Worldwide 83% of large dams are embankment structures (ICOLD, 1984), and the proportion is even greater for small dams. Embankment overtopping and breach is an important issue, and the Discusser congratulates the Author for his worthwhile contribution which complements the comprehensive study of Coleman et al. (2002). This discussion is focused on the breach development stage. It is shown that the "hourglass" profile is in fact a constant energy state (or minimum energy loss inlet design) for which simple calculations compare favourably with prototype breach flow observations

Chanson, Hubert

University of Queensland eSpace

Journal of Hydraulic Research Vol. 43, No. 4 (2005), pp. 435–438
© 2005 International Association of Hydraulic Engineering and Research
Discussion
Modeling a washout of dams
By A.L. ROZOV, Journal of Hydraulic Research, Volume 41, 2003, Issue 6, pp. 565–577
Discusser:
H. CHANSON, Reader, Department of Civil Engineering, The University of Queensland, Brisbane QLD 4072, Australia.
E-mail: h.chanson@uq.edu.au; URL: http://www.uq.edu.au/∼e2hchans
Worldwide 83% of large dams are embankment structures
(ICOLD, 1984), and the proportion is even greater for small dams.
Embankment overtopping and breach is an important issue, and
the Discusser congratulates the Author for his worthwhile contri-
bution which complements the comprehensive study of Coleman
et al. (2002). This discussion is focused on the breach develop-
ment stage. It is shown that the ‘hourglass’ profile is in fact a
constant energy state (or minimum energy loss inlet design) for
which simple calculations compare favourably with prototype
breach flow observations.
Breach development
The overtopping of an embankment is a relatively slow process.
During breach development, the breach shape exhibits a hour-
glass profile as evidenced by the data of Coleman et al. (2002)
and of the writer, and by Fig. 1. Figure 2 illustrates that a nat-
ural breach shape is very similar to inlet designs of Minimum
Energy Loss (MEL) culverts and weirs (Coleman et al., 2002;
Chanson, 2003). Basically the flow in the breach is near-critical
(i.e. 0.5 < Fr < 1.8) and the total head remains constant through-
out the breach inlet up to the throat (Chanson, 2003). Head losses
occurs downstream of the throat when the flow expands and
separation takes place at the lateral boundaries.
This analogy between natural breach and MEL inlet design
was first proposed by McKay (1970) for natural scour at bridges
and for lagoon inlet breach by Gordon (1981), and demonstrated
quantitatively by Chanson (2003). Further relevant field observa-
tions of inlet breach included Brodie (1988) and Gordon (1990)
in Australia and Kraus et al. (2002) in USA, while Visser et al.
(1990) reported a prototype experiment with a 2.2 m high dyke
breached during the rising tide.
In an MEL inlet, the flow in the approach channel is contracted
through a streamlined inlet into the throat where the channel
width is minimum (Apelt, 1983; Chanson, 1999). The inlet must
be streamlined to avoid significant form losses and flow separa-
tion, and the flow is critical from the inlet lip to the throat. At the
Figure 1 Hourglass shape of Merriespruit tailings dam breach, South
Africa (Courtesy of ProfessorAndre Fourie). The 31-m high tailings dam
was overtopped by rainfall–runoff and failed in the night of 22 February
1994.
Inlet
fan
Throat
Recirculation
zone
Separation &
scourInlet
lip
Bmin
Bmax
E
H
zlip
T.H.L.
