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Effect of plane strain on pore pressure parameters Mittal, Hari Krishan 1963

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EFFECT OF PLANE STRAIN ON PORE PRESSURE PARAMETERS by HARI KRISHAN MJTTAL B.A.Sc, UNIVERSirY OF BRITISH COLUMBIA, I96I A THESIS SUBMITTED IN PARTIAL FULFILMENT OF • THE REQUIREMENTS FOR THE DEGREE OF M.A.Sc.•• IN THE DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April , I963 In presenting th i s thesis in p a r t i a l ful f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shall , make i t free ly avai lable for reference and study. I further agree that per mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives*, I t i s understood that copying, or p u b l i  cat ion of th is thesis for f i n a n c i a l gai-n sha l l not be allowed without my written permission. Department of d/u1// £nj/sise.<zr/rij The Univers i ty of B r i t i s h Columbia,. Vancouver 8, Canada. Date Ma^t / f <?.  ABSTRACT - i - A theoretical as well as a laboratory investigation into the effects of plane strain on pore pressure parameters i s presented. Other observations relative to stress-strain relationships, intermediate principal stress values and shear strength parameters (c' , </>) i n terms of effective stresses are also reported. Experimental work consisted of the following three types of Undrained Tri a x i a l tests with pore pressure* measurements: (1) Standard t r i a x i a l tests on cylindrical specimens. (2) T r i a x i a l tests on rectangular specimens. (3) Confined tests on rectangular specimens, i n which lateral expansion was prevented i n one direction, to achieve plane strain condition. A strain-controlled t r i a x i a l machine equipped with a non-flow null indicating type pore pressure measuring device was used for a l l shear tests. pressure. The observed data show that for the s o i l tested the values of pore,,para meter A|. and shear strength parameter {c , </> ) under plane strain condition are higher than those obtained i n corresponding t r i a x i a l tests. Failure i s observed to occur, i n the case of plane strain tests, at strains much smaller than those for the corresponding t r i a x i a l tests. - v i i i - ACKNOWLEDGMENT The author wishes to express his appreciation and indebtedness to his supervisor, Mr. N.D. Nathan, for assistance i n a l l stages of this undertaking. He also wishes to thank the staff, of the Department of C i v i l Engineering Workshop, for.the help rendered i n designing and Constructing the equipment required for the experimental work of this thesis. - i i - CONTENTS Page I INTRODUCTION 1 II THEORETICAL CONSIDERATIONS 2 A. Effective stress i n soils 2 B. Prediction of Pore Pressures 3 (i) Imperial College Method 3 ( i i ) U.S. Bureau of Reclamation Method 7 III SCOPE OF EXPERIMENTAL INVESTIGATION 11 IV EQUIPMENT AND TEST PROCEDURES 12 A. Preparation of s o i l samples used i n Testing Program 12 B. Compaction Tests 12 (i) Cylindrical Specimens 12 ( i i ) Rectangular specimens 13 Description of Apparatus 13 Experimental Procedure 1^ C. Undrained T r i a x i a l Tests with Pore Pressure Measurements :1^ (i) General Equipment lk De-airing of pore pressure apparatus 15 ( i i ) Special Equipment 16 Rectangular T r i a x i a l Tests 16 Plane strain apparatus 17 ( i i i ) Testing Procedure 20 Cylindrical T r i a x i a l tests 20 Rectangular T r i a x i a l tests 21 Plane strain tests 21 V PRESENTATION OF RESULTS 22 A. Soi l Data 22 B. Presentation of Results 22 Page VI DISCUSSION 26 A. Discussion of Testing Procedure 26 B. Discussion of Results 29 (i) Stress-strain curves 29 ( i i ) Secant Modulus of deformation (M^Q) 30 ( i i i ) Intermediate Principal stress ( (J"2) 30 (iv) Pore Pressure Parameters 31 Parameter B 31 Parameter Af 32 (v) . Mohr Circles (Total stresses) 33 (vi) Mohr Circles (Effective stresses) 3^ ( v i i ) Vector curves 35 VII SUMMARY OF CONCLUSIONS 36 VIII RECOMMENDATIONS " 37 APPENDIX I - TEST RESULTS . 38 APPENDIX II - SAMPLE CALCULATIONS k2 REFERENCES kk - iv - ILLUSTRATIONS To follow Fig. 1 Anticipated Relationship Between the Parameter and the Degree of Saturation S, Bishop (1955) page 2 Fig. 2 Effect of Plain Strain on Pore Pressure Parameter A f page 6 Fig. 3 Half's Conception of Two-Phase Pore Fluid page 7 Fig. k Compaction Equipment used for Rectangular Specimens page 13 Fig. 5 A Schematic Diagram to show/the Layout for De-airing of Pore Pressure Measuring' Apparatus page 15 Fig. 6 Special Equipment for -Rectangular T r i a x i a l Tests page 16 Fig. 7 Element under Principal Stresses page 17 Fig. 8 Plane Strain Apparatus page 17 Fig. 9 A Schematic Diagram of The Transducer page 19 Fig. 10 A Rectangular Specimen i n place page 20 Fig. 11 A Specimen assembled for a Plane Strain Test page 20 Fig. 12 A Specimen set up i n the T r i a x i a l Machine for a Plane Strain Test page 21 Fig. 13 Grain Size Curve page 25 Fig. lh Compaction Curves page 25 Fig. 15 Average Stress Vs. Strain Curves for 07= 30 p.s.i.- f i g . lk Fig. 16 Average Stress Vs. Strain Curves for 6^ = 60 p.s.i. f i g . 15 Fig. 17 Average Stress Vs. Strain Curves for S~3= 75 p . s . i . f i g . 16 Fig. 18 Parameter B f i g . 17 Fig. 19 Secant Modulus of Deformation (M^Q) f i g . 17 Fig. 20 Pore Pressure Parameter A f Vs. Cell Pressure f i g . 19 Fig. 21 Mohr Circles of Total Stresses for Maximum Average Deviator Stress 'CT - Series f i g . 20 v - To follow Fig. 22 Mohr Circles of Total Stresses for Maximum Average Deviator Stress RT - Series f i g . 21 Fig. 23 Mohr Circles of Total Stresses for Maximum Average Deviator Stress PS - Series f i g . 22 Fig. 2k U.S. Bureau of Reclamation Curves f i g . 23 Fig. 25 Mohr Circles of Effective Stresses for Maximum Average Deviator Stress CT - Series f i g . 2k Fig. 26 Mohr Circles of Effective Stresses for Maximum Average Deviator Stress RT - Series f i g . 25 Fig. 27 Mohr Circles of Effective Stresses for Maximum Average Deviator Stress PS - Series f i g . 26 Fig. 28 Vector Curves CT - Series f i g . 27 Fig. 29 Vector Curves RT - Series f i g . 28 Fig. 30 Vector Curves PS - Series f i g . 29 Fig. 31 Transducer Calibration Curves f i g . 30 Fig. 32 Cylindrical T r i a x i a l Series Stress-Strain Curves Ce l l Pressure = 30 lba/sq.in. page kl Fig- 33 Cylindrical T r i a x i a l Series Stress-Strain Curves p C e l l Pressure = 60 lbs./sq.in. f i g . 32 Fig. 3k Cylindrical T r i a x i a l Series Stress-Strain Curves Cell Pressure = 75 lbs/sq.in^ f i g . 33 Fig. 35 Rectangular T r i a x i a l Series Stress-Strain Curves p C e l l Pressure = 30 lbs/sq.in. f i g . 3k Fig. 36 Rectangular Tr i a x i a l Series Stress-Strain Curves Ce l l Pressure = 60 psi f i g . 35 Fig. 37 Rectangular Triaxial Series Stress-Strain Curves p C e l l Pressure = 75 lbs/sq.in. f i g . 36 - v i - To follow Fig. 38 Plane Strain Series Stress-Strain Curves C e l l Pressure-= 30 lba/sq. i n . f i g . 37 Fig. 39 Plane Strain Series Stress-Strain Curves Ce l l Pressures 60 lbs./sq. i n . f i g . 38 Fig. kO Plane Strain Series Stress-Strain Curves C e l l Pressures 75 lba/sq. in. f i g . 39 - v i i - LIST OF TABLES Page TABLE I . SOIL PROPERTIES 22 TABLE II AVERAGE AS-MOLDED CONDITIONS' 23 TABLE III FRICTION TESTS ON TEFLON 25 TABLE IV STRENGTH PARAMETERS 3k TABLE V 0 - VALUES FOR c = 0 3h TABLE VI AS-MOLDED CONDITIONS 38 TABLE VII PORE PRESSURE PARAMETER B 39 TABLE VIII PORE PRESSURE PARAMETER A f ko - ix - NOTATIONS Pore Pressure Parameter: axial a Area ao I n i t i a l Area of Specimens B Pore Pressure Parameter: a l l round c Apparent Cohesion: effective stresses e c Compressibility of s o i l skeleton Cw Compressibility of water e Void ratio e, ao I n i t i a l void ratio E Young's modulus of el a s t i c i t y h or H Co-efficient of air solubility i n water by volume M 5 0 Secant Modulus of deformation: 50$ of maximum deviator stress N Porosity P For plane strain: suffix Pa i n i t i a l a ir pressure S Degree of saturation T For t r i a x i a l test: suffix U Pore pressure u 0 Pore pressure: a l l round Ua Pore air pressure u c Pore pressure dif f e r e n t i a l : capillary Uw Pore water pressure V Volume CT Cylindrical t r i a x i a l tests PS Plane strain tests RT Rectangular t r i a x i a l tests Angle of failure plane to major principal plane Dry density Unit axial strain Incremental change: prefix Poisson's ratio Total stress Effective stress Effective stress normal to the failure plane Major principal stress: t o t a l Major principal stress: effective Intermediate principal stress: total Intermediate principal stress: effective Minor principal stress: t o t a l Minor principal stress: effective Shear stress on the failure plane I. IICTRODUCTION As the number and size of embankments, earthdams, and other earth structures being designed and constructed increase, the study of strength characteristics of compacted cohesive soils i s gaining importance. For satisfactory and economical design, a knowledge of the behaviour of com pacted cohesive