3d plunge pool scour with protection measures

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Journal of Hydro-environment Research 4 (2010) 225e233www.elsevier.com/locate/jher

Research paper

3D plunge pool scour with protection measures

Stefano Pagliara*, Dipankar Roy, Michele Palermo

Department of Civil Engineering, Faculty of Engineering, University of Pisa, Via Gabba 22, 56122 Pisa, Italy

Received 8 January 2009; revised 1 April 2009; accepted 24 October 2009

Abstract

Plunge pool scour phenomena are well-known for destructive action at the base of hydraulic structures. An experimental study was conductedat the Hydraulic Laboratory of the University of Pisa, Italy, to investigate the hydraulics of 3D plunge pool scour in presence of simple protectionmeasures. The main geometrical scour hole parameters were investigated and various relationships are proposed for different flow conditions.These parameters include the maximum dynamic scour hole depth, the maximum scour hole width and the location of the scour hole initiationpoint. Equations for all these parameters are presented in terms of the basic scour variables including the jet densimetric Froude number, jetimpact angle, tailwater elevation above the originally horizontal sediment bed level and the protection permeability and longitudinal positions ofthe protection. Moreover, a scour hole typology and relationships for the non-dimensional longitudinal scour hole profile in presence of theprotection are also given.� 2010 International Association of Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rightsreserved.

Keywords: Plunge pool; Scour; Tailwater depth; Spillways; Stilling basin protection

1. Introduction

Plunge pool scour downstream of hydraulic structures is animportant phenomenon which received considerable attentionin the scientific literature. It is important to predict the variousscour hole characteristics to prevent the failure of a hydraulicstructure. Mih (1982) and Mih and Kabir (1983) investigatedsediment removal from a granular bed with a high-speed nozzle.Mason (1989) studied the effect of air entrainment on plungepool scour. Rajaratnam and Berry (1977) and Rajaratnam(1980) investigated the erosion by circular wall jets. Rajaratnamand Aderibigbe (1993) analyzed the effect of screen protectionstructures to reduce the scour hole depth. Mason (2002), Canepaand Hager (2003) and Pagliara et al. (2004) demonstrated thatthe scour process depends on various parameters, i.e. jetdischarge, densimetric jet Froude number, jet impact angle, jetair content, upstream flow, tailwater depth above the bed level,and granulometric characteristics of the sediment.

* Corresponding author. Tel.: þ39 50 2217717; fax: þ39 50 2217730.

E-mail address: [email protected] (S. Pagliara).

1570-6443/$ - see front matter � 2010 International Association of Hydro-environment Engine

doi:10.1016/j.jher.2009.10.014

Pagliara et al. (2006) studied the effect of ridge removal onthe geometry of the scour hole. Ridge presence plays a majorrole as it strongly affects the recirculation of the water-sedimentmixture and the suspended material in both two-dimensional(2D) and three-dimensional (3D) configurations. Tests showedthat for low tailwater conditions, continuous ridge removalresults in a deeper scour hole. Dey and Sarkar (2006a, 2006b)studied the geometrical and hydraulic parameters governing thescour process and proposed relationships to predict maximumscour hole depth without protection measures.

Pagliara et al. (2008) studied the 3D plunge pool scour tounderstand its spatial behavior and introduced a factor l todistinguish if the phenomenon is 2D or 3D. The parameterl¼ bm/b is the ratio between maximum scour hole width bm

and channel width b. For l< 1.5 the phenomenon is mainly of3D type, whereas for l> 3 is almost 2D, involving a scourhole and a ridge of cylindrical shape, while the 3D scour holeis elliptically cup-shaped with a half moon-shaped duneprofile. Fig. 1 shows longitudinal and plan views of a scourhole. Pagliara and Palermo (2008) presented a study on 2Dplunge pool scour with a protection.

ering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

mailto:[email protected]

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Fig. 1. Scheme of 3D scour hole (a) longitudinal and (b) plan views in absence of protection measures; (c) longitudinal and (d) plan views with protection measure.

226 S. Pagliara et al. / Journal of Hydro-environment Research 4 (2010) 225e233

Various hydraulic and geometrical aspects of the 3D scourwith a basin protection measure are discussed herein. Avertical protection sheet placed in the basin at various longi-tudinal positions modifies the scour process considerably bothqualitatively and quantitatively.

2. Experimental setup

The experiments were conducted at the Hydraulic Labora-tory of the University of Pisa, Italy. The rectangular channelused was 6 m long, b¼ 0.80 m wide and 0.9 m high. Oneuniform granular material was used to simulate the channel beddownstream of a spillway, involving the granulometric charac-teristics d90¼ 10.26 mm, d84¼ 10.02 mm, d50¼ 8.57 mm,d16¼ 7.49 mm and s¼ (d84/d16)0.5¼ 1.17 as the non-unifor-mity parameter. The angle of repose of the test material was37.1� under dry and 29.5� under saturated conditions.

After the preparation of the bed (see Pagliara et al., 2008), anoriginal water elevation ho above the horizontal bed level wasestablished. A circular pipe of 0.027 m outlet diameter generatedthe high-speed water jet as described by Pagliara and Palermo(2008). In these tests only black water jets (without air addition)were considered. The water discharge Q was varied from0.0025 m3/s to 0.0045 m3/s. The tailwater depth ratio Tw¼ ho/Dbetween the height of the water level ho over original bed leveland the jet diameter D was varied between 1 and 10. Theinvestigated jet discharge angles a ranged between 30� to 75�.

Two types of protection were used in these experiments: animpermeable inox sheet of 0% permeability (Type S ) anda permeable sheet with 40% opening area (Type S8) withcircular holes of 8 mm in diameter, i.e., less than d90 of thesediment. Type S8 strongly restricts the passage of sedimentsbut allows the water passage. Both protections were 70 cmwide, almost covering the channel width. There were 5 cm

gaps between the channel walls and lateral protection edges tofacilitate their placement in the stilling basin. This did notinfluence the scour process as in all the tests the scour holewidth was always less than the channel width.

Preliminary tests were carried out without any protection todefine the reference scour hole lengths for various combina-tions of the tested hydraulic and geometrical parameters. Oncethe scour hole length la3D was assessed, where the subscripta3D is relative to the 3D scour hole configuration in theabsence of any protection, various positions for the protectionwere selected. These were inserted at ls¼ 0.5la3D, ls¼ 0.75la3D

and ls¼ 1.0la3D (indicated by ‘‘þ’’ signs in Fig. 1a), where ls isthe longitudinal distance of the protection from the scour holeorigin, and the subscript s indicates the presence of a protec-tion in the stilling basin. The top of the protection wasadjusted to the original bed level (Fig. 1).

Almost 200 tests were conducted. Fig. 2(a) shows a plan viewof a scour hole without protection while Fig. 2(bed) relates toviews of scour holes with an S8 type protection placed at0.75la3D. Longitudinal and transverse profile readings wererecorded at 5, 10, 20 and 40 min from the test initiation. One testtypically ran for 40 min, as the equilibrium scour condition isgenerally reached within this period. After stopping the jet flow,profile readings also were taken referred to as the ‘‘staticcondition’’. A special point gauge was used to record theprofiles, involving a circular plate attached to the gauge toaccurately survey the scour hole profile (Pagliara et al., 2008).

3. Classification of 3D scours

3D plunge pool scour is a complex phenomenon witha radial flow beyond impact onto the sediment bed. The scourhole type is mainly determined by the jet impact angle and thetailwater depth above the sediment bed. After inserting the

Fig. 2. (a) Plan view of static scour holes for a¼ 60�, Tw¼ 10, Q¼ 2.5 l/s, without protection; (b) plan view, (c) downstream view and (d) upstream view of the

scour hole for identical Tw and Q with protection type S8.

227S. Pagliara et al. / Journal of Hydro-environment Research 4 (2010) 225e233

protection, the phenomenon becomes even more complex asthe jet is deflected by the protection. Five main scour holetypes were identified among which four are most common.Fig. 3 shows the scour hole types as a function of the non-dimensional longitudinal position j¼ ls/la3D of the protection,and the tailwater level.

