Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer

Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer

International Journal of Mining Science and Technology xxx (2018) xxx–xxx Contents lists available at ScienceDirect International Journal of Mining ...

1MB Sizes 0 Downloads 17 Views

International Journal of Mining Science and Technology xxx (2018) xxx–xxx

Contents lists available at ScienceDirect

International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst

Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer Hou Defeng a,⇑, Li Dehai b, Xu Guosheng b, Zhang Yanbin b a b

College of Resources & Safety Engineering, China University of Mining & Technology, Beijing 100083 China Institute of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454000 China

a r t i c l e

i n f o

Article history: Received 22 August 2017 Received in revised form 28 October 2017 Accepted 15 January 2018 Available online xxxx Keywords: Thick loose layer Dynamic groundsubsidence Kelvin visco-elastic rheological model Random medium Single probability integral model Superposition model

a b s t r a c t The dynamic ground subsidence due to underground mining is a complicated time-dependent and ratedependent process. Based on the theory of rock rheology and probability integral method, this study developed the superposition model for the prediction and analysis of the ground dynamic subsidence in mining area of thick loose layer. The model consists of two parts (the prediction of overlying bedrock and the prediction of thick loose layer). The overlying bedrock is regarded as visco-elastic beam, of which the dynamic subsidence is predicted by the Kelvin visco-elastic rheological model. The thick loose layer is regarded as random medium and the ground dynamic subsidence is predicted by the probability integral model. At last, the two prediction models are vertically stacked in the same coordinate system, and the bedrock dynamic subsidence is regarded as a variable mining thickness input into the prediction model of ground dynamic subsidence. The prediction results obtained were compared with actual movement and deformation data from Zhao I and Zhao II mine, central China. The agreement of the prediction results with the field measurements show that the superposition model (SM) is more satisfactory and the formulae obtained are more effective than the classical single probability integral model (SPIM), and thus can be effectively used for predicting the ground dynamic subsidence in mining area of thick loose layer. Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction The mining area of thick loose layer is widely distributed in eastern China, central China and northern China. The main geological characteristics of thick loose mining area, in general, are that the overlying bedrock is generally thin, while the loose layer is thick [1,2]. Both observed and theoretical analysis show that there has been widespread deformation of ground surface far away from the mining area and the surface subsidence is continual and slow with a long duration of movement and deformation due to underground mining of coal seam in mining area of thick loose layer. This phenomenon can cause environmental problems and damage to surface and subsurface structures [3]. In order to protect the environment and structures from these damages, precise ground movement and deformation prediction are essential. The dynamic ground subsidence caused by underground mining is a complex process dominated by time and space [4–8]. The prediction and analysis of ground subsidence due to underground mining have been studied by many scholars in this field and ⇑ Corresponding author.

several valuable results have been obtained, such as the time function method of Knothe, the time function method of XM Cui, the time function method of Sroka-Schober, the time function method of Weibull curve, the time function method of C. Gonzalez-Nicieza and the Coordinate-time function method based on probability integral method [9–12]. However, most prediction methods above, in general, consider the overlying strata as a kind of single medium. Lots of research results have shown that the strength and bearing capacity of overlying bedrock are much larger and stronger than that of loose layer, so the overlying bedrock and loose layer will have different subsidence forms due to underground mining. Therefore it will induce an inaccuracy to use a single prediction model for the surface dynamic subsidence in mining area of thick loose layer. For deep rock mass, especially in the case of water contained, the rock mass will show particularly rheological properties. Therefore the viscoelastic creep properties of rock are gradually concerned by many scholars in this field [13–15]. In the present work, the authors attempt to predict dynamic ground subsidence using a superposition model (SM). Detailed analysis was carried out to predict subsidence caused by underground mining of coal seam in mining area of thick loose layer.

E-mail address: [email protected] (D. Hou). https://doi.org/10.1016/j.ijmst.2018.02.003 2095-2686/Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003

2

D. Hou et al. / International Journal of Mining Science and Technology xxx (2018) xxx–xxx

The validation of the model has been performed by predicting the subsidence profiles for the Zhaogu mine area in China. We have found a more reasonably good match between the observed and predicted dynamic ground movement curves than the classical single probability integral model (SPIM). 2. Viscoelastic dynamic subsidence model of the overlying bedrock With the theory of rheology, the nature of the process of dynamic subsidence due to underground mining can be revealed more effectively in time and space. This paper mainly concerns the application of viscoelasticity to the dynamic subsidence of the overlying bedrock. For example, the average depth of the 11,011 working face in Zhao II mine is 690 m. The thickness of loose layer and overlying bedrock is 616 and 74 m, respectively. The overlying bedrock mainly contains of sandstone and sandy mudstone. The bedrock, subjected to water erosion in varying degrees, generally shows soft rock properties. In order to understand the properties of bedrock accurately, creep tests were carried out on the intact rock samples for sandstone and sandy mudstone from five drill holes of Zhao II mine. Fig. 1 is the experimental results, which shows that the two kinds of rock have creep characteristics obviously. Creep is the time-dependent strain or deformation under constant axial stress. Kelvin visco-elastic creep model is selected to represent the creep behavior based on the creep test results of soft rock mass [16–18]. According to the existing research results, the deformation characteristics of soft rock can be described by the Kelvin model (Fig. 2). In fact, the Kelvin rheological model has been widely used to describe viscoelastic deformation caused by underground mining. In order to predict the overlying bedrock dynamic subsidence due to underground mining, we will use Kelvin model to describe dynamic subsidence of the overlying bedrock due to underground mining by the fully-mechanized caving method [19,20]. 2.1. Basic assumptions (1) Coal seam and overlying strata are horizontal (2) The coal seam and overlying bedrock are all homogeneous medium and consistent with Kelvin rheological model (3) The vertical strain of the coal seam at any point is proportional to the deflection (i.e., subsidence) of the overlying bedrock at that point. 2.2. Dynamic subsidence prediction of the overlying bedrock According to the viscoelastic mechanics theory and engineering practice, the coal seam is considered as a visco-elastic foundation and the overlying bedrock as visco-elastic cylindrical bending plate on the foundation. Thus, the unit width beam (bedrock) can be used to characterise the cylindrical bending plate (bedrock).

Fig. 2. Kelvin rheological model.

Assuming that there is no gap between beam and foundation. According to the assumed conditions, we can choose the semiinfinite mining coordinate system shown in Fig. 3, in which the coordinate origin O1 is located at the intersection of the coal wall extension line and the bedrock upper surface, the axis of S directs the gob, and the subsidence of bedrock is vertical downward. According to engineering practice, the overlying bedrock beam could be regarded as a homogeneous viscoelastic beam [21]. The line passing through the bending beam is called the morphological line of viscoelastic bedrock beam, which can represent the deformation state of the bedrock beam (Fig. 4). From Fig. 4, we know that the external load of the bedrock beam is composed of three parts. (1) The upper surface of the bedrock beam bears the overlying thick loose layer weight Ps and the load is uniformly distributed. (2) The lower surface of the bedrock beam bears the coal seam foundation reaction force u(s, t) and the gangue reaction force w(s, t) in the gob. Based on the existing research results, the deflection (subsidence) equation of bedrock beam can be divided into two parts [22]: (1) When s < 0 or s > L, the foundation of the visco-elastic bedrock beam is unmined coal seam, and thus the dynamic subsidence equation of bedrock beam, could be described as follows:

W j ðs; tÞ ¼ expðktÞ expðps=LÞ½A3 ðtÞ sinðps=LÞ þ A4 ðtÞ cosðps=LÞ; s 2 ð1; 0 [ ½l; þ1Þ

ð1Þ

where Wj(s,t) is the dynamic subsidence of visco-elastic beam at point s at the moment t; L the length of mined-out area of the coal seam, m, and L  2rj = 2Hj/tand0; rj the major influence radius of bedrock, m; Hj the thickness of bedrock, m; and d0 the draw angle of bedrock, °. (2) When 0 < s < l, after mining, the gob (mined-out area) generally is filled with gangue, and thus the dynamic subsidence equation of bedrock beam could be described as follows:

Fig. 1. Creep tests of sandstone and sandy mudstone.

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003

D. Hou et al. / International Journal of Mining Science and Technology xxx (2018) xxx–xxx

3

gob. Assuming that the mined-out area of coal seam is equivalent to the surface subsidence space, and the deformation between the overlying bedrock and thick loose layer is synchronous. Assuming that the working face reaches at the point s at the moment t, according to the existing research results and probability integral method, the subsidence equation of the thick loose layer is as follows:

pffiffiffiffiffiffiffiffiffiffi wðxÞ ¼ wo j n1 n2 Fig. 3. Stress analysis and subsidence model of the overlying bedrock.

