Accepted Manuscript

Separation and fracturing in overlying strata disturbed bylongwall mining in a mineral deposit seam

Shaofeng Wang, Xibing Li, Shanyong Wang

PII: S0013-7952(16)30278-2DOI: doi: 10.1016/j.enggeo.2017.06.015Reference: ENGEO 4594

To appear in: Engineering Geology

Received date: 30 August 2016Revised date: 23 June 2017Accepted date: 24 June 2017

Please cite this article as: Shaofeng Wang, Xibing Li, Shanyong Wang , Separation andfracturing in overlying strata disturbed by longwall mining in a mineral deposit seam. Theaddress for the corresponding author was captured as affiliation for all authors. Pleasecheck if appropriate. Engeo(2017), doi: 10.1016/j.enggeo.2017.06.015

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Separation and fracturing in overlying strata disturbed by longwall mining in a

mineral deposit seam

Shaofeng Wang1,2,*

, Xibing Li3, Shanyong Wang

4

1School of Resources and Safety Engineering, Central South University, Changsha 410083,

China

2ARC Centre of Excellence for Geotechnical Science and Engineering, The University of

Newcastle, Callaghan, NSW 2308, Australia

Email address: wsfcumt@163.com (Corresponding); wangsf@csu.edu.cn

* Corresponding author

3School of Resources and Safety Engineering, Central South University, Changsha 410083,

China

Email address: xbli@csu.edu.cn

4ARC Centre of Excellence for Geotechnical Science and Engineering, The University of

Newcastle, Callaghan, NSW 2308, Australia

E-mail address: Shanyong.Wang@newcastle.edu.au

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Abstract Mining-induced fractures influence the stability of overburden and may provide

pathways for transferring heat and mass in underground environment. A novel approach was

proposed to quantify the separation and fracture evolution in the undermined overburden,

consisting of (1) theoretical distribution models of the void ratios of fractures (VRFs), based

on analytical evaluation of key strata subsidence, and (2) numerical modeling using the

universal distinct element code and a sequence of image post-processing procedures. For a

longwall mining panel, both theoretical calculations and numerical simulations indicated

that VRF first increased rapidly, then gradually decreased, and finally stabilized to a

minimum from the surrounding edges of disturbed strata to their centers, and gradually

decreased from deep to shallow strata. The fractures exhibited a “fracture-rich arch”

distribution type along a vertical section. Numerous fractures occurred around the arch feet

near the perimeters of mined-out area and/or arch crown near the center of disturbed strata.

The distributions of VRFs show the heights, shapes and damage intensities of fractured

zones, and can also be used as porosity parameters to determine the permeabilities of

mining-disturbed overburdens. Therefore, the VRF models can be used as a quantitative

parameter to assess the extent of possible risk zones, e.g. for water inflow into the mine or

escape of hazardous fluids to the surface.

Keywords Longwall mining, Bed separation, Stratum fracture, Void ratio, Image

post-processing, Fracture-rich arch

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Nomenclature

iS subsidence amount of the ith

key stratum ds unit length of the subsidence curve of the key

stratum

xl strike length of the mined-out area dS unit area of the curved surface of subsidence of the

key stratum

yl dip width of the mined-out area iTF transverse VRF caused by bed separation between

the ith

and (i+1)th

key strata

il length of blocky rock in the ith

key stratum iLF longitudinal VRF caused by fracture of the i

th key

stratum

M thickness of the deposit seam 1iLF longitudinal VRF caused by fracture of the (i+1)

th

key stratum

iz vertical height of the ith

key stratum , 1i iLF longitudinal VRF between the i

th and (i+1)

th key

strata

iKp bulking factor of the rock mass between the

ith

key stratum and the deposit seam ijFR VRF in the strike i

th and vertical j

th ergodic windows

ih thickness of the ith

key stratum ijFN

number of pixels whose RGB color value sums are

less than 10 in the strike ith

and vertical jth ergodic

windows

ti tensile strength of the ith

key stratum ijN total number of pixels in the strike i

th and vertical j

th

ergodic windows

iq load on the ith

key stratum iFR VRF in the strike ith

ergodic window

i average volume-weight of rock mass between

the ith

key stratum and ground surface iFN

number of pixels whose summed RGB color values

are less than 10 in the strike ith

ergodic window

H vertical height of horizontal ground surface iN total number of pixels in the strike i

th ergodic

window

fV void volume of fractures ( )N number of boxes intersected by the fracture

rV volume of rock mass side length of the measuring box

oD original distance between the i

th and (i+1)

th

key strata FD

fractal dimension

sD distance after subsidence

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1. Introduction

Longwall mining is a widely used method for excavating mineral deposit seams. The cap

strata above a longwall mined-out area will subside after undermining with different

displacements and velocities, resulting in separations between the strata and fractures in

those strata (Palchik 2003). A large number of fractures are generated and substantially alter

the fluid-flow properties of the overlying strata, including their porosities and associated

permeabilities (Schulze et al. 2001; Souley et al. 2001; Meng et al. 2016). Mining-induced

fractures or fault reactivation can penetrate aquitards and damage cap rocks, potentially

triggering influx of water or the escape of hazardous fluids, which negatively impact mining

safety (Islam and Shinjo 2009). Therefore, understanding the distribution and development

of fractures in mining-disturbed strata is important to protect the mines against water influx.

Field hydrogeological measurements have revealed that the permeabilities of strata that

overlie mineral seams increase significantly after the excavation of the seams by longwall

mining (Adhikary and Guo 2015; Karacan and Goodman 2009). Some coupled

hydro-geomechanical models have confirmed that overburden permeability is strongly

influenced by the separation and fracturing of strata and presents evident heterogeneity and

discreteness (Liu and Elsworth 1997; Karacan and Goodman 2009; Schatzel et al. 2012).

