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

Mining Science and Technology (China) 21 (2011)57. 60Contents lists available at ScienceDirectMining Science and Technology (China)ELSEVIERjournal homepage: www.elsevier.com/locate/mstcTheoretical analysis on water- inrush mechanism of concealed collapsepillars in floorTang Junhua a*, Bai Haibo', Yao Banghua a,b, Wu Yua"State Key Laboratory of Geomechanics and Deep Underground Engineering China University of Mining 6 Technologoy. Xuzhou 221008 Chinab School of Mechanics 8 Cvil Engineeng China University of Mining & Technology, Xuzhou 21116, ChinaARTICLE INFOABSTRACTArticle history:In order to study the water inrush mechanism of concealed collapse pllars from the mechanical view,Received 24 May 2010a mechanical model for water-inrush of collapse pillars has been established based on thick plate theoryAccepted 2 July 2010of elastic mechanics in this paper. By solving this model the deformation of water-resistant rock strataunder the action of water pressure and the expression of critical water pressure for collapse pillar water-Keywords:inrush have been obtained The research results indicate that: the boundary conditions and strength ofColiapse pillarwater-resistant strata play important roles in influencing water-inrush of collapse pillars. The criticalWaterinrushwater-inrush pressure is determined by both relative thickness and absolute thickness of water-resistantCritical water pressurestrata.Thick plate theoryCopyright 0 2011, China University of Mining & Technology. All rights reserved.1. Introductiondone many useful works. For instance, Yin shangxian and Wu qiangestablished 'thick wall cylinder's mechanical model' to study theAs a special vertical structure in rock strata, Karst collapse pillarsbasic condition of water-inrush from Karst collaspse pillar, as well asV common, distributing in more than 20coal fields of Shanxisummarizing the water-innrush modes in which theoretical water-Platus, Taihang mountain, Luliang mountain as well as Shandong,inrush criterions are presented |1- -5]; Xiang Yuanfa proved thatHenan, jiangsu and Shanxi province in North China. Among thenatural hydraulic fracturing effect is an important reason for water-hypothesis in the formation of Karst collapse pillars, one represen-tative explanation is carbonatite rock is gradually erased due toanalysis on water-inrush accidents and simulation experiment [6];moving groundwater, and formed Karst cave. some of them becameZhu Wancheng and Yang Tianhong simulated the process of water-larger and larger,. and then cllapsed due to the long period efctof inrush from Karst cllapse pllar, and discussed the mechanism|7.8].geological structural stress and gravity of overtying rock strata, asIn this paper, based on the research on water inrush mechanism ofwell as leading to the collapse of overlying rock strata. According toKarst collapse pillar, we built a mechanical model for water-nrush ofconductivity, Karst collapse pillars can be classifed into two types,collapse pillar according to thick plate theory of elastic mechanics,water conducted and water non-conductive (Fig. 1 ). According toobtaining elastical solution of water-resistant rock strata under thestatistical data of discovered Karst collapsoioiovererdarsrcouapsepllas aJouelars, about 90% of themaction ofvressure and the expressionotfcriticalwater pessurein North China are water non-conductive ones. Nevertheless, theof water inrush, which has some theoretical and practical meaningamount of conductive ones is also very large. In addition to seriousfor us to deeply understand the water-inush mechanism of Karstdestructive effect to rock strata, the high water pressure in water-collapse pillar and prevent this kind of water- inrush accidents inconducted Karst collapse pillar often leads to many water-inrushfuture.accidents, causing huge economical loss and serious casualties.Therefore, water-conducted Karst collapse pillars become hidden2. Physical model of a concealed Karst collapse pillartroubles which threaten and infuence the safety mining in manymining areas in China. In order to explore the water-inrush mecha-2.1. Geological modelnism ofwater-conducted Karst collapse pllar, many researchers haveAccording to statistical material about Karst collapse pillars,most of them appear as cylindrical or elliptic, with a radius of. Corresponding author. Tel: +86 355 5975512.severa中国煤化工-en more than a hundredE-mail address: tjhlJt@163.com (I Junhua).meter:paper is ylindrical ones1674-5264/5 - see front matter Copyright。2011. China University of Mining & Technology. AllYHCNMHGdol:10.1016/j.mstc 2010.12.00558T. Junhua et al / Mining Science and Technology (China) 21 (2011)57-60Coal seamSot rock TutetR一resistpoi key sf海aF网00.zFig 3. Mechanical model of damped supported wateresisant rock stata.roistantke sta3. Analytical solution of water inrush from concealedcollapse pillarsFig 1. Cllapse pllars in rok strata.We take an infinitesimal element rd0dr from the axisymmetriccircular plate (Fig. 5), and according to the equilibrium conditionEFz= 0 in z direction and axis moment equilibrium conditionconcealed under coal seams, with high water pressure inside. TheEMg = 0, we can obtain the equations satisfied by internal force ofhigh water pressure would induce a plastic deformation zonewaterresisting strataaround Karst collapse pllar. At the same time, the mining activitieswould induce a failure zones at the bottom of coal floor. Therefore,dlqr2+Pr=0(1the intact rock stratum between mining failure zone and plasticdeformation zone becomes the key rock stratum to resist the water-inrush of concealed collapse pillar, which is called the key water-dMr.1Mr-M，(2resistant stratum (Fig. 2). Moreover, in order tanalyze thisproblem,he boundary conditions for water-resistant strata areInternal force of water-resisting strata can be deduced throughclamped supported and simply-supported respectively.three-dimensional elastic mechanics equations as following:22. Mechanical modelM=(出+++20)(3In order to build the mechanical model of water inrush forconcealed waterfilling collapse pillars, several assumptions aremade based on the geological model mentioned above.(4)M=0(件→出+考别)1) The cllapse pllars present as cylindrical shape full with waterdwuniformly acting on the water-resistant rock strata.β=-∞→≌(52) The water-resistant rock strata are continuous, intact, imper-3) If the combination between water-resistant rock andvious and isotropic rock material.where:Cn= (5/6)ETIu), G;= 5Et/12(1 +4).D= E?/12(1-μ2).P=p-γsurrounding rock is intact, then the boundary condition can be(h1 + t+ h2); Mn Mg. Qr Bn w,p. r, h, t, 12. E, u represent radialapproximately considered as clamped supported; otherwise,bending moment, circumferential bending moment, shearing force,we can regard the boundary condition as simply-supported.average angle between normal of !: middle plane and Z axis,deflection water pressure, average bulk density of rock strata, failAccording to the assumptions above, the mechanical model ofzone thickness caused by mining, thickness of intact rock strata,concealed collapse pllars with water in floor can be considered asthickness of plastic failure zone in collapse pillar, elastic moduluscircular thick plate under the action of weight and uniform loadand Poisson ratio of intact rock strata.under the different boundary conditions of clamped supportedClamped supported boundary condition is(Fig, 3) or simply-supported (Fig. 4).WIr=a = 0;drr=0=0; BrlI=o=0(6)Mined Out areaFailure zoneinact rock statpa {Rock strata中国煤化工YHCNMHGFlg 2 Ceologial model for concaled clpse pla.aFg 4 Mechanical model of simply-supported waterresistant rock strata.T Junhua et aL / Mining Science and Technology (China) 21 (2011) 57-605Q_Ma/M=话(3+u)-(1+3司(17)zm/L |m/IMPa4 j[5+μ_ 2(3+μ) r2LRw=64D{年-102+aQ+(dQr +dr)ydr6(18)+5gH2(1-制)(}The maximum bending moment pointisr= 0.Fig 5. Element of circular thick plate.According to strength theory, we obtained the critical waterpressure expression isAccording to Eqs. (1)-(5) and boundary condition Eq. (6). wecan obtain the internal force for intact rock strata in clampedPc= 3023+m+ r(h+t+h2)8ost2(19)supported condition:M,="(7)4. Calculation example of concealed collapse pillar16 [(1+月-(1+ 3u蒙+ so=u()]water-inrush3μ4.1. Deformation characteristic of water-resistant strataMo='(1+)-(1+3)32 + 501-两司) ](8)Fig. 6 presents the deflection of water-resistant strata withthickness t = 20 m, elastic module E = 10 GPa, Poisson's ratioμ = 0.3, volume weight丫= 20,000, as well as water pressurew=p= 5 MPa and radius R = 25 m, under the condition of waterFor the sake of safety, we regard the water pressure numberpressure p= 5 MPa in different boundary condition of simply-supported and clamped supported. We can see from the figure thatwhich can make water-resistant strata begin to fail as the criticalthe largest deflection appears in the middle of the water-resistantwater pressure, and we assume the yield strength for water-resis-strata, and gradually decrease to 0 in edge. Moreover, the deflec-tant strata is 0s, according to strength theory:tions of water-resistant strata are different in clamped and simplysupport boundary conditions, with the former larger than the ltter.6Mmax(10) This indicates that the boundary condition plays an important roleh2in influencing water-inrush of collapse pillars.We can prove that, when(16u/5(1- μ)F)(h/a)} > 1, the maximumbending moment point isr= Othus4.2. Analysis on critical water inrush pressure infuencing factors-1心n结加把[(1+4)+ -1(83]The Fig. 7 shows that the critical water-inrush water pressure(11) increased with the growth of water-resistant strata thickness, which(2/6indicates that the thicker the water-resistant strata are, the harder8oσst2water-inrush will happen; under dfferent boundary conditions, thePc=-+ r(h +t+h2)(12)critical water-inrush water pressure appears different, with figure3a2(1+月)+ s02=(]for simply-supported smaller than that in clamped supported,which indicates that boundary condition of water-resistant strata isWhen( 16μ/5(1 - μ12(h/(a}2 < 1, the maximum bending momentan important factor affecting water-inrush of concealed collapseresisttrata bpillarsI boundary is, the easierpoint isr= a, thuspllars and the weakerwawater-inrush happen; moreover, the relationship between critical0s =t2/6(13)8orst2+r(h;+t+h2)(14)Smply spported30212 - 5iE0]、Chmpod spportedSimiarly, for the condition of simply-supported boundarycondition001W|=a= 0;dr'r=O=0; MrI=a=0obtaining:中国煤化工-M-管8+0(一国)(16)MHCNMHGmtm60Fig 6. Delection of water-resistant strata60I Jumhua et al 1 Mining Sclence and Technoloav (China)21 (2011)57-60 .a 8pChapetrepportedmped spprtedSmply spporSimply rpone051Watrwetat ttethchee()eWer.oufunt tat thhesz(mTensile strength=SMPaTensile strength=lOMpaFig 7. Critical waterinrush pressure under diferent rock strength and boundary conditions.water-resistant strata with the same relative thickness, thebehaves non-linear rule, for example, under the above conditions,larger of absolute thickness, the smaller possbility of water-the critical water pressure for water-resistant strata of tensileinrush accidents happened.strength σε = 5 MPa. 10 m thickness with simply-supported3) The critical water pressure for concealed collapse pillars is notboundary condition is about 0.85 MPa, while for that of tensileonly determined by the relatively thickness of water-resistantstrength Ot = 5 MPa, 20 m thickness with simply-supportedstrata but also related with its absolute thickness, for water-boundary condition, the critical water pressure is about 3 MPa,resistant strata with the same relatively thickness and otherwhich indicates that the critical water pressure for concealedconditions except absolute thickness, the more the absolutecolladeteed by the relatively thickness ofthickness is, the less water-inrush will happen.。 Pllarsls notonlyterminedwater-resistant strata but also related with its absolute thickness.strata can largely affect its capacity to support water pressure Acknowledgmentsthrough comparation between (a) and (b). under the above condi-tion, the critical water pressure for water-resistant strata of ensileProjects are supported by the National Basic Researchstrength σt = 5 MPa, 10 m thickness with simply supported Program of China (No. 2007CB209400). the National Naturalboundary conditin is 3.4 MPa. while that for water-resistant strata Science Foundation of China (Nos. 50974115, 50904065 andof ensile strength σt = 10 MPa is 6.5 MPa.50974107). and the 111 Project (No. B07028). These supports aregreatly acknowledged.5. ConclusionsIn this paper, based on thick plate theory of elastic mechanics, Referenceswe built a mechanical model for water-inrush of collapse pillar,obtaining elastical solution of water-resistant rock strata under the(1] Huang Kz Theory of plates and shlls. Bejing: Tsinghua University Pres: 1987action of water pressure and deriving the expression of critical [21| Qian MG Miao xx,. Mao XB. Key strara theory with rock srata control. Being:water pressure for collapse pillar water-inrush, and we obtainedChina University of Mining and Technology Press; 1994 lin Chinese].[3] Mia0 xx Liu wo, Chen zQ Mined rock mass seepage theory. Beiing Sciencethe fllowing conclusions{4| Yin sx. Wang sx Wu Q Water inush patterns and theoretic criteria of Karstic1) The analytical results indicate that: thickness and strength ofcollapse columns. Chinese Journal of Rock Mechanics and Engineering 2004:23(6):964-8 lin Chinesel.water-resistant strata are important affecting factors for its|5] Yin sx. Wu Q Studies on characters and forming mechanism of Karstic cllapsebearing capacity. Therefore, in order to reduce water-inrushcolumns 北mine asrea of poth China. Chinese Jourmal of Rock Mechanics andhould be takacidentset Collapse pillars, measures should be[6] Xiang VF. A mechanical model for the water inush of cllapse pllars. Coalenlarge the thickness and strength of water-resistant strata andreduce the floor failure induced by mining, such as floor [71 Zhu WC WelcH. Zhang FL Vang TH. Iestsgton 0 water nrush from Karstgroutingsubsidence column by using a coupled hydromechanical model. Chinese Jour-2) The crtical pressure of water inrush from a collapse pillar is81 VangTH.ChenSK zhuwC MengzrCeovF Waterusmhmechaniscntpminesnot only determined by the relative thickness of water-resis-and nonlinear fiow model for fractured rocks, Chinese jourmal of Rocktant strata but also related to its absolute thickness. For theMechanics and Engineering 2008;27(7):1411-6 [in Chunesel.中国煤化工MYHCNMHG