P Two-dimensional Modelling of Dam Breach Flooding. Miguel Ángel Corcuera Barrera 1, Peter Torp Larsen 2, Poul Kronborg 2

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1 Two-dimensional Modelling of Dam Breach Flooding. Miguel Ángel Corcuera Barrera 1, Peter Torp Larsen 2, Poul Kronborg 2 1 Aguas del Añarbe, España 2 DHI Spain Presenter: Peter Torp Larsen, ptl@dhigroup.com Keywords: Dam Breach modelling, Flood modelling. ABSTRACT The public water company Aguas del Añarbe is responsible for the safety and security of the water supply to the city of San Sebastian. The main source of water is extracted from the Añarbe reservoir located 15 km upstream of San Sebastian. The potential catastrophic failure of the Añarbe Dam and the resulting downstream flooding and damage is a subject of great concern in terms of emergency planning and preparedness. An appropriate planning of such an event requires modelling of the flood wave propagation with sufficient detail to capture both the spatial and the temporal evolution. Accurate estimates of potential flood depths, velocities and timing of the flood arrival and recession are key factors in the impact analysis. Traditionally onedimensional models have been applied to model this type of events; the problem with the 1D approach is the limited ability to capture the spatial propagation of the floodwave, both in terms of flow depth and velocity. In contrast to the 1D models, the MIKE 21 HD (landslide) provides a complete spatial and temporal description of the results in the entire flood area. This paper presents a study of different types of Dam break modelling, and an analysis of the influence of factors such as reservoir topography and the temporal evolution of the dam breach. Furthermore it compares and discusses the differences in the results of a 1D model vs. a 2D model. Introduction Several software packages for simulation of the propagation of flood waves generated by breaching dams and for inundation mapping are used for dam safety purposes. The National Weather Service modelling systems DAMBRK and FLDWAV are being widely used. Floodplain modelling efforts have moved to include unsteady-flow onedimensional (1D) models, and lately to also include steady and unsteady twodimensional (2D) models, and even dynamically coupled 1D / 2D models. The use of multi-dimensional models has also been spurred on by the increasing availability of LIDAR topography, which allows for the modeller to describe large areas of floodplain with greatly increased accuracy and greatly reduced cost. This is a major advance in terms of describing broad floodplains, as a more P081-1

2 detailed modeling effort can be meaningless in the absence of equally detailed input data. In the western U.S., the Bureau of Reclamation has applied a combined 1D and 2D modeling approach for the purpose of evaluating flood inundations of dam and levee failures at a variety of sites having complex geometries. Integrated one and two dimensional modeling systems such as MIKE 11 and MIKE 21, providing similar modeling capabilities, a user-friendly graphical user interface and GIS flood mapping features, has in the recent years become widely used for integrated simulation of reservoir inflow forecasting, dam failure, flood wave routing, inundation modeling and GIS mapping. The MIKE 11 and MIKE 21 modeling systems are approved by FEMA for flood hazard modeling and mapping under the NFIP. There have been around 200 notable dam and reservoir failures worldwide in the twentieth century. These failures have caused severe devastation in the valleys downstream both in terms of lives lost and widespread damage to infrastructure and property. The most common cause is extreme inflow events, exceeding the capacity of the spillway, but structural failures have also occurred at inflows less than the design flood. In order to prepare emergency action plans, revise dam operation strategies, prioritize dam rehabilitation, etc it is important to assess the consequences of possible dam break in terms of the affected areas, the time available to evacuate people, and the damage which the flood wave will cause. This can be most effectively assessed through model studies and flood mapping, described in the following. Model development history NWS DAMBRK and FLDWAV are widely used for 1-dimensional simulations of flood wave propagation. In the last decade several propriety software packages has been introduced. These mainly 1-dimensional modeling packages additionally offer a graphical user interface and in some cases interfaces to GIS. This provides the modeling expert with flexibility from the simplest model to the most detailed state-of-the-art modeling technology and safety against unforeseen deadlocks due to technical limitations of the software or resource constraints. More recently 2-dimensional modeling of flood wave propagation has become more commonly used not only in the US but also worldwide and lately integrated 1- and 2-dimensional models are offered. The latter allows the user to benefit from the advantages of both worlds. DHI has been an important solution provider in this development. MIKE 11, MIKE21 and MIKE FLOOD (1-dimensional, 2-dimensional and integrated 1-D and 2-D modelling tools) are approved by the US Federal Emergency Management Agency (FEMA) for flood hazard modeling and mapping under the National Flood Insurance Program. Authorities in many countries recommend MIKE 11 as the standard tool for river modeling. 1-dimensional modeling The hydrodynamic computations in MIKE 11 are based on the cross-sectional averaged Saint-Venant equations, describing the development of the water level P081-2

