Causal Analysis of Subsidence and Prediction of Damage Zone in an Abandoned Underground Limestone Mine
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(2) 2. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. ݓशࠞॠə ࣷĨًٖ ۋйČĀݓ ۆशϸ ںİ͈ॣ ˺ū ݓėʴ قڦȮ ںࠗݓ ۍěࣀॠۋۻ يʼə ġԓߎъۆ ࣷĨε ˰͆Դ رێǦɰ.. ݓ. ݗ. ܓԐ ڹًݓǴΫ࠘ڦ قॠ يԵধԵ ںԦԓॠə ġԓ ˞ ۋнݚʽ ܁ॱ ͿڷًݓĵًԜͿڷə Ìڙʪ ߿Қ ܃ ߎ֨࠘ڦ قॠČ ەɰ. ܓԐʂԜ ڹًݓই ۦDġԓق ۍսʼقًݓۿۍ رԴ ݓॠġۋ ۋΘݓرČ ϶ڷە, ݓशࠞॠ ڹًݓDġԓۍ ۋսॠş ۆۻġԓۆ ق३ . ġٰۚ ۋغΒʽ ۋًݓɰ. ۋġԓ ڹÈԓࠗ ܼҙԵধؒ ںʂԜ ͿڷÒьॠٕڷ ϶ ġߕ ۆə ॳԐĵܓę ҄ॳԐ ĵܓࡾ Ϳڷó ĵқʽɰ. ġߕ ۆʂߕ ڹॳܳ ۍۺN25-30W, ąԐə 65SW-65NE Ǵ ݓսۋݔɰ. Èԓࠗ ܼҙ Եধؒʂə 3 Òॳ ۆԐ(ًݓÀԓॳԐ, ˃ॡʴॳԐ, şʴν ॳԐ)ۋ қपॠČ ەɰ(Fig. 1, 2). ܓԐ˃ ڹًݓॡʴ ॳԐʂε ʂԜ Ϳڷġʼ϶ڷؽ, ইۦə Òьʼ؍ ݓČ ەə Ė Ϳڷġߕफ ڹ30 m ܁ʪݓۋχ ֥čۆ ق३ 80 يmū ݓȉݓرə ҙқʪ ەɰ. ݓъࠞॠ قًݓқपॠə ġ ߕت ۆԜ ڹFig. 2 ٮÏॳ҄ ۋԐĵܓε ۋΘČ ϶ڷە. Fig. 1. Geological map (circle:surveyed zone; KORES, 2002).. Fig. 2. Cross sectional view of the studied zone(KORES, 2002).. ॢĶݓĵ֨֟ࢰėॡধݓ.
(3) D ԵধԵ दġԓݓ ۆशࠞॠ ۍڙқԵ ф ٚԜॹڦĵً ٚࠑ. ٍۤ ڹ2.5 km ۋԜۋɰ. ইݓ ۦशࠞॠÀ ьԦॢ ًݓ ڹ6Úę 7Ú Ԝॠɳ ۆԜҙ Ϳڷًݓ1997ț ġٰ ۋ Βʼ ϶ڷؽই ۦÒьܼ ۋɳʽ ԜͿ Ú ۋदթʼر رەÚǴͿۿ ۆŖ ۋҝÀɠॢ Ԝۋɰ(Fig. 3).. 3. ॣ ąأٍ ڍϸۻ ͆˰ ںɳ ۋьԦॠࣷ يĨʽɰ. ̚ॢ ۼνÀ ьɵॠə ؒъقԴ ݓॠս ۆȤݓ ڹॠėʴۆ ؋܁Ձę Ìʪ֮ قÁॢ Л܃ε ьԦ֨ࢅ϶, Œَۋǣ ėŕڍ ͆˰ ںսÀ ġԓ ۆėʴۓڮ Ϳڷʼϸ ٍॢأ ߎъ ۆң͇ε ࢅڷێə ֨ь ۋ۾ʾ ս ەɰ.. ݓъࠞॠইড ݓशࠞॠ ۆѩࡾ ٮڦşə ġԓڅٖڏ ۆՙǣ ۺݗݓ څՙ ںॳٖ قыəɰ. ݓशࠞॠ قψܳ ںॳٖ ڹə ܳ څ ॢڅՙ˞ ڹԜҙݓъ˃ ۆƍ, ġԓ ۆՁ, ܳѺ ݓ ࠗ, ֩ڌʴĹ ŔνČ ҝٍ՚ϸ ˣە ۋɰ. Ϥ۹ ֮ ڹث ʪə ֱࡾক ۆՁڌۚ قॠə ܼڅ ॢڅՙܼ ۆॠǣۋ ɰ. Piggott and Eynon(1977)֮ ڹث' ڹʪə ֱࡾকۋ ҃ۋə ĖقԴҙࢢ ݓश ۆңĨ ںًݓप॥