Stability of single openings in horizontally bedded rock

Abstract This article gives the mathematical solutions of deflection, bending moment, and longitudinal fibre stress of seven different configurations of single- and multilayer roofs in horizontally bedded rock. The work, based on the theory of elastic beams on elastic supports, shows the importance of abutment compression in contributing to the deflection of the roof layers. When the ratio of the thickness of the individual layers, H , to the span of the working room, l , exceeds l /2 the theory becomes inexact. By using the finite element method it was found that the extreme fibre tensile stress is equal to the uniformly distributed load on the roof layer for H/l greater than 1.5. For ratios between these limits the actual tensile stresses can be determined from stress concentration diagrams. The theories for single- and double-layer roofs have been verified by model experiments. Two types of experimental equipment set-ups were used: ( 1 ) involving a uniform load on the top surface of the model; and ( 2 ) involving runs under controlled conditions in a high-capacity centrifuge. The model experiments in a centrifuge together with finite element theories display the difference in failure mode between thin and thick roof layers. Vertical to subvertical fissures in regions with high bending moments, that is in the roof centre and above the abutment, precede the collapse of a thin roof layer. High shear stresses appear above the abutment in thick roof layers ( H > l/2 ) which give rise to arching over the opening. The theories and results from model experiments are now being put into practice at the lead mine of Laisvall, northern Sweden. Results from present precise leveling and differential roof sag (sag differences from layer to layer) measurements in the face excavations are in accordance with results from proposed theories.