The effect of angularity on the shearing strength of sands

r·ro~ontaa.

_..

for the degree

''' c,.·~~~., ·· ·· ·.~:·,/.,:l'l

rr-...

1:~·.-.·.,·.·'II·.J• \. r .. ·.:.r·."IL)

.1.4/\\..Lt.~.'..t·. <J;..· ~ "...._ l- • .. ~·\..'f .

a- ... "" -41!UZIII • 7F'$ -• '1f a * - •• I •

ENGINEERIN8 UBMRY

TA

(10

'G:t>~~

\~5b

C/)f~

I

dnif'orm and ungraded 8f'1Hlt,'>les w·et-e also co:na!deroee ..

1 t hoa been :f'ound thnt the shearing st-rength is nffeoted

1. r.L'he Qllgulari t;!l

ot

the) snno,.

apec1ficull;/ in tho asse ;vh~re no volume chang.ea take place, 'by the cr1 tioa.l voida ratio \voids

ratio for no vol'Witle

nhnngo) ..

aN'~oting the ~o-e:fficle.at oi' blid1ng rrtot1on. Evidence h8B beP.-n found 1'or e: relati..:>nehip of.' tl\e :t'orru;

log,₀(1 + ea}

tan¢

=

H. m +a

where

llc ZliO ori·tieal voids ratio

t/J

~ munn un.glE"' of internal friction

n

IS l'OUhdneaa of E&£1nd (as defined by Wt;tdell) lQ

₌

conrrtant

COLOUR PHOTOMICROGRAPH

OF

BRIGHTON

BEACH

SAN D.

SAND SIZE: RETAINED ON A.S. T. M. 60 SIEVE.

~

.

SCALE: O·SMM.

/-·:auch. of the work t:;n.tliiled tn this the~1a

cn!JlU. not luwo Jlften done without the oo-op!.'lJ'(+tion

or the raembera of: the i~· t.s:t't' or Ca11tarbury :;;ollege

outside the ~~ivil. Engine~;.;:Pi.!!.~~ J..opurtment. Per-t1oular thanlu1 are due t.o Lr Gage of the ueology .Lepartment and. \ir lJen.r.e~i or the :J.ntlwmatico

l..,epe.l't-ment.

¥H thin the t'.~tvil r·~r,r;1neer1:ng .: epa:rt~ent Jr.

i? • ~ • Alley n.nu nh"' • ··: • i": • l'usoce al.'e ~~1'0. te~lly

thw1keO. i'ur t.l&e asiz.J1str.moe the~· b'·ve with the

\1)

\3)

( <1)

\a) :ihenrin.g .~ t..:t"Ongth \ li) Parttcle ~ihape

\a) Bh.ear Dtreni-~th An~uysis

t,b) J'('\e ura.(Jjng of' tLe ~.i~md.t>

( 1_•) Sand Samples Inveati~e.ted

\a) 1:::xper!ments Unoe:rtrzken

~a) '!he 1~irect ~htHlt' (,l.achine (b) Dhcnr T!tst:l.ng Procedure \c) ;,jeasurai•len t of tipher1c 1 'ty

\.d) ~ . .teasul~emcr. t •Jf Roundness

(e) Grauinf': Allal;yais

\ t) f~el!!r;urement of G:pecif"ic Grnvity

1. Volw;le ohunges dUl"irJg lihear~ (·md

1 1 ·'i 11 1.1 12 13 14

1?

17 22 23 24 24

the ot•i t i oal v oius ratio 46

, a) · ... ·he '>'GlU.h.le ch~wge/ time o·urvel!l 2ti

\ o) i.h:mor,,l ·.Jb:oervations on. the Upeod

o.nd AlUount ot' \/olwne Ghnnge U7 ~c) The Ird tial Voil.i.rJ .Hatio/Volume

_.

(d) 'i1

he cri ticnl voida I~atio

2. Sheal'j.ng roree vshl9s d;.rrirw lille~i!'ing Pt:r rt oCI.

.~. Adjustnien t tr.t ;::.Jlenr:ing 11'oroe curves to

r.·,ompell.ot>C te tor Volume iho.ngoe

\H) '.\'i~e i\Of!'t·s~:L\.on r'urve

\b) '~h.e Shenr Gtt~emgth 1/oluoa

28

28

33

4. r~oundfi~Bf!· ~nd ;;,:;pbetl'init:v Joluea

~D) >1oundn8St3 V~,luea

( o) ;Spi1ertci t~/ lf,•;lues

5. t:pec1f'1c l~ravi ty ~·alues

\ 5)

tTP~pha ot: Bnmis Invest:i i:~9tea

fu.::::.;:.;d::!!

~t!!

£umple C~,;loulbtiona f1.)t' He~~l*eueion i]lU'Ve

H.na c:orrip1.lnt..ion Qf Besults

;Jinc:ralo";?,i<wl C.o!upo:d tion of ;~ew Pl:l'moutl1 1ieaell Uun.d.

Page

~~.., 3.7

83

·;.-hen o soil la a a tate oi' etress auddenly f&1la, 1 t

invariably does eo as a allet.il' failure. A study

of'

shear

atx-ength 1s

therefore or

vltal lmporte.noe to the

sotence

of ooil mechuntce.

In tLl1o thesis on attempt hoe been zuade to correlate the shear atret.q;th values of various arums, (ae measured in tt.~.e

c1rect Dhear Hmch1He) with the o.ctuul shape ai~ the aund

pur-t.ioles. Ae a f~o.r1a o~ refet>ence

tor

the w ~-r:-ulor1 ty IOO&L$ure

t1hear teato we:re dooe on

unllottni

tilaaa ueoda

of

s&mi uiameter • . .J..ll1B leads us then alon. t':iO 11uea of thought, the concept of

:P1ratly ~heur i.Jtre.J,f:r;th:

French en .11 <aer (~oulomo in 1'.~76 ts

nG

rollowe:-p

=

c':o.rmnl lond

a.

1 t vir1a L·::nown in connection with liq.uef'ect.ion pher.omena

in uond that ·.,~olurJe Chall$-;es take place \\"heJl sand f'aila in

she(lr,

o:f 'J<)lume olta&lt..;e waa depe.Llo.eut OH tite 1n1 tisl voicia ratio.

\ie ,ri.otteu vol\.U:.e r~hsnge agoin~t 1n1 t1o.l voids ratio unu

:.:•ro-in 't1!1s thesis). Ttte 11.'.i t1al void.& ratio at wl11ch ,ljo volume

voiu.a ratio''. '.f;i.ia ,.;a~~t f.:Ju.nd to ue d.epeH<lent ou the e.xperi.uento~

It' the eoui'i:.ing pret;;;su.re in the case o!' t.ria.xinl

anoor, or the HOl';Jal

lona.

in tne case of' uirect shenr, was

inoreneeu, the critical voids I'atio dec~eaaed and vice

versa

':'his 1a ae one w·<;rulu 8%!-}eat.

i'he aot,;unl foroe opposing the allear1ag action is ;·,1ad.e up

of" tnreo·e:rreota:

\1) 'ihe ulldi:n~.; friction 1.,_: tl1e qQr.,.ol c~l1ti1Jil',; rr1ot11Jlc of' oue :..mteriul on SllOLher.

\, ) /i1o ro111r.>.E: f'l"tction, ns 1 ts t..oi:le 1J~tpl1es 't.l'!e

frictional .rorces developed in :roll1H,. particle&

over or~.o f)HOthar.

