Fluid Mechanics and Hydraulic Engineering of Dam Break Wave. From the Dam Busters to Self-Flowing Concrete Testing
by Hubert CHANSON (h.chanson@uq.edu.au)
M.E., ENSHM Grenoble, INSTN, PhD (Cant.), DEng (Qld), Eur.Ing., MIEAust., MIAHR, 13th Arthur Ippen awardee
School of Civil Engrg., Univ. of Queensland, Brisbane QLD 4072, Australia
Detailed photographs
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 Mohne dam 1943Presentation
Dam break waves have been responsible for numerous losses of life (e.g. Fig. 1 and 2). Figures 1 and 2 illustrate two tragic accidents : the catastrophes of the St Francis dam (USA 1928) and of the Malpasset dam (France 1959). Another situation is the bombing of the Ruhr dams by the "Dam Busters" during Word War II on 16/17th May 1943 (Fig. 3) (WEBSTER 2005). Figure 3 shows the Mohne dam breach after the bombing. Related situations include flash flood runoff in ephemeral streams, debris flow surges and tsunami runup on dry coastal plains. In all cases, the surge front is a sudden discontinuity characterised by extremely rapid variations of flow depth and velocity. Dam failures motivated basic studies on dam break wave, including the milestone contribution by RITTER (1892) following the South Fork (Johnstown) dam disaster (USA, 1889). Physical modelling of dam break wave is relatively limited despite a few basic experiments. In retrospect, the experiments of SCHOKLITSCH (1917) were well ahead of their time, and demonstrated that Armin von SCHOKLITSCH (1888–1968) had a solid understanding of both physical modelling and dam break processes. Theoretical modelling has also been limited despite the oustanding contributions of DRESSLER (1952) and WHITHAM (1954).
Herein two basic dam break wave applications are reviewed. That is, a new analytical solution of the dam break wave in a horizontal channel with bed friction, and the dam break wave motion of a non-Newtonian thxotropic fluid.

Analytical solution of dam break wave with bed friction
A dam break wave is the flow resulting from a sudden release of a mass of fluid in a channel. For one-dimensional applications, the continuity and momentum equations yield the Saint-Venant equations (BARRÉ de SAINT-VENANT 1871a,b). For a frictionless dam break in a wide, horizontal, initially-dry channel, the analytical solution of the Saint-Venant equations yields Ritter solution (RITTER 1892). The solution does not however takes into account. DRESSLER (1952) and WHITHAM (1955) solved analytically the dam break wave problem with bed friction. A simpler, newer solution was recently developed (CHANSON 2005).
Let us consider an instantaneous dam break in a rectangular, prismatic channel with bed friction and for a semi-infinite reservoir. The turbulent dam break flow is analysed as an ideal-fluid flow region behind a flow resistance-dominated tip zone (Fig. 4). WHITHAM (1955) introduced this conceptual approach that was used later by other researchers, but these mathematical developments differ from the present simple solution. In the wave tip region (x1 < x < xs, Fig. 4), the flow velocity does not vary rapidly in the wave tip zone. If the flow resistance is dominant, and the acceleration and inertial terms are small, the dynamic wave equation may be reduced into a diffusive wave equation (CHANSON 2005).
Malpasset damAssuming a constant Darcy-Weisbach friction factor in the wave-tip region, the exact, analytical solution is:
(1)   Eq. (1)
(2)   Eq. (2)
where f is the Darcy-Weisbach friction factor. The instantaneous free-surface profile is then :
(3)   Eq. (3)    Ideal fluid fow region

(4)   Eq. (4)    Wave tip, friction-dominated region
The analytical solution was compared systematically with several experimental studies. The comparative analysis suggested that the results were sensitive to the choice of the Darcy friction factor and that its selection must be based upon a match with instantaneous free-surface profiles. Alternate comparisons with wave front celerity or location data are approximate and often unsuitable.
Ultimately, a practical question is : which is the best theoretical model for turbulent dam break wave? DRESSLER's (1952) method is robust, but the treatment of the wave leading edge is approximate : "To handle the tip region accurately, some type of boundary-layer technique would be necessary [...] but no results are yet available. [...] In the absence of more satisfactory boundary layer results, we will apply [...] approximate considerations to obtain some data about the wavefront" (DRESSLER 1952, pp. 223-224). WHITHAM's (1955) method is also a robust technique, but the results are asymptotic solutions. The newer model of CHANSON (2005) with constant friction factor provides complete explicit solutions of the entire flow field. The velocity field and water depths are explicitly calculated everywhere. In practice, the selection of a suitable analytical model is linked with its main application. For example, for pedagogical purposes, the writer believes that the above model based upon a constant friction coefficient in the wave tip region is nicely suited to introductory courses and young professionals because of the explicit and linear nature of the results.

