Difference between revisions of "Pillar design"

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(4.1 Empirical Strength Formulas)
(4.1 Empirical Strength Formulas)
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The most basic method of determining pillar stability is to use the factor of safety formula which makes use of the pillar strength. The formula is the ratio of strength over stress so stable pillars have FS > 1 :
The most basic method of determining pillar stability is to use the factor of safety formula which makes use of the pillar strength. The formula is the ratio of strength over stress so stable pillars have FS > 1 :
Where the strength formula for square pillars is:
Where the strength formula for square pillars is:

Revision as of 15:32, 4 February 2015

1.0 Classification of Pillars

1.1 Support Pillars

Support pillars are load carrying. Examples of support pillars include:

Type of Pillar Description
Sill Pillar Horizontal pillars that separate levels or stopes, often used when multiple levels are mined concurrently.
Room and Pillars Pillars are left in place in a predetermined and calculated pattern as rooms are mined out.
Yield Pillars Pillars are designed to fail by going past peak load carrying capacity. Roof-strata is maintained by relieving pressure in working areas and controlling transference of load to abutments that are clear of working areas and road ways.Yielded pillars still carry load.
Post Pillars Room and pillar variation where ore is mined out in a series of horizontal slices.
Barrier Pillars Solid blocks left between two mines or sections of a mine. Provides regional support in large mines to prevent accidents due to inrushes of water, gas, or explosions or a mine fire.
Bracket Pillars Slip on discontinuities may cause rockburst within stopes, which can cause equipment damageand injury or loss of life. Ore immediately adjacent to these geological structures is left unmined to protect the structure from mining induced stresses.

1.2 Protection pillars

Protection pillars provide shelter in a mine. Examples of protection pillars include:

Type of Pillar Description
Shaft Pillars A large area that is left unworked around the shaft bottom to protect the shaft and the surface building from damage due to subsidence . Protects the shaft itself.
Crown Pillars A rock mass of variable geometry, mineralized or not, situated above an uppermost stope of the mine, which serves to permanently or temporarily ensure the stability of surface elements. Surface elements include bodies of water, soil and precipitation . Separate underground from surface mining.
Boundary Pillars Pillars left in mines between adjoining properties . Usually formed between mines.
Barrier Pillars Large pillar left unworked between two mines for security against accidents arising from an influx of water .
Bracket Pillars Slip on discontinuities may cause rockbursts within stopes, which can cause equipment damage and injury or loss of life. The most practical measure to counteract these effects involve leaving left over strips of unmined ground adjacent to the features to reduce potential for them to slip .

2.0 General Aspects of Pillars

2.1 Pillar design considerations

Pillar design considerations that need to be taken into account include :

  • Pillar load
  • Strength of pillars (failure criteria)
  • Orebody geometry
  • Geological characteristics of a mine
  • Load-deformation characteristics of the pillar and stiffness of the loading system

2.2 Pillar design basics

Pillar design basics are mainly concerned with:

  • Peak-pillar strength (load-bearing capacity)
  • Post-peak or load-deformation characteristics of a pillar

Pillar load and load distribution need to be established and potential failure models must be always kept in mind.

2.3 Potential Pillar Failure Modes

The strength of pillars are highly dependent on the geological conditions of the mine and there is no universal pillar design method. The following pictures show the potential failure modes that need to be considered for pillar design which are spalling (hourglassing), shear fracturing (geology and stress), bulking/bulging (geology) and foundation failure:


2.3.1 Hourglass Failure

The most common mode of failure is hourglassing. Hourglassing occurs when the sides of the pillar start to spall off due to high stresses, which are always highest on the boundary of the pillar. Due to this, bolting of the sidewalls of pillars is sometimes necessary. By keeping broken rock in place, it provides a form of confinement to the core and can prevent progressive failure and eventual collapse of the pillar. In the situation that there is a fault or large joint cutting the pillar, displacement on it will usually be the mode of failure .

2.3.2 Foundation Failure

The foundation of the pillar is a part of the load-carrying system and must be considered for the overall design. If the foundation rock is of low strength, it could fail prior to failure of the pillar itself. Pillar foundation is not always in the floor. For example, it can be in the hanging wall or footwall of sill pillars in steeply dipping deposits. This can be examined using numerical analysis to determine potential for foundation failure. Formulas are available for rib and rectangular pillars which relate foundation strength to the cohesion and friction angle of the foundation rock. If the foundation geology cannot be represented by a homogeneous isotropic elastic material, an analytical solution should not be used. The following picture shows the different forces associated with foundation failure and the yield zones : Please add a link to this page in the article that already exists on room and pillar mining.


