Page 595 - Rock Mechanics For Underground Mining

AVAILABLE SUPPORT LINE CALCULATIONS

C.3 Available support line calculations

C.3.1 Support stiffness and maximum support pressure for a concrete or
shotcrete lining

Input data

E c = Young’s modulus of concrete or shotcrete;
c = Poisson’s ratio of concrete or shotcrete;
t c = lining thickness (Figure A.7);
Figure A.7 Shotcrete or concrete
lining. r i = internal tunnel radius;
cc = uniaxial compressive strength of concrete or shotcrete.

Support stiffness
2 2
E c r − (r i − t c )
i
k c = 2
2
(1 + c )[(1 − 2 c ) r + (r i − t c ) ]
i
Maximum support pressure
2
cc (r i − t c )
p sc max = 1 −
2 r 2
i
C.3.2 Support stiffness and maximum support pressure for blocked steel sets
Input data (Figure A.8)

W = flange width of steel set and side length of square block;
X = depth of section of steel set;
A s = cross-sectional area of steel set;
I s = second moment of area of steel set;
E s = Young’s modulus of steel;
ys = yield strength of steel;
r i = internal tunnel radius;
S = steel set spacing along tunnel axis;

= half angle between blocking points (radians);
t B = thickness of block;
E B = Young’s modulus of block material.

Support stiffness
1 Sr i Sr 3 i
(
+ sin
cos
) 2S
t B
= + 2 − 1 +
k s E s A s E s I s 2 sin
E B W 2
Figure A.8 Blocked steel set.
Maximum support pressure

3A s I s ys
p ss max =
2Sr i
{3I s + XA s [r i − (t B + 0.5X)] (1 − cos
)}

577