Type 0: There is practically no effect of the protection onthe scour hole, similar to the case without a protection.Type A: The jet is deflected downwards after impacting theprotection directly. Scour hole is generally deeper than thatfor Type 0. It typically occurs if the protection is placedclose to the scour hole origin (0.5< j< 0.75).Type B: The jet is deflected upwards by the protection.Depending on the scour hole geometry, two categories mayresult: Type B1 if the ridge is formed mainly downstream ofthe scour hole and Type B1’ if larger ridge is observed bothdownstream and at the sides of the scour hole.Type C: The jet causes scour holes at both upstream anddownstream of the protection. Depending on the scour holegeometry, three categories may result: Type C1 if the jet isdeflected upwards and to the sides of the scour hole whichbecomes wider. One ridge is formed mainly downstream ofthe protection; Type C2 if the jet is deflected in such a waythat three distinct ridges are formed at the downstream sideand at both sides of the scour hole; Type C3 if two distinctridges are formed at the sides of the scour hole.Type D: If protection is placed near to the jet (jw0.5) andeither Tw is high and a small or a is large and Tw small. Themain scour hole is created downstream of the protection.

The upstream end of the sour hole is intercepted by theprotection, thus reducing the scour hole length.

Experiments were carried out for certain discrete values oftailwater level, protection permeability and longitudinalpositions. Therefore, only a rough delimitation for these scourhole types results as a function of a, Tw, j and p, wherep¼ Ao/At, in which Ao is the total opening (holes in theprotection) area and At is the total area of the protection.Vertical dashed double lines limit the classification becausethe minimum j value tested was 0.5 (Fig. 4).

4. Dynamic scour hole depth

4.1. Scour hole depth without protection

For black water jets and without scour hole protection,Pagliara et al. (2008) proved that the non-dimensionalmaximum scour hole depth, Zm3D¼ zm3D/D, where zm3D is themaximum scour hole depth (Fig. 1a), can be expressed as,

Zm3D ¼ f1ðFd90Þ,f2ðaÞ$f3ðTwÞ$f4ðsÞ$f5ðlÞ ð1Þ

where Fd90¼ V/( g0d90)1/2 is the densimetric jet Froudenumber, in which V¼Q/(pD2/4) is the jet velocity, Q the jetdischarge, g0 ¼ [(rs� r)/r]g is the reduced gravitationalacceleration, g the gravitational acceleration, rs and r thedensities of sediment and water, respectively. Note that jetangle a is expressed in degrees. The functions fi, where thesubscript i varies between 1 and 5, account for

Fig. 3. Scour hole types due to variation of jet impact angle, tailwater level, protection permeability and position.


Densimetric Froude number f1ðFd90Þ ¼ Fd90 ð1aÞ

Impact jet angle f2ðaÞ ¼½ � 0:38sinða� þ 22:5�Þ�,ð1:360� 0:012a�Þ ð1bÞ

Tailwater f3ðTwÞ ¼ ð1=0:30Þ½0:12$lnð1=TwÞ þ 0:45�,ð4þ TwÞð1cÞ

Granulometry f4ðsÞ ¼ �ð0:57sþ 0:33Þ ð1dÞ

3D factor f5ðlÞ ¼ 0:140 ð1eÞIn all the present tests, it was found that 0.2� l� 0.95

ensuring 3D scour holes. Eq. (1) is valid for 0.8� Tw� 10;30� � a� 60�; 4� Fd90� 30; and 0.2� l� 1.5. To extendthe validity of Eq. (1) to 30� � a� 75�, jet angle function f2(a) was modified as,

f 02ðaÞ¼½�0:38sinða�þ22:5�Þ�,�0:0004a�2�0:043a�þ1:85

�

ð2Þ

4.2. Scour hole depth with protection

In the present study only one material was used, theprotection was vertical of constant width and the top endcoincided with the original bed level. The parameters whichhave to be taken into account are the structural permeability p

and its non-dimensional longitudinal position j. Moreover,a protection modifies the scour mechanism significantly interms of the jet angle. Two additional functions accounting forthese parameters were found and Eq. (1) is thus expanded to,

Zm3Ds ¼ f1ðFd90Þ,f 002 ðaÞ,f3ðTwÞ,f4ðsÞ,f5ðlÞ,f6ðj;pÞ ð3Þ

in which

f6ðj;pÞ ¼ ½ð1:8p� 0:53Þjþ ð�1:8pþ 1:72Þ� ð3aÞ

f 002ðaÞ ¼ f 02ðaÞ$ð�0:005a� þ 1:2Þ ð3bÞEqs. (3) are valid for the tested range of parameters, as

specified above, and for 0.5< j< 1 and 0< p< 0.4. Itpredicts the experimental data with R2¼ 0.8, as shown inFig. 5 which compares the measured and calculated values ofZm3Ds¼ zm3Ds/D. zm3Ds is the scour hole depth in the presenceof a protection (Fig. 1 c). Note that f6(j, p) is a decreasingfunction of j if p¼ 0, resulting in a deeper scour hole. This isdue to the fact that an S type protection located closer to the jetstrongly affects the flow circulation, since it constitutesa physical impermeable obstacle deflecting either partially ortotally the upstream flow, generally resulting in a formation ofa strong and confined vortex. A protection thus limits thelongitudinal expansion of the scour hole, forcing the jet flow tobe strongly recirculated inside the scour hole.

If an S8 type protection of p¼ 0.40 is used, the effect of j

becomes less significant than that of the S type protection and f6(j, p)

Fig. 4. Scour hole types for (a) a¼ 30�, 45� and p¼ 0, (b) a¼ 30�, 45� and p¼ 0.40, (c) a¼ 60� and p¼ 0, (d) a¼ 60� and p¼ 0.40, (e) a¼ 75� and p¼ 0 and

(f) a¼ 75� and p¼ 0.40.


slightly increases with j, because the S8 type protection allows waterpassage. Fig. 6 shows the measured Zm3Ds values versus j with Fd90

as parameter, for both protection types S and S8, and for Tw¼ 1. Ifthe structure is placed at j¼ 1, the effect of permeability is negli-gible, i.e. the effect of permeability is no longer valid at j w 1though the value of f6(j, p) becomes slightly higher than 1 due to thecreation of a macro vortex upstream of the protection, slightlyincreasing the scour hole depth. Note from Fig. 6 that S and S8 lines

0

6

12

0 6 12

Perfect agreement±25% deviationSS8

Z m 3Ds (meas)

Z m 3Ds (calc)

SS 8

Fig. 5. Comparison between measured and calculated values of Zm3Ds for tests

with protection type S (solid circles) and protection type S8 (hollow circles).

for a fixed tailwater and Fd90 tend to cross each other at jw1 whichconfirms the above statement.

5. Dynamic scour hole length

5.1. Scour hole length without protection

The non-dimensional scour hole length, La3D¼ la3D/D isdefined as the ratio between scour hole length la3D and the jet

0

7

14

0.4 1.1 1.8

Fd90=20.57, SFd90=16, SFd90=11.43, SFd90=20.57, S8Fd90=16, S8Fd90=11.43, S8SS8

Z m 3Ds (meas) Fd 90=20.57, S

Fd 90=16.00, S

Fd 90=11.43, S

Fd 90=20.57, S 8

Fd 90=16.00, S 8

Fd 90=11.43, S 8

SS 8

Fig. 6. Zm3Ds versus j with Fd90 as parameter for both protection types S and

S8, Tw¼ 1 and a¼ 60�.


diameter D. La3D increases with Fd90 and decreases with a.Tailwater level Tw also has a significant effect on La3D.Pagliara et al. (2008) proposed for La3D under 3D conditions,

La3D ¼ 2:5½1þ 1:05expð�0:030a�ÞFd90�zLa3D ð4Þ

with

zLa3D ¼ ½0:168þ 0:062Tw þ 0:020a��,½1:217� 0:013Fd90�,½0:851þ 0:345l� ð4aÞ

subject to the following limitations: 0.8� Tw� 10;30� � a� 60�; 4� Fd90� 30; and 0.2� l� 1.5. Eq. (4)predicts the reference test data from this study for a� 75�

well, with R2¼ 0.80.