The following chart is useful in estimating stress levels below a pillar with a circular footing which is found in many soil mechanics texts:


The contours on the chart show the fraction of the original surface load magnitude. The rule of thumb of stresses being concentrated in 45 degree zone beneath the foundation can be clearly seen in the chart, as this angle approximately defines the extent of the induced stress bulbs below the foundation.

3.0 Tributary Area Method and Stresses of Pillar Design

3.1 Methodology

Tributary area method is the simplest method of determining the pillar load. This method is based on a force balance between the load carried by the pillar and the tributary area conveying load to the pillar. This method only uses average loading of the pillar not the actual stress distribution. This method is reasonable if the pillar layout is extensive otherwise this estimate is generally too high because of the arching of stresses from abundant pillars. The following pictures show the methodology for determining the tributary area:


The following pictures represents rib pillars, square pillars, rectangular pillars, and irregular pillars and their respective equations:

caption caption caption caption


The force balance on the pillar section is as follows:


This can also be expressed in terms of extraction ration r:


3.2 Stress Distribution

Stress flows around excavations do not have a constant load. Stresses are higher at excavation boundaries than in the center of pillars, so that the edge of the stress is higher than the average pillar stress that would be calculated by simple methods of tributary area. The following picture shows the real stress distribution on a three pillars:


The following diagram shows how the stress distributions are estimated on the basis of superposition and how the real stress distribution is not accounted for in the tributary method :


3.3 Load Distribution

The following pictures show an experiment that was carried out on a large pillar in which mining was carried out around it so the load is increased. In the center-height of the pillar, a slot was cut and flat-jacked where load cells were inserted. As mining around the pillar continued, the pillar height was monitored and plotted against the load which can be seen in the graph below :


The following diagrams represent the distribution of load through the pillar as it reaches and goes beyond the peak strength. It can be observed that the center of the pillar still remains load bearing, even after the peak strength has been reached. This shows the importance of confinement on effective strength along with the importance of pillar maintenance so that the load carrying capacity of the pillar is not lost .


3.4 Pillar Behavior Measurement

Tomography is a method used to determine the degree of fracturing in pillars and it involves contouring of P-wave velocity through the pillars. This is used in conjunction with observations of fracturing in open boreholes inspected using a borehole camera. Sometimes measurements of load changes are used. This form of pillar behavior measurement is very helpful in calibrating numerical models .

3.4.1 Effect of Width-Height Ratio of a Pillar

The following graph shows how post-peak strength varies significantly with the width-height ratio of a pillar. Since pillars are usually ore, the desire is to leave slender pillar which are brittle, but these pillars are the worst in terms of strength behavior .


As a guide for width-height ratios of pillars:

  • 10 : is good for barrier pillars or large protection pillars.
  • 5 : represents elastic-plastic behavior.
  • 2 : most common and there is the need for bolting based on load distribution.

3.4.2 Effect of Depth on Pillar Layout

If the span of the layout is similar or wider than the depth, the tensile zone above the layout will extend all the way to the surface. Due to this, pillars need to be designed to carry the entire weight of the overlying mass. The layout should be compartmentalized using barrier pillars for large spans, which has the same effect of breaking up the tensile zone above the layout as shown below:


The potential issues associated with shallow layouts are that tensile zones may extend to the surface and the possibility of pillar runs. In both of these cases, barrier pillars will be required.

As depth increases, pillar size becomes large and the extraction ratio decreases. Based on the stope width, a system of barrier pillars and yield pillars can be used. The transition zone between shallow and intermediate depth is dangerous as pillar yield may not always occur. The following graph, outlines the effect of extraction ratio on pillar stress :


4.0 Factor of Safety Method of Pillar Design

4.1 Empirical Strength Formulas

The most basic method of determining pillar stability is to use the factor of safety formula which makes use of the pillar strength. The formula is the ratio of strength over stress so stable pillars have FS > 1 :


Where the strength formula for square pillars is:


The constants in the empirical strength formula shown above are calibrated based on observations of stable and collapsed pillars. There is a large range of appropriate constants. The following graph shows calibrated constants in common mines:


4.2 Pillar Strength from H-B Failure Criterion

Pillar strength is calculated with the assumption that overall pillar strength is equal to average strength across the middle height of the pillar. The following graph shows how pillar strength is dependent on rock mass quality and pillar width to height ratio :


The chart can be used to estimate the Factor of Safety for a proposed pillar layout.

5.0 Application of Pillar Design