Generalization of Mauldon's and Goodman's Vector Analysis of Keyblock Rotations

Abstract

Development of the three-dimensional vector analysis of keyblock rotations is presented and described for tetrahedral blocks. The possibility to incorporate loads of every kind is introduced by using rigid body dynamics. This allows the designer to take into account couples and forces that are not applied to the centroid of the block, such as those caused by reinforcement, seepage, and external water pressures. Closed-form solutions are propounded for conditions for rotatability, mode analysis, and stability analysis. It is shown that this procedure can be added easily to the usual block theory analysis. From a design point of view, it needs to address only those keyblocks that are either stable to translation even without friction (type III) or stable to translation with sufficient friction (type II). Also it is found that blocks actually can be unstable, even if regarded as stable according to previous theories that either disregarded rotatability or assumed that the point of application of the resultant be the centroid of the block. A numerical example taken from a practical field case rounds off the presentation of the procedure.