TY - JOUR

T1 - Seepage to staggered tunnels and subterranean cavities

T2 - Analytical and HYDRUS modeling

AU - Kacimov, A. R.

AU - Obnosov, Yu V.

AU - Šimůnek, J.

N1 - Funding Information:
This work was supported by the grants DR\RG\17 and IG/AGR/SWAE/22/02 , Sultan Qaboos University , Oman, and by the Kazan Federal University Strategic Academic Leadership Program (" PRIORITY-2030 "). Helpful critiques and comments by two anonymous referees are appreciated.
Publisher Copyright:
© 2022

PY - 2022/6

Y1 - 2022/6

N2 - Darcian, 2-D flows to subterranean holes are studied analytically (by the methods of complex analysis) and numerically (by HYDRUS). For flow towards two circular or quasi-circular tunnels, reconstructed as isobars generated by two sinks under a ponded homogeneous soil surface, the flow nets, the velocity vector fields, and Riesenkampf's seepage force vectors are found. The position of the two tunnels is optimized using a criterion of the total area of the empty space comprised by the isobars with the admissible seepage flow rate as a constraint and the locus of the tunnels as a control variable. The case of a partially-filled tunnel, the contour of which is composed of two conterminous isobaric and equipotential arcs, is also analyzed. For a grouted tunnel, the refraction problem for two potential fields in two subdomains of the half-plane of the seepage flow domain is solved for an arbitrary contrast between the hydraulic conductivities of the liner and ambient soil. The tunnel grouting is, generally, eccentric with respect to the tunnel contour. High hydraulic gradients in the grouting are detected, which is a long-term seepage-harbinger for any liner materials used by geotechnical engineers.

AB - Darcian, 2-D flows to subterranean holes are studied analytically (by the methods of complex analysis) and numerically (by HYDRUS). For flow towards two circular or quasi-circular tunnels, reconstructed as isobars generated by two sinks under a ponded homogeneous soil surface, the flow nets, the velocity vector fields, and Riesenkampf's seepage force vectors are found. The position of the two tunnels is optimized using a criterion of the total area of the empty space comprised by the isobars with the admissible seepage flow rate as a constraint and the locus of the tunnels as a control variable. The case of a partially-filled tunnel, the contour of which is composed of two conterminous isobaric and equipotential arcs, is also analyzed. For a grouted tunnel, the refraction problem for two potential fields in two subdomains of the half-plane of the seepage flow domain is solved for an arbitrary contrast between the hydraulic conductivities of the liner and ambient soil. The tunnel grouting is, generally, eccentric with respect to the tunnel contour. High hydraulic gradients in the grouting are detected, which is a long-term seepage-harbinger for any liner materials used by geotechnical engineers.

KW - Complex potential

KW - Darcian velocity

KW - HYDRUS modeling

KW - Isobars

KW - Seepage force

KW - Subterranean holes

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U2 - 10.1016/j.advwatres.2022.104182

DO - 10.1016/j.advwatres.2022.104182

M3 - Article

AN - SCOPUS:85129731301

SN - 0309-1708

VL - 164

JO - Advances in Water Resources

JF - Advances in Water Resources

M1 - 104182

ER -