Theoretical analysis on water-inrush mechanism of concealed collapse pillars in floor

Mining Science and Technology (China) 21 (2011) 57e60

Contents lists available at ScienceDirect

Mining Science and Technology (China) journal homepage: www.elsevier.com/locate/mstc

Theoretical analysis on water-inrush mechanism of concealed collapse pillars in floor Tang Junhua a, *, Bai Haibo a, Yao Banghua a, b, Wu Yu a a b

State Key Laboratory of Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, China School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 May 2010 Accepted 2 July 2010

In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper. By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that: the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars. The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata. Copyright Ó 2011, China University of Mining & Technology. All rights reserved.

Keywords: Collapse pillar Water-inrush Critical water pressure Thick plate theory

1. Introduction As a special vertical structure in rock strata, Karst collapse pillars are very common, distributing in more than 20 coal fields of Shanxi Platus, Taihang mountain, Luliang mountain as well as Shandong, Henan, Jiangsu and Shanxi province in North China. Among the hypothesis in the formation of Karst collapse pillars, one representative explanation is carbonatite rock is gradually erased due to moving groundwater, and formed Karst cave, some of them became larger and larger, and then collapsed due to the long-period effect of geological structural stress and gravity of overlying rock strata, as well as leading to the collapse of overlying rock strata. According to conductivity, Karst collapse pillars can be classified into two types, water conducted and water non-conductive (Fig. 1). According to statistical data of discovered Karst collapse pillars, about 90% of them in North China are water non-conductive ones. Nevertheless, the amount of conductive ones is also very large. In addition to serious destructive effect to rock strata, the high water pressure in waterconducted Karst collapse pillar often leads to many water-inrush accidents, causing huge economical loss and serious casualties. Therefore, water-conducted Karst collapse pillars become hidden troubles which threaten and influence the safety mining in many mining areas in China. In order to explore the water-inrush mechanism of water-conducted Karst collapse pillar, many researchers have

* Corresponding author. Tel.: þ86 355 5975512. E-mail address: [email protected] (T. Junhua).

done many useful works. For instance, Yin shangxian and Wu qiang established ‘thick wall cylinder’s mechanical model’ to study the basic condition of water-inrush from Karst collaspse pillar, as well as summarizing the water-inrush modes in which theoretical waterinrush criterions are presented [1e5]; Xiang Yuanfa proved that natural hydraulic fracturing effect is an important reason for waterinrush of strong water conductive Karst collapse pillar through analysis on water-inrush accidents and simulation experiment [6]; Zhu Wancheng and Yang Tianhong simulated the process of waterinrush from Karst collapse pillar, and discussed the mechanism [7,8]. In this paper, based on the research on water-inrush mechanism of Karst collapse pillar, we built a mechanical model for water-inrush of collapse pillar according to thick plate theory of elastic mechanics, obtaining elastical solution of water-resistant rock strata under the action of water pressure and the expression of critical water pressure of water-inrush, which has some theoretical and practical meaning for us to deeply understand the water-inrush mechanism of Karst collapse pillar and prevent this kind of water-inrush accidents in future. 2. Physical model of a concealed Karst collapse pillar 2.1. Geological model According to statistical material about Karst collapse pillars, most of them appear as cylindrical or elliptic, with a radius of several meters to a few decameters or even more than a hundred meters. The collapse pillar studied in this paper is cylindrical ones

1674-5264/$ e see front matter Copyright Ó 2011, China University of Mining & Technology. All rights reserved. doi:10.1016/j.mstc.2010.12.005

58

T. Junhua et al. / Mining Science and Technology (China) 21 (2011) 57e60

Fig. 3. Mechanical model of clamped supported water-resistant rock strata.

3. Analytical solution of water-inrush from concealed collapse pillars Fig. 1. Collapse pillars in rock strata.

concealed under coal seams, with high water pressure inside. The high water pressure would induce a plastic deformation zone around Karst collapse pillar. At the same time, the mining activities would induce a failure zones at the bottom of coal floor. Therefore, the intact rock stratum between mining failure zone and plastic deformation zone becomes the key rock stratum to resist the waterinrush of concealed collapse pillar, which is called the key waterresistant stratum (Fig. 2). Moreover, in order to entirely analyze this problem, the boundary conditions for water-resistant strata are clamped supported and simply-supported respectively. 2.2. Mechanical model In order to build the mechanical model of water-inrush for concealed water-filling collapse pillars, several assumptions are made based on the geological model mentioned above. 1) The collapse pillars present as cylindrical shape full with water uniformly acting on the water-resistant rock strata. 2) The water-resistant rock strata are continuous, intact, impervious and isotropic rock material. 3) If the combination between water-resistant rock and surrounding rock is intact, then the boundary condition can be approximately considered as clamped supported; otherwise, we can regard the boundary condition as simply-supported. According to the assumptions above, the mechanical model of concealed collapse pillars with water in floor can be considered as circular thick plate under the action of weight and uniform load under the different boundary conditions of clamped supported (Fig. 3) or simply-supported (Fig. 4).

We take an infinitesimal element rdqdr from the axisymmetric circular plate (Fig. 5), and according to the equilibrium condition P F ¼ 0 in Z direction and axis moment equilibrium condition P z Mq ¼ 0, we can obtain the equations satisfied by internal force of water-resisting strata

dðQr rÞ þ Pr ¼ 0 dr Qr ¼

(1)

dMr Mr  Mq þ dr r

(2)

Internal force of water-resisting strata can be deduced through three-dimensional elastic mechanics equations as following:

  b 1þm dbr Mr ¼ D P þm r þ dr r Cn

(3)

  b db 1þm P Mq ¼ D r þ m r þ r dr Cn

(4)

br ¼ 

dw Qr þ dr Cs

(5)

where: Cn ¼ (5/6)(ET/m), Cs ¼ 5Et/12(1 þ m), D ¼ Et3/12(1  m2), P ¼ p  g (h1 þ t þ h2); Mr, Mq, Qr, br, w, p, g, h1, t, h2, E, m represent radial bending moment, circumferential bending moment, shearing force, average angle between normal of plate middle plane and Z axis, deflection water pressure, average bulk density of rock strata, fail zone thickness caused by mining, thickness of intact rock strata, thickness of plastic failure zone in collapse pillar, elastic modulus and Poisson ratio of intact rock strata. Clamped supported boundary condition is

wjr¼a ¼ 0;

dw ¼ 0; j dr r¼0

br jr¼a ¼ 0

Mined out area Failure zone Intact rock strata

t

Plastic deformation zone

p Collapse R

Rock strata Rock strata

Fig. 2. Geological model for concealed collapse pillar.

Fig. 4. Mechanical model of simply-supported water-resistant rock strata.

(6)

T. Junhua et al. / Mining Science and Technology (China) 21 (2011) 57e60

Mq ¼

w ¼

According to Eqs. (1)e(5) and boundary condition Eq. (6), we can obtain the internal force for intact rock strata in clamped supported condition:

Mr ¼

  2  Pa2 r2 8m t ð1 þ mÞ  ð1 þ 3mÞ 2 þ 16 5ð1  mÞ a a

(7)

Mq ¼

  2  Pa2 r2 8m t ð1 þ mÞ  ð1 þ 3mÞ 2 þ 16 5ð1  mÞ a a

(8)

w ¼

Pa 64D

1

2 2

r a2

 2 # 16 r2 t 1 2 þ 5ð1  mÞ a a 

(9)

For the sake of safety, we regard the water pressure number which can make water-resistant strata begin to fail as the critical water pressure, and we assume the yield strength for water-resistant strata is ss, according to strength theory:

ss ¼

6Mmax h2

(10)

We can prove that, when (16m/5(1  m)2)(h/a)2 > 1, the maximum bending moment point is r ¼ 0 thus

ss ¼ pc ¼

½pgðh1 þtþh2 Þa 16

h 2

i 8m  t 2

ð1 þ mÞ þ 5ð1mÞ

a

t 2 =6 3a2

h

8ss t 2 8m ð1 þ mÞ þ 5ð1 mÞ

 t 2 i þ gðh1 þ t þ h2 Þ

(11) (12)

a

When (16m/5(1  m)2)(h/a)2 < 1, the maximum bending moment point is r ¼ a, thus

h

ss ¼ pc ¼

½pgðh1 þtþh2 Þa2 8m  t 2 2  5ð1 mÞ a 16 t 2 =6

3a2

h

8ss

t2

8m 2  5ð1 mÞ

  Pa4 5 þ m 2ð3 þ mÞ r 2 r 4  þ 1 þ m a2 a4 64D 1 þ m  2  16 r2 t  1 þ  a 5 1  m2 a2

pc ¼

8ss t 2 2 3a ð3 þ

mÞ

þ gðh1 þ t þ h2 Þ

Fig. 6 presents the deflection of water-resistant strata with thickness t ¼ 20 m, elastic module E ¼ 10 GPa, Poisson’s ratio m ¼ 0.3, volume weight g ¼ 20,000, as well as water pressure p ¼ 5 MPa and radius R ¼ 25 m, under the condition of water pressure p ¼ 5 MPa in different boundary condition of simplysupported and clamped supported. We can see from the figure that the largest deflection appears in the middle of the water-resistant strata, and gradually decrease to 0 in edge. Moreover, the deflections of water-resistant strata are different in clamped and simply support boundary conditions, with the former larger than the latter. This indicates that the boundary condition plays an important role in influencing water-inrush of collapse pillars. 4.2. Analysis on critical water-inrush pressure influencing factors The Fig. 7 shows that the critical water-inrush water pressure increased with the growth of water-resistant strata thickness, which indicates that the thicker the water-resistant strata are, the harder water-inrush will happen; under different boundary conditions, the critical water-inrush water pressure appears different, with figure for simply-supported smaller than that in clamped supported, which indicates that boundary condition of water-resistant strata is an important factor affecting water-inrush of concealed collapse pillars, and the weaker water-resistant strata boundary is, the easier water-inrush happen; moreover, the relationship between critical

(13) (14)

a

dw ¼ 0; j dr r¼0

Mr jr¼a ¼ 0

(15)

obtaining:

Mr ¼

  Pa2 r2 ð3 þ mÞ 1  2 16 a

(19)

4.1. Deformation characteristic of water-resistant strata

Similarly, for the condition of simply-supported boundary condition

wjr¼a ¼ 0;

ð18Þ

4. Calculation example of concealed collapse pillar water-inrush

i

 t 2 i þ gðh1 þ t þ h2 Þ

(17)

The maximum bending moment point is r ¼ 0. According to strength theory, we obtained the critical water pressure expression is

Fig. 5. Element of circular thick plate.

" 4 

  Pa2 r2 ð3 þ mÞ  ð1 þ 3mÞ 2 16 a

59

(16) Fig. 6. Deflection of water-resistant strata.

60

T. Junhua et al. / Mining Science and Technology (China) 21 (2011) 57e60

Fig. 7. Critical water-inrush pressure under different rock strength and boundary conditions.

water-inrush water pressure and thickness of water-resistant strata behaves non-linear rule, for example, under the above conditions, the critical water pressure for water-resistant strata of tensile strength st ¼ 5 MPa, 10 m thickness with simply-supported boundary condition is about 0.85 MPa, while for that of tensile strength st ¼ 5 MPa, 20 m thickness with simply-supported boundary condition, the critical water pressure is about 3 MPa, which indicates that the critical water pressure for concealed collapse pillars is not only determined by the relatively thickness of water-resistant strata but also related with its absolute thickness. Moreover, we can find that the tensile strength of water-resistant strata can largely affect its capacity to support water pressure through comparation between (a) and (b), under the above condition, the critical water pressure for water-resistant strata of ensile strength st ¼ 5 MPa, 10 m thickness with simply-supported boundary condition is 3.4 MPa, while that for water-resistant strata of ensile strength st ¼ 10 MPa is 6.5 MPa.

water-resistant strata with the same relative thickness, the larger of absolute thickness, the smaller possibility of waterinrush accidents happened. 3) The critical water pressure for concealed collapse pillars is not only determined by the relatively thickness of water-resistant strata but also related with its absolute thickness, for waterresistant strata with the same relatively thickness and other conditions except absolute thickness, the more the absolute thickness is, the less water-inrush will happen.

Acknowledgments Projects are supported by the National Basic Research Program of China (No. 2007CB209400), the National Natural Science Foundation of China (Nos. 50974115, 50904065 and 50974107), and the 111 Project (No. B07028). These supports are greatly acknowledged.

5. Conclusions In this paper, based on thick plate theory of elastic mechanics, we built a mechanical model for water-inrush of collapse pillar, obtaining elastical solution of water-resistant rock strata under the action of water pressure and deriving the expression of critical water pressure for collapse pillar water-inrush, and we obtained the following conclusions 1) The analytical results indicate that: thickness and strength of water-resistant strata are important affecting factors for its bearing capacity. Therefore, in order to reduce water-inrush accidents of collapse pillars, measures should be taken to enlarge the thickness and strength of water-resistant strata and reduce the floor failure induced by mining, such as floor grouting. 2) The critical pressure of water-inrush from a collapse pillar is not only determined by the relative thickness of water-resistant strata but also related to its absolute thickness. For the

References [1] Huang KZ. Theory of plates and shells. Beijing: Tsinghua University Press; 1987 [in Chinese]. [2] Qian MG, Miao XX, Mao XB. Key strata theory with rock strata control. Beijing: China University of Mining and Technology Press; 1994 [in Chinese]. [3] Miao XX, Liu WQ, Chen ZQ. Mined rock mass seepage theory. Beijing: Science Press; 2004 [in Chinese]. [4] Yin SX, Wang SX, Wu Q. Water inrush patterns and theoretic criteria of Karstic collapse columns. Chinese Journal of Rock Mechanics and Engineering 2004;23 (6):964e8 [in Chinese]. [5] Yin SX, Wu Q. Studies on characters and forming mechanism of Karstic collapse columns at mine area of north China. Chinese Journal of Rock Mechanics and Engineering 2004;23(1):120e3 [in Chinese]. [6] Xiang YF. A mechanical model for the water inrush of collapse pillars. Coal Geology & Exploration 1993;21(5):36e9 [in Chinese]. [7] Zhu WC, Wei CH, Zhang FZ, Yang TH. Investigation of water inrush from Karst subsidence column by using a coupled hydromechanical model. Chinese Journal of Underground Space and Engineering 2009;5(5):928e33 [in Chinese]. [8] Yang TH, Chen SK, Zhu WC, Meng ZP, Gao YF. Water inrush mechanism in mines and nonlinear flow model for fractured rocks. Chinese Journal of Rock Mechanics and Engineering 2008;27(7):1411e6 [in Chinese].