Deep Mining: A Rock Engineering Challenge

There exists no universally accepted definition of deep mining. Most definitions of deep mining relate to the changes in mining conditions and mining difficulties associated with the increase in mining depth. The most noticeable effects of depth are the increase in the in situ rock stresses which result in damage to mining excavations and the increase in rock temperature which results in unfavourable environmental conditions and associated physiological stresses for the work force. Efforts to define deep mining in terms of a specific depth value have met with mixed success as the effect of depth on the rock pressure-related mining problems not only depends on the depth of mining but also on the strength of the rock mass. The same applies to the effect of depth of mining on the thermal environment in deep mines which depends on the thermal properties of the rock mass. To illustrate these points, the effects of depth on mining conditions in “deep” coal and gold mines are compared. At a depth of 1000 m below surface, the vertical in situ rock stresses are very similar in the two mining situations, namely about 25 MPa in the case of the coal mines and 27 MPa in the case of the gold mines. However, due to the very much weaker rock formations found in coal mines, the rock pressure-related problems in the coal mines tend to be much more severe than those experienced by gold mines at the same mining depths. The thermal problems in the two mining industries are also very different because of the different thermal properties of the rock formations. In the case of the geologically much younger coal deposits, the temperature increase with depth is about 3 °C/100 m depth, whereas in the case of the 3.500-million-year-old gold mining deposits in Southern Africa the rock temperature increase per 100 m depth is only about 1 °C. At the same mining depths, the virgin rock temperatures in the coal mines are, therefore, three times higher than those found in gold mines. These examples illustrate and explain the difficulties encountered in defining deep mining. A more appropriate approach from a rock pressure point of view is to define “deep mines” in terms of a rock stress to rock strength ratio. In the case of the gold mines, the use was made of the concept of a critical field stress which corresponded to 0.4 of the uniaxial compressive strength of the rock. For rocks with a strength of 150 MPa, which is an average value for rocks found in gold mining regions in Southern Africa, this would equate to 60 MPa and correspond to a depth of about 2000 m, Wagner and Salamon (1975). In the case of the coal mines, the strength values range from about 30 MPa for coal and weak shale to 80 MPa for sandstone. These strength values correspond to critical stress values ranging from 12 to 32 MPa and depth values of about 500 m and 1200 m, respectively. In the case of the heat problems in deep mines, the depth at which the virgin rock temperature exceeds 30 °C would appear to be bench mark value as at such rock temperatures measures would have to be taken to cool the ventilating air to prevent heat stress problems. One exemption is the salt mines where the acceptable air temperatures can be somewhat higher because of the very low humidity of the ventilating air, Wagner (2010). For hard rock mines, typical deep mining problems are likely to be encountered at depths below 1500 m. In the case of coal mining, it seems appropriate to speak of deep mines at depths greater than 750 m below surface.

Figure 1 gives an overview of the in situ stress situation in different regions of the world, Brady and Brown (2004). Whilst the vertical rock stresses tend to increase linearly with the depth below surface, the rate of increase is governed by the density of the overlying rock formations. The situation concerning the horizontal stresses is far more complex. The ratio k expresses the horizontal stress, p_x and p_y, in terms of the primary vertical stress, p_z. At shallow to moderate depths, 0 m < D < 1000 m, the horizontal stresses can vary in a wide range, 0.3 < k < 3.5. At depths greater than 1000 m, the horizontal stress in the earth crust tends to be equal or smaller than the vertical stresses, 1 > k > 0.3. A comprehensive overview of the topic of horizontal stresses in the earth crust is provided by Zang and Stephansson (2010). Numerous models have been proposed explaining mechanisms for the wide spread of horizontal stress values in the earth crust (McCutchen 1988; Amadei et al. 1988; Sheorey 1994). The uncertainty concerning magnitude of the pre-mining horizontal stresses constitutes a serious problem in the rock mechanics planning of new mines.

From a rock engineering point of view, the mine infrastructure comprises all excavations, i.e. shafts, raises, ore and rock passes, mine tunnels and underground chambers of various size and geometry, which are necessary to gain access to the mineral body and to prepare the mineral body for extraction, to transport men, equipment and material to and from the extraction area, to transport the mineral and waste rock from the extraction area to the surface, to ensure supply of the operating areas with energy and air, and to pump water from underground. In addition excavations are required for necessary services such as pump chambers, refrigeration plants, hoist chambers, underground workshops and store rooms, and refuge chambers. Most of these excavations have to remain operational throughout the life of mine but at least throughout the operational life of mining sections. To ensure the stability of these excavations, careful planning is essential taking into considerations the stress changes throughout the operational life of the infrastructure.

Important rock engineering decisions are:

Design of mine infrastructure for life of mine operation

Development of tertiary infrastructure in the stoping area.

The central activity of mining is the extraction of the mineral body. Since mineral deposits are anomalies in the earth crust, each deposit has to be treated separately. Notable exceptions are the relatively shallow coal deposits in Australia, South Africa and the United States of America which have similar geological and rock stress conditions or the deep tabular gold and platinum deposits in South Africa and some of the steeply dipping nickel deposits in Canada. For these deposits, some fairly common extraction systems and design criteria have evolved over time. In the majority of other cases, stoping systems have to be tailored to the local geological and stress conditions.

Critical rock engineering decisions are:

The rock stress environment in deep mines is such that rock fracturing around mining excavations often cannot be prevented. To ensure the stability of the mine infrastructure and the functionality of the mining excavations, to protect the workforce from rock falls and to facilitate the mining operations, it is necessary to support the mining excavations. In deep mines, excavation support is one of the most important, labour-, material- and resource-intensive activities. Support considerations and decisions have to be made already at the planning stages of mine infrastructure design to avoid unfavourable rock pressure situations which necessitate extensive and expensive support measures.

Central issues in the area of mine support are the selection and design of tunnel support systems taking into consideration the importance of excavation, its expected service life and stress changes throughout the life time of the excavation. In deep mines, support design not only has to consider high quasi-static rock stress conditions but also dynamic loading situations such as encountered in the event of rock bursts in the vicinity of the excavation. In seismically active mines, the ability of support to absorb significant amounts of energy is an important design and selection criterion to ensure the stability of the excavation. In the case of mine tunnels, complex-integrated support systems are required to ensure overall excavation stability under static and dynamic loading conditions. This is achieved by the yielding support tendons. The support of the fractured rock at the skin of the excavation is provided by flexible boundary or surface support elements which contain the rock fragments in the area between the support tendons, Kaiser et al. (1997)

Important aspects of mine support activities on deep mines are:

A specific feature of deep mines is the occurrence of mining-induced tremors. The first structured effort to address this problem was the establishment of the Orphirton Earth Tremor Committee in 1908, Durrheim (2010). Mining-induced seismicity is the result of instabilities in the rock mass which are triggered by the stress changes caused by the mining activities. The magnitude of the seismic event depends on the energy stored in the rock mass in the source area of the event. Mining-induced seismicity ranges in energy from 10⁵ to 10⁹ J. Seismic events radiating more than 10⁴ J can cause considerable damage to mine workings and are referred to as rockbursts, Salamon (1983). Much progress has been made in understanding mining-induced seismicity and in ameliorating the rockburst hazard in deep mines. Mine design concepts based on controlling energy changes caused by mining have been developed and are being applied (Cook 1961; Salamon 1974, 1983; Ryder and Jager 2002). The key to mitigate the rockburst hazard in deep mines is to limit mining-induced energy changes in the rock mass by means of stoping width control, use of backfill in the mined out area and by application of partial extraction systems, COMRO (1988). Particularly critical are mining activities in the vicinity of major geological structures such as faults and dykes, Gay et al. (1984). Mine support systems have to be able to absorb large amounts of energy during yielding. The substantial progress that was made in this area is summarized in the excellent textbook by Kaiser et al. (1996).

Mine-wide seismic monitoring systems are state-of-the-art and used routinely on deep mines in Australia, Canada and South Africa, Mendecki (1997). These systems can provide very valuable data concerning seismic activities in mines and the effectiveness of mining strategies. Efforts to predict reliably rockbursts in time and space have so far met with little success.

Important rock engineering decisions on seismically active mines are:

A consequence of extensive mining activities is the disturbance of the surface and surface structures. The extent of damage depends on the size and shape of mining excavation, the nature of the rock formations affected by mining operations and the type of support employed. Another important factor is the depth of mining. At relatively shallow depth, the stresses are low. This has two consequences, namely rock fracturing around excavations tends to be restricted to low-strength rock formations. The second effect concerns rock wedges in the roof of excavations which can move relatively freely because of lack of confinement due to the low horizontal stresses. As a result, subsidence is a common problem in many shallow mining situations in low-strength and intensely jointed rock masses. This type of subsidence is known as discontinuous subsidence. As the depth of mining increases the horizontal stresses in the rock mass increase and gravity-driven rock movement is restricted by frictional forces. As a result rock movement above mined out areas becomes more continuous and the pattern of surface subsidence more predictable. Apart from the vertical downward movement of the surface, horizontal strains are observed on the surface. These tend to be compressive in the middle of the mined out area and tensile close to the edges of the mined out area and beyond it. The maximum tilt of the surface occurs slightly inside the edge of the extraction area. It was found that strain and tilt on the surface were proportional to the maximum subsidence and inversely proportional to the depth of mining. Since it is the strain and the tilt which cause damage to surface structures, the deleterious effects of mining activities on the surface tend to decrease with the depth of mining, National Coal Board (1975). In the case of mining massive mineral deposits using caving methods, discontinuous subsidence is observed. This results in the formation of fracture systems which extend to the surface. Surface damage can be very severe and subsidence can be tens of metres, Henry et al. (2000). In such cases, the surface is no longer suitable for other uses and has to be evacuated. In general, mining-induced surface becomes less of a problem as the depth of mining increases. A specific problem related to the effects of deep mining activities on the surface and surface structures is the mining-induced seismicity which causes ground vibrations. In the case of mine tremors, surface structures can be damaged, Durrheim (2010).

Important issues related to surface subsidence on deep mines are

The purpose of numerical modelling in rock engineering is to analyze and evaluate the behaviour of rock and rock structures under complex loading conditions, to compare and evaluate different rock engineering designs on a rational basis to select the most appropriate design for specific mining situations, to develop semi-empirical mine design criteria using the concept of back analysis and to administer large volumes of rock engineering data. In the past, numerical analysis was confined to problems for which analytical solutions were available and where linear material behaviour was a realistic approximation of actual rock behaviour. Considerable insight into the behaviour of rock structures could be gained from this simple yet limited approach (Obert and Duvall 1967; Jaeger and Cook 1979; Brady and Brown 2004; Ryder and Jager 2002).

The development of high-speed computer equipment has impacted on all aspects of engineering design and practice, Ryder and Jager (2002). Particularly in the field of rock engineering, the availability of high-powered computer equipment and a great variety of software products and numerical techniques has opened avenues for the analysis and evaluation of complex rock engineering problems and mine designs. However, to do this effectively and efficiently the rock mechanics engineer is required to discriminate between various software products and numerical techniques. In this regard, it is important to understand the generic differences between the various numerical methods that are commonly employed in rock engineering.

A great variety of numerical methods for use in rock engineering has been developed. A detailed discussion of the various methods goes beyond the scope of this rock mechanics review and the reader is referred to comprehensive summaries of the state of numerical modelling in rock engineering (Pande et al. 1990; Ryder and Jager 2002, Brady and Brown 2004; Jing and Hudson 2002). The following methods can be distinguished in terms of numerical approach

The numerical methods can be classified into three broad categories continuum, discontinuum and hybrid continuum/discontinuum methods (Nikolic et al. 2016).

As is evident from Table 4, considerable progress was made in the development of numerical models to assist with the solution of rock engineering problems in mines. Most problems encountered with the application of numerical models in rock engineering are the area of defining the primary rock stress environment and the quantification of in situ rock mass properties. Further progress in the application of numerical methods in rock engineering will depend on progress in these areas.

A pillar system in mining comprises the pillar itself, the rock strata above and below the pillar, the stoping excavation which is supported by the pillar and the structural characteristics of the mining area where the pillars are situated. As far as pillar design itself is concerned, there are two main questions, namely how strong is the pillar and what is the load acting on the pillar?

To make progress in science and engineering often requires a major accident or disaster to happen. In the area of pillar design, it was the Coalbrook mine disaster in South Africa in 1960 which resulted in the loss of 437 lives when several thousand coal pillars collapsed affecting an area of about 3.2 km², Van der Merwe (2008). The inquiry into this disaster highlighted a number of issues in pillar design in coal mines for which there were no answers. To address these in a systematic manner the South African Government established the Coal Mines Research Controlling Council (CMRCC) and a coal mine research organization headed by M.D.G. Salamon. Within a few years, sound engineering principles for the design of room and pillar workings in coal mines were developed and became a part of the legislation governing coal mining operations in South Africa. The results of this concentrated research effort have found world-wide application (Hedley et al. 1976; Galvin 2015). Notable outcomes of this research were the coal pillar strength formula by Salamon and Munro (1967), and a method of designing room and pillar workings in coal mines, Salamon (1967).

Considerable progress has been made in estimating the strength of pillars in coal and hard rock mines. This work has shown that the strength properties of the pillar material, the geometry and the size of pillar have a strong influence on the strength of pillars. Two different pillar strength formulae have been proposed

Linear pillar strength formula

Power law strength formula

where \(\sigma_{\text{cp}}\), pillar strength (MPa); \(\sigma_{\text{c}}\), uniaxial compressive strength of pillar material (MPa); \(k_{\text{cp}}\), strength reduction factor (l); w, pillar width (m); h, pillar height (m); l, pillar length (m); α, exponent describing influence of pillar width on pillar strength; β, exponent describing the influence of pillar height on pillar strength; c, linear contribution of pillar material strength to pillar strength; d, contribution of w/h effect to pillar strength.

Table 7 gives details of more commonly used pillar strength formulae. A critical examination of the w/h ratios in the fourth column shows that without exception the formulae are based on the performance of pillars with comparatively low w/h ratios, i.e. (w/h) < 4. Several of the formulae are based on the behaviour of rectangular pillars, i.e. pillars with different base dimensions. In this connection, it has to be pointed out that most pillar strength formulae are based on the strength performance of square pillars. This raises the question of the effective width of rectangular pillars. Experience shows that the strength of long pillars is significantly greater than the strength of a square pillar of the same w/h ratio. In the literature, a number of methods to determine the effective width of rectangular pillars can be found which falls in the range

In large-scale in situ coal pillar tests, Wagner (1974) found that the unconfined periphery of coal pillars contributes relatively little to the load-bearing capability of a pillar. The greatest contribution to the strength of a pillar comes from the confined core. Based on this finding, Wagner proposed the following approach to determine the effective pillar width \(w_{\text{eff}}\)where \(A_{\text{p}}\), pillar area (m²); \(C_{p}\), circumference of pillar (m). Galvin et al. (1999) put the following constraint on this formulation, namely that \(w_{\text{eff}} = \frac{{4\; \times \;A_{\text{p}} }}{{C_{\text{p}} }}\) should be used only if w_min/h > 3.

In cases where w_min/h < 3 w_eff =  w_min.

Esterhuizen et al. (2011) proposed the following adjustment to the width of rectangular limestone pillars

where w is the minimum width of pillar and LBR is a length–benefit ratio Table 8.