\~)) .·he 1n~erlockiub affect, or 'tiie el .. :t'ect ot' :I~ovei:b.f.Jt

~~~OI18ider n sand in aheur:

the vert.icnl ctirection or~ly, ''S it. lt,; in

let n == norHtr~l load.

'.{>len equating rates of work:

sw

pta."~. Sd..A

St

=

St.

&h

±

P.A.r;t

Now tJ.;e force as :.:eaaured. on the proving ring of' the

Jirect sheur vaaohine gives a meaaure of the appnrent angle

of 1nter.·al f'r1otiof1, and Wl>~~tl multiplied by the distance sheared, .ives the work inr,ut on shearing.

&'fi == p tr:An,~

*

A • cSd

+

p.tanq~A.Sc:L= ~.tQn;.A.Sci ~

-p.A.ih.

or in ter"•a of' rntee

J.. _&_§. ,J.I Sd

tGH ~,

n

=

tGn 'f' • -:;:i

-

_I

whore

it

₌

I'(t te atruin.

-fli

=

rate i!hatsge

vert.

lLt.

l.~oth these lust ure easily lheaaured fltlU t.h.utJ the true nu~.,le o.·c inter, nl friction may be calculated..

l.ii;Jologiuts have lon~·: used the shape and row~d.l~eaa of'

aro.~.<i ~,;raia.L.> to uetermiue the r.1story of the sa:na rormntion.

·rl.e~,.. have therefore evolved i,tethod.a of hleaeuriug tuese pro-pertiea.

'io oet up a system of' sh&pe ;aeasurewent uome atHndard

of ·raferer .oe is necessary • Por this purpose the sphere is

/

..

.JOt:uy' ... i;; :i..i'J cla.sl:lii'hHJ :._;:,;;;u il.t\) l'ive ~.roupl::l w.:coruihi:

well W:? t:JiHwe n,,.u iu : Oi.. uut.li.;:ruotor~/·

face to the mean radius of ti:e Nbble.

t1r1ses llel'e o·.:ex- 't.he uof"ini tiotJ. of' 100&'1 radius, whether 1 t oe

the er1thw.et1o or geometric ;r.ean.

As ma;r be aeen those ,ru~auure~l.ients were relati ·vely ooa1ly t.Lo.no on pebblt:.;a, but aru"d · ra1{>s posed n dif'f'erent prolJleul ..

:.Jevernl experiElO• • tere t:ried • • • • usi ·:.g. visual met' )ode and oamern lr.1o1cta drawin~~s,. but nolle were entirely eat1af'actc.lry.

'•\uQ.ell ::..;J uppe~ra to hctve uee:n tt1e i~ir~t t.o (.•.1fi'aro.::t.1nte betwee.lJ. shape \. opher1c1 t:~) and l'()W.J.d.neae l r1~:.;or of wear J. lie

·..;.

corners ar.cl edt:ee of o t'Crnb•, wl:ereos eho.pe haa t.·.:> do w1 tlt the overall

fom

of tl~.e .. :rnin 1ndepende .tly of the aharpneee of

!_:.(}

Ladcll'' "' proposed to use the sphel'e ns a stru1tiard

of ref'eret.oe, ar.!li to ep!EH'l!{ of "degt'ee of' ephex-1oi ty" or

''aphor1c1 ty" as a t!le&sure of the epproBch of the ahupe of' unotller uoliti to a sphere.. i'he rutio oi' t:-,e tcurfuce o.reus

or

2 particles of the BttiYle volume

t..J•

vee o relative moueure

or

the epherici ty, but ow1n~~ to ttte uii':fio·ul ty or ~neaeurement,

t'sdell£: · .proposed ue1ng nn c.pprox1tuo.t1on.

where Cle • dif.L:J. t) 1rcle equ.ol in area to the oren

7.

th.e grain.

where di&h smo.lleat o1role airoWliJorioi:r-4::. the projeotivn.

This i'lleth,')d neceusarily .f'nlla in error in tt.1e ca.ee Of

very f'lat .~;l .. oina.

Houndness is

e.

function of the sha.~neaa o!' the e~ee ..

~.!olida iliay ho.ve perfect ruunaneaa 1n4epeHa.eutly of shape

o.~. t.m objeot of cylindrical :torm witH he.mi.opberical e ... de

hoe perfect rowl.dne&lh

Hounw:.ess. woe there~ore defined aa a value co:aputed from a projection or cross section, where t.,.,e racl1us

ot

the

1nd1V1duel corllEtra 1e divide<'. by tho re.dius o~ tJ"!e 1:i.8ximum inscribed circle

where

_r

₌

'-f-L

•

~p

ra.diut:~ ·corner.

1" :1 rodius mEix1rmll!l

1necrtoed

circle.

...

.li c:ll .uu:..1ber of' oorr:era •

a·

_•

ore often applied to ~nd particles. Pett1Joim

\ . 17

has eet up 5 l'Ound:uass ; .rndea aeoordii1g to a geometric rule, ut~ iug

~{OULdne:.:;a '{CHL.itJ.i"O OS

~ clulil~c; l_,:\l.d tu) \ iJ00.At:t:PiC .;;dti;!• ;i: d.}

.) _{·,).15 J.lJ5}

•

•. uu-i1r.\: .,, lot" >.1 ' ,:). :. 5 .t.UJJ

). 85 J.40

).4'] ) ... ~;)

·).JO 1. ·) '). ;).)0

tlu::~.t ~V•:.1J.e euo.h snnd particle Lttia its owu sphcr1t~i t:l value,

I ~

>

§ C:

<·

,,

.... iuks ~.,oulute)

n ::..> 3

II

&

_>

_~

..

_b

c

_.::::.

.., .... ~.~phnrical { eqt~luxial)

tl

.,

;•,

~- £

_<

§

I I I .:;;.

<

·lHdes <, tr 1 axial)

8 ·u

:i 'i L; ,, c

>

~ h'Od.S t :c rolate)

&

<

'5 b

ZINGG SPHEJ31CITY_·

PL0~~-1

BLADEO ROD-LIKE.

~10

;t.,::u:;r rtH:l1_{)t!l"CI>e!'a,} notabl~.; _{in t..he} phyatcol •:!hem1atry

t·ielu, ouch ae >a .. ~f<.r1:1 ana ~e;;w.)oa'~ • ·;; ' 10 hnva ;::~et up bYS teme

fioE:Jaiule :fa.ctors w~ ich r:Ir?.:J 1nf'lu.enoe the nJ~(,;le of' 1nterHal .friction~ • end consequently tlte bheur ~t.rengt.ll

'i'b.e ~;~ndtn..t-3 of th.e sand.

'l'lte ~ak groin a1ze of the sand. '.J.'he pf!rticle sh.ape co~lf;isting of~

\H) Gpl1er1e1

tv.

\ b} Houndness.

4. The purt.iole aurf'ece texture i.o~ e:rrect of

!)Ure sl1dinE frtctiorL

5. ·i''he va1do r~tio of the sample. ·;;. 1.~1e woter content of' the sample.

The WQter eon.te.nt factor h:)S ~.Jean investigated ~)Y several

wori·::era, and in the experiments cnrried out in thie work dry

: nno woe uaed for nll teuts. E:xper1uents were cnrr1ed out

~.tsiug the residue left on o.ce sieve oul~·, the effect of the

..:·eats wex-e l::::ter o.~.H-.ried out us1ug

'i'he voids rntio, apher1o1 ty, EL:o. roum.Lte&s nrc all

ef'fect8 of' these on the ahenr ~trength.

I' nus

standard vo1d~1 11nti~,, the ct•i tical void.~ r•atio.

JH shop' . J1ncl~·st.s ·of the shear strongtJl/time eurve

•;Vas also used. to prov:l de n stnndard of' tl1e tm€:le of t.nterr;al

friction.

correcteu toate over the 4 n•tnut.e teat period, l:'c;,r cny

fhua we have 4 measurements to Htlte on the l.!;ro.d.ed

1. 'l'ha i:!OWi value of'

¢>.

~~'

...

_.

~'he crit.ical voids ratio.

3. ·~lie ...:pher1c1 ty.

l~. -~'.,e _roundrtess.

\{hEm a sauc is eeporatea iuto t. ts COdmone.c;.t t.~L~es ttte relative nmount of each size group, when r1ottea. ar.,nin, .t si~e,

.'\

gives e frequency ui,;,tributio:n :t"or t.l1~~ vcrivus ei:c:-.es. :.several workers hove utter,,;pted to provide a t;,eiternlised :f'ortu:ula for

\ aee f1p enu1x 2 Urf'\ph 2) uoes uot toll ···J.s very u1uoh about the

scxJe laws relating to the f'requeucy ctietrLA• tion ot• BEwda

,,. ,''}

~,h.ockley and C::.~il"be:r'''-1 :f'Urtner elaboruted tlt.ia theory. f:L,.d

utated tlwt ti.1e dintribution of" a sn1_td is _such thu.t the

frequency of occurrence of.' t1 ~~iven grailt size decreased nt

a coru~tnnt logari thn:do rate t'or eizea coarser ar:d. l"'iner t.hr:sn

'l'hia diatribution hna three )arah.etera:

B. ri'he slope of the .:i7r<~quene;y curve f'or values co~Jl"k!er than the Hode.

3 ~ The slop.e ot• the treque.loy curve 'tor values tin•?r than the mode.

'.L'll.e~,- found furt,her thot the value of the oofll'eer slope .was reasonably constunt f'or all values of the p-~Bk g1•uin

(~·be value or the fiuer Hlope was round to lie conetvnt :ror a certain value

or

the H40de.l grain a1ze, :Jut

It should be pointed m.tt that ,,11 their teuta were carried

out with alluvial saude .frc:w the ).1aatee1pp1

taver

delta

'?he t·requency distributions of' the ;.:}•,,·JCin used in these shear

aand.$1 2 wave depout ted. ~tmds, uotll rounoe<J, OL't o.f widely

d1:ffer1ng mineralogical t.;vp~e, and ~1 nlluvir;:l snncte very different in tneir grodinEa, plus the ballotini gluwe beada.

A .full aeries ot: teets was oar•t•ied. out on ~34 uifferent art:lples, these beint selected to ehow:

1. Vuttiotion uetween tho aur~cls for one pat•ticul('Jr grudio~ si~e, an<t relating this to the equ.ivaleHt glasa

~~. \~e.riation wi tniu a s1 ;,.gle utmd o~tween the vnr _ous eradif.Lt: t\1~ee \if ~my}.

5. Variotim·t tie tween tlle grade uize and the uugruued

't'Le ui~ea with Yitioh it. wne praoti·~eble to work were somewhat 11m1ted owlrli~ to the u:1asu1ve nn1ounta o-r sond. w1;1ch

hud to be sieved !:r1 order to eolleot ~uff1o1ent to !"ill the

'l:his l1m1 ted the

expert-llieHtB f'or the ~)''lidS Cltoaen to oetweon 5) m:d l.}J ~ l ,.... .

-"'

...

;,

.

sieve o1zea 1 .. 1j. (),14v - 1 .. 35 r;an inolusivelJ.·

'i'usts were

e·,rr1ca

out on bizee~

T't~ t£l1<l()d on ;10 A.; :;.

_{at eve}

_{~ -."l:}

~). i:.'./7-'J. 35mm

• ) • • '''·*

...

"'

"

_"

0\)

.,

_"

,,

D. :mo-.>. 2J7:,l.ui

"

It _?0 >t

,,

,,

_{'.). 21··)-·.). BB}

);.J.H1

II ft

::n

"

"

11 _{0.117-0. 2'70.n'l.lil}

"

II _1,):) fl II tt _{) .14:J-;) el"'17hl1Ll}

Cgee II

mld tho re tn1Hed on 1i.J J J,.:, .1' :. · sieve 1 .. e. >'). 1•*9-J .1 . 7 ,:aN

were:

brl·. :!lton ueach ua.nd.

Glu tho. Hi ver Send.

,,

16.

aieve size of tlle Ha.ngiteta ltiver sand wae elao ti.eaaureu.,

but 1

t

was

1mpose1ble to Obtain sl..t.ff1c1ent

ror a

shear teet.

For the retained on 1:n A.B.T.'.'• a1eve etze the somplea

were:

dew Pl-:;-u1ou t.h 1 ronsand •

Hallot1n1 {.~lass A:1ada.

I I I

-~

ldl G &a.,ples were tested ungradoli, but there could of'

c~;-~ee be r1o intei'reletiuLOllip w1 tt1 the ~::;lass beads.

d1e t::ul~·;le oi' it:t,.:-rual friction f:/> of the srmutJ um::u vJ;,s

Hteaaured in t.!1e 1 .tree t. , ;te Hr 'ioch if:e •

.t'orce iueusured i.y• t_ng r 1Lg tw.o def'lec t. io.n gnuge

l. .J.:Ite tit.reC~s :.x.Ld.rolleti t.~pe.

,.,.,

(!)

-•

u.

·~

w

->

_J

<!

0::

w

z

w

l9

I

w

z

-I

u

<!

~

0::

<!

w

I

(./)

I-u

w

0::

.t<l. ,,

at.rn1n of 'i. )..;,?s 1! a/min.

e;:J",

the dept(: 0~ t:~e lowe~ section. being f.'' A!id. tlle uppel'

A perspex stdt:l"' box woe \ILE.I.de to ~:cit the

exist-c .. o nid ot' n low .oo~vered microscope 1 t was r-.opud to view t.he

A clot::iel;lr f"1 ttlng cover plnte wo.s node f'ur t ll.C t.up of'

l"i Lt1nc cover wi t11. ooll ~ocKet i'or the ~ ~1111;er woa placed.

THE DIRECT SHEAR

MCHNE.

GENERAL·

LAYOUT.

VERT. GAUGE.-•

5'

-Z6·-~1-I

19'

~·o•~

SHEAR BOX. RING.

GENERAL ARRANGEMENT WT 81 LBS

~I

0::

<{

w

I

(./)

w

I

I-it:..t.crwal friction.

on nrea o.f 5. GG~ aqu1>re in~., . :~vi flt' .. az. O'Vore.ll .nor;.ial lcx...d

of d.':J5 'lOhs/1"1;.. ~

Cri tioiam hua been levelled nt the ,1r~ct ~'ihe.ar type

or

lil;;chine in that during ah~8r there 1s tl loss of d:learing

With the lllach1ne

uaod the loe!is of nreu ·flus onl;t 1. ~1Vm1n., and t.t1e teet.a lailt.ed

4 m1nut.efll only.

'l.'ho snno swn.ple wae placed in the shear box with ti1e

holu1r... down aci•ewe t 1i--'h t, co;rer plu te and .covet- pq t on, ertcl Lho 0~~<ple vitlruted to the acsired. t:.tato ot· coup .. .:.ot.iw .. _,.·-rom o tht:r reacEtrnh cr,rried out at '.>mterb·ur;; ~;ollege a

·dniuilmi v1ura.tion period of ,.){)():J cycles/min. haa oeeu li~..>wn 1.0

be .mcet>tH:lroy fur m.axLawa coumt..ot.i:>n, and f'r'e\.LUenciea in exc~ae

cie:.•.stt:{ 1.\"0s tuiteli to 1Je the aenai ty achieved o;,• allowir•g the

tJt~h.a to fall rre·~ly fro."rl u h.eight of 21

' in to the test ttox

}H-; tt1eee V~iluea Olll~ prov iue points on a curve 'their rit>aolute

values vre not inwortant,

The compr;:cted a~:a:.ipl.c wua then placed in t.lu::: .,;Qchi"~e, lhe hftni·~er -plnced on, anl the irli tial de:.Cleetir;;nl read on i.h.t~ verttcnl r.:~erlcctioo ~~a.uf;:e. i"'rom th1& can oe cow1 uted

the voh;uue of' ~:;-no 111 LJ1e &fllr.ple. ;leigt.J.t.o up to ~:::..<J;.J li.lt$.,

tot.e.l lo;;:.o. 101ere t'· .. en placed o:n the !u1nger, the ver~ical t;UUt.z.e

vertical ga~.;;e reactiur.;a loaded. aun u.r.loadea givea a .• ueesure

;>actions some cv: solidatioJi. t ekes place.

converted to voluuiO otu~1•ge anti t•01.•co :r•ee.diiAt.B rearect.ively

A m.eaaure of the sphe~1cit;y involves th*' recording of'

linee t~H'.,;e·,tL,l to the projected vutline ot tne purticle

tile raot thr1t in. ever;~ cruse L.l1S u1D.meter came to -.vi thil•

eyepiece.

=

,):.otomicroFrnphs .~'ere tnKen of the sa;,plee and these

were vuriously EH1larged 1m ns to <ive a l.ini:f"orm ~1ze of

u;ro1n ~·•1 th 0 d.imneter of 0)1pro;,(. 'l'h.ia tU.le done so that

uocurate eor:Lperi::vms of roundness r.!mdtl ue :t~de between tha

,4pprox1m~~tely 25 r.ynina were then taKen, the racH.i

o1, their tm.1X1HiUU ina;Jorined circles 111ee.!:rure0., Ctnu t.he rau11 of

i' t.!O .:plete oer'iCH:l o:C' { .. •.> ,l ,:r

tmc1nrs left on tbe bottom sieve.

·, " endiv ',). '-_·· ,,. __ ,_ ... __ h 1-,., •

t<j:,p • .;, .,-,.~'-->.vi>

y:

:ca.

J

~~~eneutte of a~~reealtHlt is doubtless pr-esent. when t~ re.\_r·~'.H3Gion liue is cirnwn t::rough the ;. .. I"!:ICiing· p<)in t.e, 1 t taUi::.it l;e re1u.e.1JOered

t.tAat on lot:/ log p~~pr.!:r & e :;~~11 dis tonoe away i'rora ti;c L ~t ;:-l.ed

r,>oint is in

ruot

a ver~'i lurge error.

olope m1 'LLe coarser side is rousouably constaLt, while or,

~::~eerus to be in t:-,e deterr:tirmt1on of t lie w..;aol grnin si:::•e,

·.:·hese wet'e oorried out in 25:)iG. oottlee in the w-,r;;l&l

It was I'Dw~J. thnt euch grading had to buve 1 ts upec1fic gravity measureu 1Hu1 viuuolly us the :~1n.eralo'c·.icul

CCX'!l()Otd. tton vor1ed :f'rorn L<ize to size.

.!·:eaul ta Will be presented end a1acuaeed unuer the !'ollowing

heod1ngal

1. Volume changes during abesr. and the ori tical ~.;o1da ratio.

:J. Shearing fb.roe vnlue• during ahear1riti period.

3.

t1c1juatment

to

ahe~r

value , ..

w•vea

to c

A&penaate

to•

l/oluue cl\onge ~~1shop'a '~heor)' w1 th i:itatiationl

Ahal;ye1s) •

·.:. Hourtdne$a

und

a!)h.el.-'i~ity valves.

5- Sl")ee1.f1o n·rtt"lit~l valt·•j,£•

'JUI'vea

ot

slmilar

'J!ite

orl

tical voltle

although there lilQy ·be a alight corupreos1on dUI'i.t:g tho fir&t :pnrt

ot

the tinearin,g a.o t1on, ~~le i;~ tar1al e:·:hi i.l1 ts 11 .!I'lGrlt~d GJi<i l"ap1d

1ncreaae tailing off un.t11 finally . . . . the ul timnte angle of interual :f'r1et.1on is ·reached. 'l'hie expansion 1s required to

bring ti•e ~~tarial to the equival~lt plaotlc state to pel'tr.d.t olleerL..g.

l.>lm.n1ator4 later eb.owea tbot th.e volume expansion at

z)

maximum ahanr etroes tends to be relativ-ely smaller with increase

1n uol'rntll pressure.

Thie effect baa not been lOOked into.

In the loose state the material tends to dsorvaae in volw:le

rt-om the start ot the teet, out 1nvor1aL~ly aa tho ul

t1mate

a~~le of lnteJmnl fr1ctlon 1e being Peached a BIJSll aaount of expan.aion takes place.

\b) GOij!£11 O}?gem1ji,ont

on

tl)§ gpeed

and

Amqyrrt of Volwp

~-As the maxlnlum OODlJ)actlon given to

the

sample• in eaoh oaae wae approximately the •arne• a eousideratlon o~ tll'!J t:i&Xilm,m&

poa1t1ve. volume change lu. each caee anowea

\a} In general the ~t of volume cbar.ge 1ncreo.eed witll

the ctongulorl

ty"

of. the ean4 (for the graded ea:~pleo). (b) The twi:JWlt of volume change wee greater for the un{'.l'aded

eon4e than for the gl!taded ones, and inCreased as the grain atze range uecame larger v1z., 'Ihe Hang1 tato River Sr.m4,

A coneluerot1on of the speed. with which the volwne changes

reach!rlg equllibrium: oe they be emile tnore "angular". (c) 1'11! In&tial

·:oJcw

RPtio/:'olwng !::hong G\!EV!?Ji•

'ihoae ~e preaen ted f'or oU SEtflPlea in appendix 2 g-raphs 4, 7, ~~.

13, 10.

10, 22 ~om

these t.he

crl

tical vo1da

ratios t1re

obtain~d Bl4 will be cllacusaed lat.$1' •

•. ;asagruude has euggeus'tt"~Jd plotting 1n1 tiol voids rat to

the sample is clepa.r4ent on the

voids

~atio, and thus 1f"

percantnge

voids ratio is ·..:.;sed

we

nr-e in offeot introducing a double

depend-enae on the voide J'atio.

flhen tbe l'eaul ta obtained 1n t.hie work

J .

weN plot'tred ua1t1g ti.1a ~aethod ot Caaagrande1:10, uo anttsfactory graphs oou.14 bo obtaiued; the eha:pe of the curve uepei1ding on the quantity of eol1da preMmt. ·In thle work thta could not nlft7a be the e~.

It le reaaonablt' to SU!'poee that the amount of' volume ahan{:e.

aa

sb01m b~ the

1noresee

1n height

ot

the aam!'le,

should

be a

function. not of thct tot.al volume of

the

somple,

out

of th..e area be1118 sheare<l, and the actual action

ot

abearlng. (.:~rovHt.ed of

course tl~t~ e&.-l!?le ia t,:;.1oker tban the e.one of e,near1n;:; i·t.;;;el!').

B\Um1eter4 has 8boWn that this te lndeed the case. ne :rowid

that When aa.t;i.ple height

wae

varied between ·).32'• end 1.051

' , the

d1t'terenoe in flnble

of 1nteril.Ol tr1ct1on

waa

onlJ

3.;~. '.i.'ltus in this eertoe

ot

teats absolute volume ohemee bae been plotted ogainat ·the 1n1 tiul votcls ratio to Live tlle ourvee shown 1i• appendix 2 bTaphe ~k, · 'l, 10, · 13, 16, 1

v,

22.

r.J

reaeo.nnble,

altlloueh they ore

not the

atPaigbt 11nas

of'

:;aaat~roncte •

( u) IllLG£1\toal

'To

iSle

Egt&o

· :one1der1:J.&; each SEb..ple 1n turn:

1. ilr1g.l1ton Joaoll Uar4

Heto1ned on\}) .A.~h'i.' • • a1~ve ').85

"

,,

Ungraded sa .~.ple

2. Paraparaumu :...1eaoh S~md

tt _.1).88

0.84

·Retained on 100 A.u.~£·.~1. steve iloGS

Unt;rtldeci oa.:~ple 0.84

3. liow Plymouth Beach Sund

Retotned on 50 i\.2.1.'. ~. eteve ).G2

"

"

..

tt tt rt

,,

60 70

eo

100

Ungracted ealll)le

"• Oamaru ueach Sand

"

..

"

"

"

.,.i>a

rJ.G9 0.68

o.ea

l).Gf

Hetained on 0~) .A.G.T.t.~.

a1eve

0.77

Ungraded. sample

o.cG

&. R~ttata ntver San<l'.

U.t~a4ed sample

ti. Glutha

raver

SM4

netained on 50 A.~~.·r.\i.

e1eve

o.v4

"

"

"

60 70 80

i'lO

tt

,..

"

o.\15

q.

'.)5

1_J.97

1 ..

tJe

7.

0allot1n1 Olaea

.ii..eade

1~eta1ned

on

GO AeL·•"i1• i. sieve i).G5

ft

"

70 rt

"

0.65

,,

~

ao

tt If

o.e5

"

"

1·'IO

••

_"

0.66

t.rh.e apparent anomnl~! oocul'!'lng w1 th the l.-otsined on 50 A.,b.T

Mt

a1eva in tho New Plymouth Baach sand can rend11y be explatued

f'ra:1 a eoual<ierat1on

ot

the ape~1f'1c &--rav1 ty and rou.ndnesa valuea

of t::..ia san4 ( aee 'l~ablea 4 end 2 respective~) (See appendix 5

.ror m1neraloe;1cal

deterrdnDtion.

or

this sand).

'L'he uew Plymouth sand oon11ate of tvo distinct minerale

autitc e:.:.d rus.gnetite w1tb speo1f'1c gravities of 3.3 ari.d 4.9 respectively.

'ibe lighter ~Udl'al &\Q-~1 te is found onlN 1n tlle larger etaea,

almOst excluaively on

the

&0 sieve eieo and

larger.

'f:hta ie

conatuerably more

artgUlar

than the maeneti te arui co.neequentl.y

.1vee a d1t'terent value of' the crittcal voids f'atto, and ae shall oe shOWn later,

o!'

angle

of tnterr.:al

f.r1ot1on

'rhe Ufl<.:re.ded &tmJple oleo ahowa tbe

et'teot

of'

th1a,

as 1n &11

other sanda

the Cl'1t1oal voids

rntio

tor

the

uncra4e0.

ea:•ple

liea 'belQW that or the graded

erur~le. He1'e 1 t 1e above, due

to

tlle two d1rf'er1nc ant;.-ulaz-1 tiee.