5.2. Scour hole length with protection

The scour hole shape depends on the longitudinal positionand the permeability of the protection and other flow param-eters. Type C and Type D (Fig. 3) are examples where twodistinct scour holes form at both sides of the protection. TypeA and Type B (Fig. 3) are generated if the scour hole is at theupstream side of the protection only. A corrective factor zLa3Ds

accounting for the effects of protection presence includes theeffects of a as,

zLa3Ds ¼ ½ð�0:6pþ 0:2Þjþ ð0:6pþ 0:4Þ�ð�0:013a� þ 2:2Þð5Þ

For a fixed jet angle and p¼ 0, zLa3Ds increases with j, i.e.the scour hole length generally reduces if an S type protectionis placed near the jet. If an S8 type protection is used, thiseffect is reduced as the jet generates scour holes at both sidesof the protection. If p and j remain constant, zLa3Ds decreaseswith a, i.e. the scour hole length reduces with increasing jetangle, because a compact vortex is generated.

The equation for non-dimensional scour hole length inpresence of a protection is,

La3Ds ¼ 2:5½1þ 1:05expð�0:030a�ÞFd90�,zLa3D,zLa3Ds ð6Þ

where La3Ds¼ la3Ds/D, in which la3Ds is the scour hole lengthin presence of protection (Fig. 1c). Eq. (6) is valid for thetested range of parameters, as specified above, and predicts theexperimental data with R2¼ 0.75. If the protection is absent,zLa3Ds¼ 1.

6. Non-dimensional scour hole width

6.1. Scour hole width without protection

To develop an analytical formula for the non-dimensionalwidth Bm¼ bm/D of the 3D scour hole, the basic formula ofPagliara et al. (2008) was expanded. The width Bm increaseswith Fd90 and Tw and it is directly related to the scour holelength La3D. Pagliara et al. (2008) proposed the followingequation for Bm without protection, valid for 0.8� Tw� 10,30� � a� 60�, 4� Fd90� 30, and 0.2� l� 1.5,

Bm ¼ ½0:500þ 0:008a��,La3D ð7ÞEq. (7) was found to fit the present data in the range of

30� �a� 75� without modifications, i.e. its validity isextended up to a¼ 75�.

6.2. Scour hole width with protection

Similar to the scour hole length and depth, a correctivefactor zBms including protection parameters and the jet anglewas introduced in Eq. (7) as,

Bms ¼ Bm,zBms ð8Þ

where Bms¼ bms/D in which bms is the scour hole width inpresence of protection and

zBms¼½ð1:3p�0:6Þjþð�1:3pþ1:45Þ�ð�0:003a�þ1:35Þ ð8aÞ

zBms reflects the combined effects of parameters p and j, andjet angle a as described above. zBms¼ 1 if no protection ispresent. Eq. (8) is valid in the tested range of parameters andpredicts the experimental data with R2¼ 0.70.

7. Length of impact point from the scour hole origin

7.1. Length of impact point from the scour hole originwithout protection

The non-dimensional distance of the fictitious impact pointfrom the scour hole origin Li3D¼ li3D/D (Fig. 1 a) is anotherparameter investigated in the present study. For 2D scour holegeometry and without any protection, Pagliara and Palermo(2008) proposed the following relationship to determine thenon-dimensional distance of the fictitious impact point fromthe scour hole origin Li2D¼ li2D/D

Li2D ¼ð0:136Fd90 þ 5:684Þð0:0136Tw þ 0:977Þ�0:0003a�2 � 0:042a� þ 2:234

�ð9Þ

The validity of Eq. (9) was extended to the 3D condition byintroducing a function depending on l as,

Li3D ¼ Li2Dð0:6lþ 0:5Þ ð10ÞEq. (10) was validated using the Authors’ experimental

data along with those of Pagliara et al. (2008), valid for0.8� Tw� 10, 30� � a� 75� and 4� Fd90� 30 and0.2� l� 0.95. Considering the complexity of the phenom-enon, Eq. (10) predicts Li3D reasonably (R2¼ 0.6).

7.2. Length of impact point from the scour hole originwith protection

Near the scour hole initiation point, the effect of jet impactis considerably reduced as compared to the jet impact zone.Note that due to the vortex upstream of the protection thescour hole initiation point shifts slightly towards upstream ifcompared with the reference tests. This occurs for all of theprotection positions and permeabilities. For design purposes

Table 1

Coefficients of Eq. (16).

