161

. . . ...

. . , . Abstract

This research work concerns the analysis of embankment dam break and flood wave routing downstream. Especially, the partial breach of the dam and the corresponding flood wave formation are investigated. Then, the flood wave routing downstream is analyzed and finally, the prevention measures, which have to be taken in order to protect the downstream areas from the flooding consequences are examined. 1.

. , , .. , ( , RCC, , ..) (, .).

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)

) - (piping).

. , , .

, . 2.

, .

` . , , .. , .

, 162

Cristofano [7], . , .

Harris and Wagner [17] Schoklitsch [25] .

, Ponce and Tsivoglou [20] Meyer-Peter and Mller .

Fread [12], , Meyer-Peter and Mller . Manning .

Singh and Quiroga [23], Wurbs [30] ..

, , , .

, [22].

Schoklitsch [25] Dressler [9]. WES (West Experiment Station) U.S. Corps of Engineers [29]. Miller and Chaudhry [19], Towson and Salihi [27], Bellos et al. [5], Francarollo and Toro [11], Austria and Patino [2], Aurelli et al. [1] ..

, , .

. , , .

, Vasiliev [28], Fread [13], Bellos and Sakkas [3], Bellos et al. [4], Fennema and Chaudhry [10] .

Di Monaco and Molinaro [8], Katopodes [18], ..

FLDWAV. .

3.

. . b t0. [16], 43 5 m 87 m (6 5 m 30 m), :

25.0)(80.20 drhVb = (1)

9.0

47.0

0 72.4d

r

hVt = (2)

b (m), t0 (h), Vr (. ..), hd (m), .

(Fread, 1988):

5.25.1 ))(tan(2)(3 bbib hhahhbQ += (3) Qb , bi , h

163

, hb , t0, .

. (3) , cv, 0.60 , . (3) :

])(2)(3[ 5.25.1 bbisvb hhmhhbkcQ += (4) cv = , m = (/) ks = (back water effect) ht. ks :

3]67.0[8.270.1 =

b

bts hh

hhk (5)

67.0

b

bt

hhhh , ks = 1.0

bi hb . (4) :

)/( 0ttbbi = 00 tt < (6) )/)(( 0tthhhh bmddb = (7)

hbm = , , , t = = 1 - 4.

. , . , , . , , . :

) )

.

) .

) () , , , .. Manning.

, SaintVenant :

0=+

qtA

xQ

(8)

0)()/(2

=++

+

fSxhgA

xAQ

tQ (9)

Q , h , , x , t , q , ( ) Sf .

Sf . (2) Manning :

3/42

2

RQQn

S f = (10) R=/P (P = ). 4.

Saint Venant (. (8) (9)), , , x t, , h Q. , . . (8) (9) .

. , (explicit) (implicit) . Courant (C.F.L. criterion), :

, 164

cVxt

= (11)

V = Q/A = BgAc /=

. Lax-Wendroff Mac-Cormack [4,10,26].

, , . Beam-Warning, Preissmann [13,21]. Preissmann DAMBRK, NWS (National Weather Service) FLDWAV. , , (1-), ..:

+

= ++++

i

ji

ji

i

ji

ji

xxx1

111 )1( (12)

(2 2) 2 . , , , . 2 2 , Newton Raphson.

5.

, .

120 km2, 62 km2. , , , . 14 , .

,

650 m, 222 m 52 m. 40x106 m3.

FLDWAV NWS (National Weather Service). FLDWAV . . (1), (2) , , , :

t0 = 4.72(38.2350.47 )/(520.9 ) 0.75 :

b = 20.79(38.235x52)0.25 139 m ,

m=1.5, 61 m, 217 m ( 1). , 47 .

, , . 1, 139 m . , . (3) . (1) (2).

- - - - - - - -

1:

40 m 185 m, . 15 , ( 1).

165

2.5 , , . 2 , , . 1:

/

[hr]

[m]

[m]

[m3 /s] 1 1.5 170 61 21646 2 1.0 170 61 31980 3 0.75 170 61 40163 4 0.5 170 61 50669 5 0.25 170 61 64443

2: /

[hr]

[m]

[m]

[m3 /s] 1 2.5 185 40 10250 2 1.0 185 40 19790 3 0.25 185 40 28865

2, 3 4 0+ 010, 1+340 10+500 m 1. 3. . , (3) 3, 1+340 0.78 0.78-0.75=0.03 . 1.8 min.

3: /

[h]

[h] +0.01

[h] +1.34

1 1.5 1.5 1.540 2 1.0 1,00 1,020 3 0.75 0.75 0.780 4 0.50 0.50 0.525 5 0.25 0.25 0.291

/

[h]

[h] +5.15

[h] +10.51

1 1.5 1.645 1.755 2 1.0 1.110 1.22 3 0.75 0.875 0.975 4 0.50 0.653 0.773 5 0.25 0.403 0.566

5 6 .

,

, 1+340 m, , , . 6.

. .

. , .

. . , . . FLDWAV.

1. Aureli, F., Mignosa, P. Tomorotti, M., (2000). Numerical

simulation and experimental verification of dam-break flows with shocks, Journal of Hydraulic Research, Vol. 38 (N3), pp. 197-206.

2. Austria, P., Patino, C., (1997). Experimental study of flow resulting from a dam break, Ingeneria Hidraulica en Mexico, 12(1), pp. 65-75.

3. Bellos, C.V., and Sakkas, J.G. (1987). 1-D Dam-break flood-wave propagation on dry bed. Journal of Hydraulic Engineering, ASCE, 113(12), 1510-1524.

4. Bellos , C.V., Soulis, J.V., Sakkas, J.G. (1991). Computations of two-dimensional dam-break-induced flows. dvances in Water Resources, Vol 14, 1:31-41.