Figure 2 Definition sketch of embankment breach for non-cohesive
material. Cross-section through the breach centreline and view in
elevation of breach flow
435
436 A.L. Rozov
inlet lip, the flow rate into the breach equals:
Q = CD ∗ 23 ∗
√
2
3
∗ g ∗ E3 ∗ Bmax (1)
where E is the upstream specific energy above centreline dam
breach elevation and Bmax is the free-surface width at the upper
lip of the breach (Fig. 2). The coefficient CD accounts for the non-
rectangular flow cross-sectional shape and some energy loss. For
the data of Coleman et al. (2002), CD ∼ 0.6 m1/2/s. During an
overtopping event, the breach size increases with time resulting
in the hydrograph of the breach. The breach free-surface width
and specific energy are both functions of time, embankment prop-
erties and reservoir size. The re-analysis of embankment breach
data suggests that the breach dimensions satisfy:
zlip
H
= 1.08 ∗ exp
(
−0.0013 ∗ t ∗
√
g
H
)
for 100 < t ∗
√
g
H
< 1750 (2)
Bmax
H
= 2.73 × 10−4 ∗
(
t ∗
√
g
H
)1.4
for 100 < t ∗
√
g
H
< 1000 (3)
Bmin
H
= 4.01 × 10−7 ∗
(
t ∗
√
g
H
)2.28
for 100 < t ∗
√
g
H
< 1000 (4)
where zlip is the inlet lip elevation on the breach centre-
line and Bmin is the free-surface width at the throat (Fig. 2).
Equations (2)–(4) are based upon a re-analysis of the data of
Coleman et al. (2002) obtained with cohesionless materials. Note
that Eqs (3) and (4) were deduced from a limited data set.
Applications
The 9 m high Glashütte dam failed on Tuesday, 12 August 2002.
Bornschein and Pohl (2003) presented a forensic study of the fail-
ure. This flood retention system in the Elbe river catchment failed
because of inadequate spillway capacity during a heavy storm
event. Witness reports indicated that the dam wall failed com-
pletely in less than 30 min between 4:10 and 4:40 p.m. The final
breach width was about 21 m at dam crest, and Bornschein and
Pohl (2003) calculated a maximum breach outflow of 120 m3/s.
Application of Eqs (1)–(4) indicate that the reservoir emp-
tied in about 10 min with a maximum breach flow of about
200 m3/s, while the breach width at throat Bmin was more than
11 m. The results give some estimate of reservoir drainage time,
peak outflow and breach width that are consistent with witness
observations and forensic calculations. Similar comparisons were
performed successfully with prototype overtopping failures listed
by the writer. Overall the proposed development provides a sim-
ple, yet physically based system of equations to predict the breach
development for cohesionless embankment overtopping.
Acknowledgments
The discusser thanks Dr Stephen Coleman (University of
Auckland) for providing his data, and Dr Antje Bornschein (Uni-
versity of Dresden) for information on the Glashütte dam failure.
References
1. Apelt, C.J. (1983). “Hydraulics of Minimum Energy Cul-
verts and Bridge Waterways”. Aust. Civil Engng. Trans.,
I.E.Aust. CE25(2), 89–95 (ISSN 0819-0259).
2. Bornschein, A. and Pohl, R. (2003). “Dam Break dur-
ing the Flood in Saxon/Germay in August 2002”. In:
Ganoulis, J. and Prinos, P. (eds), Proc. 30th IAHR Biennial
Congress, Thessaloniki, Greece, Vol. C2, pp. 229–236.
3. Brodie, I. (1988). “Breaching of Coastal Lagoons. A
Model Study”. MSc Thesis, University of New South Wales,
Australia.
4. Chanson, H. (1999). The Hydraulics of Open Channel
Flows: An Introduction. Butterworth-Heinemann, Oxford,
UK, 512 pp.
5. Chanson, H. (2003). “History of Minimum Energy Loss
Weirs and Culverts. 1960–2002”. In: Ganoulis, J. and
Prinos, P. (eds), Proc. 30th IAHR Biennial Congress,
Thessaloniki, Greece, Vol. E, pp. 379–387.
6. Coleman, S.E., Andrews, D.P. and Webby, M.G.
(2002). “Overtopping Breaching of Noncohesive Homoge-
neous Embankments”. J. Hydraul. Engng., ASCE 128(9),
829–838.
7. Gordon, A.D. (1981). “The Behaviour of Lagoon Inlets”.
Proc. 5th Australian Conf. Coastal and Ocean Eng., Perth,
WA, pp. 62–63.