Z

1

0

2 1 pðxsÞ e r2 ds r

ð3Þ

where w0 is equivalent mining thickness of coal seam, m, and w0 = mqcosa; q the subsidence factor; j a coefficient (i.e., j = 2 or 3); n1 = K1D1/H0; n3 = K3D3/H0; K1, K3 constants (i.e., K1, K3 = 0.8); n1, n3 a coefficient of mining degree along strike and dip direction, respectively, when n1 > 1, n3 > 1, n1 and n3 = 1; D1 the length of working face advance, m; D3 the dip width of working face, m; and H0 the average mining depth, m. Substituting w0 = mqcosa into Eq. (3) and then putting Eq. (3) integral transformation, we can obtain the surface subsidence equation.

wðxÞ ¼

pffiffiffiffiffiffiffiffiffiffi i mq cos a j n1 n3 h pffiffiffiffi x p þ1 erf r 2

Fig. 4. Viscoelastic beam and external force diagram.

where erf

where b ¼

h

i1=4

Em 4IEb m

p r ¼ p2ffiffipffi

ð4Þ

0

2

eu du (i.e., probability integral function).

4. Superposition of the two theoretical models

W j ðs; tÞ ¼ expðktÞfexpðbsÞ½B1 ðtÞ sinðbsÞ þ B2 ðtÞ cosðbsÞ  mPs =Em g þ W j ðl; tÞ þ mPs =Em

pffiffiffiffi x

R rffiffipx p

ð2Þ

; k = Eb/Fb = Ep/Fp; Em the elastic modulus of

gangue, GPa; Eb the elastic modulus of the bending beam, GPa; I the moment of inertia of cross-section, m4; m the mining thickness, m; Ep the elastic modulus of the visco-elastic foundation (coal seam), GPa; Fb the viscosity coefficient of the bending beam, Pas; and Fp the viscosity coefficient of the visco-elastic foundation (coal seam), Pas. 3. Probability of integral subsidence model of the loose layer The thick loose layer formed in tertiary or quaternary almost has no bearing capacity, and thus could be regarded as random medium, that is to say, the movement of the loose surface can be regarded as a random event. So the probability integral method could be used to predict the movement and deformation of the loose surface [21–25]. Based on this, we can choose the ground movement coordinate system shown in Fig. 5, in which the origin O is located on the surface above the coal wall, the surface subsidence W(x, t) is vertically downward, and the axis X directs the

According to the existing research results, the overlying strata dynamic subsidence in mining area of thick loose layer can be divided into two parts due to the difference in subsidence characteristics between the overlying bedrock and thick loose layer. At the same time, the movement and deformation between the two kinds of medium are synchronous, so the dynamic subsidence of the bedrock can be regard as variable mining thickness input into the dynamic subsidence prediction model of loose layer. According to the principle of superposition, we can choose the theoretical model shown in Fig. 5. The dynamic bedrock subsidence Wj(s,t) can be regarded as the variable mining thickness, which is substituted into Eq. (4) (i.e., m in Eq. (4) is replaced by Wj(s,t)) [3]. After superposition, we can obtain the surface dynamic subsidence equation. 8 pffiffiffiffiffiffiffi ffiffiffiffi X < wj1 ðs;tÞqcos a j n1 n3 ½erf ðpp Þ þ 1;t 2 ½0;þ1Þ;s 2 ð1;0 [ ½l;þ1Þ; r 2 wðx;tÞ ¼ pj ffiffiffiffiffiffiffi pffiffiffiffi wj2 ðs;tÞqcos a n1 n3 : ½erf ð p Xr Þ þ 1;t 2 ½0;þ1Þ;x 2 ½0;l 2 ð5Þ

where r is the major influence radius of ground, m, which should be divided into two parts (i.e., the external major influence radius r1 and the internal major influence radius r2). r1 = Hj/tand0 + Hs/tan /, when x 2 ð1; 0Þ [ ðl; þ1Þ; r2 = H0/tan b, when x 2 ð0; lÞ; d0, / the draw angles of bedrock and loose layer, respectively; tanb the tangent of major influence angle; Hj, Hs the thickness of bedrock and loose layer, respectively; q the subsidence factor; X an arbitrary function depends on x; X = xr2/r1, when x 2 ð1; 0Þ [ ðl; þ1Þ; and X ¼ x, when x 2 ð0; lÞ. The various angle parameters above can be obtained by experience. According to Eq. (5), the dynamic slope, curvature, horizontal displacement, horizontal strain prediction curves of ground can be described by the following equations, respectively.

8 pffiffiffiffiffiffiffi < wj1 ðs;tÞqcos a j n1 n3 expðp X 2 Þ; t 2 ½0; þ1Þ; s 2 ð1; 0 [ ½l;þ1Þ r r2 iðx; tÞ ¼ pffiffiffiffiffiffiffi : wj2 ðs;tÞqcos a j n1 n3 expðp X 2 Þ; t 2 ½0; þ1Þ; s 2 ½0; l 2 r2

Fig. 5. Vertical superposition diagram of the loose layer and bedrock movement.

ð6Þ

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003

4

D. Hou et al. / International Journal of Mining Science and Technology xxx (2018) xxx–xxx

8 pffiffiffiffiffiffiffiffi <  2pwj1 ðs;tÞqcos a j n1 n3 xexpðp X 2 Þ; t 2 ½0; þ1Þ;s 2 ð1; 0 [ ½l;þ1Þ r2 r3 kðx; tÞ ¼ pffiffiffiffiffiffiffiffi 2 2pw ðs;tÞqcos a j n1 n3 : xexpðp Xr2 Þ; t 2 ½0; þ1Þ; s 2 ½0; l  j2 r3 ð7Þ 8 p ffiffiffiffiffiffiffiffiffiffi X2 j > < briðx; tÞ ¼ bwj1 ðs; tÞq cos a n1 n3 expðp r2 Þ; t 2 ½0; þ1Þ; s 2 ð1; 0 [ ½l; þ1Þ uðx; tÞ ¼ > : pffiffiffiffiffiffiffiffiffiffi 2 briðx; tÞ ¼ bwj2 ðs; tÞq cos a j n1 n3 expðp Xr2 Þ; t 2 ½0; þ1Þ; s 2 ½0; l ð8Þ

8 pffiffiffiffiffiffiffiffiffiffi 2 > brkðx; tÞ ¼  2rp2b wj1 ðs; tÞq cos a j n1 n3 x expðp Xr2 Þ; > > > < t 2 ½0; þ1Þ; s 2 ð1; 0 [ ½l; þ1Þ eðx; tÞ ¼ pffiffiffiffiffiffiffiffiffiffi 2 > > brkðx; tÞ ¼  2rp2b wj2 ðs; tÞq cos a j n1 n3 x expðp Xr2 Þ; > > : t 2 ½0; þ1Þ; s 2 ½0; l

ð9Þ

Fig. 6. Maximum subsidence value and predicted curve of surface subsidence.

where i(x,t) is the dynamic ground slope due to underground mining, mm/m; k(x,t) the dynamic ground curvature due to underground mining, 103/m; u(x,t) the dynamic ground horizontal displacement due to underground mining, mm; e(x,t) the dynamic ground horizontal strain due to underground mining, mm/m; and b the horizontal movement constant of ground. 5. Application of the superposition theoretical model to engineering examples In order to demonstrate the application of the superposition theoretical model, some examples on the application of the above theoretical results are presented. The superposition theoretical model is verified with the observed dynamic subsidence data from the Zhaogu mining area, which is located in the central part of China. The strata are horizontal in the mining area and the lithology of overlying bedrock is mainly sandstone and sandy mudstone. The mining area consists of two working faces using fullymechanized caving method. The 11,011 is the first working face of Zhaogu I mine, as well as the 11,011 working face of Zhaogu II mine. All of their geology is thin bedrock and thick loose layer, and the roof and floor of the coal seam have different thickness aquifers. According to the geological conditions in the mine, the roof (overlying bedrock) is considered as a visco-elastic plate. In the two-dimensional case, the overlying bedrock is considered as a visco-elastic beam. According to the existing research results and the analysis results of the geology data in the mining area, the two working faces belong to the ‘‘critical mining” in Zhaogu mining area because the mining width and length exceed the double thickness of the overlying bedrock. Based on the field data in the Zhaogu mining area, the modelling parameters are given in Table 1. All other engineering parameters are directly taken from geomechanics test results. In order to accurately understand the influence degree of underground mining on ground movement and deformation, Zhaogu II mine arranged two observation stations along the direction of strike and dip on the ground over the 11,011 working face, which began caving on November 7, 2010 and end on February 18, 2012. The observation dates are from November 28, 2010 to May 2014, a total of 52 measurements, in which the observation data are selected from November 28, 2010 to September 8, 2012. Fig. 6 shows the maximum subsidence value and predicted curve

Fig. 7. Predicted curves of surface subsidence and the subsidence velocity at each stage.