5. Bellos , C.V.,Soulis, J.V, Sakkas, J.G. (1992). Experimental investigation of two-dimensional dam-break induced flows. Journal of Hydraulic Research., Vol 29, 5:1-17.

6. Bellos C. and Hrissanthou V., (2003). Numerical simulation of morphological changes in rivers and reservoirs, Computers and Mathematics with Applications, Special issue entitled: Num. Meth. in Phys., Chem. and Engineering, Vol 45, 1-3: 453-467.

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, 166

8. Di Monaco, A., and Molinaro, P., (1982). Finite element solution of the Lagrangian equations unsteady free-surface flows on dry river beds. Finite Elements in Water Resources, K. P. Holz et al., eds., Springer, Berlin, Germany 4.25-4.35.

9. Dressler, R. F. (1954). Comparison of theories and experiments for the hydraulic dam-break wave, Inter. Association of Scientific Hydrology, Publ. . 38, 319-328.

10. Fennema, R.J., and Chaudhry, M.H., (1987). Simulation of one dimensional dam-break flows. Journal of Hydraulic Research, 25(1), 41-51.

11. Fraccarollo, L., Toro, E., (1995). Experimental and computational analysis for two dimensional dam break type problems, Quaderni del Dipartimento, IDR 2/1994, University of Trento, Italia, 47 pages.

12. Fread, D. L. (1984). A breach erosion model for earthen dams, Hydrologic Research Laboratory, National Weather Service, Silver Spring, Maryland.

13. Fread, D. L. (1984). DMBRK: The NWS dam-break flood forecasting model, Office of Hydrology, National Weather Service, Silver Spring, Maryland.

14. Fread, D. L., and Lewis, J.M. (1988). FLDWAV: A generalizated flood rooting mode, Proceedings of National Conference on Hydraulic Engineering, Colorado Springs, Colorado.148.

15. Fread, D. L., and Lewis, J.M. (1993). NWS FLDWAV Model: The replacement of DAMBRK for dam break flood prediction, Proceedings: 10th Annual Conference of the Association of State Dam Safety Officials, Inc., Kansas City, Missouri, pp. 177-184.

16. Froehlich, D.C. (1995). Embankment-dam breach parameters revisited, Proceedings of the First International Conferences on Water Resources Engineering, ASCE, San Antonio, August, pp. 887-891.

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19. Miller, S. and Chaudry, ., (1989). Dam-break flows in curved channel, Journal of Hydraulic Engineering, ASCE, Vl. 115(11).

20. Ponce,V.M. and Tsivoglou, A.J. (1981). Modeling of gradual dam breaches, Journal of Hydraulic Division, ASCE, 107, HY6, June, pp. 829-838.

21. Preismann A., (1961). Propagation des intou-mescences dans les canaux et reviers. First Congress of the French Ass. for Computation, Grenoble, Sept. 14-16. Procc., A.F.C.A.L., 433-442.

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23. Singh, V., and Quiroga, C. (1987). A dam breach erosion model: I Formulation. Water Resources Management, Vol I(3), pp. 177-197.

24. Singh, V., and Quiroga, C. (1987). A dam breach erosion model: II Application. Water Resources Management, Vol I(3), pp. 199-221.

25. Schoklitsch, A., (1917). Uber Dammbruchewellen, Sitzung-Berichte der k. Akademie der Wissenschaften, Vienna, Austria,126(lla), 1489-1514.

26. Terzidis, G. and Strelkoff, Th., (1970). Compu-tation of open-channel surges and shocks. Journal of Hydraulics Division, ASCE, Vol. 96, N HY12, pp 2581-2610.

27. Townson, J. . and Al-Salihi, . ., (1989). Models of dam-break flow in "R- " space, Journal of Hydraulic Engineering, ASCE, Vl. 115(5),1989.

28. Vasiliev, O.F., (1970). Numerical solution of the nonlinear problems of unsteady flows in open channels. Proc. 2nd Int. Conference on Numerical Methods in Fluid Dynamics, Berkeley, California.

29. WES (Water Experiment Station), (1960). Floods resulting from suddenly breached dams, Misc. Paper . 2-374, Report 1: Conditions of low resistance, Report 2: Conditions of high resistance, U.S. Army Corps of Engineers, Vicksburg, Mississippi.

30. Wurbs, R. (1987). Dam-breach wave models, Journal of Hydraulic Engineering, ASCE, Vol. 113, No 1, January, pp. 29-46.

0

10000

20000

30000

40000

50000

60000

70000

0 0.5 1 1.5 2 2.5 3

(hr)

(m^3

/s)

t=1.5hr t=1hr t=0.75 hr t=0.5hr t=0.25hr

2: 0+010 m

167

0

10000

20000

30000

40000

50000

60000

0 0.5 1 1.5 2 2.5 3

(hr)

(m

^3/s

)

t =1.5hr t=1 hr t=0.75 h r t=0 .5hr t=0.25 hr

3: 1+340 m

0

10000

20000

30000

40000

0 0,5 1 1,5 2 2,5 3 3,5 4

(hr)

(m^3

/s)

t=1.5hr t=1hr t=0.75 hr t=0.5hr t=0.25hr

4: 10+500 m

, 168

0

10000

20000

30000

40000

50000

60000

70000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

(Km )

(m

^3/s

)

t=1.5HR t=1HR t=0.75HR t=0.5hr t=0.25 hr

5:

0

20

40

60

80

100

120

140

160

180

200

220

240

0 1 2 3 4 5 6 7 8 9 10 11 12 13

(Km)

(m)

t=1.5 HR t=1t=0.75HR t=0.5 hr t=0.25 hr

6: . . , . . . , , 671 00 . . 25410-79613. E-mail: kbellos@civil.duth.gr.