This section summarises the existing design procedure and describes a new design methodology, which is based on the determination of zones of influence and keyblock stability analyses. Design charts for both the rockfall and the rockburst cases are given at the end of this section.
8.4.1 Existing design procedure
In the present version of SDA, there are two separate processes, namely the continuous and discontinuous analyses. Furthermore, in the current SDA version the two processes are completely independent of each other.
In the continuous analysis, a fixed zone of influence in the shape of a frustum of right cone (Figure 8.4.1) is assumed, with (R – r) typically between 1 and 1,5 m. The program works on the principle that all areas, where the zones of influence of adjacent support units do not overlap, are unstable.
) (
3
2 max 2
r Rr R
F +
= + σ π
Figure 8.4.1 Frustum of right cone zone of support influence and associated stress magnitude (σσ
max).
The discontinuous analysis checks for the stability of the hangingwall with respect to buckling, shear and rotational failure. The length of the unsupported beam is taken as the skin to skin distance between adjacent support units. The skin to skin support unit spacing under consideration here is taken in the strike direction and is denoted by s in this discussion. The spacing in the dip direction will be referred to as d. (Figures 8.4.2 and 8.4.3)
Area under consideration in the
discontinuous analysis
Face parallel fractures
s
d
Figure 8.4.2 Schematic showing hangingwall discretised by face-parallel fractures and area used in the discontinuous analysis of the current design methodology.
R F
σmax
r
d
The keyblock analysis determines if the hangingwall is stable for the strike spacing (s). An assumption of the program is that the hangingwall will be stable if d ≤ 1,5s (Daehnke et al., 1998).
8.4.2 Proposed design methodology
A proposed design method, which incorporates both the zone of influence and the keyblock theories, is described below.
A programme such as SDA can easily be modified to incorporate the discussed design procedure.
The first step in the design procedure is the definition of the following rock mass parameters:
i) Angle of extension (α) and shear fractures (β) ii) Friction coefficient (µ)
iii) In situ compressive hangingwall stress (σx)
iv) Extent of fracturing (discontinuities per metre of hangingwall)
Next, the above information is used to determine the extent of the zones of influence and the associated stress profile. This must be done for both the stope face and the support units (and backfill, where applicable). A spatial distribution of the zones of influence of the support units and stope face is established.
It is now necessary to set the support resistance criteria:
i) Fallout thickness (b) to prominent bedding plane (from rockfall back-analyses), or ii) 95 % cumulative fallout thickness (b) from fatality database (Roberts, 1995).
A cross-section of support resistance profiles is taken, also showing the support resistance criteria. Where the support resistance profile falls beneath the support resistance criteria, the effect of the zone of influence is ignored (a conservative assumption). The length of this distance is denoted by s. This unsupported section must now be analysed further to check for keyblock stability. (Figures 8.4.3 and 8.4.4).
The support design method gives insights into spacing and associated stable hangingwall spans in the strike direction only. Due to the face parallel mining induced fracture orientation in intermediate and deep level mines, the hangingwall rock is generally less prone to failure between two support units in the dip direction, compared to failure between units in the strike direction.
As discussed earlier, the current design method considers the shaded area indicated in Figure 8.4.2 in the discontinuous analysis. In the design procedure proposed here, the shaded area shown in Figure 8.4.4 must be considered for the keyblock analysis.
Probabilistic keyblock analyses (Daehnke et al., 1998) have shown that, for a typical discontinuity spacing and attitude as encountered in intermediate depth and deep gold mines, the support spacing in the dip direction can be increased by a factor of ± 1,5 compared with the strike spacing, while maintaining an equal probability of keyblock failure in the dip versus strike direction. Hence, the support spacing in the dip direction can be up to, but should not exceed, 1,5 times the spacing in the strike direction.
In the new design procedure, s is defined as the distance, in the strike direction, where the stress profiles of adjacent supports fall below the support resistance criteria. Similarly, d is defined as this distance in the dip direction. Thus, s and d no longer refer to the skin-to-skin support spacing. However, the assumption is made that if the area considered in the
discontinuous analysis is stable in the strike direction, then the area in the dip direction will also be stable, as long as d ≤ 1,5s.
Figure 8.4.3 Cross-section of support resistance profiles, illustrating the unsupported sections, which have to be checked for keyblock stability, where s
1is the spacing used in the current SDA version, and s
2is the length to be used in the proposed design method.
Figure 8.4.4 Schematic showing clamped hangingwall discretised by face-parallel fractures, zones of support influence and area to be considered in the discontinuous analysis of the new design methodology.
s2 s2
Support Resistance Criteria
s1
Zone of support influence Area under consideration in the
discontinuous analysis Face parallel fractures s
Define Rock Mass Parameters i) Angle of extension (α) and shear fractures(β) ii) Friction coefficient (µ)
iii) In situ compressive hangingwall stress (σx)
iv) Extent of fracturing (discontinuities per metre of hangingwall)
Determine σcrith using Equation 8.2.1 Establish support layout
Is the beam clamped (σh >σhcrit)?
YES NO
Determine zone of influence – Table 8.2.1 Determine zone of influence – Table 8.2.1
Determine associated stress distribution (Eq. 8.2.3) Determine associated stress distribution (Eq. 8.2.4)
Set support resistance criteria:
i) Fallout thickness (b) to prominent bedding plane (from geological investigation and rockfall back- analyses), or
ii) 95% cumulative fallout thickness (b) from fatality database (Roberts, 1995)
Determine unsupported span (s)
Calculate the stability of the hangingwall due to buckling failure:
Unstable Stable
Calculate the stability of the hangingwall due to shear and rotational failure:
Unstable Stable
STOP: Suitable support system and layout
Figure 8.4.5 Proposed design flow chart for the rockfall case.
Figure 8.4.6 Proposed design flowchart for the rockburst case.
STOP: Suitable support system and layout
Calculate dynamic hangingwall displacement (h = h1 – h2): ( ) 2
1
2 1
2 2
1
h h mg mv A dh h F
h i
i = + −
∫
Are energy absorption requirements met? i) h<0.3m; ii) F(h2)>Aρρgb; iii) (Stoping width–h2)>0.6m
NO YES
Set support resistance criteria:
i) Fallout thickness (b) to prominent bedding plane (from geological investigation and rockfall back-analyses), or
ii) 95 % cumulative fallout thickness (b) from fatality database (Roberts, 1995).
Define rock mass parameters:
i) Angle of extension (α) and shear fractures (β) ii) Friction coefficient (µ)
iii) In situ compressive hangingwall stress (σx)
iv) Extent of fracturing (discontinuities per metre of hangingwall)
Determine σhcritusing Equation 8.2.1
Establish support layout
Is the beam clamped (σh >σhcrit)?
YES NO
Determine zone of influence – Table 8.2.1 Determine zone of influence – Table 8.2.1
Determine associated stress distribution (Equation 8.2.4)
Determine associated stress distribution (Equation 8.2.3)
Calculate the stability of the hangingwall due to shear & rot. failure:
Unstable Stable
Determine unsupported span (s)
Calculate the stability of the hangingwall due to buckling failure:
Unstable Stable
Calculate effective hangingwall weight:
+
=
i i
eff h
g v b A
W 2
ρ 2