ॠݓ ͒҆ ي ॠėʴ߯ ۆʂ 10ѕū͆ݓČ ' ۆ܁ॠČ ەɰ. ۆ܁ ۋə दġԓ Ԝҙ ۆңĨȭ ٮۋġۤ Ԝҙ ң͇ ۆًݓȭۋ قŖäॢ ìۋɰ. Matheson and Eckert-Clift(1986)ə ėʴ ۆȭ(ۋh) قʂॢ Ԝҙݓъ˃ ۆƍ(m) Ҽ(h/m)ق ʂॢ Ԝěěćε ܓԐॠ يh/m ۆҼÀ 5҃ɰ ۚ ڹĖق Դə ֱࡾকرێ ۋǨ ÀɠՁ ۋϔ ڍȭČ, h/m ۆҼÀ 5قԴ 11Ԑ ˺ ێ ۋśü০ ÇՙॢɰČ ॰ɰ. ݓॠėʴ ۋԦՁʼϸ ėʴ ݔԜҙقࠗ ۆԴ ͳڿ३ѓرێ ۋǦ ɰ. ėʴܳѺߎ ۋͳڿ ۆъؒ ۆъÌʪε ߣęॠ؍ ݓ ə ॢ ėʴ ڹ؋܁ԜͿ ǫ؉ ݓەχ, ֨ ۆąę˰ ق ͆ ߎъ ۆ؋܁Ձ ڹʂőϿݓ ۆॠս ۓڮę ֨ÂܕۆՁ Ѻ ˣۆ ق३ ͳڿф ÌʪÀ Ѻজʼݓ رъ ۆңĨÀ ьԦॠó ʽɰ. ۼνǣ ɳࠗ ˣ ۆҝٍ՚ϸ˞ ۆÂüۋ ܓнॠϸ ֱࡾক ںՁॠə ʚ ψܳ ںॳٖ ڹó ʽɰ. ০ ߎъۼ ۋνǣ Œَ ˣۆ ق३ Ձʽ Ҹ͡˞Ϳ ĵ Ձʼ ںە رąڍ, սۼ ۋͳڿݔνۻ ۆɳ۹२ߣ ںę. Fig. 3. The portals of an abandoned mine in anticline.. ÚʪܳѺইড ф ࠞॠőϿ Á ܛʪϸę Лॶ˞ܓ ںԐॢ Āę Á Úʪ˞ٍۤ ۆ ڹʂ͜ 400~700 ϶ۋ, Úʪࡾşə फ 18~22 , ȭ ۋ8~10 ܁ʪ ۍìࣷ Ϳڷ؊ʽɰ. Úʪ Ԝҙݓ ۆ ڹҼİ ۺǰ ڹĵѕͿ ۋΘس ݕرʍݓ ںÀݓČ ە ϶ڷ, ՙǣИ ф ۡЀ˞ۙ ۋԦॠČ ەɰ. Ú˞࠘ڦ ۋॠ ə Ėݗݓ ڹĵॳ҄ ͿڷۺܓԐ ĵܓε Àݓə Ėڦ ق ࠘ॠ϶, Úĵҙ࠘ڦ قॠə Ȥ˃ε ࣀ३Դ ֥čۚقڌ ॢۆѕԐĵܓε ěॣ ս ەɰ(Fig. 2 ф Fig. 3). ѕԐĵܓə Օێę Եধؒ ۆąćε ՁॠČ ϶ڷە ֥čĵॳܳ ۆܓѓॳ Ϳڷġߕε ˰͆ ÚʪÀ ĹݕॠČ ەɰ. ֥ ॢ͠ۋčĵܓʪ ψ ڹŒَڮ ںʪॠۆࠗݓ ي Ìʪε أজ֨ࡎČ ݓъࠞॠ ۋۍڙ ॢ ۆʽ ìࣺ Ϳڷ ɳʽɰ. ݓъࠞॠÀ ֨ۚʼə 6Ú ÚĵŖߌقԴ Եধؒ ݓʂقԴ ėࣀ ͿڷۺՁʼə ٍۙėʴ˞ ںьþॣ ս ەɰ. ॢ͠ۋėʴ˞ʪ ݓॠ Ĺ ۋۺң͇ॣ ˺ ݓъࠞ ॠε À՚জ֨ࢅə ًॣ ں॰ ںìࣺ Ϳڷɳʽɰ. ݓъ ࠞॠə 6Úę 7Úߑܼ ۋʼə Úʪ߹ ۆѓॳ ͆˰ ںġ ѩڦॠó ьԦॠٕɰ. ࠞॠ ًٖ ॢ͟ࠑ ͆˰ ںĀę ࠞ ॠőϿə ߯ʂٍۤ أ ۋ240 mۋČ, ߯ʂ फ أ ۋ160 2 m ŔνČ ࠞॠϸ ڹۺʂ͜ 26,600 m ۋ قδɰ. ܳ ࠞॠĵً ࠞॠĵًͪˆ ۆÀ أ650 ܁ʪͿ ȉ قًٖ ڹè ߝ ࠞॠইԜ ф ݓъ ۆйǏ͠ ݙইԜ ۋьԦॠٕČ, ࠞ ॠ͟ ڹս ֯ قԴ ս ۋ قβşū ݓɰتॠó ǣ ࢍǣČ ەɰ. Úʪ Ĺݕѓॳę ݔİॠə ѓॳ ںşܵڷ Ϳ ࠞॠًٖ ۆफ ڹ140~160 ۋ قβə ìࣷ Ϳڷ؊ ʽɰ. ߯ߣݓ ۆशࠞॠə 6Úę Ԝ7ÚقԴ ġۍ Ϳڷ ३ Ձʽ ݓॠėʴ ۆԜҙߎъ ۆң͇ ॢۆ قìͿڷ ԐΒʼ϶, Ŕ ݓ ق Ϳڷॳٖ ۍۺԓԐ ۆй Ǐ͠ ݙইԜ(sliding) ۋьԦॢ ìࣺ Ϳڷɳʽɰ(Fig. 4). ݓशࠞॠ ٮ॥ƍ 2 ۍۺйǏ͠ ݙইԜ҄ ۋ०Ϳڷۺ ьԦॠٕş ˺Л قտս ࠞॠ ٮěʹʽ ѩڦε ϼঝॠó ő܁ॠşə رͷݓχ, տսॢ ࠞॠÀ ěʼə ۋًݓ Ҽİ ۺȉó Ձʼە رɰə ì ڹঝ ॣۍս ەɰ. ÚĵͿҙࢢ ݔԸäνͿ 240~260 قًݓԴ ࠞॠŪ ۋÀ ս йࢢūۋ ݓβə ֱࡾক ࠞॠε ěॣ ս ە əʚ, Ŕ फ ڹ60~80 ܁ʪࠞ ϶ۋॠɳϸ ڹWۙ ܃43ń ܃1.
(4) 4. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. Extent of slip Direction of translational sliding of the broken material. Fig. 4. Failure extent on the surface above the old workings.. ε ࠄॠČ ەɰ(Fig. 5.a). ֱࡾক ࠞॠə ġߕॳܳ ۆ ѓॳ ͠ي ͆˰ ںķʚԴ ěʼČ ەəʚ, ۋə ॠҙۆ. ܳѓ֩ ġę ܼɳң͇֩ ġۆ ق३ Ձʽ Ĺ˞ۺ ۆң͇ قşۍॠə ì܁߸ Ϳڷʽɰ(Fig. 5.b). ֱࡾক قȤʼە رə ؒԵ˞ ۋʂҙқ ॄজʼە ر ݓχ, ͠يĖقԴ йǏ͠ݙϸ֪ ͆˰ ںԸॢ ؒъ ۋŔ ʂͿ Ȥʼە رə ì ҇ ںս ەəʚ ۋə Úʪ ф Ĺ ۆۺң͇ۍ Ϳڷ३ ьԦॢ ì܁߸ Ϳڷʽɰ(Fig. 6.a). Fig. 6.b ٮÏࡾֱ ۋকǴ قǣࢍǣə ࣷթؒъęə ɵ ν Áͳؒ ۆъ˞ۻ ۋʪʼە رə ì ںьþॣ ս ەɰ. ۋìࠞ ڹॠÀ ьԦॢ ۋ ߸Àࠞ Ϳڷۺॠًݓ ܳѺԐϸقԴ ؒъۻ ۋʪʼ ںڼؽϊ३ܵɰ. ۋə ॠҙ ؒݓݓъۋ ۆę ॥ƍ Ì ڍˣ ॢۆ قԐϸۺݕ۾ ۆ ࣷĨ قş ॢۍìۋɰ. ֬ࠞ ܳ Ϳ܃ॠٽ ۆًݓĚ ս ֯ m ̆ ݕرĖقԴ ɰսۤۍ ۆŒَ ۋьԦॠČ ەə ì ںěॣ ս ؽەɰ(Fig. 7). ˰͆Դ ࠞॠ ڹًݓԓ܁Ԝ ҙ Ϳڷޅঝʂʾ ÀɠՁ϶ڷە ۋ, ć՚ݓ ͿڷۺशقԴ ۤۍ ۆŒَ ۆьت ۻԜ ф şࢍ ݓъۋʴ ݜε ěࠑ. Sinkhole. (a) Large scale subsidence (b) Sinkhole formation Fig. 5. Subsidence above the abandoned underground limestone mine site.. (a) Fresh rock along steep sides (b) Freshly broken rock with angular edges along steep sides Fig. 6. Fresh rock along steep sides due to subsidence.. ॢĶݓĵ֨֟ࢰėॡধݓ.
(5) 5. D ԵধԵ दġԓݓ ۆशࠞॠ ۍڙқԵ ф ٚԜॹڦĵً ٚࠑ. ݓъࠞॠۍڙ ۆ. Fig. 7. Tensile crack in surface.. ॣ ज़څՁە ۋɰ.. ݓशࠞॠÀ ьԦॢ ڹًݓ6Úę 7Ú Ԝॠ 3ɳܼ Ϳڷ ɳң͇֩ ġۋ ۋΘܐ رɰ(Fig. 8). ң͇֩ ġ ڹġ ߕԜҙە قə Ͽؒڮۙ ۆѺڦε آş֨ࢅə ġѓѪ Ϳڷġߕə ߎėę ьࣷ ۆठ ͆˰ قۆԜॳۋǣ ॠॳ ߎ Ϳڷėʽ ьࣷėڌۋ ںॠ يьࣷۆ ق३ Ĺʽɰ. ॢ͠ۋġѪ ڹśąԐۆ, þČॢ ġߕ ٮɰՙ ٍॢأ ؒъ ۋԜॠъ قȮە يə ąۺ قڍ०ॢ ۺɾॢ ġ Ѫۋɰ. 7Ú Ԝॠɳ֥ ڹč ۆǨÒҙ࠘ڦ قॠə ġߕε ġ ॠş ڦॠ يÚĵقԴҙࢢ Ϳڍܟқνʼ رĹݕॠə ġ֩ۋ ͿڷΘܐ رČ, 6Ú֥ ڹč۾܁ ۆҙ࠘ڦ قॠ ə ԵধԵ ںġॠş ֨ۚॠ يս і m Ĺ ݕ 7Úߌ ͤ Ϳڍܟқνʼ رġۋ ۋΘܐ رɰ. ˰͆Դ 7Úۆ ܼؖҙə ٍۙ ࢀ Ϳڷۺġܳ ۆͿ ǫó ʽɰ(Fig. 9). 7Úę 6Ú ۋĂ࠘ə ҙқ ڹ7Ú ۆԜɳ ͠ي قÒۆ cone chuteε ՁॠČ 7Ú ॠɳ قdraw pointε χ˞ر 6Ú ॠҙε ߎė ьࣷॠ يң͇֨ࢉ ׆Ϳڷġ֨֬ ں. (a) Plan view. (b) Sectional view Fig. 8. Plan and sectional view of an abandoned underground limestone mine and the zone of subsidence.. ܃43ń ܃1.
(6) 6. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. Fig. 9. Plan and cross-sectional view of a Room-and-Pillar stope(not to scale).. ॢ Ėۋɰ(Fig. 10). ॢठ cone chuteࡾ ٮ࠘ڦ ۆşə ş Ϳڷǫ؉ ؍ ݓە؉Դ ܁ঝॠó ؎ սə ݓػχ ġѓѪԜ 6Úę Ԝ・ॠ7Úߑܼ ۋʼə Ė ںؽە قì ܁߸ ͿڷʼдͿ ٚԜʼə cone chute࠘ڦ ۆə Fig. 8.a قश֨ʽ ц ٮÏɰ. Fig. 11 ڹҸ ң͇Ѫ ॢڌۺ ںġԓقԴ ьԦʼə ݓъࠞॠ ε ʪ֩ܳي҃ Ϳڷۺə Ŕρۋɰ. ġߕε ң͇֨ࡈ Ĺ॥ ͆˰ قĹߎ ۺъࣷ ۆĨÀ ьԦॣ ս ϶ڷە, ݔԜҙ ۋ˞ࠗݓս ݔѺڦε սъॠࣷ ۋ ي Ĩϸ ۋԜҙͿ ьॢۻɰ. أٍ ۋࠗݓॠČ ֮ʪÀ Ūݓ ڹ؍ą ڍĹ ۆۺң͇ݓ ڹशū ݓьۻॠ ي॥Ѓ ࠞॠÀ ьԦॠó ʽɰ. ݓ ˺ۋश ۆսۋݔʴ ڹcone chuteε ܼ֮ ͿڷьԦॠČ ġܳÀ ࠘ڦॠə ĵًݔ ۆ ԜҙقԴə Ԝʂࠞ ڹۚ Ϳڷۺॠε ࢅڷێдͿ, ؘԴ سśॢ ц ٮÏ ڹWۙࠞ ۆॠčԸۋ҃ ںó ʽɰ. Fig. 12ə ࠞॠĵًقԴ ěʽ ইԜ, ÚǴʪ, ই ġغ ՙۤ ф ęä Л ܃ġԓܛ قԐॠٕʏ قسݒ ۆڙغܛ. Fig. 10. The cross section and the transverse section of sub-level caving method of stoping at the abandoned limestone mine.. ॢĶݓĵ֨֟ࢰėॡধݓ. Fig. 11. Subsidence process associated with mine using the block caving method(Whittaker and Reddish, 1989).. Fig. 12. Sinkhole development over room and pillar mine(section B-B' in Fig. 8.a).. Ŗäॠ يٚԜॣ ս ەə ݓъࠞॠ ęۦ ں܁ইॢ ìڷ Ϳ, 6Úę Ԝ7Ú ܼɳ ںң͇֨ࡈ Եধؒ ࣷթԵ ںcone chuteε ࣀ३ ॠ7Ú ۆdraw pointͿ ধսॢɰČ À܁ॠ ٕ ںąڍ, ߯ՙ 30 m ȭ ۆۋėʴ ۋՁʾ ս ەɰ. ܼɳң͇ ˣ ġۍ Ϳڷ३ ėʴߎъ ۆң͇ ۋьԦॠϸ Ŕ Ԝҙقə ࣷթʂÀ Ձʽɰ. Œَ, ۼν ф ɳࠗę Ïؒ ڹъǴ ҝٍ՚ϸę ۋε ࣀॢ ݓॠս ۓڮ ۆф ۙ ٍ Եধؒ ėʴ ˣۍ Ϳڷॠي, ࣷ ॢ͠ۋթʂə ֨Âۋ ąę॥ ͆˰ قьۻॠ يң͇ń ۋঝʂʽɰ. ң͇ńۋ ݓशū ݓʪɵॠݓ يъ ۋ॥ЃʼČ ॥ЃܳݓѺ शࢹÀ Ĺ ۺǴҙͿ ͠ ˞رÇ ׆ͿڷĹ ۺԜҙݓ ۆशϸ.
