ROCK FRACTURE MECHANICS

Transcription

1 INTERNATIONAL CENTRE FOR MECHANICAL. SCIENCES COURSES AND LECTURES. No. 275 ROCK FRACTURE MECHANICS EDITED BY H.P. ROSSMANITH TECHNICAL UNIVERSITY OF VIENNA SPRINGER-VERLAG WIEN GMBH

2 This work is sub;ect to copyright. AII rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks by Springer-Verlag Wien Originally publisbed by Springer Verlag Wien-New York in '1983 ISBN DOI / ISBN (ebook)

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4 CONTENTS PREFACE I. BAs I CS OF RocK FRACTURE MEeHAN I CS 1 (R.A.Sahmidt - H.P.Rossmanith) 1. Introduction 2. Linear Elastic Fracture Mechanics (LEFM) The Stress Intensity Factor Fracture Criteria Fracture Toughness Crack Tip Zone of Micro-Cracking in Rock Subcritical Crack Growth Development of Fracture Toughness Testing CT-Specimen and 3PB-Specimen Testing Anisotropy Effects of Hydrostatic Compression Closure References 27 II I ANALYSIS OF CRACKS RELATED TO ROCK FRAG"ENTATION 31 (F. Ouahter lony) 1. Introduction to Blasting Configurations Idealized Crack Systems Complex Representation and Conformal Mapping ~1ethod Results Formal Approach to Uniform Growth Path-Independent Integrals Method Results and Applications References 66

5 IV III. FRACTURE TOUGHNESS TESTING OF ROCK (F.Ouahter:>Zony) 1. Review of Toughness Testing 1.1. On Specimen Geometries 1.2. Specific Work of Fracture 1.3. Griffith's Balance of Energy Rates 1.4. Fracture Toughness Validity of Metals Testing Criteria Other Aspects 1.5. J-Integral Resistance Applicability of JicTest Practice for Metals to Rock J 1 ~-Measurements on Rock 1.6. Anisotropy Effects Material Description Crack Growth Resistance Values Cone 1 us ions 2. Development of Core Bend Specimens 2.1. Single-Edqe-Crack-Round-Bar in Bending (SECRBB) Experimental Procedure Results Further Fracture Mechanics Formulas 2.2. Chevron-Edge-Notch-Round-Bar in Bending (CENRBB) 3. Crack Resistance Measurements on Core Specimens 3.1. SimpleR-Curve Approach to SECRBB Testing Prediction Formulas Energy Rate Crack Pesistance Data Conclusions 3.2. Direct R-Curve Measurements on SECRBB Specimens R-Curves from Complete Failure Curves R-Curves from Sub-Critical Failure Cycles Conclusions 3.3. Conclusions from Core Toughness Data 4. References Contents IV I Nll'fRICAL l"t..delling OF FRACTURE ~OPAGATION (A. R. Ingr:>affea) 1. Introduction 2. The Nature of Fracture Propagation in Rock 3. Stress Intensity Factor Computation 3.1. A Historical Overview 3.2. Computation by Finite Element Method 3.3. Computation by Boundary Element Method

6 Contents V 4. Theories of Mixed-Mode Fracture The cre,max-theory The S(e)min-Theory Comparison of Mixed-Mode Fracture Theories 4.4. Predicting Crack Increment Len9th Fracture Propagation Programs Numerical Methods User-Computer Interface Automatic Remeshing Example Solutions Fracture Propagation Modelling - The Future References 204 V. Iffl.w.1IC PHoTOELASTICITY AND HOLOGRAPHY 1\PPLIED TO CRACK AND WAVE PROPAGATION 209 (H.P.Rossmanith - W.L.Fourney) 1. Photoelasticity High-Speed Photography and Requirements of an Optimum Photographic System in Dynamic Photoelasticity Cranz-Schardin Camera Dynamic Holography Applications Wave Propagation Fracture Mechanics Crack-Wave Interaction References 227 VI I ELASTIC \!AVE PROPAGATION 229 (H.P.Rossmanith) 1. Waves in Unbounded Media 1.1. Plane Waves 1.2. Spherical and Cylindrical Waves Spherical Waves Cylindrical Waves 1.3. Superposition of Elastic Waves 2. Boundary Effects 2.1. Cohesive Joints 2.2. Loose Joints 2.3. Plate Waves

7 VI Contents 2.4. Surface Waves Glancing Angle Diffraction Rayleigh-Waves P-Wave Propagation in Layers 2.5. Nonplanar Wave Fronts at Boundaries and Interfaces 3. Dynamic Layer Detachment and Spallation References VI I I ANALYSIS OF DY~ lamic PHoTOELASTIC FRINGE PATTERNS (H.P.Rossmanith) 1. Identification of Isochromatic Fringes Data Analysis Boundary Conditions Wave Form Conditions Fracture Analysis Using Photoelastic Data Mixed-Mode Fracture Problem A Multiparameter Approach Crack Speed versus Stress Intensity Factor Characterization of Dynamic Fracture References VII I. DYNAMIC CRACK ANALYSIS MID THE II\'TERACTION BElWEEN CRACKS AND WAVES 271 (H.P.Rossmanith) 1. The Moving Crack 1.1. Discontinuous Change of Crack Speed 2. Crack-Wave Interaction 2.1. Cracks Subjected to Stress Wave Loading Diffraction by a Stationary Crack Crack Extension Following Wave Diffraction 2.2. Photoelastic Investigation of Crack-Wave Interaction 3. Interface Cracks and Joints 4. References

8 Contents IX. FRACTURE CONTROL BLASTING (W.L.FourneyJ 1. Introduction 1.1. Effect of Notches in a Borehole 1.2. Control of Crack Initiation 2. Photoelastic Studies of Fracture Control 3. References X, FRAGMENTATION STuDIES WITH SMALL FLI\WS (W.L.FGJurneyJ 1. Introduction 2. Fragmentation of a Homogeneous Model 3. Effects of Small Flaws 4. Summary 5. References VII XI I FRAGYIENTATION STuDIES WITH LA.HGE FLI\WS (W.L.Fourney) 1. Introduction 2. Joint Initiated Fracture 3. Time Delays Between Boreholes 4. References XI I. GAs WELL STIMJLATION STuDIES (W.L.Fourney) 1. Introduction 2. Growth of Fractures from a Wellbore and Gas Flow into them 2.1. Effect of Loading Rate 2.2. Stem Induced Fracture 3. References

9 VIII Contents XI I I I GROUND VIBRATION STuDIES 371 (W. L. Fourney) 1. Introduction Theory Results Conclusion References 381 XIV. f1bdelling A~ID DEVELOPMENT OF HYDRAULIC FRACTURING TECI-f\IOLOGY 383 (M.P. Cleary) Summary 383 Introduction Potential and Status of Fracturing Technology Mechanisms of Fracture Creation in Rock General Equations Governing Hydraulic Fracturing Models of Fracture Processes, Existing Potential Technology Modelling Field Technology First-Order Models and Design of Hydraulic Fractures Mathematical Models Equations Governing Lumped P3DH-Type Models Algebraic Solutions of Lumped Model Equations Numerical Solutions of Lumped Model Equations Summary of P3DH-Model Equations and Results Reduction of P3DH-Model to Ordinary Differential Equations Self-Similar Approximations for Storage in Latera 1 Flow Hybridisation of Self-Similar and O.D.E. Models Hydrafrac Designs Based on Lumped Model Solutions Detailed Theoretical Modelling Hydrafrac Complete Simulation for a Representative Cross Section Development of a Reference Circular Hydrafrac Model Modelling of Multiple Fractures, Interaction with Reservoir Conditions of Stress, Pore Pressure and Material Variations 443

10 Contents IX 3.3. Modelling of Multiple Fractures, Interaction with Reservoir Conditions of Stress, Pore Pressure and Material Variations Fracture Impedance Mechanisms, Branching and Slipping Fully Three-Dimensional Simulation of Fracturing Laboratory Simulation of Fracturing Interface Separation Apparatus, DISLASH Apparatus for Full 3-D-Fracture Growth and Interaction Development of Data Acquisition and Control Systems Monitoring of Fracture Growth in the Laboratory Some Studies on Fluid Rheology Laboratory Testing of Material Response High Temperature Triaxial Test Syste~ Permeability, PPIC, and High Pressure Triaxial Test Systems 466 List of References 467 AuTHOR INDEX 477 SUBJECT INDEX 4Rl

11 PREFACE The scientific branch of rock fracture mechanics serves the purpose of treating fracture problems in rock mechanics. With the known traditional fossil fuel reserves of the world being rapidly exhausted and the mushrooming of urban settlements in mining engineering areas ever increasing. attention has turned to alternative sources and also alternative and advanced technologies to be able to cope with mankind's ever growing demand and need of energy and minerals. Faster. safer and more efficient procedures for production of above and/or underground fractures and excavations with suitable extends and shapes are required. An understanding of the fracture mechanisms of rock is an essential prerequisite for designing mining excavations and civil engineering structures. for developing advanced rockbreaking processes and for establishing programs to prevent hazardous situations such as rock-bursts. The whole process of rock breakage is a complicated interaction of stress waves and crack propagation governed by material and environmental aspects. Knowledge of the basic principles of rock fracture and testing in parallel with numerical and experimental model studies allow for the development of optimal and controlled rock breakage procedures to consequently reduce the cost of mining operation. The content of this course covers the fundamentals of rock fracture mechanics and rock materials testing with a firm stronghold on the application of rock fracture to modern problems in mining engineering and related fields. Chapter I (R.A.Schmidt and H.P.Rossmanith) contains the basic principles of fracture mechanics as applied to rock. The stress analysis of radial crack systems associated with rock blasting is treated in Chapter II (F. Ouchterlony). A detailed review of fracture toughness testing of rock and

12 XII Preface and specimen development is presented in Chapter III (F.Ouchterlony). Numerical modelling of crack propagation in rock and concrete is the subject of Chapter iv (A.R.Ingraffea). The application of dynamic photomechanics techniques to fracture and wave propagation phenomena in rock is the subject of nine chapters. Chapters V to VIII (H.P.Rossmanith) contain introductory material on dynamic photoelasticity, wave propagation, fringe data evaluation, dynamic fracture, and wave-crack interaction. Experimental model studies and their in situ application to fracture control, oil shale fragmentation and gas well stimulation is considered in Chapters IX to XIII (W.L.Fourney). The final Chapter XIV (M.P.Cleary) is devoted to research and application of hydraulic fracturing of rock-type materials. On behalf of the lecturers I take great pleasure in expressing my sincere gratitude to the late Prof.Dr.H.Parkus and to the Secretary General of CISM, Prof.Dr.G.Bianchi, for having been given the challenging opportunity to organize and present this series of lectures to an interdisciplinary audience. Thanks to all members of CISM for their great hospitality which made our stay at the Centre so pleasant. Finally, I am indepted to the Fonds zur Forderung der wissenschaftlichen Forschung in Austria for kindly supporting a research program on "Rock Fracture Mechanics" at the Technical University of Vienna, Austria, which gave the incentive to these CISM-lectures. Vienna, June 1983 H.P.Rossmt~nith