- 1 Classification of Pillars
- 2 Tributary Area Method and Stresses of Pillar Design
- 3 Factor of Safety Method of Pillar Design
- 4 Application of Pillar Design
- 5 References
Classification of 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 slicesCite error: Closing
Pillar design basics
Pillar design basics are mainly concerned with:
Pillar load and load distribution need to be established and potential failure models must be always kept in mind .
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.:
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 .
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.
Tributary Area Method and Stresses of Pillar Design
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:
This can also be expressed in terms of extraction ration r:
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 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.
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.
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:
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:
Factor of Safety Method of Pillar Design
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:
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.
Application of Pillar Design
There are many different types of pillars which are used for different purposes, being for protection or stability. The main factor that pillar design is based on is factor of safety. The common design methods include tributary area, empirical calculations and modelling.
Shaft pillars are the most important excavation in an underground mine and must be protected above everything else. Failure criteria include strain limits for deformation, stress limits for failure of rock in shaft sidewalls, and for high speed hoisting. For strain limits of deformation, tilting and kinking can be used as guides. For high-speed hoisting, tilting of guides must be limited and kinks must be avoided.
In regards to determining the shaft pillar location, it is a critical decision that alters shaft stability:
For steeply dipping deposits:
For shallow dipping or tabular deposits:
The following graph shows pillar stress magnitude as a function of radial distance, r, from the center of a shaft pillar of radius R:
The graph shows the state of stress in the interior of a circular pillar of radius R with extensive mining all around it. The graph shows that circular shaft pillars have a large area in the interior of relatively constant stress. The exterior of the shaft will have increasingly high stresses. The edge of the shaft pillar will be highly stressed as it is an abutment to mining, but the interior is mostly at a uniformly lower stress level.
The following graph is based on the previous one, in which the constant interior stress magnitude region is used as a design constraint. This chart shows the size required to limit the stress to a critical magnitude. In order to use the following chart, you first have to determine the critical stress magnitude, go to the critical stress and read off the pillar radius required:
In the case of a very large depth, stress levels in the central region of shaft pillars can become too high for stability of service excavations. Depth is reached at which point the interior stress level is too high, and the radius required to protect the shaft and service excavations are too large. In order to overcome these problems, the pillar area must be mined out which can be done during mining or prior to sinking the shaft.
In order to avoid the issues of high stress in a shaft pillar is to mine it out. The major issue with this is managing displacement as opposed to stress. This can be managed by having adjustable shaft guides over a portion of the shaft steelwork that is affected by the mined-out region. By managing displacements, it eliminates the risk of rockbursts or other unpredictable effects of high stress that are associated with leaving a pillar.
In order to control displacements, unmined areas called satellite pillars can be left behind. The spacing and size of these controls the size of the interior sheltered region. Backfill is necessary of this activity for protection. In order to design satellite pillars, it is important to avoid sidewall failure or failure of shaft lining, by reducing the stress induced on the shaft. The following curve can be used to determine the induced stress level based on satellite spacing and the choice of backfill to be used inside the pillars.
Sill pillars are most commonly used in cut-and-fill mining of steeply dipping deposits. The conditions of the roof in the stope below the sill pillar gradually deteriorate as the final sill dimensions are approached. The design of sill pillars are based on:
The following graph shows case histories from Canadian hard rock mines. If it is considered stable, the factor of safety is greater than 1.4 and if it is considered failure, factor of safety is less than 1.
If the width/height ratio is greater than 5, the post-peak load-deformation curve will likely be flat. In the situation that pillars do not fail:
The way in which slender pillars fail depends on their stiffness relative to the loading system of the hanging wall and foot wall which various depending on mining geometry and geology. The overall stiffness can be determined numerically, but it is a lengthy procedure. If a fracture zone develops ahead of mining as it may in intermediate depth mining, yield pillars may be designed to have a width less than that of the fracture zone. The pillars are pre-failed and cannot burst, but can offer good local support to the roof .
The stiffness of the loading system can be determined similarly to the ground reaction curves for tunnels. The pillar is replaced by an imaginary jack in which the resistance is reduced slowly. The deformation is measured as a function of load reduction resulting in a characteristic load-line, in which the slope is the local mine stiffness. The post-peak stiffness of the pillar can be compared to that of the mine. If the pillars have a very high stiffness than the loading system, it can fail in an unstable manner. A stiff system with a softer pillar will allow the soft pillar to crush and not fail violently, whereas a stiffer pillar than loading system cannot crush, and will have excess stored strain energy. The following pictures represent the different load deformation curves based on pillar and mine characteristics:
The following picture represents a typical yield pillar layout with the use of barrier pillars:
Post pillars are used in cut-and-fill mining and they provide immediate support to the roof while enabling reasonably high extraction ratio. As the mining progresses, the pillars become more slender. This causes the stability to decrease during the first few cuts. Post pillars are designed to fail gradually with increasing height. Pillar must be stable in the first cut and gradually show signs of deterioration in the second and third cut. The backfill that surrounds the lower levels of the pillars provide confinement to keep the pillars from unravelling once yield occurs. The sizes that are used are generally designed empirically, but can also be done with modelling software. The pillar behavior must be monitored very closely, especially in the first few cuts. The following picture shoes a typical post pillar layout:
Common sizes for post pillars are 4m x 4m or 5m x 5m, with 12 m skin-to-skin. Careful blasting is important otherwise blast-induced fracturing can significantly affect performance. In very difficult ground, post pillars may be designed as ribs with cross-cuts slashed later to produce square pillars. The following picture shows an example of post pillar development:
Crown pillars consist of a rock mass of variable geometry, 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 . Golder Associates have undertaken back analysis of crown pillar stability to examine the methods for design of surface crown pillars. Based on the study, an expression from scaled span required for stability was developed. The scaled span expression takes into account span (S), thickness (T), strike length (L), foliation (q) and crown pillar rock mass unit weight (g). The following equations define the scaled span and the thickness equation is what is used for design of crown pillars:
Crown pillars, which mainly consist of hard rock mines in Ontario: