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翻译部分英文原文The influence of roadway backfill on the coal pillar strength by numerical investigationHongwei Wang a, Brett A. Poulsen b, Baotang Shen b,n, Sheng Xue b, Yaodong Jiang a(a China University of Mining and Technology, Beijing 100083, China ; b CSIRO Division of Earth Science and Resource Engineering, PO Box 883, Kenmore, QLD 4069, Australia)abstract：Stability of coal pillars and immediate rock mass is of importance in the bord and pillar extraction method underlying critical surface infrastructure. This paper describes the influence of roadway backfill on the coal pillar stability. Based on over 120 numerical models of various pillar height and backfill percentage, it is indicated that the pillar strength will increase with increasing roadway backfill, while the increase in pillar strength is greater for tall pillars than squat pillars for both cohesive and non-cohesive backfill. Modelling suggests that cohesive backfill is more effective in increasing both peak and post-peak pillar strength than non-cohesive backfill. It is also observed that the post-peak response will change from softening to hardening at a certain percentage of either cohesive or non-cohesive backfill.Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.Keywords:Roadway; backfillPillar;strengthPost-peak;responseSofteningHardening1. IntroductionIn the bord and pillar mining method, pillars are left to controlmine stability and surface subsidence, and hence to prevent damage to surface or near surface features, e.g., buildings, railways, highways, rivers, pipelines, etc. Improvement of pillar stability can be achieved by leaving large pillars or using secondary support methods such as bolts, mesh and roadway backfill. Roadway backfill as a support method may be achieved through boreholes from the surface, eliminating the need for people to work underground and allowing pillar strength improvement post-mine closure.Considerable research in the stability of pillars has been carried out particularly for coal mines. Several aspects of this research are discussed here. The coal pillar design must take into account the mechanical and physical properties of the coal. In the area where extraction of coal is mainly done by the bord and pillar mining method, empirical data on the relationship between the strength of a coal pillar and the size of the pillar is essential for the design of coal pillars. For this purpose, Bieniawski 1 in 1967 established an empirical relationship between in situstrength of coal and the size of the pillar. Furthermore, in a comprehensive study with the objective of establishing a framework for the in situ strength and deformation properties of coal pillars at a range of width-to-height ratios, Medhurst and Brown 2 in 1998 investigated the effects of size on coal strengthby a series of triaxial compression tests to provide engineers witha practical and systematic method for estimating the mechanicalproperties of a coal seam.The coal pillar strength is fundamental to pillar design: Salamon and Munro 3,4 proposed an empirical approach based on pillar width and height for pillar strength calculation in South African coal mines that has found wide international application. In the 1990s a database of Australian coal pillars 5,6 wasanalysed both in isolation and combination with the South African database used by Salamon and Munro and a similar empirical strength formula was proposed. To investigate the complete load deformation behaviour of coal pillars, a set of rectangular and square coal pillars was tested in situ by Wagner 7,8 in 1974 and 1980. The research highlights the distribution of stress in a coal pillar and the importance of the pillar core of yielded coal which may remain effective at peak strength.In a mine panel consisted of many pillars and roadways, the stability is a function of the strength of each coal pillar and the interaction between pillars. In particular, the residual strength will influence the load transfer between pillars if one of them is to fail. Consequently, pre- and post-failure mechanism of a coal pillar is essential to understand the load transfer between pillars in the mine panel. Extensive experimental test and numerical analyses have been carried out to study the post-peak strength of stress-strain response of a coal pillar 7,9-13.The stability of pillars for a period longer than mine life is of great importance to prevent damage of surface features into the failure. Deformation and strength change of a coal pillar during and after mining were analysed to establish long-term stability ofcoal pillars. An integrated design method was proposed by Bieniawski in 1994 14 to provide researchers with means to improve the stability of a coal pillar as well as to promote the gradual reduction rate of surface subsidence. Some important work has been done by