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The report presents a method of utilizing the Coulomb strength criteria for estimating the strength and stability of pillars and pit slopes containing planes of weakness. It is assumed that the Coulomb theory, as a special case of the Mohr envelope, is a satisfactory first approximation of failure in uni-axial compression or triaxial loading with low lateral loads. Accepting this assumption for brittle materials, an expression for the strength decrease of rock pillars containing a plane of weakness or fracture at any angle of orientation is derived. As few as six samples (three solid cores and three fractured cores at a failure-oriented angle) are required for testing uniaxially and triaxially to statistically determine the coefficients of friction and the shear strengths of both the solid rock and the fracture plane and the range of failure angles of the fracture plane. Plots of either the strength or strength ratios against fracture angles obtained from oriented drill core samples gives a useful first approximation of strength decrease due to fracture. Using the same test conditions for both fractured and unfractured material increases the validity of the tests. (Author)