The challenge of numerically implementing numerous force–resultant models in the stability analysis of long on-bottom pipelines

Plasticity models written directly in terms of force and displacement are finding increased popularity in describing the behaviour of offshore foundations. However, when applied to the on-bottom stability analysis of pipelines under random storm loading, hundreds, if not thousands, of models must be incorporated with structural elements in a three-dimensional analysis and simultaneously solved. This necessitates extremely efficient and accurate numerical integration techniques. This paper scrutinizes constitutive integration algorithms within both explicit and implicit frameworks, and applies them to a two-surface mixed hardening model that describes the force–displacement behaviour of a pipe partially embedded in sand. Detailed solutions are provided, allowing implementation of the pipe–soil model into any standard structural finite-element program. Through use of practical examples, the efficiency and accuracy of the solution methods are assessed.