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passive wedge failure using stereographic projection
Vol.33, No. 4, pp. 405-407, 1996 Copyright© 1996ElsevierScienceLtd Printedin GreatBritain.All rightsreserved 0148-9062/96$15.00+ 0.00
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
Pergamon
0148-9062(95)00079-8
Technical Note Kinematic Analysis of Active/Passive Wedge Failure Using Stereographic Projection C. P. N A T H A N A I L t
INTRODUCTION This technical note presents a method for assessing the kinematic feasibility of active/passive wedge failures in order to increase awareness of this failure mode and to provide a simple tool for its assessment. An active/passive wedge failure involves three surfaces defining two wedges. The upper, active wedge moves downwards and forces the lower, passive wedge outwards. A stereographic projection overlay is used to evaluate three criteria that need to be fulfilled to establish the kinematic feasibility of active/passive wedge failure.
FAILURE MECHANISMS
two-dimensional case and ignore the influence of lateral release surfaces [8, 9]. Although developed for the analysis of clay-cored embankment dams [8], the failure model has applications in rock slopes [9].
GEOLOGICAL SCENARIOS There are several geological scenarios in which active/passive wedge failure may be feasible. The simplest uppecmee
IN BRITISH OPENCAST
COAL MINES Several studies into the type of failures that have taken place in British opencast coal sites have been carried out [1-6]. The most commonly recorded failure modes are biplanar, multiplanar and planar. Failures in opencast coal sites frequently show facets of more than one failure mode and may evolve from one to another. The frequency with which a particular failure mode is cited, therefore, may be as much to do with awareness of the various models of failure in rock slopes and the ease with which they may be assessed as with the actual conditions in a given slope. This technical note presents the method for assessing the kinematic feasibility of active/passage wedge failures developed by Nathanail [7].
Fig. 1. Geometry of active/passive wedge failure mechanism.
/'~ Active/
/
//
_
Fig. 2. Geologicalscenario favourablefor active/passivewedge failure in faulted strata.
ACTIVE/PASSIVE WEDGE FAILURE
An active/passive wedge failure involves three surfaces defining two wedges (Fig. 1). The upper, active wedge moves downwards and forces the lower, passive wedge outwards. Published methods of analysis discuss the
~/////
//• / /
Active
w Pas~ve %
Qo IIII JJl //Jr
?Centre for Research into the Built Environment, The Nottingham Fig. 3. Geologicalscenario favourablefor active/passivewedge failure Trent University, Burton Street, Nottingham NG1 4BU, U.K. in folded strata. 405
406
NATHANAIL: TECHNICAL NOTE
+20 % Azimuth of
dedgn slope
-20
-20
Instability criteria: 1 loweredge of active wedge dips steeper than lower edge of passive wedge, V~ 2 lower edge of passive wedge daylights in lower face and dips less than friction angle, q)
==
3 plane separating two wedges dips steeply into face (Numbers refer to planes in Fig. 3) Fig. 4. Active/passive wedge stability assessment overlay.
scenario is where one surface, say the lowest, is a bedding plane and the other two are persistent joints. In the case of tightly folded strata, the fold limbs can form the outer boundaries of the wedges while crushed material in the core of the fold can form the inter-wedge surface (Fig. 2). Where a fault cuts bedding at a high angle, bedding on either side of the fault may form the outer boundaries of the wedges and the fault plane their inter-wedge surface (Fig. 3).
KINEMATIC
FEASIBILITY O F ACTIVE/PASSIVE WEDGE FAILURE
A stability assessment overlay, similar to those proposed by Matheson [10] for other failure modes, is proposed to evaluate the kinematic feasibility of active/passive wedge failure (Fig. 4). The overlay is
superimposed on to a stereographic projection of the poles to discontinuities. Three criteria need to be fulfilled. First, the lower edge of the active wedge (surface 1 in Fig. 1) should dip more steeply than that of the lower wedge (surface 2 in Fig. 1). Second, surface 2 should daylight in the lower face of the slope and dip at an angle less than the shearing resistance (otherwise plane failure of the passive wedge is kinematically feasible). Third, the plane separating the two wedges should dip steeply into the slope. If this plane were dipping steeply out of the face, then a non-circular failure of the passive wedge alone would be possible and the method of analysis proposed by Janbu [11] should be used. For the criteria to be fulfilled, poles must lie within each of the three shaded areas in Fig. 4. Figure 5 shows a potential active/passive wedge failure in a quarry slope. The two wedges are separated from the
NATHANAIL: TECHNICAL NOTE
407
Acknowledgements--The author acknowledges the financial support of Wimpey Environmental and the logistical support of Wimpey Mining during the research programme of which this contribution is but a small part. Accepted for publication 15 November 1995.
