Analytical solutions for gradual dam breaching and downstream river flooding

Abstract

[1] An analytical model is proposed to describe lake drainage and downstream flooding due to the gradual breaching of natural and manmade earthen dams. Erodible triangular dams are considered, undergoing gradual incision by a breaching channel of constant effective width. Adopting a simple stream power law for dam material transport, the long profile evolution of the breaching channel is governed by a diffusion equation with variable diffusion rate, proportional to the water discharge. The resulting flood is routed downstream using the kinematic wave equation. Moving boundary problems are obtained due to retrogression of the breach crest, and to the downstream propagation of the flood wavefront. For both the dam breaching and flood routing problems, explicit analytical solutions are derived. They depict a breaching process that is at first self-accelerating, then becomes self-limiting. Results include boundary paths, long profiles, and stage and discharge hydrographs. In particular, the breaching solution yields a discharge hydrograph of simple analytical shape that turns out to be ideally suited for kinematic wave routing. The model is applied to the well-documented breaching of the Tangjiashan landslide dam, Sichuan, in June 2008. Calculated results for this and other cases are in reasonably good agreement with the measured data. As the model is simple to apply, with minimal computational and data requirements, it could prove useful as a tool for rapid risk assessment. The proposed analytical approach also complements numerical models by providing more transparent links between solution outcomes and the problem data.

Kinematic wave solutions for dam-break floods in non-uniform valleys

“…In the kinematic method, one-dimensional flood routing is conducted by solving the continuity equation (Lighthill and Whitham, 1955;Whitham,1974;Hunt, 1984aHunt, , 1984bHunt, , 1995Capart, 2013;Stilmant et al, 2018) 0, AQ tx   …”

“…Currently, the most elaborate approach is to simulate flood propagation using detailed dynamic models based on the twodimensional shallow water equations (Valiani et al, 2002;Carrivick, 2006;Fan et al, 2012;Kim and Sanders, 2016;Stilmant et al, 2018). Possibly the simplest approach, by contrast, is to assume a uniform valley and model the flood using the one-dimensional kinematic wave equation (Lighthill and Whitham, 1955;Whitham,1974;Hunt, 1984aHunt, , b, 1995Kazezyilmaz-Alhan and Medina, 2007;Capart, 2013;Stilmant et al, 2018).…”

“…We find that this is indeed possible, subject to some restrictions: the upstream discharge hydrograph must produce a single shock at the wave front, and the dependences of the rating curve on discharge and distance must be separable. This last requirement is satisfied for rating curves in power law form, which is a common modeling choice (Hunt, 1984a;Kazezyilmaz-Alhan and Medina, 2007;Capart, 2013). The exponent of the rating curves must be set to describe either U-shaped or V-shaped cross sections, but the coefficient of the rating curve can vary freely with downstream distance.…”

Flood hydrograph reconstruction from the peak flow value in ephemeral streams using a simplified robust single‐parameter model

“…Models dealing with the prediction or reconstruction of flood hydrographs are common, among them palaeo-flood hydrology and rainfall-run-off process simulation and flood routing (El-Hames and Richards, 1998;Sharma and Murthy, 1998;Greenbaum et al, 2001;Morin et al, 2001Morin et al, , 2009Costelloe et al, 2003;Milewski et al, 2009;Capart, 2013;Owusu et al, 2013;Greenbaum et al, 2014). With palaeo-flood hydrology, the main issue is reconstruction of the envelope curve for peak discharge.…”

Integration Techniques for Environmental Impact Assessment of Industrial Pollutants

“…Models dealing with the prediction or reconstruction of flood hydrographs are common, among them rainfall-runoff process simulation and flood routing [7][8][9][10][11][12][13][14][15][16][17]. In the field of rainfall-runoff modelling, the focus is often on flood hydrograph prediction.…”