Factor of Safety
Introduction
This section describes the factor-of-safety calculation that can be used for stability analyses in FLAC3D and 3DEC. This calculation is based upon the strength reduction method to determine a factor of safety. The strength reduction method is an increasingly popular numerical method to evaluate factor of safety in geomechanics (e.g., see Dawson and Roth 1999, and Griffiths and Lane 1999). Although the method has been used extensively in the context of Mohr-Coulomb material, there are a few references available in the literature that extend the approach to nonlinear failure criteria in general (i.e., Dawson et al. 2000, Shukha and Baker 2003, Hammah et al. 2005, and Fu and Liao 2009). An overview of factor of safety and the strength reduction technique is given in the next section (Factor of Safety).
The strength reduction method can be applied to calculate the safety factor for a variety of different above-ground and underground structures (e.g., slopes, retaining walls, tunnels, etc.). In this section, the focus is on the factor of safety of slopes because this is the most common practical application of the method. In the section of computational methods for Factor of Safety, the strength reduction method is described and compared to other computational methods (i.e., limit analysis and the limit equilibrium technique) commonly used to determine a safety factor for slopes.
The strength reduction procedure can be conducted manually in FLAC3D and 3DEC by reducing selected strength properties until failure occurs. The method can also be performed automatically by issuing the model factor-of-safety command.
In FLAC3D 5.0 or later, and 3DEC 5.0 and later, strength properties for Mohr-Coulomb, ubiquitous-joint, and Hoek-Brown material models may be assigned with the commands zone cmodel assign, block zone cmodel assign, respectively. They also can be applied to strength properties for interfaces (FLAC3D) or joints (3DEC). The properties affected by model factor-of-safety are described Strength Reduction Properties.
In FLAC3D 7.0 or later the velocity magnitude of each grid point after each factor of safety test is stored in the model state and made available for a factor of safety contour. The limiting velocity used to determine the stable area for each factor of safety may be determined after the solution by experimentation. See the Factor of Safety Contours example.
Example factor of safety calculations based upon the strength reduction technique are also provided in this section, for both 3DEC and FLAC3D. These examples include comparisons to solutions from limit analysis and the limit equilibrium technique. The examples are described and data files are listed in the Example Factor of Safety Calculations using the Strength Reduction Method section.
Section Outline
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