linkageanalysisbetweensolid-fluidcouplingandthestrength...

Research ArticleLinkage Analysis between Solid-Fluid Coupling and the StrengthReduction Method for Karst Cave Water Inrush in Mines

Yanlin Zhao Jian Liao Qiang Liu Yang Li and Jianchao Cheng

Hunan Provincial Key Laboratory of Safe Mining Techniques of Coal MinesWork Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal MinesHunan University of Science and Technology Xiangtan Hunan China

Correspondence should be addressed to Yanlin Zhao yanlin_8163com

Received 15 January 2020 Accepted 3 February 2020 Published 4 June 2020

Academic Editor Longjun Dong

Copyright copy 2020 Yanlin Zhao et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e present paper aims to study the mechanical mechanism and characteristics of water irruption from Karst cave Combining thenonlinear seepage-pipe coupling model with the strength reduction method the linkage analysis of fluid solid coupling andstrength reduction method are constructed to study the whole process of confined Karst cave water inrush Taking the waterinrush accident of Shibaijing of the Qiyi mine in south China as an example the instability mechanism of the water-proof rockpillar and evolution of water inrush are discussed It is suggested that water discharge on the working face augments with theincrease in the reduction factor of the water-proof rock pillar before the rock pillar loses its stability Once the rock pillar becomesunstable Karst water bursts from confined Karst cave in a pipe flow shape and the water irruption quantity reaches the peak valuein a short time by adopting the pipe flow to simulate and then decreases slowly e hydraulic rough flow at the initial stagechanges into pipe laminar flow finally in the process of Karst water inrush due to the constraint of Karst cave water reserve econception for the safety factor of the water-proof rock pillar introduced the relation of the safety factor Karst cave waterpressure and thickness of the water-proof rock pillar are studied It is proposed that thickness of the water-proof rock pillar whosesafety factor equals 15 is regarded as the calculating safety thickness of the water-proof rock pillar and the safety thickness of thewater-proof rock pillar setting in mining engineering should be equal to the sum of the blasthole depth blasting disturbancedepth and the calculating safety thickness e reason leading to Karst water inrush of Qiyi Mine is that without advancedboreholes the water-proof rock pillar is set so small that it could not possess safety margin so the confined Karst cave water breaksthe water-proof rock pillar and bursts out Combining the solid fluid coupling theory pipe flow theory and strength reductionmethod the nonlinear mechanical response of confined Karst cave water inrush is studied which provides a new studymethod forthe whole process of confined Karst cave water inrush

1 Introduction

China owns many types of coal-bearing basins and has largeamounts of coal resources e stress and hydrogeologicalconditions are extremely complex during deep mining andespecially one of the main challenges associated to deepmining is the increased water pressure e coal productionreached 3700 million tons in 2012 Water inrush into coalmines is regarded as a serious detriment to mining safety InChina there have been thousands of casualties in ground-water-related coal mine accidents since 2000 Among un-derground engineering accidents including water rush

[1ndash4] gas explosion [5] rock burst [6ndash8] and time-de-pendent large deformation [8ndash10] the groundwater inrushin coal mines is second only to gas explosion in causingcatastrophic accidents according to government statistics(State Administration of Coal Mine Safety 2008) Miningdepths and mining intensity have increased causing theencountered hydrogeological conditions to become morecomplicated Water inrush threatens mine safety and coalmine productivity [11 12] Geological settings and hydro-geological conditions of the coalfields in China are verycomplicated e coalfields in north China are typicalpermian-Carboniferous coalfields Many coal seams lie

HindawiShock and VibrationVolume 2020 Article ID 5415812 14 pageshttpsdoiorg10115520205415812

above the Ordovician limestone which is a highly permeableconfined aquifer Because of the potential impacts of theconfined water in the Ordovician limestone on the miningactivities the coal seams accounting for 37 of the totalreserve are listed as prospective reserves in north China[11 12]

e coalfields in south China locally occurred in latepermian Figure 1 shows the representative stratigraphiccolumn of the region [13] e main minable coal layer liesin the late permian Longtan Formation e overall coalproducts of this region account for a small part of the na-tional total coal production Hydrogeologically south Chinais in humid region and dominated by modern Karst terrainsCoal excavation from late permian Longtan formation isseriously threatened by lower Maokou Karst aquifer andupper Changxing Karst aquifer All the times the key issuein south China is to prevent late permian Karst waterbursting

e Karst groundwater is mainly of the dissolved-caverntype and Karst-fissure type and usually forms the compli-cated systems of Karst fissures dissolved cavern pipes andKarst caves in south district [14] e distribution andstructure of underground water system are obviously ofinhomogeneity and this brings the anisotropism that theunderground hydrodynamic force is connected Althoughthe Ordovician limestone in north and the Maokou lime-stone in south are both aquifers there exist great differencesbetween them In north its Karst underground is mainly ofthe Karst-fissure water-bearing type Its hydraulic slope israther soft belonging to unified confined water-loggedstrata and once the water is exposed serious water inrushaccidents happen giving rise to the decline of water level ofaquifer [15] As for the southern area particularly in theSongzao Mine Area in Chongqing city Doulishan MineArea in Hunan province and the north area of Guizhouprovince water filling Karst caves generally exist in theMaokou limestone moreover the horizontal hydraulic re-lation among Karst caves is weak and relative independencewhich cannot form unified aquifer system [16ndash19] Withregard to the Maokou limestone of the basement in southerncoalfield its inhomogeneity of karst development in spacedistribution is found When Karst is least developedMaokou limestone strata can be seen as a relative imper-meable layer So Maokou limestone strata can be fullyutilized by adopting a scientific method At present de-velopment roadways are arranged in Maokou limestonestrata in many southern coalfields such as Xingwujing mineof Nantong Company in Guizhou province Shipingyi mineof South Sichuan Coal Industry Meitanba mine in HunanProvince Huayingshan mine of Chongqing city and so on[14 18 19] While the Karst cave development area is themajor hidden trouble for mine water inrush Karst cavewater inrush is seen as one of the coal mine flood accidentsin south China which generated to a large amount ofeconomic loss such as the ldquo4middot16rdquo accident happened in theQiyi mine of Hunan Province in 2003 (17 people died)ldquo928rdquo Karst cave water inrush accident happened in theXinmao mine of Hunan Province in 2010 and ldquo1212rdquo Karstcave water bursting in the Tianchi mine of Guizhou Province

in 2004 (21 deaths and 15 missing) which were typical Karstcave water inrush accidents in late Permian Maokoulimestone

e rock strata between the working face and Karst caveact as a geological barrier that prevents Karst cave waterfrom invading into the roadways e effectiveness of thegeological barrier depends on its thickness lithology andintegrity [20 21] Water inrushes are likely to occur whenthe geological barrier is too thin to withhold the pressure ofKarst cave water In a Karst mine the main technique forcontrolling water inrush is to leave a sufficient thickness ofthe water-proof rock pillar While the calculating methodabout safety thickness of rock pillar setting for confinedKarst cave is not given in regulations of mine water controlof China [22] a study on stability of the water-proof rockpillar and its safety thickness is of great significance forcontrolling Karst water inrush in a mine In order to do so itis of vital importance to study strata failure characteristicsand hydraulic conductivity changes due to mining andthereafter find a way to predict and prevent water inrushes

