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6.7Rock fall modeling 310Ditches 312Barriers 313Rock catch fences and attenuators 316Draped mesh 317Warning fences 317Rock sheds and tunnels 31813 Movement monitoring32013.1 Introduction 32013.2 Types of slope movement 32213.2.1Initial response 32213.2.2Regressive and progressive movement 32213.2.3Long-term creep 32413.3 Surface monitoring methods 32413.3.1Crack width monitors 32513.3.2Surveying 32613.3.3Laser imaging 32713.3.4Tiltmeters 32713.3.5Global positioning system 32713.3.6Synthetic aperture radar 32713.4 Sub-surface monitoring methods 32713.4.1Borehole probes 32813.4.2Time–domain reflectometry 32813.4.3Inclinometers 32813.5 Data interpretation 32813.5.1Time–movement and time–velocity plots 32913.5.2Slope failure mechanisms 33214 Civil engineering applications14.1 Introduction 33414.2 Case Study I—Hong Kong: choice of remedial measures for plane failure 33414.2.1Site description 33414.2.2Geology 33414.2.3Rock shear strength 33514.2.4Ground water 33514.2.5Stability analysis 33514.2.6Stabilization options 33914.3 Case Study II—Cable anchoring of plane failure 34114.3.1Site description 341334

Contentsxv14.3.2Geology 34214.3.3Rock shear strength 34214.3.4Ground water 34314.3.5Earthquakes 34414.3.6Stability analysis 34414.3.7Stabilization method 34514.3.8Construction issues 34714.4 Case Study III—Stability of wedge in bridge abutment 34814.4.1Site description 34814.4.2Geology 34814.4.3Rock strength 34914.4.4Ground water 34914.4.5Seismicity 35014.4.6External forces 35014.4.7Stability analysis 35014.5 Case Study IV—Circular failure analysis of excavation for rock fall ditch 35214.5.1Site description 35214.5.2Geology 35314.5.3Ground water 35314.5.4Rock shear strength 35314.5.5Ditch and slope design 35414.5.6Construction issues 35414.6 Case Study V—Stabilization of toppling failure 35414.6.1Site description 35414.6.2Geology 35514.6.3Rock strength 35514.6.4Ground water 35514.6.5Stability conditions 35514.6.6Stabilization method 35615 Mining applications15.1 Introduction 35715.2 Example 1—porphyry deposits 35715.2.1Design issues 35815.2.2Engineering geology 35815.2.3Rock strength and competency 35815.2.4Hydrogeology 35915.2.5Slope stability analyses and slope design 35915.3 Example 2—stratigraphically controlled deposits 36115.3.1Design issues 36115.3.2Engineering geology 36115.3.3Rock strength and competency 362357

xviContents15.3.4Hydrogeology 36315.3.5Structural domains 36315.3.6Kinematic analyses 36315.3.7Stability analyses 36415.3.8Slope design concepts 36515.3.9Preliminary design 36715.4 Example 3—deep-seated deformation in a weak rock mass 36815.4.1Design and operational issues 36815.4.2Engineering geology 36915.4.3Rock strength and rock mass competency 37015.4.4Hydrogeology and slope depressurization measures 37015.4.5Slope stability analyses 37115.4.6Slope design and operational management 37215.5 Example 4—overall slope design in a competent rock mass 37215.5.1Design aspects and issues 37215.5.2Engineering geology 37315.5.3Rock strength and competency 37315.5.4Hydrogeology 37315.5.5Slope performance 37415.5.6Slope stability analyses 37515.5.7Implementation and ongoing evaluation 37515.6 Conclusions 376Appendix II.1I.2I.3I.4I.5II.3377Introduction 377Plotting poles 377Contouring pole concentrations 377Plotting great circles 377Lines of intersection 378Appendix IIII.1II.2Stereonets for hand plotting of structural geology dataQuantitative description of discontinuities in rock massesIntroduction 381Rock mass characterization parameters 381II.2.1Rock material description 381II.2.2Discontinuity description 383II.2.3Infilling description 389II.2.4Rock mass description 389II.2.5Ground water 392Field mapping sheets 394381

ContentsAppendix IIIIII.1III.2III.3III.4III.5III.6Comprehensive solution wedge stabilityxvii398Introduction 398Analysis methods 398Analysis limitations 399Scope of solution 399Notation 400Sequence of calculations 400Appendix IVReferencesIndexConversion factors408411425

IntroductionReaders will undoubtedly recognize the similarity of this book to Rock Slope Engineering by Dr EvertHoek and Dr John Bray. We hope the following discussion of the origin and evolution of the currentbook will help to demonstrate the relationship between the two.Rock Slope Engineering was published in three editions (1974, 1977 and 1981) by the Institute ofMining and Metallurgy in London. The original research for the book at the University of Londonwas sponsored by the mining industry in response to a need to develop design methods for increasingly deep open pits. The 1960s and 1970s had seen the development of a new generation of highproduction drills, shovels and trucks that made low grade ore deposits economical to mine, and therewas a consequent significant increase in the size of open pits. The investigation and design techniquesoriginally developed in Rock Slope Engineering for mines were soon adopted in civil engineeringwhere the slopes’ heights are usually less than those in open pits, but there is a need for a high level ofreliability in terms of both rock falls and overall stability. In response to the demand for a book thatclearly presents well-proven methods to design rock slopes, Hoek and Bray’s book has continued tosell steadily around the world, and has been translated into a number of languages.In 1980, one of the authors of this book (DCW) was awarded a contract by the Federal HighwayAdministration (FHWA) in Washington to prepare a manual on rock slope design and constructionspecifically applicable to highways. At that time, I was working with Dr Hoek and he generously agreedthat his manuscript of Rock Slope Engineering could be adapted for this purpose. The manual closelyfollowed the original book, apart from chapters on slope stabilization and movement monitoring.A second FHWA contract was awarded in 1996 as part of an eleven module series on highwaygeotechnical engineering, and this opportunity was taken to embark on a major updating of themanual. The manuals have been used primarily as teaching material for a series of courses sponsoredby the National Highway Institute for highway engineers in the United States; to date over 40 courseshave been presented.It was realized that a limitation of the FHWA manuals was their focus on highway engineering, andthat their availability was generally limited to course participants. Therefore, in 2001 it was decidedthat it would be worthwhile to produce another update that would cover the wider field of rock slopeengineering, including civil and mining applications. In order to take this step, it was necessary toobtain the permission and co-operation of a number of organizations and individuals—Mr JerryDiMaggio of the Federal Highway Administration, Dr G. P. Jayaprakash of the TransportationResearch Board, both in Washington, and Dr George Munfakh of Parsons Brinckerhoff Quade andDouglas (PBQD) in New York. We are most grateful for their assistance and encouragement.Of course, the most important participant in this work has been Dr Evert Hoek who generouslyagreed that we could use Rock Slope Engineering as the basis for the new work. Since Dr Hoeklives in the same neighborhood, it has been possible to have a series of meetings to discuss both the

Introductionxixoverall approach and details of the contents and methods. We express our gratitude for the valuableassistance that we have received from Dr Hoek over the two years, as well as his pioneering workwith Dr Bray in establishing the fundamental procedures for rock slope engineering.Dr Lorin Lorig and Mr Pedro Varona of Itasca Corporation and Mr Alan Stewart and his colleaguesat Piteau Associates Engineering have also made important contributions. Dr Lorig and Mr Varonawrote Chapter 10 on numerical analysis methods, and the personnel from Piteau wrote Chapter 15 oncase studies on open pit mining. We decided these two chapters were best written by persons workingin these specialist fields, and we appreciate their hard work and dedication.One of our objectives in writing this book has been to maintain much of the original content of RockSlope Engineering, because the basic slope design methods that were developed for the 1974 editionare still valid to this day. Our approach has been to incorporate, within the original framework,technical advances and experience in rock slope design and construction projects over the past 30years. This has allowed us to maintain the structure of Rock Slope Engineering so that those who arefamiliar with Hoek and Bray can readily find their way around this book. In addition to generallyupdating the book, the following is a list of the major topics that have been added: Geological data collection—The International Society of Rock Mechanics nomenclature forstructural geology is included in Chapter 3 and Appendix II. Rock mass strength—The 2002 version of the Hoek–Brown rock mass strength criterion is includedin Chapter 4. Earthquakes—The effects of earthquakes on slope stability and design methods for slopes in seismicareas are described in Chapter 6. Probabilistic, and Load and Resistance Factor design methods—The basic principles of probabilistic and LRFD design are discussed in Chapter 1; an example of probabilistic design is includedin Chapter 6. Numerical analysis—Chapter 10 is a new chapter describing the use of numerical analysis methodsin slope design. Production blasting—Updated methods of designing production blasts have been added toChapter 11, which covers in addition, blasting methods for final walls and control of damageoutside the blast area. Slope stabilization and rock fall protection—Chapter 12 is a new chapter describing rock slopehazard assessment, slope reinforcement and rock fall protection such as ditches, fences and sheds. Slope movement monitoring—Surface and sub-surface movement monitoring methods, and datainterpretation are described in Chapter 13. Case studies in civil engineering—Case studies of plane, wedge, circular and toppling failures aredescribed in Chapter 14. Case studies in open pit mining—Four case studies demonstrating pit slope design in a variety ofgeologic environments are described in Chapter 15.It may be noticed that some material is very similar to that in the books Foundations on Rock and Landslides: Investigation and Stabilization. This duplication is inevitable when discussing fundamentals ofrock mechanics that do not change significantly over time.We would like to express our gratitude to a number of people, in addition to Dr Hoek who haveassisted us with this work. In particular, Ms Sonia Skermer and Mr George Gorczynski preparedthe illustrations, and Ms Glenda Gurtina prepared the original FHWA manual and has worked onmany of the complex portions of the text. We also appreciate the valuable input on seismic design byDr Randy Jibson and Dr Upul Atukorala, the photographs supplied by Rio Tinto Ltd and acknowledge

xxIntroductionour long associations with the Federal Highway Administration in Washington DC, the CanadianPacific Railway, and the British Columbia Ministry of Transportation.Finally, we are most grateful to our colleagues, fellow geotechnical engineers and contractors withwhom we have worked over many years on a wide range of projects. This book attempts to distillour collectively acquired experience.Duncan C. Wylliewww.wnrockeng.comChristopher W. Mahwww.cmrockeng.comVancouver, Canada, 2003

ForewordMy work on rock slope engineering started more than thirty years ago while I was Professor ofRock Mechanics at the Imperial College of Science and Technology in London, England. A four-yearresearch project on this topic was sponsored by 23 mining companies around the world, and wasmotivated by the need to develop design methods for the rock slopes in large open pit mines whichwere becoming increasingly important in the exploitation of low-grade mineral deposits. Rock SlopeEngineering, co-authored with my colleague Dr John Bray, was first published in 1974 and thenrevised in 1977 and again in 1981.While rock slope engineering remains an important subject, my own interests have shifted towardstunnelling and underground excavations. Consequently, when Duncan Wyllie suggested that he andChristopher Mah were willing to prepare a new book on rock slopes I felt that this would be anexcellent move. They have had a long involvement in practical rock slope engineering, mainly for civilengineering construction projects, and are familiar with recent developments in methods of analysisand stabilization. The evolution of their text, from Rock Slope Engineering to a manual on rock slopedesign for the US Federal Highway Administration, is described in their introduction and need not berepeated here.The text that follows is a comprehensive reference work on all aspects of rock slope engineeringand, while it embodies all the original concepts of my work, it expands on these and introduces asignificant amount of new material, for both mining and civil engineering and several new case studies.As such, I believe that it will be an important source of fundamental and practical information forboth students and designers for many years to come.I commend the authors for their efforts in producing this volume and I look forward to havinga copy on my own bookshelf.Evert HoekVancouver, 2003

Area of plane (m2 )Material constant for rock mass strength; ground acceleration (m/s2 )Burden distance for blast holes (m)Distance of tension crack behind crest of face (m); joint spacing (m)Dispersion coefficientCohesion (kPa)Disturbance factor for rock mass strength; depth (m)Diameter (mm)Deformation modulus for rock massJoint aperture (mm)Shape factorFactor of safetyShear modulus (GPa)Geological Strength IndexAcceleration due to gravity (m/s2 )Height of slope, face (m)Water level head above datum (m)Roughness angle of asperities (degrees)Joint roughness coefficientBulk modulus (GPa); hydraulic conductivity (cm/s 1 ); corrosion service life constant (µm),rate of slope movement constantSeismic coefficient; attenuation constant for blast vibrationsLength of scan line, face, borehole (m)Persistence of discontinuity (m); unit vectorUnit vectorMaterial constant for rock mass strengthmaterial constant for intact rockNumber of joints, readingsUnit vector, number of toppling blocksProbabilityPressure (kPa)External load (kN)Resultant vector; hole radius (mm)radius of piezometer (mm)

NotationSSDsTtUVWXzzwαβ xδεφγµσσcmσciσ1 σ3 τψυxxiiiShape factor; spacing distance for blast holes (m)Standard deviationSpacing of discontinuity (m); material constant for rock mass strengthRock bolt tension force (kN)Time (s, yr)Uplift force on sliding plane due to water pressure (kN)Thrust force in tension crack due to water pressure (kN); velocity of seismic waves (m/s),velocity of slope movementWeight of sliding block (kN); explosive weight per delay (kg)Loss of element thickness, corrosion (µm)Depth of tension crack (m)Depth of water in tension crack (m)Dip direction of plane (degrees)Attenuation constant for blast vibrationsWidth of toppling slab, slice in circular failure (m)Displacement (mm)Coefficient of thermal expansion (per C)Friction angle (degrees)Unit weight (kN/m3 )Poisson’s ratioNormal stress (kPa)Compressive strength of rock mass (kPa)Compressive strength of intact rock (kPa)Major principal effective stress (kPa)Minor principal effective stress (kPa)Shear stress (kPa)Dip of plane (degrees)Viscosity of water (m2 /s)

NoteThe recommendations and procedures contained herein are intended as a general guide, and prior totheir use in connection with any design, report, specification or construction procedure, they shouldbe reviewed with regard to the full circumstances of such use. Accordingly, although every care hasbeen taken in the preparation of this book, no liability for negligence or otherwise can be acceptedby the authors or the publisher.

Chapter 1Principles of rock slope design1.1 IntroductionA variety of engineering activities requireexcavation of rock cuts. In civil engineering,projects include transportation systems such ashighways and railways, dams for power production and water supply, and industrial and urbandevelopment. In mining, open pits account for themajor portion of the world’s mineral production.The dimensions of open pits range from areas ofa few hectares and depths of less than 100 m, forsome high grade mineral deposits and quarries inurban areas, to areas of hundreds of hectares anddepths as great as 800 m, for low grade ore deposits. The overall slope angles for these pits rangefrom near vertical for shallow pits in good quality rock to flatter than 30 for those in very poorquality rock.Figure 1.1 shows two typical rock slopes.Figure 1.1(a) is a rock cut, with a face angleof about 60 , supported with tensioned anchorsincorporating reinforced concrete bearing padsabout 1 m2 that distribute the anchor load onthe face. The face is also covered with shotcreteto prevent weathering and loosening between thebolts. Water control measures include drain holesthrough the shotcrete and drainage channels onthe benches and down the face to collect surfacerun-off. The support is designed to both ensurelong-term stability of the overall slope, and minimize rock falls that could be a hazard to traffic.Figure 1.1(b) shows the Palabora open pit inSouth Africa that is 830 m deep and an overallslope angle of 45–50 ; this is one of the steepestand deepest pits in the world (Stewart et al., 2000).The upper part of the pit is accessed via a dualramp system, which reduces to a single ramp inthe lower part of the pit.In addition to these man-made excavations, inmountainous terrain the stability of natural rockslopes may also be of concern. For example, highways and railways located in river valleys may belocated below such slopes, or cut into the toe,which may be detrimental to stability. One ofthe factors that may influence the stability of natural rock slopes is the regional tectonic setting.Factors of safety may be only slightly greater thanunity where there is rapid uplift of the land massand corresponding down-cutting of the watercourses, together with earthquakes that loosenand displace the slope. Such conditions exist inseismically active areas such as the Pacific Rim,the Himalayas and central Asia.The required stability conditions of rock slopeswill vary depending on the type of project andthe consequence of failure. For example, for cutsabove a highway carrying high traffic volumesit will be important that the overall slope bestabl

1.2 Principles of rock slope engineering 4 1.2.1 Civil engineering 4 1.2.2 Open pit mining slope stability 5 1.3 Slope features and dimensions 8 1.4 Rock slope design methods 8 1.4.1 Summary of design methods 8 1.4.2 Limit equilibrium analysis (deterministic) 11 1.4.3 Sens