# STABILITY ANALYSIS OF WEDGE TYPE Ly - Open ANALYSIS OF WEDGE TYPE ROCK SLOPE ... major concern in...

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Stability analysis of wedge type rock slope failures

Item Type text; Thesis-Reproduction (electronic)

Authors Sublette, William Robert, 1944-

Publisher The University of Arizona.

Rights Copyright is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

Download date 21/06/2018 14:00:31

Link to Item http://hdl.handle.net/10150/347880

http://hdl.handle.net/10150/347880

STABILITY ANALYSIS OF WEDGE TYPE ROCK SLOPE FAILURES

LyWilliam Robert Sublette

A Thesis Submitted to the Faculty of theDEPARTMENT OF MINING AND GEOLOGICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree ofMASTER OF SCIENCE

WITH A MAJOR IN GEOLOGICAL ENGINEERINGIn the Graduate College

. - THE UNIVERSITY OF ARIZONA

1 9 7 6

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below:

RICHARD D. CALL DateLecturer in Mining and Geological Engineering

ACKNOWLEDGMENTS

The author expresses his sincere gratitude to Dr. Richard D. Call, the thesis director, for guidance during the course of study. Review of the manuscript , by members of the thesis committee, Dr. Charles E.. Glass, Dr. William C. Peters, and Dr. Young C. Kim, provided meaningful constructive criticism.

TABLE OF CONTENTSPage

LIST OF ILLUSTRATIONS . .VABSTRACT....... ./....... vi

1. INTRODUCTION ........ 1Review of Literature................... 3Objectives of Thesis.......................... 7

2. STABILITY ANALYSIS ....... 93. DETERMINATION OF TETRAHEDRAL WEDGE GEOMETRY..... 194. STATISTICAL APPROACH. .... .' ........... 295. SEQUENTIAL DEVELOPMENT OF PROGRAM. ....._____ 346. EXAMPLE PROBLEM ........ 397. DESIGN APPLICATIONS AND CONCLUSIONS. ..... 43

Suggestions for Future Research. ............. 44 'APPENDIX A: PROGRAM DOCUMENT I ON. . . 46

. APPENDIX B: DESCRIPTION OF INPUT. .......... 52APPENDIX C: PROGRAM LISTING . . . ........ 57APPENDIX D: . EXAMPLE PROBLEM INPUT DATA. ......... 72APPENDIX E: RESULTS OF EACH ITERATION IN THE

EXAMPLE PROBLEM................ 74APPENDIX F: SUMMARIZATION OF THE RESULTS IN

THE EXAMPLE PROBLEM. ........____ 78APPENDIX G: PROGRAM FLOW CHART ....... 80REFERENCES ..... . . . ...... 88

iv

LIST OF ILLUSTRATIONSFigure Page

1. Typical Wedge Type Failure.......... 22. Tetrahedral Wedge ..... 103. Cross Section of the Tetrahedral Wedge

Parallel to the Line of Intersection. .... 114. Cross Section of. the Tetrahedral Wedge

Perpendicular to the Line of Intersection 125- Surface Roughness....... .......... 156. Surface Roughness Effect on the Resisting.

Shear Stress along the Potential -Failure Plane ....... 16

7. Effect of Surface Roughness (i) on theMohr's Envelope. .................... . . ......... 17

8. Rotation of Coordinate System....... . . . ...... 209. Spherical Coordinate System Used to Locate

the Exterior Surfaces and Fractures..... 2210. Determine Spherical Location Coordinates

for the Exterior Surfaces and Fractures...... 2311. Description of the Planes and Points Which

Form the Tetrahedral Wedge........... 2612. Cross Section of the Rock Slope in the

: Example Problem. ..... 4013- Schmidt Plot of Fractures. . ................... 4l

: v. . ;

ABSTRACT

An analytical method and its corresponding computer program is developed to analyze the probability of failure for a wedge-type failure in a rock slope. When analyzing the stability of a fractured or faulted rock slope, this method provides the capability of considering many possible wedge configurations that may exist in the slope and significantly influence its stability.

