Page 82 - Numerical Analysis and Modelling in Geomechanics

WAVE-SEABED-STRUCTURE INTERACTION 63

(3.2)

where S is the degree of saturation; K is the true bulk modulus of pore water,
wo
2
which is normally taken as 2 × 10 9 N/m ; P wo is the absolute static water
pressure (= γ d, d is the water depth).
w
It is well known that the elastic properties of an isotropic material can be
described by two parameters: Young’s modulus (E) and Poisson’s ratio (µ).
However, the elastic properties of an anisotropic material can be described by
five parameters (Pickering, 1970):

• Young’s modulus (E and E );
z
x
• Poisson’s ratios, µ and µ ;
xx
xz
• The modulus of shear deformation in the vertical plane (G )
z
Another two dependent parameters, Poisson’s ratio (µ ) and the shear modulus
zx
in the horizontal plane (G ) can be interrelated by
x
(3.3)

It is noted that the non-dimensional parameter n is equal to one for an isotropic
soil.
The shear modulus in the vertical plane, G , can be expressed in terms of
z
Young’s modulus E as
z
(3.4)

where m is an anisotropic constant (Gazetas, 1982) that is equal to E/2(1+µ) for
an isotropic soil. Now, the five anisotropic parameters listed above can be
changed to E , µ , µ , n and m. The possible ranges of the above parameters for
xx
z
xz
different materials have been discussed in (Jeng, 1997a, 1997b).
Based on the generalised Hooke’s law (Pickering, 1970) and under the
condition of plane strain, the incremental effective stresses and strains in a cross-
anisotropic seabed can be expressed as

(3.5a)

(3.5b)