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HYDRAULICS BRANCH OFFICIAL FILE COPY

HYD-299 oFrlcE

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BUREAU OF RZCLAMATION HYDRAULIC LABORATORY

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Memorandu.'!l

To: E. W. Lane

From: A. C. Carter

Denver, Colorado October 25, 1950

Subject: Angle of repcse of noncohes;ve material

S\.Ull:'nary

Hyd. 299

Previous studies of the stable channel problem have established a need for :nformaticn pertaintng to angles of repose of granular materials.

A review was ma.de of a.11 published data. avai.la.ble on angles of repose and internal frlct,on for dry and submerged silt, sand, and gravel; and the results ,1ere compared graphically in an attempt to determine characteristic values. The published data did not fall intcanyconsistent pattern, but instead were scattered over a wide range. An angle of repose of 34° appeared to be typical for dry sand, but no other specific values could be determined.

Angle of repose tests were performed 1n the Bureau laboratories on granular materials. Results of these measurements showed a reduction in angle of repose for sand when submerged, but practically no change for gravel. Angular gravels had angles of repose 5 to 10° greater than rounded samples.

Introduction

Studies of one phase of the stable channel problem have been made of allovable tractive forces for trapezoidal channels having various side slopes. This investlgatton determined the relationship bet·.1een tractive and gravity forces act.'..ng on particles resting on channel slde slopes. To evaluate tracti.ve forces which would not �ause scour, it was found necessary to kn0� the angle of repose of the granular material composing the banks.

A review was made of all available data on angles of repose of noncohesive material which included published values from various sources and additional information obtained by tests performed in the Hydraulic Laboratory.

Published values of angle of repose for different types of granular material showed �')nsiderable variation, and some authors gave extremely wide ranges of values for a given type of material. Soils were usually described as earth, sand, gravel, et�., instead of being cla.ssi.fied by particle sl.ze. Since the term '"earth'" is general and may refer to boulders, gravel, sand, silt, or clay, it

was ar,fttl'le:d that the more specific term silt' applied, and the substitution was made.

Noncohesjve ma.teria.ls tested in the 1a.bxatory ranged in s:1 ze fron C, .15 tu 38 mn. Angles cf repose were measured for fc,ur coniitions: (1) stacked in uir, (2) stacked ln air and then subr:,er,.r,cd, (3) stacked under water, and. (4) sta.l!ked in s.ir whi.le damp. Rounded anJ angular gravels were tested separately.

Angle of Repose

Ar.gle of repose has been def:ned as' the maximum angle of sJ ope wh 1.ch the side of a heap or _:mbankrnent of sand, earth, etc. can have without sliding.' For c0heslonless soils the angle of repoee is usually measured in the un�ompacted state and has a constant value.

Angle cf Internal Frict1-on

Angle cf internal fr let ion has been defi.ned as "the angle whose tangent is the coefficient of fr5.ction' of a material. The coefficient of friction is the ratio of normal force to shear::n� force at the point of failure in shear. Accord1n,;r, to Terzagbi _Q/ "***labora r,ory experiments have sho·..,n that the angle of internal fri..ction of sand depends to a large extent on the initial densLty. The difference between the angle of internal frjetion of a given sand tn the densest and in the loosest state may be as high as 15°." He also states that '' in engineering problems the angle of internal friction of sand can usually be considered cJnsta.nt for practical purposes. The angle of repusP. *** is always approximately equal to the angle of i.nternal friction of sand Ln the loosest state." Since channel side slopes have some degree of consolidation, the angle of internal frict.ton would probably appl:r rather t.han the angle of repose. Angles of repose and inte::-nal frict:;.on were considered interchangeable for practical purposes in this memorandum.

Procedure

Anglea of repose and int-,ernal friction for stlt, sand, and gravel -..ere selected for study from 24 references. In general, angles of repose were found 'n eng:needng handbooks and a.ngles of· internal frict·ion Ln go'.l mechanics texts. The data are presented in Tables 1 through lJ. Sources of information are indicated by numerical references to �,he bibliography. Whenever gt ven, explanations of soil conditions are included w'th the original data. Angles of repose are plotted for dry materials in Figure 1 and for submerged roo.teria.ls in Figure 2. All types of granular soils are grouped under three main classifications: s1lt, sand, 3.nd gravel. Individual angle

2

of repoce values aie represented by s·ngle lines wtth one or more mun.er icc.l bibliograyhic references. Ranges of values are indicated by arr0ws dra�n bct4een two lines �h:ch represent the limits. Explanatory notee f')r certain fate. are lncJu-ied 1 n Figures 1 and 2 correspondlnes +.o ':he lcwer ca3e le �ters near the :ceferen�e nur-.bers.

To lll11st!:'ute the eL:ect uf cor._;;,r.c':.:cr; of non,::ohes:ve materials en their s.n�;les of .�nternal fr �ct ion

;_ d,P.ta fr•)r.1 the

U.S.W.E.S. Soil Mechani.::s Fact Fin'.Lng Survey c.2; are sho•..-n in F lgure 3 by ·plotting angle of internal friction against �nl tie.l void ratio. Void rat 1.o is the vulu,ne of voids <ii\ ided by the volume of solids. A kc;y- to the syr:f''),,ls 116(,'l for different sand-a is 1ncJuled i:i Pie figure. ?he an�les cf ·nternal fricti0n ·.,:ere determined by trihxial shear tests.

2imilar t.ests we:ce pel'f()rmed ,...,n sand !'roll' Zone 2 of Trcnt..,n Da.n, by the Bureau Earth Mo.tr-:rials La.b,1rat ;ry, ?4/ and the recuJ ts a.re presented in '!':iblc- 14-A. "..'he change :n angle of' internal fr�ct 1 cn with dens:ty is shJ.n ty plott.ing inte,·nal f'ri.ctjon angle aga:nst relative d'::ns"_ty in per:::,:-nt, Figure 3-A. �r·:lati ve :ien�. ity ls def'ned by the fc·ll..:rwing ccpnt ·on:

emax e ennx - emin

h e i th · d t · .f' th '1 � +h ' . t �t t e w .• ere mBX s . e vc1 rn Jo o,. e so;t _ _ n �. e .1.ocsee:; � a. e, min is the void ratio or the soi.l in the densest state, and e is the void ratio in the state for which the relat:lve density is desired.

A number of sand and gravel sa.mp]es were obta'ned locally, and their e.nr.;les of repose •.rere measured ty pcrscnneJ. of t.he H:,-draulic Laboratory. The results of this 1n-·,�ct" .2;ation were presented. 1;y C·. S. Hanson 1n n memorandum to E. W. lane dated March 27, 1950. The fir.<it of the.;·? mec.�urer.:e!'lts ·.rcre rf'pcrtecl by E. J. Carlson in a memorandum to E. W. Lane dated Ju 1.y 18. 194 J. Phctogra.phs of the samples tested were included in the or igina.l memorand\.Lms .

Seven different slzed samples weighing approximately 80 pounds 1were obta i.ned by �crccnj ng. These sanplcs ,,.,.ere stacked in ai:r, stacked in air and then �ubmcrged, stacked una_er water, and stacked in b. �r while de.mp; the e.ngJ.es of repose were. then dctc:::-rni nca_ by c,)ord i nn.te measure­ment$ of seven points on the slope. The original data. are presented in Table 15 and Figures 4 and 5. Bar graphs are used 'n these figures to represent measur .. _d angles of repone for 5aLples of d:,fferent s� z.r:: ranges. Dotted, br)ken 1 FL'ld sol�d l.'..n•:-c: :ndtca.tec1 ,.hethcr the sample was ctacked in air, stncked in air and th<>n surmerged, or stacked under ,:fater. Valu,,G fc,r rounj_e(l ma:er :al ur>2 nhown .:n FiguY-e h and for angular material in Figure 5.

3

k; :-ihc .. �-: ';: _1 !:'igure l , anllc o f .rep,)s� ve.J ue s suggested by diffe rent au t hor i t i e s t':)r lry �, hu; : onl t: l, S :11;. t,;:r · e.. 1 d0 no+� agree very c lc s e � 1 . Fr • iU,�nt l .· , •,. : :t•.> cange-, 0 f valu"G .. ere: g .:. ven ; ;:;uch data have l i t tle prucL cul s ign.:.f lcanc? . An angle cf repoc1e of 34°

a:rp•..!arcJ. t.o be f, _ r ,. _- r.___pr .- oen ,,, ":. · \--= f'1.,r d:·y ao.u'l , but l'.L s .ngle , f'l.::.uc s for s �lt ur G!-r! \ :'. ,.,,\�r,i d i s c L. s .-:d 'J.;' thest! ·ia ta .

R(! lat ively 1 1 ttle i..nf0rma t ion wa.;; fcun:.l on angles of repose of snbmerged rmter ' oJ . Sel ··· c t i.cn of a tn:i � cal value for s ilt , sand , or grav - 1 c , ·,t· l ·l not be v.a.::le .£"_-en:. the re·.: data sh:.wn

Reference to F :gu.r1: 3 wi 11 eh, w c learly ho..- degree t. f c c:npe. c :, iun nf:'e� t: .nfle of �nternal fr ; ct :. ( n o:- f i ve nate r .:.al s r.t ,.iiicd 'by the U . S . W . :C . S . 22/ As the v• · J rat · c- increases , the fr ' ct !cn El ne;J "' tl0creef' : !'- . The &verag1: va lue f.._ r three sands tes ted ,,..as 34 . )0 and. fer 1-ravE J 32 . 7° .

J c sul ��c c_. f : aboratory rr,easui·er:-ients repc :--ted by C. . S . Hi:,m,on 23/ showed e. reduct ion in the anile cf repose for sanJ when eu"o1:1erged , but nv c·hang� for gn...v e l . Angular grave l s had angles of repose 5 to 1c0 greo.ter than rcun<h:1 saF.,ple s of the same s i ze .

1-.ckncw led gments

The a.ss .'.. stance receh'ed fron. Mr . W . G . Holtz a.nd Mr . fl . J . G lbbs of the Ear th Materials Laboratory was very helpful i.n the preparat ion of th i s rep�rt .

4

). �· . 3 .

4 .

5 . 6 . 7 . 9 . ) .

10 . 11 . 1 2 .

13 . 14 .

15 . 16 .

1, . ...

18 .

19 . 20 . 21 .

22.

23 .

24 .

AnJersor. , Fau.l , Guli s c.-uc ture _!,i�ulJ·s � ., a nl De s i. �n , 194D , p 22. Bo.ver, L . D . , So .� l Phys : '-� '-' , 1)42 . Ca.:.n, tlill.i.a.'11 , Earth Fres s"J.Te, Re te. i n i !li; Wa.J l s crn1 "lins , 1 .116, Pr J , 21L . C 0 1 rp,3 j f Lni:, i.:1ecr '-' , _ r<.,c . J f t�E: S1) 1 ls ani �'<)1, 1 lat �'-n Conference c f the U . S . 3ng � neer Dep t . , JunP , 1?38, p 221 . Goodr ich , ��ans . A . S . C . E . , v ol 5 3 , p 3 )1 . ITo�entoJl e r , C. A . , Eng · nee r in; }r0pert ! e s of Jo '. l, 1937 , p 216. TI0 ,,1e , HaJ ver.l A . , P.c. ta.in : ng ·hl: l s fL r Dc1.�· th , 1) ,4 . :Iul3c n , � -lph G . , The Engineer::; �:ar.u." l , J S:17 , p liJ2 . Kr Jn inc, S .J : 1 Me chan � ::: s, 1947. Lcye,-ue, J..nr:.a:cs ::l� s :\mts e t Chau � sees , NO'. . 1385. Ifo.saey , Guri rgc B . , The Engineer Ln:_; of EX· 'e.vat i.on , 1923. Mer::""'. mo.n , ':' . , and W:.gg � n , T . H. , A:aP-r . C ivL! .. Enginecr3 Handbook , 1 )30 , Pr ! 32 , 392 , 12)3, 200 1. lla.t lonal Rcsr•urces C rJrrrn a :;ee , I o.,,, Jams , 1938. Paa.swe ll , Ck·orge , Re Le.i.m.ng ""Jall.,. , �he · !' De ::; le;n ::nc Con2 truct . _,n, 192J , JJ 45 . P atton , W. M . , A Pract ical Tr�at L se on Found a t ions , 190? . F' lu.'TIIller, Fred L. , and Dnre , ::; +.anley J,: . , Soi l Mechen:. ,, s and .:\Jund.a Lons, 194 ), yp 115 , ZJG. Proc . of 2nd Internat ional Conference on Soi l Me :::hanics and Fc-undntiun :Cngineer.:.ng , 1949 . Taylor , Den W . , Fundamentals of Soi l Mechanics, 1948. Ter z.aghi an.i f cck, Soil Mechanics i n Engineering Practi ce, 1948 . Terzaghi , Karl , ':'heoret lca2.. Soil Mec han � cs i 1943. Urquhart , L . C . C i\ i l Engineers Ha.na.bcok , 194c, , p 603 . U . S . W . E . S . So i l Me�ha.nL: s Fat:t -F � nd::'. ng Sur-,ey , Tr i ax i.al Shear Research an,i Pre ssure I,istr ibu:.ion S '�u-L e::.i l.,n Soi ls , Apr. 1947 . Hn.n::.0:1 , C . S . , Mernoru.ndwn to Lane , E. 'rl , , Angle ·:-,f Repose of Gra.vel an i So.nd Sanple s , �..ar . 27 , 1J5n E i l: , J . W . , Contrcll.'..ng Ea.r-th..:ork Dw· : ng Conetruct:on , advance pr i nt cf pape:r :presented at Con,;t::-uc t ion Engineer ' s Conference , Denver , Colorado, February 6-10 , l95C·.

JJIGLE CF INTEFHAI. FRI·.::�I �N Dat:-i. fr::;a • . -.n: .. �r s1.;n 2_:

M.a ter ial - -dr ./ ::'ercen"'.: vo ids

C -.:,ii 1· ..3 e- ..;L:t.nl F : ne r and r.nn �:l '-

32-- - J:_.,,\.;

3r,() .., ,-CJ ,) - ) ) 3'.>o

t '. , 1 · u··: ·1.nd c -:>ttrse i.r� ";:;!_fl'l,7,

frcm /.Jner .

Te.b l,:: 2

ANC;i..E (�F :-izr :,S.E DATA rr "" ,,,. . n J, · - \,.,1.� l_..,\..t - -

EEi t. · ::.· i ,:, } l.ngl e of' repose

Dr,, ::::E:.r, l 35L·

wt>t sand 4,JO 22 • v ,. ry wi> t s1 , nd :, 9° 3 ::-. ' Dar.rp fr'.csh -::ar tL 58° 28 '

C i •. i 1 Lr.gr · ·3 ?ocke t :I:lo,Jk , T; ·au t.w i ne ' s Engr · s ?o .. �k� t 'look anJ Fa.ri.k � nc ' s Trea. t : s e s

Me i s ·: sand Wet sand vrd inary dry eo.r�h , ::-d i r1a.ry r-_:., : s ...__ t.:o ,.. r,h Ord1 nary •..-et earth Gravel ( re mu t-: angular ) A v e ruEL' c .H:h.n s Emd. - -dry A , era.;e c leEi.n s�n,1- -L1L i s v Averace c lean se.nd - - ..-e1 .Average c l ean s a.nd - - submeri::;ed Ord inary earth- -dry Ordi nar:-.,· earth - -mo i s t l rd'i nary earth- -1-re t Ord.inury cartn- -sub:c;er6ed Sand

roe - 35° 3 '1° - 45 0

? 'P l�o0

2no - 450 25 0 - 4 5 0

2'.;(, - 30°

3,,o - 4cP 3 3 u 41 ' 4h r· 3 '1 '-' 4 1 1

26° 34 •

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I'i-.b lr; 3

� N .J �..E �-�F I iJT�qN.A� FR IC I: I ·...,N 1 . _,

D t r ... � · ·¥ '" - � � .... � / _________ --,-_h_a_i. r .:1 L.�L p .... ....., .L .....,u� .a..Ob e.i.. .3 -K � ro&l �r;s s �re In:t :aJ v 0 id

Nu.riter c,f b L:;· ... s )

2'3

3 i lts , Sr· r t s , SanJs ,

. � , r._ . • .,

d.ry

t,u;. ter l nl

t .:1.i.s ,. f -c:- r-at i o E' r i c t : on angle 1 6 l 6

. (. 1-:,

. $84 , 584 . 5 :)+

A,JG.i.L vF I NTJ:: ,.NA.._. FH l :'f �,;N :ls. ta fr::im Hogent..:,gle r �1

Angl 2 c f .�nte..:·nal

Tab l·� 5

fi�1GLE ::.F lll'.'.r'cs; , 1)a ta fr;,;m Ho.re .: . ./

:,J.. . 29 . 3°

3 3 , 3° 3 1 . 8°

fr .:. c t i on

Angle of repose from Rankine ' s Ap1,1 l..:.cd r,;e .::ha.nL: s

Ear tn 14° 45°

21° - J7° 3 9° - 48°

Dr,f sand Gro.veJ. -----------------------�"'---

Dr- y : aanJ

Mat e r i.al Eart:i 1.m -�ar th

0;ri.1ve l er soi 1 cobb les

·rao l c 6

AI:r}LE uF i1.3F .JS....,

::Ja tu from Hudson �/ -----------Ang l c of repose

'l'ab le 7

.A.'1W:::..E 0F REFvGr.. l ·1 / Do.ta i'rvm Mas sey .::...::

Angle o.f repose

1 -1 /2 : l 1 - 1/3 : 1 1 - 1 /4 : 1

T1::.b l e ( - -C )n t _;_nued

-----,-----=--r-:a_t_e_r_.:.._a_l _____________ An__,,g.,__l_e __ o_1_� _r_e_p_o_s_e _____ _ Depos i ted ur.:icr ·,,utcr :

sr.nd o.n,l gru·; .s l

T9..o lc 8

\ /-Jl G I.E. ·�.F' Rl:::P vSE

2 : 1 .3 ei.r.a 4 : 1 . / ' .L - 1 . 4 : l

------·----- __ :>ata .:.'rcr:: Mc: 1-r , .. ....1..: �.n.1 w ie<, .. 1 2 / n -i-'. •1 r, _ ". · t .;. Angle e;f rep0 s e ---------

Cu�p i led 'b., Fa � l: f r Ji.1 Exper iments b y !·k-r ;.n anJ.

J;·:,; (_.!0 l t l1

� f:.. !'1 (1

S i�e - s � Jva ex�uvut �0n : f i t·r.1 f?L .. !' t-.:,(1 very sof:, earth , qu .'... cksand ::;und , c lc:a11 t::rav,2 .l r-- i 1 .. , ., ,._ .J..

Sutr10r :w: · lope s - and ) � lt.:hr.1 gra ve l S'- � l

( ,hi.:.r;,.;ed >l..te,) :

C anal bank s - - submt:rged w .:.. th current ( I nj_ :. a ) :

al lm, :�u:: .::o i. l , ·u�rJ f :.. r�: i...::ruvc l s 1� iff earth loo se e£L_r· ;:;h

Tab l e 9

14 ) - 4:5°

21 � - ·n(' 39° - 48°

1 : 1 4 : 1

33 '-' 4 1 ' 36° 5 1 ' j _f) 4 1. •

..... . �l) CfJ

2G -' 15°

)� I

54 • ., ,..., ' .) '

63° 20 ' 1.-50

2G0 30 ' t.c 18° 20 '

ANG :..E F · :BP ( SE 14 / Data .. ' r" ;m : c.t..e wcl] -' Via ti= r �al Angle c f rcpr st: ------S-a-nd______________

220 Gra vel 3 1°

,.

',

Tabl e 10

ANGLE OF REPOSE15 Data from Patton _/

Material Angle of repose from Tre.u+,wine :

shingle and gravel

Table 11

ANGLE CF REPOSE Data from Plummer and Dore 16/

Material Angle of repose Sand Muddy sand Dense sand and gravel

Table 12

A...�OLE C,F REPOSE Data from Ter zarhi 20/

300 - 400 30°

34°

Material Sand

Angle of internal fr:c t ion Angle of repose

up to 35°

Tab le 13

ANGLE OF REFUSE 21/ Data from Urguhart Material Angle of repose

from Cain _ sand, dry sand, moist sand , wet ord inary earth, dry ordinary earth, moi st ordinary earth, wet gravel, round to angular gravel , sand and clay

from Goodrich bank sand quicksand , 100 up (Tyler s i eve ) quicksand , 50-100 (Tyler s ieve ) sand , 50-100 ( Tyler s ieve ) gravel , 1/2" gravel , 1/4" bank sand sand , 30- 50 { Tyler s ieve) sand , 20 - 30 (Tyler sieve )

20° - 35°

30° - 45°

20° - 4o0

20° - 45°

25° - 45°

25° - 30°

30° - 480 20° - 37°

540 42°

37°

29°

25°

19°

19°

14°

10°

Table 13 - -Cor.tinued Mater i al Angle of repose

from B. Baker earth

from Steel earth

from Wilson banksand

Table 14

ANGL-.: OF INTERNAL F! HC'T'ION

Data from U. S . W. E . S. 22/

48°

37°

37°

Material Initial voi d ratio Angle ,..)f .i nternal fri c t i on Frank l in FaJ.ls sand 0.65

. 10

. Bo

. 85 Keystone Dam sand . J25

. 550

. 575 . 600

Chen sand .6 . 7 . 8

Sardi s Dam shell . 55 . 60 . 70 . 80

Pit Run gravel .45 . 50 , 55

Table 14 -A

AHGLE OF INTE."1tNAL FR ICTI UN

Data from Bilf 24 / l'-:aterial

Sand placed :i n

Zone 2 , Trenton Darr,

•

Relative denstty - -% Internal 23 38 50 73 84

36. 9 36 . 0 34 . 5 3 3 - 5 32 . 9 32 . 4

32 . 1 3 1 . 9 42. 0 38 . 0 3!.+ . 2 36. 1 34 . 6 32. 1 29 . 7 33 .6 32 . 7 3 1 . 7

fr tction angle , ¢

·:>ab le 15 l

.A.i.�GLE OF RE?LSE

Dn:a . fro� Hanson 23/ Sta.eke� ·i n

S i ze Shape Stacked :n a i r and Stacked S tacked in IllI:'t a i r submerp:ed under H,.,') air damp '-

19 - 38 rounded 32 32 31 29 35*

• angular 39 38 4o 40 37*

9 , 5 - 19 rounded 24 25 29 27 3 5*/

angular 37 35 34 38 33*

4. 7 - 9 . 5 rounded 25 25 26 3 3 angular 31 30 32 - 32

32* 1 : 1 : l mixt .

of above 32 28 29 2 .4 - 4. 7 rounded 34 32 33 34 1 . 2 - 2 .4 rounded 35 33 29 47 . 15 - .42 rcunded 32 27 29 90

* data from memorand\l.'.IJ of 7 - 18-49 san'ple unwashed and conta ined some sand

. ..

o• , o o,.,

0 -e-

w f/) 0 a.. w a:

LL 0

w _J

(!) z <(

50 __ _

40 __ _

30 __ _

I tV I b

C

-----<211-----1

I w (14) I

r ---.z---

20 ___ ______ ____ �---,.-L-� ---- s

d

1 0 __ _

S I LT

0 ----- 1 (y � -----

S A N D G R A V E L 0 --- ,___ __ ____, ---- .._ ___ __, ---- ,___ __ �

T Y P E O F M A T E R I A L - D R Y

ANGLE OF REPOSE DATA F R OM

TAB L E S 1 - 1 3

N O T E S ..

N u m be r s r e f e r t o b i b l i o g r a p h y

a B a k e r b f i r m e a r t h c S t e e l d s o f t e a r t h e bo n k s o n d ,

q u i c k sa n d 1 0 0 g b o n k s o n d - W i l so n ,

q u i c k s a n d 50- 100 h c o a r s e , l oo se s a n d

f i n e , d e n s e s a n d

k s a n d 5 0 - 1 00 I b o n k s o n d m q u i c k s a n d n s a n d 3 0 - 5 0 0 2 0 - 3 0 p l oo s e g r o v e l q d e n s e r I /2 " s I / 4 1 1

" I I

"

..,, G') C ::0 ,,,

OIJ O O,I �

50

I �

40

I I 30

(/) 0 a. w a:: I

LL 20 I 0

w _j (!) z <(

1 0 I I

S I LT I I

0

T Y P E

ANGLE

:,, .)

l,

I @

I I I

I S A N D I I G R AVE L

O F M AT E R I A L - S UB M E RG E D

OF REPOSE DATA FROM

TABLES I - 13

I

I

N OT E S

., ..

Nu m b e r s refer t o

b i b l i o g r a p h y

a s t i f f e a r t h ,

c u r r e n t - I n d i a

b l o o s e e a r t h ,

c u r r e n t - I n d i o

'Tl -G')

C ::n C'11

""

8 0

z 0

t- 60 u er: u..

_J

2 4 0

z

0 20

_J

z

0

•.

0

O Fr a n k l i n Fo l l s s a n d

8 K e y s t o n e D o m s a n d

'¥1 C h e n s a n d

o S a r d i s D o m s h e l l m o t e r 1 o l

O P i t r un g r o v e l

. 2 .4 .6 I N I T I A L VO I D R AT I O e p

R E L A T I O N S OF A N G LE OF

F I G U R E 3

.8 1 .0

I N T E R NA L F R I C T I O N TO V O I D R A T I O DATA FROM TABLE 14

0

-e-

50

,.40 z 0

l-o -0:: LL 30 _j <t z 0:: w 1-z 20

LL. 0

w _j

l!> 1 0 z <t

V

0 0

\

F I G U R E 3 - A

_.,.,,,-V

/ ......

