Analytical approaches for studying the stability of laminated roof strata

This paper presents two analytical approaches for studying the stability of voussoir beams by taking into account the horizontal loading condition of the beams: with and without horizontal in-situ stresses. For beams without being subjected to horizontal stresses, a bilinear truss represents the compression arch formed in the voussoir beam. The stability of the compression arch is analysed by the energy method. An iteration algorithm was proposed for the solution. The results of the approach are verified with UDEC simulations as well as experimental results. For beams subjected to horizontal in-situ stresses, the classic beam theory was employed to study their behaviour. The assumptions for the analytical approaches are verified by numerical simulations. The study shows that an increase in the Young's modulus of the beam rock improves the stability of the beams against buckling. However, it elevates the stresses in the horizontal direction within the compression arch, which may result in crushing failure in the beam abutments and the midspan. Low horizontal in-situ stress reduces the risk of beam buckling but increases the risk of sliding at the abutments. However, high horizontal in-situ stress may cause either beam buckling or crushing failure in the abutments. The developed analytical approaches would be applicable for roof stability analysis in stratified rocks.