OFR-123(3)-81 Finite Element Analysis Applied To Resin And Mechanical Roof Bolting Systems For Strata Bound Deposits - Volume III - Appendix C - An Elasticity And Finite Element Study Of The Fully-Grouted Resin Roofbolt Under Transverse Loading

A new analytical model for the shear stiffness at a joint of the fully-grouted resin roofbolt is developed using the Theory of Elasticity and an analogy to a beam on an elastic foundation, Gerdeen [2]. The model developed in this study treats the elastic foundation modulus of the resin as being composed of both an elastic rock and an elastic resin. All previous attempts have neglected the elasticity of the rock and treated only the resin. A three dimensional finite element model of the bolt-resin-rock system is developed also and comparisons are made between the predictions made by it and the analytical solution. It is found that the agreement between the two representations ranges between 1.2% and 10.5%, with the greater differences being observed for systems of very large or very small bolt diameters and resin annulus thicknesses. Since such configurations are not the rule in practice parameter studies are performed using the analytical solution with the finite element solution being used as a check. For a 0.75 in. bolt, a resin annulus thickness of 0.1375 in., a resin with E = 7 x 105 psi and -1) = 0.210, and a rock of modulus E = 6.8 x 106 psi and V = 0.159 the shear stiffness is found to be 1.220 x 106 lb,/in, from the analytical solution and 1.245 x 106 lb,/in, from the finite element model. Applying the finite element model to the problem of the axial stiffness of the fully-grouted resin roofbolt a value of 6.002 x 106 lb./in. is obtained which proves to be at least 50% higher than any of the now existing analytical predictions.