used to describe the particle kinematics. Near the coast the linear theory
may not be accurate enough, so that the forces are underestimated.
When pipelines are placed on erodible seabed, they sag and bury
themselves due to action of waves and currents. This self-burial process is
advantageous as it saves costly artificial trenching or burial of the pipes.
During the erosion process or in the presence of scour beneath the
pipelines, spanning conditions of pipelines may prevail. The pipes can
experience large static deflection or fluid-induced vibrations endangering
their structural integrity. Generally the local scour in the vicinity of
pipelines is three-dimensional. The equilibrium depth of scour Sbeneath
fixed pipes in laboratory conditions is typically 0.6 times the diameter of
the pipelines for steady currents and in the presence of waves it is
S/D0.1K (^) c(Sumer and Fredsoe, 1990; Sumer et al. 2001).
If the pipes are laid partially buried, the relative scour depth S/Dis
also a function of the relative embedment depth e/D(Hoffmanns and
Verheij (1997), Coastal Engineering Manual(US Army, 2002)).
Pipelines generally are covered using layers of materials such as
gravel, concrete blocks, and mattresses of concrete, asphalt or polypropy-
lene to protect them against erosion and mechanical damage and to
reduce their weight (Hoffmanns and Verheij, 1997); they are completely
buried to protect them from fishing trawlers.
FORCES ON CYLINDRICAL STRUCTURES 611
Fig. 14.20 Forces exerted on a submarine pipeline