The properties of mining-induced separation and fractures in overburden have been

investigated. Referencing permeability and piezometric tests, Forster and Enever (1992)

proposed a hydrogeological model that divided the mining-disturbed overburden of a

supercritical longwall panel into four zones, the caved zone, fractured zone, constrained

zone and surface zone in the vertical direction, and three areas with a mined-out area amidst

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two rib areas along the coal seam. The permeability in the fractured zone can significantly

increase, and as a result, hazardous gases or water may pass through that zone into the

mining areas. Using onsite tests of changes in natural gas emissions, Palchik (2003) used the

maximum height of the fractured zone and its ratio to the thickness of the extracted coal

seam to simply quantify the formation and development of overburden separation and

fracturing due to longwall mining. Although field data are accurate and valuable, measuring

deformation and permeability within mining-disturbed strata is a challenging and expensive

task, and large numbers of measurements that cover all overlying strata are prohibitive

(Adhikary and Guo 2014). Theoretical mathematical models have been proposed to

investigate the height of the fractured zone and the factors that influence it such as the

simplified prediction equations depicted and reviewed in Majdi et al. (2012),

time-independent energy models (Rezaei et al. 2015) and key strata models (Miao et al. 2011;

Xuan et al. 2016) that are based on field measurement data and physical models. However,

there has been a lack of further discussion regarding rock structures and their quantitative

characterization in fractured zones in those models. Fractal dimension has been used to

characterize the developmental degree of fracture networks in disturbed overburdens (Xie

1993). However, a single fractal dimension cannot easily reflect the complicated

heterogeneous distributions of mining-induced fractures in overlying strata.

Numerical modeling with multiparameter estimation can be a cost-effective approach to

assess the progressive separation and fracturing of strata in longwall mining panels.

Continuum (FEM and FDM) and discontinuum (DEM) mechanics-based numerical

simulation methods have been used in a few research programs to address that problem

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(Singh G and Singh U 2010; Yasitli and Unver 2005; Ghabraie et al. 2017; Gao et al. 2014;

Xu et al. 2016; Salmi et al. 2017). The mechanical behaviors of strata in response to

underground mining involve a complex change from continuous deformation to

discontinuous fracturing during strata subsidence, which significantly hinders the application

of FEM- and FDM-based approaches (Shabanimashcool and Li 2012; Vyazmensky et al.

2010). The DEM-based methods, especially those that utilize universal distinct element

codes (UDECs) and three-dimensional distinct element codes (3DECs), are by nature

capable of simulating discontinuous and large displacement motions of jointed and bedded

rock masses (Xu et al. 2016). Gao et al. (2014) simulated a roof as an assembly of triangular

blocks bonded via contacts using the so-called UDEC Trigon approach to capture the

progressive caving of strata above a longwall coal mining panel. In that work, a new damage

index expressed as the ratio of the total length of cracks to the total contact length was

proposed to characterize the generation of fractures and their subsequent propagation in a

longwall panel roof. Xu et al. (2016) established an equivalent jointed rock-mass model

using 3DEC software to simulate the caving and large displacement motion of strata and

surfaces induced by mining. However, the numerical studies mentioned above mostly

emphasized the progressive fracture process of strata and did not investigate the

multidimensional distributions of quantized indexes of separation and fracture

characteristics. Supported by UDEC numerical simulations, Wang et al. (2016a) recently

proposed a group of analytical models of void (pores in the caved zone, fractures in

fractured zones and ground surface fissures) fraction distributions in longwall

mining-disturbed overburden based on expressions of strata subsidence and discovered a

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fracture distribution type that they called a “fractured arch”. However, the variation in

fracture distribution with increasing depth was not quantitatively reproduced in the models.

It should be noted that few works have been published that seek to further process numerical

results, especially digital images produced using numerical software, to extract and quantify

fractures in fractured zones.

In this paper, theoretical models of three-dimensional heterogeneous distributions of the

void ratios of fractures (VRFs), which indicates the volume fraction of fissures in fractured

rock masses, are derived from subsidence differences or size increments of strata to quantify

the separation and fracturing of longwall mining-disturbed strata. In addition, a UDEC

numerical model and a set of post-processing procedures are proposed to simulate strata

fractures, extract fissures, calculate VRFs and fractal dimensions and thereby validate the

analytical results of a case study of a supercritical longwall panel, in which the panel width

was greater than the overburden thickness.

2. Overlying strata subsidence

The overlying strata of a mineral deposit seam, especially a coal seam, are composed of

numerous bedded sedimentary formations with different structure sizes, occurrences,

mechanical properties and loads. As a mining face advances, the extraction of the mineral

deposit seam will lead to deformation of the overlying strata, and unsupported strata will

periodically fracture into blocks and progressively subside in a form wherein the blocks are

hinged together (Wang et al. 2016b). Because of the varying properties of the different

overlying strata, key strata control the subsidence of the entirety or part of their overburdens,

which will subsequently subside after the key strata fracture. A key stratum must satisfy the

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condition that its fracture length is the greatest among the entirety or parts of its

corresponding overburden, which is determined by its strength, thickness and load. In

particular, the former is called a primary key stratum.

Longwall mining is a widely used method for the mechanized and large-scale extraction

of underground mineral deposit seams, especially coal seams. A longwall mining panel and

overlying strata subsidence are shown in Fig. 1. As the deposit seam in a longwall mining

panel is extracted slice by slice, a rectangular mined-out area is formed, the length of which

progressively increases with the advancing longwall mining face. Subsequently, the

overlying strata are forced to subside toward and fill the mined-out area. For a rectangular

longwall mining panel within horizontal strata, the curved surface of subsidence of the ith

key stratum was derived by Wang et al. (2016a and 2016b) based on a fitted subsidence

curve that was obtained from numerous onsite monitoring and similar material experiments

on the movement of strata, which can be expressed as

11

1

( , , )

2 42 2 41 1 1 exp 2 1 1 exp 2

21 1 exp 2

i i

yx x

i i

i i

y

i

S x y z

l yl l xM Kp z

l l

l

l

, (1)

and

=

3 3

ti tii i i

i i i

l h hq H z

, (2)

where ( , , )i iS x y z is the subsidence amount of the ith key stratum that has a vertical height

of iz ; xl is the strike length of the mined-out area; yl is the dip width of the mined-out

area; il is the length of blocky rock in the ith key stratum, which is considered to be the

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theoretical broken length of a cantilever beam; M is the thickness of the deposit seam; iz

is the vertical height of the ith

key stratum, which equals the distance between the ith key

stratum and the deposit seam; iKp is the bulking factor that quantifies the increase in the

rock volume due to caving (Palchik 2015), i.e. ratio between the volume of rock after caving

to its initial volume; ih and

ti are the thickness and tensile strength of the ith

key stratum,

respectively; iq is the load on the i

th key stratum, which is approximately represented as

the lithostatic pressure generated by the weight of the strata; i is the average volume

weight, which is defined as the weight of a unit volume of rock mass between the ith key

stratum and the ground surface; and H is the vertical height of the horizontal ground

surface.

Fig. 1

3. Bed separation between strata

From Eq. 1, it is evident that the size of the fractured block in a key stratum plays an

important role in quantifying the subsidence of the stratum. Eq. 2 shows that the lengths of

the fractured blocks in each key stratum differ owing to their varying strengths, thicknesses

and loads. Consequently, the subsidences of the key strata also differ. The different

subsidences cause bed separation between all adjacent strata in the vertical direction and

then produce fractures parallel to the stratum plane called transverse fractures, as shown in

Fig. 1a. The process of horizontal fracture formation (bed separation) along weak-strong

rock layer interfaces is accompanied by the subsidence of rock layer interface. In fact, the

aperture of horizontal fracture can be presented as a difference between a large subsidence of

top boundary of weak rock layer below the interface and a relatively small subsidence of the

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bottom boundary of strong layer above the interface (Palchik 2005). Palchik (2010) has

established that such apertures can be significant (up to 400 mm) and ratio between the

aperture of horizontal fracture and thickness of extracted coal seam is between 0.03 and 0.29

with the mean value 0.09.

Based on the definition of the void ratio, which expresses the void fraction of crack

fissures in the fractured rock masses (Wang et al. 2016a), as shown in Fig. 1b, the void ratio

of the transverse fractures, called the transverse VRF, can be represented as the ratio of the

subsidence difference to the distance between two adjacent key strata after subsidence:

1 1

1 1 1

d d

d d

f s o i i i ii

r f s o i i i i i i

V D D x y S S S STF

V V D x y D S S z z S S

, (3)

where iTF is the transverse VRF caused by bed separation between the ith

and (i+1)th

key

strata, fV is the void volume of the fractures, rV is the volume of the rock mass, oD is

the original distance between the ith and (i+1)

th key strata, and sD is the distance after

subsidence.

4. Fracturing of the strata

During subsidence, the strata will periodically fracture into rock blocks, and the rock blocks

will then rotate, resulting in separation along the fractured section between two adjacent

rock blocks in a stratum and then producing fractures that are perpendicular to or intersect

the stratum plane and that are called longitudinal fractures.

As seen in Fig. 1b, the longitudinal VRF can be expressed as the ratio of the length

increment of the stratum unit to its length after subsidence, according to the definition of the

void ratio:

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2

d d 11

d1

f

i

r fxi

V s xLF

V V s S

x

, (4)

For a curved surface of key stratum subsidence, the longitudinal VRF will

approximately be given by the square root of the ratio of the areal increment of the stratum

unit to its area after subsidence:

22

d d d 11

d1

f

i

r fi i

V S x yLF

V V SS S

x y

, (5)

where iLF is the longitudinal VRF caused by the fracture of the ith

key stratum, ds is the

unit length of the subsidence curve of the key stratum, and dS is the unit area of the

curved surface of the subsidence of the key stratum.

According to the algorithm of linear interpolation, the longitudinal VRF in strata

between the ith

and (i+1)th

key strata can be written as

, 1 1

1

ii i i i i

i i

z zLF LF LF LF

z z

, (6)

where 1iLF is the longitudinal VRF caused by the fracture of the (i+1)th key stratum, and

, 1i iLF is the longitudinal VRF between the ith

and (i+1)th

key strata.

5. Case study

Underground longwall mining methods have been adopted to extract a coal seam in a

coal mine located in Shanxi Province, northwest China. The mine focuses on the No. 4 seam,

which is closest to the ground surface. The thickness of the No. 4 coal seam is 6.5 m, the

cutting height of shearer is 3.0 m, and the top-coal caving thickness is 3.5 m. The width of

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the longwall mining is 200 m. The geological conditions of the No. 4 seam and its overlying

strata are relatively simple and without faults or hydrological impacts, and the structures of

the seam and overlying strata are essentially horizontal. The measured lithological and

geometrical properties of the coal measure strata above the No. 4 seam and the mechanical

properties of the intact rock matrices in the strata can be obtained from Wang et al. (2016a).

The mechanical properties of the rock contacts in the strata are listed in Table 1. As

estimated using Eq. 2 and supported by field monitoring of the periodic weighting of the

longwall roof, there are two key strata in the overlying strata of the No. 4 seam. The first key

stratum, which lies in the deep zone, determines the subsidence of the part of the overburden

between it and the second key stratum lying in the shallow zone, whereas the second key

stratum controls the entire overburden above it.

