RESCDAM DEVELOPMENT OF RESCUE ACTIONS BASED ON DAM BREAK FLOOD ANALYSI A PREVENTION PROJECT UNDER THE EUROPEAN COMMUNITY ACTION PROGRAMME

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1 RESCDAM DEVELOPMENT OF RESCUE ACTIONS BASED ON DAM BREAK FLOOD ANALYSI A PREVENTION PROJECT UNDER THE EUROPEAN COMMUNITY ACTION PROGRAMME 1-DIMENSIONAL FLOW SIMULATIONS FOR THE KYRKÖSJÄRVI DAM BREAK HAZARD ANALYSIS HELSINKI, 30 th June 2001 Mikko Huokuna mikko.huokuna@ymparisto.fi Finnish Environment Institute, Helsinki

2 RESCDAM DEVELOPMENT OF RESCUE ACTIONS BASED ON DAM BREAK FLOOD ANALYSIS A PREVENTION PROJECT UNDER THE EUROPEAN COMMUNITY ACTION PROGRAMME CONTENT OF THE REPORT ON THE 1-DIMENSIONAL FLOW SIMULATIONS FOR THE KYRKÖSJÄRVI DAM BREAK HAZARD ANALYSIS 1. Introduction 3 2. DYX.10 flow model Concept of DYX.10 model Solution of the 1-dimensional flow equations One-dimensional unsteady flow equations Junction algorithm Numerical solution 9 3. Structure of the Kyrkösjärvi 1-d model River reaches and cross-sections Boundary conditions Control structures Roughness coefficient Simulated breach and base flow cases Results 20 2

3 RESCDAM DEVELOPMENT OF RESCUE ACTIONS BASED ON DAM BREAK FLOOD ANALYSIS A PREVENTION PROJECT UNDER THE EUROPEAN COMMUNITY ACTION PROGRAMME 1-DIMENSIONAL FLOW SIMULATIONS FOR THE KYRKÖSJÄRVI DAM BREAK HAZARD ANALYSIS 1. INTRODUCTION The 1-d modelling for the dam break hazard analyses has been done using a DYX.10-flow model. The model is based on a four point implicit difference scheme developed by Danny L. Fread (1985) for DAMBRK model. During the 1980 s, Fread s algorithm was developed further for river networks in Finland by Consulting Engineers Reiter Ltd. and used for many dam break flood simulations. The 1-d flow model for the Kyrkösjärvi DBHA covers the area from Renko dam (upstream of Kyrkösjärvi Reservoir) to Kylänpää (about 30 km downstream of the reservoir). The map of the 1-d model area is presented in Figure 1. The cross-sections used in the model were taken either from a terrain model or they were measured cross-sections. There were over 700 cross-sections, 22 reaches and 35 junctions in the Kyrkösjärvi 1-d DBHA model (735 cross-sections for the model of breach location A and 725 for the model of breach location C). The locations of the two breach locations ( A and C ) taken in to account in the 1-d calculations are presented in Figure 2. The flow simulations of the cases where the breach was assumed to occur at location A or at location C were modelled using the 1-d flow model. The breach cases studied with the 1-d model are : -Breach location A Base flow MQ (same as RUN 1 for 2-d models) -Breach location A Base flow HQ 1/100 (same as RUN 2 for 2-d models) -Breach location C Base flow MQ -Breach location C Base flow HQ 1/100 - The breach hydrographs, used in the simulations were derived using the breach erosion model. There is a separate report available on the determination of the breach hydrograph. A constant roughness coefficient (Manning n=0.060) was used in all simulation cases. The full wetted cross-section area was used as active flow area. 1-d model was also used to run sensitivity analyses of the effect of the size of the breach hydrograph on the water level downstream of the dam. 3

4 MAP OF THE 1D MODEL AREA KYRKÖSJÄRVI RESERVOIR DAM-BREAK ANALYSIS Kitinoja Malkamäki KIIKKU WEIR # SEINÄNSUU PUMPING STATION Munakka # # PAJULUOMA POLDER RINTALA POLDER # SEINÄJOKI CITY AREA Nikkola KYRKÖSJÄRVI RESERVOIR Area of 1D cross sections N Kilometers Figure 1.

5 Ground level near the Kyrkosjarvi dam. Levels between m above sea level. Assumed breach location Location C Assumed breach location Location B Assumed breach location Location A Figure 2. Locations of the assumed breach sites

6 2. DYX.10 FLOW MODEL 2.1 Concept of DYX.10 model The DYX package consists of the flood routing program DYNET and a set of graphical user interfaces and support programs. The computational modelling part uses the conservation form of the Saint- Venant equations of unsteady flow. In their conservation form the equations consist of the conservation of mass and momentum equations. The geometry of river reaches is given by a cross section/distance concept. In network calculation, the channel is divided into reaches, starting and ending in boundary conditions or (3-way)junctions. The partial differential equations are solved using a four-point finite difference scheme. The solution method is implicit and the degree of implicity can be adjusted with the weighing factor theta ( ). The Newton-Raphson method is used as solution of the Non-linear set of equations. In the case of a single channel where there are no junctions the matrix is penta diagonal and only non-zero values are stored. If there are junctions in the system, off-diagonal elements are created. The solution of the system of equations is obtained by Gaussian elimination. The Newtonian iteration is continued until no discharge or stage changes are greater than given criteria (as well absolute as relative). The DYNET flow model also provide the capability to use internal boundary conditions and hydraulic structures including dam break components of one or two stage time dependent failure mode or erosion type of embankment dam failure. A graphical user interface (GUI) has been integrated with the computational source DYNET and is forming the modelling package DYX.10. This GUI is serving the pre-processing of input data and the development of the specific flow model, it also serves the model testing (functionality and quality) and it serves the output in many ways. The location of elevation points in cross-sections are also defined with map co-ordinates which allow the usage of digital maps in pre-processing as well as the transfer of results for presentation or usage on digital maps is possible Solution of the 1-dimensional Flow Equations One-dimensional Unsteady Flow Equations DYNET uses for solution the conservation form of the Saint-Venant equation of unsteady flow. In their conservation form the equations consist of the conservation of mass and momentum equations. The geometry of rive reaches is given by a cross section / distance concept ( Figure 3 ). 6

7 13 BC BC BC 2 Figure 3. Cross-section distance concept. ( o) Q x + A+ A t q = 0 (1) 2 ( ) [ ( ) f e ] Q t + Q A x + ga h x + S + S = / S = n Q Q A R = Q Q K f f 0 (2) (3) where A is active cross-sectional area (m 2 ) A o is inactive (off-channel storage) cross-sectional area (m 2 ) x is distance along the longitudinal axis of the waterway q is lateral inflow (positive) or outflow (negative) (m 3 /s) t is time g is gravity acceleration constant Q is discharge (m 3 /s) h is water level S f is friction slope (from Manning equation) S e is n is Manning coefficient R is hydraulic radius is channel conveyance factor. K f 7

8 In network calculation, the channel network is divided into reaches which should start and end in a boundary condition or in a junction Junction Algorithm The formulation of a junction algorithm forming the boundary of the junction (equations 4...7) (Figure 4) has the following subscripts. - upstream cross section... u - downstream cross section... a a = u + l - lateral channel cross section... r Presenting the case that the lateral inflow is positive: ( ) ( ) ( ) Qu + Qr Qa S t = 0 (4) ( ) + ( ) = ( ) + ( ) = ( ) + ( ) hu vu 2g ha va 2g hr vr 2 g (5) [ ( ) ( ) ( )] S t = x t B h u + h a + h r (6) B = B( u) + B( a) + B( r) cos( α ) (7) where B is the mean water surface width of the junction α is the angle of the lateral inflow with the main channel. Figure 4. Generalized river junction. Friction losses in the junction are included in the computation and accounting for flow dynamics within the junction is optional. 8

9 2.3 Numerical Solution The partial differential equations are solved using a four- point finite difference scheme. The solution method is implicit and the degree of implicity can be adjusted with the weighting factor theta. Theta may be adjusted from 0.5 to 1.0. The four-point weighted differential equations are (8) and (9) where K is a dummy parameter representing any variable in the differential equations (1),(2),(4) and (5) and the subscript i describes the x-position ( sequence number of cross section), and j is a subscript denoting the sequence number the time line. Thus: K(i, j) means value of K at cross section (i) and at time (j). j+ i J+ 1 j j ( i i+ 1 i i+ ) ( ) K t = K + K + K + K 1 2 t (8) j+ 1 j+ 1 j ( i)( i i ) (( ) i ) ( j + 1 i+ 1 i ) K x = θ x K K + 1 θ x K + K (9) j j ( θ)( i i+ 1 ) j+ 1 j+ 1 K = ½θ K + K + ½ 1 K + K (10) i i+ 1 9

10 Figure 4. Four-point finite difference scheme. Assuming N cross sections in a reach with two unknown variables in each cross section, discharge (Q) and water depth (y), the overall number of unknowns is 2N. Applying the above differential scheme to the flow equations we get 2N-2 non-linear equations because the equations are set up for each sub-reach between two cross sections. The two missing equations are developed for the upstream and downstream boundary conditions. If there are junctions in the river channel, we may conclude that junctions split the river into reaches. An upstream or downstream boundary condition or a junction thus limits each reach. There are three channels in each junction where flow may enter or leave. We therefore need three equations per junction, one continuity equation and two momentum equations. 10

11 3. STRUCTURE OF THE KYRKÖSJÄRVI 1-D MODEL 3.1 River reaches and cross-sections The 1-d flow model for the Kyrkösjärvi DBHA covers the area from Renko dam (upstream of Kyrkösjärvi Reservoir) to Kylänpää (about 30 km downstream of the reservoir). The map of the 1-d model area is presented in Figure 1. There are more than 700 cross-sections, 22 reaches and 35 junctions in the Kyrkösjärvi 1-d DBHA model. The locations of the reaches for the model ( breach location A) are presented in Figure 5. The model for the breach location C is almost identical to the model for the breach location A. Only the reach, which presents the geometry just downstream of the assumed dam breach site, is different in those two cases. Overall, some 735 cross-sections were used in the simulations (for breach location A) and 725 (for breach location C). Figure 6 presents the locations of the cross-sections at a distance of about 4 km downstream of the dam (model for breach location A). The cross-sections used in the model were taken either from a terrain model or they were measured cross-sections. Figure 7 presents an example of a crosssection used in the model. The information of the reaches used in the 1-d simulation is presented in Table 1. and the longitudinal profiles for the most important reaches Seinäjoki and Kyrönjoki are presented in Figures 8 and Boundary conditions The locations of the boundary conditions in the Kyrkösjärvi 1-model are presented in Figure 10. There were 7 flow and 1 stage boundary conditions in the model. Only the main inflow values were taken in to account in the study. The other inflow values are assumed to be zero. A constant water level was used at the downstream boundary in the model (about 40 km north from Seinäjoki). The backwater effect from this downstream boundary affects only a couple of kilometres upstream. 3.3 Control structures There are several overflow dams (weirs) and gates in the Kyrkösjärvi 1-d model. Fictive overflow dams were used in some locations to describe flow over a road. The locations of the control structures used in the Kyrkösjärvi 1-d model are presented in Figure Roughness coefficient A constant roughness coefficient (Manning n=0.060) was used in all simulation cases. 11

12 Reaches in the Kyrkösjärvi 1d-model Kilometers

13

14 Table 1. Information about reaches in the Kyrkösjärvi 1-d model Name of the reach Length of the reach [m] Number of CS Number of interpolated CS Mean distance between CS s [m] Seinäjoki Breach (A) Oikaisu_uoma Kyronjoki Sotaoja Tien_tak_lyhyt Sivu_uoma Pajuluoma Pajul_ala Pajulerist Pajul_oika Kiikku Kyro-Kiikku Tieksi Ioonoja Kyro-Tieksi Kitino Kyro-Kiti Kyro-Kiti Kyro-Kiti Kyro-Kiti Kyro-Kiti Seinäjoki km Elevation [m] Distance [m] Figure 7. An example of a cross-section used in the Kyrkösjärvi 1-d calculation 14

15 Figure 8. Longitudinal profiles for the River Kyrönjoki. Figure 9. Longitudinal profiles for the River Seinäjoki.

16 Boundary conditions of the Kyrkösjärvi 1d-model %U $T #S Flow %U Zero-flow $T Stage River Fictive channel Road %U %U Railroad %U #S #S #S Kilometers #S N

17 Dams and fictive dams of the Kyrkösjärvi 1-d model 17 %U %U %U %U %U %U %U %U #S Dams Fictive dams 7 %U 8 9 %U %U %U 10 4 %U %U 3 5 %U 6 %U %U 2 1 %U #S #S #S #S #S #S #S N Kilometers

