4.2.1 Zone of support influence definition
The zone of support influence is defined as the lateral extent of the vertical stress profile, induced in the hangingwall by a loaded support unit. The zone of influence can extend some distance away from the immediate support - hangingwall contact, and hence can contribute towards rock mass stability between adjacent support units. Zones of influence have some spatial distribution about the support unit, which describe the stress profile induced into the hangingwall by the support unit.
a
b
σmax
F
b a
= F
σmax (4.2.1)
Figure 4.2.1 Rectangular parallelepiped zone of support influence and associated
stress magnitude (σσ
max).
R
F
σmax
r
) (
3
2 max 2
r Rr R
F +
= +
σ π (4.2.2)
Figure 4.2.2 Frustum of right cone zone of support influence and associated stress magnitude (σσ
max).
The simplest spatial description of a zone of influence is in the form of a rectangular parallelepiped (i.e. rectangular box). The associated stress profile and magnitude are shown in Figure 4.2.1. This spatial description of the zone of influence has been used in the past (Roberts, 1999), where the parameters a and b were typically taken as 1,0 to 1,5 m.
A more complicated zone of influence stress profile in the shape of a frustum of a right cone was implemented in the support design analysis program (SDA II) developed by CSIR: Division of Mining Technology (1999). Figure 4.2.2 shows the stress profile. The radius of the support unit corresponds to r and the extent of the zone of influence from the support unit edge (R - r) is typically set between 1,0 and 1,5 m.
4.2.2 Classification of rock mass discontinuities
Mining induced and geological discontinuities govern the behaviour and deformation of the rock mass surrounding stopes. The discontinuities affect the zones of influence, and hence the following prevalent discontinuity types are considered in this study (Adams et al., 1981):
• Shear Fractures:
These fractures are associated with highly stressed rock, and are thus found in intermediate- and deep-level mines. It is estimated that the fractures initiate 6 to 8 m ahead of the advancing stope face and separate the rock into blocks of relatively intact material.
They are oriented approximately parallel to the stope face and can be regularly spaced at intervals of 1 to 3 m. Shear fractures usually occur in conjugate pairs in the hangingwall and footwall, and typically reveal distinct signs of shear movement. Their dip in the hangingwall is generally towards the back area at angles of 60 to 70 degrees (Jager, 1998; Esterhuizen, 1998).
• Extension Fractures:
These fractures initiate ahead of the stope face and are smaller than shear fractures. They form after shear fractures have propagated and generally terminate at parting planes.
Extension fractures do not normally exhibit relative movement parallel to the fracture surface and are typically oriented parallel to the stope face. They are commonly spaced at intervals of 10 cm, with lower and upper limits of 5 and 50 cm, respectively. The strike length is typically 3 m, where lower and upper limits of 0,4 and 6 m have been observed (Esterhuizen, 1998). Extension fractures normally dip between 60 and 90 degrees, where
the direction of dip (i.e. towards or away from the stope face) can be influenced by the hanging- and footwall rock types (Roberts, 1995).
• Bedding Planes:
Most reef extraction takes place in bedded quartzites. Bedding planes, which are parallel with the reef, often represent weak interfaces between adjacent strata and provide little cohesion (Jager, 1998). Bedding planes are generally spaced at 0,2 to 2,0 m intervals. The rock fall-out height is commonly governed by the position of bedding planes.
• Joints:
Apart from stress-induced fractures and bedding planes, other types of geological weaknesses transect the rock mass. The most prevalent of these are geological joints, steep-dipping faults and dyke contacts. The spacing of the geological joints generally exceeds 1 m.
In intermediate- and deep-level mines, the three most prevalent discontinuity types are extension fractures, shear fractures and bedding planes (Figure 4.2.3). In shallow mines, less stress-induced fracturing occurs, and the rock mass is generally discretised by bedding planes and joint sets.
The work presented here is applicable to both intermediate- and deep-level mines, as well as to shallow mines. Sections 4.6 and 4.7 give a summary of the zones of influence for intermediate- and deep-level mines, and shallow mines, respectively.
Shear Fractures Extension
Fractures
Bedding Planes
Stope
MiningdirectionFigure 4.2.3 Simplified schematic illustrating the three most prevalent discontinuity types in intermediate- and deep-level mines.
4.2.3 Parameter definitions
The following naming conventions are adopted to describe the basic parameters governing the zones of support influence:
Rock mass parameters:
b = height of bedding plane above hangingwall skin ϕ = friction angle of bedding plane interface
φ = friction angle of extension and shear fracture interface α = angle of extension fracture (measured from h/wall skin) β = angle of shear fracture (measured from h/wall skin) f = spacing of discontinuities such as shear fractures & joints
Support parameters:
F = support load
r = radius of cylindrical support unit (e.g. elongate, prop) w = width of rectangular support unit (e.g. pack) = 2 r Zone of influence parameters:
σ (x) = zone of influence profile in two dimensions σ (x,y) = zone of influence profile in three dimensions x = co-ordinate perpendicular to stope face y = co-ordinate parallel to stope face
z = extent of zone of influence from support unit edge
zx = zone of influence extent extending in the x-direction from the support unit edge (3D case)
zy = zone of influence extent extending in the y-direction from the support unit edge (3D case)
Figure 4.2.4 shows a schematic indicating some of the zone of influence parameters.
x Face parallel extension & shear fractures
y
b
f
β α