This paper presents the numerical formulation of an elastoplastic force-resultant model to numerically simulate the interaction of a pipe with the soil. This approach, which accounts for the load-displacement behaviour of the pipe-soil system on a macroelement level, is becoming increasingly popular in offshore engineering. The model consists of a yield surface, a non-associated flow rule, an isotropic hardening law and a description of purely elastic behaviour. It can be used to predict the behavior of one segment of pipe or numerous models can be attached to structural finite elements as nodal point elements. The latter allows the practical analysis of long pipelines. Further, by removing a number of macroelements from the pipeline, the effect of free span can be studied. To numerically incorporate large numbers of macroelements into a structural analysis, efficient and robust integration algorithms are essential. The use of both explicit and implicit integration algorithms are explored in this paper. In the explicit algorithm, the Euler forward integration scheme is adopted to achieve the real force state incrementally for each substep. On the other hand, the Euler backward integration scheme is adopted in the implicit algorithm. In this case the load state is iteratively “returned” back to the yield surface according to the end of the total displacement increment. Illustrative calculation examples are provided in this paper to demonstrate and compare the performance of the suggested algorithms.

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