Coefficients Type A Type B Type C Upstream Type C Downstream Type D Upstream Type D Downstream

30�,45�,60� 75� 30�,45� 60� 75� 30�,45�,60� 75� 30�,45� 60� 75� 30�,45� 75� 30�,45�,75�

A1 �2.23 4.70 �2.23 �4.63 0.00 �0.33 3.06 �0.56 2.75 2.37 2.80 5.61 �1.21

A2 3.48 �11.48 3.48 6.49 �3.67 �0.73 �8.98 0.94 �3.34 �1.98 �6.09 �11.53 3.77

A3 �0.66 8.28 �0.66 0.35 6.40 2.20 7.78 1.20 2.03 1.16 4.07 6.53 �1.39

A4 0.41 �0.52 0.41 �1.49 �1.88 �0.14 �0.87 �0.64 �0.49 �0.70 0.23 0.39 �0.30

A5 �1.00 �1.00 �1.00 �0.72 �0.85 �1.00 �0.98 �0.93 �0.96 �0.84 �1.00 �1.00 �0.87


the effect of p and j on Li3Ds can be included in a constantfactor zLi3Ds in Eq. (10) as,

Li3Ds ¼ Li3D,zLi3Ds ð11Þin which

zLi3Ds¼ 1:20 ð11aÞ

where Li3Ds¼ li3Ds/D and li3Ds is the distance between scourhole origin and the fictitious jet impact point on the originalbed level for the 3D case. If no protection is present, thenzLi3Ds¼ 1. Eq. (11) predicts the experimental data withprotection with R2¼ 0.65.

8. Scour hole profiles with protection

The various non-dimensional longitudinal scour hole profilesfor all angles and scour hole types were analyzed, resulting in

Type C (Upstream)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

000.20.40.60.811.2

30°, 45°, 60°

75°

c Z u

X u

Type D (Upstream)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

000.20.40.60.811.2

30°, 45°75°

eZ u

X u

Type A

-1.2

-1

-0.8

-0.6

-0.4

-0.2

000.20.40.60.811.2

30°, 45°, 60°75°

aZ u

X u

Fig. 7. Non-dimensional scour hole profile

a generalized 4th order polynomial equation. This fits the scourhole profiles with coefficients stated in Table 1, depending on jetangle and scour hole type. Fig. 7(aef) shows various non-dimensional profiles for all scour hole types and tested jet angles.For Type C and Type D, the scour hole profile was divided into anupstream and downstream part of protection. For Type A andType B, the scour hole is located only at the upstream side of theprotection (Fig. 3). Axes were made non-dimensional as,

Xu ¼ ðxs� xÞ=ðxs� xoÞ for x � xs ð12Þ

Xd ¼ ðx� xsÞ=½la3Ds� ðxs� xoÞ� for x � xs ð13Þ

where Xu and Xd are the axes for upstream and downstreamparts, respectively. x is the generic longitudinal dimensionalcoordinate, xs is the longitudinal coordinate of the structureand xo is the scour hole origin coordinate (Fig. 1 c). In Eqs.

Type B

-1.2

-1

-0.8

-0.6

-0.4

-0.2

000.20.40.60.811.2

30°, 45°60°75°

bZ u

X u

Type C (Downstream)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1 1.2

30°, 45°60°75°

d

X d

Z d

Type D (Downstream)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1 1.2

30°, 45°, 75°

f

X d

Z d

s for all tested angles and scour types.


(12) and (13), the term (xs� x o)¼ ls for all scour hole types. Ifthe scour hole is upstream of the structure (Type A and B),(xs� xo)¼ ls¼ la3Ds. In the adopted coordinate system, Xu¼ 1for x¼ xo, Xd¼ 1 at the end of the downstream scour hole andXu¼ Xd¼ 0 for x¼ xs (i.e. in correspondence of the protec-tion). Eq. (12) is valid for all scour hole types whereas Eq. (13)is valid for Type C and Type D.

