Environmental Engineering Reference
In-Depth Information
For the recovery period that is of interest here, a pressure increase of 6 MPa and
a saturation of 10% has been assumed for the reservoir center while at the boundary
the pressure also increased by 6 MPa and the saturation by 35%. Again, due to this
increase, for the center the LC curve moves from LC
1
to LC
2
, with ensuing
compaction, and then there is a slight elastic expansion moving from C to D in
Figure 7.21a. The ensuing volumetric train is ε
v
= (0.07 − 0.1)/1.35 = -0.02%.
The constitutive model BSZe (extended Bolzon, Schrefler and Zienkiewicz
model) of [SAN 06] has been adopted for these simulations, which makes use of the
generalized Bishop stress σ′
=
σ
∗
+
S
r
S
instead of the net stress, where σ
∗
is the net
stress,
S
r
the degree of saturation and
S
the capillary pressure (suction) [LEW 82].
The advantage of this stress measure is its ease in numerical applications: it has the
same form in fully and partially saturated situations. Furthermore, it is
thermodynamically consistent [NUT 08]. The material properties have been
obtained by parameter identification from curve 1 in Figure 7.12 [SIM 01]
Data
l
m
a
k
(0)
λ
(0)
v
0
i
w
Saturation
test
[PAP 98,
SIM 01]
4.816
0.85
2.56
0.0046
0.0296
1.35
1.5
0.1
Table 7.2.
Parameters identified for the constitutive model (l, m and a are material
parameters,
λ
(0) and k(0) the soil compressibility and elastic compressibility coefficients in
saturated conditions, v
0
the initial value of the specific volume and i and w come from
interpolation of experimental data)
In the second step we have imposed the compaction obtained from the
volumetric strain at reservoir level on a purely structural analyzer, with the same
geometry and material as above. This corresponds to an equivalent displacement
boundary condition also containing the pressure effects in the formation. A linear
interpolation has been used for the compaction values between the reservoir border
and center and a linear decay in the adjacent aquifer, with negligible compaction at a
distance of 3 km from the reservoir center. This “hat”-like shape obtained (see
Figure 7.22), is in line with what was observed experimentally (see Figure 7.19).
These simplified simulations show that the constitutive model used and the
material parameters adopted can perfectly model the behavior observed after
exploitation (“hat”-like shape), while conventional subsidence models are not
capable of doing so. For the results from the exploitation period, which are also
satisfactory, the reader is referred to [MEN 08].
