Consider a vertical shrinkage stope W (ft, m) wide, H (ft, m) high filled with muck having a specific weight along a strike length

Consider a vertical shrinkage stope W (ft, m) wide, H (ft, m) high filled with muck having a specific weight γ along a strike length of L (ft, m). Further suppose wall friction angle φ' and angle of internal friction φ apply. Cohesion of the muck and adhesion at the stope walls is negligible.

(a) Derive a Janssen-type formula for this specific situation per unit of strike length.

(b) If the stope is 35 ft (10.7 m) width, 120 ft (36.6 m) high, and 165 ft (56.3 m) along the strike, φ_ = 30◦, φ = 37◦, γ = 105 pcf (16.6kN/m3), estimate the vertical stress, horizontal stress, and shear stress at the bottom of the muck.

(c) If water infiltrates the stope, modify the “dry” formula from (a) and recalculate the bottom stresses in (b).