Fig. 8. Predicted curves of surface horizontal displacement at each stage.

Fig. 9. Predicted curves of surface curvature at each stage.

Table 1 Values of engineering parameters. Working face

D1 (m)

D3 (m)

M (m)

H0 (m)

Hj (m)

Β (°)

U0 (°)

Eb (GPa)

gb (GPa s)

b

q

11,011 (Zhao I) 11,011 (Zhao II)

1400 2267

180 180

3.5 3.5

570 690

49 74

76 70

42 42

2.1 2.1

2.62 2.62

0.36 0.33

0.68 0.48

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003

5

D. Hou et al. / International Journal of Mining Science and Technology xxx (2018) xxx–xxx Table 2 Maximum movement and deformation comparison between predicted values and measured values of surface. Comparison project

wmax (mm)

i (mm/m)

k (103/m)

l (mm)

e (mm/m)

Measured Predicted Inaccuracy Inaccuracy rate

2377 2389 12 0.005

4.47 4.19 0.28 0.063

+0.11 +0.09 0.02 0.182

401 376 25 0.062

+9.87 +8.08 1.79 0.181

of surface subsidence. From Fig. 6 we can draw the following conclutions: (1) The engineering actual situation is consistant with the prediction results of the SM. (2) The results of this investigation show that the SM is more apt to propagate movements due to underground mining, and better able to fit observed data than the SPIM. (3) The SM can effectively avoid the shortcomings that the curve predicted by the classical single probability integral model (SPIM) converges too fast at the ground subsidence basin boundary. The curves of surface subsidence and subsidence velocity (Fig. 7), horizontal displacement (Fig. 8), and curvature (Fig. 9) are predicted for the working face after excaving 40, 80, 120, 160, 200 d, respectively. When the face reached at the point E, compared with the SPIM, the curves of surface subsidence and horizontal displacement predicted by the SM are more consistent with the measured data. There are also two observation stations arranged along the direction of strike and dip on the ground over the 11,011 working face of Zhao I mine. The observation dates are from October 12, 2008 to October 30, 2009, a total of 16 measurements. The theoretical prediction results of the SM are compared with the measured data (Table 2). From Table 2, we can know that the engineering actual situation is consistent with the theoretical prediction results of the SM. 6. Conclusions (1) According to the actual situation, the overlying bedrock and loose layer are regarded as two different mediums, of which the subsidence should be predicted by different prediction models in mining area of thick loose layer. The predicted results of the superposition model accord with practical engineering situation. The agreement of the theoretical results with the field measurements shows that the superposition model is satisfactory and the formulae obtained are valid, and thus can be effectively used for predicting the ground movement and deformation due to underground mining. (2) The superposition model to predict the ground dynamic subsidence avoids the defect that the classical single probability integration model converges rapidly at the boundary of surface subsidence basin and improves the prediction accuracy of the ground dynamic subsidence. From the comparision between the measured data and the theoretical curves, the proposed superposition model to forecast the ground movement and deformation is in line with the actual situation of thick loose layer engineering. (3) The superposition model fully takes into account the different lithologic properties of overlying strata, and thus this theoretical prediction model is more realistic. The predicted results show that the superposition model is better than the classical single probability integral model.

(4) The author only studies the ground dynamic movement and deformation in the mining area of thick loose layer, and the overlying bedrock should have the soft rock creep characteristics. For other mining geological conditions, it remains to be further studied.

