A diffusion model for land subsidence
M. Ferronato, G. Gambolati, M. Putti, P. Teatini
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
ABSTRACT
A few assumptions suggested by the mechanism of anthropogenic land settlement
due to fuid withdrawal lead to the development of a simplified subsidence model
relying on one anisotropic diffusion equation for the vertical displacement
only. The model can be used in a generally heterogeneous porous medium,
possibly with a non linear or plastic mechanical behavior, and subject to an
arbitrary pore pressure variation. The present communication investigates the
conditions under which such a model provides an outcome of comparable accuracy
with respect to the solution of the classical equilibrium equations. The
results show that the diffusion model of subsidence gives a good prediction
above the producing field especially in case of a thin depleted reservoir
embedded within weakly heterogeneous porous media with a Poisson ratio between
0.20 and 0.30, i.e. the vast majority of real applications. The above model
allows also for a novel interpretation of the volumetric locking phenomenon
occurring for a Poisson ratio close to its limiting value of 0.50 and helps
gain a new insight in terms of equivalent "mechanical conductivities" into the
propagation of the deep compaction to the land surface.
