Establishing a UG2 Pillar Strength Formula in South African Platinum Mines

Abstract

In this study, the peak strength of chromitite pillars in South African platinum mines is re-examined by comparing laboratory tests to the Upper Group 2 (UG2) PlatMine pillar strength formula and underground measurements. The laboratory results were stronger than the underground measurements and the strength predicted by the PlatMine formula. The rock mass strength in the PlatMine formula (‘k-value’) was about 70% of the laboratory tests performed on a 50 mm diameter sample. This finding agrees with other researchers who have compared the rock mass strength to laboratory-determined uniaxial compressive strengths. The laboratory tests, underground measurements, and the PlatMine formula all show that the pillars are significantly stronger than traditionally accepted. This finding can help the UG2 mining industry to improve extraction ratios significantly by adopting the PlatMine formula, particularly at deeper levels where bord-and-pillar workings are used. The results presented in this paper will achieve significant revenue creation in the mine where the underground measurements were made.

1. Introduction

The Bushveld Complex in South Africa (Figure 1) consists of a layered igneous intrusion, which extends for about 350 km from east to west [1]. A concentration of the platinum group metals is in two shallow-dipping, tabular ore bodies known as the following:

• Upper Group 2 (UG2) chromitite seams;
• Merensky Reef, a pegmatoidal pyroxenite reef.

This paper discusses pillar design on the UG2 Reef. The PlatMine formula for UG2 pillar design [2] was developed using a maximum likelihood regression analysis on a database of failed and stable UG2 pillars. The formula is reproduced in this paper as Equation (1). An underground instrumentation site at Booysendal Mine [3] showed that the strength of a pillar loaded to failure agreed with the prediction of the PlatMine formula. However, Oates and Malan [4] suggested that this formula may overestimate pillar strengths. It was therefore important to verify the formula by further research. This was achieved using laboratory tests on a range of w/h ratio samples as described in Watson et al. [5]. All testing was performed in a servo-controlled stiff testing machine (MTS 815) at a constant deformation rate of 0.08 mm/min following the ISRM standards [6]. The paper shows comparisons between the laboratory tests [5], the PlatMine formula [2], and the underground instrumentation [3].

$$Strength=67{\displaystyle \frac{w_e^{0.67}}{h_e^{0.32}}} \mathrm{MPa}$$

(1)

where w_e is the effective pillar width and h_e is the effective pillar height.

Bord-and-pillar mining has become popular on the UG2 Reef, particularly in the newer shallow-depth mines, because of the benefits of mechanisation. Before the PlatMine formula, there were no properly researched criteria for the design of UG2 pillars. A modified version of the Hedley and Grant [7] power formula was adopted because of the success of the Salamon and Munro [8] power formula in South African coal mines. Since there was considerable uncertainty in the implementation of this formula, a conservative approach was implemented [9]. The most common adjustment to the Hedley and Grant [7] formula is shown in Equation (2), where the ‘k-value’ of the original formula was downrated to 35 MPa [10]. This value of ‘k’ is about one-third of the laboratory-determined Uniaxial Compressive Strength (UCS) of chromitite. Stacey and Swart [11] suggested that the Design Rock Mass Strength developed by Laubscher [12] may be used to determine the ‘k-value’. A similar value was generally obtained using this approach, and 35 MPa was universally accepted for ‘k’ in the design of UG2 pillars.

$$Strength=k{\displaystyle \frac{w_e^{0.5}}{h_e^{0.75}}}$$

(2)

where k = 35 MPa, w_e is the effective pillar width, and h_e is the effective pillar height.

The PlatMine formula [2] can have a meaningful impact on mines mining the UG2 reef, as pillars can be mined smaller without compromising safety. In addition, there can be improved transportation efficiencies.

2. Review of Laboratory and Rock Mass Strength Comparisons

Hoek and Brown [13] evaluated the size effect on strength for various hard rock types from several published papers. The strengths were normalised to the UCS of a 50 mm diameter sample (UCS₅₀), and the results are shown in Figure 2. The strength was shown to asymptote at about 0.7UCS₅₀ when the rock size was about 300 mm for hard rocks. A similar approach was followed by Stavrou and Murphy [14], and they found that weathered rock can have a larger drop in strength than homogeneous hard rock. Bieniawski’s [15] tests also found a larger drop in strength for soft rock (coal materials).

Kong et al. [16] found a 10% drop in strength for red sandstone from Eastern Sichuan Province in China. This researcher’s experiments were based on laboratory samples between 50 mm and 150 mm in diameter. Tests performed by Bieniawski [17] on norite showed a strength asymptote at a sample size of about 125 mm and a 25% reduction in strength between UCS₅₀ and the rock mass. York and Canbulat [18] tested 48 samples of Bushveld Merensky Reef pyroxenite from two different mines. A range of six different sizes from 50 mm to 250 mm were assessed. The samples were all prepared at a w/h ratio of one. The results showed a 28% drop in strength between 50 mm and the asymptote at 133 mm, which was similar to the results achieved by Bieniawski [17] on norite. Both the Norite and the Merensky Reef materials are from the Bushveld Complex in South Africa. Work carried out by Masoumi et al. [19] suggested that a separate evaluation of strength reduction needs to be conducted for each rock type.

Esterhuizen [20] researched the weakening effects of discontinuities on coal pillars through distinct element modelling. He found that pillar strength weakened with increasing joint frequency and decreasing joint dip angle, down to a worst-case scenario of 45°. The effects of jointing also reduce with increasing w/h ratio. The research showed that steeply dipping and sparsely spaced jointing would have little effect on the strength of a pillar with a w/h ratio of two and above (about 10%). Generally, UG2 chromitite pillars have a w/h ratio greater than two, and the joints are steeply dipping and widely spaced. The PlatMine UG2 pillar strength database [2] was collected from several mines in the Zondereinde area (Figure 1). The analysis showed a small standard deviation in strength. By implication, there was little variation in the effects of the jointing. However, pillar collapses have been recorded due to the weakening effects of a thrust structure in the top or bottom contact of pillars (parallel to the strata) [21]. These pillars are spars, and the strength of such pillars is not discussed in this paper.

3. Geomechanical Testing of UG2 Chromitite

3.1. Regional Strength Comparison

Maphosa [22] performed normal uniaxial and triaxial laboratory tests on cylindrical UG2 chromitite samples with w/h ratios of 0.4. His samples came from vertical boreholes drilled from the surface at Impala Platinum, a mine on Western Bushveld near Rustenburg (Figure 1). The results of these tests are shown by black dots in Figure 3. A curved, second-order polynomial equation provided a better fit to the data than a linear regression. Triaxial tests performed on UG2 chromitite samples from the Booysendal instrumentation site [3] (near Mashishing in Figure 1) have been plotted as red dots over the Impala Platinum results in the same figure. The results of the UG2 material from opposite sides of the Bushveld Complex were surprisingly similar. The findings suggest that the range of UG2 material strength properties could be similar across the Bushveld. The Booysendal samples were collected from horizontal boreholes drilled into a pillar, implying that the core orientation had little effect on strength.

3.2. Sample Collection

Cylindrical chromitite samples of 54 mm diameter were collected from the Booysendal instrumentation site [3], where the strength of a UG2 pillar was established from underground measurements. Samples were retrieved from horizontal boreholes drilled into the leader seam as shown in Figure 4.

3.3. Procedure for the w/h Ratio Testing

In line with ISRM standards for minimum numbers of tested samples [23], five samples were tested at each of seven w/h ratios [5]. The minimum number of grains (crystals) between the loading platens was never less than 20 through the sample thickness [5]. Endpieces were manufactured specifically for the tests from EN30B steel that was hardened to a Rockwell hardness of HRC58 with a loading diameter surface of 54.0 mm as specified by Ulusay and Hudson [23]. The tolerance of smoothness and parallelism was better than 0.01 mm. Samples were prepared according to the parallelism and smoothness standards specified by Ulusay and Hudson [23] and recorded in Appendix A. A servo-controlled MTS 815 stiff testing machine was used for the testing, and individual strength results are recorded in Appendix A. The samples were tested at a constant deformation rate of 0.08 mm/min following ISRM standards [6]. The average friction angle between the sample and the loading end-piece is also recorded in Appendix A.

3.4. Test Results

The w/h ratio strength results are shown in Figure 5 and provided in Appendix A [5]. Note that the range of strength shown in

Table 1. Results of the chromitite UCS tests [5].

Sample No.	Strength (MPa)	E (GPa)	ν (45% UCS)
Chromitite A	103.0	104.4	0.35
Chromitite B	98.9	99.0	0.30
Chromitite C	89.3	129.7	0.28
Chromitite D	80.0	87.3	0.43
Chromitite E	87.3	89.3	0.39
Mean	91.7	101.9	0.35
Standard deviation	9.2	17.0	0.06

[5] is like the Impala Platinum UCS strength range shown in Figure 3 (where the confinement is zero), and the elastic constants were also comparable. These findings reinforce the assumption that UG2 chromitite strength may be similar across the Bushveld. The results in Figure 5 suggest that the w/h strengthening effects of the laboratory data are better represented by a power rather than a linear formula.

3.5. Comparison Between the Laboratory Tests and Underground Pillars

Watson et al. [2] described a database of 33 failed and 134 stable pillars used to evaluate the exponents and ‘k-value’ of the PlatMine formula for pillar strength (Equation (1)). A maximum likelihood regression analysis was applied to the database using the same approach as Salamon and Munro [8]. The database consisted of a range in w/h ratios from about 1.5 to 4.0 [2]. However, the reef thickness or height range was restricted to between 1.5 m and 2.0 m, with a large proportion of the database at a height of about 2.0 m [2]. A comparison between the PlatMine formula (Equation (1)) and the w/h ratio laboratory tests [5] is shown in Figure 6. A constant height of 2 m was assumed in the PlatMine formula (Equation (1)) since most of the pillars in the database were at this height. Note that the underground pillar w/h ratios varied by increasing the width, whereas the laboratory tests were varied by reducing the height and maintaining a constant width.

An underground instrumentation site was set up at Booysendal Platinum Mine [3], on the eastern side of the Bushveld Complex (Figure 1). Strain cells were installed in the hangingwall above the centre of the pillar, at a position high enough to measure the average pillar stress from a point measurement. After measuring the field stress, the surrounding pillars were mined out until the instrumented pillar failed. A full stress–strain curve was determined for a pillar with an equivalent [24] w/h ratio of two [3]. Importantly, the strength of the pillar was established to be 160 MPa.

A photograph of the observed fracturing in a laboratory-tested sample with a w/h ratio of two is compared to the fracturing just before and after the instrumented pillar failed in Figure 7. The extension fracturing observed around the perimeter of the laboratory sample was identical to what was observed on the pillar underground. The pillar in Figure 7A was coated with white stone dust before failure so that fracturing could be easily observed. The black areas in the figure show where material had fallen away due to the fracturing. Large slabs were observed due to extension fracturing of the pillar in Figure 7B. Unfortunately, the observational borehole was drilled down the longer axis of the pillar, and the shear fractures observed towards the centre of the laboratory test (Figure 7D) were not observed in the pillar.

The laboratory w/h ratio tests were reduced by 28% in strength to account for the rock mass, consistent with what York and Canbulat [18] found for the Bushveld Merensky pyroxenite. The strength-reduced laboratory results are compared to Equation (1) and the underground instrumentation result [3] in Figure 8. For completeness, the adjusted Hedley and Grant formula [7], as described by Equation (2), is also included in the figure.

4. Discussion of Results

The laboratory w/h ratio tests showed higher strength than Equation (1), which is to be expected because of the effects of rock size and jointing on strength (Figure 6). The reduction in strength between a 50 mm diameter sample and the rock mass has never been determined for chromitite. Notice, though, how close the ‘k-value’ in the PlatMine Formula (Equation (1)) is to 70% of the UCS shown in Figure 3. (The PlatMine ‘k-value’ precipitated from the maximum likelihood regression analysis.) Since the Merensky Reef is located within the Bushveld Complex, the 28% strength reduction determined by York and Canbulat [18] was applied to the results shown in Figure 6. There is a remarkably close fit between these results, Equation (1), and the underground instrumentation results [3] in Figure 8, considering that there are some differences between the laboratory tests and the UG2 pillars underground:

• The pillars generally contain widely spaced, steeply dipping joints [20];
• The pillars contain some layers of pyroxenite (Figure 4);
• Metal loading end pieces with a low friction angle on the contact surfaces in the laboratory tests (Appendix A);
• Failure was not allowed to progress into the loading platens in the laboratory tests;
• The effects of draping were excluded from the laboratory tests.

The close relationship between the PlatMine formula, the instrumented pillar, and the downrated laboratory results suggests that the failure mechanism observed in the laboratory tests was like the underground pillar. An improved laboratory test could be conducted using rock loading platens to allow for foundation failure and the draping effects between pillars.

Table 2. Strength and elastic constants for chromitite and pyroxenite [22].

Sample No.	UCS (MPa)	E (GPa)	ν (45% UCS)
Chromitite	95.8	76.9	0.32
Pyroxenite	150.7	126.1	0.26

shows that pyroxenite is stronger and has a lower Poisson’s Ratio than the chromitite. The pyroxenite layers in the pillars are likely to have a strengthening effect, which was not captured in the laboratory tests.

