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Material-form relationships on talus slopes in southwestern British Columbia Evans, Stephen G. 1976

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MATERIAL-FORM RELATIONSHIPS ON TALUS SLOPES IN SOUTHWESTERN BRITISH COLUMBIA by STEPHEN G. EVANS B.Sc, A.K.C., University of London King's College, 1969 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1976 (c) Stephen George Evans, 1976 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s fo r f i nanc i a l gain sha l l not be allowed without my writ ten permission. The Univers i ty of B r i t i s h Columbia 20 75 Wesbrook Place Vancouver, Canada V6T 1W5 Department of ABSTRACT Talus slopes were investigated i n a process-material-response framework. The work was concerned with c l a r i f y i n g concepts and terminology concerning slopes of gran-ular materials and i n t e r p r e t i n g talus slope angles i n the l i g h t of th i s c l a r i f i c a t i o n ; v e r i f y i n g t h i s interpretation i n a f i e l d investigation; and seeking s t a t i s t i c a l relationships between talus slope angle and material properties. F i e l d investigations were carr i e d out i n South West B r i t i s h Columbia. Slopes were investigated i n the southern Coast Mountains and. i n the Similkameen Valley. Theoretical concepts r e l a t i n g to slopes i n granular material were discussed. Two angles of repose were d i s t i n -guished; a peak angle of accumulation (<<c) defined as the steepest angle attainable by a mass of granular material, and a lower angle, the angle of repose (<* ) to which the material s l i d e s a f t e r f a i l u r e . c< and<K were related to concepts of c r c shear resistance and the angle of i n t e r n a l f r i c t i o n (0); c<c was linked to 0 and o< r was thought to correspond to the r e s i d -ual angle of i n t e r n a l f r i c t i o n for a given m a t e r i a l . ^ andc< r were related through a regression equation of the form; ©< c = -3.29 + 1.273 ( 0 ^ ) These concepts were examined with reference to talus slope form and some of the contradictions i n the l i t e r a t u r e were presented. The c h a r a c t e r i s t i c and l i m i t i n g slope angles noted i n review were found to correspond to c<r and c<c respectively for talus material. This correspondence gave r i s e to the supp l y induced'-1 rah s format, ion . hypo the s i s which appeared to provide a suitable transformation model for rock-f a l l talus. The r e l a t i o n s h i p between material properties and slope angle was examined using parametric multivariate s t a t i s -t i c s . S i g n i f i c a n t correlations, at the 99% l e v e l , were obtained between segment angle and size (inverse) and segment angle and s o r t i n g ( d i r e c t ) . At the 95% l e v e l s i g n i f i c a n t correlations were found between segment angle and s p h e r i c i t y (inverse) and Zingg's Flatness Ratio ( d i r e c t ) . In multiple regression analysis only 37.11% of the v a r i a t i o n i n slope angle was accounted for by material properties (sorting and the v a r i -ance i n Zingg's Elongation Ratio) at the 95% l e v e l of s i g n i f -icance. Shape factors contribute very l i t t l e to the explained variance whilst f a b r i c related variables contribute nothing. Implications of these r e s u l t s for talus slope devel-opment were discussed. Rockfall talus slopes subject to supply-induced transformation processes are thought to have a d i s t i n c -t i v e morphology which may be an explanation for the t y p i c a l p r o f i l e concavity noted on such slopes. Determinants on the frequency of talus s l i d e s were examined. The problem of the basal layer cannot be ignored i n a consideration of talus slope development models. TABLE OF CONTENTS Page LIST OF TABLES V LIST OF FIGURES v i GLOSSARY OF TERMS v i i i ACKNOWLEDGEMENTS x CHAPTER 1 - INTRODUCTION . . . . 1.. 1.1 Terminology 1 1.2 The Talus Slope System . 2 1.3 Material Properties and Slope Form . . 5 1.4 Statements of the Problem and Objectives . . 6 CHAPTER 2 - REVIEW OF TALUS FORM, STRUCTURE AND SLOPE PROCESSES 9 2.1 Talus Slope Form 9 2.1.1 Gross Form 9 2.1.2 Talus Slope P r o f i l e Form . . . . 9 .2.2 E f f e c t s of P a r t i c l e Characteristics on Talus Slope Form 20 2.3 Internal Structure . . 21 2.4 Transformation Processes on Talus Slopes 28 2.4.1 Transformation Agents 28 2.4.2 Shear Processes i n the Talus System 29 CHAPTER 3 - DISCUSSION OF FIELD PROCEDURES . . . . . . . 36 3.1 F i e l d Investigations . . 36 3.1.1 I n i t i a l F i e l d C r i t e r i a 36 3.1.2 Description of I n i t i a l F i e l d Areas 36 3.1.3 Additional F i e l d C r i t e r i a . . . 39 3.1.4 Description of a Further F i e l d Area 42 Ci) Page 3.2 Sampling Plan Formulation 45 3 . 2 . 1 Alternative Sampling Plans . . . 45 3.2.2 Delimiting Sample Points within the Strata or Segments . . . . . . . . . . . . 47 3. 2 . 3 Delimiting the Length of Segment . . . . . 48 3.3 P i l o t Investigations for the Similkameen Talus 49 3 . 3 . 1 Determination of Segment Boundaries 49 3.3.2 Determination of Sample Size within Segments 56 3.4 F i e l d Measurement Techniques . . . . . 57 3 . 4 . 1 Measurement of P r o f i l e Properties 57 3.4.2 Measurement of Boulder Properties 59 CHAPTER 4 - THE INTERPRETATION OF TALUS SLOPE ANGLES . . 62 A. Theoretical Concepts and Terminology . . 62 4.1 Angle of Rest, Angle of Repose and Peak Angle of Accumulation . . 62 4.2 Factors A f f e c t i n g the Peak Angle of Accumulation 64 4.3 Concepts of Shear Resistance and Angle of Internal F r i c t i o n . . 66 4 . 3 . 1 D e f i n i t i o n s of Components of Shear Resistance . . . . 66 4.3.2 Factors A f f e c t i n g the Angle of Internal F r i c t i o n of Granular Materials . . . 69 4.4 Relationships between Peak Angle of Accumulation (=><_,) , Angle of Repose (pC ) , Angle of Internal F r i c t i o n (0) and Residual Angle of Internal F r i c t i o n (0r) . 71 4 . 4 . 1 Relationships between Peak Angle of Accumula-ti o n (oC ) and Angle of Repose (< ) . . . . . . . . 7 3 ( i i ) Page 4.4.2 Relationship between Peak Angle or Accumu-l a t i o n (oC ) and the Angle of ..Internal F r i c t i o n Resistance ( 0 ) . . . 75 4 . 4 . 3 Relationship between Peak Angle of Accumula-t i o n (d. ) , Angle of Internal F r i c t i o n (0), Angle of Repose (o< ) and Residual Angle of Inter-nal F r i c t i o n ( ^ r ) . . . . . . 76 B. Talus Slope Form 76 4.5 Interpretation of Talus Slope Angles . . . . . . . . . . . 76 4 . 5 . 1 Previous Interpretations . . 76 4.5.2 The Supply-Induced Transformation Hypothesis. . 78 C. The Case of the Similkameen Talus . . . 81 4.6 Evidence for the Operation of Supply-Induced Transformation Hypothesis 82 4 . 6 . 1 A e r i a l Photography and Slide Debris 82 4.6.2 Slope I r r e g u l a r i t i e s . . . . ' 82 4 . 6 . 3 Fabric Pattern 87 4.7 Slope Angles on the Similka-meen Talus 92 4 . 7 . 1 C h a r a c t e r i s t i c and Limiting Slope Angle . . . . 92 4.7.2 Comments on the S i m i l -kameen Talus 97 CHAPTER 5 - RELATIONSHIPS BETWEEN MATERIAL PROPERTIES AND TALUS SEGMENT ANGLES 1 0 3 5.1 Methods of Analysis 1 0 3 5.2 Variables Used i n This Analysis . . . . 1 0 6 5.3 Correlation Analysis 1 0 8 5.4 Stepwise Multiple Regression Analysis I l l ( i i i ) . Page 5.5 Comments on the Multivariate Analysis . . . . . . 112 5.5.1 The Relationship between Material Properties and Segment Angle 112 5.5.2 S u i t a b i l i t y of Indices . . . . . 113 5.5.3 Possible Sources of Oper-ator Error i n F i e l d Measurement . . . . . . . . . . 113 5.5.4 Possible Sources of Real World Noise 114 5.5.5 Relationships between Mean Material Properties and Mean Slope Angle . . . . . . . . 115 5.6 Conclusions on Multivariate Analysis . . . . . . . . . . . . . . . 115 CHAPTER 6 - IMPLICATIONS FOR TALUS SLOPE DEVELOPMENT AND CONCLUSIONS . . . . . . . . . 117 6.1 Implications for Rockwall/Talus Slope Development . . . . . . . . . . . 117 6.1.1 Talus Slope Morphology . . . . . . 117 6.1.2 Determinants on the Fre-quency of Talus Slides . . . . . 120 6.1.3 The Problem of the Basal Layer . 123 6.2 Conclusions . . . . . . « . . . « . * « . . 124 6.2.1 General 124 6.2.2 S p e c i f i c . . . . . . . . . . . . 125 LITERATURE CITED 126 APPENDIX I TALUS SLOPE PROFILES. MEASURED IN FIELD INVESTIGATIONS . . . . . . . . . . . . 140 (iv) LIST OF TABLES Table Page I Location and Lithologies of Talus Slopes on which Figures 2.1 and 2.2 Are Based . . . . 16 II C haracteristics of Slopes Studied . 40-41 III V a r i a b i l i t y of Material Properties at the Three S p a t i a l Scales Studied . 51 IV Examples of the V a r i a b i l i t y of Size and Shape Encountered by Other Workers on Talus and Similar Slopes 53-54 V L i s t of Published Peak Angles of Accumulation for Talus and Similar Materials 96 VI Variables Used i n Multivariate Analysis . . . . 105 VII Correlation Matrix for Similkameen Talus Material Properties 107 (v) LIST OF FIGURES Figure Page 1.1 Controls on Transformation Types within the System 4 1.2 Organisation of Work: Form-Material Relationships 8 2.1 Talus Cone at Lindeman Lake, B r i t i s h Columbia, Studied i n ;this3w6r.k , . . 10 2.2 Example of Sheet Talus on Norwegian Coastline, South of M§lsz>y . . . . . . . . . . 11 2.3 Example of Coalescent Cones Forming a Compound Slope, South of M§ljz>y, Norway . . . . 11 2.4 Example of Debris Slope on Norwegian Coastline, South of MSljzJy 12 2.5 Histogram of Mean Talus Slope Angles from Published Sources . . . . . . . . 14 2.6 Histogram of Published Segment Angles Measured on Talus Slopes . 15 2.7 Schematic I l l u s t r a t i o n of Talus Slope Structure 23 2.8 Talus Slope Structure; Location -Similkameen F i e l d Area 25 2.9 Talus Slope Structure; Location -Ross Dam Area, Washington State 26 3.1 Location of Talus Slopes Studied i n South Western B r i t i s h Columbia 37 3.2 Location Map of Similkameen Talus 43 3.3 Photograph Taken toward North West, of Sheet Talus on North Side of Similkameen Valley 13 Km. East of Princeton 44 3.4 I n c l i n a t i o n Diagram and Slope P r o f i l e for P i l o t Slope on Similkameen Talus . . . . . 50 3.5 Measurement of P a r t i c l e Dip on P r o f i l e D, Similkameen Talus 60 (vi) Figure Page 4.1 Schematic I l l u s t r a t i o n of the Components of Shear Resistance i n Granular Material (Adopted from Rowe, 1962) . . . 68 4.2 D i f f e r i n g Combinations of P a r t i c l e Sizes I l l u s t r a t i n g the E f f e c t i v e Matrix Problem (Modified af t e r Marsal, 1965) 72 4.3 Relationships between oC^ and <<r 74 4.4 A e r i a l Photograph of Slopes Studied on North Side of Similkameen Valley (Enlarge-ment of B.C. A i r Photograph BC 4436-213) . . . 83 4.5 Photograph of Front on Similkameen Talus . . . 85 4.6 Alternative Origins of the Fronts Observed on Talus Slope P r o f i l e s . . . . . . . 86 4.7 Orientation of Mean Vector, Similkameen Talus i n Relation to Slope Orientation . . . . 90 4.8 Dip of Mean Vector, Similkameen Talus . . . . 91 4.9 Histogram of Segment Angles on Similka-meen Talus 94 4.10 Allen's Packing Case IV for Prolate Spheroids Thought to Apply to Talus Slope Packings . . . . . . . . 95 4.11 Histogram for Calculated Values of <*c for Similkameen Talus 98 4.12 Similkameen Talus Slope Data i n Relation to <=< /U p l o t 99 c r 4.13 Histogram, of"Published Mean Talus Slope Angles/ Incorporating Data from This Inv e s t i -gation . 101 4.14 Histogram of Published Talus,Slope Segment Angles Incorporating Data from This Investigation - 102 5.1 Correlation Structure for Similkameen Talus 109 5.2 Scattergrams of Size and Sorting Variables Plotted against Segment Angles . . . . . . . . 110 6.1 Schematic Diagram of Zones on a Talus Slope Dominated by Rockfall - Debris Slide Processes 118 (v i i ) GLOSSARY OF TERMS Term or Symbol t limiting slope characteristic slope threshold slope peak angle of accumulation (<< ) c angle of repose, or rest (<<^) angle of internal friction (jz>) 0. residual angle of internal friction (J*r) Usage in this work Threshold shear strength required to resist failure (shear resistance) Applied stress great enough to exceed t. Term taken from Young (1961). Modified for usage in this work and taken to be equal to the upper value of a slope angle on slopes affected by .a particular denudation process Term taken from Young (1961). Modified for this work and used with reference to the angle which most frequently occurs on a particular landform e.g. talus slopes Term taken from Carson and Petley (1970). Used in this work as a slope that exists in equilibrium with the strength characteristics of the materials :conposing i t . May refer to a slope in equilibrium with peak or residual strength„ The maximum slope angle attainable by a granular mass for a given set of aggregate properties and depositional conditions Angle assumed by a granular mass following failure resulting from an exceedance of <<c Representative of the frictional resistance of an aggregate of soil particles. Usage as in Terzaghi (1943) The interparticulate friction component in 0 (Rowe, 1963) Dilatancy component in 0 (Rowe, 1963) The re-arranging effect component in 0 (Rowe, 1963) Residual or ultimate value of 0 Cviii) CV imbrication angle Angle of internal, friction measured when volume change in the soil material as a result of shear reaches zero. (Lambe and Whitman, 1969) Term used after Fees (1968) and is the .. angle between the slope of deposition and the mean angle of dip of the particles deposited on that slope (ix) ACKNOWLEDGEMENTS During the preparation of t h i s work I would l i k e to acknowledge the following; The Canadian Commonwealth Scholarship and Fellowship Administration under whose auspices I held a Commonwealth Scholarship at the University of B r i t i s h Columbia, 1969-1971, Dr. Olav Slaymaker for his p a r t i c u l a r patience and guidance i n the supervision of t h i s work, Dr. J. Ross Mackay for his comments and suggestions on various drafts of the work, Michael Church, Michael Patterson and Arthur Nowell for assistance i n the computing phase of the investigation, David Whiting, Jim Vickerson and Dennis Rumley for assistance i n the f i e l d , My wife, Dale, whose encouragement and assistance both i n the preparation of t h i s thesis and i n the f i e l d was invaluable. Computing time was provided through the Department of Geography. (x) CHAPTER ONE INTRODUCTION 1.1 Terminology Talus slopes appear to be a very common element of mountainous t e r r a i n where they are frequently found at the base of rock faces as an accumulation of rock debris. Talus slopes occur as a component i n valley side slopes of the highest order streams as well as those of lower order and are also seen to con-s t i t u t e a component of many summit slope systems i n the mountain environment. Such slopes are usually characterised by a slope angle intermediate between that of the rockwall above and the valley f l o o r which they may adjoin, a looseness of coarse frag-ments which cover the slope, low density or complete absence of vegetation, and a straight or concave upward slope p r o f i l e . In North American the word "talus" i s used both to des-cribe a landform and the material that composes i t . In t h i s work "talus" w i l l be used to describe the material that makes up a "talus slope", a d i s t i n c t landform. Some refe r to talus slopes as "talus s l i d e s " , or to talus as "sliderock". The use of these words conveys a fa l s e impression as to the mode of accumulation of talus (cf. Sharpe, 1960). Further, material c o l l e c t i n g i n a debris slope beneath a gravel or s i l t face i s often "referred to as talus (e.g. Rahn, 1969), but the term should be r e s t r i c t e d to that material beneath a rock face. "Talus" and "scree" tend to be synonymous i n most geo-morphological c i r c l e s although there i s a strong preference for 2 the use of scree i n the United Kingdom and for talus i n North America. 1.2. The Talus Slope System The talus slope system may be viewed as a sub-system within the mountain environment, the c h a r a c t e r i s t i c s of which give the study of mountain processes a unique place i n geomorph-ology. Some of these c h a r a c t e r i s t i c s are (cf. Hewitt, 1972); (a) The mountain environment i s a high r e l a t i v e , r e l i e f and a high energy process environment. (b) The surface of a mountain landscape i n large part consists of bare rock, rock debris, snow and i c e . (c) The great v a r i a b i l i t y i n status variables such as climate (due to elevational differences) and materials ( l i t h o -l o g i c a l variations) makes i t d i f f i c u l t to generalise about moun-ta i n processes. (d) Processes and response surfaces are not always amenable to study due to the magnitude of events (e.g. large rockslides) and i n a c c e s s i b i l i t y (mountain slopes). The study of talus slopes i n the mountain environment must be pursued with some of these c h a r a c t e r i s t i c s i n mind. Various workers i n discussing slopes, mountain slopes or otherwise, have found i t both conceptually convenient and con-ceptually useful to use a model.to i l l u s t r a t e the structure of a p a r t i c u l a r slope system (e.g.. Carson, 1969; Chorley and Kennedy, 1971). In th i s work, i t i s the intention to discuss talus slopes as a sub-system of the mountain slope system in general. Such a 3 model w i l l be s i m i l a r to a process-material-response model (Krumbein and G r a y b i l l , 1965). With reference to the talus system t h i s writer i n pre-vious work (Evans, 1969) presented a q u a l i t a t i v e process-material-response model for debris slopes i n South Wales. Towler (1969) appears to have gone further and was successful i n obtaining s t a t i s t i c a l l y s i g n i f i c a n t correlations between some of the parameters within the model. In other work Howarth and Bones (1972), present a v e r i f i c a t i o n of a general process-response model for A r c t i c talus slopes on Devon Island, N.W.T. The t y p i c a l mountain slope system has three l o c i of f a i l u r e ; the mountain slope i n general and i t s components, the rock wall and the talus slope. This work w i l l concentrate on the talus slope and w i l l be l i m i t e d to a concern for process-material-response li n k s on the talus slope i t s e l f . In consider-ing these l i n k s , i t i s necessary to make a d i s t i n c t i o n between change r e s u l t i n g from a r e d i s t r i b u t i o n of material within the l i m i t s of the slope (e.g. creep, talus s l i d e s , slush avalanches), change r e s u l t i n g from a loss of material beyond the lower l i m i t of the slope (erosion by sea, i c e , r i v e r s or transport by snow avalanches), and change achieved by gain of material through the upper l i m i t of the slope which constitutes the depositional phase of rock wall transformation. The processes involved i n these types of change vary according to environment but two basic processes are seen to be common to a l l taluses, i . e . r o c k f a l l (deposition of talus) and talus slope f a i l u r e or modification. Figure 1.1 i l l u s t r a t e s the 4 ROCK SLOPE r RESISTANCE < STRESS PROCESS OF REMOVAL THROUGH FAILURE DEPOSITION ONTO TALUS SLOPE (TRANSFORMATION TYPE 1) > TALUS SLOPE ELEMENTS OF RESISTANCE ELEMENTS OF SHEAR STRESS RT1 PARTICLE SHAPE RT2 PARTICLE FABRIC RT3 AGGREGATE DENSITY RT4 AGGREGATE SORTING RT5 PARTICLE SIZE TS1 GRAVITATIONAL STRESSES TS2 SEISMIC STRESSES TS3 IMPACT STRESSES TS4 SURFICIAL STRESSES t RESISTANCE < STRESS TALUS SLOPE PROFILE CHANGE (TRANSFORMATION TYPE 2) Figure 1.1: Controls on transformation types within the talus system 5 factors which appear to determine the process of talus slope modification. These factors have been assembled from the l i t e r -ature and t h e i r mode of presentation i s af t e r Varnes (1957). 