8. Gordon, A.D. (1990). “Coastal Lagoon Entrance
Dynamics”. In: Edge, B.L. (ed.), Proc. 22nd Intl. Conf.
Coastal Eng., Delft, The Netherlands, Vol. 3, Cahp. 218,
pp. 2880–2893.
9. International Commission on Large Dams (1984). World
Register of Dams—Registre Mondial des barrages—
ICOLD. ICOLD, Paris, France, 753 pp.
10. Kraus, N.C., Militello, A. and Todoroff, G. (2002).
“Barrier Breaching Processes and Barrier Spit Breach, Stone
Lagoon, California”. Shore Beach 70(4), 21–28.
11. McKay, G.R. (1970). “Pavement Drainage”. Proc. 5th Aust.
Road Res. Board Conf., Vol. 5, Part 4, pp. 305–326.
12. Visser, P.J., Vrijling, J.K. and Verhagen, H.J. (1990). “A
Field Experiment on Breach Growth in Sand-Dykes”. In:
Edge, B. (ed.), Proc. 22nd Intl Conf. Coastal Eng., Delft,
Netherlands, Vol. 2, pp. 2097–2100.
Reply by the Author
The author strongly appreciates the Discusser’s approach con-
cerning not only the stage of dam breach development but also
the one of initial breach formation.
Discussion: Modeling a washout of dams 437
Both the Discusser’s approach and the author’s one use the
analogy between the flow in the breach and the one in the weir.
Discusser’s equation for the water discharge through the breach
is very similar to the author’s one (19)
Q = cdg0.5BH1.5 (1)
where cd is discharge coefficient; H and B (discusser’s Bmin) are
shown in Fig. 2 of the discussion.
Both approaches differ from one another in the use of a
transversal breach characteristic. The author considers B, breach
width in the critical section, to be the best one for it can be easily
detected in experimental studies and it is used in all computer
programs for the calculations of dam-break wave parameters in
which the boundary condition at the dam section is applied.
Discusser’s Eqs (2)–(4) present a mathematical model based
on the latest experimental data of Coleman et al. (2002). The
author was aware of the experimental studies of Coleman’s
research group (Coleman et al., 1997) and their data were used
widely in the paper. However, their latest works appeared after
the author had submitted his work for publication. So, herein
the author can state general considerations only. Experimen-
tal data can certainly be used for developing a mathematical
model of the process at issue provided that full-scale conditions
of the dam washout process are satisfied in the experimental
model. One more point needs to be given proper attention to. The
use of data concerning breaching of noncohesive homogeneous
embankment in developing a mathematical model for simulating
the process of washout of dams filled with material with apparent
cohesion (typical for natural dams) needs careful substantiation.
Let us apply the methods to the investigation of the washout
process offered by the Discusser for the Glashütte dam fail-
ure case.
It was a dam Hd = 8.7 m high; its embankment consisted
of an erodible material that can be approximately identified as
one of the crushed rock type (no doubt with apparent cohesion).
The dam failure process can be reconstructed as follows. The
maximum reservoir depth at the dam was about H = 9 m. So, the
maximum difference between the levels of the water overtopping
of the dam and the dam crest was about h = 0.3 m (Bornschein
and Pohl, 2003; Fig. 4). Therefore, in this case the overtopping
of the dam led to formation of the incipient breach in the range of
the dam crest where the greatest velocities of the flow occurred
(probably in the centre of the crest). Water flowing through the
incipient breach eroded first the bottom of the breach until its
bottom reached the base of the dam along the whole of its length.
This breach is called in the paper the initial breach. Its width, B0,
is estimated as [B0 = (Hd + Hd/3)/2]
B0 = 5.8 m (2)
Because of some shortage of necessary input data we cannot
use the paper’s analytical solutions [Eqs (29)–(33) or (38)–(42)].
Nevertheless, Bornschein and Pohl (2003) presented the neces-
sary data for carrying out the theoretical analysis.