soils under load i s essential; for the laboratory measure ments of shear strength under controlled conditions of drainage, and of deformation characteristics (other than compressibility) the c i v i l engineer is usually dependent on the t r i a x i a l test. It may be noted that many practical problems approximate more closely to conditions of plane strain than to the axial symmetry obtained in the conventional t r i a x i a l test. It appears that the strength characteristics corresponding to plane strain are somewhat different from those obtained by the standard t r i a x i a l test. There i s l i t t l e direct evidence of the magnitude of this difference, which is only one of several factors influencing the relationship between laboratory measurements and the actual f i e l d values of the shear characteris t i c s of compacted clays. However, the author has made a pil o t investigation to determine the effect of plane strain on pore pressure and strength i n undrained shear. Owing to the limited amount of reliable test data so far available, only tentative conclusions can be drawn at this stage. - 2 - II. THEORETICAL CONSIDERATIONS  A. Effective stress in Soils The stresses which govern the shear strength and changes in volume of a s o i l skeleton are defined as the "Effective Stresses", /T . For saturated soils i n which the pore spaces are f i l l e d with water, i t was shown experi mentally by Terzaghi (1923) that: <f = 51 - (1) where 61 denotes the tot a l normal stress and Uy denotes the water pressure i n the void space. Thus for an equal all-round stress the relationship between the effective stress and the volume changes i n the s o i l i s given quantitatively by the expression: = -°c (<T) (2) where •—• = the volume change per unit volume of s o i l C c = the compressibility of the s o i l skeleton (Here used with respect to isotropic compression.) and i n terms of the modified coulomb criterion the shearing strength, denoted by , i s given by the expression: If = c' + qjT Tan <f>' (3) where c = the apparent cohesion ) i n terms of <(>' = the angle of shearing resistance) effective stresses. 6^ = the effective normal stress on the failure plane In the case of partly saturated soils the void space contains both air and water which, due to surface tension, may be i n equilibrium at widely different pressures. A more general form of expression for effective stress to account for this condition was put forward by Bishop (1955), 0= = 4T-(U a - X (Ug - Uw) ) (k) To follow page 2. I i X 10056 \ Figure - I. ANTICIPATED RELATIONSHIP BETWEEN THE PARAMETER X AND THE DEGREE OF SATURATION S, B I S H 0 P ( I 9 5 5 ) . - 3 - where CLQ denotes pressure of air i n the pore space and X" i s a para meter closely related to the degree of saturation, S, and varying from unity i n saturated soils to zero i n dry soils (Fig. l ) . However, the large positive pore pressures l i k e l y to lead to in s t a b i l i t y i n rolled f i l l s are only experienced at high degrees of saturation, where may be equated to unity with l i t t l e error. The additional complication of observing or predicting pore air pressure i s therefore hardly justified in such cases. B. Prediction of Pore Pressures In the design of f i l l s , then i t i s necessary to be able to predict the pore pressures that w i l l be developed at a l l points i n the f i l l , when the total pressures only are known. Current methods of doing this w i l l now be presented, and attention w i l l be drawn to the significance of the strain conditions. (i) Imperial College Method For the idealized case i n which the compressible skeleton of s o i l parti cles behaves as an elastic isotropic material and the f l u i d in the pore space shows a linear relationship between volume change and stress, Bishop and Henkel (1957) ka^e shown that the pore pressure change, for the no drainage condition in a conventional t r i a x i a l test = can be given by the equation: -LN(S£)K+5 (^1^3)1 ( 5 ) where C c =3 (l-2A)/E, the compressibility of the s o i l skeleton E = Young's modulus of e l a s t i c i t y yco = Poisson's ratio with respect to changes i n effective stress . k - AtV= change in major principal stress & S3 = change in minor principal stress N = I n i t i a l porosity C\, = Compressibility of the f l u i d i n the pore space In practice, however, i t is recognised that the volume change charac t e r i s t i c s of the s o i l skeleton are non-linear; but i t i s apparent from equation (5) that a change i n pore pressure consists of two components: (1) One due to the change in all-round pressure (2) One due to the change in deviator stress Thus the pore pressure changes are expressed i n terms of two empirical parameters A and B |skempton (195 ,^ where • A U = B ^A0~3 + A - 4 ( T 3 ) j (6) For f u l l y saturated soils the value of C w - the compressibility of pore f l u i d (water alone i n this case) - i s so small that the value of parameter B can be taken to be almost equal to unity. In the case of partly saturated s o i l s , however, the value of C i s much higher because the void space con- tains both water and air. The value of parameter B, for partly saturated s o i l s , i s , therefore, less than unity and varies with the stress range. The value of B which applies during the application of c e l l pressure (^0^) i s , thus, not equal to the value which is applicable for the duration of increase i n deviator stress (A5^ -A(J^). Hence i t i s wise not to separate the terms in the product B.A but to denote i t by a single parameter Af and express equation (6) i n the form: /MJ = BAR + A f -A<f.• ) (7) T r i a x i a l tests are performed to determine B and Af, and f i e l d pore pressures are determined on the basis of parameters so found. The Af and B values can be-established for the ^ ratio that i s expected to apply in the f i e l d , but they can only be found for the case of C~2 = ^3 i Q t n e con ventional test. It should be noted that equation (7) is derived on the basis of axial symmetry Q6~2 =A(To)) and, thus, takes no account of the change in the inter mediate principal stress ( A ^ ) . In the majority of s t a b i l i t y problems the condition approximate very closely to plane strain, i n which the intermediate principal stress (CJ2) is not equal to the minor principal stress (J3) a s i n the case of the conventional t r i a x i a l test. The pore pressure change for the idealized elastic s o i l , under the plane strain condition =M{&6y +-A<^)) may be expressed as: c c where C c = 2(1 ( l - 2]^/E, which represents the volume change characteristics i n plane strain under changes in 6\ and 0~y It i s clear from equation (6) that the basic form of expression for pore pressure change in plane strain i s the same as i n equation (7). At this stage i t may be interesting to study the effect of plane strain on the pore pressure parameters, B and A^, as defined i n equation (7), i n the case of idealized elastic s o i l . From equations (5) and (8) the expressions (l) For derivation of this equation see Bishop and Henkel (1957), p.8. - 6 - for pore pressure parameters are: A _ 1 (1 ) C 1 + N 3 ( 1 % ) ) (9) _ l ( l ) p ~ >1 + N Cw (E) < 2(1-W(1-2>T (10) a n d & = 2 & ) ^ 3 <V ( u ) i where = Parametic Af i n equation (7) for t r i a x i a l test Afp = Parametic Af i n equation (<f;) for plane strain Bp = Parametic B i n equation (7) for t r i a x i a l test Bp = Parametic B i n equation (7) for plane strain From equation (9) i t follows that A 1 (1 ) A*T ' 3 (TTW5) (12) where rf= N ( g ^ Similarly from equation (10) we obtain the following expression A f = 1(1 ) By eliminating o(from equations (12) and (13) we get A = A?T  f p 1 - ( l - ^ A f u , (lk) For an ideal material, with Poisson's ratio of 0.5, this would reduce to Afp = 1.5 A f j , and, from equation ( l l ) , i t would follow that B^ = Bp. How- (2) ever, values of Poisson's ratio for clayey soils may be of the order of O.J+5; (2) For Poisson's ratio of clayey soils see"Foundation Engineering" edited by G.A. Leonards, p. 789. -.7 - this value would reduce equation (l^) to P 1 " - 1 and figure (2) shows that this causes but a slight departure from the ideal value of 1.5 A f T > Parameter B may be expected to be substantially unaltered by a change to plane strain conditions. ( i i ) U.S. Bureau of Reclamation Method As was pointed out previously, Terzaghi (1923) showed experimentally that the effective stress was given by tf = 6t~ U w for saturated s o i l s . It was also mentioned that, i n the case of partly saturated s o i l s , there are two different "pore pressures" - the pore water pressure and the pore air pressure. Attention has already been drawn to the expression suggested by Bishop (1955), to give an equivalent pore pressure: U = U a - X (Ua - Uw). According to H i l f (1956), however, the pore pressure i s the pressure i n the f l u i d surrounding the s o i l grains and furthermore, for degrees of satura tion higher than about 25 per cent, the f l u i d surrounding the grains is. the pore water. Thus, the pore pressure i s equal to the water pressure i n the pore space, termed pore water pressure, denoted by Uw and given by the expression: Uw = U a + U c (15) where U a = Air pressure i n the pore space and Uc = Pressure di f f e r e n t i a l across a meniscus due to capillary forces. With the aid of Boyle's law of compressibility of ideal gases and Henry's law of s o l u b i l i t y of air i n water an equation for air pressure i n pore space - 8 - of compacted cohesive soils has been derived by H i l f . When a load i s applied to a p a r t i a l l y saturated s o i l under undrained conditions the pore air i s compressed and the amount of air i n solution i n the pore water i s increased. The reduction i n pore air volume i s equal to the f u l l amount of volume change i n the s o i l . The pore a i r pressure developed i n a com pacted cohesive s o i l under such a load application i s given by T T _ Pa A e u a - „ , — e a 0 + ^w ""^e t 1 6 ' where Pa = I n i t i a l air pressure A e = Change in void ratio = eo - e-j_ e a o = I n i t i a l volume of a i r i n s o i l mass of volume 1 + e Q ew = Volume of water in s o i l mass of volume 1 + e Q h = Co-efficient of air solubility i n water by volume The pressure di f f e r e n t i a l across a meniscus due to capillary forces, U"c, depends only upon surface tension and the radius of the meniscus, which, i n turn, depends upon the radius of the pore space. The value of U c is always negative except when the s o i l i s saturated, the meniscus curvature i s zero, and U c i s equal to zero. Thus for the degrees of saturation usually encoun tered i n the f i e l d with compacted s o i l s , U c may be taken equal to zero, and then the "pore pressure" i s , i n fact, the pore air pressure, as given by equation (l6). Equation (l6) gives pore pressure as a function of void ratio. A standard consolidation test i s used to relate effective normal pressure to void ratio, and then the total pressure versus pore pressure relationship can be deduced as w i l l be shown in the "presentation of Results". Thus pore pressures can be predicted from t o t a l pressures without the use of the A f and B parameters, but here stresses are again axially symmetrical. The "U.S.B.R. method", i n fact, gives results for the conditions of no later a l strain in any direction. It was mentioned that the expression for "pore pressure", ( j h , i n the case of partly saturated s o i l s , suggested by Bishop, and used i n equation (k), i s a function of the pore water pressure, and the pore air pressure, U a, whereas H i l f suggests that the "pore pressure" i s equal to the pore water pressure, for degrees of saturation higher than about 25 per cent. For low degrees of saturation, the above two methods of evaluating the pore pressure w i l l lead to different results. However, large positive pore pressures of practical significance w i l l , i n general, only occur at high degrees of saturation when the pore water pressure may be equated to the pore pressure with l i t t l e error. Both Bishop and H i l f agree that i t i s the pressure i n the f l u i d surrounding the s o i l grains, which when subtracted from to t a l normal stress gives the effective stress. Bishop believes that pore water surrounds the s o i l grains at high degrees of saturation but as the degree of saturation i s reduced, a point w i l l be reached when the s o i l particles w i l l cease to be surrounded by the pore water, and as pointed out before the equivalent "pore pressure" w i l l then be given by the expression: U = U a - DC(Ua - Uw). This implies that "pore Pressure" i s equal to "pore water pressure", and that X i s equal to unity - t i l l this point i s reached; H i l f shows that 10 - this point i s reached at a degree of saturation of about 25 percent. If oC i s equal to one for degrees of saturation higher than about 25 percent, i t cannot possibly be related to degree of saturation as shown i n figure ( l ) . Hence the writer believes that H i l f i s right when he equates the "pore pressure" to "pore water pressure" for degrees of saturation higher than about 25 percent. - 11 - III. SCOPE OF EXPERIMEHTAL INVESTIGATION The purpose of this investigation was to compare the pore pressure parameters measured under conditions of plane strain with those obtained from conventional t r i a x i a l tests. Other observations were also made, relative to stress-strain relationships, intermediate principal stress values and shear strength parameters (c , <f> ) i n terms of effective stresses. Standard undrained t r i a x i a l tests on cylindrical specimens were per formed with pore pressure measurements, at three different chamber pressures, to determine the corresponding Af and B values; similar tests were performed on rectangular speciments to check the influence on these parameters of specimen shape; f i n a l l y , a series of tests was carried out on rectangular specimens, i n which later a l expansion was prevented i n one direction, to observe the effect of plane strain. The possibility of obtaining more or less uniform plane strain conditions arose from the marketing of an almost frictionless substance - Teflon - which was used as the lining material for the restraining surfaces. The experimental investigation was limited to one s i l t y clay and a single compactive effort at a single water content. Besides the compression tests, the index properties of the tested s o i l were established, compaction tests and a consolidation test were carried out. - 12 - IV. EQUIPMENT AMD TEST PROCEDURES A T Preparation of S o i l Samples Used i n Testing Program The s o i l was obtained from Tswwassen Ferry Terminal i n the province of Brit i s h Columbia. As received i n the laboratory, i t consists of wet, medium sized chunks, some of them par t i a l l y covered with loose sand. These chunks were washed free of the sand and were ground to pass a No. 10 U.S. Standard sieve. Water was added as a fine spray to attain the desired water contents. The s o i l was again passed through the No. 10 screen and was stored i n gallon jars. The jars were kept stored i n the humid room to prevent evaporation of moisture. This method of s o i l preparation pro vided samples that remained at essentially constant water content for the period of this investigation. The s o i l was allowed to cure for a minimum period of 2k hours before compaction. In some cases, s o i l was reused: test specimens (which had lost some water during handling, but had never ' been oven-dried) were reground and re-moistened for subsequent tests. B. Compaction Tests Standard Proctor compaction gave an optimum water content of 20.0$ and a maximum dry density of 107.0 lbs./cu. f t . The intention was to devise com paction procedures which would give test specimens with a maximum dry density of the order of 95$ to 100$ of the maximum dry density for Standard Proctor compaction. (i) Cylindrical specimens (1 Cylindrical samples were compacted with the Harvard Miniature apparatus (l) "Small s o i l compaction apparatus duplicates f i e l d results closely", by S.D. Wilson, Engineering News Record, November, 1950, pp. 3k - 36. - 13 - which u t i l i z e s a mold having a volume of 1 cu.ft.and a tamper of | i n . t i p diameter. A l l specimens were compacted i n 5 layers, 25 tamps per layer with a stressed spring tamper set to 20 lbs. Optimum water content of 2 0 . 0 $ and a maximum dry density of 103*0 lbs./cu.ft. were obtained. This was con sidered satisfactory. A l l specimens were nominally 2 . 8 l 6 in. long and 1 5/16 i n . i n diameter. ( i i ) Rectangular Specimens (2) Description of Apparatus - The rectangular compaction equipment i s illustrated i n Fig. h. The compaction mold and extension collar were made from £ in. aluminum plates. The mold was 3 in« long and 1.272 i n . by 3.50 in. i n horizontal cross section. Its volume was .00773 cu.ft. The |-in. brass base plate, the mold and the extension collar were held i n place as shown in Fig.^a while the s o i l was being compacted. The tamper was essentially the same as the Harvard' : Miniature Compactor except that i t had a square t i p to give the same t i p area as that of the round rod of \ in. diameter. The extension collar was s p l i t into four plates; and the plates were removed from the compacted s o i l one at a time. This avoids shearing off the specimen and gouging below the level of the top of the mold. Similarly, the mold was taken apart and the plates were peeled off the compacted specimen one at a time. Hence the compacted specimen was removed from the mold quite conveniently and with l i t t l e disturbance. Dis turbance was cut down to a minimum i f the mold plates were coated with a (2) The apparatus used for rectangular specimens was designed and constructed i n the workshop of Dept. of C i v i l Eng., University of Bri t i s h Columbia. - Ik - thin film of o i l before the compaction was started. Experimental Procedure - The rectangular specimens were compacted with (3) different compactive efforts for a water content of 2 0 . 0 $ . The specimens compacted in 5 layers, kO tamps per layer with a stressed spring tamper set (k) at 30 lbs.had, within the experimental accuracy, the same dry density as that obtained i n the case of cylindrical tests. C. Undrained T r i a x i a l Tests with Pore Pressure Measurements (i) General Equipment A strain-controlled t r i a x i a l machine was used for a l l tests reported herein. Axial stress was applied to the specimens by means of an e l e c t r i c a l l y driven "Transmission Unit" which actuates the loading screw through a chain drive. A "Proving Ring Assembly" and "Specimen Loading Yoke" are attached to the loading screw. To attain the desir.ed rates of axial strain, a speed control d i a l i s connected, through a flexible shaft, to a variable speed clutch included i n the transmission unit. A pore pressure panel based on the Massachusetts Institute of Tech nology design, was used i n a l l tests reported herein. The pore pressure measuring device was a non-flow null indicator i n which back pressure is applied to the pore water in order to prevent moisture movements from the test specimen. The magnitude of the back pressure i s deemed to represent (3) Optimum water content as found i n cylindrical tests and Standard Proctor Compaction. (k) The purpose of this test was to find the Compactive effort required to get the dry density for rectangular specimens equal to that obtained i n case of round specimens. - 15 - the pore pressure at the location i n the specimen where the back pressure i s applied. The procedure used i n the investigation pertains to pore pressure measurements at the bottom of the specimen. Before new apparatus, or one that has not been used for some time, can be put to use, i t i s absolutely essential to make sure that the system i s free of a i r and that a l l the lines are f u l l of de-aired water. This problem i s discussed next. De-airing of Pore Pressure Apparatus - The complete layout for de- airing of the apparatus i s shown diagrammatically i n Fig. 5* The de-airing procedure i s outlined below: (1) With valves 1,2,3,^ and 6 open, and the rest of the valves shut, vacuum is applied to the system t i l l the compound pressure and vacuum gauge reads 30 i n . Hg. (2) Valve k is shut and by opening valve 5 water i s drawn from the tank, through the system, into the reservoir i n the pore pressure panel. While the water i s being drawn through the system, rapid closing and opening of valves 1,2 and 3 f a c i l i t a t e s the removal of air from the valves them selves. (3) When the reservoir i s f u l l valve 3 i s closed. Rapid opening and closing of valve k removes air from the valve i t s e l f . fk) To check that the system i s now air-free, valves 1 and 6 are closed, and valve h i s open, with valve 7 temporarily open to get a convenient level in the glass tube while there i s a positive pressure i n the Pressure Equilizer Tank. The pressure gauge indicates an i n i t i a l reading. To follow" page 15. C O M P O U N D P R t S S U R t 4 V A C U U M G A U Q E 1^  H^ TO ISO RSJ. W A T E R F 1 U . W - P L L E R V A L V E RfSEfNOiK WATER INDICATOR ' WATER R E S E R V O I R - =3= D£-AlRET> YJffTeR TANK LUCITE CYLVMOER- TRlAVlAL 6 ACU PRESSURE E Q U A L I Z E R T A N K . T R I A X I A L C H A M B E R PORE PRESSURE PANEL Figure-5. A Schematic Diagram To Show The Layout For De-airing of Pore Pressure Measuring Apparatus. - 16 - (5) Pressure i s increased by opening valve 7. A drop i n the water level i n the glass tube indicates either expansion of the apparatus, compression of air bubbles s t i l l remaining i n the system, or leakage. If the valve 7 i s adjusted to maintain constant pressure i n the pressure equilizer tank, steady creep of the water level indicates leakage. A large drop which is not f u l l y reversible generally indicates air bubbles, which pass into solution at higher pressures. A f u l l y reversible drop i n level of less than | i n . per 50 lb/sq. i n . rise i n pressure should readily be achieved. To get greater accuracy, the zero line used i n the null method i s adjusted progressively with change in pressure to allow for this deflection. This elaborate de-airing procedure i s seldom necessary once the apparatus i s i n regular use. It i s generally sufficient to check the system prior to each test by a momentary increase i n pressure. ( i i ) Special Equipment^ Rectangular T r i a x i a l Tests - The main special equipment required included a rectangular pedestal, a rectangular loading head and a rectangular porous stone. Later on i t was found d i f f i c u l t to seal the rectangular specimen inside the membrane since the circular "0"-rings did not provide enough normal pressure along the sides of the rectangular pedestal or the rectangular loading head to seal the membrane to the end f i t t i n g s . The side f i t t i n g s , as shown i n figure (6), were designed to press against the "0"-rings and thus develop the normal pressure necessary for a pressure tight seal. (5) A l l equipment refered to under "Special Equipment", was designed and con structed i n the workshop of Dept. of. C i v i l Eng., University of British Columbia. To follow page - 17 - To check that the membrane could now be sealed to the end f i t t i n g s , a dummy specimen, made of wood, was set up i n the t r i a x i a l c e l l . The specimen and the end fittin g s were coated with the paste called "McCabes - (6) Water level indicator". A rubber membrane protected the wooden block from the chamber f l u i d (in this case, de-aired water). The "0"-rings and side fi t t i n g s were used to seal the membrane to the end f i t t i n g s . A chamber pressure of 75 lb/sq.in. was applied for a period of 2k hours. At the end of this time, the block was carefully removed from the c e l l and examined for any evidence of leakage through the membrane or end f i t t i n g s . No change in colour of the paste was observed, so i t was concluded that the protective measures were adequate. Plane Strain Apparatus - When a l l the strains i n a body are parallel to a given plane, the body i s said to be i n a state of plane strain. In this case, an attempt i s made to design and construct special plane strain equip ment which allows strains only i n the direction parallel to the intermediate principal plane (plane perpendicular to $~2 a s shown i n Fig.7)» The plane strain apparatus, as shown i n Fig.8 , consists of two |-in. thick, 1.5 i n . by 3*25 i n . rectangular plates which could be assembled by means of four side bars to form a rectangular frame. This plane strain frame i s 3*25 i n . high and could be varied i n length from 3*50 i n . to 3.6O i n . (The dimensions are from inside to inside.) But, once locked at a certain length, the frame could maintain that length throughout the test, thus preventing l a t e r a l expansion i n one direction. (6) "McCabes - Water level indicator" i s widely used by the petroleum industry to detect water i n gasoline. It is green i n colour and turns bright scarlet on contact with moisture. To follow page 1J Fig. 8 Plane Strain Apparatus - 18 - If the plane strain frame as described i n the above paragraph was used i n the tests, the brass plates would have to be i n contact with the s o i l specimen. Thus during the shearing phase of the test an unknown f r i c t i o n force would develop between the s o i l specimen and the brass plates. This unknown f r i c t i o n force would affect the load d i a l readings and the true value-of the deviator stress would be hard to determine. Lateral expansion i n the (T3 direction would also be inhibited near the 6~~2 ends of the specimen, so that the assumed conditions of uniform' stress would not be obtained. To cut the f r i c t i o n to a minimum, the inside face of each brass plate was lined with .005-in. thick Teflon tape; the co-efficient of f r i c t i o n for Teflon against s o i l contained i n a rubber membrane was later found to be .05. The Teflon tape was secured on the back of the brass plate by means of two screws, as shown i n figure (8), and then i t was rolled over the top of the plate to cover the inside face of the plate. A thin film of vacuum grease on the inside face of the plate helped to keep the tape i n place. It was later decided to mount an e l e c t r i c a l pressure transducer i n the brass side plates and to measure the intermediate principal stress, 6~2> throughout the test. Now, since 6~2 was to be measured the value of the f r i c t i o n force could be calculated at any stage of the test and the load d i a l readings could be corrected accordingly to give the true average value of the deviator stress. A hole "j/Q i n » diameter was d r i l l e d i n the centre of the plate; an extra groove .020 i n . deep was provided a l l around the 7/8 i n . hole to give an - 19 - opening of one i n . diameter i n the inside face of the plate. Basically, the transducer consists of one i n . diameter pressure sensing diaphram made of Beryllium Copper. The diaphram was heat treated at 600°F and was soft soldered into place to give an even surface with the inside face of the brass plate. (7) One 120 - ohm Metal film strain gauge was glued onto the back of the diaphram. The e l e c t r i c a l wires from the strain gauge were taken out of the recess behind the diaphram through an aperture i n the side of the brass plate. As shown i n figure (9), the back of this recess was sealed by means of an "0"-ring. The e l e c t r i c a l wires were enclosed inside "Imperial poly-flow" tubing as they emerged from the side of the plate and provision was made for the wires to be taken out of the t r i a x i a l c e l l through an opening i n the base of the c e l l . Proper end fi t t i n g s were provided for the tubing so that the recess behind the diaphram would be sealed from the t r i a x i a l chamber f l u i d and s t i l l be open to atmospheric pressure; hence the reference pressure was atmospheric. The free ends of the e l e c t r i c a l wires were connected to a "Baldwin Strain Indicator", which read a unit strain i n micro inches per inch. An application of pressure caused the diaphram to deflect and actuated the strain gauge which produced a reading on the strain indicator. The transducer could be calibrated quite simply i n the t r i a x i a l c e l l by direct application of water pressure on the diaphram. (7) It was Type C6 - ikl - B Manufactured by "The Budd Company", P.O. Box 245, Phoenixville, PA. To follow page 19. - 20 - ( i i i ) Testing Procedure Cylindrical T r i a x i a l Tests - Three tests were performed at each of three different c e l l pressures - 3 0 p s i , 60 psi and 75 psi. Thus, this series consists of nine tests. A l l specimens were compacted to maximum dry density at optimum water content. The compacted specimens were extruded from the compaction mold and were placed i n the t r i a x i a l chamber i n the manner described i n "' • "Soil Testing for Engineers" by T.W. Lambe. Only one porous stone was used. The porous stone was saturated prior to the test and was placed on the pedestal. Every precaution was taken to make sure that no air bubbles were entrapped between the porous stone and the pedestal. Excess water, i f any, was very carefully removed from the pedestal and the porous stone. It was found quite convenient to r o l l the rubber membrane over the specimen and "0"-rings were used to seal the specimen. The stress changes were made i n two stages: (i) an increase i n the c e l l pressure resulting i n a uniform all-round change i n stress and ( i i ) an increase i n axial load resulting i n a change i n deviator stress. The c e l l pressure was applied using de-aired water as chamber f l u i d , i n six increments at the rate of an increment every five minutes. The pore pressure was recorded for every increment i n c e l l pressure. Thus, i t took half an hour to apply the required c e l l pressure. The upli f t on the piston due to the c e l l pressure was counterbalanced by means of dead weight. Axial loading (deviator stress) was applied at an average rate of about .27$ axial strain per minute. A d i a l gauge reading i n J_Q5Q i n « divisions was used to measure deformation. Readings of the load d i a l and pore pressure were taken at intervals of 20 divisions for the f i r s t 100 divisions, at intervals of hO divisions for the next 200 divisions and at every 100 divisions a f t e r t h a t . To follow page 20 Fig. 11 A specimen assembled for a plane strain test - 21 - Rectangular T r i a x i a l Tests - This series of tests also consisted of nine tests - three tests at each of the c e l l pressures, 30 p s i , 60 psi and 75 p s i . The test procedure followed was similar to that used i n Cylin d r i c a l T r i a x i a l Series - the only difference being that the average rate of axial strain was .23$ strain per minute. Plane Strain Tests - This aeries of tests again consisted of nine tests. The specimen was set in the t r i a x i a l chamber i n a manner similar to that used i n the Rectangular T r i a x i a l Series. (See Fig. 10) Before assembling the t r i a x i a l chamber, the plane strain apparatus was put i n place as shown in Fig. 11. The length of the plane strain frame was adjusted in a manner such that the 'Strain Indicator'showed a positive deflection, indicating that the plane strain plates were i n contact with the s o i l specimen. The testing procedure followed was the same as that used in the case of the"Rectangular Tr i a x i a l Series". To follow page 21 F i g . 12 A specimen set up i n the t r i a x i a l machine for a plane strain test - 22 - V. PRESENTATION OF RESULTS A. S o i l Data The pertinent data on the s o i l used i n this investigation are given below i n Table I. TABLE I  SOIL PROPERTIES Specific gravity 2.69 Liquid Limit 36. U$ Plastic Limit 29.2$ Plasticity Index 7.2$ The grain size curve for the s o i l along with the M.I.T. Classification scale i s presented i n Fig. 13. B. Presentation of Results The results of the tests for this investigation are mostly presented i n graphical form for ease i n visualizing trends quickly and accurately. The points used for determining the curves are shown where applicable. In Fig. Ik are presented graphs of "Dry density versus Molding Water Contents" for Standard Proctor Compaction and Harvard Miniature Compaction tests. Lines representing degrees of saturation of 80$, 90$ and 100$ are also given i n Fig. Ik. (1) Figs. 15 - 17 show average stress-strain curves for three different c e l l (2) pressures for a l l three series of tests. The average as-molded conditions, for a l l three series of tests, are given i n Table II. (1) For stress-strain curves of individual tests, see Figs. 32 - -^0 i n Appendix I. (2) For As-molded conditions for individual tests see Table VI i n Appendix I. - 23 - TABLE II AVERAGE AS-MOLDED CONDITIONS SERIES OR TYPE OF TESTS CELL PRESSURE AVERAGE MOLDING WATER CONTENT AVERAGE DRY DENSITY AVERAGE SATURATION 0 / 0 CT 30 2 0 . 0 2 102.3 84.8 60 2 0 . 3 0 103.3 8 7 . 9 75 2 0 . 0 2 102.6 8 5 . 3 RT 30 2 0 . 3 1 IO3.3 8 6 . 7 60 2 0 . 2 0 104.1 8 9 . 2 75 2 0 . 3 0 104.0 8 8 . 9 PS 30 19 .98 104.1 87 .9 60 2 0 . 0 0 103.8 87.O 75 19.91 104.6 8 8 . 6 (3) Graphs of average pore pressure parameter B versus c e l l pressure and secant modulus of deformation M50 (corresponding to 50$ of the average maxi mum deviator stress) versus c e l l pressure are plotted in Figs. 18 and 19 res pectively. (4) In Fig. 20 i s plotted the average pore pressure parameter Af, for three different c r i t e r i a of failure (maximum deviator stress, maximum effective principal stress ratio and 10$ axial strain), as a function of c e l l pressure ( 0~cj), for a l l three series of tests. (3) The B-values for a l l individual tests are given i n Table VII i n Appendix I. (4) The Af-values for a l l individual tests are given i n a tabulated form in Table VIII i n Appendix I. I - 2k - Figs. 21 - 23 are plots; of Mohr circles (in terms of total stresses), for average maximum deviator stress for a c e l l pressure. Typical pore pressure prediction curves by "U.S. Bureau of Reclamation Method" are given i n Fig. 2k. The curve e versus <f is drawn on the basis:, of a consolidation test and the curve e versus Uw is drawn with the aid of Hilf's formula, T T _ Pa (el - eg)  ^ ~ (Va + HV W)(I + e i ) - ( e i - e 2) where the symbols are the same as used previously. The other curves are drawn by combining the plots of e versus <r and e versus Uw. In Figs. 25 - 27 are plotted the Mohr circles (in terms of effective stresses) on the basis of maximum deviator stress. The vector curves (or effective stress paths) for a l l individual tests are plotted i n figures 28 - 30- They show the changing relationship between shear stress and effective normal stress on the potential failure plane, throughout the tests. They were computed on thee, assumption that the potential failure plane was inclined at 60° to the major principal plane, assuming a f r i c t i o n angle of 30 degrees. The calibration curves for the transducers used i n the plane strain apparatus are given i n Fig. 31. The results of the f r i c t i o n tests to determine the co-efficient of f r i c t i o n of teflon against the s o i l contained i n a rubber membrane are given.below i n Table III. - 25 - TABLE III FRICTION TESTS ON TEFLON NORMAL LOAD PROVING RING DIAL READINGS IN . 0 0 0 1 " FRICTION FORCE CO-EFFICIENT OF FRICTION lbs Test No. 1 2 3 Average 53 8 .0 7 .0 8 .0 3 .32(^2) = 2.45 To follow page ZS. 100 K 1 o 3 O CQ" ,0 s g 0 . 0 1 Grain Size - mm. FIG. 13 - GRAIN SIZE CURVE 0.001 0 .0001 16 18 20 22 Molding Water Content - $ FIG. lk- COMPACTION CURVES 7 b foftovi lAr c To follow fif • 7 J V - SSJJJ-S 7b follow fif. 16 7S fo//o* fijf 17 To f o l l o w f i g . 19 30 60 Cell Pressure - p.s . i . Figure 22 Mohr Circles of t o t a l stresses for Maximum Average Deviator Stress I . ' RT - Series Figure - 23 Mohr Circles of t o t a l stresses for Maximum Average Deviator Stress PS - Series TO follow Fig. 23 .625, T60 ( J - - - P.S.I, Figure - 26 Mohr Circles of Effective Stresses for Maximum Average Deviator Stress RT - Series TO ' EFFECTIVE NORMAL STRESS - p.s . i . ro Figure - 27 Mohr Circles of Effective Stresses for .^EFFECTIVE NORMAL STRESS - p. s . i . 50 AO »» 3o o to IO ! j Figure - 28 Vector Curves i . i • •-. .• • CT - Series • • i-' -•• - r — -] ' • • : • . • ; \ • ••• •] •• — ( • • " • . r -- • i i • i. i ^ ! !---V / / j. ' . A N • •' • y I f • < • I ^ "J'j . / -• / / /A / rl 1 to Zo 30 40 50 (So 70 80 S\t-- ro Figure - 29 Vector Curves RT - Series O 10 ZO 3o 40 SO (SO •*! Figure - 30 Vector Curves PS - Series Vi o 58. vo To follow Fig. : 30 FIG. 31 - TRANSDUCER CALBRATION CURVES 40 "6(5 8CT Pressure - p . s . i . - 26 - VI. DISCUSSION A. Discussion of Testing Procedure The effects of small random errors i n individual tests were minimized by using, i n each case, the average results of three identical tests. This discussion i s therefore limited to sources of error inherent i n the procedure. The method mentioned under sample preparation and compaction procedure is believed to have eliminated or reduced error to a minimum, at least to within tolerable limits. The procedure, used in preparation of the sample and storage of the s o i l i n gallon jars kept i n the humid room, made i t possible to do a test at a moments notice. Furthermore, for a l l 27 tests, the water (1) + content was quite close to 20.0$ (- .5$). It was attempted to compact a l l / ( 2 ) specimens as nearly as possible to the same dry unit weight of about IO3.O. lb/cu.ft. The average water content, average dry unit weight and average degree of saturation are given i n Table II. The specimen volume changes were not measured during the t r i a x i a l tests; and i n deducing cross-sectional areas for the computation of the deviator stress the volume changes were assumed to be negligible. In this case, since the compacted specimens were only partly saturated, there would definitely be some volume change which would put the deviator stress (calculated neglecting volume change5) in error. However, this bold decision to neglect volume changes was taken after a careful study of the scope of this investigation and the equipment available. (1) Optimum water content. (2) Dry Unit weight obtained i n Harvard Miniature Compaction. - 27 - The following were the two considerations upon which the.author based his decision: (1) Air voids i n a specimen compacted to a dry unit weight of about 103.0 lbs/cu.ft. atla water content of 20 .0$ would occupy about of the tot a l volume. Thus, the maximum change i n volume, under undrained. con ditions (as i n this case), would be at most, only 5 § $ . The actual amount of volume involved for 5§$ volume change would range from about J>\ cu.cm. (for cylindrical specimens) to about 10 cu.cm.(for rectangular specimens). With the existing t r i a x i a l chamber and the volumeter available, i t would not have been possible to measure accurately such small volume changes as these. (2) Moreover, i t was not deemed necessary to measure volume changes since the main purpose of this investigation was to study the relative difference in the shear characteristics obtained by three different types of tests - cylindrical t r i a x i a l s , rectangular t r i a x i a l s and plane strain. Thus, even though the deviator stress for a particular type of test might be i n error by as much as about 5$ (for 5§$ volume change), the relative values of deviator stress for a l l three types of tests would not be affected by the fact that the volume changes were neglected. To minimize the number of variables i t was attempted to perform a l l tests under similar conditions. Unfortunately, the rate of axial strain used i n testing cylindrical specimens (.27$ strain per minute,) was different from the axial strain rate of .23$ strain per minute used i n testing rectangular specimens. The rate of vertical travel of the motor drive used - 28 - i n a l l tests was approximately constant, but the original height of the rectangular specimen (3 in.) was different from that of the cylindrical specimen (2.8l6 in.) thus causing the axial strain rates to d i f f e r as described above. This is a possible source of error. However, the author believes that,.;since this difference i n axial strain rates was quite small i t could not cause any serious error. As described i n the 'Testing Procedure", i t was attempted to dry off any excess water around the porous stone prior to the testing phase of an experiment. Since there was no positive way of ensuring that the amount of water on the contact plane between the porous stone and the specimen was the same in a l l the tests, the author feels that this was one of the major sources of error i n the experiments. For example, excess water on that con tact plane would produce excessively high pore pressure readings during the test period. It would not affect only the parameter B but also the parameter Af. The detailed discussion of the results with this factor i n mind w i l l be given later. Moreover, i t i s explained i n reference (6) that "Porous stone end plates (except fine ceramic disks) were never satisfactory" for pore pressure measurements. Thus, the possibility that the pore pressures measured might not be 100 per cent correct should be recognized. In case of plane strain tests, as described i n the 'Testing Procedure", the length of the plane strain frame was adjusted, before assembling the t r i a x i a l chamber, i n such a way as to bring the plane strain plates into contact with the s o i l specimen. During the period of time when confining pressure was being applied, there would be some decrease in volume of the - 29 - partly saturated specimen and consequently the sides of the specimen would not be i n contact with the plane strain plates anymore. Thus i t i s believed that the plane strain condition was achieved only i n the later part of the test after such time as the plates were, once again, i n contact with the specimen. However, negative strains during the isotropic stress phase would be exactly reversed during the deviatoric stressing, so that overall strain in the direction normal to the intermediate principal plane would be zero. It was explained before under "Equipment and Testing Procedure", that teflon (an almost frictionless material having a co-efficient of f r i c t i o n of 0.05) was used as the lining material for the plane strain plates. It was therefore possible to get almost uniform plane strain condition with very l i t t l e restraint i n the direction normal to the minor principal plane. B. Discussion of Results Each of the three series (CT, RT and PS) consisted of nine experiments, with three identical tests performed at each of the c e l l pressures, 30, 60 and 75 p s i . The results of each set of three identical tests were averaged, so that each series f i n a l l y has three sets of results, each being the average of three tests. The following discussion refers, i n general, to these averaged results unless otherwise specified. (i) Stress-strain curves - In figures 15 - 17 are plotted the average stress versus strain curves. For the CT and RT series of tests, the stress- strain curves are gradually curved, reaching a maximum deviator stress at strains of 20$, reflecting a plastic flow type failure. In the case of PS tests, the stress-strain .curves are also gradually curved but reach - 30 - a maximum deviator stress at strains as low as about 10$, suggesting a shear plane type of failure. No failure planes were observed, how ever. The strains required to develop maximum deviator stress seems to be independent of the c e l l pressure. Hence i t can be concluded that the strain required to develop maximum deviator stress under plane (3) strain condition i s about 50$ of that required to develop maximum deviator stress i n the case of either RT or CT type of tests. ( i i ) M^Q - The secant modulus of deformation M50 (corresponding to 50$ of the maximum deviator stress) i s plotted i n Fig. 19- This modulus increases with increasing c e l l pressure ( The to t a l range of M^ Q i n these tests was between about 1550 and 2900 lb/sq. in . Fig. 19 does not show a consistent pattern, although a general trend i s established. It has been pointed out i n reference (5) that 'The major cause of these irregularities i n M50 m a y be the dependence of the shape of the i n i t i a l portion of stress-strain curves upon the time elapsed between the com paction of a specimen and the start of the t r i a x i a l test". The elapsed time ranged from 30 minutes to 60 minutes i n most of the tests. ( i i i ) Intermediate principal stress (0~p) - In Figs. 15 - 17 are plotted the average ( fjg - 0*3) versus axial strain curves for plane strain tests. For the f i r s t 1 $ strain in Fig. 1 5 , for c e l l pressure of 30 psi, and about f i r s t 2.5$ strain for c e l l pressures of 60 psi and 75 psi (Figs. 16, 17) the value of <5~2 - 0~3 is almost equal to zero, indicating that 0~2 is (3) Since, as explained before, the plane strain condition was probably not achieved i n the i n i t i a l stages of axial loading, this figure may be lower than 50$ for a 100$ plane strain condition. - 31 - almost equal to (X3. Hence no plane strain condition was achieved during (k) those i n i t i a l stages of the tests. In the later part of the test, however, #2 - increases at the rate of about 50$ of 0~-j_ - 0^  with strain, indicating that 0~2 i s about equal to ^ i_i_£2, 0 r , that 62 is equal to about + ^3 . 2 _ 2 As explained before, for plane strain condition can be expected to be equal to Xi{ 6j_ + $3). It i s , therfore, concluded that X)- (Poisson's ratio) for the s o i l used i n this investigation i s equal to about 0.5« (iv) Pore Pressure Parameters Parameter B - In Fig. 18 i s plotted the parameter B as a function of c e l l pressure. Results are inconsistent. It is believed that the major cause of these irregularities i n the values of B is the failure i n achieving the same amount of water on the contact- plane between the porous stone and the s o i l specimen i n every test. As described i n "Discussion of Testing Procedure" different amounts of water on this contact plane w i l l lead to different pore pressure readings, for similar c e l l pressures ( (J3); and different pore pressure readings w i l l give different values of B, hence the inconsistent results as shown in Fig. 18. In the PS series, the plane strain condition was not achieved while the all-round (cell) pressure was being applied. Thus the author was unable to study the effect of plane strain on the parameter B. (k) This confirms the explanation given i n the last part of "Discussion of testing procedure", page (29). - 32 - Parameter Af - The value of parameter Af changes throughout the axial loading phase of the tests. The overall average value, from the start of the axial loading to the load at failure , i s the one that has the most practical significance. Thus i t became important to decide at what point on the stress- strain curve failure has occured. In figure 20 are plotted curves of the pore pressure parameter Af versus c e l l pressure for a l l three types of tests. The c r i t e r i a of failure used are as follow: (1) The maximum deviator stress that the specimen can stand during the test. (2) The maximum effective principal stress r a t i o O l / f l ^ . (3) A limiting axial strain of 10$ - 10$ axial strain to represent failure was selected because of the fact that maximum deviator stress for most of the plane strain tests occured at this 10$ strain. Though the curves for the PS series i n Pig.20, for a l l three c r i t e r i a of failure, l i e above those for the CT or the RT series of tests (indicating comparatively higher values of Af for the PS tests), only tentative conclusions can be drawn at this stage, because of the following two errors i n the testing procedure: (1) The plane strain condition did not exist i n the early stages of the tests and thus the curves do not show the f u l l effect of plane strain on Af. (5) (2) As explained before, Af i s a product of A and B; and the value of B which applies during deviatoric stressing i s different from that (5) . See equations (6) and (7). - 33 - which i s applicable during application of c e l l pressure. However, as pointed out i n reference (6), the B-value which i s applicable during actual stressing i s very much dependent on the B-value obtained during the isotropic stress"phase. The value of Af, there fore i s affected by the B-value obtained during application of a l l - round pressure, which, as shown in Pig.l8, i s quite inconsistent. (v) Mohr Circles (total stresses) In Figs. 21 - 23 are plotted the Mohr circles (in terms of total stresses) for maximum deviator stress. As is apparent from the envelopes drawn in Figs.21 - 23, at small c e l l pressures the strength increases rapidly with increasing c e l l pressure .-but at large c e l l pressures the strength increases very l i t t l e with increasing c e l l pressure. It is believed that when c e l l pressures are large enough almost a l l the pore air goes into solution i n the pore water and the specimen becomes practically saturated. Any increase i n confining pressure, then, goes directly to increase the pore pressure by the f u l l amount and the effective confining pressure, thus, does not increase. Since the strength depends upon the effective confining pressure and not upon the total confining pressure, l i t t l e or no increase i n strength i s achieved by increasing the c e l l pressure once the specimen becomes nearly saturated. The so-called U.S. Bureau of Reclamation curves plotted i n Fig. 2k show this effect of large c e l l pressures on the degree of saturation of the specimens quite clearly. It i s apparent from Fig. 2kB, that after the value of 0"^  (total confining pressure) i s larger than about 90 p s i , the pore pressure increases almost by the f u l l amount of increase i n (T^ and the value of QT (effective confining pressure) stays almost constant. - 34 - (vi) Mohr Circles (effective stresses) In Figs.25 - 27 are plotted the Mohr circles (in terms of effective stresses) for maximum deviator stress. The strength envelopes drawn to touch the smallest and the largest ..circles show the following results: TABLE IV STRENGTH PARAMETERS Series c CT 10 31.5° RT 12 28.50 PS 13-5 29.00 At low confining pressures, the compacted specimens are believed to have behaved i n a manner similar to that for overly consolidated s o i l s . Thus envelopes are also drawn to pass through the origin and to touch the largest c i r c l e . The results are given i n Table V as follows: TABLE V  0 - VALUES FOR c ' = O) Series jrf CT 37-5° RT 38.50 PS 41.00 These values would be applicable at high stresses assuming that there was no cohesion at 75 psi chamber pressure. - 35 - (6) If Mohr circles were drawn for deviator stress at 10$ axial strain, the ^-values for the CT and the RT series would be much smaller than the corresponding values i n Table IV and Table V. Thus i t can be concluded that (j> -values obtained i n plane strain tests are definitely higher than that for the RT series. (vi i ) Vector Curves In Figs. 28 - 30 are plotted the vector curves for stresses on the failure plane for each individual test. They were computed on the assumption that the failure plane is inclined at 60° to the major principal plane, assuming an internal angle of f r i c t i o n of 30 degrees. The end points of a l l the vector curves lie well above the 30-degree line . (6) 10$ axial strain i s one of the c r i t e r i a of failure previously used. - 36 - VII. SUMMARY OF CONCLUSIONS Based on the data and discussions presented i n this thesis, i t may be concluded that: (1) For compacted clayey s o i l s , the strain required to develop maximum deviator stress under plane strain condition i s less than about 50$ of that required i n the case of a corresponding conventional t r i a x i a l test. (2) The value of intermediate principal stress under plane strain condition i s half way between the major and minor principal stresses. (3) The Poisson's ratio for s i l t y clay such as the one used i n this investigation i s about 0.5. (k) The value of Pore Pressure parameter A f at failure , i n plane strain i s definitely higher than that for the corresponding conventional t r i a x i a l test. (5) The values of the strength parameters (c , </) i n plane strain are higher than those for the corresponding conventional t r i a x i a l tests. In the above remarks, "Corresponding" means a test run under the same conditions(cell pressure, rate of strain, etc.) on a specimen of the same shape. - 37 - VIII. KECOI-MENDATIONS Further investigations are needed on every phase of the work reported in this thesis. The time and testing were limited, resulting i n data that need verification by investigators i n future. The following are two changes in the equipment, which could improve the quality of the results to a great extent: (1) Use of ceramic end plates instead of porous stones (as used in this investigation). (2) Provision for adjusting the length of the plane strain frame after the application of c e l l pressure. APPENDIX I  TEST RESULTS TABLE NO. VI AS-MOULDED CONDITIONS CYLINDRICAL TRIAXIAL SERIES RECTANGULAR TRIAXIAL SERIES PLANE STRAIN SERIES WATER TEST CONTENT NO. $ . DRY DENSITY lbs./cu. ft. TEST NO. W$ yj lbs/cu.ft. TEST NO. Ibs/cu. f t . 1 102.2 84.5 10 20.25 103.2 8 6 . 3 19 2 0 . 0 8 104.7 8 9 . 3 2 102.3 84.8 11 20.35 103.5 87.2 . 20 19.90 IO3.8 •' 8 7 . 1 3 102.3 85.2 12 20.33 103.3 86.5 21 19.95 103.9 8 7 . 3 Ave. 2 0 . 0 2 102.3 84.8 Ave. 20.31 103.3 8 6 . 7 •Ave. 1 9 . 9 8 104.1 8 7 . 9 4 102.8 87.4 13 104.2 89.5 22 2 0 . 1 102.9 8 5 . 0 5 103.5 88.2 .14 104.0 8 8 . 7 23 2 0 . 1 IO3.8 8 7 . 0 6 103.5 88.2 15 104.2 89.5 24 1 9 . 8 104.6 8 9 . 0 Ave. 20 .30 103.3 87 .9 Ave. 2 0 . 2 104.1 89 .2 Ave. 2 0 . 0 IO3.8 8 7 . 0 7 20.05 102.8 85 .3 16 20.5 104.0 8 9 . 0 25 2 0 . 0 8 104.5 8 8 . 4 8 2 0 . 0 0 102.2 85.2 17 2 0 . 3 103.5 87 .7 26 19-95 1 0 4 . 8 8 9 . 0 9 102.8 85.3 18 2 0 . 4 104.5 9 0 . 0 27 19.70 104.5 8 8 . 4 Ave. 2 0 . 0 2 102.6 85.3 Ave. 2 0 . 3 104.0 8 8 . 9 Ave. 19.91 104.6 8 8 . 6 Overall Ave. 102.7 8 6 . 0 Overall Ave. 20.27 103.8 8 8 . 3 Overall Ave. 19.96 104.5 8 7 . 8 TABLE NO. VII PORE PRESSURE PARAMETER B CYLINDRICAL TRIAXIAL SERIES RECTANGULAR TRIAXIAL SERIES PLANE STRAIN SERIES TEST 61 (Lc, TEST TJ TEST NO. p.s.i. p.s.i. O NO. p.s.i. p.s.i. D NO. p .s . i . p.s.i • 1 30 7" .225 10 30 1 6 ' .525 19 30 19" .625 2 30 6.5" .208 11 30 13.5 .1*50 20 30 13.0 .433 3 . 30 4" .125 12 30 I 7 . 5 .582 21 30 9-5 .317 Ave. 5-5 .186 Ave. 15.6 .519 Ave. 1 3 . 8 .458 4 60 l l + .187 13 60 19.0 .316 22 60 17.5 .292 5 60 8.5 .142 lh 60 17.0 .283 23 60 17" .280 6 60 l l " .179 15 60 14.5 .242 2k 60 2k+ .405 Ave. 10.2 .169 Ave. 16.2 .270 Ave. 19 .6 .326 7 75 12.5 .167 16 75 26.5 • 35^ 25 75 35~ .463 8 75 l 4 + .190 17 75 20.5 .274 26 75 2 7 . 0 .360 9 75 l 4 + .190 18. 75 26.0 •3^7 27 75 2 7 . 0 .360 Ave. 13.7 .182 Ave. 24.4 .325 Ave. 2 9 . 5 • 394 TABLE VIII PORE PRESSURE PARAMETER Af 7k ST j-Jo. FOR. MAX. DMVIATOR. STRESS U-Uo . 1-OAOlNi f>S.l. FOR MAX. G)/$~3 6 S~< 6]_ 63 p-s-.i. 5} psi. 4 f foR. fo'/o ST£/>/rV P3i . U-U0 f\r P-s.i. J 3 « EH \A <C O H K O 3 M EH g •a; 1 2 3 5 6 7 8 9 10 11 12 13 ll+ 15 30 30 30 60 60 60 75 75 75 30 30 30 60 60 60 17.8 17.8 17.8 21A 102.5 21.4 104.3 18.6 103.5 21.4 21.4 21.4 13.3 10.0 10.0 16.7 16.7 16.7 76.8 5.7 .074 69 76.3 4.7 .062 68 77.8 4.8 .062 66 114.5 113.5 119.5 57.3 56.9 54.0 88.0 88.0 91.0 16.5 16.5 17.O 23.2 22.3 27.7 4.2 7.0 4.2 13.7 16.5 15.5 ..066 .162 79 .158 75 .166 76 .162 .203 75 .196 76 .232 .210 75 59 42 .074 .123 .078 45 .092 .156 .187 .165 .169 72 68 75 2400 2700 2900 1550 14.20 14.2 14.2 2300 10 8.7 7.3 13.3 13.3 13.3 91.7 91.8 96.1 93-2 5.50 5.02 4.62 65.6 63.6 57.9 62.4 111.5 111.3 118.5 113.8 7.29 7.07 7.94 4.37 4.4o 3.99 16.7 18.3 20.8 18.6' 17.8 131.6 4.28 30.8 21.4 139.3 3.98 35.0 21.4 135.8 4.25 32.0 135.6 32.6 21.4 153.7 3-92 39-2 21.4 152.O 3.95 38.5 17.8 149.6 4.68 32.O 151.8 36.6 9.0 9.0 7.3 8.4 25.5 25.3 29.7 26.9 .087 .075 .073 .078 .178 .158 .166 .167 .203 .196 .244 .213 .093 .137 .104 .111 .180 .206 .178 .188 68.0 66.1 67.6 67.2 88.5 89.1 90.2 89.3 1100.2 98.8 104.4 101.1 56.6 56.9 54.O 55-8 81.0 81.6 82.7 81.8 8.4 .124 5.5 .083 5.5 .82 6.5 .096 17.O 13.1 13.8 14.6 20.6 19.8 21.1 20.5 5.2 7.0 4.3 5.5 16.3 18.0 15.8 16.7 .192 .147 .153 .164 .205 .201 .202 .202 .092 .123 .080 .098 .201 .220 .191 .204 TABLE VIII Continued Foe r4SO 'FOR f^l/IX. 6~i fof? (0°/° S T « / ? / A / TEST A / O . K i t i° f>.s.< Lt-Ua psi Tin/e ,°( <L . tf, *t Of 6;-6-3 f-s.i. P-i-i. 16 75 16 .7 9 0 . 7 2 0 . 7 .228 67 10.0 110.7 4 . 2 6 2 6 . 0 . .249 84.7 22.5 .266 17 75 16.7 94.5 2 2 . 0 .233 71 13.3 123.0 3-97 31 .0 .255 8 6 . 0 23 .2 .270 18 75 16.7 9 3 . 8 2 0 . 7 .221 .227 72 2450 13.3 118.5 117.4 4 . 5 6 2 6 . 0 2 7 . 7 .249 .251 87 .0 85.9 2 3 . 8 2 3 . 2 .273 .270 19 30 8 . 7 58.3 6.2 .108 38 6.0 60.9 13.55 4 . 5 .120 57.4 5 .2 .091 20 30 7-3 61.6 8.5 .138 30 •7-3 70 .1 8.25 8.5 .138 59.0 7 . 8 .132 21 30 8 . 7 64.0 8.2 .129 36 8 .7 70.25 6.25 12.2 .^ 129 62.4 7-3 .117 ST RA IN  .125 2200 67.1 8 . 4 .129 59 .6 6 . 8 .113 ST RA IN  22 60 10.0 81 .6 1 8 . 0 . .228 48 10.0 106.1 4.34' 2 4 . 5 .228 81.4 18.0 .221 ST RA IN  23 60 10.0 8 3 . 8 17.0 .203 44 10.0 110.0 4 . 2 0 2 6 . 2 .203 8 3 . 8 17.O .203 24 60 1 0 . 0 7 6 . 8 17-5 .221 41 10.0 95 .0 5.22 1 8 . 2 .221 7 6 . 8 17.6 .229 • 3 .217 2350 103.7 2 3 . 0 .217 8 0 . 7 17.5 .218 25 75 10.0 85.5 21.0 .246 45 8 .7 103.2 5.67 18 .2 .259 85.5 21 .0 .245 26 75 10.0 88.5 27 .0 .305 44 10.0 109.5 5.22 2 1 . 0 .305 8 8 . 5 2 7 . 0 .305 27 75 10.0 87.2 25 .0 .287 • 279 41 2600 10.0 110.2 107.6 4 .79 2 3 . 0 2 0 . 7 .287 .284 87.2 87.1 2 5 . 0 2 4 . 3 .287 • 279 To follow Fig. 3k Figure - 35 Rectangular T r i a x i a l Series - Stress-Strain Curves ,. Ce l l pressure =30 lba/sq. inf «> » Test 10 « Test 11 -"Test 12 Go •H CO CO CO / O / 2 / <S ^ < 5 AXIAL STRAIN - £ To follow Fig. 35 ! To follow Fig. 36 . 1 : — : ; Figure - 37 Rectangular T r i a x i a l Series Stress-Strain Curves g C e l l pressure = 75 lbs./sq. i n . x- o o z 4 6 0 10 IZ 14 l<o ' .18 . 20 AXIAL STRAIN - $ To follow Fig. 37 To follow Fig. .38 Figure - 39 Plane Strain Series Stress-Strain Curves ^ Ce l l pressure = 60 lba/sq. i n . AXIAL STRAIN - i To follow F i g . 39 AXIAL STRAIN - $ - h2 - APPENDIX II SAMPLE CAIiCULATICNS BASED ON DATA OBTAINED IN TEST NO. 19 A. Deviator Stress (i) Corrected Area ao where a = the area on which true deviator stress i s calculated (in.) 2 ao = the i n i t i a l area (in.) £ = the axial strain (inS'/in.) ( i i ) Vertical f r i c t i o n force because of plane strain plates. F = Average - LT3) x 2 x Side Area x f = 6.9 (2)(3.82)(.05) = 2.6 lbs. where F = f r i c t i o n force opposing the axial strain (lbs.) f = co-efficient of f r i c t i o n of teflon Then the deviator stress i s calculated as follows: 286.5 - 2.6 B. Secant Modulus of Deformation (Mqp) Max (*i -45) (psi) 2 ^5° ~ axial strain (~^ ') i n ' = = 2190 l b a / i n 2 - 1+3 - C. Pore Pressure Parameters (i) Parameter B B . 22 . i | l = . 6 2 5 3 30 where Uo = pore pressure change during the application of c e l l pressure, assuming that the pore pressure i s equal to zero before the 2 start of the test, (lbs/in.). ( i i ) Parameter Af AU = 6.2 " u~3 5 ^ 3 A f = ^ - = ^  = 0 .106 where A U = U - Uo 2 U = pore pressure at failure (lbs/in.) D. Vector Curves The most convenient method of plotting the Vector curves i s to calculate the co-ordinates of individual points analytically, using the following equations: 6£ = (T3 + (<7£ - 6~3) Cc&Jf Tf = (<J£ -0-3) &>"<fCoS<*S where , ^/ = 1+5° + |j , the angle between failure plane and major principal plane. 6f = effective normal stress on failure plane. If = shear stress on failure plane and <f> = internal f r i c t i o n angle. 67 7 ( 6 0 ) - 5.0 + 58 .3 (£) = 1 9 . 6 (lbs/in 2) 7f(6Q) - 5 8 . 3 ( - § ) ( | ) 25.3 (lbs/in 2) - Uk - REFERENCES 1. Bishop, A.W. (1955) , Lecture delivered i n Oslo, entitled "The Principle  of Effective Stress". Printed i n Tek. Ukeblad, No. 39 (1959) (Norwegian Geotechnical Institute. Publ., 3 2 . ) 2 . Bishop, A.W., Alpan, J. Blight, G. and Donald, V. ( i 9 6 0 ) , "Factors Con t r o l l i n g the Strength of Partly Saturated Soils." Research Conference on Shear Strength of Cohesive Soils Proceedings. 3. Bishop, A.W., and Bjerrum, L. ( i 9 6 0 ) , "The Relevance of the T r i a x i a l Test  to the Solution of Stability Problems" Research Conference on Shear Strength of Cohesive Soils. Proceedings. k.. Bishop, A.W., and Henkel, D.G. (1957) , "The Measurement of So i l Properties  in the T r i a x i a l Test". London, Arnold. 5. Casagrande, A., and Hirschfeld, R.C. ( i 9 6 0 ) , "First Progress Report on  Investigation of Stress Deformation and Strength Characteristics of Clays". (Report to Waterways Experiment Station.) So i l Mechanics Series No. 6 l , Harvard University, Cambridge, Massachusetts. 6. Gibbs, H.J., H i l f , J.W., Holtz, W.G. and Walker, F.C. ( i 9 6 0 ) , "Shear  Strength of Cohesive Soi l s " Research Conference on Shear Strength of Cohesive Soils. Proceedings. 7. Henkel, D.J. ( i 9 6 0 ) , "The Shear Strength of Saturated Remoulded Clays 1' Research Conference on Shear Strength of Cohesive Soils. Proceedings. - 4 5 - 8 . H i l f , J.W. ( 1956) , "An Investigation of Pore Water Pressure i n Compacted  Cohesive Soils". (Doctoral Thesis, University of Colorado), U.S. Department of the Interior, Bureau of Reclamation, Technical Memorandum 654, Denver, Colorado. 9 . Lambe, T.W. ( l 9 5 l ) , "S o i l Testing for Engineers". New York: John Wiley. 10. Leonards, G-.A. ( ), "Foundation Engineering" McGraw H i l l and Company. 11. Seed, H.B., Mitchell, J.K., and Chan, C.K. ( i 9 6 0 ) , "The Strength of  Compacted Cohesive Soils" Research Conference on Shear Strength of Cohesive Soils. Proceedings. 12. Skempton, A.W. (1954), 'The Pore Pressure Co-efficients A and B." Geotechnique, Vol. 4 , No. 4 , pp ' l 4 3 - 147. 13. Skempton, A.W. ( i 9 6 0 ) , "Effective Stress i n Soils, Concrete, and Rock". Conference on Pore Pressure and Suction i n Soils. Butterworth, London. 14. Taylor, D.W. ( 1948) , "Fundamentals of Soi l Mechanics". New York: John Wiley. 15. Terzaghi, K. (1923),"Die Berechnung der Durchlassigkeitsziffer des Tones  aus dem Verlauf der.Hydrodynamischen Spannungserscheinungenl' Sitz, Akad. Wissen. Wien Math-natunv. KL.. Abt. 11a, 132, 125 - 138. 16. Wilson, S.D. ( 1950) , "Small S o i l Compaction Apparatus Duplicates Field  Results Closely". Engineering News Record, November, 1950. 

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