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PRINCIPLES OF PRINCIPLES OF ENGINEERING GEOLOGY

P. B. ATTEWELL and I. W. FARMER University of Durham

LONDON CHAPMAN AND HALL

A Halsted Press Book JOHN WILEY & SONS, INC., NEW YORK First published 1976 by Chapman and Hall Ltd 11 New Fetter Lane, London EC4P 4EE © 1976 J. E. Attewell and L. C. Attewell Sriftcover reprillt rifthe hardcover 1ft editiolt 1976 Typeset by Preface Ltd, Salisbury, Wilts

Fletcher & Son Ltd, Norwich

ISBN-13: 978-94-009-5709-1 e-ISBN-13: 978-94-009-5707-7 DOl: 10.1007/978-94-009-5707-7

All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher.

Distributed in the U.S.A. by Halsted Press, a Division of John Wiley & Sons, Inc., New York

Library of Congress Cataloging in Publication Data Attewell, P B Principles of engineering geology.

1. Engineering geology. I. Farmer, Ian William, joint author. II. Title. TA705.A87 1975 624'151 75-20012 Contents

Preface xi Symbols xvii

Composition of Rocks 1 1.1 Origin and geological classification of rocks 1 1.2 forming 7 1.3 Clay minerals 16 1.4 Base exchange and water adsorption in clay minerals 20 1.5 Mineralogical identification 25

2 Rock Particles and Particle Systems 30 2.1 Rock particle classification 30 2.2 Typical rock particle systems 33 2.3 Physical properties of particulate systems 42 2.4 Permeability of particulate systems 45 2.5 Representation of stress in a soil mass 48 2.6 56 2.7 Frictional properties of rock particles 60 2.8 Soil deformation - drained granular media 66 2.9 Soil strength - drained granular media 75 2.10 Soil strength and deformation - clay soils 81 2.11 Pore pressure parameters 88 2.12 Rate of porewater pressure dissipation 92 2.13 The critical state concept 97 2.14 Limiting states of equilibrium 100

3 Clays and Clay Shales 104 3.1 Interparticle attraction and repulsion 105 3.2 formation and clay fabrics 109 3.3 Unstable clay fabrics 117 3.4 Glacial and periglacial clays 122 vi Contents

3.5 Depth - strength profiles 125 3.6 Macrostructure of overconsolidated clays and clay shales 130 3.7 Engineering influence of discontinuities in clay shales 143 3.8 Classification of clay shales 146 3.9 Consolidation and diagenetic considerations 150 3.10 Physical breakdown of shales 153 3.11 Suction pressure 157 3.12 Swelling pressure 162 3.13 Chemical and mineralogical analyses of clays 167 3.14 Relationship between , and geo- technical properties of clays and clay shales 175

4 Rock as a Material 182 4.1 Uniaxial strength 184 4.2 Uniaxial short-term deformation 194 4.3 Deformation mechanisms in rock 199 4.4 Complete stress - strain characteristics of rock in uniaxial compression 206 4.5 Effect of rate and duration of loading 210 4.6 Deformation and failure of rocks in triaxial compression 218 4.7 Failure criteria for rocks 224 4.8 Yield criteria 229 4.9 Rock dynamics 232 4.10 Wave transmission through rocks 234 4.11 Wave attenuation 239 4.12 Rock as a construction material 244

5 Preferred Orientation, Symmetry Concepts and Strength Anisotropy of some Rocks and Clays 250 5.1 Studies of the orientation density distribution of clay minerals and other associated minerals 251 5.2 X-ray texture goniometry 252 5.3 Symmetry concepts 260 5.4 Deformation paths 263 5.5 Deformation ellipsoid 263 5.6 Randomization 266 5.7 Symmetry elements and sub-fabrics 271 5.8 Crystallographic plane multiplicities and symmetry 272 Contents vii

5.9 Engineering influence of intrinsic anisotropy 285 5.10 Comparative degree of intrinsic anisotropy - mechanical evidence from rock experimentation 288 5.11 Intrinsic strength anisotropy of brittle and semi-brittle rocks comprising a dominant clay control 289 5.12 Intrinsic anisotropy and sedimentation 300 5.13 Anisotropy of clay shales 302 5.14 Clay strength anisotropy 302

6 Rock Discontinuity Analysis 315 6.1 The engineering interest in discontinuities 315 6.2 Genesis and modification of fissures and slickensides 317 6.3 Controls on fissuring and fissure patterns 319 6.4 Classification of discontinuities 320 6.5 Character of discontinuities 326 6.6 Test specimen size-strength relationships 326 6.7 Stereographic representation of discontinuity data 328 6.8 Direct and inverse transformations from polar to equatorial angles 329 6.9 Linear orthogonal transformations 333 6.10 Eulerian angles 336 6.11 Discontinuity survey techniques 336 6.12 Analysis of discontinuity data 344 6.13 Influence of gouge material and surface roughness characteristics of discontinuities 352 6.14 Distributions 355 6.15 Orientation density distribution of discontinuities 364 6.16 Discontinuity shear stability in a poly axial stress field 369 6.17 Shear strain energy concepts 376 6.18 Preliminary consideration of certain types of discontinuity structure in two dimensions 385 6.19 Statistics of scanlines through discontinuity distributions 388 6.20 Continuity 394 6.21 Preliminary shear stability analysis of discontinuities at the foundation interface of an earth or rock-fill 398 6.22 Stability of jointed rock in the foundation of an arch dam 409 6.23 Stability of a discontinuous clay surrounding an unlined 426 viii Contents

7 Site Investigation 427 7.1 Preliminary investigation 429 7.2 Aerial photographs 437 7.3 Terrain evaluation for highway projects 442 7.4 Geophysical exploration techniques 448 7.5 Seismic refraction surveying 453 7.6 Site exploration 457 7.7 Borehole logging 465 7.8 Sampling and testing 475 7.9 Site investigation reports 483 7.10 Mechanical tests in situ 484 7.11 Field monitoring techniques 503 7.12 Use of field seismic techniques in engineering geology 512 7.13 Analysis of ground vibrations 514 7.14 Marine geotechnical exploration 529 7.15 534 7.16 Probability theory in site investigation 547 7.17 What is 'safety' in soil and ? 557

8 560 8.1 Types of subsurface water 560 8.2 Groundwater flow 565 8.3 Seepage forces 577 8.4 Drainage and drain wells 580 8.5 Permeability tests - rock 585 8.6 Permeability tests - soils 591 8.7 Economic exploitation of groundwater 598 8.8 Ownership of groundwater and permitted abstractions 601 8.9 Groundwater exploration 601 8.10 Regional investigations 614 8.11 Simulation of groundwater regimes 618 8.12 Well losses 626 8.13 Improving aquifer yield 627 8.14 Groundwater quality 627

9 Stability of Soil Slopes 632 9.1 Planar slides 633 9.2 Circular failure surfaces 635 9.3 Slope stability case histories 645 Contents ix

9.4 Simple wedge method of analysis 661 9.5 Use of design curves 672 9.6 Pore pressure ratio 674 9.7 Oay slopes and shear strength parameters 675 9.8 Slope angle measurements in clays and clay shales 683 9.9 Classification of gravitational mass movements in clay 688 9.10 Rock breakdown and landform development 697 9.11 Geomorphological classification of slope profile development 704 9.12 General methods of preventing slope failure 705 9.13 Highway slopes 708 9.14 Protection against coastal 714 10 Rock Slope Stability 720 10.1 Geomorphological classification of rock slope instabilities 720 10.2 Classification of rock masses 730 10.3 Character of joints in rock masses 738 10.4 Engineering recognition of rock failure modes 743 10.5 Surface roughness of joints 749 10.6 Discontinuity roughness classification 753 10.7 Planar sliding and the friction cone concept 758 10.8 Instability on intersecting joint planes 765 10.9 Influence of discontinuity orientation distributions 787 10.10 Seismic influences on stability with respect to sliding 792 10.11 Instability caused by block overturning 797 10.12 General rock slope design curves 803 10.13 Slopes in highway cuttings and embankments 809 II Ground Improvement 814 11.1 Shallow compaction 817 11.2 Deep compaction 821 11.3 Pre-loading and consolidation 826 11.4 Sand drains 830 ll.5 Grout treatment 836 11.6 Fissure grouting 851 11.7 Hydrofracture 855 ll.8 Cavity grouting 863 11.9 Electro-chemical stabilisation 866 11.10 Groundwater freezing 871 x Contents

11.11 Bentonite suspension 874 1l.12 Ground anchors 879

12 Water Resources, and 887 12.1 Water requirements in England and Wales 888 12.2 Planning of water resources 889 12.3 Conjunctive use schemes 895 12.4 and dam design parameters 897 12.5 Channel protection 900 12.6 Design capacity of a storage 904 12.7 Air-photo interpretation for catchment development 907 12.8 Geological influences upon the selection of reservoir sites 908 12.9 Foundation investigations 911 12.10 Water movement into and out of a reservoir 914 12.11 Synthetic flow generation techniques 917 12.12 Dam foundations 918 12.13 Classification of dam types according to their purpose, construction and foundation geology 922 12.14 Long term stability of earth dams 944 12.15 Dam seismicity 945

References 969

Supplementary References 1022

Author Index 1025

Subject Index 1035 Preface

'Engineering geology' is one of those terms that invite definition. The American Geological Institute, for example, has expanded the term to mean 'the application of the geological sciences to engineering practice for the purpose of assuring that the geological factors affecting the location, design, construction, operation and mainten• ance of engineering works are recognized and adequately provided for'. It has also been defined by W. R. Judd in the McGraw-Hill Encyclopaedia of Science and Technology as 'the application of education and experience in geology and other geosciences to solve geological problems posed by civil engineering structures'. Judd goes on to specify those branches of the geological or geo-sciences as surface (or surficial) geology, structural/fabric geology, geohydro• logy, , soil and rock mechanics. is firmly included as a geological science in spite of the perhaps rather unfortunate trends over the years (now happily being reversed) towards purely mechanistic analyses which may well provide acceptable solutions for only the simplest geology. Many subjects evolve through their subject areas from an interdisciplinary background and it is just such instances that pose the greatest difficulties of definition. Since the form of educational development experienced by the practitioners of the subject ulti• mately bears quite strongly upon the corporate concept of the term 'engineering geology', it is useful briefly to consider that educational background. Engineering have usually received a basic training in either a geological or engineering discipline and there seems to be a popular acceptance of the potential advantages and disadvantages of both forms of training. Klaus John (1974) has summarized quite admirably the general feeling: 'They (geologists) prefer to approach a problem intuitively, indirectly, and in general qualitative terms, often preferring the problem to the results. Complexities are emphasized, xii Preface