Perm

ian

Long

tan

Mao

kou

Chan

gxin

gYu

long

shan

Tria

ssic

U

L

Figure 1 e representative stratigraphic column of the coalfieldsin south China

2 Shock and Vibration

Various research studies have been conducted in this area[23ndash26] however the mechanism of water inrushes is stillnot well-understood In this paper linkage analysis betweensolid-fluid coupling and the strength reduction methodbased on flow state conversion theory is adopted to discussthe stability of the water-proof rock pillar Meanwhile theconcept of safety factor of the water-proof rock pillar in-troduced and the safety thickness of the water- proof rockpillar setting in mining engineering is proposed

2 Solid-FluidCouplingMechanismofConfinedKarst Water Inrush

When a confined Karst cave is concealed before a roadwaydisturbance stress evokes the sharp change of stress field andseepage field of surrounding rocks ere would be strongcoupling effect in the surrounding rock mass between theKarst cave and working face is kind of coupling effect isshown as follows (1) the action of a high hydraulic gradient(high seepage stress) on the surrounding rocks results in thechange of stress field (2) also due to mining-induced fis-sures in the surrounding rocks under high hydraulic pres-sure and disturbance stress field the hydraulic conductivityof the surrounding rocks augments greatly e schematicdiagram for a water-proof rock pillar is shown in Figure 2From the angle of rock mass fluid mechanics under dis-turbance stress and high hydraulic pressure confined Karstcave water inrush can be considered as a catastrophic in-stability of the water-proof rock pillar between the Karst caveand working face accompanying with Karst cave waterinrush

21 Elastic-Plastic Analysis for a Water-Proof Rock Pillar of aConfined Karst Cave Constitutive relation of elastic-plasticmechanics for rock mass under coupling effect of stress fieldand seepage field can be denoted as

σijj + Fi +(αp)j 0 (1)

where (αp)j is equivalent volumetric stress acting on thewater-proof rock pillar which reflects the coupling effect ofseepage field on stress field

Yield criterion is the MohrndashCoulomb Criterion and theshear failure criterion is represented as

fs

σ1 minus σ31 + sinϕ1 minus sinϕ

+ 2c

1 + sinϕ1 minus sinϕ

1113971

0 (2)

e tensile failure criterion is that

ft

σt minus σ3 0 (3)

where σ1 is the first effective principal stress σ3 is the thirdeffective principal stress ϕ is the internal friction angle of therock mass c is the cohesion and σt is the tensile strength

22 Nonlinear Seepage-Pipe Flow Coupling Based on FlowState Conversion 3eory e essence of Karst cave waterinrush is the instability of the water-proof rock pillar Whenthe rock pillar is unstable the flow discharge of working face

is in the form of seepage and small-scale water flow Oncethe water-proof rock pillar becomes unstable the water inthe confined Karst cave bursts in the form of pipe flow

221 Water-Proof Rock Pillar Instability When the elastic-plastic calculation for the water-proof rock pillar is con-vergence the water inflow form is hydraulic seepage and thedifferential control equation for seepage analysis of thesurrounding rocks is represented as

zp

zt minus us

z

zxi

k(Θ p)zp

zxj

1113888 1113889 (4)

where p is the seepage pressure k(Θ p) is the hydraulicconductivity and us is the storage coefficient

e influence of seepage pressure and stress field on thehydraulic conductivity can be presented as [27 28]

k(Θ p) ξ k0eminus (Θ3minus βp)

(5)

where k0 is the initial value of the hydraulic conductivityk(Θ p) is the hydraulic conductivity by means of couplinganalysis Θ σ1 + σ2 + σ3 is the volumetric stress ξ is thesudden jump coefficient of the hydraulic conductivity and βis the coefficient

In coupling analysis for elastic units the hydraulicconductivity is looked as the negative exponential functionof the volumetric stress In equation (5) ξ is 10 and β is 05

For plastic yielding units the hydraulic conductivityenhances greatly e sudden jump coefficient of the hy-draulic conductivity enhances obviously In equation (5) ξ is1000 and β is 10

Equation (5) reflects the coupling effect of rock massstress field on seepage field Particularly the strong couplingeffect of plastic units on seepage field is reflected

222 Water-Proof Rock Pillar Instability When the elastic-plastic calculation has no convergence the water-proof rockpillar is unstable and Karst cave water bursts out to theroadway the governing law for water inrush was studied byusing the pipe flow model

Nonlinear pipe flow is a complex problem educed fromthe DarcyndashWeisbach equation

Face Rockpillar

Strong fluid-solidcoupling effcct region

Karstcave

region

Figure 2 e schematic diagram for a water-proof rock pillar

Shock and Vibration 3

ΔH fl

d

u2

2g (6)

where ΔH is the head loss f is the friction factor of headloss l is the length of the pipe d is the inside diameter of thepipe u is the mean flow velocity in the pipe and g is theacceleration due to gravity

e Reynolds number Re in the process of water inrushis represented as

Re ρvd

μ (7)

where ρ is the density of water v is water velocity in the waterinrush channel and μ is the dynamic viscosity of water

Based on Nikuradsersquos experimental curves whenRegt 100000 f is related to relative roughness of the pipewall but it is independent of Re under this situation headloss ΔH has direct ratio relations with u2 namely ldquothehydraulic rough regionrdquo and the following equation can beattained by using the Von Karman equation

f 1

[174 + 2lg(2Δd)]2 (8)

where Δ is the roughness of the roadwayWhen Relt 2300 the friction factor of head loss can be

obtained by the Hagenndashpoiseuille equation

f 64Re

(9)

In this case ΔH has a direct ratio relation with u be-longing to ldquothe laminar regionrdquo

When 2300leRele 100000 the friction factor of head losscan be obtained by the Blasius equation

f 0326Re025 (10)

In this case ΔH has a direct ratio relation with u175belonging to ldquothe hydraulic smooth regionrdquo

During the process of Karst water inrush flow velocity isfast at the initial water inrush the diameter of water-burstchannel is big and the Reynolds number Re is much morethan 100000 in the process of initial water inrush So theinitial water inrush belongs to the hydraulic rough regionWith the development of water inrush the Karst cave waterpressure drops off due to the limit of aquifers reserve in theKarst cave and flow velocity in the roadway will becomeslower the water flow in the roadway will transform fromldquothe hydraulic rough regionrdquo into ldquothe hydraulic smoothregionrdquo or even ldquothe laminar regionrdquo

With regard to a noncircular roadway the equivalentdiameter of the roadway is used which can be denoted as

d 4S

U (11)

where S is water-carrying section areas and U is the wettedperimeter

If T the porosity of pipe flow n 1 then V u

equation (6) can be expressed as follows [25 26]

V 2g d

fVJ

8gS

fVUJ (12)

Comparing equation (12) with the Darcy law theequivalent hydraulic conductivity of pipe flow is defined asfollows

KL 8gS

fVU (13)

When the pipe flow is in the turbulent state the flow lawof pipe flow can be expressed to the nonlinear Darcyrsquos lawby substituting the equivalent hydraulic conductivity KLfork(Θ p) in equation (4)

If water flow is in the laminar state the equivalenthydraulic conductivity KL transforms into the true hydraulicconductivity KL1 by submitting equations (9) into (13)

KL1 d2ρg

32μ

S2ρg

2U2μ (14)

e conception of equivalent hydraulic conductivity KL

is introduced to equation(4) and laminar region and tur-bulent region in the roadway are expressed with a unifiedlaw

zp

zt minus us

z

zxi

kzp

zxj

1113888 1113889 (15)

where the hydraulic conductivity of water-proof rock pillarinstability is k ξk0e

minus (Θ3minus βp) while for an unstable water-proof rock pillar equivalent hydraulic conductivity KL

which is considered to the hydraulic conductivity k inequation (15) is adopted to describe pipe flow in theroadway

23 Solid-Fluid Coupling ProgramDesigning e solid-fluidcoupling analysis for confined Karst water inrush in a mineis conducted by the indirect coupling method Firstly theelastic-plastic stress field is calculated when time is ti thenthe hydraulic conductivity of surrounding rocks is obtainedby using equations (5)ndash(14) which is delivered to seepagefield calculation module and then the coupling of stress fieldto seepage field is implemented Secondly the seepagevolumetric stress obtained in seepage field acts on elastic-plastic stress calculation units and then the coupling ofseepage field to stress field can be implemented e cal-culation does not stop until reaching desired calculationtime

If the calculation has no convergence Karst cave waterinrush occurs and forms pipe flow and the equivalenthydraulic conductivity KL of pipe flow is gained by FISH inFLAC3D based on equations (13) and (14)

Based on the thought of program development givenabove combining nonlinear seepage flow and pipe flow thesolid-fluid coupling analysis program is successfully con-ducted in FLAC3Dis program is composed of three partsan elastic-plastic stress calculation module seepage calcu-lation module and coupling analysis module e programflow chart is shown in Figure 2


e indirect coupling analysis method developed byFLAC3D of which merits are the fact that the couplingparameters (for example the hydraulic conductivity andseepage volumetric stress) evolve with the time steps thecoupling message of every subcoupling system (subseepagesystem and elastic-plastic stress system) can be deliveredaccurately with time steps

As for pipe flow the corresponding equation is selectedto calculate equivalent hydraulic conductivity KL based onthe Reynolds number Re From the analysis mentionedabove pipe flow of water inrush is not only considered tohave great ldquopermeabilityrdquo but also its equivalent hydraulicconductivity varies with the Reynolds number Re and it isnot a constant However node flow rates are unknownnumbers in the first time step thus the solving has to becarried out by an iterative method Owing to the fact thatinitial Karst cave water inrush belongs to the turbulent roughregion KL is assumed to be the equivalent hydraulic con-ductivity of the hydraulic rough region rough the giveninitial velocity of fluid flow Vin roughness Δ of water inrushchannel (roadway) water-carrying section areas S andwetted perimeter U of the roadway the equivalent hydraulicconductivity KL is firstly gained Water pressure p and flowvelocity Vof calculating elements are obtained by FLAC3Den the Reynolds number Re dependent of velocityVobtained by FLAC3D is used to judge the laminar region orturbulent region e friction factor of head loss f is cal-culated based on Reynolds number Re en the equivalenthydraulic conductivity KL for the next step is determined byusing equation (13) By the method given above theequivalent hydraulic conductivity KL evolves with the cal-culation time step as shown in Figure 3

24 Linkage Analysis Between Solid-Fluid Coupling and theStrength Reduction Method e basic principle of thestrength reduction method is that shear parametersc and tanφ are divided by reduction factor Fi and a newgroup of value cprimeφprime is obtained which is served as newcalculation parameters [29 30]

cprime c

Fi

(16)

φprime arctan (tanφF)i (17)

In the strength reduction method for stability of a water-proof rock pillar the shear parameters candtanφ of the rockpillar do not reduce continuously until critical state

Combing the solid-fluid coupling model and strengthreduction method the linkage analysis model between solid-fluid coupling and strength reduction method for confinedKarst cave water inrush was established e process ofrealization is illustrated in Figure 4

It is noted that although the instability of water-proofrock pillar is also related with the time-dependent failuretensile failure and crack coalescence process of water-proofrock pillar [31ndash34] in this study the plastic coalescencefailure of the water-proof rock pillar is considered based onthe strength reduction method

3 Case Analysis

31 Water Inrush Accident An example of the accident ofconfined Karst cave water inrush in the Qiyi mine in HunanProvince was studied in this paper Karst cave water inrushhappened on the heading face in the Qiyi mine with minus 160mlevel which was a typical example of water bursting fromconfined Karst cave e hydrological condition of the mineis very complex Maokou limestone strata which is a con-fined aquifer under lies in coalseam 2 Karst caves inMaokoulimestone strata always exist in the shape of moniliformstructures whose volumes are in state of half filling or fullfilling However water flow in Maokou limestone strata isless and the Maokou limestone is a hard substance whereKarst structures are less developed e heading face withminus 160m level is in No23 mining area located in Maokoulimestone strata On 16th April 2003 at 8 amsim19 pm Karstcave water poured into the heading face On 16th April at8 am the water-proof rock pillar between the working faceand confined Karst cave could not withstand the waterpressure in the Karst cave and so the water-proof rock pillarwas broken at the length A loud sound that was heard whenthe water inrush occurred indicated a sudden fracturing ofthe rock pillar and a sudden releasing of deep groundwaterpressure with abundant of water burst from Karst cave all ofsudden e inflow occurred at an estimated rate of3670m3h at the very beginning After about 2 hours waterraised as much as 25m and flooded about 2 km of theroadway e water flow was turbid along with small piecesof limestone rock flour and Karst breccias In an accident17 people died About 22 500m3 water in total burst outwithin nearly 11 h A Karst cave with volume about

Assuming velocity of fluid flow Vin in verylarge value in the 1st time step

Based on roughness ∆ of water inrush channelwater-carrying section areas S wetted perimeter U ofroadway and velocity of fluid flow Vin the equivalent

hydraulic conductivity KL is first gained

Water pressure P and flow velocity V of every elementnode are obtained by FLAC3D

Reynolds number Re is calculated

Re gt 100000 Re lt 23002300 lt Re lt 100000

KL = 8gSfV KL = 8gSfV KL = S2ρg2U2micro

Figure 3 e equivalent hydraulic conductivity KL evolved withcalculation time step


Using MohrndashColumb modelpoundnotgradullyincrease reduction factor Fipoundnotreduce

cohesion c and friction angle φ

Currenct reduction factor Fi is the safetyfactor Fs of water-proof rock pillar

Begin

Stress fieldcalculation module

Trace addresses ofcurrent yield units

Call MohrndashColumb model

Calculation moduleof seepage field

Calculate hydraulic conductivity k(t)of present time step

Call seepage calculation module of FLAC3D

Call program segment of seepage force

Coupling analysismodulus

Calculate seepage force F(t) of every unit

Whether seepageis stable or not

No Yes

Output seepage pressure p(t) of nodes

Fluid-solidcouplingsystem

Strengthreductionmethodsystem

Whether calculationis convergence or

not

Yes No

Trace reynolds number Re of calculation seepage units

Call seepage calculation model of FLAC3D

Calculate equivalent hydraulic conductivity KL

Obtain water-inrush laws based on pipe flow

Pipe flowanalysis for

rock pillar inunstability

Over

ti = tindash1 + ∆t

Figure 4 Flow diagram of linkage analysis between solid-fluid coupling and the strength reduction method based on flow state conversiontheory


20mtimes 6mtimes 20m was exposed about 3sim4m before workingface after slag clearing e geological survey indicated thatthere were some major fractures and well-developed Karstcaves around the roadway where water inrush took place thedeep confined Karst cave system exists in Maokou limestonestrata in synclinal shaft of Doulishan coal mine area eburied depth of roadway excavation is 450m more or lesse hydrostatic pressure head is about 400m the waterpressure in the confined Karst cave in Maokou limestonestrata is about 40MPa

Figure 5 illustrates the picture of water discharge of theroadway 8 h after water inrush By means of spot investi-gation after slag clearing it was found that the Karst cave wasstrongly dissolved whose walls were smooth as shown inFigure 6 the Karst water was supplied by Karst pipelinesand the Karst cave was filled with a large amount of waterand yellow mud Figure 7 is the vertical plane projection ofKarst cave development

Maokou limestone specimens were sampled from thewater inrush Karst cave It was discovered that abundantKarst fissure and pores exist in the limestone near theconfined Karst cave As the surrounding rocks near the Karstcave were deeply dissolved its integrity and continuity werepoor with high porosity and developed fissures while themechanical properties of Maokou limestone far away fromKarst cave are good

Laboratory tests were performed on rock samplesextracted from surrounding rocks near the Karst cave etests included the compressive strength and permeability ofMaokou limestone Combining the laboratory test resultsfield investigation and Hoek and Diederichsrsquos researchadvances in deformation modulus of rock mass Hoek-Brown strength theory was applied to obtain the mechanicalparameters of rock mass by using Roclab software [35ndash37]e rock mass calculation parameters of the Maokoulimestone were obtained as shown in Table 1

32 Calculation Model e numerical model is establishedbased on the in situ condition at the Qiyi coal mine in thesouth China As shown in Figure 8 the simulation domain is50m long 20mwide and 30m deep in which an excavationroadway in a semicircular arched shape is situated in themiddle of the model and confined Karst cave on the rightedge of the model has a closely simplified ellipsoidal shape

e left and right boundaries in this model are allowed tomove along the vertical direction but are restrained in thehorizontal direction e bottom of the model is fixedσ1 125MPa is applied on the upper surface of model tosimulate crustal stress

e boundary condition of seepage field is as followsKarst cave hydraulic pressure is assumed to 1MPa 2MPa3MPa 4MPa and 5MPa respectively and the hydraulicpressure of the heading face is 01MPa No 1sim5 marked inFigure 5 simulates the driving by step Footage by every stepin the numerical simulation is 5m When the water-proofrock pillar between the working face and Karst cave is lessthan 10m for the purpose of studying the stability of thewater-proof rock pillar with different thicknesses footage byevery step is 1m in numerical simulation

As for an unstable water-proof rock pillar water inrushfrom the Karst cave takes place Considering that the supplyof Karst water is not inexhaustible it is assumed that thehydraulic pressure in the Karst cave attenuates dynamicallyin the course of water inrush and the hydraulic pressure canbe denoted as

p p01 minus

t

T1113874 1113875 (18)

where p0 is the initial cave hydraulic pressure T is the wholeduration of Karst water inrush (it is assumed that T 10 h inthis simulation) and t is the different water inrush time

Figure 5 e picture of water discharge of the roadway in 8 h afterwater inrush

Figure 6 e scene photographs of the inside of the Karst cave

Figure 7 Vertical plane projection of Karst cave development


e roughness Δ of water inrush channel is assumed to01m [26]Water-carrying section areas Sof the roadway is106m2 and the wetted perimeter U is 104m Suppose thatthe initial velocity of fluid flow Vin is 01ms which is a largevalue It indicates that water flows in a hydraulic roughregion at the very beginning Using linkage analysis betweensolid-fluid coupling and the strength reduction method thepaper analyzes the stability of the water-proof rock pillarTaking the hydraulic pressure p 4MPa and the thicknessh 8m of rock pillar as an example the seepage propertiesof rock pillar and the evolution from stability to instability ofthe rock pillar are studied when the reduction factorgradually increases

4 Results

41 Water-Proof Rock Pillar Instability With gradually in-crease of the reduction factor the strength parameters of thewater-proof rock pillar gradually decrease e hydraulicconductivity which is dependent of volumetric stress hy-draulic pressure and plastic zones increases significantlyunder the action of disturbance stress and high hydraulicpressure

e strength parameters of the water-proof rock pillarare c 136MPa and tanφ 052 when Fi 110 Under the

strength the plastic region of rock pillar is less the hydraulicconductivity of the rock pillar is influenced mostly byvolumetric stress and seepage pressure e region which isnearly 15m away from the working face is the enhancedhydraulic conductivity zone which is about325 times 10minus 10 sim 1521 times 10minus 10mse hydraulic conductivityfor an undisturbed region in the middle of the rock pillar isabout 070 times 10minus 10 sim 179 times 10minus 10ms e region near theKarst cave is also an enhanced hydraulic conductivity zonewhere the hydraulic conductivity is nearly279 times 10minus 10 sim 568 times 10minus 10ms e hydraulic conductivitydistribution map when reduction factor Fi 110 is shown inFigure 9

WhenFi 154 the strength parameters of the rockpillar are c 097MPa tanφ 039 Under the strengthabout 85 of units in the water-proof rock pillar are in theplastic state and the hydraulic conductivity of rock pillarincreases at the speed of magnitude in comparison withwhen Fi 154 and it fluctuates between147 times 10minus 6 sim 280 times 10minus 6ms e hydraulic conductivitydistribution map when the reduction factor Fi 154 isshown in Figure 10

When the reduction factor Fi 110 the seepage fielddistribution is calculated as shown in Figure 11 e seepagefield of the surrounding rocks was disturbed because of

Table 1 e rock mass calculation parameters of the Maokou limestone

Density(Kgm3)

Waterabsorption

Saturatedcoefficient

Softeningcoefficient

Uniaxialcompression

(MPa)

Tensilestrength(MPa)

Youngmodulus(GPa)

Poissonratio Porosity Cohesion

(MPa)

Internalfrictionangle

(deg)

Hydraulicconductivity10minus 10 m middot sminus 1

262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1

Figure 8 Numerical calculation model


excavation e seepage field adjusts continuously for thepurpose of eliminating the high potential water pressure inthe Karst cave As Karst cave water discharges to the workingface seepage pressure progressively decreases from the Karstcave to working face e mean seepage pressure gradient ofthe water-proof rock pillar is 05MPam which brings thehorizontal volumetric stress with the direction from Karstcave to working face which is a driving force of instability ofthe water-proof rock pillar

Based on linkage analysis on solid-fluid coupling and thestrength reduction method water discharges on the workingface are achieved in the different reduction factors byFLAC3D Figure 12 illustrates that water discharge on theworking face evolves from a low flow rate to a massive flowrate with the increase of the reduction factor WhenFi 110 sim 153 the flow rate of the working face fluctuatesfrom 205times10minus 5ms (when Fi 11) to 747times10minus 3ms (whenFi 153) is implies that when the reduction factorFi 110 sim 153 the water-proof rock pillar is stable andwater discharge on the working face is more seepage thanwater inrush While the reduction factor Fi 154 sim 158water discharge on the working face increases abruptly andfluctuates from 0025m3s (when Fi 154) to 0027m3s(when Fi 158) due to nonlinear extension of the plastic

zone of rock pillar Under the action of disturbance stressand high seepage volumetric stress the displacement of theworking face is about 15 cm by coupling calculation whenthe reduction factor Fi 154 which is shown in Figure 13

42Water-Proof Rock Pillar Instability e evolution of thepercentage of plastic units in the water-proof rock pillar withthe reduction factor is visualized in Figure 14 e plasticunits in the water-proof rock pillar nonlinearly increase withthe increment of reduction factor When Fi ge 154 thepercentage of plastic units in the rock pillar mutates epercentage of plastic units in the rock pillar is about 85sim87 when Fi 154 sim 158 When Fi 159 the whole rockpillar is in the plastic state the calculation has no conver-gence rock pillar is in the instability stage and water inrushfrom the confined Karst cave in a pipe flow form happens Itindicates that when the Karst cave internal pressure p

