Scour by jets in cohesionless and cohesive soils1

Kerry A. Mazurek and Tanvir Hossain

Abstract: A technique is developed in this paper to unify the methods of analyzing scour by turbulent water jets incohesionless and cohesive soils. Data from previous studies using circular turbulent impinging jets and circular turbu-lent wall jets are used to compare the scour in low void ratio cohesive soils to that in uniform sands and gravels.Scour by these jets is related to the dimensionless excess stress on the soil bed. It is seen that this parameter willlikely work well for developing a method to predict scour for circular wall jets that is applicable to both materials.However, a circular impinging jet appears to vary appreciably in its interaction with the bed between the two types ofsoil, which makes developing a unified method to predict scour by impinging jets more difficult.

Key words: erosion, scour, water jets, cohesionless sediments, cohesive sediments, fine-grained soils, coarse-grained soils.

Résumé : Cet article présente une technique développée pour unifier les méthodes d’analyse de l’affouillement par lesjets d’eau turbulents dans les sols cohésifs et non cohésifs. Les données d’études antérieures utilisant des jets d’eauturbulents après leur rencontre avec un obstacle et des jets de parois turbulents circulaires sont utilisées pour comparerl’affouillement dans les sols cohésifs à faible indice de vides à celui de sables et graviers uniformes. L’affouillementpar ces jets est associé à une contrainte excédentaire sans dimension sur le lit de sol. Il semble que ce paramètre fonc-tionnera probablement bien pour développer une méthode servant à prédire l’affouillement causé par des jets de paroiscirculaires et qui s’appliquera aux deux matériaux. Cependant, l’interaction entre l’écoulement d’un jet après sa ren-contre avec un obstacle et le lit semble varier beaucoup selon les deux types de sol, ce qui complique le développementd’une méthode unifiée pour prédire l’affouillement causé par l’écoulement d’un jet après sa rencontre avec un obstacle.

Mots-clés : érosion, affouillement, jets d’eau, sédiments non cohésifs, sédiments cohésifs, sols à grains fins, sols à grainsgrossiers.

[Traduit par la Rédaction] Mazurek and Hossain 751

Introduction

Predicting scour by flows in the form of turbulent waterjets is of considerable importance for the design of stablehydraulic structures such as dams, culverts, weirs, and drops.Most of the work in this area has been experimental becauseof the complexities of the turbulent jet flow and its interac-tion with the sediment bed. As well, most of these studieshave been carried out in cohesionless materials. Much lessattention has been focused on the scour by jets of cohesivesoils, although as little as 10% clay in a soil can make thesoil behave as cohesive (Raudkivi 1998). Except for a fewstudies of scour by jets such as those of Abt et al. (1984)and Stein et al. (1993), cohesionless and cohesive soils havegenerally been treated as two distinct materials.

The separate treatment of the two soil types is likely dueto two reasons. The first is that a cohesive soil may show anumber of different modes of erosion, as seen in Mazurek etal. (2001, 2003). Whereas a cohesionless soil erodes by theremoval of individual particles, a cohesive soil may erode bythe removal of individual particles or aggregates of particlesfrom the soil surface, called “surface erosion,” or by theintermittent removal of lumps or chunks of soil through failureof the bed under the soil surface, called “mass erosion”(Mehta 1991). The second is that the erosion resistance ina cohesive soil is difficult to predict based on simple des-criptors of the soil characteristics. The erosion resistance ofa cohesionless material depends primarily on the particlebuoyant weight, shape, and packing (Raudkivi 1998), whereasthe critical shear stress of a cohesive material depends on anumber of physical and electrochemical properties of thematerial and the chemistry and temperature of the erodingfluid (Paaswell 1973). These parameters mainly influencethe soil structure, which is the predominant control of theamount and form of erosion of the soil. Particle weight isnot considered to influence its erosion resistance.