Dam break wave of non-Newtonian thixotropic fluid
In natural mudflows, the interstitial fluid made of clay and water plays a major role in the rheological behaviour of the complete material. Since clay-water suspensions have often been considered as thixotropic yield stress fluids, it is likely that thixotropy plays a role in some cases of natural events. Thixotropy is the characteristic of a fluid to form a gelled structure over time when it is not subjected to shearing and to liquefy when agitated. A thixotropic fluid appears as a non-Newtonian fluid exhibiting an apparent yield stress and an apparent viscosity that are functions of both the shear intensity and the current state(s) of structure of the material. Under constant shear rate, the apparent viscosity of a thixotropic fluid changes with time until reaching equilibrium. To date, it is essentially the yielding character of non-Newtonian fluid behaviour which has been taken into account for modelling either steady, slow spreading and rapid transient free surface flows (COUSSOT 1997). There is a need to explore the interplay of the yielding and thixotropic characters of mud and debris flows. Practical applications encompass also concrete tests including L-Box and J-Ring for self-consolidating (superflowing) concrete testing, preparation of industrial paints, pasty sewage sludges, and some wastewater treatment residues.
Dam break wave of bentonite suspension after stoppage.A recent work described a basic study of dam break wave with non-Newtonian thixotropic fluid (CHANSON et al. 2006. Such a highly unsteady flow motion has not been studied to date with thixotropic fluid, despite its practical applications : e.g., mudflow release, superflowing concrete flows, preparation of industrial paints. Theoretical considerations were developed based upon a kinematic wave approximation of the Saint-Venant equations down a prismatic sloping channel (Fig. 5) and combined with the thixotropic rheological model of COUSSOT et al. (2002). Theoretical results highlighedt three different flow regimes depending upon the initial degree of fluid jamming Tetao and upon the ratio do /hc. These flow regimes are: (1) a relatively-rapid flow stoppage for relatively small mass of fluid (do/hc < 1) or large initial rest period To (i.e. large Lambdao) (Cases A and B1), (2) a fast flow motion for large mass of fluid (do/hc >> 1) (Case C), and (3) an intermediate motion initially rapid before final fluid stoppage for intermediate mass of fluid (do/hc > 1) and intermediate initial rest period To (i.e. Lambdao) (Cases B2 and B3).
The physical observations of flow regimes (Fig. 6) were in remarkable agreement with theoretical considerations. In particular, exactly the same flow regimes were identified as well as same trends for the effects of the bentonite concentration and rest time. For example, theoretical considerations predict an intermediate motion with initially rapid before final fluid stoppage for intermediate mass of fluid M (i.e. do/hc > 1) and intermediate initial rest period To. The theory predicts a faster flow stoppage with increasing rest period. Similarly, it shows that an increase in bentonite mass concentration, associated with an increase in the product (Teta*Alpha), yields a faster fluid stoppage with a larger final fluid thickness. A similar comparison between theory and physical experiments may be developed for fast-flowing motion and relatively-rapid flow stoppage situations. This qualitative agreement between simple theory and reality means that the basic physical ingredients of the rheological model and kinematic wave equations are likely to be at the origin of the observed phenomena. Interestingly the Flow Type III is the only flow pattern not predicted by theoretical considerations. It is believed that this reflects simply the limitations of the Saint-Venant equations (1D flow equations) and of the kinematic wave approximation that implies a free-surface parallel to the chute invert, hence incompatible with the Type III free-surface pattern.
Basically the qualitative agreement between the present theory and experiments with bentonite suspensions (Fig. 6) suggested that the basic equations of this development (i.e. kinematic wave equation and rheology model) are likely to model correctly both fluid behaviour and flow motion.

Detailed photographs

Figure 1 - St Francis dam (USA 1928). Photo No. 1 : view of remnant part after dam collapse. Completed in 1926 near Los Angeles, the 62.5-m high gravity dam completed in 1926 was equipped with a stepped spillway (width: 67 m). The dam wall failed on 12 March 1928 because of foundation failure. More than 450 people died in the catastrophe. (Ref.: CHANSON 1995, Pergamon, pp. 191-193).

Figure 2
- Malpasset dam (Fréjus, France 1959). Photo No. 1, Photo No. 2 : in Dec. 1981 (taken by H. CHANSON). Completed at the end of 1953, the 102-m high arch dam (double curvature) had a maximum reservoir capacity of about 50 Mm3. On 2 Dec. 1959, the dam wall failed and more than 450 people died in the catastroph. The failure was caused by uplift pressures in the rock foundation (left abutment).

Figure 3
- Ruhr dams and Dam Buster campain (WWII, 1943).
Mohne dam (Germany). Completed in 1913, the curved gravity dam was 650 m long and 40 m high, with a storage capcity of 134.5 E+6 m3. The dam hit and badly damaged by the "dam busters" during Word War II on 16/17th May 1943. Almost 1,300 people died in the floods following the dam buster campaign, mostly inmates of a Prisoner of War (POW) camp just below the dam. The dam breach was 23 m high and 77 m long. Photo No. 3.1 : Mohne dam break damage during the reconstuction in less than 4 months in 1943 (Courtesy of Ruhrverband, Essen, Germany).
Sorpe dam (Germany) Built between 1926 and 1935, the embankment dam was 69 m high and 700 m long. It was built with a concrete core. The reservoir storage capacity is 70.8 E+6 m3 for a catchment area of 100 km2 [extended] (53 km2 [original]). The dam was little damaged by the "dam buster" campaign. Photo No. 3.2 : Removal of an unexploded 5-tons 1943 bomb during the Sorpe dam refurbishment in 1959 (Courtesy of Ruhrverband, Essen, Germany).