4MPa and water-proof rock pillar thickness h 8m thesafety factor of the water-proof rock pillar is 159

Karst cave water inbursts into the roadway in a pipe flowform when the water-proof rock pillar is in the instabilitystage Water irruption quantity increases rapidly in theinitial phase of water inrush ereafter with the passage of

Hydraulicconductivity

22E ndash 0920E ndash 0918E ndash 0916E ndash 0914E ndash 0912E ndash 0910E ndash 0980E ndash 1060E ndash 1040E ndash 1020E ndash 10

unit ms

Figure 9 e hydraulic conductivity distribution map when thrreduction factor Fi 110


280E ndash 06265E ndash 06250E ndash 06235E ndash 06220E ndash 06205E ndash 06190E ndash 06175E ndash 06160E ndash 06

unit (ms)

Figure 10 e hydraulic conductivity distribution map when thereduction factor Fi 154

110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025

0030Massive water flow

not water inrush

Q (m

3 s)

Seepage

Fi

Figure 12 Water discharge of the working face evolves with theincrease of reduction factor

Waterpressure(MPa)

3835322926232171411080502

Water-proofrock pillar

Figure 11 Distribution of seepage field of the surrounding rockswhen the reduction factor Fi 110


time the water irruption quantity attenuates unceasinglydue to decrease of the supply of Karst water In the calcu-lation program the evolution law of flow rate in the roadwayduring the process of water inrush is gained by pipe flowanalysis illustrated in Figure 15 Water irruption quantityreaches the peak (Qmax 127m3s) in short time(t 264 h) ereafter water irruption quantity decreasesrapidly e results of numerical simulation agree well withpractical flow law of confined Karst cave water inrush[38ndash40]

e evolution law of water pressure on roadwaytransverse sections where is 3m 8m 13m and 18m awayfrom the karst cave is visualized in Figure 16 With theincrease in water inrush time the water pressure in theroadway quickly increases and then attenuates after reachingthe peak Owing to hydraulic losses in the roadway the waterpressure in the roadway becomes smaller and smaller whenthe distance from the Karst cave is longer and longer

e water pressure distribution in the roadway is ob-tained by pipe analysis as shown in Figure 17 Due to theinstability of the water-proof rock pillar Karst water poursinto the roadway with an dramatic increase in the waterpressure in the roadway With the development of waterinrush time hydraulic gradient in the roadway declinescontinuously for example when t 353 h the mean hy-draulic gradient in the roadway is 56 much as that when

t 944 h Owing to the hydraulic gradient decaying rapidlywith the passage of time resulting in the slowing down ofwater flow in the roadway the hydraulic rough flow at theinitial water inrush process changes into pipe laminar lowfinally

43 Safety Factor of the Water-Proof Rock Pillar By thelinkage analysis of solid-fluid coupling theory and thestrength reduction method adopted the safety factor of thewater-proof rock pillar is gained when karst cave hydraulicpressure p in the Karst cave and calculation thickness h of thewater-proof rock pillar are different In Figure 14 when theKarst cave hydraulic pressures are 1MPa 2MPa 3MPa4MPa and 5MPa respectively and the calculation thick-ness of the rock pillar is 3m 4m 5m 6m 7m 8m 9m and10m separately and the relationship curves of safety factorFS and karst cave hydraulic pressure p and calculationthickness h of the rock pillar are achieved

P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36

3m from 8m from Karst cave

13m from Karst cave18m from Karst cave

Figure 16 e evolution law of water pressure on roadwaytransverse sections which are 3m 8m 13m and 18m away fromkarst cave

unit (cm)

Drivingdirection Karst

cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0

Figure 13 Horizontal displacement of the water-proof rock pillarwhen the reduction factor Fi 154

110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()

Calculation in no convergence

Figure 14 e evolution of the percentage of plastic units in thewater-proof rock pillar with reduction factor

Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)

Figure 15 e evolution law of water discharge in the roadwayduring the process of water inrush


Figure 18 displays that the safety factor FS increasesgradually with the increase of calculation safety thickness hof the rock pillar which is fitted by the exponential function

FS a + b exp(ch) (19)

where FS is the safety factor of the water-proof rock pillar his the calculation safety thickness of the water-proof rockpillar and a b and c are undetermined coefficients

e relation between safety factor FS of the water-proofrock pillar and calculation safety thickness h of the water-proof rock pillar under different Karst cave water pressures pis obtained by using equation (19) which is demonstrated inTable 2 If FS 15 is considered as the yardstick of stability ofthe water-proof rock pillar some yardsticks are educed

When FSge 15 the water-proof rock pillar is stableWhen FSlt 15 the water-proof rock pillar is unstableConclusions can be drawn from Table 2 that the cal-

culation safety thickness of the water-proof rock pillarshould be thickened with the increment of Karst hydraulicpressure such as when the Karst cave hydraulic pressures are1MPa and 5MPa respectively and the calculation safetythickness of the water-proof rock pillar is 518m and 932mrespectively e calculation safety thickness of the water-proof rock pillar is 414m more when the hydraulic pressurep 5MPa than when the hydraulic pressure p 1MPa isis because with the increase of Karst hydraulic pressure theseepage volumetric stress in the water-proof rock pillarincreases which directly leads to the enhancement of lateralthrust along the direction of the working face and thecalculation thickness should be thickened

44 Safety 3ickness of Water-Proof Rock Pillar SettingDrilling and blasting is mostly applied in mines in southernChina and the coupling analysis model is used without

considering the disturbance of blasting to the surroundingrocks before the working face Based on the experimentalresearch and numerical analysis results [41ndash43] the dis-turbance depth of ordinary blasting smooth blasting andpresplitting blasting to the surrounding rocks is about 15mmeanwhile disturbance depth increases with the incrementof a single segment explosive dosage So safety thickness ofwater-proof rock pillar setting in mining engineering is thesum of the blasthole depth h1 blasting disturbance depth h2and safety caculation thickness h3 of the water-proof rockpillar which can be denoted as follows

Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)

Figure 17 e water pressure distributions in the roadway by pipe analysis analysis in different times (a) t 014 h (b) t 353 h (c)t 944 h

9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs

5MPa Fs = 0171exp(023h) + 00434MPa Fs = 0025exp(041h) + 0843MPa Fs = 0069exp(035h) + 0732MPa Fs = 0261exp(026h) + 0341MPa Fs = 0428exp(023h) + 009

Figure 18 Variation relation curves between safe factor andcalculation safety thickness of the water-proof rock pillar


H h1 + h2 + h3 (20)

where H is the safety thickness of water-proof rock pillarsetting in mining engineering h1 is the blasthole depth h2 isthe blasting disturbance depth and h3 is the calculationsafety thickness h of water-proof rock pillar based onequation (19)

e schematic diagram of safety thickness of water-proofrock pillar setting of a confined Karst cave before a roadwayis visualized in Figure 19 e calculation safety thickness h3of the rock pillar is gained by the way proposed in this paperTable 3 illustrates safety thickness of water-proof rock pillarsetting for confined the Karst cave in the Qiyi mine based onequation (20) Based on Table 3 when hydraulic pressures ofthe Karst cave are from 10MPa to 50MPa the safetythickness of water-proof rock pillar setting is from 92m to134m According to regulations of mine water controlwhen the hydraulic pressure is less than 10MPa the ad-vanced horizontal distance of the pilot hole for detectingwater should not be less than 10m and the length of waterstop casing is more than 5m for a rock roadway with the

increase of hydraulic pressure the advanced horizontaldistance and the length of water stop casing must increasecorrespondingly when the hydraulic pressure is more than30MPa the advanced horizontal distance is more than 25mand the length of water stop casing is more than 20m Baseon the research results of this paper if regulations of minewater control are strictly executed especially regulationsabout exploring water and drilling advanced distance andthe length of water stop casing the chance for occurrence ofwater inrush would be extremely small because the advanceddistance of pilot hole for detecting water and the length ofwater stop casing regulated in regulations of mine watercontrol are more than the safety thickness of the water-proofrock pillar setting proposed in this paper In a Karst coalmine when hydrogeology condition is complicated or evenextremely complicated the rule of exploring before miningshould be obeyed