This paper attempts to develop a technique to comparescour in cohesive and cohesionless soils in the hopes ofdeveloping a unified method of predicting scour by jets thatis applicable to all soils. Data from experiments by Mazurek(2001) on the scour in cohesive soils by circular impingingjets are compared with those on scour produced by circularimpinging jets in cohesionless soils from Aderibigbe andRajaratnam (1996) and Rajaratnam (1982) using a parameter

Can. J. Civ. Eng. 34: 744–751 (2007) doi:10.1139/L07-005 © 2007 NRC Canada

744

Received 1 January 2006. Revision accepted 8 January 2007.Published on the NRC Research Press Web site at cjce.nrc.caon 10 July 2007.

K.A. Mazurek2 and T. Hossain. Department of Civil andGeological Engineering, University of Saskatchewan, 57Campus Drive, Saskatoon, SK S7N 5A9, Canada.

Written discussion of this article is welcomed and will bereceived by the Editor until 31 October 2007.

1This article is one of several papers published in this SpecialIssue on Hydrotechnical Engineering, dedicated to Dr. N.Rajaratnam.

2Corresponding author (e-mail: kam597@mail.usask.ca).

based on the dimensionless excess shear stress on the bed. Asimilar technique is used to compare data from Mazurek etal. (2002) on the scour in cohesive soils by circular wall jetswith those on scour in cohesionless soils as found by Adeand Rajaratnam (1998) and Rajaratnam and Berry (1977). Ageneral discussion of the similarities in the characteristics ofscour by jets in the two types of soil is also given.

Characteristics of scour by circular impingingjets

For this discussion of scour by circular impinging jets, weassume that the jets are vertical, fully submerged, and set ata large impingement height. When a jet is at a largeimpingement height, it will be fully developed before itimpinges on the boundary or wall. For a jet of diameter d atthe nozzle (or origin), velocity at the nozzle U0, and heightabove the soil bed H, called the impingement height, the jetcan be considered to be at a large impingement height ifH/d > 8.3 (Beltaos and Rajaratnam 1977).

For scour by circular impinging jets in cohesionless soils,it is known that the main dimensions of the scour hole growin a linear relation with the logarithm of time until the scourhole nears asymptotic state (Rajaratnam 1982). At asymp-totic state, the change in scour depth with time becomesvery small and, for all practical purposes, the scour hole canbe said to have reached its final or ultimate size. The dimen-sions of the scour hole at asymptotic state depend on theratio of the densimetric Froude number Fr0 to the relativeimpingement H/d, where Fr U gD0 0

1 2� /( / ) /�� � , in which gis the acceleration due to gravity, D is the mean grain size ofthe sediment, � is the density of the fluid, and �� is thedifference in density between the sediment particle and thefluid.

Figure 1a shows a typical scour hole shape created by acircular impinging jet in a cohesionless bed of uniform sand.The maximum depth of scour occurs along the jet centreline,and a mound of sand forms around the scour hole. The scourholes can be narrow and deep, called the strongly “deflectedjet” regime, or wide and shallow, called the “weakly de-flected jet” regime, depending on Fr0 /(H/d) (Aderibigbe andRajaratnam 1996). If Fr0 /(H/d) > 0.35, the jet will be stronglydeflected (Aderibigbe and Rajaratnam 1996). In the stronglydeflected jet regime (SD), the jet turns back on itself andthere is a lot of sediment suspended in the scour hole withinthe flow. Upon cessation of flow, these sediments settle outof suspension and fill in the scour hole. Thus for this regime,the dynamic scour depth, which is the scour depth observedwith jet flow, is significantly greater than the static scourdepth, which is observed when the jet flow is stopped. Forthe weakly deflected jet regime (WD), there is much lesssuspension of sand within the scour hole and the differencebetween the dynamic and static scour depths is small. Itshould be noted that the dynamic maximum scour depthcan be difficult to measure due to the suspended sediment.Aderibigbe and Rajaratnam (1996) simply used a rod to feelfor the bottom of the scour hole, and thus the dynamic scourdepth values are somewhat approximate.

