Model Uncertainty in Pile Axial Capacity Calculations
Authors: Lacasse S. , Nadim F. 
Published: October 2008

Abstract
The use of a probabilistic approach for pile design is described and its importance is discussed. The paper illustrates the effect of the uncertainties in pile capacity analysis methods on the reliality of a design. Suggestions are made for the value of model uncertainty to use with different analysis methods. Special emphasis is given to the American Petroleum Institute (API) RP2A approach (Ref. 1).
Relevant model tests for calibration of the model uncertainty are few and exhibit scatter. It is therefore difficult to assign values to the parameters describing the model uncertainty. In the latest API RP2A guidelines, designers are ‘encouraged to use all research advances available to them’. The designer is therefore encouraged to use substantiated alternative analysis methods. Probabilistic analyses is one of the tools that will help judge the soundness of a design.

Introduction
In the past 20 years, new and creative solutions have been developed offshore and calculation methods have been improved. And yet we have not reduced appreciably the uncertainty in pile design. There is, however, an increased awareness in the limitations in existing calculation models and the need for a rational design approach (Ref. 2). It is therefore timely in this special OTC session on Advances in Piled Foundation Analysis and Design to attempt to set numbers on the uncertainties the designer faces and the effect of these uncertainties on the designed safety margin.
Predictions of foundation response are uncertain because of spatial variation of soil properties, limited site exploration and observations, limited calculation models, uncertainties in the parameters obtained by various testing methods and not the least, uncertainties in the loads.
Current axial pile capacity calculation methods use simplified models and have been derived predominantly from onshore load tests on small piles. The uncertainties associated with the simplifications should be accounted for in design.

Geotechnical Reliability Analysis
The applicability of reliability models in geotechnical engineering has come of age after a long development started by research in the universities. The offshore industry has been a major trigger in promoting development and use of reliability methods in geotechnical engineering.
Foundation engineers have in the past looked upon reliability analysis with skepticism, as the languages of probably and geotechnical engineers were at first not compatible. Now, solutions to the complex approximations and iterations methods exist and have become routine work; more importantly, the significance of reliability, probability of failure and uncertainty has become more familiar to goetechnicians.
Figure I schematises deterministic and probabilistic analysis. Reliability analyses are not more complex than deterministic analyses, they require more input parameters: the input data are defined over a range of probable values rather than as punctual values. Failure is defined by a ‘limit state function’ which has the same form as the equation defining failure used in the deterministic calculation. Instead of a point estimate of factor of safety, the distribution of the resistance is compared with the distribution of the load.