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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 4, April (2014), pp. 82-90 © IAEME
82
LOCATION OF AIR INCEPTION POINT FOR DIFFERENT
CONFIGURATIONS OF STEPPED SPILLWAYS
Najm Obaid Salim Alghazali1
, Salam M. Jasim2
(1)
Corresponding author, Asst. Prof. Doctor, Civil Engineering Department, Babylon
University, Iraq
(2)
M.Sc. Student, Civil Engineering Department, Babylon University, Iraq
ABSTRACT
Twelve stepped spillway models have been manufactured with three downstream slope
angles: 25, 35 and 45°, and four numbers of steps: 5, 10, 15 and 20. The results of experimental work
emphasize that for the same model air inception point location moved downstream as the discharge
increased. For the same discharge, the location of air inception point was closer to the crest for larger
step heights and lesser slope angle. The location of air inception point was closer to the crest in
pooled steps compared with flat steps; this location was farther than flat steps when the gaps between
end sills and step rises were filled with gabions. Twelve empirical equations for air inception point
distance on stepped spillways were suggested based on the experimental results. The experimental
results for flat steps were compared with the results of three relationships: Matos et al. (2000),
Chanson (2001) and Boes and Hager (2003) for the prediction of the location of air inception point in
the limits of this study. The comparison showed that Boes and Hager relationship results (2003) were
the closest to the experimental results.
Keywords: Air Entrainment, Gabions Steps, Inception Point, Pooled Steps, Stepped Spillway.
1. INTRODUCTION
The stepped spillway is a spillway whose face is provided with a series of steps from near the
crest to the toe, they have gained popularity with modern construction techniques including roller
compacted concrete (RCC) and gabions [1], [2], [3], [4].
A peculiar aspect of the flow on a stepped spillway is the large aeration occurs at all nappe,
transition and skimming flow regimes. Modern stepped spillways are designed to operate with a
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
AND TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 4, April (2014), pp. 82-90
© IAEME: www.iaeme.com/ijciet.asp
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IJCIET
©IAEME

83
skimming flow regime [5].In the skimming flow regime, the determination of the exact location at
which air entrainment starts on stepped spillway is very important due to its significant effect on
energy dissipation rate, cavitation risk and training wall height [6], [7]. Air entrainment starts at the
location where the turbulent boundary layer reaches the free surface [1].
The presence of air within high-velocity flows may prevent or reduce cavitation damage. On
stepped spillway with skimming flow regime, the reduction of flow velocity and the resulting
increase of flow depth reduce also the risks of cavitation [8]. Uncertainty in this notion has
perpetuated conservative design practices [9].
The zone near the inception point of air entrainment is critical in terms of the risk of
cavitation damage. For increasing flow rates, the non-aerated region of the spillway will increase and
larger velocities will be reached that could cause unacceptable pressure fluctuations. Downstream the
inception point, the presence of an adequate percentage of air in the mixture near the solid surfaces is
expected to prevent cavitation damage [10].
In the last two decades, there has been an increasing interest in the stepped spillways in
various laboratories around the world [11]. The stepped spillway design is not limited to flat uniform
steps, some prototype stepped chutes were designed with pooled steps (e.g. Sorpe dam, Germany),
alternate sills (e.g. Neil Turner stepped weir, Australia), and weir structures designed with gabion
steps, etc.[3], [12]. Alternative stepped designs are poorly understood [3].In the recent years, the air-
water flows on pooled stepped spillways were researched in a few studies[13].Also, the hydraulics of
gabions stepped spillway has received less attention due to the complexity to evaluate the flow
patterns and flow resistance [14]. The advantages of gabions are: low cost, ease of installation,
flexibility, and ease of maintenance [15]. With proper construction practice, spillways having a
stepped downstream face built of gabions can withstand floods of up to 3 m2
/s without damage
[16].Stone size and shape have little influence on the energy loss and flow velocity as compared to
the increasing effect of the weir slope [14].
Many relationships have been developed to predict the location of air inception point for
conventional flat stepped spillway. The estimation of this point in other configurations is not yet well
understood. The objective of this study is to suggest new empirical equations for three configurations
(flat steps, pooled steps, pooled with gabions steps).
2. EXPERIMENTAL WORK
Twelve stepped spillway models were made from wood and coated with varnish to avoid
wood swelling of water and to increase its smoothness. The models have vertical upstream face with
three downstream slope angles (25°, 35° and 45°). For each slope, four models were designed as
ogee stepped spillway with 5, 10, 15 and 20 steps. All models have 0.3 m width and 0.3 m height
(from the base to the upper point in the crest).
The tests were carried out in a recirculating flume located at the fluid laboratory of
Engineering College, Babylon University, Iraq (Photo 1). The flume is 10 m length and 0.3m width.
It has transparent side walls with height of 45 cm. The flume has a pump with a discharge capacity of
30 l/s, a flow meter is installed on its pipeline for measuring the discharge of the passing flow. Two
movable carriages with point gauges were mounted on brass rail at the top of flume sides, which
have an accuracy of 0.1 mm.
The experiments were conducted for fifteen discharges runs ranging from 0.9 to 9.3 l/s
(Table 1). This range was satisfying the need of this study. Photo 2 shows a sample of the observed
locations of air inception points. Figure 1 explains the distance to the air inception point (Li) and the
step roughness height (Ks).

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 4, April (2014), pp.
The used end sills are of height equals to half step height i.e.,
height and h is the step height. Four thicknesses of end sills are used: 0.5, 1, 3 and 5 mm for the
models having number of steps: 5, 10, 15 and
Photo 1: The used flume (Civil Engineering Department, Engineering College,
Table 1:
Run No. Q (l/s)
1 0.90
2 1.50
3 2.10
4 2.70
5 3.30
6 2.90
7 4.50
8 5.10
6316(Online), Volume 5, Issue 4, April (2014), pp. 82-90 © IAEME
84
The used end sills are of height equals to half step height i.e., he = 0.5h; h
models having number of steps: 5, 10, 15 and 20 steps respectively.
The used flume (Civil Engineering Department, Engineering College,
Babylon University, Iraq)
Table 1: Discharges used in the 15 runs
q (l/s.m) Run No. Q (l/s)
3.00 9 5.70
5.00 10 6.30
7.00 11 6.90
9.00 12 7.50
11.00 13 8.10
13.00 14 8.70
15.00 15 9.30
17.00
= 0.5h; he is the end sill
The used flume (Civil Engineering Department, Engineering College,
q (l/s.m)
19.00
21.00
23.00
25.00
27.00
29.00
31.00

Photo 2a
Photo 2: Sample of the observed locations of air inception points
Figure 1: Schematic representation of the measured L
The gabion dimensions are
length and t is the end sill thickness. During testing runs, the gabions were placed into the steps and
removed alternately. Wire mesh of rhombus shape with side length of 0.68 cm and diagonals of 0.65
and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95
porosity of 41%. These types of wire mesh and gravel were selec
filled material should be larger than 1.5 times the wire mesh opening and the porosity values
between 38 and 42 are preferable as suggested by previous studies (such as
Kells (1993) cited in [17]).
3. DATA ANALYSIS
3.1 Suggested Relationships
The suggested empirical equations for the location of air inception point for flat steps, pooled
steps and pooled with gabions steps for all the slope angles 25°, 35° and 45° are presented in
Table 2. All symbols are defined in appendix 1.
85
Photo 2b
Sample of the observed locations of air inception points
a) Side view. b) Top view.
Schematic representation of the measured Li
he × (l-t) 0.3 × m, where he is the end sill height,
and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95
porosity of 41%. These types of wire mesh and gravel were selected taking into account that the
between 38 and 42 are preferable as suggested by previous studies (such as Stephenson (1979) and
All symbols are defined in appendix 1.
is the end sill height, l is the step
and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95-1.27 cm and
ted taking into account that the
Stephenson (1979) and