Although the jet behavior might be classified into thesetwo regimes, the scour hole profiles are similar. Aderibigbe

and Rajaratnam (1996) successfully developed a dimension-less scour profile using the maximum depth of scour �m asthe scale for the scour depth � and the half-width b as thescale for the radial distance from the jet centreline r, givenby

[1]�

�m

� � �

��

�

�

��

�

���

exp .0 6932

rb

The half-width b is the radial distance r where � � �m / 2(refer to Fig. 1a).

For scour by circular impinging jets in cohesive material,the main dimensions of the scour hole also grow in a linearrelation with the logarithm of time (Mazurek 2001). How-ever, there will be sudden jumps in the scour depth that areassociated with the erosion of large chunks of soil (Mazurek2001). Figure 1b shows a typical scour hole formed in afine-grained cohesive soil. The maximum depth of scour isnot necessarily along the jet centreline. No mound formsaround the edge of the scour hole. The scour hole is narrowand deep or wide and shallow, but no material stayedsuspended within the jet flow in the scour hole becausethe eroded particles were easily removed by the flow. Thedynamic and static scour depths are the same.

For cohesive soils, Mazurek (2001) found the main dimen-sions of the scour hole at asymptotic state can be shownto be a function of the parameter (X – Xc)/Xc, where X isthe erosion parameter for cohesive soils for impinging jets(= �U0

2(d/H)2), and Xc is the critical value of X below whichmass erosion is not observed. The parameter X can berelated to the maximum shear stress on the bed at the start oferosion �om using the equation for bed shear stress developedby Beltaos and Rajaratnam (1974):

[2] � �om � �

��

� �0 16 0 160

22

. .UdH

X

Equation [2] assumes that the bed is smooth, which is areasonable assumption for fine-grained soils such as clays.

Unified analysis for scour by circularimpinging jets

To develop a technique to directly compare scour bycircular impinging water jets in cohesionless and cohesivesoils, let us follow Stein et al. (1993) and Hogg et al. (1997)and use the dimensionless excess shear stress (�o – �c) / �c todescribe the potential for erosion of a particular jet flow,where �o is the shear stress on the bed, and �c is the criticalshear stress of the soil. For an impinging jet, �o varies greatlywith the distance from the jet centreline r, and therefore anappropriate value for �o must be chosen. For �o, the maxi-mum shear stress on the bed �om that occurs for the initialexperimental conditions will be used (i.e., flat bed). There-fore, (�o – �c) / �c becomes (�om – �c) / �c. Note here that, althoughthe densimetric Froude number Fr0 is frequently used to pre-dict scour in cohesionless soils, it will not work for cohesivesoils. Fr0 represents the ratio of the shear stresses on the bed(the forces causing erosion) to the buoyant weight of the par-ticle (the resistance to erosion) (Aderibigbe and Rajaratnam

© 2007 NRC Canada

Mazurek and Hossain 745

1996). For cohesive soils, particle weight does not contrib-ute to erosion resistance.

For the analysis for cohesionless sediments, the data fromRajaratnam (1982) and Aderibigbe and Rajaratnam (1996)are used. In the Aderibigbe and Rajaratnam experiments, asand and a gravel were used of average grain size D of 0.88or 2.42 mm, H varied from 1.5 to 523 mm, d varied from 4to 19 mm, and U0 varied from 2.65 to 4.45 m/s. For theRajaratnam (1982) experiments, D was 1.20 or 2.38 mm,H was 149.2–279.4 mm, d was 9.8 mm, and U0 was 2.99–4.60 m/s. For the present work, �c was calculated for thesesands using the equations that approximate the Shields curvepresented in Julien (1998).

To estimate �om for the experiments with the cohesionlesssediments, eq. [3] was developed from bed shear stress mea-surements from experiments on rough, rigid beds presentedin Rajaratnam and Mazurek (2005):

[3]��

om s s

UHd

kH

kH0

2

2 2

37 6 0 505 0�

��

� � � �

��

� � �

��

� �. . .72

with a coefficient of determination R2 = 0.69. In eq. [3], ks isthe equivalent sand roughness of the bed. In Rajaratnam andMazurek, it was shown that the dimensionless maximum bedshear stress (expressed in the form given in eq. [3]) depen-ded only the relative roughness ks / H, but no correlation wasdeveloped. The correlation found in eq. [3] is somewhat low,likely due to the difficulties in measuring bed shear stress ona rough bed. For the present analysis, to determine ks it wasassumed that ks � 2D as suggested by Yalin (1977).

The results of Mazurek (2001) are used for the analysis ofcohesive sediments. Mazurek used an apparatus that wasalmost identical to that of Aderibigbe and Rajaratnam(1996) for tests of scour by circular impinging jets in a lowvoid ratio cohesive soil of 40% clay (kaolinite and illite),53% silt, and 7% fine sand. In these experiments, U0 rangedfrom 4.97 to 25.90 m/s, d was 4 or 8 mm, and H rangedfrom 40 to 116 mm. In these tests, the soil eroded mostlyby mass erosion in small to large chunks from about 2 to140 mm in size. For the present analysis of these data,eq. [2] was used to determine �om. For �c, Mazurek found forthe soil tested that �c = 48 Pa. This was determined experi-mentally by slowly increasing the jet velocity until erosionoccurred; the jet velocity was related to the maximum bedshear stress using eq. [2].

In Figs. 2 and 3, the dimensionless maximum scour depth�m / H and radius of scour ro / H are plotted against (�om –�c) / �c, where ro is the radius of the scour hole. This scalingfollows Aderibigbe and Rajaratnam (1996) and Mazurek(2001). The data are divided into soil type and classified byflow regime (strongly deflected (SD) or weakly deflected(WD)). For the cohesionless sediments, the dynamic scourdepths are used because the cohesive sediments do not ex-hibit a static scour depth. The radius of the scour hole is forstatic scour, however, as the dynamic value for the scourhole radius was not reported by Aderibigbe and Rajaratnam(1996) or Rajaratnam (1982). Figures 2 and 3 show thateq. [3] slightly underestimates the shear stress on the bed forthe cohesionless sediments, as there are small negativevalues for (�om – �c) / �c. These negative values might also bedue to an overestimation of �c, since estimating �c using theShields curve gives only approximate values.

It appears in Fig. 2 that the values for maximum scourdepth do not differ significantly between the two materials atlower values of (�om – �c) / �c, which correspond to the weaklydeflected jet regime. At higher values of (�om – �c) / �c, whichcorrespond to the strongly deflected jet regime, the maxi-mum scour depth for the cohesive materials appears to begreater than that for the cohesionless sediments. This is likelybecause there is a lot of sediment suspended within thescour hole for the cohesionless sediments in the stronglydeflected jet regime. Scour depths are reduced becauseof the faster decay of the jet due to the suspended sand(Aderibigbe 1996).

Figure 3 shows that the radius of the scour hole for thecohesive soils experiments is always greater than that for thecohesionless soils. This may be because the radius measure-ments for the cohesionless soils are for the static scour case,where some sand may settle back out of the flow to fill thescour hole. It may also be a function of the strongly andweakly deflected jet behavior, as the wide deep scour holesproduced in a weakly deflected jet regime for cohesive sedi-ments are being compared to the narrow deep scour holesproduced by a strongly deflected jet for the cohesionlesssediments.

