Combined loading of skirted foundations M. F. BRANSBY  and M. F. RANDOLPH  The response of skirted offshore foundations to combined vertical (V), moment (M) and hori- zontal (H) loading has been studied using two- dimensional ®nite-element analysis and upper- bound plasticity analysis assuming the soil to be undrained. New information has been gained about the shape of the yield locus and the soil deformation mechanisms occurring at yield from the ®nite-element analysis. The shape of the yield locus was found to be similar to that predicted by previous workers in V±M and V± H space but differed signi®cantly in M±H space. This behaviour is explained using upper-bound plasticity mechanisms suggested by the soil de- formation mechanisms calculated in the ®nite element analysis. This procedure is then used to give a good approximation to the shape of the yield locus and thus may form the basis for future design methods. Additionally, a simplify- ing transformation is suggested for the yield locus in H±M space based on plasticity analysis, which allows use of simple mathematical expres- sions to form a design envelope. KEYWORDS: bearing capacity; footings/foundations; numerical modelling and analysis; plasticity. Nous e Âtudions la re Âponse de fondations offshore a Á jupe a Á une combinaison de charge verticale (V), instantane Âe (M) et horizontale (H) en utili- sant des analyses d'e Âle Âments ®nis en deux di- mensions et une analyse de plasticite  de limite supe Ârieure en supposant un sol non draine Â. Nous tirons de l'analyse d'e Âle Âments ®nis de nouveaux renseignements sur la forme du lieu d'e Âlasticite  limite et sur les me Âcanismes de de Âformation du sol qui se produisent a Á la limite e Âlastique. La forme du lieu se re Âve Ále comme similaire a Á celle pre Âsage Âe par les travaux pre Âce Âdents dans les espaces V±M et V±H mais conside Ârablement diffe Ârente dans l'espace M±H. Nous expliquons ce comportement en utilisant les me Âcanismes de plasticite  de limite supe Ârieure qui sont sugge Âre Âs par les me Âcanismes de de Âformation du sol cal- cule Âs dans l'analyse d'e Âle Âments ®nis. Cette pro- ce Âdure est alors utilise Âe pour donner une bonne approximation de la forme du lieu qui pourra ainsi former la base des futures me Âthodes de design. De plus, nous sugge Ârons une transforma- tion simpli®catrice pour le lieu d'e Âlasticite  limite dans l'espace H±M sur la base de l'analyse de plasticite  qui permet l'utilisation d'expressions mathe Âmatiques simples pour former une envel- oppe de design. INTRODUCTION Offshore structures may consist of multiple shallow foundations which act together in consort (e.g. jack-up rigs and tension leg platforms) or single shallow foundations (e.g. gravity based platforms). Both of these types of foundations undergo com- bined vertical (V), moment (M) and horizontal (H) loading due to environmental loadings on the superstructure. In order to predict the behaviour of an entire offshore structure the response of these individual foundations to this combined loading must be understood. The bearing capacity of shallow foundations undergoing combined vertical, horizontal and mo- ment loadings has long been a fundamental soil mechanics research problem. Solutions have gener- ally been based on plasticity (e.g. Hill, 1950; Prandtl, 1921) or use approximate/empirical meth- ods (e.g. Meyerhof, 1953; Hansen, 1970). Recent research workers working on the problem in refer- ence to offshore foundation behaviour (e.g. Tan, 1990; Murff, 1994; Butter®eld & Gottardi, 1995; Houlsby & Martin, 1992; Dean et al., 1992; Salencon & Pecker, 1995; Ngo-Tran, 1996) have analysed the combined loading response of shallow foundations using plasticity methods. Yield loci in V±M±H space have been deduced for different foundation systems in different soil types. A yield surface is introduced whereby f V As , M AsD , H As    0 (1) where A is the area of the foundation, D its Bransby, M. F. & Randolph, M. F. (1998). Ge Âotechnique 48, No. 5, 637±655 637 Manuscript received 14 April 1997; revised manuscript accepted 4 February 1998. Discussion on this paper closes 1 January 1999; for further details see p. ii.  University of Western Australia, Nedlands.