A L~BORATORY STUDY OF SETTLEMENT
CHARACTERISTICS OF SILT UliDER LOADING
by
Mumtaz H. Rehman
A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Engineering.
Department of Civil Engineering and Applied Mechanics, McGill University, Non treal.
April, 1961. ACKNOWLEDGMENT
The author ~dshes to express his gratitude to Dr. Raymond
N. Y. Yong for his support and direction of this study; and also to Professer V. W. G. Wilson for his assistance in the erection of the loading frame. C 0 N T E N T S
Page No.
HJTRODUCTION 1 THE ORY 3
P!lli"""VIOUS HORK 11
EXPER:OVLENTAL \~TORK 19
EFFSCTIVE STRESSES 34
l'iODULUS OF ITOLUHE CHANGE 40
cmrBU.fllW PRESSURE AND VALU.:!: OF 1 E 1 42
TEST RESULTS 46
SETTLEl'ŒNT ANALYSIS AriD DISCUSSION 66
PRACTICAL AP~:lLIGATION 80
CONCLUSIONS 81
SUGGESTIONS FOR FUTULΠRESEAR.CH 83
BIBLIOGRAPHY 84
APPE~'DIX 92
- i - I L L U S T R A T I 0 N S
GRAPHS Page No.
Graph No. l Settlement vs. width of pla te (after Goerner and Press) 12
Il !! 2 Grain size distribution - diameter vs. percent finer by weight 20 Il " 3 Deviator stress vs. percent strain (cell press. 15 psi) 47 Il " 4 Deviator stress vs. percent strain (cell press. 30 psi) 40
!! ,, 5 Deviator stress vs. percent strain (cell press. 45 psi) 49 " Il 6 Deviator stress vs. percent strain (cell press. 60 psi) 50 " Il 7 Deviator stress vs. percent strain (Unconfined) 52 Il rr 8 Pressure vs. void ratio (initial porosity 36.3%) 53 rr Tl 9 Il If Il Il ( 11 Il 37.4%) 54 Il Il 10 Il Tl " Il ( " Il 38.8/b) 55 Il Il ll 1[ " Il Il ( Tl " 43.4%) 56 Il !! Il Il 4::) . '') " 12 " " " ( :_). ?~b 57 fi " 13 " >1 Il " ( tl tl 5L~.l%) 58 Il Il 14 Pressure vs. modulus of volume change 59
Il tl 15 E~astic modulus vs. porosity 60
Il rr 16 Pressure vs. settlement 65
li rr 17 Elastic modulus vs. confining pressure 68
-ii - Page No.
Gr a ph No.l8 Comparison of theoretical and actual settle- ment - Loose state 75
fr fr 19 Comparison of theoretical and actual settle- ment - Medium state 76
fr Il 20 Comparison of theoretical and actual settle- ment - Dense state 77
PLATES
Plate No. l Sho1>.."'ing Triaxial Compression Apparatus 22
Il Il 2 fr Il Il Il 23 " " 3 Showing Consolidation Apparatus 26 Il fr 4 Showing Plate loading Test Ap:paratus 31
FIGURES
Fig. No. l Pore pressure coefficients A and B (after Skempton 1954) .3
fr Il 2 Pla te loading test apparatus 30
Il Il 3 Mohr circles 43
Il 11 4 Pressure bulb und er a footing 44 fr Il 5 Hairline cracks 64
- iii - APPENI!IX
TABLES Page No.
Table No. 3 Calculation of confining pressure 93
Il Il 4 Pore pressure coefficient 'A' 94 If Il 5 Values of .,( 95
li li 6 Modulus of volume change - Loose state 96
Il Il 7 If Il Il Il - l'ledium state 97
Il Il 8 Il Il Il Il - Dense state 98
Il Il 9 Settlement calculatians - Loose state 99
Il Il 10 Il If - l'!:edium state lOO
Tl Il 11 - Dense state 101
- i v - S Y N 0 P S I S
A LABORATORY STUDY OF S:E.'TTLEI-îENT
CHAR.ACTE.:l.ISTICS o:F' SILT UND1.ill LVAJING
Settlement characteristics of silt have been studied in ~elation
to those of sand and clay. This involved investigation of the immed
iate elastic settlement due to deformation occurring under constant
volume, and consolida.tion as a function oi' pore pressure dissipation.
Oedometer and Triaxial compression tests (undrained and consoli
dated-undrained) vlith pore pressure measurements vmre performed to
obtain the values of the parameters my, the modulus of volume change,
E, the elastic modulus, and pore pressure coefficient 1A1 •
Plate-load tests on dry silt using a 611 square plate were conducted
to check its behaviour pattern. For silt in dry state, it -..ras found
that settlements could be predicted according to the classical elastic
equation for immediate elastic settlement only, and that consolidation
did not play any part. However, i t is expe cted, that consoli dation "-Tiich is dependent on the pore pressures set up under the load, may greatly influence the total settlement if the silt -.;v-ere saturated or nearJy so.
Previous studies on madel plate loading tests on silt have been
critically examined i\'ith respect to the re sul ts obtained from this study.
In conclusion, suggesti ons are made to gui de further research on
the subject. I N T R 0 D U C T I 0 N
Settlement studies of structures on sand and clay have received considerable attention in the past. Little, however, is kno~n about settlement behaviour of silt under loading.
In the case of settlement, ~ of footings on sand, Terzaghi's empirical equation b 2 q ·(-) .c (Terzaghi 1943, and Yong 1959) L b+l can be used, where C is a constant.
The settlement of footings on clay is composed of three parts:-
i) Immediate elastic settlement ~nich takes place without change
in water content corresponding to the change in stresses.
ii) A primary consolidation settlement which corresponds to change
in stresses caused by dissipation of pore water pressure.
iii) A secondary compression generally kno~n as secondary time effect. (This is not very well understood at present status
of our knowledge.)
The object of this work was to study settlement characteristics of silt under loading. This entailed determination of settlement parameters
E and mv and their variation with porosity and pressure.
The behaviour of cohesive soils can be explained by electro- chemical theory (Lambe 1958, 1960, Rosenqvist 1959, Harkentin and Yong
1960, and Yong 1960) and that of frictional soils by combined stress theory, but since silt falls in between, there is a need for more data for evaluation of its behaviour.
The theory of 3ettlements on sand and clay ~~ll be examined and applied to silt. A check of the theory will be maàe by loading a moàel f ooting on silt.
It will also be necessary to examine the previous work done on compression of silt under mod.el footings.
- 2 - T H E 0 R Y
The deformation characteristics of soil are best understood by visualizing it as a compressible skeleton of solid particles enclosing voids which in saturated sail, are filled •~:L th vJater, or, in partly saturated soil, ~~th both air and water. The normal stress on any plane is in general, the algebraic sum of t-v;o components - the stress carried hy the solid particles and the pressure in the fluid in the void space called the pore pressure. To obtain a clear picture of how the pore pressure responds to the different combinations of applied stress, the concept of pore pressure coeff icients is f ound to be conven- ient. (Skempton 1954 and Bishop and Henkel 1957)
It is assu~ed that the compressible skeleton of sail particles behaves as an elastic isotropie materi al and t he fluid in the pore space shows a l:i.near relationship between volume change and stress.
l~ l à&"3 ~ t.s-,- Atrl> ~ ~+tocs-, DL + o~ + D = o_!>·b ... àu. bu 1\ àu.J_ Fig. No. 1 (after Skempton 1954) If an element of soil is originally in equilibriurn under an all-round effective pressure p, then the application of stresses t.cr, and A~>'!tcan be considered as t aking pl ace i n t~o stages. Firstly, t he element is subjected to an equal all-round increment A~0 and secondly i t is subjected
- 3 - to a deviator stress ( àSj- ACSS). Corresponding to each of these stages,
be Au. and àud. there •,;'ill pore pressure changes 4 t."here àu.
The increase in effective stress in a partially saturated sail is
::. If Cc is the compressibility of the sail structure, then the volume
change is
••• (1)
where V is the original volume.
If Cv is the compressibility of the fluid (air and water) in the voids
and n is the porosity of the soil, then the change in volume in the void
space is
••• ( 2)
But these two changes in volume are identical and hence from equations
(1) and (2)
àu.o. Il. = 1;1 = ••• (3)
In saturated soils (zero air voids) Cv = o, since the compressibility Cc
of water is negligible compared to that of soil structure;
••• B = 1 for fully saturated sail. For dry sail Cv approaches i nfinity since the compressibility of air is Cc far greater than that of soil structure, hence for dry soils, B = o.
At any time -vmen the increment of deviator stress is ( b6",-A~),
t he pore pressure due to t his increment is .6ud. and the correspond.ing
- h - changes in the principal effective stresses are
and à~• As it is assumed that the soil particles behave as an elastic material,
therefore the volume change of the soil structure under the increment
of deviator stress is
AVe a c. . v. .L ( t.i; ~ '2.6~3) - c ~
or c . v. .1. l (~e-,-.Ar )-3tuAd} ••• (4) h~ =- - c. ~ 3 And the volume change in the void space is
1::.'11 = n . ~~ ~ Il - c"" . v. . ••• (5) But these two volume changes are identical and hence from equations
(4) and (5)
=
As the sail does not behave as truly elastic material, the above
expression should be ~Titten as
Au.
= B. ôG""! + B.A. ( t:. e--1 - .t.s-"i)
= B [ ôtr~ + A. ( t..lî,- t:. cs-3 )] ••• ( 6)
A and B are called pore-pressure coefficients . Value of A is determined from un.drained tria:xial tests and depends largely on "7hether
the soil i s normally consolidated or over-consolidated and on the magni-
tude of applied stresses. (Skempton 1954).
- 5 - JJ1MEDIATE EIASTIC SETTLEI':J.ENT
The immediate elastic settlement is that ~nich takes place ~~thout change in water content corresponding to the change in stresses.
According to the classical elastic equation beginning with
Boussinesq 1 s analysis of stresses on an element due to a point load and
Terzaghi's adaptation for use, the settlement 1} is given by r:· .. '} • J, . where q = net foundation pressure b breadth or diameter of loaded area
~= Poisson 1 s ratio
E = Elastic modulus
Ip= Influence value depending on shape of loaded area.
Values of Ip have been tabulated by Steinbrenner 1934 and given by
Terzaghi 1943. E can be determined from the stress - strain relation- ship for undrained or consolidated-undrained triaxial test w~th due regard to adjustments for sample disturbances, if any.
CONSOLIDATION SETTJ.. ZI·1ENTS
For simplicity in the follow~ng analysis, only points on the axis of symmetry below a foundation v..1.ll be considered. 'rhe directions of principal stress are then vertical and horizontal.
- 6 - If, at the point under consideration, ~ is the vertical effect-
ive stress before the foundation load is applied, then the vertical
effective stress immediately after load application is - rr, =
As the pore pressure gradually dissipates to zero àuring the consoli-
dation process, the Poisson 1 s ratio (in terms of total stresses) also
decreases. This has little effect on the vertical stresses and there-
fore, so long as the foundation pressures have not changed, the vertical
effective stress 'tmen consolidation is co mpleted is =
Hence, the change in vertical effective stress during consolidation is
equal to />v., and thj_s is •·;holly an increase above the original stress ~ •
If s-~ is the horizontal effective stress before t he foundation
load is applied, then inunediately after load application, the stress
Js
But 6~ is greater than b~~( equation 6). Renee t he horizontal effective stress is reduced by the load application. During the earlier
stage of consolidation, as t he pore pressur e dissipates, the sail is subjected to a recompression in the hor izontal direction, under a stress increase equal to ( A"'-- à e-}). In tJ1e latter stage of consolidation, after the horizontal effective str ess has regained its original value ~r3 , t he soil w"ill be subje cted t o a net increase in horizontal effective stress , f rom 6'~ to - 7 - ontal total stress due to the decrease in Poisson 1 s ratio as consoli- dation takes place. Skempton and Bjerrum 1957 have r eported that, o~ing to the fore- going effects, the lateral str ains dur ing consolidation are so small that they may be neglected 1dthout involving an error of more than 20% in the value of vertical consolidation movements. In the oedomet er test , the ver tical compression of the sail is measured under t he condition of no lateral strain, and if a vertical compression ~ is caused by consolidation under an increase in effective pressure As- , then where h = t hickness of sample = mv modulus of volume change in the oedometer t est. Since the consolidation of an element of soil, beneath a found- ation, t akes place without appreciable l ateral str ain, the vertical compression of an element during consolidation, can be expressed by the equation where dz = thickness of the el ement. And the consolidation settlement f of t l1e centre of a foundation rest- i ng on a bed of soil of thickness Z j_s gi ven by z ;; = f ""v-·A~o~..c:tz ••• (7) (J - 8 - Substituting in equation (7) t he value of A<4-from equation (6), the f ollow"ing expression for { is obtained: z { ::: J m" . B. [ O,o~ + A (br>,- [).r~)J Jz D B "' 1, for saturated clay, therefore p c ••• ( 8) According to 'rerzaghi' s one-dimensional consolidation, in 1-vnich lateral strains are zero throughout the loading period as w·ell as subsequently, the settlement is ••• (9) fof.ld.. is the value obtained by standard application of the oedometer test results . Comparing equations (8) and (9) it is seen that r. t!~~ 2 /_ t'YI.~. t.s-, (A+ ~, ( •-A )jrlz where J' == « Ar, By assuming constant va lue s of mv and A ~~th depth, it is poss- i ble to express r by a siraple equati on A+.((I-A) .•• (10) 2 J: Arl · d:z. where .( == r 1 .4tr . c:h Il 1 The coefficient .{ depends on geometry of t he probl em. Skempton - 9 - and Bjerrum 1957 have tabulated values of ~ for circular and strip footings for various values of E' from i1.'hich i" could be calculated, know~ng value of A from undrained triaxial tests • .. Heyerhof 1958 ha.s reported that t he factor l" for a circular foot- ing ( -,.;hich would also hold approximately for a square cr rectangular base at any depth) can v.i. th good approximation, be represented by the simple expression: 3 (1- A) ~ = 1- 4 + "lz In general therefore, total settlement t; can be given by the equation This equation wi.ll be applied to calcula te settlements on dry silt. A check of the above theory Kill be made by mea.suring actual settlement of a 611 square plate. - 10 - PREVIOUS lrJORK Host of the laboratory work on settlement has be en done -w'i th dry soils in order to exclude the complicating factors of cohesion and rr..oisture. PRESS 1930, KOGLER 1931, and GOERNER 1932, carried out experimental work to determine the effect of the size of loaded surfaces on the settlement of footings. GOERNE:B. used circular footings of various diameters on cohesion less soils. The fill, a clean sand, was tested in a medium state (porosity = 40%) and in a dense condition (porosity = 34.8%). The methods used to produce these porosities along with the size of the con tainer used were not reported. Graph No. 1 indicates t he results of this investigation. PRESS performed similar experimenta on natural ground. The sail v.ras a bro-wn moist loam containing 46%sand along t-ri th a small amount of calcium carbonate. Square f ootings of various widths ~ere used. The results of this work are shown on graph No . 1. Both graphs reveal that, except for the smaller f ootings, a linear relationship was obtained between aize of footing anà. settlement. I n the range of footing sizes wh ere the st raight l ine r elationship did - 11 - Graph No. 1 GRAPHS OF GOERNER AND PRSSS 1------f--- -- P'fessu.Ye - f--- \.0 a..t 1'1'\o sph.ev e - \------·-f--· . o.s Q..t. '\. -- ...... ---- o. 6 o.. .t". -~ . - 0.4 a..t. - 1 o. 3 "-t. - 0·2. a...t"- - "L-j O.l a...t. 0 50 \00 OISC DIAMETER ( cm. ) · SAND P'fe ss u te -+--- 5 a..tmosp~e'f'e s ~--J_....._ -+---4 a.t. 1- ~ 30 t--+---1 :;: -+---.3 a. f; . LU ~ --1---- 2. a.t. w ..._ __ J a...lï. ~ o~~~~=±~==t=J:~ o 4o 8o WtDTH OF PLATE (cm.) --LOAM ·( 4~% SAND) - 12 - not exist, Kogler attributed this variation to the plastic movernent of unrestrained soil grains near the edge of the footing. The relative importance of this movement increased with smaller surfaces. Conse quently, only smaller surfaces on cohesive soils deviated from the linear relationship. On cohesionless soils larger footings were affected. Meyerhof 1950, wnile studying the bearing capacity of sand, reported sorne observations ntade from load-settlement curves obtained with sand. He worked with a medium uniformly graded sand and tested it at three different ranges of porosity- loose (45%), medium or compact (40%) and dense (37%). He investigated footings which were placed on the sail surface, at shallow depths and at greater depths. The f ootings used were circular, square and rectangular in shape. The size of con tainer used was such that the ratio between the width of container and width of footing was greater than 8. The following are sorne of his conclusions from the load-settlement graphs:- 1. In the dense and compact states, load-settlernent curves for shallow footings were similar to the corresponding shear stress-strain curves. A maximum value of sail reaction was obtained at a certain s ettlement beyond which the sail reaction decreased ~~th increasing settlement. 2. In the compact state, circular and square footings yielded very similar results; large areas gave similar curves to those of smaller ones of the same shape. - 13 - 3. In all three states, a line~r relation between load and settle- ment was obtained in the early stages of load-settlement curves. 4. At working loads, the settlement of footings on sand occurred largely on application of the load and progressive move ments 1-rere usually small. The total settlement at the ultimate bearing capacity depended to some extent on the rate of loading. 5. For surface tests only, the settlement per unit width decreased v.'i.th greater footing \<.'idth, apparently approaching a minimum for large areas. 6. Settlement figures and consequently factors of safety cannat be extrapolated to full scale foundations. 7. The customary use of greater factors of safety for dense sand rather for loose sand, hecause of an assumed greater settlement, is not justified; on the contrary the a.bove results indicate that a greater factor of safety should be used w-i.th loose sand if settlement consider ations govern the bearing pressure. Heigh 1950, while investigating the ultimate bearing capacity of footings on clay, cow~ented on results obtai ned from load- settlement curves. Âll tests were performed on remolded London clay having a 47% moisture content. He used four circular footings of t he dise and shaft type along \<.'i.th one square and one strip footing. The minimum size of container was adjudged to 7 D in diameter by 11 D deep where D is the footing diameter. - 14 - }1eigh, in order to have dimensionless coordinates, plotted load settlement curves as load/shear strength versus settlement/diameter. The follovri.ng are some of his findings:- 1. Four or five diameter penetration was required before the ultimate bearing capacity was reached. 2. For all size3 of circular footings tested there was only one value of ultimate bearing capacity/shear strength. Consequently, cu.rves of pr essure/shear strengti1 versus settlement/diameter should be the same for all footing sizes; experimental results proved this. 3. In the light of the ab ove, it wa.s concluded that the value of pressure/shear strength for any given value of settlement/diameter is independent of the footing size. 4. From a plot of pressure/shear strength versus settlement/diam- eter, it was seen that for equal pressures, l arger settlements occur red ~~th the strip footing than with the circular footings . However, bath load-settlement curves had a similar beginning. Brebner and Wri ght 1953 investigated the variation of subgrade modulus of sand loaded by plates of different breadths. A plot of subgrade modulus versus breadth of footing indicates that the experimental cur ve obtained with rectangular plates is of simi lar form as the curve obta:i..ned by previous investigators -v;i th circular plates . The experimental curve obt ained w"i t h circular plates follov:ed - 15 - fairly clos ely Terzaghi' s theoretical curve ~rhich was a rectangular hyper bola. More direct work on settlement of silt under madel footings was carried out by PADOPULOS 1957 and GIDJEST 1958 in the Department of Civil Engineering, McGill University, Montreal. Bath used an identical light brown silt from Niagara Falls, Ontario (S. G. = 2.58, P. 1. = 20%). It was reported that the liquid limit could not be determined. Particle size analysis indicated that 80% of the silt fell w~thin the range of medium to coarse silt (M. I. T. Classification). Oedometer tests on loose dry silt were performed with initial porosities around 62%. No rebound measurements seem to have been taken or reported. A steel circular drum measuring 22 ~ 11 in diameter and 19-f:" high served as a container for the silt. Padopulos studied the influence of the container size with refer ence to the size of loading plates vdth regard to both limiting lateral and vertical dimensions. It was reported that for a container w~dth seven times the w~dth of the plate, the percent error due to lateral limitation was 7%. For a minimum influence due to wall and depth limit ations, it Has recommended that the wi.dth of the container should be at least 8 B and depth be at least 10 B vfuere B is the widt h of the plate. Padopulos used three different ranges of average porosity - 52%, 42%, and 36%. Three madel footings 1 11 , 211 , and 311 square steel plates ~ 11 thick were used to study the influence of footing aize. - 16 - Genest also used three different ranges of porosity - 50%, 45% and 35~ . He used five footing sizes; 1~ 11 , 2", 2~ 11 , 3 11 and 3~ 11 square. The entire container "~"as mounted on a platform scale and load was applied by an adapted loading yoke. Loads \..-ere applied in small increments and left on until the rate of settlement was considered negligible. The square r oot of time fitt ing method was used Where neces sary. In general, fail ur e by excessi ve settlement occurred for t he loose and medium states of packing. Sorne localized f ailures were observed for t he loose state at about 5 psi and for the medium state at about 20 psi. Shear failure occurred at around 80 psi for the dense state of packing. Padopulos concluded t hat:- l. Load-settlement graphs f or each footing size and porosity v.-ere linear. 2. From a plot of porosity ver sus the value A defi ned as the ratio of the settlement Sf over the pressure q by t he i 3. Modul us of El asti city E for settl ement calculations coul d not be obt ai ned f rom t he relat i on E = ! , in which mv = modulus of volume IDv change obt ained i n consolidation t est. - 17 - Genestls conclusions were as follows:- 1. In the three ranges of porosity tested, a linear relationship between load and settlement was obtained. 2. The empirical equation ~ = '1·(~) 2. C may be better adapted to v+l silt in loose state. The classical elastic equation ~ = q.b.C appears best suited for a silt in medium or dense condition. 3. For the type of silt used, a relation exists between constant C = !- and the porosity of the soil. ksb 4. The variation between coefficient of subgrade reaction and the width of footing used may be of hyperbolic form. 5. The relationship p c( B = (~ )n. was established; where f = settlement B = width of footing q = pressure applied ~ = density of soil aC and n are soil parameters. All tests 0 yielded a value of 45 for n. Intercept ~ was found to vary w.'i th porosity. 6. The value of modulus of Elasticity E as used in settlement calcu- lations of silt might possibly be determined from the relat ionship E = ! , where my is the modulus of volume change obtained in consoli mv dation test. - 18 - EXPERIIvlENTAL 1vORK PROPERTIES OF THE SIL'l' The silt used waa obtained from the Island of Montreal (Dorchester and Mansfield Streets) at depth of 15-20 feet below ground surface. It was grey in colour and odourless. The specifie gravity was 2.7. The plastic and the liquid limits were 17. 9 anci. 19. 7)0 r espectivel y (Plasti city Index= 1.8). The grain size distribution curve i s shown on gr aph No. 2. 90~ of the silt fell -v;i t hin t he medium silt classifi cat i on usi ng the H. I. T. method of classification. TESTDJG ?3.0GRA1-ll".:E (A) Physical Tests: Two t es ting progr amme s -~re re mainl y carr ied out: t riaxial test- i ng and consolidation (oedomet er) t E:sting. Sorne sarr..ples Fe r e als o t ested i n t he unconfined condition. Sacb ;d l 1 be de seribe d in detail as foll ows: TRIAXIAL TESTING Preparation of Samples Samples wer e pr epared usi ng a spl it moul d 1.4" di arneter 2. 8" high - 19 - Graph No. 2 1-----+----+----4----~----~---r----T---~----- ~ ----~ l-----+----4----4----~----~---+----+---~-----r----i0o 6 i ' 1 ! 1 ' ' i . 8 ; i 1 H 1 s H . rn 1 t !=l 1 ---.· -- ---4---__,1__ --'- 1 - -i'------.. . ··-··- . -· ·· ; i 1 ' ' 1 i ~ 1-----+----+---4---4---r----+--+---- 0 H ~---+----+--~---~--r---+--~~i~ ~-, , ----·~,---1 ~ 8 H .ex: ~--t-----+----:r----t---- · ··--+--»l-i-----'---- .,--·-- 0 H 1------l-----+---t---+---t----Y/~------1-- ---· ... ··- L 1 p:; ~ -0 H rn 0 Ç:tq rn ~ i < '1 '1 E-; H 0 Ç:tq 1 0 1 1 ! Vo ~ l----1----l------+--:,.L-./--1-+---t--+--!-r-1-+ ----· -- .ex: H V' 1 t') A 1---l------1---:.~-+----+---t---+--+--t----j--/ -- · 0 ô /? 1 1-----++-/--+-'---1-----l---t------t-----f--t---j--- i ' ' 1 ~ zA -1-rf-1---+-! ---~-' ~r-1 ---+--T-' ---t- ~ --- -~--- â rn< 1 1 l--I-f-1-----+-, --If--+,· --!--....:_; --+---~1 ---r: - ·· - ··- 0 0 0 0 0 0 0 2 r- \9 rf) 0 "' ~ - 20 - and compacted in three layers. Compactive effort was varied to obtain samples of a wide range of porosities. The samples thus obtained were partially saturated. These partially saturated samples were fully saturated inside the triaxial cell by opening the top and bottom drain age valves under a confining pressure of 5-7 psi for at least 8 hours. The true initial height ofsample could be established by measuring change in height at the end of saturation. The sample ~~s then ready for test. Two types of triaxial tests were performed: Undrained and Consolidated-undrained. Undrained tests With the top and bottom drainage valves closed, cell pressures of 15, 30 and 45 and 60 psi were applied and the samples were sheared by applying deviator stress. Pore pressure measurements were taken and final water contents determined. Consolidated-undrained tests The samples were consolidated under cell pressures of 15, 30, 45, and 60 psi with the top and bottom drainage valves open for at least 12 hours, ~nich was considered more than adequate knovdng the time required for 90% consolidation from square root of time fitting method. The drainage valves were then closed and the samples were sheared by applying deviator stress. Pore pressure measurements were taken during - 21 - PLA.TE No. 1 TRIAXIAL COHPRESSI ON APPARATUS - 22 - PL.û..TE No . 2 TRH.XIAL COMPRESSION APPARATUS - 23 - the test and finalwater contents determined. A total of 30 triaxial tests were performed. Plate Nos. I and II show the triaxial cell used and the general arrangement of apparatus. CONSOLIDATION Preparation of Samples Partially saturated samples -were prepared in a split mould 2.811 diameter by compacting the sail in three layers. The porosity range from 36 to 44% was obtained by using different compacting efforts. These were later trimmed to 2 • .5 11 diameter and thickness equal to about 3/4". It was not possible to obtain a sample of high porosity (loose state) using the above method. This difficulty was resolved by pack ing the oedometer \d th loose dry sil t v..nich v;-as then saturated over night from top and bottom. The initial thickness of the sample could be easily calculated by noting the dial reading before and after the sample v..~s saturated. Two samples were thus obtained. Loading Procedure The loading and unloading cycles applied are shawn in the follow ing table:- - 24 - TABLE No. 1 Loads in Kg/sq.cm Laading 1 2 4 8 16 32 64 128 Un1oading 128 64 16 8 1 Re1oading 1 4 16 64 128 Unloading 128 32 8 1 The square root of time fitting method was used to obtain 90% consolidation for each increment of 1oading. One samp1e was taken through three 1oading and unloading cycles. Two samples (high porosity) were started with i Kg/sq.cm. and increments applied as shown i n the fo1lowing table:- TABLE No. 2 Loads in Kg/ sq. cm. Loading .1. .!.. 4 2 1 2 5 10 20 Un1oading l 20 10 5 1 4 - 25 - PLATE No. 3 CO N SOLIDO METER - 26 - A total of 6 tests were performed. Plate No. III shows the consolidometer (oedometer) used. UNCONFINED COMPRESSION TESTS Samples were prepared in Harvard Miniature compaction apparatus, the compaction effort being varied to obtain samples in 1oose, medium and dense state of packing. The moisture content of the samples was in the range 17 - 19%. Samples in loose and medium state did not yield any results as they either disintegrated as soon as load was applied or failed by bulging under their own weight. Two samples in dense state were successfully tested. (B) PLATE LOADll-JG TESTS The Fi11: The fill consisted of si1t in dry state. Three different ranges of porosity were used: loose, medium and dense. The loose state of packing was at the maximum porosity that could be easi1y produced. It was obtained by pouring the soil from a height of about one and a half feet. The test w~s commenced 24 hours later. Average porosity obtained this way was 48.9%. The medium state of packing was obtained by fi11ing the container in 6 inch layers and compacting each layer by four passes of the - 27 - vibratory tamper.".><. Average porosity obtained was 43.7 and 44.0% The dense state of packing was obtained by filling the container in 3 inch layers. Each layer in the first ! depth of the container received 4 passes; from ! depth to 3/4 depth, 6 passes, and from 3/4 to the top, 8 passes of the tamper were given. This was done to achieve a uniform density. FOOTING AND CONTADifER A steel plate 611 square and 1 11 thick was used as a footing. A small round cavity was made in the centre of one side of the plate to seat a ball bearing in order that the load could be applied without any eccentricity. The container was a 5 feet square tank, 4 f eet deep and ~~s built from 3/4" thick plywood adequately braced on all sides. LOADTIJG DEVICE The general arrangement of the loading deviee is show.n in figure No. 2 and Plate No. 4. The st eel frame was built to obtain the reacti on of a hydraulic jack so as to apply load to the plate. The two 5" x 5" columns were * Courtesy of James W. Hall & Sons, Montreal, P.Q. - 28 - secured to the floor by 3/411 diarneter cinch anchors. A 12 WF 40 bearn was connected to the top of columns by 5" x 3~ 11 x 3/811 angles. The gauge, attached to the hydraulic jack was capable of measuring up to 3,700 lbs. This gauge was calibrated prier to commencement of test- ing. On top of the plate rested a 311 steel cube which had a small round cavity in the side facing the top of the plate. The ball bearing was seated between the two cavities of the plate and the cube. There was a clearance of about 1/16 of an inch between the plate and the cube. On top of the cube was screwed a nat steel bar 1~ 11 x 3/811 x 3 1011 "Which projected towards the side of the tank. A dial gauge capable of measuring up to 0.00111 , independently supported on a rigid base, rested on top of this flat bar to register settlements. A total of 211 settlement could be measured vdth this guage. The hydraulic jack was placed on top of the cube. In the space between top of the jack and bottom flange of the bearn of the steel frame a 311 square steel plate 1/1611 thick and two blocks of wood were placed, as sho~n in plate No. 4. The weights of the plate, cube, hydraulic jack, black of wood, etc., were predetermined. Load was applied on the plate by jacking up against the bearn of the steel frame and was registered on the gauge attached to the jack. - 29 - 12W:40_/ BLOCK oF woOD ~ LEV~L .. IJ li ,.._ __ .z J~ -;s cc 1/ Il z .