A Multiplier Method for Identifying Keyblocks in Excavations Through Jointed Rock

Abstract

G. H. Shi and R. E. Goodman have recently pointed out the practical importance of the keyblock principle in supporting underground and surface excavations in jointed rock and have given an elegant procedure involving stereographic projection and graphics for identifying the shapes of keyblocks. This paper presents the mathematical analysis of an entirely different keyblock characterisation and identification algorithm. The characterisation rests upon Tucker’s Theorem of the Alternative, and the algorithm requires only the execution of a few linear programming type pivot operations and sign tests.