86
Table 2: Suggested empirical equations.
θ Equation R2
Case
45°
Li
Ks
= 5.1083Fr*
1.1731
0.7621
Flat steps
35°
Li
Ks
= 5.4641Fr*
1.2130
0.9239
25°
Li
Ks
= 6.6039Fr*
1.0395
0.8449
For all slopes
Li
Ks
= 5.8851 ሺsinθሻ-0.09572
Fr*
1.0800
0.8604
45°
Li
Kt
= 6.0784 Fr*
1.0353
0.8621
Pooled steps
35°
Li
Kt
= 7.2552Fr*
0.9515
0.9267
25°
Li
Kt
= 7.7555 Fr*
0.8830
0.8556
For all slopes
Li
Kt
= 7.6019 ሺsin θሻ-0.1023
Fr*
0.8088
0.8777
θ Equation R2
Case
45°
Li
Kt
= 9.5795 Fr*
1.0122
0.7816
Pooled steps with
gabions
35°
Li
Kt
= 10.4540Fr*
0.9880
0.8057
25°
Li
Kt
= 9.9647 Fr*
1.0149
0.7171
For all slopes
Li
Kt
= 10.4367 ሺsin θሻ-0.0999
Fr*
0.8501
0.8171

3.2 Comparison with Previous Relationships
For flat stepped spillways, the selected
present study are presented in Table 3
ones for the three slope angles (45°, 35° and 25°) are shown in the
Table 3:
Researcher
Chanson (2001)[1]
Matos et al. (2000)
(cited in [18])
Boes and Hager (2003)
Figure 2: Li/Ks and Fr
87
3.2 Comparison with Previous Relationships
For flat stepped spillways, the selected equations to be compared with the results of the
Table 3. Comparisons between the obtained data and the calculated
ones for the three slope angles (45°, 35° and 25°) are shown in the Figs. 2, 3 and 4.
Table 3: The studied relationships
Equation
Matos et al. (2000)
Boes and Hager (2003)[19]
and Fr* scatter on 45° slope angle flat models
equations to be compared with the results of the
. Comparisons between the obtained data and the calculated

Figure 3: Li/Kt and Fr
Figure 4: Li/Ks and Fr
4. CONCLUSIONS
It can be concluded that for the same model
moves downstream as the discharge increases. For the same discharge, the location of air inception
point is closer to the crest for larger step heights and lesser slope angle. The location of inception
88
or the same model the location of inception point of air entrainment
the location of inception point of air entrainment