18 4. SIMULATED BREACH AND BASE FLOW CASES The flow simulations in which the breach was assumed to occur at location A or at location C were modelled using the 1-d flow model. The assumed breach locations are presented in Figure 2. The breach cases studied with the 1-d model were : -Breach location A Base flow MQ (same as RUN 1 for 2-d models) -Breach location A Base flow HQ 1/100 (same as RUN 2 for 2-d models) -Breach location C Base flow MQ -Breach location C Base flow HQ 1/100 The base flow values for the MQ and HQ1/100 cases were taken from the hydrological model study (separate report available). For an MQ case, larger inflow values than those defined by the hydrological analyses had to be used for model stability reasons. However, this does not have a significant effect on the calculated dam break flood stages. The inflow boundary conditions for the Kyrkösjärvi 1-d model are presented in Table 3. Table 3. The inflow values used in the 1d model Name of the inflow MQ [m 3 /s] HQ 1/100 [m 3 /s] Inflow to Kyrönjoki Inflow to Seinäjoki 20 (stability reasons) 150 Inflow to Pajuluoma 3 (stability reasons) 5 The breach hydrographs, used in the simulations, were calculated using the breach erosion model. There is a separate report available of the determination of these breach hydrographs. The breach hydrographs used in the calculations are presented in Figure 12. Due to model stability reasons, a base flow of 10 m 3 /s has been used in the reach describing the river valley just downstream of the dam breach location. A constant roughness coefficient (Manning n=0.060) was used in all simulation cases. 18

19 Figure 12. Breach hydrographs used in the Kyrkösjärvi 1-d calculations.

20 5. RESULTS The results of the 1-d simulations were printed out as maps and hydrographs on selected locations. The selected locations for output are presented in Figure 13. The water level hydrographs calculated using the 1-d model for breach location A are presented in the Appendix 1: The hydrographs are for breach cases HQ 1/100 (breach location A) and MQ (breach location A) for locations 4, 9, 11, 12, 13, 17, 21, 24, 28, 29, 31, 33, 39, 40 and 42. In the Appendix 2 there are the similar values for breach location C and for locations 21, 24, 28, 33, 39 and 42. The water level profiles of the Seinäjoki river for the calculation cases HQ1 /100 A and MQ A are presented in Figures 14 and 15. The discharge profiles for the same calculation cases are presented in Figures 16 an 17. The similar profiles for the calculations of the breach location C are presented in Figures REFERENCES: Fread, D.L Channel Routing. Anderson M.G. and Burt, T.D. (ed.) Hydrological Forecasting. John Wiley and Sons Ltd., London p DYX.10 User Manual 20

21 RESCDAM project LOCATIONS OF THE OUTPUT POINTS 33 OUTPUT POINTS Kilometers

22 Water level profile for Seinäjoki HQ1/100 Case A Bottom 0.0 h h 1.5 h 2.0 h 3.0 h h Elevation [m] Distance [km]

23 Water level profile for Seinäjoki MQ Case A Bottom 0.0 h h 1.5 h 2.0 h 3.0 h h Elevation [m] Distance [km]

24 Discharge profile for Seinäjoki HQ1/100 Case A h 1.0 h h 2.0 h h 4.0 h Elevation [m] Distance [km]

25 Discharge profile for Seinäjoki MQ Case A h 1.0 h h 2.0 h 3.0 h 4.0 h Elevation [m] Distance [km]

26 Water level profile for Seinäjoki HQ1/100 Case C Bottom 0.0 h h 1.5 h 2.0 h 3.0 h Elevation [m] Distance [km]

27 Water level profile for Seinäjoki MQ Case C Bottom 0.0 h h 1.5 h 2.0 h 3.0 h Elevation [m] Distance [km]

28 Discharge profile for Seinäjoki HQ 1/100 Case C h 1.0 h 1.5 h h 3.0 h 800 Elevation [m] Distance [km]

29 Discharge profile for Seinäjoki MQ Case C h 1.0 h h 2.0 h h 500 Elevation [m] Distance [km]

30 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

31 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

32 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

33 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

34 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

35 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

36 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

37 RESCDAM 1-d model results BREACH LOCATION A APPENDIX 1

38 RESCDAM 1-d model results BREACH LOCATION C APPENDIX 2

39 RESCDAM 1-d model results BREACH LOCATION C APPENDIX 2

40 RESCDAM 1-d model results BREACH LOCATION C APPENDIX 2