Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 50

On the right-hand side of this straight line the criterion for shear failure applies while
stress states corresponding to a point on or left of this straight line lead to a tensile failure.
This combination of criteria for tensile and shear failure is referred to as the “tension cut-
off criterion”.
The Hoek-Brown criterion for tensile strength of intact rock is obtained by putting σ 1

= 0 in (3.22) and solving the resultant equation for σ 3 = - σ tIR (Hoek & Brown 1980a):

(3.24)

The tensile strength of intact rock is usually assumed to be in the order of 1/10 of the
un confi ned compressive strength. This assumption is motivated by the two-dimensional
theory of brittle failure from Griffi th (1921) predicting that the unconfi ned compressive
strength is 8 times the tensile strength, and its three-dimensional extension by Murrell (1963)
leads to the result that the unconfi ned compressive strength is 12 times the tensile strength.

Shear and tensile strength of intact rocks with planar grain structure
The Mohr-Coulomb failure criterion is also used to describe the shear strength on the
isotropic plane of intact rocks with planar grain structure. It is formulated for the resultant
shear stress

τ res in this plane and the corresponding normal stress σ n acting on this plane:

(3.25)

In the general case τ res must be determined from the three-dimensional stress

state described in the global coordinate system (x,y,z). To this end a transformation of
the stress vector {

σ n and

} in the global coordinate system (x,y,z) into the coordinate system
related to the orientation of the isotropic plane (x',y',z') according to (3.6) must be car-
ried out. Thus,

σ

σ n and τ res are functions of σ x , σ y , σ z , τ xy , τ yz and τ zx (Wittke 1990).

In the special case that the two principal normal stresses σ 3 are vertically and

horizontally oriented, respectively, and lie within the plane perpendicular to the isotropic
plane, which is inclined at an angle

σ 1 and

β , the stress components σ n and τ res are functions of

σ 1 , σ 3 and β :

(3.26)

(3.27)