Stability of Rock Wedges and Excavation Surfaces - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 303

(11.35)

Equation (11.35) still contains the unknown angles ε i which, according to Fig. 11.14,

can be expressed by the angles β Ii and ϕ i :

ε i = 90° + β Ii - ϕ i . (11.36)

Equation (11.35) thus forms a system of n equations for the 2n unknowns

ϕ i
(i = 1,...,n). 0 appearing in the equation for 1 is either equal to zero or equal to a
known external line force F with opposite sign. The corresponding angles

i and

ε 0 , β I0 and ϕ 0

are known since they are related to F (Fig 11.13).
The required anchor force A d to stabilize the rock mass is applied to the lowest block n
and therefore is equal to n (Fig. 11.13). In consideration of

(11.37)

and

(11.38)

sin( ε n + β Dn ) can be replaced by sin α and cos( ε i + β Dn ) by -cos α . Thus, setting i = n the

required anchor force is obtained from (11.35) as

(11.39)

Only if A d 0 is an anchor force required. Otherwise the rock wedge is stable.

To solve the equation system (11.35) the angles

>

ϕ i are expressed as functions of the
forces i . For this purpose, i are resolved into the components normal and parallel to
the internal failure lines (Fig. 11.14):