ERODIBILITY CRITERION FOR AUXILIARY SPILLWAYS OF ...

ERODIBILITY CRITERION FOR AUXILIARY SPILLWAYS OF DAMS

Hendrik A. D. Kirsteni, John S. .loore2. Louis H. Kirsten3 and Dart-el M. Temple4

ABSTRACTThe abilit y to reliably design auxiliary spillwavs has become a pressing requirement because of the very

large number of dams involved, An empirical classification index representing the erosional resistance ofthe overall ran ge of particulate. jointed, and intact earth materials is presented and correlated for a numberof practical cases from Arkansas and Kansas in the L nited States of America and from South Africa withthe speifle stream power of flows observed to be associated with various degrees of erosion. The UnitedStates Department of A griculture data base and the format in which the data were prepared for thepurposes herein, are described in detail. The modes of erosion that occur in spillways are defined.Guidelines are provided for evaluating the failure status of an erosion damaged spillway that enablesdetermination of whether the incident specific stream power exceeded, equalled, or fell below theerosional resistance of various sections of the ground profile affected. The correlation function betweenspecific stream power and erodibility index provides the required design criterion.

Key Words: Auxiliary spillway, Erosional resistance. Erodibiiiry index. Stream power

I INTRODUCTIONDams have been desi gned traditionally not to be overtopped during probable maximum flood events.

According to Powledge et. at, (1989), many tens of thousands of dams have, however, become potentiallysubject to overtopping as a result of improvements in the quality of flood data and in the methods fordetermining probable maximum floods for which it is not possible nor economically feasible to considermodifications to prevent overtopping. Some dams have moreover been observed to have withstoodmoderate overtopping. Efforts have as a result been concentrated in recent years on the accuratedetermination of the erodibility of natural ground in auxiliary spillways as a first step in the provision oflow cost modifications to the many dams threatened by overtopping.The Agricultural Research Service (ARS) and Soil Conservation Service (SCS), now known as Natural

Resources Conservation Service (NRCS), U.S. Department of Agriculture (USDA), has accordinglycollected a substantial body of data on erosion performance of earth spillways since 1983, Temple et. al.(1993). The data cover a range of materials from soils through rocks of varying lithology, structure, andstrength. The spillways represent a variety of widths, lengths, and gradients, in each of which thesuccessive reaches comprised engineered and natural surfaces. The engineered surfaces were either bareof vegetation or were covered with cultivated sod. The natural surfaces generally contained brush andgrassland vegetation. The erosion performance of the spillways could be divided into three classes, viz.,situations in which the flows exceeded, matched, or fell below the erosional resistance of the material.The data represent dams in II states and were collected for the general purpose of evaluating theeffectiveness of current design criteria and for recommending improvements in this regard. A specificobjective was to determine the advance rate of headcutting in earth spillways.Moore et. al. (1994) demonstrated in an initial evaluation of the data that it was feasible to develop a

criterion for the onset of erosion in terms of stream power and the classification index for ripabilitydeveloped by Kirsten (1982). The data for Arkansas and Kansas have since been evaluated in moredefinitive detail. A general classification system for hydraulic erosion has in addition been developed byKirsten et. al. (1995).

1 Steffen. Robertson. and Kirsten. Inc.; Box 55291, Northlands 2116, S. Africa2 Natural Resources Conservation Service, USDA, Box 2890, Washington, DC 200133 Civil & Structural Engineering Dept., Iscor Mining, Pretoria, S. Africa4 Agricultural Research Service, USDA, 1301 N. Western St., Stillwater, OK 74075Note: The manucript of this paper was received in mach 1999, Discussion open until March 2001.International Journal ot'Sediment Research, Vol. 15, No. 1. 2000, pp. 93-107 -93 -

The main objective in this paper is accordingly to present the format in which the field data were recastFor the purposes of the more definitive evaluation referred to. An additional objective is to present acorrelation between the specitic stream power and erodibility index for the spillways in the two states

referred to. to gether with that for spillways in hard rock in South Africa.The USDA data base is reiewed with regard to the number and size of dams, hazard class. spillway

configuration and desi gn criteria. The format in terms of which the data for Arkansas and Kansas wererecast is described briefly. The modes of erosion that occurred are defined in principle. The failurestatus of the ground profiles exposed during erosion is evaluated. The formulation of the erodibilityindex is briefly presented. The determination of erodibility classes for the spillways in the to states is

described.The definition of specific stream power for channel flow is briefly reviewed together with an evaluation

of various definitions of stream power currently in use for other purposes in river eneineering.Determination of specific stream power for the flows in the spillways considered, is presented. The plot

of specific stream power a gainst erodibility index is presented and compared simultaneously ith datafrom various other modes of hydraulic comminution for a range of materials.

2 USDA DATA BASEThe data base may be reviewed briefly as follows in terms of size, hazard class, a ge, and spillway

configuration of the dams and with regard to various aspects of design.