One of the important results of room and pillar investigations in the aftermath of the Coalbrook mining disaster was the need to isolate individual room and pillar mining panels by leaving strong continuous pillars between the panels (Salamon 1967; Wagner 1992; Galvin 2016). The importance of substantial interpanel pillars was highlighted by a pillar collapse at the Teutschenthal potash mine where in 1996 an area of 2.5 km² supported by equal sized salt pillars failed suddenly resulting in an earth tremor of Richter magnitude  M_L =  4,8 (Minkley and Menzel 1999). Interpanel pillars serve as ventilation and water barriers, and prevent the spread of pillar collapses outside the mining panel where these occur. For these reasons, it is important that the design of long inter-panel pillars is on a sound footing, i.e. that the issue of the effect of l/w ratio on the strength of strip pillars is resolved.

A point which deserves particular attention is the effect of natural discontinuities on the strength of very slender pillars, i.e. pillars with w/h < 1. Esterhuizen (1995) has analyzed the effect of jointing on the strength of pillars and found that above a w/h ratio of 5 the deleterious influence of jointing on pillar strength become insignificant. Square pillars with small w/h ratios are particularly sensitive to jointing, Esterhuizen (2006). In cases of a dominant joint direction, rectangular pillars with the long dimension oriented in the dip direction of the joints should be employed instead of square pillars. In mines extracting inclined tabular deposits, long pillars oriented in the dip direction are preferred for operational reasons and are better suited to resist down dip strata movement. Care has, however, to be taken in cases where prominent discontinuities are oriented in the dip direction. In such situations, an orientation of the long side of pillar in the strike direction is to be preferred.

There is considerable controversy as far the strength of pillars with large w/h ratios, so-called squat pillars, is concerned. Compared to more slender pillars, squat pillars have a large confined central core area and very high bearing capacities. Salamon (1982) proposed a pillar strength formula for squat coal pillars

where \(\sigma_{\text{cp}}\), strength of squat pillar (MPa); \(V_{\text{p}} = w_{\text{m}}^{2} \times h,\) (m³); \(R_{\text{m}}\), minimum width to height ratio, \({\raise0.7ex\hbox{${w_{\text{m}} }$} \!\mathord{\left/ {\vphantom {{w_{\text{m}} } h}}\right.\kern-0pt} \!\lower0.7ex\hbox{$h$}}\); \(R_{0}\), width to height ratio at which pillar is considered to become squat, \(a = \left( {\alpha + \beta } \right)/3\) and \(b = (\beta - 2\alpha )/3\) see Table 7 and Eq. (3), and \(\varepsilon\), a measure of the rate of strength increase once \({\raise0.7ex\hbox{${w_{\text{m}} }$} \!\mathord{\left/ {\vphantom {{w_{\text{m}} } h}}\right.\kern-0pt} \!\lower0.7ex\hbox{$h$}}\) exceeds R₀.

Conservative values for the transition from the standard pillar strength formula to the squat pillar formula proposed by Salamon (1979) and Wagner and Madden (1984) are

Based on the fact that there are very few reported cases of pillar failures with w/h > 3, some authors suggest that the confined core effect on the strength of pillars manifests itself already at W/H around 3 or even lower (Martin and Maybee 2000; Kaiser et al. 2011; Watson et al. 2010).

The problem of assessing the in situ strength of squat pillars stems from the fact that at higher pillar loads the circumferential portions of pillar are extensively fractured and lateral deformation of pillar increases markedly suggesting onset of pillar failure. However, there is usually little or no information available on the pillar condition in core area of pillar. In addition, there is no information available as far as overall pillar load is concerned.

