Quasistatic Poroelasticity - Continuum Mechanics of Anisotropic Materials - page 227

Fig. 8.8 Illustration of the
vertical settlement of a layer
of poroelastic material resting
on a stiff impermeable base
subjected to a harmonic
surface loading. A plot of the
absolute value of the function
c

q

i

ioL p tanh

o

L 2
c

against
frequency. See Example 8.8.3

where c and W are given by

d

K d

d 2 d

c ¼ c I W =a; W ¼ að 1 þ n Þ=ð 3 L ð 1 n Þþa ð 1 þ n ÞÞ

and c I represents the value of the constant c when the matrix material and
the pore fluid are incompressible,

K 11 3 K d

d

ð 1 n Þ

c I ¼ :

mð 1 þ n

d

Þ

8.10.2. Verify that the solution to the pressure diffusion differential equation in
Example 8.10.2 satisfies the specified form of the differential equation and
the appropriate boundary and initial conditions.
8.10.3. Determine the flux q 3 of the pore fluid from out of the top surface of the
layer in Example 8.10.2.
8.10.4. Verify that the solution to the pressure diffusion differential equation in
Example 8.10.3 satisfies the specified form of the differential equation and
the appropriate boundary conditions.
8.10.5. Determine the pressure distribution in a semi-infinite domain of poroelastic
material subjected to an harmonic surface loading T 33 ¼

o

t .
The surface of the domain is in the x 1 , x 2 plane and the x 3 positive
coordinate direction is downward. Drainage of the semi-infinite domain is
only allowed at the surface. The solution to the pressure diffusion equation,

P o e i

P ð t Þ¼

2 p

x 3 Þ¼ @ p =@ t c ð@ =@ W ð@ P =@ t Þ

for the semi-infinite domain will determine the pressure field.
8.10.6. Determine the flux q 3 of the pore fluid from out of the top surface of the
layer in Example 8.10.3.