Table 1

According to Eq. 3 and taking the above measured coal measure strata for a mined-out

length of 200 m as an example, the distribution of the transverse VRFs caused by bed

separation between the key strata can be calculated and is shown in Fig. 2. The distribution

of the longitudinal VRFs triggered by fracturing in the strata is given by Eqs. 5 and 6 and is

depicted in Figs. 3a-3d. The total VRFs of the transverse and longitudinal fractures were

obtained from Eqs. 3 and 6 and are illustrated in Figs. 3e and 3f.

Fig. 2

Fig. 3

6. Numerical simulation – support and extension of the analytical approach

The motions of the overlying strata are obviously inconsistent due to the differences in their

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structural and mechanical characteristics. Therefore, to numerically simulate the motion of

the overlying strata, the finite element method cannot be used to appropriately depict the bed

separation and fracturing of the strata. However, the UDEC numerical approach, which is

based on the discrete element method, has proven to be feasible and appropriate for

addressing the non-continuous processes of bed separation and fracturing as strata subside

(Israelsson 1996; Gao et al. 2014; Wang et al. 2016a).

Given that the strata subsidence expression of Eq. 1 is analogous from seam strike to

dip, the graphs of the VRF distribution in the x-z and y-z planes are similar. Since the motion

and VRFs of the overlying strata along the seam dip are similar to that along the seam strike,

the UDEC software program was applied to set up a two-dimensional model (Fig. 4) of the

coal measure strata above the No. 4 seam and along the seam strike. The overburden was

divided into rock layers corresponding to the strata’s thicknesses using the stratifications

between the strata. The rock layer was divided into discrete blocks that interacted with each

other through joints in the strata. Fractures could be produced at stratifications and joints.

The blocks themselves were internally divided into zones as a system of finite numerical

calculation elements using triangular meshes. Two types of rock properties were included in

the UDEC model and were used to parameterize rock matrices (blocks) and rock contacts

(joints in the strata and stratifications between the strata). The Mohr-Coulomb plasticity

model (Itasca 2014) was used to determine the mechanical behavior of the block materials,

in which the mass density, elastic properties and plastic properties were required and shown

in table in our previous publication (Wang et al. 2016a). Furthermore, the Coulomb slip

model (Itasca 2014) based on joint area contact was used to determine the mechanical

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behavior of the rock contacts between the blocks, using the properties listed in Table 1. The

block sizes of the overlying strata were calculated using the theoretical fractured lengths of

the overlying strata, expressed as Eq. 2, to determine the key strata in the overburden. There

are two key strata in the overburden of the No.4 seam. Two peaks in the support pressures,

with significant appearances of ground pressures with different intensities, were observed

periodically during field monitoring of the periodic weighting of the longwall roof. The

interval distances between adjacent peaks were 42.6 m and 23.5 m, which, respectively,

corresponded to the high and low intensities of the ground pressure appearances. Therefore,

the block sizes of the second key stratum (primary key stratum) and the first key stratum

were designed to be 42.6 m and 23.5 m in the UDEC model, respectively, the theoretical

fractured lengths of which were the greatest among the entirety and parts of their

corresponding overburdens.

Fig. 4

Because the No. 4 coal seam is prone to spontaneous combustion, boreholes at 50 m

intervals have been drilled from the ground surface to inject fire-fighting materials into the

mined-out area to prevent the spontaneous combustion of the residual coal. These boreholes

can be used as observation boreholes to determine the locations of the key strata and

investigate their subsidence values. The subsidence values of the key strata obtained from

theoretical equation Eq. 1, numerical simulation with UDEC and on-site measurements from

the observation boreholes are compared and shown in Fig. 5. It is obvious that the numerical

subsidence was remarkably consistent with and powerfully supported by the on-site

measurements. The theoretical and numerical subsidences were highly consistent, except

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when the mined-out length was only 100 m, for which the theoretical subsidence exceeded

the numerical subsidence. The reason is that the second key stratum was assumed to be a

blocky structure in the theoretical subsidence model, although it had not yet fractured. As a

result and corresponding to the bending of an elastic thin oval plate, the modified theoretical

equation was used to express the subsidence of the second key stratum (Wang and Li 2016),

the results of which are shown as the black dashed line in Fig. 5a.

Fig. 5

To simulate longwall mining using the verified UDEC model, the No. 4 coal seam was

divided into three excavation steps of 100 m apiece, which produced the 100 m, 200 m and

300 m mined-out lengths to obtain scenarios of the bed separation and fracturing of the

overlying strata.

7. Results and discussion

7.1. Theoretical calculations

Mesh and contour graphs of the distribution of the transverse VRFs between the key strata in

the x-y plane are depicted in Fig. 2. As shown in Fig. 2a, the transverse VRFs rapidly

increased at first, then gradually decreased, and finally stabilized at a minimum from the

surrounding edges of the longwall mining-disturbed strata to the interior and reached

maxima around the positions in the disturbed strata that corresponded to the four endpoints

of the rectangular mined-out area. This was due to the occurrence of the highest tensile

stresses and deformations at the edges of the mining area. In addition, the theoretical

transverse VRFs illustrated in the contour graphs shown in Figs. 2b and 2c did not change in

the vertical direction because the transverse fractures caused by bed separation were

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assumed to have a uniform vertical distribution in the theoretical model.