For the experiments with the cohesive soil, Mazurek (2001)found the scour hole profiles were similar in shape using thesame scales to nondimensionalize the profile as those usedby Aderibigbe (1996) for sand. In Fig. 4, it is seen thateq. [1], which describes the dimensionless scour profile for

© 2007 NRC Canada

746 Can. J. Civ. Eng. Vol. 34, 2007

Fig. 1. Definition sketch for scour by circular impinging jets in (a) cohesionless soils and (b) cohesive soils. �cl, scour depth at jetcentreline.

cohesionless soils, fits the data for the experiments for thecohesive soil well, except for r/b > 1.5. Since the dimen-sionless scour hole profiles for the two soil types are similar,the scale for the dimensionless profile, the half-width b, wasalso compared for the two soil types as shown in Fig. 5. It isseen that b is larger for cohesive materials. This again mightbe expected because the cohesive material is more likely tobe in the weakly deflected regime for the same (�om – �c) / �c,where the scour holes are wide and shallow.

It appears for impinging jets that relating scour in cohe-sive to cohesionless soils might not work well using thepreviously described method. Modifications to account forchanges in jet decay within the scour hole with increasingamounts of suspended sediment are likely needed. The jetdecay is also known to be affected by the shape of the scourhole (Rajaratnam et al. 1993), and this might also need to beconsidered.

Characteristics of scour by circular wall jets

For this discussion of scour by circular wall jets, weassume that the jet is deeply submerged and set to flowparallel to the bed at no vertical offset from the bed. Forcohesionless materials, the typical scour hole profile is sketchedin Fig. 6. The scour holes are similar in shape (Rajaratnamand Berry 1977). As for impinging jets, the maximum depthof scour and other significant length scales of the scour holevary linearly with the logarithm of time until the scourholes near asymptotic state (Rajaratnam and Berry 1977). Aswell, the characteristic dimensions of the eroded bed, such asthe maximum scour depth �m, the distance to the maximumdepth xm, and the length of the scour hole xo, have beenshown to depend primarily on the densimetric Froude num-ber Fr0 (Rajaratnam and Berry 1977; Ade and Rajaratnam1998).

The typical scour hole shape for fine-grained cohesivematerials seen by Mazurek et al. (2002) is shown in Fig. 7.Mazurek et al. found that the scour hole dimensions atasymptotic state could be related to the parameter (� –�c) / �c, where � is the erosion parameter for cohesive soilsfor circular wall jets (= �U0

2), and �c is the value of � belowwhich no erosion occurs. The parameter � can be related to

the shear stress on the bed by an equation in the form �o =cf � / 2, where cf is the skin friction coefficient.

Unified analysis for scour by circular wall jets

To develop a unified method of predicting scour by circu-lar wall jets, we again relate the scour hole dimensions tothe dimensionless shear stress on the bed (�o – �c) / �c. Datafrom Rajaratnam and Berry (1977) and Ade and Rajaratnam(1998) are used for the analysis for cohesionless sediments.In the experiments of Ade and Rajaratnam, the velocity U0varied from 2.2 to 5.5 m/s, and the nozzle diameter d was5.0, 19.0, or 25.4 mm. A sand and a gravel were tested. Thesand had an average grain size D of 0.242 mm, with a geo-metric standard deviation �g = (D84/D16)

1/2 = 1.46, where Diis the grain diameter at the ith percent passing. A value �g >1.35 indicates the material is just outside the range where itcan be considered a uniform sand (Breusers and Raudkivi1991). The gravel had a D = 7.2 mm and �g = 1.33. Rajaratnamand Berry used one sand of D = 1.4 mm, one nozzle diameterof 25.4 mm, and U0 = 1.28–1.81 m/s.

To estimate the bed shear stress �o for the experimentswith cohesionless sediments, we use the results from theexperiments of Wu and Rajaratnam (1990) on the behavior ofcircular wall jets on rough, rigid beds. Wu and Rajaratnamgive the variation of bed shear stress with distance from thenozzle for varying wall roughness. However, their equationsare valid for x/d > 10, where x is the distance along thelength of flow from the origin of the jet at the nozzle. Thebed shear stress �o is given by

[4] � �o f

m� cu2

2

where cf is the local skin friction coefficient, � is the densityof the fluid, and um is the maximum velocity at the given xdistance (x /d = 10) away from the nozzle. The skin frictioncoefficient cf is a function of the relative roughness ks /d andwas determined using the equations given in Wu andRajaratnam. For this analysis, as indicated earlier, it isassumed that ks = 2D. To calculate �c for the sediments usedin Rajaratnam and Berry (1977) and Ade and Rajaratnam(1998), the equations given in Julien (1998) are again used.

