Hydrological Sciences-Journal���des Sciences Hydrologiques, 46(1) February 2001 [ ]3 Numerical modelling of dam failure due to flow overtopping TAWATCHAI TINGSANCHALI & CHAIYUTH CHINNARASRI* Water Engineering and Management Program, School of Civil Engineering, Asian institute of Tecluiologv, PO Box 4, Klong Luang, Pathunithani 12120, Thailand e-mail: tawaichC��'aii.ac.Ui Abstract A one-dimensional numerical model for dam failure due to flow overtopping is developed. The MacCormack explicit finite difference scheme is used to solve the one-dimensional equations of continuity and momentum for unsteady varied flow over steep bed slopes. In the computation of erosion process, sediment transport equations are considered and the modified Smart formula developed for steep bed slope is selected. The sliding stability of the overtopped dam is checked by modified ordinary method of slices. The model has been successfully calibrated and verified using laboratory experimental data. By comparing with the experimental results, it was found that the model accuracy depends largely on the sediment transport formula and pore water pressure coefficient. The model was found to predict actual breach outflow of the Buffalo Creek Dam reasonably well and closer than other existing numerical models. Key words dam failure mathematical modelling physical models finite difference scheme: unsteady How: erosion and sediment transport Mod��lisation num��rique d'une rupture de barrage due �� un d��bordement R��sum�� Nous avons d��velopp�� un mod��le num��rique �� une dimension de rupture de barrage due �� un d��bordement. Nous avons utilis�� le sch��ma explicite aux diff��rences finies de MacCormack pour r��soudre les ��quations �� une dimension de continuit�� et de conservation des moments pour un ��coulement transitoire sur un lit �� forte pente. La stabilit�� du barrage a ��t�� test��e par une version modifi��e de l'habituelle m��thode des tranches. Le mod��le a ��t�� cal�� et v��rifi�� avec succ��s sur la base de donn��es exp��ri- mentales obtenues au laboratoire. La comparaison avec les donn��es exp��rimentales a montr�� que la pr��cision du mod��le d��pend beaucoup de la formule de transport des s��diments et du coefficient de pression de pore. Il appara��t que le mod��le peut pr��dire de fa��on r��aliste une v��ritable br��che du barrage de Buffalo Creek plus pr��cis��ment que d'autres mod��les num��riques existants. Mots clefs rupture de barrage mod��lisation math��matique mod��les physiques sch��ma aux diff��rences finies ��coulement transitoire ��rosion et transport des s��diments INTRODUCTION Failure of earth dams and embankment dams can be due to various causes such as flow overtopping and piping discharge. Dam failure due to flow overtopping has occurred frequently in the past however, in-depth knowledge of the mechanism of dam failures and measured data are still lacking. A simulation model of dam failure processes would therefore be useful. Of particular concern in this study is dam failure due to flow overtopping. In the past, most simulation models of sediment transport and river Contact address: King Monkut's University of Technology, Thonburi, Thailand. Open for discussion until 1 August 2001

114 Tawatchai Tingsanchali & Cliaiyutli Chinnarasri morphology were developed for subcritical flow in rivers and open channels with small bed slopes (Tingsanchali & Supharatid, 1996 Simons & Senturk, 1977). The physical processes of scour and deposition in rivers are different from the cases of dam failures due to flow overtopping. A number of simulation models of dam failures due to flow overtopping have been developed. Fundamentally they can be classified into three types: the first type assumes the breach to have a fixed size equal to the whole dam structure the second type assumes the breach to have a fixed chosen size and the third type determines the breach size as a function of time due to erosion, geotechnical aspect of breach stability and hydrology, etc. Meon (1989) further classified the third type models into three groups, namely parametric, physical-parametric and stochastic. The parametric models are such as the Dam Break Flood Forecasting Model of the US National Weather Service (DAMBRK) (Fread, 1979) and the model of the Hydrologie Engineering Center (HEC-1) (Singh & Snorrason, 1984). The physical-parametric models are such as that of Brown & Rogers (1981)���BRDAM, Lou's (1981) model, the model of Ponce & Tsivoglou (1981), the Breach Erosion of Earth-filled Dams and Flood Routing Model (BEED) (Singh & Scarlatos, 1989), NOAA-BREACH (Fread, 1988) and the MIKE-11 Dambreak model (DHI, 1994). An example of the stochastic models is the model of Meon (1989). Of most physical concern are the physical- parametric models. The NOAA-BREACH model considers the breach channel to have sliding failure of side walls within the limit of angle of repose, its bottom slope always parallel to the downstream face of the dam and its bottom width equal to 2-2.5 times the critical depth. Kast & Bieberstein (1997) modified the NOAA-BREACH model incorporating additional details of breach characteristics in the model computation. The MIKE-11 Dambreak model (DHI, 1994) assumes that the breach channel has a horizontal bed and there is no sliding failure of the dam surface. The weakness of these models is that none of them considers the actual mechanisms of dam surface slope failure in the form of slip circle sliding. Moreover, there is no readily available sediment transport formula for calculating erosion of dam surface due to overtopping discharge which has a shallow depth and a Froude number greater than 1 (supercritical flow). The purpose of this study is to develop a mathematical model which can satis- factorily simulate or predict dam surface erosion and slope sliding failure with time due to flow overtopping. It includes a check on the accuracy of the simulation results by comparing the model results with data from laboratory experiments as well as with observed field data (Singh, 1996) and with the existing numerical models, namely the BREACH model (Fread, 1988) and the MIKE-11 Dambreak model (DHI, 1994). The effects of model parameters on the computed results and the numerical stability are also investigated using sensitivity analysis. MODEL OF DAM BREACHING DUE TO FLOW OVERTOPPING The model of dam breaching due to flow overtopping consists of three modules: a module of unsteady flow over steep bed slopes, a dam surface erosion module, and a slope sliding failure module. The model simulation is subdivided into two reaches. Figure 1 shows the model reaches and the flow regime. Model Reach I starts from the far upstream end of the reservoir (Node a) to the front edge of the dam crest (Node c). Model Reach II starts from the front edse of the dam crest to a station located 2.4 m

Numerical modelling of dam failure due to flow overtopping i5 Model reach I Model reach II dam height and downstream slope Fig. 1 Model reaches and flow regime. downstream of the dam toe (Node d). For Model Reach I, the module of slope sliding failure, is not considered. For Model Reach II, all three modules are considered. The theory and numerical computation of each module are explained below: Module for unsteady flow over steep bed slopes The one-dimensional system of equations referred to as steep-slope shallow water equations can be applied for the case of flow over a dam. In vector form, the governing equations are: W_ dF_ dt dx in which the vectors U, F, and S are given by the following equations: h = S (1) u = F S = uh uli u1 h H���(gh2 cos 9) 0 ghismQ-S/) (2) (3) (4) where / is the depth of flow, it is the flow velocity, g is the acceleration due to gravity, 0 is the angle of the channel bed, S/- is the slope of energy grade line, x is the longitudinal distance, and t is time. In this study, the MacCormack explicit finite difference scheme (MacCormack, 1971) is used which is second-order accurate in space and time. Its main advantage is its ability to simultaneously calculate gradually varied and rapidly varied flow. The finite difference forms of the governing equations are as follows: