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The Influence of Roadway Backfill on Bursting Liability and Strength of Coal Pillar by Numerical Investigation
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 26 (2011) 1125 – 1143 www.elsevier.com/locate/procedia
First International Symposium on Mine Safety Science and Engineering
The influence of roadway backfill on bursting liability and strength of coal pillar by numerical investigation Jiang Yaodong a, Wang Hongwei a*, Zhao Yixin a, Zhu Jie a, Pang Xufeng a a* a China University of Mining and Technology, Beijing, 100083, China
Abstract The observations developed in this paper are intended to provide researchers and mining engineers with initial estimate of the burst risk of coal pillar, as the study of bursting liability is of importance in forecasting and preventing the bump of coal pillar. Bursting Energy Index (WCF) is selected in this study to describe the influence of roadway backfill on bursting liability and strength of coal pillar. For the general study undertaken in this paper, a formula derived from the combined South African and Australian databases was used to analyze the bursting liability of coal pillar. Based on over 60 numerical models of various pillar height and backfill percentage, a series of average axial stress-strain curve of 5~10m coal pillar with roadway backfill is attained. Modelling results suggest that the pillar strength will increase with increasing roadway backfill. It also can be seen that the Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the percentage of decrease amount of WCF will increase versus the percentage of roadway backfill. The increase in pillar strength is greater for the tall pillars than squat pillars. It is also observed that the central portion of coal pillar defined as elastic pillar core plays a significant role on loading capacity of pillars, increasing coal pillar strength and decreasing Bursting Energy Index (WCF).
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of China Academy of Safety Science and Technology, China University of Mining and Technology(Beijing), McGill University and University of Wollongong. Keywords: Bursting liability, Roadway backfill, Pillar strength, Elastic pillar core, loading capacity
* Corresponding author. Tel.: +86 13488689275; fax: +0-000-000-0000 . E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.2283
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1. Introduction Coal bump has always been a major concern in underground coal mines for more than fifty years in China. In general, coal bump refers to a sudden and violent failure of coal seam, which will release elastic energy contained in coal seam and expel large mount of coal and rock into the roadway or working face where men and machinery are present [1]. Therefore, coal bump can cause fatality, injury and significant economic loss of coal mining industry. One of the most challenge engineering problems for deep longwall mining is to design coal pillar that will avoid coal bump and catastrophic failure around working environment due primarily to stress concentration in coal pillar [2]. Numerous studies have been done in the past to obtain a comprehensive understanding of the coal bump in coal pillars. Several aspects of this research are discussed here. Coal pillar design must take into account the mechanical and physical properties of the coal [3]. In the area where extraction of coal is mainly done by longwall mining method, empirical data on the relationship between strength of coal pillar and the size of the pillar is essential for the design of coal pillars. For this purpose, Bieniawski [4] in 1967 established an empirical relationship between in situ strength 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 [5] in 1998 investigated the effects of size on coal strength by a series of triaxial compression tests to provide engineers with a practical and systematic method for estimating the mechanical properties of coal seam. The research of coal pillar strength is fundamental to coal pillar design. Salamon and Munro [6~7] 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 1990’s a database of Australian coal pillars [8~9] was analysed 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 [10~11] in 1974 and 1980. The researches highlight the distribution of stress in a coal pillar and the importance of the core of yielded coal pillar which may remain effective at peak strength. Bump or burst liability of coal seam and coal pillar in the bump prone mine has been studied for many years. In order to classify the potential liability of coal seam, several indices were used to evaluate the magnitude of burst possibility of prone coal. There are four indices are most popular, namely the Strain Energy Storage index (WET) [12~14], the Bursting Efficiency Ratio (η) [15~16], the Rheologic Ratio (θ) [17] and Failure Duration Index (Dt) [16~17]. Although these indices provide researchers and mining engineers with evaluation method to predict the coal bump, the shortcoming of each index limits the accuracy application to coal bump prediction in coal mine. It is a major challenge to establish an accurate burst index to indirectly predict coal bump early enough for preventative actions in underground coal mines. 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 coal pillar is essential to understand the load transfer between pillars in the mine panel. Extensive experimental test and numerical analyses were carried out to study the post peak strength of stress-strain response of coal pillar [10; 18~22]. The stability of pillars for a period longer than coal mine life is of great importance to prevent damage of surface features into the failure. Deformation and strength change of coal pillar during and after mining were analysed to establish long-term stability of coal pillars. An integrated design method was proposed by Bieniawski in 1994 [4] to provide researchers with means to improve stability of coal pillar as well as to promote the gradual reduction rate of surface subsidence. Some important work has been done by
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Salamon and Ozbay [6~7] to investigate the extent and rate of scaling of coal pillars to identify the life of a coal pillar by the methodology for assessing the long-term stability of workings. Many attempts have been made to control coal bump in underground coal mine. Coal bump prevention can be achieved through several actions. The widely approach is to conduct an active stress relief program incorporated into the mining cycle [19]. The aim of stress relief is to destroy the structure integrity of the coal seam where enough elastic energy is stored. Innacchione in 1995 proposed a method of shot firing [23] to fracture coal seam, which inject energy into stressed coal and release confinement around the surrounding rocks. Auger drilling [24] was applied by Varley in 1986 to release stress through drilling large diameter holes which is usually 100mm into the coal seam. Water infusion [23~24] is widely used in many coal mines to initiate slippage between rock surfaces, removing the state of confinement of surrounding rocks and releasing large amount of energy stored within the rocks [1]. Empirical and theoretical methods have been developed for coal pillar strength and stability, loading condition, post failure, time dependent effect and prediction and control of coal bump or burst. However, the determination of influence of roadway backfill on bursting liability of coal pillar is less widely reported in the literature. Therefore, the understanding of roadway backfill in coal pillar design and the function of controlling coal bump is a topic of this paper. In this study the function of roadway backfill and coal pillar stability is investigated by numerical analysis using the numerical code FLAC3D [25]. In this paper, three components have been conducted, which comprised the study on the relationship between coal pillar strength and the percentage of roadway backfill, influence of roadway backfill on bursting liability of coal pillar and influence of roadway backfill on elastic pillar core. The arrangement is listed as follows: in Section 2 several bursting liability indices will be reviewed to select a governing index of this study and in Section 3 numerical model and the calibration of relative parameters will be conducted. In Section 4 of this paper, numerical results, including coal pillar strength increase with increasing backfill and bursting liability of coal pillar will be presented. In Section 5 the preliminary analysis of elastic pillar core will be described and two relationships in terms of elastic pillar core will be analysed according to various percentages of backfill. 2. Selection of bursting liability indices of coal pillar The ability of natural coals to store and release rapidly elastic strain energy seems to be a fundamental condition for the occurrence of rock-bursts in deep underground coal mines [13]. Bursting liability indices of coal has been the subject of study for many years and is a crucial step for investigating the ability of natural coals to store and release elastic strain energy. Researchers have proposed several indices determined by experiment to describe this ability of coals. There are three indices are widely applied in area of the prediction of coal bump, namely the Strain Energy Storage Index (WET), the Failure Duration Index (Dt), and the Bursting Energy Index (WCF). Strain Energy Storage Index (WET) is calculated as the strain energy retained to that dissipated during a single loading-unloading cycle of uniaxial compression (see Fig. 1). This index is calculated as follow:
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stress
Uniaxial loading
Uniaxial loading
σc
σc
0.8 ~ 0.9σ c
Unloading
Uniaxial loading
Specimen
Specimen
uniaxial compression test
loading-unloading compression test
We Wp
εp
εe
Dt
strain
strain time
(b) Failure Duration Index (Dt)
(a) Strain Energy Storage Index (WET)
stress Uniaxial loading
σc Specimen
uniaxial compression test
We+Wp
Pre-failure
Wf
Post-failure
strain
(c) Bursting Energy Index (WCF)
Fig. 1 Determination of the Strain Energy Storage Index (WET), Failure Duration Index (Dt) and Bursting Energy Index (WCF)
WET =
We Wp
(1)
where We is the elastic energy retained in the specimen and Wp is the permanent strain energy which is irrecoverable [12].
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Failure Duration Index (Dt) is defined as a period of time which is from the peak strength to its failure in the complete stress-strain curve where specimen is yielding (see Fig. 1). Failure duration reflects the degree of rock failure and the energy variation in the post-peak strength process, which indicates not only the rock failure behavior (violent failure, modest failure or gentle failure), but also the bursting potential of rocks [17]. Bursting Energy Index (WCF) is the ratio of total energy which is comprised of the elastic strain energy (We) and permanent strain energy (Wp) to the energy dissipated in the process of failure during the uniaxial compression. This dimensionless value is calculated as
WCF =
We + W p Wf
=
S1 S2
(2)
where Wf is the energy dissipated in the process of failure, S1 and S2 are the areas covered by pre-failure and post-failure of complete stress-strain curve respectively (see Fig. 1). The complete stress-strain curve includes the total information of the strain energy stored and dissipated in specimen during the uniaxial or loading-unloading compression test. Statistics indicate that Strain Energy Storage Index (WET) is an index which can reflect the pre-failure part of energy state only and Failure Duration Index (Dt) could give the information of post-failure part of stress-strain curve. Therefore, Bursting Energy Index (WCF) is selected in this study since this index is obtained from the complete stress-strain curve (including the information of pre- and post failure) in the uniaxial compression experiment. 3. Numerical model and calibration of parameters 3.1. Numerical model and failure criterion FLAC3D (Fast Lagrangian Analysis of Continua in 3-Dimensions) is employed for simulating the influence of roadway backfill on coal pillar stability. The pillar analyzed 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 modeled taking advantage of symmetry [26]. Fig. 2 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 0.5m×0.5m×0.5m, whilst the thickness of roof and floor is selected as 3m in the numerical model. The chosen failure criterion is the strain softening model which is based on the FLAC3D MohrCoulomb model with non-associated shear and associated tension flow rules [26~28]. 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 [29~30], which is shown in Fig. 3. In the standard Mohr-Coulomb model, these properties remain constant.
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Detailed boundary condition
3m
Roof
5m, 6m, ...10m Pillar
y
3m
x
10m
Block Group
Plan view
10m Backfill
Roof Pillar Backfill Floor
An arbitrary coal pillar Constant velocity Roof Simulated zone
z
Pillar
z
y
x x
y
Floor
x
Cross-sectional view
Fig. 2 A sketch of FLAC3D mesh showing a quarter of a pillar as well as roof and floor
1.2
37 Cohesion (MPa) Friction Angle (°)
36 35
0.8
34
0.6
33 32
0.4
31 0.2
30
0.0
29 0
1
2
3
4 5 6 Plastic strain (%)
Fig. 3 Variation of cohesion and friction angle with plastic strain
7
8
9
10
Friction Angle (°)
Cohesion (MPa)
1.0
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3.2. Boundary conditions of numerical model According to the numerical results, in-situ stress can be ignored as it has little influence on the peak pillar strength (the different is less than 0.63% at 6m mining height at 100m depth from the surface). In order to obtain the pillar strength and complete stress-strain curve of coal pillar under the condition of uniaxial compression, reasonable boundary conditions should be set around the numerical model, as indicated on the Fig. 2. 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 compressive 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 10-5m/s. 3.3. Calibration of numerical parameters with empirical study of pillar strength 3.3.1 Governing formula for parameters calibration Pillar strength has been the subject of study for many years and is a fundamental step for investigating the influence of roadway backfill on 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 coal pillar strength in terms of their relationship between width (w) and height (h) of the pillar. In 1966, based on a large number of pillar observations a database comprising stable and unstable coal pillars was developed in South Africa. From this, Salamon and Munro [6~7] reported the results of their comprehensive study and presented the widely used coal pillar strength formula: Pillar strength = 7.20 ⋅ w
0.46
/ h 0.66
where 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. following coal pillar strength formula: Pillar strength = 8.60 ⋅ w
0.51
/ h 0.84
(3) [8~9]
developed the
(4)
It 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 [8] that produced the formula as below: Pillar strength =
6.88 ⋅ w0.50 / h0.70
(5)
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 (5) derived from the combined databases was used to calibrate the numerical parameters and to analyze the bursting liability of coal pillar in the subsequent section of this paper. 3.3.2 Determination of relevant numerical parameters In this study, formula (5) was used to calibrate the material parameters for width-to-height ratios from 2 to 4. The final calibration results give a coal uniaxial compressive strength (UCS) of 4MPa and tensile
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strength is set as 1% of the UCS. Final coal softening rates were 90% cohesion reduction over 5% plastic strain and 6 degree friction angle reduction over 0.5% plastic strain. The final mechanical parameters and softening rate used (see Fig. 3) in this study are listed in Table 1. One of a key focus of this study is the stability of 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 [26]. Fig. 4 shows the comparison between calibrated numerical result and analytical solutions calculated by formula (1) to (3). To achieve a reasonable match with the formula (3), it is found necessary to have yielding interface at pillar boundary with the roof and floor. The cohesion of interface is 0.5MPa and the friction angle is 20°. The normal and shear stiffness of this interface are 2.0GPa. A literature review of backfill [31~33] 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. A cohesive backfill with 1MPa UCS, 0.117MPa cohesion and 40 degrees friction angle is analyzed in this study. The property of backfill is shown in Table 1 as well. Table 1 Calibrated mechanical parameters used for numerical model [3]
Property
Young's Modulus (GPa)
Poisson’s Ratio
Coal Backfill Roof Floor
1.10 0.57 5.70 7.97
0.30 0.40 0.19 0.24
11
(MPa)
Tensile Strength (MPa)
4.0 1.0 \ \
0.04 0.1 \ \
Cohesion Softening rate (%) 5 \ \ \
Original value (MPa) 1.02 0.117 \ \
Residual value (MPa) 0.102 \ \ \
Original value (°) 36.0 40.0 \ \
Friction Angle Softening Residual rate value (%) (°) 0.5 30.0 \ \ \ \ \ \
Salamon and Munro Formular
10 Pillar strength (MPa)
UCS
Galvin Formula Combined Formula
9
Numerical Results
8 7 6 5 1.5
2.0
2.5
3.0 w/h ratio
Fig. 4 Comparison of pillar strength between numerical and analytical results
3.5
4.0
4.5
Dilation Angle (°) 6.0 10.0 \ \
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4. Numerical model and calibration of parameters This section describes the key numerical results including complete stress-strain curve of coal pillar, pillar strength and Bursting Energy Index. These results are analysed to understand the relationship between coal pillar strength and the percentage of roadway backfill and influence of roadway backfill on bursting liability of coal pillar. In order to quantify the influence of backfill on pillar strength and bursting liability of coal pillar in detail, 60 models are analysed for coal pillars of square cross section with pillar width of 20m, mining height of 5m to 10m, equivalent to w/h ratio of 2 to 4 and percentage of backfill from 0 to 90%. 4.1. Complete stress-strain curve of coal pillar The complete stress-strain curve includes the total information of the strain energy stored and dissipated in specimen during the uniaxial or loading-unloading compression test. In particular, the postfailure response of pillar can be classified as strain softening or strain hardening [3] depending on whether the strength of coal pillar reduces or increases after the peak of the stress-strain curve. Pillar softening or hardening is of great interest since it may influence the stability of the mining panel in that softening pillars will shed most of their load to adjacent pillars while hardening pillars will continue to carry load even after the pillar has failed [34]. Hence, the load transfer to adjacent pillars will be reduced. In Fig. 5 a series of average axial stress-strain curve of 5~10m coal pillar with roadway backfill is shown. The amount of backfill to achieve the transition between strain softening and hardening is presented in Table 2 for all mining height. The values in this table are estimated from the stress-strain curve analysed to 2.5%, 3.0% and 3.5% of plastic strain and are depended on the backfill increment which is in turn depended on the ratio of mining height to the calibrated element size 0.5m. The modelling results suggest that the average axial stress of coal pillar increases with compression until peak stress is reached. In the post-failure region, pillar stress is reduced as strain increases for all models without backfill. All the model results predict that there would be a change to strain hardening behaviour as percentage of backfill increases. For example, this transition point is 33.3% roadway backfill with 6m mining height as shown in Fig. 5 and Table 2. It can also be seen from Table 2 that tall pillars need more backfill than squat pillars to achieve the change from strain softening to hardening.
24
24 90.00%
80.00%
70.00%
60.00%
20
Average stress of coal pillar (MPa)
Average stress of coal pillar (MPa)
40.00%
16 14
30.00%
12
20.00%
10 8 0.00%
6
83.30%
66.70%
20
50.00%
18
58.30%
18 16
50.00%
14 41.70%
12 10
33.30%
8
25.00%
6 0.00%
4
4
2
2
0 0.000
91.70%
22
22
0.005
0.010
0.015
0.020
0.025
Average axial strain of coal pillar
(a) pillar height=5m
0.030
0.035
0.040
0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
(b) pillar height=6m
0.035
0.040
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24 92.90%
78.60%
20
20
18
18
16 57.10%
14 12
50.00%
10
42.90%
8 28.60% 6
68.80%
62.50%
14 12 10
50.00%
8
37.50%
6
31.30% 25.00%
4
0.00%
0.00%
2
2 0 0.000
0 0.005
0.010
0.015
0.020
0.025
0.030
0.000
0.035
0.005
0.010
0.015
(c) pillar height=7m
0.025
0.030
0.035
(d) pillar height=8m 24
24 22
88.90%
22
83.30%
90.00%
20
20
80.00%
18 Average stress of coal pillar (MPa)
18 72.20%
16 14 12
61.10%
10 8
50.00%
16 14
10
50.00% 40.00% 30.00% 25.00%
4
22.20%
0.00%
2
60.00% 8 6
27.80%
4
70.00%
12
38.90%
6
0 0.000
0.020
Average axial strain of coal pillar
Average axial strain of coal pillar
Average stress of coal pillar (MPa)
81.30%
16
21.40%
4
87.50%
22
71.40%
Average stress of coal pillar (MPa)
Average stress of coal pillar (MPa)
22
0.00%
2 0
0.005
0.010 0.015 0.020 Average axial strain of coal pillar
0.025
0.000
0.030
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
(e) pillar height=9m
(f) pillar height=10m
Fig. 5 Numerical stress-strain curve of 5~10m coal pillar with 0~90% roadway backfill Table 2 The amount of backfill to achieve the transition between strain softening and hardening Pillar height (m)
5
6
7
8
9
10
Transition backfill (%)
20.0
33.3
42.9
50.0
61.1
70.0
In order to determine the Bursting Energy Index (WCF), areas of pre-failure and post-failure of the complete stress-strain curve are calculated for each case of numerical model. Table 3 shows the numerical results of pillar strength and Bursting Energy Index (WCF) calculated though the stress-strain curve (see Fig. 5) for all the cases in this study.
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11
Table 3 Numerical results of pillar strength and Bursting Energy Index (WCF) [3]
Approximat e percentage of backfill (%)
Strength (MPa) and WCF of coal pillar 5m
6m
7m
8m
9m
10m
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
0
10.07(0.0%)
0.936
8.94(0.0%)
0.956
7.95(0.0%)
1.028
7.14(0.0%)
0.966
6.47(0.0%)
0.736
5.96(0.0%)
0.634
10
10.49(10.0%) 0.926
9.40(8.3%)
0.941
8.33(7.1%)
1.001
7.85(12.5%)
0.950
7.20(11.1%)
0.720
6.50(10.0%)
0.631
20
11.04(20.0%) 0.916
9.83(16.7%)
0.920
9.09(21.4%)
0.980
8.20(18.8%)
0.933
7.71(22.2%)
0.711
7.10(20.0%)
0.625
30
11.40(30.0%) 0.900 10.69(33.3%) 0.910
9.47(28.6%)
0.960
8.89(31.3%)
0.920
8.03(27.8%)
0.690
7.58(30.0%)
0.611
9.29(37.5%)
40
12.05(40.0%) 0.879 11.30(41.7%) 0.897 10.46(42.9%) 0.905
0.900
8.69(38.9%)
0.666
8.24(40.0%)
0.599
50
12.34(50.0%) 0.811 11.78(50.0%) 0.791 10.95(50.0%) 0.810 10.16(50.0%) 0.781
9.43(50.0%)
0.566
8.94(50.0%)
0.533
60
12.92(60.0%) 0.700 12.08(58.3%) 0.730 11.43(57.1%) 0.711 10.98(62.5%) 0.690 10.09(61.1%) 0.445
9.56(60.0%)
0.444
70
13.42(70.0%) 0.646 12.71(66.7%) 0.670 12.70(71.4%) 0.570 11.58(68.8%) 0.623 11.20(72.2%) 0.353 10.35(70.0%) 0.400
80
14.66(80.0%) 0.584 14.42(83.3%) 0.590 13.50(78.6%) 0.511 13.45(81.3%) 0.501 13.09(83.3%) 0.235 11.80(80.0%) 0.311
90
15.93(90.0%) 0.550 15.80(91.7%) 0.540 15.56(92.9%) 0.400 14.70(87.5%) 0.402 14.40(88.9%) 0.202 14.00(90.0%) 0.256
4.2. Relationship between pillar strength and roadway backfill Relationship between pillar strength and percentage of backfill in roadway is presented in Fig. 6. The raw data from Table 3 has been calculated to uniform 10% backfill as shown in Fig. 6.
140
100 80 60
20
l(
kf il
ac
fb
7
heig ht
eo
Pilla r
8
(m)
9 10
0
nt ag
6
ce
5
90 80 70 60 50 40 30 20 10
%
0
)
40
Pe r
Pillar strength inc
rease (%)
120
Fig. 6 Pillar strength increase versus percentage of backfill in roadway and pillar height for uniform 10% backfill
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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 predict that a pillar with w/h ratio of 2 is 97.9% stronger with 80% roadway backfill, while a pillar of w/h ratio of 4 is 45.6% stronger with the same relative amount of backfill. From Fig. 6, 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. 4.3. Relationship between Bursting Energy Index (WCF) and roadway backfill Because of the discreteness of WCF data for different pillar height, statistic of percentage of the WCF decrease is conducted to determine the relationship between Bursting Energy Index (WCF) and percentage of backfill in roadway, which is presented in Fig. 7. It can be seen from the Fig. 7 that the Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the percentage of the WCF decrease is increasing versus the percentage of roadway backfill. Modelling results predict a similar response that when the backfill is less than 40-50% the WCF decrease is less sensitive to amount of backfill, while over 40-50% backfill, WCF sharply decrease with percentage of backfill. In order to identify this key turning point, the relationship between Bursting Energy Index (WCF) and elastic pillar core will be discussed in section 5. 1.2
110 Percentage WCF Percentageofofthethe WCFdecrease decrease Bursting Index (WCF) BurstingEnergy Energy Index (WCF)
Percentage of theWCF decrease (%)
90
1.0
80 0.8
70 60
0.6
50 40
0.4
30 20
0.2
10 0
0.0 0
10
20
30
40
50
60
70
80
Percentage of backfill (%) Fig. 7 Bursting Energy Index (WCF) and its decreases with increase of the backfill in roadway
90
100
Bursting CF)) BurstingEnergy EnergyIndex Index(W W( CF
100
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4.4. Relationship between pillar strength and Bursting Energy Index (W CF) The data of coal pillar strength and Bursting Energy Index (WCF) of 5-7m coal pillar with 0~90% backfill, which is presented in Fig. 8 are selected to analysed the relationship between pillar strength and Bursting Energy Index (WCF). It needs to be emphasized that the increase of pillar strength is primarily due to the increase of backfill in this study rather than intrinsic properties of coal. Therefore, it can be seen from Fig. 8 that the approximate liner relation between these two parameters indicates the increase of pillar strength which is due to roadway backfill could reduce the occurrence of coal pillar burst. 1.1
Bursting Energy Index ( WCF )
1.0 0.9 0.8 0.7 0.6 0.5 0.4 6
8
10
12
14
16
18
Coal pillar strength (MPa) Fig. 8 Relationship between pillar strength and Bursting Energy Index (WCF)
5. Discussions 5.1. Elastic pillar core Wagner [10~11] in 1974 highlighted the progressive failure of coal pillar from the pillar boundary towards the centre. His work identified that a coal pillar may have an intact core when the overall pillar strength has been exceeded. In his research, Wagner indicated that the central portion of coal pillar plays a significant role on loading capacity of pillars. In this study, the intact core of pillar is defined as elastic pillar core. Fig. 9 shows the variation of elastic pillar core during the process of loading. A gradual decrease of the volume of elastic pillar core can be observed in this figure. The load-bearing capacity of coal pillar would also be reduced with decreasing volume of elastic pillar core.
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C
Average axial stress of coa pillar (MPa)
6
5
D
B
E
4
F
3
A 2
Note: shear-n shear-p tension-n tension-p
1
at shear failure now elastic, but previously at shear failure at tensile failure now elastic, but previously at tensile failure
0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
Position
A
B
C
D
E
F
Strain
0.25%
0.50%
1.00%
1.25%
1.50%
2.00%
State of the elastic pillar core
Block State
Fig. 9 Variation of elastic pillar core under compressive loading for 9m coal pillar
5.2. Relationship between elastic pillar core and pillar strength Fig. 10 presents two linear segments which illustrate the variation of coal pillar strength with 0-90% of roadway backfill at 9m mining height versus the volume of elastic pillar core calculated at approximate 2% of strain. From Fig. 10, it can be seen that the volume of elastic pillar core would increase with increasing coal pillar strength. In this process of increase, the turning point is at 40% of backfill. Modelling predicts that the volume of elastic pillar core rapidly increases above 40-50% of backfill as shown in Fig. 11. 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.
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350
90%
Volume of non-failed core (m 3)
300
250
200
150
100
40%
50
0
0 6
7
8
9
10
11
12
13
14
15
The strength of coal pillar (MPa)
Fig. 10 Variation of coal pillar strength versus the volume of elastic pillar core of 2% strain at 9m mining height with increasing backfill
500 450
Volume of pillar core (m3
400
5m
6m
7m
8m
9m
10m
350 300 250 200
Turning point: 40% Backfill
150 100 50 0 0
10
20
30
40
50
60
70
80
90
100
Percentage of backfill (%)
Fig. 11 Variation of the volume of elastic pillar core with different percentage of backfill
As the key results observed previously, 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 elastic pillar core is largely independent
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of mining height and approximately constant less than 40-50% of roadway backfill. It is concluded that roadway backfill is more effective when the percentage of backfill is more than 40-50%. According to the relationship between the volume of elastic pillar core and pillar strength of 5-10m coal pillar with 0-90% backfill, it can be seen that the proportion of elastic pillar core volume would increase with increasing roadway backfill. It is also found that volume of elastic 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 elastic 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 coal pillar. 5.3. Relationship between elastic pillar core and Bursting Energy Index (WCF) According to the discussions previously, the relationship between volume of elastic pillar core and Bursting Energy Index (WCF) is shown in Fig. 12.
ec lar pil oal
Increase
th nt rst bu
Im pro ve the
eve Pr
sta bil ity
Elastic pillar core
Backfill nce ha En
Re du ce
Coal pillar strength Reduce the occurrence of burst
Bursting Energy Index (WCF)
Fig. 13 A sketch to explain the relationships discussed in this study
Volume of the elastic pillar core will be increase with increasing backfill under the constant compressive loading. Numerical results suggest that elastic pillar core plays an important role in increasing coal pillar strength and decreasing Bursting Energy Index (WCF). This key find could provide researchers and mining engineers with evaluation method to improve the coal pillar stability and predict the burst of coal pillar.
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6. Conclusions The observations developed in this paper are intended to provide researchers and mining engineers with initial estimate of the bursting liability of coal pillar with roadway backfill. Based on the above investigations, the following conclusions can be drawn: z In satisfying the above objective, Bursting Energy Index (WCF) is selected in this study since this index is obtained from the complete stress-strain curve (including the information of pre- and post failure) in the uniaxial compression experiment. z Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the pillar strength is increase versus the percentage of roadway backfill. Model results suggest that the increase in pillar strength is approximately constant when percentage of roadway backfill is less than 40-50%, and when cohesive backfill is more than 40-50% pillar strength increases rapidly. Similar response is observed that Bursting Energy Index (WCF) decrease is less sensitive to amount of backfill when the backfill is less than 40-50%. z The central portion of coal pillar defined as elastic pillar core plays a significant role on loading capacity of pillars, increasing coal pillar strength and decreasing Bursting Energy Index (WCF). Numerical results suggest that the volume of elastic pillar core will increase with increasing backfill under the constant compressive loading. Acknowledgements The authors are indebted to National Basic Research Program (973) of China (NO.2010CB226801), the Fundamental Research Funds for the Central Universities, State Key Laboratory of Coal Resources and Save Mining and the support of CSIRO-MOE Visiting Scholar Fellowship Program. The authors would like to thank Dr. Yucang Wang and Poulsen Brett A. from CSIRO Division of Earth Science and Resource Engineering for their valuable contribution during this study.
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 26 (2011) 1125 – 1143 www.elsevier.com/locate/procedia
First International Symposium on Mine Safety Science and Engineering
The influence of roadway backfill on bursting liability and strength of coal pillar by numerical investigation Jiang Yaodong a, Wang Hongwei a*, Zhao Yixin a, Zhu Jie a, Pang Xufeng a a* a China University of Mining and Technology, Beijing, 100083, China
Abstract The observations developed in this paper are intended to provide researchers and mining engineers with initial estimate of the burst risk of coal pillar, as the study of bursting liability is of importance in forecasting and preventing the bump of coal pillar. Bursting Energy Index (WCF) is selected in this study to describe the influence of roadway backfill on bursting liability and strength of coal pillar. For the general study undertaken in this paper, a formula derived from the combined South African and Australian databases was used to analyze the bursting liability of coal pillar. Based on over 60 numerical models of various pillar height and backfill percentage, a series of average axial stress-strain curve of 5~10m coal pillar with roadway backfill is attained. Modelling results suggest that the pillar strength will increase with increasing roadway backfill. It also can be seen that the Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the percentage of decrease amount of WCF will increase versus the percentage of roadway backfill. The increase in pillar strength is greater for the tall pillars than squat pillars. It is also observed that the central portion of coal pillar defined as elastic pillar core plays a significant role on loading capacity of pillars, increasing coal pillar strength and decreasing Bursting Energy Index (WCF).
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of China Academy of Safety Science and Technology, China University of Mining and Technology(Beijing), McGill University and University of Wollongong. Keywords: Bursting liability, Roadway backfill, Pillar strength, Elastic pillar core, loading capacity
* Corresponding author. Tel.: +86 13488689275; fax: +0-000-000-0000 . E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.2283
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1. Introduction Coal bump has always been a major concern in underground coal mines for more than fifty years in China. In general, coal bump refers to a sudden and violent failure of coal seam, which will release elastic energy contained in coal seam and expel large mount of coal and rock into the roadway or working face where men and machinery are present [1]. Therefore, coal bump can cause fatality, injury and significant economic loss of coal mining industry. One of the most challenge engineering problems for deep longwall mining is to design coal pillar that will avoid coal bump and catastrophic failure around working environment due primarily to stress concentration in coal pillar [2]. Numerous studies have been done in the past to obtain a comprehensive understanding of the coal bump in coal pillars. Several aspects of this research are discussed here. Coal pillar design must take into account the mechanical and physical properties of the coal [3]. In the area where extraction of coal is mainly done by longwall mining method, empirical data on the relationship between strength of coal pillar and the size of the pillar is essential for the design of coal pillars. For this purpose, Bieniawski [4] in 1967 established an empirical relationship between in situ strength 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 [5] in 1998 investigated the effects of size on coal strength by a series of triaxial compression tests to provide engineers with a practical and systematic method for estimating the mechanical properties of coal seam. The research of coal pillar strength is fundamental to coal pillar design. Salamon and Munro [6~7] 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 1990’s a database of Australian coal pillars [8~9] was analysed 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 [10~11] in 1974 and 1980. The researches highlight the distribution of stress in a coal pillar and the importance of the core of yielded coal pillar which may remain effective at peak strength. Bump or burst liability of coal seam and coal pillar in the bump prone mine has been studied for many years. In order to classify the potential liability of coal seam, several indices were used to evaluate the magnitude of burst possibility of prone coal. There are four indices are most popular, namely the Strain Energy Storage index (WET) [12~14], the Bursting Efficiency Ratio (η) [15~16], the Rheologic Ratio (θ) [17] and Failure Duration Index (Dt) [16~17]. Although these indices provide researchers and mining engineers with evaluation method to predict the coal bump, the shortcoming of each index limits the accuracy application to coal bump prediction in coal mine. It is a major challenge to establish an accurate burst index to indirectly predict coal bump early enough for preventative actions in underground coal mines. 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 coal pillar is essential to understand the load transfer between pillars in the mine panel. Extensive experimental test and numerical analyses were carried out to study the post peak strength of stress-strain response of coal pillar [10; 18~22]. The stability of pillars for a period longer than coal mine life is of great importance to prevent damage of surface features into the failure. Deformation and strength change of coal pillar during and after mining were analysed to establish long-term stability of coal pillars. An integrated design method was proposed by Bieniawski in 1994 [4] to provide researchers with means to improve stability of coal pillar as well as to promote the gradual reduction rate of surface subsidence. Some important work has been done by
Jiang Yaodong et al.et/al/ Procedia Engineering 26 00 (2011) 1125 – 1143 Wang Hongwei Procedia Engineering (2011) 000–000
Salamon and Ozbay [6~7] to investigate the extent and rate of scaling of coal pillars to identify the life of a coal pillar by the methodology for assessing the long-term stability of workings. Many attempts have been made to control coal bump in underground coal mine. Coal bump prevention can be achieved through several actions. The widely approach is to conduct an active stress relief program incorporated into the mining cycle [19]. The aim of stress relief is to destroy the structure integrity of the coal seam where enough elastic energy is stored. Innacchione in 1995 proposed a method of shot firing [23] to fracture coal seam, which inject energy into stressed coal and release confinement around the surrounding rocks. Auger drilling [24] was applied by Varley in 1986 to release stress through drilling large diameter holes which is usually 100mm into the coal seam. Water infusion [23~24] is widely used in many coal mines to initiate slippage between rock surfaces, removing the state of confinement of surrounding rocks and releasing large amount of energy stored within the rocks [1]. Empirical and theoretical methods have been developed for coal pillar strength and stability, loading condition, post failure, time dependent effect and prediction and control of coal bump or burst. However, the determination of influence of roadway backfill on bursting liability of coal pillar is less widely reported in the literature. Therefore, the understanding of roadway backfill in coal pillar design and the function of controlling coal bump is a topic of this paper. In this study the function of roadway backfill and coal pillar stability is investigated by numerical analysis using the numerical code FLAC3D [25]. In this paper, three components have been conducted, which comprised the study on the relationship between coal pillar strength and the percentage of roadway backfill, influence of roadway backfill on bursting liability of coal pillar and influence of roadway backfill on elastic pillar core. The arrangement is listed as follows: in Section 2 several bursting liability indices will be reviewed to select a governing index of this study and in Section 3 numerical model and the calibration of relative parameters will be conducted. In Section 4 of this paper, numerical results, including coal pillar strength increase with increasing backfill and bursting liability of coal pillar will be presented. In Section 5 the preliminary analysis of elastic pillar core will be described and two relationships in terms of elastic pillar core will be analysed according to various percentages of backfill. 2. Selection of bursting liability indices of coal pillar The ability of natural coals to store and release rapidly elastic strain energy seems to be a fundamental condition for the occurrence of rock-bursts in deep underground coal mines [13]. Bursting liability indices of coal has been the subject of study for many years and is a crucial step for investigating the ability of natural coals to store and release elastic strain energy. Researchers have proposed several indices determined by experiment to describe this ability of coals. There are three indices are widely applied in area of the prediction of coal bump, namely the Strain Energy Storage Index (WET), the Failure Duration Index (Dt), and the Bursting Energy Index (WCF). Strain Energy Storage Index (WET) is calculated as the strain energy retained to that dissipated during a single loading-unloading cycle of uniaxial compression (see Fig. 1). This index is calculated as follow:
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stress
Uniaxial loading
Uniaxial loading
σc
σc
0.8 ~ 0.9σ c
Unloading
Uniaxial loading
Specimen
Specimen
uniaxial compression test
loading-unloading compression test
We Wp
εp
εe
Dt
strain
strain time
(b) Failure Duration Index (Dt)
(a) Strain Energy Storage Index (WET)
stress Uniaxial loading
σc Specimen
uniaxial compression test
We+Wp
Pre-failure
Wf
Post-failure
strain
(c) Bursting Energy Index (WCF)
Fig. 1 Determination of the Strain Energy Storage Index (WET), Failure Duration Index (Dt) and Bursting Energy Index (WCF)
WET =
We Wp
(1)
where We is the elastic energy retained in the specimen and Wp is the permanent strain energy which is irrecoverable [12].
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Failure Duration Index (Dt) is defined as a period of time which is from the peak strength to its failure in the complete stress-strain curve where specimen is yielding (see Fig. 1). Failure duration reflects the degree of rock failure and the energy variation in the post-peak strength process, which indicates not only the rock failure behavior (violent failure, modest failure or gentle failure), but also the bursting potential of rocks [17]. Bursting Energy Index (WCF) is the ratio of total energy which is comprised of the elastic strain energy (We) and permanent strain energy (Wp) to the energy dissipated in the process of failure during the uniaxial compression. This dimensionless value is calculated as
WCF =
We + W p Wf
=
S1 S2
(2)
where Wf is the energy dissipated in the process of failure, S1 and S2 are the areas covered by pre-failure and post-failure of complete stress-strain curve respectively (see Fig. 1). The complete stress-strain curve includes the total information of the strain energy stored and dissipated in specimen during the uniaxial or loading-unloading compression test. Statistics indicate that Strain Energy Storage Index (WET) is an index which can reflect the pre-failure part of energy state only and Failure Duration Index (Dt) could give the information of post-failure part of stress-strain curve. Therefore, Bursting Energy Index (WCF) is selected in this study since this index is obtained from the complete stress-strain curve (including the information of pre- and post failure) in the uniaxial compression experiment. 3. Numerical model and calibration of parameters 3.1. Numerical model and failure criterion FLAC3D (Fast Lagrangian Analysis of Continua in 3-Dimensions) is employed for simulating the influence of roadway backfill on coal pillar stability. The pillar analyzed 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 modeled taking advantage of symmetry [26]. Fig. 2 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 0.5m×0.5m×0.5m, whilst the thickness of roof and floor is selected as 3m in the numerical model. The chosen failure criterion is the strain softening model which is based on the FLAC3D MohrCoulomb model with non-associated shear and associated tension flow rules [26~28]. 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 [29~30], which is shown in Fig. 3. In the standard Mohr-Coulomb model, these properties remain constant.
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Detailed boundary condition
3m
Roof
5m, 6m, ...10m Pillar
y
3m
x
10m
Block Group
Plan view
10m Backfill
Roof Pillar Backfill Floor
An arbitrary coal pillar Constant velocity Roof Simulated zone
z
Pillar
z
y
x x
y
Floor
x
Cross-sectional view
Fig. 2 A sketch of FLAC3D mesh showing a quarter of a pillar as well as roof and floor
1.2
37 Cohesion (MPa) Friction Angle (°)
36 35
0.8
34
0.6
33 32
0.4
31 0.2
30
0.0
29 0
1
2
3
4 5 6 Plastic strain (%)
Fig. 3 Variation of cohesion and friction angle with plastic strain
7
8
9
10
Friction Angle (°)
Cohesion (MPa)
1.0
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3.2. Boundary conditions of numerical model According to the numerical results, in-situ stress can be ignored as it has little influence on the peak pillar strength (the different is less than 0.63% at 6m mining height at 100m depth from the surface). In order to obtain the pillar strength and complete stress-strain curve of coal pillar under the condition of uniaxial compression, reasonable boundary conditions should be set around the numerical model, as indicated on the Fig. 2. 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 compressive 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 10-5m/s. 3.3. Calibration of numerical parameters with empirical study of pillar strength 3.3.1 Governing formula for parameters calibration Pillar strength has been the subject of study for many years and is a fundamental step for investigating the influence of roadway backfill on 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 coal pillar strength in terms of their relationship between width (w) and height (h) of the pillar. In 1966, based on a large number of pillar observations a database comprising stable and unstable coal pillars was developed in South Africa. From this, Salamon and Munro [6~7] reported the results of their comprehensive study and presented the widely used coal pillar strength formula: Pillar strength = 7.20 ⋅ w
0.46
/ h 0.66
where 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. following coal pillar strength formula: Pillar strength = 8.60 ⋅ w
0.51
/ h 0.84
(3) [8~9]
developed the
(4)
It 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 [8] that produced the formula as below: Pillar strength =
6.88 ⋅ w0.50 / h0.70
(5)
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 (5) derived from the combined databases was used to calibrate the numerical parameters and to analyze the bursting liability of coal pillar in the subsequent section of this paper. 3.3.2 Determination of relevant numerical parameters In this study, formula (5) was used to calibrate the material parameters for width-to-height ratios from 2 to 4. The final calibration results give a coal uniaxial compressive strength (UCS) of 4MPa and tensile
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strength is set as 1% of the UCS. Final coal softening rates were 90% cohesion reduction over 5% plastic strain and 6 degree friction angle reduction over 0.5% plastic strain. The final mechanical parameters and softening rate used (see Fig. 3) in this study are listed in Table 1. One of a key focus of this study is the stability of 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 [26]. Fig. 4 shows the comparison between calibrated numerical result and analytical solutions calculated by formula (1) to (3). To achieve a reasonable match with the formula (3), it is found necessary to have yielding interface at pillar boundary with the roof and floor. The cohesion of interface is 0.5MPa and the friction angle is 20°. The normal and shear stiffness of this interface are 2.0GPa. A literature review of backfill [31~33] 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. A cohesive backfill with 1MPa UCS, 0.117MPa cohesion and 40 degrees friction angle is analyzed in this study. The property of backfill is shown in Table 1 as well. Table 1 Calibrated mechanical parameters used for numerical model [3]
Property
Young's Modulus (GPa)
Poisson’s Ratio
Coal Backfill Roof Floor
1.10 0.57 5.70 7.97
0.30 0.40 0.19 0.24
11
(MPa)
Tensile Strength (MPa)
4.0 1.0 \ \
0.04 0.1 \ \
Cohesion Softening rate (%) 5 \ \ \
Original value (MPa) 1.02 0.117 \ \
Residual value (MPa) 0.102 \ \ \
Original value (°) 36.0 40.0 \ \
Friction Angle Softening Residual rate value (%) (°) 0.5 30.0 \ \ \ \ \ \
Salamon and Munro Formular
10 Pillar strength (MPa)
UCS
Galvin Formula Combined Formula
9
Numerical Results
8 7 6 5 1.5
2.0
2.5
3.0 w/h ratio
Fig. 4 Comparison of pillar strength between numerical and analytical results
3.5
4.0
4.5
Dilation Angle (°) 6.0 10.0 \ \
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4. Numerical model and calibration of parameters This section describes the key numerical results including complete stress-strain curve of coal pillar, pillar strength and Bursting Energy Index. These results are analysed to understand the relationship between coal pillar strength and the percentage of roadway backfill and influence of roadway backfill on bursting liability of coal pillar. In order to quantify the influence of backfill on pillar strength and bursting liability of coal pillar in detail, 60 models are analysed for coal pillars of square cross section with pillar width of 20m, mining height of 5m to 10m, equivalent to w/h ratio of 2 to 4 and percentage of backfill from 0 to 90%. 4.1. Complete stress-strain curve of coal pillar The complete stress-strain curve includes the total information of the strain energy stored and dissipated in specimen during the uniaxial or loading-unloading compression test. In particular, the postfailure response of pillar can be classified as strain softening or strain hardening [3] depending on whether the strength of coal pillar reduces or increases after the peak of the stress-strain curve. Pillar softening or hardening is of great interest since it may influence the stability of the mining panel in that softening pillars will shed most of their load to adjacent pillars while hardening pillars will continue to carry load even after the pillar has failed [34]. Hence, the load transfer to adjacent pillars will be reduced. In Fig. 5 a series of average axial stress-strain curve of 5~10m coal pillar with roadway backfill is shown. The amount of backfill to achieve the transition between strain softening and hardening is presented in Table 2 for all mining height. The values in this table are estimated from the stress-strain curve analysed to 2.5%, 3.0% and 3.5% of plastic strain and are depended on the backfill increment which is in turn depended on the ratio of mining height to the calibrated element size 0.5m. The modelling results suggest that the average axial stress of coal pillar increases with compression until peak stress is reached. In the post-failure region, pillar stress is reduced as strain increases for all models without backfill. All the model results predict that there would be a change to strain hardening behaviour as percentage of backfill increases. For example, this transition point is 33.3% roadway backfill with 6m mining height as shown in Fig. 5 and Table 2. It can also be seen from Table 2 that tall pillars need more backfill than squat pillars to achieve the change from strain softening to hardening.
24
24 90.00%
80.00%
70.00%
60.00%
20
Average stress of coal pillar (MPa)
Average stress of coal pillar (MPa)
40.00%
16 14
30.00%
12
20.00%
10 8 0.00%
6
83.30%
66.70%
20
50.00%
18
58.30%
18 16
50.00%
14 41.70%
12 10
33.30%
8
25.00%
6 0.00%
4
4
2
2
0 0.000
91.70%
22
22
0.005
0.010
0.015
0.020
0.025
Average axial strain of coal pillar
(a) pillar height=5m
0.030
0.035
0.040
0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
(b) pillar height=6m
0.035
0.040
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24 92.90%
78.60%
20
20
18
18
16 57.10%
14 12
50.00%
10
42.90%
8 28.60% 6
68.80%
62.50%
14 12 10
50.00%
8
37.50%
6
31.30% 25.00%
4
0.00%
0.00%
2
2 0 0.000
0 0.005
0.010
0.015
0.020
0.025
0.030
0.000
0.035
0.005
0.010
0.015
(c) pillar height=7m
0.025
0.030
0.035
(d) pillar height=8m 24
24 22
88.90%
22
83.30%
90.00%
20
20
80.00%
18 Average stress of coal pillar (MPa)
18 72.20%
16 14 12
61.10%
10 8
50.00%
16 14
10
50.00% 40.00% 30.00% 25.00%
4
22.20%
0.00%
2
60.00% 8 6
27.80%
4
70.00%
12
38.90%
6
0 0.000
0.020
Average axial strain of coal pillar
Average axial strain of coal pillar
Average stress of coal pillar (MPa)
81.30%
16
21.40%
4
87.50%
22
71.40%
Average stress of coal pillar (MPa)
Average stress of coal pillar (MPa)
22
0.00%
2 0
0.005
0.010 0.015 0.020 Average axial strain of coal pillar
0.025
0.000
0.030
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
(e) pillar height=9m
(f) pillar height=10m
Fig. 5 Numerical stress-strain curve of 5~10m coal pillar with 0~90% roadway backfill Table 2 The amount of backfill to achieve the transition between strain softening and hardening Pillar height (m)
5
6
7
8
9
10
Transition backfill (%)
20.0
33.3
42.9
50.0
61.1
70.0
In order to determine the Bursting Energy Index (WCF), areas of pre-failure and post-failure of the complete stress-strain curve are calculated for each case of numerical model. Table 3 shows the numerical results of pillar strength and Bursting Energy Index (WCF) calculated though the stress-strain curve (see Fig. 5) for all the cases in this study.
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11
Table 3 Numerical results of pillar strength and Bursting Energy Index (WCF) [3]
Approximat e percentage of backfill (%)
Strength (MPa) and WCF of coal pillar 5m
6m
7m
8m
9m
10m
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
Strength (MPa)
WCF
0
10.07(0.0%)
0.936
8.94(0.0%)
0.956
7.95(0.0%)
1.028
7.14(0.0%)
0.966
6.47(0.0%)
0.736
5.96(0.0%)
0.634
10
10.49(10.0%) 0.926
9.40(8.3%)
0.941
8.33(7.1%)
1.001
7.85(12.5%)
0.950
7.20(11.1%)
0.720
6.50(10.0%)
0.631
20
11.04(20.0%) 0.916
9.83(16.7%)
0.920
9.09(21.4%)
0.980
8.20(18.8%)
0.933
7.71(22.2%)
0.711
7.10(20.0%)
0.625
30
11.40(30.0%) 0.900 10.69(33.3%) 0.910
9.47(28.6%)
0.960
8.89(31.3%)
0.920
8.03(27.8%)
0.690
7.58(30.0%)
0.611
9.29(37.5%)
40
12.05(40.0%) 0.879 11.30(41.7%) 0.897 10.46(42.9%) 0.905
0.900
8.69(38.9%)
0.666
8.24(40.0%)
0.599
50
12.34(50.0%) 0.811 11.78(50.0%) 0.791 10.95(50.0%) 0.810 10.16(50.0%) 0.781
9.43(50.0%)
0.566
8.94(50.0%)
0.533
60
12.92(60.0%) 0.700 12.08(58.3%) 0.730 11.43(57.1%) 0.711 10.98(62.5%) 0.690 10.09(61.1%) 0.445
9.56(60.0%)
0.444
70
13.42(70.0%) 0.646 12.71(66.7%) 0.670 12.70(71.4%) 0.570 11.58(68.8%) 0.623 11.20(72.2%) 0.353 10.35(70.0%) 0.400
80
14.66(80.0%) 0.584 14.42(83.3%) 0.590 13.50(78.6%) 0.511 13.45(81.3%) 0.501 13.09(83.3%) 0.235 11.80(80.0%) 0.311
90
15.93(90.0%) 0.550 15.80(91.7%) 0.540 15.56(92.9%) 0.400 14.70(87.5%) 0.402 14.40(88.9%) 0.202 14.00(90.0%) 0.256
4.2. Relationship between pillar strength and roadway backfill Relationship between pillar strength and percentage of backfill in roadway is presented in Fig. 6. The raw data from Table 3 has been calculated to uniform 10% backfill as shown in Fig. 6.
140
100 80 60
20
l(
kf il
ac
fb
7
heig ht
eo
Pilla r
8
(m)
9 10
0
nt ag
6
ce
5
90 80 70 60 50 40 30 20 10
%
0
)
40
Pe r
Pillar strength inc
rease (%)
120
Fig. 6 Pillar strength increase versus percentage of backfill in roadway and pillar height for uniform 10% backfill
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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 predict that a pillar with w/h ratio of 2 is 97.9% stronger with 80% roadway backfill, while a pillar of w/h ratio of 4 is 45.6% stronger with the same relative amount of backfill. From Fig. 6, 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. 4.3. Relationship between Bursting Energy Index (WCF) and roadway backfill Because of the discreteness of WCF data for different pillar height, statistic of percentage of the WCF decrease is conducted to determine the relationship between Bursting Energy Index (WCF) and percentage of backfill in roadway, which is presented in Fig. 7. It can be seen from the Fig. 7 that the Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the percentage of the WCF decrease is increasing versus the percentage of roadway backfill. Modelling results predict a similar response that when the backfill is less than 40-50% the WCF decrease is less sensitive to amount of backfill, while over 40-50% backfill, WCF sharply decrease with percentage of backfill. In order to identify this key turning point, the relationship between Bursting Energy Index (WCF) and elastic pillar core will be discussed in section 5. 1.2
110 Percentage WCF Percentageofofthethe WCFdecrease decrease Bursting Index (WCF) BurstingEnergy Energy Index (WCF)
Percentage of theWCF decrease (%)
90
1.0
80 0.8
70 60
0.6
50 40
0.4
30 20
0.2
10 0
0.0 0
10
20
30
40
50
60
70
80
Percentage of backfill (%) Fig. 7 Bursting Energy Index (WCF) and its decreases with increase of the backfill in roadway
90
100
Bursting CF)) BurstingEnergy EnergyIndex Index(W W( CF
100
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4.4. Relationship between pillar strength and Bursting Energy Index (W CF) The data of coal pillar strength and Bursting Energy Index (WCF) of 5-7m coal pillar with 0~90% backfill, which is presented in Fig. 8 are selected to analysed the relationship between pillar strength and Bursting Energy Index (WCF). It needs to be emphasized that the increase of pillar strength is primarily due to the increase of backfill in this study rather than intrinsic properties of coal. Therefore, it can be seen from Fig. 8 that the approximate liner relation between these two parameters indicates the increase of pillar strength which is due to roadway backfill could reduce the occurrence of coal pillar burst. 1.1
Bursting Energy Index ( WCF )
1.0 0.9 0.8 0.7 0.6 0.5 0.4 6
8
10
12
14
16
18
Coal pillar strength (MPa) Fig. 8 Relationship between pillar strength and Bursting Energy Index (WCF)
5. Discussions 5.1. Elastic pillar core Wagner [10~11] in 1974 highlighted the progressive failure of coal pillar from the pillar boundary towards the centre. His work identified that a coal pillar may have an intact core when the overall pillar strength has been exceeded. In his research, Wagner indicated that the central portion of coal pillar plays a significant role on loading capacity of pillars. In this study, the intact core of pillar is defined as elastic pillar core. Fig. 9 shows the variation of elastic pillar core during the process of loading. A gradual decrease of the volume of elastic pillar core can be observed in this figure. The load-bearing capacity of coal pillar would also be reduced with decreasing volume of elastic pillar core.
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C
Average axial stress of coa pillar (MPa)
6
5
D
B
E
4
F
3
A 2
Note: shear-n shear-p tension-n tension-p
1
at shear failure now elastic, but previously at shear failure at tensile failure now elastic, but previously at tensile failure
0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
Average axial strain of coal pillar
Position
A
B
C
D
E
F
Strain
0.25%
0.50%
1.00%
1.25%
1.50%
2.00%
State of the elastic pillar core
Block State
Fig. 9 Variation of elastic pillar core under compressive loading for 9m coal pillar
5.2. Relationship between elastic pillar core and pillar strength Fig. 10 presents two linear segments which illustrate the variation of coal pillar strength with 0-90% of roadway backfill at 9m mining height versus the volume of elastic pillar core calculated at approximate 2% of strain. From Fig. 10, it can be seen that the volume of elastic pillar core would increase with increasing coal pillar strength. In this process of increase, the turning point is at 40% of backfill. Modelling predicts that the volume of elastic pillar core rapidly increases above 40-50% of backfill as shown in Fig. 11. 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.
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350
90%
Volume of non-failed core (m 3)
300
250
200
150
100
40%
50
0
0 6
7
8
9
10
11
12
13
14
15
The strength of coal pillar (MPa)
Fig. 10 Variation of coal pillar strength versus the volume of elastic pillar core of 2% strain at 9m mining height with increasing backfill
500 450
Volume of pillar core (m3
400
5m
6m
7m
8m
9m
10m
350 300 250 200
Turning point: 40% Backfill
150 100 50 0 0
10
20
30
40
50
60
70
80
90
100
Percentage of backfill (%)
Fig. 11 Variation of the volume of elastic pillar core with different percentage of backfill
As the key results observed previously, 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 elastic pillar core is largely independent
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of mining height and approximately constant less than 40-50% of roadway backfill. It is concluded that roadway backfill is more effective when the percentage of backfill is more than 40-50%. According to the relationship between the volume of elastic pillar core and pillar strength of 5-10m coal pillar with 0-90% backfill, it can be seen that the proportion of elastic pillar core volume would increase with increasing roadway backfill. It is also found that volume of elastic 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 elastic 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 coal pillar. 5.3. Relationship between elastic pillar core and Bursting Energy Index (WCF) According to the discussions previously, the relationship between volume of elastic pillar core and Bursting Energy Index (WCF) is shown in Fig. 12.
ec lar pil oal
Increase
th nt rst bu
Im pro ve the
eve Pr
sta bil ity
Elastic pillar core
Backfill nce ha En
Re du ce
Coal pillar strength Reduce the occurrence of burst
Bursting Energy Index (WCF)
Fig. 13 A sketch to explain the relationships discussed in this study
Volume of the elastic pillar core will be increase with increasing backfill under the constant compressive loading. Numerical results suggest that elastic pillar core plays an important role in increasing coal pillar strength and decreasing Bursting Energy Index (WCF). This key find could provide researchers and mining engineers with evaluation method to improve the coal pillar stability and predict the burst of coal pillar.
Jiang Yaodong et al.et/al/ Procedia Engineering 26 00 (2011) 1125 – 1143 Wang Hongwei Procedia Engineering (2011) 000–000
6. Conclusions The observations developed in this paper are intended to provide researchers and mining engineers with initial estimate of the bursting liability of coal pillar with roadway backfill. Based on the above investigations, the following conclusions can be drawn: z In satisfying the above objective, Bursting Energy Index (WCF) is selected in this study since this index is obtained from the complete stress-strain curve (including the information of pre- and post failure) in the uniaxial compression experiment. z Bursting Energy Index (WCF) will decrease with increasing roadway backfill while the pillar strength is increase versus the percentage of roadway backfill. Model results suggest that the increase in pillar strength is approximately constant when percentage of roadway backfill is less than 40-50%, and when cohesive backfill is more than 40-50% pillar strength increases rapidly. Similar response is observed that Bursting Energy Index (WCF) decrease is less sensitive to amount of backfill when the backfill is less than 40-50%. z The central portion of coal pillar defined as elastic pillar core plays a significant role on loading capacity of pillars, increasing coal pillar strength and decreasing Bursting Energy Index (WCF). Numerical results suggest that the volume of elastic pillar core will increase with increasing backfill under the constant compressive loading. Acknowledgements The authors are indebted to National Basic Research Program (973) of China (NO.2010CB226801), the Fundamental Research Funds for the Central Universities, State Key Laboratory of Coal Resources and Save Mining and the support of CSIRO-MOE Visiting Scholar Fellowship Program. The authors would like to thank Dr. Yucang Wang and Poulsen Brett A. from CSIRO Division of Earth Science and Resource Engineering for their valuable contribution during this study.
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