A second factor which makes assessment of the behaviour of squat pillars difficult is the phenomenon of foundation failure. Given the high strength of squat pillars, the failure in pillar mining area system failure is often caused by foundation failure and not pillar failure. This is particularly the case when the rock strata immediately above and/or below the pillar are weak. The problem of weak floor strata in room and pillar mining is well known in the Australian coal mining industry and has resulted in considerable mining difficulties and accidents, Galvin (2016). Even in situations of massive strong rock foundation, failure is observed and needs to be considered in the design of pillar mining systems, Wagner and Schümann (1971). Foundation failure is a critical issue in connection with the implementation of stabilizing pillars as a means of controlling energy changes in ultra-deep tabular hard rock mines in an effort to ameliorate the rock burst hazard in deep mines (Salamon and Wagner 1979; Ryder and Jager 2002).

The bearing capacity of weak floors, q_b, is usually expressed in terms of stress or pressure. For a uniformly loaded strip pillar on a half-space, bearing capacity is given by classical plasticity analysis, Brady and Brown (2004)

where c is cohesion (MPa); \(\gamma\) is unit weight of loaded medium (N/m³) and \(w_{\text{p}}\) is width of footing (pillar) (m).

Bearing capacity factors

where \(\phi\) is friction angle of loaded medium (°).

Watson et al. (2010) employing the above approach investigated the bearing capacity of the footwall strata in a crush pillar section at the Impala Mine and found the bearing capacity of the Merensky Reef footwall strata to be as low as 33 MPa. This value corresponds to a cohesion value between 0.4 and 1.1 MPa, and a friction value between 30° and 40°. Salamon and Wagner (1979) reported on the successful implementation of the concept of stabilizing pillars to reduce the rock burst hazard at the ERPM gold mine by limiting elastic stope closure. To achieve this objective, long pillars with w/h > 20 are left between individual stoping areas. The average pillar stresses often exceed 200 MPa. As far as this could be established at the time, no foundation failure took place in the massive and strong quartzite in the footwall strata of the gold reef. More work is required to clarify this important aspect of pillar design in deep mines. In the light of the complex foundation failure mechanism observed by Wagner and Schümann (1971), the question has to be asked whether the classical plasticity-based models used to determine bearing capacity of foundations in soils are suited to assess the bearing capacity of strong brittle rock formations.

The second major issue in the rock engineering design pillar systems concerns the average stress acting on pillars. In deep mines, this is in the majority of cases a statically indeterminate problem as the pillar stress depends on the stiffness of pillar, the local deformation of rock strata immediately above and below the pillar, and the stiffness of the mining layout, Salamon (1974). The commonly applied tributary area model of pillar load assessment which assumes the weight of rock strata above the pillar mining area is supported by each pillar in the area by the same amount

where \(\sigma_{\text{p}}\) is the average pillar stress (MPa), \(\rho\) the density of overburden strata (kg/m³), g the gravitational acceleration (9.81 m/s²) and e is the proportion of total area of the pillar panel which has been extracted.

What is commonly overlooked is that a number of criteria have to be satisfied to apply the tributary area model of pillar loading. These are

In practice, these requirements can only be met in mechanized room and pillar situations in coal and salt mines. In hard rock mines where the rock is excavated by means of drilling and blasting, the requirement of constant mining dimensions is difficult if not impossible to achieve.

Figure 2 illustrates the pillar loading situation and the parameters governing pillar load. As a general rule, the stiffness of the mining system increases with the depth of mining and the deformation modulus of rock mass, and decreases with the width of mining panel. Pillar stiffness is directly proportional to the deformation module of pillar material and the pillar area, and inversely proportional to pillar height. In deep mines, tributary area loading conditions are the exception because \(W_{\text{mp}}\) << 1.3D. As a result, a significant proportion of the rock strata above the pillar panel is supported by the abutments of the mining panel, i.e. actual pillar stresses tend to be lower than those determined by tributary area model. The real problem arises when the width of mining panel is increased as this will result in an increase in actual average pillar stress. In situations where pillars are already stressed close to the point of their ultimate strength, the increase in panel width can lead to unexpected regional pillar failures. The situation is particularly critical in post-pillar mining situations. Post-pillar mining is often applied in irregular mineral deposits of considerable height. Room and pillar mining takes place in ascending slices commencing in the deepest portion of the deposit. After a slice of about 3–5 m height has been mined, it is backfilled and working on the backfill the next slice is mined. There are known cases where 30 slices and more have been mined in this manner, Wagner et al. (2016). The specific feature of this system of mining is that with every mining step the stiffness of pillars and its strength are reduced. Given the generally small panel width found in post-pillar mining applications, this means that pillar loads decrease as mining progresses, and more and more of the overburden strata are supported by the panel abutments. Considering that with every mining slice w/h becomes smaller the pillar strength decreases. Any significant increase in panel width in an advanced mining stage can result in regional pillar failure.

