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in the roof as outlined by Obert and Duvall in 1967. The beam <br />theory utilized in this model does not adequately account for pre- <br />existing fractures and discontinuities in the rock. State of the art <br />engineering procedures in roof design today indicate that these <br />discontinuities are extremely important in controlling the behavior <br />and performance of the roof area. However, detailed information on <br />such discontinuities will not be available until such time as the <br />actual mining process has begun. Therefore, the beam theory approach <br />has been utilized solely to illustrate the relative effects of various <br />different t}°pes of roof reinforcement in the strata observed at the <br />location of Test Boring No. 3. <br />This procedure does assume that the rock strata in the roof area <br />will deform as elastic beams, with their deflection and the develop- <br />ment of stresses controlled by the density, thickness, and the value <br />of Young's modulus for each strata. It is further assumed that the <br />strata will reach a point of incipient failure when the theoretical <br />bending stresses developed in each strata reach the modulus of rupture. <br />Our first analysis deals entirely with stresses developed in <br />an unsupported, unreinforced roof section. Tunnel drifts and inter- <br />section areas were considered separately. Maximum indicated safe <br />spans were determined over a factor of safety range of from 9 to 6. <br />we have also considered separately the condition of the removal of <br />the thin shale layer immediately above the coal, and the suspension <br />of the shale layer. Results of this analysis will be found in Table <br />No. 1 in Appendix C. This indicates that ignoring the effect of pre- <br />existing fractures and discontinuities in the rock, fairly large <br />unsupported spans would be plssible in the tunnel drifts with rela- <br />tively large factors of safety. [when one accounts for the stress <br />S <br />