Similarly, for the Z axis,

Zu ¼ z=z0m3Ds ð14Þ

Zd ¼ z=z00m3Ds ð15Þ

where Zu and Zd are the non-dimensional vertical coordinatesfor the upstream and the downstream parts of the scour holes,respectively, z is the dimensional vertical coordinate, z0m3Ds

and z00m3Ds are the maximum scour hole depths of theupstream and downstream scour holes respectively.z0m3Ds¼ zm3Ds except for Type D, where z00m3Ds¼ zm3Ds, as themaximum scour hole depth occurs downstream of theprotection. Original bed level was fixed as vertical origin. Allprofiles pass through Zu¼�1 and Zd¼�1 whereas Xu and Xd

range from 0 to 1.The generalized polynomial equation for scour hole profiles

is,

Zx ¼ A1X 4x þA2X 3

x þA3X 2x þA4Xx þA5 ð16Þ

where x¼ u for upstream profile and x¼ d for downstreamprofile. A1, A2, A3, A4 and A5 are the coefficients given in Table1 in terms of scour hole type and jet angle.

For Type A, Type B and Type C the maximum scour holedepth occurs upstream of the protection, whereas for Type D itoccurs downstream of it.

9. Prototype applications and recommendations

The previous findings can be applied to prototypes to deter-mine the main lengths of the scour hole geometry in presence ofa protection. Knowing the hydraulic and geometric site condi-tions, the same procedure may be adopted as for a 3D plungepool scour, as illustrated by Pagliara and Palermo (2008), toselect the efficient protection position and type. Generally,experimental tests showed that S8 protection has to be preferredover S to minimize scour hole depth. Moreover, it was observedthat if the protection is located close to the jet impact its effect ismore prominent, thus it has to be preferably located at j¼ 0.5.

10. Conclusions

This study deals with the 3D behavior of plunge pool scourin presence of two protections at selected positions, as anextension of the previous studies on 2D and 3D plunge poolscour. An analysis of the scour hole types was conducted. Inpresence of a protection the phenomenon becomes even morecomplex as the jet is deflected and five main scour hole typeswere observed: Type A, Type B, Type C, Type D and Type 0. Atypology was presented and the effects of flow and protection

parameters were highlighted. The proposed classificationpredicts the scour hole types if the main geometrical andhydraulic parameters are known, i.e., jet angle, structuralpermeability, tailwater level and protection position.

The main scour hole lengths were analyzed and relation-ships were proposed to predict them. These include themaximum dynamic scour hole depth, the maximum dynamicscour hole length, the maximum scour hole width and thedistance of the scour hole initiation point from the fictitious jetimpact point on the original bed material. Experimental testsshowed that S8 protection has to be preferred over S tominimize scour hole depth if located close to the jet impact.

The scour hole profiles were also analyzed and equationswere furnished to predict the profiles for each scour hole typeand tested jet angle.

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List of symbols

Ao: total opening area (holes in the protection);

At: total area of the protection;

b: channel width;

bm: scour hole width;

B: relative channel width b/D;

Bm: relative scour hole width bm/D;

d: particle diameter of basin material;

D: diameter of the jet;


Fd90: V/( g0d )1/2 densimetric Froude number;

g0: reduced gravitational acceleration, [(rs� r)/r]g;

ho: original water elevation over initial bed level;

la: scour hole length;

La: relative scour hole length la/D;

li: distance of the fictitious jet impact point on the original bed surface;

Li: relative distance of the fictitious jet impact point on the original bed

surface, li/D;

ls: longitudinal distance of the protection from the scour hole origin;

p: structural permeability;

Q: discharge;

Tw: tailwater, ho/D;

xo,xs: longitudinal coordinate of the scour hole origin and protection,

respectively;

Xu, Xd: non-dimensional longitudinal coordinate for upstream (u) and down-

stream (d ) part of scour hole profile, respectively;

zm: scour hole depth;

Zm: relative scour hole depth zm/D;

Zu, Zd: non-dimensional vertical coordinate for upstream (u) and downstream

(d ) part of the scour hole profile respectively;

a: jet angle (in degrees);

rs, r: specific gravity of sediment and water, respectively;

s: sediment non-uniformity parameter;

l: 3D factor, bm/b;

j: non-dimensional longitudinal position of the protection ls/la3D;

z: correction factor.

Subscripts

2D: two-dimensional;

3D: three-dimensional;

m: maximum (without protection);

s: with protection.

3d plunge pool scour with protection measures

Documents