| Since block theory was brought forward formally by Richard. E. Goodman and Gen-hua Shi in 1982, it has been becoming an important method in analysis of rock engineering stability as more and more scholars research and use it. The dissertation reviews and summarizes systematically the status of research and application of block theory at present, analyzes the problems or difficulties which should be studied further. Based on these, as well as the computational codes collected up, some basic problems are studied and new methods are developed, containing morphological analysis of concave block, geometrical search and statistical analysis of stochastic block, block reliability analysis considering simultaneously randomness of mechanical and geometric properties of discontinuities, development of engineering analytical software, and approaches of application in engineering as well. The achievements of the dissertation are creative and of theoretical and practical values.1. Morphological analysis of concave block. The issue was involved less in the past and is critical in application of block theory. Two methods are put forward in the dissertation. The fist fulfills the morphological analysis by means of proposed classification of the concave zones of concaves, proposed discriminant rules of existence of intersections of face and face, sorting of intersections, and some other procedures. The volume of block and area of block faces are calculated also. The second method is named as block adding and block subtracting. The basic operation rules of block adding and subtracting, algorithm of adding and subtracting of face and face as well are brought forward. And with the procedures of uniformly numbering of faces and intersections and so on, the much more complex block can be created by putting the comparatively simple blocks together. At last, the methods of morphological analysis of complex block are used to construct located block in slope and cavern, a number of located blocks in slope or cavern can be shown visually and simultaneously. The methods of morphological analysis of concave block are useful supplements to block theory and can be referred by the same researches.2. Geometrical analysis of stochastic block. The complicated features and statistic distributions of mechanical parameters of discontinuities in rock messes are discussed, as well as the geostatistic analysis methods and probabilistic distributions of trace lengths, spacings and orientations. Then, based on the latest research works, three-dimensional simulating network of joints is accomplished. On the basis of simulating network, the realistic 3-D stochastic blocks are searched by means of the procedures of analysis of relations between half-plane of trace and half-space of joint, tree cutting, closed loop searching, analysis of the probable maximum region of blocks, and the proposed method of combination of intersections, the proposed judgment method of rotation directions or spatial positions of intersections. Some other problems are studied such as blocks searching which are located in the crosses of slope surfaces or the arch roof of cavern. Hence, the technologies of geometrical analysis of stochastic blocks in slope or underground space are achieved.On the basis of the geometrical searching of stochastic block, the size, average size of block, and ratio of overlay area of faces of blocks to excavation surface are analyzedstatistically and the contribution characteristics are obtained. Then the probabilistic distribution models are inferred and validated. The statistic analysis of stochastic blocks is valuable for quantitative estimations of harmfulness of blocks and analysis of support design.3. Reliability analysis of stochastic block. The reliability analysis method is put forward which takes simultaneously the random variations of the geometrical and mechanical parameters of geological discontinuities into account. The dip, as well as friction modulus and cohesion are considered as random variables in th...
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