Seepage Through Dams (Casagrande, 1937)

LIST OF CONTRIBUTIONS FROM THE HARVARD ENGINEERING SCHOOL A list of titles of publications No. 1-200 in this series will be sent upon request.

HARVARD UNIVERSITY

No.

201. Studies in Sewage Treatment. I. Observations on the Digestion of a Sewage Sludge over a Wide Range of Tempratnrs. Gordon M. Fair and Edward W. Moore. II. The 0XJ'gen Demand of Mixtures of Aeth·ated Sludge and Sewage. Edward W. Moore. Sewage Works Journal. January, 1937. 202. Vibration in Industry. J.P. Den Hartog. Journal of Applied Physics. :February, 1937. 203. Bending of an Infinite Beam on an Elastic Foundation. M.A. Biot. Journal of Applied Mechanics. March, 1937. 204. The Physics of the Ionosphere. Harry Rowe Mimno. Reviews of Modern Physics. January, 1937. 205. Sound Analysis. H. H. Hall. Journal of the Acoustical Society of America. April, 1937. · 206. The Application of Paschen's Law to the He-Ignition of an Are. J. D. Cobine and R. Burton Power. Journal of Applied Physics. April, 1937. 207. Air-Borne Infection. William F. Wells and Mildred W. Wells. Journal of the American Medical Association. Nov. 21 and Nov. 28 1 1936. 208. Exploration of Soil Conditio.ns and Sampling Operations. H. A. Mohr. Soil Mechanics Series No. 4. June, 1937. 209. Seepage through Dams. Arthur Casagrande. Journal of the New England Water Works Association. June, 1937.

Requests for reprints will be granted, so jar

a&

poss-ible, on

SEEPAGE THROUGH DAMS BY

ARTHUR CASAGRANDE

payment of

twenty-five cent.! a copy.

Reprinted from

Journal of the New England Water Works Association June, 1937

- i \

PUBLICATIONS FROM THE GRADUATE SCHOOL OF ENGINEERING 1936-37

No. 209

Soil Mechanics Series No. 5

PRINTED IN U. 8, A,

New England Water Works Association ORGANIZED

1882.

june, 1937.

Vol. LI.

No.2

This Association, as a borly, is not respons-ible for the statements or opwions of any of its members

SEEPAGE THROUGH DAMS. BY ARTHUH CASAGRANDE.* [Read February 1!8, 1935.]

CONTENTS.

A. Introduction. B. Darcy's Law for the Flow of Water through Soils. C. General Differential Equation for the Flow of Water through Homogeneous Soil. D. Forchheimer's Graphical Solution. E. Seepage through Dams; General Considerations. ·F. Seepage through' Homogeneous Isotropic Earth Dams. a. Appro:dmate Solution for a30°. c. Solution for a Horizontal Discharge Surface (a = 180°). d. Approximate Solutions for Overhanging Discharge Surfaces (90°

.h = - beh,·ern

2 9:?

L1he o/ Seepa9~ Tcm9enf fo Ot'schar9e ,cace. 0

ci)

----

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e)

I')

--~---~--

---~

Daf!echOn of' Line o/ See,va9e cd Boundan1 helwean Soils- of D.tl'rerenf Perrneoht!lr't;~

"

·~

1';::

:~

'

k,

.1::<

'' l' T.Jiscon ·1/nuif!:/ t.hua/

any two neighboring equipotential lines. __'l'l_1e s_e~nc{concli_!io]:l__!'efersJQJl!S',_§.!()_[Je __()f_tlle line of §_ee_plig(:) ILL the point of i:rl~en:{_'~tio~\jj:ll__[tllJ'bcmncl~I'YL~ls for exan_lpJe [j,t_tg~_poiilts of -e~tr~a~l-~e nncl there has been plotted m Figure 11 the relatwnslnps between the \·atw a

a+ t>a

and the angle a.

The quantity

n+ M

-

11 - ·-,

a.+t>a

f o - - - - - FOR 90'rhPrP the quantities of suitable material for tlw drainagP layer are \'Pry IimitPcl. To obtain thP ftmr nPt, the tntP sPrtion was tran~formed into a steeper seetion, using a~ transformation factor vk,/ k,, = v3. Tlw flow nPt was thrn obtained by Forchheinwr's graphical method, by gradual approximation. KotP tlw Pqui-distant horizontal lines intPrsecting the line of Reepage. These \\'E'l'