RISK-BASED PROCEDURE FOR DESIGN AND VERIFICATION OF DAM SAFETY

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1 4 th International Symposium on Flood Defence: Managing Flood Risk, Reliability and Vulnerability Toronto, Ontario, Canada, May 6-8, 2008 RISK-BASED PROCEDURE FOR DESIGN AND VERIFICATION OF DAM SAFETY M Anhalt 1, and G Meon 1 1. Leichtweiss-Institute for Hydraulic Engineering and Water Resources, Dept. Hydrology, Water Management and Water Protection, University of Braunschweig, Germany ABSTRACT: In this paper an overview and the results of the project Risk-based methods to guarantee adequate flood safety for reservoirs are presented. The project is part of the program on Risk management of extreme flood events (RIMAX) funded by the German Federal Ministry for Research and Education. The focus lies upon risk assessment methodologies and the development of advanced design procedures regarding dam failure caused by flood loads. Key Words: dam safety; risk analysis; reliability; dam breach; flood 1. INTRODUCTION Flood events of recent years clarified that hydraulic structures like dams impose a risk of failure with potential disastrous consequences. Absolute safety of a dam cannot be achieved. Therefore methods of risk-based design of dams become more important. Dams are systems with large hazard potential due to the high potential energy accumulated within the water body. Statistic evaluations show that dam failures are mainly caused by overtopping of the dam crest. According to Hable (2001) 35% of dam failures occurred due to overtopping. This failure type is essential to be addressed in dam design and verification of dam safety. Many countries are currently exploring the possibilities of incorporating risk assessment as a part of their dam safety guidelines. Several required methods, models and applications of risk analysis of dam safety are still being reviewed and developed. Fundamental contributions of comprehensive dam risk assessment in terms of a Portfolio Risk Assessment can be found in Bowles (1987, 2006). International trends and progresses are summarized e.g. in McGrath (2000) and DEFRA (2002). In Germany, Meon (1989) and Bachmann et al. (2007) developed comprehensive risk-based procedures applied to dams. The German DIN standard represents the state of the art regarding dams and diversion structures in Germany. A complex safety proof concept has been introduced in the revised standard from Safety requirements for extreme floods and earthquakes are considered. The new safety proof concept considers conditions beyond the current design limits. Thus, the new DIN offers the possibility of qualitative risk assessment in dam safety evaluation (Sieber, 2004). However, there is still a lack of methods and guidelines to assess the residual risk and appropriate measures to minimize the risk of dam failure. Statements and guidelines concerning the risk of dam overtopping do not yet exist in a comprehensive form. Therefore, further investigations of risk analysis of reservoir-dam systems in 154-1

2 Germany are necessary to obtain practicable and standardized risk-based procedures which can be used for the design of new dams and also for a safety verification of existing dams. In the following chapters, the concept of such a comprehensive procedure will be described. Within this paper only the key aspects and approaches as well as a brief presentation of some results can be illustrated. 2. CONCEPT The submodules M i of a risk-based procedure against dam failure caused by flood loads are shown in Figure 1. The procedure includes a risk analysis and assessment embedded in a dam risk management. The assessment includes the estimation of failure probabilities (M1, M2), potential dam breaching (M3), downstream propagation of flood hydrographs caused by a dam break (M4), damage analysis (M5), and the determination of risk indices (M6). Figure 1: Comprehensive risk-based procedure embedded in a risk management of a dam The developed procedure includes three types of hydro-meteorological failure of a reservoir-dam system: large spillway discharges (failure type 1), overtopping without dam breaching (failure type 2) and overtopping with dam breaching (failure type 3). Following investigations of existing methods, suitable approaches were adopted and partially modified as described in the following chapter. 3. MODULES OF THE PROCEDURE 3.1 Synthetic flood event The first module of the procedure is the determination of synthetic flood events (inflow into reservoirs). A stochastic model based on Treiber (1977) for the simulation of reservoir inflows is used. Observed daily flows covering a period of 46 years were used to apply the model. It consists of two parts: a stochastic simulation of input pulses, and a deterministic part that transforms rainfall into runoff. The pulse generation model has cyclic variable parameters with one parameter set for each month. After the calibration for two study areas (see chapter 4), the model yields artificial series of reservoir inflow with the statistical properties of the historical records

3 3.2 Probability of hydro-meteorological failure The total water level in the reservoir is a result of three random variables: the water level at the beginning of a flood event h 0, the water level h R resulting from the retention of a flood event (inflow Q in ), and the corresponding and coincidental wind related freeboard h F. In the proposed concept (see Figure 2) the hydro-meteorological failure occurs if: [1] h 0 + h R + h F > H max. Figure 2: Chart of submodule M2 determination of hydro-meteorological probability The theoretical solution of the overtopping probability P F is given by a triple integral (Pohl, 1997), in which the three heights h 0, h R and h F are assumed to be independent (Equation 2): [2] P = P(h + h + h > b) = f (h ) d f (h ) d f (h ) d F 0 R f h0 0 h0 hr R hr hf F hf A closed solution of the integral is not practical, so that a Monte Carlo Simulation is used. The basic concept follows the one developed by Pohl (1997) and modified by Hable (2001). The major difference of the concept refers to the main load size which defines h R. Generated daily inflows from submodule M1 with a length of at least one million years are used. If necessary, the daily inflows can be disaggregated in smaller time steps. It is possible to simulate the complete time series or to consider every annual flood with differentiation based on the highest peak discharge or the highest volume. At the beginning of every flood event the initial water level h 0 must be determined. The level h 0 depends on the reservoir management and previous floods or droughts. By using historical data of measured daily water levels, empirical cumulative density functions of the initial water level were determined on a monthly basis. Thus, the variation of the initial water level within a year is considered and adequate to the generated inflow which occurs in a certain month. On the basis of several series of observed wind velocities and corresponding wind directions, an applicable cumulative density function of freeboard has been evaluated to determine the third random variable h F

4 Figure 2 summarizes the procedure for the three main load sizes h 0, h R and h F. The main output obtained from submodule M2 is the total height of the water level with respect to the flood routing in the reservoir corresponding to certain probabilities P i (nwl). The water level WL is specified as a normalized factor nwl (actual water level WL divided by spillway crest elevation). By doing so, the results of different scenarios and different dams become comparable. Then the failure probability of overtopping P F can be expressed by: [3] PF = 1 P(nWL) 3.3 Dam breach modelling Models used to predict breach formation vary in complexity and basis. Breach models can be divided in: non-physically based (empirical) models, semi-physically based (analytical and parametric) models and physically based models. An overview is given in Mohamed (2002). There are many models for detailed dam-break analysis. However, the calculated results often include considerable uncertainties. In this study a simplified dam breach model was developed on the basis of Meon (1989). In the model the discharge is estimated by combining stochastic, parametric and physical approaches. The initial water level of the reservoir is directly integrated in the dam breach model from submodule M2. In case of critical conditions the calculation procedure of dam breach modelling starts. The outflow hydrograph is simulated using a Monte Carlo technique. The initial top width and depth of the initial breach b 0 is considered as a percentage of the potential maximum breach width b max. This value is assumed as a random variable ranging between a minimum value b 1,max and a maximum value b 2,max based on dam break statistics. Different probability density functions can be assumed for b max. A stochastic outflow hydrograph Q i (t) is computed for the generated initial top width. The algorithm is divided into three parts: calculation of discharge using a broad crested weir formula, calculation of sediment transport using the Meyer-Peter- Müller transport formula, and calculation of the breach growth using parametric breach curves. Based on a statistical analysis of the obtained outflow hydrographs, a representative stochastic outflow hydrograph is derived. 3.4 Flood Routing To investigate the consequences of a dam failure, information about the hydrodynamic indicators (water depths, inundated areas and the flow velocities downstream of the dam) is required. Within the study, the 2D model MeadFlow was applied. It is a finite element model optimally adapted to simulate steady or unsteady flows of complex river systems. Characterized by short computation time and little numerical instability (Leismann and Meon, 2002), MeadFlow provides inundation areas of high accuracy. Applying sophisticated numerical algorithms, the Saint Venant equations are efficiently solved by neglecting the convective inertial term. If necessary the full equation can be applied. The use of this model for dam failure studies could be verified. It is suitable for both, the failures of overtopping scenarios with or without dam break. To validate the applicability of the model the failure of the Möhne Dam was used. During the World War II the Möhne Dam failed due to intensive bombing. Immense damages were caused and 1200 people died (Euler, 2007). The peak discharge of the flood wave accounted for almost m³/s. The downstream hydraulics of the flood wave was simulated using the model described above. Figure 3 shows the good conformance of the flood extent

5 Figure 3: Aerial photograph (Euler, 2007) of area downstream of the Möhne Dam (destruction of dam on May 17 th 1943) with simulated extension of inundated area (blue) 3.5 Consequences and risk parameters Many methods for determining the consequences of a dam failure exist. Almost all of them involve a mapping of the inundated area as a result of specific types of failure as well as the identification of the number of people (population at risk), and the infrastructure and landuse in the inundated area. Dam failure consequences are estimated according to the population at risk (PAR) and the financial impact. The socio-economic and the ecological impacts are assessed subjectively (from insignificant to extreme). For this, hydrodynamic indicators obtained from the 2D simulations were superimposed with landuse data and associated damage functions by using a geographic information system (GIS). The damage functions are formulated for different categories of land use like residential areas, industry, agriculture or infrastructure. A relative damage is calculated for each category. The monetary value of the direct damage was obtained by using the capital value of the categories. For example Messner (2007) presents a good overview about current possibilities and recommendations for flood damage analysis. By means of analyzing damage data of the flood event in 2002 of the river Elbe, the damage functions could be improved for infrastructures. As a result of the developed risk-based procedure the following risk parameters can be derived: Failure probabilities Risk as a product of failure probability and potential damage People at risk (PAR) Subjective risk in the field of socio-economic and ecological impact 154-5

6 4. APPLICATION The risk-based procedure was applied to two existing dams located in the Ruhr river basin in Germany: The Möhne Dam is a gravity dam with a height of approx. 40 m and a crest length of 650 m. The reservoir has a capacity of million m³ and a drainage area of 436 km². Some smaller villages are located downstream the dam. The river Möhne joins the river Ruhr after 12 km. The Henne Dam is an earthfill dam with a height of 60 m and a crest length of 376 m. The reservoir has a capacity of 38.4 million m³ and a drainage area of 98 km². An urbanized area having about inhabitants is located directly downstream the dam. The river Henne joins the river Ruhr after 2 km. For the existing systems, the estimated failure probabilities of overtopping (failure type 2 without dam breaching) are in the order of per year or less. In order to show the applicability of the procedure, additional virtual scenarios (e.g. changed spillway capacities, different reservoir operating rules, etc.) were created in order to get results for all modules of the risk-based procedure. Figure 4 shows two of these scenarios applied to the Möhne Dam. Figure 4: Cumulative distribution function of simulated maximum water levels for different variants The left diagram (a.) displays the results of a scenario with varying capacities of the spillway. In case of a reduction of the spillway capacity to 50 %, the probability of overtopping the dam crest (see Equation 3) increases to about per year. The right diagram (b.) displays the results of a scenario with different operating rules. A comparison of the curves (Variant 4 A and 4 B) shows, that the mode of operating strongly influences the probability of failure type 1 (spillway discharges). Due to the large flood protection storage, the influence on the other failure types is comparatively low

7 5. CONCLUSION AND OUTLOOK A scientifically validated and practicable risk-based procedure for design and verification of dam safety has been developed by combining traditional and risk-based components. The risk-based design concept and cognitions from the application to several case studies will support further developments of design standards. The procedure allows for a safety evaluation of dams with respect to risk on a practicably and economically significant basis. It can also be used as a part of an integrate flood risk management of the entire project river basin. It further provides tools for the selection of risk reduction measures like emergency plans. 6. ACKNOWLEDGEMENT The results in this paper are based on the research project Risk based methods to guarantee adequate flood safety for reservoirs funded by the German Ministry for Education and Research (BMBF). The project is part of the program on Risk management of extreme flood events (RIMAX) and was undertaken in cooperation with the Institute for Water and River Basin Management of the University of Karlsruhe, the Ruhrverband (Ruhr River Association) and the State Reservoir Administration of the State of Saxony, Germany. 7. REFERENCES Bachmann, D., Kutschera, G., Niemeyer, M., Köngeter, J Risk assessment for hydraulic structures: Procedure and application. In: Reducing the Vulnerability of Societies Against Water Related Risks at the Basin Scale (ed. by Schumann, A., Pahlow, M.). IWRM Bochum, Germany, September IAHS-Red Book, IAHS Press, Oxfordshire, UK. Bowles, D.S A Comparison of Methods for Integrated Risk Assessment of Dams. In: Engineering Reliability and Risk in Water Resources, L. Duckstein and E. Plate (Eds.), M. Nijhoff, Dordrecht, The Netherlands, pp Bowles, D.S Dam Safety Portfolio Risk Assessment And Management. US Society on Dams Annual Conference, San Antonio, Texas. DEFRA Reservoir Safety - Floods and Reservoir Safety Integration. Department for Environment, Food and Rural Affairs (DEFRA). (Final Report, Ref. XU0168 Rev A05). Euler, H Wasserkrieg. Motorbuch. Stuttgart, Germany. (in German). Hable, O Multidimensional probabilistic design concept for the estimation of the overtopping probability of dams. Schriftenreihe zur Wasserwirtschaft 37, Technische Universität Graz. Austria. Leismann, M., Meon, G Das Modell MeadFlow für die praxisgerechte 2D-Modellierung von Strömungen in Flusslandschaften. Wasserwirtschaft, Vol. 92, No. 6. (in German). McGrath, S To study international practice and use of risk assessment in dam management. The Winston Churchill memorial trust of Australia. Meon, G Sicherheitsanalyse einer Talsperre für den Hochwasserfall. Mitteilungen des Instituts für Hydrologie und Wasserwirtschaft, Universität Karlsruhe (TH), Heft 35. (in German). Messner F., Penning-Rowsell E., Green C., Meyer V., Tunstall S., van der Veen A., Evaluating flood damages: guidance and recommendations on principles and methods. FLOODsite-Report T , 176 pp

8 Mohamed, M.A.A Embankment Breach Formation and Modelling Methods. PhD. Thesis, The Open University, HR Wallingford, UK. Pohl, R Überflutungssicherheit von Talsperren. Wasserbauliche Mitteilungen, Heft 11, Institut für Wasserbau und Technische Hydromechanik, TU Dresden. Germany. (in German). Sieber, H.U Was bringt die neue DIN für die Sicherheitsbewertung? Wasserwirtschaft, Vol. 95, No. 1/2, (in German). Treiber, B., Plate, E.J A stochastic model for the simulation of daily flows. Hydrological Sciences, Bull. 22 (1), pp