Water inrush accident induced by confined waterbreaking rock pillar happened on the heading face withminus 160m level of the Qiyi mine e investigation suggestedthat the Karst cave with a volume of 20mtimes 6 mtimes 20m was

Table 2 e relation between safety factor FS and thickness h of the water-proof rock pillar under different karst cave water pressures

Karst cave waterpressure (MPa)

e relation between safety factor FS and thickness ofwater-proof rock pillar h

e calculation safety thickness of water-proof rockpillar when safety factor FS 15 (m)

1 Fs 0428 exp(023 h) + 009 5182 Fs 0261 exp(026 h) + 034 5733 Fs 0069 exp(035 h) + 073 6894 Fs 0025 exp(041 h) + 084 7985 Fs 0171 exp(023 h) + 0043 932

Workingface

Karst cavesregion

h1 h2 h3

Figure 19 Schematic diagram of safety thickness of water-proof rock pillar setting in mining engineering

Table 3 Safety thickness of water-proof rock pillar setting in the Maokou limestone for the Qiyi coal mine

Kars waterpressure (MPa)

Blasthole depthh1 (m)

Blasting disturbancedepth h2 (m)

Calculation safety thickness ofrock pillar h3 (m)

Safety thickness of water-proof rockpillar setting (Hm)

10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332


some 3sim4m away from the face at is to say the water-proof rock pillar between the Karst cave and working facewas about 3sim4m Even worse as the surface water connectedwell with the Karst cave water the hydraulic pressure in theKarst cave was about 35sim40MPa Based on Table 3 thesafety thickness of water-proof rock pillar setting should be11sim12m e water-proof rock pillar with a thickness of3sim4m did not have the ability of preventing water inrushlet alone safety margins

5 Conclusions

(1) e linkage analysis of solid-fluid coupling and thestrength reduction method to study the Karst cavewater inrush is proposed e interaction of dis-turbance stress and high seepage volumetric stress tothe water-proof rock pillar gives rise to instability ofthe water-proof rock pillar Accompanying withmechanical instability of water-proof rock Karstcave water inrush is deemed a conversion process ofthe ldquoseepage to pipe flowrdquo

(2) Equivalent hydraulic conductivity of pipe flow forconfined Karst cave water inrush is introduced and anonlinear seepage-pipe coupling model of confinedKarst cave water inrush is established Combiningthe nonlinear seepage-pipe coupling model with thestrength reduction method the linkage analysis offluid solid coupling and the strength reductionmethod is constructed to study the whole process ofwater inrush

(3) Taking the water inrush accident of Shibaijing of theQiyi mine as an example it is proposed that thethickness of the water-proof rock pillar whose safetyfactor equals 15 is regarded as the calculating safetythickness of the water-proof rock pillar and safetythickness of water-proof rock pillar setting in miningengineering is equal to the sum of the blastholedepth blasting disturbance depth and the calcu-lating safety thickness of the water-proof rock pillar

(4) e reason leading to Karst water inrush of the Qiyimine is that due to the absence of advanced bore-holes the water-proof rock pillar is set so small that itcannot possess a safety margin and the confinedKarst cave water breaks the water-proof rock pillarand bursts out

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (nos 51774131 and 51274097) and theCRSRI Open Research Program (CKWV2017508KY)

References

[1] Q Wu andMWang ldquoCharacterization of water bursting anddischarge into underground mines with multilayeredgroundwater flow systems in the North China coal basinrdquoHydrogeology Journal vol 14 no 6 pp 882ndash893 2006

[2] Q Wu M Wang and X Wu ldquoInvestigations of groundwaterbursting into coal mine seam floors from fault zonesrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 4 pp 557ndash571 2004

[3] B Yu W Zhu and J Xu ldquoNumerical simulation of surfacesubsidence characteristics during deep miningrdquo Journal ofMining and Safety Engineering vol 24 no 4 pp 422ndash4262007

[4] Y Zhao L Zhang W Wang J Tang H Lin and W WanldquoTransient pulse test andmorphological analysis of single rockfracturesrdquo International Journal of Rock Mechanics andMining Sciences vol 91 pp 139ndash154 2017

[5] Y X Wang S Y Wang Y L Zhao P P Guo Y Liu andP Cao ldquoBlast Induced Crack Propagation and Damage Ac-cumulation in Rock Mass Containing Initial Damagerdquo Shockand Vibration vol 2018 pp 1ndash18 2018

[6] L Dong D Sun X Li J Ma L Zhang and X Tong ldquoIntervalnon-probabilistic reliability of surrounding jointed rockmassconsidering microseismic loads in mining tunnelsrdquo Tunnel-ling and Underground Space Technology vol 81 pp 326ndash3352018

[7] L J Dong W Zou D Y Sun and X J Tong ldquoSome De-velopments and New Insights for MicroseismicAcousticEmission Source Localizationrdquo Shock and Vibrationvol 2019 pp 1ndash15 2019

[8] Y Zhao Y WangWWangWWan and J Tang ldquoModelingof non-linear rheological behavior of hard rock using triaxialrheological experimentrdquo International Journal of Rock Me-chanics and Mining Sciences vol 93 pp 66ndash75 2017

[9] Y L Zhao L Y Zhang W J Wang W Wan and W H MaldquoSeparation of elastoviscoplastic strains of rock and a non-linear creep modelrdquo International Journal of Geomechanicsvol 18 no 1 2018

[10] K Peng J Zhou Q Zou and X Song ldquoEffect of loadingfrequency on the deformation behaviours of sandstonessubjected to cyclic loads and its underlying mechanismrdquoInternational Journal of Fatigue vol 131 Article ID 1053492020

[11] J Zhang and B Shen ldquoCoal mining under aquifers in China acase studyrdquo International Journal of Rock Mechanics andMining Sciences vol 41 no 4 pp 629ndash639 2004

[12] Y L Gong and F Z Wan ldquoImpact of karst water on coalmining in North Chinardquo Environmental Geology vol 49pp 449ndash457 2006

[13] C S Wang H B Bai and S C Liu ldquoMine water issues inChinardquo in Proceedings of the IMWA 2010 Symposium Sydneyvol 445ndash448 Mine Water and Innovative inking NovaScotia Canada 2010

[14] H Keqiang Y Jia F Wang and Y Lu ldquoOverview of karstgeo-environments and karst water resources in north andsouth Chinardquo Environmental Earth Sciences vol 64 no 7pp 1865ndash1873 2011

[15] X X Miao A Wang Y J Sun et al ldquoResearch on theory ofmining with water resources protection and its application toarid and semi-arid mining regionrdquo Chinese Journal of RockMechanics and Engineering vol 28 no 2 pp 217ndash227 2009

[16] K Q He R L Wang and W F Jiang ldquoGroundwater inrushchannel detection and curtain grouting of the Gaoyang iron


ore mine Chinardquo Mine Water and the Environment vol 31no 4 pp 297ndash306 2012

