A Comparative Study of Different Approaches for Factor of Safety Calculations by Shear Strength Reduction Technique for Non-linear Hoek–Brown Failure Criterion

The shear strength reduction technique is becoming more and more popular to determine the factor-of-safety for geotechnical constructions, especially for slopes. At present, two in principal different procedures are used to apply the numerical shear strength reduction technique for materials characterised by non-linear failure envelopes, like the Hoek–Brown criterion. One procedure is based on the determination on local stress and strength values, whereas the other is based on a global linearization of the non-linear failure envelope. This article shortly describes and discusses these two different procedures and compares results for a broad spectrum of parameter constellations based on slope stability calculations. The local approach is physically more correct. The global approach can be considered as a first approximation. A comparison of both methods reveal that the global approach in comparison to the local approach, can leads to a deviation of up to 15 % in both directions. If one considers the local approach as the ‘correct’ one, depending on the parameters the results of the global approach can lie on the safe or unsafe site. The practical conclusion is that evaluation of slope stability using the global approach can result in uneconomic slope design or overestimation of safety margin. The use of the local approach instead of the global should be preferred. In case of small safety margins (e.g. 20 % or less) the use of the local approach is strictly recommended.