, :ons1de~1rlg tile read te for the aunde in genernl. eeveral points eme~:

3/

2 • ~he crl tical vo ida ratio of the ungra4e4 ss:.aplee is

1n general leas them

that

of' the ~aded material, tba

pt'oport1on teud1ng

to

'be relatively smaller ae the

urad:S.ng

becomes

leas uni~orm.

critical voids ratio (0.94) is

ve~

oloee to

the

r~tnlne4 0t1 GO steve a1~ { :) • 85); whereae 1n the

oemaru. T:1eaoh sEU'ld t~y d1f'hl' gt'eatly (0.6£:.> to

o.77).

The dif:f'erenoe in the srnding curves 1e ahOWn in

A:r!'entUx

2 Graph 2.

1111e consii..Jtent value nppear1ng

tor

the gleaa b•a4a le

interesting no one r'light expect th1B

to contorm

to a particular type

ot

sphere pockinc:·:.

Graton and '7'ru'Z.er7 an.d later

He~:wood

11

h~ve

ehown tbat there are etx possible typee of' sphere pecldngs,

corHepond.iu.s

to

tour

dttterent

voids ratioa.

Thtuse aix oaooe

with

tlle1P volde

re.t1oa

are shown below• · . \r,o1do

_Ratio

1.

~c~ubic _puck1:ng (.).910 )

.,

...

orthorll0mb1 c pecking

fitlU~;l'$

').654 )

Layer

a

3. RllQit&Uohedrnl pacldna c)a350 )

4. ;Jrthorhomblo

paok1ng

J •. ~56

\ fib.omb1C

5. ·~etragonal

-

er;he!'Lo1dt1l packing 0.•132

G, Hhombobedrr•l

packing

0.350 } L~re

'

The or! t1anl voids ratio oorreeponda to the voids ratios

of Gaaee 2 or 4~

'

of equu~e layers (:c'!aaea

1, 2

and 3) a·od tJlOM aampoaecl

ot

r)l.or.).b1c lB)ters \Coeea 4, 5 nnd 6).

'J:hua

,}

.CASES

1,_~-- ~ ~--~

A

a

the

shear

box is square 1 t ~v be as8Ufl04 the packing tu of' the square layer t~lP• rntb<Jl' thon rhombic layer type.

''l'he packing in ~.;tute 2 will there'fOl'e oe cona1dere4 ln. more uetoil. The packing oona1ete of J ~'1uare layer' arrantlemente lying et angles

ot

60° to eaoh otber Probably the alulpleet wuy to cone1uer 1 t, is to 1nlog1ne 2 equare laye!l'a lying uireot.ly

I

on top

ot

0:1G f.lnotner w1 th the spheres u1rectl:; over oHe a:.otber. 1_{l'he upper layer 1a then : ... oved porallel to the edge of}

the squnre

so.

that the 1 ;ottc:xne o~ tlle upper

layer

lii.e ln the hollows of the

lower layer.

'.i.'he un1 t acllt or ru1A.i:.i&Wlll conf1gurnt1m~ which ehowe the

'l'lle call iu n aix sided form., f'our of

wooae tsoe•

are squurea of' aide 2 R and

two

of whose t'aoea B.J'tt almple rhombe of aide

~m;

the volume

of auoh

a cell 1a 6.93

a

3•

A et~1ot mntller.mtieal analysis ot th• forces aot1t1g during ehe~u~in.f; with t ~10 co!d"iguration te etatioally

This V'ariation 1e shown tor the same aaaples ae the J)

vol. cht:mc:~e/t:lme

curveD.

They appear in appendix 2 graphs

5, s,

11, 14,

1?,

20, 23.

Var1at1ona in &hearing torce

tor

the auu.plos nut shown ure

ot

the aome

torm,

an4 the valuoa

obtnined.

~am

tlleee hnve been ueed

to

provide thO values of

all4t~le ot: int.erru:~l friction pnaented ovel'lea!' ( ·rable 1).

!J"i~om

a oon&iuernt1on

of

these

p;r~ha

taken in conjUnction

~;1 th the volume ehange/t1me aurvee, an 1ntimnte connection

~ beat be thought of aa a abeor compensator.

shear ·force is high, the re.t.e

ot

change

ot

volume

ts

1n the positive dipeotion, a.ud when the ahOar toroe is 10\f t.he rate of .volun~e ch.anFe is 1n the negat1 ve direotior.~.t

All the grophe e11ow a prelinl1nt.u7

4ecreaae

1n \lOlume when the force is firat eppltea, tllue corn~..,ensating for the

ird tially low

ferae

reaci1:tl£ on the proving ring.

This etrect hr:s already been mentioned 1n

the

u1eouas1or.1.

~

toottr

w.t•6j'

.Go

-

:·~-.GG

...

,

,~,=~

tfO

~

~r:g

....

~·o

••

..

Ofii•o

~--··-

_eK

·"

_t•o

_•

"'··~ .~.,..

...

_:,

:.,. .. . 1

:Sr.-ct·o

.Pf

~-•te•o 4"ta

_..

~

•

"'-'*0

,pr.

••

CPJ•o

•" oK

._ .. :

.Ll:JJ'

·-"

as-o

·"

..

-o

·• · oil(

Si'aoo

, . . 6

I .

•

:lei(

'"::

....

l

.Ctt ••

·"

~

;-o

..

,

.,

.

.,

tta~o

fi

•u

.-o

~··tll

...

,~. . 'ilt •

••

:tt·-"·

m·~l

.n·~

•v

M

•"

•o

i'::f

m:~

,,tft-00\

-.·o

,~

..

•o

...

... 0

,

..

...,

.~

...

*,;) • 8 .

~-~

~•a I

...

~~0

.oo.g

...

,

:1~1

··o

~---~ .

....

•o

•fto~

;;r-o·

·~ ,..,ft.~

oe

~~

~---

•·a

..

~

•;>(

eril • ...., .. 0

...

!

...

m-o

•

"

•

..

,.01

:V

~

=r::

~ -$:i ~

:1:1

·o

·"eK

..loll

""''~

OL

... J

·•*

~'

.

.,

9'C

....-a

we~

~ I

i

=·o

...

~.

:g.~~

&G.I. .

.,t)

••

~

~-~

,....

..

(J.•-.

B

==~

;reo

lit·o

~1~~

.:

·.. .

~~:

•o

taJ'•o

••

~

M

•"

:~:~

9h, ...

09

.• ,.0

iJiC

.oa

D•o;

...,.0

•"'"

i/12.

..,.0

.ot

....

...

...,..

..

~ .--· ._ r

... .1!!

Ole

to{

-2~

'11''"0

.

tf>-... ,i;

,

..

·"

-~

.JO

·etl!

!3"

;.,

....

·~ .;,;

·"' ;aa

.'10

;,1

0

-~

tp

,.._

~--1

fJ

;-.

;

{i·iet

rp

p-.

~ ~at

-rp

~--

_p

••

;

••

.. ..

I

---..

. !10

.

.,.

... ...

111111 . .. .. .

...,..

•t~

-

I

(e)' 'th~_ji~~ret~eion Jurve.

An

exru...ple

will

shoW the

u1ethod

uaed

to oeet

etf'eota

tan

t/>.

It-

•

tan.

' "''.&A

't'. St

•

rate of

at~sln

&

_s.t

•

rate

ot

cn~ns• o~

vert.

height

¢1 • o.ppnrent angle internal f'r1ot1on

rf' .

•

true anglo internal friction.

•

8-il.. Of) l-D8

Rhte

ot

b,trtl1n

•

o.

J-472 ~min.

Gona1de~ing a 10 eeoond period

!At ttate ohange vert. height in 10 sec&.

•

¥

1n~10 aeoe. • G:t~ 1nD/m1n ,

Let overage proving ring dial gauge "ad1ng in

this 10 second period • x ins • Gonverting this

to

force

1 diviaion ~

o.o

lbe,

X 1UD a 8\'):)0 X lbs.

Tnn :oppuroat a:P:sle 1ntur:rml friction

/

ten¢

=

q~;Jfli

•

'J5.3x

04-.05

Since

tan¢

I

-

+

tan

t/>

x o.0472 •

9fh~x

x 0.0479

+

e,

-The

reaaon

for

the

a1gn convention s.n the t1nal tem

1e

that

it

the matel'ial

1•

ex;pand1ng,

the ttnal tel'm

must be

tan

¢ •

fl5.3x

-

+

127y

•· E• Aaauming

Average proving

rtr4g

dial gauge hading •

o.ooao

ina

I

{giving tan¢

ot

o.76S).

