Analytical Expression for Vertical Stress within an Inclined Mine Stope with Non-parallel Walls

Arching is a phenomenon that occurs in many situations in geotechnical engineering. When underground mine stopes are backfilled, a significant fraction of the self-weight of the backfill is carried by the side walls. As a result, the vertical stress at the bottom of the stope is significantly less than its overburden pressure. Few analytical expressions published in the literature can be used to determine the vertical stresses of stope with parallel walls. The objective of this paper is to extend the analytical solution previously developed by the authors to long plane-strain stopes with non-parallel walls with both slopes leaning to the same side. Different combinations of wall inclination are examined using the new analytical expression developed. To validate the analysis, the proposed results are compared with numerical model results. The results show that the proposed analytical expression is capable of estimating the vertical stress within mine stopes when the inclination of the hangingwall to the horizontal (α) is less than that of footwall (β). An important behavioural trend for the stress distribution is observed, where with the same overburden pressure and base width, the stress magnitude experienced by fill material significantly varies depending on the wall inclination.