Stability of asymmetric roof wedge under non-symmetric loading

An analytical method is presented for the calculation of the load carrying capacity of two-dimensional asymmetric rock wedges when the loading on the joint faces is non symmetric, such as the case of an asymmetric wedge formed in the roof of a circular tunnel in an inclined stress field. The pull out force that causes yield at one of the joint faces is evaluated from formulae based on the limiting equilibrium conditions assuming a purely frictional joint resistance. Next, the total pull out force required for the secondary face to yield is calculated. During this step, the wedge is further displaced and while the primary yielding face is plastically deformed, the other face is still in the elastic range until failure. Validation of the analytical procedure is obtained with the UDEC code, which provides an implementation of the Distinct Element Method in two dimensions. When the assumptions made in the analytical procedure are valid, the analytically calculated values for the pull out resistance of the wedge are computed to be close to the numerically obtained ones.