Bate

or

change

ot

vert.

height

tn

10

aeoond period •

o.0017

1na

e:zpan41ng

tan

¢ •

95.3

x

o.ooao ..

127

x

o.0017

Uatng average

valuee f~

the 10

aeoond

reading period,

a table of dial

rea41nga to be eubtraoted trom or adc!t4

to

tl'le

to.-ce

gauge readings 18

eae1ly oomputed.

roq then be dona 41NOtlJ' from the dinl gauge readings.

Theee

oorrectea

valuea, When averaged tor

th~parttcular tifl1At11 provide the valuea uae4

tor

the

regression

QUrvea (or

t~

OUPVea tor

cr1t1oal vo14s

ratio).

Theee

are

shown

dott•4 in appendix 2 gpaphs

n, e,

11,

14,

17, 20, 23.

(b) ThJ

§beer

.§\rer+gth Va),ylg

l n'C

vnryiru: aetween on y ~v

gre~<tf:r• the mnxirm.l!il nn-.:<:le of intorrwl friction

band.

the :aevn u:n.gle or .intel.,~~ctl friction temh1 to ir!creas,

I·,

us the t:-rro ln &i~e decreases in any particulnr &tutd. ·

1. Tbe ovel":r:ll mmm vnlue of'

tp

over oll. corl"ected

z.

1_{i·he <f•c,an val1""e of' the ult1ii1nte vr.alue of!}

rp

_{tlt. tue}

or~d of the f' our• minute to at per>io(l.

)'6 .

SAlllf'L'E UR!OfiTON _PARAPARA- rEW ~)AMARU ~ANGI-

i:Lrr.rrlA

c.

FADS

mm

PLY:t;UTH 'l'A'I'A

-

~ .

-··-·

R~ta:ined

0.42 ').:..30

60 sieve

Retained

J.2G 0.51 t . !,;,3 0.31 O.l\.1

?-.OO

,jQ _sieve . '

Retained

0.54 .J.l9

1.vu

70 sieve

Retained

J.54 0.18 1. )0

so

sieve

Retained _,).25

0.28

o.M

).17 1 •. )J

100 sieve

1--'--·

oi~t.e diatrLj, tion. 1 t:t :naco~Hmr•y i'O!' thj u to ,;ct:o;rie very appal"'Or.tt•l

/ n in 7,;r)X'tlU tii: , f'sct OITi.';;!".r'es when tl!<:~Se vnlnee are

For ~tll the

(b)

'~he spheric! t.'/ valU:oe ne

for oo~upn.riuon. 'i'ho nalt.rulnted

value

haa been der1 vea

t._rom

6pher1o1 ty f'lot iu excellent.

The

diameter

vall:tea hnve been includ.ed ·to ahow the

agreement

ot·

the tJ~termedicte diameter w1 th the up er l1m1 t

ot

the eiove aize on vhieh it. was retained..

50

sieve size

Int. clit\Ill.

rce.a1nt',eu

Gluthn

=

0.2Y7 - J.350 J.36J li~n

r - - - · - · · - · · c - - - - --..---:-.,,,,-.,-·-t-·-~"--r-,-, -. ~--~-:---:--r- ' . ,' ' ~.)t!- '{;(.,_;_1

~)~~~1(;!,1.:-~: ), t-·j\_;-i_~'·,~--_}J:,~-\~i\- .;..-H ~_j\' .. _J'r,l\() _i·,J~ ·\ ... 1- • ... d., .. d'L ;.l'1 ·_;. f !~ •. ~

'··*Jl

..).301 J.:J2)

·).'74. J.74

) • !)lJ

'). ~)(~~~)

\J. ;J2f!

o.

5'""~

<>. :.; :;):)

·~). 2G1 :).64

). ~35

). 4Jt~

' j):k " •

J. f/J'..J

). 7';)

J.·?'d

;

.

.;.,,:)

). ,);j\J

). :.i"-'4

o.

_'""

_·~

h 72

). ').L;

).34c5

• 11'1

::).'15

).76

]. ;'k~2

,). _3Vk

,). ... ~1

J. I:J

J. ?fj

+---+-- · - - -·---t---ii---+----1~

; •. :54 ).l·._.JU ·J.121 ).72 J.72

}. :~07

l.2llj ·).14:\ ). 72 ,.73 J.835 ).182 ).112 :).72 ).'73

) • ?3':} ).1'!7' ).110 1.78 J. 72 J.:SJG .).~;;;:.; 0.85 J.86 J.~V4 ).211' ).2)3 ).-35

'). 8~2 J.H:iS

J.1'7:.J

J •... 5 0.05

le jl'l'

.>.846 ).24a ).;;35 ).85 J.482 .J.37G

J. ~131 1.72 J. '7'3

'i.3,.J2 .J. ~53

,J. :~JG

J • ., ••

J.14 .).331 J.BKj 1.1l·~ ). '73 ;.74

J. ~;~4

).17.3

.. -). '/8 j . '7'::.

).IJ.:J? }.ti32

1.3:}G J. B~-~c

).27:) ).8:)8

).74 ).?2

}.'7'4 l.?\S

1. 3.)

l.J:J

1. ) ,!

1.J)

J.J'Vi?:hton

t\f)W PlytilqUth

<)rt~:lfi"rl1

~(fl.Ilgl to.t~r

Glutha

Glutha

J < tY.'i Plyn4<JU th

Clutha

Dr1t·hton

Parepernumu

New

Plymouth GluthE

<.). ;:,<)1 lfi\ll 0, :;BO itllil

o.

3:5o ,~.~ ) • 314 Hlffi

.). H52 mm

• J,177 - 0.210 )i}ilh

.). H11 H.'\U

0. ;,3Q{j fillll

o.1!>B

mn

1,182 n:tn

·J.1·~;e

_m.n

0.1'78 rnm

r4".hh~ intermediate di~TZ.eter 1& the one Which detal"minea

the e1eve on which the pert1ole: is :retninea.. and the agreement

ehown givaa t't good verifioa.tion of the accux-acy

or

t11e

resulte.

and thUili of the w~thc.d by wh1cll the diwuetere were measUI"ed..

'l'he sphei•io1 ty values for all the quatttz aamia a:ve

p.ronou..noed cloo:vage planes ..

These are shown in '!!able 4 !"or the EJ0..'1!J)loe teateu.

'l'het.~e emwll 'Vt'riotione will be due to vurir)U$ a:~all pe:raen. tagee

<l ... bD

~;Ii{:~,;:::

'"'~:. '.t' .. ,(J

1!~-·J...t JO

~Iii.\\/f~

H,i

i/d(;-' ·:.; ?:)

l~~I !, vr~:

.

.c'Ali·•-.1.' 1.})

..:,I ·n;:

. ..._,.

~.~.G5 , •• J2

·1.54

;:.G5 ,;.::.A

1]

,)A'.J/b iJ :nl\.;,.; I- JJ,, L .:;~ 1.~ i\Lv

':,.A'l.lt

2.67

nno thus the unql~ of' 1nterm1l f'rtcn;ion h~ relnti vel::~ les~.

the cri tieul ·.r·.)hn:." rntio ..

voias to the v<.>lurr.e or solids in the COHtnlute a8mple.

Th.UB

v.,

...,-o's a, the voida Patio

NQW the tan Vt:il..:.e ia actint·; •Jnly over the: ao t..ual

nrea of solids during ~htmr. :. Let theor-ottoG.l tan

¢ =

=

41 \

)

tau ~ ''

=

tn.n

¢ \

l + ec:J whet•e o₀

=

or•i tical voids ret:i.o

shown. in tble 5.

••

1. 'l'he oif't'erence in minoralog1cel CQtCiPOSi tion and thus

or

valuo o:r alidirl'~~ J'r1et1pn.

'the aeoon.d pokjeillil1 t.y is ruled ou't as ttie glaes bt3&de 11e

011. the upper line Bl though tile1r ephcf'1o1 t,.y <11f1~ere tram that

ot' "t.he quortz

aano.

r,rho value C~f' sliding t'z.1etton tor dry qutn•tz on quart0 ia gi ve.n 'by 'J.'&oh.ioo·t.ol,ioft' aa 0.11.

tor

mag .not 1 t.e on uu~gne t i te.

ho

vnl·ue o

ou.ld be oo

ta1neo

It should

oo

~toted

that the valuee plotted e.ro tor the

ungraded i:lm.t.ue as well as the p:-raded S!li!lPlea and

all

l1e on

'~' 1 ' ' ' . . . ·' . . ,., ' ' ' ~ " 1 ·. 'l' ' tp_ ., i "~

1 h~U •. .: ' · -'-t\ll l.t<.l:l 'fl ₁ ~ t \ +e ) 'A.· , F .,oJ J.t

---·---·----

... ~- -·---~-...

---_ ---_ ---_ ---_ t - - " _ _ _ _

~--~---1"·

--·

---l:J.~.i1.·~ ,. 'l\Ji,.}/·. '. ~. -r ·'

' j ' ··.j ~- ;· ~! -'\:-~- .~;j·tr:.,· _{~ ~ (,' ,':_~ 1·-} ! '1./ .. ;'ld, ' ~ ,"· .'j .J..'" I ~

I I'~-) ;','·.~ •'. u _,, ~' 1 i'LY _:4, t'~rf ~ ~ ':')\l'/l

I

----

_"-

--··-

-·---

1---tnn

_t/>

).4:j~J ;J.552

i

~

_~· J. 8[: .J. :J4

()

:.1+& I ,_-sn~ .).8'~0 1. t)'lO

...

!

C.:)

b: ) .... 2 'J.:JJ

¢1 ~-(1;"'~

---

-·-

-

-

-

_

... _.

__

t---1!

tf.Ul

f

).588 .).48S J.53~

.).f3.i5 ').•i!· )1

~~ J.S5 ·J.68 .)

.

P1 ).95 ). C5

...

_{(;1+' \}

l8!it/J 1.:)33 '')• (320 ).955 1.1')~ ) • OG2

(Q !';,, .. ...,

.,

..,

~:2~ H 1).26 0.51 J.43 1.1':.1 l.·J')

I

-C) _{ton- J.492} ;). 5cl5 J.4t.;·:l.

~!

Et· ) • 68 J. J~) J.05

Cl Q

J,.Hx~Hr.nf J.81J 1.1')!3 ) . '()

...,

I

-~) (.:

)a 54 J.1·;J 1. ) f

...

""

1{

1

E

tuu r/J ). l88 ). 55·-.~ ) . 4 4 )

~-- 1.GS J.'J7 .) .. ~5

,-s

_{\lfct>..) 1ac.} ).810 1.115 .). 720

.e~s T.'t ).54, ).18 l. ))

~~

"

-,

i!

tan; ).bd7 J.551 ).4;2 :). 5'/G .).441

etc ~].~~.~a ). B~3 O.GS :J.:A) .).05

... eli

1~1+~)

ten;

1.1r)4 1. )35 ,).826 1.121 ) • ·,.Y;Jt7

Bg

tD ..,

r~ >.25 ').28 J.64 ·J.17 1.

u

~·

ton;

iJ.5f;;J6 ,). 5'74 ,).512 ). 57"-) J.JJ3 J.o84

I

ec

,}.84 ; .. 84 ).67 ·). G-j .··). {)8 _{:. f~}

IJ.+

c)\&;;,

1.0'75 1.U56 J.:u56 ·). <Jv2 1. ·J40 1.;)74

i

i\ ). :;5 ).DB J. -~i.J .J • .!J.~~ ,).20 ).ld

~

1•2

l

RELATIONSHIP BETWEEN

I

ROUNDNESS

I· I I ~of I • I . + +

-AND

{1

+ec)tan

¢

1•0 ~---~---1---r~~~---+---+---r---+---~---~--~---;

0·9

-0•8

---+-~~~----·+---~---~

.

c

c:

L ' .

;

I

:::!...6·7

_w"

---·-

---~-~~---+

'

I • BRIGHTON sAND. --~

--+---__...•

+

0 PARAPARAUMU SAND.

' - '

0•6 ... , _ _

0·5

0

I • NEW PLYMOUTH SAND.

X OAMARU SAND.

---1-- a RANGITATA SAND.

+

CLUTHA SAND. • GLASS BEADS.

0·1 0·2 0·3

'

0·4 0·5 0·6 0·7 0•8 0•9 1•0

ROUNDNESS.

GR.

I.

.f.,

#:;rent.

rou·nd;;etH.1 wh:l ·Ji; ht:ts tefln m:-.:.r~tL:r···tl by eoveral WQX"kers t sec

rot. 1'7 p,,,; 5·1), i:.IUt it OPP•'Hire t.o •N1ry ~.:olBilieruLl,v 1tJ1th the

1. ~n~o nrul<> ()f' inte-p·r~l i'rict:ion for ary ar:~,tds o.t

v·,,

Clrj ti ~nl vt"~1ds t-r>tio vroriee according to:

(e) '~t~o t-onndnese o~ tim tHu dt on which ia d~P<~udent

t!•e ett:ittcal voids rr:~tl.o.

(b) 'l'ho f!,radiro~ of' the armd., on

w

hioh is O.ep~.l~d.e:n.t

the 01"1 tical voidc rr1.ti<J.

( n) 'I''\'lt'l m1nernlog1col oompord.tion of the tlllnd,

;~hr·1nt: the Vfllue o:f pure sliding :rr1ct1on. 't'be ~~l~tionBhip ia

ot

the rorrru

lo;::: ₁₀ ( 1 + ee ) tan

4

and in the ease of the iron enhda

log,₀(1 +

fJoJ

tancfJ • •0.:335 H • 1.),0:$85

~r

in the ease of' the qunrtz sands

., BALLOTINI GLASS

BEADS.

-1

RETAINED 60 SIEVE. _{RETAINED 70 SIEVE. RETAINED 80 SIEVE.} RETAINED 100 SIEVE .

PARAPARAUMU

RETAINED 100 SIEVE.

SCALE:

BEACH SAND.

•

_{· I MM.}

•

_UNGRADED.

!APPENDIX

I

BRIGHTON BEACH

SAND.

'

RETAINED 60 SIEVE. ' RETAINED 100 SIEVE. _UNGRADED.

OAMARU

SAND.

1

RAN·GITATA SAND.

'

,-RETAINED 60 SIEVE . . UNGRADED. UNGRADED.

SCALE:

-.MM. FIG.2.

'""

NEW

PLYMOUTH

BEACH

SAND.

---- - ~

-RETAINED SO SIEVE. RETAINED 60 SIEVE. RETAINED 70 SIEVE . RETAINED 80 SIEVE.

RETAINED 100 SIEVE

SCALE:

I MM. UNGRADED. FIG.3.

..

'

4 :·'

l

RETAINED 50 SIEVE.

CLUTHA

RIVER

SAND.

J

RETAINED 60 SIEVE. RETAINED 70 SIEVE. RETAINED 80 SIEVE.

RETAINED 100 SIEVE .

sc

_{A E}

_{L :}

•

•

I MM. UNGR ADED. F!G .4.

Jl

COMPARISON SHOWING RETAINED

60

SIEVE SIZE.

--~

GLASS BEADS: NEW PLYMOUTH.

RANGITATA.

{NOT SHEARED)

_{SCALE: ..}

_{I MM~}

OAMARU.

CLUTHA.

FIG.S.

100---~----~---~----~---~---r----~

v;

z

-~

SAMPLE SIEVING CURVE.

I

BRIGHTON

SAN~!>.

,("') 80

I\

PE~CENTAGE ~F

BOTT0

1

M SlEVE

1

TAKINGS

~ALLING

o

1

N

I

BOTTOM SIEVE IN 3 MIN. PERIOD PLOTTED AGAINST

TIME.·

(1:

7.

RETAINED IN 102 MINUTES.) .

z

060~

. UJ

I

-z

--r---i~

~

I

1

u2o~

a:

LLI

Q.

.

0

0 IS 30 45 60 75 90 lOS

MINUTES.

I

APPENDIX

li

~

GR.t.

...,

·*-325 100

""0

90

fT1

:::0

80

()

fT1

:z,o

:~

')>

I G)

6o

1'11

50

~

c.n

40

c.n

-'Z

30

G) •

20

10

0

0·05

..;.

A.S:t:M. SIEVE NOS.

200 100 50 30

'

16 8

1. PARAPARAUMU BEACH SAN D. 2.BRIGHTON BEACH SAND. J.NEW PLYMOUTH BEACH SAND . 4.CLUTHA RIVER SAND.

5. OAMARU BEACH SAND. 6. RANGITATA RIVER SAND,

-0·10 0·50 1·00

DIAMETER. (MM.)

GRADING CURVES FOR

SANDS TESTED.

IOO%

so%----

ol-

osloz-w

u

a:

w

Q.

GRAIN

0· OS

%----c---1

5

•

I + BRIGHTON SAND. 2 • PARAPARAUMU SAND.

• RANGITATA SAND.

0 CLUTHA SAND.

5 • NEW PLYMOUTH SAND.

6 X OAMARU SAND.

GRAIN SIZE

t

M.)

'GR.3.

-r 0·150

+0·120

~

+0·090 V)

z

-.

:J

+0·060

u

..._

+0·030 0·000 -0·030 -0·060 0·66

lLI

C)

z

~

I

u

.

0

>

BRIGHTON

BEACH SAND.

1

+

I

I

')l

VOL. CHANGES ON SHEARING

FOR VARYING VOIDS.

• RETAINED ON 60 SIEVE.

)t II ₁₀₀ II

'

0 UNGRADED SAMPLE .

I

I

! •

~J-

_________ [___ ---

- - -

~-I I

I

0

INITIAL VOIDS RATIO.

0·70 0·74 0·78 0·82 0·86 0·90 0·94 0·98

I·OOr---~~---~---~-r---~---~---~---~---,

. BRIGHTON BEACH SAND.

RETAINED 60 SIEVE.

O·BOJ

I

ee-?'1" ~

I

=-

I

I

I

I

I

I

.;-:..-0·601 .

~~

±=

1=:_

t

I I

~

-e-z

~

t...=

0-401 '

II' · .-r 1 :z=

_ - •• r .,_ > I

0·20tl(---t----~--t---~---~----~--~---~----TIME (SECONDS)

o.ooL---~---~---~---~---~---~---~---~

0 30 60 90 120 ISO 180 210 240

SHEAR STRENGTH OVER SHEARING · PERIOD .

+0·120r---~~==~r----=~~~r-~~-=----r---r---r---~---~---.

VOL. CHANGE DURING SHEAR PERIOD.

I

I

BRIGHTON SAND. · RETAINED 60 SIEVE.

I

I

+0·090

I

I

I

:::::;;:;;o--t

I

,__

_.

Cl)

z

_{- +0·06ol}

I /'I _,~~,... I J.,....__...-- I

I

:)

~

./ 1:7...,.... ~1 I __..,.,...-- I

L&l

+0·03ol

I ~ 7

C)•

z

<(

:r

_u

0•000~

_~ 1 ...

~·832

~

----=1

I

I

·

I

•

...J

0

>

-0·03011-

'-l-t====rl==lt£:·8~64=f=l

=i=l

- ·

==4=d==~

· I

I

1

TIME . (SEC.ONDS.)

-o·o6oL---J.--__._ _ _

_.___..;..._....___....;....~..

_ _

__._ _ _

..._ _ ____,

0

30

60

90

120

ISO

180

210

240

+Od20-_____,---,..----,--~-~-_____,....---PARAPARAUMU- BEACH

SAND.

+0·090~---t---t---t---+---+---+---__j

0

" "

I .

X

VOL. CHANGES ON

~

CIS

+0·060~

z

-:j

u

+0·030t-...-.

L&J

'-'

_z

O·OOof" ~

X

u

"'{

SHEARING FOR

o . o

~:RYING

VOIDS.

.·~

. ,r'

~-•

- 0· 0301-

.J

-0

>

-0·060~

~ I

x RET~INED ON 100 SIEVE.

0 UNGRADED SAMPLE.

I~

I

- 0 · 0 3 J

I

INI~IAL V~IDS R~TIO.

J

I

I

0•68 0·72 0·76 0·80 0·84 0·88 0·92 0·9~

I·OQP---~~---T---~~---~---~---~---~

PARAPARAUMU

BEACH SAND.

I

RETAINED 100 SIEVE.

I

0-80

··---&

I

i

x~ ! C4c:·8IS

0~0

~

·. i ..

~·85_0_

I

I

~

0·401

t~!fz-~·

! • .

~

...

~

I

-~

,~

I II - - - ' - - - -- - '

I

I

I

0·20 1

-TIME (SECONDS.)

0·00~---~---~---~----~~---~~---._---~---~

0 30 60 90 120 ISO 180 210 240

-SHEAR STRENGTH OVER -SHEARING

PERIOD.

+0·120

,...

en

z

-+0·09

=>

+0·06

u

...,,

lJJ

C) +0·03

z

c(

J:

u

.

0·00

_J

~

-0·03 I I 0 :> -0·060 0

I I I I 1

VOL. CHANGE DURING SHEAR PERIOD.

PARAPARAUMU

SAND.

RETAINED 100 SIEVE.

~

~

v

~

/

~

~

v

v

&i_:::O'~~..,

~

---

_::::;

-~

~

~

~ -~-:::::::::::: e.;.-·918 . /

TIME (SECONDS.)

30- 60 90 t20 ISO 180 210 240

+O·I20r---~---~---~----~----~---~---r---~---~---,

NEW

PLYMOUTH

BEACH

SAND.

VOL. CHANGES ON SHEARING 'FOR VARYING VOIDS.

+0.09

I

_,...,.

•

eli

z

_-

_•

+0·060~

-•

J

g

_•

w

+0·0301- C)

z

~

:r

o-oooru

• • RETAINED ON

so

...J

• II ₆₀

0

.>

-0·030

•

II 70

..

~"

1'\

•

_'

+

_"

80

)(

"

100

0 UNGRADED- SAMPLE.

-0·060 .

INITIAL VOIDS

RATIO.

-0·09oL---~---~---~---~---~---~---~---~---~

o-s2

o-s6

o-6o

-

0·64

o-68

o-12

0·76

o-eo

0·84

o·e8

-&

z

1-0or---~---~---~---~---~~---~---T---~

NEW

I

PLYMOUTH

BEACH SAND.

•

RETAINED

60

SIEVE.

0~0

I

I

-+

- - - + - - - - + - - - - + - - - i

I I

! I

I

I

I

I

L I &i"' _;;;!..-l!J

....I:?---0·60 7 ! =" lo=:--~

I ,

--t---1--- - - t

REGR~SSION CURVE.

----

---~---4C( 0·40

~ I

i I

!

I

I

.

'

t----~---·

. I I

TIME (SECONDS.)

0·00~---~---~---._---~---~---~---~---~

0 30 60 90 120 lSO l80 210 240

SHEAR STRENGTH OVER SHEARING

PERIOD.

+().120

\J

,_._ +0·09,

vi

z

-::) +0·06 ... ..,

~

UJ

C)

+0·03 )

z

~

:I:

0

.

_.

g

0·00

·--0·03 )

-0·060 0 r, I I

l--I I

· VOL. CHANGE

I I I _{I I}

DURING SHEAR

PERIOD.·

NEW · PLYMOUTH SAND.

RETAINED

60

SIEVE.

'

Cj,~ • 573

----'

~~---

«6.::.. 598

/I~

~~~

_I

I _{«.&.=· 631}

____-r---~/

~ : I ~=·&SA l I

'----~~~

L---~--·

-

/

~

«;.••690

1--- .

i

.

---Cj,=a •722

-

_.

---~ Tl~E

_{... (SECONDS.) ·}

30 60 90 120 lSO 180 210

I

I

I

240

+0-lSO~---~~---T---r---~---~---~---r---~---~

+-0·120

i

0

. .

~

: 0

: OAMARU BEACH

SAND.

+-0·090'

·~

VOL. CHANGES ON SHEARING

I i " ' -

FOR VARYING VOIDS RATIO.

-- - -- --- 1 ---

-r-'l ---

!

----~

r-- --

-1·

~ ~

z

~

-•

:::>

+0·06

u

.,_,.,

UJ

C) +0·030t-

z

-0·00 ~

:I:

u

.

...J

0

>

0

-- ---- t

• RETAINED ON 60 SIEVE.

o UNGRADED SAMPLE.

-0·03CHI---~---~--r--INITIAL

I -. .

j

'

·1-:

I

.

I

+----'--- -

-~

---

j

I

·o

I

---- ---~

i

I

.

VIOIDS

RATIO.

I

0·52 0·56 0·60 0·64 0·68 0·72

-0·0'~:---~~---~---_L ______ _ L

0·48 i ---·-' ' ' .

0·76 O·SO 0·84