3.2 Results of numerical modelling
3.2.1 Influence of horizontal clamping stress on hangingwall stability
In this analysis, the orientation of the extension fractures is kept constant and the shear fractures’ angles are varied between 30° and 90°.
3.2.1.1 Extension fracture orientation: αα = 30°°
The results for the fracture combinations of α = 30° with β = 90°, β = 60° and β = 30° are given in Figures 3.2.1, 3.2.2 and 3.2.3 respectively.
From Figure 3.2.1, it can be seen that the horizontal clamping stress has very little influence on the stability of the hangingwall. However, it is clear that the hangingwall can be stabilised by reducing the support spacing. For a support spacing of 1 m, a small percentage instability occurs. For this combination, the support spacing should be very small since the hangingwall is inherently unstable when intersected by these sets of fractures.
For the 30°/60° and 30°/30° combinations, the horizontal clamping stress also has little or no influence. The support spacing should be small to prevent any falls of ground from the hangingwall.
0 10 20 30 40 50 60 70 80
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.1 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 30°°/90°° combination.
0 10 20 30 40 50 60 70
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.2 Influence of horizontal clamping stress and support spacing on
stability of hangingwall for the 30°°/60°° combination.
0 10 20 30 40 50 60 70 80
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.3 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 30°°/30°° combination.
3.2.1.2 Extension fracture orientation: αα = 60°°
The results for the 60°/90°, 60°/60° and 60°/30° combinations are shown in Figures 3.2.4, 3.2.5 and 3.2.6 respectively.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.4 Influence of horizontal clamping stress and support spacing on
stability of hangingwall for the 60°°/90°° combination.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.5 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 60°°/60°° combination.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.6 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 60°°/30°° combination.
For the 60°/90° and 60°/60° combinations, a horizontal clamping stress of 1 MPa reduces the percentage instability to zero. This occurs even at a support spacing of 4 m.
From Figure 3.2.6, it can be seen that for a clamping stress of 1 MPa, the hangingwall, containing extension fractures dipping at 60° and shear fractures dipping at 30°, is completely
stable for support spacings less than or equal to 2 m. Support spacings greater than 2 m result in unstable hangingwall conditions.
Thus, to achieve hangingwall stability in rock masses, which contain a combination of extension fractures that dip at 60° and shear fractures that dip at 30°, 60° or 90°, and where a horizontal stress of approximately 1 MPa is acting, a support spacing of 2 m is indicated for rockfall conditions.
If the horizontal clamping stress is closer to zero, a support spacing of no greater than 1 m is indicated for rockfall conditions.
From Figures 3.2.4, 3.2.5 and 3.2.6, it can be seen that when the horizontal clamping stress is smaller or equal to 0,1 MPa and the support spacing is equal to or greater than 2 m, the hangingwall is completely unstable.
From these results it is evident that the horizontal clamping stress plays a major role in the stability of the hangingwall.
3.2.1.3 Extension fracture orientation: αα = 75°°
The results for the combinations 75°/90°, 75°/60° and 75°/30° are shown in Figures 3.2.7, 3.2.8 and 3.2.9, respectively.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.7 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 75°°/90°° combination.
The relationships that are obtained for these combinations are similar to those that were obtained for the combinations that involved the 60° extension fractures.
As is the case for the 60° extension fracture, a horizontal clamping stress of 1 MPa reduces the percentage instability to zero for the 75°/90° and 75°/60° combinations. The hangingwall, intersected by extension fractures dipping at 75° and shear fractures dipping at 30°, is completely stable for support spacings less than or equal to 2 m and when the horizontal clamping stress is 1 MPa.
From Figures 3.2.7, 3.2.8 and 3.2.9, it can be seen that if the horizontal clamping stress is less than or equal to 0,1 MPa and the support spacing is equal to or greater than 2 m, the hangingwall is unstable.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.8 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 75°°/60°° combination.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.9 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 75°°/30°° combination.
3.2.1.4 Extension fracture orientation: αα = 90°°
The results for the 90°/75°, 90°/60° and 90°/30° combinations are shown in Figures 3.2.10, 3.2.11 and 3.2.12, respectively.
From these figures, it can be seen that the combinations of shear fractures with extension fractures dipping at 90° are the most stable of all the combinations that were considered in this analysis. The combination of 90°/75° is stable at a support spacing of 4 m and a 0,1 MPa horizontal stress. The 90°/60° combination is stable up to a support spacing of 3 m with a horizontal stress of 0,1 MPa. The 90°/30° combination is stable at 2 m support spacing with a horizontal stress of 1 MPa.
The results show that the shallow fracture orientations tend to be less stable than the steeper orientations. This is as a result of the angle between the horizontal stress and the fracture orientation. If this angle is closer to 90°, the normal stress on the fracture is increased and the fracture interface more effectively clamped.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.10 Influence of horizontal clamping stress and support spacing on stability of hangingwall for the 90°°/75°° combination.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa
Figure 3.2.11 Influence of horizontal clamping stress and support spacing
on stability of hangingwall for the 90°°/60°° combination.
0 10 20 30 40 50 60 70 80 90 100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Support Spacing (m)
% Instability
0 MPa 0.01 MPa 0.1 MPa 1 MPa