2.1 Number of damsThe NRCS pursues a broad range of programs in which dams form an integral part of the conservation

systems implemented. Most of the dams are constructed as single- or multi-purpose structures for floodwater retarding and storm water management, storage of water for livestock, recreation facilities, fishponds, wildlife habitat, irrigation, grade stabilization of gullies, and sediment control. A few dams havebeen built for municipal and industrial purposes and for hydraulic power generation.According to a recent estimate a total of 24,822 dams have been installed in the past 60 years with

assistance from the NRCS (Federal Emergency Management Agency [FEMA],1997). A dam wasdefined as any artificial barrier that impounds or diverts water, exceeds 25 ft. 7.6 m, in height, has a

capacity greater than 50 ac-ft, 30,800 m3 , or classifies as high hazard (FEMA, 1997). Although theNRCS provides technical assistance to project sponsors in the form of planning, design. constructionmanagement, and financial assistance, the agency does not own, operate, or maintain any dams.

2.1 Hazard and age of damsAccording to the hazard classification defined by NRCS, (SCS, 1985), 84 percent of its inventory

classifv as low hazard, 8 percent as significant hazard, and 8 percent as high hazard installations.Twenty-one percent were constructed before 1960, 43 percent in the 1960's, 30 percent in the 1970's and6 percent since the 1980's. Older dams are not necessarily the more hazardous. The rate at which newdams have been constructed has evidently declined in recent years. Only 160 new dams have been builtin the last seven years. The weighted average age of NRCS designed dams is somewhat more than 30years, which compared to the average design life of 50 years, implies that most of the dams have enteredthe second half of their expected life.

2.3 Size of damsUnpublished NRCS data from a 1990 inventory show that 9 dams exceed 150 ft. 46 m, in height,

compared to an average height of 30 ft. 9.1 m, and compared to a height of less than 40 ft. 12 m. for 883percent of the dams. The volume of earth fill in 39 of the dams exceeds 1.0 million yd'. 760.000 m.

compared to an average volume of fill of 60,500 yd, 46,300 m', and compared to a volume of fill of lessthan 46.300 yd, 38.200 m. for 75 percent of the dams. Thirty-four reservoirs have storage capacitiesexceeding 25.000 ac-ft, 31 x 10 6 m 3 , compared to an average capacity of 676 ac-ft. 834.000 m', andcompared to a capacity of less than 1,000 ac-ft. 1.23 x 106 m 3 , for 84 percent of the dams. There are

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sites of which the drainage area exceeds 100 mi 2 , 940,000 ha. compared to an avera ge area of 3.6 mi,940 ha, and compared to an area less than 5 mi, 1,300 ha, for 89 percent of the dams.

2.4 Configuration and protection of spillway systemsNearly all of the dams desi gned by NRCS include auxiliary spilla systems to safely convey flood

flows around the installations. The spillways typicall y comprise a broad trapezoidal channel with inlet.control, and exit sections.The channels are excavated in natural ground in one or both abutments. Approximately 80 percent of

the systems are vegetated and less than I percent are structurally protected with concrete linin gs. Twopercent of the spillways are excavated entirely in rock, the remainder largely comprising compositechannel beds of rock and other earth materials.The spillways are usually located in topographic saddles or other favourable natural features that

provide a maximum bulk of material a gainst breaching of the spillway by the freeboard hydrograph. Thespillways may be curved, provided the return flows will not impinge on the dams, should the channelsfail at the curve..The spillways may release the discharge at the breakpoint where it intersects the natural hill slope or it

may be graded to the valley floor so as to contain the discharge on the natural slope above the floodplain.Most of the spillways exit to hill slopes, a situation that may give rise to considerable erosion below thebreakpoints where the streams are incident on the downhill slopes.

2.5 Design flowMost of the spillway channels are designed to operate in the 25- to 100- yr storm recurrence interval.

Since the 1950's, approximatel y 5 percent of NRCS constructed dams have experienced spillwa y flows,some more than once. More than 1500 spillways flows have been reported. Of these, most of thereservoir heads were less than 3 ft, I m, and little or no damage was observed (Ralston and Brevard,1988).

2.6 Spillwa y design approachBoth the hydraulic characteristics and structural competence of the spillways are considered in designs

carried out by NRCS. Conventional methods are used for the h ydraulic design to ensure stable flowcondition.,. As far as structural competence is concerned, the occurrence of some erosion or scour isaccepted pro'. ided it is expected to be infrequent, maintenance facilities are available, and the spillwaywould not he breached during passage of the freeboard flood. A threshold level of erosion for a givendesign flood f relatively low recurrence interval is used for this purpose.

out.

CS formed the Auxiliary Spillway Flow Study Task Group to conduct on-site evaluations of.jected to flows. Field studies were conducted jointly with researchers from the Plant

Water Conservation Laboratory , ARS, USDA, Stillwater, OK, and occasionally withs of the US Army Corps of Engineers. The objectives of the team included documentingtTected spillway performance for every flow event, evaluating the etiectiveness of currentn criteria, and submitting recommendations for improving design criteria and technical

;isited some 125 spillway sites in 11 states, viz., in Arkansas, Kansas, Kentucky, Mississippi,ia, Virginia, Oklahoma, Texas, Michigan, Indiana and Missouri representing 14 flood events.

chosen for evaluation that had been subjected to reservoir heads in excess of 3 ft, 0.9 m, or toions exceeding seven days, or to significant erosion damage to the spillway channels. A

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2.7 Co -r of data baseNRC:d collecting information on performance of earth spillways in 1957. Until 1983, the detail of

the in:r.n was limited in principle to the flow parameters and erosion damage that could be readilyobtained-built records were relied on for the required detail because on-site investigations wererarely c:

In 198Sspillwa'Sciencereprese;factorsNRCSguidelir

The tz.West \Sites vflow c

particular region may occasionally experience dozens or even hundreds of spillway flows during thepassage of a single storm system. In these instances the team visited only those sites that were expectedto provide new or essential information on spillway performance.

3 DATA FORMATThe data for 16 dams in Arkansas and 29 dams in Kansas were prepared in various categories as shown

typically for a particular site referred to as WFPR in Arkansas in Tables I through 6. Abbreviations inthe tables are defined under Nomenclature. Longitudinal shapes of the spillways before and after erosionare typically illustrated in Figure I. Categories referred to in Tables I through 6 comprise information onthe site location, general topography of the dam and surrounding terrain, flood flow, (2eometry, vegetation,geology, geological structure, and erosion damage sustained on each of the successive reaches. Theinformation enabled the erodibility index and specific stream power to be calculated at various points

along the spillway as illustrated in Tables 7 and S.REACH

a) BEFORE EROSION1.2.

REACH

I

NUMBER

4.(ii) & (lii)

(I) FORWARD EROSIONNb) AFTER EROSION

"T Ji,-KNIO(lNT EROSION

(iv)DATA POINT NUMBER

HEADCUT EROSION""JET EROSiONDIREMON OF

FORWARD EROSION4.

'REVERSEGRADIENT EROSION

Fig. 1 Illustration of longitudinal shape of spillway at WFPR, AK,Before and after erosion damage

Table I General Geometric and Flow Data for Spillway at WFPR, ArkansasElevationsSpillway crest (m) 165.6End exit reach (m) 164.4Floodplain (m) 136.7FlowDepth (m) 1.3Width (m) 26.2Rate (cms) 38.52Unit rate (cms/m) 1.47

Table 2 Geometric Data for Various Reaches for Spillway at WTPR. ArkansasReach 123 4

Length (m)36.518.262.073.0Gradient (%)-2.00.01.918.0Surface typeengengengnat

Shape strstrstrnatNote: engengineered; natnatural, strstraight

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Table 3 Data on Vegetation on Various Reaches for Spillwav at WFPR. ArkansasReach 2 3 4Type cover cultNatStand -VrdDensity/cover fair-CI;CF 6: 0.5-Irreg/discont. nonenoneType; species trs: -vdd: -Growth habit bncliSpaced (m) - -Root depth (m) -

Note: cultcultivated vrdvarieJ grsrass, wdd = ooded. bnch=bunch

Topographic data in Table 1 comprise entries on elevations of the spillwa y crest, end of exit reach andfloodplain. Flood data include depth. width, and 'rate of flow at key locations. Data on the spillwaygeometry, given in Table 2, include detail on length, gradient, and shape in plan, and the natural orconstructed nature of the surface of each reach. Table 3 gives information on the ty pe. variability, density,uniformity, species, growth habit, plant spacing and root depth of the vegetal cover.Information on geology in Table 4 comprises the depth. strength. structure, and material type and origin

for each layer. Provision was made to some extent to enable alternative determination of the parametersto Suit the form in which the source data may be available. For example, degree of weathering,unconfined compressive strength and unit weight are related to each other and enable the strength of rockto be determined in a number of ways depending on the available information. The purpose of the dataon the size, shape, and shape ratio of potentially erodible units, is to enable estimates of the rock qualitydesi gnation and number ofjoint sets that may intersect the material, to be made. The number ofjoints perunit volume was available in some instances. On that basis, rock quality designation was evaluatedalternatively.

Table 4 Data on Geology of Various Reaches for Spillwa y at WFPR, ArkansasLayer Top SecTopSecReach 3 left 3 ri ght4 4Depth (ft) 0.5Weathering - III Ill IIIConsistency firrnlstf- - -UCS (MPa) 0.14 1.25-201.25 20Material type loamrockrockrockOrigin sapsapSs SsMean diameter (m) 0.7 0.7 0.9Shape ratio 0.04?0.04?0.04?RQD (core) (%) 5RQD (equiv) (%) 90 90 92Number of joint sets 3 3 3Joint set number, .1,,

2.73 2.73 2.73Note: Sec=second, stt\stiff, sap=saprolite, Ss =sandstone, UCS—mnconflned compressive strength,

RQDRock quality designation

Table 5 contains data on the structure of rock that ma y be involved. These data duplicate those given inTable 4 with respect to the size and shape of the potentially erodible material unit, but in addition includedetail on the relative orientation of the structure and the separation and strength of the joints and gougemulling. Table 6 contains an assessment of the extent and status of erosion of the spillway It is the mostcrucial aspect because it determines the usefulness of the data with regard to the correlation between thespecific stream power and the erodibilitv index. The various considerations in this regard are dealt withspecifically in Sections 4 and 5.

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Table 5 Data on Geological Structure for Various Reaches for SpReach 1 2 3Joint set 1:2:3 1:2:3 1:2:3(-,-;bj)Strike (°)Dip direction (°)Dip angle (°)Spacing (m)SeparationGouge typeGouge consistencyRoughness. JrAlteration. J

at WFPR. Arkansas41:2:3

0;90;0090:90:00.11; 0.18; 0.1Open toploam11cm

Because the data were not collected originally for the purposes considered herein, the data base isconsidered incomplete. However, the provisions in Tables I through 6, especiall y with regard toduplicative data, were retained to serve as field recording format for future applications.

