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Discussion to “Model Study of a Roller Compacted Concrete Stepped Spillway” by Jorge Matos

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CHANSON, H. (1997). "Model Study of a Roller Compacted Concrete Stepped Spillway."
Journal of Hydraulic Engineering
, ASCE, Vol. 123, No. 10, pp. 931-933
(ISSN 0733-9429).
M
ODEL
S
TUDY OF A
R
OLLER
C
OMPACTED
C
ONCRETE
S
TEPPED
S
PILLWAY
A
Discussion by Hubert CHANSON
b
The authors presented the results of one particular laboratory study. The work is helpful in understanding the various aspects of the hydraulics of stepped channels. The discusser wishes to point out that the paper is however incomplete. It deals with one particular case and it should not be considered as the state of the art in model study of stepped spillways. Several important bibliographic references were not considered (e.g. ESSERY and HORNER 1978, FRIZELL 1992, PEYRAS et al. 1992). Altogether the results, presented by the authors, is within the scatter of numerous existing laboratory investigations.
Some history of stepped channels
The discusser (CHANSON 1995, pp. 23-43) reviewed recently the history of stepped spillways and stepped spillway design since the Antiquity. He noted that, during the 19-th century, stepped (or staircase) weirs and channels were quite common. Numerous dam engineers described indeed the construction of stepped spillways
1
: e.g., HUMBER (1876), SCHUYLER (1909), WEGMANN (1907, 1911, 1922). The discusser noted that, in Europe and in the USA, nearly one-quarter to one-third of the dams built during the 19-th century included a stepped spillway ! It is felt that the authors were narrow-minded in stating that "there was little interest in the (stepped) spillways prior to 1982" !
A broader bibliography
For the past 30 years, numerous investigations of stepped spillways were performed over the world. Some are related here for completeness. In United Kingdom, the CIRIA conducted comprehensive laboratory tests (ESSERY and HORNER 1978). The tests were posterior to the construction of the Clywedog dam (completed in 1968) which included a stepped spillway (h = 0.76-m, Ho = 73 m). Soviet engineers were among the first to propose a stepped concrete protection (fig. 1) on the downstream face of dam to pass flood discharges under the leadership of P.I. GORDIENKO (e.g. GORDIENKO 1978). The concept of overflow earth dam incorporates a spillway system which consists of a revetment of precast concrete blocks laid on a filter and erosion protection layer (PRAVDIVETS and BRAMLEY 1989, PRAVDIVETS 1992). The channel bed is very flexible and allows differential settlements as individual blocks do not need to be interconnected, and high discharge capacity can be achieved.
a
by RICE, C.E., and KADAVY, K.C.,
Jl of Hyd. Engrg.
, ASCE, 1996, Vol. 122, No. 6, pp. 292-297.
b
Senior Lecturer in Fluid Mechanics, Hydraulics and Environmental Engineering, Department of Civil Engineering, The University of Queensland, Brisbane QLD 4072, Australia.
1
Ancient names for the spillway include : waste waterway, wastewater weir, idle-discharge outlet, byewash or bywash.
CHANSON, H. (1997). "Model Study of a Roller Compacted Concrete Stepped Spillway."
Journal of Hydraulic Engineering
, ASCE, Vol. 123, No. 10, pp. 931-933
(ISSN 0733-9429).
In South Africa, several applications of gabion stepped weirs (e.g. STEPHENSON 1979, 1980) and stepped RCC weirs (e.g. HOLLINGWORTH and DRUYTS 1986, STEPHENSON 1991) were investigated. GERINGER (1994) documented and illustrated several stepped spillways of RCC dams which have been built since 1985. In France, similarly, the construction of RCC stepped spillways (e.g. M'Bali dam, h = 0.8 m, Ho = 29 m; Riou dam, h = 0.43 m, Ho = 22 m) and gabion stepped weirs (fig. 1) instigated a comprehensive series of experiments (BaCaRa 1991, PEYRAS et al. 1992). Numerous investigations have been performed elsewhere, including in Australia, India, Spain. Stepped channels are used commonly also for stormwater drainage (e.g. CHANSON 1995, pp. 13-14), for river training and control of debris flows. Associated applications include water treatment plants (e.g. for the re-oxygenation of Calumet waterway), stepped fountains and road gutters in steep areas.
Similitude and physical modelling of stepped spillway flow
Recently several important laboratory studies of stepped channels provided significant contributions to the understanding of stepped channel flows : i.e., ESSERY and HORNER (1978), FRIZELL (1992), PEYRAS et al. (1992). Although open channel flows are commonly modelled with a Froude similitude, similarity of stepped channel flows is more complex because of : 1- the various flow regimes (nappe and skimming flow regime), 2- the role of the steps in enhancing turbulent dissipation and 3- the substantial amount of free-surface aeration. Considering a skimming flow (fig. 2), a dominant feature is the momentum exchange between the free-stream (i.e. flowing waters) and the cavity flow within the steps. At each step, a turbulent momentum transfer mechanism takes place in the separated flow region of the triangular cavity. The recirculation within the cavity is associated with turbulent and viscous dissipation. Basic dimensional analysis yields :
F
1(V, yn, h, l,
α
, k s, g,
µ
w,
ρ
w) = 0 (1) where V and yn are the mean flow velocity and flow depth, h, l and
α
characterise the triangular cavity geometry, k s is the skin roughness height, g is the gravity acceleration, and
µ
w and
ρ
w are the dynamic viscosity and density of water respectively. For horizontal steps,
α
= tan-1(h/l) but three parameters are required to defined the cavity geometry in the general case of inclined steps. In dimensionless term, equation (1) can be rewritten as :
F
2
⎝ ⎜⎛ ⎠⎟ ⎞
Vg yn ;
ρ
w V yn
µ
w ; hl ;
α
; k sh = 0 (2) where the first term is a Froude number, the second is a Reynolds number, the third and fourth parameters characterise the cavity shape, and the last term describes the skin friction effects on the cavity walls. It must be noted that the above analysis neglects the interactions between adjacent steps and the effect of free-surface aeration. Altogether a Froude similitude cannot describe the complexity of stepped spillway flows. In the re-analysis of a large number of experimental data, the discusser (CHANSON 1994a,1995) showed that the Froude number has no effect on the flow resistance, that the Reynolds might not have substantial effect and that the form drag was related primarily to the step cavity geometry. Further BaCaRa (1991) described a systematic laboratory investigation of the M'Bali dam spillway. Several identical models were built with the scales of 1/10, 1/21.3, 1/25 and
CHANSON, H. (1997). "Model Study of a Roller Compacted Concrete Stepped Spillway."
Journal of Hydraulic Engineering
, ASCE, Vol. 123, No. 10, pp. 931-933
(ISSN 0733-9429).
1/42.7. For the scales 1/25 and 1/42.7, the developing flow region and the flow resistance were not correctly reproduced. It is believed that similitude considerations of stepped spillway flows require more in-depth analysis and the considerations, presented by the authors, are grossly incomplete.
Energy dissipation
Several researchers investigated the energy dissipation above stepped spillways. The author (CHANSON 1994b, 1995) re-analysed a large number of experimental results. And a more detailed presentation is shown on figure 3. Figure 3 presents the dimensionless residual energy as a function of the crest elevation divided by the critical depth. For skimming flows, the experimental results indicate consistently that : - the residual energy increases with the discharge for a given dam height, and - the relative residual energy decreases with increasing dam height for a given flow rate. The data are compared with an analytical formulation developed assuming that uniform equilibrium flow conditions are reached at the downstream end of the stepped channel (CHANSON 1994b) : Ho - HHo = 1 -
⎝ ⎛ ⎠ ⎞
f 8 sin
α
1/3 cos
α
+ 12
⎝ ⎛ ⎠ ⎞
f 8 sin
α
-2/332 + Hdamyc (3) where Ho is the upstream total head, H is the downstream total head, Hdam is the crest elevation above the toe, yc is the critical flow depth and f is the friction factor. On figure 3, equation (3) is plotted for f = 1 (as proposed by CHANSON 1995). Note that, on figure 3, the authors' data (only three points) fit within the scatter of other results.
REFERENCES
BaCaRa (1991). "Etude de la Dissipation d'Energie sur les Evacuateurs à Marches." ('Study of the Energy Dissipation on Stepped Spillways.')
Rapport d'Essais
, Projet National BaCaRa, CEMAGREF-SCP, Aix-en-Provence, France, Oct., 111 pages (in French). BINDO, M., GAUTIER, J., and LACROIX, F. (1993). "The Stepped Spillway of M'Bali Dam."
Intl Water Power and Dam Construction
, Vol. 45, No. 1, pp. 35-36. CHANSON, H. (1994a). "Hydraulics of Skimming Flows over Stepped Channels and Spillways."
Jl of Hyd. Res.
, IAHR, Vol. 32, No. 3, pp. 445-460. Discussion : Vol. 33, No. 3, pp. 414-419. CHANSON, H. (1994b). "Comparison of Energy Dissipation between Nappe and Skimming Flow Regimes on Stepped Chutes."
Jl of Hyd. Res.
, IAHR, Vol. 32, No. 2, pp. 213-218. Errata : Vol. 33, No. 1, p. 13. Discussion : Vol. 33, No. 1, pp. 114-143. CHANSON, H. (1995). "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways."
Pergamon
, Oxford, UK, Jan., 292 pages
(ISBN 0-08-041918-6)
. Reviews : RAJARATNAM, N. (1995),
Jl of Hyd. Engrg.
, ASCE, Vol. 121, No. 12, p. 923; DE JONG, R.J. (1996),
Jl of Hyd. Res.
, IAHR, Vol. 34, No. 2, p. 259. CHRISTODOULOU, G. C. (1993). "Energy Dissipation on Stepped Spillways."
Jl of Hyd. Engrg.
, ASCE, Vol. 119, No. 5, pp. 644-650. Discussion : Vol. 121, No. 1, pp. 80-87.
CHANSON, H. (1997). "Model Study of a Roller Compacted Concrete Stepped Spillway."