3 s and the discharge Q or the mean flow speed U. The Saint-Venant equations in 1-D reads: A Q + = FS t x (1) Q gq Q + Q A + ga h + 2 ( α / ) 2 t x x C AR = 0 (2) where h is the water depth, Q is the discharge, α is the velocity distribution coefficient, x is stationing, t is time, FS is a source term, g is gravitational acceleration, C is the Chezy number, A=f(h) is the area of wet cross-section, P=g(h) is the wet perimeter, both depending on the water depth and R=A/P is the hydraulic radius. Briefly, the numerical solution is obtained from a finite difference formulation of the equations, using a scheme, which is based on alternating Q and h points (Abbott, 1979). The graphic and interactive MIKE 11 dam breach module allows the user to define: Failure moment: at a specified time or related to certain hydraulic conditions such as the reservoir water level. Failure mode: breach development, piping failure leading to erosion, or erosion through overtopping. The breach flow calculation routine is based on the energy equation looking at the loss of energy as the flow passes through the breach. This gives the following equation: 2 2 v + 1 v = + s A + 1 h h s ζ in 1 (3) 2g 2g As h is water surface elevation in the reservoir, v 1 is flow velocity in the reservoir, h s is water surface elevation in the breach, ζ in is head loss factor for inflow contraction, A 1 is the flow area in the reservoir and A s is the flow area in the breach. In a simplified version this equation corresponds to the breach flow equation used in DAMBRK and FLDWAV. For most dam breach cases the flow velocity in the reservoir is small, i.e. the velocity head can be neglected, and if the inflow head loss factor is set to zero the equation simplifies to: 2 vs h = hs + (4) 2g Assuming critical flow is present at the breach (i.e vs = g ys where y s is the water depth in the breach) following equation holds: Q b s s s s i i 3 2 s = v A = g y y b = g b y (5) P081-3

4 Combining (4) and (5) yields: Q b = g bi ( h hb )2 (6) 3 Using g=32.19ft/s 2 this equation becomes ( ) 1. 5 as used in DAMBRK and FLDWAV. Q b = 3.1 bi h hb which is the same This has been verified by applying DAMBRK and MIKE 11 on the same case. The inflow head loss factor in MIKE 11 has been set to , with such a setting MIKE 11 compares well to the DAMBRK breach flow calculation. The routing of the breach flow downstream of the dam is in MIKE 11 as in DAMBRK done by solving the Saint Venant equations. One of the differences between the two is the finite difference scheme used to solve the equations. The difference between MIKE 11 and DAMBRK originating from the method of solving to the Saint Venant equations has been investigated by comparison of the results in another case with flow routing. The breach flow from DAMBRK has been used as boundary condition for MIKE 11. Mapping of 1-dimensional results The conventional output from hydraulic models comprises time series, longitudinal profiles and plans plots of discharge, flow velocity and water level. While these are meaningful to engineers, they lack a spatial dimension and are less readily understood by planners, emergency organizations and the general public. MIKE 11 is integrated with GIS for automated model development and flood mapping. The automated and integrated GIS process provides a very efficient modeling environment that allows the engineer to establish a wellorganized production line. Flood mapping provide highly visual presentations of flood plain inundation, FEMA flood zones, etc and can be overlaid with other GIS data such as topography, roads, tax lots, etc. This information is thus readily available to flood managers, concerned organizations and the general public, for both planning purposes and in emergency situations. Flood maps and video animations are key results of dam break studies, illustrating the floods simulated for the different failure modes, hydraulic conditions etc., in combination with other GIS information on infrastructure, location of emergency services, etc. Generating flood maps basically requires two set of input: a DEM and MIKE 11 simulation results. These informations are combined into a flood map as shown in Figure 1. P081-4

