Page 81 - Numerical Analysis and Modelling in Geomechanics

62 D.S.JENG
history. However, many materials show more limited forms of anisotropy. A
cross-anisotropic material is an example. This material has the same properties in
all horizontal directions, but different properties in the vertical direction. When
soils are deposited vertically and subjected to equal horizontal stresses, they will
exhibit a vertical axis of symmetry and be transversely isotropic (Pickering,
1970; Graham and Houlsby, 1983).
The mechanism of the wave-seabed-structure interaction has been studied from
the aspect of either coastal or geotechnical engineering. The wave forces
(pressure) acting on the marine structure have been the main concerns of coastal
engineering. Although some researches have considered the sediment transport
around the structures, only the movement of sediment along the seabed surface
was considered. On the other hand, geotechnical engineers have focused on the
distribution of stress under the structure loading, rather than wave loading.
However, the interaction between wave, structure and seabed has rarely been
linked from both the coastal and the geotechnical point of view. This study
attempts to link wave loading, seabed response, and marine structure in a single
model.
This chapter is divided into two parts. In the first part, a general finite element
model for the wave-seabed-structure interaction is proposed. The full finite
element formulations are presented. Also, a detailed numerical procedure used
for the simulation of wave-seabed-structure interaction is included. In the second
part, two practical examples (pipelines and caissons) are used to demonstrate the
application of the proposed model.

Theoretical formulations

Boundary value problem
In this study, the consolidation equation (Biot, 1941), which has been generally
accepted as the governing equation for the flow of a compressible pore fluid in a
compressible porous medium, is adopted to treat the wave-seabed-structure
interaction with variable permeability as

(3.1)

where p is the wave-induced pore pressure, K is permeability in all directions, n'
is soil porosity, and γ is the unit weight of the pore fluid.
w
In equation (3.1), the volumetric strain (ε) and compressibility of pore fluid
(β) are defined as