Transp Porous Med DOI 10.1007/s11242-017-0908-y

Analysis of Broken Coal Permeability Evolution Under Cyclic Loading and Unloading Conditions by the Model Based on the Hertz Contact Deformation Principle Cun Zhang1,2,3 · Shihao Tu4 · Lei Zhang4

Received: 26 March 2017 / Accepted: 20 July 2017 © Springer Science+Business Media B.V. 2017

Abstract The permeability of the caved zone in a longwall operation impact many issues related to ventilation and methane control, as well as to interaction of gob gas ventholes with the mining environment. Insofar as the gob is typically inaccessible for performing direct measurements of the stresses and permeability, the latter values of the caved zone have to be assessed indirectly, which requires the application of the most reliable prediction techniques. To study the permeability evolution of the broken coal and its influencing factors during the coal seam group repeating mining, the particle deformation of the broken coal sample (BCS) is assessed in this study based on the Hertz contact deformation principle. Using the experimental results of the BCS cyclic loading and unloading seepage tests, the effect of BCS parameters on the stress sensitivity for permeability is analyzed. The laboratory test results imply that the re-crushing, re-arrangement, and compressional deformation of particles in the loading process lead to a drastic drop in the caved zone porosity causing the permeability reduction. During the unloading process, only the permeability loss caused by the particle deformation can be recovered. The secant modulus of BCS during unloading is stable and can be assessed by fitting the permeability stress curves. The stress sensitivity of the BCS permeability during unloading process drops with an increase in the secant modulus, while the re-crushing capacity and re-arrangement ability of BCS particles gradually deteriorate due to an increase in the secant modulus with the number of loading cycles. The effect of

B B

Shihao Tu [email protected] Lei Zhang [email protected]

1

Beijing Key Laboratory for Precise Mining of Intergrown Energy and Resources, China University of Mining and Technology (Beijing), Beijing 100083, China

2

School of Resource and Safety Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China

3

State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology (Beijing), Beijing 100083, China

4

Key Laboratory of Deep Coal Resource Ministry of Education of China, School of Mines, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

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Poisson’s ratio on the permeability stress sensitivity at the later loading/unloading stages is found to be quite feeble, while the stress sensitivity is indirectly related to the particle size via the secant modulus: the greater the particle size, the higher the unloading stress sensitivity. Keywords Broken coal sample · Stress sensitivity · Caved zone · Permeability · Hertz contact deformation principle

1 Introduction The overburden strata above the mining seam are conventionally subdivided (from the bottom to the top) into “four vertical zones,” and they are caved zone, fractured zone, continuous deformation zone and surface zone from the bottom to the top (Palchik 2003, 2010; Cheng et al. 2017). The caved zone is made up of the crushed rock and coal, and its porosity is up to 30–45%, according to laboratory measurements (Pappas and Mark 1993). According to the Booth and Greer (2011), the continuous advance of working face causes a rapid subsidence of the overlying strata and ground surface, as well as produces a subsidence trough over the advancing panel. In the process of the overlying strata subsidence, the rock masses of the gob are compacted gradually by the gravity and overlying strata pressure. When there are multilayers of the coal seams, the stress and permeability of the gob will be disturbed again during the following coal seam mining. The repeated unloading and compaction result in the further break of the caved coal and rock in the gob, with the respective porosity variation, which in turn affects the permeability value. Thus, the relationships between stress and permeability of the caved zone during the group coal seam mining differ significantly or each particular coal seam mining. Comprehensive methods, including the theoretical analyses of production data, field trials, and numerical simulation, are used to evaluate such gob parameters as stress, strain, permeability. Several models have been proposed to assess the gob reservoir properties and the gas extraction performances (Palchik 2002, 2014; Karacan 2009; Schatzel et al. 2012; Zhang et al. 2015, 2016). The gob permeability can be derived via the following empirical equation, which fits the stress permeability behavior of the post-failure rocks (Jozefowicz 1997): K g0 = −4 × 10−16 εvol 3 − 6 × 10−15 εvol 2 − 7 × 10−14 εvol + 10−11

(1)

where εvol is the volumetric strain of the caved coal and rock in the gob. Similar simple models based on the Carman–Kozeny (C–K) and Happel (H) equations (Li and Logan 2001; Esterhuizen and Karacan 2007) are also used for the gob permeability prediction. Besides, the fractal permeability model was proposed by Karacan (2010), which approach envisaged the porosity and permeability prediction based on the size distribution of broken rock material in the gob using flow and fractal crushing equations for granular materials. Fan and Liu (2017) proposed to subdivide the total compression process into four consecutive stages, described as follows: (1) the rock particle contact area remains in a stable state, while the secant modulus of the broken rock is unchanged; (2) shear failure happens at some weak contact points, while the secant modulus of the broken rock mass experiences an upward trend; (3) compacted rock mass is considered as a continuum of a porous medium, while the secant modulus of broken rocks and elastic modulus of particles are derived as E = α/(2λ + 1)E b ; (4) the main rock particles start to break up, and new fractures occur, while the secant modulus of broken rocks will continuously increase. Here the permeability ratio is given as follows:

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Analysis of Broken Coal Permeability Evolution Under Cyclic...

k = k0



V0 − Vs /(1 −

3 σz aσz +b )

(2)

V0 − Vs

where k/k0 is permeability ratio; V0 is initial volume of gob material; Vs is volume of particles; σz is vertical stress; a and b are fitting coefficients, which can be derived from the following equation E = aσz + b =



Eb

(2λ + 1) 1 +

(1−s1 ) s2



(3)

f

where E b is particle elastic modulus; λ is confining coefficient; f is roughness coefficient; s1 and s2 the proportion coefficients of the elastic deformation frictional slip contact length. From the four consecutive stages of the permeability evolution proposed by Fan and Liu (2017), variations of s1 and s2 at the each stage cause the secant modulus variation and, thus, affects the permeability. Other models describing the creep behavior patterns can also be used to study the permeability evolution in the long-term gob compaction (Yang et al. 2015). However, it has been experimentally proved that for the relatively low-strength coal, the particle re-crushing and re-arrangement occurs during the total compaction process, which is the main factor affecting the permeability reduction. Noteworthy is that, in the presence of multi-layers in the coal seam, the stress and permeability of the caved zone will be disturbed again during the following coal seam mining. The repeated mining causes the unloading and loading of the caved zone, so that the pore structures of caved zone change accordingly, and thus affect the permeability value, which controls the gas migration in the caved zone. The main factors affecting the permeability of the unloading process are different from those controlling it during loading. In order to study the permeability evolution of the broken coal and its influencing factors during the coal seam group repeating mining, the particle deformation of the BCS was calculated by the Hertz contact deformation principle. Using the experimental results of the BCS cyclic loading and unloading seepage test, the effect of BCS parameters on stress sensitivity for permeability is analyzed in this paper.

2 Laboratory Experimental Analysis The test samples are collected from the 13-1 coal seam in the Huainan coalfield, which is located to the west from Huainan city of Anhui Province in China. The Huainan coalfield location is depicted in Fig. 1a, while the borehole diagram of the longwall face with various seams including the 13-1 coal seam is presented in Fig. 1b together with the respective thickness and lithology details, which mainly include sandy mudstones with a few sandstone layers. The 11-2 coal seam was chosen as the protective seam, in order to exclude the coal and gas outburst hazards associated with the 13-1 coal seam, which has been mined (Zhang et al. 2017; Qin et al. 2015). The gas content and the maximal gas pressure of the 13-1 coal seam are 8.78 m3 /t and 3.7 MPa, respectively. The original permeability of 13-1 coal seam is 0.002 md and belongs to the outburst coal seam. Physical and mechanical parameters of the coal samples are shown in Table 1, while the coal proximate analysis and adsorption of a and b constant determination results are shown in Table 2. According to the particle size of coal samples, the BCSs are divided into six groups (Table 3). The sample size of the BCS is 50 × 100 mm, as shown in Fig. 2, the crushing particles filled in the sealant sleeve

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Thickness (m)

Lithology

3.49

Fine sandstone

0.40 1.91 5.67 2.43 2.00

Coal line Mudstone Powder sandstone Sandy mudstone Mudstone

4.58 4.32 0.39 2.12 10.4 8.51 8.61 10.38 13.8 6.44 1.24 2.18 1.43 0.63 3.87 0.85 25.44

13-1 Coal Mudstone Coal line Fine sandstone Mudstone Powder sandstone Mudstone Sandy mudstone Powder sandstone Mudstone 11-2 Coal Mudstone Powder sandstone 11-1 Coal Mudstone Sandy mudstone Powder sandstone

Beijing

Huainan mining area

Anhui

Protected coal seam

Protective coal seam

(a)

(b)

Fig. 1 The Huainan coalfield location in China (a) and the borehole diagram (b) of the longwall face (Zhang et al. 2017) Table 1 Physical and mechanical parameters of the coal samples Elastic modulus

Poisson’s ratio

Cohesion

Tensile strength

Friction angle

Em

νm

cm

tm

ϕm

Compressive strength σm

1.59 GPa

0.15

1.14 MPa

1.09 MPa

37.13 ◦

15.98 MPa

Table 2 Coal proximate analysis and adsorption of a and b constant determination results Mad (%)

Aad (%)

Vad (%)

St.ad (%)

TRD (g/cm3 )

a

b

1.70

18.28

29.75

0.10

1.67

8.521

2.133

Table 3 Subdivision of the BCSs into 6 groups

Diameter /mm

5–8

8–12

12–15

15–18

18–22

22–25

Sample ID

G1

G2

G3

G4

G5

G6

and shake to make it uniform. The fluid (CH4 ) pressure is 0.2 MPa. The main boundary conditions are depicted in Fig. 2. Based on the design of the stress path, BCS with different particle size stress permeability test would be conducted in this paper; the test results are shown in Fig. 3. In situ stress measurement results show that the horizontal stress is equal to the vertical one. Thus, the axial stress in the experiment is equal to the confining stress. As shown in Fig. 4, the permeability of the BCS deceases rapidly with the effective stress during the first loading but can still exceed 100 md in the high stress state. The unloading stress sensitivity of permeability is smaller than that in a single cyclic loading/unloading process. With an increase in the number of cycles, the permeability loss and its stress sensitivity decreases gradually. The permeability of BCS increases with the particle size under the same

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Analysis of Broken Coal Permeability Evolution Under Cyclic... Fig. 2 Structure of BCS and experimental boundary conditions

Downstream pressure Axial pressure Confining pressure

50mm

Sleeve Perforated plate Metal screen

100 mm

Broken coal

Metal screen Perforated plate

Upstream pressure

18 Axial stress

16

Confining stress

Stress/MPa

14

Gas pressure

12 10 8

6 4 2

0 0

2

4

6

8

10

12

14

Testing time/h Fig. 3 Single loading and unloading path of the broken coal

effective stress. However, with an increase in the effective stress, the permeability difference between particles of different size decreases gradually. This indicates that larger sizes of particles size correspond to higher stress sensitivity of the permeability during the total cyclic loading/unloading process.

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C. Zhang et al. 1,200

800 600

Permeability/md

Permeability/md

600

G1 Load G2 Load G3 Load G4 Load G5 Load G6 Load

1,000

400 200

G1 Unload G2 Unload G3 Unload G4 Unload G5 Unload G6 Unload

500 400 300 200

100

0

0 0

2

4

6

8

10

12

14

16

0

2

4

Effective stress/MPa

6

(a)

12

350

G1 Load G2 Load G3 Load G4 Load G5 Load G6 Load

500

400 300

Permeability/md

Permeability/md

10

14

16

(b)

600

200 100

G1 Unload G2 Unload G3 Unload G4 Unload G5 Unload G6 Unload

300 250 200 150

100 50

0

0 0

2

4

6

8

10

12

14

16

0

2

4

Effective stress/MPa

6

8

10

12

14

16

Effective stress/MPa

(c)

(d)

350

250

G1 Load G2 Load G3 Load G4 Load G5 Load G6 Load

300

250 200

Permeability/md

Permeability/md

8

Effective stress/MPa

150 100 50

0

G1 Unload G2 Unload G3 Unload G4 Unload G5 Unload G6 Unload

200 150 100

50 0

0

2

4

6

8

10

12

Effective stress/MPa

(e)

14

16

0

2

4

6

8

10

12

14

16

Effective stress/MPa

(f)

Fig. 4 Permeability–effective stress curves for BSCs with different particle sizes under cyclic loading (a, c, e) and unloading (b, d, f) seepage tests: first loading (a) and unloading (b) cycle; second loading (b) and unloading (c) cycle; third loading (e) and unloading (f) cycle

3 Theoretical Analysis of the Permeability Evolution in the Laboratory Test In order to illustrate the permeability evolution of the BCS and its influencing factors during the total cyclic loading and unloading process, the particle deformation of the BCS was calculated by the Hertz contact deformation principle (Lei et al. 2014). Pore and structural changes of the BCS under cyclic loading and unloading axial seepage test are shown in Fig. 5. It is assumed that coal particles are spherical, and the composite particle structure in Fig. 5 is three dimensional.

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Analysis of Broken Coal Permeability Evolution Under Cyclic...

Fig. 5 Pore and structure changes of the broken coal and rock samples under cyclic loading and unloading axial seepage test

Fig. 6 Fragmentation of BSCs after cyclic loading and unloading seepage tests

It can be seen from Fig. 5 that at the early stage of the broken particles accumulation, the BCS contains multi-particle composite structure (PCS), and the larger the particle, the higher the composite number and pore volume. Due to the absence of cohesive force acting between particles, the PCS is easily damaged by the increased stress. The pore area reduced by 18.79 and 7.44% when four and five PCS, respectively, were damaged and reduced to three PCS. Besides, the particle re-crushing in the loading process, as shown in Fig. 6, will also drastically reduce the porosity of BCSs. The size of the re-crushing particle will be greatly decreased, and the pore area will also be reduced, respectively. Some smaller recrushing particles will fill the pore space of the larger particles composite structure, as shown in Fig. 5. Thus, the particle re-crushing of the BCS also greatly reduces its permeability. The permeability loss caused by the above two factors is very difficult to compensate in the process of unloading, which results in a great loss of the BCS permeability during the first loading and unloading cycle. In addition to re-arrangement and re-crushing of particles, their compressional deformation can also cause the porosity reduction, but the latter can be recovered in the unloading process. The porosity variations of G1 BCS during the three loading and unloading cycles are shown in Fig. 7. The particle re-crushing and re-arrangement of the BCS greatly reduce its porosity (0.1102, 0.0316 and 0.0218 for the first, second, and

123

Load-1

Unload-1

Porosity loss by re-arrangement and re-crushing of particles

Porosity loss by deformation of particles

0

2

4

6

8

10 12 14

0.50 0.45 0.40 0.35 0.30 0.25 0.20

Effective stress/MPa

Load-2

Unload-2

Porosity

0.50 0.45 0.40 0.35 0.30 0.25 0.20

Porosity

Porosity

C. Zhang et al.

0

2

4

6

8

10 12 14

0.50 0.45 0.40 0.35 0.30 0.25 0.20

Load-3

0

2

4

6

8

Unload-2

10 12 14

Effective stress/MPa

Effective stress/MPa

(b)

(c)

(a)

Fig. 7 Porosity loss curves by re-crushing, re-arrangement and particle deformation of the particles during first (a), second (b) and third (c) loading/unloading

third loading cycles, respectively), while the porosity loss caused by the particle deformation accounted for a small share of the total loss (0.0427, 0.0160 and 0.0144 for the first, second, and third loading cycles, respectively). The re-crushing capacity and re-arrangement ability of BCS particles gradually deteriorate due to continuous increase in the secant modulus of broken coal with the number of cycles, which results in the porosity loss and gradual drop of its stress sensitivity. Meanwhile, the secant modulus increases after loading also caused a gradual reduction of the stress sensitivity during the unloading process. Due to re-crushing and re-arrangement of small particles in the unloading process, the secant modulus can be considered as practically unchanged, so that the particle deformation of three, four, and five PCS (Fig. 8) can be calculated based on the Hertz contact deformation principle. According to the Hertz contact deformation principle (Gangi 1978; Li 2009), the radius of the particle contact area can be calculated by Eq. (4).    2 3 3F R 1 − v a= (4) 4E where E is the elastic modulus of the broken particle; ν is Poisson’s ratio; R is particle radius; F is the pressure on the particle. The latter is derived from Eq. (5) F3 =

