Numerical Investigation Of Coal And Gas Outbursts In Underground Colliery

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International Journal of Rock Mechanics & Mining Sciences 43 (2006) 905–919 www.elsevier.com/locate/ijrmms

Numerical investigation of coal and gas outbursts in underground collieries T. Xua,b, C.A. Tanga,c,, T.H. Yangc, W.C. Zhuc,d, J. Liud a

Center for Material Failure Modeling Research, Dalian University, Dalian, 116622, PR China School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China c Center for Rock Instability and Seismicity Research, Northeastern University, Shenyang 110006, PR China d School of Oil and Gas Engineering, the University of Western Australia, 6009, Australia b

Accepted 1 January 2006 Available online 3 April 2006

Abstract Coal and gas outbursts are a complex catastrophic unstable phenomenon that involve the ejection of large volumes of coal, and are often accompanied by gas, such as methane, carbon dioxide or a mixture of the two. Coal and gas outbursts are prevalent in deep and gassy mines where face advance rates are rapid, and where gas drainage is either poor or absent. The occurrence of progressively larger coal and gas outbursts, and the potential for the catastrophic collapse of coal pillars, is of increasing importance as mining is extended deeper in seams rich in methane and other hydrocarbons. A unique coupled gas flow and solid deformation numerical model, viz., RFPA2D-GasFlow, has been developed and is applied to simulate the evolutionary process of such catastrophic coal failures in underground collieries. The finite element model, which incorporates the physics of gas flow in the coal seam, the physics of coal deformation and instantaneous failure, and the cross-couplings between them, is proposed. The model also incorporates small-scale variability in deformation modulus and strength of the coal and surrounding rock. The variability in modulus and strength is distributed via a fine-scale resolution model according to the Weibull distribution, where the distribution parameter determines the level of heterogeneity. This numerical model is applied to simulate the whole process of coal and gas outbursts, including stress concentration, coal fracturing, gas pressure-driven expansion, and outburst. The instantaneous outburst process and associated stress fields, gas pressure gradients and displacement vectors are presented step by step. The numerical simulations indicate that the instantaneous outburst is a complex phenomenon involving interactions between gas pressure, stress and the physico-mechanical properties of the coal, and it can occur under a variety of conditions. Successful numerical simulation of the whole coal and gas outburst process provides the basis for identifying the outburst mechanisms, parameterizing the causative processes, and to defining potential precursors of failure. r 2006 Elsevier Ltd. All rights reserved. Keywords: Coal and gas outburst; Underground mining; Failure process; Numerical simulation

1. Introduction Underground collieries have long experienced sudden, usually unexpected, expulsions of coal or rock and gas away from freshly exposed working face during underground mining, either while breaking into or during development of a seam—normally resulting in a cavity in the coal or rock mass. These are commonly known as coal Corresponding author. Center for Rock Instability and Seismicity Research, Northeastern University, Shenyang 110006, PR China. Tel.: +86 411 8740 3700; fax: +86 411 8740 3588. E-mail address: [email protected] (C.A. Tang).

1365-1609/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2006.01.001

or rock and gas outbursts. They have occurred in virtually all the major coal producing countries of the world and have been the cause of major disasters in the world mining industry. Such coal and gas outbursts range in size from a few tones to thousands of tones of coal with corresponding gas volumes from tens of cubic meters to hundreds of thousands of cubic meters. In fact, coal and gas outbursts can release over one million cubic feet of gas, fractured and even pulverized coal and rock (Fig. 1). The occurrence of coal and gas outburst in coal mines and caverns poses a major potential threat to facility operators and has challenged many researchers in the rock mechanics and

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Fig. 1. Coal and gas outbursts induced by underground mining.

rock engineering community. In the last 150 years, since the first reported coal and gas outburst occurred in the Issac Colliery, Loire coal field, France, in 1843 [1], as many as 30,000 outbursts have occurred in the world coal mining industry. The most outbursts, more than one-third of the total, have occurred in China. These disastrous mine outbursts have resulted in much loss of equipment, production time, even entire mines, and the lives of numerous miners all over the world. For instance, on October 20, 2004 at the Daping coal mine in Xinmi city, Henan province, China, 148 fatalities resulted from an outburst. A large component of the disaster was due to secondary factors, such as the succeeding gas explosion, suffocation, and poisoning. Similar disasters have befallen coal mines in many other countries. These have forced mining leaders and researchers to develop an understanding of the complex outburst phenomenon, and develop procedures to minimize the effect of outbursts or eliminate them completely. However, some safety procedures that have been adopted lead to reduced production rates. For almost half a century now, considerable attention has been paid to this complex problem [2]. The preliminary investigations relating to the coal and gas outburst mechanism, which were conducted through in situ observation, physical and theoretical studies, and numerical modeling, were made to prevent coal and gas outburst hazard during recent decades. Some empirical hypotheses, criteria and analytical models have been proposed for the understanding, analysis and prediction of the coal and gas outburst conditions. Kidybinski [3] took into consideration the three components of gas content and flow, stress, and coal failure and proposed the presence of three zones in the coal seam ahead of the mining operations starting at the coal face: (1) protection/degassed zone, (2) high gas pressure/active zone and (3) abutment pressure zone. Within this model, three fundamental conditions are assumed to be met for an outburst to occur: (1) failure of the coal in compression within the active zone, (2) penetration of a hole through the