89
point of air entrainment is closer to the crest in pooled steps compared with flat steps; this location is
farther than flat steps when the gaps between end sills and step rises are filled with gabions.
The comparison of experimental results for flat steps with the results of three relationships:
Matos et al. (2000), Chanson (2001) and Boes and Hager (2003) for the prediction of the location of
air inception point in the limits of this study showed that Boes and Hager relationship results (2003)
were the closest to the experimental results.
REFERENCES
[01] Chanson, H., The Hydraulics of Stepped Chutes and Spillways, Balkema, Lisse, the
Netherlands, 2001.
[02] Gonzalez, C. A., An Experimental Study of Free-Surface Aeration on Embankment Stepped
Chutes, Ph.D. Thesis, University of Queensland, Australia, 2005.
[03] Felder, S. and Chanson, H., Air Entrainment and Energy Dissipation on Porous Pooled
Stepped Spillways, International Workshop on Hydraulic Design of Low-Head Structures
(IWLHS), Aachen, Germany, (87-97), 2013.
[04] Guenther, P., Felder, S. and Chanson, H., Flat and Pooled Stepped Spillways for Overflow
Weirs and Embankments: Cavity Flow Processes, Flow Aeration and Energy Dissipation,
IWLHS, 2013.
[05] Gonzalez, C.A. and Chanson, H., Experimental Study of Turbulence Manipulation in Stepped
Spillways. Implications on Flow Resistance in Skimming Flows, Proceeding of the 31st
IAHR
CONGRESS, Soul, Korea, 2005.
[06] Hunt, S. L. and Kadavy K.C., Inception Point Relationship for Flat-Sloped Stepped
Spillways, J. Hydr. Eng., ASCE, 137(2): 262-266, 2011.
[07] Jian-hua, W., Bin, Z. and Fei, M., Inception point of air entrainment over stepped spillways,
ScienceDirect J. hydrodynamics 25(1):91-96, 2013.
[08] Chanson, H., Hydraulics of Stepped Spillways and Cascades, International Conference on
Hydraulics in Civil Engineering, University of Queensland, Brisbane, Australia: 217-222,
1994.
[09] Frizell, K.W., Renna, F.M. and Matos, J., Cavitation Potential of Flow on Stepped Spillways,
J. Hydr. Eng., ASCE, 139(6): 630-636, 2013.
[10] Amador, A., Sanchez-Juny, M., and Dolz, J., Developing Flow Region and Pressure
Fluctuations on Steeply Sloping Stepped Spillways, J. Hydr. Eng., ASCE, 135(12):
1092-1100, 2009.
[11] Khatsuria, R.M., Hydraulics of Spillways and Energy Dissipators, Marcel Dekker, New
York, U.S.A., pp. 95-127, 2005.
[12] Chanson, H. and Gonzalez, C.A., Stepped Spillways for Embankment Dams: Review,
Progress, and Development in Overflow Hydraulics, Proc. Intl Conf. on Hydraulics of Dams
and River Structures, Tehran, Iran, Balkema Publ., The Netherlands, pp. 287-294, 2004.
[13] Felder, S., Guenther, P. and Chanson, H., Air-Water Flow Properties and Energy Dissipation
on Stepped Spillways: A Physical Study of Several Pooled Stepped Configurations, Research
Report No. CH87, School of Civil Engineering, the University of Queensland, Brisbane,
Australia, 2012.
[14] Chinnaarasri, C., Donjadee, S. and Israngkura, U., Hydraulic Characteristics of Gabion-
Stepped Weirs, J. Hydr. Eng., ASCE, 134(8): 1147-1152, 2008.
[15] USACE, Use of Gabions in the Coastal Environment." CETN-III-31, 12/86, 1986.
[16] Peyras, L., Royet, P. and Degoutte, G., Flow and Energy Dissipation over Stepped Gabion
Weirs, J. Hydr. Eng., ASCE, 118(5): 707-717, 1992.

90
[17] Salmasi, F., Sattar, M. and Pal, M., Application of data mining on Evaluation of Energy
Dissipation over Low Gabion-Stepped Weir, Turkish Journal of Agriculture and Forestry
No. 36: 95-106,2012.
[18] Sarfaraz, M. and Attari,J., Selection of Empirical Formulae for Design of Stepped
Spillways on RCC Dams, World Environmental and Water Resources Congress, ASCE:
2508-2517,2011.
[19] Boes, R. and Hager, W., Two-Phase Flow Characteristics of Stepped Spillways, J. Hydr.
Eng., ASCE, 129 (9): 661-670, 2003.
Appendix 1: Symbols
Symbol Unit Definition
Fr* [‒‒‒‒] Roughness Froude number =q /ටg (sin θ)(h cos θ)3
g [m/s2
] Gravity acceleration
h [m] Step height
he [m] End sill height
Ks [m] Step roughness height perpendicular to the pseudo bottom
Kt [m] Equivalent roughness height perpendicular to the pseudo bottom
Li [m] Distance from the upper point on the spillway crest to the inception point
q [m2
/s] Discharge per unit width
R2
[‒‒‒‒] Coefficient of determination
yc [m] Critical flow depth above spillway crest
θ Degree Downstream slope angle

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