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Constant volume friction angle of granular materials Wijewickreme, Dharmapriya 1986

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CONSTANT VOLUME FRICTION ANGLE OF GRANULAR MATERIALS By DHARMAPRIYA WIJEWICKREME 3.Sc. (Eng) Hons., U n i v e r s i t y of Peradeniya S r i Lanka, 1982. THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of C i v i l Engineering We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA February 1986 © Dharmapriya Wijewickreme, 1986 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) A B S T R A C T The p o s t u l a t e that the constant volume f r i c t i o n angle </>cv of a granular m a t e r i a l i s unique i s v e r i f i e d e x p e r i m e n t a l l y . The constant volume f r i c t i o n angle of a wide spectrum of granular g r a n u l a r m a t e r i a l s i s measured using the r i n g shear d e v i c e , e n a b l i n g the m a t e r i a l to be sheared to l a r g e , i n f a c t u n l i m i t e d s t r a i n s at which 0 c v i s m o b i l i z e d . Granular m a t e r i a l s t e s t e d were composed of p a r t i c l e s ranging from m i n e r a l s to metals. The e f f e c t s of c o n f i n i n g p r e s s u r e , i n i t i a l packing d e n s i t y , p a r t i c l e s i z e , g r a d a t i o n and p a r t i c l e shape on the value of tf>cv are s t u d i e d . The p o s s i b l e i n f l u e n c e of the presence of pore water i s a l s o i n v e s t i g a t e d . The t e s t r e s u l t s i n d i c a t e that f o r a given m a t e r i a l , <Pcv i s independent of c o n f i n i n g p r e s s u r e , i n i t i a l packing d e n s i t y and p a r t i c l e s i z e . N e i t h e r p a r t i c l e c r u s h i n g nor change in shape of the p a r t i c l e had any n o t i c e a b l e e f f e c t on the observed value of 0 C V« These experimental r e s u l t s suggest that the constant volume f r i c t i o n angle i s a fundamental property of a g r a n u l a r m a t e r i a l which i s dependent only on the m i n e r a l c o n s t i t u e n c y of the m a t e r i a l . A comparison of <j> and the f r i c t i o n angle m o b i l i z e d at the p o i n t of maximum c o n t r a c t i o n i n drained shear (a t r a n s i e n t constant volume s t a t e ) as w e l l as the f r i c t i o n angle m o b i l i z e d at phase t r a n s f o r m a t i o n s t a t e i n undrained i i shear (a t r a n s i e n t constant pore pressure s t a t e ) i s a l s o made, i n an attempt to seek a broader fundamental s i g n i f i c a n c e of <p rcv i i i CONTENTS Chapter Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i INDEX OF NOTATIONS x i ACKNOWLEDGEMENT x i i DEDICATION x i i i 1 . INTRODUCTION 1 2. LITERATURE REVIEW 6 2.1 General 6 2.2 Drained Shear Strength of Coh e s i o n l e s s M a t e r i a l s 6 2.3 Large S t r a i n Tests 13 2.4 T r a n s i e n t Constant Volume State s During Shear 23 3. EXPERIMENTAL ASPECTS 27 3.1 Measurement of Constant Volume F r i c t i o n Angle 27 3.1.1 Laboratory Shear T e s t i n g Devices 27 3.1.2 UBC Ring Shear Device 30 3.1.3 M o d i f i c a t i o n s to UBC Ring Shear Device 32 3.1.4 Measurements of Loads and Displacements 36 3.2 Determination of M o b i l i z e d F r i c t i o n Angle at Maximum C o n t r a c t i o n 38 3.2.1 T r i a x i a l Apparatus 38 i v 3.2.2 Measurement of Loads, Displacements and Volume Change 3.3 M a t e r i a l s Tested 3.4 T e s t i n g Procedure and Sample Pr e p a r a t i o n 3.4.1 Ring Shear T e s t s 3.4.2 T r i a x i a l T e s t s 4. RESULTS AND DISCUSSION 4.1 Constant Volume F r i c t i o n Angle 4.1.1 Ring Shear T e s t s on Ottawa Sand 4.1.2 Ring Shear T e s t s on Brenda and Lornex Mine T a i l i n g s 4.1.3 Ring Shear T e s t s on Granular Copper 4.1.4 Ring Shear T e s t s on Lead Shots and Glass Beads 4.1.5 Review of the Test R e s u l t s in R e l a t i o n t o Previous Work 4.2 F r i c t i o n Angle at Maximum C o n t r a c t i o n 4.2.1 Drained T r i a x i a l T e s t s on Medium Ottawa Sand 4.2.2 Drained T r i a x i a l T e s t s on Other M a t e r i a l s 4.2.3 Review of the Test R e s u l t s in R e l a t i o n to Previous Work 4.3 C r i t i c a l S t ate, Steady State and Phase Transformation S t a t e 5. SUMMARY AND CONCLUSIONS REFERENCES L I S T OF TABLES T a b l e No. Page 3.1 P h y s i c a l P r o p e r t i e s o f t h e M a t e r i a l s T e s t e d 41 4.1 C o n s t a n t Vo lume F r i c t i o n A n g l e O b s e r v e d f o r D i f f e r e n t M a t e r i a l s 75 4.2 C o m p a r i s o n o f C o n s t a n t Vo lume F r i c t i o n A n g l e a n d F r i c t i o n A n g l e m o b i l i z e d a t P h a s e T r a n s f o r m a t i o n 98 v i L I ST OF F IGURES F i g . No. Page 2.1 Components of Shear R e s i s t a n c e of Sand (A f t e r Rowe, 1962; Lee and Seed, 1967). 8 2.2 T h e o r e t i c a l R e l a t i o n s h i p s between Constant Volume F r i c t i o n Angle and I n t e r p a r t i c l e F r i c t i o n Angle Compared with Experimental R e s u l t s ( A f t e r Home, 1969) 11 2.3 Experimental Observations on Constant Volume F r i c t i o n Angle and I n t e r p a r t i c l e F r i c t i o n Angle compared with Previous T h e o r e t i c a l R e l a t i o n s ( A f t e r Skinner, 1969) 12 2.4 Re s u l t s of Simple Shear T e s t s on 1 mm S t e e l B a l l s with a Normal Stress, of 1.4 kg/cm 2 ( A f t e r Roscoe et a l . , 1958) 15 2.5 V a r i a t i o n of Volumetric S t r a i n with Shear S t r a i n During Drained T r i a x i a l T e s t s on Leighton Buzzard Sand. (A f t e r Roscoe e t . a l . , 1963) 16 2.6 S t r e s s S t r a i n Data f o r Three Large S t r a i n Tests on Leighton Buzzard Sand at the Same Average V e r t i c a l Normal S t r e s s of 1.33 kg/cm 2 ( A f t e r C o l e , 1967) 17 2.7 Resu l t s of Drained T r i a x i a l T e s t s on Ottawa Banding Sand ( A f t e r C a s t r o , 1969) 19 2.8 Peak F r i c t i o n Angle f o r Chattakoochee R i v e r Sand Tested at D i f f e r e n t Normal S t r e s s Le v e l s ( A f t e r V e s i c and Clough, 1969) 21 2.9 T y p i c a l S t r e s s S t r a i n Behaviour f o r a Drained T r i a x i a l Test on a Dense Sand (A f t e r Atkinson and Bransby, 1978) 25 3.1 Major Components of UBC Ring Shear Device ( A f t e r Bosdet, 1980) 31 3.2 M o d i f i c a t i o n s to the Upper Ring Assembly of the Ring Shear Apparatus 34 3.3 M o d i f i c a t i o n s to the Lower Load C e l l Connection Measuring Side F r i c t i o n Forces i n the Ring Shear Device 35 v i i Schematic of the Measuring Devices i n the Ring Shear Apparatus Schematic of the Measuring Devices i n the T r i a x i a l Apparatus P a r t i c l e S i z e D i s t r i b u t i o n s f o r Sands Used i n the t e s t i n g Program Test on a Saturated Sample with a Surrounding Water R e s e r v o i r Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) a. I n i t i a l R e l a t i v e Density - 30% b. I n i t i a l R e l a t i v e D e n s i t y - 55% c. I n i t i a l R e lat ive D e nsity - 64% d. I n i t i a l R e l a t i v e Density - 75% e. I n i t i a l R e l a t i v e Density - 80% f. I n i t i a l R e l a t i v e Density - 85% Constant Volume f r i c t i o n Angle vs I n i t i a l R e l a t i v e Density Medium Ottawa Sand (Oven Dry) Grain S i z e D i s t r i b u t i o n of Medium Ottawa Sand Before and A f t e r Ring Shear T e s t s Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Saturated) with an I n i t i a l R e l a t i v e D e n s i t y = 30% Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Fine Ottawa Sand (Oven Dry) with an I n i t i a l R e l a t i v e D e n s i t y = 30% Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Brenda Mine T a i l i n g s (Oven Dry) with an I n i t i a l R e l a t i v e d e n s i t y = 54% Grain S i z e D i s t r i b u t i o n of Brenda Mine T a i l i n g s Before and A f t e r Ring Shear Tes t s v i i i 4.8 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Lornex Mine T a i l i n g s (Oven Dry) with an I n i t i a l Dry Density = 1.4 g/cm3 68 4.9 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Fine Copper (Oven Dry) with an I n i t i a l Dry Density = 6.95 g/cm3 70 4.10 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Coarse Copper (Oven Dry) with an I n i t i a l Dry Density = 6.14 g/cm3 71 4.11 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Lead Shots (Oven Dry) with an I n i t i a l Dry Density = 7.74 g/cm3 73 4.12 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Glass Beads (Oven Dry) with an I n i t i a l Dry d e n s i t y = 1.53 g/cm3 74 4.13 Stress-Strain-Volume Change Data For Medium Ottawa Sand from Drained T r i a x i a l T e s t s , E f f e c t i v e C o n f i n i n g Pressure = 200 kPa a. I n i t i a l R e l a t i v e Density = 30%, Diameter of the Sample = 51mm 79 b. I n i t i a l R e l a t i v e Density = 30%, Diameter of the Sample = 63.5 mm 80 c. I n i t i a l R e l a t i v e Density = 54%, Diameter of the Sample = 51 mm 81 d. I n i t i a l R e l a t i v e Density = 80%, Diameter of the Sample = 63.5 mm 82 4.14 M o b i l i z e d F r i c t i o n Angle at Maximum C o n t r a c t i o n vs I n i t i a l R e l a t i v e Density -Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa 83 ix 4.15 M o b i l i z e d F r i c t i o n Angle at Maximum Co n t r a c t i o n vs E f f e c t i v e C o n f i n i n g Pressure - Medium Ottawa Sand, I n i t i a l R e l a t i v e Density = 50% (Af t e r Negussey et a l . , 1986) 85 4.16 Stress-Strain-Volume Change Data from Drained T r i a x i a l Tests - E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, Sample Diameter - 51mm a. Fine Ottawa Sand, R e l . D e n s i t y = 35% 86 b. Brenda T a i l i n g s , R e l . D e n s i t y = 25% 87 c. Lornex T a i l i n g s , Dry Densit y = 1.27 g/cm3 88 d. Fine Copper, Dry Densit y = 5.00 g/cm3 89 e. Coarse Copper, Dry Densit y = 5.23 g/cm3 90 f. Lead Shots, Dry Densit y = 6.64 g/cm3 91 g. Glass Beads, Dry Densit y = 1.52 g/cm3 92 4.17 M o b i l i z e d F r i c t i o n Angle at Maximum Co n t r a c t i o n i n T r i a x i a l T e s t s ( I n i t i a l l y Loose Samples) vs Constant Volume F r i c t i o n Angle 93 4.18 Ultimate F r i c t i o n Angle i n T r i a x i a l T ests vs Constant Volume F r i c t i o n Angle 95 x INDEX OF NOTATIONS R a t i o Between the Major and Minor P r i n c i p a l E f f e c t i v e S t r e s s e s Volumetric S t r a i n Accumulated During Drained Shear i n a T r i a x i a l Test A x i a l S t r a i n During Shear i n a T r i a x i a l Test Maximum D i l a t i o n Angle During Drained Shear M o b i l i z e d F r i c t i o n Angle at Any General Instant During the Shear Process of a S o i l M o b i l i z e d F r i c t i o n Angle at Constant Volume State ( C r i t i c a l State) During the Drained Shear Process of a Granular M a t e r i a l M o b i l i z e d F r i c t i o n Angle Less the Component Due to Volume Changes During the Drained Shear Process of a Granular M a t e r i a l M o b i l i z e d F r i c t i o n Angle at the Inst a n t of Maximum C o n t r a c t i o n During the Drained Shear Process of a Granular M a t e r i a l M o b i l i z e d F r i c t i o n Angle at the Instant of Phase Transformation During the Undrained Shear Process of a Granular M a t e r i a l Angle of I n t e r p a r t i c l e F r i c t i o n Major P r i n c i p a l E f f e c t i v e S t r e s s Minor P r i n c i p a l E f f e c t i v e S t r e s s x i ACKNOWLEDGEMENTS The author wishes to express h i s most s i n c e r e thanks to h i s s u p e r v i s o r P r o f e s s o r Yoginder Va i d f o r h i s guidance during t h i s r e s e a r c h . A couple of sentences cannot adequately convey the measure of g r a t i t u d e which i s due to him for h i s i n v a l u a b l e a s s i s t a n c e . The author i s g r a t e f u l to Dr. Dawitt Negussey not only f o r the p a i n s t a k i n g e f f o r t s taken i n l a y i n g the foundation f o r t h i s r e s e a r c h but a l s o f o r h i s continued i n t e r e s t and h e l p f u l c r i t i c i s m . A s s i s t a n c e and advice given by P r o f e s s o r Peter Byrne du r i n g the author's stay i n Canada i s deeply a p p r e c i a t e d . S p e c i a l thanks are due to Mr. Fred Zurkirchen f o r h i s patience and hardwork i n equipment development. The f i n a n c i a l support provided by the N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. x i i DEDICATED TO MY PARENTS CHAPTER 1 INTRODUCTION F r i c t i o n a l c h a r a c t e r i s t i c s of c o n s t i t u t i n g minerals have a s i g n i f i c a n t i n f l u e n c e on the s t a b i l t y of a c o h e s i o n l e s s s o i l mass. The drained shearing r e s i s t a n c e . o f a granula r m a t e r i a l can be represented by a s i n g l e parameter, the m o b i l i z e d angle of f r i c t i o n . A granular s o i l s u b j e c t e d to d r a i n e d shearing w i l l normally e x h i b i t an i n c r e a s i n g m o b i l i z e d angle of f r i c t i o n with i n c r e a s i n g s t r a i n upto peak v a l u e . Continued s t r a i n i n g beyond the peak may or may not cause a drop in the m o b i l i z e d angle of f r i c t i o n , while tending towards a constant value at l a r g e s t r a i n s . At t h i s stage the s o i l can deform i n d e f i n i t e l y without any change i n v o i d r a t i o or s t r e s s s t a t e . T h i s s t a t e i s g e n e r a l l y r e f e r r e d to as the constant volume or c r i t i c a l s t a t e and the corresponding f r i c t i o n angle i s c a l l e d the constant volume f r i c t i o n angle <j> 3 c v The concept of c r i t i c a l s t a t e and the a s s o c i a t e d constant volume f r i c t i o n angle has an important r o l e both at fundamental s o i l p r operty c h a r a c t e r i z a t i o n s and in the design and a n a l y s i s of g e o t e c h n i c a l problems. Rowe (1962) in h i s formulation of the s t r e s s d i l a t a n c y theory has shown that the maximum d i l a t i o n angle J> „ and <6 , can adequately d e f i n e the 3 max cv ^ •* peak f r i c t i o n angle of a gr a n u l a r m a t e r i a l . With proper c o n s i d e r a t i o n given to t h i s Hughes et a l . (1977) obtained the 1 s o l u t i o n t o the a x i s y m m e t r i c p l a n e s t r a i n problem a s s o c i a t e d w i t h the expansion of a p r e s s u r e m e t e r . T h i s s o l u t i o n c o u l d be used t o o b t a i n the i n s i t u peak f r i c t i o n a n g l e from p r e s s u r e m e t e r r e s u l t s p r o v i d e d the v a l u e of 0 c v of the s o i l d e p o s i t i s known. The v a l u e of </> i s a l s o r e q u i r e d i n s o l v i n g boundary v a l u e problems w i t h the use of s l i p l i n e methods. The c o n s t a n t volume f r i c t i o n a n g l e p r o v i d e s a d e f i n i t e boundary f o r the domain of v i a b l e s t r e s s s t a t e s i n the f o r m u l a t i o n of s t r e s s s t r a i n models f o r sands. S i n c e i t c o r r e s p o n d s t o a s t a t e of z e r o volume change, i t may be of p o t e n t i a l use as a r e f e r e n c e s t a t e i n the development of c o n s t i t u t i v e models, whereby any o t h e r p o i n t i n the s t r e s s space c o u l d be d e s c r i b e d as a d e v i a t i o n from the r e f e r e n c e s t a t e . Use of 4> as a cv d e s i g n parameter i n s t e a d of the peak f r i c t i o n a n g l e i n the s o l u t i o n of s t a b i l i t y problems would a l l o w the d e s i g n e r t o use lower s a f e t y f a c t o r s ; even as low as 1 . 0 p r o v i d e d the v a l u e of <PCV i s e s t i m a t e d a c c u r a t e l y . These a s p e c t s c l e a r l y demonstrate t h a t the c o n s t a n t volume f r i c t i o n a n g l e of g r a n u l a r m a t e r i a l s i s a m a t e r i a l parameter of c o n s i d e r a b l e i n t e r e s t from both t h e o r e t i c a l as w e l l as p r a c t i c a l p o i n t s of view. The c o n s t a n t volume f r i c t i o n a n g l e i s an i n d i c a t i o n of the l o w e s t shear r e s i s t a n c e p o s s e s e d by the m a t e r i a l , and has been suggested to be a fundamental p r o p e r t y of the m a t e r i a l , dependent o n l y on the m i n e r a l c o n s t i t u t i n g the g r a i n s . P r e v i o u s work c l e a r l y i n d i c a t e t h a t no such e x p e r i m e n t a l v e r i f i c a t i o n of the uniqueness of <j> has been p o s s i b l e . T h i s 2 i s p r i m a r i l y because of the d i f f i c u l t i e s a s s o c i a t e d with shear t e s t i n g over l a r g e s t r a i n s at which <j>cv i s m o b i l i z e d . T r i a x i a l or simple shear t e s t i n g techniques can only y i e l d an upper bound to the value of 0 C V . Moreover, the s t r e s s s t a t e at l a r g e s t r a i n s i n these d e v i c e s would be f a r from homogeneous, thereby i n t r o d u c i n g f u r t h e r u n c e r t a i n i t y i n measured 4>cv. On the other hand, <f>cv has been i n f e r r e d i n d i r e c t l y from drained t e s t data with no need to shear the g r a n u l a r m a t e r i a l to very l a r g e s t r a i n s at which the constant volume s t a t e i s r e a l i z e d . These i n d i r e c t techniques are based e i t h e r on the assumed v a l i d i t y of the s t r e s s d i l a t a n c y theory or by (Rowe, 1962; Skinner, 1969) e x t r a p o l a t i o n of peak f r i c t i o n angle corresponding to zero d i l a t i o n r a t e . However, the p o s s i b l e fundamental nature of tf>cv f o r a g r a n u l a r m a t e r i a l can be e s t a b l i s h e d only by d i r e c t measurements in a shear device capable of imposing l a r g e , and p r e f e r a b l y u n l i m i t e d shear s t r a i n s . Skempton (1964,1985) r e p o r t e d the use of the r i n g shear apparatus i n the d i r e c t measurement of r e s i d u a l shear s t r e n g t h of c l a y s of v a r y i n g p l a s t i c i t y . Examination of the past work on t h i s d e v i c e , c l e a r l y shows i t s p o t e n t i a l i n l a r g e s t r a i n measurements. The r i n g shear d e v i c e seems to provide an e x c e l l e n t means of shearing with u n l i m i t e d s t r a i n s and s t i l l p r e s e r v i n g a homogeneous s t r e s s s t a t e on the plane of shear. These c o n s i d e r a t i o n s along with the observed need to i n v e s t i g a t e the value of <f>_ f o r g r a n u l a r m a t e r i a l s r e s u l t e d 3 i n the evolvement of the main theme of t h i s t h e s i s . In t h i s t h e s i s the value of <6 , i s d i r e c t l y measured with the use of cv J the r i n g shear device, f o r a wide spectrum of granular m a t e r i a l s ranging from minerals to metals. For each m a t e r i a l p o s s i b l e e f f e c t of c o n f i n i n g p r e s s u r e , i n i t i a l packing d e n s i t y and p a r t i c l e s i z e on <£ c v are i n v e s t i g a t e d . P o s s i b l e i n f l u e n c e of the presence of pore water i n the vo i d s as opposed to the dry m a t e r i a l i s a l s o i n v e s t i g a t e d . At the c r i t i c a l s t a t e , the r a t e of volume change i s zero. In the d r a i n e d shear response of granula r m a t e r i a l s , except at very low d e n s i t i e s and high c o n f i n i n g s t r e e s e s , there i s always a d i l a t i v e behaviour u n t i l c r i t i c a l s t a t e f o l l o w i n g an i n i t i a l c o n t r a c t i o n . T h i s p o i n t of maximum c o n t r a c t i o n corresponds to a t r a n s i e n t s t a t e of zero volume change. In analogy with t h i s d r a i n e d response, a granular mass when sheared undrained passes through a t r a n s i e n t constant excess pore pressure s t a t e (phase tr a n s f o r m a t i o n ) before i t reaching steady s t a t e a f t e r a decrease i n excess pore pressure (which i s e q u i v a l e n t to a d i l a t i v e b e h a v i o u r ) . As both these undrained s t a t e s correspond to a n u l l r a t e of volume change tend e n c i e s , i t i s of fundamental i n t e r e s t to i n v e s t i g a t e f o r any a s s o c i a t i o n between these s t a t e s and the l a r g e s t r a i n d r a i n e d constant volume s t a t e . In order to i n v e s t i g a t e the above p o s s i b l e a s s o c i a t i o n , a s e r i e s of d r a i n e d t r i a x i a l t e s t s on granular m a t e r i a l s are 4 performed. The f a c t o r s t h a t may have r e l e v a n t i n f l u e n c e on m o b i l i z e d f r i c t i o n a n g l e a t t r a n s i e n t c o n s t a n t volume s t a t e are examined and p o s s i b l e c orrespondence between m o b i l i z e d f r i c t i o n a n g l e s a t maximum c o n t r a c t i o n and c r i t i c a l s t a t e i n d r a i n e d shear and the m o b i l i z e d f r i c t i o n a n g l e a t phase t r a n s f o r m a t i o n i n u n d r a i n e d shear i s i n v e s t i g a t e d i n an attempt t o seek a broader fundamental s i g n i f i c a n c e of <f> . 5 CHAPTER 2 L ITERATURE REVIEW 2.1 G e n e r a l Many researchers have c o n t r i b u t e d to the ex p l a n a t i o n of ex p e r i m e n t a l l y observed phenomena r e l a t e d to s t r e s s s t r a i n and s t r e n g t h response of sands. Most of the l a b o r a t o r y work c a r r i e d out on granular m a t e r i a l s to examine i t s shear behaviour has produced r e l i a b l e i n f o r m a t i o n at small to moderate s t r a i n s . On the other hand, the amount of research work that has been c a r r i e d out toward understanding the f r i c t i o n a l behaviour at c r i t i c a l s t a t e i s r a t h e r l i m i t e d . T h i s chapter reviews the re p o r t e d work on the shearing r e s i s t a n c e of g r a n u l a r m a t e r i a l s with p a r t i c u l a r r e f e r e n c e to the i n v e s t i g a t i o n s p e r t a i n i n g to the constant volume f r i c t i o n angle. Experimental o b s e r v a t i o n s r e g a r d i n g the s t r e s s c o n d i t i o n s at constant volume s t a t e s encountered during d r a i n e d shear l o a d i n g of a c o h e s i o n l e s s mass are a l s o c o n s i d e r e d h e r e i n . 2.2 D r a i n e d S h e a r S t r e n g t h o f C o h e s i o n l e s s M a t e r i a l s The drained shear r e s i s t a n c e of a gr a n u l a r mass at any stage of shear can be represented by a s i n g l e parameter, the m o b i l i z e d angle of f r i c t i o n . At a given r e l a t i v e d e n s i t y three main components of shear r e s i s t a n c e that comprise the peak m o b i l i z e d f r i c t i o n angle have been i d e n t i f i e d (Rowe 1962, Lee 6 and Seed 1967); v i z . i n t r i n s i c s l i d i n g f r i c t i o n ( c o n t r o l l e d by <t>^, the angle of i n t e r p a r t i c l e s l i d i n g f r i c t i o n ) , r e s i s t a n c e to d i l a t i o n and the r e s i s t a n c e to p a r t i c l e rearrangement. T h i s i s s c h e m a t i c a l l y i l l u s t r a t e d in F i g . 2.1. The angle of i n t e r p a r t i c l e f r i c t i o n <f>^ i s g e n e r a l l y b e l i e v e d to be a m a t e r i a l c o n s t a n t , independent of s t r e s s l e v e l and packing d e n s i t y of the g r a n u l a r m a t e r i a l . However, Bowden and Tabor(1964) have observed that the i n t e r p a r t i c l e s l i d i n g f r i c t i o n i s very s e n s i t i v e to s u r f a c e c o n d i t i o n s . In u l t r a c l e a n s u r f a c e s , the j u n c t i o n growth at c o n t a c t p o i n t s were observed to be high, r e s u l t i n g i n an i n c r e a s e d <p^ v a l u e s , whereas su r f a c e contaminations reduced these values remarkably. I n v e s t i g a t i o n s by Horn and Deere (1962) have shown that the presence of pore f l u i d s on s l i d i n g s u r f a c e s g r e a t l y i n c r e a s e d the f r i c t i o n a l c o e f f i c i e n t s of m i n e r a l s having massive c r y s t a l s t r u c t u r e s , such as quartz and f e l d s p a r . On the other hand, minerals having l a y e r l a t t i c e s t r u c t u r e s showed a decrease in f r i c t i o n i n the presence of pore f l u i d s . However, i t was observed that with i n c r e a s i n g s u r f a c e roughness a n t i - l u b r i c a n t e f f e c t of f l u i d on massive s t r u c t u r e d minerals diminished r a p i d l y . D i r e c t shear t e s t s by the same re s e a r c h e r s revealed that p a r t i c l e moisture had no a p p r e c i a b l e i n f l u e n c e on the drained shearing r e s i s t a n c e of sands composed of massive s t r u c t u r e d m i n e r a l s . On the other hand, the d r a i n e d shear r e s i s t a n c e of powdered mica decreased with i n c r e a s i n g surface moisture. 7 Relative Density-percent O 50 100 Initial Porosity F i g . 2.1 Components of Shear Resistance of Sand ( A f t e r Rowe, 1962; Lee and Seed, 1967). 8 The magnitude of shear r e s i s t a n c e c o n t r i b u t i o n due to d i l a t i o n i s known to depend on f a c t o r s such as voids r a t i o , s t r e s s l e v e l , g r a i n a n g u l a r i t y and g r a i n s i z e d i s t r i b u t i o n . At very l a r g e s t r a i n s , granular m a t e r i a l s shear at constant volume and s t r e s s e s . T h i s s t a t e i s r e f e r r e d t o as c r i t i c a l or constant volume s t a t e . T herefore, at t h i s s t a t e the shear s t r e n g t h does not have a d i l a t a n c y component, and the corresponding f r i c t i o n angle i s r e f e r r e d t o as the constant volume f r i c t i o n angle <f> 3 cv Rowe (1962) in h i s s t r e s s d i l a t a n c y theory expressed the a s s o c i a t i o n of the e f f e c t i v e s t r e s s r a t i o o\/o\ (=R) with the s l i p s t r a i n increment r a t i o r e s u l t i n g i n the equation R = K.D, where R = E f f e c t i v e S t r e s s R a t i o D = 1 - d e v / d e a and R = t a n 2 (45+tf>f/2) where e y = volumetric s t r a i n , e a = a x i a l s t r a i n and <j>^ i s the m o b i l i z e d angle of f r i c t i o n l e s s the d i l a t a n c y . I t was observed that the value of tf>f l i e s between the bounds of <j>^ and <t>cv- For loose m a t e r i a l approached <t>cv s i n c e at l a r g e s t r a i n s the corresponding d i l a t a n c y component of the m o b i l i z e d f r i c t i o n angle would tend towards zero. The constant volume f r i c t i o n angle </> at c r i t i c a l s t a t e 3 cv re p r e s e n t s a lower bound of shearing r e s i s t a n c e , and has been suggested to be unique f o r each granular m a t e r i a l , c o n t r o l l e d 9 only by the mineral c o n s t i t u t i n g the g r a i n s . Home (1969) proposed a t h e o r e t i c a l r e l a t i o n s h i p between 0^ and tf>cv and showed ( F i g . 2.2) that the r e l a t i o n s h i p has a c l o s e agreement with experimental o b s e r v a t i o n s . F i g . 2.2 a l s o shows other t h e o r e t i c a l r e l a t i o n s suggested by Caquot (1934) and Bishop (1954). Home's theory was d e r i v e d f o r an assembly of equal rotund p a r t i c l e s . I t s u r p r i s i n g l y agreed with the r e s u l t s f o r rotund p a r t i c l e s of s i m i l a r r e l a t i v e s i z e . He a t t r i b u t e d t h i s to the s t o c h a s t i c nature of the treatment of p a r t i c l e s i n the d e r i v a t i o n of h i s theory. C o n s i d e r i n g the dominant dependence of <p^ on the c o n d i t i o n of s u r f a c e s , agreement of Home's t h e o r e t i c a l r e s u l t s with experimental data would l i k e l y appear to be f o r t u i t o u s . In c o n t r a d i c t i o n to Home's r e s u l t , Skinner (1969) showed that the value of 4>cv does not i n c r e a s e m o n o t o n i c a l l y with i n c r e a s i n g i n t e r p a r t i c l e angle of f r i c t i o n F i g . 2.3. He recognized that the mechanism of p a r t i c l e movement with respect to one another comprised of s l i d i n g and r o l l i n g . Mechanism of r o l l i n g predominates i f the value of <t>^ i s high whereas low «/»^  values cause more s l i d i n g to occur than r o l l i n g . By observing the behaviour of g l a s s b a l l o t i n i i n the shear box under dry and f l o o d e d c o n d i t i o n s , ( w h i c h had corresponding 4>^ values of about 3 and 33 degrees) he observed that the o v e r a l l energy d i s s i p a t i o n was u n a f f e c t e d by <j>^. Skinner i n f e r r e d the value of <t>cv u s i n g the data from shear box t e s t s . T h i s was achieved by e x t r a p o l a t i n g a p l o t of peak 10 40 1 - Home (1969) 2 - Caquot (1934) 3 - B i s h o p (1954) > 20 J I ! I 20 40 C r u s h e d G l a s s F e l d s p a r ( R o s e ) Q u a r t z ( W e l l a n d R i v e r ) Q u a r t z ( M e r s e y R i v e r ) Z i r c o n B r o n z e S p h e r e s 0 G l a s s B a l l o t i n i 1 Range o f V a l u e s f o r S t e e l B a l l s F i g . 2.2 T h e o r e t i c a l R e l a t i o n s h i p s between Constant Volume F r i c t i o n Angle and I n t e r p a r t i c l e F r i c t i o n Angle Compared with Experimental R e s u l t s ( A f t e r Home, 1969) 1 1 F i g . 2.3 Experimental Observations on Constant Volume F r i c t i o n Angle and I n t e r p a r t i c l e F r i c t i o n Angle compared with Previous T h e o r e t i c a l R e l a t i o n s ( A f t e r Skinner, 1969) 12 f r i c t i o n angle vs a non dimensional volume change parameter r e p r e s e n t i n g d i l a t a n c y . E x t r a p o l a t e d value of f r i c t i o n angle corresponding to zero d i l a t a n c y was considered as 0 C V * However, the shear box always underestimates the peak f r i c t i o n angle because of the nature of non uniform d i s t r i b u t i o n of s t r a i n s across the plane of shear. Thus, the numerical value of d , i n f e r e r r e d from these t e s t s would be l i a b l e to e r r o r , cv I t i s recognized by Home (1969) as w e l l as many others that the measurement of and tf>cv i n the l a b o r a t o r y i s a s s o c i a t e d with c o n s i d e r a b l e amount of d i f f i c u l t i e s . Values of <p^ reported i n l i t e r a t u r e show a wide s c a t t e r , probably due to the f a c t o r s d i s c u s e d e a r l i e r . On the other hand, no attempt has been made to o b t a i n enough experimental evidence i n support of the p o s t u l a t e d uniqueness of </> f o r granular m a t e r i a l s . T h i s i s p r i m a r i l y because of the d i f f i c u l t i e s a s s o c i a t e d with shear t e s t i n g over l a r g e s t r a i n s at which <j>cv i s m o b i l i z e d . Given below i s a b r i e f overview of the r e p o r t e d experimental work r e l a t e d to l a r g e s t r a i n d r a i n e d t e s t s on granular m a t e r i a l s , i n an attempt t o d e f i n e 0 C V « 2.3 Large S t r a i n Tests Roscoe et a l . (1958) i n v e s t i g a t e d the v a l i d i t y of the s t a t e boundary s u r f a c e and c r i t i c a l v o i d s r a t i o concepts f o r granular m a t e r i a l s . I n i t i a l l y they c a r r i e d out t r i a x i a l t e s t s on granular media and found that the s c a t t e r of the observed v o i d r a t i o s at c r i t i c a l s t a t e were h i g h due to sample non 13 u n i f o r m i t i e s at l a r g e s t r a i n s , e s p e c i a l l y f o r dense samples. A l t e r n a t i v e use of the simple shear apparatus y i e l d e d c r i t i c a l v o i d r a t i o s with a l e s s e r s c a t t e r f o r t e s t s on lead shots ( F i g . 2.4) and g l a s s beads. However, the simple shear t e s t s on rounded Leighton Buzzard sand and e s p e c i a l l y on angular Hauxton sand produced r e s u l t s with an i n c r e a s e d s c a t t e r . Roscoe et a l . ( l 9 6 3 ) have a l s o r e p o r t e d the r e s u l t s of d r a i n e d t r i a x i a l t e s t s c a r r i e d out on Leighton Buzzard sand, i n t h e i r attempt to i n v e s t i g a t e a y i e l d c r i t e r i o n f o r sands. The volume change c h a r a c t e r i s t i c s f o r the d r a i n e d compression t e s t s are reproduced i n F i g . 2.5. These r e s u l t s c l e a r l y show that the o v e r a l l volume change of the specimens were s t e a d i l y i n c r e a s i n g even a f t e r an a x i a l s t r a i n of 30-40%, and thus no approach to 0 c v i s i n d i c a t e d . Cole (1967) conducted l a r g e s t r a i n t e s t s on Leighton Buzzard sand using the simple shear apparatus. He found that the average voids r a t i o of i n i t i a l l y loose samples a t t a i n e d a constant value at l a r g e s t r a i n s , but the v o i d s r a t i o s of i n i t i a l l y medium to dense samples were s t i l l i n c r e a s i n g at l a r g e s t r a i n s . I t was a l s o observed that the s t r e s s r a t i o s t a r t s to r i s e again at very l a r g e s t r a i n s , probably due to the e x c e s s i v e d i s t o r t i o n of the sample, F i g . 2.6. Cole's measured value of 6 f o r loose sand overestimated the same cv obtained from t r i a x i a l t e s t s . The value of <p . i s a lower cv bound to the shearing r e s i s t a n c e of a g r a n u l a r mass. The above r e s u l t s t h e r e f o r e i n d i c a t e that the values of <p estimated by 14 5 10 15 Displacement of shear box (mm) F i g . 2.4 Re s u l t s of Simple Shear T e s t s on 1 mm S t e e l B a l l s with a Normal S t r e s s of 1.4 kg/cm 2 ( A f t e r Roscoe et a l . , 1958) 15 F i g . 2.5 V a r i a t i o n of Volumetric S t r a i n with Shear S t r a i n During Drained T r i a x i a l T e s t s on Leighton Buzzard Sand. ( A f t e r Roscoe e t . a l . , 1963) 16 0.8 2 Vol / to » 0.4 I?/ 0 Dense •f. Medium Dense X Loose 0-75 0.65 •O 0.60] 0.55 02 0.4 0.6 0.8 IO 1.2 / / / o / o / / F i g . 2.6 S t r e s s S t r a i n D a t a f o r Th 17 the simple shear apparatus would be even f u r t h e r away from t h i s a c t u a l lower bound, suggesting t h i s to be no b e t t e r a l t e r n a t i v e to the t r i a x i a l apparatus in the measurement of In order to study the l i q u e f a c t i o n phenomena of sands, Castro (1969) c a r r i e d out a s e r i e s of l a b o r a t o r y t e s t s on three sands of d i f f e r e n t minerology. Large s t r a i n d r a i n e d t e s t s conducted in order to o b t a i n i n f o r m a t i o n on c r i t i c a l v oids r a t i o are c o n s i d e r e d h e r e i n ( F i g . 2.7). For d r a i n e d t r i a x i a l t e s t s on i n i t i a l l y dense specimen ( t e s t 1-4) a f a i l u r e plane developed i n the sample at moderate s t r a i n s during shear, and on f u r t h e r shearing the s t r a i n s were concentrated i n the volume of the sand adjacent to t h i s plane. Due to t h i s the volume change measured for the e n t i r e sample was not r e p r e s e n t a t i v e f o r the zone of shear f a i l u r e i n which the increase i n v o i d s r a t i o i s c o n s i d e r a b l y g r e a t e r . His r e s u l t s c l e a r l y show that even a f t e r shearing to l a r g e s t r a i n s (above 20% - a x i a l ) the o v e r a l l volume response of the sample i s s t i l l d i l a t a n t . T h i s i s i n agreement with the o b s e r v a t i o n s by Roscoe et a l . (1963). For a t e s t on a l o o s e sample ( t e s t 1-1, with an i n i t i a l r e l a t i v e d e n s i t y < 30%) a constant volume s t a t e appears to be approached a f t e r an a x i a l s t r a i n of about 20%. These o b s e r v a t i o n s i n d i c a t e that the accurate determination of 4>CV f o r an i n i t i a l l y dense t r i a x i a l sample i s a v i r t u a l l y impossible task. F u r t h e r , L u p i n i et a l . (1981) have repo r t e d the o b s e r v a t i o n s on the t e s t i n g of c l a y s by 18 F i g . 2.7 R e s u l t s of D r a i n e d T r i a x i a l T e s t s on Ottawa Banding Sand ( A f t e r C a s t r o , 1969) 19 Herrmann and Wolf s k i l l (1966) and Blondeau and Josseaume (1976). They concluded that the t e s t i n g of c l a y s in the t r i a x i a l apparatus always overestimated the r e s i d u a l shear s t r e n g t h . Vesic and Clough (1968) have conducted an e x t e n s i v e i n v e s t i g a t i o n on the drained t r i a x i a l shear behaviour of Chattahoochee r i v e r sand, over a c o n f i n i n g s t r e s s e s ranging from about 100 kPa to 300 MPa. I t was observed that the d i l a t a n c y e f f e c t s g r a d u a l l y d i m i n i s h e d with i n c r e a s i n g confinement. The value of the peak f r i c t i o n angle ( f r i c t i o n angle at f a i l u r e ) observed f o r loose and dense samples at d i f f e r e n t s t r e s s l e v e l s are reproduced i n F i g . 2.8. Above a p a r t i c u l a r s t r e s s l e v e l (which i s recognized as the breakdown s t r e s s by V e s i c and Clough) samples s u b j e c t e d to shearing c o n t r a c t e d a l l the way upto f a i l u r e , i r r e s p e c t i v e of the i n i t i a l packing d e n s i t y . No d i s t i n c t f a i l u r e plane was observed f o r dense samples, even at l a r g e s t r a i n s . They a l s o n o t i c e d that the m o b i l i z e d f r i c t i o n angle at f a i l u r e was v i r t u a l l y constant f o r c o n f i n i n g s t r e s s l e v e l s above the breakdown s t r e s s . I t i s i n t e r e s t i n g to note that the peak f r i c t i o n angle f o r loose samples y i e l d e d almost an i d e n t i c a l value to the above, throughout the whole s t r e s s range. These r e s u l t s i n d i c a t e the e x i s t e n c e of a constant volume f r i c t i o n angle independent of the value of the s t r e s s l e v e l and i n i t i a l d e n s i t y , provided the s t r e s s l e v e l i s very l a r g e (above the breakdown s t r e s s ) . However, at lower c o n f i n i n g s t r e s s e s t h i s 20 50 • Dense samples ' I 1 I ' ' I I I I J I L 102 IO 3 10 4 IO5 P'(kN m" 2 ) F i g . 2.8 Peak F r i c t i o n Angle f o r Chattahoochee River Sand Tested at D i f f e r e n t Normal S t r e s s L e v e l s ( A f t e r V e s i c and Clough, 1969) 21 was not observed, as the peak f r i c t i o n angle was found dependent on the i n i t i a l d e n s i t y and thus having no coi n c i d e n c e with the constant volume f r i c t i o n angle. The experimental work d e s c r i b e d above, attempt to make a d i r e c t measurement of 0„„ from the o b s e r v a t i o n s . On the other cv hand, an i n d i r e c t assessment of 0 c v can be made by e x t r a p o l a t i o n of t r i a x i a l t e s t data. The same approach on d i r e c t shear data by Skinner (1969) was d e s c r i b e d e a r l i e r . However, i n order to study the p o s s i b l e uniqueness of 0 c v i t i s e s s e n t i a l to have a d i r e c t measuring technique. The t e s t i n g device used i n the measurement of 0 should possess the a b i l i t y to shear a sample to very l a r g e s t r a i n s while e x e r t i n g the l e a s t d i s t o r t i o n to the sample geometry. T h i s would imply a homogeneous s t a t e of s t r e s s a d m i n i s t e r e d on the plane of shear. Among the shear t e s t i n g d e v i c e s the r i n g shear apparatus seem to meet these requirements i n many r e s p e c t s . Saada and Townsend (1981) have recognized the use of r i n g shear device i n the measurement of l a r g e s t r a i n behaviour. T e s t s on non p l a s t i c c l a y s by Skempton (1985) have f u r t h e r supported these views. The c r i t e r i a f o r a s s e s s i n g the achievement of 0 c v s t a t e i n t r i a x i a l t e s t s should be viewed both i n terms of s t r e s s e s and v o l u m e t r i c s t r a i n . T r i a x i a l r e s u l t s i n terms of s t r e s s e s achieve a s e n s i b l y constant s t a t e at l a r g e s t r a i n s . However the v o l u m e t r i c s t r a i n does not reach a constant s t a t e i n most 22 of the c a s e s . On the o t h e r hand, i n the r i n g shear d e v i c e the c r i t e r i a f o r # c v i s o n l y of s t r e s s , s i n c e the sample c o u l d be sheared i n d e f i n i t e l y u n t i l the c r i t i c a l s t a t e which a u t o m a t i c a l l y e s t a b l i s h e s the c o n s t a n t volume c o n d i t i o n . The concept t h a t # c v r e p r e s e n t s the lower bound of s h e a r i n g r e s i s t a n c e would suggest t h a t <j>cv from r i n g shear t e s t s would be i n v a r i a b l y l e s s than t h a t from the t r i a x i a l t e s t s . A b r i e f r e v i e w of a p p l i c a b i l i t y of d i f f e r e n t t e s t d e v i c e s i s a l s o g i v e n i n the next Chapter. From the s e o b s e r v a t i o n s i t can be c o n c l u d e d t h a t none of the p r e v i o u s work have p r o v i d e d r e l i a b l e i n f o r m a t i o n on the c o n s t a n t volume f r i c t i o n a n g l e of g r a n u l a r m a t e r i a l s . Having i d e n t i f i e d the s t r o n g need and the p o t e n t i a l of u s i n g the r i n g shear d e v i c e i n t h i s r e s p e c t , i t was d e c i d e d t o i n v e s t i g a t e the c o n s t a n t volume f r i c t i o n a n g l e f o r a wide range of g r a n u l a r m a t e r i a l s , which i s the main o b j e c t i v e of t h i s t h e s i s . 2.4 T r a n s i e n t C o n s t a n t Vo lume S t a t e s D u r i n g S h e a r A ve r y l o o s e g r a n u l a r m a t e r i a l s u b j e c t e d t o d r a i n e d shear w i l l c o n t r a c t a l l the way u n t i l the c r i t i c a l s t a t e i s a t t a i n e d . C o n t r a c t i v e b e h a v i o u r i s not o n l y governed by the i n i t i a l p a c k i n g d e n s i t y but a l s o by the c o n f i n i n g p r e s s u r e d u r i n g s h e a r . A d i l a t i v e sample under one c o n f i n i n g p r e s s u r e c o u l d e x h i b i t c o n t r a c t i v e b e h a v i o u r when sheared under a 23 higher c o n f i n i n g pressure (Lee and Seed, 1967). At most packing d e n s i t i e s and c o n f i n i n g pressures, there i s an i n i t i a l c o n t r a c t i o n which i s followed by d i l a t i o n u n t i l the c r i t i c a l s t a t e i s a t t a i n e d . The po i n t of maximum c o n t r a c t i o n corresponds to a s t a t e of t r a n s i e n t constant volume. A q u a l i t a t i v e correspondence between the m o b i l i z e d f r i c t i o n angle tf> at the i n s t a n t of maximum c o n t r a c t i o n and the value 3 mc of 0 c v was suggested by Atkinson and Bransby (1978), F i g . 2.9. However, no experimental evidence i n support of t h i s concept has been presented. Undrained behaviour of sands has been the focus of a t t e n t i o n i n the recent past mainly due to many c a t a s t r o p h i c f a i l u r e s a s s o c i a t e d with l i q u e f a c t i o n of s a t u r a t e d sands due to earthquakes and impact l o a d i n g . On undrained shearing a satur a t e d g r a n u l a r m a t e r i a l u l t i m a t e l y reaches a steady s t a t e c h a r a c t e r i z e d by deformation at constant volume, s t r e s s e s and v e l o c i t y (Poulos, 1981; Castro et a l . , 1982). The f r i c t i o n angle m o b i l i z e d at steady s t a t e has been shown to be unique f o r a given g r a n u l a r m a t e r i a l . A c l e a r analogy can be e s t a b l i s h e d between the dr a i n e d shear c h a r a c t e r i s t i c s of a granular mass and the undrained behaviour of the same. Undrained shearing of a loose c o n t r a c t i v e g r a n u l a r m a t e r i a l w i l l r e s u l t i n r i s i n g excess pore pr e s s u r e s a l l the way u n t i l the steady s t a t e i s a t t a i n e d , where the pore pressure remains constant. In g e n e r a l , over a range of v o i d s r a t i o and s t r e s s e s , undrained shear causes the pore pressure to r i s e 24 Expansion F i g . 2.9 T y p i c a l S t r e s s S t r a i n B ehaviour f o r a D r a i n e d T r i a x i a l T e s t on a Dense Sand ( A f t e r A t k i n s o n and Bransby, 1978) 25 i n i t i a l l y a n d t h e a p p r o a c h t o s t e a d y s t a t e o c c u r s a f t e r a d i l a t i v e b e h a v i o u r a s s o c i a t e d w i t h p o r e p r e s s u r e d r o p . I s h i h a r a (1975) d e s i g n a t e d t h e p o i n t o f maximum p o r e p r e s s u r e m e n t i o n e d a b o v e ( w h i c h i s a t r a n s i e n t c o n s t a n t p o r e p r e s s u r e s t a t e ) a s t h e p h a s e t r a n s f o r m a t i o n s t a t e . I n v e s t i g a t i o n s by V a i d a n d C h e r n (1985) h a v e r e v e a l e d t h a t t h e f r i c t i o n a n g l e s , 0 p T ' m o b i l i z e d a t t h e i n s t a n t o f p h a s e t r a n s f o r m a t i o n a n d a t s t e a d y s t a t e a r e i d e n t i c a l a n d a u n i q u e p r o p e r t y o f t h e m a t e r i a l . A l t h o u g h much r e s e a r c h work h a s b e e n c a r r i e d o u t on t h e b e h a v i o u r o f s a n d s u n d e r d r a i n e d a n d u n d r a i n e d c o n d i t i o n s i n i s o l a t i o n , n o t many a t t e m p t s h a v e b e e n made t o draw any c o r r e s p o n d e n c e b e t w e e n t h e two d r a i n a g e c o n d i t i o n s . L u o n g (1980) h a s s u g g e s t e d t h a t t h e f r i c t i o n a n g l e <t>mc m o b i l i z e d a t maximum c o n t r a c t i o n i n d r a i n e d s h e a r i s i d e n t i c a l t o t h e f r i c t i o n a n g l e a t p h a s e t r a n s f o r m a t i o n i n u n d r a i n e d s h e a r . T h i s i m p o r t a n t o b s e r v a t i o n h a s n o t . b e e n c o r r o b o r a t e d by c o n c l u s i v e e x p e r i m e n t a l e v i d e n c e . U n d r a i n e d s t e a d y s t a t e a n d t h e d r a i n e d c r i t i c a l s t a t e a p p e a r i n t u i t i v e l y a n a l o g o u s . Y e t , no s u g g e s t i o n h a s b e e n made a s t o t h e i r e q u i v a l e n c e n o r a n y e x p e r i m e n t a l e v i d e n c e s o u g h t w h i c h m i g h t i n d i c a t e s u c h an e q i v a l e n c e . 26 CHAPTER 3 EXPERIMENTAL ASPECTS 3.1 Measurement of Constant Volume F r i c t i o n angle 3.1.1 Laboratory Shear T e s t i n g Devices Shear t e s t i n g d e v i c e s s h o u l d enable development of l a r g e u n i - d i r e c t i o n a l shear d i s p l a c e m e n t s i n the measurement of <p cv Homogeneous s t r e s s and s t r a i n c o n d i t i o n s s h o u l d p r e v a i l a l o n g the shear p l a n e d u r i n g the p r o c e s s of d e f o r m a t i o n . In the study of s t r e s s s t r a i n and s t r e n g t h b e h a v i o u r of s o i l s i n the l a b o r a t o r y , t r i a x i a l , d i r e c t shear and s i m p l e shear a p p a r a t u s ar e commonly used. These a p p a r a t u s a r e n o r m a l l y i n t e n d e d f o r the measurement of peak shear s t r e n g t h of s o i l s . H e r e i n , i t would be i n o r d e r t o a s s e s s t h e performance of t h e s e d e v i c e s as t o t h e i r a b i l i t y f o r shear t e s t i n g over l a r g e s t r a i n s . Saada and Townsend (1981) have p r e s e n t e d an e x t e n s i v e review and e v a l u a t i o n of the advantages and l i m i t a t i o n s of v a r i o u s l a b o r a t o r y shear t e s t i n g d e v i c e s . Given below i s a b r i e f o verview of the performance of shear t e s t i n g d e v i c e s , w i t h r e f e r e n c e t o measurements a t l a r g e s t r a i n s i n p a r t i c u l a r . C o n v e n t i o n a l t r i a x i a l t e s t a p p r o x i m a t e s the i d e a l i z e d assumptions of homogeneity of s t r e s s and s t r a i n , p r o v i d e d the d e f o r m a t i o n s a re s m a l l . However, a t pos t peak s t r a i n l e v e l s , samples may d e v e l o p e x t e n s i v e non homogeneity of s t r e s s and s t r a i n . The degree of non homogeneity a t pos t peak s t r a i n s i s 27 more s i g n i f i c a n t i n the case of d i l a t i v e or dense samples, when compared to the c o n t r a c t i v e or loose samples. S t r e s s non u n i f o r m i t y at l a r g e s t r a i n s in t r i a x i a l t e s t i n g c o u l d a l s o develop due to end r e s t r a i n t s , which i n h i b i t the f r e e r a d i a l deformation of the sample. Use of l u b r i c a t e d or f r i c t i o n l e s s end p l a t e n s s i g n i f i c a n t l y reduce t h i s e f f e c t , s t i l l w i t h i n bounds of a f i n i t e s t r a i n l e v e l (Rowe and Barden, 1964). Very l a r g e s t r a i n s cannot be achieved without the expense of homogeneity of s t r e s s and s t r a i n c o n d i t i o n s . Therefore the t r i a x i a l t e s t may be l e s s d e s i r a b l e f o r use in the determination of the constant volume f r i c t i o n angle, which i s m o b i l i z e d at l a r g e s t r a i n s . D i r e c t shear .test has been used f o r the measurement of r e s i d u a l s t r e n g t h of c l a y s . In the case of c l a y s l a r g e s t r a i n s are obtained by repeated r e v e r s a l of the s h e a r i n g d i r e c t i o n or by repeated u n i d i r e c t i o n a l shear. Clay samples are sometimes pre-cut along the shear plane in order to achieve the c r i t i c a l s t a t e e a s i l y . However i n a t e s t c a r r i e d out on a granular m a t e r i a l these techniques become i m p r a c t i c a l . In a d d i t i o n , under d i r e c t shear the d e f i n i t i o n of the s t r e s s s t a t e i s q u i t e e r r a t i c e s p e c i a l l y at l a r g e s t r a i n s due to c o n t i n u o u s l y changing c r o s s s e c t i o n a l area of the shear plane. The simple shear device has been found to be an a t t r a c t i v e a l t e r n a t i v e to the d i r e c t shear t e s t in the measurement of shear s t r e n g t h on account of i t s a b i l i t y to 28 impose more uniform s t a t e of s t r a i n . The l i m i t a t i o n s of the simple shear apparatus i n the measurement of </>cv i n terms of Cole's (1967) experimental work have a l r e a d y been d i s c u s s e d i n Chapter 2. The f o r e g o i n g aspects r e v e a l that the shear t e s t i n g d e v i c e s i n common use have c o n s i d e r a b l e drawbacks as regards to the measurement of p r o p e r t i e s at l a r g e s t r a i n s . In order to o b t a i n , more r e l i a b l e i n f o r m a t i o n at these s t r a i n l e v e l s the need to u t i l i z e an a l t e r n a t i v e form of a shear device cannot be overemphasized. In the r i n g shear apparatus, the s o i l sample posseses an annular geometry. The normal load i s a p p l i e d i n the a x i a l d i r e c t i o n and the shear f o r c e i s a p p l i e d as a torque about the c e n t r a l a x i s . Due to t h i s the top part of the annular sample shears a g a i n s t the bottom. The a t t r a c t i v e f e a t u r e of the r i n g shear apparatus i s i t s a b i l i t y to impose u n l i m i t e d u n i - d i r e c t i o n a l shear s t r a i n s on the sample while p r e s e r v i n g a uniform s t r e s s s t a t e on the plane of shear. The s t r a i n r a t e r a d i a l l y a c r o s s the shear plane i s not uniform as the sample i s subjected to a constant angular displacement r a t e . However t h i s c o u l d be minimized by s e l e c t i n g the sample with l a r g e diameter and small annular t h i c k n e s s . The v a r i a t i o n i n s t r a i n r a t e c o u l d have a s i g n i f i c a n t i n f l u e n c e i n t e s t i n g of c l a y s , as i t a f f e c t s the d i s s i p a t i o n of excess pore p r e s s u r e s . However, i n the case of a g r a n u l a r m a t e r i a l excess pore 29 pressures w i l l normally not develop due to i t s high p e r m e a b i l i t y . Admittedly, the r i n g shear device does not provide u s e f u l i n f o r m a t i o n r e g a r d i n g small deformation response and thus i t s use i s l i m i t e d to l a r g e displacement measurements at which </> , i s m o b i l i z e d . Based on these c o n s i d e r a t i o n s , the r i n g shear d e v i c e was c o n s i d e r e d s u i t a b l e for t h i s i n v e s t i g a t i o n of constant volume f r i c t i o n angle of granular m a t e r i a l s . 3.1.2 UBC Ring Shear Device The UBC r i n g shear apparatus was designed and developed by Bosdet (1980), with the main o b j e c t i v e of measuring r e s i d u a l s t r e n g t h of c l a y s . Only a b r i e f account of the device w i l l be given here. A more d e t a i l e d d e s c r i p t i o n may be found in Bosdet (1980). Sine the d e v i c e was o r i g i n a l l y designed to c a t e r f o r t e s t s on c l a y s , c e r t a i n m o d i f i c a t i o n s were r e q u i r e d before the t e s t s on granular m a t e r i a l s c o u l d be performed. D e t a i l s of these changes are given i n s e c t i o n 3.1.3. A schematic s e c t i o n of the UBC r i n g shear device i d e n t i f y i n g main components i s given i n F i g . 3.1. An annular s o i l sample i s c o n f i n e d between an upper and lower p a i r s of c o n f i n i n g r i n g s . Inner and outer r a d i i of the sample are 44.5 and 70 mm, r e s p e c t i v e l y . The height of the sample v a r i e s s l i g h t l y f o r each t e s t , but on the average equals about 20 mm. Top and bottom faces of the sample are i n c o n t a c t with annular porous s t a i n l e s s s t e e l p l a t e n s having p r o t r u d i n g r i b s f o r 30 Major Components 1. A n n u l a r S o i l S ample 2. U p p e r a n d Lower O u t s i d e C o n f i n i n g R i n g s ' 3. U p p e r a n d Lower I n s i d e C o n f i n i n g R i n g s 4. P o r o u s S t a i n l e s s S t e e l P l a t e n s 5. T u r n t a b l e 6. T u r n t a b l e B a s e 7. Moment T r a n s f e r Arms 8. Moment M e a s u r i n g F o r c e T r a n s d u c e r s 9. C o n f i n i n g R i n g Gap 10. A i r P i s t o n 11. W a t e r R e s e r v o i r Major Components of UBC R i n g Shear D e v i c e ( A f t e r B o s d e t , 1980) t r a n s f e r i n g shear. The lower c o n f i n i n g r i n g and the porous d i s c are fastened to the t u r n t a b l e which i s r o t a t e d at a s e l e c t e d r a t e . The t u r n t a b l e i s d r i v e n by a d.c. servo motor with a heavy duty gear head and a c h a i n d r i v e . The movement of the upper c o n f i n i n g r i n g and the upper porous d i s c i s r e s t r a i n e d by the moment t r a n s f e r arms, which r e s t a g a i n s t two l o a d c e l l s used i n the measurement of the r e s i s t i n g torque. T h i s r e s t r a i n t on the upper r i n g and the r o t a t i o n of the lower r i n g along with the t u r n t a b l e causes the shearing of the sample i n a h o r i z o n t a l p l a n e . A small gap between the upper and lower r i n g s (about 0.025 to 0.050 mm) i s maintained i n order to a v o i d metal to metal co n t a c t between the two r i n g s while minimizing the l o s s of m a t e r i a l d u r i n g s h e a r i n g . The normal load i s a p p l i e d to the sample by an a i r p i s t o n e x c i t e d with a r e g u l a t e d a i r supply. 3.1.3 M o d i f i c a t i o n s to UBC Ring Shear Device As mentioned i n s e c t i o n 3.1.2 c e r t a i n m o d i f i c a t i o n s were r e q u i r e d on the o r i g i n a l r i n g shear d e v i c e i n order to f a c i l i t a t e the t e s t i n g of g r a n u l a r m a t e r i a l s . For p r e p a r a t i o n of c l a y samples, the remoulded s o i l i s p l a c e d u n i f o r m l y w i t h i n the upper c o n f i n i n g r i n g which i s f i x e d to the moment t r a n s f e r arms. T h i s u n i t i s then f l i p p e d upside down, mounted on the r i n g shear device and the s o i l s lowly pushed i n t o the lower c o n f i n i n g r i n g u n t i l i t s i t s on the lower porous p l a t e . C l e a r l y , t h i s procedure cannot be adopted i n the p r e p a r a t i o n 32 of a c o h e s i o n l e s s sample. For p r e p a r i n g samples of granular c o h e s i o n l e s s m a t e r i a l s , the upper c o n f i n i n g r i n g i s p o s i t i o n e d over the lower c o n f i n i n g r i n g and both are h e l d t i g h t l y in v e r t i c a l alignment by means of an a d j u s t a b l e s t e e l t e n s i o n b e l t . Granular sample i s then p l u v i a t e d i n t o the sample c a v i t y . A f t e r l e v e l l i n g the s u r f a c e the moment arm with the upper porous d i s c i s lowered on to the sample. The moment arm i s connected to the upper c o n f i n i n g r i n g by means of the connecting b o l t s as shown in Fig.3.2. I t i s necessary to make sure that the holes i n the moment arms and the upper c o n f i n i n g r i n g are p r o p e r l y a l i g n e d i n order to accomodate the b o l t s . T h i s i s achieved by having two l o c a t i n g p i n s on the moment arm as shown in F i g . 3.2. In order to c a l c u l a t e the normal s t r e s s on the plane of shear dur i n g the s h e a r i n g process, the values of the a p p l i e d normal load as w e l l as the s i d e f r i c t i o n on the w a l l s of the upper c o n f i n i n g r i n g are r e q u i r e d . The o r i g i n a l design of the r i n g shear device had the c a p a b i l i t y to measure the s i d e f r i c t i o n p r ovided i t i s a c t i n g downwards ( i . e . a compressive lo a d on the lower l o a d c e l l ) . In the case of granular m a t e r i a l s , upward a c t i n g side f r i c t i o n i s o f t e n encountered due to g e n e r a l l y d i l a t i v e behaviour u n t i l r e a l i z a t i o n of constant volume c o n d i t i o n . The measurement of s i d e f r i c t i o n (upward or downward) i s achieved by c o n n e c t i n g the bottom lo a d c e l l to both the c e n t r e support s h a f t and the base p l a t e by means of a threaded con n e c t i o n . ( F i g . 3 . 3 ) . 33 F i g . 3.2 M o d i f i c a t i o n s t o the Upper R i n g Assembly of the Ring Shear A p p a r a t u s C e n t r a l S u p p o r t i n g S h a f t T h r e a d e d C o n n e c t i o n F i g . 3.3 M o d i f i c a t i o n s t o t h e L o w e r L o a d C e l l C o n n e c t i o n M e a s u r i n g S i d e F r i c t i o n F o r c e s i n t h e R i n g S h e a r D e v i c e 35 In t e s t i n g g r a n u l a r metals, the f o r c e s exerted on the r i b s on the porous p l a t e s at the sample ends are much g r e a t e r . T h e r e f o r e for t e s t s on copper p a r t i c l e s and lead shots, the o r i g i n a l porous p l a t e with t r a c t i o n blades was replaced by an annular m i l d s t e e l d i s c machined to have r i b s i n m o n o l i t h i c c o n n e c t i o n . The torque r e q u i r e d to shear a g r a n u l a r m a t e r i a l i n the r i n g shear device i s c o n s i d e r a b l y higher than that r e q u i r e d f o r shearing c l a y s . T h i s r e q u i r e d an upgrading of the d r i v e system by i n c r e a s i n g the speed of the servo motor, and c a p a c i t i e s of the gearhead and the c h a i n d r i v e . Shearing r a t e s i n the upgraded system can be v a r i e d between 80 mm/year to 1 m/hr. Granular m a t e r i a l s can be sheared at a much f a s t e r r a t e . Because of t h e i r high p e r m e a b i l i t y , no excess pore pressure would develop i f the m a t e r i a l was s a t u r a t e d . 3.1.4 Measurement of Loads and Displacements A schematic r e p r e s e n t a t i o n of the measuring devices i n the r i n g shear apparatus i s giv e n i n Fig.3.4. A l l the tran s d u c e r s were e x c i t e d by a common power supply of 5 v o l t s . Load c e l l s were used to measure the top normal load a p p l i e d by the a i r p i s t o n and s i d e f r i c t i o n i n the upper c o n f i n i n g r i n g . Torque was obtained by f o r c e measurement on two load c e l l s r e s t i n g a g a i n s t the moment arms. The angular displacement of the t u r n t a b l e was converted to a v e r t i c a l displacement through a spur gear and screw arrangement. T h i s displacement as we l l 36 Turntable LC2 LVDT1 Power Input Power Supply S t r i p Chart Recorder LCI Load C e l l Measuring A p p l i e d Load LC2 Load C e l l Measuring Side F r i c t i o n TLC1 Load C e l l f o r Torque Measurements TLC2 Load C e l l f o r Torque Measurements LVDT1 To Measure Changes i n Sample Height LVDT2 To Measure Sample Shear Displacement F i g . 3.4 S c h e m a t i c o f t h e M e a s u r i n g D e v i c e s i n t h e R i n g S h e a r A p p a r a t u s 37 as changes i n height of the sample due to compression during normal s t r e s s a p p l i c a t i o n , d i l a t i o n or c o n t r a c t i o n and minor l o s s of sand g r a i n s , were measured using displacement t r a n s d u c e r s . A l l transducer s i g n a l s were recorded on two s t r i p c h a r t r e c o r d e r s . 3.2 D e t e r m i n a t i o n o f M o b i l i z e d F r i c t i o n A n g l e a t Maximum C o n t r a c t i o n 3 .2 .1 T r i a x i a l A p p a r a t u s T r i a x i a l apparatus was used i n the determination of the m o b i l i z e d f r i c t i o n angle at maximum c o n t r a c t i o n d u r i n g d r a i n e d shear. A schematic diagram of the t e s t setup i s shown i n F i g . 3.5. Saturated t e s t specimens were shear loaded i n i t i a l l y i n s t r e s s c o n t r o l l e d mode fo l l o w e d by s t r a i n c o n t r o l l e d l o a d i n g at post peak s t r a i n s . S t r e s s c o n t r o l l e d l o a d i n g was done with an a i r p i s t o n , whereas duri n g s t r a i n c o n t r o l l e d l o a d i n g , the a i r p i s t o n was hel d at i t s top dead centr e and the b a s a l p l a t f o r m was r a i s e d at a d e s i r e d r a t e . Test specimens were 5 cm i n diameter and 10 cm i n h e i g h t . 3 . 2 . 2 Mea su rement o f L o a d s , D i s p l a c e m e n t s and Vo lume Change E l e c t r o n i c t r a n s d u c e r s were used to measure the a x i a l l o a d, pore and c e l l p r e s s u r e s , a x i a l displacement and volume change. Both a x i a l and vol u m e t r i c s t r a i n s c o u l d be determined to a comparable accuracy of 10"" which allowed p r e c i s e d e f i n i t i o n of p o i n t s of maximum c o n t r a c t i o n . F u r t h e r 38 C o m p r e s s e d A i r S u p p l y A i r P i s t o n L o a d C e l l To R e c o r d e r LVDT Sample L o a d i n g P l a t f o r m To R e c o r d e r D i f f . P r e s s u r e T r a n s d u c e r P o r e P r e s s u r e T r a n s d u c e r To R e c o r d e r F i g . 3.5 S c h e m a t i c o f t h e M e a s u r i n g D e v i c e s i n t h e T r i a x i a l A p p a r a t u s 39 c o n s i d e r a t i o n s and improvement of apparatus f o r small s t r a i n s have been d i s c u s s e d by Negussey (1984). Transducer s i g n a l s were fed i n t o a Fluke Data A c q u i s i t i o n system coupled to an IBM p e r s o n a l computer. Acquired data was reduced simultaneously and both the a c q u i r e d and reduced data were s t o r e d in magnetic d i s k e t t e s . 3.3 Materials Tested A wide spectrum of g r a n u l a r m a t e r i a l s were s e l e c t e d f o r t h i s i n v e s t i g a t i o n . In order to minimize the l o s s of g e n e r a l i t y , g r a n u l a r m a t e r i a l s ranging from minerals to metals were t e s t e d . M a t e r i a l s used i n the study and t h e i r r e l e v a n t p h y s i c a l p r o p e r t i e s are given i n Table 3.1. Medium Ottawa sand, a p r i m a r i l y quartz m a t e r i a l from Ottawa, I l l i n o i s , was used as the c o n t r o l m a t e r i a l f o r t h i s i n v e s t i g a t i o n . The p a r t i c l e s i z e d i s t r i b u t i o n of t h i s m a t e r i a l , conforms to the l i m i t s s p e c i f i e d by ASTM d e s i g n a t i o n C-109-69, i s i l l u s t r a t e d i n F i g . 3.6 along with the g r a d a t i o n s f o r the other sands used i n t h i s study. Medium Ottawa sand has a D 5 0 value of 0.4 mm. Fine Ottawa sand with i d e n t i c a l minerology but with a D 5 0 of 0.2 mm was used to study the p o s s i b l e e f f e c t of p a r t i c l e s i z e on the value of <t>cv- F i n e r and coarser p a r t i c l e s of g r a n u l a r copper were a l s o used to study the e f f e c t of p a r t i c l e s i z e on <j> . 40 T a b l e No. 3.1 P h y s i c a l P r o p e r t i e s o f t h e M a t e r i a l s T e s t e d Material Composition G s e max e m i n (mm) Shape Ottawa sand (C 109) 100% quartz 2.67 0. 82 0. 50 0.4 Rounded Ottawa sand (Fine) 1002 quartz 2.67 0. 86 0. 56 0.2 Rounded T a i l i n g Sand (Brenda Mines) ~652 feldspar ~ 35% quartz 2.70 1. 060 0. 688 0.A Angular T a i l i n g Sand (Lornex Mine) ~63% feldspar ~33% quartz 2.70 0.4 Angular Granular Copper (Coarse) 8.92 1.0 Rounded Granular Copper (Fine) 8.92 0.6 Cylind-r i c a l Lead Shots 11.35 1.4 Rounded Glass Beads 2.50 0.4 Rounded 41 F i g . 3.6 P a r t i c l e S i z e D i s t r i b u t i o n s f o r Sands Used i n the t e s t i n g Program T a i l i n g s sands obtained from two copper and molybdenum mines i n B r i t i s h Columbia (Brenda and Lornex) were employed in the t e s t i n g program i n order to i n v e s t i g a t e the i n f l u e n c e of minerology on </»cv« V i s u a l i n s p e c t i o n i n d i c a t e d that both t a i l i n g s sands have v i r t u a l l y the same minerology and composed of about 2/3 f e l d s p a r and the remainder q u a r t z . The orebody compositions r e p o r t e d by Waldner et a l . (1976) and S o r e g a r o l i (1974) fo r Lornex and Brenda mines r e s p e c t i v e l y r e v e a l that the parent rocks were predominantly f e l d s p a r with a quartz component of about 25%. T a i l i n g s sand i s the r e s i d u a l product of the orebody a f t e r removal of the copper and molybdenum e x t r a c t s . T h i s j u s t i f i e s the s l i g h t i n c r e a s e i n the percentage of quartz i n r e s i d u a l t a i l i n g s . Lead shots and g l a s s beads were a l s o t e s t e d , i n an attempt to broaden the r e p r e s e n t a t i o n of d i f f e r e n t g r a n u l a r m a t e r i a l s . 3.4 T e s t i n g Procedure and Sample P r e p a r a t i o n 3.4.1 Ring Shear T e s t s Medium Ottawa sand was i n i t i a l l y t e s t e d i n an oven dry s t a t e . A known weight of sand was d e p o s i t e d i n the annular space by p l u v i a t i n g i n a i r . During the p l u v i a t i o n process the height of f r e e f a l l of sand p a r t i c l e s was about 1 to 2 cm. A f t e r d e p o s i t i n g enough sand the top s u r f a c e of the sample was l e v e l l e d by s i p h o n i n g o f f the s u r p l u s p a r t i c l e s using a vacuum d e v i c e . T h i s l e v e l l i n g method has been used at UBC i n constant volume simple shear t e s t i n g and a l s o by Cole (1967). A f t e r 43 c a r e f u l l y mounting the upper porous p l a t e along with moment arm followed by the l o a d i n g system, the upper r i n g assembly was r a i s e d by approximately 0.025 mm from the o r i g i n a l p o s i t i o n with the use of the screw connection on the c e n t r e support s h a f t . T h i s small gap between the upper and lower c o n f i n i n g r i n g s prevented any f r i c t i o n a l torque due to metal to metal contact between the two r i n g s d u r i n g shear. A height reading of the bracket mounted on the s h a f t of the a i r p i s t o n was taken with r e s p e c t to a r e f e r e n c e l e v e l with the use of a d i a l gauge. T h i s enabled c a l c u l a t i o n of the sample height as the d i a l gauge was p r e v i o u s l y c a l i b r a t e d a g a i n s t a dummy sample of known h e i g h t . Ring shear t e s t s were performed at d i f f e r e n t r e l a t i v e d e n s i t i e s f o r samples of medium Ottawa sand prepared as mentioned above. D e n s i f i c a t i o n of the samples was done with a high frequency low amplitde v i b r a t o r . A d d i t i o n a l g e n t l e tapping with a s o f t hammer was needed to achieve higher r e l a t i v e d e n s i t i e s . A l l d e n s i f i c a t i o n s were performed a f t e r s e a t i n g the top porous p l a t e on the l e v e l l e d sand s u r f a c e of the sample. For a sample at a given r e l a t i v e d e n s i t y , shear t e s t s were done at d i f f e r e n t normal s t r e s s e s on the plane of shear, as d e s c r i b e d below. I n i t i a l l y the sample was loaded to a normal s t r e s s of about 200 kPa and sheared u n t i l the constant volume s t a t e was reached. Then the normal s t r e s s was i n c r e a s e d by about 250 kPa 44 and the t e s t was repeated. In t h i s manner the value of <t> was r cv determined at d i f f e r e n t normal s t r e s s l e v e l s ranging to a maximum value of about 1200 kPa. (This maximum was l i m i t e d by the c a p a c i t y of the l o a d i n g p i s t o n and the shear mechanism). A f t e r reaching the maximum s t r e s s l e v e l , a s i m i l a r set of measurements of </»cv were made during the d e c r e a s i n g phase of the normal lo a d i n s t e p s . The above mentioned sequence of o p e r a t i o n s i n l o a d i n g and unloading w i l l be r e f e r r e d to as a " c y c l e of shear t e s t i n g " i n the subsequent d i s c u s s i o n s i n Chapter 4. A shearing displacement rate of 1 m/hr was used in the t e s t i n g program. However, some t e s t s were c a r r i e d out at low shearing r a t e s (about 10 times slower) to determine p o s s i b l e i n f l u e n c e of shearing r a t e on ^ c v - Shearing was continued u n t i l the constant volume s t a t e , which occured when the lower load c e l l and the LVDT monitoring the d i l a t i o n or c o n t r a c t i o n of the sample readings a t t a i n e d steady v a l u e s . That such constant volume and s t r e s s c o n d i t i o n s was reached c o u l d be i n f e r r e d from transducer t r a c e s on the s t r i p c h a r t r e c o r d e r s . One t e s t on medium Ottawa sand was c a r r i e d out on a loose s a t u r a t e d sample prepared by p l u v i a t i n g sand i n d e a i r e d water in order to i n v e s t i g a t e the p o s s i b l e i n f l u e n c e of s a t u r a t i o n on 0 C V« As the l e v e l l i n g of the top sand s u r f a c e of t h i s s a t u r a t e d specimen c o u l d not be achieved by the s u c t i o n technique, a f l a t blade was used to remove the s u r p l u s sand. 45 Throughout the process of p r e p a r a t i o n and s h e a r i n g , the s a t u r a t i o n of the sample was maintained by a surrounding water r e s e r v o i r as shown in F i g . 3 . 7 . Shearing was c a r r i e d out at both f a s t and slow r a t e s . No d i f f e r e n c e i n t e s t r e s u l t s was noted, i n d i c a t i n g that shearing r a t e s were slow enough to achieve f u l l drainage. Although the t e s t was performed f o r only one i n i t i a l packing d e n s i t y , the t * c v measurements were done over the same range of confinement used f o r dry samples. S i m i l a r r i n g shear t e s t s were c a r r i e d out on f i n e Ottawa sand over a range of normal s t r e s s e s on the plane of shear. T h i s was done to i n v e s t i g a t e p o s s i b l e e f f e c t of p a r t i c l e s i z e on 0 c v f o r i d e n t i c a l p a r t i c l e minerology. T e s t s were a l s o performed on granular copper samples of two d i f f e r e n t g r a i n s i z e s , f o r s i m i l a r reasons. The s t r e s s range used i n these t e s t s was the same as that used f o r medium Ottawa sand. Furt h e r t e s t s were conducted on samples of t a i l i n g s sand from the two mines, Brenda and Lornex, under the same c o n d i t i o n s and s t r e s s l e v e l s d e s c r i b e d above. No pore f l u i d was used i n the t e s t i n g of these m a t e r i a l s and the samples were at oven dry c o n d i t i o n s . Mechanical s i e v e a n a l y s i s was performed on the samples of medium Ottawa sand and Brenda mine t a i l i n g s ; o btained both before and a f t e r the r i n g shear t e s t s . These r e s u l t s p r o v i d e d a q u a l i t a t i v e e v a l u a t i o n on the degree of c r u s h i n g due to s h e a r i n g . Ring shear t e t s on l e a d shots and g l a s s beads were a l s o performed under the same c o n d i t i o n s as fo r the above m a t e r i a l s . However there was a l i m i t a t i o n on the 4 6 F i g . 3.7 Test on a S a t u r a t e d Sample w i t h a Su r r o u n d i n g Water R e s e r v o i r a p p l i e d c o n f i n i n g s t r e s s l e v e l d u r i n g shear. Lead shots underwent c o l d welding when sheared at normal s t r e s s l e v e l s i n excess of about 700 kPa. Aggregates formed i n the shear zone due to c o l d welding had s i z e s comparable to sample dimensions, whereas the m a t e r i a l away form the shear plane was not subjected to such c o l d welding. Due to these non u n i f o r m i t i e s development of unsteady behaviour was observed during shear and the 0 c v c o u l d not be estimated r e l i a b l y . As w e l l , e x c e s s i v e c r u s h i n g of g l a s s beads under high s t r e s s l e v e l s l i m i t e d t h e i r t e s t i n g only i n the re g i o n of low s t r e s s e s . Maximum a p p l i e d s t r e s s on the plane of shear d i d not exceed 700 kPa f o r these two m a t e r i a l s . 3.4.2 T r i a x i a l T e s t s Drained t r i a x i a l t e s t s were c a r r i e d out on medium Ottawa sand, under an e f f e c t i v e c o n f i n i n g p r e s s u r e of 200 kPa. Saturated samples were prepared by p l u v i a t i n g sand i n d e a i r e d water contained w i t h i n a s p l i t former l i n e d with rubber membrane of 0.03 mm t h i c k n e s s . D e n s i f i c a t i o n of the sample was achieved with a high frequency low amplitude v i b r a t o r . However, very dense samples (greater than ~80% r e l a t i v e d e n s i t y ) c o u l d only be achieved by a d d i t i o n a l tappings with a s o f t hammer. A l l d e n s i f i c a t i o n s were c a r r i e d out a f t e r s e a t i n g the top cap over the sample and with p r o v i s i o n f o r both top and bottom drainage. 48 A l l samples were i s o t r o p i c a l l y c o n s o l i d a t e d to an e f f e c t i v e s t r e s s of 200 kPa a g a i n s t an a p p l i e d back pressure of 50 kPa. C o n s o l i d a t i o n was done i n e f f e c t i v e s t r e s s increments of 50 kPa, to reach the f i n a l 200 kPa va l u e . The shearing process was i n i t i a t e d with a load c o n t r o l l e d system. I n c r e a s i n g the a x i a l load i n sm a l l e r steps p r o v i d e d a b e t t e r c o n t r o l over the measurement of displacement and volume change at small s t r a i n l e v e l s . Enough time was allowed f o r the sample to reach e q u i l i b r i u m under each increment. A f t e r passing the poi n t of maximum c o n t r a c t i o n , the l o a d i n g mode was changed from s t r e s s to s t r a i n c o n t r o l l e d at an a x i a l s t r a i n r a t e of 0.17%/min. The samples were sheared past the peak s t r e n g t h u n t i l the reading of the d e v i a t o r s t r e s s reached an approximately steady v a l u e . T r i a x i a l t e s t s on medium Ottawa sand prepared at r e l a t i v e d e n s i t i e s of 30% and 54% were performed on 51 mm diameter x 102 mm high samples. However, as the po i n t of maximum c o n t r a c t i o n f o r very dense samples occured at very small values of a x i a l and vol u m e t r i c s t r a i n s , a l a r g e r sample s i z e (63.5 mm diameter x 127 mm high) was used f o r t e s t s on dense sand i n order to increase the s e n s i t i v i t y of deformation measurements. To ensure c o n s i s t e n c y i n t e s t r e s u l t s a t e s t was a l s o performed on 63.5 mm loose sample ( r e l a t i v e d e n s i t y = 30%) and r e s u l t s were compared with those obtained from the t e s t on smal l e r 51 mm diameter sample. 4 9 S i m i l a r d r a i n e d t r i a x i a l t e s t s on a l l o t h e r m a t e r i a l s l i s t e d i n Table 3.1 were performed on 51 mm diameter samples. The sample p r e p a r a t i o n and the t e s t i n g p r o c e d u r e was the same as mentioned above. However, a l l the samples were t e s t e d under l o o s e c o n d i t i o n s w i t h o u t any d e n s i f i c a t i o n by e x t e r n a l means. 50 CHAPTER 4 RESULTS AND DISCUSSION 4.1 C o n s t a n t Volume F r i c t i o n A n g l e 4.1.1 R i n g Shear T e s t s on Ottawa Sand The measured values of <f>cv which were m o b i l i z e d at shear displacements of the order of 1 t o 2 cm f o r the oven dry medium Ottawa sand are i l l u s t r a t e d i n F i g u r e s 4.1.a to 4.1.f. Each f i g u r e shows the constant volume f r i c t i o n angle m o b i l i z e d as a f u n c t i o n of a p p l i e d normal s t r e s s on the plane of shear, for a f i x e d i n i t i a l r e l a t i v e d e n s i t y . I t may be noted in these f i g u r e s that f o r each i n i t i a l d e n s i t y </>cv i s e s s e n t i a l l y independent of the normal s t r e s s . The maximum d e v i a t i o n from the mean value does not exceed ±1 degrees at any d e n s i t y . The magnitude of c o n f i n i n g s t r e s s ranged from about 200 to 1200 kPa. The average value of </>cv o b t a i n e d from each f i g u r e ( i . e . F i g s . 4.1.a to 4.1.f) i s p l o t t e d a g a i n s t the corresponding r e l a t i v e d e n s i t y i n F i g . 4.2. The r e s u l t s i l l u s t r a t e v i r t u a l independence of the constant volume f r i c t i o n from the p a r t i c l e packing d e n s i t y . The p a r t i c l e s i z e d i s t r i b u t i o n of a t y p i c a l sample f o l l o w i n g shear t e s t i n g under the highest c o n f i n i n g s t r e s s i s compared with the g r a i n s i z e d i s t r i b u t i o n of the untested sand i n F i g . 4.3. L i t t l e change i n the gr a d a t i o n of t h i s sand may be noted f o l l o w i n g shearing to <f> s t a t e under v a r i o u s l e v e l s 5 1 33 cn 0) Q JU cn c < c o o > CJ 32 31 H 30 29 -28 -27 0.2 —1 1 1 1 0.4 0.6 (Thousands) Normal Stress kPa 0.8 1.2 F i g . 4.1.a Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 30% 33 ui co cn cu Q CJl c < c o o > (J 32 31 -30 -29 -28 -27 -• 0.2 —I 1 1 1 0.4 0.6 (Thousands) Normal Stress kPa 0.8 1.2 F i g . 4 . 1 . b Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 5 5 % cn v Q cr> c < c o o > (J 33 32 H 31 30 -29 -28 -27 0.2 F i g . 4.1.c + + + — i 1 1 1 1 i r 0.4 0.6 0.8 1 (Thousands) Normal Stress kPa Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 64% T 1 1 1 1 1 1 r 0 0.2 0.4 0.6 0.8 1 1. (Thousands) Normal Stress kPa F i g . 4.1.d Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 75% 33 cn 0) a cn c < c o o 'L. > (J 32 -31 -30 -29 -28 -27 0 T T 0.2 0.4 0.6 (Thousands) Normal Stress kPa 0.8 1.2 F i g . 4.1.e Constant Volume F r i c t i o n A n gle v s Normal S t r e s s on the P l a n e of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 80% 33 <u Q V CP c < c o u "l_ u. > 32 -31 -30 -29 -28 -27 0 + + + + 0.2 —I 1 1 1 0.4 0.6 ( T h o u s a n d s ) N o r m a l S t r e s s k P a 0.8 1.2 F i g . 4-1 - f Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Oven Dry) I n i t i a l R e l a t i v e D e n s i t y - 85% 33 oo 0) Q Q) cn c < c o o U-> (J 32 -31 -30 29 H 28 27 T T T 20 40 60 Relgtive Density % 80 100 F i g . 4.2 Constant Volume f r i c t i o n A n g l e vs I n i t i a l R e l a t i v e D e n s i t y Medium Ottawa Sand (Oven Dry) F i g . 4.3 G r a i n S i z e D i s t r i b u t i o n of Medium Ottawa Sand B e f o r e and A f t e r R i n g Shear T e s t s of confinement. Such a behaviour c o u l d be expected due to the quartz minerology of t h i s rounded Ottawa sand. The r e s u l t s of a r i n g shear t e s t on a s a t u r a t e d sample of medium Ottawa sand are presented i n F i g . 4.4. As f o r the oven dry sand, <£ c v may seen to be e s s e n t i a l l y independent of the normal s t r e s s and i t s mean equals the value f o r the oven dry m a t e r i a l . That the f r i c t i o n a l c h a r a c t e r i s t i c s of minerals are unchanged i n the sat u r a t e d s t a t e when compared to dry s t a t e i s in agreement with the o b s e r v a t i o n s of Horn and Deere (1962) for massive s t r u c t u r e d m i n e r a l s , and those of T a y l o r (1948) on sands. F i g . 4.5 shows the r e s u l t s of r i n g shear t e s t s on f i n e Ottawa sand ( D 5 0 = 0.2 mm compared to 0.4 mm f o r medium Ottawa sand) over the same range of c o n f i n i n g s t r e s s e s . I t i s i n t e r e s t i n g to note that the average value of the constant volume f r i c t i o n angle i s about 30 degrees, which i s i d e n t i c a l to the value found for medium Ottawa sand. The above obse r v a t i o n s l e a d to the f o l l o w i n g c o n c l u s i o n s . The constant volume f r i c t i o n angle of Ottawa quartz sand depends n e i t h e r on the i n i t i a l packing d e n s i t y nor the l e v e l of c o n f i n i n g s t r e s s on the plane of shear. Neither the presence of pore water nor the changes i n p a r t i c l e s i z e d i s t r i b u t i o n had any n o t i c e a b l e i n f l u e n c e on the observed value of 0 C V « These important f i n d i n g s r egarding <j>cv f o r a granular m a t e r i a l of a f i x e d minerology are now i n v e s t i g a t e d 60 d) Q V cn c < c o v* u 'l_ > CJ 33 32 31 -30 -29 -28 -27 0.2 F i g . 4.4 + + + + ~ ~ l 1 1 1 1 1 1 1 0.4 0.6 0.8 1 1 (Thousands) Normal Stress kPa Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Medium Ottawa Sand (Saturated) with an I n i t i a l R e l a t i v e D e n s i t y = 30% CTi to Q _QJ CP c < c o °-4-> o U . > CJ 33 32 -31 -30 -29 -28 -27 0 1 1— 0.2 F i g . 4.5 + + + + _! j 1 1 1 1 1 — i 0.4 0.6 0.8 1 1 ( T h o u s a n d s ) N o r m a l S t r e s s k P a Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Fine Ottawa Sand (Oven Dry) with an I n i t i a l R e l a t i v e D e n s i t y = 30% f o r g r a n u l a r m a t e r i a l s composed of other m i n e r a l s , metals and g l a s s beads. 4.1.2 Ring Shear Tests on Brenda and Lornex Mine T a i l i n g s Both Brenda and Lornex mine t a i l i n g s are angular i n shape and are composed of about 6 6 % f e l d s p a r and 3 3 % q u a r t z . The f e l d s p a r sands were found to be more s u s c e p t i b l e to c r u s h i n g due to t h e i r lower toughness, when su b j e c t e d to both c o n f i n i n g s t r e s s e s and shear (Chern, 1 9 8 4 ) . I t i s t h e r e f o r e expected that the r i n g shear t e s t s on these sands would r e f l e c t both the i n f l u e n c e of minerology and p a r t i c l e c r u s h i n g on 0 c y . The r e s u l t s of r i n g shear t e s t s on oven dry Brenda mine t a i l i n g s are shown in F i g . 4 . 6 . The average value of t * c V over the range of c o n f i n i n g s t r e s s e s used may be noted to be about 3 5 degrees; with a s c a t t e r of about ± 1 degree about the mean. The o b s e r v a t i o n s from t r i a x i a l t e s t s i n d i c a t e that the 0 cv value f o r f e l d s p a r sands i s higher than that f o r quartz sands (Rowe, 1 9 7 1 ) , and thus the above r e s u l t s on Brenda mine t a i l i n g s are i n agreement with Rowe's o b s e r v a t i o n s . Brenda mine t a i l i n g s experienced a s i g n i f i c a n t amount of cr u s h i n g d u r i n g the process of shear. A q u a l i t a t i v e estimate of the degree of crus h i n g c o u l d be obtained by comparing the p a r t i c l e s i z e d i s t r i b u t i o n s before and a f t e r the t e s t s . Mechanical s i e v e a n a l y s i s were performed on two samples at v a r i o u s stages of shearing. The f i r s t sample comprised of 6 3 38 cn C7» V Q JU cn c < c o u u. > d 37 -36 -35 -34 -33 -32 + + ++ + T T 0.2 0.4 0.6 (Thousands) Normal Stress kPa 0.8 + + 1.2 F i g . 4.6 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Brenda Mine T a i l i n g s (Oven Dry) with an I n i t i a l R e l a t i v e d e n s i t y = 54% t a i l i n g s a f t e r completing one c y c l e of shear, i . e . a f t e r t e s t under the normal s t r e s s of 1200 kPa was completed. The second specimen was subjected to two c o n s e c u t i v e c y c l e s of shear t e s t i n g . The p a r t i c l e s i z e d i s t r i b u t i o n s are i l l u s t r a t e d i n F i g . 4.7 which appears to i n d i c a t e that the degree of c r u s h i n g i s predominantly governed by the amount of shearing displacements imposed. C a r e f u l examination of the sample a f t e r the r i n g shear t e s t showed that the p a r t i c l e s i n the shear zone were h e a v i l y crushed. However, the p a r t i c l e s near the ends of the specimen were v i r t u a l l y i n t a c t . T h e r e f o r e , the percentage of c r u s h i n g i l l u s t r a t e d i n F i g . 4.7 i s an underestimate of the a c t u a l value on the plane of shear. In c o n t r a s t , Ottawa sand, as a l r e a d y noted e a r l i e r d i d not s u f f e r observable p a r t i c l e c r u s h i n g . S i m i l a r o b s e r v a t i o n s regarding d i f f e r e n c e s in p a r t i c l e c r u s h i n g due to shear are reported by Chern (1984) from undrained t r i a x i a l t e s t s on Ottawa sand and Brenda mine t a i l i n g s . F i g . 4.6 shows that d e s p i t e major p a r t i c l e breakage, the value of 0 remains e s s e n t i a l l y constant over the e n t i r e c o n f i n i n g s t r e s s range. More c r u s h i n g occured during the second c y c l e of shear t e s t i n g , but with no a l t e r a t i o n i n the magnitude of the constant volume f r i c t i o n angle, 0CV'. T h i s implies that the process of p a r t i c l e c r u s h i n g has no i n f l u e n c e on the 0 C V value r e g a r d l e s s of the l e v e l of c o n f i n i n g s t r e s s or the magnitude of shear displacement. F u r t h e r , t h i s o b s e r v a t i o n supports the independence of <j> from p a r t i c l e 65 F i g . 4.7 Grain S i z e D i s t r i b u t i o n of Brenda Mine T a i l i n g s Before and A f t e r Ring Shear Tests s i z e e s t a b l i s h e d e a r l i e r f o r Ottawa sand. A f r e s h sample of Brenda mine t a i l i n g s i s angular i n shape. I t i s reasonable to b e l i e v e that the shape of the p a r t i c l e would change in the process of shear due to c r u s h i n g ; an aspect which i n d i r e c t l y suggests that the value of </>cy may a l s o be independent of the shape of the p a r t i c l e as long as minerology remains constant. Brenda and Lornex mine t a i l i n g s possess e s s e n t i a l l y i d e n t i c a l minerology (about 66% F e l d s p a r and 33% Quartz) but d i f f e r e n t p a r t i c l e s i z e s and g r a d a t i o n ( F i g . 3.6). I t i s i n t e r e s t i n g to note that the r i n g shear t e s t on Lornex mine t a i l i n g s y i e l d e d c&cv values e s s e n t i a l l y i d e n t i c a l to those observed f o r Brenda mine a i l i n g s ( F i g . 4.8). These r e s u l t s suggest that the value of <Pcv i s a d i r e c t r e f l e c t i o n of the minerology of the m a t e r i a l and independent of - the p a r t i c l e s i z e , g r adation or shape. 4.1.3 Ring Shear Tests on Granular Copper Two types of granular copper were used. In the f i r s t type p a r t i c l e s were rounded i n shape with a uniform gradation having a D s o of 1.0 mm. The second type c o n s i s t e d of c y l i n d r i c a l p a r t i c l e s , with a D 5 0 of 0.6 mm. These m a t e r i a l s would thus enable f u r t h e r o b s e r v a t i o n of the i n f l u e n c e of p a r t i c l e s i z e and shape on the value of # c v « C l e a r l y the shearing process w i l l not cause p a r t i c l e breakage f o r such a m a t e r i a l . 67 38 cn co cn <D Q ju cn c < c o u "c > 37 36 35 -34 -33 -32 0.2 T" T 0.4 0.6 ( T h o u s a n d s ) N o r m a l S t r e s s k P a 0.8 1.2 F i g . 4.8 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Lornex Mine T a i l i n g s (Oven Dry) with an I n i t i a l Dry D e n s i t y = 1.4 g/cm 3 Ring shear t e s t r e s u l t s on both f i n e and coarse copper are presented in F i g s . 4.9 and 4.10, r e s p e c t i v e l y . Both f i g u r e s do not show evidence of the e f f e c t of c o n f i n i n g pressure on the value of ^ c v . Maximum d e v i a t i o n of the observed d . values does not exceed 1.5 degrees from the mean, cv 3 The average <j>cv f o r f i n e g r a i n copper i s 32.0 degrees and f o r coarse copper i s 32.9 degrees. The range of c o n f i n i n g pressure used was i d e n t i c a l to that f o r sands, ( i . e . 200-1200 kPa). E s s e n t i a l l y constant values of <j>cv observed f o r granula r copper s t r o n g l y supports the c o n c l u s i o n s d e r i v e d from t e s t s on sands. These a d d i t i o n a l r e s u l t s are i n favour of the independence of <PCW from the i n f l u e n c e of c o n f i n i n g pressure and p a r t i c l e s i z e . 4.1.4 R i n g S h e a r T e s t s on L e a d S h o t s and G l a s s Beads Ring shear t e s t s on these m a t e r i a l s serve to expand the range i n the v a r i e t y of gr a n u l a r m a t e r i a l s . Some <&cv measurement on these m a t e r i a l s have been r e p o r t e d i n the past and t h i s would provide a good b a s i s f o r comparison of r i n g shear t e s t r e s u l t s with those r e p o r t e d i n l i t e r a t u r e . Lead shots had a D 5 0 of 1.4 mm and g l a s s beads 0.4 mm. As mentioned i n s e c t i o n 3.4.1 the c o n f i n i n g s t r e s s used i n t e s t s on these m a t e r i a l s was l i m i t e d to a maximum of about 700 kPa. The le a d shots experienced c o l d welding and g l a s s beads showed ex c e s s i v e breakage at high s t r e s s e s . 69 o cn V Q 0) cn c < c o O > 35 34 H 33 32 -31 -30 -29 + + 0.2 F i g . 4 . 9 + —I 1 1 1 1 1 1 1 1 I 0.4 0.6 0.8 1 1.2 (Thousands) Normal Stress kPa Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Fine Copper (Oven Dry) with an I n i t i a l Dry Densit y = 6 . 9 5 g/cm3 3 6 V Q ft) cn c < c o u > 3 5 H 3 4 3 3 H 3 2 31 H 3 0 + + + + + + + 0.2 —I 1 1 1 0.4 0.6 (Thousands) Normal Stress kPa 0.8 1.2 F i g . 4.10 Constant Volume F r i c t i o n Angle vs Normal S t r e s s on the Plane of Shear -Coarse Copper (Oven Dry) with an I n i t i a l Dry De n s i t y = 6.14 g/cm 3 The t e s t r e s u l t s on these two m a t e r i a l s i l l u s t r a t e d i n F i g s . 4.11 and 4.12 a l s o show 4> to be independent of the a p p l i e d normal s t r e s s . During the process of shear of g l a s s beads the a s s o c i a t e d c r u s h i n g would have very l i k e l y changed i t s shape from rounded to angular. The u n a l t e r e d value of # c v observed under such changes favour the suggestion on the absence of shape e f f e c t . Lead shots y i e l d e d an average value of 4>cv of 33 degrees and g l a s s beads 24.3 degrees. These o b s e r v a t i o n s r e i n f o r c e f u r t h e r the uniqueness of <4>cw f o r a given g r a n u l a r m a t e r i a l . The o b s e r v a t i o n s made above suggest that n e i t h e r p a r t i c l e s i z e , shape or g r a d a t i o n nor p a r t i c l e c r u s h i n g have a c o n t r o l l i n g i n f l u e n c e on the value of 0 C V« Test r e s u l t s presented thus, s t r o n g l y i n d i c a t e that 0 c v would be changed i f and only i f the m i n e r a l c o n s t i t u t i n g the granular m a t e r i a l i s changed. 4.1.5 Review of the Test Results i n R e l a t i o n to Past Work The measured average values of t * c v f o r a l l m a t e r i a l s used i n t h i s program are summarized i n Table 4.1. The r i n g shear r e s u l t s d i s c u s s e d i n the previous s e c t i o n s c l e a r l y i n d i c a t e that the constant volume f r i c t i o n angle i s a unique p r o p e r t y f o r a g r a n u l a r m a t e r i a l and i t depends only on the mi n e r a l c o n s t i t u t i n g the g r a i n s . At t h i s stage i t i s a p p r o p r i a t e t o eval u a t e these r e s u l t s i n r e l a t i o n to previous experimental r e s u l t s and t h e o r e t i c a l p o s t u l a t e s . 72 3 6 CA) cn cu Q V cn c < c o v» CJ u. > d 3 5 3 4 -3 3 -3 2 -31 -3 0 + + T T T 2 0 0 4 0 0 Normal Stress kPa 6 0 0 8 0 0 F i g . 4.11 Constant Volume F r i c t i o n A n gle vs Normal S t r e s s on the P l a n e of Shear -Lead Shots (Oven Dry) w i t h an I n i t i a l Dry D e n s i t y = 7.74 g/cm 3 0 T 1 1 1 1 1 r 2 0 0 4 0 0 6 0 0 8 0 0 Normal Stress kPa F i g . 4.12 Constant Volume F r i c t i o n A n gle vs Normal S t r e s s on the P l a n e of Shear -G l a s s Beads (Oven Dry) w i t h an I n i t i a l Dry d e n s i t y = 1.53 g/cm 3 T a b l e No. 4.1 C o n s t a n t Vo lume F r i c t i o n A n g l e O b s e r v e d f o r D i f f e r e n t M a t e r i a l s Material •cv <De8'> Ottawa Sand (C 109) 29.9 Ottawa Sand (Fine) 30.2 Lornex Mine T a i l i n g s 35.1 Brenda Mine T a i l i n g s 34.7 Granular Copper (Coarse) 32.9 Granular Copper (Fine) - 32.0 Lead Shots 33.0 Glass Beads 24.3 75 <P values given i n Table 4.1 f o r quartz sand and g l a s s beads agree reasonably w e l l with some of the values reported in l i t e r a t u r e ; Mersey r i v e r quartz sand - 32 degrees; g l a s s b a l l o t i n i - 23 degrees; (Rowe, 1971). A 0 c v f o r a f e l d s p a r sand of 43 degrees has been reported by Rowe (1971). T a i l i n g s sands used i n t h i s study with 66% f e l d s p a r y i e l d e d a value of only 35 degrees. Rowe (1971) does not i n d i c a t e the percentage of f e l d s p a r i n the sand used. It may be reasonable to expect the measured 0 C V f o r a qua r t z f e l d s p a r mixture to l i e between 4>cv v a l u e s of pure quartz and f e l d s p a r . On the other hand the reported values of 0 c v by Rowe (1971) were not obtained by a d i r e c t measurement technique, but i n f e r r e d from d r a i n e d t r i a x i a l t e s t data based on the assumption that the s t r e s s d i l a t a n c y theory i s v a l i d . Average values of 0 c v obtained f o r Ottawa quartz sand, granular copper and l e a d shots are 30, 32.5 and 33 degrees, r e s p e c t i v e l y . According to the t h e o r e t i c a l r e l a t i o n s h i p proposed by Home (1969), the corresponding values of 0^ f o r the above m a t e r i a l s should be i n the order of 25 degrees. On the other hand, the r e p o r t e d values of 0^ f o r metals as opposed to minerals l i k e quartz and f e l d s p a r are c o n s i d e r a b l y lower than 25 degrees, (Rowe, 1962; Horn, 1962). Therefore the measured val u e s of 0 c v do not appear to support the proposed r e l a t i o n s h i p between 0^ and 0 C V i f the above. trend i n the value of 0^ i s t r u e . A d i f f e r e n t p i c t u r e on the value of ^ emerges from Skinner's (1969) work, where he observed a 76 r a d i c a l change i n the v a l u e of (from 3 degrees t o 33 d e g r e s s ) f o r g l a s s beads when exposed t o water as compared t o the dry s t a t e . I t was f u r t h e r o b s e r v e d t h a t the o v e r a l l energy d i s s i p a t i o n d u r i n g shear was u n a l t e r e d under such changes. Q u a n t i t a t i v e l y , S k i n n e r ' s e s t i m a t e of c&cv may be l i a b l e t o e r r o r as mentioned i n Chapter 2 . However i n a q u a l i t a t i v e sense h i s r e s u l t s show t h a t a d i r e c t r e l a t i o n s h i p between 0 c v and <t> i s not v i a b l e . The f r i c t i o n a l b e h a v i o u r i n the r i n g shear t e s t s does not e x c l u d e the i n f l u e n c e of i n t e r p a r t i c l e f r i c t i o n on 0 C V « However, i t i s c l e a r t h a t d i r e c t correspondence cannot be e s t a b l i s h e d between the c o n s t a n t volume f r i c t i o n a n g l e and <j>^, which i s supposedly c o n s i d e r e d as the s o l e i n d i c a t o r of the i n t e r p a r t i c l e f r i c t i o n . C o n s i d e r i n g the o b s e r v a t i o n s on the r e p o r t e d v a l u e s of i n t e r p a r t i c l e f r i c t i o n a n g l e s <p^, i t i s a l s o e v i d e n t t h a t the d e t e r m i n a t i o n of c> i s d i f f i c u l t due t o i t s h i g h s e n s i t i v i t y t o the s u r f a c e c o n d i t i o n s . Thus, the use of <fi^ as a fundamental p r o p e r t y of the m a t e r i a l may not be d e s i r a b l e and p r a c t i c a l . On the o t h e r hand, the c o n s t a n t volume f r i c t i o n a n g l e which i s governed o n l y by the m i n e r a l c o n s t i t u t i n g the m a t e r i a l would be a more s t r a i g h t f o r w a r d and p r a c t i c a l l y v i a b l e fundamental p r o p e r t y compared t o the a n g l e of i n t r i s i c s l i d i n g f r i c t i o n . 77 4 .2 F r i c t i o n A n g l e a t Maximum C o n t r a c t i o n The conceptual analogy between c r i t i c a l s t a t e and t r a n s i e n t constant volume s t a t e ( s t a t e at maximum c o n t r a c t i o n ) i n d r a i n e d shear with respect to m o b i l i z e d f r i c t i o n angle, i n g r a n u l a r m a t e r i a l s has been a l r e a d y i d e n t i f i e d i n Chapter 2. The f o l l o w i n g s e r i e s of d r a i n e d t r i a x i a l t e s t s p r i m a r i l y on Ottawa sand are intended to seek experimental v e r i f i c a t i o n of t h i s analogy, which was o r i g i n a l l y suggested by Atkinson and Bransby (1978). 4 . 2 . 1 D r a i n e d T r i a x i a l T e s t s on Medium O t t a w a Sand R e s u l t s of d r a i n e d t r i a x i a l t e s t s on medium Ottawa sand are shown i n F i g s . 4.13.a to 4.13.d. Test r e s u l t s correspond to the samples sheared at r e l a t i v e d e n s i t i e s of 30, 54 and 80 percent and a f i x e d c o n f i n i n g pressure of 200 kPa. The m o b i l i z e d f r i c t i o n angle '6 at the i n s t a n t of maximum 3 mc c o n t r a c t i o n d e r i v e d from F i g s . 4.13.a to 4.13.d i s p l o t t e d a g a i n s t r e l a t i v e d e n s i t y i n F i g . 4.14. I t may be noted that 0 m c decreases with i n c r e a s i n g i n i t i a l r e l a t i v e d e n s i t y f o r sand sheared under constant l a t e r a l confinement. However, i t s value f o r the loose sand (30% r e l a t i v e d e n s i t y ) i s almost equal to the c* c v value of the sand. T h i s trend i s i n agreement with Rowe's (1962) concepts regarding p a r i c u l a t e m a t e r i a l behaviour. Rowe suggests that i f the sample i s very dense the degree of rearrangement i s very small and the predominant cause of shear r e s i s t a n c e would be s l i d i n g and d i l a t i o n . But 78 40 35 -30 -+ + ++ + + + + + + + W Q 25 -20 -c < c o o 15 10 -5 -1.5 -T -2 - I 1 1 4 6 A x i a l S t r a i n % —1— 10 1 -K c 'o L . V) u V •*-> E O > 0.5 + + - 0 . 5 - + + + + ++ + + + -1 - 1 . 5 -- 2 ~i 1 1 4 6 A x i a l S t r a i n % T " 8 - i — 10 2 F i g . 4.13.a Stress-Strain-Volume Change Data from Drained T r i a x i a l T e s t s on Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l R e l a t i v e Density = 30%, Sample D i a . = 51 mm. 79 40 35 -30 + + + + + + CP 4) Q 25 -cn c < c o 20 -15 10 -5 -4 6 T -8 - 1 — 10 1.5 - A x i a l S t r a i n % 1 -o 0.5 -to _o L . <-* t) E JJ o > - 0 . 5 -+ + + + + + + + -1 -•1.5 -- 2 6 2 4 i 8 I 10 A x i a l S t r a i n % F i g . 4.13.b S t r e s s - S t r a i n - V o l u m e Change Data from D r a i n e d T r i a x i a l T e s t s on Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g P r e s s u r e = 200 kPa, I n i t i a l R e l a t i v e D e n s i t y = 30%, Sample D i a . = 63.5 mm. 80 « a v cn C < c o 40 35 -30 -25 -20 -15 -10 -5 -+ + • + + + + + + + + + + + + + + + 2.5 -2 4 6 A x i a l S t r a i n % T 8 c 'a to o E O > 2 -1.5 -1 -0.5 --0.5 --1 2 4 6 A x i a l S t r a i n % 8 10 F i g . 4.13.C S t r e s s - S t r a i n - V o l u m e Change Data from D r a i n e d T r i a x i a l T e s t s on Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g P r e s s u r e = 200 kPa, I n i t i a l R e l a t i v e D e n s i t y = 54%, Sample D i a . = 51 mm. 81 40 35 -+ + + + + + + + + + + + + + + + + + 30 -« Q 25 -cn c < c o _u u U. 20 - • 15 -10 -5 -c 2 -in u "C E O > 1 -2 6 -r-8 i 10 3 -A x i a l S t r a i n % -1 -r 6 8 ~r 2 " T-4 I 10 A x i a l S t r a i n % F i g . 4.13.d Stress-Strain-Volume Change Data from Drained T r i a x i a l T ests on Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l R e l a t i v e Density = 80%, Sample D i a . = 63.5 mm. 82 1 ] \ 1 r—= 1 1 i i I 0 20 40 60 80 100 Relative Density % F i g . 4.14 M o b i l i z e d F r i c t i o n A n g l e a t Maximum C o n t r a c t i o n v s I n i t i a l R e l a t i v e D e n s i t y -Medium Ottawa Sand, E f f e c t i v e C o n f i n i n g P r e s s u r e = 200 kPa below the peak s t r e n g t h and p r i o r to commencement of d i l a t i o n , 0 m c would l i k e l y approach <p^, the i n t e r p a r t i c l e f r i c t i o n angle with i n c r e a s i n g d e n s i t y . Drained t r i a x i a l t e s t s on Ottawa sand have re v e a l e d that <t>mc at a given r e l a t i v e d e n s i t y i n c r e a s e s with the i n i t i a l c o n f i n i n g pressure •(Negussey et a l . 1986). T h i s data i s reproduced i n F i g . 4.15 and i l l u s t r a t e s that the value of 4>mc approaches 4>cv with i n c r e a s i n g c o n f i n i n g s t r e s s l e v e l . I n c r e a s i n g confinement promotes c o n t r a c t i o n and whether or not <t>mc approaches c* c v w i l l depend both on i n i t i a l d e n s i t y and c o n f i n i n g s t r e s s l e v e l . 4.2.2 Drained T r i a x i a l T e s t s on the Other M a t e r i a l s Drained t r i a x i a l t e s t s s i m i l a r to medium Ottawa sand were a l s o c a r r i e d out on a l l remaining m a t e r i a l s l i s t e d i n Table 3.1. Saturated specimens were prepared by p l u v i a t i n g granular m a t e r i a l i n d e a i r e d water. Samples were not d e n s i f i e d f o l l o w i n g d e p o s i t i o n so as to achieve a loose i n i t i a l packing and enable a b e t t e r d e f i n i t i o n of <b and a more c o n t r a c t i v e mc sample. A l l specimens were sheared under an e f f e c t i v e c o n f i n i n g s t r e s s of 200 kPa. The t e s t r e s u l t s are given in F i g s . 4.16.a to 4.16.g. The 0 m c values obtained from these t e s t s are p l o t t e d a g a i n s t the constant volume f r i c t i o n angles measured i n r i n g shear t e s t s , i n F i g . 4.17. I t may be noted that 6 of granular m a t e r i a l s 84 CD OI 3 0 -cn to Q JQJ cn C < c o v< o O 25 -100 F i g . 4.15 , r j 1— 2 0 0 3 0 0 Confining Pressure kPa M o b i l i z e d F r i c t i o n Angle at Maximum Co n t r a c t i o n vs E f f e c t i v e C o n f i n i n g Pressure - Medium Ottawa Sand, I n i t i a l R e l a t i v e D e n s i t y = 50% (A f t e r Negussey et a l . , 1986) cn Q cn c < c o c. '6 i_ *J cn o « E 3 O > 40 35 30 -25 -20 -15 -10 -1.5 -1 -0.5 -- 0 . 5 --1 -- 1 . 5 -- 2 + ++ + + + + + + + + + + T -2 i i i 4 v 6 A x i a l S t r a i n % 10 + + + + + +++++++ + 2 ~I 1 1 4 6 A x i a l S t r a i n % 8 i 10 F i g . 4.16.a Stress-Strain-Volume Change Data from Drained T r i a x i a l T e s t s on Fine Ottawa Sand, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l R e l a t i v e Density = 35%, Sample D i a . = 51 mm. 86 Axial Strain % F i g . 4.16.D Stress-Strain-Volume Change Data from Drained T r i a x i a l Tests on Brenda Mine T a i l i n g s , E f f e c t i v e C o n f i n i n g P r e s s u r e = 200 kPa, I n i t i a l R e l a t i v e Density = 25%, Sample D i a . = 51 mm. 87 V O cn c < c o c "o L . IS) o "k-V E O > 50 40 -30 20 -10 -+ + + + + + + + •1 -- 2 -- 3 -- 4 -- 5 1 1 1 1 1 1 1 1 1 1 — \ 2 4 6 8 10 ++ ++ A x i a l S t r a i n % i i i r 12 14 — I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — 0 2 4 6 8 10 12 14 16 A x i a l S t r a i n % F i g . 