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Excavation process - time dependent

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Hi,
I am trying to model a real-time excavation of a borehole. Assuming that at the time t = 0, the drilling begins and at time t = 1 day, the tunnel advancement is 1 m (drilling velocity = 1m/day). Imagine that I build a cylindrical mesh inside a cubbic mesh. The outer surface of the cylinder is where the drilling is initiated. The drilling advancement is along the cylinder. What the boundary conditions I should use in the outer surface of the cylinder to simulate the drilling process? Thanks.

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