通过压力拱理论和区域回采率进行煤柱荷载计算外文文献翻译

翻译部分 外文原文：Coal pillar load calculation by pressure arch theory and near field extraction ratio（B.A. Poulsen CSIRO Earth Science and Resource Engineering,P.O.Box 883,KENMORE 4069 Qld,Australia）ABSTRACTA method for calculating the load acting on a pillar of coal in a bord-and-pillar mine is described for the purpose of back analysing pillar failure or assessing the stability of a panel of pillars. The method is applicable to pillars of arbitrary plan shape and accounts for the spatial position of the pillar with respect to the other pillars, un-mined coal, and the network of roadways. Calculation of the extraction ratio within the pillars zone of influence defined by the depth dependent load transfer distance accounts for the pillars spatial position in the mine layout. An advantage of this approach is its suitability for computer programming for the automated analysis of hundreds of pillars. In this paper, pillars are analysed by the new method, and by tributary area theory, with the results from the new method comparing favourably to elastic three dimensional numerical analysis. Finally, an example of coal mine pillar failure from the literature that neither could be satisfactorily back-analysed by the traditional factor of safety approach nor by two-dimensional numerical modelling is considered. With the proposed, approach 42 of the 54 pillars in the observed failed pillar region are predicted to have a safety factor below the recommended value for long term stability and of these, three pillars are predicted to have an FoS of 1.18. With tributary area theory every pillar, including all those outside the failed pillar region, is predicted to have an FoS less than 1.2.1 Introduction Pillars in bord-and-pillar mining are formed during the extraction process and remain to provide stability to the overlying strata1. Conventional theory proposes that local stability is ensured if the pillars strength exceeds the stress placed upon it. The ratio of a pillars estimated strength to the pillars stress is expressed as the factor of safety （FoS）. The nominal FoS for a pillars design is dependent on the consequence of failure of that pillar. It has been proposed 2 that pillars in a coal mine in Australia should have a safety factor of at least 1.6, where it is desirable that they provide stability in the long term and the consequences are not serious if they fail. A safety factor of 2.1 usually applies to situations, where the consequences of failure are severe 3.Pillars designed to a nominal FoS require estimates of both strength and stress. Pillar strength has been a subject of research for many years with analytical formulas and increasingly numerical methods 4 used to estimate the strength of a pillar based on its geometric shape, mining height and material strength. In comparison with pillar strength, less research is reported in the literature on estimating a pillars stress 14.Pillar stress may be calculated from the beam theory, numerical methods, or photoelastic techniques, but is most commonly estimated by the tributary area theory 5,6 and is expressed as a multiplier based on the extraction ratio of the in situ vertical stress, which in turn is a function of an average overburden density.With estimates of a pillars strength and the pillars stress, it is then possible to estimate an FoS for the pillar, although extrapolating this safety factor to a grouping of pillars or a panel is problematic for a number of reasons: （a） pillars or roadways may not be of uniform dimensions within a panel; （b） pillar load will be dependent on a pillars proximity to barrier pillars and unmined coal, while tributary theory assumes the pillar is one of an infinite array of pillars; （c） pillar load is also dependent on depth-of-cover, which will vary for a seam with a non-zero dip or due to topographic change; and （d） pillar stability probabilities are not independentfailure of any pillar will influence the loading, and hence FoS and stability of adjacent pillars 7.A conceptual theory for pillar loading is based on the pressure arch formed by an excavation in a pre-stressed material. According to this theory stresses arch over an excavation with abutment stresses reducing to pre-mining levels at some distance from the excavation.The present paper introduces the concept of a zone of influence centred on the pillar and based on the load transfer distance to estimate the limit of the pressure arch formed from the creation of the pillar. Within this zone of influence, it will be shown that the redistribution of in situ stress is dependent on the extraction ratio, allowing estimation of an average vertical stress, including the pillar stress for the pillar under consideration. A pillars zone of influence and the associated extraction ratio can be determined from the data typically available from a mine CAD system. With this method, it is possible to automate the estimation of pillar stress, so that a pillars stress and the pillars strength are calculated uniquely on a pillar-by-pillar basis for every pillar in a mine under investigation.2 Pillar strengthCoal pillar strength has been a focus of research for many years, although the work of Salamon and Munro 8 following the Coalbrook mine disaster in South Africa in 1960 9 led to the development of an analytical formula that continues to find wide use in the industry with over one million coal pillars designed with it to date 5,10. Research on coal pillar strength in Australia likewise followed a series of mine accidents in the late 1980s 11. Following on from the work in South Africa, a database of both failed and unfailed Australian pillars was analysed both in isolation and in combination with the South African database.The original, 1966, analytical mine pillar strength formula of Salamon and Munro 8 is reported in SI units as 10where w pillar=width and h=mining height. Formula （1）,updated with the Australia pillar database by Galvin and Hebblewhite 11 from UNSW in 1995, is expressed asThe Galvin and Hebblewhite formula was further modified with a revised statistical approach in 1996 by Salamon, Galvin, Hocking and Anderson 11 Also in 1996, the original South African database was updated and reanalysed with the revised statistical techniques to give 11Finally, in 1999, the combined Australian and South African data sets were analysed with the revised statistical method and the pillar strength formula expressed as 11Graphically, Eqs. （1）（5） are presented in Fig. 1.The results of the work conducted at the UNSW led the authors to note that there is remarkable consistency between the design formulas developed from back-analysis of the two separate national pillar databases, containing many different coal seams and geological environments 11.There are several points of note in these formulas. The dimensionally correct form of each is where k is the strength of a cube of width w and height h, and hence the parameter k in Eqs. （1）（5） is the strength of a representative sample of unit volume and not necessarily the mass strength of coal. Salamon 10 describes the multiplier k, thus is not a property of the material （i.e., of the coal）, but the property of the involved system.Secondly, the width w in Eqs. （1）（5） is an effective width for non-square pillars. Wagner 12 invoked the concept of hydraulic radius to define the effective width we as 13where Ap area of pillar and Cp pillar circumference.Eqs. （1）（5） have been found to underestimate pillar strength when a pillars width to height ratio exceeds five 11. A squat pillar formula has been proposed for a width to height ratio greater than five 11. Likewise, at a width to height ratio less than two, researchers have concluded that pillar strength becomes increasingly sensitive to geological structure 2. Galvin et al. 11 have suggested the application of Eqs. （1）（5） is suitable only within the range w/h2w/h5.3 Pillar stressIn this section, a new method for calculating a pillars stress is presented based on the idea that a zone of influence surrounds a pillar, in which load redistributed by excavations interact to determine the stress in the pillar under analysis. In the following section, we discuss tributary area theory and the inherent assumptions of the method. Secondly, we define the extent of the zone of influence, in which shed load influences a pillars stress and show that the stress magnitude is related to the extraction ratio within this zone of influence. Finally, with idealised examples and a study from the literature, the approach is compared with tributary area theory and alternative analysis methods.where H is depth of cover, e is the extraction ratio between zero （no extraction） and one （100% extraction） and to keep consistency with an original expression of Eq. （1）, g =10 m/s2 and = 2488 kg/m3.The original work of Salamon and Munro calculates the loading on square pillars of width w, bord width B and depth of mining H with tributary area theory asImplicit in Eq. （12） is that the stress is fully contained on the pillars that are uniform in size with constant bord width 15,7, a conservative assumption 13 that is acceptable if the panel width to depth ratio exceeds unity 6.A comprehensive study on pillar loading 6 identifies other techniques to determine pillar stress, including beam theory, electrical analogue, numerical methods and photo elastic physical studies. Roberts et al. point out that pillar FoS calculations with loading calculated by methods, other than Eq. （12）, calls into question the validity of the FoS given that the empirical strength calculation is based on tributary area theory.In the approach that follows is a local method for calculating an extraction ratio e in Eq. （11）. The motivation is to develop a simple analytical methodology that can be automated, yet account for an individual pillars position in the mine. The assumption is made when calculating pillar FoS that the pillar strength formula of Salamon and Munro and its refinements are valid and the pillar strength can be determined from the pillars effective width and its height.It is recognised that the conservative tributary area theory has been successfully applied to the design of many pillars since 1967 and is appropriate in that role. However, it will be shown that in the back analysis of pillar failure, little useful information on pillar loading is given from a tributary area approach, and more so if only average pillar properties are considered.3.1 Load transfer distanceA bord-and-pillar mine will have barrier pillars and unmined seam, pillars of irregular geometry and varying bord width, and it is likely the seam will dip such that the stress acting on any one pillar will vary dependent on the pillars position and geometry.Abel 16 introduced the concept of the load transfer distance （LTD） in estimating the lateral extent of the base to the pressure arch between pillars. The LTD is defined as the maximum distance any stress can be laterally transferred and is determined by measuring the maximum distance that any effect of mining can be detected. Within the distance, defined by the LTD, stress can be shed between pillars. Excavations outside of the LTD will not shed stress and the full tributary area load will act upon the pillar.The LTD from 55 measurements in flat lying sedimentary deposits is presented in 16 with the relationship between LTD and depth of mining, in meters, presented in Fig. 2 and expressed asPillars within the LTD of each other will be able to interact and shed load as shown in Fig. 3. Typically a