Calculations to ensure a submarine pipeline is stable on the seabed have traditionally used Morison’s equations . The equations aim to satisfy two stability conditions:
- the submerged weight of the pipe has to be greater than the lift force; and,
- the horizontal frictional force should exceed the combined drag and inertia forces.
The equations are empirical relations, relating the hydrodynamic forces (lift, drag and inertia) to the pipe diameter. The outcome is an appropriate thickness of a concrete weight coating to ensure pipeline stability, Figure 1.
Figure 1. Line pipe coated in concrete.
The pipe is stable when :
- the submerged weight is greater than the lift force; and, at the same time,
- the frictional force exceeds the combined drag and inertia forces.
Morison’s equations include hydrodynamic coefficients. These are determined using model testing and are a function of Keulegan-Carpenter Number (related to maximum wave velocity), Reynolds Number (related to total flow velocity), embedment or trench depth, and pipe roughness.
Stability is assessed using a model. Those with increasing complexity are 2D static, 3D dynamic, and 3D transient dynamic. There are also various commercial programs available for assessing pipeline stability.
Note standard tools and methods are not appropriate for the breaking wave zone which occurs close to the shore.
- J R Morison et al, ‘The Forces Exerted by Surface Waves on Piles’, Journal of Petroleum Technology, vol. 189, pp. 149-154. 1950.
- F Van den Abeele, J Vande Voorde, ‘Stability of Offshore Pipelines in Close Proximity to the Seabed’, 6th Pipeline Technology Conference. Berlin. Germany. 2011.