Seepage to staggered tunnels and subterranean cavities: Analytical and HYDRUS modeling

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.