Figure 4
- Sketch of a dam break wave in a horizontal channel with bed friction (after CHANSON 2005)

Figure 5
- Dam break wave down an inclined channel with bed friction (after CHANSON et al. 2004)

Figure 6
- Dam break wave of non-Newtonian thixotropic fluid - Sudden release of bentonite suspension on an inclined plane (15 deg.) (Ref. CHANSON et al. 2004, 2006). Photo No. 6.1 : Test 3, 15 deg. slope, 15% bentonite mass concentration, dam break after 1 minute relaxation, photograph taken after fluid stoppage. Photo No. 6.2 : Test 15, 15 deg. slope, 17% bentonite mass concebtration, dam break after 1 min. relaxation, photograph taken after fluid stoppage. Photo No. 6.3 : Test 5, 15 deg. slope, 15% bentonite mass concentration, dam break after 1 minute relaxation, "roll waves" formed during clean upof the channel.

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Sabo check dams

Air bubble entrainment in turbulent shear flows References

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CASTRO-ORGAZ, O., and CHANSON, H. (2017). "Ritter's Dry-bed Dam-break Flows: Positive and Negative Wave Dynamics." Environmental Fluid Mechanics, Vol. 17, No. 4, pp. 665–694 (DOI: 10.1007/s10652-017-9512-5) (ISSN 1567-7419 [Print] 1573-1510 [Online]). (View only) (PDF file) (Reprint at UQeSpace)
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The writer acknowledges the asssitance of Dr P. COUSSOT (LMSGC).


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Hubert CHANSON is a Professor in Civil Engineering, Hydraulic Engineering and Environmental Fluid Mechanics at the University of Queensland, Australia. His research interests include design of hydraulic structures, experimental investigations of two-phase flows, applied hydrodynamics, hydraulic engineering, water quality modelling, environmental fluid mechanics, estuarine processes and natural resources. He has been an active consultant for both governmental agencies and private organisations. His publication record includes over 800 international refereed papers and his work was cited over 3,700 times (WoS) to 13,500 times (Google Scholar) since 1990. His h-index is 32 (WoS), 35 (Scopus) and 56 (Google Scholar), and he is ranked among the 150 most cited researchers in civil engineering in Shanghai’s Global Ranking of Academics. Hubert Chanson is the author of twenty books, including "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways" (Pergamon, 1995), "Air Bubble Entrainment in Free-Surface Turbulent Shear Flows" (Academic Press, 1997), "The Hydraulics of Open Channel Flow : An Introduction" (Butterworth-Heinemann, 1st edition 1999, 2nd editon 2004), "The Hydraulics of Stepped Chutes and Spillways" (Balkema, 2001), "Environmental Hydraulics of Open Channel Flows" (Butterworth-Heinemann, 2004), "Tidal Bores, Aegir, Eagre, Mascaret, Pororoca: Theory And Observations" (World Scientific, 2011) and "Applied Hydrodynamics: an Introduction" (CRC Press, 2014). He co-authored two further books "Fluid Mechanics for Ecologists" (IPC Press, 2002) and "Fluid Mechanics for Ecologists. Student Edition" (IPC, 2006). His textbook "The Hydraulics of Open Channel Flows : An Introduction" has already been translated into Spanish (McGraw-Hill Interamericana) and Chinese (Hydrology Bureau of Yellow River Conservancy Committee), and the second edition was published in 2004. In 2003, the IAHR presented him with the 13th Arthur Ippen Award for outstanding achievements in hydraulic engineering. The American Society of Civil Engineers, Environmental and Water Resources Institute (ASCE-EWRI) presented him with the 2004 award for the Best Practice paper in the Journal of Irrigation and Drainage Engineering ("Energy Dissipation and Air Entrainment in Stepped Storm Waterway" by Chanson and Toombes 2002). Hubert Chanson edited further several books, including the recent monograph "Energy Dissipation in Hydraulic Structures" (Chanson 2015, IAHR Monograph, CRC Press). He chaired the Organisation of the 34th IAHR World Congress held in Brisbane, Australia between 26 June and 1 July 2011. He chaired the Scientific Committee of the 5th IAHR International Symposium on Hydraulic Structures held in Brisbane in June 2014. He chairs the Organisation of the 22nd Australasian Fluid Mechanics Conference in Brisbane, Australia on 6-10 December 2020.
 His Internet home page is http://www.uq.edu.au/~e2hchans. He also developed a gallery of photographs website {http://www.uq.edu.au/~e2hchans/photo.html} that received more than 2,000 hits per month since inception.

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