Rock falls can be a public safety issue. This book provides comprehensive information on identification of these hazards, and design and construction of protection methods. Rock Fall Engineering describes first, the theoretical background to rock fall behaviour in terms of the impact and trajectory phases of rock falls, and second, how this information is applied to modelling of rock falls and the design of ditches, fences and sheds. The theory of rock fall behaviour is verified by comparing the calculations with five carefully documented case studies.
Rock falls can be a public safety issue. This book provides comprehensive information on identification of these hazards, and design and construction of protection methods.
Rock Fall Engineering describes first, the theoretical background to rock fall behaviour in terms of the impact and trajectory phases of rock falls, and second, how this information is applied to modelling of rock falls and the design of ditches, fences and sheds. The theory of rock fall behaviour is verified by comparing the calculations with five carefully documented case studies.
The book covers four main topics as follows:
Describes causes of rock falls, including geology, climate and topography, and provides detailed documentation on rock fall impacts and trajectories at five sites with a wide variety of topographic and geologic features
Discusses theory of impact mechanics, and its application to velocity and energy changes during impacts and trajectories
Reviews methods of modelling rock fall events, and presents analyses for the five case studies
Examines rock fall protection in terms of selecting appropriate method(s) for site conditions, and design principles in which the objective is to absorb impact energy in an efficient manner
This book, which contains many worked examples, is of interest to practitioners and researchers working in the fields of geological engineering and natural hazards.
Table Contents
About the Author
Introduction
Foreword
Nomenclature
1 Rock Falls—Causes and Consequences
1.1 Source Zones and Topography
1.2 Geology
1.3 Weather Effects on Rock Falls
1.4 Vegetation Effects on Rock Falls
1.5 Seismic Effects on Rock Falls
1.6 Human and Animal Influences on Rock Falls
1.7 Consequences of Rock Falls
2 Documentation of Rock Fall Events
2.1 Impacts on Rock Slopes
2.1.1 Mt. Stephen, Canada—2,000 m High Rock Slope
2.1.2 Kreuger Quarry, Oregon—Rock Fall Test Site
2.1.3 Ehime, Japan—Rock Fall Test Site
2.2 Impact on Talus and Colluvium Slopes
2.2.1 Ehime, Japan—Rock Fall Tests on Talus
2.2.2 Tornado Mountain—Rock Falls on Colluvium
2.3 Impact on Asphalt
2.4 Impact on Concrete
2.5 Summary of Case Study Results
3 Rock Fall Velocities and Trajectories
3.1 Trajectory Calculations
3.1.1 Trajectory Equation
3.1.2 Nomenclature—Trajectories and Impacts
3.1.3 Rock Fall Trajectories
3.1.4 Trajectory Height and Length
3.1.5 Field Trajectory Heights
3.2 Rock Fall Velocities
3.2.1 Field Velocity Measurements
3.2.2 Effect of Friction and Slope Angle on Velocity
3.3 Variation of Trajectories with Restitution Angle
3.3.1 Calculated Trajectories for Varying Restitution Angles (θ0)
3.3.2 Field Values of Restitution Angles (θ0)
3.4 Angular Velocity
3.4.1 Field Measurements of Angular Velocity
3.4.2 Relationship between Trajectories and Angular Velocity
3.5 Field Observations of Rock Fall Trajectories
3.5.1 Rock Falls down Gullies
3.5.2 Run-Out Distance
3.5.3 Dispersion in Run-Out Area
4 Impact Mechanics
4.1 Principles of Rigid-Body Impact
4.1.1 Rigid-Body Impact
4.1.2 Kinetics of Rigid Bodies
4.2 Forces and Impulses Generated during Collinear Impact
4.3 Energy Changes during Impact
4.4 Coefficient of Restitution
4.5 Frictional Angular Velocity Changes during Impact for Rough Surface
4.6 Impact Behavior for Rough, Rotating Body
4.6.1 Impulse Calculations
4.6.2 Final Velocities for Rock Fall Impacts
4.6.3 Example of Impact Mechanics Calculation
4.6.4 Effect of Angular Velocity on Trajectories
4.7 Calculated versus Actual Restitution Velocities
5 Coefficient of Restitution
5.1 Newton’s Coefficient of Restitution
5.2 Normal Coefficient of Restitution
5.2.1 Theoretical Relationship between Impact Angle and Normal Coefficient of Restitution
5.2.2 Field Data Showing Relationship between Impact Angle and Normal Coefficient of Restitution 68
5.2.3 Application of [θi – eN] Relationship to Rock Fall Modeling
5.3 Tangential Coefficient of Restitution and Friction
5.3.1 Field Values of Tangential Coefficient of Restitution
5.3.2 Application of eT to Rock Fall Modeling
6 Energy Changes during Impacts and Trajectories
6.1 Impact Mechanics Theory and Kinetic Energy Changes
6.1.1 Kinetic Energy Changes for Normal Impact, Nonrotating Body
6.1.2 Kinetic Energy Changes for Inclined Impact, Rotating Body
6.2 Rotational Energy Gains/Losses
6.3 Total Energy Losses
6.4 Energy Loss Diagrams
6.4.1 Energy Partition Diagram for Potential, Kinetic, and Rotational Energies
6.4.2 Energy Head
6.5 Loss of Mass during Impact
6.6 Effect of Trees on Energy Losses
7 Rock Fall Modeling
7.1 Spreadsheet Calculations
7.2 Terrain Model—Two-Dimensional versus Three-Dimensional Analysis
7.3 Modeling Methods—Lumped Mass
7.3.1 Rock Fall Mass and Dimensions
7.3.2 Slope-Definition Parameters
7.3.3 Rock Fall Seeder
7.3.4 Normal Coefficient of Restitution
7.3.5 Tangential Coefficient of Restitution and Friction
7.3.6 Surface Roughness
7.3.7 Rotational Velocity
7.3.8 Probabilistic Analysis
7.3.9 Data Sampling Points
7.4 Modeling Methods—Discrete Element Model (DEM) 102
7.5 Modeling Results of Case Studies 102
7.5.1 Rock Fall Model of Mt. Stephen Events 103
7.5.2 Rock Fall Model of Kreuger Quarry, Oregon, Test 105
7.5.3 Rock Fall Model of Ehime, Japan, Test Site 106
7.5.4 Rock Fall Model of Tornado Mountain Events
7.5.5 Rock Fall Model of Asphalt Impact Event
7.6 Summary of Rock Fall Simulation Results
8 Selection of Protection Structures
8.1 Impact Energy—Deterministic and Probabilistic Design Values
8.2 Impact Energy—Service and Ultimate States Energies
8.3 Impact Energy—Probability Calculations
8.3.1 Probability Distribution of Rock Fall Mass
8.3.2 Probability Distribution of Rock Fall Velocity
8.4 Determination of Rock Fall Return Periods
8.4.1 Gutenberg–Richter Cumulative Annual Frequency
8.4.2 Gumbel Extreme Value Theorem
8.5 Risk Management of Rock Fall Hazards
8.5.1 Definitions of Hazard and Risk
8.5.2 Inventories of Hazard and Risk
8.5.3 Probabilities of Rock Falls
8.5.4 Calculation of Relative Risk
8.5.5 Decision Analysis—Selection of Optimum Mitigation
9 Design Principles of Rock Fall Protection Structures
9.1 Structure Location with Respect to Impact Points
9.2 Attenuation of Rock Fall Energy in Protection Structures
9.2.1 Velocity Changes during Impact with a Fence
9.2.2 Energy Changes during Impact with a Fence
9.2.3 Energy Efficiency of Fences
9.2.4 Configuration of Redirection Structures
9.2.5 Hinges and Guy Wires
9.3 Minimizing Forces in Rock Fall Protection Fences
9.3.1 Time–Force Behavior of Rigid, Flexible, and Stiff Structures
9.3.2 Energy Absorption by Rigid, Flexible, and Stiff Structures
9.4 Design of Stiff, Attenuator Fences
9.5 Model Testing of Protection Structures
9.5.1 Model-Testing Procedure
9.5.2 Model Test Parameters
9.5.3 Results of Model Tests
10 Rock Fall Protection I—Barriers, Nets, and Fences
10.1 Ditches and Barriers
10.1.1 Ditch Design Charts
10.1.2 Ditch Geometry
10.1.3 Gabions
10.1.4 Concrete Block Barriers
10.1.5 Impact Energy Capacity of Gabions and Concrete Blocks
10.2 MSE Barriers
10.2.1 MSE Barriers—Design Features
10.2.2 MSE Barriers—Design Principles
10.2.3 Base Sliding and Overturning Stability
10.2.4 Punching Stability
10.2.5 Global Stability
10.2.6 Repairs to Face Elements
10.3 Slide Detector Fences
10.4 Wire Mesh—Draped and Pinned
10.4.1 Draped Mesh
10.4.2 Mesh Pinned to Face with Pattern Bolts
10.5 Nets and Fences
10.5.1 Fence Components
10.5.2 Attenuators and Hanging Nets
10.5.3 Debris Flow Barriers
11 Rock Fall Protection II—Rock Sheds
11.1 Types of Rock Sheds
11.2 Reinforced Concrete Sheds
11.2.1 Energy Absorption—Weight and Transmitted Impact Forces
11.2.2 Properties of Cushioning Layer
11.2.3 Tests to Measure Weight and Transmitted Impact Forces
11.2.4 Shed Design—Flexibility and Cushioning
11.2.5 Typical Rock Shed Design
11.2.6 Static Equivalent Force
11.3 Cantilevered Structures
11.4 Sheds with Sloping Roofs
11.5 Wire-Mesh Canopies
Appendix I: Impact Mechanics—Normal Coefficient of Restitution
Appendix II: Impact Mechanics—Impact of Rough, Rotating Bodies
Appendix III: Energy Loss Equations
Appendix IV: Conversion Factors
References
Index