Discussion on “GIS-based kinematic slope instability and slope mass rating (SMR) maps: application to a railway route in Sivas (Turkey)” by Işık Yilmaz, Marian Marschalko, Mustafa Yildirim, Emek Dereli and Martin Bednarik, Bulletin of Engineering Geology and the Environment 71 (2012), 351–357, doi:10.1007/s10064-011-0384-5

Excerpt

We read the original paper entitled ‘‘GIS-based kinematic slope instability and slope mass rating (SMR) maps: application to a railway route in Sivas (Turkey)’’ by Yilmaz et al. (2012), Bulletin of Engineering Geology and the Environment. The paper shows the potential use of kinematic stability and slope mass rating (SMR) maps using a geographical information system (GIS). However, there are several aspects in the paper regarding the SMR geomechanical maps elaboration that are debated on this note. As the authors explain in their paper, SMR (Romana 1985) is a slope geomechanical classification based on Bieniawski’s (1989) classification. This geomechanical index is computed adding to basic Rock Mass Rating (RMR) index, calculated by characteristic values of the rock mass, several geometrical correction factors (F ₁, F ₂, F ₃) and a fourth factor (F ₄) depending on the excavation method, respectively. Focusing our attention on F ₁, F ₂ and F ₃ parameters, we can see that these parameters are computed in a different way depending on the failure mode. F ₁ depends on the parallelism (A) between discontinuity dip direction, α _j , (or the trend of the intersection line, α _i , in the case of wedge failure) and slope dip direction, α _s . Factor F ₂ depends on the discontinuity dip, β _j , in the case of planar failure and the plunge of the intersection line, β _i , in wedge failure (B). For toppling failure, this parameter always adopts the value 1.0. F ₃ depends on the relationship (C) between slope, β _s , and discontinuity, β _j , dips (β _j  + β _s for toppling and β _j  − β _s for planar failure cases) or the plunge of the intersection line β _i (β _i  − β _s for wedge failure case). As a consequence, for computing SMR index through a GIS, the geometrically compatible failure modes for each pixel have to be previously known in order to be considered for estimating the correcting parameters (Tomás et al. 2009, 2012). Rigorously, for each pixel of the map, we can compute as many SMR values as discontinuities are affecting the rock mass (that can cause planar of toppling failures) plus the combinations of pairs of discontinuities (that can cause wedge failures). So, for n discontinuities affecting a rock mass, the total number of potential failure mechanisms is equal to n × (n + 1)/2. However, many of these combinations can be not feasible (e.g. when the line of intersection of two discontinuity planes dips inwardly of the slope). This means that we can compute at most n × (n + 1)/2 values of SMR (from this number we have to subtract the non-feasible wedges). For example, considering a pixel of a rock mass map affected by four discontinuity sets (J ₁, J ₂, J ₃ and J ₄; Fig. 1) and performing a simple geometrical analysis (not strictly a kinematic analysis), we can compute as maximum 4 × (4 + 1)/2 = 10 different SMR indexes (Table 1). However, the real number of SMR values is six because J ₁‐J ₄, J ₂‐J ₃, J ₂‐J ₄ and J ₃‐J ₄ wedges are not possible as they dip to inside the slope. Examining Table 1, we can state that for the considered pixel, we have three different SMR indexes associated to planar failure mode (SMR_P = 36), toppling failure mode (SMR_T = 56) and wedge failure mode (SMR_W = 51). These values have been obtained considering the lower SMR value for each possible failure. The “global” SMR of this pixel (SMR_G) is the minimum value of the whole computed values for the different compatible failures (González de Vallejo and Ferrer 2011): SMR_G = min [SMR_P, SMR_T, SMR_W] = 36, value that, for the pixel used in the example, corresponds to a planar failure. As a consequence, in general, for each pixel on the map, the SMR_G value is controlled by a different failure mode. In other words, for an individual pixel, the failure will be caused for the more unfavourable failure mode that provides the minimum SMR index. This means that we can elaborate a SMR map for wedge failures, a different failure map of toppling failures, a third map showing the SMR values associated with the feasible wedge failures and even a final map showing the global minimum SMR value for each pixel. In Fig. 8 of the original paper authors compare the SMR value (although it is not explained in detail we think it is the global SMR—SMR_G) with the areas affected by wedge and planar failures computed by means of conventional kinematic slope stability analysis. However, this direct comparison does not take into account the failure mode associated with the SMR value of the pixel and as a consequence in some pixels they can be comparing a SMR value corresponding to a wedge failure with a planar kinematic failure and vice versa. It would be more realistic to elaborate two different SMR maps showing the SMR values associated to planar and wedge failures for each pixel and compare them with their respective results of the conventional kinematic slope stability analysis. Furthermore, authors can also consider in the future the toppling failure mode for both the kinematic analysis and the elaboration of SMR maps providing a wider vision for the different failure modes. Finally, we think that the use of continuous slope mass rating (Tomás et al. 2007) instead of original discrete functions for the elaboration of SMR maps can considerably simplify the implementation of SMR through a GIS.

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