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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
NEMCCO CONSULTING

Optimisation de l'installation de câbles pour l'éponte supérieure d'un chantier ouvert

Le boulonnage par câbles de l'éponte supérieure des chantiers ouverts à pendage relativement peu prononcé est une pratique courante pour le soutènement des ouvertures souterraines. Cela permet de contrôler la dilution (et donc de réduire les coûts) et d'augmenter le roulement des chantiers. Le but de cet exemple est de démontrer l'effet des câbles sur la stabilité d'une éponte supérieure d'un chantier ouvert dans un massif bloceux et comment améliorer un patron de boulonnage de câble donné.

Comportement d'une zone de cisaillement (faille) adjacente aux excavations minières souterraines et son implication sur la planification minière

La plupart des mines souterraines ou à ciel ouvert présentent des discontinuités géologiques, notamment des failles majeures et des zones de cisaillement qui pourraient avoir une incidence sur la séquence d'exploitation, la récupération et les conceptions de contrôle de terrain. Cet exemple montre que l'analyse du glissement de faille est sensible à l'orientation et à l'amplitude des contraintes in-situ, ainsi qu'à la géométrie et aux propriétés géotechniques de la zone de cisaillement.

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
NEMCCO CONSULTING

Cut and fill mining method is the preferred choice for steeply dipping, irregular, thin and relatively high grade orebodies. Underhand cuts (using backfill) provide several advantages from a production and safety perspectives. In fact, underhand cuts provide an additional mining horizon while the overcuts are progressing upwards. They also force stresses to be in the floor, and since backfill (usually paste) is an engineered material, it is preferred to be the roof of the cut rather than a potentially unstable rock mass (as it is the case of overcuts).
To increase the production rate, different levels may be excavated in parallel. As the underhand and overhand cuts approach each other, the diminishing pillar, referred to as ‘sill pillar’ is subject to increasing stresses. Therefore, the last planned overcut is usually subject to high stresses in the back, making it a difficult cut to mine from a production rate and workers safety standpoints.
This example propose a method to decide the ground support in such overcuts. 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 cut and fill horizon. The remaining sill pillar is 40 m in vertical height. The cuts are 5m in width and height each. The particularity of the geometry is the existence of a main ore vein with an East-West strike and a series of smaller veins sub-perpendicular to the main vein, with a North-south strike. The ore body is located approx. 1,500m below surface.

The pre-mining stress state is characterized by a major principal stress direction of 45° (Notheast-Southwest) and a plunge of 0°. Stresses of the major principal stress (σH max) increase linearly with depth by 50 kPa/m with a constant stress of 8 MPa. The vertical and the minor principal stress components also increase linearly with depth by 30 kPa/m without an initial constant stress.
Modeling Procedure
The software used in this example is Map3D (Wiles, 2017). The first mining step of the simulation corresponds to the situation where twelve (12) underhand and four (4) overhand cuts have been already mined out. At this point, the sill pillar is about 45 m vertical distance. The second mining step models the progression of mining by adding an additional overcut, reducing the height of the sill pillar to a 40m vertical distance. Several results grid have been generated but we will only focus on analyzing longitudinal and cross sections to the main ore vein.
Results and Discussion
Contours of the major principal stress ratio (σ1/UCS), deviatoric ratio (q/UCS) and vertical displacement are presented in Figures 2 and 3. One can easily notices that the excavation damage zone (EDZ), as shown in figure 2(a) and (b) and illustrated by the gray area (σ1/UCS>0.8), has increased from step 1 to step 2. This result is to be expected as stresses at the back of the excavation increase the more we mine overcuts sub-perpendicularly to the major principal stress direction. At this point, we accumulate more damaged ground in the back and one could expect that the advancement rate of this last overcut to be much slower than the previous ones. The stresses below the undercuts haven’t changed much as compared to the sill pillar stresses at the core and certainly the back of the overcut.
Figures 3 (a) and (b) show the isocontours of deviatoric ratio at step 1 and step 2 respectively. As the pillar is diminished in height, the deviatoric stresses increased one increment (from 0.32 to 0.38) and seismic activity (micro and macro) is expected to increase more as compared to the activity shown in figure 3 (a).
Figure 3 (c) shows the isocontours of vertical displacement, indicating a potential for floor heave in the undercut and larger displacements near the intersection (large spans) in the last overcut. Although, it is important to note that the displacement values are very sensitive to Young’s Modulus assigned to the host rock and to the Elastic nature of the model (high displacement values for high concentrated stresses) and therefore, displacement values should be interpreted with caution.
If we consider the perpendicular grid to the main vein (i.e. parallel to the major principal stress direction) shown in figures 4(a) and (b), it is shown that the damaged zone (EDZ) in the back of the overcut is approx. 2.2m in step 1 and increases to 3m after mining the next and last overcut. This is extremely important results for the design of the ground support as it should be able to hold the damaged zone from a static and dynamic type of failures. One can also notice the ‘destressed’ zone in the HW of mining, which is also of extreme interest in designing strategies to recover the remaining ore in the zone.

Figure 5 shows the deviatoric stresses at the back of the last overcut at three different locations. This figure suggests there is a loss of confinement at the back where sub-perpendicular excavations to the main vein have been mined. In fact, by mining the secondary veins, which are oriented sub-perpendicularly to the minor principal stress direction, σ3 has to change trajectory and is therefore reduced in this location. This is particularly important to know and to understand since the confinement stress relaxation (loss of clamping stresses) increase the potential for gravity controlled instabilities. Consequently, the ground support design should consider this important observation (Jian, 2010; Kaiser et al. 2012).
In this example, it has been determined that EDZ corresponds to σ1/UCS>0.8. This might be different for each site depending on ground conditions. Again, calibration of the model is of the essence. Ideally, the depth of fracturing (or EDZ) should be monitored as much as possible for each overcut to note the progression of this parameter. This can easily be performed by drilling observation holes and installing a borehole camera. Obtained values should be compared to the suggested EDZ from the simulation in order to provide confidence into the model.
Recommendations for Ground Support (Part 2)
In the next issue, we will contemplate how to use these modeling results into the design of ground support of the overcut. Dynamic calculations (energy release and bolt energy absorption) will be shown along with selection of surface and bolt support.