We shall use the paper’s equation for the rate of the breach-
width enlargement [Eq. (27)]
dB
dt
= α√g A
H¯1/3
H0.5 (3)
Water depth at the dam during the failure process from 1610 to
1640 can be approximated (Bornschein and Pohl, 2003; Fig. 4) by
H = H0 − ct (4)
where
H0 = 9 m at t0 = 0; Hk = 2 m at tk = 30 min;
c = 3.9 × 10−3 m/s (5)
Substituting (4) into (3) and performing the integration one
obtains
B = B0 + 2α
√
gA
3cH¯1/3
(
H1.50 − H1.5
) (6)
According to the paper [Eq. (47), Table 4, crushed rock]
α = 0.05; A = 3.6 × 10−2 m1/3 (7)
Analytical solution (6) with the help of (2), (5) and (7) gives
for the final breach width Bk(H¯ = 5.5 m)
Bk = 19 m (8)
Here (8) correlates with historical data (Bk = 21 m at dam
crest) that are the result of the observations which were made
some time after dam failure, when the material from the top of
the breach might to a certain extent be crumbled, transforming
the rectangular form of the breach into a trapezoidal one.
It is of value to estimate the value of Qmax, peak outflow
discharge through the breach. Substitution of (2)–(6) into (1) after
some mathematical manipulations gives [assuming cd = 0.5,
Eq. (22); corresponding breach width and water depth at the dam:
B = 10 m and H = 7 m]
Qmax ∼ 300 m3/s (9)
Calculated value Qmax by Bornschein and Pohl (2003) is
Qmax = 120 m3/s (10)
According to their calculations breach outflow discharge after
the completion of the process of washout (1640) was (Fig. 4)
Q ∼ 37 m3/s (11)
On the other hand, according to the same Fig. 4 at time 1640
one has
H = 2 m (12)
Time 1640, one should have (B = 19 m)
Q = cdg0.5BH1.5 = 84 m3/s (13)
Comparing (13) and (11) we have a right to conclude that
Bornschein and Pohl (2003) somehow undervalued the breach
outflow discharge.
Compare the Discusser’s Fig. 2 and Fig. 6 in the paper. The
diagram in Fig. 6 is used for the case of breach (lateral) devel-
opment. The diagram in Fig. 2 of the discussion can be used for
438 A.L. Rozov
two cases: uniform washout of the whole length of the dam crest
and formation of initial breach. The former is a very rare one.
Johnson and Illes (1976) in their detailed classification of dam
failures did not even mention it. This process needs particular
conditions for its realization. In the case of Glashütte dam failure
these conditions were absent. Therefore the diagram in Fig. 2 can
be used for the case of formation of initial breach. Figure 2 dis-
plays an important feature of this process. As a consequence of the
more intensive erosion of the downstream slope of the embank-
ment (where the highest flow velocities take place) there is some
low speed displacement of the topmost section of the breach in
the direction of the upstream wall. This phenomenon shows the
complexity and the importance of the problem at hand. The prob-
lem embraces several allied aspects. For example, according to
known data values of discharge coefficient cd depend on the ratio
of reservoir’s and breach’s widths to some degree. The method
proposed by the Discusser, which includes both experimental and
theoretical techniques, is especially suitable for the study of this
problem.
Acknowledgments
The author thanks Dr Vitaliy Klimovich (VNIIG B.E. Vedeneev)
for providing information.
References
1. Bornschein, A. and Pohl, R. (2003). “Dam break during the
Flood in Saxon/Germay in August 2002”. In: Ganoulis, J.
and Prinos, P. (eds), Proc. 30th IAHR Biennial Congress,
Thessaloniki, Greece, Vol. C2, pp. 229–236.
2. Johnson, F.A. and Illes, P. (1976). “A Classification of Dam
Failures”. Water Power Dam Constr., December, 43–45.


Discussion: Modeling a Washout of Dams by A. L. Rozov.

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