PIAHSProceedings of the International Association of Hydrological SciencesPIAHSProc. IAHS2199-899XCopernicus GmbHGöttingen, Germany10.5194/piahs-372-519-2015On the possible contribution of clayey inter-layers to delayed land subsidence above producing aquifersIsottonG.g.isotton@m3eweb.itFerronatoM.GambolatiG.TeatiniP.Università degli Studi di Padova, Padova, ItalyG. Isotton (g.isotton@m3eweb.it)12November2015372372519523This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://piahs.copernicus.org/articles/372/519/2015/piahs-372-519-2015.htmlThe full text article is available as a PDF file from https://piahs.copernicus.org/articles/372/519/2015/piahs-372-519-2015.pdf
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.
Introduction
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.
Mathematical model
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:
∇k∇h=Ss∂h∂t+q
where k is the hydraulic permeability tensor, h is the hydraulic head change,
t is time, q the source/sink and Ss the specific elastic storage defined
as Ss=γcM+φβ with γ the
specific weight of water, cM the oedometric compressibility of the
porous medium, φ the porosity and β the volumetric fluid
compressibility. A nonlinearity is present in Eq. (1) since Ss is a
function of the vertical effective stress σz, hence h, via cM.
Equation (1) is solved in space by the finite element method using linear
tetrahedral elements and in time by an implicit finite difference scheme,
with the nonlinearity addressed by a Newton-like iterative method.
The values of the four parameters used in the simulations: depth
Ha and permeability of the producing aquifer, thickness of the sandy
(ΔSs) and clayey (ΔSc) layer, ratio between the
oedometric compressibility in first and second loading cycle and ratio
between the sandy and the clayey hydraulic conductivity.
Ha (m)50010002000Permeability (mD)20010050ΔSs (m)105090ΔSc (m)45255Cr358Rk1×10-21×10-41×10-6
Pressure change predicted by the groundwater flow model along the
symmetrical axis in the case with Ha=1000 m, ΔSc=45 m, Rk=1×10-6 and Cr=8.
The incremental pore pressure variation p=h⋅γ induced by water
pumping is implemented into the geomechanical model to compute the medium
displacements. The equilibrium equations along the coordinate directions
x, y and z in an isotropic medium can be written in terms of incremental soil
displacement u (Verruijt, 1969):
G∇2ux+λ+G∂ε∂x=∂p∂xG∇2uy+λ+G∂ε∂y=∂p∂yG∇2uz+λ+G∂ε∂z=∂p∂z
where ux, uy and uz are the components of u along the
coordinate directions, λ and G are the Lamé constant and
shear modulus of porous medium, respectively, and ε is the
volume strain. A nonlinearity is introduced in Eq. (2) since λ and G
are functions of σz, and hence u, via cM as λ=ν/1-νcM and G=1-2ν/21-νcM with ν the Poisson ratio.
Using data based on field and lab measurements the compressibility cM
is related to σz, with a different relationship in first and
second loading cycle accounting for geomechanical hysteresis (Baù et
al., 2002). Equation (2) is solved by the finite element method using the
same tetrahedral elements as the groundwater flow model. The nonlinearity is
solved by a Newton-like iterative method.
Maximum vertical displacement Uz normalized with respect to the
displacement at the end of the pumping period (10 years) Uz(10) in the case
with Ha=500 m and ΔSs=10 m. In the left panel Rk=1×10-6 and Cr=3, 5 and 8. In the right panel Cr=8 and Rk=1×10-2,
1×10-4 and 1×10-6.
Maximum vertical displacement Uz normalized with respect to the
displacement at the end of the pumping period (10 years) Uz(10) in the case
with Ha=1000 m and ΔSs=10 m. In the left panel Rk=1×10-6 and Cr=3, 5 and 8. In the right panel Cr=8 and Rk=1×10-2,
1×10-4 and 1×10-6.
Maximum vertical displacement Uz normalized with respect to the
displacement at the end of the pumping period (10 years) Uz(10) in the case
with Ha=2000 m and ΔSs=10 m. In the left panel Rk=1×10-6 and Cr=3, 5 and 8. In the right panel Cr=8 and Rk=1×10-2,
1×10-4 and 1×10-6.
Maximum vertical displacement Uz normalized with respect to the
displacement at the end of the pumping period (10 years) Uz(10) in the case
with ΔSs=10 m Cr=8, Rk=1×10-6 and Ha=500 m, 1000 m and 2000 m.
Modeling set-up
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 R=10 km and height H=5 km, with zero
displacements prescribed on the bottom and the outer boundaries. An aquifer
is located at depth Ha and confined by two clayey layers. An accurate
discretization of 1 m thick elements is used to simulate the pore pressure
propagation at the sand-clay interface and the in less permeable units along
the vertical direction. A zero pore pressure is prescribed on the side
surface and the natural condition is prescribed on the top and bottom
boundaries. The aquifer permeability decreases with depth as summarized in
Table 1 with typical values of a Quaternary sedimentary basin.
A 10-year constant water withdrawal rate Q∗ is prescribed from a 500 m-radius
cylindrical aquifer volume to simulate the pore pressure decline
experienced by several producing wells. The fluid-dynamic simulations last
for 10 years after the cessation of the production. The value Q∗ is
calibrated to have a uniform 100 bar pressure decline in the produced volume
at the end of the withdrawal period.
The sensitivity analysis takes into account four parameters:
the depth Ha of the sandy layer;
the ratio between the sandy and the clayey layer thickness, ΔSs
and ΔScrespectively, with ΔSs+2ΔSc=100 m;
the ratio Cr between the oedometric compressibility in first e second loading cycle;
the ratio Rk between the sandy and the clayey layers permeability.
The values of the four parameters used in the simulations are summarized in
Table 1.
Numerical results
Figure 2 shows the pore pressure variation along the symmetry axis for the
case with Ha=1000 m, ΔSc=45 m, Rk=1×10-6
and Cr=8: the pore pressure recovery in the clay layers is
significantly delayed relative to the aquifer. The pore pressure in the
aquitards may still decline after the shutdown of the producing wells,
possibly causing a delayed land subsidence.
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 (t=10 years). A normalized displacement
larger than 1 highlights a delay between the pore pressure in the aquifer
and the land settlement. The results obtained for the investigated Ha
values and ΔSs=10 m are shown in Figs. 3–6.
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 Rk and ΔSs and large values of Ha and
Cr enhance a delayed land settlement because the pore pressure propagates in
the clay more slowly. For all the investigated Ha values the delay
between the pore pressure recovery and the land settlement is maximum with
ΔSs=10 m, Cr=8 and Rk=1×10-6.
With these configurations, a 9 and 20 % of the final land subsidence takes place
after the cessation of withdrawal for Ha=1000 and 2000 m,
respectively. With Ha=500 m subsidence is almost unvaried after the
well closure.
Conclusions
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 Ha,
thickness of the sand ΔSs and of the clay ΔSc units,
ratio between the oedometric compressibility in first e second loading
cycle Cr, and ratio between the aquifer and the aquitard permeability
Rk. The range of variability of these parameters is typical of a
Quaternary sedimentary basin.
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 Ha increases;
the sandy layer thickness ΔSs decreases relative to the aquitard thickness;
the ratio between the oedometric compressibility in first and second loading cycle Cr rises;
the ratio between the sandy and the clayey layers permeability Rk decreases.
Within the investigated configurations the maximum subsidence occurring
after the well shutdown amounts to 20 % and therefore must be taken into
account for reliable subsidence evaluation and prediction.
Coupling this process with a visco-plastic mechanical behaviour of the
depleted layers might cause an enhancement of the land subsidence delay.
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