The distribution mesh graphs of the longitudinal VRFs in the first and second key strata

in the x-y plane are shown in Figs. 3a and 3b, respectively. According to the linear

interpolation algorithm, the longitudinal VRFs between the two key strata were estimated,

and their distribution contour graphs in the x-z and y-z sections are illustrated in Figs. 3c and

3d, respectively. The longitudinal VRFs rapidly rose and reached maxima, then quickly

decreased, and finally stabilized at a minimum from the perimeters to the interior area. Four

ridges with maxima and four hollows with minima emerged in the positions that

corresponded to the middle segments of the four edges and the four endpoints of the

rectangular mined-out area, respectively, as illustrated in Figs. 3a and 3b. These results were

the result of the fracturing of the strata that were disturbed by the rectangular mined-out area,

which presented an “O-type” (Wang et al. 2016a). As shown in Figs. 3c and 3d, the

longitudinal VRFs gradually decreased from the deep to shallow strata, and the positions

with maxima occurred in the two subsidence segments with maximum gradients, the

distance between which slowly diminished as the embedded depths of strata decreased.

Adding the transverse and longitudinal VRFs together, the total VRFs between the key

strata were obtained and are shown in Figs. 3e and 3f. It is evident that the fractures were

concentrated around the perimeters of the longwall mining-disturbed strata, where the

subsidence curves had the maximum gradients, the VRFs around which gradually decreased

from the deep to shallow strata.

7.2. Numerical simulations

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It can be seen from the original images of strata motion shown in Fig. 6 that the excavation

of the coal seam caused varying subsidences and heterogeneous bed separation and fractures

in the overlying strata and then produced a large number of fractures. The distribution of

fractures was clearly discontinuous and heterogeneous. In the early stage, when the second

key stratum had not fractured, the fractures mostly occurred near the perimeter and center of

the disturbed strata. Correspondingly, those fracture-rich zones were located above the

boundaries and center of mined-out area. However, in the middle and late stages, after the

fracturing of the second key stratum, the fractures were concentrated around the two

boundaries of the longwall mining-disturbed strata between the two key strata. Those

fracture-rich zones lied obliquely above the boundaries of the mined-out area. It is evident

that the fracture-rich zone presented an “arch” type. Therefore, a “fracture-rich arch”

fracture distribution type was proposed to depict the distribution and development of the

longwall mining-induced fractures in the overlying strata. As the mined-out length of the

coal seam increased, the “fracture-rich arch” extended vertically and along the strike. More

specifically, before the primary key stratum fractured, a large number of fractures occurred

around the arch feet and arch crown, and the “fracture-rich arch” extended vertically and

along the seam’s strike. However, the fractures thereafter were primarily concentrated

around the arch feet, and the “fracture-rich arch” extended only along the strike of the seam.

Fig. 6

The original images of strata motion produced from the UDEC simulations only show

the qualitative performance of the opened cracks, such as the rough locations and densities

in the distribution. To quantify the void fraction of the opened cracks in the fractured rock

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masses between the key strata, a post-processing procedure was used to process the original

images to achieve images of the VRF distribution. The details of the procedure are shown in

Figs. 6a and 6b and are as follows.

(a) An original image obtained from the UDEC numerical simulation was read to

generate a three-dimensional image matrix that included the pixel positions and three

primary color values of red-green-blue (RGB).

(b) The image between the first and second key strata and the boundary positions of the

key strata were extracted.

(c) The fractures were identified to produce an image of the fracture distribution under

the condition that the sum of RGB color values, Isum, obeyed Isum<10.

(d) The VRF in a 5×10 pixel ergodic window was calculated using Eq. 7, and by

moving the window pixel by pixel along the ergodic direction vertically and along the strike

of the seam, a VRF distribution nephogram was obtained.

ij

ij

ij

FNFR

N , (7)

where ijFR is the VRF in the strike ith and vertical j

th ergodic window, ijFN is the

number of pixels whose RGB color value sums are less than 10, and ijN is the total

number of pixels in the ergodic window.

Using the above post-processing procedure, the distribution images of the fractures

and corresponding VRF for mined-out lengths of 100 m, 200 m and 300 m were obtained

and are shown in Figs. 6c-6h. The VRFs were large around the perimeters and center of

disturbed strata when the mined-out length was 100 m. For the mined-out lengths of 200 m

and 300 m, the VRFs were large around both sides of the disturbed strata. Because VRFs

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can reflect the number and sizes of fractures, the results are suitable for quantifying the

development of bed separation and fracturing in the strata and to further evaluate the

excavation damage zone. Damage in the stratum increased with increasing VRF. Overall,

the distributions of the VRFs from the UDEC numerical simulations and theoretical models

had uniformly shaped distributions. However, the values of the distribution nephograms for

the VRFs obtained by the former were evidently dispersed and discontinuous, which is

more consistent with the real situation.

7.3. Comparison of the results

To further compare the theoretical and numerical results, another post-processing procedure

was used to obtain the changes in the VRF along the seam strike. The detailed procedure is

shown in Figs. 6a and 6b and as follows.

(a) An original image from the UDEC numerical simulation was read to generate a

three-dimensional image matrix that included the pixel positions and RGB color values.

(b) The image between the first and second key strata and the boundary positions of the

key strata was extracted.

(c) The fractures satisfying the condition of the sum of RGB color values, Isum<10, were

identified to obtain an image of the fracture distribution.

(d) The VRF in an ergodic window of 2×all pixels was calculated using Eq. 8, and by

moving the window pixel by pixel along the ergodic direction of the seam strike, a scatter

diagram of the VRFs was obtained.

ii

i

FNFR

N (8)

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where iFR is the VRF in the strike i

th ergodic window,

iFN is the number of pixels

whose summed RGB color values were less than 10, and iN is the total number of pixels

in the ergodic window.

Using the above procedure, the scatter diagrams of the VRFs distributed along the seam

strike for the mined-out lengths of 100 m, 200 m and 300 m were obtained and are

illustrated in Fig. 7. Correspondingly, the VRF distribution curves obtained using the

theoretical models are also shown in Fig. 7 for comparative analysis. The curves show that

the distributions of the VRFs between the key strata along the seam strike from the

theoretical and numerical methods presented an “M-type” with two peaks, which indicates

that the VRF first increased and then decreased from the two boundaries to the center of

disturbed strata and finally stabilized at a minimum value. The theoretical and numerical

results were in good agreement, except when the mined-out length was only 100 m, where

the theoretical VRFs were obviously less than the numerical values. The reason for that case

was that the second key stratum had not yet fractured but was assumed to be a blocky

structure in the theoretical models. This difference can be greatly reduced when the second

key stratum is modeled as an elastic thin oval plate (Wang and Li 2016). The modified

theoretical results are depicted as a red dashed line in Fig. 7. In fact, the bed separation and

fracturing of the strata was stochastic and discrete, which resulted in the distinct randomness

and discreteness of the numerical results. The theoretical VRFs can be considered to be the

statistical and expected values of the numerical results.

Fig. 7

The global properties of mining-disturbed overburdens are useful for estimating the

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overall development level of fractures to quantify the intensity of roof damage induced by

undermining. Fractal dimension can be used to characterize the developmental degree of

fractures in rock and soil and can reflect the fractal properties of an entire crack network

(Xie 1993; Perfect 1997; Lu et al. 2016). The box-counting dimension, which is easily

programmed and applicable to crack patterns with or without self-similarity (Peitgen et al.

2004), was used in this study to determine the fractal properties of the bed separation and

fracture of overburden. As shown in Fig. 8, each fracture distribution image identified from

the original image of strata movement was covered by a sequence of square grids with

ascending sizes through a measurement box of scale along the horizontal and vertical

measurement directions. For each grid, the number of boxes intersected by the fracture

network, ( )N , and the lengths of the sides of the boxes, δ, were recorded. The slope of the

straight-line fit obtained by plotting log( ( ))N against log(1/ ) indicated the fractal

dimension, FD , per Eq. 9:

log( ( )) log(1/ )FN D C . (9)

Referencing the straight-line regressions shown in Fig. 8b, the fractal dimensions were 1.314,

1.203 and 1.099, respectively, for the 100 m, 200 m and 300 m mined-out lengths. The

average VRFs from the theoretical models and UDEC numerical simulations can also be

used to quantify the overall fracture intensity as global parameters. The average theoretical

VRFs in the fractured zones above the mined-out areas with lengths of 100 m, 200 m and

300 m were 0.1489, 0.0857 and 0.0717, respectively. The average numerical VRFs were

0.1496, 0.1072 and 0.1014. The fracture properties had the same degree of descent as the

mined-out lengths were increased from 100 m to 300 m, as indicated by the fractal

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dimensions, theoretical VRFs and numerical VRFs. The reason for this was that the

fractured zone was gradually compacted by the overburden above the primary key stratum

after fracturing at the mined-out length of 100 m.

Fig. 8

Overall, the resulting VRF distribution of the key strata disturbed by the longwall

mining of the coal seam from the theoretical calculations were in good agreement with those

from the UDEC numerical simulations. With regard to quantitatively depicting the bed

separation and fracturing of the strata, the accuracies of the theoretical models were

confirmed by the UDEC numerical simulation. Therefore, the theoretical models of VRF

distributions in fractured rock masses, which quantitatively reflect the crack intensit ies of

fractured rock masses, can be used as evaluation indexes to quantify the size scale and

fracture intensity of excavation damage zones in longwall mining-disturbed overburdens of

mineral seams to estimate roof reliability. In addition, the VRFs can be used as direct inputs

to control equations for analytic and numerical investigations of heat and mass (groundwater,

natural gas, oxygen, grouting materials or fire-fighting materials) transfers in underground

environments disturbed by mining activities.

8. Conclusions

Based on subsidence expressions for key strata, theoretical models that govern the

three-dimensional distribution of VRFs were derived from the subsidence differences or size

increments of key strata to quantify the separation and fracturing of strata. In addition, a

numerical model and post-processing procedures were proposed to obtain fracture networks,

VRF distributions and fractal dimensions for comparison with theoretical results. It is

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evident that the theoretical models when supported by UDEC numerical simulations

validated by onsite subsidence measurements can clearly depict the heterogeneous

distributions of mining-induced fractures. Therefore, the VRF models can be used as a

quantitative parameter to determine the scales, sizes and shapes of the fractured zones and as

direct inputs to control equations for numerical investigations of underground heat and mass

transfers. From this study, the following conclusions can be drawn.

(a) For a rectangular mined-out panel produced by longwall mining of a mineral seam,

theoretically, the VRFs that quantify the void fraction of cracks caused by bed separation

and fracturing of overburden typically have maxima around the edges of the

mining-disturbed strata. The VRFs first rapidly increase, then gradually decrease, and finally

stabilize to a minimum from the surrounding edges to the center of strata and gradually

decrease from deep to shallow strata. A sequence of UDEC numerical simulations supported

those theoretical results and shed light on the arch-type distribution of undermining-induced

fractures in the overburden, which can be called a “fracture-rich arch” in two dimensions

and further inferred to be a “fracture-rich dome” in three dimensions. This type of

distribution indicates that longwall mining-induced cracks are rich around arch feet near

perimeters of mined-out area and arch crowns near the centers of disturbed strata. The

“fracture-rich arches or domes” will extend vertically and horizontally directions with

increases in the mined-out lengths of seams prior to the fracturing of primary key stratum.

Subsequently, cracks are primarily concentrated around arch feet, and “fracture-rich arches

or domes” extend only horizontally.

(b) A series of post-processing procedures based on digital images produced using the

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UDEC software program was proposed in this paper to identify key strata above mined-out

seams, extract crack fissures in fractured zones, calculate void ratios of fissures, and regress

the fractal dimensions of fracture networks. The numerical VRFs presented distinct

randomness and discreteness because the bed separations and fracturing of the strata were in

fact stochastic and discrete. It is considered that theoretical VRFs can be regarded as the

statistical and expected values of numerical VRFs. Average VRF, which is similar to fractal

dimension, can be as a global parameter to estimate the overall developmental level of

fractures to quantify roof damage intensity induced by undermining. For the mentioned case,

the fracture degrees of overburden had the same descending trend as the mined-out lengths

increased from 100 m to 300 m, as indicated by the fractal dimensions and average VRFs.

The fractal dimensions dropped from 1.314 to 1.099, the theoretical VRFs dropped from

0.1489 to 0.0717, and the numerical VRFs dropped from 0.1496 to 0.1014. The proposed

post-processing methods provide a novel approach for extracting information from the

output images of DEM-based numerical software. In addition, those can be especially used

to further investigate the dynamic development of mining-induced fractures in overburden

and its influencing factors, which include mining speed, mining height, mined-out scale,

geomechanical and geometrical properties of overburden, and geological conditions.

(c) VRF distributions can not only reflect the heights, shapes and fracture intensities of

fractured zones, but can also serve as porosity parameters to determine the hydraulic

conductivities of mining-disturbed overburden. Furthermore, by coupling the required

permeabilities of flowing gas/water and the distribution field of VRFs calculated using the

proposed models in our work, the development heights of gas/water-conducting zones can

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be determined.

(d) The results can provide some engineering guidance for mining safety in practical

mining processes. In fractured zones induced by longwall coal mining, high VRFs indicate

that rich gas/water-conducting fissures exist around the edges and/or tops of

mining-disturbed overburdens. Therefore, fire-prone zones for coal spontaneous combustion

and influx-prone zones for groundwater usually appear around the perimeters of mined-out

areas. Furthermore, pipes or borehole outlets used to inject fire-fighting and plugging

materials should be arranged near those zones. In addition, for methane extraction, gas

drainage boreholes inlets should be placed near the tops of fractured zones in the early

stages of mining when the primary key stratum has not yet fractured. Subsequently, however,

these inlets should be arranged around the edges of mining-disturbed overburdens.

Acknowledgments

This work was supported by the State Key Research Development Program of China (grant

number 2016YFC0600706) and the National Natural Science Foundation of China (grant

numbers 41630642, 11472311). The first author would like to thank the Chinese Scholarship

Council for financial support toward his joint Ph.D. at the University of Newcastle, Australia.

We would also like to acknowledge the editors and reviewers for their invaluable comments.

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Table 1 Mechanical properties of rock contacts in the overlying strata

Type Contact Normal stiffness (GPa/m)

Shear stiffness (GPa/m)

Tensile strength (MPa)

Friction angle

(°)

Cohesion (MPa)

Joint in stratum

Soil 0.1 0.04 0 27 0

Mudstone 5.8 2.1 1.2 28 1.4

Sandstone 60.4 18.9 2.4 31 2.9 Shale 10.1 4.0 0.9 15 1.2

Coal seam 9.3 3.8 0.6 20 1.0

Stratifi-cation

Soil - Mudstone 2.8 0.9 0.4 27 0.6 Mudstone - Sandstone 20.1 8.4 1.9 28 1.9

Sandstone - Shale 27.7 10.0 1.4 20 1.7 Shale - Coal seam 9.5 3.8 0.6 18 1.1

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Figure Captions

List Figure captions

Fig. 1 Cut-away view of a longwall mining panel and stratum motion

Fig. 2 Distribution graphs of the theoretical VRF of transverse fractures caused by

bed separation between the first and second key strata for a mined-out length

of 200 m

Fig. 3 Distribution graphs of theoretical VRF of longitudinal fractures caused by the

fracturing of strata and of the total fractures between the first and second key

strata for a mined-out length of 200 m

Fig. 4 UDEC model of coal measure strata

Fig. 5 Subsidence of a the second key stratum and b the first key stratum from

theoretical, numerical, on-site measurement and modified theoretical results

Fig. 6 Post-processing procedure and numerical simulation results

Fig. 7 Comparison between the total VRFs of transverse and longitudinal fractures

between key strata determined by theoretical and numerical methods

Fig. 8 Fractal dimensions of the fracture network in the fractured zone

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Strike x

yLongwall

mining face

Mined-out area

Deposit seam

Stratum 1

Stratum 2

Stratum 3

Stratum 4

Stratum 5

Stratum 6

Ground surface

Fracture

Starting line

z

Vert

ical

(i+1)th key stratum

Primary key stratum

ith key stratum

Bed-separation

(a)

ith key stratum

(i+1)th key stratumzi+1

zi

Original distance Do

Distance after subsidence Ds

Subsidence Si+1

Subsidence Si

dx

(b)

Fig. 1 Cut-away view of a longwall mining panel and stratum motion showing a subsidence,

bed separation and fracturing of stratum and b subsidence curves of key strata

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-500

50100

150200

250

-150-100

-500

50100

150

0.00

0.05

0.10

0.15

0.20

(a)(b)

(c)

Seam dip – y/m

Seam strike – x/m

Ver

tica

l–z/

mV

erti

cal–

z/m

VRF

VRF

VR

F

Fig. 2 Distribution graphs of the theoretical VRF of transverse fractures caused by bed

separation between the first and second key strata for a mined-out length of 200 m, which

involves a mesh graph in the x-y plane, contour graphs b in the y=0 section and c in the

x=100 m section

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-500

50100

150200

250

-150-100

0

1001500.00

0.05

0.10

0.15

0.20

-500

50100

150200

250

-150-100

0

1001500.00

0.02

0.04

0.06

0.08

(a)(c)

(d)

