Model Uncertainty in Axial Pile Capacity Design Methods
Authors: Lacasse Suzanne , Nadim Farrokh , Langford Thomas , Knudsen Siren , Yetginer Gülin Luis , Guttormsen Tom Reidar , Eide Asle 
Published: June 2014

Abstract
To estimate the safety level associated with the axial capacity of a pile, one needs to know the bias and uncertainty in the calculations made the design method. This model uncertainty is usually obtained by comparing the predicted axial pile capacity with the measured axial pile capacity in reliable pile load tests. Model uncertainty can have a strong influence on the calculated annual probability of failure of a piled foundation, and thus on the estimation of the safety margin. This paper studies the model uncertainty for the API-method and the NGI, ICP, Fugro and UWA methods for predicting the axial pile capacity in clays and in sands. The study also shows that the selection of the parameter to quantify the uncertainty influences the values of the mean and standard deviation. A significant factor in the evaluation of model uncertainty is the reference database of pile load tests used to quantify the uncertainty. The paper suggests an approach for quantifying model uncertainty for pile calculation methods. There is a need to quantify specific uncertainties, such as the reduced capacity in low plasticity clays and pile diameters and lengths that become much larger than the dimensions used for the pile load tests in the reference database(s). The paper recommends that an international joint industry project be initiated to look into the databases of pile model tests and to establish a consensus on the reliable pile load tests, the soil characterization and the interpretation to be used for the evaluation of the model uncertainty.

Introduction
The model uncertainty in a calculation method is usually quantified in terms of a mean (or bias), a standard deviation (and/or coefficient of variation) and the probabilistic density distribution that best fits the data. For methods predicting the ultimate axial pile capacity, the model uncertainty is obtained by comparing the predicted axial pile capacity with the measured axial pile capacity in reliable pile load tests. A companion paper in the same session at OTC 2013 (1) demonstrated the importance of model uncertainty in the probabilistic calculation of axial pile capacity and probability of failure. The model uncertainty was especially significant in the probabilistic analyses of the axial pile capacity of piles in sand (1).
The study of model uncertainty was undertaken as part of the design of pile foundations on jackets in the North Sea. The aim was to document compliance with governing regulations in terms of annual failure probability. This paper studies the model uncertainty for the API-method and four newer design methods. Table 1 lists the methods considered and the references for each method: the current API method, the pre 1987 API method, the NGI-05 method, the ICP-05 method, the Fugro 96/05 method and the UWA-05 method. These methods became of greater interest when API RP2A RP2GEO (2) and ISO 19902 (3) introduced them as alternative methods to the API method for the design of piles in sand.