Jackup Units on Clay: Structural Analysis With Realistic Modelling of Spudcan Behaviour
Authors: Martin C.M. , Houlsby G.T. 
Published: October 2008

Abstract
A plasticity-based numerical model is developed for predicting the behaviour of a spudcan foundation on clay under combined (V, M, H) loading. The consequences of including this model in the structural analysis of a jackup unit are demonstrated, and predictions are compared with those of a traditional pinned footing analysis.

Introduction
The most important criterion which governs the assessment of a jackup unit for a site in a harsh environment is often the moment developed at the lower leg guide. This moment depends on a complex process of interaction between the jackup and the soil, and is significantly affected by the "moment fixity" at the spudcans. This problem has led to a considerable amount of research, notably the Joint Industry Study (Ref. 1) which was an important precursor to the current SNAME guidelines (Ref. 2), which in turn are likely to be a major influence on ISO guidelines which are currently under discussion.
In the early stages of addressing this problem, thes tructural engineers tended to ask the geotechnical engineers for the values of the "springs" that could be used to model moment fixity. The geotechnical engineers correctly pointed out that this view was an over-simplification, and that the soil response was much more complex than could be represented by linear (or even nonlinear) springs. Unfortunately, however, the procedures they were able to offer to evaluate foundation behaviour under a complex regime of combined loading were complicated, largely based on semi-empirical methods, and quite inappropriate for combining with structural analyses. This unsatisfactory situation can be resolved if both groups are prepared to make some compromises. If the geotechnical engineers re-cast their understanding of foundations under combined loading within the context of work-hardening plasticity theory, then it is possible to form the incremental stiffness matrix for the foundation in a form that can be used by structural engineers in their analyses. For their part, the structural engineers need to accept that the nonlinearities of the work-hardening plasticity model mean that time-stepping incremental analyses are required for jackups, and that more efficient spectral decomposition methods are inappropriate.
The purpose of this paper is to set out a procedure for expressing the behaviour of a jackup foundation on clay in terms of work-hardening plasticity theory. The model is based on a database of experimental results, and where appropriate it also makes use of relevant theory. It is suitable for incorporation in numerical analysis of a jackup, and a simple illustration of a quasi-static analysis is given.

"Model B" Description of Spudcan Behaviour
The numerical model of spudcan response is based on work-hardening plasticity principles (early spudcan models of this type were proposed in Refs 3 and 4). Model B is capable of predicting load"displacement behaviour for combined vertical, moment and horizontal loading within a single vertical plane. Fig. 1 shows the sign convention used for the loads (V, M, H) and their work-conjugate displacements (w, ?, u). In describing the model it is easiest to begin with the case of a fully penetrated spudcan, as shown in Fig. 1(a). Extension to the case of a partially penetrated footing, Fig. 1(b), is then relatively straightforward. In both cases the embedded part of the underside of the spudcan is treated as a single "equivalent conical footing" with an equal radius and equal volume.