ML20137Z018

Informs That Responding to Proposed Rainfall Duration Curve for Umtrap Embankments Reviewed.Regression Equation for Rainfall Duration Acceptable & Time Concentration of Less than 2.5 Minutes Not Necessary

ML20137Z018
Person / Time
Issue date:	01/30/1986
From:	Higginbotham L NRC OFFICE OF NUCLEAR MATERIAL SAFETY & SAFEGUARDS (NMSS)
To:	Themelis J ENERGY, DEPT. OF
References
REF-WM-39 NUDOCS 8603120455
Download: ML20137Z018 (13)

Text

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Mr. John G. Themelis, Project flanager UMTRAP Project Office U.S. Department of Energy P.O. Box 5400 Albuquerque, New Mexico 87115

Dear Mr. Themelis:

We have reviewed your letter of December 13, 1985, responding to our proposed rainfall-duration curve for UMTRAP embankments. We acknowledge a typographical error in the equation presented in our October 18, 1985 letter. A term, F jwas inadvertently omitted from the equation and table. The revised table (Enclosure 1) includes the corrected equation and a column of F, values. The curve fit originally presented was correct.

We have compared the NRC spline fit to the regression equation suggested by 00E. We note, however, that there is an apparent error in the DOE equation.

The exponents of both coefficients should be preceded by minus signs. Our comparison shows a discrepancy of up to 11% for the 2.5 minute time of concentration, but much closer agreement at the 5 minute time of concentration.

The DOE letter urged that the analyses not require a titre of concentration for the rainfall-duration curve of less than 2.5 minutes. We have previously indicated that 2.5 minutes was probably short enough for typical embankments.

As backup to this assertion, we performed a simulation using the finite difference runoff model described in Enclosure 2, a paper by R. Codell of our staff to be presented in February at the Colorado State University symposium on geotechnical and geohydrological aspects of waste management. We simulated runoff for the cases of a local PMP with minimum times of concentration of 2.5 and 5 minutes. The peak runoff rate for the 2.5 minute case was only about 1%

greater than the 5 minute case. This indicates that the peak runoff would not be sensitive to the 11% discrepancy between the DOE and NRC curves, and that shorter times of concentration should not be necessary.

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I We therefore conclude that DOE's regression equation for rainfall-duration is  !

acceptable. Furthennore, we conclude that a time of concentration of less than i 2.5 minutes is not necessary for calculation of design basis runoff at tallings "

embankments. i Sincerely,  !

Leo B. Higginbotham, Chief Low. Level Waste and Uranium Recovery Projects Branch l Division of Waste Management Office of Nuclear Material Safety and i

Safeguards l

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Enclosures:

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ENCLOSURE 1 l 4

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Table 1 - Cubic Spline Curve for Rafnfall Intensity ,

vs. Duration i

8" mjn. mi i 1,1 01 ,2 01 .3 F i

i 1 0.0 0.0 - 1.0 .1616205E+00 0. .782049 2-02 0.0 2 1.0 1.0 - 5.0 .1381590E+00 .2346148E-01 .7820493E-02 0.1538 3 5.0 5.0 -15.0 .3967789E-01 .1158403-02 .7820493E-02 0.45 4 15.0 15.0 -30.0 .1923221E-01 .88574812-03 .7820493E-02 0.74 5 30.0 30.0 -45.0 .4822097E-02 .74906285-04 .7820493E-02 0.89 6 45.0 45.0 -60.0 .3479401E-02 .1460674E-04 .7820493E-02 0.95 i

EQUATION:

R = (( C 9,3 x0+C 1,2) x 0 + C f 1 ) x 0 + rg F l where R = fraction of one hour PMP accumulation.

0 = Ouration - t,, min.

I l

ENCLOSURE 2

. ARMOREO SLOPES my Runoff from armored slopes ~ " * *i l

l Richard 8. Codell

! U.S. Nuclear Regulatory Commission, Washington D.C. 20555 Byg 1 INTRODUCTION Uranium mill tailings embankments in the United States are required to be l stabilized and protected from natural phenomena for a period of 200 to 1000 years (EPA 1985). Embankments and diversion channels are often pro-tected from erosion by rock armor, which must withstand runoff from in-tense precipitation. Protection from the effects of the Probable Maximum

Flood (PMF) adjacent to the site and the runoff from the local Probable l Maximum Precipitation (PMP) would satisfy this requirement. Lesser i events would also be acceptable if they could be adequately justified.

