Integrated Foundation and Structural Reliability Analysis of a North Sea Structure
Authors: van Langen H. , Swee J.L.K. , van Efthymiou M. , van Overy R. 
Published: October 2008

ABSTRACT
In cases where the reliability of fixed offshore structures in extreme storms is influenced by both structural and foundation failure, appropriate interpretation of foundation model prediction uncertainty becomes particularly important. To account for this type of uncertainty, a technique is introduced which can be incorporated into a structural reliability analysis to give confidence limits on reliability predictions and thus ensure correct interpretation of structural reliability. Application of the technique is demonstrated by considering a case study of a North Sea structure.

INTRODUCTION
In previous studies (Refs.1, 2), it was demonstrated that the failure probability calculated using highly validated models for environmental loading and ultimate strength is consistent with the performance of structures in extreme hurricanes and can therefore be used as a basis for making operational decisions, for example judging the need for structural upgrades or developing evacuation strategies (Ref.3). However, as will be explained in the following, probability of failure can only be used to provide an absolute measure of structural reliability (as opposed to a relative measure for comparing structures) when uncertainty is properly accounted for.
Analogous to Bea's definitions (Ref 4.), two types of uncertainties are distinguished, namely a) physical uncertainty and b) model prediction uncertainty. Physical uncertainty is the inherent natural uncertainty associated with a random variable, e.g. the a-priori uncertainty about the value of the annual extreme load on a structure. This uncertainty cannot be reduced by improving the physical understanding of the phenomenon or by measurement. Model prediction uncertainty, on the other hand, is the uncertainty about the validity of the predicted structural response, e.g. including uncertainty about the pile group bearing capacity. This type of uncertainty is composed of two parts, namely a) uncertainty associated with the model itself and b) uncertainty about the value of the model variables, e.g. material properties. In contrast to physical uncertainty, model prediction uncertainty can be reduced by improving our physical understanding and/or measurement.
As the probability of failure is usually calculated by integration of the probability distributions of load and esistance, will be influenced both by physical uncertainty and model prediction uncertainty. However, the actual reliability of a structure can not be changed by physical insight or measurement and can therefore in reality only depend on physical uncertainty. This implies that the failure probability obtained from such integration can only be used to provide an absolute measure of reliability when physical uncertainty dominates over model prediction uncertainty.
Assessment of the API recommended methods for determining pile axial bearing capacity by Tang (Ref.5)shows that the above requirement may not be met for foundation analyses. Uncertainty about validity of the foundation model and the values of the soil parameters used, proves in some cases to be of the same order of magnitude as the physical uncertainty in theenvironmental load. Hence, in order to obtain an bsolute measure for the reliability of a structure in such cases we need to either be able to exclude foundation failure from the analysis or derive.