Smith, JV 2013, 'Interpreting local critical orientations of structural weakness in relation to stress and dilatancy in rock slopes', in PM Dight (ed.), Slope Stability 2013: Proceedings of the 2013 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics, Perth, pp. 177-188, https://doi.org/10.36487/ACG_rep/1308_06_Smith
(https://papers.acg.uwa.edu.au/p/1308_06_Smith/)
Abstract: The orientation of structural weaknesses, such as faults, joints, bedding and foliation, is a major influence on the stability of rock slopes. In the unloaded parts of benches, the critical orientation of structures is typically considered with respect to gravity. In the toe of each bench and the zone of rock behind the benches the critical orientations must be considered with respect to the local stress trajectory. In this zone the maximum principal compressive stress (1) is approximately parallel to the slope, in a two dimensional cross-section. This principal stress orientation approximates the inter-ramp slope angle for a series of benches with local steepening of the trajectory behind the lower part of each bench and local flattening behind the top part of each bench. The critical structures will be those with orientations favourable to slip with respect to the local 1 trajectory. The orientation of surfaces favourable to slip is also related to the friction angle and dilatancy of a material. 
Materials which undergo no volume change during deformation typically slip on surfaces at 45° to 1. Materials undergoing volume increase during deformation slip on surfaces at lower angles. This can be observed in conjugate pairs of structures where the slip occurs simultaneously on ‘mirror image’ structures. The angle between conjugate structures in rocks is typically around 60°, that is, each structure is inclined 30° to 1. Experiments and field observations have shown that this angle decreases at lower confinement and increases at higher confinement. 
Based on these relationships, a slope of 50° would have 1 inclined at approximately 50° (with local variations) and the conjugate critical structures would therefore be oriented at 20 and 80° out of the slope. The low-angle structure would have a resolved shear displacement of sliding out of the slope. The high angle structure would have the opposite shear sense, that is, the block behind the slope moving down relative to the block nearer the slope face. Movement on the high-angle structures can appear to be a toppling failure. At the toe of the overall slope, where stresses are at their most concentrated, 1 will progressively flatten to horizontal as it goes under the pit floor. In the zone of greatest stress concentration, the 1 trajectory will approximate half the slope angle, depending on factors including the in situ stress ratio. At this location, 1 would be, for example, inclined at approximately 25° and the conjugate critical structures would be oriented at approximately 5° into the slope and 55° out of the slope. Movement on the low angle structures can be upward into the pit and may appear to be heave in the pit floor. Movement on the high-angle structures can also appear to be heave in the pit floor. 
Rock slopes which contain structural weakness oriented in one or both of the local critical orientations will undergo plastic yield at a lower threshold than other rock masses. The susceptibility of structures to this effect can be assessed from a stereograph using the down-dip line of the slope as a surrogate for the maximum principal compressive stress direction and half this angle for the overall slope toe. Numerical modelling of confining stress and consideration of the friction angle and dilatancy of the rock mass will also assist in identifying the sensitivity of a rock mass to local critical structural orientations.