1.3 Material Properties and Slope Form The rel a t i o n s h i p between material properties and slope form has been investigated i n pioneer work on London clay slopes i n South England, by Skempton and De Lory (1957), Skempton (1964) and Hutchinson (1967a)who demonstrated the relationships between the incidence of mass movement processes, material properties and observed slope angles on slopes i n the Tertiary sediment. Other work along s i m i l a r l i n e s has been car r i e d out by Chandler (1970 a,b) on Lias clay slopes in.England, by Lohnes and Hardy (1968) on loess slopes i n Iowa, and by Carson and Petley (1970) on debris covered h i l l s l o p e s i n two upland areas i n B r i t a i n . Swanston (1970) conducted studies on g l a c i a l t i l l slopes on Prince of Wales Island, Alaska whilst Carson (1972) looked at debris-covered h i l l s l o p e s i n the Laramie Mountains of Wyoming with a s i m i l a r conceptual framework. U n t i l recently the material-form l i n k had not been studied on talus slopes s p e c i f i c a l l y and the work of Rouse (undated ms.) and Chandler (1973), working i n South Wales and Spitzbergen respectively, represent the f i r s t work i n that d i r e c t i o n . The importance of material properties and t h e i r e f f ects on slope form i s i m p l i c i t i n the statements of Strahler"(1952) and Chorley (1966.) who comment on the role of stress-strength 6 relations i n process studies. Strahler (1952) noted that " a l l geomorphic processes that we observe... are b a s i c a l l y the v a r i -ous forms of shear, or f a i l u r e . . . of materials" (p. 924). Chor-ley (1966), stressed the importance of force-resistance r a t i o s since they expressed "the effectiveness of the force i n produc-ing change i n materials of a given strength a t t r i b u t e " (p. 283). A geomorphic event, the sum of which over a period of time represents a geomorphic process, occurs when an applied stress (Y c) i s greater than a threshold shear strength (V) required to r e s i s t f a i l u r e . Material properties should be related to slope form i n the following ways: (a) A threshold must e x i s t for a l l slopes where f c > "E , i . e . a l i m i t i n g value for strength, and t h i s threshold must have a morphometric manifestation. This manifestation would correspond to the l i m i t -ing slope. (b) Equilibrium conditions, where t = \ , i . e . a lower bound for the operation of a process, must e x i s t for a l l slopes and t h i s must have a morphometric manifestation. This manifestation would correspond to the threshold slope as defined by Carson and Petley (1970). (c) Changes i n form take place as a r e s u l t of a process where Xc> X . 1.4 Statement of the Problem and Objective Most workers i n the past have been preoccupied with 7 petrologic aspects of talus accumulation (viz. s i z e , shape, etc.) and have not related these properties to the mechanical proper-t i e s of the talus or d i r e c t l y to slope form. A considerable gap exists i n knowledge concerning the relationship between mechan-i c a l properties of talus, talus slope processes and slope form. Confusion also continues to be rampant (vide recent texts on slopes and slope processes) with respect to concepts of angle of repose, shear resistance, and t h e i r r e l a t i o n to values of threshold and l i m i t i n g slopes. The major objective of t h i s work i s to investigate relationships that e x i s t between material properties and talus slope form on selected r o c k f a l l talus slopes i n southwestern B r i t i s h Columbia. I t w i l l be met i n two ways; (a) By c l a r i f y i n g concepts and terminology OTWerhing slopes of granular materials and interpreting talus slope angles i n the l i g h t of th i s c l a r i f i c a t i o n , (b) By seeking s t a t i s t i c a l relationships between talus slope angle and material properties of p a r t i c l e s that make up the slope. The work w i l l be car r i e d out i n a way suggested i n Figure 1.2. 8 FORM Observations on c h a r a c t e r i s t i c and l i m i t i n g slopes REVIEW FORM F i e l d slope survey - character-i s t i c and l i m i t i n g slopes FIELD MATERIALS Eff e c t s - shear of s i z e , shape, resistance f a b r i c REVIEW MATERIALS E f f e c t s - shear of s i z e , shape, resistance f a b r i c FIELD FORM MATERIAL Figure 1.2; Organisation of work: form-material r e l a t i o n s h i p s 9 CHAPTER TWO REVIEW OF TALUS SLOPE FORM, STRUCTURE AND PROCESSES 2.1 Talus Slope Form 2.1.1 Gross Form; The d i s t i n c t i o n between various types of tauls slopes has been noted i n works by Rapp (1960 b) and Stock (1968) and the implications for process-form relationships have been examined by Howarth and Bones (1972). Rapp (1960 b) distinguished three gross forms exhib-i t e d by talus slopes; the cone form as i l l u s t r a t e d i n Figure 2.1 which occurs at the outlet of a rock chute, mountain gully or co u l o i r , the sheet form (Figure 2.2) which accumulates at the foot of a continuous rock face, and a compound slope which occurs where several cones coalesce as i l l u s t r a t e d i n Figure 2.3. Stock (1968) has much the same basis for his c l a s s i f i c a t i o n except that he distinguishes a fourth type, a debris slope, the common feature of which i s the apparent thinness of the debris mantle over the bedrock beneath which controls p r o f i l e char-a c t e r i s t i c s (Figure 2.4). 2.1.2 Talus Slope P r o f i l e Form (a) Slope Angle; In reviewing the l i t e r a t u r e , i t was found that talus slope measurements have been presented, confus-ingly, i n two forms i . e . on the p r o f i l e scale which may represent either the mean angle of slope calculated from segment data or the o v e r a l l angle of slope, and on the segment scale consisting of measurements on discrete parts of the p r o f i l e . The length of 10 F i g u r e 2.1 T a l u s cone a t L i ndeman L a k e s t u d i e d i n t h i s wo rk 11 Figure 2.2 Example of sheet talus on Norwegian coastline south of M§10y Figure 2.3 Example of coalescent cones forming a compound slope, south of MaljZ>y, Norway Figure 2.4 Example of debris sloge on Norwegian coastline, south of Malsziy 13 these segments may vary from scarcely 1 metre to over 100 metres. As a r e s u l t of t h i s d i f f e r e n t i a t i o n the two sources of data have to be treated separately. With regard to p r o f i l e measurements, slope angles were obtained from e x i s t i n g works where slope angles were given and are i l l u s t r a t e d i n histogram form i n Figure 2.5. Many other works give i l l u s t r a t i o n s of p r o f i l e s but do not give slope angle data. Details of the slopes on which Figure 2.5 was based are given i n Table I. From an examination of Figure 2.5 the follow-ing points a r i s e ; ;.(i) Based on published sources the mean p r o f i l e angle of talus slopes i s 29.6° with n = 181. ( i i ) The data appear to be almost unimodal at 32.0° (modal strength of 13.2%). A weak secondary mode i s seen at 27.0° (modal strength of 6.5%) but i f data from Evans (1969) i s excluded i t would not be evident, ( i i i ) 35.9% of the observations occur between 32° and 35° i n c l u s i v e l y , (iv) The range of the data i s 29° i . e . between 11.0° and 40.0°. The implication of these observations w i l l be discussed below. There have been indications that p r o f i l e angle i s related to the "dominant process" within a p a r t i c u l a r talus system. White (1968) recognises r o c k f a l l talus, avalanche talus and a l l u v i a l t a l u s . He reports that t h e i r mean slope angles are, respectively, 14 30 n 25 H SLOPE ANGLE Howarth and Bones (1972) — 1 DO Koons (1955) 2 CE1 Stock (1968) 1 CZl Gardner (1970) 1 123 Caine (1969) 3 E3 Evans (1969) 1 L±D Fair (1948) 1 LX| Rapp (1960 b) 2 S Chandler (1973) — 3 • I Andrews (1961) 3 1 - Reported as means 2 - Mean of means 3 - Calculated from mean of segments Figure 2.5 Histogram of mean talus slope angles from published sources (n - 181) 40 rr\ Tinkler (1966) E 3 Andrews (1961) • i Frankfort (1968) LXI Caine (1963) EmQ Caine (1967) SCaine (1969) CElRapp (1960 a, b) CDWorobey (1972) [^Chandler (1973) ^1 Thornes (1971) Figure 2.6 Histogram of published segment angles measured on talus slopes (n = 207) 16 TABLE I. LOCATION AND LITHOLOGIES OF TALUS SLOPES ON WHICH FIGURES .2.5 AND 2.6 ARE BASED Source Location Lithology Howarth & Bones (1972) Devon Island, N.W.T. Limestone Koons (1955) Various Locations i n Arizona, New Mexico Basalts, Limestones Sandstones Stock (1968) B a f f i n Island, N.W.T. Schists, G r a n i t i c Gneiss Gardner (1970) Lake Louise, Rocky Mountains, Alberta Q u a r t i z i t e s , Shales Carbonates Evans (1969) Fforest Fawr, South Wales, U.K. Quartzites Caine (1969) Southern Alps, New Zealand Sandstone Caine (1967) North East Tasmania Do l e r i t e Rapp (1960 a) Karkevagge, Sweden Gneisses Rapp (1960 b) Spitsbergen Chert, Limestones Chandler (1973) Spitsbergen Schi s t s , Limestones Andrews (1961) Lake D i s t r i c t U.K. Andesites Ti n k l e r (1966) Eglwysweg, North Wales, U.K. Limestones Frankfort (1968) Central Connecticut Basalt Worobey (1972)^ Similkameen Va l l e y , B r i t i s h Columbia Cherts, Lavas and Limestones Thornes (1971) Iceland Massive Basalts F a i r (1948) Karoo, Natal, S. A f r i c a Shale, Sandstone, D o l e r i t e 17 within the ranges 37°-40°, 35°-38° and 30°-38° (30°-35° for lower portion, 35°-38° for upper portion). Howarth and Bones (1972) contend i n s i m i l a r fashion that r o c k f a l l talus p r o f i l e s are steeper (33.5°-35.5°) than meltwater-affected slopes (30.3°-31.0°). As Howarth and Bones (1972) point out, " i n most cases s i g n i f i c a n t differences i n geometrical form occur between slopes subjected to d i f f e r e n t dominant processes" (p. 151). Figure 2.5 must be viewed with t h i s i n mind. Segment angles show subst a n t i a l l y d i f f e r e n t character-i s t i c s , and the results from the l i t e r a t u r e review are seen i n histogram form i n Figure 2.6. Details of the slopes are found in Table I. The following comments can be made on the data; (i) Based on published sources the mean segment angle on talus slopes i s 30.9° with n = 207. ( i i ) The data appear to be strongly unimodal at 35°. The modal strength for t h i s mode i s 17.9%. ( i i i ) 50.7% of the observations occur between 33° and 36.9°. 32.9% occur between 34° and 35.9°. (iv) The range for the data i s 28.9° ( i . e . between 11.0° and 39.9°). According to Young's d e f i n i t i o n s the c h a r a c t e r i s t i c slope angle i s that angle "which most frequently occurs either on a l l slopes under p a r t i c u l a r conditions of rock types or 18 of climate or i n a l o c a l region" (p. 126). Limiting angles of slopes are "those that define the range within which p a r t i c u l a r types of ground surface occur, or p a r t i c u l a r denudational pro-cesses operate"(p. 127). Viewing the data with Young's (Young,'1961)' terminol-ogy i n mind i t can be concluded that on the basis of published data that the c h a r a c t e r i s t i c slope angle for talus slopes i s 35° fcf. Chandler, 1973) whilst the l i m i t i n g slope angle appears to be 40°. (b) P r o f i l e Shape; Visual inspection of published talus slope p r o f i l e s confirirs, that, i n general they tend to be concave upward. This pervasive c h a r a c t e r i s t i c of talus slopes has attracted the imagination of many geomorphologists several of whom have theorized on i t s possible o r i g i n (e.g. Penck, 1924; Kirkby i n Carson and Kirkby, 1972; Scheidegger, 1970). Penck, among others, explained the concavity as being due to the size gradient downslope ( i . e . fine at the top, coarse at the bottom). Kirkby has obtained a sim i l a r concavity i n laboratory experi-ments designed to simulate talus slope development and contends that distance'travelled.by each rock i n the r o c k f a l l process i s the determining factor. Scheidegger thought that packing v a r i a -tions and t h e i r r elationship to the angle of repose might account for the observed concavity. A second impression derived from an examination of slope p r o f i l e s i s the existence of "mini-concavities" superim-posed upon the general slope concavity. Andrews (1961) and Scheidegger (1970) have also noted t h e i r existence. I t may be 19 noted that these are far more evident i n the f i e l d than by-v i s u a l examination of a published slope p r o f i l e (cf. Morisawa, 1966). As a r e s u l t of t h i s review of talus slope form certain general comments can be made; (i) Other processes may be active on talus slopes apart from r o c k f a l l processes. These other processes have been shown to be e f f e c t i v e i n producing a char-a c t e r i s t i c response. (cf. King, 1966). ( i i ) Whilst the c h a r a c t e r i s t i c slope angle for talus was found to be 35° there i s no basis for the generalisation put forward by such workers as Carson (1969) that talus slopes stand at 35°. ( i i i ) The l i m i t i n g slope angle for talus slopes i s considerably higher than 35° i . e . 4 0°. (iv) The talus p r o f i l e i s concave upward i n general which gives r i s e to a consider-able range of segment angles within the slope. F i n a l l y , i t may be noted that on some occasions where basal processes are active i n eroding the base of the slope a convexity may r e s u l t at the foot of the slope, (e.g. King, 1956). In instances where the top of the slope i s under an extremely steep rockface talus slopes often show a s l i g h t upward convexity (Ryder, 1968) near the top of the slope. 20 2.2 '•>• Eff e c t s of P a r t i c l e C haracteristics on Talus Slope Form; Many workers have reported that large boulders are present at the base whilst smaller ones are found at the top of the slope. These workers include early geomorphologists and geologists such as Thoulet (1887) who believed that size was an important variable i n the determination'of slope angle. Behre (1933) believed that size was not only important but that talus slope angle varied d i r e c t l y with p a r t i c l e size. Behre's conclu-sions were severely c r i t i c i z e d by Bryan (1934). Van Burkalow (1945) concluded that " i t i s doubtful that v a r i a t i o n i n slope angle i s caused by the contrast i n size of fragment" (p. 699) and c i t e d such factors as shape, height of f a l l , density of the aggre-gate and surface roughness as the important controls. F a i r (1948) commenting on talus i n Natal reported "the angle of slope i s i n d i r e c t proportion to p a r t i c l e s i z e " , (p. 72). Andrews (1961) i n the Lake D i s t r i c t of England found an inverse r e l a t i o n s h i p between slope angle and size whilst Frankfort (1968) found no r e l a t i o n -ship between slope angle and s i z e . I t i s of intere s t to note that Rapp (1960 a,b), Caine (1969), Stock (1968), Gardner (1970 a,b), Luckman (1971) , ...and Bones (1973) a l l i n f e r by virtu e of the shape of the talus slope p r o f i l e s presented i n t h e i r works ( i . e . concave upwards) and the size gradients they note downslope, that slope angle varies inversely with the size of the talus material. Thornes (1971) reported work.from Iceland to which the same i n f e r -ence applies. Worobey (1972) reporting r e s u l t s from a talus cone i n southwest B r i t i s h Columbia concluded that some po s i t i v e corre-l a t i o n between size and angle was implied i n his data. 21 Although Ryder (1968) and Van Burkalow (1945) .think that there are no simple re l a t i o n s between slope angles and material properties, workers such as Piwowar (1903) who con-tended that more angular p a r t i c l e s seemed to support steeper slopes than rounded and Koons (1955), who reported from South-western USA that basalt talus slopes were less steep because of the more rounded nature of the blocks, conclude that p a r t i c l e shape i s important. This i s also noted by King (1966). Frank-f o r t (1968) found that "slope s t a b i l i t y " tended to increase with p a r t i c l e angularity. Thornes (1971) i n a rare attempt to examine other material c h a r a c t e r i s t i c s and t h e i r possible e f f e c t s , found no systematic v a r i a t i o n i n slope angle and the sorting, slope and orientation of p a r t i c l e s (which Davison (1888) had contended to be an important f a c t o r ) . Caine (1967) found " l i t t l e i n t e r -r e l a t i o n , between the talus variables (shape, size and f a b r i c ) . . . and that the arrangement of the blocks i n talus i s (no) more than fortuitous" (p. 501) . In retrospect there has been a d e f i n i t e pre-occupation with the role of size of talus p a r t i c l e s and not, as one would expect, i n r e l a t i o n to slope angle per se, but with respect to pos i t i o n on slope. Material-response relationships i n talus systems, appear to be contradictory and imperfectly understood. 2 . 3 Internal Structure The slope evolution models of Lehmann (1933), Bakker and LeHeux (1946, 1947, 1950, 1952) and Scheidegger (1970) amongst others assume that talus slope materials at depth are si m i l a r to those found on the surface, i . e . loosely packed rock 22 fragments without a subsidiary matrix. Other workers, such as Wallace (1968) and Worobey (1972), have calculated volumes of talus cones on the assumption that the material i s homogeneous throughout. Further, many d e f i n i t i o n s of talus slopes i n f e r that a talus slope i s a p i l e of rock rubble largely composed of rock fragments. A non-homogeneous structure would a f f e c t the calculated volumes of talus, not only compromising some of the theories of the mode of talus development, but also the rates of talus deposition calculated from f i e l d data. F i e l d observations by t h i s writer and other workers give an impression that talus slopes i n general appear to be heterogeneous i n structure. The material beneath the surface i s not rock rubble throughout i t s depth but a structure s i m i l a r to that as i l l u s t r a t e d i n Figure 2.7. This observation i s not only lim i t e d to low a l t i t u d e mountain valleys-but i s also noted i n sub-alpine or even alpine talus slopes. The top layer (A), or mobile layer, i s usually loose angular talus fragments which give a talus slope i t s t y p i c a l external appearance. Layer (B) i s an intermediate zone where pockets of fine material form a patchy matrix. The larger frag-ments s t i l l maintain inter-fragment contact. A t h i r d layer (C), i s a basal layer where the fine grained matrix i s predominant and encloses the larger talus fragments completely so that i n t e r -fragment contact i s minimal. Previous workers have noted elements of t h i s s t r a t i f i -cation. I t may be pointed out that the intermediate layer does not always occur, or at least i f i t does occur i t may be .<:,..-... Figure 2.7 Schematic illustration of talus slope structure 24 extremely thin. Von Moos (1953), i n reporting materials encoun-tered i n a g a l l e r y driven into a talus slope i n the Swiss Alps, noted an increase i n the sand f r a c t i o n toward the rock boundary and the lack of a fin e matrix near the surface. Ritchie (1963) presents photographs showing the fi n e r matrix of the intermediate and basal layer beneath the mobile layer which had been stripped o f f i n the course of highway construction i n Washington State, whilst B a l l (1966) and Hutchinson (1967 b) show photographs of similar materials beneath the mobile and intermediate zones i n Wales and Ireland. Breth (.1967) describes what i s apparently a landslide i n the basal layer of a talus slope i n the Austrian Tyrol whilst Branthoover (1972) encountered similar s t r a t i f i c a -t i o n to that i n Figure 2.7 during an investigation of talus slopes near Lewiston, Pa. Morisawa (.1966) i n Colorado and Bailey (1971) in Wyoming note crude layering p a r a l l e l to the surface of talus slopes whilst Gerber and Scheidegger (1974) mention the fact that loose talus material "forms only a r e l a t i v e l y t h i n cover" (p. 26) on talus slopes i n Austria. Examples of my own observations from the f i e l d area near Princeton, B.C. and the Ross Dam Area, Wash-ington State, are given i n Figures 2,7 and 2.9 respectively. It i s not intended to consider the o r i g i n of t h i s s t r a t -i f i c a t i o n i n d e t a i l , although the o r i g i n of the matrix i n p a r t i c -ular and the basal layer generally would aid i n an assessment of th e i r s t a b i l i t y c h a r a c t e r i s t i c s . The following alternatives appear to present themselves i (a) A g l a c i a l o r i g i n : i n which t i l l from the f i n a l Figure 2.8 Talus slope structure; location - Siirdlkameen field area (N.B. Transition from open, loose mobile layer to basal layer, to left of Figure, exhibiting the finer matrix) 26 27 g l a c i a t i o n i n a l l the areas mentioned above has mantled the bed-rock slope and which has been mantled i n turn by post g l a c i a l talus accumulation. If t h i s i s the case i n B r i t i s h Columbia, for example, post g l a c i a l talus accumulation has been su r p r i s i n g l y l i t t l e . The appearance and the density of the basal layer, how-ever, would tend to support t h i s hypothesis. (b) A weathering o r i g i n : i n which the material i n the basal layer and i n scattered pockets i n the intermediate layers are the re s u l t s of weathering and material breakdown of older talus accumulations. The lack of d i s t i n c t boundaries i n the talus and also the fact that the matrix gets more persistent with depth, i . e . a gradation change, would tend to support the idea of a weathering p r o f i l e o r i g i n for the layering or zonation. (c) The sieving e f f e c t : an o r i g i n proposed by Gerber and Scheidegger (1974) whereby the f i n e r material such as frag-ments and dust f i l t e r s through the talus to c o l l e c t at the bottom, i . e . i n the basal layer. The grain size d i s t r i b u t i o n i n v e r t i c a l section would support t h i s hypothesis but the volume and source of dust and small fragments required to form the widespread matrix i s d i f f i c u l t to v i s u a l i s e . Examples e x i s t of g l a c i a l deposits such as g l a c i o -l a c u s t r i n e s i l t s being found beneath the lower portions of the slopes (e.g. Kicking Horse Canyon, B.C.). F l u v i a l sand and gravel has also been found i n the toe portions of talus (e.g. Worobey, 1972, Breth, 1967). Wahrhaftig (1958) also notes that t i l l i s sometimes found beneath talus i n the Alaska Ranges and 28 Lewis (1969) notes a s i m i l a r s i t u a t i o n i n the East Kootenays of B r i t i s h Columbia. It i s s u f f i c i e n t to note that although the s t r a t i f i c a -t i o n may be due to one or more of the processes noted above i t s presence seems to be common. It i s , therefore, considered v i t a l to acknowledge the existence of the s t r a t i f i c a t i o n i n a treat-ment of material-process l i n k s , talus slope s t a b i l i t y , slope development and attendant transformation processes. 2.4 Transformation Processes on Talus Slopes 2.4.1 Transformation Agents; A variety of transformations can be operative on talus slopes. Rapp (1960 b) l i s t s some of the more important ones which are reproduced with modification as follows: (a) Individual p a r t i c l e movement r e f l e c t i n g thermal changes, creep, or movement , caused by the impact of f a l l i n g rock. (b) Talus s l i d e s which are described as f a i l u r e s i n the talus material i t s e l f . (c) Snow avalanches, the e f f e c t of which has been noted by White (1967) and Luckman (1972) . (d) Alpine mudflows which may emanate from the g u l l i e s that feed many talus slopes ( s p e c i f i c a l l y talus cones), Rapp 1960 b, Behre, 1933, F r y x t e l l and Horburg, 1 9 4 3 ) . (e) Overland flow, (Howarth and Bones, 1972; Dingwall, 1972) . 29 The r e l a t i v e importance of these various processes w i l l vary necessarily with the environment i n which the talus slope has developed. The main concern i n t h i s work w i l l be talus s l i d e s and shear processes within the slope i t s e l f . 2.4.2 Shear Processes i n the Talus System; A d i s t i n c t i o n w i l l be made i n t h i s review discussion between f a i l u r e i n the mobile layer and f a i l u r e i n the basal layer although i n Section 2.4.1 they are both referred to.as talus s l i d e s . I t i s thought that the intermediate layer does not have a d i s t i n c t i v e f a i l u r e mode since i t shares c e r t a i n properties with both the mobile and the basal layers; (a) Failures i n the Mobile Layer: Two scales of f a i l u r e can be distinguished i n the mobile layer, ;the movement of in d i v i d u a l par-t i c l e s and the occurrence of talus s l i d e s involv-ing rock fragments i n the mobile layer. The d i f -f e r e n t i a t i o n , however, may r e f l e c t the scale of observation and measurement rather than i n t r i n s i c differences i n the scale of the process. (i). Movement of in d i v i d u a l p a r t i c l e s : Measurement of the movement of in d i v i d u a l p a r t i c l e s on talus slopes has been car r i e d out by many workers. Results have been presented with very l i t t l e accompanying rationale for the movements observed. Barnett (1966) found that movement was extremely e r r a t i c and concluded that i t did 30 not vary i n a systematic way. Stock (1968), on talus slopes on B a f f i n Island found sim-i l a r behavior. Worobey (1972) working i n the Similkameen Valley of B r i t i s h Columbia found no systematic behavior i n the move-ment of p a r t i c l e s , but noted that coarse debris moved more than fine debris. Rapp (1960. a), found that the movement of i n d i -vidual p a r t i c l e s was i r r e g u l a r both i n space and time. Gardner (1969) has con-cluded that the movement measured i n the Alberta. Rockies was "very e r r a t i c " . He states that the e r r a t i c movement of small groups of p a r t i c l e s or i n d i v i d u a l ones sug-gests that the forces producing the move-ment are i s o l a t e d i n certa i n parts of the slope. He did f i n d , however, that the rate of movement df the p a r t i c l e s was greater toward the top..of talus slopes than toward the base, an observation which has considerable significance i n the l i g h t of discussions i n succeeding chapters. As Gardner (1969) i s ri g h t to point out, the forces producing movement may include such diverse processes as r o c k f a l l , snow avalanches or f a i l u r e s i n the mobile layer 31 (as described by Rapp, 1960 b). To t h i s should be added thermal e f f e c t s , s e t t l i n g , seismic forces or movements i n the basal layer. In fact, there i s l i t t l e reason to expect that measurements of the movement of i n d i -vidual p a r t i c l e s should show a systematic v a r i a t i o n since t h e i r movement appears to be related to many processes which may involve.an aggregate of p a r t i c l e s of which the measured p a r t i c l e s are only a part. Studies of t h e i r movement would appear to remain inconclusive i f other factors such as the incidence of talus slides or basal layer processes are not considered, ( i i ) Talus Slides A larger scale of f a i l u r e than the above has been noted on talus slopes and i s " termed talus s l i d e by Rapp (1960 b) and debris s l i d e by Gerber and Scheidegger (1974). They occur as a movement of a mass of material on the surface of the slope and form a lobe or tongue-shaped deposit which, according to Gerber and Scheidegger, are observed "everywhere on talus slopes" (p. 34). 32 In his investigation of talus slopes i n Spitzbergen, Rapp noted d i r e c t l y 12 such debris s l i d e s which occurred i n "unstable t a l u s " . They occurred largely i n the upper portions of the slope and came to rest not very far below t h e i r point of o r i g i n . This observation i s also of importance i n the l i g h t of subsequent discussion. Large boulders were invariably found near the front and the sides of the s l i d e mass. Most sli d e s were narrow i n width, shallow i n depth but varied i n length. Rapp describes them as s l i d i n g down " i n slow motion i n which larger stones s l i d on top", (p. 61) and noted that they were sim i l a r i n prin-.. c i p l e to tongue-like s l i d e s which often occur i n gravel p i t s and mounds of tipped ore. Worobey (1972) attributed the very marked strip.ingj of talus slopes i n his f i e l d area to the operation of talus s l i d e s . In Allen's opinion (Allen (1970 a)) such debris s l i d i n g , or as he terms i t "avalanch-ing", i s the dominant process shaping many screes". (p. 348). Morisawa (1966) also 33 deems talus s l i d e s to be "the most import-ant mechanism for s h i f t i n g large amounts of material on talus slopes" (p. 113) at high a l t i t u d e s i n Colorado. It w i l l be noted i n succeeding chapters that the process of talus s l i d i n g may be linked both to properties of material depos-i t e d on talus slopes and to the form of the slopes themselves, (b) F a i l u r e i n the Basal Layer Direct observations of f a i l u r e s i n the basal layer of a talus slope do not exi s t as such but movements i n talus slopes referred to by Rapp (1963), Terzaghi and Peck (1967), Bjerrum and Jorstad (1968), and Branthoover (1972) are most c e r t a i n l y not i n the mobile layer as defined e a r l i e r i n t h i s chapter. The presence of water played a large part i n these f a i l u r e s and i t i s probable that the basal layer was involved since i t i s the only part of the slope where pore pres-sures could be expected to develop. Rapp (1963) documents the s l i d e s at Ulvadal following extremely heavy rains. Terzaghi and Peck (1967) note that such s l i d e s often occur during periods of snow melt when large quantities of free water are available,.whilst Bjerrum and Jorstad (1968) 34 comment on the f a i l u r e of a talus slope at Modalen, Norway, which was caused by a very large boulder f a l l i n g onto the talus surface the impact of which caused l i q u e f a c t i o n of the apparently saturated basal layer. The material i n the Modalen s l i d e was described as "stones and boul-ders with the pores between these fragments being f i l l e d with f i n e material" (p. 6). As Hutchinson (19 67 b) notes, gradation curves of material that i s very probably from the basal layer do not obviate the p o s s i b i l i t y of such material being prone to l i q u e f a c t i o n e s p e c i a l l y under dynamic loading conditions such as seismic forces or the impact of a f a l l i n g rock. A notable example of a s l i d e i n the basal layer i s given by Breth (1967). Although he terms the stratum i n which the f a i l u r e took place "moraine", the s t r a t i g r a p h i c p o s i t i o n of the material beneath the mobile layer and i t s properties as described by Breth make i t very probable that the s l i d e , caused by reservoir f i l l i n g i n the Kauner Valley, Austria, was a f a i l u r e i n the basal layer. A further example has been described recently by Azimi and Desvarreux (1974) i n the French Alps. Note must also be made of an " a r t i f i c i a l " basal layer being e f f e c t i v e i n causing water promoted 35 f a i l u r e i n a zone above the actual basal layer. In areas of permafrost, the permafrost table could provide an impermeable layer s u f f i c i e n t to cause some displacement i n the mobile layer (cf. Bones, 1972 and Chandler, 1973). Movements caused by i n s t a b i l i t y of the basal layer are of a very large scale compared to other forms of i n s t a b i l i t y and very often go beyond the boundary of the talus slope i n question and deposit material i n areas of the va l l e y f l o o r , e.g. the Modalen Slide. Lack of d i r e c t observa-t i o n , however, hinders a more detailed discussion of f a i l u r e i n the basal layer. 36 CHAPTER THREE DISCUSSION OF FIELD PROCEDURES 3.1 F i e l d Investigations 3.1.1 I n i t i a l F i e l d C r i t e r i a ; to meet the objectives out-l i n e d i n Chapter 1 these were: (a) that the talus slopes to be investigated should be dominated by rock f a l l processes, (b) that the material forming the talus slopes should be of a constant l i t h o l o g y both within the free face above each slope and between in d i v i d u a l slopes. (c) that the talus slopes should be accessible and l o g i s t i c a l l y v i a b l e . appeared to s a t i s f y the above c r i t e r i a were studied i n the Coast Mountains near Pemberton and Garibaldi, and i n the Skagit Ranges at Lindeman Lake. A l l slopes were developed on granite or gran-o d i o r i t e . The slopes were at elevations where snowfall was thought to be low enough that snow avalanches would not assume dominance as a slope process. The locationsof slopes selected are shown i n Figure 3.1. Six slopes were chosen i n the Pemberton area because several colleagues were also involved i n geomorphic investigation in the area (see Slaymaker, 1972; G i l b e r t , 1972, 1973; Ponton, 1972) and access was therefore f a c i l i t a t e d . Two slopes i n the Cheakamus Valley, south of Garibaldi, and one slope at Lindeman 3.1.2 Description of I n i t i a l F i e l d Areas; Talus slopes which Figure 3.1 Location of slopes studied in South West British Columbia 38 Lake were also selected. Brief descriptions of the slopes studied are as follows: (a) Sheet taluses: (i) L i l l o o e t Lake No. 2; a sheet talus on the east shore of L i l l o o e t Lake which termin-ated about 35 m. above water l e v e l . No observable processes were active at i t s toe. The slope was quite active i n that the noise of f a l l i n g rock was a constant companion i n the f i e l d . ( i i ) Poole Creek; two very short talus slopes developed at the foot of a rockface above Poole Creek F l a t s , 3.2 km. south of Birken. No fresh debris was observed on these slopes and i n many places s o i l and organic matter f i l l e d the interfragmental voids. ( i i i ) Spetch; active talus slopes developed at Spetch on the north side of the Birkenhead River, 8 km. north of Mount Currie. Partly vegetated but active talus accumulation taking place. At Spetch No. 2 a recent rockslide had deposited fresh debris on the slope. (iv) Cheakamus Valley; two active talus slopes developed just north of Brohm Lake on the east side of Highway 99. 39 (b) Cone taluses: (i) L i l l o o e t Lake No. 1; a cone talus on the west side of L i l l o o e t Lake the foot of which terminated i n the water of L i l l o o e t Lake. Evidence of snow avalanche a c t i v i t y was found. ( i i ) Lindeman Lake; a cone talus (see Figure 2.1), developed at the outl e t of a cou l o i r on the east side of Lindeman Lake. E v i -dence of snow avalanche a c t i v i t y observed but r o c k f a l l very intense. 3.1.3 Additional F i e l d C r i t e r i a ; After examining the results of the i n i t i a l i nvestigation i t was thought that the qu a l i t y of the r e s u l t s r e f l e c t e d amongst other factors the physiographic .  v a r i a t i o n i n the environments i n which the talus slopes were located, e.g. v a r i a t i o n i n slope aspect, elevation, gross geom-etry, etc. The following f i e l d requirements were imposed on the sel e c t i o n of a further f i e l d area: (a) that talus cones be excluded, (b) that talus slope orientation be held as constant as possible, (c) that talus slopes with l i t t l e or no vegetation be selected, (d) that talus slopes with comparable gross geometries be preferred, (e) that the talus slopes be located i n a low snowfall area to obviate the p o s s i b i l i t y of snow avalanche TABLE II. CHARACTERISTICS OF SLOPES STUDIED Talus Slopes Studied - Coast Ranges Name (Nos. on Fig. 3.1 Follow in Brackets) Location Activity (Input) Basal Con-ditions Base Ej vation' Le- Height1 Mean Angle No. of Segments Length of Segments No. of Particle^ Measured Remarks Orienta-tion Lillooet Lake #2(5) East side of L i l l -ooet Lake Active Road along shore 245 m. asl 156 m. 35. .5° 8 30 m. 80 Sheet talus 180° Poole Creek #1(3) S.E. side of Poole Crk. Flats Non-Active Poole Crk. Flats 305 m. asl 24 m. 29. .6° 7 6 m. 70 i i 290° Poole Creek #2(3) 11 it I I Non-Active I I I I 305 m. asl 12 m. 27. ,2° 4 6 m. 40 I I 340° Spetch #1(2) N.W. side of Bir-kenhead River Active Birkenhead River 335 m. asl 125 m. 32. 1° 5 4x30 l x l l m. m. 50 it 120° Spetch #2(2) I I it Active I I I I 335 m. asl 85 m. 28. .9° 7 6x152 1x20 m. m. 70 I I 110° Cheakamus #1(1) East side of Highway 99 Non-Active Road along bench 365 m. asl 94 m, 34. 2° 5 30 m. 50 I I 250° Cheakamus #2(1) n I I Active I I ti 365 m. asl 60 m. 34. .1° 7 15 m. 70 n 270° Lillooet Lake #1(4) West side of Lillooet Lake Active Lake 215 m. asl 200 m. 32. .8° 9 5x30 4x60 m." m. 90 Cone talus 150° Lindeman Lake (6) S.E. corner of Lindeman Lake Active Morainic ridge 855 m. asl 127 m. 34. .8° 6 5x30 m. 60 I I 270° Notes: 1: In some cases the survey was not taken to the top of the 2: Estimated : from 1:50,000 topographic maps to the nearest 5 metres. slope because of the fact that the loose talus terminated 3: Total number of particles measured on each slope, some way down from the top and because of the danger from falling rock near the top of some slopes. TABLE II (cont'd.). CHARACTERISTICS OF SLOPES STUDIED Talus Slopes Studied - Similkameen Valley Name Location Activity Basal Con- Base Ele- Height Mean No. of Length of No. of Remarks Orient-(Input) ditions vation^ Angle Segments Segments Particles ation Measured-^  Similkameen #1(A) North Side of Active No 610 Similkameen Valley Process 13 m. east of Active Princeton //2(B) " " " " 610 //3(C) " " " " 610 //4(D) " " " " 610 //5(E) " " " " 610 //6(F) " " " " 610 //7(G) " " " " 610 //8(H) " " " " 610 //9(I) " " " " 610 Similkameen Pilot " " " " 610 m. asl 66 0 m. 33 5° 4 4x30 m. 199 Sheet talus 185° m. asl 67 2 m. 34 2° 4 4x30 m. 198 " 175° m. asl 68 4 m. 34 6° 4 4x30 m. 199 166° m. asl 84 0 m. 34 0° 5 5x30 m. 249 174° m. asl 62 4 m. 32 7° 4 4x30 m. 199 167° m. asl 62 4 m. 32 5° 4 4x30 m. 200 179° m. asl 65 4 m. 33 6° 4 4x30 m. 200 " 190° m. asl 112 2 m. 32 5° 7 7x30 m. 350 " 184° m. asl * 27 3° 2 2x30 m. 99 180° m. asl 49 2 m. 33 0° 3 3x30 m. 149 185° Notes: 1: In some cases the survey was not taken to the top of the 2: Estimated from 1:50,000 topographic maps to the nearest 5 metres, slope because of the fact that the loose talus terminated 3: Total number of particles measured on each slope, some way down from the top and because of the danger from falling rock near the top of some slopes. * Only lower portions investigated. 42 a c t i v i t y which had been observed on some ' . i n i t i a l slopes studied. 3.1.4 Description of a Further F i e l d Area; A location which appeared to f i t the above requirements for further testing of the hypotheses was found on the north side of the Similkameen Valley between Hayes Creek and Stevens Creek approximately 12.8 km. east of Princeton and 20 km. west of Hedley. Talus slopes have developed on the margins of the Thompson Plateau (Holland, 1964) where the Similkameen Valley has been incised into i t (Figure 3.2). The slopes met the more stringent f i e l d require-ments as follows: (a) Talus slope development i n the area has been of the continuous sheet variety and forms an apron along the Plateau edge. Talus cones were not i n evidence (Figure 3.3). (b) The talus slopes have developed with a southerly aspect and t h i s r e s u l t s i n an almost constant slope orientation (see d e t a i l s i n Table I I ) . (c) Vegetation did e x i s t on the slopes but was sparse and scattered. (d) The slopes were of comparable geometries i n that slope heights were not widely variable. (e) The slopes i n the Similkameen appear to be part of a s i m i l a r process environment. There i s no great elevational difference along t h i s section of v a l l e y and further,.no basal processes are active. Thus i t could be assumed that the slopes are subject Figure 3.2 Location map of Similkameen talus slopes. Shaded area indicates sheet talus developed on north side of Similkameen Valley, 13 km. east of Princeton. Slopes studied are marked A and B. Figure 3.3 Photograph taken towards northwest, of sheet talus on north side of Similkameen Valley, 13 km. east of Princeton. Profiles were measured on slopes A, B, C. Note fresh debris on slopes. \ 45 to the same variety of processes. Rockfall pro-cesses were seen to be very active as was e v i -denced by the large number of fresh boulders present on the slopes, (f) The area has low snowfall compared to locations i n the Coast Mountains. Mean annual snowfall at Princeton and Hedley i s 156 cm. and 75 cm. respec-t i v e l y . This compares with 282 cm. at Pemberton Meadows and 422 cm. at G a r i b a l d i . Although there may be no d i r e c t c o r r e l a t i o n between mean annual snowfall and avalanche occurrence the.'talus' slopes developed i n the Similkameen probably have less l i k e l i h o o d of being subject to avalanche processes than the slopes investigated i n the .. Coast Mountains. 3. 2 Sampling Plan Formulation The existence of d i f f e r e n t i a t i o n i n talus slopes with respect to material, form and process would suggest i n turn that some s t r a t i f i c a t i o n be e s s e n t i a l i n a plan to sample material properties and form elements. A preference e x i s t s , therefore, for a sampling unit,or stratum,smaller than the whole slope pro-f i l e i n order that intra-slope variations may be detected i n the f i e l d investigations. 3.2.1 Alternative Sampling Plans; In reviewing sampling plans used i n previous work i t has become clear that the delimitation of a stratum i s not always an objective exercise. 46 The following methods have been used to delimit samp-l i n g units or segment boundaries: (a) on the a r b i t r a r y basis of where breaks i n slopes have occurred (e.g. Bones, 1973), (b) on the basis of "environmental conditions" (e.g. Thornes, 1971).-(c) a proportional sampling approach where segments on d i f f e r e n t slopes w i l l be of d i f f e r e n t lengths but w i l l be of the same proportionate length i n r e l a t i o n to the t o t a l length of the slope (e.g. Evans, 1969; Garner, 1971), (d) a systematic sampling method where'on talus slopes of approximately s i m i l a r dimensions a fixed length of segment i s adopted. Unfortunately, a l l four of these approaches have draw-backs. Breaks of slope are not always c l e a r l y defined on talus slopes and are d i f f i c u l t to detect i n the f i e l d . Breaks of slope may also occur at too small a scale to be distinguishable. "Envir-onmental conditions" are not always definable on talus slopes p a r t i c u l a r l y when they are not i n a state of high a c t i v i t y . The proportional sampling plan, although i t has ce r t a i n i n t u i t i v e benefits has disadvantages i n that sample size must be changed from slope to slope as the length of the segment and therefore the target population changes. I t also requires a pre-survey to define the length of the proportional segments. On too long a segment important variations i n slope angle and material proper-t i e s may be missed. F i n a l l y , a systematic approach may suffer from the fact that the length of segment selected may not detect 47 meaningful-changes i n materials and slope angles. A systematic approach to delimiting the boundaries of the s t r a t a may be the most b e n e f i c i a l , however. In terms of detecting changes i n slope angle and material properties obvi-ously the length of segment has to be t a i l o r e d to the magnitude of change i n these properties within a given set of slopes. This can be ca r r i e d out i n a p i l o t study which would examine the v a r i a b i l i t y of these variables at d i f f e r i n g s p a t i a l scales. The systematic approach therefore appears to be sympathetic to the v a r i a b i l i t y of the parameters under examination i n a way that the other three methods are not. I t also lends i t s e l f to a r i g i d system of within-stratum sampling more readi l y than the others. The f i e l d investigations were based on two d i f f e r e n t sampling plans. A rather loose proportional sampling plan was adopted i n i t i a l l y . The method involved the estimation of the slope length by eye and the adoption of one quarter of t h i s length as the segment length. However, i t i s very d i f f i c u l t to e s t i -mate slope length from the base of the slope and frequently the i n t e r v a l selected was much too short. Further, the proportional slope segments were so variable i n length, because of the variable lengths of the talus slopes studied, (see Table II;):, that the fixed sample size adopted did not r e f l e c t the v a r i a b i l i t y of the target population being sampled. Based on t h i s experience and the argument presented above a systematic sampling plan was ; subsequehtly; adopted. 3 . 2 . 2 Delimiting Sample Points within the Strata or Segments; A transect sampling approach was adopted. Selection of sample 48 points by random numbers and by a f i x e d - i n t e r v a l method was con-sidered. The random method, although desirable i n many ways, has the following disadvantages; (a) time consumed i n locating positions determined by the,random numbers, (b) time wasted by several /concurrent random numbers f a l l i n g on a large boulder i n blocky talus. The f i x e d - i n t e r v a l method on the other hand, whilst not completely solving the d i f f i c u l t y of several points f a l l i n g on the same boulder does ensure that the p a r t i c l e s are measured over the whole length of the segment and i s far more e f f i c i e n t . 3.2.3 Delimiting the Length of Segment; In defining the length of segment for the investigation three factors were con-sidered : (a) The length of the segment should be representa-. t i v e of a slope of deposition and thus should be mechanically meaningful. (b) The length of segment should be long enough to include-an ample number of boulders from which to draw a sample. (c) The length of the segment should be such that given conditions (a) and (b) the v a r i a b i l i t y of the p a r t i c l e properties should be kept at a mini-mum. . This factor assumes importance because i n t e r n a l s t r a t i f i c a t i o n i n material properties exists and the v a r i a b i l i t y of the sample would increase with an increase i n segment length. 49 3.3 P i l o t Investigations for the Similkameen Talus A p i l o t investigation was c a r r i e d out i n the Similka-meen to obtain data which would lead to a selection of optimum segment length and optimum sample s i z e . A slope was selected that appeared to be of a constant angle over a large part of i t s length. 3.3.1 Determination of.Segment Boundaries; The top and bottom of the talus were defined as the points where a matrix of vegetal debris and/or fine material obscured the i n t e r p a r t i c l e contacts of the talus material. Using f i e l d techniques outlined i n the following section.a tape and Abney l e v e l were used to measure slope angles on d i f f e r i n g lengths of segments. (Figure 3.4). Four distance scales were used to measure slope angle. The general slope angle over 90 m. was 33°; three segments of 30 m. were a l l 33°; at the 15 m. scale the range was 32.0° to 34.5°; at the 7.5 m. scale the range increased to 4.0° (31.0° -35.0°). Thus as the segment length decreased the range of meas-ured segment angles increased (cf. i n c l i n a t i o n diagram i n Figure 3.4). The parameters of a x i a l measurements and f a b r i c data were measured on p a r t i c l e s at 3 s p a t i a l scales (The 7.5 m. scale was omitted because of i n s u f f i c i e n t boulders.) A sample size of 50 was used for the three scales, a figure which deter-mined the sample point location i n the systematic sampling plan discussed above. The v a r i a b i l i t y was calculated using the c o e f f i c i e n t of variation.(see Carson, 1967) for size and shape 50 Figure 3.4 Inclination diagram and slope profile for pilot slope on SimiLkameen talus 51 TABLE I I I . VARIABILITY.OF.MATERIAL. PROPERTIES AT THE THREE SPATIAL SCALES STUDIED Rotational Length of ^ 2 Vector Segment Mean Size Size c.v. Mean Shape Shape c.v. Strength 15 -7.7130 81.8% 0.6310 15.0 70.0% 30 -7.7643 80.6% 0.6336 15.2 69.6% 90 -7.8180 82.6% 0.6330 13.3 73.0% ^tean of long axes measurements i n Phi-units 2 — c.v. = sample coefficient: of v a r i a t i o n .(c.v. = S/X, where S i s the sample standard deviation and X i s the sample mean) 3 Mean of Krumbein's Intercept S p h e r i c i t y 4 Value df s i g n i f i c a n t r o t a t i o n a l vector strength 52 and for f a b r i c , a comparison of s i g n i f i c a n t vector strengths.was considered a suitable index for v a r i a b i l i t y . The re s u l t s are seen i n Table III and from them the following conclusions are made; (a) The v a r i a b i l i t y of size at the three l i n e a r scales i s high whilst the magnitude of that var-i a b i l i t y i s si m i l a r at the three scales, (b) The v a r i a b i l i t y i n shape, by contrast, i s low and the magnitude of the v a r i a b i l i t y i s similar at the three scales, (c) The length of the segment does not a f f e c t the value of the vector strength which at a l l scales i s high and s i g n i f i c a n t at the .01 l e v e l , (d) The length of the segment does not produce sub-s t a n t i a l differences i n the v a r i a b i l i t y of mater-i a l properties under examination. At t h i s juncture i t i s perhaps i n s t r u c t i v e to compare the v a r i a b i l i t y encountered i n t h i s study with the v a r i a b i l i t y reported by other workers i n the size parameters they obtained by using d i f f e r i n g sampling plans and i n d i f f e r i n g process envir-onments. The data are summarized i n Table IV. Size data are highly v a r iable except where point data has been c o l l e c t e d (Caine, 1967; Thornes, 1971). Lateral sampling produces great v a r i a t i o n i n the case of Melton (1965) and Gardner (1970), whilst G r i f f i t h s (1959) using the same method finds a low c o e f f i c i e n t of v a r i a b i l i t y . Because of the d i f f e r e n t measures of size used i n the investigations and the variety of process-environments they TABLE IV. EXAMPLES OF VARIABILITY OF SIZE AND SHAPE ENCOUNTERED BY OTHER WORKERS ON TALUS AND SIMILAR SLOPES SIZE Author L i t h -ology Measure of Size Sample Size i n each Strata Sampling Method Coe f f i c i e n t of Varia t i o n Melton (1965) G r a n i t i c "B" Axis (ins.) Y ? Steepest part of slope, randomly se l e c t point sample h o r i z o n t a l l y from this point 29.41%-90.24% (Mean 57.75%) Gardner (1971) Sandstones, Shales, Carbonates "Mean Nominal Diameter" 25 Point (Proportion samp-lin g ) , one at centre l i n e , 12 either side, l a t e r a l l y , selected by random numbers 50.0%-120.0% (Mean 80.00%) Caine (1967) Dol e r i t e s "Phi-Measure" At a point (no word on sampling plan) 50.0%-9.3% (Mean 7.06%) Thornes (1971) Basalts Mean Log "A" 50-120 Point-metre grid .' 5.42%-147 70% .(Mean=13.2%) G r i f f i t h s (1959) Quartzite Phi-"B" Axis 64-88 L a t e r a l l y along l i n e 7.64%-0.97% (Mean 8.80%) Frankfort (1968) Basalt "B" Axis 25 20' gri d 42.78%-101.53% (Mean 65.7%) Carson (1967) - D 5 Q by Vol-ume Within slope 34.00% Evans ( P i l o t ) G r a n i t i c Phi-"A" Axis Line downslope 15 metre seg. 81.80% 30 metre seg. 80.63% Total slope 82.60% TABLE IV. (cont'd.) EXAMPLES OF VARIABILITY OF SIZE AND SHAPE ENCOUNTERED BY OTHER WORKERS ON TALUS AND SIMILAR SLOPES SHAPE Author L i t h -ology Measure of Shape Sample Size i n each Strata Sampling Method Co e f f i c i e n t of Var i a t i o n Thornes (1971) Basalts Krum-bein's Y 50-120 Point-metre grid 5.03%-18.45% (Mean 16.45%) Evans ( P i l o t ) G r a n i t i c Krum-bein's ¥ 50 Line downslope 15 metre seg. 14.99% 30 metre seg. 15.15% Total slope 13.27% Ul 55 encompass, very l i t t l e i n t erpretation can be placed on the data, but i t does provide comparative information on the v a r i a b i l i t y of the "size variable", however defined, used by other workers. In comparing the data i n Table I V . i t i s seen that one of the highest c o e f f i c i e n t s of v a r i a t i o n i n the size variable has been obtained for the Similkameen data, despite the use of the Phi-transformation which would reduce the value of the c o e f f i c i e n t . This may be due to the fact that the sampling plan, i . e . down-slope sampling, used i n t h i s study i s i t s f i r s t reported use i n talus slope investigations. A more variable sample i s to be expected from such a plan since a much larger section of the slope i s sampled compared to point,, g r i d or transverse sampling plans. I t i s noted that s p h e r i c i t y measurements by Thornes (1971) exhibit a sim i l a r v a r i a t i o n to the ones from the Similka-meen P i l o t Study. In selecting the segment length i t was f e l t that (a) at the 7.5 m. l e v e l the slope angle measurement r e f l e c t e d to a large extent the differences i n fragment elevation above the general slope of deposition, p a r t i c u l a r l y at the base of the slope i n the v i c i n i t y of very large boulders. Further, at t h i s scale there were often very few boulders from which to sample, and (b) at the 15.0 m. scale again the lack of a v a i l a b i l i t y of s u f f i c i e n t boulders near the base of the slope presented problems. Three factors had a bearing on the decision to adopt the 30 m. segment length; (a) i t appeared to represent a "general depositional surface" within the talus slope which was 56 considered important i n view of intra-slope processes, (b) i t provided an ample accessible population, (c) i t provided a scale of measurement compatible with the geometries of most of the slopes i n the area. 3.3.2 Determination,of Sample Size within Segments; In deter-mining the optimum sample size for p a r t i c l e measurement within a segment i t i s pointed out that three basic sets of data are obtained d i r e c t l y and i n d i r e c t l y , i . e . s i z e , shape and f a b r i c , each set having d i f f e r e n t degrees of v a r i a b i l i t y , a fact which i s already apparent i n Table I I I . For a sampling program, there-fore, the optimum sample size determined by the most variable parameter w i l l be the operative sample size for each segment. In the case under consideration the most variable parameter i s siz e , more s p e c i f i c a l l y , the length of the long axis i n Ehi-units. Calculations for an operative sample size were c a r r i e d out with respect to t h i s parameter. Indications from e x i s t i n g l i t e r a t u r e (e.g. Bones, 1973) were that an i n i t i a l sample size of 50 p a r t i c l e s would be s u f f i c -i e nt to estimate s i z e . With respect to the 30 m. segments the resu l t s of the p i l o t study indicate that there i s a 95% proba-b i l i t y that the sample mean d i f f e r s from the population mean by an amount less than 2.3 cm., and a 99% p r o b a b i l i t y that the sample mean d i f f e r s from the population mean by an amount less than 9.7 cm. Given the accuracy of the measurement technique out-li n e d i n the following section, these errors are well within 57 those l i m i t s tolerable. A sample size of 50 p a r t i c l e s within each segment was, therefore, considered s t a t i s t i c a l l y acceptable. In summary, the sampling plan adopted as a r e s u l t of the P i l o t Investigation was as follows: (a) 30 metre segments as the basic sampling unit within the slope as a whole, (b) 50 p a r t i c l e s were measured at 60 cm. i n t e r v a l s along a transect upslope within the basic samp-l i n g unit or slope segment. 3.4 F i e l d Measurement .Techniques 3.4.1 Measurement of P r o f i l e Properties; P r o f i l e measurement was carried out using Abney l e v e l and tape. At certa i n locations p r o f i l e measurement was ca r r i e d out using a rangefinder f i t t e d with a clinometer. However, t h i s method was not very r e l i a b l e and checks on measured distances with a tape found the error i n the operation of the rangefinder to be i n the order of 10%. In the Similkameen the sampling plan described above was adopted. The selection of a p r o f i l e for measurement was based on ease of access and the absence of vegetation. Following the selection of a suitable p r o f i l e i t s measurement was under-taken i n the following manner: (a) The base of the p r o f i l e was marked with a stake (base stake) and flagging tape, (b) A bearing was taken with a Brunton compass to the top of the p r o f i l e , (c) The f i e l d assistant proceeded to the 15 m. mark 58 where a slope angle reading was taken with a hand-held Abney l e v e l sighting onto a marked pole. (d) The f i e l d assistant continued onto the 30 m. mark where the slope angle was again taken from the base stake. The f i e l d assistant flagged the 30 m. loca-t i o n . (e) P a r t i c l e c h a r a c t r i s t i c s were measured at 60 cm. i n t e r v a l s and at the 15 m. mark another slope angle was taken. (f) This operation continued upslope with periodic readings being taken to control .the d i r e c t i o n of the movement up the slope. Once the top of the talus (as defined above), was reached a check was made on the qu a l i t y of the p r o f i l e ' s r e c t i l i n e a r -i t y by aligning the flagged 30 m. stations with the base stake. This method of slope angle measurement was.adopted because the 15.0 m. check on the slope angles would point out any great discrepancy i n the 30.0 m. reading. I t would not be unreasonable to suggest that slope angles measured i n t h i s way were accurate to within ±1°. A problem encountered on slopes where the boulders were very large was the coincidence of a measuring station with the top of a boulder that was much higher than the general slope surface. If measured according to the c r i t e r i a outlined above the resultant reading would give an exaggerated value and i n such cases the f i e l d assistant was directed to either side of the 59 massive boulder or just behind i t . 3.4.2 Measurement of Boulder Properties; Within one 30 m. segment the tape was secured at both ends. A x i a l and f a b r i c measurements were carried,out on the boulder that was d i r e c t l y underneath the 60 cm. mark and i n t h i s way approximately 50 boulders were measured for every segment. In some cases the rock fragment was of such a size that i t extended beyond the sampling point over two or three sampling stations. In these cases only one p a r t i c l e measurement was taken at that loc a t i o n . The three p r i n c i p a l axes of the rock fragments were measured by hand tape following procedures well established i n sedimentary petrology (e.g. Krumbein, 1941) . The "a" axis i s the longest axis of the fragment, the."b" axis i s the intermediate axis i n the same plane as "a" but perpendicular to i t , and "c" i s the shortest axis perpendicular to the plane of "a" and "b". Obviously problems aris e with equidimensional boulders and sev-e r a l e f f o r t s to discern the p r i n c i p a l axes, of these boulders may be necessary. Access to the large majority of fragments was comparatively easy since they tend to l i e on the surface with a l l faces exposed. A Suunto compass/clinometer was used to measure the o r i -entation of the long axis ("a") and i t s dip r e l a t i v e to the h o r i -zontal (Figure 3.5).. Measurement of the orientation of the long axis was made r e l a t i v e to north. Equidimensional boulders pre-sented problems for reasons recounted above. Dip was measured by aligning the base of the compass with the approximate plane of the long axis. The Suunto compass provides an accuracy i n Figure 3.5 Measurement of particle dip on Profile D, Similkameen talus. Clinometer on Suunto instrument faces camera. Base of clinometer is 5 cm. 61 both orientation and dip i n the order of ±5 since the gradation on both the compass and the clinometer i s i n 5° i n t e r v a l s . A l -though the measurements obtained with t h i s instrument appear coarse the instrument has d i s t i n c t advantages with regard to ease of manipulation, ruggedness, and e f f i c i e n c y i n use. In com-parison with other f a b r i c measurements on talus slopes, Caine (1967) does not specify the methods he used, whilst Thor.nes • (.197.1) using a si m i l a r instrument on Icelandic talus claims that the possible error i s not more than ±3°. Gardner (1971) does not discuss error problems i n his report on talus p a r t i c l e orienta-t i o n i n the Moraine Lake area, Alberta. 62 CHAPTER FOUR THE INTERPRETATION OF TALUS SLOPE ANGLES An e s s e n t i a l part of material-response investigations i n talus slopes i s an examination of the uses of such concepts as angle of repose, angle of rest and angle of i n t e r n a l f r i c t i o n i n the int e r p r e t a t i o n of talus slope form, s p e c i f i c a l l y talus slope profiles.''' Relationships between these terms w i l l be investigated and longstanding misconceptions concerning these relationships w i l l be examined and hopefully corrected. Factors c o n t r o l l i n g the various parameters w i l l be examined and the implications for the inte r p r e t a t i o n of talus slopes w i l l be looked at. A. THEORETICAL.CONCEPTS AND TERMINOLOGY 4.1 Definitions of Angle of Rest, Angle Of Repose and Peak Angle of Accumulation Misconceptions have arisen from the use of "angle of rest" and "angle of repose" both i n the geomorphological and the engineering l i t e r a t u r e . As Carrigy (1967) has pointed out, although the term "angle of rest" appears i n many publications i t s use has been ambiguous (cf. Van Burkalow , 1945). The f i r s t source of confusion occurs where some workers have used the term to describe the angle of slope of an i n c l i n e d plane at which a p a r t i c l e r e s t i n g on i t w i l l begin to s l i d e , whilst others have See Glossary of Terms 63 used the term to express the angle at which a mass of loose gran-ular material w i l l stand when p i l e d or dumped. I t i s apparently not r e a l i z e d that the differences between these angles are sub-s t a n t i a l since one describes p a r t i c u l a t e behavior whilst the other describes mass behavior and two d i f f e r e n t thresholds are therefore involved. Usage of the angle of rest (or repose) i n t h i s work w i l l be lim i t e d to that describing mass behavior but a second source of confusion i s immediately encountered. Van Burkalow (1945), Sharpe (1960) and Carrigy (1967) have pointed out there are two "angles of repose" which are rarely distinguished; the steepest angle that can be achieved by the granular material when p i l e d or dumped and a lower angle to which the material w i l l slump when the steeper angle i s exceeded and f a i l u r e has taken place. These two angles can be re a d i l y appreciated by tipping a sugarbowl u n t i l the sugar contained therein moves and achieves, f i r s t the higher slope angle, then the lower one. The two angles have been variously defined and i n t e r -preted. Bagnold (1941), The American Geological Ins t i t u t e (1957), The American Society for Testing Materials (1966), Metcalf (1966), Simons (undated ms.), Rahn (1969), to. .mention a few, ref e r to the higher angle as the "angle of repose". Carson and Kirkby (1972) on the other hand term the lower angle "the angle of repose" and the higher one "the angle of maximum slope". Both Van Burkalow (1945) and Carrigy (1967) refer to the higher angle as the "maxi-mum angle of repose" whilst the lower angle has been defined as the "angle of rest a f t e r avalanching" (Carrigy (1967)), "the 64 angle of shear" (Bagnold, 1941), "the residual angle of shearing" (Allen, 1970 a,b,c) and the "minimum angle of repose" (Van Burkalow.. 1945 X -Terzaghi (194 3) defined the angle of repose as follows, "the material w i l l s l i d e . . . and not come to rest u n t i l the angle of i n c l i n a t i o n of the slope becomes equal to a .certain angle which i s c a l l e d the angle of repose" (p. 4). The inference seems to e x i s t ( i . e . a f t e r sliding) that the angle of repose thus defined by Terzaghi i s the lower angle of repose discussed above. For the purposes of t h i s work i t i s intended to adopt the following d e f i n i t i o n s and notations for the two d i f f e r e n t angles, which w i l l be used i n subsequent discussion: (a) the peak angle of accumulation (s*^) ; the steepest angle that a mass of granular material w i l l stand at without shearing taking place, (b) the angle of repose (or rest) (»<r) ; the angle assumed by granular material aft e r shearing has taken place following an exceedance of threshold conditions as defined by<?< . J c 4.2 Factors Aff e c t i n g the Peak Angle of Accumulation (<^ -c) Investigation of the factors a f f e c t i n g the peak angle of accumulation (c<c) have largely been studied i n the laboratory using model techniques and a r t i f i c i a l conditions of accumulation. The emphasis has been on the e f f e c t s of material on the values of o<c obtained, or material-response re l a t i o n s h i p s . 65 Van Burkalow (1945) experimenting with a wide variety of materials found that <<c varied with material properties i n the following manner; (a) inversely with size of fragments i n p e r f e c t l y sorted materials but d i r e c t l y with those imper-f e c t l y sorted, (b) inversely with density of fragments, (c) d i r e c t l y with t h e i r angularity, roughness and degree of compaction, (d) inversely with height of f a l l of materials onto accumulation surfaces. Carrigy (1967) found that size and sorting had l i t t l e or no e f f e c t , that<K c increased with increased p a r t i c l e angular-i t y and surface roughness. He concluded that values o f ^ are dependent mainly on shape. A l l e n (1970 a,b,c) a f t e r looking at an i d e a l case of prolate spheroids both i n theory and experiment, found that oi increased with departure from the spherical form; increased with p a r t i c l e concentration (aggregate density); and decreased with p a r a l l e l i s m of the long axes of p a r t i c l e s with the d i r e c t i o n of maximum slope of the deposits and surface. A l l e n found that the difference between c < c and c<r, increased with aggregate density which he contended r e f l e c t e d the increase i n the d i l a t a n t compon-ent of shear resistance of the materials considered. Simons (undated ms.), i n a comprehensive survey involv-ing laboratory and f i e l d measurements, noted that c< can be viewed as a function of size, shape, surface texture, mass density 66 and gradation. He concluded that the primary variables i n f l u -encing <?<c seem to be shape, size and, probably, surface texture of the p a r t i c l e s . Metcalf (1966) also found shape to be an important factor. 4.3 Concepts of Shear Resistance and Angle of Internal F r i c t i o n At t h i s stage i n the discussion some well known con-cepts of shear resistance are introduced since elements of shear resistance are presumably important i n determining the behavior of slopes at the thresholds denoted by c< and c< . c r 4.3.1 Definitions of Components of Shear Resistance: The shear resistance, or shear strength, of slope forming materials determines the behavior of that material under shear stresses. In i t s most basic form the shear resistance (t) of a material can be expressed by Coulomb's Law as follows; t = c + fftan^ (Eq. 4.1) where c i s the cohesion of the material, 0 i s the angle of int e r n a l f r i c t i o n and a i s the normal pressure on the f a i l u r e plane. Normally, however, i n t e r p a r t i c u l a t e cohesion, which may ex i s t i n clays and s i l t s , does not ex i s t i n granular materials and the law i s s i m p l i f i e d to; t = 0"tan 0 (Eq. 4.2) As w i l l be seen below, however, granular material does not behave as a purely f r i c t i o n a l material as implied i n Equation 4.2. Further, at high-.normal pressures the f a i l u r e envelope defined by Equation 4.2 departs from the li n e a r form. 67 Workers such as. Rowe (1963), Lee and Seed (1967) and Koerner (1970 a,b) have attempted to e s t a b l i s h by experiment additional components i n the shear resistance of granular mater-i a l s beyond that of simple f r i c t i o n . The following components have been i d e n t i f i e d ; (a) strength due to i n t e r p a r t i c u l a t e f r i c t i o n approx-imating to the angle of s o l i d f r i c t i o n of one p a r t i c l e on another and which was the f r i c t i o n a l component envisaged by Coulomb i n Equation 4.2 denoted by 0^ . (b) strength due to dilatancy e f f e c t s where energy has to be expended to create the volume increase necessary for one p a r t i c l e to pass over another i n the shear process denoted by 0^ . (c) strength due to re-arranging e f f e c t s (or crushing e f f e c t s under high shear stresses) denoted by 0 . a The various components are i l l u s t r a t e d i n Figure 4.1 and 0 can be expressed as follows; 0 = 0 f + 0 d + 0 a (Eq. 4.3) It should be noted that 0, the angle of i n t e r n a l f r i c -t i o n , corresponds to the peak angle of i n t e r n a l f r i c t i o n . During the shear process the d i l a t a n t component i s "removed" and the value of the angle of i n t e r n a l f r i c t i o n f a l l s to the so-called ultimate or residual value (0r) (Lambe and Whitman, .1969)... In the post shear state, therefore, the components i n the residual shear resistance of a mass of granular material are as follows; 0 r = 0 f + 0 a (Eq. 4.4) MEASURED ANGLE OF •* INITIAL POROSITY Figure 4.1 Schematic illustration of the components of shear resistance in a granular material. (Adopted from Rowe, 1962). 69 In the residual condition the material i s also i n the c r i t i c a l state.where the void r a t i o remains constant with further deforma-tion (Lambe and Whitman, 1969, Bishop, 1971). I t i s to be noted that the magnitude of the d i l a t a n t component varies d i r e c t l y with the bulk density of the granular mass, since the denser the aggre-gate, the greater the expansion needed to shear i t , and the greater the value of the angle of - i n t e r n a l • f r i c t i o n . 4.3.2 Factors Affecting the Angle of Internal F r i c t i o n of Granular Materials: Most of the work on the measurement of shear resistance i n granular materials, such as r o c k f i l l , has been done i n connection with the design and construction of rock-f i l l dams. Casagrande (1936) was one of the f i r s t workers i n the f i e l d of s o i l mechanics to point out the e f f e c t s of p a r t i c l e c h a r a c t e r i s t i c s on the angle of i n t e r n a l f r i c t i o n of cohesionless materials. Holtz and Gibbs (1956) and Vallerga et a l . (1957) found the p a r t i c l e shape very important i n accounting for variations i n the angle of i n t e r n a l f r i c t i o n and found that i t increased d i r e c t -l y with angularity. Morris (1959) found similar r e l a t i o n s with angularity and surface roughness of p a r t i c l e s . Mackey (1964) found that shape affected the shear resistance of a granular mass in contrasting ways. He found more spherical p a r t i c l e s could be compacted to a greater degree than angular ones thus increasing the value of 0. Farouki and Winterkorn (19 64) and Du Terte and Winterkorn (1966) found that 0 varies d i r e c t l y with angularity and with dispersion on the Zingg shape diagram. Size was not considered important. Marsal (1967) and Fumagalli (1969) found 70 that shape i s an important factor i n accounting for strength variations at similar densities whilst Nichiprovich and Rasskazov (1967) found .:~ - density an important control on shear r e s i s t -ance. Anagosti (1967) i n a general report, stated that the : shear strength of coarse cohesionless material l i k e l y depends on; mean and maximum grain s i z e , gradation shape, mode of packing, strength of grains, normal strength, porosity, and e f f e c t s of time (weathering, s t r a i n softening, e t c . ) . Al-Houssaini (1972), Mogami and Yoshikoshi (1971), Marachi et a l . (1972), Pike (1973) and Bishop (1971) a l l believe shape to be very important. Indeed, Bishop goes so far as to say " p a r t i c l e shape which influences p a r t i c l e r o l l i n g plays an overriding part i n the behavior of cohesionless s o i l s " (p. 22). Leps (1970) i n a review work concluded that 0 varies inversely with normal stress and sph e r i c i t y but d i r e c t l y with r e l a t i v e density and crushing strength df the constituent p a r t i c l e s . Oda (1972) found that grain f a b r i c affected mobilized strength and dilatancy r e l a t i o n s . In summary, therefore, the following factors are thought to control the value of the angle of i n t e r n a l f r i c t i o n (0) i n cohesionless materials such as r o c k f i l l or talus; (a) Size: The e f f e c t of size seems to be ambiguous. This fact may r e f l e c t the many d i f f e r e n t measures of size used i n the investigations reviewed above. It may also r e f l e c t confusion over the role of the e f f e c t i v e matrix and i t s r e l a t i o n to density and packing properties., (Figure 4.2) . 71 (b) Sorting (Gradation): The e f f e c t s of sorting also seem to be ambiguous. The majority of reports indicate an increase i n the range of sizes e x i s t -ing i n a given aggregate leads to an increase i n 0. This may be related to the higher densities that can be achieved with such a gradation or the increase i n contact forces brought about by increased i n t e r p a r t i c l e contact. Other reports indicate that an improvement i n sorting ( i . e . a decrease i n gradation) leads to an increase i n of an aggregate possibly r e f l e c t i n g the role of an e f f e c t i v e matrix, (Figure 4.2). (c) Shape: This variable i s seen by most workers to be very important i n determining the shear r e s i s t -ance of a granular mass. The angle of i n t e r n a l f r i c t i o n has invariably been observed to increase with angularity. Further, 0 increases with v a r i -ation i n shape. (d) Surface Roughness: Increased p a r t i c l e roughness seems to lead to an increased value of 0. (e) Fabric: Increased p a r a l l e l i s m of the major p a r t i c l e axis with the d i r e c t i o n of shear increases the value of 0. 4 . 4 Relationships between Peak Angle ^of Accumulation (g<_) # Angle of Repose (c<r) , Angle of Internal F r i c t i o n (0 )  and Residual Angle of Internal F r i c t i o n ) The nature of the relationships among c/ •> 0 , c<, and 72 Case One: Well sorted cohesionless material. A l l p a r t i c l e contacts contribute to shear strength of material. Mean s i z e of p a r t i c l e s accurate i n d i c a -t i o n of p a r t i c l e s determining shear resistance. Case Two: Poorly sorted cohesionless material. Large p a r t i c l e s with a f i n e r matrix. Contacts of larger fragments e f f e c t i v e i n c o n t r o l l i n g shear resistance. Matrix properties are subsidiary i n t h e i r e f f e c t , and do not contribute to shear resistance. Mean s i z e of p a r t i c l e s not an accur-ate i n d i c a t i o n of p a r t i c l e s determining shear resistance. May y i e l d s i m i l a r standard deviation of s i z e measurements as Case Three. Case Three: Poorly sorted cohesionless material. Large p a r t i c l e s enclosed i n a f i n e r matrix. Con-tacts of larger p a r t i c l e s do not contribute to •shear strength of material which i s c o n t r o l l e d by matrix properties. Mean s i z e of p a r t i c l e s not an accurate i n d i c a t i o n of p a r t i c l e s determining shear resistance. Figure 4.2 Differing combinations of particle sizes illustrating the effective matrix problem (Modified after Marsal, 1965) 73 0 assume c r i t i c a l importance i n the understanding not only of shear processes on slopes consiting of granular materials but of the values of threshold slopes i n such materials and the factors that control them. 4.4.1 Relationships between Peak Angle of Accumulation (o^) and Angle of Repose : From the work of A l l e n (1970 a) and Carrigy (1967), and the data they present i t i s possible to obtain a s t a t i s t i c a l r e l a t i o n s h i p between oCc and oc^ .. A l l e n has i l l u s t r a t e d the re l a t i o n s h i p thus; c< = cK + AoC (Eq. 4.5) c r * M ' where AoC i s the d i l a t a n t component incK»c. If the data from Carrigy and Allen's work i s plotted with o( c as the ordinate and °^ as the abcissa as i n Figure 4.3 i t appears that a re l a t i o n s h i p exists between the two variables. Contrary to Allen's curious contention thatc< c i s invariant there appears to be wide range of values, i . e . between 25° and 40°. 2 Using the data from Carrigy (1967) a value of r = 0.96 was obtained from the following equation; o£c = -3.290 + 1.273 U r ) (Eq. 4.6) The importance of the d i l a t a n t component i s seen at higher peak angles of accumulation. Data from B u t t e r f i e l d and Andrawes (1972) have been added to Figure 4.3 due to the correspondence that i s thought to ex i s t between t h e i r " s t a t i c and k i n e t i c angles of f r i c t i o n " , the values of <f> and <f>^, and <>C and e< . The, suggestion i s apparently confirmed by the location of t h e i r data points. Of addit i o n a l 74 1 1 ' 1 r 1 1 T 5 15 25 35 45 E q u a t i o n s f o r L i n e s ; LINE 1 ( C a r r i g y ' s d a t a o n l y ) : o< c = -3.29 + 1.273 (<*r)--r2 = .962 LINE 2 ( C a r r i g y and A l l e n ' s data) : «* = 2.60 •+ 1.198 («rf.)--r2 = LINE 3 ( A l l d a t a on p l o t ) : ©< c = 0.1320 + 1.290 (*rYr2 = -904 Figure 4.3 Relationships betweenc<c andcAr 75 int e r e s t i s the location of the two peaks noted i n studies by-Melton (1965) and Rahn (1969) .., 4.4.2 Relationship between Peak Angle of Accumulation (c<c) and the Angle of Internal F r i c t i o n (0); A slope of cohesionless material standing at the peak angle of accumulation, as defined i n Section 4.1, i s standing at the steepest angle that can be formed without shearing taking place. This being the case, the slope i s i n a state of l i m i t i n g equilibrium a n d ^ denotes the threshold slope for that material. In a state of l i m i t i n g equilibrium the shear forces acting on a slope are p r e c i s e l y balanced by available shear resistance, i . e . the r a t i o of strength to stress is, unity. F o l -lowing convention i n s o i l mechanics th i s i s expressed i n a Factor of Safety (F) as follows; shear resistance tan <6 F = ^ : = = 1.00 (Eq. 4.7) shear stresses tane< c According to t h i s argument, therefore, the peak angle of accumu-l a t i o n i s equal to the angle of i n t e r n a l f r i c t i o n , for those p a r t i c u l a r conditions of aggregate packing and density. Workers have found contradictory relationships between << and the angle of i n t e r n a l f r i c t i o n . Metcalf (1966) using c somewhat unconventional testing procedures, found that was co r r e l a t i v e with the angle of i n t e r n a l f r i c t i o n of the material i n i t s densest state. Chandler (1973) found that c< c was equal to the angle of i n t e r n a l f r i c t i o n of the material i n a loose state at constant volume (^ c v)• It i s thought by t h i s writer, however, that both extremes are not generally applicable. 76 Rather, the rel a t i o n s h i p between d> and << i s s p e c i f i c a l l y related to the c h a r a c t e r i s t i c s of the mass being examined (cf. Nanda-kamuran et a l . / .1974). 4.4.3 Relationships between Peak Angle of Accumulation (^ c), Angle of Internal F r i c t i o n (#) , Angle of Repose ( g < r ) and Residual Angle of Internal F r i c t i o n (^r) When f a i l u r e takes place at the threshold defined by Equation 4.7, the d i l a t a n t component of shear resistance i s expended and the material comes to res t i n i t s loosest state where shear strength i s at a minimum or residual value (Equa-tion 4.4). The angle assumed by t h i s material corresponds to the angle of repose of the material (e<.) i . e . the post shear angle. Thuso< r would appear to correspond with ^ for those p a r t i c u l a r conditions of aggregate packing and;.density which are ef f e c t i v e i n c o n t r o l l i n g the d i l a t a n t component i n ^  (or 0) . The two angles <s< c and ^  can therefore evidently be treated i n much the same way as the peak and residual angle of in t e r n a l f r i c t i o n respectively (cf. Bishop, 1971). There i s an exception to the above argument and t h i s occurs where the depositional density of the granular material under consideration i s very low and approaches the c r i t i c a l density. In t h i s case <XC would be equal to and cf> would equal ^ (tf . B. TALUS SLOPE FORM 4.5 4.5.1 Interpretation of Talus Slope Angles Previous Interpretations; I n s u f f i c i e n t d i s t i n c t i o n has 77 been made i n the l i t e r a t u r e between c< and oi , and between 0 c r and 0 . r Many workers have asserted that the angle of a talus slope i s equal to the "angle of repose" for the talus material. As has been pointed out elsewhere (e.g. Andrews, 1961) these investigations ignore the fact that talus slopes are not gener-a l l y r e c t i l i n e a r i n p r o f i l e and that slope angles within the slope show considerable v a r i a t i o n generally r e s u l t i n g i n a con-cave upward p r o f i l e . At the same time they rarely define which "angle of repose" (cf. Section 4.1) i s being referred to. Work-ers who are s p e c i f i c as to which angle of repose they refer present contradictory impressions. For example, G i l u l l y et a l . (1959) observe that "talus slopes... (stand at) the angle of .. repose because i t i s the steepest slope on which the material w i l l stand without r o l l i n g downward..." (p. 1 7 8 ) . In t h i s case the angle of repose i s the peak angle of accumulation (c^  ) . Carson and Kirkby (1972) on the other hand state that "talus and scree... stand at the angle of repose of the coarse material"., (p. 33 3 ) . The usage of the term "angle of repose" i n t h e i r work indicates that i n t h i s case the angle of repose i s ^ . Workers have equated the angle of repose with the talus slope angle and have gone on to equate the angle of repose with the angle of i n t e r n a l f r i c t i o n . I t i s i n t h i s regard that prob-lems created by not distinguishing between 0 and 0^ (and i n c i -dentallyc< c and c-Cr) become extremely important.; Ward ( 1 9 4 5 ) , for example, inferred i n his early work on slope s t a b i l i t y , that the l i m i t i n g slope for talus (otc) was determined by the angle of 78 i n t e r n a l f r i c t i o n of the material i n a loose state. Carson (1969) on the other hand noted that the l i m i t i n g slope (c*^ ,) was determined by 0. In a l a t e r paper, Carson and Petley (1970) note that the angle of repose of bouldery rock fragments i s equal to rytx but i n the same paper indicate that slope angle, v i s - a - v i s the angle of repose i s equal to 0. The lack of d i s t i n c t i o n .. between residual shear strength values and values of shear strength above that threshold also detract from studies by . Scheidegger (1970) and Carson (1971). Problems have also arisen i n attempts to interpret the value of the c h a r a c t e r i s t i c slope angle for talus, i . e . 35°. Obviously t h i s interpretation i s linked to the discussion above and frequently the three relationships are discussed together, v i z . talus slopes stand at the angle of repose - the angle of repose i s equal to the angle of i n t e r n a l f r i c t i o n - the slopes stand at 35°. Many workers have erroneously thought that 35° represents the l i m i t i n g slope for talus (e.g. Ward, 1945';, Carson, 1969, 1971) which i s c l e a r l y not the case/ (Figure 2.5). The l i m i t i n g slope i s obviously higher than 35° although Carson and Petley (1970) do suggest that 35° affords an estimate of the ultimate angle of shear resistance (0 ) for bouldery rock frag-ments . 4.5.2 The Supply Induced Transformation Hypothesis; To resolve the obvious contradictions l i s t e d above i t remains to determine the following which are central to the interpretation of talus slope angles; (a) l i m i t i n g slopes for talus materials corresponding to the peak angle of accumulation (c<^) , 79 (b) t h e r e a s o n f o r t h e f a c t t h a t 3 5 u seems t o be t h e c h a r a c t e r i s t i c s l o p e a n g l e f o r t a l u s . The l i m i t i n g s l o p e f o r t a l u s m a t e r i a l s i s , a s d e f i n e d a b o v e , t h e p e a k a n g l e o f a c c u m u l a t i o n (<*-c) a n d i n o r d e r t o a s c e r t a i n t h i s v a l u e , a r e v i e w o f t h e v a l u e s o f o<c f o r v a r i o u s t y p e s o f t a l u s - l i k e m a t e r i a l s was c a r r i e d o u t . The r e s u l t s a r e p r e s e n t e d i n T a b l e V . V a l u e s f o r <K w e r e f o u n d t o be b e t w e e n c 4 0 . 8 a n d 4 2 . 0 on t h e b a s i s o f p u b l i s h e d i n f o r m a t i o n w h i c h c o r r e -s p o n d s q u i t e w e l l t o 0 f o r l o w c o n f i n i n g p r e s s u r e s a n d l o w d e n -s i t i e s f r o m t h e w o r k o f L e p s (1970) a n d N i c h i p r o v i t c h a n d R a s s -k a z o v ..(1967) . I t a l s o c o r r e s p o n d s t o t h e v a l u e s o f max imum t a l u s a n g l e s p u b l i s h e d i n t h e l i t e r a t u r e ( 4 0 ° - b y M i n e r , 1 9 3 4 ; R a p p , 1960 b; H o w a r t h a n d B o n e s , 1 9 7 2 ) . I f i t i s a s s u m e d t h a t t h e v a l u e f o r i>( f o r t a l u s m a t e r -c i a l s t a k e n f r o m T a b l e V i s 4 1 ° i t i s p o s s i b l e t o e s t i m a t e t h e v a l u e o f t h e a n g l e o f r e s t (oC^) , v i s - a - v i s t h e r e s i d u a l a n g l e o f i n t e r n a l f r i c t i o n (0^) b y t h e u s e o f E q u a t i o n 4 . 6 . I n E q u a -t i o n 4 . 6 w i t h = 4 1 . 0 ° , oi i s c a l c u l a t e d t o be 3 5 . 0 ° . T h i s C 10 v a l u e i s c o i n c i d e n t w i t h t h e c h a r a c t e r i s t i c t a l u s s l o p e a n g l e n o t e d a b o v e . 35° w o u l d , t h e r e f o r e , a p p e a r t o r e p r e s e n t t h e " c h a r -a c t e r i s t i c " a n g l e o f r e p o s e (e< ) f o r t a l u s m a t e r i a l s a n d w o u l d a l s o c o r r e s p o n d t o t h e a n g l e o f i n t e r n a l f r i c t i o n o f t h e same m a t e r i a l i n a l o o s e s t a t e . I t f u r t h e r c o r r e s p o n d s w i t h t h e r e s i d u a l a n g l e o f i n t e r n a l f r i c t i o n o f c o a r s e s i n g l e m i n e r a l s o i l s a s r e p o r t e d b y K e n n e y ( 1 9 6 7 ) . The f a c t t h a t 3 5 ° i s i n t e r p r e t e d t o be t h e g e n e r a l 80 angle of r e s t (oC^) by i t s r e l a t i o n s h i p to o( through Equation 4.6 for talus materials has led t h i s writer to formulate the supply  induced transformation hypothesis which relates process material and form for the mobile layer i n r o c k f a l l talus slopes. Under the terms of t h i s hypothesis, supply of debris takes place from the rockwall above with deposition occurring near the top of the slope u n t i l the peak angle of accumulation i s exceeded. Fa i l u r e takes place and by downward movement the debris i s deposited at a slope equivalent to rX.^ or 0r« The fact that a relationship was found to e x i s t between c< c and oCr for talus materials i s an i n t e r e s t i n g prima f a c i e confirmation of the hypothesis (Figure 4.3). The hypothesis has further supportive evidence. In Chapter 2 i t was noted that observable movement on talus slopes both i n terms of i n d i v i d u a l p a r t i c l e s and the incidence of talus s l i d e s i s concentrated i n the upper portions of the slope, i . e . near the rockwall. This together with what i s known about depositional patterns.on talus slopes (Gardner, 1970; Caine, 1969) would indicate that the supply induced transformation hypothesis may have a basis i n observed r e a l i t y as well as i n the r e l a t i o n -ships between the threshold slopes noted above. F i e l d evidence given by Rapp (1960 b) from Spitzbergen i s of further note. Slopes which, he considered as being domin-ated by talus s l i d e s stand at angles of 34.9°, 34.8°, and 34.2° respectively, angles which compare favorably with the value of ^ r o r 0 r obtained above ( i . e . the angle assumed afte r f a i l u r e has taken place). 81 Work by Alle n (1972) reports the r e s u l t s of investiga-tions into the i n t e n s i t y df deposition from debris s l i d e s i n model experiments. He concluded that "the high i n t e n s i t i e s of deposition... correspond to degrees of packing...that are very nearly the loosest possible for natural materials" (p. 105). Applying t h i s to talus s l i d e s i t tends to suggest the idea that the material deposited by talus s l i d e s exists i n a c r i t i c a l state, i . e . 0 = d> = c< . ' cv " r r The c h a r a c t e r i s t i c slope angle and the l i m i t i n g slopes for talus i n general appear to correspond toc< r and oi^ respec-t i v e l y . These values are related through Equation 4.6 which appears to be a suitable transformation model for r o c k f a l l talus and relates the three factors noted i n Section 1.3. As far as th i s writer i s aware the transformation process described above has not been s a t i s f a c t o r i l y explained before, and the observed d i s t r i b u t i o n of talus slope angles seems to afford a confirmation of t h i s process. C. THE CASE OF THE SIMILKAMEEN TALUS Under the terms of the supply induced transformation hypothesis, the c h a r a c t e r i s t i c slope angle exhibited by r o c k f a l l talus slopes can be assumed to be equal to the angle of repose (<*r) for that material, thus affording an interpretation of rock-f a l l talus angles. The hypothesis was investigated with reference to the Similkameen talus slopes which, for reasons outlined i n Chapter 3, were considered well suited for the purpose. 82 4.6 Evidence for the Operation of Supply Induced Transformation Processes A necessary precursor to a discussion of slope angles i s an examination of the evidence for the operation of supply induced transformation processes, i . e . talus s l i d e s . Since d i r e c t observations of talus s l i d e s were not c a r r i e d out, i n f e r -ences must be made based upon the int e r p r e t a t i o n of response elements such as s l i d e debris, slope p r o f i l e s and f a b r i c patterns. 4.6.1 A e r i a l Photography and Slide Debris; Fresh deposits of debris can be seen on a e r i a l photographs (Figure 4.4) on the talus slopes on the north side of the Similkameen Valley between Stevens Creek and Hayes Creek. These deposits give the char-a c t e r i s t i c striped pattern to the talus slopes s i m i l a r to that observed by Worobey (1972) on talus slopes further east i n the Similkameen Valley near Keremeos. Alternative origins for the deposits could be rock s l i d e debris, the r e s u l t of snow ava-lanches, debris avalanches or flows, as well as being products of talus s l i d e s . In the f i e l d the debris does not appear:rto be a r e s u l t of rockslide deposition since the deposit i s too narrow. Whilst the p o s s i b i l i t y of the deposits being the r e s u l t of snow avalanche does e x i s t t h i s must be considered very unlike l y i n view of the l i g h t snowfall i n the area. 4.6.2 Slope I r r e g u l a r i t i e s ; A d i s t i n c t feature observed on the Similkameen slopes was the existence of "fronts" or l o c a l -ised steep sections of the slope p r o f i l e . These tended to give the p r o f i l e i n some cases a stepped appearance evident i n a series of mini-concavities. As can be seen i n Appendix I and Figure 4.4 Aerial photograph of slopes studied on north side of Similkameen Valley. Note Lobate forms (arrowed) on sheet talus and lighter tone of fresh deposits. (From B.C. Air Photograph BC 4436-213; Scale 1 cm. =£= 150 m.) 84 and Figure 4.5. these fronts may vary i n height from 1.5' m. - 3 m. The o r i g i n of these fronts may be explained by one of the following alternatives; (i) i t could represent the scar of a movement i n ..the material downslope from i t , as indicated i n Figure 4.6, ( i i ) i t could represent the "front" of a mass of debris s l i d e material that has s l i d on the slope as indicated i n Figure 4.6. Andrews (1961) noted a s i m i l a r phenomenon i n the scree slopes he studied i n the Lake D i s t r i c t . He suggested that they were the r e s u l t of slope f a i l u r e "producing l o c a l i s e d movements of the scree material and r e s u l t i n g i n a steep f r o n t a l slope and a more gentle back slope" (p. 223). He further noted that the f a i l u r e plane was p a r a l l e l to the slope and the steep fore^ slope was formed by the moving scree overriding the natural down-slope. Gerber and Scheidegger (1974) also noted the existence of these "fronts" i n ,;the investigations i n the Austrian Alps. They f e l t that the i r r e g u l a r i t i e s i n the p r o f i l e are the r e s u l t of small r o t a t i o n a l s l i p s occurring i n the mobile layer which "explains the observed overlapping tongue shaped structure of the deposits on scree slopes" (p. 34). From the evidence of shear phenomena i n cohesionless materials, however, i t i s very u n l i k e l y that the f a i l u r e would be r o t a t i o n a l with a curved f a i l u r e surface but more l i k e l y to be planar as Andrews (1961) speculates * The location of these fronts, between a t h i r d and two thirds downslope (see for example Similkameen E or Spetch No. 1 85 Figure 4.5 Photograph of front on Siirdlkameen talus MOVEMENT "FAILED MASS (A) The scar of a movement of material downslope from i t MOVEMENT FAILED MASS FRONT (B) Front of a mass of debris that has moved downslope from above Figure 4.6 Alternative origins of the fronts observed on talus slope profiles 87 i n Appendix I) tends to indicate that o r i g i n ( i i ) above would be more applicable p a r t i c u l a r l y since, as noted i n Chapter 2, movement of talus materials has generally been reported to have been concentrated i n the upper portions of the slope. 4.6.3 Fabric Pattern; Note was made i n Chapter 3" that very high vector strengths were obtained i n the Similkameen talus that were also highly s i g n i f i c a n t . This was i n contrast to other workers who had been unsuccessful i n obtaining such r e s u l t s (e.g. Caine, 1967,, 1969; Thornes, 1971; Gardner, 1972) although e a r l i e r observations by Davison (1888), Hamelin (1958), Rapp (1960 a) and Andrews (1961) had reported, q u a l i t a t i v e l y , the _ existence of preferred orientations on talus slopes. The lack of "success" encountered by the authors men-tioned above i s pa r t l y explained by t h e i r sampling design (two used g r i d sampling .at a point and one measured orientations on a l i n e transverse to the p r o f i l e ) , and pa r t l y i n the fact that they were dealing with talus slopes which may have been affected by such processes as intense snow avalanching, slush avalanching and mudflows that would tend to produce d i f f e r e n t f a b r i c patterns. Fabric measurements were taken as described i n Sec-ti o n 3.4.2, and were analysed using the.technique outlined by Mark (1971) as explained i n Section 5.2. As noted i n that section the vector strength and f a b r i c data used here were the re s u l t of Rotational Vector Analysis. The objective of a f a b r i c investigation was to i n v e s t i -gate whether the Similkameen slopes were dominated by supply induced transformation processes and exhibited f a b r i c s similar 88 to those produced by analagous shear processes i n dry slopes of sand. Work pioneered by Rees has led to the discovery that d i s t i n c t f a b r i c patterns r e s u l t from shear processes i n dry cohesionless materials, i . e . when c< c i s exceeded. The character-i s t i c s of these f a b r i c patterns are as follows; (a) a pa r a l l e l i s m of p a r t i c l e long axes i n the dir e c -t i o n of shear, i . e . downslope, (b) the long axes of the p a r t i c l e s slope less steeply than the surface of deposition, or slope, and have a mean angle of imbrication r e l a t i v e to the plane of deposition, of 25°. The production of these d i s t i n c t i v e f a b r i c s i s apparently due to the e f f e c t s of repeated intergranular c o l l i s i o n s which occur when a concentrated dispersion of p a r t i c l e s i s sheared (Rees, 1966, 1968; Hamilton, Owens and Rees, 1968). The r e s u l t s of the f a b r i c analysis are found i n Figure 4.7 and Figure 4.8. In Figure 4.7 the orientations of the mean vectors are given i n r e l a t i o n to slope aspect. A l l vectors are s i g n i f i c a n t at the .05 l e v e l and at the corrected l e v e l of s i g n i f -icance given by Mark (1973). In order to ascertain whether or not a p a r a l l e l i s m exists i n the fa b r i c pattern the P a r a l l e l i s m Index of Cailleux, as used by Caine (1969), was employed. The Index i s the percentage of observations lying within 45° of the slope d i r e c t i o n . A value of. 91.2% was obtained for the talus as a whole ( i . e . the mean of the Index values for each segment). This value of the Pa r a l l e l i s m Index i s considered evidence to support the suggestion that p a r a l l e l i s m exists i n the Similkameen talus. 89 to those produced by analagous shear processes i n dry slopes of sand. Work pioneered by Rees (1966) has led to the discovery that d i s t i n c t f a b r i c patterns r e s u l t from shear processes i n dry cohesionless materials, i . e . when i s exceeded. The character-c i s t i c s of these f a b r i c patterns are as follows: (a) a p a r a l l e l i s m of p a r t i c l e long axes i n the di r e c t i o n of shear, i . e . downslope, (b) the long axes of the p a r t i c l e s slope less steeply than the surface of deposition, or slope, and have a mean angle of imbrication r e l a t i v e to the plane of deposition, of 25°. The production of these d i s t i n c t i v e f a b r i c s i s apparently due to the e f f e c t s of repeated intergranular c o l l i s i o n s which occur when a concentrated dispersion of p a r t i c l e s i s sheared (Rees, 1966, 1968; Hamilton, Owens and Rees, 1968). The r e s u l t s of the f a b r i c analysis are found i n Figure 4.7 and Figure 4.8. In Figure 4.7 the orientations of the mean vectors are given i n r e l a t i o n to slope aspect. A l l vectors are s i g n i f i c a n t at the .05 l e v e l and at the corrected l e v e l of s i g n i f -icance given by Mark (.1973) . In order to ascertain whether or not a p a r a l l e l i s m exists i n the f a b r i c pattern the P a r a l l e l i s m Index of Cailleux, as used by Caine (1969), was employed. The Index i s the percentage of observations l y i n g within 45° of the slope d i r e c -t i o n . A value of 91.2% was obtained for the talus as a whole (i. e . the mean of the Index values for each segment), This value of the P a r a l l e l i s m Index i s considered evidence to support the suggestion that p a r a l l e l i s m exists i n the Similkameen talus. H i \ \ 166 174 167 179 190 184 Figure 4.7 Orientation of mean vectors on Similkameen talus in relation to slope orientation (given at base of slope line) F i g u r e 4.8 D i p o f mean v e c t o r ( i n r e l a t i o n t o h o r i z o n t a l ) , S i m i l k a m e e n t a l u s 92 In Figure 4.8 the dip of the mean vectors i s given i n r e l a t i o n to the horizontal. In general the dip of the mean vec-tors i s less steep than the slope surface. Negative angles of dip (Figure 4.8) occur at six locations and can be considered anomalous since they may represent boundaries of talus s l i d e s . If these negative angles of, dip are excluded the mean angle of dip for vectors calculated for the Similkameen talus i s 25.6°. If t h i s value i s subtracted from the mean slope angle of 33°, the mean angle of imbrication as used by Rees (1968) i s 7.4°. Although the existence of a p a r a l l e l i s m i n the f a b r i c would indicate a correspondence with a sheared f a b r i c as derived by Rees and his co-workers the mean imbrication angle i s not as high as predicted. The high degree of p a r a l l e l i s m would tend to indicate, however, a response to a mass downslope movement and the p o s s i b i l i t y exists that higher imbrication angles that may have been created by t h i s movement have been decreased by the s e t t l i n g or creep of p a r t i c l e s within the sheared mass. The fa b r i c evidence, t h e r e f o r e f o r the occurrence of shear processes on the Similkameen ta l u s , whilst not t o t a l l y conclusive, i s suggestive of t h e i r operation. 4.7 Slope Angles on the Similkameen Talus 4.7.1 C h a r a c t e r i s t i c and Limiting Slope Angles; In view of the evidence presented above for the operation of shear processes on the Similkameen talus i t would be i n order to interpret the ch a r a c t e r i s t i c slope angle i n terms of the angle of repose («< ) of the material making up the slopes. A histogram was constructed 93 (Figure 4.9) and a mode i s noted at 33° (modal strength = 28.8%). This value being the c h a r a c t e r i s t i c slope angle for the Similka-meen slopes i s therefore the angle of rest for the material mak-ing up those slopes under the terms of the supply induced trans-formation hypothesis. To obtain the l i m i t i n g angle (e>< ) for the talus i n the Similkameen use i s made of Equation 4.6 because of the evidence presented i n Section 4.6. By in s e r t i n g the value f or c(r, obtained above a peak angle of accumulation of 38.7° i s obtained. In assessing the quality of t h i s estimate i t i s s i g n i f i c a n t that no slope angle over 3 7° was measured i n the f i e l d . An additional method of assessing the value of the c< c obtained i s available i n the work of A l l e n (1970 b) who developed relationships between the a x i a l dimension, a and b, and values of o ( c for various peaking arrangements of cohesionless prolate spheroids . Packing Case VI given by Al l e n (1970 b) was thought to apply approximately to the packing arrangements observed i n the talus examined (Figure 4.10). For t h i s case A l l e n (1970 b) gives c<c as being calculated thus; tan<X = --7=- (Eq. 4.8) 2f/3 b c When mean values of a and b for p a r t i c l e s i n each seg-ment studied on the Similkameen talus were inserted i n Equation 4.8, the values obtained did not appear r e a l i s t i c and were much lower than expected. It was concluded that t h i s equation did not provide a good estimate for ^ c > This perhaps arose because i n Allen's t h e o r e t i c a l treatment the surface of the spheroids was 94 SEGMENT ANGLE Figure 4.9 Histogram of segment angles on Similkameen talus 95 Figure 4.10 Allen's packing case IV for prolate spheroids thought to apply to talus particle packings 96 TABLE V. LIST OF PUBLISHED.PEAK ANGLES OF ACCUMULATION (oC) FOR TALUS AND SIMILAR MATERIALS Source Ma t e r i a l c Simons (Undated ms.) Crushed Limestone 42.0° Talus (Stockpile) 42.0° Talus (Stockpile) 41.0° Crushed Granite 40.8° Bl i g h t (1969) Quartzite R o c k f i l l 41.0° 97 considered to be smooth which would i n e f f e c t neglect the f r i c -t i o n a l strength gained by i r r e g u l a r p a r t i c l e surfaces. Based on Allen's (1970 b) investigations which sug-gested a relationship between a x i a l dimensions and the value of oi. further examination of the relat i o n s h i p was carr i e d out. I t c was found that i f mean values of a and b for the material i n each slope was inserted i n Equation 4.9 below and the values obtained were plotted against the mean slope angle (taken to equal, on the evidence presented above, to be equal to a mean ) , the resultant data points are very close to the l i n e derived from Carrigy's (1967) data (Figure 4.11). tancx! = .54 (a/b) (Eq. 4.9) Whenc<c was calculated using Equation 4.9 for each set-ment, the modal value obtained was 39.0° (Figure 4.12) which i s in good agreement with the value of<5< c obtained using Equation 4.6. The above would therefore indicate that Equation 4.9 provides an empirical approximation f o r ^ c i n the Similkameen talus. 4.7.2 Comments on the Similkameen Talus (a) I t would appear from the above discussion that slope angles on the Similkameen talus can be interpreted i n terms of the supply induced transformation hypothesis. As such th i s work has v e r i f i e d a general process-material-response model. (b) Since s l i d e processes si m i l a r to those envisioned i n the supply induced transformation hypothesis were shown to be 98 5 5 H 45 H Data from Similkameen slopes (o< calculated from a x i a l data c using Equation 4.6;oi mean slope angle for each s l o p e ) r Meant* and mean oir for Similkameen talus C h a r a c t e r i s t i c and l i m i t i n g slope angles for t a l u s slopes taken from review i n Chapter 2 3 H 2 5 4 15 H 54 - r 15 T " 25 35 45 Figure 4.11 Similkameen talus slope data in relation to °^/c^c plot 99 Figure 4.12 Histogram of calculated values for for Similkameen talus 100 active on the basis of the inter p r e t a t i o n of response elements, the d i s t i n c t mode' shown i n the d i s t r i b u t i o n (33°) was taken to be the angle of rest for the Similkameen material. (c) The l i m i t i n g slope was obtained using Equation 4.6 and Equation 4.9. This enables a statement to be made whereby an upper and lower bound can be set for the operation of talus s l i d e processes on the Similkameen talus slopes. These corres-pond to the l i m i t i n g slope of 39° and a lower bound (the char-a c t e r i s t i c slope) of 33° although there may be some overlap i n these figures with transformation events (cf. Hutchinson, 1967 a). These slope angles then define the thresholds for talus s l i d e processes on the Similkameen talus. (d) The talus slopes studied i n the Similkameen appear to be i n equilibrium with the residual strength of the materials composing them. I t i s in t e r e s t i n g to compare t h i s conclusion with those of Skempton (1964) and others who suggest that natural slopes tend toward an equilibrium determined by the residual strength. (e) For the purposes of completing the review process . begun i n Chapter 2 mean slope angles and segment angles from investigations i n the Coast Mountains and the Similkameen are added to Figures 2.5 and 2.6 and are presented i n Figures 4.13 and 4.14 respectively. 101 30 T • 1 Data from t h i s i n v e s t i g a t i o n CZl Data from Figure 2.5 £ 20 o io H 40 10 20' 25 SLOPE ANGLE 30 35 Figure 4.13 Histogram o f published mean t a l u s slope angles incorporating data from t h i s i n v e s t i g a t i o n 102 SEGMENT ANGLE Figure 4.14 Histogram of published talus slope segment angles incorporating data from this investigation 103 CHAPTER FIVE RELATIONSHIP BETWEEN MATERIAL PROPERTIES  AND TALUS SEGMENT ANGLE As outlined i n Chapter 1, a second objective of t h i s work i s to seek s t a t i s t i c a l relationships between talus slope angle and the c h a r a c t e r i s t i c s of the material that forms the slope (cf. Caine, 1967; Thornes, 1971). Relationships are thought to e x i s t between talus slope angle and material proper-t i e s such as size, shape and f a b r i c , which were shown to be important controls on the shear resistance of cohesionless mater-i a l s s i m i l a r to talus i n Chapter 4. These relationships w i l l be explored here with r e f e r -ence to the 30 m. segments from the Similkameen slopes. 5.1 Methods of Analysis The objectives of the exploratory analysis are twofold; (a) To e s t a b l i s h whether material properties and seg-ment angle co-vary i n a systematic manner, (b) To e s t a b l i s h the group of variables that are most important.in accounting for variations i n segment angle. It may be noted that attention i s focussed on the seg-ment scales since they form the elements of slope p r o f i l e s as discussed i n Chapter 3. An appropriate t o o l to explore the above objectives would appear to be multivariate s t a t i s t i c s , s p e c i f i c -a l l y multiple c o r r e l a t i o n and stepwise multiple regression 104 analysis. Many workers have used these methods to i n i t i a l l y "sort out" geomorphic problems; indeed Carson (1969) ,has remarked on "the e f f i c i e n c y of the s t a t i s t i c a l approach i n detecting the relevance of alt e r n a t i v e models" i n slope process-response studies. The uses of these methods and the interpretation of the re s u l t s are r e s t r i c t e d by c e r t a i n assumptions. In c o r r e l a -t i o n analysis, for example, the variables are assumed to be random samples from a bi v a r i a t e normal population. In regression analysis three basic assumptions are involved; (a) The sample data must be from a population for which the variance i s homogeneous, i . e . the v a r i -ance of the Y values about the regression surface must be the same at a l l points, (b) The deviation of the Y values from the regression surface must be independent of each other and normally d i s t r i b u t e d , (c) Independent variables must be measured with no error. As the objectives, of t h i s part of the analysis are exploratory i t i s thought s i g n i f i c a n t information can be obtained from the use of these methods even though a formal test of these r e s t r i c t i v e assumptions w i l l not be c a r r i e d out. This view i s shared for si m i l a r situations by King (1969) and Snedecor and Cochran (1967). However, because the variables used are means, and i n some cases the mean of means, there i s some j u s t i f i c a t i o n , for example, for assuming that the same variables form normal TABLE VI. . VARIABLES, USED. IN MULTIVARIATE ANALYSIS SEGANG - Segment Angle of 30 m. segments Size Related Variables PHISIZ - Mean, i n Phi-units of 'a' axes measurements PHIDEV - Standard deviation, i n Phi-units, of PHISIZ Shape Related Variables SPHERI - Mean value of Krumbein's Intercept S p h e r i c i t y ( f ) , where Y = bc-^/^/a 2 PZINGG - Mean value of Zingg's Flatness Ratio, P. where P = c/b PZVARI T. •...•Variance: i n PZINGG QZINGG.. - Mean value of Zingg's Elongation Ratio, Q, where Q = b/g QZVARI - Variance i n QZINGG FZINGG - - Mean value of Zingg's Shape Factor, F. where F = ca/b FZVARI - Variance i n FZINGG Fabric Related Variables SLODEV - Deviation of Mean Vector from Orientation of Slope DIPVEC - Dip of Mean Vector VECSTR - Vector Strength 106 populations. With, the above l i m i t a t i o n s i n mind the methods outlined above w i l l hopefully supply convenient approximations of the relationships between segment angle and material prop-e r t i e s . 5.2 Variables Used i n Analysis In Chapter 4 , three basic groups of material v a r i -ables were established as being important i n c o n t r o l l i n g shear resistance, peak angle of accumulation and angle of repose of granular materials, they being, s i z e , shape and f a b r i c . To obtain parameters related to these groups for each segment certai n indices established mainly i n the f i e l d of sedimentary petrology were derived and are l i s t e d i n Table VI. Size and shape variables were obtained using a variant of C0BLAN, a com-puter programme developed by Michael Church and a ZINGG programme developed by Michael Patterson who were both at the time c o l -leagues i n the Department of Geography at the University of B r i t i s h Columbia. Fabric variables were obtained by using a 3-Dimensional Rotational Vector Analysis Programme developed by David Mark, also of the Geography Department, which subsequently appeared i n the l i t e r a t u r e (Mark, 1971). The significance tests used i n the f a b r i c analysis were those i n the 1971 programme which were l a t e r corrected by Mark. .(Mark, 1973). This writer has reviewed the paper by Mark (1973) and has consulted the author as to the status of the results from his o r i g i n a l programme. Mark notes i n his 1973 paper that the re s u l t s of the " e a r l i e r programme TABLE VII. CORRELATION MATRIX FOR SIMILKAMEEN TALUS MATERIAL PROPERTIES 1 2 3 4 5 6 7 8 9 10 11 12 13 SEGANG PHISIZ PHIDEV SPHERI PZINGG PZVAR QZINGG QZVAR FZINGG FZVARI SLODEV DIP VEC VECSTR 1 2 . 5 1 * - - - - - - - - - - -3 . 5 5 * . 8 5 * - - - - - - - - -4 - . 3 4 * - r - . 5 8 * - r 5 6 * - - - - - - - - -5 - . 3 2 + - . 3 8 + - . 5 2 * . 6 6 * - - - - - - - - - -6 - . 2 0 .04 - . 0 9 .05 .18 - - - - - - - -7 - . 2 4 - . 5 4 - . 4 3 * . 8 8 * .24 .17 - - - - - - -8 .05 - . 3 1 - , 36+ .29 . 23 .21 .32+ - - - - - -9 .01 .12 - . 1 1 - . 2 0 . 5 7 * .25 - . 5 9 * .14 - - - - -10 .16 .14 .03 - . 5 0 * .06 .27 - . 5 3 * .30 .57 - - - -11 .04 - . 0 6 - . 0 6 - . 1 2 - . 0 7 - . 2 4 - . 1 2 - . 2 0 .01 - . 0 6 - - -12 .08 .18 .19 - . 1 2 - . 1 2 - . 0 8 - . 1 1 - . 1 3 - . 0 5 - . 0 5 .17 - -13 .08 — . 06 - . 2 0 - . 0 8 - . 0 3 - . 1 9 .05 .14 .13 - . 1 9 - . 4 3 -^Value of r s i g n i f i c a n t at the 99% l e v e l Value of r s i g n i f i c a n t at the 95% l e v e l 1 - Segment Angle 8 - Variance of Q 2 - Size i n Phi-units 9 - Zingg's Shape Factor (F) 3 - Standard Deviation i n Size: a measure of sorting 10 - Variance of F 4 - Sphericity (Krumbein's Intercept Sphericity) 11 - Deviation of mean vector from slope o r i e n t a t i o n 5 - Zingg's Flatness Ratio (P) 12 - Dip of Mean Vector 6 - Variance of P 13 - Vector Strength 7 - Zingg's Elongation Ratio (Q) o 1 0 8 agree f a i r l y well with those produced by the eigenvalue method" (p. 1 3 7 2 ) . I t has not proved possible to re-analyse the f a b r i c data using the eigenvalue method proposed by Mark ( 1 9 7 3 ) , but vector strengths have been checked for significance using pro-cedures i n Mark's paper. A l l the vector strengths obtained i n the Similkameen talus remain s i g n i f i c a n t at the 9 9 % l e v e l . The rotation i n t e r v a l used i n the analysis was 2 0 ° based on Mark's (Mark, 1 9 7 1 ) statement that "the 2 0 ° rotation i n t e r v a l should be accurate enough for most purposes, e s p e c i a l l y i n view of the fa c t that f i e l d measurements so often 'considered to have an accuracy of ± 5 ° ' (Andrews and King, 1 9 6 8 , p. 4 3 7 ) " (p. 2 6 6 3 ) (cf. Section 3.4.2 above). 5.3 Correlation Analysis The res u l t s of the c o r r e l a t i o n analysis are contained i n Table VII and a diagrammatic representation of the c o r r e l a -tion structure i s given i n Figure 5 . 1 . The following conclusions can be suggested following an inspection of the r e s u l t s : (a) S t a t i s t i c a l l y s i g n i f i c a n t correlations do e x i s t . At the 9 9 % l e v e l of sig n i f i c a n c e , negative corre-latio n s are found between slope angle and siz e , whilst p o s i t i v e correlations are found between segment angle and sorting, the values of the c o e f f i c i e n t being .51 and .55 respectively (Figure 5 . 2 ) . (b) At the 9 5 % l e v e l of significance negative c o r r e l a -tions e x i s t between slope angle and sph e r i c i t y 109 SEGMENT ANGLE PHISIZ QZINGG PHIDEV SPHERI QZVARI — FZINGG I — PZINGG • 1 FZVARI Value of R s i g n i f i c a n t at 99% l e v e l Value of R s i g n i f i c a n t at 95% l e v e l PHISIZ - Size in Phi units QZINGG - Zingg's elongation ratio (Q) PHIDEV - Standard deviation of size (sorting) QZVARI - Variance in Q SPHERI - Krumbein's sphericity FZINGG - Zingg's shape factor (F) PZINGG - Zingg's flatness ratio (P) FZVARI - Variance in F Figure 5.1 Correlation structure for Sirrdlkameen talus 37 H • •• mm ~ l 1 1 -7.0 -8.0 SIZE IN PHI UNITS 9.0 37 36 35-34-33-32-31-O < 30 z 111 E 29 o U J 28-27-2 6 -25-24-- 6 . 0 YTWO DATA POINTS • • •• • • • • ¥ • •••• • •• • ••• • 1 ' r -7.0 -8 .0 SORTING IN PHI UNITS -9.0 Figure 5.2 Scattergrams of size and sorting variables plotted against segment angle I l l and between slope angle and Zingg's Flatness Ratio, (r = -.34 and -.32 re s p e c t i v e l y ) . (c) Many s i g n i f i c a n t correlations e x i s t within the size and shape groups and between them, (e.g. size and sphe r i c i t y , r = -.58). (d) There i s a lack of s i g n i f i c a n t c o r r e l a t i o n between fa b r i c variables and segment angle or between fa b r i c variables and other material variables. (e) A c o r r e l a t i o n does e x i s t between vector strength and the mean vector dip. 5.4 Stepwise Multiple Regression Analysis Stepwise multiple regression was used in.the next stage of the analysis to discover whether a combination of mater-i a l variables could account for a v a r i a t i o n i n slope angle. This involves a d i f f e r e n t i a t i o n between a dependent variable and a set of independent variables. Whilst acknowledging the comments of Melton (1958) on the subject of cause and e f f e c t i n slope studies and r e a l i s i n g that both slope angle and material proper-t i e s are i n a sense " e f f e c t s " , i t can be argued that due to the demonstrated relationships between material c h a r a c t e r i s t i c s and shear resistance and between shear resistance and slope form, that slope form can be considered a dependent vari a b l e . Using stepwise multiple regression, only 37.11% of the va r i a t i o n i n segment angle could be accounted for by v a r i a t i o n i n material c h a r a c t e r i s t i c s at the 95% l e v e l of sig n i f i c a n c e . 