Identification of modes of slope instability

Different types of slope failure are associated with different geological structures and it is important that the slope designer be able to recognize potential stability problems during the early stages of a project. Some of the structural patterns that should be identified when examining pole plots are outlined on the following pages.

Figure 1: Main types of block failures in slopes, and structural geology conditions likely to cause these failures: (a) plane failure in rock containing persistent joints dipping out of the slope face, and striking parallel to the face; (b) wedge failure on two intersecting discontinuities; (c) toppling failure in strong rock containing discontinuities dipping steeply into the face; and (d) circular failure in rock fill, very weak rock or closely fractured rock with randomly oriented discontinuities.

Figure 1 shows the four types of failure considered in this book, and typical pole plots of geological conditions likely to lead to such failures. Note that in assessing stability, the cut face of the slope must be included in the stereo plot since sliding can only occur as the result of movement towards the free face created by the cut. The importance of distinguishing between these four types of slope failure is that there is a specific type of stability analysis for each and it is essential that the correct analysis method be used in design. The diagrams given in Figure 1 have been simplified for clarity; an actual rock slope may contain a number of different types of geological structures, and this can lead to a range of additional types of failure. For instance, again referring to Figure 6 of the topic Stereographic Analysis of Structural Geology, there could be a plane failure on joint set A, but toppling failure on the same slope formed by the bedding.

In a typical field study, for example, where structural data have been plotted on stereonets, a number of significant pole concentrations may exist.

It is useful to be able to identify those that represent potential failure planes, and to eliminate those that represent structures unlikely to be involved in slope failures. Tests for identifying important pole concentrations have been developed by Markland (1972) and Hocking (1976). These tests establish the possibility of wedge failure where sliding takes place along the line of intersection of two planar discontinuities, as illustrated in Figure 1(b). The plane failure, shown in Figure 1(a), is also covered by this test since it is a special case of wedge failure. In the case of a wedge failure, there is contact in both planes but sliding along the line of intersection between the two planes. For either plane or wedge failure to occur, it is necessary that the dip of the sliding plane in the case of plane failure, or the plunge of the line of intersection in the case of wedge failure, be less than the dip of the slope face (i.e. ψi < ψf) (Figure 2 (a)). That is, the sliding surface "daylights" in the slope face. 

Figure 2: Identification of plane and wedge failures on stereonet: (a) sliding along line of intersection of planes A and B is possible where the plunge of this line is less than the dip of the slope face, measured in the direction of sliding, that is, ψi < ψf; (b) wedge failure occurs along line of intersection (dip direction αi) on slope with dip direction αf because dip directions of planes A and B (αA and αB) lie outside included angle between αi and αf; (c) plane failure occurs on plane A (dip direction αA) on slope with dip direction αf because dip direction of planes A lies inside included angle between αi and αf.

The test can also differentiate between sliding of a wedge on two planes along the line of intersection, or along only one of the planes such that a plane failure occurs. If the dip directions of the two planes lie outside the included angle between αi (trend of intersection line) and αf (dip direction of face), the wedge will slide on both planes (Figure 2 (b)). If the dip direction of one plane (A) lies within the included angle between αi and αf, the wedge will slide on only that plane (Figure 2 (c)).

Kinematic analysis

Once the type of block failure has been identified on the stereonet, the same diagram can also be used to examine the direction in which a block will slide and give an indication of stability conditions. This procedure is known as kinematic analysis. An application of kinematic analysis is the rock face shown in Figure 1(b) of the topic Structural Geology & Data Interpretation where two joint planes form a wedge which has slid out of the face and towards the photographer. If the slope face had been less steep than the line of intersection between the two planes, or had a strike at 90◦ to the actual strike, then although the two planes form a wedge, it would not have been able to slide from the face. This relationship between the direction in which the block of rock will slide and the orientation of the face is readily apparent on the stereonet. However, while analysis of the stereonet gives a good indication of stability conditions, it does not account for external forces such as water pressures or reinforcement comprising tensioned rock bolts, which can have a significant effect on stability. The usual design procedure is to use kinematic analysis to identify potentially unstable blocks, followed by detailed stability analysis of these blocks using the procedures.

An example of kinematic analysis is shown in Figure 3 where a rock slope contains three sets of discontinuities. The potential for these discontinuities to result in slope failures depends on their dip and dip direction relative to the face; stability conditions can be studied on the stereonet as described in the next section.

Figure 3: Kinematic analysis of blocks of rock in slope: (a) discontinuity sets in slope; and (b) daylight envelopes on equal area stereonet

Plane failure In Figure 3 (a) plane AA forms a potentially unstable planar block dipping at a flatter angle than the face, ψA < ψf, and is said to "daylight" on the face. On the other hand, sliding is not possible on plane BB which dips steeper than the face, ψB > ψf and does not daylight. Similarly, discontinuity set CC dips into the face and sliding cannot occur on these planes although toppling is possible. The poles of the slope face and the discontinuity sets (symbol P) are plotted on the stereonet shown in Figure 3 (b) assuming that all the discontinuities strike parallel to the face. It can be seen that the position of these poles with respect to the slope face indicates that all the poles of planes that daylight and are potentially unstable lie inside the pole of the slope face. This area is termed the daylight envelope and can be used to identify quickly potentially unstable blocks.

The dip direction of the discontinuity sets will also influence the stability. Plane sliding is not possible if the dip direction of the discontinuity differs from the dip direction of the face by more than about 20◦. That is, the block will be stable if |αA − αf| > 20◦, because under these conditions there will be an increasing thickness of intact rock at one end of the block which will have sufficient strength to resist failure. on the stereonet this restriction on the dip direction of the planes is represented by two lines defining dip directions of (αf + 20◦) and (αf − 20◦). These two lines indicate the lateral limits of the daylight envelope on Figure 3 (b).

Wedge failure

Kinematic analysis of wedge failures (Figure 1 (b)) can be performed in a similar way to that of plane failures. In this case the pole of the line of intersection of the two discontinuities is plotted on the stereonet and sliding is possible if the pole daylights on the face, that is. The direction of sliding of kinematically permissible wedges is less restrictive than that of plane failures because there are two planes to form release surfaces. A daylighting envelope for the line of intersection, as shown on Figure 3 (b), is wider than the envelope for plane failures. The wedge daylight envelope is the locus of all poles representing lines of intersection whose dip directions lie in the plane of the slope face.

Figure 4: Combined kinematics and simple stability analysis using friction cone concept: (a) friction cone in relation to block at rest on an inclined plane (i.e. φ > ψp); and (b) stereographic projection of friction cone superimposed on “daylighting” envelopes.

Toppling failure

For a toppling failure to occur, the dip direction of discontinuities dipping into the face must be locked within about 10 of the dip direction of the face so that a series of slabs are formed parallel to the face. Furthermore, the dip should be steep enough for interlayer slip to take place. Slip will only occur if the applied compressive stress is oriented at an angle greater than фj with the normal to the layers, where фj is the friction angle of the faces of the layers. The trend of the major principal stress in the cut is parallel to the face of the cut, at an angle ψf to the horizontal, so Shear and toppling failure on planes with dip ψp will occur when the following conditions are met for interlayer slip and toppling, as Goodman and Bray stated in 1976:

(90◦ − ψf) + φj < ψp             (1)

These conditions on the dip and dip direction of planes that can develop toppling failures are defined on Figure 3 (b). The envelope defining the orientation of these planes lies on the opposite side of the stereonet from the sliding envelopes.

Friction cone

Having determined from the daylight envelopes whether a block in the slope is kinematically permissible, it is also possible to examine stability conditions on the same stereonet. This analysis is done under the assumption that the sliding surface has only friction and cohesion is zero. Consider a block at rest on an inclined plane with an angle of friction, φ, between the block and the plane (Figure 4 (a)). For an at-rest condition, the force vector normal to the plane must lie within the friction cone. When only gravity is applied to the block, then the pole to the plane is parallel to, and in the same direction as, the normal force. Hence the block will be stable if the pole lies within the friction circle. The envelopes shown on Figure 4 (b) illustrate the range of possible positions of poles which form unstable blocks. Envelopes have been drawn for slope face angles of 60◦ and 80◦, which point out that the risk of instability increases as the slope becomes steeper as indicated by the larger envelopes for the steeper slope. In addition, the envelopes grow larger as the friction angle diminishes. The envelopes further highlight that, under simple gravity loading conditions, instability will only occur for a limited range of geometric conditions.

