Stress Distribution and Fault Development Around...

Title Stress Distribution and Fault Development Around NepalHimalaya by Means of Finite Element Method

Author(s) Alam, Md. Mahmudul; Hayashi, Daigoro

Citation 琉球大学理学部紀要 = Bulletin of the College of Science.University of the Ryukyus(73): 15-54

Issue Date 2002-03

URL http://hdl.handle.net/20.500.12000/2621

Rights

BulLFELc・Sci.，Univ､Ryukyus,No.73815-鼬（2002） 1５

StressDistributionandFaultDevelopmentAroundNepal

HimalayabyMeansofFiniteElementMethod

Ｍｄ･MahmudulAlamandDaigoroHayashi

oftheRyukyusINishihara。DepartmentofPhysicsandEarthSciences，Universityofthe

Okinawa，903-0213,Japan

Abstract

Thereareanumberofmethodstoanalysegeologicalstructures・Ｆｍｉｔｅｅｌｅｍｅｎｔ

ｍｅｔｈｏｄｉｓｏｎｅｏｆｔｈｅｍ・Numericalmodelingbasedonfiniteelementanalysisisan

effectivetoolforstudyingtheelasticbehaviorsofearth，Bcrustduetotectonicmove‐

ment・Ｔｈｉｓｓｔｕｄｙｄｅｓｃｒｉｂｅｓｈｏｗｔｏｕｓｅａｎａｄvancednumericalmodelingtechnique，thefiniteelementmethod，ｔｏｃｏｍｐｕｔｅｒｏｃｋｄｅｆｏｒｍａｔｉｏｎａｎｄｔopredictstressand

faultdevelopｍｅｎｔａｓａｆｕｎｃｔｉｏｎｏｆｍａｔｅｒｉａｌｐｒｏpertieB，cohesionandfrictionangle・Stressdistributionandfaultdevelopmentof2dimenBionalplanestrainFEMmodB1s

offourHimEL1ELyancrosssectionsaredescribed・ＳＷ（southwest）ｔｏＮＥ（northeast）horizontalshorteninguptomaximuｍ３７５ｍ（equivalentdisplacementat7､５

ｃｍ/yrof5000yr)isappliedatthesouthwesternendofthecrosB-Bections・ProposedmodelsshowthatthedirectionofmaximumprincipalstressBs（ｏ,）arehorizontal

alongtheshallowｅｒｐａｒｔｏｆａｌｌｔｈｅｍｏｄｅｌＢ・Variationofthevelocityboundarycon-ditionindicatesthechangesofdirectionofprincipalstressesalongthedeeperpart

whilethatalongtheshallowerpartmmainunchangＢｄ

ＡｃｃｏｒｄｍｇｔｏｔｈｅＭｏｈｒ‐Coulombcriterion，failureisobservｅｄａｌｏｎｇｔｈｅＢｈａｌ－ｌｏｗｅｒｐａｒｔｏｆＳｉｗalik，TethysandGraniticlByer，ａｎｄａｖｅｒｙｆｅｗｎｅａｒｔｈｅｓｕｒｆａｃｅｏｆＭＢＴ，ＭＣＴａｎｄＳＴＤＳ，FailurehasnotoccurredinthedeeperpartcfHigher

HimalayaandLesserHimalaya，inspiteofchangingphysicalparametersofrockformations，becauseofthehydrostaticconditionthatisobsewedalongthemodels・PreviousstudiesonfocalmechanismBolutionBofearthquakeBintheHimalBLyan

regionprovidethBexistenceofthrustfaultsalongitBEWBtretchingwithoneplanedippinggBntlynorthbeneaththeHimalaya，SimulationBhowsthesamedistributionofthrustfaultBaloｎｇｔｈｅｕｐｐｅｒｐａｒｔｏｆｔｈｅｍｏｄｅｌｓａｓｓｈｏｗｎｂｙｔｈｅｆｏｃａｌｍｅｃｈａ‐niRmsolutions．

AbbreviationsandNotations

Sub-Himalaya

LesserHimalaya

LesserHimalayanThrust

LesserHimalayanSequence

HigherHimalayas

HigherHimBulayasSequence

MainBoundaryThrust

MainBoundaryFront

MainCentralThrust

●●Ｏ■Ｏ●●●●●ロロＧＣ●●甲●

Ｓｍ”⑪

顕、血蠅躯叩ＭＭＭ

1６ＭｄMahmudulA1amandDaigoroHayashi

Ｍ２ｉｎＤｅｔＲｃｈｍｅｎｔＴｂｎｕｇｔ

Ｍ且inFront21Thrust

SouthTibetanDet2chment

SouthTibetanDetachmentSystem

Tethys-Himalayas

TibetanTethysseries

lndusTsangpo

lndusTsangpoSuture

Sedim⑨nt

Gneig巳

Normnlfflln1t

Fini他Ｆ１②mentMethod

MaximumPrincipalStress

lntermediatePrincipalStress

MinimumPrincipalStress

ＭＤＴ３

ＭＦＴ：

STD：

SＴＤａ

ＴＨ：

ＴＴＳ：

IＴ：

ITS8

Sed．：

Ｇｎ８

ＮＦ：

ＦＢＭ：

ぴ１：

｡２：

◎３：

Introduction

TheNepalHimalayas，ｗｉｔｈａｎｅｘｔｅｎｓｉｏｎｏｆ８００ｋｍ，coverthemountainrangeslying

withintheKingdomofNepaLSincel949，ｗｈｅｎＮｅｐａｌｏｐｅｎＧｄｉｔｓｂｏｒｄｅｒｔｏｔｈｅｆoreigners，

anintensegBologicalinvestigationhastakenplace，ａｎｄｉｎａＳｈｏｒｔｔｉｍｅＮｅｐａｌｈａｓｂｅｃｏｍｅ

ｏneofthegeologicallywellknowntractsoftheHimalayanrange，Theearliestreported

visitorwasHooker,whoinl848crossedtheTamurVallyineasternNepal（Hooker,1854)．

HewasfollowGdbyMedlicott,whoinvestigatedtheKatmandureg1onandtheTriSuliGanga

(Medlicott,1875)．ThefirstcomprehensiveaccountofNepalesegeologyhasbeeng1ven

bｙＡｕｄｅｎ（1935)．HeimandGanSSer（1939）enterednorthwestemNepalinl939・Ｉｎｌ９５０

ＨａｇｅｎｂｅｇａｎｈｉｓｆｉｅｌｄｗｏｒｋｆｏｒｔｈｅＧｏｖｅｍｍｅｎｔｏｆＮｅｐａＬＤｕｒｉｎｇｌＯｙｅarsofintensive

investigationsinpracticallyallpartsofthenowaccessiblekingdomheaccumulateda

wealthofgeologicalfacts,unequalinthehistoryofgeologicalexplorationintheHimalayas、

TheexcellentgeologicalresultsbｙＬｏｍｂａｒｄ（SwissEverestexpedition）andBordet'ｓ

(FrenchascentsofMakalu)expeditionsareEwaluablecontributionofthehighestmountain

group･Inl962theDutchgeologistsEgelerａｎｄＤｅＢｏｙ,ｉｎｅａｒｌｙｌ９６３Ｇ・FuchsofAustralian

expedition，ｉｎｌａｔｅｌ９６３ＢｏｒｄｅｔｗｉｔｈＲｅｙｍａｎｄａｎｄKrummenachercoveredtheThakkhola

reglon

HimalayasiStheworl｡'shighestmountainchain，itconstitutesthegreatestattraction

toclimbersandtrekkersthroughouttheworld・Butmorethananythingelse，theHimalayas

representtheawe-inspiringpower，beauty，andgrandeurofnature・Ｆｏｒｍingadistinct

geographicaldividethatseparatesthelndiansubcontinentfromCentralAsia，theHimalayas

extendfromwesttoeastinELmassivearc(Fig.１）forabout2500kilometersterminating

attheYunnanandthePamirsyntaxes・Coveringanastoundingareaof612,O21sq．ｋｍ，

StressDistributionandFaultDevelopmentAmundNepalHimalayabyMeansofFimiteElementMethodl7

ＴＴＢｎＢｏｎｌｍ■lpyBＢ■tholith

I■｡、-醜angpo．＆Ｎ⑨r0h＄r■SlDqnrezone35.

蕊!;蕊liiLiih義liilllllliⅢ●可

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KGlibman

90。８０。Ｅ

SimplifiedgeologicmapoftheHimalayashowingthemajortectonostratigrELphicdivisions･ModifiedfromGansser（1964)，ＬｅＦｏｒｔ（1975)，BarnicotandTreloar，ParrishandHodges，Kaneko（1997)．

Ｆｉｇ．１．

thevastmountainchainpassesthroｕｇｈｔｈｅｌＩＤｄｉａｎＳｔａｔｅＳｏｆＪａｍｍｕａｎｄＫashmir，

HimachalPradesh，UttarPradesh，SikkimandthoHimalayankingdomsofNepaland

Bhutan、TheTibetanP1ateau‐ｔｈｅｒｏｏｆｏｆｔｈｅｗｏｒｌｄ‐formsthenorthernboundaryof

thismagnificentmountainsystemwhilelowerextensionsoftheHimalayasbranchoff

fromeasternandwesternfrontiersofthesemountains・

Thecontinent‐ContinentcollisionmodelfortheupliftoftheTibeteLnPlateauhas

beentreatednumericallybyEnglandandothers（EngalandandMcKenzie，1982,1983；

EnglandandHousemanl985,1986)．Inthisstudies,theyassumedthelndianandAsian

cruststobeincompressiblenon-Newtonianfluidsandanalysedthecollisionin3-dimension

bymeansofathinviscoussheetanalysisandhadtheintentionofexplainingthestructure

oftheinterioroftheAsianContinent、Itisimpossible，howcver，ｔounderstandtheuplift

oftheHimalayasdirectlyfromtheirmodel，althoughitmayrepresentsoneofthemost

reasonablecollisionmodel＆

ThelargestnegativegravityanomEL1iesovertheGangaBasinandtheHimalayaare

reproducedbyamodelwherethelndiancrustunderthrustsHimalayaatshallowangles

ofl5｡±5．alongvariousthrustzones（IndusSutureZone，ＭＣＴａｎｄＭＢＴ)．Ｉｎｔｈｉｓ

ｍｏｄｅｌｔｈｅＨｉｍａｌａｙａｒｅｇｉｏｎｉｓisostaticallyuncompensatedandthecrustalshorteningof

300to400kmiscalculatedtohaveoccurredacrossthemountain（Warsi＆Molnar,1977)．

Hayashi（1987,1988,1992）numericallysimulatedtheupliftoftheTibetanplateau

andtheHimalayasassumingthatthenortherlymigrationofthelndianplatedeforms

theoverlyingAsiancontinentalcrustwhichbehavesasanincompressibleNewtonianfluid

ofAsiaabovetherigiduppermantle・Inthesemode1s，theuppermantlelithosphereis

1８Ｍｄ・MahmudulA1amandDaigoroHayashi

arigidbodyforthefirstapproximationandthedeformablecrustoverliestheupper

mantle・ＴｈｅｄｅｆｏｒｍａｔｉｏｎｏｆｔｈｅｃｒｕｓｔｉｓｔｈｅｎexpectedtoformplateausELndmountain

ranges・Undersuchanassumption，isostaticreadjustmentbeComesimpossibleandthe

calculatedvaluesｏｆｓｕｒｆａｃｅｕｐｌｉｆｔｔｅｎｄｔｏｂｅoverestimated、Further，therigidplate

assumptionprohibitssimulationforaperiodlongerthａｎ0.1Ｍa・Thenumericaltechnique

usedinsimulationpurposeisbasedonthewellknownfiniteelementmethod･

TheHimalayas,ｔｈｅworld'syoungestandhighestmountai、range,aremorphogenetically

stillactivetodayandup-going、Therearebasicallytwocausesforthis:（ｉ）activefault-

ingintheSiwalikhillsinthesouthernfrontalpartan。（ii）１ongwEwelengthchromcup-

heavalinthecentralHigherHimalayaTheｕｐｎｆｔｏｆｔｈｅＳｉｗａｌｉｋｈｉｌｌｓｉｓｑｕｉｔｅａrecent

eventresultingfromintermittenteELrthquakessincethelateP1eistocene，whereasthe

HigherHimalayastartedtoupliftinassociationwiththeMCTactivefromthemiddle

MioceneanｄｃｏｎｔｉｎｕｅｓｔｏｄｏｓｏａｔｐｒｅｓｅｎｔｗｉｔｈｅpisodicrapidrisesduringthespELn．

TheriseofthemountainsshiftedsuccessivelyfromtheTibetanMarginalMountains

inthenorthintheO1igｏｃｅｎｅｔｏｔｈｅＨｉｇｈｅｒＨｉｍａｌａｙａｉｎｔｈｅＭiocene，theMahabharat

RangeintheearlyP1eistoceneinassociationwiththesouthwardjumpofthethrustfaults

(IT1S→MCT-全l1fBT-受MFT)．

Numericalmodelingbasedonfiniteelementanalysisisaneffectivetoolforstudying

theelasticbehaviorsofearth,scrustduetotectonic（epirogenicandorganic）movement・

Generally，thedeformationthatoccurswithintheearth'scrustisinhomogeneousfinite

deformation・Thegeologicaldeformationishowevertoocomplextobeanalyzed・

Thestrainmarkerswithintherocksandtheirstrainanalysisgenerallyprovides

valuablemessagesaboutthenatureoftectonicmovementwhichtherockexperienceｄｉｎ

ｔｈｅｐａｓｔ・

ＨｉｍａｌａｙａｉｎＮｅｐａｌｉｓａｃｏｍｐｌｅｘｆｉｅｌｄwhererocksequencearefolded，faultedand

thrustedinresponsetoaseriesofupliftmentoftheHimalayaduetosubductionoflndian

platebeneaththeEurasiaplate・Thesedimentaryandmetamorphicrocksarefolded，

faulted,jointedandthrusteddifferentlyaccordingtotheintensityofstressdeveloped

withinit・Thestudyoftheserocksequencesandstructurescertainlymayprovidesvarious

cluestoanalysethestress，elasticbehELvioroftherocksandtectonichistoryoftheregion・

Ｔｈｅａｉｍｏｆｔｈｅｓｔｕｄｙｉｓｔｏａｎａｌｙｓｅｔｈｅfollowings：

（ｉ）TheintensityanddirectionofprincipalstressesalongtheNepalHimaｌａｙａａｒｅｃｏｍ‐

putedinvariousboundaryconditions．

（、）Developmentoffaults

（iii）Comparisonthesimulatedstressdistributionwiththefocalmechanismsolution

happenedwithintheregion．

StressDistributionandFaultDevelopmentAroundNepalHimalayabyMean8ofFiniCoE1ementMethodl9