Acknowledgments Financial support for this work, is provided by the National Natural Science Foundation of China Youth Found of China (No.41102169), the doctoral foundation of Henan Polytechnic University of China (No. B2014-056), both of which are gratefully acknowledged. We also would like to express our acknowledgements to the anonymous reviewers and editor lilyduan who provided valuable help that improved an earlier version of the manuscript. References [1] Liu YX, Dai HY, Jiang YD, Zhang YF, Peng Z. Study on surface movement law of coal mining under thick loose layer. Coal Sci Technol 2013;41(05):117–20. [2] Hou DF, Li DH, Xu GS, Zhang YB. Impact of mining thickness on dynamic subsidence characteristics in condition of mining under thick unconsolidated layers. Coal Sci Technol 2016;44(12):191–6. [3] Yu HZ, Li DH, Li JM. A modified model of probability integral method for mining under thick loose layer. J Jiaozuo Inst Technol (Nat Sci Ed) 2004;23 (04):255–7. [4] Feng YX, Hu QF, Deng XB, Li LC. Study on dynamic surface subsidence prediction system for multi working face. Coal Mine Saf 2013;05:72–5. [5] Guo WB, Huang CF, Chen JJ. Dynamic surface movement characteristics of fully mechanized top coal caving under thick and wet loose layer. J China Coal Soc 2010;35(S1):38–43. [6] Huang YT, Wang JZ. Study on deformation law and calculation method of surface dynamic subsidence. J China Univ Min Technol (Soc Sci) 2008;10 (02):211–5. [7] Liu YC, Cao SG, Liu YB. Time function model of the dynamic process of surface subsidence. Rock Soil Mech 2010;31(03):925–31. [8] Zhang G, Wu Y, Wang L, Zhang K, Daemen Jaak JK, Wei L. Time-dependent subsidence prediction model and influence factor analysis for underground gas storages in bedded salt formations. Eng Geol 2015;187:156–69. [9] Chang ZQ, Wang JZ. Study on time function of surface subsidence—the improved Knothe time function. Chin J Rock Mech Eng 2003;22(9):1496–9. [10] Cui XM, Miao XX, Zhao YL. Discussion on the time function of time dependent surface movement. J China Coal Soc 1999;24(5):453–6. [11] Peng XZ, Cui XM, Zang YQ, Zhang Y, Yuan DB. Time function and prediction of progressive surface movements and deformations. J Univ Sci Technol Beijing 2004;26(4):341–4. [12] Zhu GY, Shen HX, Wang LG. Prediction function of surface dynamic deformation. Chin J Rock Mech Eng 2011;30(09):1889–95. [13] Zhu SP, Zhou CL. Visco-elastic mechanical analysis of surrounding rock stability of underground circular tunnel. J Tongji Univ 1994;22(03):329–33. [14] He M. Latest progress of soft rock mechanics and engineering in China. J Rock Mech Geotech Eng 2014;6(3):165–79. [15] Jang H, Topal E. A review of soft computing technology applications in several mining problems. Appl Soft Comput 2014;22:638–51. [16] Li WX, Guo YG, Hou XB. A visco-elastic model for analysis of ground subsidence due to underground mining by pillarless sublevel caving method. Eng Mech 2009;26(7):227–31. [17] Liu B. Introduction of mining rock mechanics. Changsha: Hunan Science & Technology Press; 1982. p. 9. [18] Hebei university. Experimental study on the mechanical properties of soft rock of deep mine; 2009. p. 221. [19] Zhang WX. Xin method in visco-elastic mechanics. Dalian: Dalian University of Technology; 2007.

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003

6

D. Hou et al. / International Journal of Mining Science and Technology xxx (2018) xxx–xxx

[20] Carranza-Torres C, Fairhurst C. The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion. Int J Rock Mech Min Sci 1999;36(6):777–809. [21] Zeng Z, Kou X. Application of viscoelasticity to study the time-dependent surface subsidence caused by underground mining. Eng Geol 1992;32 (4):279–84. [22] Li WX, Gao CY, Yin X, Li JF, Qi DL, Ren JC. A visco-elastic theoretical model for analysis of dynamic ground subsidence due to deep underground mining. Appl Math Model 2015;39(18):5495–506.

[23] Donnelly LJ, La De, Cruz H, Asmar I, Zapata O, Perez JD. The monitoring and prediction of mining subsidence in the Amaga, Angelopolis, Venecia and Bolombolo Regions, Antioquia, Colombia. Eng Geol 2001;59(12):103–14. [24] Li W, Li J, Wang Q, Xia Y, Ji ZH. SMT-GP method of prediction for ground subsidence due to tunneling in mountainous areas. Tunn Undergr Space Technol 2012;32:198–211. [25] Wu K, Ge JX, Wang LD. Mining subsidence is expected to integration method. Xu Zhou: China Mining University Press; 1998.

Please cite this article in press as: Hou D et al. Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer. Int J Min Sci Technol (2018), https://doi.org/10.1016/j.ijmst.2018.02.003