2σ1 πb2 , 3

F4 =

σ1 πb2 , 2

F5 =

2σ1 πb2 5

(5)

where σ1 is effective stress; F3 , F4 and F5 are the pressures for the cases of three, four and five PCS, respectively; b is the radius of the model after deformation. b = R2 − a2 (6) The pore areas of the PCS before and after deformation can be calculated by Eqs. (7) and (8), respectively.

√ √ 2 π R2 3π R 2 2 2 , A40 = 4R − π R , A50 = 25+10 5R 2 − (7) A30 = 3R − 2 2   √ 3 π a R 2 A4 A3 = 3b2 − 3ab − − 2 arctan 2 3   a b R2 = 4b2 − 4ab − π − 4 arctan b

 a  √ 3π − 5 arctan R2 A5 = 25 + 10 5b2 − 5ab − (8) 2 b

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Analysis of Broken Coal Permeability Evolution Under Cyclic...

O1 R b

a

O2

O3

(a)

O1

O2

O3

O4

(b)

O2

O1

O3

O5

O4

(c) Fig. 8 The deformation of PCS with different combined particle number. a Three PCS, b four PCS, c five PCS

After substituting parameters a and b into Eq. (8), the pore area is derived as the function of R, E, v,and σ1 . Because the formula is quite cumbersome, the pore areas before and after deformation are further referred to as A(R, E, v, σ1 ), and A0 (R, E, v, σ1 ), respectively. Given this, the porosity ratio (of pore areas before and after deformation) can be calculated by Eq. (9).

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C. Zhang et al. 1.0 Three particles Four particles Five particles

0.9

0.8 0.7

k/k0

0.6 0.5

0.4 0.3 0.2

0.1 0.0 0

5

10

15

20

Effective stress/MPa Fig. 9 Permeability ratio–effective stress curves of the three, four and five PCS

√ √ 3 3

A (R, σ1 , E, v) 2 ϕ A0 (R, σ1 , E, v) − A (R, σ1 , E, v) = 1− = √ ϕ0 A0 (R, σ1 , E, v) A0 (R, σ1 , E, v)

(9)

where ϕ and ϕ0 are the porosity values of the BCS before and after deformation, respectively. The relationship between porosity and permeability based on the cubic law can be expressed by Eq. (10) (Palmer 2009; Perera et al. 2011).

3 k ϕ = (10) k0 ϕ0 Thus, the permeability of the BCS after deformation can be calculated by Eq. (11).

9 A (R, σ1 , E, v) 2 k = k0 A0 (R, σ1 , E, v)

(11)

The permeability ratio–effective stress curves (Fig. 9) of three, four and five PCS were constructed, according to the coal physical and mechanical parameters listed in Table 1. In Fig. 9, the particle radius is 5 mm. The stress sensitivity of the BCS permeability decreases with the number of combined particles: that of three PCS is much higher than those of four and five PCSs. It means that the permeability stress sensitivity should gradually increase for three PCSs in the later stages of the cyclic loading process. However, this is not consistent with the experimental results. From the above analysis, the permeability loss caused by the particle deformation accounted for a small share of the total permeability loss. This is because the coal particles are broken coal samples, whose elastic modulus is much higher than that listed in Table 1, which has been directly measured via the uniaxial compression test of an intact coal sample. The elastic modulus in this model should be replaced by the secant modulus (Fan and Liu 2017), which is derived via Eq. (3) and is increased with the stress. Moreover, there is a negative exponential relationship between the secant modulus and the size of rock, as shown in Fig. 10. When the rock size is less than that of representative volume element, which corresponds to point D in Fig. 10, the secant modulus of the particle is affected greatly by the particle size (Wang and Zou 1998). The elastic modulus is 17.9–55.3 GPa, with an average of 34.3 GPa, when the coal particle size is about 0.1 mm (Zhao et al. 2005). The size of the coal particles decreases gradually due to their re-crushing with an increase in the

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Analysis of Broken Coal Permeability Evolution Under Cyclic... Fig. 10 The correlation between size and elastic modulus of rock mass

E

y=aebx+c D

Rock size

number of loading/unloading cycles, and thus, the secant modulus of the particle increases continuously. Figure 11 shows the permeability ratio–effective stress curves of the three PCS with various secant moduli (10–50 GPa). The stress sensitivity of the permeability sharply drops with the secant modulus increase. The smaller the secant modulus was, the greater the influence on permeability. The permeability ratios at 20MPa effective stress are equaled to 0.044, 0.405, 0.563, 0.643, 0.694, 0.729, and 0.755 when the secant modulus increased from 1.5 to 50 GPa, as shown in Fig. 11b. This implies that the stress sensitivity of the BCS permeability gradually decreases during the loading process. Insofar as only the permeability loss caused by the particle deformation can be recovered in the unloading process, the stress sensitivity of the permeability during the unloading is equal to that calculated for the particle deformation. The unloading stress sensitivity of the permeability reduces with the number of cycles in the laboratory measurements because of the secant modulus increase. Besides, Poisson’s ratio can also affect the stress sensitivity of the BCS permeability, as follows from Eq. (9). The permeability ratio–effective stress curves of the three PCS with various Poisson’s ratios are shown in Fig. 12. In Fig. 12a, the secant modulus equals to 30 GPa and the particle radius is 5 mm. The influence of Poisson’s ratio on the permeability stress sensitivity is much lower than that of the secant modulus. The permeability ratios were 0.065, 0.062, and 0.050 (which corresponded to the increase by 28.8, 12.7, and 7.8% of the original values) for Poisson’s ratio increase from 0.1 to 0.5 under the secant moduli of 5, 15, and 30 GPa, as shown in Fig. 12b. This implies that with an increase in the secant modulus during the loading, Poisson’s ratio varies slightly in the loading process and its effect on permeability decreases gradually. Thus, the effect of Poisson’s ratio on the permeability stress sensitivity at the later loading/unloading stages is quite feeble. The comparison of permeability curves with different particle sizes constructed via Eq. (11) reveals no significant differences between them. This can be accounted for by further simplification of Eq. (11). Since direct substitution of Eqs. (4)–(9) into Eq. (11) is too cumbersome, the following assumption is: due to the high value of elastic modulus of the broken particles, the deformation a is very small relative to R. Then, assuming that b is equal to R, Eq. (11) can be reduced to the following form. A/A0 = f (F), where F = πσ1 (1 − v 2 )/E

(12)

As can be seen from Eq. (12), the particle size R is no longer present in the formula, so that the value A/A0 is controlled only by secant modulus E and Poisson’s ratio v. However,

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1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

k/k0

k/k0

C. Zhang et al.

E=10GPa E=20GPa E=30GPa E=40GPa E=50GPa E=60GPa

0

5

10

15

20

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

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20

30

40

50

60

0.5

0.6

Effective stress/MPa

Elasticity modulus/GPa

(a)

(b)

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

k/k0

k/k0

Fig. 11 Permeability ratio–effective stress curves with various secant modulus

v=0.1 v=0.2 v=0.3 v=0.4 v=0.5

0

5

10

15

Effective stress/MPa

20

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

secant modulus 5GPa secant modulus 15GPa secant modulus 30GPa

0

0.1

0.2

0.3

0.4

Elasticity modulus/GPa

(a)

(b)

Fig. 12 Permeability ratio–effective stress curves with various Poisson’s ratio

the laboratory experiments indicate that larger sizes of particles correspond to higher values of the permeability stress sensitivity during the total cyclic loading/unloading process. This can be attributed to the following main factors: (1) an increase in the initial pore area of the PCS with the particle size causes the initial permeability rise, according to Eq. (7); (2) since the permeability loss during the loading is mainly caused by the particle re-crushing and re-arrangement, the re-crushing capacity and PCS damage ability of BCS are gradually increased with the particle size. (3) There is a negative exponential relationship between the secant modulus and the particle size, while the stress sensitivity of the permeability increases significantly with the secant modulus reduction. Thus, although the particle size R does not directly affect the stress sensitivity of the permeability, it exhibits an indirect effect via the secant modulus. Since the stress sensitivity of the permeability during the unloading cycle is equal to that calculated for the particle deformation, the unloading stress sensitivity also increases with the particle size. Therefore, the secant modulus is the main factor controlling the deformation of particles, which finding has been confirmed by Fan and Liu (2017). In this paper, the secant modulus of broken coal sample during unloading is calculated by fitting the permeability stress curves via Eq. (12), as shown in Fig. 13. As can be seen from Fig. 13, the fitting effect of Eq. (12) is good for the unloading curve of broken coal samples, which indicates that the permeability variation during the unloading

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1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

G1 Unload G3 Unload G5 Unload G1 Fitting curve G3 Fitting curve G5 Fitting curve

0

2

4

Permeability ratio

Permeability ratio

Analysis of Broken Coal Permeability Evolution Under Cyclic...

G2 Unload G4 Unload G6 Unload G2 Fitting curve G4 Fitting curve G6 Fitting curve

6

8

10

12

14

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

G1 Unload G3 Unload G5 Unload G1 Fitting curve G3 Fitting curve G5 Fitting curve

0

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4

Effective stress/MPa

G2 Unload G4 Unload G6 Unload G2 Fitting curve G4 Fitting curve G6 Fitting curve

6

8

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Secant modulus/GPa

Permeability ratio

70

G1 Unload G3 Unload G5 Unload G1 Fitting curve G3 Fitting curve G5 Fitting curve

G2 Unload G4 Unload G6 Unload G2 Fitting curve G4 Fitting curve G6 Fitting curve

6

8

10

12

Effective stress/MPa

(c)

12

14

16

(b)

(a) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

10

Effective stress/MPa

14

16

60 50

Unload 1 59.6

Unload 2

55.4

Unload 3

40

35.9 32.6

30

24.5 19.6

20 10

13.6 8.2 3.6 4.6

6.4

8.6

10.6

21.6 16.4

15.6 12.1

9.1

0 G6

G5

G4

G3

G2

G1

(d)

Fig. 13 Fitting results of the broken coal sample during unloading process. a First unload, b second unload c third unload, d fitting results of secant modulus

process of broken coal samples is mainly controlled by the deformation of coal samples. The smaller the coal particle size, the greater the secant modulus of the broken coal sample. This reduces the effective stress influence on the permeability, which is consistent with the experimental results. For broken coal particles of different sizes, the increased secant modulus is not equivalent to the effect of increase in the number of cycles: the former is less pronounced for larger particles, but its increase rate does not decreases gradually with number of loading cycles. This is mainly due to the fact that the loading stress is less than the strength of the large-sized particle, so that the latter still occupy a large part of the original volume after the repeated loading, as shown in Fig. 6. Therefore, when the number of cycles or effective stress reaches their threshold levels, the secant modulus of all broken coal particles will stabilize, irrelevant of their size, and the properties of broken coal samples become similar to those of porous media. The above comprehensive analysis strongly suggests that calculations based on the Hertz contact deformation principle can well describe the permeability evolution of the BCS during cyclic loading and unloading, especially the permeability variation of during unloading.

4 Discussion The caved zone consists of the crushed rock and coal, whose physical and mechanical properties control the permeability of this zone. The re-crushing, re-arrangement, and compressional deformation of particles in the loading process drastically reduce the caved zone porosity

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and, thus, its permeability. Similar models, such as proposed by Karacan (2010) and Fan and Liu (2017), can be used for gob permeability calculations, especially for the case of broken rock loading. However, it has been experimentally proved that for a relatively low-strength coal, the particle re-crushing and re-arrangement occurs during the total compaction process, which is the main factor affecting the permeability reduction. While the permeability model proposed by Karacan (2010) is based on the size distribution of broken rock particles, it is not convenient for permeability prediction, since fragmentation of broken coal samples is difficult to obtain during loading. In the model of Fan and Liu (2017), the only situation under study is when the broken rock mass is stable and contains no unstable pile-induced large voids, so that the shear failure occurs only at some weak contact points between the rock masses. Thus, the coal particle re-crushing and re-arrangement, which occur in the total compaction process, is neglected. Besides, the parameters f, a and b in Eq. (3) still need to be matched with the available experimental results. Moreover, when there are multi-layers of the coal seams, the stress and permeability of the caved zone will be disturbed again during the following coal seam mining. The repeated mining causes unloading and loading of the caved zone, where in the pore structures of caved zone change accordingly and affect the permeability value. In order to study the permeability evolution of the broken coal and its influencing factors during the coal seam group repeated mining, the particle deformation of the BCS was calculated by the Hertz contact deformation principle. Using the experimental results of the BCS cyclic loading and unloading seepage test, the effect of BCS parameters on stress sensitivity for permeability is analyzed in this study. The laboratory test analysis results strongly indicate that the re-crushing, re-arrangement, and compressional deformation of particles in the loading process drastically reduce the BCS porosity and permeability. Only the particle deformation-induced permeability loss, which accounts for a small share of the total one, can be compensated in the unloading process. Thus, the permeability model expressed by Eqs. (11) and (12) cannot be directly applied for fitting the permeability and stress curves in the loading process. Instead, the secant modulus of broken coal, which exhibits a continuous increase during the particle re-crushing and re-arrangement in the loading process, can be derived via Eq. (3) proposed by Fan and Liu (2017), the value obtained being substituted into Eq. (12) for the permeability prediction. In such way, the permeability model proposed in this study can properly describe the permeability evolution characteristics in both loading and unloading processes. Noteworthy is that the gas pressure variation in the broken coal samples can also contribute to the deformation of particles (Xie et al. 2015), but due to a small-scale gas pressure variation in the caving zone, no further research of this issue has been carried out in this study. Since the deformation of coal particles containing different gas types (for example, CH4 and CO2 ) is also different (Ranathunga et al. 2017), this issue requires more comprehensive analysis and should be addressed in the future works.

5 Conclusions (1) The BCS permeability and its sensitivity to stress is shown to increase with the particle size during the total cyclic loading and unloading process. Within the first loading/unloading cycle, the stress sensitivity of permeability in the loading half-cycle exceeded that in the unloading one. With an increase in the number of cycles, the permeability loss and its stress sensitivity decreased gradually, which can be attributed to gradual deterioration of the re-crushing and re-arrangement abilities of BCS particles due to the secant modulus increase with the number of cycles.

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(2) The permeability loss during the loading process is mainly caused by the particle recrushing and re-arrangement, while that caused by the particle deformation is quite small. The stress sensitivity is shown to drop with the secant modulus increase caused by particle re-crushing and re-arrangement during the loading process. Only the permeability loss caused by the particle deformation can be compensated in the process of unloading. Thus, the stress sensitivity of the permeability during the unloading is equal to that calculated for the particle deformation. (3) The permeability loss caused by particle deformation is calculated via the Hertz contact deformation principle. Based on this model, the effect of BCS parameters including combined particle number, secant modulus, Poisson’s ratio and particle size on permeability stress sensitivity during the unloading process is analyzed in this paper. There is a feeble effect of Poisson’s ratio on the permeability stress sensitivity at the later loading and unloading stages. The secant modulus of BCS continuously increases during the loading process due to stress sensitivity of the BCS permeability reduction. The secant modulus of broken coal sample during unloading is stable, and it can be assessed by fitting the permeability stress curves. The particle size indirectly affects the stress sensitivity via the secant modulus: the greater the particle size, the higher the unloading stress sensitivity. Acknowledgements Financial support for this work was provided by the National Key R&D Program of China (2016YFC0600708, 2016YFC0801401), the National Natural Science Foundation of China (NO. 51374200) and the Natural Science Foundation of Jiangsu Province (NO. BK20140208).

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