Rock Mechanics - Design for Bolting Stratified Roof

Research on roof bolting has developed significant information with respect to the functions that can be performed by properly installed bolts and the methods that can be used to ensure that effective installation has been achieved. The present paper brings together results that are pertinent to the design of a bolting system for reinforcing horizontally stratified mine roof with vertical bolts. The design approach is based on the use of bolts to decrease the maximum bending stress within an arbitrary sequence of roof strata (see Fig. 2) in which the only loads are the weights of the individual beds. The use of rock bolts to achieve other objectives, such as to stabilize a fractured rock mass on the periphery of a mine opening,3 is excluded from consideration herein. Reinforcing effect of bolts consists of a friction effect and a suspension effect in combination. "Friction effect" refers to reduction of bending in a stratified roof due to clamping action of tensioned bolts, which compress the strata, thereby creating frictional resistance to displacement along planes of stratification. (The flexure of a sequence of strata is necessarily accompanied by horizontal displacement of each bed with respect to its neighbor, along mutual surfaces of contact.) Although the sliding of the beds tends to exert a shearing effect on the bolts, tests show that this has negligible influence on the bending stresses, probably because the bolts are so far apart. "Suspension effect" refers to the transfer of part of the weight of the weaker or thinner strata to one or more thick strata, which occurs when strata with differing tendencies to deflect are constrained to have equal deflection. The term "suspension" is used irrespective of whether the thin strata are above or below the thick strata, because tests show that the supporting effect of the flexurally more rigid roof strata is for practical purposes independent of their position in a bolted sequence of strata. An earlier paper4 dealt with a bolted unit in which all strata had equal flexural rigidity; bolting could develop a friction effect but no suspension effect. The present paper deals primarily with a bolted unit in which all strata do not have equal flexural rigidity, so that bolting can develop both a friction effect and a suspension effect. The reinforcing effect of the bolts was determined by a combination of experimental and theoretical stress analysis.4'6'7 The experimental method consisted of loading a model by rotating it in a centrifuge to simulate the gravity forces exerted about an underground excavation. Models were made from two different limestones, although the results are independent of the material because the elastic constants were taken into account in the data analysis. Electric resistance strain gages were bonded to the highest and lowest members of the bolted unit to determine the outer-fiber bending strains at the center and at the supports. The quantitative results presented herein are based on tests of 56 different models, which included a range of values for the structural parameters. Each model was tested several times, with different combinations of spacing and tension of the bolts. DESIGN EQUATIONS The effects of friction and suspension on the flexure of a bolted stratified roof can be expressed by the following equations, which give the maximum bending stress, the deflection, the friction effect, the suspension effect and the transferred load for any (the i-th) member of the bolted unit in terms of the structural parameters: