Steel catenary risers (SCRs) are used to transport hydrocarbon products between offshore floating platforms and the seabed. Like many offshore structures, SCRs are subjected to gross cyclic movements during operation, which remould the seabed soil. The fatigue life of these structures is highly sensitive to the stiffness and strength of the seabed response. Accurate modelling of this behaviour requires a framework that can capture the changes in soil strength and stiffness that occur throughout the design life, accounting for remoulding during extreme events, and reconsolidation during the intervening periods. This paper describes such a framework, which is couched in effective stress terms. Soil softening during remoulding is predominantly associated with excess pore pressure generation, and the subsequent regain in strength is linked to the dissipation of excess pore pressure. The framework can describe the variation of resistance on a cylinder (i.e. a pipe) during any sequence of vertical cyclic motion, interspersed with pause periods. The framework is based on a critical state approach, with the current strength being linked to the current moisture content. The framework is shown to capture well the load-penetration response during an episodic T-bar penetrometer test. The operative soil strength is shown to vary dramatically throughout this event, with the softening effect of remoulding being almost entirely negated by a regain in strength associated with periods of partial or complete reconsolidation. The framework provides a basis for capturing these dramatic effects to aid pipeline and riser design (and other processes that involve gross remoulding and reconsolidation), without recourse to a full numerical simulation of the entire soil domain.