The deflection and factor of safety against snap through of an underground roof rock beam depends on its geometry, on its mechanical properties and on its lateral constraint at the abutment. The solution for a rigid abutment is known. For a complying abutment the lateral resistance will provide a lower resisting couple. The deflection of the rock beam, the lateral strain at the abutment and the safety factor against snap through are investigated analytically. Finally numerical model studies are performed in order to evaluate and illustrate the trends in deflection increase and factor of safety decrease due to the compliance of the abutment.


La deflexion et Ie facteur de securite d'une poutre de toit au flambage dependent de sa geometrie, ses proprietes mecaniques et ses contraintes laterales a I'aboutement. La solution pour un aboutement rigide est connue. Pour un aboutement tendre la resistance laterale fournit un couple de resistance plus faible. La deflexion de la poutre rocheuse, la deformation latera Ie a I'aboutement et Ie facteur du securite au flambage ont ete examinees analytiquement. Enfin, pour I'evaluarion et I'illustration de I' agrandissement de la deflexion et la diminution du facteur de securite a cause de la deformation de I' aboutement, plusieurs models numeriques ont ete etudies.


Die Durchbiegung und der Sicherheits Faktor zu Verbiegung einer unterirdischen Firstenkappe hangt von seiner Geometrie, seiner mechanische Eigenschaften und seinen Seitenzwang am Widerlager an. Das Ergebniss fur einen steifen Widerlager ist bekannt. Fur einen weichen Wider lager der Seitenwiderstand erweist ein kleineres Widerstand Moment. Die Durchbiegung des Felsbalkens, die seitliche Verformung am Widerlager und der Sicherheits Faktor zur Verbiegung sind theoretisch untersucht. Zum Ende, sind, mit dem Vortrag rechnerischen Modellen, die Vergrosserung der Durchbiegung und die Verkleinerung des Sicherheits Faktors bewertet und graphisch presentiert.


Orebodies in sedimentary environments are usually conformable with the stratification, which is conferred by persistent bedding planes. The latter have low or zero tensile strength in their normal direction and low shear strength of their surfaces. Models of jointed roof beds showed that beds near the immediate roof of an underground opening behave as individual ones, whereas the stresses due to the weight of the overlying strata are deviated to the sidewalls, a phenomenon called arching. Natural cross joints or induced transverse fractures do not allow the simulation of roof rock beams as continuous ones; the stability against bending of such a beam depends on a couple of constant thrust forces at two cross sections and a changing with distance from the abutment lever arm of the thrust line. The lower the lever arm the larger has to be the thrust and the compressive stress in the rock in order to obtain stability of the roof beam. These beams usually fail in shear or crushing or buckling. Sofianos (1996) developed a closed form solution for the bearing capacity of the hard rock voussoir beam roof supported at rigid abutments. This depends on the span s and the thickness t of the rock beam, the modulus of deformability E, the unit weight y of the rock mass and the limiting strain or strength parameters of the rock at the fracture planes. In table 1 the minimum values of the beam thicknesses t against snap through failure, according to this solution, are given for four selected spans and for the chosen modulus of deformability and unit weight of the rock.

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