1．GeologicalSetting

ThegreatHimalayasextendforabout2500kmfromthePunjabHimalayainthewest

totheArnachalHimaIayaintheeastalongtheWNWdirectionlikeaborderingwallalong

thesouthernedgeoftheTibetanPlateau・

ＴｈｅgeomorphiccrosssectionintheN-Sdirectionisalmostsimilarthroughoutthe

Himalayas・AtypicalsectionfroｍｔｈｅＮｅｐａｌＨｉｍａｌａｙａｉｓｓｈｏｗｎｉｎＦｉ９．２．Fromnorth

Ｈ唾ＴＤｍＴＭＣｒ

Ｆｉｇ、２．SimplifiedcrosssectionoftheHimEL1ayas、ＭＦＴ：MainFrontalThrust，ＭＢＴ：MainBoundaryThrustiMCT：MainCentralThruBt・

tosouth,theTibetanHimalaya（5000ｍ),theHigherHimalaya（70006000ｍ),theLesser

Himalaya（1500-2000ｍ）withtheMahabharatRange（3000ｍ）atthesouthernborder，

theSiwalikhillsintheSub-Himalaya（1000ｍ）andtheTeraiP1ainarezonallyarranged

Thegeomorphicdivisionsarewellcorrelatedwiththezonaldistributionofthegeologic

formationsandstructuralarrangementsalongtheHimalayantrend

lntheTibetanHimalayazonemthenorth，theTethyssedimentsofthePalaeozoic

totheearlyCenozoicagespreadovertheareawhichisunderlainbyavastamountof

granitebodies・TheHigherHimalayanzoneisoccupiedbythehighmountainscovered

withsnowandglaciersincludingpeakshigherthan8000msuchasKanchanjangha，

Makalu，Everest，Cho-Oyu，Manaslu，AnnapurnaandDhaulagiri・Ｔｈｅｕｐperpartsof

thesemountainsareformedbytheTethyssedimentswhichareunderlainbytheCentral

Crystallinescomposedofhighgrademetamorphics・Boththesedimentsandgneisses

thrustuptheLesserHimalayansedimentｓａｌｏｎｇｔｈｅＭＣＴ（MainCentralThrust),ｗｈｉｃｈ

ａｐｐｅａｒｓｔｏｂｅｏｎｅｏｆｔｈｅｓｉｇｎｉｆicanttectonicboundariesthroughouttheHimalayas・Ｔｈｅ

lesserHimalayanzoneintheMidlandisadiSSectedhighlandborderedbytheMahabharat

Rangetothesouth，ｍａｄｅｕｐｏｆｔｈｅＬｅｓｓｅｒＨｉｍａｌａｙａｎｓｅｄimentsandtheGondwana

ＮＳ

■”四

岬鉈ｌ》

面岳

悪､￣

I丘ｅ■ｎｄＳｎｏＷＺｏ正

----------ＳｎｏｗＬ１Ｊｕｅ

AlPlneZone

Sub-AIplneZmhe

TempernteZone

Subtropl亜ｌＺｏｎｅ

1℃ralsub･皿、血ｍｙ、 Ⅱ紀霞ｅｒＨ迩白lay■、 I､ゆcrmmala” rIbemnHimnmya Ｇｅｏｍ⑨rphMoglc山Ｄｉ７．

ＧａｎｇＥｓＡ１ｌｖ．ＳＩＷ曰ｌｌｋＳｅｄ． u－ＺＵ－Ｓｃｄ n.Ｇｎ． TeOhysSed． GeoUcgicaIDlv．

2０Ｍｄ、MahmudulA1amandDaigoroHayashi

sedimentsaswelLThelesserHimalayansedimentsofthePrecambriantotheearly

Palaeozoicageshowmonotonousdepositionsandarebarreninfossilsexceptforafew

occurrencesofstromatolites・TheSub-HimalayanzoneislimitedbｙｔｈｅＭＢＴ（Main

BoundaryThrust）tothenorthalongthesouthernfootoftheMahabharatRange，ａｎｄ

ｔｈｅＭＦＴ（MainFrontalThrust）ｔｏｔｈｅｓｏｕｔｈａｔｔｈｅｓｏｕｔｈｅｍｅｄｇｅｏｆｔｈeSiwalikGroup・

TheLesserHimalayansedimentsthrｕｓｔｕｐｔｈｅＳｉｗａｌｉｋＧｒｏｕｐｏｆｔｈｅＳｕｂ－ＨimalayGLThe

sedimentsoftheGrouprepresentmolassedepositsresultedfromtherapidupheavalof

theHigherHimalayafromthelateTertiaryｔｏｔｈｅｅａｒｌｙＱuaternary・Thegrouphasalso

thrustoverthealluvialformationoftheGangeticsedimentsalongtheMFTwhichis

presentlyactivealongtheMBT．

１．１EUC山tioJzq/Himalqyq

Overtwohundredfiftymillionyearsago，India，Africa，Australia，andSouth

AmericawereallonecontinentcalledPangea・OverthenextseveraImillionyears，this

giantsoutherncontinentproceededtobreakup，formingthecontinentsweknowtoday・

Pangeaessentiallyturnedinsideout，theedgesoftheoldcontinentbecomingthecollision

zonesofnewcontinents・Africa，SouthAmerica，andAntarcticabegantofragment・

About60minionyearsago，wasthempidmovementofIndianorthwardtowardthe

contmentofEurasia,Indiachargedacrosstheequatoratｒａｔｅｓｏｆｕｐｔｏｌ５ｃｍ/yr.，inthe

processclosinganoceannamedTethysthELthadseparatedfragmentsofPangea・This

oceanisentirelygonetoday，althoughthesedimentaryrocksthaｔｓｅｔｔｌｅｄｏｎｉｔｓｏｃｅａｎ

ｆｌｏｏｒａｎｄｔｈｅvolcanoesthatfringeditsedgesreｍａｉｎｔｏｔｅｎｔｈｅｔａｌｅｏｆｉｔｓｅｘｉｓｔｅｎｃｅ・

ThelndiansubcontinentiSmovingtowardtherestofEurasianconｔｉｎｅｎｔａｔａｒａｔｅ

ｏｆａｂｏｕｔ５０ｍｍ/yr．（LePichon，1968,MinsteretaL，1974)．Therelativemotionof

thesetwocontinentalmassesduringthepast40m.y・apparentlyhascauseddeformation

throughoutmuChofcentralandeasternAsia，ａｎｄｔｈｅｃｒｅａｔｉｏｎｏｆｔｈｅＨｉｍａｌａｙａａｒｅonly

oneconsequenceofthisconvergence（MolnarandTapponnier,1975)．Intheearlytertiary

andoceanbasiｎＩａｙｂｅｔｗｅｅｎｌｎｄｉａａｎｄｔｈｅｒｅｓｔｏｆＥｕmsiaandwaspartofthelndian

plate、SubductionofthelndianplateoccurredalongthesouthernmarginoftheEurasian

continent,untilapproximately40to50m.ｙ・ago，whenthetwocontinentalmassescollided

witheachother（DeweyandBird,1970,LeFort,1975,PowellandConaghan,1973)．The

lowdensityofcrustalrockstogetherwiththemuchgreaterthicknessofcontinentalthan

oceaniccrustpresumablyrenderssimplesubductionofcontmentalcrustimpossible（Isacks

eta1.,1968,McKenzie,1969)．AsaresulttheconvergEnceofthetwocontinentalmasses

mustoccurbyprocessesotherthansubduction‐suchascrustalshorteningandmounｔａｉｎ

ｂｕｉｌｄｉｎｇａｓｉｎｔｈｅＨｉｍａｌａｙａｏｒｂylatera1movementsoflargeblocksalongstrikeslip

faultsandoutofthewayoftheimpingingcontinentsａｓｉｎｍｕｃｈｏｆｔｈｅｒｅｇｉonnorthof

theHimalaya（MolnarandTapponnier,1975,TapponnierandMolnar,1977)．

Foratleast80millionyearstheoceaniclndianP1atecontinueditsinexorablecollision

StressDistributionandFaultDevelopmentAroundNepalHimaLByabyMeansofFiniteElementMethod21

withsouthernAsia，includingTibet・Theheavyoceanfloornorthoflndiaactedlikea

giantanchor，plungingrapidlyintothemantle，anddraggingthelndiancontinentalong

withit，northward，towardsTibet、

Astheplatescollided，thesinkingoceanfloorgeneratedvolcanoesinsouthernTibet

becaｕｓｅｔｈｅｒｏｃｋａｔｔｈｅｔｏｐｏｆｔｈｅｄｅｓｃｅｎｄingplatemelted，fromfrictionandthehuge

pressureｓｏｆｃｏｌｌｉｓｉｏｎ・However，ｂｙ２５ｍｉｌｌｉｏｎｙｅａｒｓａｇｏｔｈｅｆａｓｔｍｏｖinglndiancontinent

hadalmostentirelyclosedovertheinterveningocean，squeezmgthesedimentsonthe

oceanfloor・Sincethesedimentswerelightweight，insteadofsinkingalongwiththe

plate，theycrumpledintomountainranges-theHimalayas・

ＢｙｌＯｍｉｌｌｉｏｎｙｅａｒｓａｇｏｔｈｅｔｗｏｃｏｎｔｉnentswereindirectcollisionandthelndian

continent，becauseofitsenormousquantityoflightquartz-richrocks，wasunableto

descendalongwiththeｒｅｓｔｏｆｔｈｅｌｎdianplate・Ｉｔｗａｓａｔａｂｏｕｔｔｈｉｓｔｉｍｅｔｈａｔｔｈｅ

ａｎｃhorchainmusthavebroken；thedescendinglndianplELtemayhavefallenoffand

foundereddeepintothemantle・A1thoughwedon'tfullyunderstandthemechanismof

whathappenednext，ｉｔ,sclearthatthelndiancontinentbegantobedrivenhorizontally

beneathTibetlikeagiantwedge，forcingTibetupwards・Tibet，meanwhile，isbehaving

likeagiantroadblockthatpreventstheHimalayafrommovingnorthward

TheHimalayanorganicｂｅｌｔｈａｓｌｏｎｇｂｅｅｎｒｅｇａｒｄｅｄａｓｔｈｅｗｏrldstandardofanor-

ganicbeltforｍｅｄｂｙｔｈｅｃｏｌｌｉｓｉｏｎｏｆｔｗｏｌａｒｇｅｃｏｎtinents（DeweyandBird，1970,

Windley,1984,1995)．Forthisreason,theHimalayanorganicbelthasbeeninvestigated

bymanyearthscientists,includinggeologists（Gansser,1964,Ｈａｓｈｉｍｏｔｏｅｔａ1.,1972,Ｌｅ

Ｆｏｒｔ，1975,Stocklin，1980,Sakai，1983,1985,ＣｏｌｃｈｅｎｅｔａＬ，1986,Ｓｅａｒｌｅｅｔａ1.,1987,

BurchfieletaL，1992)．AfterthecollisionbetweenthelndianandEurasiancontinents

duringtheEocene，thelargecrustalshorteningcausedbyconvergencewastakenupin

majorintercontinentalsubductionwhiｃｈｌｅａｄｔｏｔｈｅｆｏｒｍａｔｉｏｎｏｆｔｈｅＨｉｍａｌayanchain

(Pecher,1989)．AseriesofschematicdiagramBinFi9.3showingthetectonicevolution

oftheHimalayanMetamorphicbeltinNepaL

BasedonfieldandlaboratoryStudies，numericalmodelingofvariousaspectsof

continentalcollisionandensuingBubductionhasbeenachieved（EnglandandThompson，

1984,MolnarandTapponier，1975,Ｃｈｅｍｅｎｄａｅｔａ1.,1995)．Nevertheless，theorganic

processoftheHimalayamountainrangearenotyetfullyunderstood．

ＨＬｍｒｅｑﾉｫﾉＺｅＨｉｍｑＺｑｏ'α

Overperiodsof5-10millionyears，ｔｈｅｐｌａｔｅｓｗｉｌｌｃｏｎｔｉｎｕｅｔｏｍｏｖｅａｔｔhesame

rate，whichanowsustoforecastfairlyreliablyhowtheHimalayawindevelop・ＩｎｌＯ

ｍｉｌｌｉｏｎｙｅａｒｓｌｎｄｉａｗｉｌｌｐｌｏｗｉntoTibetafurtherl80km、Ｔｈｉｓｉｓａｂｏｕｔｔｈｅｗｉｄｔｈｏｆ

Ｎｅｐａｌ・BecauseNepal,sboundarieｓａｒｅｍａｒｋｓｏｎｔｈｅＨｉｍａｌａｙａｎｐｅａｋｓａｎdontheplains

oflndiawhoseconvergencewearemeasuring，Ｎｅpalwilltechnicallyceasetoexist・Ｂｕｔ

ｔｈｅｍｏｕｎｔａｉｎｒａｎｇｅｗｅｋｎｏｗａｓｔｈｅＨｉｍａｌａｙａｗｉｌｌｎｏｔｇｏａｗａｙ・Ｔｈｉｓｉｓｂｅｃａｕｓｅｔｈｅ

Ｍｄ・MahmudulA1amandDaigoroHayashi2２

(A）Ｃａ、６０Ｍa：Pre-colliSionstage

lndianplate…正dionaTymmpIex EumsianpIate

(B）Ｃａ、２０

Ｂｂ

5-11Ｍa：MountainBuildingstageに）

■■

ﾛﾛ

Present(D）

SchematicdiagramsshowingthetectonicevolutionoftheHimalayanMetamorphicbeltinNepal．（Ａ）sub-ductionofthelndiancontinent；（Ｂ）subhorizontalextrusionoftheHHSａｎｄｔｈｅＬＨＳｍｅｔａｍｏｒｐｈｉｃｕｎｉｔｓｂｙｓｙｎchronouspairednormalfaultingonthetopandreversefaulting（MCT）atthebottom・Ｔｅctonicjuxtapositionofthesemetamorphicunitsatmid-crustalleveL（C）＆（Ｄ）ｄｏｍｉｎｇｏｆａｌｌｔｈｅｓｅｔｈｒｅｅｕｎｉｔｓ，byjacking-upduetounderthrustingofthesub-Himalayas，andrelatedBecondaryhigh-anglenormalfaulting、ModifiedfromKaneko（1997)．

Ｆｉｇ．３．

StressDistributionandFaultDevelopmentAroundNepaIHimalayabyMeansofFiniteElementMethod23