Table 6 Data on Erosion Damae on Various Reaches for Spillway at WFPR. ArkansasData point (See Fig I I (i)(ii)(iii)(iv)(v)(vi)(vii)Reach 2-33 left3 right3-44 top4 sec4 sec altDepth (m) 0.3Nil 3.6Width (m) 2.2 29.2Length (m) 45.6 89.3Vol. (M 3)11.3 133.1nilLocation nckptsipSIPNckptSIPheadbaseShape gui/nIType nckptfwdrvgrdnckptfwdhdctjetSequence simsimsimsimLayer eroded 1111ILayer erodedRel power 1112I22

UUUUUEENote: Sec alt--second alternative, nckptknick point, slpslope, f\wdforward, rvgrd=reverse gradient, simsimplar,

hdctheadcut, gulgully, rilnills, ReIrelative

Table 7 Determination of Erodibilitv Index at Various Locations on Reaches for Spillway at WFPR. ArkansasReach 2-33 left 3 right3-44 topMass strength. K.0.090.09 0.99-200.990.99Particle/block size, KbII 1818ISJoint strength, Kd0.30.3 0.30.30.3Relative structure. KI1 0.930.90.81Erodibiiitv index. K0.030.03 4.65.354.8

4 MODES OF EROSIONThe following modes of erosion can in principle occur along an unlined spillway:

4.1 Forward erosionForward erosion is the failure and entrainment of material that occur from the bed surface in straight

channels under normal conditions of supercritical flow.

4.2 Jet erosionJet erosion results from impact of a relatively inclined stream and can be initiated directly by the

incident stream at the point of impact or by front and back rollers into which the stream divides, as

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illustrated in Figure 2. Jets occur at overfull situations that can arise in a number of ways in addition tobeing due to the natural topography.

Table 8 Determination otLocationx-Coordinate(m)y-Coordinate (m)Critical depth (m)Flow depth (in)Enerv level (m)Velocit y (m/s)Spec. Power (kW/m1Erodihilirv IndexReachRouihness (n)Bed slope 1%)Critical bed slope 1%>Flow typeEnergy slope %)Spec, Power (kW/m-)Erodihility Index

tic Stream Power at Various Locations on Reaches Oir S0-I-22-3 3-..() 30.4745.71 00.610.61-0.370680 (,$0.68

1)95 0.680.6879I .63 11,95

2.582580.3 1)

0.032 3 4

0.0350.03 5 (1.035004

(11) .9 8.0->81I .5811.4811.9,4

Su bSupSup07221.89:16.767

01:70,352 2.9424.64.8

llwav at WFPR. Arkansas4-5 5-6

57.52-1 1.070.68(1.33

6

- DIRECTION OF FLOW

FLOW SEPARATIONAND RAISEDTURBULENCEINTENSITY

INITIATION OFPOTENTiAl. HEADOJTEROSION

SCOUR HOLE

HOLE

Fig. 2 Illustration ofJet erosion at Fig. 3 Illustration of knickpoint erosion andpoint of impact and under front initiation of potential headcut erosionand back rollers at abrupt increase in bed gradient

4.3 Knickpoint erosion

Knickpoint erosion occurs immediately downstream of an abrupt increase in slope where the streamdeparts temporarily from the bed in a parabolic trajectory

and rejoins it shortl y further at an obtuse angle.A counter rotational roller develops underneath the jet on the upstream side of the point of impact thaterodes the bed material in reverse directed tangent flow as shown in Figure 3. Knickpoint erosion is selfaggravatin g in that an increase in the depth of the resulting scour hole gives rise to an increase in the rateof turbulence energy production.

4.4 Headcutting

Headcuning represents an advanced stage of knickpoint erosion in some instances as illustrated inFigure 4, at hich the upstream boundary of the scour hole forms a sub-vertical head, the toe of which isattacked by the counter rotational roller underneath the overfallin g jet. Headcurting also can occur atnatural topographic overfalls. The head can be of substantial vertical dimensions and can migrate

International Journal of Sediment Research. Vol. 15, No. I, 2000. pp. 93-107 -99-

upstream for extensive distances. Geological profiles that allow the toes of the heads to be underminedare particularly prone to this mode of erosion.

AILNG OIRECTicr OF F Ow

OISCONflNUIOEMARCATIADVANCEDPOSMON

SCOUR HOLE

UNDERCUTscouR HOt

Fig. 4 Illustration of headcut erosionFig. 5 Illustration of reverse gradient erosionin overfall situation potentially aggravated by hydraulic jump

at abrupt decrease in bed gradient

4.5 Reverse gradient erosionReverse gradient erosion occurs at an abrupt decrease in slope gradient and is due to the stream

impacting as an inclined jet on the downstream slope as shown in Figure 5. The situation may in additionbe associated with a hydraulic jump of which the, turbulence may aggravate or even dominate thescouring action. The downstream boundary of the scour hole that results under normal forward erosion issubject to reverse gradient erosion provided the depth of flow is not very much larger than that of thescour hole. Otherwise, the scour hole simply represents an irregularity in the surface.

5 EVALUATION OF FAILURE STATUSThe main consideration in the evaluation of spillway damage is to assess the magnitude of the incident

stream power relative to the erosional resistance of the material through which erosion has occurred. It isimportant to decide in which sections of the exposed ground profile did the incident stream power exceed,equal, or fall below the erosional resistance of the material. It is useful in this regard to determine whatmode of erosion occurred and if more than one mode occurred, how these may have progressed from theone to the other. It is also useful to evaluate the ground profile in terms of the following observations.

Spillway erosion primarily affects the top of the ground profile that in practice can be considered eitherto increase gradually in erosional resistance or to comprise two strata of which the one is erodible and theother not. Very often the relatively erodible stratum occurs on the top and is underlain by the relativelyresistant bed. On occasion, particularly in headcut situations, resistant layers occur at the top and bottomof the eroded profile and are separated by a relatively incompetent layer.If the ground profile varies gradually in resistance to erosion, material at the bottom of a scour hole very

likely matches the power of the incident flow. In the dual material situation, it is usually reasonablycertain that the power of the incident stream exceeds the resistance of erodible layer and falls below thatof the relatively resistant layer. In headcut situations in which a resistant capping occurs at ground level,it is usually not clear what the actual situation in this regard is.The modes of erosion at the various dam sites in Arkansas and Kansas were evaluated on this basis.

The evaluation was started by preparing a longitudinal section of the erosion damage as shown typicallyin Figure 1. The various arrow heads in the figure designate the direction of the incident flow in terms ofwhich the mode of erosion was assessed and in terms of which it was determined whether the power of

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the flow exceeded, matched, or fell below that of the material at the various horizons in the profileattacked by the flow. Layers that were eroded and on which erosion stopped. ere noted as shown inTable 6.

In practice, many more data points that represent situations in which the incident stream power eitherexceeds or falls below the erosional resistance of the ground, can he identified than data points thatrepresent situations in which the incident flow accuratel y matches the erosional resistance of the material.The usefulness of the 'over or 'under supplied data points lies therein that the marg ins by which theerodibility of the material is exceeded or undershot, are statistical parameters of' which the respectivelower and upper limits approach the data points that represent situations in which the incident lowmatches the erodibility of the material. The objective herein in terms of this observation. 'as accordinglyto identify as many 'over' and under data points as possible from the various dam sites investi gated. Thedifficulties encountered in this re2ard are briefly as follos.The auxiliary spillways considered were in some instances very wide and long. As a result, considerable

variation in ground conditions across and along the reaches gave rise to uncertaint y in the evaluationthereof. Surface irregularities in the torm offence posts, vehicle tracks, boulders, and concrete structures,that caused local raisers in turbulence intensity , occurred in a significant number of instances, but werenot specifically accounted for. Gentle undulations in surface topography gave rise to accelerated localflow velocities that detracted from the uniform onset of erosion across the widths of the relatively broadchannels.

The effect of the foliage of the vegetation was accounted for in the surface roughness considered indetermining the flow characteristics. The root reinforcing effect of the ve getation was, however, notconsidered.The forward erosion damage along the beds of the spillways generall y comprised scars of relativelylimited width that did not represent uniform flow conditions across the widths of the channels. Not many

headcut situations could be identified with certainty . Headcuts are particularly sensitive to the relativegeologic structure of the material. Structure could not be determined with sufficient reliability on thebasis of the scant information recorded originally in this regard. It also was not certain whether thefinally exposed geometry of the scour holes was in fact representative of an overfall situation duringactual flow and whether it applied over the relatively extensive widths of the spillwa ys. The depth offlow was generally very much larger than that of the scour holes caused by forward erosion. No usefulreverse gradient modes of erosion could as a result be identified. The data points identified mostlyrepresented forward erosion and to a lesser extent knickpoint erosion. The erosion damage of thespillways in Arkansas was generally more varied than that recorded in Kansas.

6 FORMULA FOR ERODIJ3ILITy INDEXAn empirical classification basically represents the constitutive behaviour of a material and characterises

the relationship between the imposed excitation and the resulting response of the material with regard to aparticular process, erosion in this instance. The parameters on which the process depends and to which itis most sensitive are the strength of the mass, the size of potentiall y erodible units, the bond strength ofthe interfaces between the units, and the relative orientations of the interfaces to the incident stream-last three of these parameters may be considered as detractions of the mass strength of the material asprimary aspect of its erosional resistance. The most directly sensitive and appropriately weighted wa y inwhich this concept can be expressed is accordingly in a series of multiplications of representative factorsas follows:

K=Km.Kb.Kdjc (I)The factors Km, K b, K. and K. respectively represent the mass strength. block size, discontinuity orinterparticle bond strength, and relative orientation of the discontinuities, Kirsten (1995) developedprocedures for the determination of the values for each of the these parameters for particulate soils,jointed and intact rocks and intact materials in general. Moore (1997) developed a procedures guide forthe field determination of the parameters,

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7 DETERMINATION OF ERODIBILITY INDEXInformation on the geolo gy of the ground was generally inadequate, mainl y because it was not collected

for the specific purposes of this paper. Particularly heavy reliance on experiential jud gernent for thequantitative determination of the various parameters was as a result required.

