Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 78

el is reversible, while all other strain components

ε IR vp ,

The elastic strain component ε

ε D1 vp ,…, ε DN vp are irreversible. The total strain

tot of jointed rock is obtained by the

ε

superposition of all these strain components.

Figure 3.23 Rheological model and strain components of a jointed rock mass with N discontinuity sets

Elastic behavior
The elastic constants of the rock mass in a homogeneous model are related to the ave-
rage stresses and strains. They differ generally from the elastic constants of the intact
rock. This particularly applies to Young's moduli and shear moduli which, in general, are
smaller than those of the intact rock due to the higher deformability of the discontinuities.

The infl uence of discontinuities on the deformability of a rock mass separated by one
discontinuity set is demonstrated in Fig. 3.24. If a compressive stress

σ n is applied nor-
mal to the discontinuities the total normal strain of the rock mass according to the
homogeneous model is composed of the normal strain of the intact rock

ε n,IR and the

normal strain ε n,D of the discontinuities leading to

(3.84)

where δ n,D is the change of apertures

of the discontinuities. s is the spacing of the discontinuities, which is assumed to be a
constant and E n is the so-called “equivalent Young's modulus”, also referred to as the
“deformation modulus”, for a loading normal to the discontinuities. If the rock mass is
subjected to a shear stress

δ n,IR is the compression of the intact rock and

τ res parallel to the discontinuities the total shear strain of the
rock mass according to the homogeneous model is composed of the shear strain of the
intact rock

γ res,IR and the shear strain γ res,D of the discontinuities leading to

(3.85)