stress distribution and fault development around...
TRANSCRIPT
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
16 MdMahmudulA1amandDaigoroHayashi
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.
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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
18 Md・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.
20 Md、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‐
26 Md、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ビノ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
30 Md、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.
34 Md・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
36 Md・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
4 G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
StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFiniteElementMethod37
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
【周回ご吻詞H駒I動
←皿 75m40m
●」△10mぞ ̄
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
38 Md・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).
StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFiniteElementMethod39
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
40 Md・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.
StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFiniteElementMethod41
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.
42 Md・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.
44 Md、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
StressDistributionandFaultDevelopmentAroundNepalHimalayabyMeansofFiniteElementMethod45
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
46 Md・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 24 97 92 06 23520 33016 1925 28724 9160
03 26SEP1964 29 96 80 46 4030 22060 22015 4075 1350
04 210CTl964 28 04 93 75 3575 17785 17740 35750 870
05 l2JANl965 27 40 87 01 015 18075 18030 060 900
06 27jUN1966 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 79 19066 1024 19021 1069 1000
09 z0FEBl967 33 63 75 鋼 16825 4250 1014 12357 27228
10 l4MAR1967 28 41 9H1 29 310 18380 18335 355 930
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
50 Md. Mahmudul Alam and Daigoro Hayashi
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.
References
Arita, K., Hayashi, D., Yoshida, M., 1982. Geology and structure of the Pokhara-Piuthan
Stress Distribution and Fault Development Around Nepal Himalaya by Means of Finite Element Method 51
area, central Nepal. Jour. Nepal Geol. Soc. 2, 5-29.
Arita, K., Shiraishi, K. Hayashi, D., 1984. Geology of western Nepal and a comparison with
Kumaun, India. Jour. FAc. Sci., Hokkaido Univ. Ser. IV. 21(1), l-20.ture of thePokhara-
Piuthan area, central Nepal. Jour. Nepal Geol. Soc. 2, 5-29
Arita, K., 1983. Origin of the inverted metamorphism of the lower Himalaya, central Nepal.
Tectonophysics, 95, 43-60.
Armbraster, J.f Seeber, L., Jacob, K.H., 1978. The northwestern termination of the Himalayan
mountain front: Active tectonics from microearthquakes. J. Geophys. Res. 83, 269-282.
Banghar, A.R., 1974. Focal mechanisms of earthquakes in China, Mongolia, Russia, Nepal,
Pakistan, and Afghanistan. Earthq. Notes, 45, 1-11.
Banghar, M. Isacks, B.L., 1976. Spatial distribution of earthquakes and subduction of the
Nazca plate beneath South America. Geology, 4, 686-692.
Bashyal, R.P., 1981. Geology of Dhangarhi-Dandeldhura road section and its regional
significance. JNGS, 1, 15-28.
Bordet, P., Colchen, M., Le Fort, P., 1972. Some features of the geology of the Annapurna
renge, Nepal Himalaya. Him. Geol., 2, 537-563.
Bmnet, M., 1986. Ductile thrusting in the Himalayas: Shear sense criteria and stretching
lineations. Tectonics, 5, 247-265.
Burg, J.P., Chen, G.M., 1984. Tectonics and structural zonation of southern Tibet, China.
Nature, 311, 219-223.
Chandra, U., 1981. Focal mechanism solutions and their tectonic implications for the eastern
Alpine-Himalayan region. Geodynamics series, 3, 243-271.
Chemenda, A.I., Mattaure, M. Malavieille, J., Bokun, A.,N., 1995. A mechanism for syn-
collisional rock exhumation and associated normal faulting: Results from physical
modeling. Earth Planet. Sci. Lett., 132, 225-232.
Chen, W.P., Molnar, P. 1977. Seismic moments of major earthquake and the average rate of
slip in central Asia. J. Geophys. Res., 82, 2945-2969.
Colchen, M., LE Fort, P., Pecher, A., 1986. Geological research in the Nepal's Himalaya:
Annapurna-Manaslu-Ganesh Himal, notice of the geological map on 1/200000. Centre
National de la Recherche Scientifique, Paris.
Dewey, J.F., Bird, J.M., 1970. Mountain belts and the new global tectonics. J. Geophys. Res.,
75, 2625-2647.
England, P., Houseman, G., 1985. Role of lithospheric strength heterogeneities in the tectonics
of Tibet and neighbouring regions. Nature, 315, 297-301.
England, P., Houseman, G., 1986. Finite strain calculations of continental deformation, 2,
comparison with the India-Asia collision zone. J. Geophys. Res., 91, 3664-3676.
England, P., Mckenzie, D., 1982. A thin viscous sheet model for continental deformation.
Geophys. J.R.Astr.Soc, 70, 295-321.
England, P., Mckenzie, D., 1983. Correction to a thin viscous sheet model for continental
deformation. Geophys. J.R.Astr.Soc, 73, 523-532.
England, P.C., Thomson, A.B., 1984. Pressure - temperature-time paths of regional meta
morphism, part-I: Heat transfer during the evolution of regions of thickened continental
crust. Jour. Petrol., 25, 929-954.
Evans, P., 1964. The tectonic framework of Assam, J. Geol. Soc. India, 5, 80-98.
Fitch, T.J., 1970. Earthquake mechanisms in the Himalaya, Burmese and Andaman regions
and continental tectonics in Central Asia. J. Geophys. Res., 75, 2699-2709.
Fuchs, G., Frank, W., 1970. The geology of west Nepal between the rivers Kali Gandaki and
Thulo Bheri. Jahrb. Bundesanst. Sonderb. 18, 1-103.
52 Md. Mahmudul Alam and Daigoro Hayashi
Fuchs, G., 1980. The Lesser Himalayan geology of west Nepal and its regional importance.
In: stratigraphy and correlations of Lesser Himalayan formations, Hindustan Pub., Delhi,
163-173.
Ganseer, A., 1984. Geology of the Himalayas. Interscience, London 289p.
Ganseer, A., 1966. The Indian Ocean and the Himalayas: a geological interpretation, Eclog.
Geol. Helv., 59, 831-848.
Gill, W.D., 1952. The stratigraphy of the Siwalik Series in the northern Potwar, Punjab,
Pakistan. Q.J. Geol.Soc. London, 107(4), 375-394.
Glennie, K.W., Ziegler, M.A., 1964. The Siwalik formation in Nepal. Intern. Geol. Cong.
22nd Sess. Rep. Pt., 15, 82-95.
Hagen, T., 1969. Report on the geological survey of Nepal, Vol.1. Denkschr. Schweiz. Naturf.
Gesell., Bd. 86(1), 1-185.
Hashimoto, S., et al., 1973. Geology of the Nepal Himalayas. Saikon, Tokyo, 286p.
Hayashi, D., 1979. Finite element formulation of viscous fluid on a variational principle.
Bull. Coll Sci. Univ. Ryukyu, 28, 119-130.
Hayashi, D., 1980. Variation of field of viscous stress around diapir calculated by the finite
element method. Bull Coll. Sci. Univ. Ryukyu, 30, 11-21.
Hayashi, D., 1980. Simulation of Himalayan orogeny and tectonophysics. Monthly Earth, 2,
787-796.
Hayashi, D., 1987. Numerical simulation of the uplift of the Tibetan Plateau. Jour. Geol.
Soc. Jap., 93, 587-595.
Hayashi, D., Kizaki, K., 1972. Numerical analysis on migmatite dome with special reference
to the finite element method. Jour. Geol. Soc. Jap., 78, 677-686.
Hayashi, D., Kizaki, K., 1979. Numerical experiments of migmatite rise based on continuum
dynamics. Tectonophysics, 60, 61-76.
Hayashi, D., Fujii, Y., Yoneshiro, T., Kizaki, K. 1984. Geology of the Karnali-Bheri region,
west Nepal. Jour. Nepal Geol. Soc, 2, 29-40.
Hayashi, D., Talbot, C, 1991. Numerical simulation of a Himalayan profile. Essays in
Geology, Professor Hisao Nakagawa Commemorative Volume, 53-63.
Hiroshima, M., 1972. Topography of Marsyandi River, Symposium: Nepal , 1, 45-50.
Ichikawa, M., Srivastava, H.N., Drakopoulos, J., 1972. Focal mechanism of earthquakes
occuring in and around Himalayan and Burmese mountain belt. Papers in Meteorology
and Geophysics (.Tokyo), 23, 149-162.
Isacks, B.L., Oliver, J., Sykes, L.R., 1968. Seismology and the new global tectonics. J.
Geophys. Res., 73, 5855-5900.
Itihara, M. Shibasaki, T., Miyamoto, N., 1972. Photogeological survey of the Siwalik Ranges
and the Terai Plain, southeastern Nepal. Jour. Geosci. Osaka City Univ., 15, 77-98.
Ito, H., 1972. Change of topography due to flow of the crust under the condition of isostasy.
Jour. Geol. Soc. Jap., 78, 29-38.
Kamada, K., Yashida, M., Arita, K., 1982. Jurassic ammonites from the Muktinath region.
Jour. Nepal Geol. Soc, 2, 149-154
Kaneko, Y., 1994. Metamorphic P-T path of the Higher Himalayan Sequence in the Annarnapurna
region, central Nepal Himalaya. Proceeding of the Himalaya Symposium, Tok&i University
Press.
Kaneko, Y., 1995. Thermal structure in the Annapurna region, central Nepal Himalaya:
implication for the inverted metamorphism. Jour. Mineral. Petrol. Econ. Geol., 90, 143-
154.
Kano, T., 1977. Origin of augen gneisses and related mylonitic rocks in the Hida metamorphic
Stress Distribution and Fault Development Around Nepal Himalaya by Means of Finite Element Method 53
region, central Japan. Plutonism in relation to volcani&m and metamorphism (7th
C.P.P.P. meetings), 206-229.
Le Fort, P., 1975. Himalayas: the collided range. Present knowledge of the continental arc.
Amer. Jour. Sci., 275, 1-44.
Le Pichon, X., 1988. Sea floor spreading and continental drift. J. Geophys. Res. 73, 3661-
3698.
McKenzie, D., 1969. Speculations on the consequences and causes of the plate motions.
Geophys. J. Roy. Astr. Soc, 18, 1-32.
Menke, W.H., Jacob, K.H., 1976. Seismicity patterns in Pakistan and northwestern India
associated with continental collision. Bull. Seismo. Soc. Amer. 76.
Minster, J.B., Jorden, T.H., Molnar, P., Haines, E., 1974. Numerical modeling of instanta
neous plate tectonics. Geophys. J. Roy. Astr. Soc, 36, 541-576.
Molnar, P., Fitch, T.J., Wu, F.T., 1973. Fault plane solutions of shallow earthquakes
contemporary tectonics of Asia. Earth Plan. Sci. Lett., 16, 101-112.
Molnar, P., Fitch, T.J., Wu. F.T., Chen, W.P., Warsi, W.E.K., Tapponnnier, P., 1977.
Structure and tectonics of the Himalaya; A brief summary of relevant geophysical obser
vations. Himalaya, Science de la Terre, Centre National de la Recherche Scientique,
Paris, 269-294.
Molnar, P., Tapponnnier, P., 1975. Cenozoic tectonics of Asia: effect of a continental collision.
Science, 189, 419-426.
Pecher, A., 1989. The metamorphism in the central Himalaya. Jour. Metamorphic. GeoL, 7,
31-41.
Powell, P., Conaghan, P.J., 1973. Plate tectonics and the Himalayas. Earth Plan. Sci. Lett.,
20, 1-20.
Rastogi, B.K., 1974. Earthquake mechanisms and plate tectonics in the Himalayan region.
Tectonophysics, 21, 47-56.
Sakai, H., 1985. Geology of the Kali Gandaki Supergroup of the Lesser Himalaya in Nepal.
Mem. Fac. Sci., Kyushu Uniu., Ser. D. GeoL, 25, 337-397.
Searly, M., Windley, B.F., Coward, M.P., Cooper, D.J.W., Rex, A.J., Rex, D., Tingdong,
L., Xuchang, X., Jan. M.M.Q., Thakur, V.C. and Kumar, S., 1987. The closing of Tethys
and the tectonics of the Himalaya. Bull. GeoL Soc. Amer., 98, 678-701.
Seeber, L., Armbruster, J.G., Quittmeyer, R.C., 1981. Seismicity and Continental subduction
in the Himalayan Arc. Geodynamics series, 3, 215-242.
Sharma.T., Merh, S.S., Vashi, N.M., 1978. The Terraced Conglomerates of Pokhara Vally in
central Nepal, Symposium on Morphology and Evolution of Landforms, Department of
Geology, University of Delhi, 226-240.
Sharma.T., Upreti, B.N., Vashi, N.M., 1980. Kali Gandaki gravel deposits of central West
Nepal - their neotectonic significance, Tectonophysics, 62, 127-139.
Stauder, W., 1968. Tensional character of earthquake foci beneath the Aleutian trench with
relation to sea-floor spreading. J. Geophys. Res., 73, 7693-7703.
Stocklin, J., 1980. Geology of Nepal and its regional frame. Jour. GeoL Soc. London, 137,
1-34.
Tandon, A.N., Srivastava, H.N., 1975. Focal mechanisms of some recent Himalayan earth
quakes and regional plate tectonics. Bull. Seismo. Soc. Amer., 65, 963-969.
Tandon, S.K., 1976. Siwalik sedimentation in a part of the Kumaun Himalaya, India. Sed.
GeoL, 16, 131-154.
Tandon, S.K., Narayan, D., 1981. Calcrete conglomerate, case-hardened conglomerate and
cornstone, a comparative account of pedogenic carbonates from the continental Siwalik
54 Md. Mahmudul Alam and Daigoro Hayashi
Group, Punjab, India. Sedimentology, 28, 353-367.
Tapponnier, P. Molnar, P., 1977. Active faulting and tectonics in China. J. Geophys. Res.,
82, 2905-2930.
Uemura, T., 1971. Some problems on tectonic flow of rocks. Jour. Geol. Soc. Jap. 77, 273-278.
Valdiya, K.S., 1980. Geology of Kumaun Lesser Himalaya. Wadia Institute of Himalayan
Geology, Dehra Dun, India, 291p.
Valdiya, K.S., 1977. Structural set-up of the Kumaun Lesser Himalaya. In: Himalaya,
C.N.R.S., Paris, 449-462.
Valdiya, K.S., 1980. Outline of the structure of Kumaun Lesser Himalaya. In: Tectonic geology
of the Himalaya. Today and Tomorrow Pub., New Delhi, 1-14.
Wadia, D.N., 1975. Geology of India, 4th Edition. Tata McGraw-Hill Publishing Co., New
Delhi, 508p.
Warsi, R.I., Molnar, P., 1977. Plate tectonics and gravity anomalies in India and the Himalaya.
Science de la Terre, Centre National de la Recherche Scientique, Paris.
West, R.M., Lukacs, J.R., Munthe, J.Jr., Hussain, S.T., 1978. Vertebrate fauna from Neogene
Siwalik Group, Dang Vally, western Nepal. Jour. Paleont,, 52, 1015-1022.
Widely, B.F., 1984. The evolving continents, 2nd ed. John Wiley and Sons, Inc., 399p.
Widely, B.F., 1995. The evolving continents, 3rd ed. John Wiley and Sons, Inc., 526p.
Yamanaka, H., Iwata.S., 1982. River terraces along the middle Kali Gandaki and Marsyandi
Khola, central Nepal. Jour. Nepal Geol. Soc, 2, 95-111.
Yamanaka, H., Yoshida, M., Arita, K., 1982. Terrace landform and Quaternary deposit
around Pokhara vally, central Nepal. Jour. Nepal Geol. Soc, 2, 113-136.
Yashida, M., Arita, K., 1982. On the Siwaliks observed along some routes in central Nepal.
Jour. Nepal Geol. Soc, 2, 59-66.