Applications of kinematic analysis

The techniques shown on Figures 1– 4 to determine both potentially unstable blocks of rock on the slope and the type of instability can easily be applied at the initial stages of slope design. This is demonstrated in the two examples following.

Highway: A Proposed highway on a north–south alignment passes through a ridge of rock in which a through-cut is required to keep the highway on grade (Figure 5 (a)). Diamond drilling and mapping shows that the geological conditions in the ridge are consistent so that the same structure will be exposed in each face. The predominant geological structure is the bedding, which strikes north–south, parallel to the highway alignment and dips to the east at angles of between 70 and 80. By convention, a way of describing the attitude of a plane Geological monitoring and instrumentation in rock masses The stereonets in Figure 5 (b) show poles representing the dip and dip direction of the bedding, and great circles representing the orientations of the left and right cut faces.

Also plotted on the stereonets is a friction cone representing a friction angle of 35◦ on the bedding. These stereonets show that on the left, west face, the bedding dips towards the excavation at a steeper angle than the friction angle so sliding can occur on the bedding. This cut face has been made along the bedding, ensuring a stable face. On the right hand (east) face the bedding dips steeply No into the face and there is a possibility that the slabs formed by these joints will fail by toppling. According to equation (1), toppling is possible if (90◦ − ψf) + φj < ψp. If the face is cut at 76◦ (0.25V:1H) and the friction angle is 35◦ then the left side of this equation equals 49◦, which is less than the dip of the bedding (70◦–80◦). As the poles to the bedding planes lie inside the toppling envelope the potential for toppling is indicated. This preliminary analysis indicates that the right-hand (east) cut slope has potential stability problems, and that more detailed investigation of structural geology conditions would be required before finalizing the design.

Figure 5: Relationship between structural geology and stability conditions on slope faces in through-cut: (a) photograph of through-cut showing two failure mechanisms—plane sliding on left side (west), and toppling on right side (east) on Route 60 near Globe AZ; (b) stereographic plots showing kinematics analysis of left and right cut slopes.

The first step in this investigation would be examination of the spacing of the bedding planes and determination if the center of gravity of the slabs will lie outside the base, in which case toppling is likely. Note that it is rarely possible to change the alignment sufficiently to overcome a stability problem, so it may be necessary to either reduce the slope angle on the right side, or stabilise the 76◦ face. 

Open pit slopes: During the feasibility studies on a proposed open pit mine, an estimate of the safe slope is required for the calculation of ore-to-waste ratios and the preliminary pit layout. The only structural information that may be available at this stage is that obtained from diamond drill cores drilled for mineral evaluation purposes, and from the mapping of surface outcrops. Scanty as this information is, it does provide a basis for preliminary slope design. A contour plan of the proposed open pit mine is presented in Figure 6 and contoured stereo plots of available structural data are superimposed on this plan.

Two distinct structural regions, denoted by A and B, have been identified and the boundary between these regions has been marked on the plan. For the sake of simplicity, major faults have not been shown. It is, however, important that details of faults should be recorded on large-scale plans of this nature and that the stability problems likely to arise from such faults should be assessed. Drawn on the stereonets are great circles showing the orientations of the east and west pit faces assumed overall slope angle of 45◦.

A friction cone of 30◦ is also plotted on the stereonets which is assumed as the average friction angles of the discontinuity surfaces. According to the stereonets, it will be anticipated that the western and southern portion of the pit can be stable at the proposed slope of 45◦. It would, therefore, seem probable that if the rock is of good quality and free from major faults these slopes could be steepened or, alternatively, this sector of the pit wall could be utilized as a haul road location with steep faces above and below the haul road. 

Figure 6: Presentation of structural geology on stereonets, and preliminary evaluation of slope stability of proposed open pit mine

The northeastern part of the pit contains a number of potential slope problems. Plane sliding on discontinuity set A1 can be expected in the northern face since this set will daylight in the face at an angle steeper than the friction angle. Wedge failures on the intersection of sets A1 and A3 are possible in the northeastern corner of the pit, and toppling failure on set A2 may happen in the eastern slopes. Indications of potential instability would suggest that flattening the slopes in the northeastern part of the proposed pit should be considered.

It is interesting that the same structural region of a slope might be responsible for three types of structurally controlled slope failures, depending upon the orientation of the slope face.