10.4122/1.1000000426
Ferronato, Massimiliano
Massimiliano
Ferronato
ferronat@dmsa.unipd.it
Gambolati, Giuseppe
Giuseppe
Gambolati
gambo@dmsa.unipd.it
Putti, Mario
Mario
Putti
putti@dmsa.unipd.it
Teatini, Pietro
Pietro
Teatini
teatini@dmsa.unipd.it
Ferronato, Massimiliano
Massimiliano
Ferronato
ferronat@dmsa.unipd.it
A diffusion model for land subsidence
XVI International Conference on Computational Methods in Water Resources
2006
2006
In classical hydrogeology land subsidence due to fluid withdrawal is typically
predicted by decoupling the flow model from the structural model. The pore
pressure solution obtained from the flow model is used as an external source
of strength in the structural equations to compute the porous medium
deformation. Though the horizontal displacement can be of some interest as
well, usually the attention is devoted to the vertical displacement, which
allows for the prediction of subsidence at the ground surface.
A careful inspection of the equilibrium equations, together with a few
assumptions related to the subsidence mechanism, leads to the development of
a simplified model based on one anisotropic diffusion equation for the
vertical displacement only. The model can be applied to a generally
heterogeneous porous medium, possibly with a non linear or plastic mechanical
behavior, and subject to an arbitrary pore pressure variation. The aim of the
present paper is to investigate the conditions under which such a model
provides results of comparable accuracy with respect to the solution of the
classical equilibrium equations. A sensitivity analysis is performed on the
Poisson ratio, which controls the model anisotropy, the depleted reservoir
depth and shape, and the rock mechanical heterogeneity. The results show that
the diffusion model of subsidence gives a good prediction especially in case
of a thin depleted reservoir embedded within homogeneous or generally
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 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.