Stability of Rock Wedges and Excavation Surfaces - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 293

to obtain the so-called “design values” of φ D and c D , where γ φ > 1 and γ c > 1 are

denoted as “partial safety factors” of φ D and c D . This method of reducing the shear

strength, known as the “Fellenius rule”, was introduced by Fellenius (1927) when inves-
tigating the stability of slopes.
In order to assess stability of the wedge the so-called “utilization factor” μ is intro-

duced, defi ned as

(11.6)

where T D is the driving shear force acting parallel to the sliding surface and T R is the
resisting shear force along the sliding surface resulting from the shear strength of the
discontinuity. The wedge is considered stable if μ ≤ 1. At limit equilibrium μ is equal to

1. For μ < 1, a higher safety margin, as required, is available. If μ > 1, the wedge is not

considered stable and is equivalent to the reciprocal value of the safety factor used in

the global safety concept setting the partial safety factors equal to 1.
The geometry of the wedge illustrated in Fig. 11.5 defi ned by h,

μ

δ and ε leads to a weight

per meter that can be calculated as (Wittke 1990)

(11.7)

in which is the unit weight of the rock wedge.

Equation (11.6), in consideration of (11.2) and (11.3), indicates that for c D,d = 0

γ

μ is

independent of G and thus of size and shape of the wedge:

(11.8)

Condition μ ≥ 1 applied to Equation (11.8) is equivalent to the condition φ D,d ≤ β D that

is the condition for sliding on a plane inclined with angle β D .

If the wedge, in addition to self-weight, is loaded by a water load W per meter resulting
from hydrostatic uplift and seepage forces (Fig. 11.6) the stability of the wedge is as-
sessed by means of the following utilization factor:

(11.9)

W acts normal to D and therefore has no component parallel to D (Fig. 11.6). W can be
approximated by a linear distribution of water pressure acting along the sliding surface
up to its intersection line with the phreatic surface. The location of the phreatic surface
can be calculated by an FEM seepage fl ow analysis (Sections 10.6 and 10.7.2). Using the
notation given in Fig. 11.6 yields: