umbrella vault is an architectural term, I think I would say arched back in a mining context, the idea being the same in both cases: arched roofs are stronger than flat ones, and they are mining in bad ground.

This (aka "tubes préforés") involves drilling horizontal/subhorizontal holes ahead of the face of the adit/tunnel, along the line of the roof (usually arched), and installing steel pipes in them which may be mechanically anchored or grouted into place, then excavating beneath them. They therefore serve to consolidate the roof the excavation pre-excavation.

From my notes: a variety of terms gleaned from the literature (Tunnels&Tunnelling International, Civil Engineering International, ICE Proceedings on the Channel Tunnel, etc.) over the years, take your pick:

Tubes préforés Ou voûte parapluie q.v. Forepoling (steel), spiling ("reinforcing rods form a canopy to stabilize the crown", CW,1.9.93,p11) [TTI,9.99,p.7], pipe injection protection shield [TTI,11/98,p.35], spile bars [TTI,5/99,p.21,64], spile pins [CEi,4/2000,p.14], canopy of interlocking steel pipes [TTI,12/99,p.33], canopy tubes [TTI,2/00,p.8]

Tubes de soutènement Voir Voûte parapluie, tubes préforés

Voûte parapluie Also tubes préforés Forepoling, "Umbrella" pipe shield, forward-driven spiles [ChanTun1,p30,P5] - technique used to start tunnels or in the vent of cave-ins, involving drilling holes approx. 20cm outside the roofline and inserting pipes (spiles: BS, Waltham) which support the roof while excavation takes place beneath, until permanent lining is erected. Cf. Protective hood (axial holes), protective umbrella (radial holes) [Channel Tunnel 1,p74], forward umbrella, horizontal micropiles, micropile arch [CEi,10/96p24], umbrella [CEi2/97p24 ], umbrella jet grouting [CEi,10/96p18], spile bars [TTI,5/99,p.64], pipe roof [TTI,9.98p.29], pipe arch [TTI,9.98p.38; Jubilee,p.37]; pipe-jack umbrella, pipe-jacked arch [Jubilee,p.44], umbrella arch [Web]