Rock Mechanics.pdf - Mining and Blasting

Figure 4.47 Coulomb friction, linear
deformation joint model; (a) normal
stress (n)–normal closure (v)
relation; (b) shear deformation ()–
shear displacement (u) relation.
ROCK STRENGTH AND DEFORMABILITY
(d) The shear strength of a filled discontinuity does not always depend on the thickness
of the filling. If the discontinuity walls are flat and covered with a lowfriction
material, the shear surface will be located at the filling-rock contact.
(e) Swelling clay is a dangerous filling material because it loses strength on swelling
and can develop high swelling pressures if swelling is inhibited.
4.8 Models of discontinuity strength and deformation
In section 4.7, discussion was concentrated on the factors influencing the peak and
residual shear strengths of discontinuities. When the responses of discontinuous rock
masses are modelled using numerical methods such as joint-element finite element
or distinct element methods (Chapter 6) it is also necessary that the shear and normal
displacements on discontinuities be considered. The shear and normal stiffnesses of
discontinuities can exert controlling influences on the distribution of stresses and displacements
within a discontinuous rock mass. Three discontinuity strength and deformation
models of varying complexity will be discussed here. For simplicity, the
discussion is presented in terms of total stresses.
4.8.1 The Coulomb friction, linear deformation model
The simplest coherent model of discontinuity deformation and strength is the Coulomb
friction, linear deformation model illustrated in Figure 4.47. Under normal compressive
loading, the discontinuity undergoes linear elastic closure up to a limiting value
of vm (Figure 4.47a). The discontinuity separates when the normal stress is less
than the discontinuity tensile strength, usually taken as zero. For shear loading (Figure
4.47b), shear displacement is linear and reversible up to a limiting shear stress
(determined by the value of the normal stress), and then perfectly plastic. Shear load
reversal after plastic yield is accompanied by permanent shear displacement and hysteresis.
The relation between limiting shear resistance and normal stress is given by
equation 4.11.
This model may be appropriate for smooth discontinuities such as faults at residual
strength, which are non-dilatant in shear. The major value of the model is that it
provides a useful and readily implemented reference case for static discontinuity
response.
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