The Effect of Shape on the Failure Envelope of the Cross-Shaped Foundation â€“ Numerical Analyses-Paper

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The paper uses three-dimensional finite-element analyses to examine how the width and height of a cross-shaped steel foundation (CSF) affect its vertical–horizontal (VH) and vertical–horizontal–moment (VHM) failure envelopes. The foundation is intended for offshore structures on soft clay and is designed as a modular system that can be adapted to superstructure loads.<br /><br />The authors modelled the CSF and normally consolidated clay under undrained conditions, comparing five geometries with different wing dimensions. They also assessed structural feasibility, representing the wings as steel plates reinforced by vertical stiffeners. A 25 mm unstiffened plate proved too flexible and developed unacceptable stresses; a thinner, stiffened plate provided a suitably rigid and structurally compatible design.<br /><br />The results show that geometry affects both load capacity and installation. Horizontal resistance generally varies with wing area, while vertical resistance also reflects the increase in clay strength with depth. No single shape is best across all criteria: some geometries offer comparable or improved capacity, while others can penetrate fully under their own weight and avoid additional ballast. Soil-deformation patterns indicate a transition between behaviour resembling a solid pile and behaviour dominated by shear along the individual wings.<br /><br />For the reference geometry, analyses with the load applied above the foundation showed that increasing the load application height substantially reduces maximum horizontal resistance. This suggests a close relationship between horizontal load and moment capacity, although further analyses are needed to establish it.<br /><br />Overall, the study finds that CSF geometry can be tailored to balance capacity, structural demands, and ease of installation. The authors identify serviceability studies, physical model testing, and further validation of analytical methods as priorities for future work.

Keywords

cross-shaped steel foundation

finite-element analysis

failure envelopes

offshore foundations

soft clay

undrained conditions

wing dimensions

structural stiffeners

horizontal resistance

moment capacity