To safely and efficiently carry out the discharge of excavated earth and sand resulting from the propulsion of a propelling apparatus in a construction work of laying a deeply sloped pipeline, etc., using the muddy-water-supplied propelling apparatus.

Highly concentrated muddy water is supplied from a ground unit to stabilize a working face 5 that the front face of the propelling apparatus 10 faces. Excavated earth and sand resulting from cutting work by the working face 5 of the propelling apparatus 10 on excavation is taken into a discharged soil reservoir 15 in the propelling apparatus 10. Excavated earth and sand reserved in the discharged soil reservoir 15 is then mixed in a mud transfer/discharge pipeline, which is constructed by connecting a mud transfer pipe to a mud discharge pipe 22, to form circulating muddy water. This circulating muddy water is sucked under negative pressure into the mud discharge pipe 22 by a spiral pump 29 disposed therein, and is pressure transferred up to the ground through the mud discharge pipe 22.