Engineering Rock Mechanics

380 Design of underground excavations

proaches the maximum allowable, it will induce shearing immediately
below the horizon and hence the injected water will flow downwards. As
a result, if the water is to be retrieved, the production boreholes will need
to be located below the injection boreholes.

420.4 A circular tunnel of radius 4 m is to be driven in a weak
rock mass subjected to an in situ hydrostatic stress field of 9 MPa.
The triaxial compressive strengths of the rock mass in its initial and
fractured states are given by u1 = 8+4u3 (MPa) and u1 = 3u3,
respectively.
A preliminary analysis for design is to determine the relative in-
stabilities of the roof, sidewalls and floor.
Plot the ground response curves for the roof, sidewalls and floor,
taking G = 2.1 GPa, f = 1.4 and y = 25 kN/m3, and comment on the
appropriate support pressure.

A20.4 The ground characteristic for this tunnel has two parts: a linear
part, extending from the in situ conditions to the point at which frac-
turing starts at the tunnel boundary; and a nonlinear part thereafter.
We start by finding the support pressure below which a fracture zone
develops. This is given by

2P - Cfl

l+b

PI = ~

and for this case we have p = 9 MPa, C,, = 8 MPa and b = 4 (because the
strength of the unfractured rock is 01 = 8 + 4a3 = C, + bq). The critical
pressure is then

2p-Co-2x9-8 10

• 
  
  
  
  • 
    
    
    
    • 
      
      
      
      • = 2 MPa.
        1+4 5
        PI = ~
        l+b
        The radial deformation at the boundary of the fractured zone is given by
      
      
      
      
    
    
    
    
  
  
  
  

P - PI

u, = --

2G re

where re is the radius of the fractured zone. For the case of the critical

pressure, which is when the fracture zone just starts to develop, we have

re = a = 4 m and p1 = 2 MPa. With G = 2.1 GPa we find that

u, = -

9-2 28

x4= = 0.0067 m.

2 x 2.1 x 103 4.2 x 103

The linear part of the ground characteristic therefore extends from

(0,9) to (0.0067,2) - in (displacement, pressure) co-ordinates.

For the nonlinear part of the ground characteristic, we choose a series

of support pressure values, and then compute re, ur, proof and paoor for

each value. The appropriate equations are