/ 0

/ /· V

V

/

'

20 4 0 60 80 100 R E L AT I V E D E N S I T Y - P E R C E N T, D r

R E L AT I O N OF I N T E R N A L F R I C T I O N A N G L E

T O R E L A T I V E DE N S I T Y

0 S A N D , Z O N E 2 , T R E N T O N DA M

, ,

OiJ 'l .:. ,u

0 -&

w (/)

50_

40_

Q. , .. . . .. . . . . UJ 30 a:: -

� 0

uJ _J

<.!> 20_ z

I Q __

-- -- --

. 15 - .42

o _ , ___ _

� - - - -

1 .2 - 2.4 2.4-4 .7

I I I

m i x t u r e , __

o f 3

l a r g e s t

s i z e s

4.7 -38

t-,... ... ... -.... .,,,.

4 7-9.5

R A N G E OF S I ZE m m

AN G L ES OF R E POSE

F ROM

FOR ROUNDE D

TABLE 1 5

· · ·¥<·#· · · . . · * . . . .

ti,--.., .. ....... ..

. . . ... . ... .. . #

� -- - - 1·

9.5 - 1 9 1 9 - 38

MAT E R IAL

N OT E S

· • · • • · • · S t o c k e d i n

a i r

- - - - S t o c k e d , n

a i r a n d

s u b m e r g e d

- S t o c k e d , n

w a t e r

* M e m o o f

7 - 1 8 - 4 9

•

# U n w a s h e d - ­

c o n t a i n e d

s o m e s a n d

.,, G') C ::0 "' �

' ..... '.

�-- � , .. .-;,

0

-e-

lJJ (/)

50 ___ _

40. ___ _

I- - - - -

. . . * · . . .

t:": ::-: .;. ::-: �

N O T E S

• • • · • · • • S t o c k e d 1 n a i r

- - - - S t a c k e d 1 n a i r

a n d s u b m e r g e d

--- S t o c k e d i n w a t e r

0 a.. w er. 30. ____ r:�::: : . .-.::� ---- * M e m o o f 7 - 1 8 - 49

LL 0

w _J (.!) z 20 ____ _

1 0 ___ _

4,7-9.5 9.5 - 1 9 1 9 - 38 o _______ ..___--J-_____ �-��---�--

A N G L E S OF

R A N G E O F S I Z E m m

R E PO S E F O R F RO M TAB L E

A N GULAR M AT E R I A L 1 5

.,, G) C ::lJ rn

.0,

Denver , Colorado

�,arc h 27 , 19 50

To E . �·I . Lane

From 0. :3 . Hanson

S ubject : Ane-le of repo�· e of gravel and f: and srurples

1. In c onnec tion with the prelimina ry work on stable cr,annel invet�tigat ions t he angle of repose of various cravel c1nd s ;-md sampler: ,,:R.s measured under n variety of condit ion!"' . The firft of thec-e me;:i suremi=.nt s were made by E . J . Carlson and reported in a memorandum to you diited July 18 , 1949 . '.I'he ne original measurement s were all made on dry gravel samples 5tncked in Hir .

2 . The program was cont im.1.ed nt r:i l8ter date by meaf:uring these and additiona.l sampleG stac ked in air , stacked in air and then subn:erged , stacked under water, and stacked in air ·while damp . 'I'he:ce mea surements were made using apJ.,roxi�ntely 130 pounds of each sample and f't ncking the grnvel a gain,t the wnll of a t in lined bo:x . The angle of repose v.-as determined from nat urnl ti ngent s calcu l2ted by mnking hori­zont al and vert ical measurement s at seven point s on the slope .

3 . The following table shows the result s o.f these mea , urer.ient " inc luding those covered by the memorandum of July 18 , 1949 . Photog-raphi· of "' ,3J'Ilr,les meM ured are attached .