Typical embankments at these sites have surface areas of only a few acres, with gentle top slopes (0-2%) and a steep side slope (10-205).

The tailings are generally covered with a 6-to-8 f t layer of compacted silt and clay to reduce tne diffusion of radon into the atmosphere. Rock 1 armor is usually placed on top of the radon barrier in thicknesses of 12 ft, with a mean diameter d of 1-2 in on the gentle slopes, and 3-12 in 50 on the steeper slopes.

Models exist for calculating overland flow on hillsides (Morris 1980) but no models have been found which explicitly deal with runoff from ar-i mored slopes. Flow on armored slopes differs from overland flow, because substantial flow occurs beneath the surf ace of the rock layer at low run-

! of f, and both above and below the surface for high runof f. In addition to the lack of a suitable model, no estimates of the PMp exist for such I

l small areas and for very short durations, This paper develops a model for calculating runof f from armored embank-ments. The model considers the offect of slope, drainage area and " flow concentration" caused by irregular grading or slurrping. A rainfall-duration curve based on the PMP is presented which is suitable for very small drainage areas. The development of the runof f model and rainfall-duration curve is presented below, along with a demonstration of the mod-el on the design of a hypothetical tailings embankment.

2 RUN0FF MODEL -

Rain falling on an armored slope will flow downhill except for the frac-tion infiltrating the ground which for the present case can be neglected.

Referring to Fig.1, the flow of water on the slope may be described for a two dimensional case by a macroscopic mass balasice and the kinematic ap-proximation of the energy balance (Overton, 1976). The kinematic

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Figure 1. Embankment in profile approximation neglects acceleration, which can be shown to be small, and balances friction versus hydraulic gradient only. The kinematic equa-tions for runoff are stated:

a((u) . 8(lv) ,R,g ax ay at 0 1-+K"]"

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(2) gnada - S* = 0 l O( Kv/u2 +va ay 3 ,

• S y =0 (3) where ( = water depth above an impermeable layer, u a flux of water

' across the slope, v = flux of water down the slope, n a rock void porost-ty, t = time, R = rainfall rate, g = acceleration of gravity, K = fric-i tion factor, and da = representative rock diameter.

For flow over the top of the rock layer, the depth ( becomes a virtual depth; that is, the depth which the water would have to assume if the rock layer were infinitely thick. The factor e is used to adjust the gradient of the virtu.11 water surface for flows which overtop the rock layer. It is equal to unity if flow is below the level of the rock layer and equal to the porosity n if flow is above the rock layer surface.

The coefficient K for flows confined below the surface of the rock is a function of rock shape, roughness and Reynolds number Re = Ud*/no, where v is the kinematic viscosity, and U is the water flux in the direction of l flow. For the large Reynolds numbers (i.e., greater than 1000) expected through the rock layers, Stephenson (1979) observed that K is a function only of roughness and shape:

K= +K g (4) where Kg = 1 for smooth polished spheres, 2 for sem;-rounded rocks, and 4 for angular rocks.

ARMORED SLOPES i

2.1 Flow over top of rocks The resistance to flow through the rock layer is much higher than flow i

resistance for open channel or overland flow. Therefore, the effective resistance will decrease once the water depth exceeds the thickness of tha rock layer.

Consider for the time being only the flow down a slope, which is cov-ered by a uniform layer of rock. The total flow Q past a point on the slope is the sum of the flows through the rock layer, Q and over the rock layer, Q 2

Q=Qg*Q2 * *1 N * '2 (( - H) n (5) where v layer, g andis the flun in the rock layer, .2 is the flux in the over-top H is the thickness of the rock layer. The velocity over the top of the rock layer is calculated using the Carcy-Weisbach equation for i

flow resistance in open channels: -

r 8gRIb h y

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2" f l

(6) where R is the hydraulic radius, and f is the Darcy-Weisbach friction factor,hlhe hydraulic radius is approximated as the water depth over the top of rock:

Rh * " (b ~ H) (7)

Hey (1979) presents a correlation of f for flow in gravel river beds, in terms of Rh and the d 84 r ek diameter:

1/Vf = 2.03 log 10 13.46 R h /3.5 d 84 (8)

An effective resistance factor K' for the total flow in and over the rock layer can be derived by combining Eqs. 4 through 7:

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d' (2 H(d*/K) + (( - H) (8 (( H)n) i f I

l Equations 1,2, and 3 are solved with the effective value, K' substituted for K when ( is greater than the rock layer thickness H. Since friction is likely to only decipase as the flow overtops the rock layer, the value of K' is limited to K:

K' K (10)

Rating curves for flowrite vs. water depth at steady-state for the exam-pie are shown in Fig. 2. The much higher t irrying ability of the over-top layer is evident from this figure.

The upper end of the top slope is assummed to be a no-flow boundary:

v = 0, f" = 0 dy (11) i

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j Figure 2. Rating curves for example - 2% top and 20% side slopes f .

l The water level is continuous across the slope break. Free slip and no.

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• flow are assummed at the lateral boundaries. The flow boundary conditic'1 j l at the base of the lower slope considers that the depth of the water lay- <

er is determined only by the balance between friction and gravity:

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&"f( g S) y (12) 1 l The partial differential equattuns 1, 2, and 3 are reduced to their fi- '

l nite difference form in a staggered grid, and are solved by th'e '" Leap-i frog" explicit algorithm (Roache 1972). The model is presently limited to slopes which can be represented by up to 4 tilted subslopes, i

! 3 PRECIPITATION MODEL

The rainfall-duration curve is developed from Hydrometerological Report i

49 (NOAA 1977) for durations of 15 minutes to 2 hours2.314815e-5 days <br />5.555556e-4 hours <br />3.306878e-6 weeks <br />7.61e-7 months <br />. and from estimates

! made by the staff of the U.S. National Weather Sevice (NWS) for durations I i shorter than 15 minutes (Hansen 1985). It is most suited to the Colorado 1 and Great Basin drainages of the Western United States.-but rainfall- I j duration curves for other regions could be developed along similar Ifnes.

' l The NWS estimated that the 5 minute duration PMP for the area covered [

l by HMR-49 was 45 15% of the 1 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> PHP. For durations shorter than 5  !

minutes, NWS advised that maximum rainfall ,ates could be estimated from i record rainfall amounts measured at mid-latitudes on the globe. NRC, j therefore, used the U.S. record fur 1 minute of 1.23 in, measured at

Unionville, MO, July 4, 1956. ,

l Recognizing that conditions which saturate the rock layer are likely to  :

l produce the greatest flows, the design basis hyetograph (time rate of  !

! precipitation) for the slope was formulated so that there would be an in-l creasing intensity of precipitation, with the last 2.5 minutes of the first hour and the first 2.5 minutes of the second hour being the most

} Intense. Total precipitation for the first hour was 8 inches. Precipi- ,

l l tation for the second hour was 14% of that for the first hour. The l

hyetograph is presented in Fig. 3.

1 I

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ARMORED SLOPES 5- 7 Nb 4 MODEL RESULTS The modeled embankment is typical of those found at uranium mill tail-ings sites. The embankment is assumed to be triangular and symmetrical around the vertical centerline, similar to that shown in Fig.4a. It is 700 feet long from top to bottom, and 1200 feet wide at the base. The top portion of t!.e embankment is 440 ft long, with a slope of 2% and a rock-layer thickness of 1 ft. The lower portion of the embankment is 260 f t long with a slope of 20% and a rock layer thickness of 1.5 f t. The harmonic mean diameters of the rock are 0.1 ft and 0.3 ft for the top and side slopes respectively. The d g4 diameters are 0.32 and 0.75 ft respectively. Friction factor for flow through the rock is assumed as K = 2.0.

Runoff per unit width from the toes of the top and side slopes of the sample embanlunent are shown in Fig. 3. These and subsequent results are also summarized in Table 1. In the present case, the top and side slopes are assumed to be unfailed. Peak flow is nearly coincident with the peak precipitation rate. Runof f fron the side slope shows a small disturbance after its peak, which is caused by the routing of the peak flow from the top slope.

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i E, i i i Figure 3. Hyetograph and runoff from benchmark embankment 1 4.1 Flow concentration i

Flow concentration is a term to describe the preferential flow paths on the embankments caused by nonuniformities of the embankment profile, fhe most likely cause of flow concentration, given that good grading and rock

] placement practices are followed, is a failure or differential settlement of the earthwork with subsequent subsidence or slumping. Such a failure could create a depression toward which water running off the slope would collect. The nature of such a fatture is highly speculative.

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. j ARMORED SLOPES mra

<l wI The smaller grade and lower water carrying ability on the top slope would accentuate the effects of settlement on flow concentration, Settle-ment of from one to several feet might be possible (Wardwell 1984). The effect of settlement can.probably be overcome by good engineering Table 1 - Summary of model experiments Peak runoff, cfs/ft Experiment Top slope Side slope Benchmark, 0% slump 0.15 0.35 Halve d* 0.29 0.28 Double da 0.16 0.42 is layer thickness 0.45 0.40

\% slump 0.55 0.90 1% slump 1.03 0.55 infinite layer,1% slump 0.20 0.46 i

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2 00ED SLOPES , , ,

. . ~l~ s practice. Nevertheless, several scenarios of embankment failure have been postulated and studied with the numerical runoff model. Figure 4b shows a uniform inward slumping of the embankment toward the centerline. Mul-tiple failures as 1.11ustrated in Fig. 4c would probably cause less severe flow concentration, because the drainage area for each sub-basin is smaller than the single 'a11ure case. Other failures are possible, such as the opening of a trough by slumping and erosion of an otherwise-unfailed slope (Fig.4d).

Two cases of embankment slumping of the type illustrated in Fig. 4b are presented in order to demonstrate flow concentration:(1) Uniform inward slope of 1% toward centerline and (2) Uniform inward slope of 1%.

Flow concentrations resulting from steady rainfall are presented in Fig. 5 as the ratio of runoff per unit width at the embankment centerline to runoff per unit width from an infinitely-wide slope with no slumping.

Flow concentrations for the unfailed (Benchmark) case are less than uni-ty, especially on the top slope, and are relatively insensitive to the rate of precipitation.

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Figure 5. Flow concentrations at steady state Flow concentration for the it and 1% slump scenarios are all greater than unity, and depend on the rainfall intensity. The high degree of.

flow concentration from the top slope is explained largely by the satura-tion and overtopping of the rock layer. Resistance to flow is greatly reduced once overtopping occurs. In addition, the inward slope in each case is a significant fraction of the 2% downward gradient of the origi-nal slope. There is significantly less flow concentration on the steep side slopes. Overtopping would occur only at points above the slope break. Peak flow rates are attenuated within the rock layer of the side slope.

Transient runoffs fron the top and side slopes resulting from the local PMP are presented in Fig. 6 for the 1% slump scenario. There is a con-siderable degree of flow concentration in this case, particularly on the top slope. An interesting dbservation is that peak runoff may occur at the toe of the top slope rather than at the toe of the side slope. The m __

t ARMORED SLOPES design of the rock layer on the side slope may therefore be controlled-by runoff from the top slope.

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.reet les eaes Figure 6. Flow concentration for transient case - 1% slump case 4.2 Sensitivity of runoff to design parameters and uncertainties Peak runoff is sensitive to the ability of the flow to remain confined to the rock layer rather than overtop it. The ability of the rock layer to store and transport most of the runoff is a critical factor in the at-tenuation of peak flow from the slope. This effect will be diminished however rosity too small.

if the rock layer is too thin, its friction too great or its po-The capacity of the rock layer to conduct flow is related to its thick-ness and on the grouping of terms KU2/gd*n2 Reducing porosity n would both increase friction and reduce the water-carrying ability of the rock layer, forcing more flow to the surface, all other factors being equal.

The effect of doubling and halving the estimate of d* is given in Table

1. Doubling d* lowers the internal frictiori, increasing the peak runoff.

Interestingly, halving da increases friction, but causes the flow on the top slope to exceed the carrying capacity of the rock layer, resulting in an increase in the peak runoff at the toe of the top slope.

The grouping is directly proportional to the friction factor K. This factor depends largely on rock surface angularity; e.g. , a layer of crushed rock will carry less water than a layer of rounded alluvial grav-el, all other factors being equal.

The transient case was rerun for the 1% slump scenario, but with an es-sentially infinite layer thickness which eliminates the possibility of overtopping. The results of this run are shown in Fig. 6 along with the runoff for the normal rock layer thickness. Peak runoffs for this case are dramatically lowered. Furthermore, the peak runoff occurs at the toe of the side slope and is no longer controlled by runoff from the top slope. The maximum rock layer thicknesses necessary for the example em-bankment.to completely contain the peak flows are about 3 ft. on the top slope and 1.3 ft. on the side slope.

