Rock slope stability is analysed assuming toe planar failure surfaces. Dimensionless magnitudes and a non-linear Hoek and Brown strength law are used, and constant dilatancy depending on the degree of fracturing and weathering of the rock mass is assumed. The strength law, which is verified by the stresses on the failure plane, is stablished depending on dilatancy. The values proposed by Hoek and Brown (1977) are adopted for the angle of dilatancy. These hypotheses are applied to some simplified cases for volcanic materials, and different charts are obtained that associate the slope height and slope inclination with their safety coefficient. These values are compared with the results of computer calculations using a well known software code; nonlinear failure and constant dilatancy also being applied for these calculations.


The original Hoek and Brown criterion (1980) can be regarded as being of the "Mohr type", because it represents the envelope of Mohr's circles when failure occurs. The values of the stresses on the failure plane are given by a "Coulomb type" strength law.

6.1 Nomograms

The values yielded for different safety factors can be drawn in nomograms on the basis of the assumed strength parameters υ and ζ. In these nomograms it can be seen for different values of the slope's angle (δ) the normalised height (N) which correspond to a slope safety factor equivalent to the unit. Examples of these kind of nomogram are shown in figures 5. The nomograms can also show the theoretical safety factor corresponding to different slope layouts, (Figs. 6). More information is given in Serrano & Olalla (1998).

6.3 Comparison with computer-assisted calculation

Same example is calculated with computer, using a commercial software code that applies limit equilibrium theory. The calculations are done dividing the sliding mass into slices and solving according to Morgernstern-Price method. The same Hoek and Brown strength law and parameters are used. The safety factor obtained for a slope angle of 47° is S.F. = 0,98, and for a slope angle of 40° is S.F = 1,195. The main difference between these calculations and the ones with the previous nomograms is that, as stated in Apt. 2.1, the failure normal and shear stresses in the failure plane are assumed to be uniform to draw the charts, while in the computer calculations these stresses are not constant. In figure 7 there are represented the values of the stresses in the failure, together with a schematic representation of the slope and the failure plane AB.


A Hoek and Brown non-linear strength law has been adopted, with constant dilatancy and graphs that link the height and the gradient of a slope on rock with its safety coefficient have been obtained using certain simplified hypotheses. The findings have been compared with the results obtained from calculations that were made using the Morgernstern-Price limit equilibrium method with the aid of a well known computer program. The same findings are obtained.

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