Various alternative procedures are available in the erodibility classification system for the determinationofsome of the parameters. The purpose of the alternative procedures is not to alternatively determine thevalue for any particular parameter, but rather to enable determination of the parameter in terms of theform in which the basic data may be available. When sufficient data are available that enable more thanone procedure for the dete rmination of a parameter to be applied. cognisance should be taken in the finalselection of an applicable value, of the si gnificance of the various procedures with re gard to the contextof the problem.None of the various parameters related to the stren g th of the ground was ori g inalk recorded. The

values for these various parameters, presented in Fable -L were assessed from in depth knowled ge of thevarious sites and with the assistance of' photo g raphs. In some instances the estimates were confirmed hsubsequent field inspections. The determination of the mass stren g th number is overall considered to hereasonably reliable.Unit size and shape ratio for potentially erodible units were recorded originally. The joint spacings and

numbers of Sets were, however, subsequentl estimated from a knowledge of the site and fromphotographs. The two sources of data from which rock quality designation and resulting block sizenumber were determined gave somewhat contradictory results in some instances. This was considered tobe due largely to the definition of the shape ratio used in the original data. The shape ratio referred to theshape of the units as determined by the bedding that, although generally closel y spaced, did not representactual bedding fractures. Engineering jud gement aided by the photo graphs ' relied upon in suchinstances to estimate the applicable block size.Joint strength was not determined strictly in terms of the procedures prescribed for the evaluation of the

joint roughness and alteration numbers. No information was in any event recorded in this regard in theoriginal data base. It was rather estimated on the basis of an empirically established practical range of'values for the equivalent friction angle of 16° to 38°, the lower limit representing conditions in whichstrength is dominated by cohesive properties and the upper limit conditions in which strength isdominated by frictional properties of the material.No explicit information was contained in the original data base in terms of which the relative structure

number could be determined. This did not pose a problem with regard to the soils considered, in whichinstance a value of unity was selected for the structure number. It also did not present a problem withregard to the rocks, that in most instances were generally known to contain three joints sets of which oneset was by and large sub-horizontal.The component parameter values used for the determination of the erodibility index were recorded as

shown typically in Table 6. A range of values was found for the index in some instances owing to arange of values in one or more of the underlying parameters. A final value was then selected from therange in terms of an overall assessment of ground conditions.

8 DEFINITION OF SPECIFIC STREAM POWERKirsten and Kirsten (1995) reviewed the fundamental considerations and practical applications of stream

power that have been advanced in channel flow and confirmed that it generally is a representativemeasure of the rate of turbulence energy production that causes erosion. They also found that sixdefinitions of stream power are in general referred to in the literature on river engineering, the first five ofwhich represent measures of the energy supplied and the sixth, a measure of the energy applied in thedissipation process.

Total stream power is given by the product of the average flow velocity . V, the energy gradient. S, andthe weight of the body of water being displaced in channel flow. (y.y 0 .131), where y denotes the unitweight of water, y' 0 and b the depth and width of flow respectively, and L the length of the reach overwhich the power is expended. Specific stream power represents the total stream power per unit area of

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channel and is given bv(V.S.y.y)). Stream power per unit length is given by (V.S.y.v.b) and represents acondition of dynamic equilibrium in streamflow in which energy is spent at a constant minimum ratealong the len gth of the stream. Stream power isgkcn by (V.S.y ) .h) and unit stream power by (V.S).Unit stream power represents uniform flow across the section of a stream and corresponds to acharacteristic spatial constant.The rate at sshich enerey is dissipated may alternatively be refrred to as the rate of turbulence energy

production of which a good measure is unit applied stream power. It may in eneral he determined byintegrating the product of the shearing stress,and the vertical gradient of the horizontal velocit\.,

over the depth of flow. u denotes the horizontal flow velocity and (V the vertical Cartesiancoordinate. In quasi uniform flow the unit applied stream poser is equal to the spec

ific stream power.

The determination of unit applied stream power in general requires that the shearing stress and velocitydistributions he knoss n accuratel y . The fact that these parameters are usually not known with sufficientaccuracy renders the use of unit applied stream power intractable from a practical point of view.Total stream power contains the sidth and length of the channel and does not allow spillways of

different dimensions or dilfrent modes of erosion in any particular spillssa' to be compared. Streampower per unit len gth and stream power contain the width of the channel and represent characteristicconditions for streamtlow under dynamic equilibrium. Spillways of different widths therefore cannot becompared in terms of these expressions of stream power. The flow conditions in spillways subject toerosion do not necessaril y represent dynamic equilibrium, especially not at points at which the turbulenceenergy is raised locally. Stream power per unit length and stream power therefore also cannot be used asdefinitive measures of the rate of turbulence energy production for this reason. Since unit stream powerrepresents uniform flow that may not necessarily apply to spillways. it is also not a suitable measure ofthe excitation that causes erosion.Specific stream power is the only measure of therate of turbulence energy production that is not subject

to any of these disqualifications. Dynamic equilibrium does not have to be satisfied for it to be applicable.The fact that specific stream power enables different modes of erosion to be compared is of particularimportance in comparing the erosion damage in various applications. Examples include channel flow;free fallin g jets as in overfall situations; and pressure induced, continuous, plain and abrasive entrainedwater jets.

9 DETERMINATION OF SPECIFIC STREAM POWERThe hydraulics of the flow was determined in the following sequence of steps. The coordinates for the

beginning and end points of the successive reaches in a spillway were determined from data given inTables I and 2. Roughness coefficients of 0.035 and 0.040 were selected for the constructed and naturalsurfaces respectively. These values corresponded to rock cuts and natural vegetation consistin g ofgrassland and brush. The geometry of the spillway together with the surface roughness values assignedand the flow rate given in Table 1, enabled the flow depth and velocity profile for every reach to beestimated. The energy heads at the change in gradient points were consequentl y determined whichenabled the energy slopes for every reach to be determined on the assumption that the effect of thegradually varying flow profile in proximity of the change in gradient, was negligible. The critical depthand slope were calculated for each spillway in terms of the recorded flow data and selected surfaceroughness values. This enabled the sub or super critical nature of the flow on every reach to be evaluated.Values for the key parameters in terms of which the specific stream power was determined, are showntypically in Table S. The relative magnitude of the specific stream power with regard to exceeding,matchin g, or falling below the erosional resistance of the ground was assessed in addition as shown in thetable.

10 CORRELATION OF SPECIFIC STREAM POWER AND ERODIBILITY INDEXThe erodibility index and specific stream power for the data points identified, are shown plotted in

Figure 6. The three classes of points representing excessive, matching, and deficient specific streampower relative to the erosional resistance of the bed material are clearly distinguished as expected.

International Journal of Sediment Research, Vol. 15, No. I. 2000, pp. 93-107 - 103 -

Dooge (1993) examined the occurrence and extent of erosion damage to a variety of spillways in 29dams in South Africa. Ten different rock types of variable consistency were identified. Damage wasassociated with either channel flow or free overfall into a plunge pond and was identified in a number ofzones in each spillway . Doo ge (1993) described the severity of the damage in terms of three intervals ofdepth. viz. 0 - 0.2 m as zero damage. 0.2 - 2 m as little to moderate damage. and > 2 m as excessiveerosion damage, which is very similar to the approach adopted herein with regard excessive, matchiniz,and deficient specific stream power. Doo ges data points are plotted in Figure 6 after Kirsten et. al.(1995).The South African data points evidently represent more resistant materials, but are otherwise similarly

disposed relative to a potential threshold criterion compared to the data points from the two Americanstates. Kirsten et. al. (1995) further showed the threshold criterion for jointed rock forms part of ageneric threshold criterion that extends from very weak soils through jointed rock, as dealt with herein, tovery stron g intact materials as shown in Figure 7. The generic nature of the data for the jointed rock,displayed in Figure 7, was in fact partl y relied on to locate the threshold criterion in Figure 6 which maybe expressed as follows:

= (81 .K)°, (2)where.

K o.(RQDfJ,).(c ± 0.5.J,JJa).Ks (3)P denotes specific stream power, K, the erodibilitv index, a c the uniaxial compressive strength of thepotentially erodible unit of material, o the tensile strength of the discontinuities demarcating adjoiningunits. RQD, the rock quality designation, J, the joint set number, Jr, the joint roughness number, J 3, thejoint alteration number, and K, the relative structure number which represents the shape and orientationof the erodible blocks relative to the direction of the incident stream. Criteria are presented by Kirsten et.al. (1995) which enable these parameters to be determined.

Ii ACKNOWLEDGEMENTSThe manuscript of the paper was reviewed with regard to hydraulic and geotechnical content prior to

submission for publication by Brian Middleton and Dr. Graham Howell, Principals and Directors ofSteffen Robertson and Kirsten, (SRK). Their contributions in this regard as well as the permission fromSRK to publish the paper, are greatly appreciated. Thanks are due to Sandra Warner for the linedrawings in the figures. Acknowled gement is due to both of the USDA agencies, NRCS and ARS, forgeneral information on auxiliary spillways and for the specific data on spillway performance in Arkansasand Kansas. Permission from USDA to publish the paper is also gratefully noted.

REFERENCESABT, S.R.. KHATTAK, MS., NELSON, J.D., RUFF, J.F., SHAIKH, A., WITTLER, R.J., LEE, D.W., and

HINKLE, N.E. May 1987 and Sep. 1988, Development of riprap design criteria by riprap testing in flumes:phases I and II: Colorado State University and Oak Ridge National Laboratory Report NUREG/CR465 IOR.NL.rrM-io 100, n. p.

DOOGE, N., Nov. 1993, Die hidrouliese erodeerbaarheid van rotsmassas in onbelynde oorlope met spesiale'erwysing na die rol van naatvulmateriaal: unpublished Master of Science thesis in Afrikaans with Englishabstract, Pretoria University, Pretoria, South Africa, 121 p.

KIRSTEN, H.A.D. Jul. 1982, A classification system for excavation in natural materials: The Civil Engineer inSouth Africa, 24(7), 292-308.

KIRSTEN, H.A.D. KIRSTEN, L.H., and KIRSTEN, A.H. 1995. General classification system for hydraulic erosion:Steffen Robertson and Kirsten Report No. 197083/1, n.p.

KIRSTEN, H.A.D and KIRSTEN, L.H. 1995, Stream power as measure of the excitation causing hydraulic erosion:Steffen Robertson and Kirsten Report No. 197083/2, n.p.

LEPP, L.R., KOGER, C.J., and WHEELER, J.A. 1993, Channel erosion in steep gradient, gravel-paved streams:Bull. Assoc. Eng. Geol., 30(4), 443-454.

