# Crown pillars

## Contents |

## **Introduction**

When designing underground mines, it is necessary to consider a crown pillar, which provides a barrier between the surface activity and underground. A crown pillar, defined as a rock mass situated above an uppermost stope of the mine, can be one of two types: a “surface crown pillar” and “crown pillar between open pit and underground” ^{[1]}. Both types of crown pillars have similar purposes to protect the surface land and the underground mine, and those working in it from inflows of water, soil, and rock ^{[2]}. To ensure safety, it is critical to leave a pillar of adequate thickness, while still maximizing ore recovery. Designing crown pillars involves understanding the rock mass characteristics of the ore zone and host rocks, along with the conditions in the near-surface weathered zone ^{[3]} .

### **Surface Crown Pillar**

A surface crown pillar is used when an underground mine is constructed directly below surface, where no open pit mining has occurred as shown in Figure 1.

The primary purpose of a surface crown pillar is to protect the surface from subsidence, and the mine from any material inflows, such as water, soil, and rock ^{[2]}. It is vital that the surface crown pillars remain stable throughout their life to protect the surface land users. Often roads are built overtop of these underground areas to provide service to the mines and nearby towns. As roads have very little tolerance to subsidence, this is a concern for post-mine closure, as long term pillar stability may have not been considered ^{[4]}.

### **Open Pit to Underground Crown Pillar**

Often when there is a deposit near surface with a considerable vertical extent, a combination of open-pit and underground mining will be used. These deposits will generally be exploited first by open-pit, due to the increased production capacity and safety, as well as the decreased capital and operating costs in comparison to underground. If it is determined economical, the mine may choose to progress to underground methods, rather than deepening the open-pit. In this case, a crown pillar between open pit and underground is required. As shown in Figure 2, the crown pillar is rock directly under the open pit, up to the start of the underground workings.

Crown pillars between open-pit and underground mining are required to prevent water from entering from the bottom of the open pit into the underground stope ^{[2]}. In some cases, the open pit may be mined simultaneously with the underground operations. If this occurs, careful consideration must occur on the required crown pillar thickness, as the pillar will be reduced in thickness as mining progresses.

## **Pillar Sizing**

It is important to determine the optimum thickness for crown pillars, ensuring both safety and maximum ore recovery. To design these crown pillars, an understanding of the rock mass characteristics of the ore zone and host rocks is required ^{[3]} . Several key factors for pillar sizing include ^{[2]}:

- Orebody geometry (especially dip and width)
- Most likely failure mode of crown pillar
- Most likely failure mode for the hanging wall and footwall rocks
- Water accumulation, either in base of open pit, or from surface runoff
- Loads from equipment and stockpiles on the crown pillar
- Rock mass strength
- General competence of pillar and wall rocks
- Geotechnical conditions inducing weakness (groundwater, variations in rock strength, intersecting planes), and their likely impact on crown pillar stability
- Influence of open pit blasting on pillar integrity

Three methods that can be used for determining pillar stability are: empirical methods, numerical modelling, and limit-equilibrium equations ^{[6]}
. Empirical methods and numerical modelling will be discussed below, while limit-equilibrium equations will only be introduced.

### **Empirical Methods**

#### **Scaled Span Method**

There are several empirical methods used for determining the crown pillar thickness, the most common being the Scaled Span Method. The Scaled Span concept was developed using case studies of previous designs, and gives a procedure for empirically dimensioning the geometry of crown pillars mine openings ^{[3]}. In order to determine the scaled crown span, the following equation is used:

Where:

- Cs represents the scaled crown span,
- S represents span,
- T represents thickness of crown pillar,
- L represents strike length is L,
- θ represents foliation/ore zone dip, and
- γ represents crown pillar rock mass unit weight.

With the scaled crown span determined, Figure 3 can be used along with the RMR classification to determine if the crown pillar is stable or not.

The chart above is based on 70 cases of crown pillars, most from Ontario in hard rock mines ^{[7]}. Based on the chart, if the point where scaled crown span and RMR meet is below the critical span line, it is considered to be stable. It should be noted that this method does not provide any factor of safety ^{[3]}. The critical span can also be calculated by using Equation 2:

If the scaled crown pillar span if less than critical span, the crown pillar is considered stable ^{[8]}. To determine the thickness, Equation 1 and 2 can be combined to:

Where T, S, L, γ, and θ are the same as those used in Equation 4, with the addition of:

- Jn represents joint set number
- Jr represents joint roughness number
- Ja represents joint alteration number
- Jw represents joint water reduction number
- SRF represents stress reduction factor

When a crown pillar is proposed where mining strike length is more than 10 times the span, Figure 4 can be used. To determine thickness, RMR can be used in combination with the opening span size.

It is noted that the minimum thickness of crown pillars is approximately 3m, to ensure consistency with empirical guidelines that are practical to excavate ^{[3]} . This plot can only be used when the strike length is at least 10 times the span, and aids in determining if the pillar is stable, requiring support, or unstable. The curves offer no factor of safety, and have been assumed based on minimum controlling rock mass quality ^{[3]} .

#### **Probabilistic Method**

One application of the scaled span method is using a probabilistic approach to assess pillar stability. Crown pillar stability at several mines, along with mine hazard risk assessments, was compiled to allow for quantification of risk and uncertainty ^{[9]}. Probabilities for pillar failure were calculated and plotted against the quotient of Critical Span divided by the scaled crown span ^{[8]}. Shown in Equation 4, the probability of pillar failure can be calculated:

Pf is the probability of failure, while erf is the error function, also known as Gaussian error function ^{[8]}. This equation is an approximation, and has a standard deviation of 10 RMR units.

#### **Dimensional Analysis**

With the deepening of several open pit mines, the popularity of expanding to a caving mine method below the open pit is rising. This creates the need to determine the optimum pillar thickness required between an open pit and underground block caving operations ^{[2]}. The dimensional analysis approach is an application of the scaled span approach, shown below in Equation 5, which considers the most effective parameters to block caving.

Where

- C represents cohesion strength,
- S represents Stope Span,
- h represents stope height,
- γ represents the unit weight of the rock.

This formula is based on several case studies, and is applicable wherever for block caving mining underneath an open pit.

### **Numerical Modelling**

Numerical modelling is a flexible solution for analyzing pillar stability, and can consider a large number of influencing factors such as stresses, rock mass properties, geometry, and more ^{[6]}. These models can be done either in 2D or 3D, depending on what is to be modelled. For example, a regular shaped orebody can be modelled in 2D using axis symmetry, while a shaft or stope, if not continued indefinitely in one direction, must be modelled in 3D.

#### **RS2 (Phase2) Modelling**

An example of software that can be used for numerical modelling of pillars is RS2 by Rocscience. By setting the behaviour to plastic, therefore allowing failure to occur, the model can be used to determine the location of yielded elements. An example of this is shown in Figure 5, where an open excavation is created in a cylindrical, vertical orebody.

As no shaft or stopes are used in this case, only half of the model is constructed, utilizing axis symmetry used to reduce computational time. To determine the minimum crown pillar size required, the excavation size is increased incrementally by 1m, therefore decreasing the crown pillar thickness by 1m. After each increment, the yielded elements are examined to determine when pillar failure occurs. In Figure 5, the red sections represent that 100% of elements have yielded. Figure 5A shows the pillar prior to failure, and it can be observed that the yielded areas have not connected, as there is competent (0% yielded) rock between. Figure 5B is considered the critical minimum thickness prior to failure, as shown in Figure 5C.

### **Limit-Equilibrium Equations**

This technique uses analytical limit-equilibrium equations, each developed for a specific failure mechanism ^{[6]}. These failure mechanisms are further discussed in the “Pillar Failure” section. Equation 6 shows the general setup for each equation.

The forces resisting and inducing movement vary depending on failure method, and can include normal stress, shear stress, gravity, and the effect of groundwater ^{[6]}. Forces can be determined through the use of free body diagrams.

## **Pillar Failure**

There are six main pillar failure types that have been observed ^{[6]}:

- Rock Fracturing: Rupture of surface crown pillar and collapse into stope
- Plug Failure: Sudden fall of the crown pillar (delineated by its boundary planes) by gravity into the stope
- Ravelling: Block by block rock mass failure without a self-supporting cavity being reached
- Delamination: Ravelling failure involving sliding or buckling of thin rock layers, leading to destabilization of the crown pillar
- Strata Failure: Tensile failure of stratified rick at wall contacts or along the crown pillar span
- Chimneying: An upwards progression within a weak rock mass forming a cavity with limited lateral extend, developing from underground opening towards surface

These pillar failures, excluding rock fracturing, are shown in Figure 6.

One cause of failure is related to improper backfill material. In Timmins, Ontario, several sinkholes and crown pillar collapses where observed where stoping had been close to the surface ^{[11]}. Most of these stopes were mined using cut and fill methods, with sand used as the fill material. It was determined that a rise in water levels caused the fill to become saturated, which lowered the angle of repose and allowed it to flow into lower levels in the mine ^{[11]}. As a result, these stopes were left unsupported, resulting in subsidence or a full collapse.

## **References**

- ↑ E. Bakhtavar, "Transition from Open-Pit to Underground as a New Optimization Challenge in Mining Engineering," Journal of Mining Science, vol. 45, no. 5, pp. 485-494, 2009."
- ↑
^{2.0}^{2.1}^{2.2}^{2.3}^{2.4}E. Bakhtavar, "Determination of the Optimum Crown Pillar Thickness Between Open-Pit and Block Caving," in 29th International Conference on Ground Control in Mining, Morgantown, 2010. - ↑
^{3.0}^{3.1}^{3.2}^{3.3}^{3.4}^{3.5}^{3.6}^{3.7}T. Carter, "A New Approach to Surface Crown Pillar Design," Golder Associates, Toronto, 1992. - ↑ M. Betournay, "Highway Stability Considerations and Site Work Associated with Abandoned North American Mines," Post-Mining, Nancy, France, 2008.
- ↑ D. Whittle, "Determining the open pit to underground transition: A new method," University of Melbourne , Parkville, 2015.
- ↑
^{6.0}^{6.1}^{6.2}^{6.3}^{6.4}M. Betournay, "A Canadian Standard for Hard Rock Mine Shallow Stope Decommissioning," CANMET Natural Resources Canada, 2001. - ↑ S. McKinnon, MINE 469 Course Notes: Pillars, Kingston: Queen's University, 2017.
- ↑
^{8.0}^{8.1}^{8.2}T. Carter, "An Update on the Scaled Span Concept for Dimensioning Surface Crown Pillars for New or Abandoned Mine Workings," Golder Associates, Toronto, 2000. - ↑ T. Carter and R. Miller, "Crown-pillar risk assessment - planning aid for cost effective mine closure remediatiom," Instution of Mining and Metallurgy, England, 1995.
- ↑ T. Carter, "Guidelines for use of the Scaled Span Method for Surface Crown Pillar Stability Assessment," Golder Associates, Toronto, 2014.
- ↑
^{11.0}^{11.1}Beauchamp, "Addressing Mine Hazards under Transportation Corridors - The Timmins Experience," Golder Associates, Sudbury, 2006.