In recent years, measurements of land subsidence above pumped aquifers by permanent GPS and InSAR have exhibited some delay relative to drawdown ranging from months to years. The current modeling approaches accounting for water fluid dynamics and porous medium geomechanics may fail to predict such a delay and may underestimate the land settlement after the well shutdown. In the present communication, an investigation is made on the residual compaction of the intervening clayey formations as a possible contribution to retarded land subsidence. The pore pressure variation within the aquifer and its propagation in the clay are simulated by a finite element flow model, with the resulting pore pressure decline used as input data in a hypo-plastic geomechanical model. A proper sensitivity analysis on (i) aquifer depth, (ii) ratio between the sandy and the clayey layers thickness and hydraulic conductivity, (iii) oedometric compressibility in first and second loading cycles, is performed for a typical geology of a Quaternary sedimentary basin. The results show that a certain fraction, up to 20 % of the overall land subsidence, can take place after the shutdown of the producing wells depending on actual basin, litho-stratigraphy and parameter values.

A major consequence of groundwater pumping is anthropogenic land subsidence. This can be a matter of concern if the affected areas are highly urbanized, with the loss in ground elevation generating possible structural problems to the buildings. If the aquifers underlie the coastland, the environmental problems are the exposure to flooding during high tides and severe sea storms. Hence, land subsidence must be investigated, monitored and reliably predicted to implement adequate remedial measures.

Extensometric records of soil deformation combined with land subsidence measurements by permanent GPS stations and InSAR techniques have provided evidence of some delay between the well shutdown or a significant reduction of the pumping rates and the resulting land settlement (Hettema et al., 2002; Teatini et al., 2006; Wu et al., 2010; Galloway and Sneed, 2013; Chang et al., 2014). While pore pressure in the aquifers progressively recovers, the subsidence may still continue, with a delay ranging from a few months to a few years. This suggests that the clayey layers confining the aquifer may keep on depressurizing and depleting after the shutdown of the producing wells. In the present study an investigation is made on the possible correlation between the delayed subsidence and the depletion of the clayey inter-layers of a multi-aquifer system.

The current standard modelling approach accounting for water fluid-dynamics and porous medium geomechanics usually does not accurately address these inter-layers (or aquitards) and tend to underestimate the land settlement after field abandonment. Before using a more complex modelling approach, such as visco-elastic or visco-plastic (Wu et al., 2010; Chang et al., 2014), a sensitivity analysis is performed with the aid of a 1-way coupled hysteretic hypo-plastic model (Gambolati et al., 2001) in which the pore pressure variation propagates in the clayey inter-layer. The sensitivity analysis takes into account the main parameters controlling land subsidence: aquifer depth, ratio between the sandy and the clayey layers thickness and hydraulic conductivity, and oedometric compressibility in the first loading and second unloading-loading cycle.

Aquifer dynamics and land subsidence caused by water withdrawal is theoretically described by the coupled process involving mechanics and flow in porous media (Biot, 1941). Uncoupling the flow field from the stress field is a usual assumption in groundwater hydrology. Gambolati et al. (2000) have shown that uncoupling has generally no measurable influence over any timescale of practical interest. Hence, in the present analysis a 1-way coupled approach is followed where the pore pressure variation is first simulated by a 3-D groundwater flow model, and then the land settlement is predicted by a 3-D geomechanical model with the pore pressure change used as an external distributed source of strength.

Geomechanical model used in the numerical simulations.

The aquifer hydrodynamics relies on the classical groundwater flow equation:

The values of the four parameters used in the simulations: depth

Pressure change predicted by the groundwater flow model along the
symmetrical axis in the case with

The incremental pore pressure variation

Maximum vertical displacement

Maximum vertical displacement

Maximum vertical displacement

Maximum vertical displacement

The geometry of the porous system used as test problem for the sensitivity
analysis is shown in Fig. 1. The cylindrical domain of the geomechanical
model is characterized by a radius

A 10-year constant water withdrawal rate

The sensitivity analysis takes into account four parameters:

the depth

the ratio between the sandy and the clayey layer thickness,

the ratio

the ratio

Figure 2 shows the pore pressure variation along the symmetry axis for the
case with

The results of the geomechanical model are presented in terms of the maximum
vertical land displacement normalized with the respect to the value at the
end of the water abstraction (

Note that the sudden increase of the aquifer stiffness at the well shutdown generates an abrupt increase of land subsidence although the pore pressure recovers in the aquifer. This 3-D deformation process, which is mainly accounted for the Poisson ratio and, subordinately, the depth of the depleted layer, was already pointed out by Ferronato et al. (2001).

Small values of

A set of numerical simulations are performed using a 3-D 1-way coupled groundwater flow and geomechanical model to investigate the possible contribution of clayey inter-layers to the delayed land subsidence measured above deep pumped aquifers.

The parameters addressed by the analysis include: aquifer depth

The results show that the delay between the pore pressure variation and land
settlement can partly be accounted for by the delayed pressure propagation
in the clayey layers confining the aquifer. The delay increases if:

the aquifer depth

the sandy layer thickness

the ratio between the oedometric compressibility in first and second loading cycle

the ratio between the sandy and the clayey layers permeability

Coupling this process with a visco-plastic mechanical behaviour of the depleted layers might cause an enhancement of the land subsidence delay.