Application of the First Order Reliability Method to Planar-Type Failure in a Hard-Rock Slope to Assess the Probability of Failure

Author: Charlie Harrison
Conference: Geohazards 7
Date: June 3-6, 2018

The First Order Reliability Method (FORM) is a semi-probabilistic reliability analysis method devised to evaluate the reliability of a system. The stability of the system must be a function of two or more probabilistic variables that have a mean, and standard deviation. The correlation between the probabilistic variables must be determined, which can be difficult, as will be show, independent variables can be functions of independent variables. The FORM considers any deterministic variables also included in the stability function as having a mean equal to their value, and a standard  deviation of zero.

The equations for quantifying the stability of a planar-type failure mechanism in a hard-rock slope are available in close-form and can be easily implemented in a spreadsheet, and checked against a commercially available limit equilibrium method software program. The author uses a worked example to show the application of FORM to a hard-rock slope susceptible to the planar-type failure mechanism. The author provides commentary on the application of the FORM in engineering practice given that the user will find it difficult to define or measure the correlation factor(s) and reduction factors.


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