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BEHAVIOUR OF DISCONTINUOUS ROCK MASSES

                                          The progressive reduction in shear stress is represented by

                                                                       1            p
                                                                 m =− (  m −   b ) u
                                                                       R
                                        where   m is the prevailing mobilised friction angle,   b is the basic friction angle, and
                                        R is a parameter with the dimension of length, related to joint roughness.
                                          The response to normal loading is expressed incrementally as
                                                                       n = K n  v

                                        where the normal stiffness K n is given by

                                                                     K n =   n     n
                                                                             n
                                        in which   n and   n are further model parameters.
                                          The shear stress and shear displacement increments are related by

                                                                       = FK s  u

                                        where the shear stiffness may also be taken to be a function of normal stress, e.g.
                                                                     K s =   s   n   s

                                        in which   s ,   s are further model parameters.
                                          The continuously-yielding joint model has been shown to have the capability to
                                        represent satisfactorily single episodes of shear loading and the effects of cyclic
                                        loading in a manner consistent with that reported by Brown and Hudson (1974).


                                        4.9 Behaviour of discontinuous rock masses

                                        4.9.1 Strength
                                        Thedeterminationoftheglobalmechanicalpropertiesofalargemassofdiscontinuous
                                        in situ rock remains one of the most difficult problems in the field of rock mechanics.
                                        Stress–strain properties are required for use in the determination of the displacements
                                        induced around mine excavations, and overall strength properties are required in, for
                                        example, assessments of pillar strength and the extent of discontinuous subsidence.
                                          A first approach to the determination of the overall strength of a multiply jointed
                                        rock mass is to apply Jaeger’s single plane of weakness theory (section 4.6) in several
                                        parts. Imagine that a rock mass is made up of the material for which the data shown
                                        in Figure 4.33b were obtained, but that it contains four sets of discontinuities each
                                        identical to the cleavage planes in the original slate. The sets of discontinuities are
                                                          ◦
                                        mutually inclined at 45 as shown in the sketches in Figure 4.49. A curve showing the
                                        variation of the peak principal stress difference with the orientation angle,  , may be
                                        constructed for a given value of   3 by superimposing four times the appropriate curve
                                        in Figure 4.33b with each curve displaced from its neighbour by 45 on the   axis.
                                                                                               ◦
                                        Figure 4.49 shows the resulting rock mass strength characteristics for three values of
                                          3 . In this case, failure always takes place by slip on one of the discontinuities. Note
                                        that, to a very good approximation, the strength of this hypothetical rock mass may
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