The failure criteria and deformational moduli of granular rock

Analytical solutions of stress for composite material are obtained by means of mathematical theory of elasticity, assuming spherical inclusions and uniform displacements of boundaries of representative elements. These solutions show that the failure criteria of composite materials are complicated functions of the elastic moduli of matrix, inclusion and composite, and the volume ratio of matrix and inclusion. Combining this theory with Griffith\u27s theory gives a new criteria for brittle failure of granular rook. This theory appears to provide a nearly perfect model for granular rooks, inasmuch as: a) most assumptions used in other criteria are eliminated, b) most phenomena in failure of brittle rocks can be described theoretically, and c) it is the most logical so far. A simple formula that relates the elastic moduli of inclusion and matrix to the effective moduli of the composite is also derived as a part of the thesis. Comparison with experimental data indicates that it approximates the value better than other approximation formulas --Abstract, Page ii