4.16.C Stress-Strain-Volume Change Data from Drained T r i a x i a l T ests on Lornex Mine T a i l i n g s , E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l Dry D e n s i t y = 1.27 g/cm 3, Sample D i a . = 51 mm. 88 50 40 -30 -20 -10 -+. ++ + + + + + + + + - | 1 1 1 1 1 +~ 2 4 6 + Axial Strain % + + + + + + + + + 3 -1 1 1 I I : I I 0 2 4 6 8 Axial Strain % 4.16.d Stress-Strain-Volume Change Data from Drained T r i a x i a l T ests on Granular Copper ( F i n e ) , E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l Dry Density = 5.00 g/cm 3, Sample D i a . = 51 mm. 89 50 cn O cn c < c o u *c li-fe? c 'o in u ' L . *J 4) E O > A x i a l S t r a i n % F i g . 4.16.e Stress-Strain-Volume Change Data from Drained T r i a x i a l T e s t s on Granular Copper (Coarse), E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l Dry D e n s i t y = 5.23 g/cm 3, Sample D i a . = 51 mm. 90 Ol <0 Q <n v a> c < c o c '5 CO E 3 50 40 -30 -20 10 1 --1 -- 2 T -2 - i 1 1 4 6 A x i a l S t r a i n % ++ + + + + + + + + + + + + + 8 —r— 10 T " 2 -1 1 1 4 6 A x i a l S t r a i n % 8 I 1 0 F i g . 4.16.f Stress-Strain-Volume Change Data from Drained T r i a x i a l T ests on Lead Shots, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l Dry D e n s i t y = 6.64 g/cm 3, Sample D i a . = 51 mm. 91 cn 0) O cn c < c o c 'a L_ .*-# 10 o v E O > 50 40 -30 -20 -+ + 10 -1 -+ + + + + + + + + + + + + + + + ~~\ 1 1 1 — 2 4 x -Axial Strain % + . + 6 2 • :—I 4 Axial Strain % ~T~ 6 8 F i g . 4.16.g Stress-Strain-Volume Change Data from Drained T r i a x i a l Tests on G l a s s Beads, E f f e c t i v e C o n f i n i n g Pressure = 200 kPa, I n i t i a l Dry Density = 1.52 g/cm 3, Sample D i a . = 51 mm. 92 50 CO 40 ,.cn CU Q cn C < c o .y 3 0 LJL c_> 2 20 2 0 l 4 0 p G l a s s B e a d s + O t t a w a S a n d o F i n e O t t a w a S a n d A F ine C o p p e r X C o a r s e C o p p e r • L e a d S h o t s B r e n d a M i n e T a i l i n g s L o r n e x M i n e T a i l i n g s I 60 8 0 C V . F r i c t i o n A n g l e D e g . F i g . 4.17 M o b i l i z e d F r i c t i o n Angle at Maximum C o n t r a c t i o n i n T r i a x i a l T e s t s ( I n i t i a l l y Loose Samples) vs Constant Volume F r i c t i o n Angle i n the loose s t a t e represent a very good estimate of t h e i r corresponding 0 C V'. Thus, the need to run la r g e s t r a i n t e s t s fo r d i r e c t measurement of 0 may not be necessary, s i n c e good estimates of 0 c v can be made by measuring 0 m c i n the loose s t a t e s . However, 6 from dense c o n d i t i o n s would underestimate mc r c v 4.2.3 Review of the Test R e s u l t s i n R e l a t i o n to Previous Work The d r a i n e d t r i a x i a l t e s t s as d i s c u s s e d above have re v e a l e d that the m o b i l i z e d f r i c t i o n angle at maximum c o n t r a c t i o n i s a parameter that depends on the i n i t i a l c o n f i n i n g pressure and the r e l a t i v e d e n s i t y of the granular mass. The suggested correspondence between 0 m c and 0 c v by Atkinson and Bransby (1978) w i l l be v a l i d only i f the i n i t i a l s t r e s s s t a t e and d e n s i t y c o n d i t i o n s of the granular m a t e r i a l are biased towards a c o n t r a c t i v e behaviour. T r i a x i a l t e s t s i n t h i s i n v e s t i g a t i o n were continued to a x i a l s t r a i n s g e n e r a l l y i n excess of 10%. Sample deformations appeared s e n s i b l y uniform throughout and value s of m o b i l i z e d f r i c t i o n angles were computed at the l a r g e s t s t r a i n s at which the t e s t s were terminated. At t h i s s t r a i n l e v e l most specimens were s t i l l d i l a t i n g and t h e r e f o r e 0 c y c o n d i t i o n was not q u i t e approached. A comparison of a p p r o p r i a t e 0 c v values obtained from r i n g shear and l a r g e s t r a i n 0 m o b i l i z e d i n t r i a x i a l t e s t s i s shown in F i g . 4.18. I t may be observed that the t r i a x i a l t e s t 0 values i n each case are g r e a t e r than or about equal to the 0 94 G l a s s B e a d s O t t a w a S a n d F i n e O t t a w a S a n d F i n e C o p p e r C o a r s e C o p p e r L e a d S h o t s B r e n d a M i n e T a i l i n g s L o r n e x M i n e T a i l i n g s 2 0 4 0 6 0 8 0 Ring Shear ( Deg. ) F i g . 4.18 Ultimate F r i c t i o n Angle i n T r i a x i a l T ests vs Constant Volume F r i c t i o n Angle v a l u e s f r o m r i n g s h e a r t e s t s . T h u s t h e d e v e l o p m e n t o f tf>cv f o r some t r i a x i a l t e s t s w o u l d a p p e a r t o have r e q u i r e d even l a r g e r s t r a i n i n g and t h e r i n g s h e a r t e s t r e s u l t s a p p e a r t o r e p r e s e n t a l o w e r bound on s h e a r r e s i s t a n c e . 4.3 C r i t i c a l S t a t e , S t e a d y S t a t e and Pha se T r a n s f o r m a t i o n S t a t e The f r i c t i o n a n g l e m o b i l i z e d a t s t e a d y s t a t e , w h i c h i s t h e u l t i m a t e s t a t e a c h i e v e d by a g r a n u l a r m a t e r i a l s u b j e c t e d t o u n d r a i n e d s h e a r , h a s been shown t o be u n i q u e f o r t h a t m a t e r i a l ( P o u l o s , 1981; C a s t r o e t a l . , 1 9 8 2 ) . S i n c e t h i s s t a t e c o r r e s p o n d s t o a c o n s t a n t p o r e p r e s s u r e and s t r e s s c o n d i t i o n , i t c a n be c o n s i d e r e d a c o u n t e r p a r t o f t h e c r i t i c a l s t a t e i n d r a i n e d s h e a r w h i c h r e p r e s e n t s t h e u l t i m a t e c o n s t a n t vo lume s t a t e . A c o n t r a c t i v e s a n d r e a c h e s s t e a d y s t a t e f o l l o w i n g a c o n t i n u o u s i n c r e a s e i n p o r e p r e s s u r e u n t i l s t e a d y s t a t e . On t h e o t h e r h a n d a p a r t i a l l y c o n t r a c t i v e or d i l a t i v e s a n d r e a c h e s s t e a d y s t a t e a f t e r a d r o p i n p o r e p r e s s u r e f o l l o w i n g an i n i t i a l c o n t r a c t i v e b e h a v i o u r and p o r e p r e s s u r e i n c r e a s e . I s h i h a r a (1975) i d e n t i f i e d t h i s c o n d i t i o n a t t h e i n s t a n t o f maximum p o r e p r e s s u r e ( t r a n s i e n t c o n s t a n t p o r e p r e s s u r e s t a t e ) d u r i n g u n d r a i n e d s h e a r o f g r a n u l a r m a t e r i a l s a s t h e p h a s e t r a n s f o r m a t i o n s t a t e . V a i d and C h e r n (1985) f o u n d t h a t b o t h p h a s e t r a n s f o r m a t i o n and s t e a d y s t a t e s a r e i d e n t i c a l i n t e r m s o f t h e m o b i l i z e d a n g l e o f f r i c t i o n . A p o s s i b l e c o r r e s p o n d e n c e be tween cf> and t h e m o b i l i z e d f r i c t i o n a n g l e a t p h a s e 96 t r a n s f o r m a t i o n or steady s t a t e i s i n v e s t i g a t e d h e r e i n i n an attempt to seek an equivalence between c r i t i c a l s t a t e , steady s t a t e and phase t r a n s f o r m a t i o n s t a t e . Values of f r i c t i o n angles obtained at the s t a t e of phase t r a n s f o r m a t i o n f o r Brenda mine t a i l i n g s and medium Ottawa sand by Chern (1984) are compared- with t h e i r c orresponding 0 c v values from the r i n g shear d e v i c e , i n Table 4.2. I t may be noted that a c l o s e agreement e x i s t s between the two angles f o r both sands. T h i s confirms a fundamental equivalence of undrained phase t r a n s f o r m a t i o n or steady s t a t e and the d r a i n e d c r i t i c a l s t a t e of granular m a t e r i a l s with respect to the mo b i l i z e d f r i c t i o n angle. Phase t r a n s f o r m a t i o n s t a t e has been c a l l e d the c h a r a c t e r i s t i c t h r e s h o l d by Luong (1980). Luong a l s o observes that the m o b i l i z e d f r i c t i o n angle at maximum c o n t r a c t i o n i n a drain e d t e s t i s i d e n t i c a l to the f r i c t i o n angle m o b i l i z e d at phase t r a n s f o r m a t i o n i n an undrained t e s t . The r e s u l t s shown i n F i g s . 4.14 and 4.15 however i n d i c a t e t h a t # m c i s not unique f o r a given m a t e r i a l , but would vary with c o n f i n i n g s t r e s s l e v e l and d e n s i t y . Hence the correspondence between <f>mc and 0 p T should be q u a l i f i e d to perhaps r e f e r to i n i t i a l l y c o n t r a c t i v e s t a t e s f o r which 0 m c and </>pT may be c l o s e or i d e n t i c a l . The value of 0 p T would l i k e l y be underestimated by d> f o r d i l a t i v e s t a t e s , mc 97 T a b l e No . 4 .2 C o m p a r i s o n o f C o n s t a n t Vo lume F r i c t i o n A n g l e and F r i c t i o n A n g l e M o b i l i z e d a t P h a s e T r a n s f o r m a t i o n Mater ia l •cv •pT Deg. Ottawa Sand 29.9 29.4 Brenda Mine T a i l i n g s 34.7 36.5 98 CHAPTER 5 SUMMARY AND CONCLUSIONS T h e m a i n o b j e c t i v e o f t h i s r e s e a r c h was t o i n v e s t i g a t e t h e u n i q u e n e s s o f c o n s t a n t v o l u m e f r i c t i o n a n g l e , 4>cvr o f g r a n u l a r m a t e r i a l s . R i n g s h e a r d e v i c e was a d o p t e d i n t h e m e a s u r e m e n t a n d s t u d y o f c* c v due t o i t s i n h e r e n t a d v a n t a g e s i n l a r g e d e f o r m a t i o n m e a s u r e m e n t o v e r o t h e r s h e a r t e s t i n g d e v i c e s . A v a r i e t y o f g r a n u l a r m a t e r i a l s e x t e n d i n g f r o m m i n e r a l s a n d s t o m e t a l s a n d g l a s s b e a d s were u s e d i n t h e t e s t i n g p r o g r a m . R i n g s h e a r t e s t s on medium O t t a w a s a n d ( C - 1 0 9 ) ( p u r e q u a r t z , D 5 0 = 0 . 4 mm) i n an o v e n d r y s t a t e r e v e a l e d t h a t t h e c o n s t a n t v o l u m e f r i c t i o n a n g l e ^ c v » i - s i n d e p e n d e n t o f t h e c o n f i n i n g p r e s s u r e a n d t h e i n i t i a l p a c k i n g d e n s i t y o f t h e m a t e r i a l . No o b s e r v a b l e c h a n g e i n t h e v a l u e o f 0 C V was f o u n d due t o t h e p r e s e n c e o f p o r e w a t e r d u r i n g a t e s t on a s a t u r a t e d s p e c i m e n o f t h e same s a n d . F i n e O t t a w a s a n d w h i c h h a d t h e same m i n e r o l o g y a s medium O t t a w a s a n d b u t w i t h a D 5 0 o f 0 . 2 mm, when t e s t e d i n r i n g s h e a r i n d i c a t e d t h a t t h e v a l u e o f 0 c y f o r a g i v e n m i n e r a l w o u l d a l s o be i n d e p e n d e n t of p a r t i c l e s i z e . T e s t s on two m i n e t a i l i n g s w h i c h h a d t h e same m i n e r o l g y a n d a p r e d o m i n a n t p r e s e n c e o f f e l d s p a r , y i e l d e d i d e n t i c a l v a l u e s o f <t>cv' The r e s u l t s f o r t h e s e two s a n d s showed t h a t 4>c v i n a d d i t i o n i s n o t i n f l u e n c e d by p a r t i c l e c r u s h i n g , g r a d a t i o n o r 99 shape. The measured valu e s of # c v f o r granular copper a l s o i n d i c a t e d that the constant volume f r i c t i o n angle i s u n a f f e c t e d by the changes in c o n f i n i n g pressure, and p a r t i c l e shape and s i z e . T e s t s on l e a d shots and g l a s s beads f u r t h e r r e i n f o r c e d the observed uniqueness of 4>cv f o r other m a t e r i a l s . I t c o u l d be concluded that # c v i s a fundamental property of the gran u l a r m a t e r i a l and would depend only on the min e r a l c o n s t i t u t i n g the g r a i n s . The constant volume f r i c t i o n angle provides a lower bound to the shear r e s i s t a n c e of a granula r m a t e r i a l . R e s u l t s of tf>cv obtained from the r i n g shear device- were g e n e r a l l y lower than or equal t o the u l t i m a t e f r i c t i o n angle at the l a r g e s t imposed s t r a i n ( i n excess of about 10%) i n the t r i a x i a l apparatus f o r the same m a t e r i a l . These o b s e r v a t i o n s c l e a r l y i l l u s t r a t e d the p o t e n t i a l of the r i n g shear apparatus f o r e s t i m a t i n g lower bound f r i c t i o n a l r e s i s t a n c e which occur at l a r g e deformations. Drained t r i a x i a l t e s t s on medium Ottawa sand i n d i c a t e d that the mobilzed f r i c t i o n angle <Pmc at the point of maximum c o n t r a c t i o n , i s not a fundamental m a t e r i a l p r o p e r t y . The value of <t> f o r medium Ottawa sand increased with c o n f i n i n g *mc 3 pressure and decreased with i n i t i a l packing d e n s i t y . The upper bound of <t> would be equal to <t> , and as a r e s u l t a good mc ^ cv 3 estimate of # c v c o u l d be obtained by measuring the 0 m c f o r a c o n t r a c t i v e sample without r e s o r t i n g to larg e s t r a i n t e s t s . 100 A c l o s e agreement was observed between the c o n s t a n t volume f r i c t i o n a n g l e c* c v o b t a i n e d from r i n g shear t e s t s and the m o b i l i z e d f r i c t i o n a n g l e 0 p T a t phase t r a n s f o r m a t i o n or steady s t a t e r e p o r t e d from u n d r a i n e d t r i a x i a l t e s t s , f o r medium Ottawa sand and Brenda mine t a i l i n g s . These o b s e r v a t i o n s i n d i c a t e d t h a t the m o b i l i z e d f r i c t i o n a n g l e s a t c r i t i c a l s t a t e and s t e a d y s t a t e are e q u i v a l e n t and unique f o r a g r a n u l a r m a t e r i a l . 101 REFERENCES Atkinson, J.H. and Bransby, P.L. (1978). 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R e s i d u a l Strength of Clays i n L a n d s l i d e s , Folded S t r a t a and the Laboratory, Geotechnique 35, No. 1, pp. 3-18. Skinner, A.E. (1969). A Note on the In f l u e n c e of I n t e r p a r t i c l e F r i c t i o n on the Shearing Strength of a Random Assembly of S p h e r i c a l P a r t i c l e s , T e c h n i c a l Notes, Geotechnique, V o l . 19, pp. 150-157. S o r e g a r o l i , A.E. (1974) . Geology of the Brenda Copper-Molybdenum Deposit i n B r i t i s h Columbia, Canadian Mining and M e t a l l u r g i c a l (CIM) B u l l e t i n , V o l . 67, No. 750. T a y l o r , D.W. (1947) . Fundamentals of S o i l Mechanics, John Wiley and Sons, Inc., New York V a i d , Y.P. and Chern, J.C. (1985) . C y c l i c and Motonic Undrained Response of Sat u r a t e d Sands, Session No. 52, Advances i n the Art of T e s t i n g S o i l s Under C y c l i c C o n d i t i o n s , Annual Convention and E x p o s i t i o n , D e t r o i t , Michigan. V e s i c , A.S. and Clough, G.W. (1968) . Behaviour of Granular M a t e r i a l s Under High S t r e s s e s , J o u r n a l of the S o i l Mechanics and Foundation En g i n e e r i n g D i v i s i o n , American S o c i e t y of C i v i l E ngineers, V o l . 94, No. SM3, pp. 661-688. Waldner, M.W., Smith, G . D . and W i l l i s , R . D . (1976). Lornex, Canadian I n s t i t u t e of Mining and M e t a l l u r g y , CIM S p e c i a l Volume 15, Paper 13, pp. 120-129. 104 

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