The discussion has shown that there are a number of critical situations that have to be considered when applying pillar systems in mines. One aspect of pillar mining at depth which deserves particular attention is that of rock bursts. When the stress acting on a mine pillar reaches the level of ultimate pillar strength, the pillar loses its resistance to deformation and yields. Salamon (1970, 1974) has shown that at this critical moment the mode of failure depends on the post-failure characteristics of the pillar and the local stiffness of the mining system. Up to the point of failure, external work has to be done to deform the pillar and the system is stable. Beyond this point, pillar stability will depend on the local mine stiffness at the position of pillar and the pillar post-failure stiffness, Brady and Brown (1981, 2004). The practical difficulties in assessing pillar stability stem from the lack of reliable information concerning in situ post-failure behaviour of pillars. This is an area requiring urgent attention.

Closely linked to the issue of pillar stability is that of crush pillars. The concept of crush pillars is receiving considerable attention in the South African platinum mining industry. The concept of crush pillars is to develop undersized stope pillars which fail in a stable manner close to the stope face and to use their residual strength to provide the required support resistance to keep the stope hanging wall stable and to prevent back breaks, Watson et al. (2010). Critical design issues are the stiffness of the rock strata close to the stope face and its change with distance from the face, and the w/h ratio which determines peak and residual strengths of the pillars. Another critical dimension is the distance between pillars which should be such that stability of stope hanging wall is ensured.

Design of room and pillar systems is usually based on the classical engineering concept of a factor of safety, \(F_{\text{s}}\), which is defined as the ratio of the strength of the structure and the load acing on the structure. In the case of pillars

where \(\sigma_{\text{cp}}\) is the pillar strength and \(\sigma_{\text{P}}\) is the average pillar stress.

In coal mining, the safety factor of pillars in extraction panels is typically 1.6, in secondary developments about 2 and in main developments 2.2–2.5, Wagner (1992). For South African and Australian coal pillars, there exist statistically reliable data concerning the probability of pillar failure for different safety factors, Salamon and Munro (1967), Galvin et al. (1999). In deep German potash mines, pillar safety factors of 2.5 are being used. For hard rock pillars, reliable data on the probability of pillar failure for different factors of safety are largely missing. Particularly uncertain is the situation for very slender pillars, w/h < 0.8, which is not uncommon in hard rock mines, Esterhuizen et al. (2011). The reason for this is the strong influence of discontinuities on the strength of slender pillars.

One of the main findings of the investigations into the causes of the Coalbrook mining disaster and the regional pillar failure at the Teutschenthal potash mine was the absence of inter-panel pillars. This facilitated the mine-wide pillar collapse. Today, standard practice in the design of room and pillar workings in coal mines is to leave a continuous pillar between adjacent room and pillar panels. Experience has shown that a width of such pillars equal to the size of panel pillars is sufficient to prevent spread of pillar collapse from one panel into the adjacent panel, Salamon (1967), Wagner (1992). In salt mines, there tends to be a resistance to the use of inter-panel pillars which is based on the concern that inter-panel pillars are stiffer than the panel pillars and act as stress raisers which adversely affect the strength of the roof strata and can facilitate water inflow into the mine, Knoll (1995). This issue deserves further investigation.