Discussion of Papers Published Prior to 1956 - Analysis of Roof Bolting Systems Based on Model Studies

If we assume that testing of the model started at time t1, that time t2 was the instant at which the elastic limit of the material was passed at the points of the maximum stress, and that at time t3 the failure of the model was completed as shown in the typical photograph (Fig. I), then actually the photograph shows the final results of what took place between time t2 and t3. By the principle of similitude all conclusions drawn from the behavior of the model were applicable and valid for actual mine roofs up to the time t2 after time t2 motions and friction came into play during the destruction of the model. The events between t2 and t3 and the photograph itself are not representative of the events expected in an actual mine roof unless corrections imposed by the principle of similitude are made. It can therefore be stated that all conclusions and observations of the author from the photographs are applicable only to his small-scale experiments and not to actual mine roofs. Without investigation of the true stresses or the combined maximum stress induced in the beds it has been assumed by the author that failure occurred solely due to bending stress caused by loading of the beds. (The author states that D was taken to be the theoretical strain given by elementary beam theory.) Fig. 1 shows that the beds were clamped together. This clamping was necessary to prevent slipping of the beds due to the horizontal shear. However, this clamping caused an uncontrolled and undertermined com-pressive stress S at the end of the beds, and this com-pressive stress caused a true tensile stress ?S (? PoiS-son ratio). This true tensile stress combined with the tensile stress produced at the end of the beds due to loading (fixed beam uniformly loaded), and the horizontal shear which is maximum at the end appears to be the most probable maximum stress produced in the beds. It is therefore evident that the author in performing this experiment has introduced stresses in the model not existing or dissimilar to actual mine roofs, and therefore his conclusions may be applicable to his small-scale experiments but inapplicable to actual mine roofs. Louis A. Panek (author's reply)—The discusser's difficulty is related to mechanics of materials rather than similitude. The effect of time did not enter into the tests in any way, being simply excluded from consideration in this study, because all quantitative results entering into the design equations are based on measured (between time t1 and time t2) bending strains that are well below the breaking strain (i.e., in the elastic range) for the model material. Time does not become a significant factor until the rock stress reaches 80 to 90 pct of the breaking stress." The objective of this investigation was not to predict that bolted roof will fail after time t, but was instead to develop a safe roof, that is, roof in which the bending strain is much less than (say less than 50 pct of) the breaking strain. The models tested to failure had no direct bearing on the design equations. Although for some rocks time may influence the magnitude of stress or strain at which fracture occurs, breaking stress or breaking strain values were not employed for any purpose in this investigation. Tests to failure were made only to obtain additional evidence regarding the behavior of the bolted laminae' as evinced by the locations of the cracks. As stated in the last paragraph of the paper, if one wishes to predict the time or stress conditions for which the roof will fail, additional information is required. The reason for clamping the laminae is to make them behave liked clamped beams, which closely approximate the clamped-plate condition of the actual mine roof beds (Ref. 5, p. 1; Ref. 6). The writer has previously demonstrated that the bending stresses induced by centrifugal loading in a clamped model beam are in agreement with those predicted by theory;' hence clamping has no significant effect on the bending ,trains measured during a test. Moreover, actual ,in, roof beds are likewise subject to a clamping effect due to weight of superincumbent strata carried by the pillars or ribs on each side of the opening. It is emphasized that this study was restricted to evaluating only the reinforcing effect produced by the bolts. Procedures employed in the experiments and in the data analysis were such as to deliberately exclude the effects of other factors. The objections offered are therefore invalid,