Environmental Engineering Reference
In-Depth Information
The assumed boundary conditions were a fixed potential with zero horizontal
displacements at the external vertical boundary. The assumption for the fluid mass
balance equation appears to be reasonable as the aquifers are recharged landward.
The base of the system was taken to be impermeable, with zero vertical
displacements. An impermeable surface with free displacements was assumed at the
top of the model. The initial conditions were assumed to be the 1930 values of the
variables.
As far as the mechanical properties are concerned, the solid skeleton is assumed
to be linear elastic, with different behavior in compaction and expansion. The fluid
transport parameters were also linear. These hypotheses were essentially due to the
fact that there were no sufficient data available for considering a more refined
mechanical behavior. Permeability values were determined through a trial-and-error
analysis, where the aim was to match the decline in the piezometric levels recorded
in Venice until 1969 in the numerical simulation. The identification procedure
provided the permeability values used in the following applications: the range of
these values was 2.765-13.82 m per day for the aquifers and 0.00173-0.0432 m per
day for the impermeable layers (aquitards). Compressibility modulus was 817 MPa
for aquifer sands, whereas was in the range 8.6-26.4 MPa for aquitards. Extension
modulus (used in a second analysis to model the rebound phase) was assumed to be
10 times larger than the value for compression.
Several trial runs have been carried out to determine the optimal value of time
increment necessary for an accurate integration of equations [5.5]. For the first
model (Figure 5.8a) a time step of 91 days showed no oscillation in the pore
pressures in space or time. At the same time this limited the costs of the analysis.
5.1.4.3.
Subsidence of Venice: results
As previously stated, material parameters for the numerical simulation have been
identified by using a trial-and-error procedure on the basis of experimental measures
recorded in the period 1930-1969. This step has been carried out by using the mesh
shown in Figure 5.8a.
Under the assumption of a constant pumping rate from 1969 to 2000 and equal
to the maximum historical value, comparison has been performed between the
responses of the coupled model previously presented and an uncoupled one [GAM
74]. The results of this comparison are presented in Figure 5.9.
Taking into account the experimental data, the coupled solution is much more
realistic: the model indicates a tendency towards steady-state conditions once the
pumping rate is kept constant, as experimentally observed. The agreement between
the calculated piezometric decline for the pumping rate history of Figure 5.4 and
measured values is remarkable for the first aquifer, for which field values were