REFERENCES
Fig. 5. Active/passive wedge geometry formed by joints.
rock mass by joints; a joint also forms the plane separating the two wedges.
1. Stimpson B. and Walton G. Clay mylonites in English Coal Measures: Their significance in open-cast slope stability. Proceedings First International Congress of International Association of Engineering Geology, Paris 3, 1388-1393 (1970). 2. Walton G. and Taylor R. Likely constraints on the stability of Technical Society Conference on Rock Engineering. Newcastle 329-349 (1977). 3. Walton G. and Atkinson T. Some geotechnical considerations in the planning of surface mines. Trans Inst. Mining Metall. 87A, A147-A171 (1978). 4. Cobb O. Slope stability assessment in British sur[ace coal mines. Ph.D. Thesis, University of Nottingham, England (unpublished) (1981). 5. Scoble M. Studies of ground deformation in British surface coal mines Ph.D. Thesis, University of Nottingham, England (unpublished) (1981). 6. Stead D. An evaluation of the factors governing the stability of surface and coal mine slopes. Ph.D. Thesis, University of Nottingham, England (unpublished) (1984). 7. Nathanail C. P. Systematic analysis and modelling of digital data for slope and foundation engineering. Ph.D. Thesis, University of London, England (unpublished) (1994). 8. Seed H. B. and Sultan H. A. Stability analysis for a sloping core embankment. Proceedings American Society of Civil Engineering 93, SM4, 69-84 (1967). 9. Goodman R. E. Methods of Geological Engineering in Discontinuous Rocks. West Publishing, St Paul (1976). 10. Matheson G. D. Rock stability assessment in preliminary site investigations--graphical methods. TRRL Report 1039, Crowthorne (1983). 11. Janbu N. Slope stability computations. In Embankment Dam Engineering, Casagrande Volume (Edited by Hirschfield R. C. and Poulos S. J.), pp. 47-86. John Wiley, New York (1972).
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
Pergamon
0148-9062(95)00079-8
Technical Note Kinematic Analysis of Active/Passive Wedge Failure Using Stereographic Projection C. P. N A T H A N A I L t
INTRODUCTION This technical note presents a method for assessing the kinematic feasibility of active/passive wedge failures in order to increase awareness of this failure mode and to provide a simple tool for its assessment. An active/passive wedge failure involves three surfaces defining two wedges. The upper, active wedge moves downwards and forces the lower, passive wedge outwards. A stereographic projection overlay is used to evaluate three criteria that need to be fulfilled to establish the kinematic feasibility of active/passive wedge failure.
FAILURE MECHANISMS
two-dimensional case and ignore the influence of lateral release surfaces [8, 9]. Although developed for the analysis of clay-cored embankment dams [8], the failure model has applications in rock slopes [9].
GEOLOGICAL SCENARIOS There are several geological scenarios in which active/passive wedge failure may be feasible. The simplest uppecmee
IN BRITISH OPENCAST
COAL MINES Several studies into the type of failures that have taken place in British opencast coal sites have been carried out [1-6]. The most commonly recorded failure modes are biplanar, multiplanar and planar. Failures in opencast coal sites frequently show facets of more than one failure mode and may evolve from one to another. The frequency with which a particular failure mode is cited, therefore, may be as much to do with awareness of the various models of failure in rock slopes and the ease with which they may be assessed as with the actual conditions in a given slope. This technical note presents the method for assessing the kinematic feasibility of active/passage wedge failures developed by Nathanail [7].
Fig. 1. Geometry of active/passive wedge failure mechanism.
/'~ Active/
/
//
_
Fig. 2. Geologicalscenario favourablefor active/passivewedge failure in faulted strata.
ACTIVE/PASSIVE WEDGE FAILURE
An active/passive wedge failure involves three surfaces defining two wedges (Fig. 1). The upper, active wedge moves downwards and forces the lower, passive wedge outwards. Published methods of analysis discuss the
~/////
//• / /
Active
w Pas~ve %
Qo IIII JJl //Jr
?Centre for Research into the Built Environment, The Nottingham Fig. 3. Geologicalscenario favourablefor active/passivewedge failure Trent University, Burton Street, Nottingham NG1 4BU, U.K. in folded strata. 405
406
NATHANAIL: TECHNICAL NOTE
+20 % Azimuth of
dedgn slope
-20
-20
Instability criteria: 1 loweredge of active wedge dips steeper than lower edge of passive wedge, V~ 2 lower edge of passive wedge daylights in lower face and dips less than friction angle, q)
==
3 plane separating two wedges dips steeply into face (Numbers refer to planes in Fig. 3) Fig. 4. Active/passive wedge stability assessment overlay.
scenario is where one surface, say the lowest, is a bedding plane and the other two are persistent joints. In the case of tightly folded strata, the fold limbs can form the outer boundaries of the wedges while crushed material in the core of the fold can form the inter-wedge surface (Fig. 2). Where a fault cuts bedding at a high angle, bedding on either side of the fault may form the outer boundaries of the wedges and the fault plane their inter-wedge surface (Fig. 3).
KINEMATIC
FEASIBILITY O F ACTIVE/PASSIVE WEDGE FAILURE
A stability assessment overlay, similar to those proposed by Matheson [10] for other failure modes, is proposed to evaluate the kinematic feasibility of active/passive wedge failure (Fig. 4). The overlay is
superimposed on to a stereographic projection of the poles to discontinuities. Three criteria need to be fulfilled. First, the lower edge of the active wedge (surface 1 in Fig. 1) should dip more steeply than that of the lower wedge (surface 2 in Fig. 1). Second, surface 2 should daylight in the lower face of the slope and dip at an angle less than the shearing resistance (otherwise plane failure of the passive wedge is kinematically feasible). Third, the plane separating the two wedges should dip steeply into the slope. If this plane were dipping steeply out of the face, then a non-circular failure of the passive wedge alone would be possible and the method of analysis proposed by Janbu [11] should be used. For the criteria to be fulfilled, poles must lie within each of the three shaded areas in Fig. 4. Figure 5 shows a potential active/passive wedge failure in a quarry slope. The two wedges are separated from the
NATHANAIL: TECHNICAL NOTE
407
Acknowledgements--The author acknowledges the financial support of Wimpey Environmental and the logistical support of Wimpey Mining during the research programme of which this contribution is but a small part. Accepted for publication 15 November 1995.
REFERENCES
Fig. 5. Active/passive wedge geometry formed by joints.
rock mass by joints; a joint also forms the plane separating the two wedges.
1. Stimpson B. and Walton G. Clay mylonites in English Coal Measures: Their significance in open-cast slope stability. Proceedings First International Congress of International Association of Engineering Geology, Paris 3, 1388-1393 (1970). 2. Walton G. and Taylor R. Likely constraints on the stability of Technical Society Conference on Rock Engineering. Newcastle 329-349 (1977). 3. Walton G. and Atkinson T. Some geotechnical considerations in the planning of surface mines. Trans Inst. Mining Metall. 87A, A147-A171 (1978). 4. Cobb O. Slope stability assessment in British sur[ace coal mines. Ph.D. Thesis, University of Nottingham, England (unpublished) (1981). 5. Scoble M. Studies of ground deformation in British surface coal mines Ph.D. Thesis, University of Nottingham, England (unpublished) (1981). 6. Stead D. An evaluation of the factors governing the stability of surface and coal mine slopes. Ph.D. Thesis, University of Nottingham, England (unpublished) (1984). 7. Nathanail C. P. Systematic analysis and modelling of digital data for slope and foundation engineering. Ph.D. Thesis, University of London, England (unpublished) (1994). 8. Seed H. B. and Sultan H. A. Stability analysis for a sloping core embankment. Proceedings American Society of Civil Engineering 93, SM4, 69-84 (1967). 9. Goodman R. E. Methods of Geological Engineering in Discontinuous Rocks. West Publishing, St Paul (1976). 10. Matheson G. D. Rock stability assessment in preliminary site investigations--graphical methods. TRRL Report 1039, Crowthorne (1983). 11. Janbu N. Slope stability computations. In Embankment Dam Engineering, Casagrande Volume (Edited by Hirschfield R. C. and Poulos S. J.), pp. 47-86. John Wiley, New York (1972).