Engineering Rock Mechanics

2 70 Rock reinforcement and rock support

1.06 -

1.04 -

5 1.02 -

9

g 1.00 -

2

u- 0

0

0.98 -

0.96 -

0.94

If we consider T cos p to be a positive restraining component, then we
have

N= Wcos@+fsinj?, andS= Wsin@

leading to

(W cos y? + T sin /I) tan @ + T cos j?

W sin y?

F, =

for the factor of safety.

(b) For the case of a factor of safety of 1, these expressions rearrange to

sin@ -cos@tan@

cosj? + sinp tan@

sin @ - cos @ tan@

cosp + sinj? tan@

T, = W and Tr = W

which are identical. With W = lo00 kN, j? = 15", @ = 42" and @ = 36",

the bolt tension required is 112.0 kN.

(c) Evaluating the two expressions for factor of safety over a range of

values for the tension gives the results shown in the table below. These

results are plotted in the following diagram.

• Negative actuating component


• 
  
  
  
  • 
    
    
    
    • Positive restraining component
    
    
    
    
  
  
  
  

T (I&): 87.0 97.0 107.0 117.0 127.0 137.0