Journal of Japan Society of Civil Engineers, Ser.
B1 (Hydraulic Engineering), Vol. 69, No. 4, I_79-I_84, 2013.

HYDRAULIC DESIGN OF IN-GROUND STILLING
BASIN UNDER SUBMERGED JUMP CONDITIONSFOR FLOOD MITIGATION DAMS
Mohammad MESHKATI SHAHMIRZADI1, Tetsuya SUMI2
1Member of JSCE, Ph.D. Student, Disaster Prevention Research Institute, Kyoto University (Gokasho, Uji, Kyoto
611-0011, Japan)
2Member of JSCE, Professor, Disaster Prevention Research Institute, Kyoto University (Gokasho, Uji, Kyoto
611-0011, Japan)

Forced submerged jumps within a non-prismatic stilling basin, named in-ground stilling basin, wereexperimentally investigated. An in-ground stilling basin (ISB) is a newly popular concept for stilling basin
downstream of flood mitigation dams (FMDs). In FMDs usually one bottom outlet is located in thecenterline and the width of the stilling basin is much wider than the width of the bottom outlet, whichleads to a small expansion ratio, k, for the outflow. This study experimentally investigates the flow
patterns and velocity reduction, within ISB downstream of FMDs, under different hydraulic and geometricconditions. Finally, an innovative design guide-line is proposed considering downstream flow
requirement.
Key Words: Flood mitigation dam, submerged hydraulic jump, in-ground stilling basin.

1. INTRODUCTION
Stilling basin is a well-known hydraulic structure
located below dam’s bottom outlet, chutes andculverts. The main objective of this structure is todissipate the excess energy of outflow to reduce therisk of undesirable scouring in river system.
However, the function of stilling basin in a flood
mitigation dam (FMD) is not only to dissipate theexcess energy of flow in flood events, but to let theflow, sediment and fish pass through the structure
unobstructed during normal river flow condition.
Thus, it is highly necessary to improve the design ofstilling basin, in order to fulfill the advantages of
FMDs.
These facts bring the authors to conduct anexperimental investigation on the numbers ofproposal solutions. The solution discussed in thispaper is to dig out the apron of stilling basin andcreate what it has been called, in-ground stillingbasin (ISB), a non-prismatic stilling basin with asudden transversal enlargement combined with avertical abrupt drop at its upstream end. The
schematic side and plan view of constructed model
setup and the main governing parameters consideredin this study was shown in Fig. 1.
State of art provides considerable number ofexperimental studies devoted to hydraulic jumps in

non-prismatic stilling basins. Past studies can beclassified into three main categories as: hydraulicjump in case of only sudden enlargement in the
flume width1), 2), 3) only abrupt drop at the bed4) andcombination of both sudden expansion and abrupt
drop 5), 6), 7).
The past studies on hydraulic jump in sudden
expansion and abrupt drop, mostly conducted byadjusting the tail-water level, being far from the realcondition; whereas in present study there is nocontrol on tail-water and the hydraulic jump wasforced by an end-sill, similar to the real condition. A
forced hydraulic jump within a confined andcomplex structure such as ISB has yet to be solvedin the literature. This study specifically focused on asmall expansion ratio (=bottom outlet width/ ISB
width) of 0.2, as it is more practically common andcauses a periodic and unstable flow pattern rather
than larger expansion ratios 2).
Present research experimentally investigates thehydraulic characteristics of the forced hydraulicjump in an ISB and attempts to classify the possible
flow patterns within it under different hydraulic andgeometry conditions. Lastly, using successful
experimental results a design procedure wasdeveloped for the forced submerged jump within
ISB, concerning the flow requirements at ISB
downstream.

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Table 1 Experimental condition.

