Accounting for partial material factors in numerical analysis

The concept of a safety factor in the design of geotechnical structures has traditionally been developed within the framework of classical soil mechanics, where the analysis methods for its calculation involve simple limit equilibrium or limit analysis approaches. Therefore the inclusion of a safety factor within an advanced analysis method, such as finite elements or finite differences, is a more complex issue. In particular, the problem arises with design codes, such as Eurocode 7, in which partial factors on soil strength (or partial material factors) must be accounted for. Eurocode 7 implies that a numerical analysis should be performed accounting for a characteristic strength, which is reduced by partial factors. There are two ways in which such partial factors can be included in numerical analysis: one in which the strength is reduced at the beginning of the analysis, and the other in which this is done during the analysis. Eurocode 7 gives no guidance as to which one of these two approaches is more appropriate to apply. More importantly, there is no guidance on the appropriate numerical procedure that should be implemented in any software in order to perform the required strength reduction during the analysis in the latter approach. Therefore different software programs account for this in different ways, and mostly only for simple constitutive models. This paper presents, first, a consistent methodology for accounting for partial material factors in finite-element analysis, which can be applied to any constitutive model. It then demonstrates the implications of the two ways the partial material factors can be introduced in any analysis, using the example of a bearing capacity problem and employing constitutive models of increasing complexity. The paper shows that the two approaches for accounting for partial material factors may lead to different results, and that it is therefore necessary to develop a rational set of guidelines for their inclusion in advanced numerical analysis.