simplifications are only hesitatingly accepted' and, in the case of engineers, '(they) are trained to be analytical, to depend on theory, and rely on numerical data, on abstractions of natural conditions ... often carried to excess with a tendency to unduly simplify in order to be able to numerically analyse a problem because, due to training and environment, (they) are dominated by their orientation toward results.' There is also a widespread feeling that a university training often tends to be given and received in a form and in an environment that is rather remote from the professional world where major design decisions have to be taken under pressures that are of both an economic and time-dependent nature. In Great Britain, it would appear that most of the entrants to the profession of engineering geology arrive with a background in geological science. With that in mind, it could be argued that the fundamental objectives of an engineering geology education should be: (a) to provide an adequate analytical and numerical framework within which the observational skills of the professional can be harnessed to produce information that will be immedi• ately useful in engineering design procedures; (b) to emphasize the geological, physical and structural variants inherent in both undisturbed and excavated earth materials and to indicate the manner in which the inevitable departures from an ideal material behaviour may constrain and cause to be modified any formalized process of design and construction of earth and rock structures; and (c) to underline the importance of water and particularly ground• water as an economic asset to be conserved and as a problem in ground engineering design. To these fundamental objectives should perhaps be added the express wish that the at all times maintain a socia-environmental awareness of the possible ramifications of his professional work and advice. It is with the three primary objectives in mind that the authors have attempted to structure the book by isolating a series of main headings which, it is felt, cover in a reasonable manner the very wide field of interest that is vested in the term 'engineering geology'. It should be stated that during the early planning of this book it soon became apparent that there were at least two possible ways of Preface xiii

tackling the work. One option, which had a certain attraction, would have been to present what might well have developed into a simple text on Quarternary and combined with a compendium of engineering geology case histories and supported by some very basic and undemanding analysis. Readers would have been expected to absorb the broad experience of others and, by interpolation and extrapolation, to use that experience in order to solve their own particular problems. Necessarily, such an approach to the subject would be qualitative and broadly descriptive, it would probably encompass numerous examples of rather simple geological structures, and it would no doubt be very acceptable to many geologists. On the other hand, one may question the requirement for a formalized collation of case histories when the proceedings of most of the engineering geology and rock mechanics conferences provide such case history expositions in easily-accessible and easily-readable form. An alternative option, which is in line with the arguments expressed earlier and which is the one adopted for this book, attempts to treat many of the more basic engineering geology concepts at a rather greater analytical depth and where possible uses case history evidence to back-up those concepts. It attempts to indicate to the reader how he can solve his own problems more immediately by a knowledge of some of the underlying principles moderated by an appreciation of the physical nature of the materials with which he is dealing. The present method of presentation therefore integrates many of the contributory disciplines in both the geological and engineering sciences upon which engineering geology must draw, but it retains those disciplines for a service function rather than allowing them to dictate the form of that presentation. Much of the text is written at university undergraduate level and, it is hoped, will be particularly appropriate reading for students in the final year of a first degree course in geological science. Some of the material should be of interest and use to students engaged in higher degree taught courses and to first degree civil engineering students. But since the text is geologically orientated throughout, students in these latter categories would need to supplement their reading with much more extensive study in the subjects of soil mechanics, rock mechanics, rock engineering and . In writing and organizing the text, the authors have drawn to some extent on their experience of lecturing to higher degree students in xiv Preface

engineering geology, to geology undergraduates of all levels, and to civil engineering science students, mainly, but not exclusively, in the University of Durham. However, certain lecture material that would normally be presented to M.Sc. students in Engineering Geology and to the B.Sc. students in Engineering Science has been omitted from the text on the grounds that it has rather less direct geological relevance. Typical examples of such omissions would be greater in-depth studies of stress analysis and dynamics, excavation tech• niques and support systems. Temptations to engage in discussions on aspects of foundation engineering have usually been firmly resisted, and there has been a conscious decision not to include either formalized descriptions of geological structures or general concepts in structural geology on the grounds that these subjects and their implied relationship to engineering geology are adequately covered in other books. Similarly omitted are the simple trigonometrical con• structions used to resolve information on geological maps since, as before, these procedures are dealt with elsewhere. Mathematical demands on the reader have been set generally at a low level and rarely in the book do they rise above pre-university standard. On a very few occasions, the going does become a little heavier and probably of more specialist research interest at the present time, but the treatment of the subject is such that those particular sections may be ignored if necessary by the average reader without incurring any penalty throughout the subsequent text. Quantities are usually expressed in S.1. units but in most instances an equivalent alternative is given at an appropriate point in the text. Where imperial units have been used the authors justify their decision on the grounds both that S.I. units have not yet been adopted universally and also that it is really no major task to convert one to the other. Symbols are defined in the text when used and are also separately listed in the book. Because of the extent of the subject coverage many of the symbols are re-used one or more times, occasionally in the same chapter. Care has been taken, however, to ensure that the reader is not faced with ambiguities that might be attributed to the allocation of the same symbols to different parameters. There are twelve chapters in the book and they have been arranged in such a way as to minimize the degree of forward reference as the subject is developed. Chapter I examines the composition of rocks and earth materials generally and highlights the importance of silicates and clay minerals in engineering geology. Chapter 2 Preface xv considers the physical properties of rock particles and covers the basic mechanics of particle systems or soils. This development is extended in Chapter 3 to a rather more detailed study of clays and clay shales, the latter with particular reference to mineralogy and chemistry and to the physical processes influencing breakdown. Chapter 4 looks at rock as a material in a materials science context and Chapter 5 examines some of the controls on and implications of intrinsic anisotropy in rock and clay. Chapters 6 and 7 form a particularly important part of the book. They cover respectively the subjects of rock discontinuities and site investigation techniques ~ the major interface between classical geology and civil engineering. These chapters include practical examples of discontinuity analysis and site appraisal. Chapter 8 is devoted to groundwater in both its engineering and economic roles. It includes a general theoretical appraisal of flow regimes and permeability measurement, aquifer abstraction and a consideration of water requirements. The remaining chapters are generally illustrative. Chapters 9 and 10 cover respectively soil and rock slope engineering problems with an emphasis on case history description and subordinate analytical backing. Chapter 11 describes in some detail various ground improvement techniques such as consolidation, grouting and freezing, the successful adoption of which is quite intimately dependent upon the geological character of the ground to be treated. The final Chapter 12 is concerned with dams, reservoirs and water resources. The authors wish to record help and encouragement from several sources. They extend very warm thanks to Dr. R. K. Taylor, a colleague of several years' standing, for many enlightening discussions on varied topics in engineering geology. The work on clay shales in Chapter 3 in particular has benefited from his experience in that field. Special thanks must also be accorded' to Mr. J. P. Woodman for his work with P.B.A. in the formulation and solution of rational discontinuity models -- a subject which is introduced in Chapter 6 ~ and to both he and Mr. J. C. Cripps for discussions on the use of decision theory in site investigation. The work of Engineering Geology M.Sc. Advanced Course students at Durham is acknowledged at appropriate points in the text and the authors express their appreciation of this contribution. They are also grateful to Dr. D. M. Hirst for reading through and xvi Preface commenting on Chapters I and 5 and to Dr. J. A. Hudson for performing the same operation on Chapter 4. The authors also feel that the final product has benefited from a first draft reading by Professor T. H. Hanna to whom they also express their thanks. Needless to say, they accept full responsibility for any inevitable errors that remain. The authors wish jointly to acknowledge their debt to Dr. Albert Roberts, formerly of the University of Sheffield, England and the University of Nevada, U.S.A. He encouraged and supported their early work at the University of Sheffield and they will always be grateful for the research opportunities and the research environment that he provided. In acknowledging the facilities at Durham University the authors have also appreciated the encouragement and support given by Professors G. M. Brown and M. H. P. Bott of the Department of Geological Sciences and by Professor G. R. Higginson of the Department of Engineering Science in the University. P.B.A. has also appreciated the tangible support provided during the development of Engineering Geology at Durham University by Professor Sir Kingsley Dunham, formerly Head of the Department of Geology in the University and Director of the Institute of Geological Sciences. Much of the research described in the text was possible only with outside support. Singly and jointly the authors acknowledge the following bodies for grants and contract support: Natural Environ• ment Research Council (U.K.), Transport and Road Research Laboratory, Department of the Environment (U.K.), European Research Office, U.S. Army. Technical assistance with some of the previously unpublished work outlined in the text was provided by Messrs. A. Swann, C. B. McEleavey and P. A. Kay. Messrs. G. Dresser and J. Clayton were responsible for some of the photographic printing. Finally, the onerous task of typing - and sometimes interpreting - the draft manuscript was performed most patiently and efficiently by Mrs. P. Farmer and Mrs. A. Taylor. Very special thanks are extended to them.

August 1974 P. B. Attewell I. W. Farmer Symbols

Chapter Symbol Meaning Reference

A Porewater pressure parameter 2 A Total capillary discharge area 2 ~i Asperity contact area 2 A Porewater pressure parameter 2 A Cross-sectional area of cylindrical rock specimen 4 A Creep constant 4 A Wavefront area 4 A Area factor 6 A* Predicted value in probability analysis 7 Ai Mutually exclusive events in probability analysis 7 A Shape factor in flow equation 8 A 1. .. n Strip areas in soil slopes for ru evaluation 9 A Total area of shear plane 10 Aj Total joint area within shear plane 10 A Cross-sectional area of river channel 12

B Pore water pressure parameter 2,9 jj Porewater pressure parameter 2,9 B Constant in strength anisotropy criterion 5 B Width of strip footing or foundation 7 B An event in probability analysis 7 B Maximum width of a slide 9

C Areal coefficient 2 C Porewater pressure parameter 2 C Torsion strain in vane tests 7 CR Cone resistance in standard penetration tests 7 C Capillary constant 8 C Drawdown constant 8 C Electrical capacitance in groundwater analogue models 8 C Explosive charge factor 11 C Constant in blasting compaction law 11 C Constant in pressure grouting uplift analysis II Ch Coefficient of consolidation due to radial flow 11 C Coefficient in Creager flood discharge formula 12 xviii Symbols

Chapter Symbol Meaning Reference

Dr Relative density 2 D Diameter of rock cylinder 4 D Maximum thickness of a slide 9 D Depth parameter in Taylor's slope design curves 9 D~ Underground excavation span parameter 10 D Dielectric constant II D Depth of water in river channel 12 E Young's modulus of elasticity 2,4,7 ER Attraction and repulsion energy between plates 3 Em Deformation modulus from Boussinesq rigid punch test 7 Ed Deformation modulus from plate (central hole) jacking test 7 Es Secant modulus 7 Er Elastic modulus from pressure chamber test 7 Er Energy ratio in vibration 7 E Potential difference 11 Ei Potential gradient 11 oE Grout input energy 11 oEs Stored strain energy in rock and grout fluid 11 oEr Irrecoverable energy during hydro fracture 11 En Evaporation parameter for month n in synthetic flow generation 12 F Dimensionless strength ratio 6 F Force dimension in dimensional analysis 7 F Factor of safety 9,10 FR Pull-out resistance of a grouted anchor 11

Gw Specific gravity of water 2 Gs Specific gravity of solids 2 G Rigidity modulus 4,7 G Dimensionless parameter in limit equilibrium analysis on stereographic projection 6

H Half thickness of a consolidating layer 2 He Height of collapse rock 7 H Vertical distance between standing piezometric level and base of abstraction or test borehole 8 H Slope height in Taylor's slope design curves 9 H Trough-to-crest wave height 9 H Slope height in rock 10 Hw Height of water table in slope 10 H Depth of wedge in diaphragm wall analysis 11 HI Height of dam from crest to top of foundation 12 Symbols xix

Chapter Symbol Meaning Reference

H2 Impounded head of water from base of dam 12

Ia Brittleness index 4 I Normalized diffracted X-ray intensity 5 I Electrical current in resistivity investigation 7 Ir Influence factor 7 !,/j Edge formed by planes PO!, P/j on stereographic projection 10

In Joint structure number in Tunnelling Quality Index equation 10 Ir Joint roughness number in Tunnelling Quality Index equation 10 la Joint alteration number in Tunnelling Quality Index equation 10 Iw Joint water reduction factor in Tunnelling Quality Index equation 10

Ko Coefficient of earth pressure at rest 2,3,7 Ka Coefficient of active earth pressure 2, 11 Kp Coefficient of passive earth pressure 2,7 K Bulk modulus 4,7 Ks Stiffness of rock specimen on unloading 4 Km Unloading stiffness of rock testing machine 4 K Constant in Griffith crack stability criterion 5 K U3/Ul ratio 5,11 Dimensionless parameters in limit equilibrium ~l } analysis on stereographic projection 6 K2 K Multiplying factor in rock slope stability analysis 10

L Length of cylindrical rock test specimen 4 L Length standardization multiplying factor for discontinuity scanlines 6 L Length dimension in dimensional analysis 7 L Beam span 7 L Length of flow path in seepage analysis 8 L Length along a borehole 8 L Leakage parameter in non-steady state drawdown under leaky aquifer conditions 8 L Maximum length of a slide up-slope 9 L Length of cylindrical injection source 11 L Path length in stabilisation 11 L Effective length of grouted anchor 11 L Width of wedge 11 xx Symbols

Chapter Symbol Meaning Reference

M A strength ratio 6 M A fraction between 0 and 1 6 M Total moment (Lm) of rotationally-shearing soil in slope stability analysis 9 M Catchment area 12

N Normal force 2,9 N Number of capillary tubes 2 N Number of fatigue cycles 4 N Accumulated microseismic activity 4 N Number of poles to discontinuities 6 N A fraction between 0 and 1 6 N A constant 6 N-y Bearing capacity factor 7 Nq Bearing capacity factor 7 N Number of blows in penetration testing 7 N Number of prior distributions 7 N f Number of flow lines 8 ND Number of equipotential lines 8 N Taylor stability number in soil slope stability analysis 9 N Number of fissures per metre 11 p Uniaxial force on a rock specimen 4 p Probability function 6,7 P Projection point of pole on a sphere 6,10 p Total force applied in plate bearing test 7 p A resultant vector in friction circle method of analysis 9 P Designated as the applied normal force on a plane in stereographic analysis of rock slope stability 10 P Myers percentage rating for 12 Pn,n-l Precipitation indices 12

Q Total volume flow rate 2,8,11,12 Q Activation energy in Arrhenius equation 4 Quit Ultimate bearing capacity 7 Q-l Material friction parameter (seismic wave transmission) 7 Q Tunnelling Quality Index 10

R Gas constant in Arrhenius equation 4 R Angle of refraction of a wave at a boundary 4 R Radius of projection sphere 6 Symbols xxi

Chapter Symbol Meaning Reference

Re Reliability of an estimate on an exponential utility function 7 Rq Reliability of an estimate on a quadratic utility function 7 R Drawdown radius (cone of depression) in pumping 8 tests 8 R Reciprocal of transmissivity (lIT) 8 R Resultant vector of weight and porewater force in slope stability analysis 9 R Skempton's 'residual factor' 9 Pa, P(J Ra} Normal reactions to forces on planes in rock R(J slope stability analysis 10 R Radius of grout penetration 11 R Electrical resistance 11 Rs Skin friction resistance of a grouted anchor 11 Rp End-bearing resistance of a grouted anchor 11 Rn Rainfall in month n (synthetic flow generation) 12

S Asperity shear resistance 2 S Saturation 2 So Specific surface area per unit volume of particles 2,11 Sc Particle crushing strength and unconfined compressive strength of rock 4,7,10,11 St Tensile strength 4,7 SAR Compressive strength of rock specimen having aspect ratio AR 4 S Fatigue strength 4 SRT Ultimate compressive strength at room temperature 4 Su Ultimate compressive strength at any temperature 4 Ss Strength of rock in direct (double) shear 4 S Storage coefficient of an aquifer 8 Sa} Boulton's aquifer storage coefficients 8 Sy S Shear force along a plane 9 Sc Cohesive element of shear force 9 Ss Shear strength of soil during rotational failure of embankment caused by seismicity 12 S Slope of stream or river 12

Tv Time factor in one-dimensional consolidation 2 T Surface tension 3 T Absolute temperature in Arrhenius equation 4 T Time dimension in dimensional analysis 7 T Time lag in permeability 8 T Transmissivity of an aquifer 8 xxii Symbols

Chapter Symbol Meaning Reference

T Weight resolved into a plane of shear 9 Th Time factor in radial (sand drain) consolidation 11

Vw Volume of water in pores of a soil 2,8 Vy Volume of voids in a soil 2 Vs Volume of solids in a soil 2 V Specimen bulk volume 2,4 V Electrical voltage in resistivity investigation 7 V Cost parameter in probability analysis 7 oV Volume of grout fluid injected per unit time during hydrofracture 11

Ww Weight of water 2 Ws Weight of sohds 2 W Energy in compression testing 4 Wi Input energy to a wave 4 Ws Stored energy in a wave 4 Wk Kinetic energy in a wave 4 Wo Source energy of a diverging wave disturbance 4 Wr Energy per unit area of wavefront at distance r from source 4 W standardizing multiplying factor for discontinuity scanlines 6 W Total shear strain energy due to shear movements along discontinuities 6 W Energy released by explosive (charge weight) 7,11 W Weight of soil or rock in slope stability analysis 9,10 W Weight of wedge in diaphragm wall analysis 11 W Width of river channel at water surface 12

X Slope angie function in rock slope design curves 10

y Slope height function in rock slope design curves 10

Z Zeta potential 11

a Graphical ordinate intercept in p-q space 2 aw Volume ratio of water phase 2,11 a Area of new cracks per unit volume of rock 4 a Area on plane of projection 6 a Inter-electrode spacing for resistivity investigation 7 at Radius of central hole in plate (bearing test) 7 a2 Radius of plate 7 a Internal radius of pressure chamber 7 Symbols xxiii

Chapter Symbol Meaning Reference a Ground acceleration 7,12 ap Radius of piezometer 8 a Borehole radius 8,11 ao Radius of grout injection source 11 a Capillary radius 8,11 aw Volume ratio of water phase 11 a Catchment area 12 an Constant of proportionality in synthetic flow generation 12 a Lever arm parameter in Newmark's seismic stability analysis 12 b Effective principal stress difference ratio 4 b' Saturated thickness of an aquitard 8 b Slice width in 2-dimensional soil slope stability analysis 9 b Constant in synthetic flow generation equation 12 b Distance parameter in Newmark's seismic stability analysis 12

C Cohesion 2,4,11 Ci Cohesion at asperity contact point 2 Cu Undrained shear strength 2,9,11 Cv Coefficient of consolidation 2,11 C Crack half-length 4 cp 1 (or Cj ) P-wave (or wave) velocity in medium I 4,7,10 Cp 2(orc2) P-wave (or wave) velocity in medium 2 4,7 Cc Crack length in anisotropic failure criterion 5 Ce Effective cohesion along a partially discontinuous surface 10

d Clay mineral particle/plate diameter 1 d Capillary diameter 2 do Particle diameter parameter 2 d Interparticle distance 3 d Vane diameter 7 d Jacking plate diameter 7 d Thickness of block in rotational stability analysis 10 de Drain spacing 11 dw Drain diameter 11 dp Maximum particle diameter 11 d Anchor diameter 11 d Induced dynamic distortion in a structure 12 xxiv Symbols

Chapter Symbol Meaning Reference e Void ratio 2 f Frequency 7, 12 fo Janbu correction factor in soil slope stability analysis 9 f Wave fetch (coastal protection) 9

Water head 2,8 Capillary water height above water table 2,8 Head of water above dam foundations or block 6,10 Height of vane 7 Seam thickness 7 Artesian head 8 Height of block of rock in rotational stability analysis 10 Grout hydraulic injection head 11 Head losses due to shear resistance 11

Hydraulic gradient 2,8,11 Angle of incidence of a wave at a boundary 4 Angle of critical incidence in seismic refraction 7 Standard deviation 7 Current in analogue simulation of groundwater 8 Average angle of incidence of surface undulations in direction of shear displacement 10 Slope angle in rock slope design curves 10

k Coefficient of permeability 2,8 k Equal area projection parameter 6 k Constant 7 ks Constant expressing sampling and testing cost 7 kt Constant expressing the degree of loss due to error 7 ke Effective permeability of anisotropic strata 8 kOt«(3) } Constants in rock slope stability analysis 10 k(3(Ot) ke Equivalent permeability of fissured strata 8,11 kh Coefficient of horizontal permeability 8,11 kv Coefficient of vertical permeability 8,11 ke Electro-osmotic coefficient of permeability 11

Length of principal axes of deformation ellipsoid 5 Quantum number of Legendre polynomial equation 5 Length of a discontinuity intersection on a plane 6 Slice length parameter along a shear plane 9 Symbols xxv

Chapter Symbol Meaning Reference

Length of chord of a failure arc in slope stability analysis 9 Base width of dam 12 m Moisture content 2 m Poisson's number 2 mv Volume compressibility of a soil 2,11 m Constant 4,10 m Quantum number in Legendre polynomial equation 5 m Fractional height of a water table above a reference surface 9 m Moment of a force along a slope failure arc 9 mOl Parameter in soil slope stability analysis 9 n Porosity 2,4,11 n Exponent in creep equation 4 n Number of variables in probability analysis 7 n Fraction of vertical force (W) exerted horizontally (specifically by seismic waves) 7,9,10,12 nOi. Parameter in soil slope stability analysis 9 n Constant in rock slope stability analysis 10 n* Ratio between sand-drain spacing and diameter 11

P Half sum of principal stresses 2 p Suction pressure 3 Px Event probability 6 P Scanline angle parameter 6 POl,{3 Designation of a plane 10 Pa Average injection pressure acting in a fissure 11 Po Internal grout pressure in a borehole 11 Pr Fluid pressure at radius r 11 P Basic forcing frequency 12 q Half principal stress difference 2 qu Yield strength or unconfined compressive strength 2,6,9 q Scanline direction constant 6 q Bearing pressure 7 q Flood discharge per unit area 12 r Radius or radial distance 1,3,4,6,7,8, 9,11 ru Pore pressure ratio 9 xxvi Symbols

Chapter Symbol Meaning Reference

S Average specific surface area of clay minerals S Material parameter 6 S Settlement 7 S Drawdown as a function of radius from pumped well 8

St Total drawdown due to pumping 8 sd Dynamic shear strength 12

Clay mineral thickness 1 Consolidation time 2 t Temperature 3 t Time 4,7,8,11 Beam thickness 7 Torque at failure in vane test 7 tn,n+ 1 Interslice shear forces in slope stability analysis 9

U Porewater pressure 2,8,11 Ua Pore pressure change under hydrostatic consolidation 2 Ub Pore pressure change due to deviator stress 2 Ug Pressure of gas phase in partially-saturated soil 2 Uw Pressure of water phase in partially-saturated soil 2 Ue Excess porewater pressure in consolidation 2 U Surface or particle displacement 7,12 U Parameter in Theis equation 8 ~: } Parameters in Boulton's equation 8 v Particle, ground surface, or water discharge velocity 2,4,7,8 v Voltage in analogue simulation of groundwater 8 w Weighting constant used in computer fabric analysis 6 w Weight of slice of soil in slope stability analysis 9 x Specimen displacement axis in graph of uniaxial compression test 4 Coordinate axes 6,7 Projection of measured discontinuity length h on to horizontal axis 6 x Value of a variable in probability analysis 7 X Mean value of a variable 7 y Geophone distance from source of seismic pulse 7 yc Critical distance in seismic refraction 7 Symbols xxvii

Chapter Symbol Meaning Reference

Z Interatomic charge Z Depth 2,4,7,8,11 Zj Projection of measured discontinuity length Ii on to vertical axis 6 Depth of tension crack 10 Depth to water table and of water in tension crack 10

Volumetric strain 2,4 Vibration intensity 7

1\ Defines projection domain of discontinuity length onto a reference axis (p) 6

Defines projection domain of discontinuity length onto a reference axis (8) 6 Dimensionless area factor in seepage flow 11

Summation symbol 2,6,9

Function in dimensional analysis 7

Electrical potential 3 Thermal diffusivity 11

Effective hydraulic radius 2,11 Slope of p-q envelope 2 Soil-water contact angle 3,8 Variable parameter in extended Tresca law 4 Wave attenuation coefficient 4 Direction cosine angle 6 Bedding or shear plane inclination to horizontal (passive wedge in soil slope stability analysis) 7,9 Reciprocal of delay index (leaky water-table aquifer condition) 8 a* Analogue model mesh length 8

A reflection angle in wave transmission 4 Angle formed by an anisotropic plane and a major principal stress direction 5 Dip angle of pole to a discontinuity from the vertical and also direction cosine angle 6 Measured dip to horizontal of discontinuity intersection with scanline measurement plane 6 xxviii Symbols

Chapter Symbol Meaning Reference

Embankment slope angle 8 Shear plane inclination to horizontal (neutral wedge in soil slope stability analysis) 9 Angle in Newmark's dynamic stability analysis 12

'Y Bulk density 2,4,7,8 'Yd Dry density 2,4 'Yf Fluid density 2 'Yb Submerged density 2,8,11 'Yw Density of water 2,3,6,8,9,11 'Y8 Density of solids 2 'YC Density of concrete 6 'Yr Density of rock 6 'Y Direction cosine and equatorial angle on projection 6 'Yk Density of collapse rock 7 'Y Shear plane inclination to horizontal (active wedge in soil slope stability analysis) 9 'Yg Density of grout suspension 11

Equatorial angle (small circle) on projection 6 Mathematical function 7 Displacement of rock at depth z beneath plate 7 Fissure thickness 8,11 Displacement along undulating surface 10 Fissure thickness before injection extension 11 Fissure thickness at edge of extension front 11 Average fissure width extension 11

€x,y,z Strain 2,4,5,10,11 €o Elastic strain 4 €c Long-term creep strain 4 €L Lateral strain 4 €a,{3 Azimuth angle between two planar full-dip directions 10

Angle defining surface of no finite longitudinal strain 5

TI Fluid viscosity 2,8,11 TI Latitude angle of poles to crystallographic planes in texture-goniometry 5 TI Eulerian angle in transformation of axes 6 TIe Fraction of coal extraction from a seam 7 TI Storativity ratio parameter in Boulton's non-steady state water table type curves 8 TIp Bingham viscosity of grout 11 Symbols xxix

Chapter Symbol Meaning Reference

T/g Grou t viscosity 11 T/w Water viscosity 11 T/a Apparent viscosity 11

(} Angle defining plane in principal stress space 2 (} Azimuth angle of poles to crystallographic planes in texture-goniometry 5 (} Azimuth angle of a discontinuity pole (direction of planar full dip) 6 (} Scanline direction angle referenced to an arbitrary axis 6 (} Angle in construction of parabola 8 (} Wedge angle 11

A Wavelength of transmitted waves 4 A Angle formed by a shear failure plane and a major principal stress direction 5 A Eulerian angle in transformation of axes 6 A Wavelength of undulations on discontinuous surfaces 10

Ji Coefficient of friction (tangent of friction angle) 2,4 Jic Friction coefficient along a crack 5 v Poisson's ratio 2,4,7,10 Vo 'Elastic' Poisson's ratio 4 Vc Crack dilation portion of /I 4

~ Designation of a crystal face 5 ~ Eulerian angle in transformation of axes 6 ~ General shear plane angle to horizontal 6 Inclination angles of joint shear planes to horizontal ~a } ~[3 in rock slope stability analysis 10 ~I Dip angle from vertical of Pa, P[3 planar intersection line Ia ,[3 in rock slope stability analysis 10 p Specific surface energy per unit length of crack 4 p Electrical resistivity 7,11 a Stress (also ax, ay , az along coordinate axes x, y, z) 2,4 a Hydrostatic (all-round) stress 2 a1,2,3 Principal stress 2,4 an Normal stress on a plane 2,4 I aVID Maximum historical overconsolidation pressure 2 I avo Initial vertical geostatic pressure on a soil 2 xxx Symbols

Chapter Symbol Meaning Reference

Ut Tensile stress concentration 4 U3L Limiting confining pressure 4 Uo Critical stress value in distortional strain energy law 4 U Pressure in a wave 4 Ui Stress in incident wave 4 ur Stress in wave reflected from a boundary 4 Utr Stress in wave transmitted through a boundary 4 unc Normal stress on a crack 5 Ut Tangential stress around a borehole 11 ur Radial stress around a borehole 11 Uto Tangential stress around a hole with zero internal pressure 11 uR Radial pressure distribution around a borehole with seepage flow of injectant 11 uT Tangential pressure distribution around a borehole with seepage flow of injectant 11

T Shear stress 2,4,7,9,11,12 TA Shear resistance of asperities 2 Tf Shear stress at failure (function of normal pressure) 4,12 Tr Residual shear strength 4,9 Tc Shear stress along a crack 5 Tp Peak shear strength 9 f Mean shear strength 9 Ts Shear strength of grout 11

X An even t in fracture analysis 6 X Angular measurement on stereo graphic projection for rock slope stability analysis 10

1/101,/1 Azimuthal angle for planar full dip direction 10 1/11 Azimuthal angle for planar intersection line direction 10 w Circular frequency 12