(2 FIG. No. 1 PLATE LOADING TEST DE VICE - 30 PLATE No. 4 PLATE LOADING TEST APPARATUS - 31 - TESTING PROCEDURE In all, five loading tests were performed; two each for dense and medium states and one for loose state of packing. Load was applied in small increments and was maintained till 90% consolidation was reached. This was determined by the square root of time fitting method. The soil at the top was levelled off by screeding with a plane board 211 x 4". The centre of the tank was marked; the plate and 3" steel cube, ~~th the ball bearing seated between them, were placed on the soil in the centre of the tank as quickly as possible. The zero reading of the dial gauge for measuring axial compression ~~s instantly taken. This was the first load in each case. After 90% consolidation was reached, the hydraulic j ack was placed over the st eel cube and the wooden block and Y' square thin plate inserted between the jack and bottom flange of the bearn. This was the 2nd increment of load in each case. All the subsequent increments of load were obtained by j acki ng up against the bearn of the frame. In the loose state, load increments of 20 lbs. were applied up to a total of 250 l bs. The increments were then increased to 30 l bs. and continued until failure occurred. Failure ~~s assumed to have been reached when a small increment of load produced excessive settlements. I n the medium state, t he load increments of 50 lbs. were applied - 32 - up to a total of 200 lbs. The increments were then increased to 200 lbs. and continued until failure was reached. Shear failure occurred 11 11 as explained in the chapter Test Results • In the dense state, the load increments of 200 lbs. were applied up to 950 lbs. followed by increments of 600 lbs. up to 3,650 lbs., beyond which load could not be measured. Failure ~~s not reached, although sorne hairline cracks around the plate were noticed. - 33 - EFFECTIVE STRESSES The fundamental principle underlying all work on strength or deformation characteristics of soils is that the mechanical properties are controlled by intergranular forces. If ~ denotes the total normal stress acting on any plane in a sail and if u. is the pressure in pore water, then to a close approximation, the effective stress ~ is given by - fr = rr-- u. In this expression CS" is the sum of the intergranular forces normal to the plane per unit area of the plane. This has been established by Terzaghi 1936 for sand, clay and concrete, Hvorslev 1937, Rendulic 1937, and Taylor 1944 for clays, and Bishop and Eldin 1950 for sands. The Coulomb-Hvorslev failure criterion can be expressed by S = c.e. + ( 10 - "'" ) tan ~TfZ wtlere c~ = true cohesion .h = and r~ true angle of internal friction. Cohesion By "cohesion" is meant shear resistance which can be mobilized between two adjacent particles wnich cohere to each other w~thout the necessity of any externally derived normal pressure, i.e. bonding between adjacent particles is from forces arising w~thin the particles - 34 - themselves. (These are physico-chemical forces.) The magnitude of cohesion is dependent upon several factors. The follo~~ng are sorne important characteristics of cohesive strength: (Lambe 1960) l) Cohesion can be variable - van der Waals and electrostatic cohesion can be sensitive to environment. 2) Cohesion may merely make larger soil particles out of smaller ones; thus a highly cemented soil may show its improved strength by an increase in the friction angle rather than cohesion intercept on an effective stress-strength plot. 3) Cohesion is generally mobilized at relatively low strains. Thus in a natural soil, cohesion can be mobilized and destroyed before the other components of strength become active. I f the water content of a clay were plotted against the effect ive major principal stress, all points conform to a single curve, independent of the magnitudes of the minor and intermediate principal stresses. (Triaxial Research Program, Unit ed States War Department, 1947). If the compressive strength, determined in the triaxi al apparatus - 35 - were plotted against the water content at failure, all points would fall on or near a single curve independant of method of test, pore water pressures etc. This led Bjerrum 1950 to propose the following hypothesis: l. The water content of a clay element is dependent solely on the magnitude of the effective major principal stress. 2. If by shear the total external stresses are changed so quickly that the water content of the clay element remains constant, an excess hydrostatic pore water pressure will arise, the magnitude of which w~ll adapt itself in such a way that the effective major principal stress remains unaltered. 3. Provided that the pore water can escape, the effective inter granular stresses will, after a certain time, be equal to applied external pressures. This working hypothesis is not valid for all soils; it is known that it cannet be applied to non-saturated or preconsolidated clays. In the case of unsaturated soils, there exists a pressure defic iency in the pore water (negative pore pressure). Aitchison and Donald 1956 found that there is no fixed relationship in incompressible (granular) soils between pressure deficiency in the pore water and the effective intergranular stress due to such pressure deficiency. In such soils, the maximum effective intergranular stress is determined by the - 36 - pore water stress at initial pore drainage. Any further increase of the pore water stress does not cause a substantial change of effective stress. In unsaturated fine sands the maximum effective intergranular stress due ta moisture films, is of the arder of 1 - 2 psi. Effective stresses in unsaturated compressible (clay) soils are related directly ta the pressure deficiency in the pore water. Pressure deficiencies of the arder of 400 psi can produce effective stresses of equal magnitude in clays. The normal concept of effective stress ( i" = cr- v..) is there fore unacceptable in incompressible unsaturated soils at pressure deficiencies of magnitude sufficient ta cause pere drainage. At the other extreme, in fully compressible soils, the normal effective stress concept is completely valid, even at pressure deficiencies in the pore water (negative pore pressure) of a very high arder. In the case of preconsolidated clays, if strength is plotted against water content at failure, the points do not fall on a single curve. If the applied load is less than the preconaolidation pressure the possibility of pore pressure build up is unlikely, and a strength plot will yield higher value of shearing strength. These facts account for the inapplicability of the hypothesis. Internal Friction Internal friction is derived principally from actual friction of grain on grain. During shear displacements, the moving particles tend to interfere with each other both electrically and physically. If the - 37 - interference results in a tendency toward a volume increase, a higher shear resistance is mobilized. Hoving the particles can cause a change in electrical forces thus requiring a change in volume or change in some other pressure, such as ..- or u. , to main tain equilibrium. This phenomenon can result in a dilatancy component to the shear resistance. A most important characteristic of both dilatancy and friction is that the shear resistance which can be mobilized is a direct function of the force acting normal to the shear surface. The greater the normal force, the closer the surfaces, and thus the greater the influence of electrical force fields, one on another. (Lambe 1960). It is seer., therefore, that effective or intergranular stress is the most important factor in the determination of strength and deformation behaviour of soils. In the case of soil in dry state, the effective or intergranular stress iS is equal to total normal stress cs- as excess pore ,,;ater pressure ~ in the equation is zero. The friction component of the Coulomb-Hvorslev equation depends upon the true angle of internal friction ~ and the i nter granular stress vJhich, in the dry state, as stated above, is the total normal stress. - 38 - As intergranular stress, by definition, signifies stress betw~en particles in contact, the results of triaxial tests on saturated sarr~les expressed in terms of intergranular stresses, will yield a value of elastic modulus E which could be applicable to a sail in dry state. - 39 - HODULUS OF VOLUME CHANGE Redefining consolidation as a gradual process involving drainage, compression, and stress transfer under complete saturation and not merely compression under static loading, and modulus of volume change as representing the compression of soil per unit of original thickness due to a unit increase of pressure, an equation for settlement can be used which embodies both phenomena. In the oedometer test, consolidation takes place at zero lateral strain, with free drainage to atmosphere (one-dimensional consolidation). Assuming that the sample is under an initial stress equal to tr , an increase of ~ sets up excess pore-water pressure A~ and the effect- ive stress immediately after the stress increase is (see Theory, page 7 ) The excess pore-water pressure gradually dissipates to zero through