Stress Ratios in Entire Mine Stopes with Cohesionless Backfill: A Numerical Study

Evaluation of stress states in backfilled mine stopes (or similar openings), using arching theory, can be largely impacted by the value selected for the earth pressure coefficient, K = σh/σv. Recently, the current study’s authors addressed the debate about the value of K near the opening center, based on Rankine’s active coefficient (Ka) and at-rest coefficient (K0). Here, stress ratios in vertical backfilled stopes are numerically assessed (in two dimension, 2D), considering both the independent and related backfill internal friction angle (φ′) and Poisson’s ratio (ν). Emphasis is placed on the backfill state near stope walls, where local rotation of stresses occurs, so the coefficient (K) and principal stress ratio, Kps (= σ3/σ1), should be distinguished. Parametric analyses indicate that values of K and Kps depend on the position and the relationship between φ′ and ν. Near the opening center, K (= Kps) is close to Ka when ν or φ′ is below a critical value; otherwise the value approaches K0, defined from ν. Near both walls, Kps is always close to Ka, while K is near K0 for related ν − φ′ cases and depends on their respective values for independent ν and φ′. Additional simulations conducted with interface elements indicate that the stress ratios near the opening center line are insensitive to interface roughness and are almost identical to values obtained without interfaces, but the stress ratios near walls may change for less rough or smooth interfaces.