Page 84 - Numerical Analysis and Modelling in Geomechanics

WAVE-SEABED-STRUCTURE INTERACTION 65

(3.9b)

in the x- and z-directions, respectively.
Appropriate boundary conditions are required to solve the governing equations
(3.1) and (3.9). For a porous flow in a seabed, the boundary conditions at the
impermeable rigid bottom require that the dynamic fluctuations of all the
physical quantities vanish, i.e.,

(3.10)

For the lateral boundaries of the computation domain, since the existence of the
structure only affects the wave-induced soil response near the structure, the
disturbed components due to the existence of a structure will vanish far away
from the structure. Thus, the soil response at these points should be that induced
by waves without any structures (see Yamamoto et al., 1978; Jeng, 1997b).
These lateral boundary conditions should be determined before including the
structure into the whole model. The details of the numerical procedure will be
described in the section headed ‘Numerical procedure’.
Besides the bottom boundary conditions, the seabed surface conditions are
also required for the wave-seabed-structure interaction. Since these
boundary conditions will vary with the type of structure, they will be described
in each example.

General finite element model for wave-seabed-structure
interaction (GFEM-WSSI)
Since the wave-induced oscillatory soil response fluctuates periodically in the
temporal domains under harmonic wave loading, the wave-induced soil response
can be assumed to take the form

(3.11)

where subscripts “r” and “c” represent the real and imaginary parts of the soil
response, respectively.
Substituting (3.11) into (3.1) and (3.9), then directly applying the Galerkin
method (Zienkiewicz and Taylor, 1989) to these equations, the finite element
analytical formulations can be expressed in matrix form as