(7) D ԵধԵ दġԓݓ ۆशࠞॠ ۍڙқԵ ф ٚԜॹڦĵً ٚࠑ. قԴə ࠞॠĵً ۋঝʂʼČ ąԐϸۋ ںΘó ʽɰ. ҆ ۆًݓąݓ ڍश ܓԐĀę ֥čۋǣ ۼν ٮÏؒ ڹъ Ǵ ҝٍ՚ϸę ՙőϿ ɳࠗ, Եধؒ ٍۙėʴ ˣ ۆࠗݓ Ìʪε أজ֨ࢅə ݗݓĵܓε ÍČ ەɰ. Ӽχ ؉ɦ͆ 6Úę ݓशū˃ࠗݓ ۆݓƍə 50~100 mݓ قǣڹ؍ ݓ ʚ ъ३ ݓॠĹėʴ ۆȭۋə أ50 mۋ قβş ˺Л ݓ قъࠞॠÀ ֖ó ьԦॣ ս ؽەʏ ìࣺ Ϳڷɳʽɰ. Fig. 13 ڹġغՙࠑقԴ ࠑ͟ॢ ۙΒε ц ͿڷĵՁ ॢ Fig. 8 ۆAA' ɳϸʪۋɰ. 6Ú ڍܟ ۆÚʪ ݔԜҙق Դ ߯ʂ ࠞॠÀ ьԦॠٕ ϶ڷÚʪ Ԑۋə ġܳݓݓ ۆ ͳۍ Ϳڷ३ Ԝʂ ڹۺ ͿڷۺőϿݓ ۆъ ࠞॠÀ رێ ǣ Wۙ ࠞ ۆॠčԸۋ ںΘČ ॣ߸ ںڼەս ە ɰ. 6Ú ࠑڍÚʪ ݔԜҙقԴ 17 mۋ قβə ߯ʂ ࠞॠ À ьԦॠٕ϶ڷ, ۋĖقԴ 6Ú ߎъū ۆݓäνə 103 mۋ قδɰ. Ĺėʴ ң͇ݓ ॢۍ Ϳڷश॥Ѓ ۋÚʪ ۆÀۤ ؋ޅ (ÚĵͿҙࢢ Àۤ Ϥ ق)ޅԴҙࢢ ֨ۚʼؽə ݓ؉ɦϸ ÚĵقޅԴҙࢢ ֨ۚʼؽəݓə ঝ֬ॠ؍ ݓɰ. ɰχ ێ ҙ ġܳÀ ңĨʼϸԴ ݓъ ۋͳڿęʪॠó ܼݚʼٍ ر թ Ϳڷۺɰδ ġܳ˞ʪ ࣷĨʼČ, ۍ Ϳۋ३ Á cone chute˞ ܳѺ قьԦॢ ėʴ˞ٍ ۋĀʼ رʂőϿ ң͇ Ϳڷь ॢۻì܁߸ Ϳڷʽɰ. قًݓ ۋԴݓ ۆशࠞॠęܛ ں܁०ॠϸ ɰڼę Ïۋ ٚԜॣ ս ەɰ(Fig. 14). ֱࡾকۆ ق३ ݓशࠞॠͿ ۋ ݓرə ߎъңĨ ۆÀɠॢ ۍۺʹێԐæ˞ ڹԜՃॢ ě ࠑۋ ۋΘݕرɰϸ رɗ ܁ʪ ঝ֬Ձ ںÀݓČ Ժ܁ʾ ս ݓەχ, ێъݓ Ϳڷۺशࠞॠ ٮěʹʼə ۦ३܁ ۆ ঝॢ ۤՙ֨ ٮ ںٚԜॢɰə ìر ڹͷɰ. ҆ ܓԐݓ ًܼ ڹɳң͇֩ ġۆ ق३ Ձʽ Ĺߎ ۋۺъۆ ۍۺݕ۾ңĨε ࢅڷێČ ŕɳࡾֱ Ϳڷۺক Ϳ ݓ श قǣࢍǣó ʽɰ. ̚ॢ दġԓ Ԝҙ ۆąԐݓ ݕۋ. 7. Fig. 14. The possible sequence of surface failure above the abandoned limestone mine.. ܼ ںॣً ॢڅॠó ʼر, ġߕ ۆǚ͇ۙ ۍÚʪۓĵ ҙ қ ڹԜҙݓश˃ ۆƍÀ Çՙॠó ʼݓ رशϸقԴ ֱࡾ ক ۆսε ݒÀ֨ࢇɰ. ݓ ۆąԐε ˰͆ َ ۆε ÀݓČ ǣࢍǣə ֱࡾক˞ݓ ڹъأ ۆজইԜ͒ߣ ںॠ ó ʼ϶, Ԝҙݓъॄ ۆজۚۆ قڌ३ ܳѓ֩ ġۚغ ۤ ࡾֱ ۆڦক˞ ںԴͿ Кó χ˜ɰ. ॄজ֮ ۆʪə ş ܓæ ںॳٖ قыó ʼČ, ψ ڹÌս ܓæ ̚ॢ ॄজۆ ֮ʪε ݒÀ֨ࢇɰ. υݓφࠗݓ Ϳڷ॥Ѓ ۋقə 2 ͿڷۺԓԐ ٮÏ ڹйǏ͠ ݙইԜ҄ ۋ० ͿڷۺьԦ ॠٕɰ. ۋə ݓश ॥ЃͿ ۋࠗݓİ͈ʼݓ رъۻ ۆɳ ÌʪÀ ۹ॠʿ ׆Ϳڷशࢹࠗݓ ۋĵѕε ˰͆ ۋʴॢ ìࣺ Ϳڷɳʽɰ. Ĺߎ ۺъࣷ قթʂÀ ՁʽɰČ ॠʌ͆ʪ ܁ۺġ ܳε ҃ॢۻɰϸ ġܳ قьԦʼə ߿ ںܼݚ ͳڿқ০ þ˩ ս ەş ˺Лߎ قъ ң͇֖ ۋó ݓशū ݓьۻॠ ݓə ؍əɰ. Ŕ͠ǣ ҆ ġԓ ۆąقڍə ġ ۆ؋ۻ ںČͲॠߏ ڹ؍ ݓսॠϸԴ ġܳ˞ ںęۖ Ϳڷ Ĺ॥ ׆Ϳڷġܳݓݓ ۆɠͳࡾ ںó Çՙ֨ࡈ Ԝۦॠܼ ںþ˥ ݓЇॠČ ġܳÀ տÂࣷ ͿڷۺĨʽ ìࣺ Ϳڷ ɳʽɰ.. ࠞॠٖॳѩڦ. Fig. 13. Sectional view in the zone of subsidence(section A-A' in Fig. 8.a).. ܁߸ ۺۋ ࠞॠÀ ьԦॠə şÂ ڹĹܓæę ܓݗݓæ ŔνČ Ìսܓæ ͆˰ قսțقԴ ս֯ ț ۋèπ ս ەş ˺Л قćࠑ ںॠş قۻə ݓъٰ ۋےݔړ ۆΒʼə ֨۾ ںɳ ॣ܁ս ػɰ. ҆ ġԓ ۆąقڍʪ ࠞॠÀ ьԦʼČ ܃43ń ܃1.