5 Figure 1: Example of flood map generated using MIKE 11 GIS 2-dimensional modeling The two-dimensional MIKE 21 model is based on the depth averaged Saint- Venant equations, describing the evolution of the water level s and two Cartesian velocity components U and V. See equations 7,8 and 9. s + Uh + Vh = FS t x y s U U + U + V + g x s t x y g 2 2 U U + U U + V + ( K ) ( ) 2 xx + K yy = FSU C d x x y y s V V + U + V t x y s g 2 2 V V + g + V U + V + ( K ) ( ) 2 xx + Kyy = FV S x C d x x y y S S (7) (8) (9) where s is the elevation, h is the total water depth, U and V are depth averaged Cartesian velocity components, C is the Chezy number, K xx and K YY are eddy viscosities, F S is a source term and U S and V S are the velocity at the source. The numerical solution is obtained from a finite difference form of the equations using a staggered C-grid and a semi-implicit ADI two-step algorithm. By rewriting the convective and friction terms a robust and accurate solution can be obtained (Abbott, 1979). This enables an efficient solution consisting basically of consecutive line sweeps across the domain. Two extensions to the numerical solution method are important for the present applications to flood plain flows, namely the ability to describe flooding and drying of computational nodes and to describe propagation of flood waves across initially dried or very shallow areas. The basic problem with dried out cells, i.e. cells where the water level falls to or below the bed level yielding a zero or negative total water depth, is to develop P081-5

6 methods that provides stable and physical sound solutions and conserves mass. Several methods has been suggested such as clipping of the water depth to a small positive value, artificially increased friction for small water depths or implementation of slots, where the cell area diminishes when the water level falls below the bed level. McCowan et al. (2002) has demonstrated that within the present solution method a modification of the scheme suggested by Stelling et al. (1998), which utilize an upwinded discretisation of the water depth, combined with a positive and monotone scheme for the water depth, provides a reasonable solution. The use of spatially centered discretization of the convective terms provides a high accuracy of the numerical solution, but restricts for stability reasons the flows to be sub-critical, i.e. the Froude number F = U / gh must be less than 1. For coastal applications this is usually not a serious restriction, but for flood waves propagating over dried or very shallow areas, critical or super critical conditions often arise. A remedy is to introduce extra dissipation of short wave energy locally either by introducing an artificial eddy viscosity or numerical filters (Abbott, 1979) or through the numerical scheme (Lax, 1954). By introducing an upwind weighting of the convective terms McCowan et al. (2002) has demonstrated that the present solution method can be stable also for super critical flows and avoids artificial wiggling of both velocities and water levels. The weighting is selected based on the local Froude number such that for F < 0.25 a centered scheme is used and a gradually increasing upwinding until F>1.0 where a fully upwinded scheme is used. To enable modeling of landslide and dambreaks a landslide module has been incorporated into MIKE21 HD which allows the user to use temporal variation in the model bathymetry. This makes it possible to describe the dam breach via the bathymetry, instead of the conventional MIKE 11 Dam Break method. The effect of Dam Break is modelled by forcing terms representing the dynamic vertical deformation of the bathymetry plus additional terms to represent the effect of the dam break due to viscous and inertia forces. Regarding the high velocities that can occur during a Dam break, MIKE 21 model engine incorporated a calculation scheme which allows it to model both sub- and supercritical flows.ref /7/ Combined 1- and 2-dimensional modeling In recent years, MIKE 21 has been dynamically linked to MIKE 11, into a single package called MIKE FLOOD. MIKE 11, MIKE 21 and MIKE FLOOD are approved by FEMA for flood hazard modeling (river, flood plain and coastal storm surge) and mapping under the NFIP. Combining the two models provides a highly efficient system as the benefits of both models are utilized while the downsides are eliminated, i.e. detailed modeling and accuracy where needed without sacrificing computational or model development time. With MIKE FLOOD it is no longer necessary to compromise between choosing between the number of horizontal dimensions and the often-prohibitive resolution requirements of modeling in a detailed 2D grid. Now it is possible to use internal subgrid structures from the MIKE 11 system in a MIKE 21 domain (ie culvert, bridges, channels, weirs, etc). Also, it is possible to link MIKE 11 river reaches to MIKE 21 open boundary conditions. Further, it is now possible to embed a river reach within a MIKE 21 model domain, and have automatic over bank connections P081-6

