LIMITING STRENGTH OF ROCKS UNDER STRESS 123 
The systems of surfaces of shear corresponding to each of the 
above cases are shown as (i), (ii), and (iii) in Fig. 1. The cracks 
developed by failure in each of the above ways as they would 
appear on the cylindrical surface, over a cross-section perpendicular 
to the axis and over a section through the axis are represented by 
the diagrams (i), (ii),-and (iii). 
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Fic. 1 
The surfaces of shear developed in a cylinder under test will 
depend on which of the stress-differences is a maximum, a condition 
determined by the elastic constants of the rock and also by the 
nature of the nickel-steel boundary. As soon as this maximum 
stress-difference has attained a limiting value characteristic of the 
material, and determined to some extent by the boundary conditions 
the corresponding families of surfaces of shear will make their 
appearance. 
Considering first the stresses in the rock specimen, the radial 
displacement U satisfies the equation 
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