S i ze Shape

19 mm t o 38 Ir.IIl rounded ( 3/4 to l 1/2 in . )

angular

9 . 5 mm to 19 mm rounded ( 3/8 to 3/4 in. )

angular

4 . 7 mm t o 9 . 5 mm rounded ( 0. 18 5 to 3/8 in . ) angula.r

1 : 1 : l mixture of above

2 .4 mm to 4 - 7 mm rounded

1 . 2 mm to 2 .4 mm rounded

. 15 mm to . 42 nnn rounded

Angle in derree s from -Stacked Stac ked

in air

32 3 5* " Q

37,r

24 3 5*# 37 33-:f

2 5 31 32-:�

32

34

3 5

32

in air and

submerged

32

2 5

3 5

2 5 30

32

27

-1 � data from memorandum of July 18 , 1949

the hor i ;:,ontal Stacked jtac ked under in air water dEimp

;l 29

40 40

29 27

'34 38

26 33 'l� _,,{ 32

28 29

'l 'l 34 29 47

29 90

#' t his srun:i:,le ·as unwri shed and cont? ined some sand

Photograph No .

H-84 5-12

H-845-7

H-845-11

H-845-8

H-845-10 H-845-9

r-;-5676

h-5675

l';-5 589

•

4 . Result s of the i: e mea::urement s f3how that for the gravel 1::ample s there is practic ally no chc'lnge in the angle of repose in air or under water . The sand samples , however, do show a reduction in ane;le of repose when submerged . The magnitude of this reduction increases as t he diameter decreases . The smaller sands also showed an appreciable inc rease in angle when piled while damp •.dth the 0 . 15 mm to 0 . 42 mm sand standing vert ical . The effect of shape iE sho�n by t he angular gravels having a greater angle of repo�e than the rounded samples by 5 to 10 degrees .

/s/ Odin S . Hanson

ROUNDED

ANGULAR

1 9 mm TO 3 8 mm 3 I 4 in . TO 1 / 2 in .

ROUNDED

ANGULAR

9 . 5 mm TO 1 9 mm 3 / 8 in . TO 3 / 4 in .

ROUNDED

ANGU LAR

4 . 7 mm TO 9 . 5 mm 0 . 1 8 5 in . TO 3 / 8 in .

2 . 4 mm TO 4 . 7 mm

1 . 2 mm TO 2 . 4 mm

ENLARGED PHOTOGRAPHS OF SAND SAMP LE S

0 . 1 5 mm TO O . 4 2 mm

E N LARGED PHOTOGRAPH OF SAND SAMP LE

•

To E . W. Lane

From E . J . Carlson

Denver , Colorado

July 18 , 1949

Subject : Angle of repose of gravel samples

J. . On July 5 , t he angle of repose was mea sured of several grBvel samples that were on the Bureau Laboratories unlonding docks . To determine this angle an adjustable square with a protractor head , together -..-ith a 5-foot metal straight­edge was used in the manner shown in enc losed Photograph l! -84 5-1 .

2 . Tabulated belo ... · i s a list of the samples fiv ing the Jngle of repose ( in nir) , s ize classification , and the number of the enc los ed photo£rRph which is a picture of the material .

J . All the samples were obtained from the J . B . Bertrand 3and and Gravel Company, 4295 York 0treet , on Clear Creek . :3 &.rr.ples No . 1 and 2 were in the condition as delivered . ::irunples No . 3 to 5, inc lusive , were rewashed and graded in the Bureau' s Materials Laboratory . .3 ample No . 2 had some sand remaining in the gravel .

LIST OF 3A.MPLES

Angle of repose average of 3 i ze

Sample No . 3 msmt s clafsif ication Photograph No . 1 3 5 .0° 3/4 in to 1-1/2 in H-845-2

2 34 - 9° 1/4 in to 3/4 in H-84 5-5

3 32 . 2° No 4 mesh to 3/8 in H-845-6

4 33 - 3

° 3/8 in to 3/4 in H-e4 5-4

5 37 . 0° 3/4 in to 1-1/2 in H-84 5-3

Enclosure ( 1)

ROUNDED ANG LE OF REPOSE 3 4 . o0

ANGULAR ANGLE OF REPOSE 3 7 . o0

3 / 4 in . TO 1 - 1 / 2 in . GRAVE L

•

3 / 8 in . TO 3 / 4 in . GRAVEL ANGLE OF REPOSE 3 3 . 3 o

1 / 4 in . TO 3 / 4 in . GRAVE L ANGLE OF REPOSE 34 . go

0 . 1 8 5 in . TO 3 / 8 i n . GR AVE L

ANGLE OF REPOSE 3 2 . 2 °

,.