Bearing capacity of a cohesive-frictional soil under non-eccentric inclined loading Mohammed Hjiaj * , Andrei V. Lyamin, Scott W. Sloan Department of Civil, Surveying and Environmental Engineering, The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia Received 19 June 2003; received in revised form 17 June 2004; accepted 18 June 2004 Abstract This paper applies numerical limit analysis to evaluate the bearing capacity of a strip footing, subjected to a non-eccentric inclined load, resting on a ponderable cohesive-frictional soil. Accurate lower and upper bounds are calculated rigorously using finite elements and nonlinear programming. By adopting typical values for the friction angle, the inclination angle, and a dimen- sionless parameter related to the self-weight, most cases of practical interest are treated. The results are presented in the form of tables. As the gap between the bounds does not exceed 3%, the average limit load provides a good estimate of the exact ultimate load and can be used with confidence for design purposes. The numerical results are compared with ultimate loads predicted by the theories of Meyerhof, Hansen and Vesic ´. The comparison shows that the Meyerhof and Vesic ´ theories results are unconservative for inclined loading. In particular, the inclination factors from the Meyerhof theory appear to be inaccurate, whilst the Vesic ´ theory does not take proper account of the self-weight. For a ponderable soil under vertical or inclined loading, the collapse mechanism from the rigorous upper bound analysis is different to that assumed by previous authors. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Bearing capacity; Strip footing; Inclined load; Limit analysis; Finite element; Mathematical programming 1. Introduction The stability of foundations under inclined loads is a fundamental problem in geotechnical engineering. The type of loading, which is often known as combined load- ing, is particularly important in oil industry where off- shore foundations are subjected to vertical and horizontal loads as well as moments. Typically, the ver- tical force stems from the weight of the superstructure (or a part of it), while the horizontal load comes from wind and wave forces. Generally speaking, the idealized case of a foundation under a central vertical load is a gross simplification of what actually occurs in practice. Even in a simple multistory building, suspended slab floors generate horizontal forces that are transmitted to the foundation by load bearing walls. Fortunately, in these cases, the horizontal forces are usually not com- parable in magnitude to the vertical ones and it is often safe to ignore them. The ultimate bearing capacity of surface strip footing, subjected to an inclined load and resting on a ponderable cohesive-frictional soil, has been studied by numerous investigators. Traditionally, the inclination of the load is taken into consideration through a semi-empirical modification of the theory available for a vertical load. In turn, most of the bearing capacity theories for a verti- cal load are derived using the superposition principle introduced by Terzaghi [27], which assumes that contri- butions from the cohesion, the surcharge and the unit weight can be summed independently. Key papers that have influenced various national design standards in- clude those of Meyerhof [14,15], Hansen [11] and Vesic ´ 0266-352X/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2004.06.001 * Corresponding author. Tel.: +61 2 4921 5582; fax: +61 2 4921 5582. E-mail address: mohammed.hjiaj@newcastle.edu.au (M. Hjiaj). www.elsevier.com/locate/compgeo Computers and Geotechnics 31 (2004) 491–516