201414288677 A description turning now to the detailed description of the preferred arrangement or arrangements of the present invention it should be understood that the inventive features and concepts may be manifested in other arrangements and that the scope of the invention is not limited to the embodiments described or illustrated the scope of the invention is intended only to be limited by the scope of the claims that follow the mode i stress intensity factor k i is given for 2 d plane strain crack geometries by or its mathematical equivalent in which u03c3 is the driving stress or pore fluid pressure and a is crack half length although this expression can be modified for non plane crack geometries e g three dimensional 3 d crack shapes by either a multiplicative factor or polynomial expression or by a more complete stress analysis e g kanninen and popelar 1985 it is not necessary since that will be incorporated directly into the calculation of crack opening displacements widths below the stress intensity factor for a perfectly brittle rock is given by 6 with u03c3 being the yield strength corresponding to the rock 39 s tensile strength and ei 1 0 substituting the value of peak or ultimate stress into 6 provides an estimate of the apparent stress intensity factor for the ductile rock k ductile this approach is justified because it implicitly incorporates the inelastic deformation mechanisms that control the value of ultimate failure strength in a ductile rock combining 3 and 6 leads to which illustrates.