(8) 8. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. ьۻ३٣ ęܳͲ؎ ں܁ə ۙΒÀ ä ϶ڷػ ۆćࠑʪ ֬֨ʽ ػ ۋۺş ˺Лࠞ قॠÀ ٰΒʼؽə ݓ؉ɦϸ ć՚ʼČ ەə قݓʂ३Դə ҆ ܓԐقԴə э৩ ս ػ ɰ. ɳݓ ݓश ܓԐ ٮąॹࣀ ں३Դ Ԝɾ ҙқ ۆĹۺ ۋң͇Нۆ قॠ ںܐڗ يì܁߸ ͿڷʼдͿ ॳ ߸Àࠞ ۍۺॠÀ ьԦॠʌ͆ʪ Ŕ őϿə ࡾ ں؍ ݓì ࣺ Ϳڷɳʽɰ. Ĺėʴ ॥Ѓۆ قॠ يՁʽ Ҿ ė ॥Ѓ şˊ ݔ ۆą ڹң͇ ߣşقə ݓॠ ėʴ(W)قԴǣ ݓश(D) ԜقԴ ʴ ॣێìۋдͿ D=WÀ Ձςॢɰ(Fig. 15). ġ ԓߎъߣ ۆşң͇ę ʴ֨ࣷ قթʽ ؒԵ˞ٍ ڹĀʽ Ĺ Ϳڷۺ͠˞رÀԴ ؋֩Á Ϳ ּۋó ʼČ, ࣷթ ؒۺߕ ۆऋۍ Ϳڷ३ ǣϢ ݓ॥Ѓ şˊڍ ںó ʽ ɰ. ۋə ߯ݓ ͿڷۺܛशԜ قǣࢍǣə ՜ԜًٖͿڷԴ ࠞॠ ٖॳѩ(ڦDs)ε ॢۆ܁ɰ. ݓशԜ ق՜Ԝʂݔ ۆąڦ ں܁߸ ں३ Whittakerٮ Reddish(1989)À ܃؋ॢ ąॹ ۺशই֩ ॣڌۋ ںս ەɰ. . . (1). يşԴ, ԜҙݓъČ( ), K=ऋέ, ێъͿڷۺ 1.3~ 1.5(Church,1981; Blyth & De Freitas,1990; Bell & Stacey, 1992; Whittaker & Reddish, 1993), Ĺ ۺफ( ), ĹČ( ), ࣷթؒ ۆ؋֩Á, Ŕ νČ ң͇ʂݔ ۆąۋɰ. ֩ (1)Ϳҙࢢ ֱࡾক ও ڹң͇ʂݔ ۆą ə ɰڼ. (2)֩ę Ïɰ. . . (2). şۙܕΒ ф ইܓݓԐε ࣀ३ , , , , ˣ ͿڷÁÁ ԓ ॢ܁Ā ę ՜Ԝ ًݓѩ ۍڦң͇ʂݔ ۆą ڹ26 Ϳ ćԓʼؽ ɰ. ۋə ܳѓ֩ ĹѪقԴ Àɠॢ ࣷĨ تԜ ێս ە ɰ. Ŕ͠ǣ êࢹ ʂԜ ԵধԵġԓ ۆąܳ ڍѓ֩ ĹѪ χ ॢڌۺ ںì ۋ؉ɦ͆, ܼɳ ң͇Ѫʪ Ԑ ॢڌঔ०ۺ ۍġѓѪڌۺ ںॠٕɰ. ۋə ܳѓ֩ ĹѪڌۺ ق ॠə ąॹ֩( ֩ ۍ1) ںԐڌॠəʚ ۋأ܃ʾ ս ڷە ǣ, Ŕ Òȝ ںটڌॠ يऋέ ࣷ ۍթؒݓ ۋॠə ߕ ۺф ںۺߕ ߕۻԓ܁॥ ׆Ϳڷң͇ʂݔ ۆą ںć ԓॣ ս ەɰ. ۋə ݓशقԴ ěॣ ս ؽەʏ ࠞॠٮ ԓԐ(landslide)҄ ۆ० ۺইԜ ںőϼॠşۺ ق०ॢ ۿŖѪࣺ ͆ۋɳॠٕɰ. ъ˚֨ ČͲ३ܳ ॣ آʽ ۙۍ ࣷ ۍɳÁ(angle of break) ə ݔą 26ࡾֱ ۍক ܳ Ѻ ؒъࣷ ۺݕ۾ ۆĨͿ ۍ३ ࢀ É ںÀ ݗս ںڼە ঝ ॣۍս ەɰ. ݔą Ϳ Ձʽ ֱࡾক ǴͿ शࢹࠗࣷ ۋĨʼ߸ رÀ Ϳڷۺ͠˞ر ߕ ڹۺɰ( ڼ3)֩ę Ï ۋशইʽɰ. . . . . . . . . . . . . (3). ࣷթؒ ݗڗ Ϳڷս ەə ߕۻė ڹɰ( ڼ4)֩ę Ïɰ. Ds . (4). ң͇Ū ۋε 2 Ϳ À ॣ܁ąࣷ ڍթؒݓ ۋॠə ߕ ڹۺɰ( ڼ5)֩ę Ïɰ. . . (5). ۺߕ ߕۻę ۆěćͿҙࢢ ɰ ڼˣ֩ ۋՁςॢɰ.. φ Fig. 15. Basic considerations in estimating the extent of damage due to subsidence by sinkhole formation.. ॢĶݓĵ֨֟ࢰėॡধݓ. . (6). ŔνČ ε Ԝş ֩ Ϳڷशইॠϸ ɰڼę Ïɰ..
(9) 9. D ԵধԵ दġԓݓ ۆशࠞॠ ۍڙқԵ ф ٚԜॹڦĵً ٚࠑ. . (7). Ԝş ֩ ںɳտজ֨ࢅϸ ɰ ڼěć֩ ںص ںս ەɰ. . (8). . ֩(8) ں؉͒ ࠑ܁É˞ڌۋ ںॠ يिϸ ঝۤʽ ՜Ԝ ʂ ۆѩࠞ ڦॠٖॳѩ ڦε ںصս ەɰ. ěॢ ॢ ܼ ۾ݓĖ قʂ३ , , , , , ŔνČ. ێą ͿڍԺ܁ॠ يćԓॢ Āę, ۋʽɰ. ۋÉق۾ݓڌۺ ڹԴ ěʽ ࠞॠफ, ࠞ ॠ ٖॳ ѩ أ ڦ70 Ǵ ͿٽǣࢍǦ ìę ۞ ҙ०ॢɰ. ˰ ͆Դ ३ɾ ق۾ݓԴ࠘ͳۓ ۆÀ Ҽİࢍ ۺɾॢ É˞ںے ঝ ॣۍս ؽەɰ. Ŕ͠ǣ ۋս࠘ə Á ًݓѻ ң͇Ūۋ ࣷ ٮթؒ ۆऋέۋ قÀ ںەս ەČ şॠॡ܁ ۺ ҃˞ قʂॢ ֬ࠑ࠘˞ ۋҾأॠ϶ Úʪ قʂॢ ۆ҃܁ ֪Ձ ۋɰՙ ̆϶ݓر, ࠞ ۻॠًٖێ قέۺ Ϳڷۺ ڌॠş رͷş ˺Л ͳۓ ˞ۋ قѺ͟˞ قʂॢ ঝέۺ êࢹÀ ज़څॠɰ. ঝέ܁߸ ۺ ң͇Ūۋ, ؒԵऋέ, ؋֩Á ˣ Á ϔÒѺս ۆқप ф ࣀć͟ ںইۤܓԐ Āę ф ֬ࠑ࠘ε ࢹʂͿ À܁ॠ Č, Monte Carlo ֨бͪۋՎ şѪڌۋ ںॠ ي՜Ԝʂۆ. ѩ قڦʂॢ қपε ؽصɰ. ̚ॢ, ࠞॠŪ ٮۋ՜Ԝʂ, ࠞॠॳٖ ۆѩ ۆٮڦěćε ֨бͪۋՎࣀ ں३ ڮʪॠ ࠞ يॠইԜ ф ѩ قڦʂॢ ۿ ۺۋŖ֨ ںʪॠٕɰ. ڍԸ ҃սۿ ۍۺŖڦ ں३ ң͇Ū ۆۋथŒę शܵठ ε 3 m ٮ2 mͿ Âܳॠٕؒ ϶ڷԵऋέ ۆąقڍ ə थŒ 1.45, शܵठ 0.1Ϳ Ժ܁ॠٕɰ. ࢹࠗ ۆऋ έ ڹथŒ 1.15, शܵठ 0.05, ŔνČ ؋֩Á ۆथŒę शܵठə Á Á 30 4 Ϳ Ժ܁ॠٕČ, қपə ܁őқ पε ڌۋॠٕɰ. शࢹࠗ ˃ƍ, ң͇Čə ս࠘ݓʪ ε ڌۋॠ يŔ қपε ϶ڷؽصÁ ϔÒѺսѻ қपə Fig. 16ę Ïɰ. ˞ۋϔÒѺսѻ Ǧսε ڌۋॠࠞ يॠ ٖॳń قʂ३ ঝέ ۺқԵ ںսॱॠࠞ يॠŪ ٮۋѩ ۆٮڦěć֩ ںĵॠٕɰ(Fig. 17 ф Table 1). ֨бͪۋՎ ĀęۙΒ قʂ३ ࠞॠ Ū(ۋ )ॳٖ ٮѩ (ڦ) ۆěćϿʝͿԴ 1 ݓսÇկ Ͽʝę 2 ݓսÇկ Ͽʝ ںČͲॢ Āę, 2 ݓսÇկ Ͽʝ ۋԜěՁ ۋȭó ǣࢍǮ϶ڷ, ۋə ȭڮۙ ڹʪε ৠԦ३Դ ڹصĀęͿ ҇ ս ەɰ. Ā܁ć ս ܼ ق ۆНνۆ ۺйə ң͇ݔąڮ قԐॢ ۆйε ݓɦ϶ ݓशŖߌ ۆң͇ݔą ۋėʴǴ ۆң͇ݔą ٮ ڮԐॠɰə ì ڹң͇ ࠞॠėʴǴε ࣷթؒۋǣ शࢹࠗ ڐ ۋս ەə ߕ ۋۺÇՙॠş ˺Л قǰࣷ ڹթÁ ںÀݓó ʿۆ ںйॢɰ. 2 ݓսÇկ Ͽʝڌۺ ںॠ يÁ cone chuteÀ ࠘ڦ ॣ ì ͿڷٚԜʼə ق۾ݓʂॢ ٖॳѩڦε ԓ܁ॠٕڷ ϶, Ŕ Āęε Fig. 18 قʪ֨ॠٕɰ. ॳٖ ॢ͠ۋѩڦə ߸ ͿڷؘÀ ͿڷۺьԦॣ ս ەə ݓशң͇ѩڦε Ժ܁ ॠə şܵ ۋʼ϶, Fig. 18Ϳҙࢢ Ժ߸ ॢ܁À ࠞॠͲڍ ĵً ڹFig. 19 ٮÏɰ. ࠞॠ Ͳڍĵً ڹǫ ޅф ǫʴޅ قԴə ইࠞ ۆۦॠĵً ąć҃ɰ 10~20 m ܁ʪ ȉر ϶ݓ, ҚԴѓॳͿڷə 30~40 m ঝۤʾ ս ەə ìͿڷ ǣࢍǮɰ. Қʴ ѓॳͿڷə ֬ࠞ ܃ॠًٖ ۋćԓۆ ق. Table 1. Correlation models between the depth of subsidence and the effective range Model . R2 parameters. Exponential decay model I. Exponential decay model II. ⋅ . ⋅ ⋅ . 160.65. 114.18. 0.891. 0.923. A=205.42. A1=216.41. B=0.97. B1=0.32. C=43.47. A2=100.14 B2=2.54 C=27.56. ܃43ń ܃1.
(10) 10. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. (a) Depth of subsidence ( ). (b) Bulking factor of rock ( ). (c) Bulking factor of soil ( ). (d) Angle of repose ( ) Fig. 16. Assumed distribution models of various parameters. Fig. 17. Correlation between a depth of subsidence and an effective range.. ३ ĵॢ ٖॳѩ҃ڦɰʪ ʌ ࡾó ǣࢍǮəʚ ۋə ĵܓ أٍ ۍۺʂ ۆьɵͿ ॢۍìࣺ Ϳڷɳʽɰ. ࠞॠĵًۆ ʴ ޅѓॳͿڷə ݓश॥ЃͿ śąԐ Ԑϸ ۋԞͿ ۋՁ ʼݓ رъࠞॠٮə Иěॠó ؒъॄ ۆজܼݚ ٮͿڍ. ॢĶݓĵ֨֟ࢰėॡধݓ. Fig. 18. Effective range of subsidence associated with each cone chute.. ۍ३ ԓԐ ٮÏ ڹԐϸࣷ ۺݕ۾ ۆĨÀ ॱݕʾ ìڷ Ϳ ࣺɳʽɰ. ֬ ۋ Ϳ܃ĵً ǴقԴə ࠞॠًٖ ѓق ьۻॠČ ەə ɰսۤۍ ۆŒَ ˣ ںěॣ ս ەɰ..
(11) 11. D ԵধԵ दġԓݓ ۆशࠞॠ ۍڙқԵ ф ٚԜॹڦĵً ٚࠑ. Ϳ ׆शࢹٍࠗۙ ۋąԐϸۋ ͆˰ ںʴॢ ìۋɰ.. Fig. 19. Hazard map of subsidence and landslide over the abandoned limestone mine.. Ā. . - ݓъࠞॠ ইড ݓъࠞॠə 6Úę 7Úߑܼ ۋʼə Úʪ߹ ۆѓॳں ˰͆ ьԦॠČ ϶ڷە, ࠞॠĵً ڹٍۤ ۆ240 mۋČ 2 ߯ʂ फ ڹ160 mͿԴ Ŕ ϸ ڹۺ26,600 m ۋɰ. ࠞॠĵ ً ǴقԴ ॥Ѓ ࠞॠ ۋۺɰս ьþʼ϶ ࠞॠ ق ݓъ ۋԓԐ ٮÏ ڹйǏ͠ ݙইԜ ۋьԦॢ ҄०ۍۺ ࠞॠε ǣࢍǴČ ەɰ. ࠞॠɳϸ ڹʂߕͿ Wۙ ε ࠄॠəʚ ۋə cone chute ԜҙقԴə ؒъң͇ۋ ψ ڹъϸ ġܳÀ ॢ࠘ڦĖقԴə Ԝʂࠞ ͿڷۺॠÀ ۺó ьԦॠٕş ˺Л ۍìࣺ Ϳڷɳʽɰ. ݓ ۋąԐ ە ܋ş ˺Л قČʪÀ ǰ҃ޅ ڹɰ ȭقޅ ڹԴ ݓъۆ սۋ ݔʴ͟࠶ ۋԴ ࠞॠ ۆًݓʴ ޅąćҙقə śąԐ Ԑϸ ۋՁʼۍ Ϳۋ ϶ڷؽ३ ۺݕ۾ԐϸࣷĨÀ ॱݕ ʼČ ەɰ. - ݓъࠞॠ ۍڙ Ԝ 7ÚقԴ 6Ú Ԑ قۋġߕε cone chuteͿҙࢢ Ĺ ॥߯ ׆Ϳڷՙ 30 m ȭ ۆۋėʴ ۋՁʽ ъϸ ݓशū ֮ ۆݓʪə 50~100 mݓ قǣ؍ ݓ؉ ėʴߎъ ۆң͇ ͿڷՁʽ ࣷթʂÀ ԴͿ ٍĀʼϸԴ ġܳÀ ॠܼں þ˥ ݓЇॠČ ࣷĨʼ ر॥Ѓ ࢇڷێ ںì܁߸ Ϳڷʽ ɰ. ̚ॢ Եধٍؒۙ ۆʴĹę ɳࠗ ф ֥čę Ïأٍ ڹ ॢ ݗݓĵܓÀ ॥Ѓ ںÀ՚জ ֨ࢇ ìࣺ Ϳڷɳʼ϶, И ҃ؼɰʪ ߏսॠϸԴ ġܳε ęۖ Ĺॢ ìۍۺۿݔ ۋ ۍۍڙìࣺ Ϳڷɳʽɰ. ࠗݓ॥Ѓ ۋقə 2Ϳڷۺ ԓԐ ٮÏ ڹйǏ͠ ݙইԜ ۋьԦॠٕəʚ, ۋə ݓ श ॥ЃͿ ۋࠗݓİ͈ʼݓ رъۻ ۆɳÌʪÀ ۹ॠʿڷ. - ߸ÀࠞॠٚԜ ঝέۆ ق܁߸ ۺॠϸ ࠞॠ Ͳڍĵً ڹǫ ޅф ǫ ʴقޅԴə ইࠞ ۆۦॠĵً ąć҃ɰ 10~20 m ܁ʪ ȉ϶ݓر, ҚԴѓॳͿڷə 30~40 m ঝۤʾ ս ەə ì ͿڷǣࢍǦɰ. ҚʴѓॳͿڷə ֬ࠞ ܃ॠًٖ ۋćԓق ۆ३ ĵॢ ٖॳѩ҃ڦɰʪ ʌ ࡾó ǣࢍǮəʚ ۋə ĵ أٍ ۍۺܓʂ ۆьɵͿ ॢۍìࣺ Ϳڷɳʽɰ. ࠞॠĵ ً ۆʴ ޅѓॳͿڷə ݓश॥ЃͿ śąԐ Ԑϸ ۋԞͿۋ Ձʼݓ رъࠞॠٮə Иěॠó ؒъॄ ۆজܼݚ ٮ ۍ Ϳڍ३ ԓԐ ٮÏ ڹԐϸࣷ ۺݕ۾ ۆĨÀ ॱݕʾ ìࣺ Ϳڷɳʽɰ. ćࠑۙΒÀ رػইࠞ ۦॠܛ ۆΒيҙə ҝқϼॠд Ϳ ߸Àࠞ ۍۺॠʪ ѕ ॣ܃ս ػɰ. ̚ॢ Ԑ͊˞ॱࣀ ۆ ˚ ۋЛ ĖۋдͿ ॥Ѓݕ߿ ݓę Ï֨ ڹśॢ ҄ĵə ज़ ڹ؍ ࠘څìࣺ ͿڷɳʼдͿ ҄ĵʂࠞ ڹॠÀ ٰΒʼ ݓ رъ ۋ؋܁জʽ ۋ قսςॠə ì ۋц͊ݔॠν͆ ҆ɰ. ąćًٖ Ǵ ݓъ॥