112 The equation obtained i s as follows: Segment Angle = 45.7122 + 2.6542 (Sorting) + 181.005 (Variance i n Elonga-t i o n Ratio) (Eq. 5.9) Sorting contributed 30.10% and the variance i n the elongation r a t i o 7.01%. As a r e s u l t of the multiple regression analysis we are led to the following conclusions: (a) A large amount, i . e . 62.89% of the variance i n segment angle i s not explained by the v a r i a t i o n i n material c h a r a c t e r i s t i c s as measured i n t h i s investigation, (b) Sorting i s the single variable that contributes a major amount to the explained variance i n seg-ment angle, i . e . just over 80.00%, (c) Shape factors contribute very l i t t l e to the explained variance, (d) Fabric factors do not contribute to the explained variance. 5.5 Comments on the Multivariate Analysis 5.5.1 The Relationship between Material Properties and Seg-ment Angle; With reference to the second objective of thi s work, s t a t i s t i c a l l y s i g n i f i c a n t correlations were obtained that indicated segment angle varied inversely with size and d i r e c t l y with sorting. The l i n k between shape (sphericity) and segment angle i s less marked. S i g n i f i c a n t correlations at the 113 95% l e v e l suggested that segment angle varies inversely with sp h e r i c i t y . No s i g n i f i c a n t correlations were found to indicate that slope angle varied d i r e c t l y with v a r i a t i o n i n shapes. A s i m i l a r absence of s i g n i f i c a n t correlations existed with segment angle and f a b r i c variables contrary to expectation. Increased sorting was related to an increase i n slope angle and t h i s v a r i -able was also the dominant material variable i n accounting for 80.00% of the explained variance i n segment angle which was con-trary to expectation. This could possibly be explained by the greater i n t e r l o c k i n g between fragments (Mackey, 1964) of a more uniform sized aggregate and the lack of a matrix of smaller frag-ments. The low l e v e l of "explanation",, however, i s surprising. I t was thought that because.of the demonstrated relationships between material properties and various threshold properties i n Chapter 4 that a larger percentage of explained variance i n seg-ment angle would be attributable to material properties. 5.5.2 S u i t a b i l i t y of Indices; The p o s s i b i l i t y e xists that the indices used to approximate the parameters such as shape, which were thought to be important controls on segment angle, were not appropriate for that purpose. The measures of shape used here, e s s e n t i a l l y based on a x i a l measurements, have been open to question for some time by such workers as Lees (19 64), Fleming. (1965), Mackey (1965) and Mogami and Yoshikoshi (1971), and t h i s fact could contribute to the low c o r r e l a t i o n obtained. 5.5.3 Possible Sources of Operator Error in F i e l d Measure- ment ; A further cause for the low l e v e l i n the explan-ation of segment angle v a r i a t i o n i s the p o s s i b i l i t y of operator 114 error i n f i e l d measurement. Whilst i t i s claimed that because of the author 1s f a m i l i a r i t y with the technique of a x i a l measure-ment the operator error would be very small, i t i s conceded that errors could have occurred p a r t i c u l a r l y on very large boulders ( > 3 m.) and boulders of equidimensions as discussed i n Sec-t i o n 3.4.2. With reference to slope angle measurements problems r e l a t i n g to p r o f i l e roughness have already been discussed i n Section 3.4.1. Attention i s drawn to the checks made at 15 m. within the 30 m. segment. Whilst the method appears to reduce errors a cer t a i n amount of error could arise and t h i s could be i n the order of +1° for the 30 m. segment. Also i n Section 3.4.2 reference i s made to the i n s t r u -ment used i n f a b r i c measurements. An error of ±5° i s considered to e x i s t i n the data. It i s r e a l i s e d that some operator error must e x i s t i n the data. However, i t i s suggested that due to the r i g i d f i e l d procedure used that t h i s would be at a minimum and would not be a major factor i n the low l e v e l of explanation obtained i n the analysis. 5.5.4 Possible Sources of Real World Noise; One of the pre-conditions for f i e l d testing of the hypothesis was that the talus slopes i n question would be dominated by the r o c k f a l l process. The low l e v e l of explanation obtained i n the analysis may r e f l e c t the operation of snow or slush avalanches, or a l l u v i a l processes not so much as a dominant process, but as a subordinate process the a c t i v i t y of which i s far i n excess, of that envisioned by t h i s 115 writer. 5.5.5 Relationships between Mean Material Properties and Mean Slope Angle; Mean material properties for each slope studied were plotted against mean slope angle. No pattern was discovered i n the scatter, r e f l e c t i n g perhaps the variations i n material-form relationships within the slope i t s e l f . 5.6 Conclusions on Multivariate Analysis Low le v e l s of explanation were found i n the analysis. In some ways these re s u l t s are c h a r a c t e r i s t i c of s t a t i s t i c a l morphometric studies(Melton, 1958; Carson, 1966) where c o r r e l a -t i o n c o e f f i c i e n t s tend to have low values and scatter diagrams attempting to rel a t e the.variables show considerable disarray (Carson, 1966). I t may be that the high degree of scatter and the lack of a substantial, functional relationship r e f l e c t s samp-l i n g or measurement error, the fac t that the variables may not represent those c h a r a c t e r i s t i c s which were desired, or the fac t that material properties/segment angle relationships may obtain at a d i f f e r i n g scale (perhaps "between areas") than that studied here. It i s possible that a morphological systems approach (cf. Chorley and Kennedy, 1971) i s not appropriate to study a problem of material-form l i n k s . The assumption of the approach i s that co-variance exists i n the data whilst the implication of a material-form l i n k i s that i t exists at a threshold which, i n the same environment and i n the same li t h o l o g y , would tend to be invariant or at least clustered i n a very narrow range of slope 116 angles. Notwithstanding the above, however, s i g n i f i c a n t r e l a -tionships were found between segment angle and sorting together with s i z e . Shape variables were less important i n accounting for variations i n segment angle. The s i g n i f i c a n t nature of s i z e , sorting and segment angle relationships are i n contrast to some previous attempts to re l a t e form and material properties (Caine, 1967; Thornes, 1971). 117 CHAPTER SIX IMPLICATIONS FOR TALUS SLOPE  DEVELOPMENT AND CONCLUSIONS 6.1 Implications for RockwalT/Talus Slope Development Models 6.1.1 Talus Slope Morphology; The re s u l t s noted above have considerable import i n both the evaluation of the talus p r o f i l e dominated by r o c k f a l l and talus s l i d e processes, and the change of slope geometry over time, i . e . slope development. Talus slopes i n the Similkameen and i n the Coast Ranges have been noted to be b a s i c a l l y concave. In other areas such as Colorado, Spitzbergen and Devon Island slopes dominated by rock-f a l l processes would appear to be s i m i l a r l y concave (White, 1967; Rapp, 1960 b; Howarth and Bones, 1972, r e s p e c t i v e l y ) . I t i s proposed here that the concavity observed i n r o c k f a l l taluses i s largely the r e s u l t of two stages i n the supply-induced transformation process, v i z . the accumulation pro-cess beneath the r o c k f a l l and the r e d i s t r i b u t i o n of t h i s accumula-tio n through talus s l i d e processes. I t i s s i g n i f i c a n t that Rapp (1960 b) and Howarth and Bones (1972), noted the existence of debris s l i d e lobes on the r o c k f a l l taluses they studied. The talus slope affected by such processes would have i d e a l l y , 3 d i s t i n c t zones as indicated i n Figure 6.1. Zone A would represent the zone of accumulation. A wedge of material builds up i n t h i s upper zone u n t i l the i n c l i n -ation reaches a value of e< for the material i n that condition 118 Figure 6.1 Schematic diagram of zones on a talus slope dominated by rockfall-debris slide processes (for explanation see text) 119 and f a i l u r e takes place downslope. Such a. designation for Zone A i s consistent with observed patterns of accumulation on talus slopes (e.g. Evans, 1969; Caine, 1969; Carson and Kirkby, 1972). Zone B represents the area of deposition of debris from the f a i l u r e i n Zone A and according to arguments presented i n Chapter 3 and findings reported e a r l i e r i n t h i s chapter, would assume an angle equivalent to or 0 r. Zone C would be at a lesser angle because of an end e f f e c t of the v a l l e y f l o o r , terrace, g l a c i e r , etc. I t would be the c o l l e c t i n g area for boulders that break free from the s l i d i n g mass above (as noted by Rapp, 1960 b), for large r o c k f a l l s that bypass the upper two zones, or for large debris s l i d e s that go beyond the usual l i m i t s of such s l i d e s ( i t has been noted that debris s l i d e s are usually confined to the upper two-thirds of the slope). The slope outlined i n Figure 6.1 could contain two threshold slopes. In Zone A the threshold or l i m i t i n g slope would be equivalent to the peak angle of accumulation of the material at i t s depositional density. The slope of deposition assumed by the debris following the exceedance of c/-c i s then equivalent to c^r, or the angle of rest or the angle of i n t e r n a l f r i c t i o n i n a looser state. This slope i s then equal to the residual threshold slope. The upper threshold, or peak threshold slope and the residual threshold slope as outlined i n t h i s chapter, i l l u s t r a t e the importance of considering residual strength factors i n d i s -cussions of threshold slopes and slope development (cf. Rouse, undated ms;).. - ' 120 6.1.2 Determinants on.the Frequency of Talus Slides; Varia-tions i n the a c t i v i t y of the talus s l i d e process take place as a r e s u l t of v a r i a t i o n i n a number of factors, the most important of which i s primary fragment supply rate. A l l e n (1970 b) has carri e d out experiments on the e f f e c t of primary fragment supply rate, i . e . i n t h i s case deposition from the rock face, on the ch a r a c t e r i s t i c s of debris avalanches including frequency and thickness of accumulation. The supply rate has i t s greatest e f f e c t i n c o n t r o l l i n g the depositional density of an accumulation (cf. Kolbuszewski, 1948). Four supply situations are thought to apply to talus slopes dominated by r o c k f a l l processes; (a) I f the fragment supply rate i s high ( i . e . extreme frequency) the density of the wedge w i l l be very low. I t i s possible that primary deposition, of high frequency r o c k f a l l s r e s u l t s i n a slope near to cC. or jz^. At lea s t a very small d i l a t i o n angle i s presumed to form and as a r e s u l t debris s l i d e s w i l l be very infrequent. (b) If the fragment supply rate i s smaller ( i . e . intermediate frequency) the depositional density angle would be higher. An increase i n wedge volume res u l t s which i n turn r e s u l t s i n a greater debris s l i d e thickness. Greater s l i d e v e l o c i t y ... also r e s u l t s a f t e r f a i l u r e and the debris travels a greater distance downslope. (c) I f the fragment supply rate i s less than (b), i . e . low frequency, a smaller wedge builds up, 121 although the d i l a t i o n angle is.high. Small f a i l -ures take place and "freeze" i n the upper portions of the slope building up a secondary wedge which i n turn f a i l s by progressive f a i l u r e i n i t s fore-slope. A l l e n (1970 b) believes t h i s to be the _ type of debris s l i d e behavior that i s common on talus slopes and works on an example given by Rapp from Spitzbergen. (d) No supply. A further important variable would also be length of slope, the bottom of which acts as an "end e f f e c t " for the pro-cesses outlined i n a, b and c above. A consideration of the rate of supply i s p a r t i c u l a r l y i n t e r e s t i n g i n the l i g h t of indications of decreasing supply rates i n p o s t g l a c i a l time (e.g. Worobey, 1972). It i s proposed here that following the i n i t i a t i o n of present talus accumulation processes with the retreat of the gl a c i e r s 10,000(±) years B.P., talus slopes i n southern B r i t i s h Columbia went through the spec-trum of supply conditions a-c. Some have probably reached the i n e r t i a l state of no supply (d). The implication of t h i s statement for the magnitude and frequency of debris s l i d e processes i s that immediately following the retreat of the ic e , through stress release and high in t e n s i t y rockwall transformation, r o c k f a l l was so frequent and depositional densities so low that accumulation wedges did not form, or at least did not form with any high frequency. The slope would under these conditions approximate to a r e c t i l i n e a r 122 form with a concave base i n the presence of an end e f f e c t . The slope of the r e c t i l i n e a r portion would be equal to 0^ or 0 because the depositional density would approximate to the loose condition. As the frequency of the r o c k f a l l subsided as i n case (b) wedges had the opportunity to develop due to the higher depo-s i s i o n a l density and debris s l i d e s were more frequent. The con-cavity would have been.more pronounced because of the higher angle of slope i n the upper portions of the slope developed.on the wedge surface. The frequency further subsided and case (c) became operative. Small wedges gave the slope an i r r e g u l a r p r o f i l e , the so-called mini-concavities; s l i d e s are limited to the upper portions of the slope. Smaller s l i d e s b u i l d up a secondary wedge further down the slope which subsequently f a i l s on a much larger scale than the primary wedge. The talus slopes studied i n the Similkameen seem to have entered t h i s phase of development. Some talus slopes are inactive with respect to debris s l i d e processes because the rockwalls above them have become s t a b i l i z e d and no longer produce appreciable quantities of rock fragments. In t h i s s i t u a t i o n features noted i n case (c) became f o s s i l i z e d and vegetation often invades the slope giving the ppearance of an inactive talus slope. However, lobes and i r r e g u l a r i t i e s are s t i l l evident. The p r o f i l e w i l l obviously assume a d i f f e r e n t form i n the absence of an "end e f f e c t " , e.g. where the base of the slope i s eroded by waves, r i v e r s and g l a c i e r s , since the basal 123 concavity w i l l not develop. It w i l l also assume d i f f e r e n t forms i f other slope processes such as mudflows, snow avalanches and overland flow assume dominance as transformation process. Under these condi-tions the processes mentioned would tend to mitigate against wedge development. 6.1.3 The Problem of the Basal Layer; The model of slope development proposed above i s r e s t r i c t i v e i n that i t only con-siders the mobile layer and the r o c k f a l l - d e b r i s s l i d e process as a transformation mechanism. As Kirkby and Carson (1972) point out, however, the problem of slope p r o f i l e development i s . a multi-process one. The problem here i s no exception for i t has been noted i n Chapter 2 that the structure of talus slopes i n general include a basal layer that i s susceptible to pore-pressure e f f e c t s . I t i s i n t h i s context that the o r i g i n of the basal layer discussed i n Section 2.2 becomes an important consid-eration because i f the layer i s t i l l very l i t t l e change can be expected to take place i n . i t s properties. If i t i s the r e s u l t of -weathering, or the sieving e f f e c t , change can be expected to take place. An increase i n the thickness w i l l r e s u l t from the advancement of the weathering front and also by the addition of more material through the sieving e f f e c t . However, even the sieving process w i l l become inoperative i n time as supply decreases to zero. Under the conditions of no supply, however, weathering w i l l continue. It w i l l be appreciated that i f the basal layer increases i n depth the layer w i l l tend to increase i n density, and, whilst adding to i t s shear strength would leave 124 i t more susceptible to pore water pressures in a similar way to that described by Carson (1969, 1971). In time this process would result in differing shear strength thresholds being deter-minants on the morphometry of talus slopes. Thus the existence of the basal layer cannot be discounted in a slope evolution model of talus/rockwall systems. 6.2 Conclusions 6.2.1 General (a) The verification of a material-response model detailed in this work, both using review and f i e l d data, indi-cates once more the importance of studying material variables in rationalising the form of various landforms, (cf. Strahler, 1952; Chorley, 1966). (b) The study illustrates an example of a remarkable correspondence between predicted values of threshold slopes based on the model experiments of other workers in the laboratory and the values of characteristic and limiting slope angles in the f i e l d . (c) The problems of cause and effect, the selection ofindependent and dependent variables and the definition of response elements in a slope system were encountered in this study. These d i f f i c u l t i e s would appear to be common to investi-gations based on the familiar process-material-response framework and are particularly acute in studies of strength-stress relation-ships as noted by Chorley (1966). (d) The value of the systems approach in seeking 125 alternative explanations i n form-material relationships was also seen. 6.2.2 Sp e c i f i c (a) Based on an evaluation of published works and the d i s t r i b u t i o n of published talus slope angles, the supply-induced transformation hypothesis was proposed to account for observed c h a r a c t e r i s t i c and l i m i t i n g slope angles on talus slopes. These were found to correspond to the angle of repose (<?<r) and the peak angle of accumulation (°^) respectively. Testing the hypothesis i n the f i e l d on talus slopes i n the Similkameen Valley, character-i s t i c and l i m i t i n g slope angles were thought to correspond to and<^c respectively for the Similkameen material, and together with other evidence, the supply-induced transformation hypothesis was v e r i f i e d for the Similkameen slopes. 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YOUNG, A., 1961, Char a c t e r i s t i c and Limiting Slope Angles: Z e i t s c h r i f t fur Geomorphologie, Bnd. 5, pp. 126-31. 140 APPENDIX 1 TALUS SLOPE PROFILES MEASURED IN FIELD INVESTIGATIONS 

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