7 between the MIKE 11 river and the MIKE 21 domain. This is achieved using continuous lateral links along the embankment, which can be described by various weir formulations. With this capability it is possible to relax many of the constraints on grid spacing that 2D modeling once posed. One example of the Dam Break in MIKE 11 is by using the structure option to include the flow between the Dam break cells. Figure 2 shows the structure coupling from M11-M21: Figure 2: Incorporation of a Dam Break in MIKE FLOOD using structure links. Another possibility is to calculate the hygrogram directly in MIKE11 and incorporate it as an internal boundary condition in MIKE 21. Application example modeling of the Añarbe Dam break In this example we will focus on the MIKE 21 landslide method, meaning incorporating the Dam Break directly into the model bathymetry, as described above. Furthermore, we ll undertake a comparison with the 1D method. Description of the area and the Dam The studied dam is partly located in the north eastern part of Navarra and partly in the province of Gipuzkoa, in the Basque Country. P081-7

8 Figure 3: The location of the Añarbe Dam The dam was built in 1978 partly as a flood protection measure and partly to secure the water supply to San Sebastian. The Añarbe reservoir has a maximum extension of 201 Ha, a max depth of 65 m and a medium depth of 26m. The maximum capacity of the reservoir is 44hm3 It s a gravity dam with a height of 79m and a length of 304 m, the bottom outlet has a capacity of 520m3/s Figure 4: The Añarbe Dam seen from downstream. P081-8

9 Input data: The model topography was defined by LIDAR data with a resolution of 1x1m, and the reservoir bathymetry was defined by a 5x5m grid. A spatial distribution of the Manning number was applied. The Manning number was defined based on the available land use maps. The downstream boundary was defined by a max tidal level for the Cantabrian Sea. Definition of the breach Dam Break was defined based on the general guidelines set out by the Ministry of Environment of Spain and the following breach equations and parameters: Time of Breach=15 min Shape of breach = Rectangular Depth of breach = 75m Longitude: m Side slope: 1:1 NMN =156 m Initial water level in the reservoir =156.5 m Volume of reservoir at NMN =37 Hm 3 Figure 5: The dam before the breach (t=0 min) and after the breach (t=15 min) (upstream view) Modeling results Comparison of 1D-2D model and excl reservoir or incl. reservoir A normal way of describing the storage capacity of a reservoir is by a relation between the stored volume and water level in the reservoir (or surface and water level). Therefore a typical assumption in Dam Break simulations is that the volume can be defined in one calculation point, just upstream of the dam, which means that the topography and of the reservoir and the dynamics of the upstream moving wave is not taken into consideration. In this study we did however have very fine reservoir topography, so it was possible to analyze the effect this assumption on the outflow from the dam. We therefore ran two MIKE 11 DB simulations, one with the volume located in one point just upstream of the dam, and one where the reservoir volume is defined by cross sections extracted from the reservoir bathymetry. These results were then compared to the outflow hydrograph calculated by the 2D model (MIKE21). The result can be observed on: P081-9

10 Figure 6: Outflow hydrographs. As it can been seen the inclusion of the reservoir topography plays quite an important role in the peak outflow. The discharge is considerably higher than the two other simulations. The reasons can be found in the assumption made in the DAMBrk formula, that V=0m/s in the reservoir (and therefore no energy outflow loss), which as can be seen in figure 7 is not the case. Actually velocities of up to m/s are predicted. Figure 7: Flow pattern in the Añarbe Reservoir The difference between the M11 with reservoir and the M21-landslide is caused by the differences in flow path. The M11 do not include the meanders of the reservoir, in fact the flow path will change depending on the water level. P081-10

11 Results of the 2D simulations including the reservoir topography Figures 7- through 11 show water depth and velocity output from the model at the initiation of the dam breach, and then at times of 10min, 30min, 1 hour and 2 hours after the breach. Figure 8: Water levels at t=0 Figure 9: Water levels at t=10min P081-11

12 Figure 10: Water levels at t=30min Figure 11: Water level t=1hour P081-12

13 Figure 12: Water level t=2 hours The flood will travel down the upper reach (the first 15 km) where the river is relatively step 0.8 % but winding. On this part the flood will attain a maximum depth of 20-25m, and a max speed of velocity of m/s, until the point where the river widens (Ereñozu San Sebastian) and is less steep the flood spreads out and attain a max depth of 8-10m and a velocity of 5-8 m/s. Considering the relatively high velocity at the edge of the advancing flood wave it is considered characterized by supercritical flow in the upper part of the river, but as it can be observed from the variations in velocity (fig 13) the front wave is unable to completely follow the bending riverbed and is reflected of the valley sides causing a possible creation of hydraulic jumps and a transition to subcritical flow. Figure 13: velocity at t=10min P081-13