Journal of Hydraulic Engineering
, ASCE, Vol. 123, No. 10, pp. 931-933
(ISSN 0733-9429).
ESSERY, I.T.S., and HORNER, M.W. (1978). "The Hydraulic Design of Stepped Spillways."
CIRIA Report No. 33
, 2nd edition, Jan., London, UK. FRIZELL, K.H. (1992). "Hydraulics of Stepped Spillways for RCC Dams and Dam Rehabilitations. "
Proc. 3rd Specialty Conf. on Roller Compacted Concrete
, ASCE, San Diego CA, USA, pp. 423-439. GERINGER, J.J. (1994). "The Evolution and Development of RCC Dams in South Africa."
Intl Jl of Hydropower and Dams
, Vol. 1, Nov., pp. 35-41. GORDIENKO, P.I. (1978). "Reinforced-Concrete-Earth Overflow Dams."
Dams & Spillways
, Collection of Works No. 61, Issue 2, MISI, Moscow, pp. 3-17 (in Russian). GRINCHUK, A.S., PRAVDIVETS, Y.P., and SHEKHTMAN, N.V. (1977). "Test of Earth Slope Revetments Permitting Flow of Water at Large Specific Discharges."
Gidrotekhnicheskoe Stroitel'stvo
, No. 4, pp. 22-26 (in Russian). (Translated in Hydrotechnical Construction, 1978, Plenum Publ., pp. 367-373). HOLLINGWORTH, F., and DRUYTS, F.H.W. (1986). "Rollcrete : Some Applications to Dams in South Africa."
Intl Water Power and Dam Construction
, Vol. 38, No. 1, Jan., pp. 13-16. HUMBER, W. (1876). "Comprehensive Treatise on the Water Supply of Cities and Towns with Numerous Specifications of Existing Waterworks."
Crosby Lockwood
, London, UK. NOORI, B.M.A. (1984). "Form Drag Resistance of Two Dimensional Stepped Steep Open Channels."
Proc. 1st Intl Conf. on Hyd. Design in Water Resources Engineering
, Channels and Channel Control Structures, Southampton, UK, K.V.H. SMITH Ed., Springer-Verlag Publ., pp. 1.133-1.147. PEYRAS, L., ROYET, P., and DEGOUTTE, G. (1992). "Flow and Energy Dissipation over Stepped Gabion Weirs."
Jl of Hyd. Engrg.
, ASCE, Vol. 118, No. 5, pp. 707-717. PRAVDIVETS, Y.P. (1992). "Stepped Spillways in World and Domestic Hydraulic Engineering."
Gidrotekhnicheskoe Stroitel'stvo
, No. 10, Oct., pp. 28-32 (in Russian). (Translated in Hydrotechnical Construction, 1993, Vol. 27, No. 10, Plenum Publ., pp. 589-594). PRAVDIVETS, Y.P., and BRAMLEY, M.E. (1989). "Stepped Protection Blocks for Dam Spillways."
Intl Water Power and Dam Construction
, Vol. 41, No. 7, July, pp. 49-56. SCHUYLER, J.D. (1909). "Reservoirs for Irrigation, Water-Power and Domestic Water Supply."
John Wiley & sons
, 2nd edition, New York, USA. SORENSEN, R.M. (1985). "Stepped Spillway Hydraulic Model Investigation."
Jl of Hyd. Engrg.
, ASCE, Vol. 111, No. 12, pp. 1461-1472. Discussion : Vol. 113, No. 8, pp. 1095-1097. STEPHENSON, D. (1979). "Gabion Energy Dissipators."
Proc. 13th ICOLD Congress
, New Delhi, India, Q. 50, R. 3, pp. 33-43. STEPHENSON, D. (1980). "The Stability of Gabion Weirs."
Intl Water Power and Dam Construction
, Vol. 32, No. 4, pp. 24-28. STEPHENSON, D. (1991). "Energy Dissipation down Stepped Spillways."
Intl Water Power and Dam Construction
, Vol. 43, No. 9, Sept., pp. 27-30. TOZZI, M.J. (1992). "Caracterização/Comportamento de Escoamentos em Vertedouros com Paramento em Degraus." ('Hydraulics of Stepped Spillways.')
Ph.D. thesis
, University of Sao Paulo, Brazil (in Portuguese). WEGMANN, E. (1907). "The Design of the New Croton Dam."
Transactions
, ASCE, Vol. LXVIII, No. 1047, pp. 398-457. WEGMANN, E. (1911). "The Design and Construction of Dams."
John Wiley & Sons
, New York, USA, 6th edition.
CHANSON, H. (1997). "Model Study of a Roller Compacted Concrete Stepped Spillway."
Journal of Hydraulic Engineering
, ASCE, Vol. 123, No. 10, pp. 931-933
(ISSN 0733-9429).
WEGMANN, E. (1922). "The Design and Construction of Dams."
John Wiley & Sons
, New York, USA, 7th edition.
NOTATION
H = total head (m) at the spillway toe; Hdam = crest elevation (m) above the stilling basin; k s = skin roughness height (m) of the step facing;
µ
w = dynamic viscosity of water (Pa.s);
ρ
w = density (kg/m3) of water.

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