[17] W J Wang Y L Zhao Q F Li et al ldquoDisaster mechanism ofkarst water bursting in minerdquo Journal of China Coal Societyvol 35 no 3 pp 443ndash448 2010

[18] G JWang ldquoe discussion of karst water dam age preventionin Huayingshan mine areardquo Journal of North China Instituteof Science and Technology vol 6 no 4 pp 96ndash100 2009

[19] S H Zhou ldquoMaokou limestone karstic water flooding andharnessing in Songzao coalmine chongqingrdquo Coal Geology ofChina vol 17 no 5 pp 65ndash77 2005

[20] Y L Zhao J Z Tang Y Chen L Y Zhang W J Wang andJ P Liao ldquoHydromechanical coupling tests for mechanicaland permeability characteristics of fractured limestone incomplete stressndashstrain processrdquo Environmental Earth Sci-ences vol 76 no 1 pp 1ndash18 2017

[21] C LWang L Pan Y Zhao Y Zhang andW Shen ldquoAnalysisof the pressure pulse propagation in rock a new approach tosimultaneously determine permeability porosity and ad-sorption capacityrdquo Rock Mechanics and Rock Engineeringvol 52 no 11 pp 4301ndash4317 2019

[22] Ministry of Coal Industry Regulations for Mine Water Pre-vention and Control Coal Industry Publication Press BeijingChina 2009

[23] H Q Zhang Y N He C A Tang B Ahmad and L J HanldquoApplication of an improved flow-stress-damage model to thecriticality assessment of water Inrush in a mine a case studyrdquoRock Mechanics and Rock Engineering vol 42 no 6pp 911ndash930 2009

[24] Y Wang Q Chen and Y Y Wei ldquoApplication of infraredacquisition technology to prediction of water inrush inYuanliangshan tunnelrdquo Chinese Journal of Rock Mechanicsand Engineering vol 22 no 5 pp 855ndash857 2003

[25] C X Chen ldquoGroundwater flowmodel and simulationmethodin triple media of karst tube-fissure-porerdquo Earth Sciencesvol 20 no 4 pp 361ndash366 1995

[26] S H Liu and S C Yu ldquoEffect of turbulent boundary layer to asmall step change in wall roughnessrdquo Journal of Hydrody-namics vol 13 no 1 pp 35ndash40 1998

[27] Y L Zhao Y Wang and L Tang ldquoe compressivendashshearfracture strength of rock containing water based on Dru-kerndashPrager failure criterionrdquo Arabian Journal of Geosciencesvol 12 p 452 2019

[28] Y Zhao P He Y Zhang and C Wang ldquoA new criterion for atoughness-dominated hydraulic fracture crossing a naturalfrictional interfacerdquo Rock Mechanics and Rock Engineeringvol 52 no 8 pp 2617ndash2629 2019

[29] J J Meng Y X Wang Y L Zhao H Ruan and Y LiuldquoStability analysis of earth slope using combined numericalanalysis method based on DEM and LEMrdquo Tehnicki Vjesnikvol 25 no 5 pp 1265ndash1273 2018

[30] Y Zhao L Zhang W Wang C Pu W Wan and J TangldquoCracking and stress-strain behavior of rock-like materialcontaining two flaws under uniaxial compressionrdquo RockMechanics and Rock Engineering vol 49 no 7 pp 2665ndash2687 2016

[31] C Wang Y Zhao Y L Zhao and W Wan ldquoStudy on theinteraction of collinear cracks and wing cracks and crackingbehavior of rock under uniaxial compressionrdquo Advances inCivil Engineering vol 2018 pp 1ndash10 2018

[32] Y X Wang H Zhang H Lin Y Zhao and Y Liu ldquoFracturebehaviour of centralndashflawed rock plate under uniaxial com-pressionrdquo 3eoretical and Applied Fracture Mechanicsvol 106 2020

[33] Y Zhao Y Wang W Wang L Tang Q Liu and G ChengldquoModeling of rheological fracture behavior of rock crackssubjected to hydraulic pressure and far field stressesrdquo 3eo-retical and Applied Fracture Mechanics vol 101 pp 59ndash662019

[34] L J Dong W W Shu X B Li Z Zhou F Gong and X LiuldquoQuantitative evaluation and case study of risk degree forunderground goafs with multiple indexes considering un-certain factors in minesrdquo Geofluids vol 2017 pp 1ndash15 2017

[35] Q Wu L Chen B Shen B Dlamini S Li and Y ZhuldquoExperimental investigation on rockbolt performance underthe tension loadrdquo Rock Mechanics and Rock Engineeringvol 52 no 11 pp 4605ndash4618 2019

[36] Y L Zhao L Y Zhang W J Wang et al ldquoCreep behavior ofintact and cracked limestone under multi-level loading andunloading cyclesrdquo Rock Mechanics and Rock Engineeringvol 50 no 6 pp 1ndash16 2017

[37] J Chen H Peng J Fan X Zhang W Liu and D JiangldquoMicroscopic investigations on the healing and softening ofdamaged salt by uniaxial deformation from CT SEM andNMR effect of fluids (brine and oil)rdquo RSC Advances vol 10no 5 pp 2877ndash2886 2020

[38] X R Liu X D Zhang and M Huang ldquoDelay characteristicsand risk mitigation of karst water burst flood of tunnelsrdquoChinese Journal of Geotechnical Engineering vol 33 no 9pp 1326ndash1332 2011

[39] L Zhang and J A Franklin ldquoPrediction of water flow intorock tunnels an analytical solution assuming an hydraulicconductivity gradientrdquo International Journal of Rock Me-chanics and Mining Sciences amp Geomechanics Abstractsvol 30 no 1 pp 37ndash46 1993

[40] T Li T Mei X Sun Y Lv J Sheng andM Cai ldquoA study on awater-inrush incident at Laohutai coalminerdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 59pp 151ndash159 2013

[41] J Y Qi ldquoe Influence of tunnel blasting method for sur-roundingrdquo Railway Engineering vol 7 pp 4ndash7 1979

[42] G Wang Y Luo X Li T Liu R Ma and D Qu ldquoStudy ondynamic mechanical properties and meso-damage mecha-nism of jointed rock under impact loadrdquo European Journal ofEnvironmental and Civil Engineering vol 45 pp 1ndash17 2019

[43] W X Zheng Y L Zhao and Q W Bu ldquoe coupled controlof floor heave based on a composite structure consisting ofbolts and concrete antiarchesrdquo Mathematical Problems En-gineering vol 2018 pp 1ndash14 2018


above the Ordovician limestone which is a highly permeableconfined aquifer Because of the potential impacts of theconfined water in the Ordovician limestone on the miningactivities the coal seams accounting for 37 of the totalreserve are listed as prospective reserves in north China[11 12]

e coalfields in south China locally occurred in latepermian Figure 1 shows the representative stratigraphiccolumn of the region [13] e main minable coal layer liesin the late permian Longtan Formation e overall coalproducts of this region account for a small part of the na-tional total coal production Hydrogeologically south Chinais in humid region and dominated by modern Karst terrainsCoal excavation from late permian Longtan formation isseriously threatened by lower Maokou Karst aquifer andupper Changxing Karst aquifer All the times the key issuein south China is to prevent late permian Karst waterbursting

e Karst groundwater is mainly of the dissolved-caverntype and Karst-fissure type and usually forms the compli-cated systems of Karst fissures dissolved cavern pipes andKarst caves in south district [14] e distribution andstructure of underground water system are obviously ofinhomogeneity and this brings the anisotropism that theunderground hydrodynamic force is connected Althoughthe Ordovician limestone in north and the Maokou lime-stone in south are both aquifers there exist great differencesbetween them In north its Karst underground is mainly ofthe Karst-fissure water-bearing type Its hydraulic slope israther soft belonging to unified confined water-loggedstrata and once the water is exposed serious water inrushaccidents happen giving rise to the decline of water level ofaquifer [15] As for the southern area particularly in theSongzao Mine Area in Chongqing city Doulishan MineArea in Hunan province and the north area of Guizhouprovince water filling Karst caves generally exist in theMaokou limestone moreover the horizontal hydraulic re-lation among Karst caves is weak and relative independencewhich cannot form unified aquifer system [16ndash19] Withregard to the Maokou limestone of the basement in southerncoalfield its inhomogeneity of karst development in spacedistribution is found When Karst is least developedMaokou limestone strata can be seen as a relative imper-meable layer So Maokou limestone strata can be fullyutilized by adopting a scientific method At present de-velopment roadways are arranged in Maokou limestonestrata in many southern coalfields such as Xingwujing mineof Nantong Company in Guizhou province Shipingyi mineof South Sichuan Coal Industry Meitanba mine in HunanProvince Huayingshan mine of Chongqing city and so on[14 18 19] While the Karst cave development area is themajor hidden trouble for mine water inrush Karst cavewater inrush is seen as one of the coal mine flood accidentsin south China which generated to a large amount ofeconomic loss such as the ldquo4middot16rdquo accident happened in theQiyi mine of Hunan Province in 2003 (17 people died)ldquo928rdquo Karst cave water inrush accident happened in theXinmao mine of Hunan Province in 2010 and ldquo1212rdquo Karstcave water bursting in the Tianchi mine of Guizhou Province

in 2004 (21 deaths and 15 missing) which were typical Karstcave water inrush accidents in late Permian Maokoulimestone

e rock strata between the working face and Karst caveact as a geological barrier that prevents Karst cave waterfrom invading into the roadways e effectiveness of thegeological barrier depends on its thickness lithology andintegrity [20 21] Water inrushes are likely to occur whenthe geological barrier is too thin to withhold the pressure ofKarst cave water In a Karst mine the main technique forcontrolling water inrush is to leave a sufficient thickness ofthe water-proof rock pillar While the calculating methodabout safety thickness of rock pillar setting for confinedKarst cave is not given in regulations of mine water controlof China [22] a study on stability of the water-proof rockpillar and its safety thickness is of great significance forcontrolling Karst water inrush in a mine In order to do so itis of vital importance to study strata failure characteristicsand hydraulic conductivity changes due to mining andthereafter find a way to predict and prevent water inrushes

Perm

ian

Long

tan

Mao

kou

Chan

gxin

gYu

long

shan

Tria

ssic

U

L

Figure 1 e representative stratigraphic column of the coalfieldsin south China









fs


+ 2c


1113971

0 (2)


ft

σt minus σ3 0 (3)





zp

zt minus us

z

zxi

k(Θ p)zp

zxj

1113888 1113889 (4)




(5)







Face Rockpillar


Karstcave

region



ΔH fl

d

u2

2g (6)



Re ρvd

μ (7)



f 1

[174 + 2lg(2Δd)]2 (8)



f 64Re

(9)



f 0326Re025 (10)




d 4S

U (11)




V 2g d

fVJ

8gS

fVUJ (12)


KL 8gS

fVU (13)



KL1 d2ρg

32μ

S2ρg

2U2μ (14)



zp

zt minus us

z

zxi

kzp

zxj

1113888 1113889 (15)











cprime c

Fi

(16)





3 Case Analysis







Re gt 100000 Re lt 23002300 lt Re lt 100000







Begin











No Yes





not

Yes No







Over












p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References






















































fs


+ 2c


1113971

0 (2)


ft

σt minus σ3 0 (3)





zp

zt minus us

z

zxi

k(Θ p)zp

zxj

1113888 1113889 (4)




(5)







Face Rockpillar


Karstcave

region



ΔH fl

d

u2

2g (6)



Re ρvd

μ (7)



f 1

[174 + 2lg(2Δd)]2 (8)



f 64Re

(9)



f 0326Re025 (10)




d 4S

U (11)




V 2g d

fVJ

8gS

fVUJ (12)


KL 8gS

fVU (13)



KL1 d2ρg

32μ

S2ρg

2U2μ (14)



zp

zt minus us

z

zxi

kzp

zxj

1113888 1113889 (15)











cprime c

Fi

(16)





3 Case Analysis







Re gt 100000 Re lt 23002300 lt Re lt 100000







Begin











No Yes





not

Yes No







Over












p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References















































ΔH fl

d

u2

2g (6)



Re ρvd

μ (7)



f 1

[174 + 2lg(2Δd)]2 (8)



f 64Re

(9)



f 0326Re025 (10)




d 4S

U (11)




V 2g d

fVJ

8gS

fVUJ (12)


KL 8gS

fVU (13)



KL1 d2ρg

32μ

S2ρg

2U2μ (14)



zp

zt minus us

z

zxi

kzp

zxj

1113888 1113889 (15)











cprime c

Fi

(16)





3 Case Analysis







Re gt 100000 Re lt 23002300 lt Re lt 100000







Begin











No Yes





not

Yes No







Over












p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References


















































cprime c

Fi

(16)





3 Case Analysis







Re gt 100000 Re lt 23002300 lt Re lt 100000







Begin











No Yes





not

Yes No







Over












p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References


















































Begin











No Yes





not

Yes No







Over












p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References























































p p01 minus

t

T1113874 1113875 (18)







4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References
















































4 Results







Density(Kgm3)

Waterabsorption



Uniaxialcompression

(MPa)


Youngmodulus(GPa)


(MPa)


(deg)


262 022 056 068 127 082 126 035 025 15 297 085

x

yz

1 2 354 P

σ1











unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References























































unit ms




unit (ms)


110 115 120 125 130 135 140 145 150 155 1600000

0005

0010

0015

0020

0025


not water inrush

Q (m

3 s)

Seepage

Fi


Waterpressure(MPa)

3835322926232171411080502









P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References




















































P (M

Pa)

1 2 3 4 5 6 7 8 9 10 110Inrush time (h)

00

04

08

12

16

20

24

28

32

36




unit (cm)


cave

ndash80

ndash87

ndash94

ndash10

1

ndash10

8

ndash11

5

ndash12

2

ndash12

9

ndash13

6

ndash14

3

ndash15

0


110 115 120 125 130 135 140 145 150 155 1600

20

40

60

80

100

Fi

Perc

enta

ge o

f pla

stic u

nits

()



Q (m

3 s)

0001020304050607080910111213

1 2 3 4 5 6 7 8 9 10 110Inrush time (t)











Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References























































Waterpressure(MPa)

363228242161208040

(a)

Waterpressure(MPa)

19618918217516816115414714

(b)Waterpressure

(MPa)0201901801701601501401301201101

(c)


9327986895735183 4 5 6 7 8 9 10 112

h (m)

05

10

15

20

25

30

35

40

45

Fs




H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References















































H h1 + h2 + h3 (20)










Workingface

Karst cavesregion

h1 h2 h3








10 25 15 518 91820 25 15 573 97330 25 15 689 108940 25 15 798 119850 25 15 798 1332



5 Conclusions





Data Availability




Acknowledgments


References
















































5 Conclusions





Data Availability




Acknowledgments


References















































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