TY - JOUR
T1 - Slumping of groundwater mounds
T2 - Revisiting the Polubarinova-Kochina theory
AU - Kacimov, Anvar
AU - Al-Jabri, Salem
AU - Sherif, Mohsen
AU - Al-Shidi, Salem
PY - 2009
Y1 - 2009
N2 - Decay or rise of the water table from a disturbed (mound or trough) position to a quiescent flat state is studied by a linear potential theory that does not rely on the Dupuit-Forchheimer vertical averaging but is a solution to the full Laplace equation. We consider an unconfined aquifer of high (infinite) thickness disturbed by a linear or point hydrodynamic dipole and assemblies of dipoles, which generate two- and three-dimensional seepage. Hydrologically, the dipoles mimic a channel (or circular-recharge basin), which generates the mound. The dipole ascends (descends) and the corresponding free surface, on which the isobaricity and kinematic conditions hold, slumps. A solvability condition, which stipulates no singularities in the seepage domain, is explicitly presented. The mound signal is defined as the time peak of the water table at any piezometer located away from the original recharge area. The flow net and isotachs prove the Bouwer caveat that the Dupuit-Forchheimer theory is specious if applied to high-thickness aquifers accommodating mounds originating from short infiltration events. The analytical value of the water table peak and the time of its arrival are compared with piezometric observations in recharge experiments conducted in a coastal aquifer of the United Arab Emirates, where the hydraulic conductivity is assessed from hydrographs. The inversely determined hydraulic conductivity fits well with those found from infiltration double-ring experiments and MODFLOW simulation.
AB - Decay or rise of the water table from a disturbed (mound or trough) position to a quiescent flat state is studied by a linear potential theory that does not rely on the Dupuit-Forchheimer vertical averaging but is a solution to the full Laplace equation. We consider an unconfined aquifer of high (infinite) thickness disturbed by a linear or point hydrodynamic dipole and assemblies of dipoles, which generate two- and three-dimensional seepage. Hydrologically, the dipoles mimic a channel (or circular-recharge basin), which generates the mound. The dipole ascends (descends) and the corresponding free surface, on which the isobaricity and kinematic conditions hold, slumps. A solvability condition, which stipulates no singularities in the seepage domain, is explicitly presented. The mound signal is defined as the time peak of the water table at any piezometer located away from the original recharge area. The flow net and isotachs prove the Bouwer caveat that the Dupuit-Forchheimer theory is specious if applied to high-thickness aquifers accommodating mounds originating from short infiltration events. The analytical value of the water table peak and the time of its arrival are compared with piezometric observations in recharge experiments conducted in a coastal aquifer of the United Arab Emirates, where the hydraulic conductivity is assessed from hydrographs. The inversely determined hydraulic conductivity fits well with those found from infiltration double-ring experiments and MODFLOW simulation.
KW - Analytical solution
KW - Artificial recharge
KW - Phreatic surface
KW - Potential theory
KW - Seepage
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U2 - 10.1623/hysj.54.1.174
DO - 10.1623/hysj.54.1.174
M3 - Article
AN - SCOPUS:65649133615
SN - 0262-6667
VL - 54
SP - 174
EP - 188
JO - Hydrological Sciences Journal
JF - Hydrological Sciences Journal
IS - 1
ER -