1、A plasticity model for the behaviour of footings on sand under combined loadingG.T.HOULSBY1, M.J.CASSIDY2(1.Departmen of Offshore Engineering, Oxford University, UK; 2.Center for Offshore Foundation Systems, University of Western Australia(formerly at Oxford University)ABSTRACTA complete theoretical
2、 model is described for the behavior of rigid circular footings on sand, when subjected to combined vertical, horizontal and moment loading. The model, which is expressed in terms of work-hardening plasticity theory, is based on a series of tests specifically designed to allow evaluation of the vari
3、ous components of the theory. The model makes use of the force resultants and the corresponding displacements of the footing, and allows predictions of response to be made for any load or displacement combination. It is verified by comparison with the database of tests. The use of the model is then
4、illustrated by some demonstration calculations for the response of a jack-up unit on sand. This example illustrates the principal purpose of the development, which is to allow a realistic modelling of foundation behaviour to be included as an integral part of a structural analysis.KEYWORDS: footings
5、/foundations; model tests; numerical modelling and analysis; offshore engineering; plasticity; sandsINTRODUCTIONThe purpose of this paper is to describe a theoretical model, based on strain-hardening plasticity theory, which is capable of describing the behaviour of a circular footing on sand when i
6、t is subjected to all possible combinations of drained vertical, horizontal and moment loading. The motivation for this work comes principally from the offshore industry, specifically arising from the problem of assessment of jack-up units under extreme loading. The applications are, however, much b
7、roader, since the model could be applied to many instances of combined loading of a footing on sand.Structural engineers carry out detailed analyses of jack-up units, and ask geotechnical engineers to provide them with the values of spring stiffnesses to model the foundations. Geotechnical engineers
8、 tend to take the view that such a simplistic view of foundation behaviour is unrealistic. Unfortunately, however, they often describe the complexities and non-linearities of foundation behaviour by a series of ad hoc procedures, which a structural engineer cannot implement within a standard analysi
9、s. The purpose of the model described here is to provide a means by which the structural and geotechnical engineers can communicate. Geotechnical engineers must be prepared to re-cast their knowledge of foundation behaviour within a terminology (plasticity theory) that is amenable to numerical analy
10、sis. Structural engineers must accept that soil behaviour cannot be described merely by springs, but can be accommodated if they are prepared to use strain-hardening plasticity theory within their analyses.The ad hoc procedures for describing foundation behavior under combined loading have their roo
11、ts in the work on bearing capacity by Meyerhof (1953), and are typified by the procedures described by Brinch Hansen (1970) and Vesic (1973). These methods are adequate for predicting failure under combined loads, but they are unsuitable for numerical analysis, principally because they formulate the
12、 problem using a series of factors applied to the bearing capacity formula for vertical loading, modifying it to account for horizontal and moment loading. This renders the analysis unsuitable for direct inclusion in numerical analysis programs. Furthermore the conventional analyses pay no attention
13、 to the issue of plastic strains pre-failure, since they treat only the failure problem.An alternative is to address the problem directly as one of loading within a three-dimensional (V , M , H ) load space, and to explore, for instance, the shape of the yield surface in this space. This approach wa
14、s pioneered by Roscoe & Schofield (1956), who were also concerned with a problem of soil structure interaction: that of calculating the fully plastic moment resistance of a short pier foundation for a steel framework. The general framework of plotting load paths in (V, M, H) space has been adopted b
15、y the offshore industry, but the formulae used to derive the failure surfaces are often based on the shape a nd inclination factor approach (see e.g. Hambly & Nicholson, 1991).Recently there has been considerable interest in the development of models based on plasticity theory, and on the experiment
16、al work necessary to support this approach (e.g. Schotmann, 1989; Nova & Montrasio, 1991: Gottardi & Butterfield, 1993, 1995; Houlsby & Martin, 1992; Martin, 1994). The model described here is intended for the description of drained loading of a circular foundation on dense sand, subjected to an arbitrary combination of vertical, horizontal and moment loads. It is complete in the sense that any load or deformation path can be applied to the footing and the correspondin
