q accord. to exptl, data site i

site iiI

0,19 0,15 0,14

0,71 055 0,29

Qf/Q accord, to hydraulic calc. data

I

0,26 0,18 l 0.14 0,09 0,14 0,12

Three series of experiments made up the bulk of the investigations on the model. Each series corresponded to one of the floods of 0.01, 0.I, and 1% probability and included an investigation of the hydraulic characteristics of the channel and floodplain flows under conditions of a natural regime and also with complete (~c/~ = i) and partial (~c/~ = 0.5) construction of the cross-sectional area of the main channel at the three sites. Partial contraction was achieved by symmetric damming of the channel at both banks over the entire depth of the stream. At the same time, we examined the problem of the effect of a forest on the results of investigating the passage of floods over floodplains. For this purpose the aforementioned experiments performed on a model reproducing only the relief of the terrain were repeated with consideration of the floodplain forest tracts. The diameter of cylindrical bars (i0 mm) simulating trees and the distance between them (ii cm) were selected in conformity with the prototype data on the density of the forest and real possibility of taking the necessary measurements on the model. The first condition consists in providing on the model the prototype value of the ratio of the part of the area of a forested floodplain occupied by tree trunks to the part free from trunks. An evaluation of the effect on the hydraulic characteristics of the flow of the diameter of the model trunks and of the distance between them corresponding to the adopted condition requires additional studies. Some considerations in connection with such calculations for a known prototype value of the hydraulic resistance are given in [3]. Conduction of the main series of experiments was preceded by the obtainment of the total discharge curves (Fig. 3). The difference between them for the model with and without the forest and, consequently, the effect of the forest on the discharge capacity of the floodplain and channel are negligible only in the case of comparatively small inundations of the floodplain. During such floods the forest apparently has a smaller effect on the hydraulics of the flow than complex planar forms and morphological elements of the channel and floodplain in the stretch of investigations. With a further increase of discharges and water levels the relative role of the forest tracts among the elements governing the hydraulic resistance of the floodplain intensifies, particularly owing to worsening of the conditions of flow around the tree trunks when the velocities of the floodplain flow increase. A comparison of the rating curves of the main channel plotted from the results of the main series of experiments elucidates the essence of the contradictions between the total discharge curves and reveals new aspects of the effect of forests on the flow in the channel and floodplain. For the same floods the ratios of the floodplain discharges Qf to the total Q with and without consideration of the forest differ little (Table i). However, the experimental rating curves of the main channel for these conditions have a substantial qualitative difference (Fig. 3). For example, at site II! in the experiments without the forest when the water spilled over onto the floodplain the discharge at first decreased with increase of the levels and then their increase is again observed. On the model with the forest a monotonic decrease of the discharge in the channel part of the flow occurs with increase of inundation of the floodplain. The calculated curve differs even more substantially from the experimental rating curve of the main channel. The main, in fact total, load in the calculations is assigned to the channel. This circumstance permits the conclusion that the coincidence of the experimental and calculated curves of the total discharges at site III is accidental. The premises underlying the calculation do not correspond to the experimentally established physical essence of the investigated process. One could hardly foresee and take into account in the calculations for the site the effect on the hydraulics of the flow of the complex relief and marked change in the planar forms of the floodplain directly below

696

site III. The stretch of the floodplain within which site I is located is simpler for schematization. Probably for this reason the calculation and experiment gave closer results for this site (Table 2). Figures 4-6 give characteristics of the discharges, levels, and velocities of greatest interest for solving the problem of passage of floods over the floodplain for various degrees of contraction of the main channel at the three sites in the series of experiments w i t h o u t a forest. A comparison of these characteristics with the corresponding results obtained in experiments with a forest (Table i) leads to the conclusion that a forest has an effect on the absolute values of the discharges in the channel and floodplain, but with rare exception hardly changes their ratio. In the experiments with a forest a regular decrease of the absolute values of the maximum velocities compared to the results of experiments without a forest is noted. However, in certain cases the forest causes a redistribution of the velocities over the width of the flow. Therefore in experiments with a forest an increase of velocities in the near-channelpart of the flow compared to the corresponding experiments without the forest was observed for certain regimes despite the general decrease of the discharge capacity of the channel and floodplain. The results obtained give grounds to state that site III experiences the least effect from the introduction of structures in the main channel. The maximum velocities of the floodplain flow at this site do not exceed 1.6 m/sec under any conditions. The velocities of the floodplain flow at all sites are not so great that one should fear local erosion of the floodplain directly threatening the structures during a short period and, the more so, a shift of the channel flow and channel around the hydrostation. Thus, on the basis of the conditions of the floodplain flow regime we can recommend as the best place for siting the hydrostation site III at which the construction of channel structures leads to a minimum increase of floodplain discharges and velocities and, consequently, requires a minimum number of outlets and hence minimum expenses. The exceptional complexity of the effect of the floodplain relief and forested floodplains on the hydraulic regime of the flow is characterized by the preceding data. The results of the investigations make doubtful the possibility of determining the roughness coefficient from a visual evaluation of the hydraulic resistances of a channel and floodplain and, consequently, the reliability of calculating other hydraulic characteristics dependent upon it. The given example of a laboratory investigation of the passage of floods over a floodplain shows the expediency of using modeling, especially when solving problems related to selecting the main site or to a comparative evaluation of competing sites for constructing structures on the basis of hydraulic features. LITERATURE CITED 1.

2. 3. 4. 5.

V. S. Gvozdev, Passage of a Flood over a Floodplain in the Case of Low-Head Dams [in Russian], Gosizdat Lit. Stroit. Arkhit., Moscow (1956). Yu. N. Sokolov, "Morphological indices of vegetation in connection with an investigation of the hydraulic resistance of a floodplain," Tr. TsNIIKIVR, No. 2 (1976). L. G. Begam, V. S. Altunin, and V. Sh. Tsypin, Streamflow Regulation When Designing Roads [in Russian], Transport, Moscow (1977). A. P. Zegzhda, Similarity Theory and Method of Calculating Hydraulic Models [in Russian], Gosstroiizdat, Leningrad-Mosocw (1938). M. M. Gendel'man and Z. D. Kopaliani, "Experience in modeling the channel forming processes on the basis of hydraulic resistances," in: Summaries of Reports of the Scientific-Technical Conference "Increase of Efficiency and Quality of Transportation Construction on the Baikal--Amur Mainline and in Other Regions of Siberia and the Far East" [in Russian], VNII Transp. Stroit., Moscow (1979).

697