General stability criteria for unsupported cavity cross-sections in bedrock are given. For a special class of cross section then terms and statements are discussed by the aid of which stability investigations on the cavity contours are to be carried out. This is followed by the introduction of an optimization model serving for the determination of stable and optimal forms of cross section. Simultaneously, this model yields a new method for estimating the support load. With the aid of a graphic method of solution and using example the practical significance of the research results is pointed out.

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