Block theory and its application

Block theory is a geometrically based set of analyses that determine where potentially dangerous blocks can exist in a geological material intersected by variously oriented discontinuities in three dimensions. It applies ideally to hard, blocky rock in which blocks of various sizes may be potential sources of load and hazard in an excavation or foundation. Block theory also can apply to rocks that are highly porous, weathered and fissured, and it may have applicability to some soils. The lecture discusses problems faced in attempting to characterize blocky rock and reviews some methods for gaining adequate data about joint systems. The underlying assumptions of block theory are examined in relation to recent developments and refinements. The main ideas of block theory are reviewed, as are their application to finding and describing key-blocks of tunnels, slopes and foundations. Both translational and rotational analysis are covered, the latter being a recent enlargement of block theory. Examples of practical problems that can be solved using block theory are identifying and analysing problems of safety posed by actual blocks in foundations of existing dams, finding design blocks for laying out and selecting supports for tunnels in complexly jointed rock masses, finding the minimum safe thickness of a pillar between parallel excavations, estimating real key-block regions for tunnels of different size in joint systems that are not infinitely long, and finding the optimal directions for tunnelling or shafting through a rock mass. Some illustrative cases are introduced.