Review of Historical Dam-Break Events and Laboratory Tests on Real Topography for the Validation of Numerical Models

Dam break inundation mapping is essential for risk management and mitigation, emergency action planning, and potential consequences assessment. To quantify flood hazard associated with dam failures, flooding variables must be predicted by efficient and robust numerical models capable to effectively cope with the computational difficulties posed by complex flows on real topographies. Validation against real-field data of historical dam-breaks is extremely useful to verify models’ capabilities and accuracy. However, such catastrophic events are rather infrequent, and available data on the breaching mechanism and downstream flooding are usually inaccurate and incomplete. Nevertheless, in some cases, real-field data collected after the event (mainly breach size, maximum water depths and flood wave arrival times at selected locations, water marks, and extent of flooded areas) are adequate to set up valuable and significant test cases, provided that all other data required to perform numerical simulations are available (mainly topographic data of the floodable area and input parameters defining the dam-break scenario). This paper provides a review of the historical dam-break events for which real-field datasets useful for validation purposes can be retrieved in the literature. The resulting real-field test cases are divided into well-documented test cases, for which extensive and complete data are already available, and cases with partial or inaccurate datasets. Type and quality of the available data are specified for each case. Finally, validation data provided by dam-break studies on physical models reproducing real topographies are presented and discussed. This review aims at helping dam-break modelers: (a) to select the most suitable real-field test cases for validating their numerical models, (b) to facilitate data access by indicating relevant bibliographic references, and (c) to identify test cases of potential interest worthy of further research

Reply to AlQasimi, E.; Mahdi, T.-F. Comment on “Aureli et al. Review of Historical Dam-Break Events and Laboratory Tests on Real Topography for the Validation of Numerical Models. Water 2021, 13, 1968”

This is the reply to the comments by Mahdi (2021) on the classification attributed to the Lake Ha! Ha! real-field test case by Aureli et al. (2021) in their review of historical dam-break events useful for the validation of dam-break numerical models. While admitting that this test case is affected by the data shortcomings reported by the Discusser, in the authors’ opinion, it should remain included in the group of well-documented test cases due to the large and complete dataset available in digital format. This conclusion is also supported by the fact that the Lake Ha! Ha! case was chosen as a benchmark in the framework of the 2001–2004 IMPACT (Investigation of Extreme Flood Processes and Uncertainty) European project and was then widely used in the literature for the validation of one-dimensional and two-dimensional geomorphic flood models

Experimental and numerical evaluation of the force due to the impact of a dam-break wave on a structure

Flood events caused by the collapse of dams or river levees can have damaging consequences on buildings and infrastructure located in prone areas. Accordingly, a careful prediction of the hydrodynamic load acting on structures is important for flood hazard assessment and potential damage evaluation. However, this represents a challenging task and requires the use of suitable mathematical models. This paper investigates the capability of three different models, i.e. a 2D depth-averaged model, a 3D Eulerian two-phase model, and a 3D Smoothed Particle Hydrodynamics (SPH) model, to estimate the impact load exerted by a dam-break wave on an obstacle. To this purpose, idealised dam-break experiments were carried out by generating a flip-through impact against a rigid squat structure, and measurements of the impact force were obtained directly by using a load cell. The dynamics of the impact event was analyzed and related to the measured load time history. A repeatability analysis was performed due to the great variability typically shown by impact phenomena, and a confidence range was estimated. The comparison between numerical results and experimental data shows the capability of 3D models to reproduce the key features of the flip-through impact. The 2D modelling based on the shallow water approach is not entirely suitable to accurately reproduce the load hydrograph and predict the load peak values; this difficulty increases with the strength of the wave impact. Nevertheless, the error in the peak load estimation is in the order of 10% only, thus the 2D approach may be considered appropriate for practical applications. Moreover, when the shallow water approximation is expected to work well, 2D results are comparable with the experimental data, as well as with the numerical predictions of far more sophisticated and computationally demanding 3D solvers. All the numerical models overestimate the falling limb of the load hydrograph after the impact. The SPH model ensures good evaluation of the long-time load impulse. The 2D shallow water solver and the 3D Eulerian model are less accurate in predicting the load impulse but provide similar results. A sensitivity analysis with respect to the model parameters allows to assess model uncertainty

Galilean-Invariant Expression for Bernoulli’s Equation

The Bernoulli principle is one of the basic and most famous concepts in fluid mechanics, and the related equation is an extremely useful and effective tool in the solution of a wide range of practical engineering problems. However, the Bernoulli equation is not Galilean-invariant (i.e., it does not remain the same as a result of a change in the inertial frame of reference when the new frame moves with constant velocity relative to the original one). In this paper, a frame-independent expression of the Bernoulli equation is obtained from the Euler equation of inviscid motion for the case of steady flow, for the two classic versions valid along a streamline, and for irrotational flow. Compared to the conventional formulation of the equation, an additional term is present in the definition of the Bernoulli constant. An interpretation of the new equation is provided on the basis of the first law of thermodynamics. Some classic applications are presented, and the results found are in accordance with the consolidated knowledge of fluid mechanics

2D numerical modelling and physical modelling of unsteady free surface flows

The thesis presents experimental and two-dimensional (2D) numerical results of four tests concerning rapidly varying free surface flows induced by the sudden removal of a sluice gate. For the acquisition of the experimental data, an imaging technique capable of providing spatially distributed information was adopted: a coloring agent was added to the water, the opalescent bottom of the facility was backlighted, and photographs of the area of interest were taken. The gray tones of the acquired images were converted into water depths by means of transfer functions derived from a static calibration. The potential sources of error of the proposed procedure are discussed. A local comparison with an ultrasonic device showed a 20% maximum deviation in 95% of the observations. The tests were simulated through a 2D MUSCL-Hancock finite volume numerical model, based on the classic shallow water approximations, in which the intercell water depths are estimated according to the surface gradient method. A global analysis of the relative frequency distributions of the deviation between numerical and experimental results is performed. Despite some evident differences at a local scale, the adopted 2D numerical model is capable of reproducing the main features of the flow fields under investigation

Seismic-generated unsteady motions in shallow basins and channels. Part II: Numerical modelling

In this paper, unsteady motions generated by seismic-type excitation are simulated by a 2D depth-averaged mathematical model based on the classic shallow water approximation. A suitable time-dependent forcing term is added in the governing equations, and these are solved by a MUSCL-type shock-capturing finite volume scheme with a splitting treatment of the source term. The HLL approximate Riemann solver is used to estimate the numerical fluxes. The accuracy of the numerical scheme is assessed by comparison with novel exact solutions of test cases concerning sinusoidally-generated sloshing in a prismatic tank, a rectangular open channel, and a parabolic basin. A sensitivity analysis is performed on the influence of the relevant dimensionless parameters. Moreover, numerical results are validated against experimental data available in literature concerning shallow water sloshing in a swaying tank. Finally, real‐scale applications to a reservoir created by a dam and an urban water-supply storage tank are presented. The results show that the model provides accurate solutions of the shallow water equations with a seismic-type source term and can be effectively adopted to predict the main flow features of the unsteady motion induced by horizontal seismic acceleration when the long wave assumption is valid

New formulation of the two-dimensional steep-slope shallow water equations. Part I: Theory and analysis

Two-dimensional (2D) depth-averaged shallow water equations (SWE) are widely used to model unsteady free surface flows, such as flooding processes, including those due to dam-break or levee breach. However, the basic hypothesis of small bottom slopes may be far from satisfied in certain practical circumstances, both locally at geometric singularities and even in wide portions of the floodable area, such as in mountain regions. In these cases, the classic 2D SWE might provide inaccurate results, and the steep-slope shallow water equations (SSSWE), in which the restriction of small bottom slopes is relaxed, are a valid alternative modeling option. However, different 2D formulations of this set of equations can be found in the geophysical flow literature, in both global horizontally-oriented and local bottom-oriented coordinate systems. In this paper, a new SSSWE model is presented in which water depth is defined along the vertical direction and flow velocity is assumed parallel to the bottom surface. This choice of the dependent variables combines the advantages of considering the flow velocity parallel to the bottom, as can be expected in gradually varied shallow flow, and handling vertical water depths consistent with elevation data, usually available as digital terrain models. The pressure distribution is assumed linear along the vertical direction and flow curvature effects are neglected. A new formulation of the 2D depth-averaged SSSWE is derived, in which the two dynamic equations represent momentum balances along two spatial directions parallel to the bottom, whose horizontal projections are parallel to two fixed orthogonal coordinate directions. The analysis of the mathematical properties of the new SSSWE equations shows that they are strictly hyperbolic for wet bed conditions and reduce to the conventional 2D SWE when bottom slopes are small. Finally, it is shown that the SSSWE predict a slower flow compared with the conventional SWE in the theoretical case of a 1D dam-break on a frictionless channel with fixed slope. The capabilities of the proposed model are demonstrated in a companion paper on the basis of numerical and experimental tests

Seismic-generated unsteady motions in shallow basins and channels. Part I: Smooth analytical solutions

In this paper time-dependent water motions generated by seismic-type horizontal excitation in shallow basins and channels are modelled by the two-dimensional depth-averaged shallow water equations in which a specific source term is added in order to include an earthquake-induced forcing effect. Sinusoidal excitation is considered as a first approximation, and the response of shallow basins and channels to this simple external forcing is characterized. The nondimensional form of the governing equations shows that the Strouhal number and a ratio representing the amplitude of the forcing acceleration are the influential dimensionless parameters. Novel exact solutions of sinusoidally-forced smooth waves in a prismatic tank, a rectangular open channel, and a parabolic basin are presented. In the first two cases, a sway motion occurs, and reflections take place at the side walls. In the last case, the water sloshes back and forth flowing up the sloping sides of the basin; the free surface remains planar and a moving circular shoreline is present. These analytical solutions provide useful standards for assessing the accuracy of the numerical models used to solve the two-dimensional shallow water equations with source terms

A Probabilistic Approach for Dam-break Flood Hazard Assessment

The storage of water provided by dams offers numerous benefits associated with the different uses of the resource (irrigation, energy production, water supply, etc.). However, in the event of a dam-break, a large amount of water may be released with catastrophic consequences for the population and the economic and environmental assets located downstream of the dam. For this reason, flood risk assessment is fundamental to planning emergency responses and developing mitigation measures. A key step of the flood risk evaluation is flood hazard assessment, which consists in the identification of the area prone to flooding and in mapping hydraulic parameters (e.g. maximum water depth, maximum flow velocity, flood arrival time, etc., or a suitable combination of these) representative of flood intensity. Usually, dam-break flood hazard is assessed deterministically considering only one dam-break scenario. In particular, for concrete dams, the collapse is considered total and instantaneous with the water level behind the dam at the spillway crest level. However, this approach does not take into account uncertainties in dam-break parameters and their effect on flood hazard estimation in the downstream area. To this end, we propose a probabilistic approach based on a set of dam-break scenarios characterized by different reservoir levels and breach widths. These parameters are actually the most important in defining the breach outflow hydrograph and the resulting inundation extent. Each scenario is characterized by a probability conditional to the dam-break event. For each scenario, the dam-break wave propagation is simulated via a finite volume hydrodynamic model based on the 2D shallow water equations. The flood inundation maps calculated for each scenario, along with the associated probabilities, are then combined to produce probabilistic inundation maps: a probabilistic flood extent map; probabilistic hazard level maps (with reference to pre-selected flood hazard classes); a probability-averaged flood hazard index map and a probability-weighted dam-break wave arrival time map, both coupled with a map representing the spatial distribution of the associated uncertainty. The probabilistic method is applied to the case study of the Mignano concrete gravity dam in northern Italy