Seam dip – y/m

Seam strike – x/m

Ver

tica

l–z/

mV

erti

cal–

z/m

VRF

VRF

VR

F

(b) (e)

(f)

Seam dip – y/m

Seam strike – x/mV

erti

cal–

z/m

Ver

tica

l–z/

mVRF

VRF

VR

F

Fig. 3 Distribution graphs of theoretical VRF of longitudinal fractures caused by the

fracturing of strata and of the total fractures between the first and second key strata for a

mined-out length of 200 m, which include the mesh graphs of longitudinal VRFs a in the

first key stratum in the x-y plane and b in the second key stratum in the x-y plane, the

contour graphs of longitudinal VRFs between the first and second key strata c in the y=0

section and d in the x=100 m section, and the contour graphs of total VRFs e in the y=0

section and f in the x=100 m section

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10

6.9

m

500 m

Soil

Stratification between strata Block (Rock matrix)Joint in strata

Mudstone1Sandstone1

Mudstone2

Sandstone2Sandstone3a

Sandstone4Sandstone5Sandstone6b

ShaleCoal seamFloor

Mined-out length of 100m

Mined-out length of 200m

Mined-out length of 300m

x

z

O

a The second key stratum (primary key stratum)b The first key stratum

Fig. 4 UDEC model of coal measure strata

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-50 0 50 100 150 200 250 300 350-7

-6

-5

-4

-3

-2

-1

0

-50 0 50 100 150 200 250 300 350-7

-6

-5

-4

-3

-2

-1

0

Subsi

den

ce/m

Subsi

den

ce/m

Seam strike – x/m

Mined-out length of 100 mMined-out length of 200 m

Mined-out length of 300 m

Theoretical results Numerical results On-site measurement values Modificatory theoretical results

(a)

(b)

Mined-out

length of 100 m

Mined-out

length of 200 mMined-out

length of 300 m

Mined-out

length of 100 m

Mined-out

length of 200 mMined-out

length of 300 m

Fig. 5 Subsidence of a the second key stratum and b the first key stratum from theoretical,

numerical, on-site measurement and modified theoretical results

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-50 0 50 100 150 200 250 300

0

20

40

60

80

100

-50 0 50 100 150 200 250 300

0

20

40

60

80

100

(c)

(d)

Seam strike – x/m

Ver

tica

l–z/

m

Seam strike – x/m

Ver

tica

l–z/

m

VR

F

Fracture-rich arch Arch crown

Arch foot

Second key stratum

First key stratum

-50 0 50 100 1500

0.1

0.2

0.3

0.4

Original imageImage matrix Image extraction

between key strata

Fracture

distribution

Fracture

distribution

Identification

Result Result

Distribution of VRF

Seam strike – x/m

VR

F

Ergodic window

Ergodic direction

Mined-out length100 m

(a)

Fracture-rich arch

-50 0 50 100 150 200 250 300

0

20

40

60

80

100

-50 0 50 100 150 200 250 300

0

20

40

60

80

100

(e)

(f)

Seam strike – x/m

Ver

tica

l–z/

m

Seam strike – x/m

Ver

tica

l–z/

m

VR

F

Mined-out length of 200m

Original imageOriginal image

Image matrix

Image between key strata

and boundaries of key strta

Image read

Image extraction

Image of fracture distribution

Fracture

identificationIsum<10

Distribution curve of

VRF along seam strike

Distribution

nephogram of

VRF

Ergodic window:

2×all pixels

Ergodic direction:

seam strike

Ergodic window:

5×10 pixels

Ergodic direction:

seam strike and vertical

(b)

Fracture-rich arch

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-50 0 50 100 150 200 250 300

0

20

40

60

80

100

-50 0 50 100 150 200 250 300

0

20

40

60

80

100

(g)

(h)

Seam strike – x/m

Ver

tica

l–z/

m

Seam strike – x/m

Ver

tica

l–z/

m

VR

F

Mined-out length of 300m

Original image

Fracture-rich arch

Fig. 6 Post-processing procedure and numerical simulation results, which include

post-processing a procedure and b flowchart, fracture distribution images with c 100 m, e

200 m and g 300 m mined-out lengths, and VRF distribution images with d 100 m, f 200 m

and h 300 m mined-out lengths

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-50 0 50 100 150 200 250 300 350

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Numerical results Theoretical results

Mined-out length of 100 mMined-out length of 200 m

Mined-out length of 300 m

Seam strike – x/m

VR

F

Modificatory

theoretical

result

Fig. 7 Comparison between the total VRFs of transverse and longitudinal fractures between

key strata determined by theoretical and numerical methods

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-50 0 50 100 150 200 250 300

0

20

40

60

80

100

Seam strike – x/m

Ver

tica

l–z/

m

1

2

n

3

δ

log(1/δ)

logN

(δ)

R2=0.98 R2=0.99 R2=0.99

Mined-out length lx/m

Fra

ctal

dim

ensi

on D

F

Measuring box

Measuring direction

Mea

suri

ng d

irec

tio

n

(a)(b)

(c)

Aver

age

VR

F

Fig. 8 Fractal dimensions of the fracture networks in the fractured zones, including a the

post-processing to count the number of boxes N(δ) intersected by the fracture network using

a square mesh comprised by many measuring boxes of scale δ (its increment Δδ is equal to

the scale of a pixel of 0.4956 m) to cover the entire target area, b the calculation of box

dimensions and c the changes of box dimensions and average VRFs with the increasing

mined-out lengths

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41

Highlights:

Theoretical heterogeneous distribution models of void ratios of fractures (VRFs) were

proposed

A numerical model for simulating the bed separation and fracturing of strata was

established

Image post-processing procedures were proposed to calculate the VRFs and fractal

dimensions

A fracture-rich arch/dome illustrates the distribution and development of

mining-induced fractures

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