F . .

~ ARMORED SLOPES '

77[kl5 Qh One area of uncertainty is the effective diameter d*, which is neces-sary to calculate resistance for flow through the rock layer. Leps (1973) suggests the d r ck diameter. Staphenson recommends the 50 harmonic mean (i.e., the mean weighted by the inverse) diameter d I Differences between d 50 and the dr can be large. The ratio d #d" 50 calculated for anticipated rock grades specified for the example is about

1. 3. Ratios calculated on typical grades of crushed rock are in the range d50/d" = 2 to 3. The harmonic mean diameter places heavier emphasis on the smaller rock sizes.

5 CONCLUSIONS Runoff from armored compound slopes on tailings embankments resulting from intense precipitation has been studied by means of a mathematical model for kinematic flow. Several interesting conclusions can be drawn from the mathematical experiments with the model:

1.~

The calculation of runoff must consider flow both through and over the top of the armor layer.

2. Irregularities in the surface of the slopes may lead to large concen-trations of flow along preferential paths.

~

3. .The peak runoff from the gentler top slope can frequently be greater than the peak runoff from the steeper side slope, thereby controlling the design of the armor on both slopes. This condition may occur when the ability of the rock layer to carry the flow is inadequate, forcing the flow to overtop the rock layer. The most severe hydrologic stresses on the armor are likely to occur at the break between the top and side slopes for this situation.

This observation indicates that the larger armor used on the side slope should extend a distance above the break in the slope, onto the less steep slope.

4. The use of larger-diameter rock and thicker rock layers tends.to di-minish peak runoff from the top slope.

5. The effects of flow concentration caused by geotechnical failure or slumping can be greatly diminished by having an adequate rock layer thickness.

Several uncertainties were identified during the development of an ana-lytical method for the determination of runoff and design of :.he rock layer. Simplifying approximations had to be made in order to pursue the development of the methods. To evaluate the significance of these uncer-tainties, NRC is sponsoring technical assistance at Colorado State Uni-versity to collect experimental data on flow resistance of typical rockfill layers, and the ability of the rock to withstand the erosive ef-fects of the runoff.

6 DISCLAIMER The opinions expressed in this paper are those solely of the author, and do not necessarily represent the official policy of the Nuclear Regu-latory Commission.

n .

( . . .

ARMORED SLOPES REFERENCES EPA, 1985, Title 40 Code of Federal Regulations Part 192, Washington D.C., U.S. Government Printing Office Hansen, E.M., 1985, Personal communication with E.M. Hansen and D. Fenn, U.S. , National Weather Service, Silver Spring MD, July 31, 1985 Hey, R.D. 1979, Flow Resistance in gravel bed rivers, Journal of the Hydraulics Division ASCE, HY4: 365-379 Leps, T.M., 1973, Flow through rockfill in Embankment Dam Engineering, Casagrande Volume, by R.C. Hirshfeld~and S.J. Paulos (Editors), New York, John Wiley and Sons :87-108 Morris E.M., & D.A. Woolhiser, 1980, Unsteady one-dimensional flow over a plane: partial equilibrium and recession hydrographs, Water Resources Research, 16, no.2: 355-360 NOAA, 1977, Hydrometeorological Report No. 49 - Probable Maximum Precipitation estimates,. Colorado River and Great Basin drainages, Silver Spring, MD, U.S. Dept. of Commerce Olivier, H. 1967, Through and overflow rockfill dams new design techniques, Proceedings, Institute of Civil Engineers, March 1967:

433-471 Overton, D.E., & M.E. Meadows, 1976, Stormwater Modeling, New York, Academic Press Roache, P.J., 1972, Computational Fluid Dynamics, Albuquerque NM, Hermosa Publishers Stephanson, D., 1979, Rockfill in Hydraulic Engineering, Amsterdam, Elsevier Wardwell, R.E., J.D. Nelson, S.R. Abt, & W.P. Staub, 1984, Design Considerations for long-term stabilization of uranium mill tailings, in Management of Uranium Mill Tailings, Colorado State University, Fort Collins, Colorado

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