Salamon and Ozbay 15 to investigate the extent and rate of scaling of coal pillars to indentify the life of a coal pillar for assessing the long-term stability of workings. Empirical and theoretical methods have been developed for pillar strength and stability, loading condition, post-failure and time dependent effect. However, the determination of influence of roadway backfill on the coal pillar stability is less widely reported in the literature. Therefore, the understanding of roadway backfill in the coal pillar design is a topic of this study. In this paper, the function of roadway backfill and the coal pillar stability is investigated by numerical analysis using the numerical code FLAC3D 17.This paper presents a study on the influence of backfill on the coal pillar stability and the relationship between the coal pillar strength and the percentage of roadway backfill. The arrangement is listed as follows: in Section 2 empirical formulas used to calculate the coal pillar strength will be discussed and in Section 3 the preparation of this numerical study and the comparison between theoretical and numerical results will be conducted. In Section 4 of this paper, numerical results, including pillar strength increase with increasing cohesive and non-cohesive backfill, will be presented. In Section 5 the relationship between non-failed pillar core and pillar strength and the preliminary analysis of post-failure of the pillar will be investigated at various percentages of backfill.2. Empirical study of pillar strengthPillar strength has been the subject of study for many years and is a fundamental step for investigating the influence of roadway backfill on the coal pillar stability. Researchers have proposed empirical formulae to describe the strength of coal pillars. The common feature of many of these formulae is that they define the coal pillar strength in terms of their relationship between width (w) and height (h) of the pillar and the units for strength in these formulae is MPa.In 1966, based on a large number of pillar observations a database comprising stable and unstable coal pillars was devel-oped in South Africa. From this, Salamon and Munro 3,4 reported the results of their comprehensive study and presented the widely used the coal pillar strength formula:Pillar strength 7:20w0:46 =h0:66 1where w and h are the width and height of the pillar, respectively. In 1996, a similar database of Australia pillars was compiled and Galvin et al. 5,6 developed the following coal pillar strength formula:Pillar strength 8:60w0:51 =h0:84 2It was found that the formula derived from the Australian database resemble closely the results obtained by Salamon and Munro. The similarity in the pillar strength formulae derived from the two national databases prompted a study based on the combined databases in 1999 5 that produced the formula as below:Pillar strength 6:88w0:50 =h0:70 3By comparing the coal pillar strength calculated using formulae (1)-(3), respectively, for width-to-height ratio from 2 to 4, it is found that the coal pillar strength calculated by these three formulae resembled each other closely and the difference is less than 8.3%. At w/h ratio less than 2 Galvin et al. 5 reported geological structure start to dominate pillar strength and when w/h ratio is over 4, pillar strength increase is greater than that produced by formula (3).The original extensive South African database used by Salamon and Munro is widely accepted under the geological conditions of South Africa and likewise the Australian database is accepted under Australian geological conditions. For the general study undertaken in this paper, formula (3) derived from the combined databases was used to calibrate the numerical model and to analyse the stability of pillar in the subsequent section of this paper.3.Numerical model and determination of parameters3.1.Numerical model and failure criterionFLAC3D (Fast Lagrangian Analysis of Continua in 3-Dimen-sions) is employed for simulating the influence of roadway backfill on the coal pillar stability. The pillar analysed in this simulation is one of an infinite number of pillars extending in both axis directions of plan section. Based on this assumption, only a quarter of pillar needs to be modelled taking advantage of symmetry 16. Fig. 1 is an example of the FLAC3D mesh showing a quarter of pillar as well as roof and floor in this study. The element size of pillar is kept constant as 0.5 m 0.5 m 0.5 m,whilst the thickness of roof and floor is selected as 3 m in the numerical model.The chosen failure criterion is the strain softening model which is based on the FLAC3D Mohr-Coulomb model with non-associated shear and associated tension flow rules 16-19. In this model the cohesion, friction, dilation and tensile strength may soften after the onset of plastic yield by a user defined piecewise linear function 20,21, as shown in Fig. 2. In the standard Mohr-Coulomb model, these properties remain constant.3.2.Boundary conditions of numerical modelBecause the focus of this study is the strength of pillar, in situ stress can be ignored as it has little influence on the peak pillar strength(according to the modelling results, thedifferent is less than 0.63% at 6 m mining height at 100 m depth from the surface). In order to obtain the pillar strength under the condition of uniaxial compression, reasonable bound-ary conditions should be set around the numerical model, as indicated in Fig. 1. Since the area represents a quarter of a pillar with symmetry, the displacement of four vertical symmetry planes of model is restricted in the normal direction, and zero vertical displacement is set at the base of model. A constant velocity is applied to the top of the model in the negative z-direction to generate a vertical loading on this model. In this study, the magnitude of constant velocity has been set as 10-5 m/s.3.3.Determination of relevant material parametersIn this study, formula (3) was used to calibrate the material parameter for width-to-height ratios from 2 to 4. The final calibration results give a coal uniaxial compressive strength (UCS) of 4 MPa and tensile strength is set as 1% of the UCS. Final coal softening rates were 90% cohesion reduction over 5% plastic strain and 61 friction angle reduction over 0.5% plastic strain. The final mechanical parameters and softening rate used (see Fig. 2) in this study are listed in Table 1. The focus of this study is the stability of a coal pillar, hence the roof and floor are assumed to be stiffer than coal and are able to deform but not to yield as recommended by Fama et al. 16. Fig. 3 shows the comparison between calibrated numerical result and analytical solutions calculated by formulae (1)-(3). To achieve a reasonable match with formula (3), it is found necessary to have yielding interface at pillar boundary with the roof and floor. The cohesion of interface is 0.5 MPa and the friction angle is 201. The normal and shear stiffness of this interface are 2.0 GPa.Fig. 2. Variation of cohesion and friction angle with plastic strain. Fig. 3. Comparison of pillar strength between numerical and analytical results3.4. Property of backfillA literature review of backfill 22-24 in a coal mining context identified several examples from China where backfill is used to reduce surface subsidence and from America where backfill is used to dispose fly-ash and reduce acid mine drainage. There are two different types of backfill considered in this study, a cohesive backfill of 1 MPa UCS and a non-cohesive backfill with friction angle of 421. The property of backfill used in this study is shown in Table 2. It is believed that a typical backfill strength will be within this range.4. Results of the numerical analysisIn order to quantify the influence of backfill on pillar strength in detail, 120 models (60 models for cohesive backfill and 60 models for non-cohesive backfill) are analysed for coal pillars of square cross section with pillar width of 20 m, mining height of 5-10 m, equivalent to w/h ratio of 2-4 and percentage of backfill from 0% to 90%. Table 3 shows the results of pillar strength for all the cases in this study.4.1. Relationship between pillar strength and cohesive backfillRelationship between pillar strength and cohesive backfill in roadway is presented in Fig. 4.The raw data from Table 3 have been calculated to uniform 10% backfill as shown in Fig. 5.The modelling results suggest that the pillar strength will increase with increasing roadway backfill, while the percentage increase of pillar strength is greater for the taller pillars than squat pillars. For example, modelling predicts that a pillar with w/h ratio of 2 is 97.9% stronger with 80% roadway backfill, while apillar of w/h ratio of 4 is 45.6% stronger with the same relativeamount of backfill. From Fig. 5 it is observed that when the backfill is less than 40-50% the pillar strength increase is less sensitive to pillar height or w/h ratio, while over 40-50% backfill, pillar strength rapidly increase with pillar height. Modelling results suggest this is more pronounced for tall pillars than squat pillars. This observation will be further discussed in section 5.1.4.2. Relationship between pillar strength and non-cohesive backfillRelationship between pillar strength and non-cohesive backfill in roadway is presented in Fig. 6. The raw data from Table 3 have been calculated to uniform 10% backfill as shown in Fig. 7.Modelling results predict a similar response from non-cohesive backfill although the effectiveness is reduced in comparison with cohesive backfill. For example, at w/h ratio of 2 with 80% non-cohesive backfill, pillar strength is increased by 27.8% compared to 97.9% with cohesive backfill. From Fig. 7, it can be seen that when the backfill is less than 40-50% the pillar strength increase is largely independent of pillar height or w/h ratio, while over 40-50% backfill pillar strength rapidly increase at lower w/h ratio.4.3. Comparison of effects of cohesive and non-cohesive backfillAs seen in Fig. 8, it is observed that the pillar strength increase is greater for cohesive backfill than that for non-cohesive backfill either with percentage of backfill or pillar height. The difference between cohesive and non-cohesive backfill increases gradually with increasing backfill as well as coal pillar height. As an example, if the factor of safety (FOS) of a pillar need to be increased from 1.4 to 1.6, then at 100 m depth from the surface, the required strength increase of a 6 m high coal pillar is approximate 14.0% and modelling suggests it will need 33.3% cohesive roadway backfill compared with 66.7% non-cohesive backfill. However, although cohesive backfill is more effective to improve the stability of a coal pillar than that of non-cohesive backfill, the latter could still satisfy the needs of preventing coal pillar failure and surface subsidence depending on geology or other conditions.Regression of modelling results has generated general for-mulas for pillar strength from cohesive and non-cohesive road-way backfill. These formulas are applicable to the pillar dimensions and backfill strengths considered in this study and care should be exercised in using the results outside these parameters.Given the general pillar strength equationPillar strength Kwa =hb4If cohesive roadway backfill of UCS 1.0 MPa is placed to height hbf in roadways surrounding a pillar of width w 20 m and height h such that:then pillar strength can be expressed asPillar strength Kwa =hb 0:842e2:361hbf =h 5If non-cohesive backfill is placed in roadways surrounding pillars to greater than 50 percent roadway height then pillarstrength can be expressed asPillar strength Kwa =hb 0:334e2:356hbf =h 65. Post-failure behaviour of a coal pillar5.1. Relationship between pillar core and pillar strengthWagner 7,8 in 1974 highlighted the progressive failure of a coal pillar from the pillar boundary towards the centre. His work indentified that a coal pillar may have an intact core when the peak pillar strength has been exceeded. In his research, Wagner indicated that theFig. 9. Variation of pillar core under compressive loading for 9 m coal pillar.central portion of a coal pillar plays a significant role on loading capacity of pillars. In this study, the intact core of pillar is defined as pillar core.Fig. 9 shows the variation of the pillar core during the process of loading. A gradual decrease of volume of pillar core can be observed in this figure. The load-bearing capacity of a coal pillar would also be reduced with decreasing volume of pillar core. Fig. 10 presents two linear segments which illustrate the variation of the coal pillar strength with 0-90% of cohesive roadway backfill at 9 m mining height versus the volume of pillar core calculated at approximate 2% of strain. The turning point is at 40% of backfill. Modelling predicts that the volume of pillar core rapidly increases above 40-50% of backfill as shown in Fig. 10. In this example the pillar strength and core volume are linearly related above and below this value. Similar results are also observed at other mining height.From Fig. 10, it can be observed that the volume of the pillar core would increase with the increase in the coal pillar strength. As observed previously, modelling suggests the increase in pillar strength is approximately constant when the percentage of cohesive backfill is less than 40-50%, while more than 40-50% backfill pillar strength increases rapidly. From Fig. 11 it is observed that the volume of pillar core is largely independent of mining height and approximately constant less than 40-50% of backfill. It is concluded that the roadway backfill is more effectivewhen the percentage of backfill is more than 40-50%. According to the relationship between the volume of the pillar core and the pillar strength of 5-10 m coal pillar with 0-90% backfill, it can be seen that the proportion of pillar core volume would increase with increasing roadway backfill. It is also found that volume of the pillar core is largely independent of pillar height when the percentage of backfill is less than 40-50% of backfill. Since a large amount of backfill lead to a significant improvement of pillar stability, the volume of pillar core would increase with increasing pillar height when the percentage of backfill is more than 40-50%. This means that the high percentage of backfill has a great efficiency for improving the stability of a coal pillar.Fig. 10. Variation of coal pillar strength versus the volume of pillar core of 2% strain at 9 m mining height with increasing cohesive backfill.5.2. Ana
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