TY - JOUR
T1 - Analytical solutions for steady-state, axisymmetric seepage to toroidal and disk-shaped drainages and tunnels
T2 - the Gauss and Weber legacy revisited
AU - Kacimov, Anvar
AU - Houben, Georg
N1 - Publisher Copyright:
© 2023 IAHS.
PY - 2023/5/4
Y1 - 2023/5/4
N2 - Axisymmetric, steady-state, Darcian flows in homogeneous and isotropic aquifers towards a toroid or disk intake are analytically studied. Both unbounded (infinite) and bounded (by an equipotential soil surface or by an impermeable horizontal caprock-bedrock) aquifers are considered. The Gauss closed-form solution from astronomy for a gravitating circle having a uniform mass distribution and the Weber solution from electrostatics for an equipotential disk are utilized. The scalar/vector fields of piezometric head (potential)/specific discharge allow for reconstruction of stream lines, isobars, isochrones, and isotachs. An air-filled toroid drains much more water than equipotential, or–inversely–at a given flow rate, the size of an empty toroid is much smaller than that of a water-filled one. The hydraulic gradients in the vicinity of modelled wells/tunnels are very high, triggering colmation and suffusion. The functionals of dissipation and drawdown over a specified zone in the far field are evaluated.
AB - Axisymmetric, steady-state, Darcian flows in homogeneous and isotropic aquifers towards a toroid or disk intake are analytically studied. Both unbounded (infinite) and bounded (by an equipotential soil surface or by an impermeable horizontal caprock-bedrock) aquifers are considered. The Gauss closed-form solution from astronomy for a gravitating circle having a uniform mass distribution and the Weber solution from electrostatics for an equipotential disk are utilized. The scalar/vector fields of piezometric head (potential)/specific discharge allow for reconstruction of stream lines, isobars, isochrones, and isotachs. An air-filled toroid drains much more water than equipotential, or–inversely–at a given flow rate, the size of an empty toroid is much smaller than that of a water-filled one. The hydraulic gradients in the vicinity of modelled wells/tunnels are very high, triggering colmation and suffusion. The functionals of dissipation and drawdown over a specified zone in the far field are evaluated.
KW - Dirichlet boundary value problems
KW - Gaussian quasi-toroidal tunnel
KW - Weber’s disk-shaped well
KW - dissipation and integral drawdown functionals
KW - gravitational and specific discharge potentials
KW - streamlines–isotachs–isochrones
KW - superposition principle for harmonic function of piezometric head
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U2 - 10.1080/02626667.2023.2193296
DO - 10.1080/02626667.2023.2193296
M3 - Article
AN - SCOPUS:85158850757
SN - 0262-6667
VL - 68
SP - 938
EP - 953
JO - Hydrological Sciences Journal
JF - Hydrological Sciences Journal
IS - 7
ER -