Geotechnical Probability: From FOSM to RFEM

For geotechnical professionals, the words "risk" and "probability" should not be confused, since risk is the probability of design failure weighted by its consequences. An obvious implication of this definition is that if the consequences of a failure are serious in terms of loss of life and/or cost to infrastructure, the allowable or target probability of failure for design must be commensurately low. Conversely, if the consequences of failure are relatively less important, a higher allowable or target probability for design can be allowed. Risk is therefore inextricably linked to quantitative probability estimates. Geotechnical engineers have a toolbox of methods available for estimating probability, ranging from hand calculation methods such as the First Order Second Moment (FOSM) method, to mildly computational method such as the First Order Reliability Method (FORM) to intensively computational numerical methods such as the Random Finite Element Method (RFEM). This paper reviews these methods, offers an alternative approach to FORM, and highlights some of their characteristics that can be taken into account when applying them to probabilistic geotechnical applications.

Keywords: Probability, Risk, First Order Methods, Monte-Carlo, Random Finite Element Methods