14 The changing of flow conditions along the river, can have an important effect on the water depth of the flood water, and thus highlights the importance of a dynamic 2D momentum balance for dam break simulations, which allows wave action such as shocks and backwater profiles to be resolved. Comparison with a real Dam Breach of the results Due to the nature of a Dam break it s seldom possible to calibrate the model, although data might be available. In order to verify/validate the results we have compared the simulation results to a real Dam break flood event, of a similar magnitude, the San Francis Dam Break. The Saint Francis dam was a concrete dam constructed between 1924 and 1926 by LA bureau of waterworks and supply. Failure occurred at 23:57:30 h on March , when the reservoir was first filled to its crest level. Following the collapse, a wave of water traversed roughly 87 km towards the Pacific Ocean. The flood destroyed over 1000 homes, ten bridges, roads, and caused over 500 fatalities. Ref. /6/ The similarities in size and design can be observed on table 2: Furthermore the topography is similar, hilly monotonous on the first stretch and flat with a small gradient on the last part. Table 1: Dam and reservoir data Dam Volume Height of dam Width Max. Discharge (m3/s) (Simulated) Añarbe Dam 44 hm3 61m 300m m3/s San Francis 47 hm3 57m 213m m3/s The Dam break On the Figure below the 2 Dam breaches- situation before and after, to the left the theoretical Breach of the Añarbe Dam and to the right the San Francis dam break of 1927 (ref./6/) P081-14

15 Figure 14: Illustration of the two Dam breaches. Figure 15 shows the location of the stations where arrival time was recorded (Outland 1963) and the left figure shows the points at the corresponding PKs in the Añarbe model. Figure 15: Location and layout of the topography of the two Dams P081-15

16 Table 2 shows the observed arrival time for the San Frances DB, and the corresponding simulated times for the Añarbe simulation. Table 2: Observed arrival time Ref/6/. Station ID (Ref. /6/) Station Añarbe Pk. (Estim.) Arrival time (Obs.) Arrival time simulated A-A:Power House A-A: min 4.5 min B-B: Saugus Subst B-B: Ereñozu min 46 min C-C: Edison Camp C-C: P. Carteles h 22min 1h 45 min Interestingly the arrival times of the flood wave are very similar, even though its two different locations and two different dam break. Of course it s difficult to conclude based on these results, other than the simulation a result from MIKE 21 Landslide seems to be realistic. 3. Conclusions This paper presents a short description of theoretical background of different Dam break modelling approaches 1D, 2D and a combination of 1D & 2D and the. MIKE11-MIKE21 and MIKEFLOOD The fully dynamic 2D method (MIKE21 Landslide) is applied to a real dam break study, and the flood maps generated by the model are presented. In order to validate the simulation results the outflow hydrograph is compared to the results of a 1D simulation using the well know and widely used DAMBRK formula in MIKE 11. Furthermore the influence of the inclusion of the reservoir topography was analysed by running M11 simulations with and without and comparing the results to the results from the 2D simulation Finally the results were compared to the observation from the St Francis dam break that occurred in 1928, in California, and is very well described by various sources. The two dams are very similar in both in size and topographical configuration. The results showed a surprisingly good correspondence between the arrival times observed in the St. Francis study. But as they are different in many ways the comparison only serves as a validation of the modelling results, which must be considered to be realistic. P081-16

17 REFERENCES 1. Abbott, M. B. (1979). Computational Hydraulics. Pitman, London. 2. Lax, P. D Weak solutions of non-linear hyperbolic equations and their numerical approximations. Comm. Pure and Applied Mathematics, No McCowan, A.D., Rasmussen, E.B. and Berg, P. (2002) Improving the performance of a two-dimensional hydraulic model for floodplain applications. Proc. Conf. on Hydraulics in Civil Engineering, The Institution of Civil Engineers, Australia. 4. Soares, S. and Zech, Y Effects of a sharp bend on dam-break flow. Paper B9, Proceedings 28th IAHR congress, Graz, Austria. 5. Stelling, G., Kernkamp, H. W. J. and Laguzzi, M. M Delft Flooding System. In: Babovic, V. and Larsen, L. C. (eds.), Hydroinformatics 98, Balkema, Rotterdam. 6. Lorenzo Begnudelli and Brett F. Sanders Simulation of the St. Francis Dam-Break Flood, Journal of Engineering Mechanics, November Henrik Kofoed Hansen, (2000) Numerical Modeling of landslide generated waves in reservoirs, DHI. P081-17