2. MATERIALS AND METHODS
b1/B(1) Experimental setup
The model setup constructed for this study isthe scale representation (length scale ratio equal to1/40) of the hydraulic flow situation of three flood
mitigation dams in Japan (Masudagawa, Tsuzuki
and Mogamioguni). This model consists of ahorizontal rectangular flume, 0.5 m width, 0.5 m
deep and 9 m long. A centrifugal pump was
employed to support the recirculating water systemthroughout the model. The upstream supply tankwas equipped by a calibrated 90 degree V-notch
weir. To measure the water head above the V-notch
weir a point gage was used, and then averagetime-volume method was utilized to obtain therelationship between water head and the pertinent
discharge. Two pierced plates, also, were installedinside of the main reservoir to attain the laminaroutflow discharge from its bottom outlet; so that a
uniform supercritical flow with a thickness equal tothe bottom outlet was finally plunged into the ISB.

0.2

L/B

s/h1

he/h1

Fr1

1.5

3

0, 0.8, 1.6 & 2.4

2.8-5.1

2

1, 2 & 30, 0.8, 1.6, 2.4 & 2.7

2.8-5.1

2.5

30, 0.8, 1.6 & 2.4

2.8-5.1(3) Experimental condition
The experiments were carried out under different
ISB geometries as follows: ISB length (L= 75, 100
and 125 cm), drop height (s= 5, 10 and 15 cm),
however, the ISB width for all experiments was thesame B= 50 cm equal to the width of flume. For
each ISB geometry configuration, different
geometry of end-sill with various heights (he= 0, 4,
8, 12 and 13.5 cm) has been systematicallyexamined to obtain the optimum case. The end-sills
were placed vertically above the positive step andperpendicular to the longitudinal axis of flume. In
addition to the three different Froude number ofsupercritical flow at the bottom outlet (namely Fr1=
2.8, 4.9 and 5.1), only one dimension of bottom
outlet (h1= 5 cm and b1= 10 cm) was examined,
thus, creates an expansion ratio of k=0.2 (k=b1/B),
similar to the average practical expansion ratio for
FMDs. Table 1 shows the experimental condition
considered in present study.

(2) Experimental measurement
The basic data collection procedure was the samefor all of the experiments run. For each test digital
photographs were taken from side and plan view of
ISB and visual observations were recorded using
high resolution digital camera. A water level meter
was used to measure the water depth and its
fluctuation throughout ISB. The sampling frequency
for water level meter was set to 50 HZ. Using anelectro-magnetic current meter the 3D component ofvelocity was measured in different transversal andlongitudinal cross sections for each test run. At
every section the velocity was measured at 2.5 cm
interval. Accordingly, the sampling frequency was
set to 50 HZ.

3. RESULTS AND DISCUSSION(1) Flow pattern classification
Depending on the geometry of ISB, five different
jump types have been observed within ISB
including: B-jump, S-jump, U-jump, periodic
submerged jump and steady submerged jump 7) (Fig.
2). It can be determined that the type of hydraulicjump was less dependent on Fr1, and more
dependent on the end-sill height he.

Upstream
supply tank

W.L.M.
PC

C.M.

Main
reservoir

Hw(I), (III)

h1

(II)

h3

h2

(IV)

he

h4

s
b)

Side view
Outletb1
a)Plan view

4B

L

B

In-ground stillingFig. 2 Hydraulic conditions for five flow patterns with change
of normalized end-sill height and normalized ISB length, fors/h1=3, Fr1=2.8-5.1

End-sill

basin

Fig. 1 Schematic side and plan view of the model setup.

2

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Flow pattern 1: B-jump was observed only in caseof the ISB without end-sill (Fig. 3a and b), in which
a non-submerged nape plunges into the ISB. At thelateral side of the nape air entrained into the waterand minor jumps were created in two parallel lines.
By getting far from the outlet the surface roller
becomes wider and occupied whole the width of thechannel.
Flow pattern 2: For a short ISB length (L/B<2) andshorter end-sill height (0.7<he/hc<1.2), the expanded
supercritical outflow turned to the left side andformed an oblique spindle of rollers at the surface ofwater (Fig. 3c). Simultaneously, at the opposite sideof the channel, right side, a big eddy was formed.
This flow pattern is known as asymmetric S-jump,which was distinguished as a dominant flow pattern
for short ISB with low end-sill height.
Flow pattern 3: A longer ISB with low end-sillheight established a different type of flow pattern(Fig. 3d), named U-jump. In this case, a narrow andsymmetric super critical current was observed along
the centerline of ISB, in which the rollers front were
continuously converging and diverging. Two eddies
with approximately equal size, also, formed at bothside of the central super critical current.
Flow pattern 4: A short ISB length (L/B<2)combined with a medium height of end-sill (Fig.
3e), established a steady and symmetric flow,
named steady submerged jump. While, the longer
one (L/B>2) turned to be much unstable andperiodic, named periodic submerged jump (Fig. 3f).
The shorter ISB with medium height of end-sill may
be an optimum case as a point of view of jumpstability and compactness.
Flow pattern 5: Lastly, in case of a very tall
end-sill (2.5<he/hc<3.5), variation of length did notconsiderably effects on flow pattern within ISB(Fig. 3g and h).

he/hc, in comparison with the longer ISB. The
overall trend shows that increasing the normalized
ISB length may increase the magnitude of velocity
reduction. Moreover, for a given normalized end-sillheight, he/hc, the longer ISB shows a greater valueof normalized velocity reduction (Fig. 5). Moreover,the effect of normalized end-sill height, he/hc, on
normalized velocity reduction may differ between
short and long ISB length. In case of shorter ISB, byincreasing the he/hc, velocity reduction always
increased while in case of longer ISB after he/hc=2
the normalized velocity reduction did not change
and remained constant. It reveals that a longer ISB
may provide us a shorter end-sill height.
Fig. 6 and 7 depict the influence of drop number(s/h1) on velocity reduction within ISB respectively
for Froude number equal to 2.8 and 4.3. With an
overall view on the data plotted in Fig. 6, it can beestablished that a shallower ISB (s/h1=1) withmedium height of end-sill (he/hc=1.8) is an optimum
geometry for end-sill and step (highest velocity
reduction). Having said that, increasing the Froudenumber from 2.8 to 4.8 slightly shifted the optimum
drop number from s/h1=1 to s/h1=2 (Fig.7). In
general, for a Froude number between 2.4 to 4.3, themaximum performance of ISB regarding to velocity
reduction, may occur for s/h1=1 to 2 and he/hc=1.8
to 2.9.
L/B
<2
(a)

> 2

he/hc=0(b)

0.7<he/hc <1.2
1.6<he/hc <2.4

(2) Dissipation effect of in-ground stilling basin
The normalized velocity reduction is plottedagainst different normalized parameters to provide a
better vision in their individual effects on
dissipation mechanism within ISB.
Fig. 4 illustrates the normalized velocity
reduction, U1-U2/U1, between section I and II, as afunction of the normalized ISB length (L/B). U1 is
the initial outlet velocity and U2 is the maximum
velocity just upstream of end-sill. In short ISB cases(L/B=1.5) the change in end-sill height causes alarge change in normalized velocity reduction,
however, for long ISB (L/B=2, 3) the changes in
end-sill height results in very small changes innormalized velocity reduction. It demonstrates thatin shorter ISB, the normalized velocity reduction
depends more on the normalized end-sill height,(e)

2.5<he/hc <3.5

B-jump(c)(g)

B-jump(d)

U-jumpAsy. S-jump(f)Periodic submerged jump

Steady submerged jump

Steady submerged jump(h)

Steady submerged jump

Fig. 3 Schematic side and plan view of the flow patterns under
different hydraulic and geometric conditions.

3

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Fig. 8 The normalized velocity reduction between section I andIV versus he/hc.

Fig. 4 The normalized velocity reduction within ISB versus L/B
for periodic and steady submerged jump with Fr= 2.8-5.1 ands/h1=3.

0.6

Additionally, for a given drop number (s/h1) ataller end-sill provides better velocity reduction.
However, increasing the normalized end-sill heightfrom he/hc =1.8 to 2.9 did not significantly change
the magnitude of normalized velocity reduction
within ISB. Thus, the drop number (s/h1) equal to 2
and the normalized end-sill height (he/hc) equal to
1.8 may are the optimum test cases.
Fig. 8 illustrates the normalized velocity
reduction between section I and IV (downstream of
ISB). U4 is the average velocity of flow at section
IV. The overall trend of data plotted in this figure
shows by increasing the normalized height ofend-sill the normalized velocity reduction is
reducing. In other words, in contrary with thenecessity of taller end-sill to create a steadysubmerged jump within a confined space, the taller
end-sills negatively reproduce the higher flow
velocities at ISB downstream.

0.4

(3)

0.2

a) Determining the sequent depth
So far, in preceding sections, it was shown thatconsidering a medium end-sill and drop height for
ISB could effectively reduce the velocity of flow.
Also, this combination of end-sill and drop resulted
to stable and steady flow known as steadysubmerged flow. Thus, hereafter the design guidelien producer is proposed only for steady submergedflow.
To calculate the sequent depth, h2, for the forced
submerged hydraulic jump, the momentum equation
was applied, neglecting the bed shear stress,
between section I and II in (see in Fig. 1).

Fig. 5 The normalized velocity reduction within ISB versus
he/hc for periodic and steady submerged jump with Fr= 2.8-5.1
and s/h1=3.
1

he/hc=0he/hc=1.8

he/hc=0.9
he/hc=2.9

U1‐U2/U1

0.8

0
0

1

s/h1

2

3

4

Fig. 6 The normalized velocity reduction within ISB versus s/h1
for Fr=2.8 and L/B=2.
1
he/hc=0he/hc=1.8

he/hc=0.9
he/hc=2.9

U1‐U2/U1

0.8

0.6

0.4

Design procedure of in-ground stilling basin

0.2

(1)
0
0

1

2

3

4

s/h1

where h is the submergence depth at the face ofdrop, h is the sequent depth upstream from theend-sill, U1 is the initial outlet velocity,
U1=Q/(b1×h1), andis the average velocity at

Fig. 7 The normalized velocity reduction within ISB versus s/h1
for Fr=4.3 and L/B=2.

4

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section II,=Q/(B×h2), Q is the outflow discharge,
is the density of water, and is the specificsubstitutionofweightofwater. After
non-dimensional parameters in Eq. 1 andsimplification, the preceding equation can be
expressed as:
2

2

2

0

(2)

where Y2 is the normalized sequent depth, Y2=h2/h1,
S is the drop number, S=s/h1, and k is the expansion
ratio, k =b1/B. Fig. 9 shows the comparison between
the predicted h2 using Eq. 2 and the measured
sequent depth. As can be seen, Eq. 2 provides anamenable prediction of measured sequent depth.

Fig. 9 Predicted normalized sequent depth, Y2, using Eq.4
versus the measured sequent depth.

b) Determining the end-sill height
The end-sill height is obtained using Fig. 10,
selecting a desire Froude number for thedownstream from end-sill (Fr4) on the horizontal
axis, and then finding a corresponding he/h4 value on
the vertical axis. The water depth at ISB
downstream, h4, can be calculated from the selected
Fr4 and the design discharge. It should be taken into
account, the energy loss over the end-sill (free fallflow) is not negligible and it is varied depend on theend-sill height. The energy over the end-sill can becalculated using critical depth (hc) and end-sillheight (he). If it assumed that, there is no energy loss
for free fall flow over the end-sill, the energy
downstream of ISB is equal to the energy at the topof end-sill as below:

Fig. 10 end-sill height relationship with downstream
boundary condition.

(3)
where hc is the critical depth, B is the width of thechannel, h4 is the water depth at ISB downstream, Q
is the design discharge and g is gravity acceleration.
The comparison between the measured values ofenergy at section IV, and the results obtained bytheoretical method (Eq. 3) demonstrates that theexistence of considerable energy loss over theend-sill (Fig. 11). Therefore, empirical equations
were proposed to map the h’4 assuming no energy
loss over the end-sill to the measured values of h4.
By knowing the h4, the width of channel, B, as wellas the design discharge, Q, all the necessary
parameters for the boundary condition at thedownstream of end-sill would be completed.

Fig. 11 Predicted downstream water depth assuming noenergy loss, h’4..

long ISB is not cost-efficient. In practice, the lengthof a classical hydraulic jump (Lj), 4 to 6 times ofsequent depth (h2), is being used for design
purposes. This method may not suitable to obtain
the ISB length herein, due to the presence of tall
end-sill and submerged hydraulic condition. The
ISB length (L) can be obtained using Eq.4 proposedby Ohtsu et al. 2).

1.7c) Determining the ISB length
The proper estimation for the ISB length (L), or inother words end-sill location, is crucial. If end-sill
locates too close to the outlet, the jump would nothave enough space to be induced. In other hand, a

1.79

(4)

where HL is the head loss due to submerged
hydraulic jump and H1 is the total head at the drop
face, which can be define as:

5

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4. CONCLUSION(5)This paper investigates forced hydraulic jumps
within an in-ground stilling basin (ISB). The
observed flow patterns within ISB were classified
into five main groups. The main governingparameters were found to be the height ofend-sill, he, and the ISB length, L, while thevariation of Fr1 did not lead to a considerable
effects on the flow pattern and energy loss
function within ISB.
It was concluded that the presence of end-sill isvital to establish a compact hydraulic jump,
although a tall end-sill can negatively accelerate
the downstream velocity due to the free fall flow
over the end-sill. A medium ISB length combinedwith a medium end-sill height (1.6<he/hc<2.4)
provides a stable symmetric submerged jumpwith greater velocity reduction.
The effect of drop number (s/h1), also, wasexamined in this study. It was found that,considering a medium depth for ISB canpositively improve the velocity reduction, whilefurther increasing the depth showed benefit inneither velocity reduction nor design cost. The
optimum drop number may differ by varying the
Froude number; a higher Froude number requireda deeper ISB, in general. The next step of thisstudy is to examine the performance of ISB incase of extreme flood events.

U1 is the initial outlet velocity, andis theaverage velocity at section II. The Eq. 6 is thenon-dimensional form of Eq. 5 considering
expansion ratio, k, as well as drop number, S, topredict the energy loss within ISB. The value
obtained by Eq. 6 is input for Eq. 4.
/(6)d) Determining the drop heightThe drop height, s, can be found using steadysubmerged jump data in Fig. 12. The known valuesof hc, L, B and he with the linier equation fitted tothe steady submerged jump data may provide anappropriate estimation of drop height to be used indesign procedure.
8

B‐jumpU‐jump
Perio. Submerged jump
Steady Submerged jump
Linear (Steady Submerged jump)(he/s)

6

4

2

he/s = -0.7366(heL/hcB) + 5.4815
0
0

0.5

1

1.5

2

2.5

3

3.5

REFERENCES(he/hc)(L/B)

1)

Fig. 12 ISB geometrical parameters and jumps types.

e) Proposed design procedure of ISB
For a horizontal apron of ISB with a negative step
at upstream end and an end-sill at its downstream
end, following design procedure can be proposed:2)3)1) Given the upstream boundary condition
including the design discharge, Q, dimensionsof bottom outlet, b1 and h1, approach Froudenumber, Fr1, and river channel width, B.
2) Use the upstream boundary condition to
calculate the critical depth, hc.
3) Select a suitable he and L and then s by referringfrom Fig. 10 to 12 as well as Eq. 4 to 6,
considering stable submerged hydraulic jump.
4) Check the obtained water depth downstream
from the end-sill, h4, and downstream Froudenumber, Fr4, under assumption of no energy
loss. If necessary, modified h’4 can becalculated with Fig. 11 by considering theenergy loss by free fall flow over end-sill.
5) Repeat steps 2 to 3 until the downstream
condition will come to be acceptable level.

4)

5)

6)

7)

6

I_84

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(Received September 30, 2012)