The Author

Nawfal El Mkadmi, P.Eng., M.A.Sc.
Senior Consultant in Mining Geomechanics and Backfill
nawfal.mkadmi@nemcco-international.com
NEMCCO CONSULTING

Conception d'un système de soutènement pour une galerie supérieure dans une opération de coupe et de remblai en profondeur (partie 1 de 2)

La méthode d'extraction par coupe et remblai est le choix préféré pour les gisements à fort pendage, irréguliers, minces et à teneur relativement élevée. Au fur et à mesure que les coupes du bas et en surplomb se rapprochent, le pilier décroissant, appelé «pilier de sill», est soumis à des contraintes croissantes. Par conséquent, la dernière coupe prévue est généralement soumise à des contraintes élevées au toit, ce qui en fait une coupe difficile à exploiter du point de vue de la cadence de production et de la sécurité des travailleurs.

Conception d'un système de soutènement pour une galerie supérieure dans une opération de coupe et de remblai en profondeur (partie 2 de 2)

Dans cette section, nous examinerons comment utiliser les résultats de modélisation de la partie 1 dans la conception du soutènement de la galerie supérieure. Les calculs dynamiques (libération d'énergie et absorption d'énergie du boulon) sont abordés ainsi que la sélection de la surface et du patron de boulonage.

The main objectives of backfilling are to improve ground stability and reduce ore dilution (Li and Aubertin, 2014). Consequently, the placed backfill in a stope must possess a minimum strength to remain self-standing during mining of an adjacent stope.
3D Numerical modelling represents a valuable tool to understand the behaviour of the rock mass, the placed backfill and the interaction of these two elements. In fact, numerical modelling can be used in conjunction with empirical analysis (Mitchell et al 1982; Li Li 2013), field observations, model calibration and experience to evaluate the dilution potential and further optimize backfill strength requirements in an underground mine.
The purpose of this example is to evaluate the behavior of the backfill in an underground stope following mining adjacent block and exposing the end wall. Another simulation is performed to evaluate the factor of safety associated with mining underneath the backfill. 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 shape of the opening is based on stope CMS that has been performed before backfilling the stope. Block 2 (Figure 1-b) is the planned stope that will be mined adjacent to the backfilled stope 1.
Three (3) backfill strengths have been modeled to analyze the stability of backfill when exposing the end wall from the extraction of block 2. The scenarios are listed in Table 1:
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 10, 5 and 3.5 MPa for the major, intermediate and minor principal stress components respectively. It is assumed that the stress redistribution due to mining do not affect the stresses within the backfill. Other analyses, using the same methodology as presented here, can be conducted to understand the impact of convergence of the rock walls on the stresses within the backfill.
The modelled stope is 30 m long (strike-length), 30 m in height, 15m in width and has a 80° HW dip angle. The adjacent face that will be exposed is 15m width and 30m height.
Modeling Procedure
The software used in this example is FLAC3D (Itasca, 2020). 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.
Three types of backfill have been studied in this example: 1)- low strength (e.g. soft paste for example); 2)- medium strength (e.g. consolidated paste); 3)- high strength backfill (e.g. cemented rock fill). Note that these descriptions are used for illustration purposes and do not represent the general characteristics of backfill.
Results and Discussion
Figures 2 (a) and (b) show the contours of vertical stresses of the backfill after placement in the stope. It can be noted that vertical stresses at the bottom of the stope are significantly higher for backfill 1 (250 kPa) as compared to backfill 2 (130 kPa). This is explained by the significant arching effect that takes place in backfill 2 due to the higher friction angle and cohesion, translated to higher shear stress in the backfill-rock wall interface and the transfer of load to the adjacent rock.
Figure 2 (c) shows the contours of displacement in backfill following mining block 2 and the end wall exposure of the backfill. A factor of safety can be calculated based on the shear strength reduction method. The variation of the safety factor in function of the backfill strength is shown in Figure 3.

Similarly, we can evaluate the stability of the backfill with a certain strength by mining underneath and design a ground support system to obtain satisfactory factors of safety. Figure shows the displacement induced by mining underneath the backfill and the corresponding displacement
In this example, the backfill strength required for safe extraction of adjacent blocks and to minimize backfill dilution can be determined from numerical modelling with FLAC3D. The same type of exercise can be used to determine what is the required ground support for remnant mining strategies or to mine underneath or around a placed backfill with a given strength.

The Author

Nawfal El Mkadmi, P.Eng., M.A.Sc.
Senior Consultant in Mining Geomechanics and Backfill
nawfal.mkadmi@nemcco-international.com
NEMCCO CONSULTING

Détermination des exigences de la résistance du remblai dans les chantiers souterrains à face ouverte

Dans cet exemple, la résistance du remblai requise pour une extraction sûre des blocs adjacents tout en minimisant la dilution de celui-ci peut être déterminée à partir de la modélisation numérique avec FLAC3D. Le même type d'exercice peut être utilisé pour déterminer quel est le support de terrain requis pour l'extraction du minerai restant récupérable ou sous/autour d'un remblai avec une force donnée.