Journal of Engineering Science and Technology Review 9 (1) (2016) Research Article
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1 Jest Jounal of Engineeing Siene and Tehnology Review 9 () (6) 66-7 Reseah tile Effet of Stesses and Stains of Roadway Suounding Roks on Boehole itightness WU Wei, *, WNG Zhaofeng, and JEN n JOURNL OF Engineeing Siene and Tehnology Review Engineeing Cente of the inisty of Eduation of Coal ine Disaste Pevention and Disaste Relief, Henan Polytehni Univesity, Jiaozuo 454, China College of Safety Siene and Engineeing, Henan Polytehni Univesity, Jiaozuo 454, China RIT Univesity, elboune, ustalia Reeived 8 Januay 6; epted Febuay 6 bstat t pesent, many high gas and outbust mines have poo gas dainage effets. n impotant eason influening the gas dainage effet is a poo hole-sealing effet. ost studies on gas dainage boehole sealing fous on loal and foeign boehole sealing methods, boehole sealing euipment, and boehole sealing mateials. Numeial simulations of initial dilling sealing depth ae insuffiient beause studies on this subjet ae few. Howeve, when the initial sealing depth of the boehole is not hosen easonably, ai an ente the gas dainage dill hole though the iumfeential ak of oadway suounding oks unde the influene of sution pessue of the dainage system. This phenomenon ultimately affets the hole-sealing effet. To impove the dilling hole sealing of gas dainage boing, we dedued the expession fomulas of the ushing zone, plasti zone, and elasti zone aound the oal-seam floo stone dift and onduted a stess stain analysis of the oal-seam floo stone dift of the 45 woking sufaes of the Sixth Coal ine of Hebi Coal ine Goup Company by using theoetial analysis, numeial simulation, and on-sene veifiation. Finally, we obtain the initial dilling sealing depth, whih is a main ontibution of this study. The esults pove the following. The pefomed hole-sealing poess with an initial dilling sealing depth of 8 m has a gas dainage effiieny of 55%. Compaed with the pevious 6.8 m initial dilling sealing depth with a gas dainage effiieny of less than %, whih was adopted by the mine, the initial sealing depth of 8 m hosen in the numeial simulation is easonable and onfoms to the atual situation on the spot. Theefoe, the initial dilling sealing depth hosen in the numeial simulation will podue patial and effetive guidane to study the field hole-sealing depth. Keywods: Gas Dainage, Hole Sealing, Numeial Simulation, Initial Dilling Sealing Depth. Intodution Coal is one of the main enegy esoues in ou ounty. long with ineasing mining depth, the pobability of gas aidents also ineases. In the 95s, ou ounty teated gas dainages as an impotant measue to pevent and ontol oal mine gas. fte deades of development, gas dainage tehnology has made signifiant pogess. t pesent, the main hole sealing ways in the ounty and aboad inlude mehanial ement mota hole sealing [,], hemial gouting mateials hole sealing [,4], and hole sealing with hole pake. Howeve, many gas and outbust mines still have a poo gas dainage effet in ou ounty and the gas dainage ate annot meet the standads. These defiienies an be attibuted to the poo gas pemeability [5] of oal seams, impope hoie of the gas dainage method, and poo effet of the boehole seal of gas dainage. If the initial sealing depth of gas dainage boing is not hosen easonably, the hole-sealing effet will be dietly influened. The so-alled initial dilling sealing depth denotes the distane fom the oifie of the oadway dill hole inwad up to the loation whee the adoption of the hole-sealing devie begins. t pesent, studies on gas dainage boehole sealing fous on loal and foeign boehole sealing methods, boehole sealing euipment, and * addess: hpuwuwei@6.om ISSN: Easten aedonia and Thae Institute of Tehnology. ll ights eseved. boehole sealing mateials. Numeial simulations ae insuffiient beause studies on initial dilling sealing depth ae few. Hene, this study investigates the initial dilling sealing depth of gas dainage by onduting theoetial analyses, numeial simulations, and on-sene veifiations. This study obtains an initial dilling sealing depth that is easonable and mathes with the atual situation; this esult is one of the main ontibutions of this atile. The following fatos mainly ause the ouene of the uneasonable hoie of the initial sealing depth of gas dainage dill hole. The pevious hoie of the dill-hole initial sealing depth lagely depends on the fatos of on-site expeiene and geologial onditions to judge the initial sealing loation of the dill hole; this eseah inludes theoetial analysis and numeial simulation, patiulaly the haateistis of the oadway suounding stess stain. Without investigation, the oadway suounding stess stain annot be auately judged only by on-site expeiene. Futhemoe, the hosen initial sealing depth annot evade the fissue of the oadway suounding ok. Thus, the ai leakage hannel annot be fixed when the dill hole is sealed. Unde the influene of sution pessue of the dainage system, the ai in the oadway an ente the tube used fo gas dainage, theeby leading to the poo gas dainage effet though the fissue of oadway suounding oks [6 ]. Theefoe, this wok studies the effet of the stess stain of oadway suounding oks on boehole seal depth by analyzing the stess stain of oadway suounding oks. This wok also finds easonable hole-sealing positions and impoves the whole
2 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) 66-7 sealing effet to ahieve the aim of impoving the gas dainage ate. Ò. Stess stain Relation of Roadway Suounding Rok Ò Fo ok mass, the oh Couloumb stength iteion is usually adopted. The shea stength τ of the ok mass depends on positive stess on the slip plane and the shea stength t is expessed as the funtion [] of positive stess, i.e., τ f ( ) () ÒE o Å ä Fig.. Stess stain elation uve with desending banh Å If the envelope line is a staight line, the following is obtained (Fig. ): Ó Ñ K ( Ð ) Ñ o Ò Ò Ò Ò In Fomula (6), is the modulus of the desending banh and is the defomation of the elasti egion. The following is obtained if the lateal defomation oeffiient is intodued: / (7) Theeafte, Fomula (6) is tansfomed into the following: om / (8) Suppose ξ /E. The following ievesible defomations ae obtained: Fig.. Envelop of oh s iles of pinipal stesses τ tan ρ K () Beause n Δ ( ξ ) E E ( ξ ) ( om ) and (9) π τ sin( ρ) os ρ π os( ρ) sin ρ () n Δ ( ξ ) E E ( ξ ) ( om ) () Fo elasti defomation, the Poissons atio is ν.5; Theeafte, Hene, sin ρ ot ρ K (4) sin ρ sin ρ e e e ( ), () 4E The total defomation is expessed as follows: If om is epesented as the ompessive stength of ok, when the elasti stage is eahed. Fomula (4) is then tansfomed as follows: om (5) Thus, the shift to the stess stain elation is epesented by pinipal stess, as shown in Fig.. The following fomula is fo the desending banh: om (6), a b a b whee e n e a (.5ξ ), a.5ξ b ξ (.75), b ξ (.75) om ( ξ ), om ( ξ ) n () 67
3 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) Stess stain of Roadway Suounding Rok Theoy Gound stess auses the fomation of elasto-plasti ange in the oadway suounding ok [, ]. The elasto-plasti ange of the oadway mainly inludes the elasti egion, plasti zone, and ushing zone. In the oiginal ok stess fa away fom the oadway, the hoop stain, appoximating the stess ondition with eual omponent of stess, i.e.,, wheeas the oiginal ok stess nea the oadway is, ; the stess ondition an be met in the bounday between the elasti egion and initial stess aea: () On the stess level, the stength of the ok mass is detemined by the snap-in foe, ohesive foe, and fition foe of the ok. fte enteing the elasti egion, with ineasing defomation and the bevelment of the unevenness on the slip plane, the snap-in foe gadually deeases. Hene, the hadness of the ok diminishes until the esidual stength is eahed on bounday between elasti egion and plasti zone. The value of esidual stength is detemined by the ohesive foe and fition foe of the ok mass. The stess ondition is met on the following bounday: (4) The defomation annot be unestitedly ineased, and y is in the plasti zone. When the limit value is eahed, the inne ohesive foe is hanged to zeo, i.e., ; the ok mass will ompletely ente the ollapse behavio, i.e., the bounday of the ushing zone. The plasti and ushing zone is 4. The ondition is met in the ushing zone, i.e., (5) The aea influening the boehole seal effet is mainly elasto-plasti ange. The stess, stain, and size of the displaement in the aea ae theoetially analyzed as follows. In the elasti zone, assume that the onstitutive elationship is desibed by the following euation:, (6) The total defomation should be witten as follows: ( ) E and (7) ( ) (8) E The following euation is solved by onsideing Fomulas (7) and (8): d (9) d The following stain epesentation in the elasti zone is obtained on the basis of bounday onditions and : ( ) E ( )( ) () We substitute Fomula () into Fomula (6) and F : epesent the stess omponent with stess funtion ( ) F df, () d df d We obtain F ( ) ξ () ( )( ) In Fomula (), ξ / E. We solve Fomula () by onsideing on bounday and plaing the solution as follows: [( )( ) ξ ] ( ) ξ ( )( )( ) ( )( ) ( ) ξ ( )( ) τ ξ ( ) () In Fomula (), is the stess on the bounday. We obtain fom the stess analysis of the plasti zone as follows. The defomed omponent in the plasti zone is detemined in the following fomula fom (7) to (): ( ) E ( ) E (4) 68
4 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) Thus, by esoting to geometi euations d du / and u /, we an obtain the adial displaement as follows: ( ) E u (5) If the ievesible defomation on bounday is ( ) /, the elation between and fom Fomula () is expessed as follows: ) ( ) )( )( ( ξ ξ (6) In the plasti zone, the govening euation is a balane euation and physial euation:, d d (7) On the basis of the above-mentioned euation, with espet to the stess 4 on the bounday with ushing zone 4, the stess epesentation of the plasti zone is as follows:, τ (8) The defomed omponent in this aea is obtained by the defomation ontinuity euation ( ) / / d d, inompessible ondition Δ Δ, and defomation bounday ondition on bounday : ( ) ( ) E E (9) The adial dispesion is obtained by u / : ( ) E u () On bounday 4 between the plasti zone and ushing zone, the adial displaement o iumfeential defomation eahes a etain limit; the ohesive foe is zeo in the ok mass. Fom Fomula (9), whee and 4, the following elation between and 4 an be obtained as follows: d d,. () In the ushing zone, the govening euation is a balane euation and physial euation: ( ) [ ] ( ) ( ) 4 ξ ξ () On the oadway bode when the bounday ondition is satisfied, p, i.e.,,, τ p p () The defomed omponent by ( ) / / d d, inompessibility ondition Δ Δ, and on 4 obtains the following: 4 4 (4) The oesponding adial displaement is expessed as follows: 4 (5) The stess on the bounday 4 is expessed as follows: 4 p (6) Thus, the following is obtained fom Fomulas (8) and (5), whee : 4 4 p (7)
5 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) 66-7 Thus, the stess stain state in the elasto-plasti zone depends on its adius. Suppose Fomulas () and () ae eual when, we obtain the following when onsideing Fomula (7): p ( ) [( )( ) ξ ] ξ ( ) ( )( ) ξ ( ) ξ ( ) (8) fte detemining, and 4 an be ompletely detemined by Fomulas (6) and (). The ideal plastiity solution is obtained when the abovementioned solutions is ξ,, and. The ideal bittleness of the ok mass an be obtained when ξ,,, and 4. In both ases, the bode adius in the elasti zone and oiginal ok stess zone is expessed as follows. Fo an ideal bittle mateial: p p Fo an ideal plasti mateial: p p (9) (4) In both ases, the adial displaement in the ushing zone is: u E ( ) (4) In the ushing zone, the ok mass is in a state of destution. We ely on fitional esistane to maintain stability. Fitional esistane is aused by tangential stess, whih is aound the oadway geneated by the blok. In the plasti zone, the ok mass is in the plasti stage of the ompession defomation. Unde the influene of stess edistibution, an intenal ak podues a new etain dietion of the fatue weak plane. Both the size of the aea of the physial and mehanial popeties of ok mass and oiginal ok stess field distibution of the state have a lose elationship. This elationship has been peviously analyzed. In the elasti zone, the ok mass is at the stage of elasti defomation unde the ation of extenal foe. The majoity of the inteio ak is loated in the initial fissue weak plane, whih is unde the ation of new stess [4, 5]. The spatial sale of the fatue weak plane has etain hanges, but the ok mass is still in the stage of elasti defomation. oding to the theoetial analysis, gound stess will inease in the elasti zone and the ok mass will have etain pemeability. In tems of distane away fom the oadway, is the oiginal ok stess zone is beyond the elasti egion. The ok mass an be teated as an aea that is unaffeted by oadway fomation. Thus, the oadway suounding ok mass within the boehole seal must bypass the elasto-plasti ange beause the pemeability and mehanial state of the ok mass will hange in the elastoplasti ange of the oadway. oe ai leakage passages exist beause the egion fatues ae geate in numbe. Boehole sealing should not be pefomed in this aea, even if hole sealing is onduted in this aea. The effet of this poess is also poo. 4. Stess stain of Roadway Suounding Rok Numeial Simulation and Initial Sealing Depth On the basis of the theoetial investigation of the elasti, plasti, and ushing zones of the oadway, we pefom the numeial simulation eseah on the stess stain of the seam-floo stone-dift suounding ok by adopting COSOL multiphysis numeial simulation softwae. On the basis of the esult of the oadway suounding ok stess stain obtained fom the simulation omputation, the easonable dill-hole initial sealing depth is finally hosen. We used 45 woking sufaes of the oal-seam floo of the stone-dift ossing dill hole of Hebi Coal ine Goup Company s Sixth Coal ine, e.g., pefomed the sample numeial simulation. oding to the alulation esults, the easonable initial sealing depth is detemined fo the oal-seam floo of the dill hole of the stone-dift ossing. The ove depth of the 45 woking sufaes of the oalseam floo stone dift of Hebi Coal ine Goup Company s Sixth Coal ine is 5 m o so with a stike length of 98 m loated in the sandstone ok statum. We pefom the stess stain numeial simulation of the oadway with a ove depth of 5 m and adius of.5 m by adopting the oh Coulomb iteion. The oadway ove depth is 5 m; thus, the gound stess is 5 Pa. gound stess of 5 Pa should be imposed on the uppe, left, and ight boundaies of the model established by hoie(fig. and Fig.4). The lowe bounday is set as a fixed bounday. The physial mehani popety of the sandstone will be hosen as the physial paamete of the oadway suounding ok mass (as shown in Table ) beause the oadway is aanged in the ok statum of sandstone. S shown in the table, Young s modulus is 4 Pa, the ohesive foe is 9 Pa, intenal fition angle is 9, Poisson atio is., and the density is.5 g/m. The balane euation adopting the elastiity of solid defomation is expessed as follows: ( i, j,, ) ij, j F i, (4) In Fomula (4), volume foe. ij is the stess tenso and Table. ehanial paametes of the model Intenal Young s Cohesive Rok fition Poisson modulus foe type ngle atio (Pa) (Pa) (unit ) Fi is the Density (unit g/m ) Sandstone
6 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) 66-7 Fig.. Numeial simulation modeling diagam The meshing model is shown in Fig. 4. wheein the elasti-plasti behavio is shown, the elastoplasti ange is.5 m. The elasto-plasti ange is 8 m fom the oadway side wall whee the ok mass defoms, and the gas pemeability of suounding ok is ineased to a etain extent. The gas dainage boehole sealing in the oal-seam floo stone dift must avoid a mining-influened aea beause the oiginal ok exavated will destoy the oiginal stess state of the oadway suounding ok and lead to stess edistibution. On one hand, adial stess deeases the oadway peimete to zeo; on the othe hand, the tangential stess ineases, thus poduing the stess onentation. Futhemoe, the stess state of the suounding ok beomes an appoximately two-dietion foe. The pevious state is a thee-dietion foe, and stess onditions deteioate. If the value of stess onentation is geate than the stength of the loose suounding ok, a suounding ok fatue will ou. This fatue fom the oadway peimete begins to gadually expand downwad until a new thee-dietion foe state of euilibium is eahed. t this point, the suounding ok aea will appea in a egion. The egion is alled the elasto-plasti ange, whih is a poess of ouene, development, and stability. The value afte the elasto-plasti ange stabilizes eflets the suounding ok stess and suounding ok stength fatos, suh as the esult of joint ation. Fig. 4. eshing figue diagam Finally, we obtain the oadway suounding ok stess diagam (Fig. 5) and the oadway suounding ok stain diagam (Fig. 6). Fig. 6. Roadway suounding ok stain diagam Fig. 5. Roadway suounding ok stess diagam In Fig.6, nea the stone dift of the 45 seam floo, patiulaly the aea with the stone-dift ente of ile as the efeene fame, i.e., the ok mass in the geen aea lage numbe of field test esults show the following. The destution of oadway suounding ok in oal-mine podution is inevitable. Even in a low stess field, the suounding ok of oadway unde the effet of gound stess is also had to stabilize. The mehanial haateistis of the oadway suounding ok show that the stesseduing aea inludes the ushing, plasti, and elasti zones. The loose ok mass mainly ontains mioaks, whih will inease gadually. Defomation suddenly ineases, and ohesion and angle of intenal fition and defomation modulus ae edued. The loose ok mass fatue system develops, and a low stess value will have advese effets on dill-hole sealing. On one hand, holesealing gout leaks outwad along the elasto-plasti ange of fatue system. On the othe hand, the development of the fissue system is diffiult to ahieve full bloking fo sealing. Thus, at the pesent stage, gas dainage boehole sealing must be onduted outside the oadway elasto-plasti ange. In this egion, fatue develops, ai leakage passage ineases. Unde negative pessue gas dainage, outside ai 7
7 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) 66-7 an ente the aks on the intenal gas dainage pipe, whih will seiously affet the gas dainage. If the aea is hosen fo the hole sealing, even if the hole sealing is ompleted, the effet an be poo unde the sution pessue of the dainage system. i leakage an esult in this aea. Thus, we avoid the aea when seleting the initial sealing loation, i.e., the boing initial sealing depth shall not be lowe than 8 m. dilling field ontains a seven-ow gas dainage dill. Eah ow has five gas dainage dills. The total dilling is 5. The distane between one end of the dill hole and anothe is 5 m. We dilled using ement mota hole sealing. The initial sealing depth of gas dainage dilling is 8 m. Eah goup of the five gas dainage dills is onneted. We use one dainage poe plate to investigate the dainage onentation and flow oifie. In the end, the uent olleto was onneted to the dainage pump station. In the 45 woking sufae oal-seam floo stone dift on the site veify gas dainage effiieny. Compaed with the pevious ase of onsite hole sealing, the initial sealing depth is less than 8 m. When the initial sealing depth of the on-site hole sealing is moe than 8 m, gas dainage effiieny is fom less than % 55%. The umulative dainage gas data ae.4 million m. The hole is sealed losely. single goup of gas dainage onentation is moe than %. Compaed with the pevious gas dainage onentation, the obtained dainage onentation is enhaned by nealy two times. Dainage negative pessue is kpa, whih has made signifiant dainage effet. Thus, the initial sealing depth of 8 m is easonably and eliably hosen in the numeial simulation, whih is in line with the atual situation. 5 Disussion s a basi tehnial means fo ontolling gas, gas dainage dilling sealing has extensive appliation anges in mine aeas. In ou ounty, howeve, the sealing uality of vaious dillings is unsatisfatoy. Thus, eseah on initial dilling sealing depth should inlude the study of the stess stain theoy and numeial simulation of the seam-floo stone dift suounding ok. To impove the utilization atio of sealing, aeleate elimination outbust ate of oal seam, edue the numbe of dilling, and save podution ost, studies on initial dilling sealing depth have vey impotant ealisti signifiane in peventing seious aidents, suh as gas outbust and gas explosion. t pesent, gas dainage boehole sealing studies fous moe on boehole sealing depth, boehole sealing euipment, and boehole sealing mateials in the ounty and aboad beause studies on initial dilling sealing depth ae few, and numeial simulations ae insuffiient. Hene, this atile studies gas dainage initial dilling sealing depth using theoetial analysis, numeial simulation, and on-sene veifiation. we have obtained initial dilling sealing depth that is easonable and in line with the atual situation, whih is also the innovation of this atile. The main esults in this thesis ae as follows: we analyzed the distibution of the stess field and stain field aound the oal-seam floo stone dift, dedued the expession fomulas of the ushing zone, plasti zone, and elasti zone aound the oal-seam floo stone dift. Some onlusions ae obtained fom the theoetial analysis and numeial simulation. Sealing ok fatue is fomed aound the oal-seam floo stone dift. On the basis of the eseah on the stess stain theoy of the seam-floo stone dift suounding ok, we simulate the stess stain of the seamfloo stone dift suounding ok by adopting the COSOL multiphysis numeial simulation softwae. We ombine the 45 woking sufaes of the oal-seam floo of stonedift field ases of the Sixth Coal ine of the Hebi Coal ine Goup Company aoding to the esults of numeial simulation. easonable and eliable initial sealing depth of 8 m is hosen fo the seam-floo stone-dift ossing dill hole, with efeene to the atual hole-sealing depth of 8 m adopted in the field. The gas dainage effiieny is 55%, in ontast to the hole-sealing depth of 6.8 m, whih was peviously adopted by the mines. The gas dainage effiieny of less than % indiates that the eseah on hole-sealing depth with numeial simulation an auately pedit the elasto-plasti zone of the oadway. The same an be used as the basis of hoie of the hole-sealing depth fo the oal-mine seam-floo stone-dift ossing dill hole, whih lays the foundation in enhaning the hole-sealing uality and effet, as well as gas dainage effiieny, boasting wothwhile advanement and appliation pospets. knowledgements This eseah was suppoted by the Speialized Reseah Foundation fo the Dotoal Pogam of National Natual Siene Foundation of China (No and 5749) and Key Laboatoy of Gas Geology and Gas Contol of Henan Povine, Povinial Depatment of Constution of State Key Laboatoy Beeding Base Open Funded Pojets (WSB). Refeenes. Ogilvie, ihael L., Gas dainage in ustalian undegound oal mines, ining Engineeing: Littleton, Coloado, 47(), 995, pp Hebble White B K, Rihmond J, llan J., ustalian expeiene in long-hole in-seam dilling tehnology fo seam gas dainage, Symposia Seies-ustalasian Institute of ining and etallugy,, 98, pp.-7.. Noak, Klaus, Contol of gas emissions in undegound oal mines, Intenational Jounal of Coal Geology, 5(/4), 998, pp Wanghua Sui, Jinyuan Liu, Wei Hu, et al, Expeimental investigation on sealing effiieny of hemial gouting in ok fatue with flowing wate, Tunnelling and Undegound Spae Tehnology, 5, 5, pp Chao Zhang, Baiuan Lin, Yan Zhou, et al, Study on fatuingsealing integation tehnology based on high-enegy gas fatuing in single seam with high gas and low ai pemeability, Intenational Jounal of ining Siene and Tehnology, (6),, pp anhao He, Physial modeling of an undegound oadway exavation in geologially 45 inlined ok using infaed themogaphy, Engineeing Geology,,, pp Baiuan Lin, Fazhi Yan, Chuanjie Zhu, et al, Coss-boehole hydauli slotting tehniue fo peventing and ontolling oal and gas outbusts duing oal oadway exavation, Jounal of Natual Gas Siene and Engineeing, 6, 5, pp Zhiyong Hao, Baiuan Lin, Yabin Gao, et al, Establishment and appliation of dilling sealing model in the spheial gouting mode based on the loosing-ile theoy, Intenational Jounal of ining Siene and Tehnology, (6),, pp
8 D WU Wei, WNG Zhaofeng and JEN n/ Jounal of Engineeing Siene and Tehnology Review 9 () (6) Jianbing Peng, Liwei Chen, Qiangbing Huang, Physial simulation of gound fissues tiggeed by undegound fault ativity, Engineeing Geology, 55,, pp Yabin Gao, Baiuan Lin, Wei Yang, et al, Dilling lage diamete oss-measue boeholes to impove gas dainage in highly gassy soft oal seams, Jounal of Natual Gas Siene and Engineeing, 6, 5, pp Tingkan Lu, Zhaofeng Wang, Hongming Yang, et al, Impovement of oal seam gas dainage by unde-panel ossstata stimulation using highly pessuized gas, Intenational Jounal of Rok ehanis and ining Sienes, 77, 5, pp.-.. Chengzhi Qi, Qihu Qian, Basi Poblem of Dynami Defomation and Fatue of Rok ass, Siene pess, China, Beijing, 9.. Wenxiu Li, Chongyang Gao, Xia Yin, et al, viso-elasti theoetial model fo analysis of dynami gound subsidene due to deep undegound mining, pplied athematial odelling, 9, 5, pp Lan Cui, Junjie Zheng, Rongjun Zhang, et al, Elasto-plasti analysis of a iula opening in ok mass with onfining stessdependent stain-softening behavio, Tunneling and Undegound Spae Tehnology, 5, 5, pp Z.B. Liu, S.Y. Xie, J.F. Shao, et al, Effets of deviatoi stess and stutual anisotopy on ompessive eep behavio of a layey ok, pplied Clay Siene, 4, 5, pp
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