Ѓ ф ࠞॠইԜę ʴ ޅԐϸق Դ ۆҼϸ йǏ͠ ݙইԜ߸ ۆÀ ۍۺьԦيҙǣ ݓъ ؋܁জيҙ ۆঝڦ ںۍॠٍ ي՚ ۍۺćࠑ ф ܳşۺ ইۤě ۋज़څॠɰ.. ČЛॶ 광업진흥공사(KORES), 2002, 정밀조사보고서(석회석: 영월 -토교, 제천-두학지구), DS2002-LS(IV), 자원탐사처, p.115. Bell F.G. and Stacey R., 1992, Subsidence in Rock Masses. Chap. 13, Engineering in Rock Masses, ButterworthHeinemann. Blyth F.G.H. and de Freitas M.H., 1990, A Geology for Engineers, Edward Arnold. Church H.K. 1981, Excavation Handbook, McGraw-Hill International Book Company. Matheson G.M. and Eckert-Clift A.D., 1986, Characteristics of chimney subsidence and sinkhole development from abandoned underground coal mines along the Colorado Front Range, Proceedings of the 2nd Workshop on Surface Subsidence due to Underground Mining, West-Virginia University, Morgantown, WV, pp.204- 214. Piggott R.J. and Eynon P., 1977, Ground movements arising from the presence of shallow abandoned mine workings, Proceedings of the Conference on Large Ground Movements and Structures, UWIST, Cardiff, Geddes J.D.(ed), Pentech Press, pp.749-80. Sowers G.F., 1976, Mechanisms of subsidence due to underground openings, in Subsidence over mines and. ܃43ń ܃1.
(12) 12. Ը ߺڍբڙą Ϊʴ ڍU.M. Rao Karanam. caverns, moisture and frost actions, and classification: Washington, D.C., Transportation Research Board Record 612, National Academy of Science, pp.2-8. Whittaker B.N., Reddish D.J., 1993, Subsidence Behaviour. of Rock Structures, Chap. 28, Vol. 4, Comprehensive Rock Engineering. Pergamon Press. Whittaker B.N. and Reddish, D.J., 1989, SubsidenceOccurrence, Prediction and Control, Elsevier, p.528.. Ը ߺ ڍ. բ ڙą. 1978ț Դڐʂॡİ ۙڙėॡę ėॡԐ 1984ț Դڐʂॡİ ʂॡڙۙ ڙėॡę ėॡԵԐ 1988ț ॒͎֟ ࣷν VIʂॡİ ėॡчԐ. 1982ț Դڐʂॡİ ۙڙėॡę ėॡԐ 1985ț Դڐʂॡİ ʂॡڙۙ ڙėॡę ėॡԵԐ 1996ț قƞʚлʂ ॒͎֟, ėॡчԐ. ইॢ ۦĶٍڙۙݗݓĵݓ ڙъ؋ٍۻĵҙ ٍےĵڙ (E-mail; [email protected]). ইॢ ۦĶٍڙۙݗݓĵݓ ڙъ؋ٍۻĵҙ ٍےĵڙ (E-mail; [email protected]). Ϊ ʴ ڍ. 6. 3BP ,BSBOBN. 1994ț Դڐʂॡİ ۙڙėॡę ėॡԐ 1996ț Դڐʂॡİ ʂॡڙۙ ڙėॡę ėॡԵԐ 2000ț Դڐʂॡİ ʂॡݓ ڙĵঞą֨֟ ࢰėॡҙ ėॡчԐ. 1983ț Osmania University ėॡԐ 1987ț Banarus Hindu University ėॡ ԵԐ 1994ț Indian Institute of Technology ėॡчԐ. ইॢ ۦĶٍڙۙݗݓĵݓ ڙъ؋ٍۻĵҙ Ըٍےĵڙ (E-mail; [email protected]). ॢĶݓĵ֨֟ࢰėॡধݓ. ই ۦIndian Institute of Technology, ġԓॡę İս (E-mail; [email protected]).
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