stiffer pillar, generally of greater width to height ratio such as a barrier pillar, will carry a greater proportion of the load than smaller production pillars within its zone of influence. From Fig. 3, it can be seen that a pillar of effective width w e has a lateral zone of influence measured from the pillar centroid ofIn the plan view, Eq. （14） is the radius of a circular zone of influence.3.2 Average stress with a pillars zone of influenceAt depth H, the average pre-mining vertical stress is commonly estimated in sedimentary strata of average density r ashence an average vertical force in a pillars zone of influence defined by Eq. （14） will beIf excavation of area al is made in a pillars zone of influence, then an average stress in the region, including the pillar is given byor more simply Eq. （11）, where the excavation ratio el is now calculated within the pillars circular zone of influence.4 Example of pillar loading calculationTo examine and compare pillar loading estimated by pressure arch and traditional tributary area theory, a numerical model of square pillars of width 20 m, bord width 5 m and mining height 6 m is subject to 3.75 MPa in situ stress （equivalent to 150 m mining depth）. Making use of quarter symmetry, the average stress is calculated for the central pillar as 1, 9, 25, 49 and 81 pillars are formed （Fig. 4 and 5）. As expected, the numerical and pressure arch methods asymptote to the tributary area stress of 5.86 MPa when the fourth row of pillars, the first wholly outside the pillars zone of influence, are excavated.To examine the pillar loading calculated by the two approaches for an array of irregular pillars, the layout in Fig. 6 is formed with quarter symmetry and the stress calculated after all pillars are created （Fig. 7） Eqs. （7） and （11） are used to estimate pillar effective width and the pillar stress, respectively. Pillar stresses in Fig. 7 are referenced to stresses calculated by elastic three dimensional analysis and an average absolute stress difference is calculated as 0.30 MPa for the pressure arch method and 2.37 MPa for the tributary area theory.5 Back-analysis of pillar failure in the Emaswati coal mine, Swaziland Located approximately 80 km from Mbabane, the capital of Swaziland, the Emaswati mine extracts coal with bord-and-pillar mining of the Main seam in the Karoo Supergroup.As reported by Mokgokong and Peng 17, the failed pillar area of the mine is a panel of approximately 104 pillars of side length 6 m separated by bords of 6 m as shown in Fig. 8 and 9. Mining height is reported as 3 m, with the seam dipping approximately 4to the east with 71 m depth-of-cover in the region of failed pillars.A dolerite intrusion trending north-east, south-west is located in the southern section of the panel, and is associated with shearing observed in the seam and possible weakening from the heating effect of the intrusion 17. Mokgokong and Peng report that the bearing capacity of pillars proximal to the intrusion is significantly reduced. From Fig. 8, it is observed that the boundary of the failed pillar zone abuts the intrusion supporting this observation.A row of cement block stopping extends north south through the panel with roadways to the west forming part of South 2 Mains escapeway with increased reinforcement.5.1 Factor of safety analysis Emaswati coal mine with tributary area theoryWith the average representative properties reported in Mokgokong and Peng, the pillars FoS from Eq. （5） is estimated as 1.11. （Mokgokong and Peng calculate 1.12 with Eq. （1）. While probabilities of failure are not reported for either Eq. （1） or （5）, 2 reports probability of failure for similar Eq. （4） as 50% for FoS 1.0 and 10% for FoS 1.22, hence of the 104 pillars in the panel, it is predicted that more than 10 pillars are likely to fail although there is no knowledge of which are those pillars.A digital model of the failed pillar panel has been created in the mine planning package Vulcan and is displayed in Fig. 10. The surface is represented as a horizontal plane, while the seam is modelled with 41 dip to the east and 71 m below the surface at the centre of the failed pillar region. From the digital model, it is possible to calculate each pillars effective width based on Eq. （7） and depth-of-cover at the pillars centroid.For pillars defined by a closed polygon with n sides and n nodes, the pillars area iswhere each sum is taken from i 1 to n1.With this data and using tributary area theory, pillar FoS is estimated as 1.03 in the deeper southeast corner of the panel and 1.16 in the east （Fig. 10）.5.2 Factor of safety analysis Emaswati coal mine with pressure arch theoryThe rest of the analysis of Emaswati failed pillar panel is undertaken with an FoS approach and pillar stress estimated within each pillars zone of influence as defined by the load transfer distance （pressure arch theory）.Both the concrete stoppings and dolerite intrusion, as shown in Fig. 11, are digitised in the mine plan. The dolerite intrusion is modelled as a void approximately 1 m wide recognising the reduction in strength in proximal pillars.A program was written to read the mine plan in DXF format and calculate pillar area and circumference with Eqs. （18） and （20）, and hence each pillars effective width Eq. （7）. Depth of mining is calculated at the pillars centroid defined by Eq. （19）, and hence the LTD with Eq. （13） and the pillars ZI, Eq. （14）. An example of the calculation of the extraction ratio within the ZI of pillar number 36 is presented in Fig. 11.Each pillars FoS is estimated with Eq. （5） and range 1.182.90. Pillars with FoS below 1.6 show a high correlation with the highly stressed pillars observed in the panel as shown in Fig. 12. Of the 54 pillars observed to be highly stressed, the pressure arch str