The laboratory w/h ratio tests clearly showed a non-linear relationship between w/h ratio and strength, which was well described by a power formula. Similarly, Maphosa noted a non-linear relationship between strength and confinement [22] at low confining pressures. These findings differ from those of some previous authors for different rock types, where a linear equation seems to have provided a better fit [18,25,26,27]. The different fits suggest that some material strengthening effects are better described by a power formula while others follow a more linear relationship.

The results of the laboratory tests suggested that the metal loading platens provided a significant confining effect on the specimen. The ‘k-value’ in the power formula refers to the strength of a sample with a w/h ratio of one (Figure 6), which was shown by the laboratory tests to be significantly greater than that of a standard test sample with a w/h ratio of 0.4 for chromitite. An average friction angle of about 14° was measured for the interface between the samples and the metal loading platens (Appendix A). In contrast, the contact surfaces underground will likely be about 30° [28]. The low friction angle in the laboratory tests probably acted to reduce the strength results. In contrast, fracturing was not allowed to develop into the foundation in the laboratory tests, which may have had a strengthening effect. Further testing is thus required using rock platens with the same material properties and contact surface friction angles as the pillar foundation materials.

All three analyses shown in Figure 8 suggest that Equation (2) underestimates UG2 pillar strength while the PlatMine formula provides better strengths for the range of pillars within the database [2]. Nothnagel [29] calculated that by using the PlatMine formula, Booysendal, which is a comparably small UG2 mine, will realise an additional USD 1.3 billion over the 25-year life-of-mine (using the January 2020 Platinum Group Metals (PGM) basket price [30]). Consequently, an increase in Net Present Value (NPV) will be realised and the life of the mine will be extended by 4.5 years. Van Schalkwyk [31] calculated that the additional ounces would provide the community with about USD 0.5 billion through labour and procurement (excluding taxes and royalties). These benefits accrue as a direct result of applying the PlatMine formula. According to Baxter [32], more than two jobs are created both up- and downstream for each job in the mines. In addition, each mining employee supports an average of seven people. The significant financial effects of using the PlatMine formula on a single small mine suggest that the UG2 mining industry could gain enormously from its universal implementation. However, it should be noted that there is a variation in material strength, discontinuity orientation, and frequency. Pillar strength will therefore vary from the average strength. The current practice of applying a safety factor of 1.6 [8] should be applied to the calculated pillar strengths during design.

Following a successful instrumentation result, Booysendal and Saffy Shaft (Sibanye Stillwater) have implemented the PlatMine formula to design pillars for about six and three years, respectively. Over 14,400 pillars have been cut at Booysendal at a depth range between 270 m and 550 m below the surface without a single failure [33]. Similarly, 1500 pillars have been cut at the Saffy Shaft at about 700 m below the surface, with an extraction ratio of 82% [34].

5. Conclusions

Laboratory tests were carried out to validate the PlatMine formula [2]. The results showed a greater, but remarkably similar, strength profile to the formula when 2 m high UG2 pillars are assumed in Equation (1). A reduction of 28% in the strength of the laboratory tests [5] was made to account for the rock mass conditions. The results showed a remarkably close fit to the PlatMine formula (Figure 8). In addition, the ‘k-value’ in Equation (1) is close to 70% of the material UCS shown in Figure 3. Importantly, the down-rated results of the laboratory tests (Figure 8) and the instrumentation results [3] suggested that the traditionally used formula [9], as shown in Equation (2), significantly underestimates the strength of pillars.

A change from the traditional formula for pillar design to the use of the PlatMine formula can have a substantial impact on the South African Bushveld platinum industry. Nothnagle [29] calculated an additional revenue of USD 1.3 billion over the 25-year life of Booysendal (a relatively small mine) as a direct result of implementing the PlatMine formula (assuming the January 2020 Platinum Group Metals (PGM) basket price [30]). A higher NPV has therefore been realised for that mine due to the cutting of smaller pillars. In addition, the life of the mine will be extended by 4.5 years and the community will receive an additional USD 0.5 billion through labour and procurement [31].

The laboratory tests showed that a power formula provided a better fit to the data than a linear equation. This result confirms the power fit used in the PlatMine formula. Other authors have found that the w/h ratio strengthening effects may be better described using a linear formula for some materials.

The research suggests a significant effect of the loading surfaces on material strength when using metal loading platens. The results showed considerably stronger samples at a w/h ratio of one compared to a normal UCS test. Further tests are therefore recommended using rock platens with the same material properties as the pillar foundations. In this way, damage will be permitted to propagate into the foundation materials and draping effects can also be included. The true ‘k-value’ also needs to be established for chromitite by testing a range of sample sizes, each with a w/h ratio of one.