protection zone and (3) fluidized bed outflow of the products from the outburst cavity. Gray [4] considered two gas-initiated failure mechanisms existed: either tensile failure of unconfined coal or piping of sheared material. Paterson [5] took the general view that, when gas is released from coal, there are body forces on the coal equal to the pressure gradients of the flowing gas. His models were based therefore on the fundamental assumption that an outburst is the structural failure of coal due to excess stress resulting from these body forces. A model proposed by Litwiniszyn [6] was based on the gas existing in a condensed state within the coal. When a shock wave passes through the coal, a phase transformation occurs of the liquid substance into a gaseous state. This sudden creation of gas causes the skeleton of the medium to be destroyed and an outburst to be initiated. Support for this model is found in the following observations: (1) sometimes ‘bumps’ and instantaneous outbursts occur together, and some ‘bumps’ are regarded as initiation of instantaneous outbursts, and (2) in hand-working, especially without the ambient noise of machinery, successive ‘knocks’ in the coal were often precursors to an instantaneous outburst [7]. However, Paterson [5] identified several flaws in this model, in particular cause and effect, where do the shock waves originate? Thermodynamic descriptions have also been proposed for outburst modeling [8]. Williams and Weissmann [10] used a schematic of an outburst in frequently encountered Australian conditions to discuss gas content thresholds for outbursts. They placed emphasis on a gas pressure gradient existing ahead of the working face. However, they also believed that ‘‘the most important parameter is gas desorption rate, in conjunction with the gas pressure gradient ahead of the face’’. Jiang and Yu [10], based on many laboratory tests, presented the ‘spherical shell losing stability’ model during outbursts (as shown in Fig. 2). They believed that the outburst process consists of six phases, viz., (1) intact stress phase, (2) stress concentration phase, or abutment pressure phase, (3) coal crushed by rock stress, (4) coal split by gas pressure, (5) expulsion of coal and gas due to spherical shell losing stability, and (6) movement of coal and gas desorption. In addition, many previous studies have considered tectonic deformation and the microstructure of the deformed coal to be important factors influencing outburst occurrence. Farmer and Pooley [11] found that outbursts only occur in districts subject to severe tectonic movement—hence, their association in many places with anthracite—and in association with such deformation and depositional structures as folds, faults, rolls and slips and in particular with rapid fluctuations in the seam thickness. Shepherd et al. [12] reported on outburst occurrences in Australia, North America, Europe, and Asia, and found that probably over 90% of significant outbursts have been concentrated in the narrow strongly deformed zones along the axes of structures such as asymmetrical anticlines, the hinge zones of recumbent

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Fig. 2. ‘Spherical shell losing stability’ model during outbursts (after Jiang [9]).

folds, and the intensely deformed zones of strike-slip, thrust, reverse, and normal faults. These narrow deformed zones, whether in mesoscopic or mine-scale geological structures, form the loci for stress and gas concentration. Similar studies in China revealed that outbursts nearly always occurred in long, narrow outburst zones along the intensely deformed zones of strike-slip, reverse or normal faults, within which coal has been physically altered into cataclastic, granular, or mylonitic microstructures [13]. The other occurrences are associated with bedding-plane faults and intense folds, which may produce these microstructures in broader zones. In either case, the outburst-prone zones generally cover no more than 20–30% of the mine area. Some fault zones do not exhibit altered microstructure, and these are not prone to outburst. Thus, the presence of these altered microstructures is considered as the first essential factor for outburst occurrence, and outburst-prone districts could be predicted by studying the spatial distribution of altered coal and geological structures. It has also been found that outburst danger increases with the intensity of deformation and alteration of the coal microstructure. Many studies have compared coal actually expelled from an outburst cavity to coal in situ with similar microstructure, based on their physical and morphological characteristics. To date no significant difference has been found [14,15]. There has been a fairly widely accepted view that a deeper understanding of outbursts mechanism and reliable methods for the prediction of outbursts must be not only based upon long years of practical experience in mines, but also on scientific research and experimentation. Despite extensive research about violent coal and gas outbursts occurring in coal mines, surprisingly little progress have been achieved in the past 150 years towards understanding or prediction. Especially, a quantitative model that describes progressive failure process as well as violent outbursts process in coal mines has not appeared. It is the aim of this paper to present such a model and to show how the model explains the observations associated with outbursts. For example, the coal is often in pulverized form

and appears to flow, although some incidents are merely large face slumps or floor heaves and associated gas release. In addition, the mechanical and seepage properties of gassy coal specimens, such as deformation and strength behavior, and the evolution of coal permeability, are also covered in this paper. The rapid advance of computer technology has enabled applied mathematicians, engineers and scientists to make significant progress in the solution of intractablecoupled mining and rock mechanics-associated problems. Thus, in this paper, a quantitative model, RFPA2DGasFlow model, is proposed to describe the coupled gasflow and rock failure problems associated with coal/rock and gas outbursts, and correspondingly, an advanced powerful numerical tool, RFPA2D-GasFlow code, has been developed on the basis of the RFPA2D-Flow code to investigate the mechanism of the complex outbursts and to try to gain an insight into the coupling mechanism between gas flow and coal/rock deformation.

2. Theoretical model When formulating the model in mathematical language, various levels of complexity can be incorporated into each component, with the accuracy and versatility of the model depending on the refinement of the components description. For coal and gas outbursts in mining or drilling, gas migration problems in gas drainage, and gas disposal in engineering practice, which can all be attributed to fluid flow and deformation problems in porous media, the coupled effect of the medium deformation and fluid flow may be important for understanding the mechanism of coal and gas outbursts and the methane gas flow during gas drainage. As pointed by Paterson [5], for a model that can be used to predict outbursts, three components must be accounted for: (i) a gas flow description, (ii) a stress description, and (iii) a failure description. Hereby, the descriptions of gas flow, stress and failure in the RFPA2DGasFlow model are presented in this section.

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2.1. Flow of gas

Substitution of Eq. (5) into (4) leads to:

The fundamental assumption behind the outburst model presented here is that the coal is saturated with gas; thus, the equations for two phase flow in porous media should be used. In 1856, Henry Philibert Gaspard Darcy [16] first developed the equation to describe fluid flow through a porous media. Based on Darcy’s Law, Zhou [17] further developed the gas filtration equation followed by a linear law. qi ¼
lij

dP , dn

(1)

where, qi denotes gas filtration rate (i ¼ 1; 2; 3) in m/s; lij is the coefficient of gas filtration (i; j ¼ 1; 2; 3) in m2/(MPa2 s); and P is the square of gas pressure in MPa2. Generally, gas exists within coal in two distinct forms: usually referred to as free gas and adsorbed gas. The adsorbed gas typically accounts for over 95% of the gas within a coal seam, depending on the pressure at which the gas is adsorbed, while the free gas, only a small fraction of the total gas, is stored in the pore or cleat space, either free or in solution. The total gas content in coal can be approximated by the empirical equation [17,18] pffiffiffi X ¼ A p, (2) where X is the gas content in gassy coal in m3/m3; A is the empirical coefficient of the gas content in m3/(m3 MPa1/2), and p is the gas pressure in MPa. According to the basic seepage theory of gas flow in porous media, the following equation for the isothermal filtration gas flow in gassy coal and rock can be obtained: aP r 2 P ¼

qP , qt

(3)

where aP ¼ 4lA
1 P3=4 . 2.2. Deformation of the solid Secondly, we consider the stress description, which can be formulated in a number of ways. For a stress analysis in terms of effective stress, the stress equilibrium equations take the form [19]: sij;j þ f i ¼ 0,

(4)

where sij is the stress tensor, (i; j ¼ 1; 2; 3) in MPa, fi is the body forces per unit volume in MPa. We now use the generalized effective stress principle based on Terzaghi’s law [20] in the stress equilibrium equations from one- to two-phased materials: sij ¼ s0ij þ apdij ,

(5)

where sij is the solid total stress tensor, sij0 is the solid effective stress tensor, p is the gas pressure, and a is a positive constant equal to 1 when individual grains are much more incompressible than the grain skeleton, dij is the Kronecker delta function.

s0ij;j

þ f i þ ðapdij Þ;j ¼ 0.

(6)

Thus, the equilibrium equation is expressed according to the effective stress principle. According to the continuous conditions, for a perfectly elastic isotropic continuum, the geometrical equation can be expressed as 1 eij ¼ ðui;j þ uj;i Þ, (7) 2 where eij is the strain tensor, (i; j ¼ 1; 2; 3), ev is the volumetric strain, ev ¼ e11 þ e22 þ e33 , and u is the displacement of an element. The constitutive equation for the deformation fields can be expressed for elastic isotropic materials as s0ij ¼ Kdij ev þ 2Geij ,

(8)

where G is the shear modulus and K is Lame’s constant. On the basis of the above, the equilibrium, the continuity, and the constitutive equations, the governing equations for the mathematical model of coal/rock deformation considering the gas pressure in coal/rock can be represented as ðK þ GÞuj;ji þ Gui;jj þ f i þ ðapÞ;i ¼ 0.

(9)

2.3. Failure of the solid Finally, the failure description of the RFPA2D-GasFlow model is given here. In the RFPA2D-GasFlow code, we rely on the finite element method to perform the stress analysis in the model. The model is discretized into a large number of small elements to take into account the local variations of the material heterogeneity. The basic elements of the RFPA2D-GasFlow model can be generalized as follows: (1) By introducing the heterogeneity of rock properties into the model, the model can simulate the non-linear deformation of a quasi-brittle rock with an ideal brittle constitutive law for the local material; (2) By recording the event-rate of failed elements, the model can simulate seismicity and fracturing events associated with the progressive fracture process; (3) By introducing a reduction of the material mechanical parameters (strength, elastic modulus, etc.) after elemental failure, the model can simulate strain-softening and discontinuum mechanics problems in a continuum mechanics mode; (4) By introducing the relational equation for stress and gas permeability, the model can simulate the stressinduced variation of gas permeability, especially the sudden jump of gas permeability in the post-failure regime. For the details of the heterogeneity and failure event-rate of the material, the reader can refer to published papers

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[21,22]. Here the other two aspects of the failure description, damage induced stiffness degradation and damageinduced permeability increase, are presented as below. In the model, only an elastic constitutive law with linear behavior has been introduced for all elements, which have been assigned different strength and elastic constant parameters depending on the heterogeneity of the rock materials. The elastic constitutive relation for an element under uniaxial compressive stress and tensile stress is illustrated in Fig. 3. When the stress in the element satisfies the strength criterion (such as the Coulomb–Mohr criterion), the element becomes damaged. In elastic damage mechanics, the elastic modulus of the element may degrade gradually as damage progresses. If the element and its damage are assumed to be isotropic, the elastic modulus of the damaged element is defined as follows:

Similarly, for tension, the maximum tensile stress criterion is chosen as the strength criterion for the elements:

E ¼ E 0 ð1
DÞ,

2.4. Evolution of permeability

(10)

where D represents the damage variable, E and E0 are the elastic moduli of the damaged and undamaged elements, respectively. The parameters E, E0 and D are all scalar. For compression, Mohr–Coulomb criterion is chosen as the strength criterion for the elements: s1
s3

1 þ sin f Xf c , 1
sin f

(11)

where s1, s3, are the maximum principal stress and minimum principal stress, respectively; f is the internal friction angle and fc is the threshold of the compressive strength of elements. Correspondingly, the damage variable D in compression can be expressed as ( 0; eoec0 ; D¼ (12) fcr 1
E 0 e ; ec0 pe; where fcr is the residual compressive strength of elements, e and ec0 are the compressive strain and the compressive threshold strain of the elements, respectively.


1

Compression

fc Elastic

Degraded tu 3

Tension

t0

fcr -ftr

c0

cu

1

-ft

Fig. 3. Elastic damage constitutive law for element under uniaxial compression and tension.

s3 p
f t ,

(13)

where ft is the threshold for the tensile strength of elements. Correspondingly, the damage variable D in tension can be expressed as 8 0; et0 pe; > < f tr (14) D ¼ 1
E 0 e ; etu peoet0 ; > : 1; epetu ; where ftr is the residual tensile strength of the elements; et0 and etu are the tensile threshold strain of damage elements and the final tensile strain of the failed elements, respectively.

For damage-induced permeability change, most of the theories are only valid in the pre-failure regions. During elastic deformations, the rock permeability decreases when the rock compacts, and increases when the rock expands. However, a dramatic and remarkable increase in rock permeability can be expected as a result of the generation of numerous microfractures on reaching the peak load. Then, the permeability may gradually drop again should the failed rock be further compacted, or the permeability may increase continuously should the failed rock be further extended. The gas permeability coefficient in uniaxial compression and tension can be described in the following equations [23]. The gas permeability of the elements in compression can be described as ( l0 e
bðs1
apÞ ; D ¼ 0; l¼ (15) xl0 e
bðs1
apÞ ; D40; where l0 is the initial gas permeability for unloaded coal and rock, b is the coupling factor of stress to pore pressure, a is the coefficient of pore pressure, and x is the coefficient of sudden jump of gas permeability for loaded elements in compression. For elements in tension, the gas permeability–stress equation is expressed as 8 l e
bðs3
apÞ ; D ¼ 0; > < 0
bðs3
apÞ 0oDo1; xl e ; 0 l¼ (16) > : x0 l0 e
bðs3
pÞ ; D ¼ 1; where x0 is the coefficient of sudden jump of gas permeability for failed elements in tension. The other parameters are the same as the earlier equations. In this way, the damage-induced stiffness degradation and damage-induced permeability variation are presented in the RFPA2D-GasFlow model. In the simulations using the RFPA2D-GasFlow code, the numerical sample is loaded either in a displacement control

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mode or in a load control mode. At each loading increment, the stress and strain, and the stress and gas permeability in the elements are calculated; then, the stress field and flow field are examined and those elements, which are strained beyond the pre-defined strength threshold level are broken irreversibly. If some elements have failed, then the model with new parameters for some of its elements moves to a new equilibrium. The next load increment is added only when there are no more elements strained beyond the strength threshold level at an equilibrium strain field. Thus, numerical loading on the model can be performed in this way—as a direct analog to the laboratory-testing machine

1 Normalized Stress

910

Experimental Curve Numerical Curve

0.8 0.6 0.4 0.2 0 0

(a)

0.5

1 Normalized Strain

1.5

2

3. Validation of the RFPA2d-gasflow model Validation of RFPA2D-GasFlow model was conducted for the failure process of coal or rock and the gas flow process in the coal or rock failure process. Several coal specimens, 50 mm in width and 100 mm in length, were prepared from blocks of coal, which were taken from the Gushuyuan mines in Jincheng city, Shanxi province, PR China. The ISRM Suggested Methods [24] were kept in mind while preparing the specimens. The coal specimens were conducted on the RMT-150B servo-controlled rocktesting machine and the uniaxial compressive strength, the strain at the peak stress, and the complete stress–strain curves were obtained. Meanwhile, several model specimens with the same scale parameters, such as failure strength, elastic modulus, but with different homogeneity indices were numerically tested under uniaxial compression. The model specimens, with geometry of 100 mm  50 mm in size, were all discretized into 20,000 elements. Based on the experimental results on two coal specimens in uniaxial compression and numerical simulations with RFPA2D-GasFlow code, the dimensionless stress–strain curves were obtained as shown in Fig. 4a. It can be seen that the numerically simulated curves in uniaxial compression tallied well with the experimental curves, except for the initial portions of the curves. The main reason for the diversity at the initial portions of the numerical curves and experimental curves was the adjustment of the gaps in the steel platens, coal specimen and loading cell at the beginning of loading, and the closure of the extensively distributed preexisting microcracks in the specimens. Moreover, the numerical simulation method replicates the complete process of deformation and failure of rock, especially the localization of deformation and failure, as illustrated in Fig. 4b. From the comparisons of the numerical simulations and experimental results, it can be seen that the numerical method is not a simple replication of theoretical or analytical methods, but an effective method of reproducing the entire process of deformation and failure and investigating the mechanical behavior of rock under loading.

(b) Fig. 4. Comparison of experimental curves and numerically simulated curves for specimens.

10m

p=0.1MPa 10m

p=3MPa

p=3MPa Numerical model for radial gas flow in coal seam Fig. 5. Numerical model for a radial open-hole cavity well.

For the validation of the gas flow in the coalbed, the classical well-pumping test for the steady gas flow around a circular borehole in a homogeneous, isotropic, elastic material subjected to far-field gas pressures was adopted

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10 nm–10 mm. As a result of the geometry of the cleat (the fracturing) structure, the permeability of coal is anisotropic. Furthermore, the permeability of coal is stress dependent. An increased confining stress causes the cleats to close, reducing the absolute permeability: reductions of two-orders of magnitude have been observed. So, the evolution of the permeability of gassy coal was numerically investigated to gain an insight into its effect on coal and gas outbursts.

here. A radial numerical model, 10m  10 mm, was constructed with a cavity borehole of 0.5 m in diameter in the center (Fig. 5). The numerical model was discretized into a 200  200 (40,000 elements) mesh. The initial gas pressure in the coalbed was 3 MPa, the borehole pressure was equal to the atmospheric pressure. The gas flow process in the coalbed and the changing curves of gas pressure with duration are illustrated in Figs. 6a and b, respectively. It can be seen from Fig. 6b that the gas pressure around the borehole gradually decreases with duration and finally stabilizes in a new equilibrium state. This tallies well with the theoretical predictions [17]. As can be seen, the numerically simulated results of the failure process of coal and the gas flow in the coalbed show that the RFPA2D-GasFlow is an appropriate tool for studying coupled gas flow during the coal or rock failure process, as well as outbursts. Furthermore, the numerical results can be displayed as an ‘animation’ to provide an improved perception and understanding of the deformation and failure mechanisms of the progressive failure process of coal, as well as outbursts.

4.1. Mechanical properties 4.1.1. Numerical model The mesh for the plane strain numerical sample consists of 200  100 elements with a geometry of 100 mm  50 mm in size (as shown in Fig. 7), and all the elements have the same size (and are square in shape). The pore pressure in the rock specimen is denoted as P, and the confining pressure and axial pressure acted on the numerical rock specimen are respectively denoted as s0 and s1. In order to incorporate the heterogeneity of the rock specimen, the widely used Weibull distribution [25] was introduced to describe the material properties of the elements, such as failure strength, Young’s modulus, and Poisson’s ratio at the mesoscopic level. The input material mechanical property parameters used for the numerical model rock specimen are listed in Table 1 below. An external displacement at a constant rate of 0.002 mm/ step in the axial direction was applied to the rock specimen

4. Numerical simulation of the failure of gassy coal For a number of reasons, gassy coal is far from being a straightforward material to model. Coal has a dual porosity nature: it has a micropore system with pore diameters in the range 0.5–1.0 nm and a macropore system with pores somewhat larger, in the range about

t =1d

t=12d

t=40d

3 2.5 2 p/MPa

(a)

1.5 t=1d

1

t=12d 0.5 0 (b)

t=40d 0

1

911

2

3

4

r/m Fig. 6. Numerically simulated results in radial open-hole cavity well.

5

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and the stress acting on the rock specimen as well as the induced deformation in each element were computed in the numerical tests.

Fig. 7. Numerical model for gassy coal.

Table 1 Mechanical parameters of the numerical model Parameters

Rock

Homogeneity index, m Mean elastic modulus, E0, GPa Mean compressive strength,s0, MPa Internal friction angle, f1 Ratio of compressive to tensile strength, C/T Poisson’s ratio, m Pore pressure, a Coefficient of stress influence, b Confining pressure, MPa

1.5 30 200 30 10 0.25 1, 3 0.1 0, 2, 4, 8, 16

4.1.2. Numerical results Fig. 8 shows the numerically simulated macroscopic failure patterns of the model specimens under different confining pressures and the correspondingly numerical complete axial stress versus axial strain curves of rock at constant confining pressure up to 16 MPa with no pore pressure are presented in Fig. 9. As shown in Fig. 8, the angle between the failure plane and the maximum principal stress direction in uniaxial compression is about 301, and the angle between the macroscopic failure plane and the maximum principal stress direction gradually increases with the increase of confining pressure acted on the rock specimens—which agrees well with theoretical predictions. It can be seen from the stress–strain curves in Fig. 9 that the rock deforms linearly and elastically at axial stresses below the yield strength, which is dependent on the confining pressure. Further compression leads to inelastic deformation up to the peak strength. At low-confining pressures, the curves show defined peak strength and a gradual strength decrease in the post failure region until final deformation occurs at a roughly constant axial stress, i.e., residual strength. At higher confining pressures, the rock exhibits work hardening and the Young’s modulus of the rock is higher than that of the rock at lower pressures. Meanwhile, the transition from brittle to ductile deformation in rock with an increase in confining pressure is also intimated in Fig. 9. Fig. 10 provides the relation between peak strength of the rock specimens and the confining pressure at failure and Fig. 11 is the numerically obtained failure envelopes of the rock specimens. As can be seen from Figs. 10 and 11, the ultimate compressive failure strength, i.e., the peak strength of the numerical rock specimens gradually increases with confining pressure. Even though the linear Mohr–Coulomb failure criterion with tension cut-off is adopted in the model, the macroscopic failure envelope is concave towards the s axis. The numerical results thus indicate that macroscopic non-linear phenomena, such as

Fig. 8. Macroscopic failure patterns of model specimens with given pore pressure of 1 MPa under various confining pressures.

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For rock materials, fracture and friction are macroscopic manifestations of the same processes: e.g., grain crushing, crack growth, healing, and plastic yielding. When viewed in this way, it is not surprising that the difference between the intact strength and residual (or frictional) strength should vanish with increasing confining pressure. That is to say, the rock will ideally exhibit a state of plastic flow at extremely high confining pressure.

70 0 2 4 8 16

60

σ1/MPa

50 40

913

30 20

4.2. Seepage properties

10 0

0

0.1

0.2 ε1/%

0.3

0.4

Fig. 9. Complete stress–strain curves of coal/rock with fixed pore pressure under various confining pressures.

70 60 50 UCS/MPa

40 30 20 10 0

-5

0

5

Tension

10

15

20

Compression Confining pressure/MPa

Fig. 10. Relation between the compressive strength of coal/rock and confining pressure for given pore-pressure.

35 Mohr failure envelope

30 τ/MPa

25 20

Rock permeability is important in coal mining engineering. As mentioned, disastrous coal and gas outbursts into excavations pose a potential significant risk to mining and civil engineering projects. Gas flow in rock strata also influences the regular construction and daily servicing of geo-engineering projects. In the last several decades, hydrogeological and petroleum engineers have become increasingly involved in the study of the permeability of underground rocks and reservoirs [26–28]. These efforts have led to the development of a wide range of mathematical models for permeability and stress or strain interaction. In the present study, considering the mutual interaction between stress and permeability, an attempt is made to investigate the evolution of rock permeability, as well as the relation between permeability and the stress in connection with the complete strain–stress process of loaded rocks using the gas pressure incorporated in the RFPA2D-GasFlow code. 4.2.1. Numerical model In this paper, three different numerical rock specimens with different homogeneity indices (m ¼ 1:5, 3 and 5) representing materials from relative heterogeneity to relative homogeneity (Table 2) are established. The specimen geometry is 100  50 mm and has been discretized into a 240  120 (28800 elements) mesh. In all cases, the specimens undergo plane strain compression, imposed by a relative motion of the upper and lower loading plates, as shown in Fig. 12. Although the specimens are more or less Table 2 Mechanical and seepage parameters

15 10

Parameters

Rock

Homogeneity index, m Mean elastic modulus, E0, GPa Mean compressive strength, s0, MPa Internal friction angle, f1 Ratio of compressive to tensile strength, C/T Possion’s ratio, m Gas permeability K, m2 (MPa2 d) Coefficient of gas content A, m3 (m3 MP1/2) Coefficient of pore pressure, a Coefficient of stress influence, b Confining pressure, MPa Inlet pressure, P1, MPa Outlet pressure, P2, MPa

1.5, 3, 5 50 100 30 10 0.3 0.1 2 0.5 0.1 0 2 0.1

5 0

0

10

20

30 40 σ/MPa

50

60

Fig. 11. Simulated failure envelope for model rock specimens.

rock failure in nature, can be described and revealed through some simple linear rules at the mesoscopic level. In addition, it is noticed that the residual strength (or friction) of rock, is also dependent on the confining pressure, and increases with confining pressure.

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heterogeneous on the microscale, they are statistically homogeneous on the macro-scale since the mechanical property parameters are randomly distributed throughout the whole specimen with many elements.

4.2.2. Numerical results The final simulated stress–strain curves and the corresponding permeability–strain curves of the model specimens are shown in Figs. 13a and b. It can be seen from Fig. 13 that the heterogeneity of the model specimens has a remarkable influence on the strength characterization, the shape of stress–strain curves and permeability evolution. Simulated tests also reveal that the maximum compressive strength of the specimens is proportional to the homogeneity index. The higher the values of the homogeneity index, the higher the values of the peak stress and the peak permeability of the rock samples. One method of observing damage or microcracking during rock deformation experiments is by monitoring acoustic emissions (AE) or seismic events produced during deformation. In the RFPA2D-GasFLow code, a single AE event represents a microcrack-forming event to indirectly assess the damage evolution and the AE events change with the development of microcracking [29]. The simulated failure process, gas pressure gradients and displacement

Fig. 12. Numerical model for seepage tests.

60 m=1.5 50

Stress/MPa

m=3 40

m=5

30 20 10 0 0

0.0005

0.001

(a)

0.0015

0.002

Strain

0.25 Permeability/(m2/(MPa2d))

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0.2 0.15 0.1

m=3 0.05 0

(b)

m=1.5

m=5 0

0.0002

0.0004

0.0006

0.0008 Strain

0.001

0.0012

0.0014

0.0016

Fig. 13. (a) Simulated stress–strain curves and (b) the corresponding permeability–strain curves.

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deviation of stress–strain curve and permeability–strain curve from linearity and an increase of the AE events rate. A sharp increase in the AE events rate and the permeability due to the macroscopic fracturing plane can be observed after the peak strength is reached. Finally, the eventual failure of the specimen is characterized by disintegration of the specimen into pieces by a combination of axial splitting and local shearing or faulting, with the AE events rate sharply decreasing, the stress–strain curve approaching a

vector for a model specimen (m ¼ 1:1) under compression are shown in Figs. 14a, b and c, and the corresponding stress–strain curve, AE characteristics and permeability– strain curve are shown in Fig. 15. It can be seen from Fig. 15 that the stress–strain curve and permeability–strain curve linearly develop with a small increase in axial stress and, at the same time, AE events linked to damage randomly occur throughout the specimen. Further increases in the axial strain lead to the

8

0.18

7

0.16 0.14

6

0.12

5

Normalized AE

4

Permeability-strain Stress-strain

0.1 0.08

3

0.06

2

0.04

1

0.02

0

0

0.0002

0.0004

0.0006

0.0008

Permeability/(m2/(MPa2•d))

Stress/Mpa Normalized AE/counts

Fig. 14. (a) Simulated rock failure process and (b) gas pressure gradients for rock specimen (m ¼ 1:5).

0 0.001

Strain Fig. 15. Numerically simulated stress–strain curves, normalized AE counts, and the corresponding permeability–strain curves for rock specimen with homogeneity index, m ¼ 1:5.

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residual strength and permeability approaching a relative stable value. The simulated results agree well with the findings in laboratory testing [30].

5. Coal and gas outbursts A coal and/or gas outburst is a complex mechanical process in which the fracture splitting and ejection of coals in gassy coal seam are to a large extent dependent on the gas pressure, in situ stress and physico-mechanical properties of coal and surrounding rock. Therefore, it is of great importance to investigate the mechanism of coal and gas outbursts based on the stress field in the rock roof, floor and coal seam. The instantaneous outburst of coal and gas away from the working face during coal mining or drilling is a complex phenomenon. The coal and gas instantaneous outbursts were therefore simulated using RFPA2D-GasFlow model. The numerical model shown in Fig. 16 is designed to simulate instantaneous outbursts occurring in the course of crosscutting induced by drilling. In the model, the gassy soft coal seam is enclosed by impermeable and hard rock roof and floor. Moreover, a layer of thick hard rock acts as a protective screen ahead of the coal seam. The layer of hard rock is instantaneously opened by drilling and the coal seam behind the protective screen is therefore exposed in the course of crosscutting. The model is discretized into a 150  200 mesh (30,000 elements). The gas pressure saturated in the coal seam is 2.1 MPa and the Young’s modulus and strength of the coal are 10 GPa and 15 MPa, respectively. In addition, the Young’s moduli and strength of the rock roof and floor far exceed those of the coal seam. The mechanical and seepage parameters of the numerical model are presented in Table 3. Figs. 17a and b show the crosscutting-induced instantaneous outbursts and the associated stress fields distributions in the rock roof, floor and gassy coal seam. Compared with Figs. 2 and 17, it can be seen that the numerically simulated instantaneous outbursts agree well with the ‘spherical shell losing stability’ model mentioned earlier.

Fig. 16. Numerical mechanical and seepage model of coal and gas outbursts induced by crosscut penetration.

Table 3 Mechanical and seepage parameters for numerical model for instantaneous outbursts Mechanical and seepage parameters

Coal seam

Roof and floor

Crosscut

Heterogeneity index, m Mean elastic modulus, E0, GPa Mean compressive strength,s0, MPa Internal friction angle, f1 Bulk weight/(103 kg/m3) Ratio of UCS to UTS Poisson’s ratio, m Gas permeability, l, m2 (MPa2 d) Coefficient of gas content, A Coefficient of pore pressure, a

2 5 100

10 50 300

2 10 150

30 2.7 20 0.3 0.1

32 1.4 10 0.25 0.001

30 2.0 10 0.3 0.01

2 0.5

0.1 0.01

0.1 0.1

It can be seen from the numerically simulated results induced by crosscutting that the whole process of coal and gas outbursts can be divided into four stages: (1) Stress concentration stage: At the beginning of crosscutting, the loads from the upper rock strata are mostly carried on the freshly exposed coal due to stress concentrations. It is worth noting that the stress in the coal is not uniformly distributed at the meso-scope scale because of the incorporation of the heterogeneity of model materials. (2) Coal/rock fracture and splitting induced by rock stress: Microfractures in coals are predominantly under the abutment stress at this stage. The mechanical properties of coals progressively degrade due to the effect of stress concentration and creep, as well as the three-dimensional stress state in the coals near the working face gradually transforming into a two-dimensional stress state. As a result, fracturing and splitting parallel to the free exposed face occur first in coals near the working face. In the course of splitting, the stress in coals near the coalface decreases and the stress peak gradually moves away from the coalface and into the deep coals with the release of the elastic energy stored in the coal. It is noticeable that a cluster of cracks begins to develop along with the transfer of the stress peak in the coals. (3) Crack propagation driven by gas pressure: Highpressurized gas saturated in the coal seam gushes into the ‘gas way’ and quickly and violently splits the fractured coal. The effect of high gas pressure eventually leads to the formation of the ‘gas way’ during the propagation and coalescence of clusters of cracks. (4) Ejection of coals induced by gas pressure, i.e. outbursts: During the process of crack propagation and coalescence induced by gas pressure, the cracks volumetrically expand and the gas gushes into the cracks. There is a large gas pressure gradient because the gas pressure

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Fig. 17. Numerically simulated coal and gas instantaneous outbursts process and numerically simulated shear stress distributions during instantaneous outbursts (Steps 1–9 stand for the ninth calculated failure step in the first time step for modeling the outbursts process. The steps continue in incremental time steps indicating the failure of coal or rock with duration).

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saturated in the cracks is far beyond the pressure in the freshly exposed coalface, which causes the ejection of the fractured and splitting coals, i.e. coal and gas outbursts. As listed above, the stress concentration, coal/rock fracture and splitting induced by stress, crack propagation driven by gas pressure, and ejection of coals induced by gas pressure are the four major stages of coal and gas outbursts derived from the numerical simulations in this paper. The numerical simulated results reveal that in situ stress, gas pressure and the physico-mechanical properties of coal and rock are the main contributing factors affecting coal and gas outbursts. In addition, numerical simulated results not only trace the initiation, propagation and coalescence of cracks in coals, but also present the associated evolution of the stress field in the coal seam and the roof and floor of the rock strata, i.e., the stress redistribution in the coal seam and rock roof and floor at every stage. 6. Discussion and conclusions Instantaneous outbursts in underground coal mines continue to pose a hazard to safe, productive extraction of coal. The problem results from a combination of the effects of stress, gas content and physico-mechanical properties of the coal. Research and operational experiences have provided the opportunity to test theories on the mechanisms of an instantaneous outburst. Therefore, in the present paper, firstly, the elastic constitutive law for element at a meso-level was proposed considering the heterogeneity of coal and rock; meanwhile, considering the relational equation between damage induced gas permeability and stress and the time-dependent equation for creep damage evolution, the solid–gas coupling model (RFPA2D-GasFlow) for gaseous coal and rock was established, and the numerical FEM implementation for the model was also given. Furthermore, the coupled model was also validated via two aspects of the failure process of coal and rock and gas flow in the coal and rock. Using the RFPA2D-GasFlow code, numerical tests on the basic mechanical characteristics of gaseous coal and rock, such as deformation and strength, heterogeneity, rheology and seepage, were also conducted. The mechanical properties of gaseous coal and rock and the gas permeability evolution of gaseous coal and rock under different stress were also numerically investigated to gain a better understanding of the factors that control the behavior of gas flow in rocks or rock masses. Such intensive studies of gas flow in stressed heterogeneous rocks are useful as initial approaches to many engineering problems in mining and petroleum industries. Numerical results indicate that heterogeneity plays an important role in affecting the evolution of permeability in rock. As the more homogeneous rock sample fails in a more brittle manner, which results in a bigger stress drop, a more significant increase in the overall permeability of the

sample is thus obtained. The simulated permeability variations in stressed heterogeneous rocks agree well with the observed results in the laboratory. Finally, instantaneous outbursts induced by crosscut driving were numerically simulated. Numerical results reproduced the whole process of microcracking, propagation, coalescence and ejection of coal or rock. In addition, the associated stress fields, displacement vectors, gas pressure and microseismicities during the outbursts were clearly visualized. It is noted that the numerical simulations obtained using RFPA2D-GasFlow in this paper capture most of the experimental and in situ-observed phenomena, especially the outburst cavity in a coal and gas outburst. The successful reproducion of the experimentally and in situ observed outburst failure phenomena with a numerical method implies that our understanding of the mechanisms of coal and gas outbursts has reached a more reasonable level which, in turn, will help us to make further progress in better understanding of the mechanism of instantaneous outbursts and controlling and preventing their occurrence as induced by underground mining. Acknowledgments The work presented in this paper was financially jointly supported from the General Project of the National Natural Science Foundation of PR China (Grant No.50504003, 50374020, and 50504005), the Key Project of the National Natural Science Foundation of PR China (50139010), the Major Project of the National Natural Science Foundation of PR China (Grant No. 50490274) and the Open Project of the National Laboratory for Geological Hazard Prevention and Environment Protection (GZ2004-01). Professor John A Hudson is thanked for his editorial assistance. References [1] Lama RD, Bodziony J. Management of outburst in underground coal mines. Int J Coal Geol 1998;35(1):83–115. [2] Beamish BB, Crosdale PJ. Instantaneous outbursts in underground coal mines: an overview and association with coal type. Int J Coal Geol 1998;35(1):27–35. [3] Kidybinski A. Significance of in situ strength measurements for prediction of outburst hazard in coal mines of Lower Silesia. Symposium on the occurrence, prediction and control of outbursts in coal mines. Aust Inst Min Metall, Melbourne 1980:193–201. [4] Gray I. The mechanism of, and energy release associated with outbursts. Symposium on the occurrence, prediction and control of outbursts in coal mines. Aust Inst Min Metall, Melbourne 1980:111–25. [5] Paterson L. A model for outburst in coal. Int J Rock Mech Min Sci Geomech Abstr 1986;23(4):327–32. [6] Litwiniszyn J. A model for the initiation of coal-gas outbursts. Int J Rock Mech Min Sci Geomech Abstr 1985;22(1):39–46. [7] Hargraves AJ. Instantaneous outbursts of coal and gas: a review. Proc Aust Inst Min Metall 1983;285:1–37. [8] Jagiello J, Lason M, Nodzenski A. Thermodynamic description of the process of gas liberation from a coal bed. Fuel 1992;71:431–5.

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