Numerical Analysis for Foundations of Offshore Structures With Special Reference to Progressive By Deformation
Authors: Zienkiewicz O.C. , Lewis R.W. , Norris V.A. , Humpheson C. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the SPE-European Spring Meeting 1976 of the Society of Petroleum Engineers of AIME, held in Amsterdam, The Netherlands, April 8–9, 1976. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal, provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Introduction
The art and science of soil mechanics is based on logical deduction adjusted by observation and experience of actual performance. In conventional foundation performance. In conventional foundation problems such experience is widely available problems such experience is widely available and acceptable design procedures have long been established. In offshore work to date such experience is slight and attention has to be focused on theoretical predictions based on the best models and solutions available. As such solutions can usually be obtained only by using numerical methods and, in particular, the most widely successful Finite Element Method, an attempt is made to outline some of the approaches used and the parametric studies carried out at the authors' parametric studies carried out at the authors' institution with the aim of determining successful numerical procedures and also appropriate constitutive relationships.
In many respects the offshore foundation problem is similar to conventional 'footing'situations and some of the studies are equally applicable to both. However, in one respect the situation is not parallel 'on load shore'. This is manifest in cyclic horizontal loads due to wave action. Such relatively slow load cycling is seldom encountered elsewhere and under certain circumstances, as will be demonstrated, can lead to progressive deformation. Such progressive deformation is well-known in progressive deformation is well-known in structural engineering whenever plasticity occurs, but has not been studied to any extent in the area of soil plasticity. We shall, therefore, focus some attention on this important problem.
The length of the present paper inhibits covering the field exhaustively and some important aspects of behaviour will not be considered. Amongst these are the phenomenon of liquefaction and the response to rapid, dynamic (earthquake) forces.

2. THE GENERAL MODEL AND ITS FINITE ELEMENT DISCRETISATION.
Offshore structures are always founded on saturated soil. Thus, in general, it is necessary to consider the coupled behaviour of the soil skeleton and the pore fluid. The fluid is characterised by the significant stress of hydrostatic pressure p. Further, the assumption is made that the effective stress*
(1)