In the development of design methods for single-pile flexible dolphins used for the berthing of bulk carriers, the design stress has been gradually increased to the yield stress to employ the elastic energy absorption capacity of the pile more optimally. In recent guidelines, e.g. EAU 1996 [3] and PIANC 2002 [5], also the plastic yielding capacity is implicitly or explicitly included in the ultimate load-bearing capacity. This movement towards plastic design is not accompanied by the development of calculation models and design criteria to assess the plastic load-bearing capacity and relevant failure modes such as local buckling and ovalisation of the cross-section. To investigate the nonlinear load-deflection behaviour of a dolphin, a numerical model was developed based on the Beam on Nonlinear Winkler Foundation (BNWF) method [7] and extended for the plastic range of the steel pile using plasticity theory, which has been verified and confirmed by FEM analysis. The resulting Bruijn model enables the assessment of the elastic and plastic load-bearing capacity in terms of energy absorption including all significant failure modes, resulting in an improved assessment of the safety against failure and allowing more optimal designs. Case study calculations with the Bruijn model show that buckling, and to a lesser degree ovalisation, are significant failure modes for a diameter-wall thickness (D/t) ratio of 62 and 83, and should therefore be included in the design guidelines. The use of the plastic yielding capacity is limited to a low diameter-wall thickness ratio (about 40), where an increase in the elastic energy absorption capacity of up to 1,37 times the original elastic energy absorption capacity can be obtained after some plastic yielding. At a larger D/t ratio the buckling sensitivity reduces the advantages of plastic design.

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