Rock Mechanics.pdf - Mining and Blasting

Figure 11.6 Calculated required
support line for the sidewalls in a sample
problem.
ROCK SUPPORT AND REINFORCEMENT
Table 11.1 Required support line calculations for sample problem.
pi(MPa) 10 4 2 1.222 1.0 0.5 0.2 0.1
re(m) — — — — 3.316 4.690 7.415 10.487
i(m) 0 0.015 0.020 0.022 0.027 0.063 0.228 0.632
(re − a)(MPa) 0 0 0 0 0.008 0.042 0.110 0.187
proof = pi + (re − a)(MPa) 10 4 2 1.222 1.008 0.542 0.310 0.287
pfloor = pi − (re − a)(MPa) 10 4 2 1.222 0.992 0.458 0.090 (−0.087)
To determine the ground characteristic or required support curve, substitute successive
values of pi in equation 7.15 to obtain a series of values of re which are then
substituted into equation 11.7 to obtain the corresponding values of i =−ui. The
results so obtained are tabulated in Table 11.1 and plotted in Figure 11.6. The critical
support pressure below which a fractured zone will develop is found by putting re = a
in equation 7.15 which gives pi cr = 1.222 MPa. In order to restrict radial displacements
to values of i, calculated for sidewall support pressures of pi, roof and floor
pressures of pi + (re − a) and pi − (re − a) will be required.
The complete solution of a rock–support interaction problem requires determination
of the support reaction or available support line in addition to the ground
characteristic or required support line considered so far. Using methods introduced
by Daemen (1975), Hoek and Brown (1980) have presented methods of calculating
support reaction lines for concrete or shotcrete linings, blocked steel sets and
ungrouted rock bolts or cables. Details of these calculations are given in Appendix C.
Figure 11.7 shows the results of a set of calculations carried out for a sample
problem using the material model of Figure 11.5. A 5.33 m radius access tunnel is
driven in a fair quality gneiss at a depth of 120 m where the in situ state of stress
is hydrostatic with p = 3.3 MPa. The properties of the rock mass are c = 69 MPa,
m = 0.5, s = 0.0001, E = 1.38 GPa, = 0.2, f = 4.2, mr = 0.1, sr = 0 and r =
20 kN m −3 . In this problem, the self-weight of the fractured rock around the tunnel
has an important influence on radial displacements, as shown in Figure 11.7.
The support reaction or available support line for 8I23steel sets spaced at 1.5 m
centres with good blocking was calculated using the following input data: W =
0.1059 m, X = 0.2023 m, As = 0.0043 m 2 , Is = 2.67 × 10 −5 m 4 , Es = 207 GPa,
ys = 245 MPa, S = 1.5 m, = 11.25 ◦ , tB = 0.25 m, EB = 10.0 GPa and i0 =
0.075 m. The available support provided by these steel sets is shown by line 1 in
Figure 11.7 which indicates that the maximum available support pressure of about
0.16 MPa is quite adequate to stabilise the tunnel. However, because the set spacing
of 1.5 m is quite large compared with the likely block size in the fractured rock, it
will be necessary to provide a means of preventing unravelling of the rock between
the sets.
The importance of correct blocking of steel sets can be demonstrated by changing
the block spacing and block stiffness. Line 2 in Figure 11.7 shows the available
support line calculated with = 20 ◦ and EB = 500 MPa. The support capacity has
now dropped below a critical level, and is not adequate to stabilise the tunnel roof.
Since it has already been recognised that some other support in addition to steel
sets will be required, the use of shotcrete suggests itself. Line 3 in Figure 11.7 is
the available support curve for a 50 mm thick shotcrete layer calculated using the
following data: Ec = 20.7 GPa,c = 0.25, tc = 0.050 m, cc = 34.5 MPa. Because
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