Himalayawillprobablylookmuchthｅｓａｍｅｉｎｐｒｏｆｉｌｅｔｈｅｎａｓｉｔｄｏｅｓｎｏｗ･Therewill

betallmountainsinthenorth,smalleronesinthesouth,andthenorth/Southwidthof

theHimalayawillbetｈｅｓａｍｅ・WhELtwillhappenisthattheHimELlayawillhave

advancedacrossthelndianplateandtheTibetanplateauwillhavegrownbyaccretion・

ＯｎｅｏｆｔｈｅｆｅｗｃｌｕｅｓａｂｏｕｔｔｈｅｒａｔｅｏｆｃｏｌlisionbetweenlndiHandTibetbeforetheGPS

measurementsweremadeｗａｓｔｈｅｒａｔｅｏｆａｄｖａｎｃｅｏｆＨｉｍａｌａｙａｎsedimentsacrossthe

Gangesplain・Thereisanorderlyprogressionofsedimentsinfrontofthefoothills・

Largerbouldersappearfirst，followedbypebbles，andfurthersouth，sand-grains，siltS，

andfinallyveryfinemuds・ＴｈｉｓｉＢｗｈａｔｙｏｕｓｅｅｗｈｅｎｙｏｕｄｒｉｖｅｆromthelasthillsof

theHimalayasoｕｔｈｗａｒｄｌＯＯｋｍ、Thepresentisobvious，butthehistoricalrecordcannot

beseenonthesurfacebecausethesediｍｅｎｔｓｂｕｒｙａｌｌｆｏｒｍｅｒtracesofearliersediments

However，indrillholesintheGangesplain，ｔｈｅｃｏａｒｓｅｒｒｏｃｋｓａｒｅａｌｗａｙｓｏｎｔｈｅｔopand

thefinerpebblesandmudsareｏｎｔｈｅｂｏｔｔｏｍ，showingthattheHimalayaarerelentlessly

advancingonlndia．

Ｌ２ＺＯ"atioJLq／ｔｈｅＨＺｍｑＪｑｙａＳ

Ｆｏｒａｐｒｏｐｅｒstudy，itisnecessarytoclassifythevastareacoveredbythemountains

intosmallersub-sections・ThegeometriccrosssectionintheN-Sdirectionisalmost

similarthroughouttheHimalayas・

TheHimalayascanbeclassifiedinavarietyofways・Ｆｒｏｍｓｏｕｔｈｔｏnorth，the

mountainscanbegroupedintofourparallel,longitudinalmountainbelts（Gansser,1964)，

eachwithitsuniquefeaturesanddistinctivegeologicalhistory：

（ｉ）TheSubHimalayas

（ii）TheLesserHimalayas

（iii）TheHigherHimalayas

（iv）TheTethysHimalayas

1.2.ＩＺ１ｈｅＳｕｈＨＺｍａＺｑｙａｓ

ＦｏｒｍｉｎｇｔｈｅsouthernmostbeltoftheHimalayanrange，ｔｈｅＳｉｗａｌｉｋｓａｒｅａｌｓｏｔｈｅ

ｌｏｗｅｓｔａｎｄnarrowestrangeintheentireHimalayansystem，havinganaverageelevation

ofabout900‐１２００ｍａｎｄｉｎｐｌａｃｅｓ，ａｗｉｄｔｈｏｆｏｎｌｙｌ６ｋｍ・TheSiwaliksrisesteeply

fromthegreatnorthemplainsoflndiaandPakistanandrunparalleltothemainranges

oftheHimalayastowardsthenorth，fromwhichtheyareseparatedbyhighmountains

anddeepvalleys・TheSub-HimalayanzoneislimitedbytheMainBoundaryThrust

(ＭBT）tothenorthalongthesouthernfootoftheMahabharatRangeandtheMain

FrontalThrust（MFT）ｔｏｔｈｅｓｏｕｔｈａｔｔｈｅｓｏｕｔｈｅｒｎｅｄｇｅｏｆｔheSiwalik（Churia）Group・

TheLesserHimalayansedimentsthrｕｓｔｕｐｔｈｅＳｉｗａｌｉｋＧｒｏｕｐｏｆｔｈｅＳｕｂ－Ｈimalaya，The

sedimentsoftheGrouprepresentmolassedepositsresultedfromtherapidupheavalof

theHigherHimalayafromthelateTertiarytoearlyQuaternary、ＴｈｅＧｒｏｕｐｈａｓａｌｓｏ

Ｍｄ・MahmudulA1amandDaigoroHayashi2４

thrustoverthealluvialformationoftheGangeticsedimentsalongtheMFTwhichis

presentlyactivealongｗｉｔｈｔｈｅＭＢＴ．

1.2.2mheLesseF･HZmajCqyas

TheLesserHimalayaｓｈａｓｂｅｅｎｖａｒｉｏｕｓｌｙｎａｍｅｄｔｈｅＭａｉｎｃentralthrust（MCT）zone

andMidlandsedimentaryzone（Arita,1983),MidlandFormation（LeFord,1975),Lesser

Himalaya（Brunel，1986）andLesserHimalayanSequence（Kaneko，1994,1995)．Lying

betweentheHigherHimalayasｒｅｇｉｏｎｉｎｔｈｅｎｏｒｔｈａｎｄｔｈｅＳｉｗａｌｉｋｓｔｏｔｈｅｓｏｕｔｈ，the

LesserHimalayaregionformsthemiddlesectionoftheHimalayanmountainchain・

ＬｏｗｅｒｔｈａｎｔｈｅＨｉｇｈｅｒＨｉｍａｌａｙａｓｏｒｔheGreatHimalayas，thisregionhasanaverage

altitudeｏｆ３７００‐４５００mabovesealeveLItextendssoutheastfromPakistanandextends

throughlargepartsofthelndiansｔａｔｅｓｏｆＪａｍｍｕａｎｄＫａｓｈｍｉｒ，HimachalPradesh，

WesternUttarPradesh，NepalEmdtheNorth-EastemHimalayas・TheLesserHimalayan

zoneintheMidlandisadissectedhighlandborderedbytheMahabharatrangetothe

south，ｍａｄｅｕｐｏｆｔheLesserHimalayansedimentsandtheGondwanasedimentsaswelL

TheLesserHimalayansedimentsofthePrecambraintotheEarlyPalaeozoicageshow

monotonousdepositionsandarebarrenmfossilsexceptforafewoccurrencesof

stromatolites，whiletheGondwanasedimentsofthePalaeozoictotheEarlyTertiaryage

haveabundantfossilswhicharescatteredandexhibitanarrowdistributionalongfaults

insomeplaces・

TheupperpartoftheLesserHimalayanSequencerocksaremyloniticwithlocalized

foliation-parallelbandsofhighstrain・Therocktypesincludingpsammiticschist，augen

gneiss,phyllite，peliticschist，calc-silicateschist，marbel，siliceousschistandamphibolite．

L2.3Ｔ１ｈｅＨｉｇｌｂ”Ｈｉｍａｌｑｙａｓ

ＴｈｅＨｉｇｈｅｒＨｉｍａｌａｙａｓｉｓｂｏｕｎｄｅｄｔｏｔｈｅｓｏｕｔｈｂｙｔｈｅＭａincentralthrust（which

separatesitfromtheLesserHimalayansequence）ａｎｄｔｏｔｈｅｎｏｒｔｈｂｙｔｈｅＳｏｕｔｈＴｉｂｅｔａｎ

detachmentsystem・TheSouthTibetandetachmentsystem，aseriesofnormalfaultson

thenorthernflankoftheHimalaya，formsthecontactbetweentheTibetanTetyessediment

andunderlyingHigherHimalayanSequence（Burchfieleta1.,1992,BurgChen,1984,Richard

andJeffrey，1993,HashimotoetaL，1973)．TheHigherHimalayahasbeenvariously

namedHimalayanGneisszone（Arita,1983),Tibetanslab（LeFord,1975,Ｂｏｒｄｅｔｅｔａ1.,

1971)，andHigherHimalayanSequence（Kaneko，1994,1995)，UpperCrystallineNappe

(Fuchs＆Frank，1970)，KathmanduNappesandKhunbuNappes（Hagenl969)．The

northernmost，longestandthemostcontinuousbeltintheHimalayansystem，theHigher

HimalayanbeltformsthebackboneoftheHimalayas・Ｌｙｉｎｇｗｅｌｌａｂｏｖｅｔｈｅｓｎｏｗｌｉｎｅ

ｗｉｔｈａnaverageelevationofabout6100m（20,000ｆｔ)，theHigherHimalayadominates

theextremenorthernfrontiersoflndiaandtheentirenorthernboundaryofＮｅｐａＬＩｔ

ｒｉｓｅｓｔｏｉｔｓｍａｘｉｍｕｍｈｅｉｇｈｔinNepalcontainingnineofthefourteenhighestpeaksin

StressDistributionandFaultDevelopmentAroundNepalHimaIayabyMeansofFiniteElememtMethod25

theworld，ａｌｌａｂｏｖｅ８０００ｍａｂｏｖｅｓｅａｌｅｖｅＬＴｈｅｕpperpartsofthesemountainsare

formedbytheTethyssedimentswhichareunderlainbytheCentralCrystallinec⑨mposed

ofhighgrademetamorphicrock・BoththesedimentsandgneissesthrustuptheLesser

HimalayansedimentsalongtheMainCentralThrusｔ（MCT),whichappearstobeoneof

thesignificanttectonicboundariesthroughouttheHimalayas・Bothgroupshaveslipped

andspreadｏｖｅｒｔｈｅＭＣＴｔｏｔｈｅｓｏｕｔｈｐｒｏｄｕｃｉｎｇｎappeandklippeontheLesserHimalayan

sedimentsintheMidlnnd

1.2.4ＴﾉieLthysHZmcMqycLs

lntheTibetanHimalayanzone，theTethyssedimentsofthePalaeozoictotheearly

CenozoicagearedistributedalongthesouthemmostmarginofthehugeTibetanTethys

basin,suchastheSagarmatharegion,theLangu-Manangbasin，theSaipal‐Amlangbasin，

theSpitibasinaｎｄｔｈｅＫａｓｈｉｍｉｒｂａｓｉｎｗｈｉｃｈｉｓｕnderlainbyavastamountofgranite

bodies・ThenorthernborderoftheTethyssedimentsisrepresentedbyafaultzonewhich

stretchesalongthelndusandTsangporiversIreferredtoasthelndus-TsangpoSuture，

whichsignifiesthecollisiontraceofthelndiansubcontinentwithEurasia・Ｓｏｍｅｔｉｍｅ

ａｇｏ，theGondwanasedimentsattributedtothelndiansubcontinentwerereportedfrom

thearealyingtothenortｈｏｆｔｈｅｓｕｔｕｒｅｚｏｎｅ・Iti8possiblethatanothercollisiontrace

ofthecontinentsolderthanthelndus-TsangpoSutureexists．

L3Lithostmtigmpﾉｉｙｑ／1VbpaZHjmalqya

Accordingtothegeologistandgeophysiciststhosewhosuweyedandtillnow

engagedindifferentpartsofNepalHimalaya，suchasArita，HayashiandYoshida

(1982)，Ｓａｋｏｅｔａｌ．（1968)，Hashimotoetal．（1973)，Hagen（1969)，Fuchs＆Franｋ

(1970),Gansser（1964),Ｂｏｒｄｅｔｅｔａｌ.（1971),surveyedthePokhara-Piuthanarea,Central

Nepal；Ｋａｎｏ（1977,1980＆1982)，ＰｅｃｈｅｒａｎｄＬｅＦｏｒｔ（1977),surveyedthemaincentral

thrustzoneoftheAnnapumaRange,CentralNepal；Arita＆Yoshida（1982),ＳａｋｏｅｔａＬ

(1968)，Hashimotoetal．（1973)，Hagen（1969)，Fuchs＆Frank（1970)，surveyedthe

Ramdighat,CentralNepal;Yoshida＆Arita（1982),Wadia（1975),Tandon（1976),Tandon

andNarayan（1981)，Ｏｐｄｙｋｅｅｔａｌ．（1979)，ＪｏｈｎｓｏｎｅｔａＬ（1979)，Gill(1952)，Gansser

(1964)，Powel＆Conaghan（1973)，Siwalikrange，CentralNepal；Iwata，Yamanaka＆

Yoshida（1982)，Hazen（1968)，Ｂｏｒｄｅｔｅｔａｌ．（1971)，ＬｅＦｏｒｔ（1976)，Takkholaregion，

CentralHimalaya；Yamanaka＆Iwata（1982)，Hiroshima（1976)，ＳｈａｒｍａｅｔａＬ（1980)，

Hagen（1969),ＬｅＦｏｒｔ（1976),MiddleKaliGandakiandMarsyandikhola,CentralNepal；

Yamanaka,Yoshida＆Arita(1982),Horman(1974),Hagen（1969),PokharaVally,Central

Nepal；Yokoyama＆Ｏｍｕｒａ（1982)，DanaandKerabari,CentralNepal；Kamada，Arita

＆Yoshida(1982),Ｒｅｅｄ(1908),Arkell（1965),Hagen（1968),Ｂｏｒｄｅｔｅｔａｌ.（1971),Gansser

(1964)andRyf(1962),Muktinathregion,CentralNepal；thelithostatigraphyoftheNepal

Hｉｍａｌａｙａｃａｎｂｅｓｕｍｍａｒｉｚｅｄｉｎｔｈｅｆｏｌlowingtable‐

2６Ｍｄ、MahmudulA1amandDaigoroHayashi

TableLGeologicalunitsandageofrocksinNepalHimalELya（Gansser，1964,1983,Valdia，1980,SinhiandRoy，1982)．

Ｚｏｎｅ

1.3.ＪＳｉｕ,ａＺｉｈ（Churm）GroUp

TheChuriagroupcanbedividedonthebasisoflithologicnatureintothreeparts，

i､e､，ｔｈｅlower，themiddleandtheupperformations・ThreedivisionsoftheChuria

groupｗｅｒｅａｌｓｏａｔｔｅｍｐｔｅｄｂｙｌｔｉｈａｒａｅｔａＬ（1972)，Hagen（1969)，Wadia（1975)，Ｗｅｓｔ

ｅｔａｌ.，（1978＆1981)，GlennieandZiegler（1964）dividedtheSiwaliksinNepalintothe

lower“sandstoneFacies，，ａｎｄｔｈｅｕｐｐｅｒ“ConglomerateFacies"、

Thelowerformationconsistsofirregularlyalternatingbedsofmuddy，ｆｉｎｅsand‐

stoneandsiltstone、Variegatedsiltstonesandcoaly，blacksiltstonesareintercalated

frequently．Ｓandstoneismoderatelyindurated

Themiddleformationconsistsmainlyofthickbeddedmassivesandstoneand

subordinatelyofsiltstoneandthin-beddedalternationofsandstoneandsiltstone、

Variegatedsiltstone，irregular-bedded，aresometimesintercalated・Sandstoneisless

indurated，ｍｅ｡iumtosometimescoarse-grainedwhiterockwithblackspecks（mostlyof

biotite)，showingasalt-and-pepperappearance・Therearealsofoundwell-consolidated

calcareoussandstonebedswhichexhibitsomeconcretionarystructures・Sandstoneis

abundantinmica，rareinclaymatrixandpartlycalcite-cemented，belongingtolithic

arenite・

Theupperformationiscomposedpredominantlyofgravelbedsandsubordinatelyof

sandandsiltlayersMostlytheyareunconsolidated・Wellconsolidatedcalcareoussand‐

stonebedsarerarelyfoundintheupperpart・Gravelsrangeinsizefrompebbletoboulder

andcobblegravelsarecommoｎＡｃｃｏｒｄｉｎｇｔｏＡｒｉｔａｅｔａＬ（1984,ArjunKhola,Jajarkot-

Piuthanarea）ｔｈｅｌｏｗｅｒｐａｒｔｏｆｔｈｅＣｈｕｒｉａＧｒｏｕｐｃｏnsistsmainlyof“brickcolored'，

fine‐tomedium-grainedsandstoneandcontainssomeintercalationsofmuscovite-bearing

coarsed-grainedsandstone・Ｔｈｅｍｉｄｄｌｅｐａｒｔｉｓｍａｄｅｕｐｏｆｔｈｅｆｉｎｅ‐tomedium-grained

calcareoussandstoneinthelowerportionandtofine-tomedium-gramedbrickcolored

mottledsandstoneintheupperportion・Theupperpartislargelycomposedofconglomerate．

Himalaya Zone Group Geologicalageofrocks

SｕｂＨｉｍａｌａｙａ MainBoundaryThrust

Siwalik TertiarytoQuarternarymolasgesedimentS

LesserHimalaya MninCentral

Thrust

MidIHnd MainlyEocambrianclasticsedimentswithlimestoneandquartzite，mostlyalteredtophylliteandmetasandstone

HigherHimalaya Unconformity HimalayanGneiss RejuvenatedPrecambrianbasement，

mostlypolymetamorphosedandmigmatizedattheA1pinestagebytheintrusionoftourmalinegranites

TibetanHimalaya Indus-TsangpoSuture

TibetanTethｙｓ MainlylowerPaleozoictoMesozoicclasticandc2lcareoussediments

StressDistributionandFaultDevelopmentAroundNepalHimB1ayabyMeBnBoIFiniteElementMethod27

Sub-angulartosub-roundandpebUe‐tocobble-sizegravelsconsistsofbrick，greyand

whitechertyquartziteconsistsofgreylimestoneandcalcareoussandstoneandblack

shalyslate・

IntheKarnali-Bherireglon，sandstone，mudstone，conglomirateandlimestoneare●

found（Hayashi,FujiilYoneshiro,＆Kizaki,1984,Va1diya,1977-78,1982,Fuchs＆FrBLnk，

1970,Fuchs，1977,80,andBashya，1981)．

1.3.2ＭｉｃＪＺｃｍｄｇｍｕｐ

Ｔｈｅｇｒｏｕｐｉｓｒｏｕｇｈｌｙdividedintotwosub-groups；thequartziteandsandstonesub‐

groupandthesandstoneandphyllitesubgroup（Kawamitsu＆Hayashi,1991,Annapuma

region)．

Thequartziteandsandstonesubgroupismainlycomposedofquartzitewithsand‐

stoneinterbeds・Thequartziteiswhiteincolor，includingmuscovite，biotiteandplagio‐

clase、Crenulationcleavagesa”shownonbeddingplanea

ThesandstoneandphyllitesubgroupismainlyexposedintheMidlandarea・The

groupconsistsmainlyofbiotitebearingblackphyllitewithquartzveinS，Crenulation

cleavagesandkinkfoldsareseenonbeddingplBLnes，

AccordingtoAritaetaL（1984,Jajarkot-Piuthanarea),Sakai(1982-84,Tansenarea)，

Gansser,1964,Hagen，1969,Ｈａｓｈｉｍｏｔｏｅｔａ1.,1973ａｎｄＦｕｃｈｓ＆Frank，１９７０（Jajarkot

area)，Garnet-mica-chloritephylliteschist，black-greenphyllite，crystallinelimestone，

blastomyloniticaugengneiss，１imestone，dolomite，calcareoussandstonearefoundinthe

JajarkotCrystallineklippe・Quartz,sand8tone,greenphyllite,blackphyllite,slate,shale，

dolomite，limestoneandcalcareousshale，conglomerateandamphibolitearefoundinthe

Dunaihi,MaikotandRoli-Sallyanarea、AndQuartz，sandstone，shale，dolomite，ｌｉｍｅ‐

stoneandvariegatedrocksarefoundinthePiuthan，Musikot，DalliandDhorpatanzone・

BlastomyloniticaugengneissesalsｏｏｂｓｅｗｅｄｏｎｔｈｅＢｈｅririverjustsouthofJajarkot

(HayashietaL，1984)．

Phyllite，quartzite/quartz-conglomerate，siliceoussandstone，amphibolite，１imestone

andslatearefoundintheKarnali-Bheriregion（Hayashi,Fujii，Yoneshiro，andKizaki，

1984,Valdiya，1977-78,1982,FuchsandFrank,1970,Fuchs,1977,80,andBashya,1981)．

１.ａ３ＭｂｚｍＯｅ"tｍＪＺＶｉｍｓｔＧｍＵｐ（ＭＣＴＧｍＵｐ）

Ｔｈｅgrouphasinsertedandconsistsoftheblackandgreenphynitesubgroup，augen

gneisslsubgroup，amphibolitesubgroup，quartzitesubgroupandcalcariousphylliteschist

subgroup（Kawamitsu＆Hayashi，1991,Annapurnaregion)．

Theblackandgreenphyllitesubgroｕｐｉｓｃｏｍｍｏｎｌｙｅｘｐｏｓｅｄｉｎｔｈｅａｒｅａａｎｄｉｓｃｏｍ‐

posedofbiotite-graphite-phyllite，wavygreenphylliteandbiotite-chloritephylliticschist

withorwithoutgamet，Thephylliticschistischaracterizedbywavymicaceouslayers

withirregularfoldedlenticularquartzaggregates・Thetypicalmineralassemblageis

ＭｄMahmudulA1amandDaigoroHayashi2８

garnet-biotite-muscovite-Kfeldspar-plagioclase-quartz・

TheaugengneisslsubgroupisseenatUnerialongtheKaliGondakiriver・The

augengneissconsistsofmediumtocoarse-grainedminerals・Theaugenstructurecom‐

prisesKfeldspar-porphyroblastsand/orporphyroclasts、ＴｈｅｇｎｅｉｓｓｗａｓcalledUlleri

augengneissbyLeFort・Therepresentativemineralassemblageisbiotite-muscovite-K‐

feldspar-plagioclase-quartz・Theamphibolitesubgroup；severalamphibolitesheetsareplaced

betweenthelowerandmiddleparｔｓｏｆｔｈｅＭＣＴｇｒｏｕｐ、Typicalmineralassemblageis

hornblend-biotite-quartz-Kfeldspar・

Thequartzitesubgroup；afewquartzitelayersareplacedbetweenthemiddlehori‐

ｚｏｎｓｏｆｔｈｅＭＣＴｇｒｏｕｐａｌｏｎｇｔｈｅＫａｌｉＧandakiandModiKholarivers・Thecolorsofthe

quartzitesarewhite，bluishgreyandgreen・Thesequartzitearefinetomedium-grained

sandsize，includingthinmicaceouslayers・Thecalcareousphyllite-schistsubgroupis

exposedclosetotheupperＭＣＴ・

Limestone，garnettwomica-schist/quartzite，granitearefoundintheKarnali-Bheri

region（HayaShi，Fujii,Yoneshiro,andKizaki，1984,Valdiya，1977-78,1982,Fuchsand

Frank，1970,Fuchs,1977,80,andBashya，1981)．

1.3.4Hinml町aJzGFzeiSsGroUp

ThegroupconsistsofvariouskindsofgneissesandthrustsovertheMCTgroup

alongtheupperMCT、Ｔｈｅｇｒｏｕｐｉｓｂａｓｅｄｏｎｔｈｅｆｉｅｌｄｓｕｗｅｙ，dividedintothreesub‐

groups；gneissl，gneissllandaugengneissllsubgroups（Kawamitsu＆Hayashi，1991,

Annapurnaregion)．Structureofthesegneissesisgenerallyconcordantwiththatofthe

upperMCm

Thegneisslsubgroup；basalpartoftheHimalayanGneissgroupiscomposedofthe

gneisslsubgroup，whichisrepresentedbythealternationofpeliticandpsammiticgneisses

Thepeliticgneisspossessesmediumtocoarse-grainedminerals，especiallygarnet，while

thepsammiticgneissconsistsoffine-grainedparticles・Thetypicalmineralassemblage

isgarnet-biotite-muscovite-Kfeldspar-plagioclase-quartz・

Thegneissllsubgroupiscomposedoffinetomediumgrainedcalc-silicategneissand

overliesthegneisslsubgroup、Thetypicalmineralassemblageisbiotite-muscovite‐

kyanite-calcite-plagioclase-quartz・

Theaugengneissllsubgroupwhichiscomposedofmigmaticgneisswithaugenstructure，

occupiestheupperpartoftheHimalayanGneissgroup、Thetypicalmineralassemblage

isbiotite-muscovite-Kfeldspar-quartz

AccordingtoSakai（1982-84,Tansenarea),Gansser,1964,Hagen,1969,Hashimotoet

a1.,1973ａｎｄＦｕｃｈｓ＆Frank（1970,Jajarkotarea),thebasalpartofthegneissesconsists

ofmylonitizegneissincludingcrushedgarnetporphyroblastsandisfollowedbythekyanite‐

garnet-micagneiss・Ｔｈｅ“argillo-arenaceous，,gneissgraduallygradeupwardintocalcareous

gneissesofthemiddlecalcareousgneissesinthenortheast、AccordinｇｔｏＡｒｉｔａｅｔａＬ

StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFiniteElementMethod29

(1984,JajarkotDailekh-Raraarea),theHimalayangneissesaremadeupofgarnet-mica

gneiss，kyanite-garnet-micagneiss，siliceousgneissandcalcareousgneiss、

Migmatitegneiss，Augengneiss，calc-siliceousgneiss，gametbiotitegneissarefound

intheKarnali-Bheriregion（Hayashi,Fujii,Yoneshiro,andKizaki,1984,Valdiya，1977‐

78,1982,Fuchs＆Frank，1970,Fuchs，1977,80,andBashya,1981)．

1.3.5Ti6etα〃TbﾋﾞﾉｈｙｓＧｍｕｐ

Ｔｈｅｇｒｏｕｐｉｓｃｏｍｐｏｓｅｄｏｆｔｈｅcrystallinelimestonesubgroupandthealternationof

quartziteandmudstonesubgroup（Kawamitsu＆Hayashi,1991,Annapurnaregion)．The

groupoverliestheHimalayanGneissgroupandseemstobeintenselydeformedThe

groupiscalledtheLarjungFormationbyBordetetal.（1980)．

Thecrystaninelimestonesubgroup；basalpartoftheTibetanTethysgrouplsrepre‐

sentedbythenonfossiliferouscrystallinelimestonesubgroup、Thealternationofquartzite

andmudstonesubgroupoverliesthecrystallinelimestonesubgroup・

ThesedimentaryrocksoftheTibetanTethysbasinextendfromthehighestpartof

thegreatHimalayastothenorthintheChineseTibetanterritory,overlyingtheHimalayan

gneisseswhicharethrustedsouthwardsontotheMidlandmetasediments、Therocksof

thisbasindiscussedsepamtelyfromtheMidlandmeta-sedimentarybasinandtectonic

unitsindependentfromthoseoftheMidland（Hagen，１９６９andFuchs'1967)．Rocks

foundintheKaliGandaki，ShishaPangma，SagarmathaandDhaulagiriareaareimpure

limestone，dolomite，argillaceousandcalcareouspelitCs・

ThecalcareousschistisfoundintheKarnali-Bheriregion（Hayashi,Fujii,Yoneshiro，

andKizaki，1984,Valdiya，1977-78,1982,Fuchs＆Frank，1970,Fuchs，1977,1980,and

Bashya，1981)．

２．NumericalSimuIation

2・ＩＦＶｉ几iteEZeme"ｔＭｅｔｂｏｄ（FEⅢ）

Finiteelementmethodisawellknowｎｍｅｔｈｏｄｂｒｏａｄｌｙｕｓｉｎｇｉｎｍｏｓｔｏｆｔｈｅbranches

ofappliedsciences，Engineering，MedicalsciencesoreveninEconomics・Itisalsorapidly

usingfornumericalcalculationinstructuralgeologyandtectonics、

Anadequatemodelisobtainedusingafinitenumberofwelldefinedcomponentsin

manysituationsandsuchproblemisknownasdiscrete・Inotherwords，thesubdivision

iscontinuedindefinitelyandthisleadstodifferentialequationsorequivalentstatements

whichimplyaninfinitenumberｏｆｅｌｅｍｅｎｔｓａｎｄｓｕｃｈｓｙｓｔｅｍｉｓｔｅｒｍｅdascontinuous・

Ａｓｔｈｅｃapacityofallthecomputersisfinite，discreteproblemcanbesolvedreadily

(evenifthesamplesizeislarge）butcontinuousproblemcanonlybesolvedexactlyby

mathematicalmanipulation・Thefirsthavedevelopedgeneraltechniquesapplieddirectly

todifferentialequationsgoverningtheproblemsuchasfinitedifferenceapproximation

(Ｒ､Ｖ・Southwell，1946,,.Ｎ・ＤＥ・GA11en，1955)，variousweightedresidualprocedures

3０Ｍｄ、MahmudulA1amandDaigoroHayashi

(S､Ｈ・Crandall,1956,Ｂ・AFinlayson，1972)．Inthefieldofsolidmechanics,reasonably

goodsolutiontoacontinuumproblemcanbeobtainedbysubstitutingsmallportions

(elements）ofthecontinuumbyanarrangementofsimpleelasticbars（McHenry，1943,

Itrenikoff,1941,Newmark,1949,Argyris,1960,Turnereta1.,1956)．C1ough(1960)appears

tobethefirstterm“finiteelementmethod"･

Thecivilengineerandstructuralgeologistsaredealingwiththestructuresfirst

calculatestheforce-displacementrelationshipforeachelementofthestructureandthen

proceedstoassemblethewholefollowingawelldefinedprocedureofestablishinglocal

equilibriumateach“､ode”orconnectingpointofthestmcture・Fromsuchequations

thesolutionsoftheunknowndisplacementsbecomespossible・

Thefiniteelementprocessasamethodofapproximationtocontinuumproblems，the

followingstepssufficetodescribethisapproach：

（ｉ）Dividethecontinuumintoafinitenumbersofsubgroups（orelements）ｏｆｓｉｍｐｌｅ

ｇｅｏｍｅｔｒｙ（triangles,rectanglesandsoon)．

(ii）Ｓｅｌｅｃｔｋｅｙｐｏｉｎｔｓｏｎｔｈｅｅｌｅｍｅｎｔｓｔｏserveasnodes,whereconditionsofequilibrium

andcompatibilityaretobeenforced．

(iii）AssumedisplacementfunctionswithineachelementsothatthediSplacementsat

eachgenericpointaredependentuponnodalvalues．

(iv）Satisfystrain-displacementandstress-strainrelationshipswithinatypicalelement．

（ｖ）Determinestuffinessandequivalentnodalloadsforatypicalelementusingworkor

energyprinciples．

(vi）Developequilibriumequationsforｔｈｅｎodesofthediscretizedcontinuumi、terms

oftheelementcontributions

(vii）Solvetheseequilibriumequationsforthenodaldisplacements．

(掴）Calculatestressesatselectedpointswithintheelements．

（ix）Determinesupportreactionsatrestrainednodesifdesired

TheprimarydisadvantageofthismethodiStodiscretizationofthedifferential

equationsforwhichtheboundaryconditionsaredifficulttosatisfy・Aseconddisadvantage

isthataccuracyoftheresultsisusuallypoor，

Thispotionhavebeenchosenfromthｅｐａｐｅｒ（HayashiandKizaki,1972）toexplain

theFEMforelasticity・Thenumericaltreatmentofthegeologicalprocesshasalready

beenadvancedinthemodernstructuralgeologyaswellasintherockmechanics、Since

thegeologicalprocess，however，areconspicuouslyslowphenomenaandhistories，ｉｔｉｓ

ｒｅquiredinthenumericalanalysiscarefullytotakeaccountofthephenomenaandhistory

ofthegeologicalstructuraAnattemptwasmadeinthisstudytoanalyzethestress

distributionsintheNepalHimalayaregionｂｙｍｅａｎｓｏｆＦＥＭ・InperformingtheFEM

analysis，itisassumedthatthegeologicalmaterialsinvolvingintheanalysisarehoｍｏ‐

geneousandperfectlyelastic，althoughitiscertainthatthegeologicalrockbodymust

beregardedasvisco-elasticbodyasalreadymentionedbyUemura，Ｔ・（1971)，Ito，Ｈ、

StressDistributionandFaultDevelopmontAroundNepalHimalayabyMeansofFiniteElementMethod31

(1972）ａｎｄothers、ThhBmaymaketheresultsdifferfromthetrueoncertainpointsbut

itwouldbeconsideredtobeanapproachtothebetterunderstandingofthenature・

Foratypicalelement（Fig.４),assuminghomogeneousstresswithintheelement,ｔｈｅ

Ｖ

Ｘ

Ｆｉｇ．４．Atriangularfiniteelement・

vectorofnodaldisplacementsuBeandthevectorofnodalforcesF・canbeexpressinmatrix

formas；

凡凡鴎脇堅脇

周一I|‐ (1)，Ⅳ．－皿ｅ＝

Bycontinuityofdisplacementwithintheelementandwithadjacentelements，a

displacementfunctionoftwolinearpolynomialscanbechosenforthecaseoftwo

dimensions・Soitcanberepresentedasfollows；

嶢':j=[:::::}'１ (2)

ｕ：innerdisplacementvector

Eq2maybｅｗｒｉｔｔｅｎｉｎｔｈｅｆｏｒｍａｓ；

、〕□Ⅱワ□ｎ』ｑⅡ⑪

ａαロ。、。、Ｕ●、

←[;iiiI::］ (3)＝［R']･ａ

Ｍｄ、MahmudulA1amandDaigoroHayashi3２

Thereforethevectorofnodaldisplａｃｅｍｅｎｔｉｓｌ遁tedasaproductofmatrixandvector．

臼 (4).α＝［Ｒ]･ａ虹ｃ＝

[Ｒ］：shapefunctionmatrix；α：generalizeddisplacementvector・

ＵｓｉｎｇＪｒｉＵｌｆｏｒｔｈｅｘ‐ａｎｄｙ‐coordinateatthenodalpointi，theshapefunctionmatrix

[RJatthepointisrepresentedby;

皿-[;:ｉｌ:Ｊ…（`’Foreq4thegeneralizeddisplacemeｎｔｖｅｃｔｏｒａａｒｅｇｉｖｅｎｂｙ

α＝［Ｒ]-1.88゜（６）

勾翰輪

１１１

眺眺鮪

theinversematrix［Ｒ]-1willbeexpressed；Using△ｆｏｒ

訂巫詞

０００△△△△

△△△０００

１２３

１１１

０００△△△△

０２３

１１０

副漣海

０００△△△

、浬濁

△△△０００

則鐘詞

△△△０００

[R]－１＝上△

(7)

where△ｅｑｕａｌｓｔｏｔｗｏｔｉｍｅｓａｒｅａｏｆｔｈｅｔｒｉａｎgleelementsand△ｄｉｉｓｔｈｅｃｏｆａｃｔｏｒｏｆｉ，

'…･…｡…･…'…-に|………………。innerdisplacementofthetriangleisequatedasfollows；

秘＝［Ｒ'].α （８）

＝［R'].[R']-1.88.

Ｎowstrainvectoreisrepresentedas；

一日＋

-ＩｉＩＩ叶馴。＝［B]･[Ｒ]-1.㎡

(9)

StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFinitenlementMethod33

Wherethematrix［B］iscalledthestrain-generalizeddisplacementmatrixanditscompo‐

nentsarenotfunctionsofvariableｓｘａｎｄｙ，ｓｏｔｈａｔｏｎｅｃａｎｓｅｅｔｈａｔｔｈｅｓｔｒａｉｎｉｓ

constantineachelement・

Therelationofstressvectorpandstrainvectoreis；

一日

'Ｐｌｗ１

Ｅ(１－"）⑩１０

１－２ｙ

Ｏ２(１－ｼ）

(1＋"）（1-2ｼ）

0

＝［Ｋ]･e

WhereyisthePoisson'８ratio,EistheYoung，smodulusand［Ｋ］isthestress-strain

matrix・ＥｑｌＯｉｓｖａｌｉｄｆｏｒｔｈｅｃａＳｅｏｆｐｌａｎｅｓｔrain、

Letthevirtualdisplacementbeoz函whentheelementisdeformed，thestrainenergyUof

thiselementiｓｇｉｖｅｎｂＷ

Ｕ＝J上．〃｡ｖ

＝ル．)T･[K]･ｅａｖ

＝Ｌ(灘..)γ･([R]-1)『･[B]『･[X]･[B]･[R]-1ＷＶ

＝い゛.)T･[B･]『･[K]･[B､]･[R]-1W・dVwhere［Ｂ､］ｉｓｅｑｕａｌｔｏ［Ｂ､］[R]~Ｉａｎｄｇ･isthevectorofvirtualstrain・

Asthenodalforcesarealreadydefiｎｅｄｂｙｅｑ、１，theexternalworkis：

ｗ＝（皿.｡)了･Ｆｏ

Ａｎｄｔｈｅｓｔｒａｉｎｅｎｅｒｇｙｉｓｅｑｕａltotheexternalwork，sothatthefonowingequation

holds．

(u､｡)『･F｡＝J,(卿.霞)『･[B・]ｱ･[K]･[B・]･灘｡｡Ｖ

＝(鰹..)了(L[B・]?.[K]･[B・]｡v)･拠・Ｗｈｉｌｅｔｈｅｖｅｃｔｏｒｏｆｎｏｄａｌｆｏｒｃｅｉｓｒｅpresentedby；

F`＝{J鋤[B､丁･[K]･[B・]｡v}･灘.｝Ｎｏｗ，ｔｈｅstiffnessequationisobtained

F．＝［Ａ]･rwhereAiscalledthestiffnessmatｒｉｘａｎｄｃａｎｂｅｗｒｉｔｔｅｎｉｎｔｈｅｆｏｒｍ；

Ａ＝{L[B･]『.[K].[B･]｡V｝Ｉｎｔｈｉｓｃａｓｅ，eachmatrixisconstantintheelement，thentheproductofmatricesi.e・

［β・]T･[Ｋ]･[B・］，isconstant，Consequently,ｉｔｉｓｐｏｓｓｉｂｌｅｔｏｔａｋｅｏｆｆｔheintegralmark，

Ａ＝［Ｂ･]T･[Ｘ]･[Ｂ･]｡Ｖ，ｗｈｅｒｅＶｉｓｔｈｅｖｏｌｕｍｅｏｆｔｈｅｅｌｅｍｅｎｔ．

3４Ｍｄ・MahmudulAlamandDaigoroHayashi

Bysolvingtheabovestiffnessmatrix，onecangetundecidednodalforcesandnodal

displacementsforeveryelement・Moreove】P，usingthesenodaldisp1acements，thevalues

ofstressandstmincouldbeobtained・FurtheranddetaileddisclI息QinnsonFEMare

referredtosuchpublicationsasZienkiewiｃｚｅｔａｌ．（1967）ａｎｄｓｏｆｏｒｔｈ．

2.2ＭbdbZing

Fourdifferentcrosssectionsareusedtojustifytheeffectofmaterialpmpertiesof

rockformationsappliedonthesecrosssections・Referringpaperswhichwerepublished

duringl979tol999，wehaveselectedthesecrosssectionsforfourmodelstoverifythe

adequatestressdistributionandfaultdevelopmentamongthemodels・Thefourcross

sectionsaretypicalfortheprofileofNepalHimalaya．

》》》ｖ》

。ｑｕ

岫岬》一一一ｎ頤、》》一一叩くⅧ”騒騒』ＤＤｖａ１，

》》》》ｎｏ

ｓｏ１

・に此

□圏露■

冗罪ｅ３

叩醍

７ｒ

ｐｃ

７の（巴

。》・伽吻汕

ｏＰ１ｎ

２Ｔ

’とい－N齢…圖

F…EIF鷲鵠瀞鉗Ｉｌｉｆ:RHI:１.醗職綴粥隠麓:fi：iRl;M;VModifi.｡…S…

(ii）Model‐２

ｕ■

０

ｍｌｎＵＣ『］｛０丘一》｛Ｕで

ｍｌｓ叱る皿Ⅲ己必罰

Ｓ

Ｏｋｍ

－５

・１０

・1５

Ｓ

Ｆｉｇ．６．GeologicalsectionacrossthecentralHimalayaofNepal・ModifiedfromBrunel（1986)，Ｐａｎｄｅｙｅｔａｌ．（1999)．

StressDistribuIionandFaultDevelopmentAroundNepalHimalayabyMeanSofFiniteEIementMethod35

(iii）Model‐３（Ａ）

ＴＴＳ

Ｆｉｇ．７．PresentstageofthegeologicalcrosssectionfOrthetectonicevalutionoftheHimalayanMetamorphicbeltincentralNepaLModlfiedfromKaneko（1997)．

(iV）Model‐３（B）

－しteCtoSPbCre

Fig.８．Mountambuildingstage（5-11Ｍa）ofthegeologicalcrosssectionforthetectonicevalutionoftheHimalayanMetamorphicbeltincentralNepal・ModifiedfromKaneko（1997)．

Thegeometryofallthecross-sectiｏｎｓａｒｅｍｏｒｅｏｒｌｅｓｓｓａｍｅａｌｔｈｏｕｇｈｅａchhasbeen

takenfromdifferentphenomenon・ItisdifficulttodistinguishtherochSbelongingto

thelayeraccordingtotheirgeologicalmeaning・Ａｎｕｍｂｅｒｏｆｒｏｃｋｓｂｅｌｏｎｇｔｏｔｈｅｌａｙｅｒs

canbeselectedinthefollowingformula

()‐〃！

⑪AC!("－k)！

ｗｈｅｒｅｎｉｓｔｈｅｎｕｍｂｅｒｏｆｒｏｃｋｓｂｅｌｏｎｇｉｎｇｔｏｔｈｅｌａｙｅｒａｎｄｋｉｓｔｈｅｎｕｍｂｅｒｏｆlayer

(､＞k)．

Thefollowingtablesareshowingthematerialpropertiesfordifferentmodels

Table2、MaterialpropertiesofModel-1ＣｈＥＢｉｎＭＰａ

、ﾛ■■、ｎ日■

ｒｎｕＤ iiiiM2Ｆ面Euﾛ⑥ｎ

ｎｎｇＩｅｄＢ歴Ｂ

ＬｉＬｈｏｌＤｇｙＬｒａｔＩｇｒＢｐＵＥｕｎＩ

ｇｎｎｄＢｔｏｎＢＳｉｌぃnnmEMuu北tｎｍＲ

曰､。■ＬｏｎＢｉｍ蕗hｎｎＢ

ｌ空目亜ｒ

Ｈｉｍｍａ

MmbEl

GraniteⅡＬ亟産、､■

ｌｌｉｈＨｉｍＢｌＢ.、

ＳＦｎＮｐｈｍｎｅ

ｌｍＰｕｍＵｍ璽亟、巴

Ｔ巴ｔｈｓＨｉｍ＆'四

St『a濡冊pｈ●

BＣ Layer Lithology Ｐ⑥i稗onUBratio lｌｉｌ１ｉＷｉ N{i鐘i：）

9111冊;1Ｗ

sub

Himalaya６ SandgtoneI

Siltstone0MmdBtone

0.25 2500 4０ 3５ 1８

Ｈｉ４ SandgtoneD

Lim唾to亟０，３０ 2700 7０ 5０ 1７

面溌l:;。５ MarbeIO

GraniteoLimeBton⑧

035 2900 8０ 5８ 1０

IIE:11M(;。1．２．３ Sandgtone，

!i腰鵬。0.25 2600 5０ 4５ 2０

3６Ｍｄ・MahmudulA1amandDaigoroHayashi

Table３．MaterialpropertiesofModel‐２

Ⅱ至旦円里ｒ

ｉｍＢＥ■

ＳＦｎｒＵ■ｍｍＤ

ｉｍｅＢｔｎｎロ

Table4MaterialpropertiesofModel‐３（Ａ＆Ｂ）

囚､土ヒロ回⑭

ｉｍｅ四t□、

2.2.2Ｂｏｍｄ(zが００"ditio〃

ＩｎａｌｌｍｏｄｅｌｓｔｈｅｕｐｐｅｒｓｕｒｆａｃｅｉｓｆｒeetodeformhorizontanyandverticaUy、The

lowerboundaryisrestrictedtomoveverticallybutallowedtodeformhorizontally・The

nodesattheleftboundarycanmoveonlyvertically、Ｔｈｅｎｏｄｅａｔｔｈｅｊｏｉｎｉｎｇｏｆｌｏｗｅｒ

ａｎｄｔheleftboundaryisfiｘｅｄＳＷ（southwest）ｔｏＮＥ(northeast)horizontalshortening

upto375miBappliedinincrementalstepsof75m，equallydividedoverthecross-section・

Model‐１containB352nodes，５６４elementsandthematerialpropertiｅｓａｒｅｓｈｏｗｎｉｎ

Ｔａｂｌｅ２；model-2contains501nodes，８８４elementsandthematerialpropertiesare

showninTable3；model‐３（Ａ＆Ｂ）contains353nodes,６２４elements,and491nodes，

８８０elementsrespectivelyandthematerialpropertiesareshowninTable4・

Accordingtotherulesdescribedabove，theboundaryconditionsforallthemodels

areasfollows8

MOdbZ-LForｔｈｅｎｏｄｅｓｌ，２and3displacementalonghorizontaldirectionisonly

permitted；ｎｏｄｅｎｏ、346,347,348,349,350,351arepermittedtomoveonly

verticany；ｎｏｄｅｎｏ、３５２isrestrictedtomovetoalldirections；ｎｏｄｅｎｏ、６，

StrBtigrBphicunit

Layer LithoIogy Ｐ⑪i且已⑪nCS

ratioDGnBity(kg/､｡）

Young`sModuU亟

(GPa）

Friction

angle(degme）

Ｃｃｈｃｇｉｏｎ

(MPa）

sub

Ｈｉｍａｌａｙａ

３ SandStoneoSiItBtone。M1ndgtone

0.25 2500 4０ 3５ 1８

Ｕ杢匁－P

Himalaya

２ SandstoneoLim⑭gtone

0.30 2800 7０ 5０ 1７

HigherHimalaya

１ MarbeIO

Granite，Lime2to正

0.35 2900 8０ 5８ 1０

TethysHimalaya

４ SandBtone，

Impu”liwT⑤二t⑪no

０.露 2600 5０ 4５ 2０

Stratigraphicuｎｉｔ

Layer Lithologｙ PoisBon0B

rａ

Ｄｅ

(kg/､o）Young`ｓＭ⑥｡ⅢUu2

(GPa）

Ｆ面ctioh

angle(degrpe）

Cohesion

(MPa）

sub

Himalaya

２ Sandstone，

SiltStono0Mudstono

0.25 2600 4０ 3５ 1８

ＬＥ２空r

HimaIaya

３ SandstoneoLim餌t⑪Tb⑨

0.30 2600 6０ 4８ 1５

HigherHimalaya

４Ｇ聖i唾

Granito，Ｌｉｍ函t⑪亟

０．３５ 2900 8０ 5０ 1７

TethyBHimalaya

５ Sand8tone，

ImpurBli価､巳to幼ｅ

０．２５ 2600 5０ 4５ 2０

Ｇｒａ

ｌ沮

nitic

ｙｅｒ

１ GraniteoＭ亜h⑭！

Ｔ』imE=tＯｎｅ

0.35 2900 8０5８

10


９，１２，１５，１９，２３，２７，３１，３５，３９，４３，４７，５１，５５，５９，６３，７３，７８，８８，９５，１０５，111,

120,125,133,140,147,154,160,174,183,188,196,200,204,208，212,219,

224,237,242,248,254，２５９，２６０，２６５，２７２，２８４，３０４，３１５and326canmove

horizontallyandvertically（Fig.９)．Othernodesarefree．

弓(G伝

．Ｃ埒

～■

｡●

と鐘}

一一

:‐ヨコ椒醇f…，｡Ｔ守わ

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nＯＤ２１I．】２０函ＤＢ４’１０５

禿tmdzOm）

Ｆｉｇ．９．Ｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｏｆｍｏｄｅｌ－１・Ｉｔｃｏｎｔａｉｎｓ３５２ｎｏｄｅｓａｎｄ５６４ｅｌｅ:ments・Thelowerboundaryisrestrictedtomoveverticallybutallowedtodeformhorizontally・Thenodesattheleftboundarycanmoveonlyvertically・ＴｈｅｎｏｄｅａｔｔｈｅｊｏｉｎｉｎｇｏｌｌｏｗｅｒａｎｄｔheleftboundaryisfixedSW（southwest）ｔｏＮＥ（northeast)horizontalshorteninguptomaximuｍ３７５ｍ（equivalentdisplacementat7､５ｃｍ/ｙｒｏｆ５０００ｙｒ）isappliedinincrementalstepsof7５ｍ，atthesouthwesternendofthecrosssection．

ModeＺ‐２：Ｆｏｒｎｏｄｅｎｏ、１，２，３，４，５，６，７and8deformationtakesplacealonghorizontal

directiononly；ｎｏｄｅｎｏ、１６，１７，３２，３３，３４，５０，５１，７４，７５，９１，９２，１０２，１０３，

１２３，１２４，１６６，１６７，１８７，188,206,239,240,264,265,296，297,314,316,347,

348,366,368，382,383,406,407,413,414,439，４４１，４４２ａｎｄ４６５ｃａｎｍove

horizontallyandvertically；、ode、０．４６６isforbiddentomovetoalldirections；

ｎｏｄｅｎｏ、467,468,469,486,487,488,489，４９０，５０１and500canmoveonly

verticaldirection；ｏｔｈｅｒｎｏｄｅｓａｒｅｆｍｅｅｔｏｍｏｖｅｔｏａｌｌｄｉrections（Fig.１０)．

一一｜｜

山副ロ卸山【Ｃ筒灼

有ロ己圓ゼロ丁由

王一一王

王￣

△f-10Trl

・0’２００．幻1600800】ＣＯ

零！】：｡ﾖ(k､）

Ｆｉｇ．１０．Boundaryconditionofmodel-2whichcontains501nodesand884elements、Thelowerboundaryisrestrictedtomoveverticallybutallowedtodeformhorizontally・Thenodesattheleftboundarycanmoveonlyvertically・Thenodeatthejoiningoflowerandtheleftboundaryisfixed,８Ｗ(southwest)ｔｏＮＥ(northeast)horizonIalshortenmguptomaximum３７５ｍ（equivalentdisplacementat7､５ｃｍ/ｙｒｏｆ５０００ｙｒ）isappliedinincrementalstepsof7５ｍ，atthcsoutllwesternendofthecrosssection．

3(Ａ)：Ｆｏｒｎｏｄｅｎｏ、１，２，３，４，５and6deformationtakesplacealonghorizonta］

directiononly；ｎｏｄｅｎｏ、１７，１８，４０，４１，５７，６９，７０，８４，１０６，107,118,119,135,

136,157,158，１８０，２０６，２０７，２６１，２６２，２８４，２８５and307canmovehorizontally

andvertically；ｎｏｄｅｎｑ３５３ｉｓｆｏｒｂｉｄｄｅｎｔｏｍｏｖｅｔｏａｌldirections；ｎｏｄｅｎo、

３４３，３４４，３４５，３４６，３４８，３５０，３５１and352canmoveonlyverticaldirection；

ｏｔｈｅｒｎｏｄｅｓａｒｅｆｒｅｅｔｏｍｏｖｅｔｏａｌｌｄｉrections（Fig.１１)．

jlJoapl

3８Ｍｄ・ＭａｈｍｕｄｕｌＡｌａｍａｎｄＤａｉｇｏｒｏＨａｙａｓｈｉ

ｗ純一ロ劇一山鄙一○司一、一□

自倒ご駒百円了閃

正一一主

工

Ｚ

Ｉ】Ｂｕ３０ｕ輯ＩＯＯｕ７５’９０

x-,1.0画D

Boundaryconditionofrnodel‐３(Ａ)．１ｔcontains353nodesand624elements・The

lowerboundaryisrestrictedtomoveverticallybutaIlowedtodeformhorizontally・Thenodesattheleftboundarycanmoveonlyvertically・mhenodeatthejoiningoflowerandtheleftboundaryisfixed・ＳＷ(southwest)ｔｏＮＥ(northeast)horizontalshorteninｇｕｐｔｏｍａｘｉｍｕｍ３７５ｍ（equivalentdisplacementat7亀５ｃｍ/ｙｒｏｆ５０００ｙｒ）isappliedinincrementalstepsof7５ｍ，ａｔｔｈｅｓｏｕｔｌｌｗｅｓｔｅｒｎｅｎｄｏｆｔｈｅｃｒｏsssection．

【０

F埴,111

ModeZ-3(β)：Ｆｏｒｎｏｄｅｎｏ、１，２，３，４，５and6deformationtakesplacealonghorizontal

directiononly，ｎｏｄｅｎｑｌ２，１３，２６，２７，５７，５８，７８，７９，８１，９６，９７，114,115,

134,135,157,158,209，210,231,232,252,253,273,274，331,332,334,335,

340,341,351，３５４，３５６，４１５，４１６，ａｎｄ４１７ｃａｎｍｏｖｅｔｏｂｏｔｈｈｏｒｉｚｏｎｔａｌａ､d

verticaldirection；４４２isforbiddentomovetoalldirections；ｎｏｄｅｎｏ、443,

463,464,465,479,480,481，４８８，４８９，and491canmoveonlyverticaldirection；

othernodesarefree（Fig.１２)．

園一日一℃【｜昌一⑭ｌＣ

ａ３旦目ム

乱．一一

ｒ

］○

」

、・zＵｏｄＯｏＯＤｕ８０u1OOU120

秀nxlmmD

Boundaryconditionofnlode1-3(B）whichhave491nodesand880elements・The

lowerboundaryisrestrictedtomoveverticallybutallowedtodeformhorizontally、Thenodesattheleftboundarycanmoveonlyvertically・Ｔｈｅｎｏｄｅａｔｔｈｅｊｏｉｎｉｎｇｏｆｌｏｗｅｒａｎｄｔheleftboundaryisfixed・ＳＷ(southwest)ｔｏＮＥ(northeast)horizzontalshorteninguptomaximuｍ３７５ｍ（equivalentdisplacementat7､５ｃｍ/ｙｒｏｆ５０００ｙｒ）isappliedinincrementalstepsof7５ｍ，atthesouthwesternendofthecrosssection．

Ｆｉｇ．１２．

22.3qZ6e7io〃／brSeZectio〃ｑ/DiSpZtzcemelztBou几ｄｔｚＵ'００"dition

MarinegeophysicaldatafromtheAtlanticandIndianOceansallowreconstructionof

IndiaandEurａｓｉａｆｏｒｔｈｅｌａｓｔ７０Ｍａ，ArapiddecreaseinconvergencefroｍａｂｏｕｔｌＯＯ

ｍｍ/ｙｒｔｏ５０ｍｍ/yroccurredapproximately40Maago，approximatelyorslightlylaterthanthedateinferredgeologicallyforthecollisiｏｎ・TheHimalayanmountainoriginated

asaresultofcollisionbetweenthelndianandEurasianplates・Thelndianplate

convergesnorthwaｒｄａｔａｎａｖｅｒａｇｅｒａｔｅｏｆ５０ｍｍ/yrandisunderthrustingbeneathTibet

(Thakureta1.,2000)．Ofthetotalconvergence，～２０ｍｍ/yｒ（Lave＆Avouac，1998；

BilhametaL，1997）isaccommodatedacrosstheHimalayaandtheremainingconvergenceistakenupfarthernorth（Peltzer＆Saucie，1996；Yeats＆Thakur，1998)．


Ｔａｋｉｎｇｔｈｅｅｓｔｉｍａｔｅｔｈａｔ３００ｔｏ４００ｋmofshorteninghasoccurredintheHimalaya

(Gansser,1966;Mattauer,1975；Warsi＆Molnar,1977）andassumingthatunderthrusting

beganintheOligoceneorlateEocene（Gansser,1964；Ｈａｍｅｔ＆A11egre,1976),theaverage

rateofshorteningisabｏｕｔｌＯｍｍ/yr、ThisrateisconsistentwiththeratｅｏｆｌＯ－２０

ｍｍ/yrinferredfromrelevelingdataofChugh,1974,withgeodeticmeasurementsaciross

onefault（SinvaletaL，1973)，andfromseismicmomentsofearthquakes(Chen＆Molnar，

1977)．Alloftheratesaresubstantiallylessthantheconvergencebetweenlndiaand

EurasiaforthelastlOMa(LePichon,1968;MinsteretaL,1974)．TheHimalaya,therefore，

seemtoabsorbonlyfractionoftheconvergence；theremainderoccursapparentlyby

deformationofthepartofAsianortｈｏｆｔｈｅＨｉｍａｌａｙａ（Molnar＆Tapponnier，1975)．

Hayashi（1987,1988andl992）numericallysimulatedtheupliftoftheTibetanplateau

andtheHimalayasassumingthatthenortherlymigrationofthelndianplatedeforms

theoverlyingAsiancontinentalcrustwhichbehavesasanincompressibleNewtonianfluid

ofAsiaabovetherigiduppermantle・Ｉｎｔｈｅｓｅｍｏdels,theNewtoniansialiccrustisdeforｍｅｄ

ｂｙａ６０ｋｍｄｅｅｐｒａｍｐｄｉｐｐｉｎｇ４５ｄｅｇreesnorthwardsinarigidmantleasthenosphere

movingatlOOmm/yr･

Gatheringourknowledgeandimproveourskillness,３ｃｍ/yr,５ｃｍ/yr,７．５ｃｍ/ｙｒａｎｄ

ｌＯｃｍ/yrdisplacementhadbeenappliedforallthemodels・Consideringallthecases

mentionedabove,７．５ｃｍ/yrdisplacementhavebeentakenforthepresentanalysis．

ProcedUre／bro6taininginputa几ｄｏＩＬｔｐ叫tdbutq

Primarilybasedontheseismiccross-sectionbutalsoincorporatingfielddata，a2

dimensionalfiniteelementmodelhasbeenconstructed・Theelementsusedarethree-nodes，

triangles（Fig.４),withlinearshapefunctionsandthusconstantstrainandstress・The

finiteelementcodeusedfortheelasticcalculationise！[ES､f

Toproduceinputdata，thecross-sectionsaredividedintotriangleelementsforiden‐

tifyingthecoordinatesofthenodalpointsandimposingtheboundaryconditionsaccording

tothestructuralandtectonicenvironment・

Inputdatacanbemademanuanyusingsectionpaperorthetabletmechanismunder

Macintoshcomputersystem･Ｉｔｉｓｉｍｐｏｒｔａｎｔｔｏｎｏｔｅｔｈａｔｔｏｌｅｔｔｈex-axisandy-axisin

thecross-secｔｉｏｎｂｅｐａｒａｌｌｅｌｔｏｔｈｅｆｒａｍｅｓｉｄｅｓｏfthetabletasmuchaspossible、Then

usingthetabletthecoordinatesofallthenodeswillbeobtained・Therefore，aftergetting

thecoordinatesofannodes，thedeterminationofelementconnectiondatawillbemade

manually・Basedonthecoordinatesofthenodes，ａｓｉｍｐｌｅｐｒｏｆｉｌｅｍａｐｗｉｔｈｔｈｅｓａｍｅ

ｓｃaｌｅｏｆｘ－ａｘｉｓａｎｄｙ－ａｘｉｓｃａｎｂｅｄrawnbyusingaFortranprogram（"et./UJzc)．After

thattheinputdatawillbeobtainedfinally・

Ｗｅｃａｎｖｅｒｉｆｙｔｈｅｓｈａｐｅｏｆｔｈｅｍｏｄｅｌｗｉｔｈｔｈｅｃｒｏｓｓｓｅｃｔｉｏｎｌｆｓｏｍｅｔｈｉｎｇｗrong

withthecrosssection,ｉｔｗｉｌｌｂｅｅａｓｉｌｙｌｏｃａｔｅｄｂｙｔｈｅｓｏｆｔlzet・んJOC・

Aftergettingtheinputdata，finiteelementmethodprograms，ｅｍＭ６αｿZ｡./ａｎｄ

4０Ｍｄ・ＭａｈｍｕｄｕｌＡ１ａｍａｎｄＤａｉｇｏｒｏＨａｙａｓｈｉ

几et､/tmcwritteninFortranareappliedtoobtainthestressfieldofallthemodels，Program

〃et・か"cisusedtoshowthegeometricalstructureoビthecross-sectionundertriangles

only、Program6a7zd・ノisusedtodeterminethehighestvalueofthedifferenceamongthe

nodesofrespectivetriangles、Ａftercomputing,ｉ６ｚｕ（ljhehighestdifference）isobtainand

isunique・Computingtimedependsonthevalueｏｆｔｈｅｉｂｗ・Ｉｆｉ６ｍｉｓｌａｒｇｅ，computing

timewillbelong，ProgrameZas./ｉｓｕｓｅｄｔｏｃｏｍｐｕｔｅｔｈｅｓｔｒｅｓｓｆｉｅｌｄｏfthemodeLIn

thisprogram，boundaryconditionfile，materialpropertiesanddatafilesareusedto

simulatethemaximumprincipalstress（０，）andminimumprincipalstress（ｏ２)．Using

theprincipalstresses，ａｓｏｆｔｗａｒｅ（st7ess・んjzc）ｃａｎｂｅａｐｐｌｉｅｄｔｏｆｉｎｄｏｕｔｔｈｅｓｔｒｅｓｓ

distributionwhichidentifiesthedeformationpatternalongtheregion．

３．Result

Inthenumericalexperimentspresentedinthisstudy，thefaultdistributionandstress

patternaredescribedbytwoparameters：displacementboundaryconditio、and，cohesion

andfrictionangle・Thenumericalexperimentsshowthatacceptabledistributionofdefor-

mationcanbecalculatedforsomechoiceofdisplacementboundarycondition（７５ｍ／

l000yr，１５０ｍ/2000yr,２２５ｍ/3000yr,３００ｍ/4000yr，ａｎｄ３７５ｍ/5000Ｗ）andalsoforthe

valuesofcohesionstrengthandfrictionangleAgeneraldiscussionismadeforallthe

modelsanalyzingthepointsmentionedaｂｏｖｅｏｆｔｈｅＨｉｍａｌａｙａｕｎｄｅｒＦＥＭ．

3.IModeZ-I

HbrizoJztaZdiSpJaceme"ｔｉｓ巧加/IOOOy/瓠.（Fig.１３)：Principalstressesarestrongerinthe

deeperportionthantheshallowerone、Maximumprincipalstressesaredistributednear

verticallywhileminimumprincipalstressesaredistributednearhorizontallyalloverthe

region・HydrostaticconditionoccursbelowtheTethysHimalayathaｔｂｅｌｏｎｇｓｔｏ６ｔｏｌ２

ｋｍｄｅｐｔｈｏｆｔｈｅＨｉｇherHimalaya・ＬｅｆｔｓｉｄｅｏｆｔｈｅｕｐｐｅｒｈａｌｆｏｆＭＣＴａｎｄＭＢＴ，o1is

distributedhorizontallybutverticallyattherightside・Principalstressesarecompressive

alongalltheregion、ＩｎｔｈｅｓｈａｌｌｏｗｅｒｐａｒｔｏｆｔｈｅＳｉｗａｌｉｋandtheTethys,principalstresses

areverysmall（nearaboutO)．Thevaluesofcompressiveo1arefrｏｍＯｔｏ４５０ＭＰａ

(elemontno､541）andthevaluesofcompreSsiveO2areｆｒｏｍＯｔｏ３５０ＭＰａ（elementnq418)．

u▲

Tctl1yo ・ざの､－２ドシ山口皐繍

一蝋繊》鱗繊

業婆莎

辮》州鮴膨讓鑪ii鑿艤}iliiiiji3〆

iiiilM:！|NNN

lハ

ii：繍ｉｉ'iｉＷＫ

ＸSjmEMEI

印■一■■■⑪

>At／

閂と一

Fig.１３.Stressdistributionofmodel‐１７５mdisplacementboundaryconditionｉｓｓｕｂｊｅｃｔｅｄｔｏｔｈｅｂｏｔｔｏｍｏｆｔｈｅｍｏｄelduringlOOOyear．


Hbrizo几taZdjSpm“、…ｉＳ３巧加/5DDOyr.（Fig.１４)：Principalstressesarestrongerin

thedeeperportionthantheshallowerone・Maximumprincipalstressesaredistributed

horizontallyandminimumprincipalstressesaredistributedverticallyallovertheregion・

HydrostaticconditionoccursbeneａｔｈｔｈｅｄｅｅｐｅｒｐａｒｔｏｆｔｈｅＨｉｇｈｅｒＨｉｍalaya，ｔｈａｔｉｓ

ｎｅａｒｔｈｅＭＣＴａｎｄｂｏｕｎｄｅｄｂｙｌｏwerboundary・Principalstressesarecompressivealong

alltheregionexcepteleｍｅｎｔ、。．２３７，２４８and249TheseelementsshownegligibleextenSive

stress（lessthanlOOMPa）ｆｉｅｌｄｌｎｔｈｅｓｈａｌｌｏｗｅｒｐａｒｔｏｆｔｈｅＳｉwalikandtheTethys

area,minimumprincipalstressesareverｙｓｍａｌｌ（nearaboutO)．ＴｈｅｌｉｍｉｔｓｆｏｒＯｊａｒｅ

ｆｒｏｍ４０ＭＰａ（elementｎｏ,442）ｔｏＬ１ＧＰａ（element、0.418）ａｎｄｆｒｏｍＯｔｏ５００ＭＰａ

(element、0.418）ｆｏｒｍ．

i篝鑪妻蕊 ii義i曇鑿霊鯵懸鎌i：('7/杙ﾆト

≠ -卜

｣て＋＋

－１■■■

Stressdistribution⑥f]mIodel‐1.375mdisplacementbounda]PyconditionissubjectedtothebottomoftUlemodelduring5000year，Redblocksindicatingextensivestressfi⑨1．

Ｆｉｇ．１４

3.2j1fodeJ-2

HOrizo"tclJdjSpZCzceme"ｔｉＳ恋加/IOOOyr.（Fig.１５)：Principalstressesarestrongerinthe

deeperportionthantheshalloweroneMaximumprincipalstressesaredistributednear

verticallybutminimumprincipalstressesaredistributednearhorizontallyoverallthe

regionHydrostaticconditionappearsbelowtheTethysHimalayathatbelongsto5to

lOｋｍｄｅｐｔｈｏｆｔｈｅｕｐｐｅｒｐａｒｔｏｆｔｈｅＨｉｇｈｅｒＨｉｍａｌａｙａａｎｄｓｏｍｅｐａｒｔｓｏｆｔｈｅＳｉｗalik

andtheLesserHimalayaalongtheboundarybetweenthemAlongtheshallowerpartof

theHigherHimalaya，LesserHimalayaandtheSiwalik，Ｃｌisdistributedhorizontally

whereＯ２ｉｓｖｅｒｙｓｍａｌｌ（nearOOMPa)．Principalstressesarecompressivealongallthe

reglon・ThelimitsofcompressiveOlarefroｍ３０ＭＰａ（element、0.289）ｔｏ６３０ＭＰａ

(element、0.825）ａｎｄワョａｒｅｆｒｏｍＯｔｏ３９０ＭＰａ（element、。,792,825,826ａｎｄ827)．

｝

申

Fig.１５.ShPessdistributionofmodel‐２．７５mdisplacementboundaryconditioｍｉｓｓｕｂｊｅｃｔｅｄｔｏｔｈｅｂｏｔｔｏｍｏｆｔｈｅｍｏdelduringlOOOyear．

4２Ｍｄ・MahmudulAlamandDaigoroHayashi

HbrizoJztaZdiSpkz“melLtis3庵、/5DOOyr.（Fig.１６)：Principalstressesarestrongerinthedeeperportionthantheshallowerone･Maximumprincipalstressesaredistributedhori-

zontallyandminimumprincipalstressesaredistributedverticallyallovertheregion・HydrostaticconditionoccuｒｓｉｎｔｈｅｄｉｐｐｅｒｐａｒｔｏｆｔｈｅＨｉｇｈｅｒＨｉmalaya，andsomepartsoftheLesserHimalayａａｌｏｎｇｔｈｅｄｅｅｐｅｒｐａｒｔｏｆｔｈｅＭＣＴａｎｄMBTregion・Principalstressesarecompressivealongalltheregionexcepteleｍｅｎｔ、０．２５１，２５６，４４０，４７６，６６１，and66aTheseelementsshownegligibleextensivestress（1essthanlOOMPa）field、Ｉｎ

ｔｈｅｓｈａｌｌｏｗｅｒｐａｒｔｏｆｔｈｅＳｉｗａｌｉｋandtheTethysarea，minimumprincipalstressesareverｙｓｍａｌｌ（nearaboutO)．ＴｈｅｌｉｍｉｔｓｆｏｒＯＩａｒｅｆｒｏｍ９０ＭＰａ（element、0.871）ｔｏ６８０ＭＰａ（element、0.820）ａｎｄｆｒｏｍＯｔｏ６５０ＭＰａ（element、0.819）ｆｏｒ０２．

Ｆロnｍﾛﾛ、ｕ■［■

］qnLLB 、Ⅱ

3.3MbdbZ‐３（Ａ）（P7℃…tstCUge）

HO7吃olztaJdiSpZCuceme〃ｔｉｓ市、/I〃Ｏｙｒ.（FZgI7)：Principalstressesarestrongerinthedeeperportionthantheshallowerone、A1ongtheSiwalikregion，Ojisdistributedhori-

zontally（Gangaticplane）ｗｈｅｒｅａｓｉｎｔｈｅｄｅｅｐｅｒｐａｒｔｉｔｉｓｄｉｓｔributednearvertically･IntheLesserHimalaya，ワ，tendstohorizontaltoverticaldirectionalongtheshallowerparttodeeperpart・ＩｎｔｈｅＨｉｇｈｅｒＨｉｍａｌａｙａｍｓｈｏｗｓｔｈｅｓａｍｅｔｅｎｄｅｎｃｙａｓｔｈｅＳｉｗａｌｉｋ

ａｎｄｔｈｅＬｅsserHimalayabutthedeepermostpartobtaininghydrostaticcondition．A1ongalltheregionsoftheTethysHimalaya，◎，isdistributedhorizontally・Ｍｏｓｔｏｆｔｈｅａｒｅａ

ｏｆｔｈｅＧｒａｎｉｔｉｃｌａｙｅｒｍｉｓdistributednearverticallybut｡２isnearhorizontalexceptthepartjustbelowtheSiwalikregion,whereO1isdistributedhorizontally・HydrostaticconditionoccursinsomepartsoftheGraniticlayer・PrincipalstressesarecompressivealongalltheregionThelimitsofcompressiveDlarefrom３０（element、｡､283）ｔｏ５３０ＭＰａ（element、0.305）ａｎｄＯｇａｒｅｆｒｏｍＯｔｏ３４０ＭＰａ（element、｡､526)．

巳

Fig.１７.Stressdistributionofmodel-3(Ａ).７５mdisplacementboumdaryconditiOnissubjectedtothebottomofthemodelduringlOOOyear．

StressDishibutionandFamltDevelopmentAroundNepalHimalayabyMeansolFiniteElementMethod43

Hb7izo几tQZdiSpZaceme"ｔＺｓ３面、/5000ｙｒ．（Fig.１８)：Principalstressesarestrongerin

thedeeperportionthantheshallowerone・Maximumprincipalstressesandminimum

principalstressesaredistributedalmosthorizontallyandvertically，respectivelyoveran

theregionbuthydrostaticconditionisobservedalongthedeeperpartofHigherH1Th輿laya，

LesserHimalayaIandsomepartsofGraniticlayer・PrincipalstresseSarecompressive

alongalltheregmnexceptelementｎｏ、１６３，１８７ａｎｄ190．Theseelementsshownegligible

extensivestress（lessthanlOOMPa）ｆｉｅｌｄＴｈｅｌｉｍｉｔｓｆｏｒｍａｒｅｆｒｏｍ４０（element、0.

283）ｔｏ７４０ＭＰａ（elementｎｏ,529）ａｎｄｆｒｏｍＯｔｏ４９０ＭＰａ（elementｎｏ’572）ｆｏｒの．

蕊鑿議篝鑿篝議警護蕊「

ZN7△Ｎ

塗心支

一己一

Fig.１８．Stressdis放ibutionofmodel‐３(Ｂ)．３７５mdisplacementboundaryconditionｉｓｓｕｂ‐jectedtotllebottomofthemodelduring5000year・IRedbIocksindicatingextensivestrSssfield．

3.4jlrodeJ‐３（B）（ﾙfOU刀tai7z6uiZdt7zgsmge）

Hb7izo几tQJdiSpZQceme"ｔｉｓ７５ｍ/１０００Ｗ.（Fig.１９)：Principalstressesaremorestronger

inthedeeperportionthantheshallowerone，AlongtheSiwalikregion，misdistributed

horizontally（Gangaticplane）whereasinthedeeperpartitisdistributedvertically・In

theLesserHimalaya，O1tendstohorizontaltoverticaldirectionalongtheshallower

parttodipperpart・ＩｎｔｈｅＨｉｇｈｅｒＨｉｍａｌａｙａＯ１ｓｈｏｗｓｔｈｅｓａｍｅｔｅｎｄｅｎｃｙａｓｔｈｅＳｉｗａｌｉｋ

ａｎｄｔｈｅLesserHimalayabutthedippermostpartobtaininghydrostaticconditionmnthe

TethysHimalaya，misdistributedhorizontallyalongtheshallowerpartbutthedeeper

partshowsnearverticaldirection・ShanowerpartoftheGraniticlayer，Ｄ，showshori‐

zontaldirectionwllileinthedeeperitshowsverticaldirection・Hydrostaticconditionoccurs

insomeplacesoftheGraniticlayer・Principalstressesarecompressivealongalltheregions、

Thelimitsofcompressivemarefrom２０（elementｎｏ､４５）ｔｏ５９０ＭＰａ（elementｎｏ､723）

and◎２ａｒｅｆｒｏｍＯｔｏ４２０ＭＰａ（elementｎｏ，719)．

ii霧議篝鑿篝i鑿鑿

冒上

＄

ＰＢＯヰユェ的一・

ザ

■T

、玉■

３(B)．７５１１１modelduring

Ｆｉｇ．１９．Stressdistributionofmodelsubiedｆｅｄｔｏｔｈｅｂｏｔｔｏｍｏｆｔｈｅ

displacementboundaryconditionislOOOyear．

4４Ｍｄ、MahmudulAIamandDaigoroHayashi

Hbrizo"tclZdiSpmcem…iS3乃加/〃ＯＯｙ７.（Fig・卯)：Principalstressesaremorestronger

inthedeeperportionthantheshallowerone・ojando2aredistributedhorizontallyandvertically，respectivelyallovertheregionexceptalongthedeeperpartoftheGranitic

layer，whereobtainingreversedistributionofぴ,ａｎｄ０２．Hydrostaticconditionisobsewed

alongthedeeperpartofHigherHimalaya，LesserHimalaya，andsomepartsofGranitic

layer・Principalstressesarecompressivealongallthereglonsexceptelemeｎｔｎｏ、521．

Thiselementshowsnegligibleextensivestress（lessthanlOOMPa）ｆｉｅｌｄＴｈｅｌｉｍｉｔｓｆｏｒ

ＯｌａｒｅｆｒｏｍｌＯＯ（elementｎｏ､６６）ｔｏ８８０ＭＰａ（element、0.719）ａｎｄｆｒｏｍＯｔｏ６４０ＭＰａ

(elementno719）ｆｏｒ０２．

１

■ 血

Fig.２０．Stressdistributionofmodel‐３(B)．３７５mdisplacementboundaryconditionissub‐jectedtotllebottomofthemodelduring5000year,Redblocksindicatingextensivestressfield．

４．Discussion

4.ISeismiCityα"ｄＦｂｍｍ`ccﾉbCz"iSmSbZUtio〃

Himalayaisseismicallyactiveatteststocurrenttectonicactivity・Fourearthquakes

withmagnitudemorethan8occurredsincel897andallappeartoberelatedtomountain

buildingprocessesintheHimalaya・A1thoughearthquakesoccurinneighboringreglons，abeltofseismicityfollowstherangealongtheentirelength・Accordingtolnternational

SeismologicalCenterandthelnternationalOceanicandAtmosphericAdministrationfor

theperiodl961-1970，mostoftheepicentersfallneartheｔｒａｃｅｏｆｔｈｅＭＣＴａｎｄｎｏｔｔｈｅ

ＭＢＦ・Ｆｒｏｍｔｈis，ｉｔｉｓｔｅｍｐｔｉｎｇｔｏｃｏｎｃｌｕｄｅｔｈａｔｔｈｅＭＣＴｉｓａｃｔｉｖｅｂｕｔｎｏｔｔｈｅＭＢＥ

Ｈｏｗｅｖｅｒ,whenoneconsidersthattheMBFdipsgentlytothenorthornortheast(Gansser，

1964),ELndthattheearthquakesoccuratfinitedepth,itseemsmorereasonabletoconclude

thatalongmostoftheHimalaya，theactivityisassociatedwithMBFandtheZone

surroundingit・

ＴｈｅｓｅｉｓｍｉｃｉｔｙａｔｂｏｔｈｅｎｄｓｏｆｔｈｅＨｉｍａｌayaappearstobemorecomplicatedwith

diffusezonessouthofmamrange、Ｉｎｔｈｅｅａst，seismicityisdistributedovertheShillongplateauandit,smargins（Fig.２１)．Inthenorthwest,usingadensenetworkofstations，ArambrusteretaL，（1976）ａｎｄＪａｃｏｂｅｔａＬ，（1976）locatedearthquakesinabroadarea

ｆｒｏｍ５０ｋｍｎｏｒｔｈｏｆｔｈｅＭＣＴｔｏｌ５０ｋｍｓｏuthofitandextendingtodepthsgreaterthan60kmTheyconsiderboththｅＭＣＴａｎｄｔｈｅＭＢＦｔｏｂｅａｃｔｉｖｅ，andinfactusedthe

earthquakeepicenterstomapthewestwardcontinuationoftheMBFbeyondwhereitｉｓ


90゜鋼。期｡的●７５●

ShallowfDcusseismicityoftheHimalayaregion・SelectedwelllocatedepicentersfromlSCorNOAAfroml961-1970andmajorshoCksSincel897(Molnareta1.,1977)．

Fig.２１．

recognizedgeologically・A1thoughthetectonicsofthissegmentoftheHimalayaisprobably

morecomplicatedthantothesoutheast，thelessontobelearnedisprobablythatseismicity

alongtheentirerangeisnotrestrictedtoasinglenarrowfaultzone、

SeveralpublishedstudiesoffocalmechanismsolutionsofearthquakesmtheHimalaya

regiongivethesamegeneralpatternofthrustfaulting，withoneplanedippinggently

beneaththeHimalaya（ArmbrusteretaL,1976;Banghar,1974；BenMenahenetaL,1974；

Ｃｈｅｎ＆Molnar，1977；Fitch，1970；ＩｃｈｉｋａｗａｅｔａＬ，1972；ＭｏｌｎａｒｅｔａＬ，1973；Rastogiet

aL，1973；Tandon,Srivastava，1975)．Amongthesestudiesslightlydifferentapproaches

havebeentaken，ａｎｄｉｎａｆｅｗｃａｓｅｓ，differentsolutionsforthesameearthquakewere

reported，butthegeneralpatternisobservedfornearlyalLExceptpossiblyforthel950

AssamearthquakeaUtenofthefocalmechanismsolutionsforevenｔｓｉｎｔｈｅＨｉmalaya

showlargecomponentsofthrusting（Fig.２２)．Assumingthatdipsapproximatelynorth

9軒DOP、●７５･８５０

Focalmechanismsolutions・SinglearrowsshowpresumeddirectionOnmnder‐thrusting・Opposingarrowsfbrevent2showapproximatedirectionofmaximumcompressionanddivergingarrowsforevent7showapproximatedirectiOnofleastcompression・Numbe顕correspondtotable5・Circesshowlowerhemisphereplotsoffocalsphere-darkareasrepresentquadrantwithcompressionalfi霜tarrivals(Ｍｏｌｎａｒｅｔａ1.,1977)．

Ｆｉｇ．２２．

JＧ

I．．

◆＄。

●

ロ

●■

８食●１

4６Ｍｄ・MahmudulA1amandDaigoroHayashi

ornortheastisthefaultplane，theslipvectorsarefairlywelldeterminedandshowan

underthrustingtothenorthornortheast,Ｔｈｅｄｉｐｓｏｆｔｈｅｆａｕｌｔｐｌａｎｅｓａｐｐｅａｒｔobeshal-

lowerforearthquakesinthesoutheELstportionoftheHimalayathanelsewhere、The

solutionsarebasedonfirstmotiｏｎｓｏｆｐｗａvesand，ｗｈｅｎpossible，swaves，from

recordingsoflongperiodseismograms、Parametersforthesesolutionsaregivenin

Table5．

Table５．Catalogoffocalmechanismsolutionparameters

１９ＵＲＶ１９６３

80.46

177４０

ｌＺＪＡＮ１９６５

ＵＩＷ１９６６ 196４９

ＩＡＲ１９６６

100

１０１４

1６７４０

Azimuth（Ａｚ.）andplunges（pL）aregivenforpolesofeachpossibleｎｏｄａｌｐｌａｎｅａｎｄｆｏｒＰ，Ｔ，ａｎｄＢａｘｉｓ，whichroughlyapproximatethedirectionsofmaximum，minimumandinter‐mediatecompressivestresses．

InnorthernPakistan，wherefocalmechanismsolutionsofsmallerearthquakeshave

beenexaminedindetail（Arambrustereta1.,1976,Ｊａｃｏｂｅｔａ1.,1976)，thesamebasic

patternprevailsbutgreatercomplexity・Theseismicityalsoscattersattheeasternend

oftheHimalayaneartheShillongplateau・Apoorlydeterminedsolutionwasobtained

forasmallevent（June19,1963）neartheDaukifault（Evens，1964)，whichseparates

thecrystallinerocksoftheShillongplateaufromtheCenozoicsedimentssouthofit・

Drillingdatasuggestasmuchas250kmofrightlateralstrikeslipmotiｏｎｏｎｔｈｉｓｆａｕｌｔ

(Evans，1964)．

TheAugustl5，１９６６earthquakeoccurredlOOkmsouthwestofHimalayanfront，the

GangaBasin、Normalfaultingoccurredonaplanethatstrikesapproximatelyparallel

totheHimalaya、TheinterpretationthatStauder（1968)，Isacks，oliver，Sykes（1968）

gave，ｔｈａｔｔｈｅｎｏｒｍａｌｆａｕｌｔｉｎｇｉｓｄｕｅｔｏａｓtretchingoftheupperpartofthelithosphere

asitbendsdownatthetrenchMenke＆Jacob（1976）locatedmanyearthquakesbeneath

tｈｅＧａｎｇａｂａｓｉｎａｎｄｓｏｕｔｈｏｆｉｔ、Inthissensethel966earthquakeisnotunusual

(Ｍｏｌｎａｒｅｔａ1.,1979)．

4.2ＭOﾉｶr-CbuZom6／ｂｌｊｍ"ePLueZOPe

Mohr-Coulombfailureenvelopeisamethodwhichhelpstoidentifythelocationof

ＮＯ Earthquakeｄａｔｅ

Laｔ（Ｎ） Long(E）ＰｏＩｅ

Ａｚ．ｐ】．

Ｐｏｌｅ

Ａｚ．ｐＬ

PoIe

Ａｚ．ｐＬ

T-axis

Ａ２．ｐ1．

Ｂ･ＲＸｉ色

Ａｚ．ｐ1．

01 l５ＡＵＧｌ９５０ 28.50 96.70 351１２ 1７１７８ 1７１３３ 351５７ 8１０

0２ l９ＪＵＮ１９６３ 2４９７ 9２ 0６ 235２０ 330１６ 192５ 287２４ 9１６０

0３２６ＳＥＰ１９６４ 2９ 9６ 8０ 4６ 4０３０ 220６０ 220１５ 4０７５ 135０

0４２１０ＣＴｌ９６４ 2８ 0４ 9３ 7５ 357５ 177８５ 177４０ 357５０ 8７０

0５ l２ＪＡＮｌ９６５ 2７ 4０ 8７０１０１５ 180７５ 180３０ 0６０ 9００

0６２７ｊＵＮ１９６６ 2９ 6２ 8０ 8３ 3６４１ 196４９ 207４ 9Uｌ８６ 297１０

0７ l５ＭＡＲ１９６６ 2８ 1７ 7８ 9３ 4２５９ 222３１ 222７６ 4２１４ 132０

0８ l６ＤＥＣｌ９６６ 2９ 6２ 8０ 7９１９０６６ 1０２４ 190２１ 1０６９ 100０

0９ z０ＦＥＢｌ９６７ 3３ 6３ 7５鋼 168２５ 4２５０ 1０１４ 123５７ 272２８

1０ l４ＭＡＲ１９６７ 2８ 4１ 9H1 2９３１０ 183８０ 183３５３５５ 9３０

11 l９ＦＥＢ１９７０ 2７ 4０ 9３ 9９ 347５ 167８５ 167４０ 347５０ 7７０

1２ O３ＳＥＰ１９７２ 3５ 9８ 7３ 4２ 0５０ 180４０ 0５ 180５０ 9００

StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeanBofFmiteElementMethod47

faultplanewithinthecrustorinthesurface・ＳｉｎｃｅＦＥＭｈｅｌｐｓｔｏｃｏｍｐｕｔｅｔｈｅ２Ｄｓｔｒess

field（｡,ａｎｄＯ３）underemslprogramforanthemodels,thethirdunknownprincipal

stress（０｡）canbeobtainedbyusingtheequatioｎ

ｏ＝ソ(o,＋ｏｈ）⑫●

where，ｌ’isPoisson'ｓratio（Tilnoshenko＆Goodier，1970,HayashiandKizaki，1972)，

ロ‘ａｎｄ◎2（cEL1culatedbyFEM）aretheprincipalstresses・Aftergettingthevaluesof

C,，Ｏ２ａｎｄび゛foreachelement，itiseasytocomputewhichprincipalstresses，、，

Ｄ２，ａｎｄ◎。ａｒｅｔｈｅｍａｘｉｍｕｍ，intermediateandminimum・Accordingtotheorderof

magnitude，anewlydefinedstressfieldcanbeobtainedbyusingthenewlyobtainedprincipal

stressesO1，Ｏ２ａｎｄＯ８、

TheMohr-CoulombfailureenvelopeｉｓｓｈｏｗｎｉｎＦｉｇ、２３．Ｉｔｉｓｂａｓｅｄｏｎａｌｉｎｅａｒ

/づて、

Ｆｉｇ．２３．Mohrcircleconstructiondemonstratmgtheconceptofproximitytofailure・

relationshipbetweenthesharestress「ａｎｄｔｈｅｎｏｒｍａｌｓｔｒｅｓｓｏｈ：

T)h…＝ｃ＋ohtan‘㈹wherecisthecohesivestrengthoftｈｅｒｏｃｋａｎｄｄｉｓｔｈｅａｎｇｌｅｏｆｉｎｔｅｒｎａｌfriction、

FailureoccurswhentheMohrcirclefirsttouchesthefailureenvelope・Thisoccurswhen

th…dius･ftheMohrcircle,凸-百一望,isequaltoth．p…diculardiS…fr･ｍｔｈｏ

…｡f…廼。'…且-票L`｡…ilu…､．'。p･，

(且L云竺ﾙ冠-.…+(且L苧)…伽Ａｓｔｈｅｎｅｗｌｙｄｅｆｉｎｅｄｓｔｒｅｓｓｆｉｅｌｄｏｆeachmodelisavailable，ｉｔｉｓｐｏｓｓｉｂｌｅｔｏｌｏｃａｔｅｉｎ

ｗｈｉｃｈｅｌｅment，faultwillbedevelopedaccordingtoMohrcircle、

TheproximitytofailureP「，ｃａｎｂｅｄｅｆｉｎｅｄａｓｔｈｅｒａｔｉｏｂｅｔｗｅｅｎｔheactualradiosofthe

M゜hrcircle,些百~里,andthomd…tfanure，

(二二;;二）昨（｡,

48 Md. Mahmudul Alam and Daigoro Hayashi

One can evaluate whether faulting develops in certain element according to the value of

the parameter Pr. Whenever the value of Pr<X the stress state is within the failure

envelope ( i.e., no fault develops), but when Pf>\, failure occurs. Thus Pr is taken as

an indicator to define whether the fault develops or not. Using the eq. (19 it is easy to

find out the location of failure element.

Some experiments have done for choosing the material properties according to the

layer using eq. (ID. Table 2-4 show the required material properties for our numerical

modeling. We have imposed some boundary conditions like 3 cm/yrf 5 cm/yr, 7.5 cm/yr

and 10 cm/yr; among these we describe only 7.5 cm/yr during 1000 to 5000 yr period.

According to the boundary condition 75 m/lOOOyr, the average limits for O\ and a» are

from 20-500 MPa and 0 to 360 MPa, and for 375 m/5000yr, average limits for O\ and

a% belong to 60 - 800 MPa and 0 to 600 MPa respectively, which indicates that the

difference between maximum principal stress ( tfi) and minimum principal stress ( o») is

comparatively high if the convergence rate is relatively high and the deformation rate is

also strong. The results are observed from the stress field over the Granitic layer, Tethys

Himalaya, Higher Himalaya, Lesser Himalaya and Siwalik that the principal stresses are

stronger in the deeper part than the shallower one. For models 3(A) and 3(B) hydrostatic

condition is observed along the granitic layer beneath the Siwalik for the boundary condition

75 m during 1000 yr but for 375 m during 5000 yr hydrostatic condition belongs to some

parts of granitic layer and deeper most part of Higher Himalaya and Lesser Himalaya.

For model - 2, hydrostatic condition is observed along the upper part of Higher Himalaya

and some parts of Lesser Himalaya for the boundary condition 75 m/lOOOyr. But for 375

m/5000yr hydrostatic condition is obtained in the deeper part of Higher Himalaya and

Lesser Himalaya along the MCT and MBT zones. Hydrostatic condition is obtained along

the deeper and upper most part of Higher Himalaya according to the boundary condition

375 m/5000yr and 75 m/lOOOyr, respectively for the model - 1. It is obvious from the

discussion that no deformation is observed along the deeper part of Lesser Himalaya,

Higher Himalaya and Granitic layer due to hydrostatic condition. May be, lower parts

of these layers belong to a high grade metamorphic rock.

The occurrence of faulting under Mohr circle depends on the values of displacement

boundary condition, cohesive strength (c) and friction angle (0). The values of cohesive

strength (c) and friction angle ( <f>) are shown in Tables 2-4. When the displacement

boundary condition is equal to 75 m/lOOOyr no failure may occur for all the models but

if gradual change of boundary condition i.e. 150 m/2000yr, 225 m/3000yr then a few failure

may occur at the shallower level. For the proposed models, displacement boundary

condition has been taken as 375 m/5000yr. Depending on this condition some failure occur

along the shallower level of all the models and most of the failure occur at the sub

Himalaya and the Tethys Himalaya (Fig. 24-27). According to the predetermined great

thrusts (MBT, MCT, LHT and STDS), failure occur along two boundaries (Fig. 24-27).

Stress Distribution and Fault Development Around Nepal Himalaya by Means of Finite Element Method 49

Tdliy

Fig, 24, Failure elements of model - 1. Red blocks indicate failured.

Fig. 25. Failure elements of model - 2. Red blocks indicate failured.

1 100

Fig. 26. Failure elements of model - 3(A). Red blocks indicate failured.

Fig. 27. Failure elements of model - 3(B). Red blocks indicate failured.

By 'tuning' different controlling parameters, we did not succeed in obtaining in a model

where failure occurred at the deeper part of Higher Himalaya and Lesser Himalaya, due

to hydrostatic condition.

Several published studies of focal mechanism solutions of earthquakes in the Himalaya

region give the same general pattern of thrust faulting, with one plane dipping gently

beneath the Himalaya (Armbruster et a]., 1976; Banghar, 1974; Ben Menahen et al., 1974;

Chen & Molnar, 1977; Fitch ,1970; Ichikawa et al., 1972; Molnar et al., 1973; Rastogi et

al., 1973; Tandon & Srivastava, 1975).

This study also shows the same pattern of thrust faulting along the shallower part


of all the models. The boundary condition, whatever it might be (75 m during lOOOyr

or 375 m during 5000 yr), it shows thrust faulting along the shallower region of the

Himalaya. Changing of displacement boundary condition changes the direction of principal

stresses along the deeper part but the upper part remain unchanged.

Conclusion

(1) Variation of the velocity boundary condition indicates changes of direction of principal

stresses along the deeper part while that along the shallower part remain unchanged.

(2) Nature of stress pattern is most likely compressive for all the models but if conver

gence rate is high then some extension ( less than 100 MPa) may happen on the shallower

part.

(3) The difference between maximum principal stress ( ad and minimum principal stress

( as) is comparatively high if the convergence rate is relatively high.

(4) Hydrostatic condition occurs within the deeper part of the Higher Himalaya, Lesser

Himalaya and some parts of the Granitic layer (no deformation may occur within the

region).

(5) General tendency of the direction of principal stresses ( <J\ and a3) are complicate to

determine. Along the upper part of the whole region the maximum principal stress is

horizontal. Comparatively, in the lower part, the direction of principal stress is vertical

(except for the boundary condition 375m).

(6) According to the Mohr - Coulomb criterion, failure is observed along the shallower

part of Siwalik, Tethys and Granitic layer, and a very few near the surface of MBT,

MCT and STDS.

(7) Inspite of changing the controlling parameters, failure did not occur in the deeper

part of Higher Himalaya, Lesser Himalaya and Granitic layer, because of hydrostatic

condition.

(8) Previous studies on focal mechanism solutions of earthquakes in the Himalayan

region show the existence of thrust faults along its EW stretching with one plane dipping

gently north beneath the Himalaya. Simulation provides the same distribution of thrust

faults along the upper part of the models as shown by the focal mechanism solutions.

Acknowledgment

Md. Mahmudul Alam would like to express his gratitude to MONBUSHO for financial

constraint during the study period. The encouragement and suggestions for him received

from honorable teacher Professor Massaki Kimura, Department of Physics and Earth

Sciences, University of the Ryukyus, Okinawa, Japan.

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