drainage and after consolidation is completed the effective or intergranular stress is This means that the effective stress on completion of consolidation under the increased load, is equal to the total applied load. This is the mechanism of consolidation. For this soil system (silt), it is not certain vmether surface - 40 - forces ~~ll prevzil under loading conditions. In view of the fact that silt exhibits sorne plasticity, there may be sorne influence. On the ether hand, in terms of particle size the surface forces will not be important. It may therefore, be inferred that the compressibility characteristics of wet and dry silt w~ll not be materially different. Nash 1953, while investigating the shearing strength of fine sand, reported that the compressibility characteristics of we t or air dry fine sand were the same. In the light of the above remarks, and assuming that the viscosity effects in silt are negligible, it may be possible to use the values of my obtained for saturated and partially saturated samples to calculate consolidation settlement of dry silt. - 41 - CONFINING PRESSURE AND VALUE OF 11 E11 In order to obtain value of E from triaxial test results, it is necessary that effective confinement applicable to plate loading tests at any one depth be known. (This follows from graph No. 15 which shows that E increases with increase in confining pressure.) If an elastic prism of sail having unit weight t' on a perfectly frictionless base is considered, the pressure due to its mm weight causes not only vertical compression but also lateral expansion. If this prism is laterally confined between perfectly smooth vertical walls or within a layer of identical material on a rough base, no lateral expansion can occur. Therefore, at any depth z, every vertical side of the prism w~ll be acted upon by a horizontal pressure 6" 3 per unit of area -v:hose intens ity suffices to restrict lateral expansion of the prism at any depth z; this horizontal pressure is given by 5'"~ = "t' z 1(0 where Ko = coefficient of earth pressure at rest. When an external pressure is applied to the soil through a foot ing, tendency to expand laterally increases. To maintain equilibrium ~ must increase to counteract the increased tendency for lateral expansion. Passive resistance of sail is thus mobilized and 11~ is given by ~3 = "{ 'Z. 1(~ ••• ( 12) - b2 - SHEAR STRESS VS NOnl-1AL STRESS / / Consolidélted - undrained / / triaxicù tests ./ (!) ./ ...... Effective Stresses t>=1 ;po {"'Total Stresses ::0 ., "" .....,_ ~ (!) VJ >-:3 " ::;:J '"'\ t.:j \ (!) ' '\ \ {f) ' " \ \ ' \ \ \ (!) " H"' \ \ \ \ \ \ N 0 R N A L S T R E S S PSI Fig. 3 t10HR CIHCLE PLOT OF TOTAL A.t~DEFFECTIVE S'rRF.SSES 4b 3b 3b 4b z.b 5b 6b ' J!----;1i- 7b l 8b 1 ·--+---1 ------' - IO b 1---,-----"'" ,--r----i ! --;---j Il b ~0 r----1 --:---t----t--1i __ ' "'0..., "' . ·"'fJ 1 Il ~~----+' r-~~----,r---~--~---~--~~--~~· 11~ 4b :'l lh b 0 'lb ?>.b 4b Fig. 4 PRESSURE BULB Contours of equal vertical stress beneath a square foundation of width b, computed by We s tergaard's formula , after Sower s & Sowers (30 ) - 44 ------, where ~~ is coefficient of passive earth pressure. KP is equal to tan2 (45 +f/2). f, the angle of internal friction, if determined from a plot of MOHR circles for consolidation-undrained tests (see fig. No. 3), is called fcq in terms of total stresses and r' in terms of effective stresses. It is worth noting here that there is very little difference in the total and effective strength plot for the sail under consideration. If the pressure bulb under a square footing is examined (fig. No. 4), it is seen that for a footing 611 square, contours of O.l'i and 0.01~ pass 10.511 (1. 75b) and 34.5 11 (5. 75b) respectively below the base of the footing. The limiting value of significant stresses beneath a footing may vary from 0.1~ to 0.01~ , depending upon the nature of problem. A more commonly used value of 0.01~ is adopted here. The centre of pressure of the effective pressure bulb is located at H/3 from the top of soil, where H is defined as the limiting depth below which the stresses are neglected. In the equation (12) z can, there fore , be replaced by H/3 "'34.5 x l/3 = 11.5", say 1 1 • The confining pressure f or each state of packing is det ermined in table No . 3, and an average value obtained v.nich is 2 psi. - 45 - TEST RESULTS 1. TRIAXIAL TESTS The results of the triaxial tests, undrained and consolidated drained, are plotted as deviator stress ( ~ - ~3 ) versus %strain (see graph nos. 3 to 6). It is seen that the curves do not start smoothly at the origin. This is probably due to 11 seating errer". It is gener ally difficult to effect a positive seating of the caps when the test specimens are remolded or compacted samples. The fact t hat this effect is more pronounced for the smnples in the loose state supports this view. In determining the strain used to compute E, proper allow atlce has be en made for the 11 seating errer" as sho"'n by the dashed part of curve. The point "'nere the dashed curve cuts the abscissa has been trucen as zero strain. The elastic modulus E for each t est is calculated by taking one-hal f the deviator stress at failure and dividing by the correspond ing strain. This is quite arbitrary but within the limits of the conventional straight line stress-strain curve. Skempton 1948 has used this criterion t o calculate the elastic modulus. The values of E for each test are noted on the gTaph. The variation of elasti c modulus E with porosity and lateral pressure (confining pressure for the sample ) has been studied (see - 46- Cro ph ::.:). 3 DEVIATOR STRESS VS STRAIN 160 CELL PRESSURE 15 PSI -i------l------ El---Cl Consolidated undrained test o~---o Undrained test 140 For n • 38. 55;, E = 315 TSF ( 5) 120 ~------4---~-----+------~-----~----~------1 ! H ! Cl) 0.. ~9.'/%, E =,230 TSF (l) lOO ~------~~-----,______~------~or n ~-~~% 1 E = 120 TSF (2) 1 ~0 ~------1-----.F-+-----~---·r 1 60 For n = 46.8%, E = 60 TSF(4) 40 20 . 1 1 1 1 1 1 1 1 1 8 12 16 /0 % ST,RA!N DEVIATOR STRESS VS STRAIN - CELL PRESSURE 15 PSI - 47 - Graph Ho. 4 ------,-·------,-~0---lt~ . 1 1 i" 1 i1 1 1 i ' 1 ·--74---"ç;.-:~'---+-~---!-_:______J__. --~ 180 1------+------+ 1 . ' i - l-o-~ 1 1---El'-+ ~ . f'oi ; ! ,1 l o--; 1 -o---- o-t-D 1 1 o--- ! l 140 ~---1-----~----' 1 1 -H Cl) P-t 1 1 1 .i 120 1 ~~~~~~~ Cl) ' 1 i 1 Cl) 1 1 fï:l = 46.2 %, E =265 TSF:(6) 1 p:; 1 1 8 lOO = 43.2 %, E = 250 TSF: ( 8) ~ Cl) 42.0 % E = 315 TSF: (7) ! 1 : = 39.1 % E = 560 TSFi ( 12) i 1 : 1 1 For n = 80 ~--t--- ·------+- 37.2 %, E = 780 TSFI(lO)I ! l 1 1 1 1 ------;---~ - - 1 1 1 1 DEVIATOR STRESS vs STRAIN CELL PrŒSSURE 30 PSI 1 j o,--~o Consolidated-undrained test! ------+-o__ o Un1~-r~ined.:__:t;est _____f ___ i 1 : 1 1 1 ! ! 1 ! ' ' 1 1 1 1 i ! 8 10 12 % S T R A I N DEVIATOR STRESS VS STRAIN - CELL PFŒSSUHE 30 PSI -48_ 200~------r------~------ ! 1 18or------,-- l (/) (/) 43.8 % E ::540 TSF ( 15) !il lOO -..... __ . For n 43.3 % E =580 TSF (16) Çt: <.____ ...... ___ For n = 40. 6 % E : 980 TSF (13) 8 i <.___ (/) For n .. 39. 2 % E =670 TSF ( 14 ) ;z___ ' For n ... 38. 4 % E =1 040 TSF (18 ) Çt: 80 +------cl-+-+-+-- 1 0 i 1 8 1 < / 1 : 1 H ! '- --+ 6 1 ·f-+1----L------+-----j --· ---: ------1-- -·------r > W ~ ! A t---+---w-l--+------1------tl DEVIATOR S'l' R:;:<; SS VS CELL PHF:SSUR E 45 PSI D----ll Consolio a t ed- und rain ed t e r; t : i o Undra i ned t e s t 1 1 .~~~--~------74------~------~------~~-----~~---- % STRAIN DEVIAT OR STRESS VS STHAIN -CELL PRESSUR E 45 PSI - 49 - · Graph No. 6 240~------~------+------f------r------+------~------1 . --o- H Cf) 200 ~ Cl) Cf) r:il 160 et: 8 For n E ::1100 TSF (20) Cf) = 43.2 %' For· n = 41.0 % E =1390 TSF (23) et: 120 For n E =1030 TSF (21) 0 = 38.0 %' 8 = 37 .o %' E =1440 TSF ( 22) 1 <: = 36.3 % E =1840 TSF (19) 1 H 80 > r:il A DEVIATOR STRESS VS S'rRAIN CELL PRESSURE 60 PSI e o Consolidated-undrained t est ~ Undrained test 0 2 4 6 8 10 12 14 % STRAIN DEVIATOR STRESS VS STRAIN - CELL PRESSURE 60 PSI - 50 ":"' graph No. 15). E is found ta increase with: a) a decrease in porosity - the denser the sail, the greater the elastic modulus. b) an increase in confining pressure - as would be predicted for cohesionless materials according to the classical theory. 2. UNCONFllŒD CŒlPRESSION TESTS The results of the unconfined compression tests are shawn in graph No. 7. E has been calculated in the same i•;ay as triaxial tests. 3. CONSOLIDATION TESTS The results of consolidation (oedometer) tests are plotted as pressure versus void ratio (see graph Nos. 8 to 13). Graph No. 14 shows variation of modulus of volume change, M., with pressure. mv is found ta decrease hyperbolically with increase in applied pressure. For purposes of comparison on an equal basis, mv must be determined for the same restrictions as E from triaxial tests. The value of~v, therefore, is read off against the pressure equal to one-half the deviator stress. (70 psi or about). - 51 - Graph No. 7 UN CONF ItlliD COHPH.SSS ION 7 STY?.ESS VS STRAIN Porosit;r 37.3% 6 E = 10'T/sq. ft. 1 2 -~~----1 1 -+--J----i 0 4 8 12 16 20 % STRAIN - 52- 0-4 0-4 ..,., ..,., 0 0 Pl Pl ro ro '1 '1 ::r ::r 'd 'd 200 200 IO IO . . 100 100 AT R 36.3% 36.3% VOID VOID Unloading Unloading Loading Loading Reloading Reloading o o VS VS a a :6 :6 POROSITY POROSITY 50 50 T " l.O - - -- A A o o INITIA~ INITIA~ i"k i"k . . PRESSUIŒ PRESSUIŒ JO JO cm 1 1 20 20 kg/sq. kg/sq. ---- ]-~ . . --. --. -·-- •• •• RESSURE RESSURE P 10 10 -----1 -----1 :=---0. :=---0. i i 1 1 4 4 5 'f 'f 3 3 2 2 ----j_··----l---L-- 1 1 1 1 1--- 50 50 o45 o45 ~55 ~55 oJ5 oJ5 • • .40 .40 o60 o60 - > > 0 0 ~ ~ 0 0 0 0 1-3 1-3 ::0 ::0 H H H H 1 1 l.>J l.>J Vl Vl .C,2 . --~--~---~------~------~------.-----~--~------~~------~ .~o PRESSURE VS VOID RATIO . ' J INITIAL POROSITY 37.41o · .sB . -Î -- --~--- ·-·------·- - "' n Loading _____L__ !- ~ ~ Unloading . SC:. J ' l 0- Ci> Reloading -- ,------r ' . 54 ------1 ------t------~-l 1 1 1 . ~--- 1 V1 . 5'2. ·- jl ----- .. 1ï ·-- . ij ·-· ------· .p. < 1------··___ - ---- . --+----,----_. ··- --- - ·---'----. ------1 D 1 1 ' 1 - 1 1 ' 0-50 ------_[ . _j ______- -L - _ J i 1 l i i ----- .. ·----•- ~No ------·-·i· -- .' . . · • 1 1 ' ! __J=-r ~~------~ i 1 ·. 1 . -- ! ! 1 1 0 .4~ --1-.. -i- :------· -----l--. ! ! i 1 .44 . ______l ______i-- --~------1------1 ! ! 1 1 j 1 ' ·4"- . 1 1 . ·------l--- - 0 1 l 1-i ' ---,..___ ,1 1 lb 'd ·4b : 1 1 : p· ---r-- - -: ~ - .--i -i ' ' ' ------:z: 0 • ·38 "-!) r------1 - 1. r 1· - ·· r- -- , --1--t -r------r----- '1- 3 4 S lD 2-o '30 4o 50 160 '2.1::.>0 PRE:SSO RE- K~/Ctn?- ·5~~------~--~~--~~------~------~----~--~--~------~------~ PRESSURE VS VOID RATIO ·~··--- INITIAL POROSITY 38. 8% .5.<\-+------+--- · -- 1-- l'] c:J Loading A &l. Unlo ad ing ·52. ------0 0 Heloading - < ·'50·------· ·-- -- -· 1 0 D ·4-B t----·-- - Vl Vl 1 ;{)·4(,~ --- ?{ ·~-~J ·····~··~-]---- 0 ·4+ ! -~~ •4-7- " 1 i v~ ~h 40 ...... · ------i L------+' -- i ~. ' p fi •.Ya '0~ ::Y ~ .~ç.r-- 0 --- • 1---' 0 ·34 ·--- -··· '2. '20 3o 5D 1co 200 Cll) "2... Q Q ~ ~ ~ ~ 0 0 ::r' ::r' 'i 'i f--' f--' f--' f--' . . '0 '0 0 0 ' ' 1 1 j j 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -- 20 -- -·-- IO IO 4% 4% . ng ng 43 RAT -- di - 100 100 eloél VOID VOID Unloading Unloading Loading Loading R - VS VS POROSITY POROSITY 0 0 D D 6 6 ~ ~ ~ ~ r--_ r--_ 50 50 -- ·· N!"TIAL N!"TIAL RESSunE RESSunE 0 0 ~ ~ 1 1 P ' ' I 6, 6, n n - l~O l~O "' -j -j ~~ ~~ - A A -- ~1 ~1 ' ' _[ _[ 30 30 __ __ - ____ ___:_ ___:_ cm. cm. ~ ~ 1-- ' ' 20 20 -- - " 1 - /sq. /sq. ,G ~ ~ -- l< --c:-... --c:-... URE URE 1 1 1 1 1 1 1 1 1 ~' ~' 1 1 r r 10 10 j _ . . PRESS -- . . --· --· - - -- -- . . t-- r--;J r--;J - ...... ' ' f-- 1 1 4 4 5 -- --1---- - - -- --- --- -- r--Q-__ r--Q-__ J- 1 1 N N 3 3 ·-- - 1 1 1 1 1 1 i i 1 1 1 1 1 1 1 1 i i 1 1 : : 1 1 1 1 1 1 1 1 i i 1 1 2 2 - r . . . . - . . -- 1>-- ~ ~ 1 1 55 55 .5 .5 .45 .45 .4 .4 . .6 .6 .65 .65 - <: <: t::l t::l 0 0 ;t> ;t> 0 0 >-3 >-3 H H ::0 ::0 H H a- V1 V1 o9 1 PRESSURE VS VOID Rf,TIO DJITIAL POROSITY 48. 7% oB i a c Loading 6: A Un1oading ~ 0 0 Re1oading 0 H t::l 1 l 1 1 o7 -- -. i +-- ·---- -~--- - ::0 . ;t-. >-3 H 0 \J1 -.J r.. .6 " A ~- !~ 1 - - - + 1 1' --1- --·--- --1- --·------+ ····· ·----- .5 --- -+------'------+---r---~------ 1 l Üo1 Q.2 0.5 1 2 3 4 5 10 20 30 0 '1 :J-' '0 ;::r' PRESSURE kg/s q . cm. z: .0 1-' /:\) loO PRESSURE vs VOID RATIO ----- INITIAL POROSITY54.1% ·~. .9 o o Loading ~ .o. Unloading ~ o o Reloading -~- .8 . . ·- ·--·- ·---- - ~ ------1 < ·--· --- - 0 IJlH --~r CXl t;:l f~ . 1 s: 1 >-3 H 0 ~~ o7 ------~ -- f------·- ----~ ~- f- -·· - · .6 . ···-· ...... -- . ~~ --~-- -- 1 -~ . 1 ~- 1 0 1 '1 -- ·- 'd o5 0.1 ;:;s'"' 0.2 0.5 1 2 3 4 5 10 20 30 z 0 0 1-' PRESSù~kg / sq . cm. \...) Graph No. 14 PRESSURE VS MODULUS OF VOLU~E C HA~GE Q a Poros ity .. 07 54.1% (!) (:) Porosity 48. 7 ~~ 6 6. Porosity 43. 4% 0---0 Porosity 38. 8% . o5 I!J---<:J Porosity 37.4% 1 . ! ~ ~ 1 l ...... ' • 1 6 .03 t>. r----~.-:-- -r-----~ 1. o' Cil ! ' 1 l 1 1'1 Ç::::1 l 1 1 . 01 1 l " W----~------+------r--· ----1------,------~-'---1 - ~ i 1 < 1 :::::: i ! 1 ' ' 0 1 1 : i Ç::::1 j ! . 008 ------r------:------;-1 -- ;:g 1 : t 1 ' i ::::::> 1 1 H 1 0 > .006 li. i 0 1 1 ' Cl) ::::::> 1 i H • 004 ::::::> A 0 ~ . 002 20 30 40 50 60 P R E S S U R E kgjsq.cm. - 59.- ·49 ~-----~--~--~~~~~~~---~~--~--~--~~~~--~~~ 1 20 1 50 100 1 200 j 1 500 j 1 1 jlOOO 2000 0 1/mv \ l4 \ ·41 \ ---4---~-----<-'1 1 1 ·--j ---- \ \ ! \ 1 ·45 J:------·------·------, 'l:J 0 ::0 0 (/) H ~ 1 0\ ' 1 1 li0 .39 .___ ~~-l___ 0 j -- - 1 'dIll o e Conso1idated-undrained P" · l\ITP. ········ ·N !2: 0 0 . 0 Undrained • 1-' ~ 1 1\111 \J1 •----• E from 1/mv • 37 f-- ELASTIC 110DULUS tons/sq. ft • • 35" The values of 1/mv are plotted against the corresponding porosity on graph No. 15 to afford an easy comparison between 1/mv from consolidation tests and E from triaxial undrained and consoli- dated-undrained tests. 4. VALlTE OF E AND 1/mv In comparing the reciprocal of modulus of volume change with the elastic modulus it is evident that any relationship would be coincidental. It is expected that the main difference lies in the characteristics of one dimensional,as opposed to three dimensional testing. It is lmown that for elastic material •••• (11) •·:here V is the initial volume and 4ë;, etc. are given by 6i"~ = A~- 4 14 ; .t.s-"" , A•, and Ari are increases in the three princi- pal stresses and 4"'" is the consequent increase in pore pressure. In the triar.ial test u-!1 = .6~ ; equation (11), therefore, reduces to E = ( t.rr.._ +Z 6~ )(1 - 21() •••• (12) bNjv The modulus of volume change mv is given by - 61- ffiv = e - e1 Ap(l+e) v-ihere e initial void ratio el final void ratio and 6p = t.~x.- 2. ~~z If Vs = volume of solids Vv initial volume of voids and Vv1 = final volume of voids, then Yv/v, vv, /vs m-v = (à~-c Zàlfz )(l +- YJ< ) Ys Y-Vs v, -Vs = y~ Vs (_bi-~ZAi .) (1 +~) 1 Ys (2:::.-r) -(!:! -r) = Va vs (t>r.._-26rz)( ,.,.. y_ •) V,s = v-v, v or mv = •... (13) From (12) and (13) E =~x Ai'x. + z..45z. ( 1-2. v) 'O'Iv à~x. -2.4i'z which proves that E is not equal to Ymv. Referring to graph No. 15, it is seen that no agreement exists between E and ~ as borne out by theory. mv Genest 1958, suggested tr~t the relation E = ~ could be used to mv - 62 - determine the value of E for settlement calculations. The author feels that the suggested relationship may be fortuitous. Padopulos 1957 also reported that the value of E could not be determine ct from the relation E = 1 mv The value of E, for settlement calculations, should be deter- mined from undrained, consolidated-undrained or isotropically consoli- dated-undrained triexial tests (Skempton and Rj errum 19)7 , Simons 1957, etc.) with due regard to adjustments for sample disturbances, if any. - 63 - 5. PlATE LOADDJG TESTS The results of plate loading tests are plotted as applied pressure versus settlement (see graph No. 16). A linear relationship, in the loose state, existed throughout the penetration capacity of the loading deviee. · Failure was not well defined and was i nterpreted as the load causing excessive settlement ï-ri. th a small increment of load. In the medium state of packing, shear failure occurred and was better def'ined - small hairline ~ \ 1 / cracks around the plate developed ~ -<~::·.·- / - •'!!t :',•·---- into larger cracks extending to about 1211 all around the plate ---:/~~~~~) ·~ as shawn in fig. No. 5. In the dense state of packing , failure could not be reached due to limi ted capacity of loading apparatus. A linear relati onship existed between load and settlement t.hroughout the l oading range. Surface cracks around the plate were noticed. - 64 - 0 10 20 30 40 50-,- 60 70 80 90 lOC p R E S S U R E 'PSI • 2 ...... . 4 ~ --- -1- ~() .s -- 3;'1 • 6 ~:z:. --- 1- -+- -- Ç::4 ~ Ç::4 H LOAD vs SETTLEMENT .8 1_.8 ~ :6 Test # 1 Loo se n = 48.9 % ~------8 0 0 Il 2 Medium = Ç::4 Test n 44.0 % o------0 Test # 3 Medium n = 43.7 % lm . vt. El Il 4 Dense 0 Test # n = 3 7 • 3 ; lfl 1.0 . +- o---- -tl Test # 5 Dense n = 37. 1 % n> d ::J ~~ 1-' 0'\ 1.2 ll_l ____ -- -t--·- --·- -- ·-+------4-----· \ SETTLE~~TT ANALYSIS AND DISCUSSION In arder to appraise the basis of settlement analysis of found- ations on silt and as developed in the theory section, the total settlement given by has been compared to the actual settlement from loading tests. a) D1NEDThTE ELASTIC SETTLEMENT Immediate elastic settlement is given by l. ,., b 1- y I 'z· = ~ · . ~ . p b For a square footing, value of the influence factor ~ for computing settlement of a b corner of a loaded area is equal to 0.56 as given by Terzaghi 1943; hence, the settle- ment of centre of the area is Fig. 6 2. 1-11" 4- 1( o. 56 x 2. or 1.12. x ~ . b. 1-f:v The settlement of a co rner is '/4111 that of centre an à the average settlement of the s quare area is 0.848 x settlement of centre of the area 2 1 or 0. 848 x 1.12 x 9 x b -e.'lf ( Terzaghi 1943) - 66 - z. or 0.95 x , . .b. 1-lf' E Yang 1959, has given values of Poisson's ratio for silt as follows: v = 0 for loose state v = .1 for medium state v = .2 for dense state The above equation for average value of immediate elastic settle- ment becomes simplified for the three states of packing as follows: Loo se f. = 5.7 ~~E Nedium f . •••• (lh) • = 5.643 'tfE Dense ,P. 7 = 5.472 '1 le The value of E in the above equation for the calculation of ~ for plate loading tests on dry silt is the most important determin- ation. In explaining the role of effective stress principle it was shawn (see pages 38 & 39 ) that in the case of dry soils, the total normal stress is equal to the intergranular or effective stress. It is apparent, therefore, that the results of triaxial tests on saturated samples of silt in terms of effective stresses would yield a value of E no different from the one obtained from dry sail. The value of E can thus be obtained from graph No. 15. This value has to be adjusted in relation to the confinement applicable to the plate loading tests. As all triaxial tests ivere performed at confinements of 15, 30, - é7 - Graph No. 17 • 2000 E-< li< a. ELASTIC MODULUS VS u:l ...... u:l CONFINING PRESSURE 8 E-< 1600 POROSITY 37.3% 0 Ill POROSITY 43.7% A J. POROSITY 48.9 % Il El / (.) H w ·eoo ~ ...:1 / / ~ / / / y 400 1 ------~---~~--~------+------~~------/- .... ~ / · .-- 0 10 20 30 40 50 60 C 0 N F I N I N G P R E S S U R E PSI Note: Dashed parts of curves are extrapolated values. - 68 - 45 and 60 psi, it is necessary to study the variation of elastic modulus viith confining pressure to obtain relationship a.t lower confinements. From graph No. 15, values of E are obtained for n equal to 37.3%, 43.7% and 48.9%. E for unconfined condition is avail able for sail in dense state only (n = 37.3%, graph No. 7). It was reported earlier (page 27) that unconfined compression tests at higher porosities were not possible. Graph No. 17 shmvs plot of E versus confining pressure. The àashed parts of curves for sail in loose and medium states have been extrapolated. The following table gives values of E at confining pressure of 2 psi (average value of confinement applicable to plate loading tests; see table No. 3):- Porosity % Elastic Modulus tons/sq.ft. 48.9 7 extrapolated 43.7 35 11 37 .2 60 The above values of E are substituted in equation (14) to get immediate elastic settl ement. - 69 - b) CONSOLIDATION SETTLEf-IENT Consolidation settlement is given by p C! = /'· foed. z A~>, . d..z. = fl · J I'V\v · ( see The ory, page 9 ) 0 = ~- m.,.Cf.H where f =A +oC(l - A) mv = modulus of volume change (units sq.cm./kg. or sq.ft./tons) q = applied load H = thickness of stratum A = pore-pressure coefficient z 1 Alr3 .c!z. and oC = 0 jz A&-;. c:l.z. " The average value of pore pressure coefficient A, which depends on the stress history and the magnitude of the applied stresses, has been calculated and sho~n in table No. 4. The values are calculated at failure (maximum deviator stress). It is seen that the value of A is negative. In the undrained tests for fully saturated samples, increase in cell pressure is carried by the pore ~"'a.ter pressure and does not cause an increase in effective pressure (Penman 19.53). As the major principal stress is increased, the pore pressure at first increases under the ne"t,- load but as strain increases, there is a tendency for dilatancy, and - 70 - the pore pressure decreases tc counteract this potential expansion. This fall in pore pressure continues, causing an increase in effective pressure and then becomes constru1t as the sample fails (Penman 1953 ). Ta the equation for pore pressure B = 1 for fully saturated s~1ples and hence A = Due to the fall i>'1 pore pressure durine; straining, (~ 14 - ~~3) becomes a negative quantity, giving negative value of A. Skempton 1954 has quoted negative values of A for some soils. The amount of potential dilatancy is governed mainly by void ratio and effective pressure. Penman 1953 has reported f ronr undrained tests that the re is an approxima tely linear relation bet-,.;een maximum fall i:1 pere pressure and the void ratio of the sample. Because of this, at the same consolidation pressure and void ratio, several samples at various cell pressures "W-ill develop the sa'lle fa.ll in pore pres sure and hence have the s~e strength, unless the pore pressure drops to a very low value. The coefficient ~ depends only on the geometry of the problem and bas been computed for circular and strip footings by Skempton and Bjerrum 1957 ~ith various ratios of the thickness of soil to the breadth of the footing (~). These values are given in the t able No. S. b - 71- Assuming that oC is the same for a circular and a square footing (Meyerhof 1958), it is seen from table No. 5 that for z = 8 ~ • 0.27; -b ' from table No. 4, A = -0.0454. Substituting the value of oC. and A in the equation j- =A+o((l-A) gives t- = 0.24 The modulus of volume change mv is generally determined from results of standard oedometer test. Under each increment of load for a normally consolidated soil, pore pressure builds up and is dissipated through drainage to atmosphere until equilibrium is reached. This means that, on completion of consolidation under the load pore pressure is equal to zero, and the total normal stress is equal to the intergranular stress except for particle rearrangement if the sail is affected by soil-water reaction. However, for the ca se of granular materials, the effect of body forces is large b~r comparison and surface forces result- ing in interaction and particle rearrangement may have little effect. For the soil in question, the plasticity index is very small (1.8) and hence it seems probable that surface forces w"ill not effect its behaviour to any marked degree. In view of the foregoing remarks and absence of full scale load- ing tests ( -wtdch alone could determine its true behaviour), it seems reasonable to assume that modulus of volume change for the silt in w~t and dry state may be same. - 72 - In table Nos. 6 to 8, mv has be en worked out for each state of packing, namely loose, medium and dense, respectively, for appropriate increments of pressure as applied in the plate loading tests. Kno~'ing jJ- and mv, { can be calculated for any applied load. - 73- The values of the immediate elastic settlement ~ and the consolidation settlement ( have been computed for the complete range of applied pressure and presented in columns 2 and 4 of table Nos. 9 to 11 for the three states of packing. Values of ( t; + !; ) and the actual settlement from plate loading tests for each state of packing are given in columns 5 and 6 respectively. For examination and appraisal of theory applicable to settlement of dry silt, load-settle- ment curves obtained from plate load tests are compared ~~th those based on ":· and : + t:_ ( see gr a ph Nos. 18 to 20). Referring to graph No. 18 for silt in loose state, it is seen that failure occurred under a load of about 6 psi. This is a local shear failure. The theoretical curve based on ~ agrees fairly l closely with the actual load-settlement curve within the range of experimental accuracy until the failure occurred. This shows that consolidation settlement ;: does not contribute to the total settle- ment of dry silt in loose state. For silt in dense state of packing, (refer to graph No. 20) throughout the entire loading range, the actual load-settlement curve from the plate loading tests agrees closely with the theoretical curve based on f'. • J. - 74 - Graph #18 .. .. 0 r-i 1 ,. 1 Il.." / ~ ~"' ~... ~/ 1~ 1 ~/ ' "// ,.! N r ~ 1 lv 1 ~ ;{ 1 / 1 v / Q_\1 H j/ A/ en ..... i- o.. / ~... ~"' ( 1 ~ / 1 '7 .-1 5'""' 4:/ r-i m U) / 0 0 ·ri ·ri"' .p ~ / .;J g:: j' E-t .-1 Cl) Cl) "/ :z: H H /"" 0 0 - 71 2 Cl) .f5"' Cl) - 7.5 - 0 5 10 15 20 25 30 35 40 PRESSURE PSI ~J------tl . "" " ------.2 --'( " " "-. . ------{---Lr: . " -q,.._ - ...._ - ...._ (/.) " ... 1 _ ._ tz; .4 1 "1------·------~-- - cv-...._ >-3 ------.Jt-' >-3 ------.. -- 0\~ fij z >-3 1 1 1 1 ~-----t---t~~-:~~-- Hz .6 0 ~ (/.) .8 1 . 1 1 --~ LOAD vs SETTLE11ENT 1\ Medium State 1.0 t-- 'iQ El [3 lb Actual -g. ~ 1-' 0------0 f>_• Theoretica1 - l '-0 ~- -:_t. Theoretical - t;· +ft 1.2 araph # 20 -. " ' 1 1 1 1 1 v 1 1 ~ 1 ij ,/ 0 1: 1 /~ to 'i v1 1 / i 1 ' 1 ! 1 1 1 1 1 i Ir 1 v- 1 1 1 ~0 1 i- / ' 1 . ~.. / 1 ( L 1,r A- 1 1 1 1 / 1 1 1 1 1 J ,/ AL 0 ···- • 1.("\ Ji '/" / 1 1 1 / / ;1 1 <\._V H 1 / .... U) (].., 1 / / ~ ~... .. 1 0 1~ 1 1 ....:t ~ ~~ / ~ / ri r-l ëf5 r; rd cd i Cl) / (.) () r=:l / •r-i •ri / E-< +' ..p 8:: z ri C) ·. Q) / ~ h H / ...:.. ~ 0 0 Q) Q) ...~ +' f- " ~ (.) ..c: ~ v Q) / E-< ~ E...., E-t 1 E-< +' ~N 1 !. 1 ~ 1 U) .s \y/ / U) Cil Q) 1 > Cil 1 1 s:: Q) 1 1 0 0 0 ~ ~ 1 C\l ;/' 0 1 ....:l 1 1 1 1 v/ 1 1 1 1 1 f/ Q ~ / I / ;J _.. / 0 ,-; f/Y J///, 0 ri C\l C"'\ ....:t '-0 0 0 0 . 0 SETTLEtJ.iENT INCHES - 77 - The failure does not seem to have been reached due ta limited capacity of the loading deviee. Hoï-rever, surface cracks around the loading plate were noticed as mentioned earlier. Here again, consoli dation settlement f does not contribute to the total settlement of dry silt. For silt in the medium state of packing (see graph No. 19), it is seen that failure occurred under a load of about 17 psi. However, the load-settlement curve based on ;;. does not show a very good accord ~~th the actual load-settlement curve. This might be due ta non- uniform packing of sail in the container for plate loading tests, ~~th the result that the porosity of 43.7% on which value of E is based, was over-estimated. The actual porosity could have been around 41%. The curve based on~· +{ shows much greater deviation from the actual plate loading curve and it may therefore, be said that { does not contribute to the settlement of dry silt in medium state of packing. The above examination has revealed that consolidation settle ment ~ , which is a function of pore pressure dissipation under the load, does not contribute ta the settlement of dry silt. However, consolidation may play a dominant role if the silt is saturated or - 78 - nearly so. It v-rould appear from the foregoing analysis, that for silt in the dry state, prediction of settlement may be made according to the classical elastic equation '1 ,_v 1 = 'l· b . E . p wnere E is the elastic modulus. Genest 1958 also reported that the above equation could be used to predict settlement of footings on silt in medium and dense states. - 79 - PRACTICAL APPLICATION The behaviour of dry silt under loading can be predicted by the application of classical elastic equation ,_v %. b 1· . E which gives settlement for any point in a foundation. !~, in the above equation,is the appropriate influence value, as given by Steinbrermer 1934, q is the net pressure, b is the width of foundation, and E is determined from undrained triaxial or iso- tropically consolidated-undrained tests ldth a correction for sample disturbances, if necessary. - 80 - C 0 N C L U S I 0 N S From the foregoing observations and results, it is concluded that: 1. Load-settlement relationship is linear for all the tests con- ducted. 2. The behaviour of dry silt under loading may be similar to that of sand. The classical elastic equation for immediate elastic settle- ment 2 ;;. = q.b.l -v I 0 E . ~ may be used to predict settlement of dry silt under loading. In the above equation q ~ net foundation pressure b c. breadth or diameter of loaded area ~ c Poisson's ratio E elastic modulus and Ip = influence value depending upon shape of loaded area. 3. Consolidation settlement given by which is a function of pore pressure dissipation under the load does - 81 - not contribute to the total settlement of dry silt. It is expected, however, that it may greatly influence the total settlement if the silt were saturated or nearly so. In the above equation Î = A + ..C. (1 - A), where A is pore pressure coefficient and oC. depends upon the geometry of the problem. 4. The value of the elastic modulus for calculation of the immed- iate elastic settlement, cannat be obtained f rom the relation E = ! , illv ~omere mv is the modulus of volu.rn.e change obtained by standard application of oedometer test results. E should be determined from undrained or isotropically consoli- da.ted-undrained triaxial tests w~th due regard to sample disturbances, if any. - 82 - SUGGESTIONS FOR FUTURE RSSEA.RCH 1. The programme of triaxial compression and consolidation testing should be continued on silt obtained from different locations and sources. 2. Plates of various sizes over 6" squar e should be used for loading tests. 3. Full scale loading tests on silt be carried out. - 83 - B I B L I 0 G R A P H Y BISHOP, A. W. and G. ELDIN, 1950. 11 Undrained Triaxial Tests on Saturated Sands and their significance on the General Theory of Shear Strength" Geotechnique Vol. 2 BISHOP, A. lv" . and D. J. llli'NIŒL, 1957. "The Triaxial Test" Arnold, London BJERRUM, L. 1950. 11 Fundamental considerations on the Shear Strength of Soils" Geotechnique Vol. 2 BREBNER, A. and W. \rJRIGHT, 1953. "An experimental mvestigation to determine the variation in the subgrade modulus of a sand loaded by pl ates of different breadths" Geotechnique Vol. III, No. 8 BURHISTER, D. Iv!. 1936. "In terpret ation of Loading Tests for Footings" First International Conference on Soil Mechanics and Foundation Engineering, Vol. III - 84 - G~~EST, G. L. 1958 . "Compression of silt under madel footings" ~1. Eng. The.sis, aubmitted to the Faculty of Graduate Studies and Research, IJlcGill Uni ver sity, l":ontreal (Unpublished) GOLDBR, H. Q. 1941. "The Ultimate Bearing Pressure of Rectangular Footings" Journal, Instituts of Civil Engineers, Vol. 18, paper 5274, pp. 161-174 h~ORSLEV, M. J. 1937. 11 Uber die Festigkeitseigenschaften gestoerter bindiger Boeden" ("On the strength properties of disturbed cohesive soils") Ingeniorvidenskabelige Skrifter A No . 45 JU.R.GENSüN, L. 1934. "The application of theories of elasticity and pl asticity to Foundation Problems" Journal, Boston Society of Civil Engineers 21 pp. 206-41 KOGLER, .L". 1936. "Pressure Distribution" First International Conference on Soil Vechanics and Foundation ~ngineerin g , Vol. III KRYt·iL.IJ'E, D. D. 1936. Dis cussion of "Pressure Distribution" by F. Kogler. First International Conference on Sail :tvlechanics and Foundation Engineering, Vol. III _85 - LAMBE, T. W. 1958. 11 The Structure of Compacted Clay" 11 The Engineering behaviour of Compacted Clay" Journal, Soil E:echanics and Foundation Division A.S.C.E. Vol. 84, SM 2 LA~IDE, T. W. 1960. "A :r-'1echanistic Picture of Shea.r Strength in Clay11 A.S. C. E. Research Conference on Shear Strength of Cohesive Soils }ŒIGH, A. C. 1950. 11 Hodel Footing Tests on Clay" M.Sc. Thesis, University of London MEYERHOF, G. G. 1948 11An investigation of the bearing capacity of shallow footings on dry sand" Proc. 2nd International Conference on Soil Mechanics and Foundation Engineering, Vol. I i•JEYERHOF, G. G. 1950 11 The Bearing Capacit y of Sand" Ph.D. Thesis, University of London BEYERHOF, G. G. 1951. "The U1timate Bearing Capacity of Foundations 11 Geotechnique, Vol. 2 - 86 - ~ŒYERHOF, G. G. 1956. 11 Settlement analysis of six structures in Chicago and London" Discussion, Proc. Institute of Civil Engineers, Part I, Vol. 5 MEYERHOF, G. G. 1958. 11 Correspondence on 1A Contribution to the settlement analysis of foundations on clay'" by Skempton & Bjerrum Geotechnique Vol. 7 NASH, K. L. 1953. "The shearing resistance of a fine closely graded sand" III International Conference on Soil Mechanics and Foundation Engineering NE\1if.1ARK, N. M. 1935. 11 Simplified Computations of Vertical Pressures in Elastic Foundations11 University of Illinois Eng. Expt. Station Bull. No. 24 PADOPUI.OS, D. 1957. "Compression of silt under model footings" M.Eng. Thesis, submitted to the Faculty of Graduate Studies and Research, McGill University Montreal (Unpublished) PECK, R. B., and H. E. TJYANIK, 1955. 11 0bserved and computed settlements of structures in Chicago 11 University of Illinois Eng. Expt. Station, Bull. No. 24 - 87 - PENHAN, A. D. M. 1953. "Shear Characteristics of Saturated Silt Measured in Triaxial Compression" Geotechnique, Vol. III, No. 8 ROSENQVIST, I. Th. 1959. 11 Physico-Chemical Properties of Soils, Soil-Water Systems" Journal, Soil :tliechanics and Foundation Division, ASCE Vol. 85, SH 2 RENDULIC, L. 1937. 11 Ein Grundgestz der Tonmechanik und sein experimenteller Beweis" Bauingenier 18: 459-467 SIMONS, N. 1957. "Settlement studies on two structures in Norway" 4th International Conference on Soil Mechanics and Foundation Engineering, Vol. I, pp. 431-36 SKE1.-JPTON, A. ti. 1948. "The effective stresses in saturated clays strained at constant volume" Proc. 7th International Congress on App. Mech. 1 : 192-196 SKEHPI'ON, A. W. 1948. "The f = o Analysis of stability and i ts Theoretical basis" Proc. 2nd International Conference on Soil Mechanics and Foundation Engineering, Vo. 1 -88 - SIŒMPI'ON, A. ~f., and A. I·J. BISHOP, 1950. "The measurement of shear strength of soils" Geotechnique, Vol. 2 SKEHPI'ON, A. H. 1954. "The Pore-Pressure Coefficients A and B11 Geotechnique, Vol. 4 SKEr-1PI'ON, A. W., R. B. PECK, and D. H. McDONALD, 1955. 11 Settlement analysis of six structures in Chicago and London" Proc. Institute of Civil Engineers, Vol. 4, PP• 525-44 SIŒMPTON, A. W. and L. BJERRUN, 1957. "A contribution to the settlement analysis of fonndations on clay" Geotechnique, Vol. 7 SOWERS, G. B. and G. F. SŒiERS, 194.5. 11 Introductory Soil He chanj_cs and Foundations11 MacMillan STEINBRENNER, W. 1934. 11 Tafeln zur setzongsberechnung" Die Strasse, 1~ pp. 121-24 TAYLOR, D. W. 1944 M. I .T. Triaxial Report No. 10 TAYLOR, D. W. 1948. 11 Fundamentals of Sail Mechanics" l'l[iley TI:RZAGHI, K. 1936. "The shearing resistance of saturated soils and the angle between planes of shear" Proc. lst International Conference on Sail Mechanics and Foundation Engineering, Vol. 1 TERZAGHI, K. 1936. 11 Settlement of Structures" lst International Conference on Sail Mechanics and Foundation Engineering, Vol III TERZAGHI, K. 1943. "Theoretical Sail Hechanics" lfliley TERZAGHI, K. and R. B. PJCK, 1948. 11 Soil Hechanics in Engineering Practice11 Wiley \iARIŒNTIN, B. P. and R. N. Y. YONG, 1960. 11 Shear strength montmorillonite and kaolinite related to ihter particle forces" 9th National Clay Conference, Purdue University - 90 - YONG, R. N. Y. 1959. "A Study of settlement characteristics of madel footings on silt 11 lst Pan-American Conference on Sail Mechanics YONG, R. N. Y. l96o. 11 A physico-chemical approach ta analysis of clay sail behaviour11 Symposium on Foundation Engineering, Indian Institute of Science, Bangalore, India ADDITIONAL AITCHISON, G. D., and I. B. DONALD, 1956. "Effective stresses in unsaturated soils" Proceedings, 2nd Australian - New Zealand Conference on Sail Mechanics UNITED STATES WAR DEPART MENT, 194 7. 11 Triaxial Shear Research and Pressure Distribution on Soils" United States Haterway Experimental Station PP• 332 -91 - A P P E H D I X - 92 - TABLE NO. 3 Calculation of Confining Pressure for loose, medium and dense state of packing s; = ~z. "~ where ~~ ,.. tan2 ( 45 + f /2 ) Porosity Dry density z = H/3 Confining t ki' n 1f = (l-n)G5· rw pressure % lbs .jc.ft. ft. 0 psi 48.9 86 l 29 2.88 1.7 43.7 95 l o~-34 3.54 2.3 37.3 105 l 38 4.02 2.9 Average confinement E 6.9 x l/3 = 2.3 say 2 psi "'A- This value obtained from Jviohr circle plot (see fig. No. 3). ~ for the loose and dense states assumed from commonly known values. - 93 - TABLE NO. 4 PORE FRESSURE COEFFICIENT 'A 1 From Undrained Triaxia1 Tests 6L.L= B(bo~+A(à.O.-lo.s-!>)) where B = 1 (fu11y saturated samp1e) Test n% ., cel1 press. ( A5ï -A';) (t."- -àr~) 'A' No. psi ( psi psi 1 2 43.0 15 92.0 -4.2 -0.0457 3 41.1 15 83.5 -3.9 -0.0468 6 46.2 30 120.0 -4.8 -0.0400 8 43.2 30 135.0 -6.2 -0.0460 13 40.6 45 190.0 -8.8 -0.0463 15 43.8 45 181.0 -8.2 -0.0453 16 43.3 45 172.5 -7.9 -0.0458 20 43.0 60 214.0 -9.8 -0.0458 23 41.0 60 222.0 -10.5 -0.0474 AVERAGE VALUE OF PORE PRESSURE COEFFICIENT 'A' a -0.0454 - 94 - TABLE NO. 5 Values of oC in the equation p= A +oC(l- A) after Skempton and Bjerrum (195 7) z cmcuiAR STRIP b FOOTING FOOTING 0 1.00 1.00 0.25 0.67 0.74 0.5 o.5o 0.53 1 0.38 0.37 2 0.30 0.26 4 0.28 0.20 10 0.26 0.14 oC 0.25 0 - 95 - TABLE NO. 6 VALUES OF HODULUS OF VOLUME CHANGE LOOSB STATE OF PACKING POROSITY 48.7% (GRAPH NO. 12) q e de 1 + ë dq. Inv = de x _1_ psi Qq 1 + ë sq.cm/kg. 1 2 3 4 5 6 1 0.856 0.008 1.852 1 0.0625 2 0.848 0.007 1.844 1 0.0625 3 0.841 o. oo6 1.838 1 0.0526 4 0.835 o.oo5 1.832 1 0.0454 5 0.830 0.005 1.827 1 0.0384 6 0.825 0.005 1.822 1 0.0384 7 0.820 o.oo5 1.817 1 0.0384 8 0.815 o.oo5 1.812 1 0.0384 9 0.810 - 96 - TABIE NO. 7 VALUES OF EODULUS OF VOIDME CHANGE HEDIUM STATE OF PACKING POROSITY 43.4% (GRAPH NO. 11) q e de 1 + e àq. mv = de x 1 psi dq J~ + e sq.cm/kg. 1 2 3 4 5 6 5 0.668 0.019 1.658 5 0.0322 10 0.649 0.011 1.6l_J-3 5 0.0192 15 0.638 0.008 1.634 5 0.0138 20 0.630 o.oo6 1.627 5 0.0105 25 0.624 0.005 1.621 5 0.0088 30 0.619 0.004 1.617 5 0.0071 35 0.615 - 97 - TABlE NO. 8 VALUES OF EODULUS OF VOLlJlvlE CHANGE DENSB STATE OF PACKll~G POROSITY 37.4% (GRAPH NO. 9) q e de 1 + e dq. mv = de x 1 psi dq 1 + e sq.cm/kq. 1 2 3 4 5 6 10 0.587 o.oo8 1.583 10 0.00714 20 0.579 o.oo6 1.576 10 0.00540 30 0.573 0.005 1.570 10 0.00454 40 0.568 0.004 1.566 10 0.00364 50 0.564 0.004 1.562 10 0. 00364 60 0.560 0.004 1.558 10 0. 00364 70 0. 556 0.004 1.554 10 0.00364 80 0.552 0.003 1.)50 10 0. 00274 90 0.549 0.003 1.547 10 0.00274 lOO 0.546 - 98 - TABLE NO. 9 LOOSE STATE OF PACKING (Test No. 1) for n = 48.9% E = 7 tons/sq.ft. (see Page 69) q ~'r rn v f"' 5.1 fjjE ~ = )<- .;:ed. '!;·'~{ from plate 1oading psi in sq. cm/kg in in tests in 1 2 3 4 5 6 l 0.0587 0.0625 0.0506 0.1093 0.028 2 0.1174 0.0625 0.1012 0.2186 0.09 3 0.1761 0.0526 0.1279 0.3040 0.19 4 0.2348 0.0454 0.1473 0.3821 0.225 5 0.2935 0.0384 0.1558 0.4493 0.29 6èL" 0.3522 0.0384 0.1869 0.5391 0.355 7 0.4109 0.0384 0.2180 0.6389 0.53 8 0.4696 0.0384 0.2492 0.7188 0.81 9 0.5283 0.0384 0.2804 0.8087 1.08 ~~ Failure occurred at 6 psi - 99 - TABLE NO. 10 HEDIUH STATE OF PACKING (Test Nos. 2 and 3) for av. n = 43.7% E = 35 tons/sq.ft. (see page 69) fr from plate 1oading q e.- 5 · '=-43 1~ Mv ,{ :: ,f-. l:oJ.. 1 E t;. -t ;:. tests psi in sq.cm/kg in in . Test.No.2 Test.No.3 ln lU 1 2 3 4 5 6 7 1 5 0. 0 58 0.0322 0.13 0.188 0. 036 0.03 10 0.116 0.0322 0.261 0.377 0.072 0.045 15 0.174 0.0192 0.233 0.407 0.11 0.084 -~- 20 0.232 0.0138 0.225 0.457 0.215 0.185 25 0.290 0.0105 0.213 0.503 0.53 0.47 30 0.348 0.0083 0.215 0.563 0. 87 0.79 35 0.406 0.0071 0.201 0.607 1.20 1.10 -l<- Failure between 15 and 20 psi - lOO - TABLE NO. 11 DENSE STATE OF PACKING (Test Nos. 4 and 5) for av. n = 37.2% E = 60 tons/sq.ft. (see page 69) tT q from plate 1oading l,'· = s.+n ~ mv 1;, " f' ·f..aJ. Pz · r~ E tests psi in sq.cm/kg in in Test No.4 Test. No.s 1n 1n / 1 2 3 4 5 0 7 10 0.0657 0.00714 0.0578 0.1235 0.075 0.075 20 0.1314 0.00714 0.1156 0.2470 0.14 0.14.5 30 0.1971 0.0054 0.1313 0.3284 0.196 0.205 40 0.2628 o.oo454 0.1471 0.4099 0.255 0.2.57 50 0.328.5 0.00364 0.1474 0.4759 0.312 0.31 60 0.3942 0.00364 0.1769 0.5711 0.37 0.365 70 0.4599 0.00364 0.2064 0.6663 0.43 0.42 80 0.5256 0.00364 0.2359 0.7615 0.49 0.47 85 0.5583 0.00274 0.1886 0.?469 0.52 - 90 0.5913 0.00274 0.1997 0.7910 - 0.525 100 0.6570 0.00274 0.2219 0.3789 - 0.58 - 101 -