© 2007 NRC Canada

Mazurek and Hossain 747

Fig. 3. Radius of scour hole for circular impinging water jets incohesive and cohesionless soils.

Fig. 2. Maximum depth of scour for circular impinging waterjets in cohesive and cohesionless soils. SD, strongly deflected jetregime; WD, weakly deflected jet regime.

The data from Mazurek et al. (2002) are used for thecohesive sediments. In these experiments, two clays weretested. The first was made up of 37% clay, 48% silt, and15% fine sand and had a critical shear stress of 42 Pa. Thesecond was made up of 33% clay, 38% silt, and 15% fine

sand and had a critical shear stress of 52 Pa. These values of�c were measured experimentally by noting the velocity atwhich (mass) erosion first occurred. The mineralogy of theclay in both materials was shown to be made up of kaoliniteand illite. In the experiments, U0 = 2.98–15.62 m/s and dwas 4.90, 5.97, or 12.18 mm.

The experimental work of Rajaratnam and Pani (1974) onthe behavior of circular wall jets on smooth, rigid beds wasused to estimate �o for the cohesive soil experiments. Thebed shear stress �o can be calculated from (Rajaratnam andPani 1974)

[5] � �o f

0� CU2

2

where Cf is the global skin friction coefficient. Rajaratnamand Pani plotted Cf with the dimensionless distance x / d.From this work, it is found that the global skin frictioncoefficient is Cf = 0.003 at a distance of x / d = 10.

© 2007 NRC Canada

748 Can. J. Civ. Eng. Vol. 34, 2007

Fig. 5. Half-width for scour by circular impinging jets in bothcohesionless and cohesive soils.

Fig. 4. Scour profiles from experiments in cohesive soils from Mazurek (2001), with dimensionless profile used for cohesionless soils.

Fig. 6. Sketch of scour hole created by circular wall jets in sand.

Fig. 7. End view of typical scour hole shape for a cohesive soil(width of sample is 170 mm).

A plot of a comparison of the maximum depth of scour,given in dimensionless form as �m /d, produced by circularwall jets in cohesionless and cohesive sediments is shown inFig. 8. The dimensionless distance to the maximum scourdepth xm and the length of the scour hole xo are shown inFigs. 9 and 10, respectively. Although there are not a lot ofdata in an overlapping range of (�o – �c) / �c, the figures showthat the maximum depth of scour and its location are similarin cohesive and cohesionless soils. However, the scour holeis longer for cohesive materials. This is likely because thereis no mound formation at the end of the scour hole for cohe-sive materials, which would change the dynamics of the jetflow at the end of the hole.

Use of the developed method to estimatescour in practice

As an example of how the unified method of assessingscour as presented earlier might be used in practice, we dis-cuss how one might estimate scour downstream of a circularculvert using the method. If the culvert is not set at an offsetfrom the bed, the scour below the culvert can be modeledclosely as scour by a circular wall jet. For a soil that is notfissured, one would (i) determine the average velocity offlow at the culvert outlet; (ii) determine the average grainsize of the bed and then relate this to the bed roughness ksby ks � 2D (if the material is fine grained (clay-size parti-cles), assume the bed is smooth); (iii) use the velocity offlow, bed roughness, and diameter of the culvert to deter-mine the shear stress �o created by the flow on the bed at adistance x/d = 10 (if the bed is smooth, use eq. [5] with Cf =0.003; if the bed is rough, use eq. [4] and estimate cf usingthe equations presented in Wu and Rajaratnam (1990) thatrelate cf to ks /d); (iv) estimate the critical shear stress �c forthe soil (use the Shields curve for cohesionless materials orthe equations that approximate the curve such as those pre-sented in Julien (1998); for cohesive material, it is recom-

mended that �c be determined using a field measurementtechnique such as the impinging jet test of Hanson and Cook(2004)); (v) express �o and �c in terms of the dimensionlessexcess stress (�o – �c) / �c; and (vi) use Figs. 8–10 to obtainestimates for the size of the scour hole.

It is noted here that the described technique still needs tobe verified with additional experimental data.

Discussion and conclusions

The results from experiments in the scour by circular im-pinging water jets and circular wall jets in cohesionless andcohesive soils were compared using a parameter in the formof a dimensionless excess stress. It was seen that this methodmight not work well for predicting scour in these materialsby impinging jets because of differences in the interaction ofthe impinging jet within the sediment beds for each material.

© 2007 NRC Canada

Mazurek and Hossain 749

Fig. 8. Dimensionless maximum scour depth for circular walljets.

Fig. 9. Dimensionless distance to the maximum scour depth forcircular wall jets.

Fig. 10. Dimensionless length of scour hole for circular walljets.

For circular wall jets, however, it appears this method mightwork well to predict scour in these soils, as the maximumscour depth and location were similar for both materials.The length of the scour hole was greater in cohesive, fine-grained materials, likely due to the lack of mound formation.To better evaluate this method, more experiments should beperformed at lower shear stress ranges for the cohesionlesssediments and higher shear stress ranges for the cohesivesediments. Also, further study is needed to better understandthe bed shear stresses created by jet flow over rough beds.

Acknowledgements

The authors gratefully acknowledge the financial supportof the Natural Sciences and Engineering Research Councilof Canada for this project in the form of a Discovery Grantto the first author. The authors also acknowledge the helpfulcomments of the reviewers.

References

Abt, S.R., Kloberdanz, R.L., and Mendoza, C. 1984. Unified scourdetermination. Journal of Hydraulic Engineering, 110(10): 1475–1479.

Ade, F., and Rajaratnam, N. 1998. Generalized study of erosion bycircular horizontal turbulent jets. Journal of Hydraulic Research,IAHR, 36(4): 613–635.

Aderibigbe, O.O. 1996. Contributions to erosion by jets. Ph.D.thesis, Department of Civil Engineering, University of Alberta,Edmonton, Alta.

Aderibigbe, O.O., and Rajaratnam, N. 1996. Erosion of loose bedsby submerged circular impinging jets vertical turbulent jets.Journal of Hydraulic Research, IAHR, 34(1): 19–33.

Beltaos, S., and Rajaratnam, N. 1974. Impinging circular turbulentjets. Journal of the Hydraulics Division, ASCE, 100(HY10):1313–1328.

Beltaos, S., and Rajaratnam, N. 1977. Impingement of axisym-metric developing jets. Journal of Hydraulic Research, IAHR,15(4): 311–327.

Breusers, H.N.C., and Raudkivi, A.J. 1991. Scouring. A.A. Balkema,Rotterdam.

Hanson, G.J., and Cook, K.R. 2004. Apparatus, test procedures,and analytical methods to measure soil erodibility in situ.Applied Engineering in Agriculture, 20(4): 455–462.

Hogg, A.J., Huppert, H.E., and Dade, B.W. 1997. Erosion by planarturbulent wall jets. Journal of Fluid Mechanics, 338: 317–340.

Julien, P.Y. 1998. Erosion and sedimentation. Cambridge Univer-sity Press, New York, N.Y.

Mazurek, K.A. 2001. Scour of clay by jets. Ph.D. thesis, Depart-ment of Civil and Environmental Engineering, University of Al-berta, Edmonton, Alta.

Mazurek, K.A., Rajaratnam, N., and Sego, D.C. 2001. Scour ofcohesive soil by submerged circular turbulent impinging jets.Journal of Hydraulic Engineering, 127(7): 598–606.

Mazurek, K.A., Liu, Y., and Rajaratnam, N. 2002. Scour of cohe-sive material by circular wall jets. In Proceedings of the 16thHydrotechnical Conference of the CSCE, Burlington, Ont. CD-ROM. Canadian Society for Civil Engineering, Montréal, Que.pp. 1–12.

Mazurek, K.A., Rajaratnam, N., and Sego, D.C. 2003. Scour of acohesive soil by submerged plane turbulent wall jets. Journal ofHydraulic Research, IAHR, 41(2): 195–206.

Mehta, A.J. 1991. Review notes on cohesive sediment erosion. InCoastal Sediments ’91: Proceedings of a Specialty Conferenceon Quantitative Approaches to Coastal Sediment Processes,Seattle, Wash., 25–27 June 1991. Edited by N.C. Kraus, K.J.Gingerich, and D.L. Kriebel. American Society of Civil Engi-neers, New York, N.Y. Vol. 1, pp. 40–53.

Paaswell, R.E. 1973. Causes and mechanisms of cohesive soilerosion: state of the art. In Soil Erosion: Causes and Mecha-nisms, Prevention and Control: Proceedings of a Conference–Workshop, Washington, D.C., 26 January 1973. Special Report135, Highway Research Board, National Research Council,Washington, D.C. pp. 52–74.

Rajaratnam, N. 1982. Erosion by submerged circular jets. Journalof the Hydraulics Division, ASCE, 108(HY2): 262–267.

Rajaratnam, N., and Berry, B. 1977. Erosion by circular turbulentwall jets. Journal of Hydraulic Research, IAHR, 15(4): 277–289.

Rajaratnam, N., and Mazurek, K.A. 2005. Impingement of circularturbulent jets on rough boundaries. Journal of Hydraulic Research,IAHR, 43(6): 688–694.

Rajaratnam, N., and Pani, B.S. 1974. Three dimensional turbulentwall jets. Journal of the Hydraulics Division, ASCE, 100(HY1):69–83.

Rajaratnam, N., Johnston, G.A., and Barber, M.A. 1993. Energydissipation by jet diffusion in stormwater drop shafts. CanadianJournal of Civil Engineering, 20: 374–379.

Raudkivi, A.J. 1998. Loose boundary hydraulics. A.A. Balkema,Rotterdam.

Stein, O.R., Julien, P.Y., and Alonso, C.V. 1993. Mechanics of jetscour downstream of a headcut. Journal of Hydraulic Research,IAHR, 31(6): 723–738.

Wu, S., and Rajaratnam, N. 1990. Circular turbulent wall jets onrough boundaries. Journal of Hydraulic Research, IAHR, 28(5):581–589.

Yalin, M.S. 1977. Mechanics of sediment transport. 2nd ed. PergamonPress, New York, N.Y.

List of symbols

b half-width of scourcf local skin friction coefficientCf global skin friction coefficientd jet diameterD average grain sizeDi diameter at the ith percent passing

Fr0 densimetric Froude numberg gravitational accelerationH impingement height (height of jet above original bed

level)ks equivalent sand roughnessr radial distance from jet centreline

ro radius of scour holeR2 coefficient of determinationum maximum velocity of jetU0 velocity of jet at the nozzle

x distance from the jet origin along the length of flowxm distance from the jet origin to the maximum depth of

scourxo length of scour holeX erosion parameter for cohesive soils for impinging jets

Xc critical value for erosion parameter X� scour depth

�cl scour depth at jet centreline

© 2007 NRC Canada

750 Can. J. Civ. Eng. Vol. 34, 2007

�m maximum scour depth� erosion parameter for cohesive soils for circular wall

jets�c critical value for erosion parameter � for cohesive soils

for circular wall jets� density of eroding fluid

� � difference in density between sediment particle anderoding fluid

�g geometric standard deviation of grain size of sediment�c critical bed shear stress�o bed shear stress

�om maximum bed shear stress

© 2007 NRC Canada

Mazurek and Hossain 751