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BEHAVIOUR OF DISCONTINUOUS ROCK MASSES

                                        illustrate the criterion’s application in practice. A further update was given by Hoek
                                        et al. (2002). The summary of the criterion given here is based on these accounts and
                                        those of Marinos and Hoek (2000) and Brown (2003).
                                          In effective stress terms, the generalised Hoek-Brown peak strength criterion for
                                        jointed rock masses is given by:

                                                                                   2 a

                                                                =   + m b   c   3 + s                 (4.37)



                                                               1   3               c
                                        where m b is the reduced value of the material constant m i (see equation 4.25) for the
                                        rock mass, and s and a are parameters which depend on the characteristics or quality
                                        of the rock mass. The values of m b and s are related to the GSI for the rock mass (see
                                        section 3.7.4) by the relations
                                                          m b = m i exp{(GSI − 100)/(28 − 14D)}       (4.38)
                                        and


                                                             s = exp{(GSI − 100)/(9 − 3D)}            (4.39)
                                        where D is a factor which depends on the degree to which the rock mass has been
                                        disturbed by blasting or stress relaxation. D varies from 0 for undisturbed in situ rock
                                        masses to 1.0 for very disturbed rock masses. For good quality blasting, it might be
                                        expected that D ≈ 0.7.
                                          In the initial version of the Hoek-Brown criterion, the index a took the value 0.5 as
                                        shown in equation 4.25. After a number of other changes, Hoek et al. (2002) expressed
                                        the value of a which applies over the full range of GSI values as the function:

                                                           a = 0.5 + (exp −GSI/15  − exp −20/3 )/6    (4.40)

                                        Note that for GSI > 50, a ≈ 0.5, the original value. For very low values of GSI, a →
                                        0.65.
                                          The uniaxial compressive strength of the rock mass is obtained by setting   to

                                                                                                        3
                                        zero in equation 4.37 giving
                                                                       cm =   c s a                   (4.41)

                                        Assuming that the uniaxial and biaxial tensile strengths of brittle rocks are approx-
                                        imately equal, the tensile strength of the rock mass may be estimated by putting
                                          =   =   tm in equation 4.37 to obtain


                                         1    3
                                                                                                      (4.42)
                                                                     tm =−s   c /m b
                                        The resulting peak strength envelope for the rock mass is as illustrated in Figure 4.50.
                                        Because analytical solutions and numerical analyses of a number of mining rock
                                        mechanics problems use Coulomb shear strength parameters rather than principal
                                        stress criteria, the Hoek-Brown criterion has also been represented in shear stress-
                                        effective normal stress terms. The resulting shear strength envelopes are non-linear
                                        and so equivalent shear strength parameters have to be determined for a given normal
                                        stress or effective normal stress, or for a small range of those stresses (Figure 4.50).
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