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![Cable bolting the HW of relatively shallow dipping open stopes is a common practice for the support of underground openings. This helps control dilution (thus reducing cost) and increases stopes turnover.
3D Numerical modelling represents a valuable tool to understand the behaviour of the rock mass, ground support and the interaction of these two elements. In fact, numerical modelling can be used in conjunction with empirical analysis (Mathews, 1981; Potvin 1988; Hadjigeorgiou and al. 1995), field observations and experience to further optimize cable bolting practice in an underground mine.
The purpose of this example is to demonstrate the effect of cable bolting on the stability of an open stope’s hanging-wall (HW) in a blocky ground and how to improve a given cable bolting pattern. It is important to note that there are other methods for achieving the same results. This example has been published for educational purposes and not to replicate the same recommendation for a given mine without proper tailored engineering.
Figure 1 shows the geometry of the studied area. The stope is modelled to be mined using a top and bottom accesses. Two drifts in the hanging wall of the stope have also been modelled. Cable bolts will be installed from the top HW access, so the cable bolts can be as perpendicular to the orebody as possible.
The rock mass is characterized by weakness planes as shown in figure 2. It is assumed that the weakness planes are joint discontinuities, weathered and infilled with stiff clay material. It is assumed in this example that Equivalent Linear Overbreak Slough (ELOS) analysis has been carried out and that there is a fairly good correlation between this parameter and the displacement magnitude of the HW (obtained from numerical modelling) from previous mined-out and reconciled stopes.
The pre-mining stress state is characterized by a major principal stress direction of 90° (East-West) and a plunge of 0°. The stress magnitude in the study area is 40, 20 and 20 MPa for the major, intermediate and minor principal stress components respectively.
The modelled stope is 40 m long (strike-length) and 30 m in height and has a 65° HW dip angle.
Modeling Procedure
The software used in this example is FLAC3D (Itasca, 2018). FLAC3D is an explicit finite difference program to study, numerically, the mechanical behaviour of a continuous three-dimensional medium as it reaches equilibrium or steady plastic flow.
Two types of boundary conditions have been used: roller boundaries along the sides and bottom of the model and applied stresses corresponding to the principal stresses.
The first step of the simulation is to model the in-situ stress prior to any mining. Results are verified to ensure initial boundary conditions have been properly assigned. The next step is to excavate the top and bottom drifts and to run the model to reach equilibrium. Ground support installation (in this case cable bolts) is then added using structural elements. This example illustrates an installation of cable bolts from the HW access drift as illustrated in figures 2(a) and (b). The model is run into equilibrium again to account for in situ stresses on the structural elements. The last step is to excavate the stope.
Four scenarios have been studied in this example: 1)- Linear elastic model without cables; 2)- Ubiquitous Joint Model without cables; 3)- Ubiquitous Joint Model with cable bolting according to pattern 1 : 3 cables per ring (twin cables), 12 rings spaced at 2m; 4)- Ubiquitous Joint Model with cable bolting according to pattern 2 : 3 cables per ring (twin cables), 10 rings spaced at 2m.
Results and Discussion
Contours of the major principal stress Sxx on a vertical and horizontal cross-section, as well as on a 3D view are presented in figure 3 for scenario 1 (linear elastic model). One can easily notices that the excavation of the stope induced a large relaxation zone (loss of confinement) in the HW of the opening, particularly as the major principal stress direction is sub-perpendicular to the ore body. Figure 4 shows the difference in displacement isocontours in the HW of the stope between an elastic and a plastic model using Ubiquitous joint model that accounts for planes of weakness. As one would expect, given the unfavourable joint orientation relative to the HW of the stope, the results clearly indicate a much larger displacement expected for the plastic model as compared to the elastic. In fact, the maximum displacement at the HW stope center is shown to be around 10cm for the elastic model, whereas it could reach 55cm approx. for the plastic model that accounts for the weakness planes.
Figures 5(a) and (b) represent displacement isocontours for scenario 3 and 4 which call for cable bolts in the HW of stope. These figures show that adding cable bolts reduces significantly the displacement of the HW boundary. The cable bolting pattern 1 (scenario 3) was able to reduce the displacement to 37 cm in between cable bolts set 2 and 3 and even further reduction around cable bolts set 1 (30cm max).
On the other hand, a tighter patter in the middle and with higher angle between the cable bolts and the HW dip of the stope yields even better results as shown in figure 5 (b). The displacement is reduced to less than 20cm in at the center of the stope HW and up to a maximum of 27.5cm in localized areas.
Figure 5(b) also shows the axial force on each structural element. It is shown that all cable bolts are carrying load because of the HW displacement and that the range of this axial load on each cable is from 200 to 500 kN, suggesting factors of safety between 1.1 to 2.7. The same plot could be generated for the grout state. This also suggests that further optimization of the cable bolting pattern is possible.
Figure 6 illustrates the cable state of element of pattern 2 (scenario 4) suggesting that none of the simulated cables reached the yield zone (assumption of failure).
In this example, it has been determined that cable bolting pattern influences the performance of the HW of a 65° dipping stope given the assumptions stated above. Again, calibration of the model is of the essence. Ideally, each stope should be reconciled to increase site-specific ground condition awareness and to improve cable bolt practices. Calibration will also help correlate host rock displacement magnitude obtained from numerical modelling to expected ELOS to further provide confidence to the model.
The Author
Nawfal El Mkadmi, P.Eng., M.A.Sc.
Senior Consultant in Mining Geomechanics and Backfill
nawfal.mkadmi@nemcco-international.com
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Optimization of Cable Bolting Installation for the HW of an Open Stope
Cable bolting the HW of relatively shallow dipping open stopes is a common practice for the support of underground openings. This helps control dilution (thus reducing cost) and increases stopes turnover. The purpose of this example is to demonstrate the effect of cable bolting on the stability of an open stope’s hanging-wall (HW) in a blocky ground and how to improve a given cable bolting pattern.
![The response of a shear zone to mining an ore body following pyramid sequence is studied in this example using Map3D software (BEM stress analysis). The analysis is carried out in 3D and suppose the geometry of the shear zone is properly identified based on a series of exploration and geotechnical diamond drill holes (DDH). The shear zone is characterized by local variation of dip angles ranging between 5 to 20° and has an overall north-south dip direction.
The underground method used in this example is a longitudinal long hole with a bottom-up sequence (Figure 1-a). The accesses are placed in the HW of the ore body as shown in Figure 1 (b).
The average height of stopes is 30m with a HW dip angle of 68°. The ore body is located approx. 850m below surface.
The pre-mining stress state is characterized by a major principal stress direction of 90° (East-West) and a plunge of -20°. Stresses of the major principal stress (σH max) increase linearly with depth by 25 kPa/m with a constant stress of 20 MPa. The vertical stress component also increase linearly with depth by 20 kPa/m with a constant stress of 7 MPa.
Modeling Procedure
The first step of the simulation corresponds to the situation where the bottom two levels are already mined-out. At this point, a fault slip is not expected as mining is still relatively distant from the structure (at this stage, seismicity is considered low in the location of the shear zone). The second and third steps model the progression of mining towards the shear zone.
In this example, the fault is assigned a heterogeneous strength distribution (functionality in Map3D) in such way that the structure is marginally stable (at the point of failure) (wiles, 2014). This assumption could be conservative as the fault becomes sensitive to adjacent mining. However, it could be a realistic assumption in cases where seismicity starts occurring on the shear zone following a certain level of mining adjacent to it (seismicity could be a cluster of micro-seismicity or macro-seismic events in the vicinity of the fault).
Results and Discussion
Contours of the major principal stress are presented in Figure 2. It is clearly shown that the major principal stresses are increased towards the shear zone as mining progresses. Depending on the local orientation of the shear zone and the trajectory of σ1, some areas of the shear zone will be subject to more shear stress than others. Figure 3 presents the excess shear stress occurring on the shear zone. It is interesting to note that most of the ESS occurs on the HW of the ore and has relatively large footprint. Figure 4 presents the shear displacement (i.e. fault ride) at different mining steps. There is little induced displacement in step 1 and step 2 as the influence of mine induced stress changes haven’t reached the shear zone yet. On the other hand, step 3 indicates that a shear displacement around 15 mm on the fault could occur in this example.
While it is noteworthy to mention that fault slip analyses are very sensitive to underlying model assumption (particularly the orientation and magnitude of far field stresses, as well as the geometry and the geotechnical properties of the shear zone), this type of analysis gives a good overall appreciation of where the potential unstable area of the shear zone could occur (Cooke 1997; Ryder 1988). Furthermore, a properly calibrated plastic fault-slip model will provide a good representation of the actual site response and will be extremely valuable for rock engineering and mine planning purposes. In fact, to preserve the integrity of the top access, it is recommended to opt for an end access or a FW access rather than a HW access. This latter would be in the close proximity to the problematic area of the shear zone (Figure 5) and is not recommended.
Efforts should be made to characterize the geometry of the shear zone, particularly the part adjacent to mining (adjacent to stopes, accesses and infrastructures). This is key in assigning different strength distribution along the shear zone as it has been carried out in this example.
Calibration of the model is also of the essence. The modeled stresses on the shear zone should be correlated with the observed instrumentation and seismic data as mining progresses.
The Author
Nawfal El Mkadmi, P.Eng., M.A.Sc.
Senior Consultant in Mining Geomechanics and Backfill
nawfal.mkadmi@nemcco-international.com
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Behavior of a Shear Zone (fault) Adjacent to UG Mining Excavations and its Implication on Mine Planning
Most of underground or open pit mines have geological discontinuities including major faults and shear zones that could impact the mining sequence, recovery and ground control designs. This example shows that fault-slip analysis is sensitive to the orientation and magnitude of far field stresses, as well as the geometry and the geotechnical properties of the shear zone.
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