MOORE, J.S. 1997, Field procedures guide for the headcut erodibility index: Trans. ASAE, 40(2), 325-336.MOORE, J.5., TEMPLE, D.M., and H.A.D. KIRSTEN. 1994, Headcut advance threshold in earth spillways: Bull.

Assoc. Eng. Geol., 31(2), 277-280.

- 104- International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 93-107

POWLEDGE, OR., RALSTON, D.C., MILLER, P., CHEN, Y.H., CLOPPER. P.E.. and TEMPLE. DAM. Aug1989, Mechanics of overflow erosion on ëmbankments, Part I, Research Activities: Jour. Hydr. En., ASCE,115(8),1040-1055.

POWLEDGE, OR., RALSTON. D.C., MILLER. P., CHEN, Y.H., CLOPPER. P.E. and TEMPLE. D M. Aug. 1989Mechanics of overflow erosion on embankments, Part [I. Hydraulic and Desi g n Considerations Jour. Hydr. Eng.,ASCE, 115(8), 1056-1075.

RALSTON. D.C., and BREVARD, J.A. Sep. 1988. SCS's 40 year experience with earth auxiliary spillwavs: Proc.of the FifthAnnual Meetin g of the Assoc. of State Dam Safety Officials, Manchester, NH. 19 pp. (available asSCS National Bulletin No. 210-9-2. 17 October 1983. NRCS, NHQ, Box 2890, Washin gton, DC).

SOIL CONSERVATION SERVICE USDA. 23 Feb. 1984. National Bulletin No 210-4-14, Arkansas. December1982: Spillway Performance Report, np.

October 1985, Earth Dams and Reservoirs: Technical Release No. 60, '1 0-VI. np .17 July 1991, National Bulletin No. 210-4-13. Kansas, 10-1I June 1989: Spillway Performance Report, np.

TEMPLE, D.M., BREVARD, J,A., MOORE, JS.. HANSON. G.J., GRISSINGER. E.H. and BRADFORD, J.M.September 1993, Analysis of veitetated earth spillwa ys, Proc. 10th Ann. Meeting of Assoc. State Dam SafetyOfficials, 225-230, Kansas City. MO.. Lexington. KY.: Assoc. State Dam Safety Off.

FEDERAL EMERGENCY MANAGE.\IENT AGENCY. Au g. 1997, National Dam Safety Program, 1996 and 1997,A Progress Report; Vol. I and 2, Washington, D.C.

YANG, C.T. Oct. 1973, Incipient motion and sediment transport: Jour. H ydr. Div., Proc. ASCE, 99(10), 1679-1704.

Appendix I

Abbreviations Used in Tables i-S

P1retri IRQDrvgrdsapsecsimSIPssSpecstfstrtrajUUCSvrdwdd

altbjbrichCFC,cultdiscontEengequivfwdgrsguihdctHIirreg

natnckpt

alternativebedding jointbunchvegetal cover factorvegetal retardarice curve indexcultivateddiscontinuitiesequalengineeredequivalentforward

grassgully

headcutweathering class III, II, etc.

irregularitiesManning's flow resistance coefficient

naturalknickpoint

Plasticity indexrelative

rutsrock quality designationreverse gradient

saprolitesecond

similarslope

sandstonespecificstiffstraight

trajectoryunder suppliedunconfined compressive strength

variedwooded

International Journal of Sediment Research, Vol. 15, No. 1, 2000, pp. 93-107 - 105 -

K Index

Fig. 6 Plot of specific stream power against erodibilily index forspillways in Arkansas, Kansas and South Africa

000

•0

0

00180

10000

1000

("1

E100

a)

o100.ECoa)U)0

0(I)a01(I)

a3

0

0

9

0

CIL

-I

is5•1-a

0 E•C1

OL

zCl)

p•

-C.)0)

o (1)

.9

0-.1

0-4

1e9

1e6 S

100000 Intact materialsin jet cutting

10000 Jointed rockIn splllway flow

1000

-- Key to Figure 70.1 0River sediment, thiesliold power, Yang (1973)+Sand and gravel, threshold power, K irsten ci at (1995)

001 ......'.. ... ..,......,,.,,.....,..,LIGravel, threshold power, Lepp et at (1993)0

0Angular and rounded riprap, threshold power, AN ci at (1987)0.00i....... ......... ......... .LI Jointed very soft rock, ilueshmild lsosr, Aikansas and Kansas

+Jornicil vc' soft tuck, excessive prover, Arkansas and Kansas•

00001 Jointed very softso rock insufficient poou Arkansas and Kansas- . S '• Jointed soil rock - hard rock, little to moderate erosion, Dooge (1993)0 Particulate media . jojtites sol)- hard rock, excessive erosion, Dooge (1993)

le-5 .-" in river flow ......................Jointed 51)11 - hard rock no erosion, l)imoge (1993)•Intact materials, threshold power

le-6'-'-- • I..I...,..- ,.-- .•..•.•005 N(Cl1$),- 0000C

.-.--.-0 C)N- 0)0'7 1d28 g22 d °8 -.K Index

Fig. 7 Plot of specific stream power against translbrtiicd crod i bit ily indexFor particulate media, jointed rock and intact materials

I

I