A probability approach is necessitated when many wedge configurations are considered in the determination of a slope's stability. The analytical method presented in this Thesis first determines the probability that failure is kinematically possible for randomly selected wedge configurations. Next it determines the probability of failure for those wedge configurations which have a kinematic possibility of failure. The total probability of failure is then determined by multiplying the two previously mentioned probabilities together.

A vector analysis is used to determine the factor of safety for each wedge analyzed. The resisting shearing stresses developed along each fracture plane is determined from the Mohr-Coulomb strength equation.

CHAPTER 1

INTRODUCTION

The stability of fractured rock slopes is a major concern in open pit mining and engineering projects. This is especially true in open pit mining where mine depths are increasing and the pit slope inclination becomes a significant factor in the economics of the open pit operation. As the pit slope inclination is increased the cost of stripping the overburden is decreased, however this increases the probability of a slope failure. Since a slope failure can be very costly, both the stripping costs plus the slope failure costs should be considered in determining the optimum pit slope inclination.

The subject of this thesis is the development of a analytical method which uses a three dimensional vectoral stability analysis to determine the probability of failure for a wedge-type block failure in a fractured rock slope. The wedge-type failure is a common type of failure in rock Slopes (Fig. 1). With this method and its corresponding computer program the design engineer can determine the probability of a wedge failure for various pit slope inclinations.

1

2

Line o f In tersec t ionT o p

Surface

[etrahedral Wedge

Slope Face

Botto m Surface

Figure 10 Typical Wedge Type Failure

' . ..... 3;Review of'Literature >

Two distinct approaches may be taken in the analysis of a rock slope. The rock mass in question may be considered as a continuum and the stresses and strains throughout the region of influence within this continuum may be Calculated , or the rock mass may be described as a discontinuum whose stability calculation involved the statics and kinematics of a rigid block or an accumulation of rigid blocks. This paper will deal only with the mechanics of a discon- tinuum.

The analysis of discontinuous rock slopes is a product of a mostly European workers; most prominently Pierre Londe, Walter Wittke, J.E. Jennings, Klaus John, and Evert Hoek. Significant American contributions are from Richard Goodman and Robert Taylor.

Wittke (1965) developed a comprehensive vectoral stability analysis for a rock slope containing one or two fracture sets. Wittke discussed the stability Of blocks having cohesive as well as frictional shear strength on their boundaries, and considered rotational as well as translational failure mechanisms. Goodman and Taylor (1967) reviewed the development of the concepts and applications of the two contrasting methods of approach stability of a discontinuum and mechanics of a continuum.

. 4In their paper they discussed both the finite element and vector analysis approaches. In the vector approach they analyzed possible rotational and translation wedge failures.

Klaus John (1968) used equal area hemispheric projections to evaluate the stability of a. slope with two planes of weakness. With this method he was able to determine the direction of movement and its factor of safety. Since forces can not be considered in his approach, it has the following limitations: shear is only frictional, andall forces such as hydraulic thrust, and retaining forces (rock anchors, retaining walls, buttresses, etc.) must be expressed in proportion to the weight of the rock mass.It was also assumed that no deformation takes place in the failing rock mass. Klaus John (1970) considered a modified wedge bounded by two mean failure planes. The analy-- sis was a graphical approach based on a reference hernia sphere. Cohesion, friction, and other forces,. such as hydrostatic forces, were considered in this approach.

Londe, Vigier, and Vormeringer (1969) used spherical coordinates to develop a three dimensional approach to analyze the stability of a slope. This method allowed for an estimation of the relative influence of the various strength parameters and internal water pressure on

;stability. In their "approach they assumed the following: no deformation of the failing rock mass; negligible.cohesion and tensile strength; and no moments produced by the forces. In 1970 Londe, Vigier, and Vormeringer approached the stability problem by representing the three dimensional wedge on a plane and presenting the results on simple graphs. The major advantage of graphic representation of limit equilibrium conditions is the easy appreciation of t

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