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地质岩土英文文献翻译
InternationalJournalofRockMechanicsandMiningSciences
Analysisofgeo-structuraldefectsinflexuraltoppling
failure
AbbasMajdiandMehdiAmini
Abstract
Thein-siturockstructuralweaknesses,referredtohereinasgeo-structural
defects,
suchasnaturally
inducedmicro-cracks,
are
extremely
responsive
to
tensile
stresses.Flexuraltopplingfailureoccursbytensilestresscausedbythemoment
dueto
the
weight
ofthe
inclined
superimposed
cantilever-like
rock
columns.
Hence,
geo-structuraldefectsthatmaynaturallyexistinrockcolumnsaremodeledbya
series
of
cracks
inmaximumtensile
stress
plane.
Themagnitudeandlocation
of
the
maximumtensile
stress
inrock
columns
with
potential
flexural
toppling
failure
are
determined.
Then,the
minimumfactor
of
safety
for
rock
columnsare
computedbymeans
ofprinciples
of
solid
andfracture
mechanics,
independently.
Next,
anewequation
isproposedtodeterminethelengthofcriticalcrackinsuchrockcolumns.Ithas
beenshownthat
if
the
length
ofnatural
crackis
smaller
thanthelength
ofcritical
crack,thentheresultbasedonsolidmechanicsapproachismoreappropriate;
otherwise,
the
result
obtained
basedonthe
principles
offracture
mechanics
is
more
acceptable.
Subsequently,
for
stabilization
oftheprescribed
rock
slopes,
somenew
analyticalrelationshipsaresuggestedfordeterminationthelengthanddiameter
oftherequiredfully
groutedrockbolts.Finally,forquick
designof
rockslopes
againstflexuraltopplingfailure,agraphicalapproachalongwithsomedesign
curves
arepresented
by
whichanadmissibleinclinationofsuchrockslopesand
or
length
of
all
required
fully
grouted
rockbolts
are
determined.
In
addition,
acase
studyhasbeenusedforpracticalverificationoftheproposedapproaches.
KeywordsGeo-structuraldefects,In-siturockstructuralweaknesses,Critical
cracklength
...
1.
Introduction
Rockmassesarenaturalmaterialsformedinthecourseofmillionsofyears.
Sinceduringtheirformationandafterwards,theyhavebeensubjectedtohigh
variablepressuresbothverticallyandhorizontally,usually,theyarenot
continuous,andcontainnumerouscracksandfractures.Theexertedpressures,
sometimes,producejointsets.Sincethesepressuressometimesmaynotbe
sufficientlyhightocreateseparatejointsetsinrockmasses,theycanproduce
microjointsandmicro-cracks.However,theresultscannotbeconsideredas
independentjointsets.Althoughtheeffectsofthesemicro-cracksarenotthat
pronouncedcomparedwith
large
sizejointsets,yet
theymaycauseadrasticchange
ofin-situgeomechanicalpropertiesofrockmasses.Also,inmanyinstances,due
todissolutionofin-siturockmasses,minutebubble-likecavities,etc.,are
produced,whichcauseaseverereductionofin-situtensilestrength.Therefore,
oneshouldnotreplacethisin-situstrengthbythatobtainedinthelaboratory.
Ontheotherhand,measuringthe
in-situ
rock
tensile
strength
dueto
the
interaction
of
complexparametersis
impractical.
Hence,
anappropriate
approach
for
estimation
ofthetensilestrengthshouldbesought.Inthispaper,bymeansofprinciplesofsolidandfracturemechanics,anewapproachfordeterminationoftheeffectofgeo-structuraldefectsonflexuraltopplingfailureisproposed.
2.Effectofgeo-structuraldefectsonflexuraltopplingfailure
2.1.Criticalsectionoftheflexuraltopplingfailure
Asmentionedearlier,MajdiandAmini[10]andAminietal.[11]haveprovedthattheaccurate
factorofsafetyisequaltothatcalculatedforaseriesofinclinedrockcolumns,which,by
analogy,isequivalenttothesuperimposedinclinedcantileverbeamsasshowninFig.3.According
totheequationsoflimitequilibrium,themomentMandtheshearingforceVexistinginvarious
cross-sectionalareasinthebeamscanbecalculatedasfollows:
（5）
（6）
Sincethesuperimposedinclinedrockcolumnsaresubjectedtouniformlydistributedloads
...
causedbytheirownweight,hence,themaximumshearingforceandmomentexistattheveryfixed
end,thatis,atx=Ψ:
（7）
（8）
IfthemagnitudeofΨfromEq.
（1）issubstituted
ofshearingforceandthemaximummomentofequivalent
intoEqs.（7）and（8）,thenthemagnitudesbeamforrockslopesarecomputedasfollows:
（9）
（10）
whereCisadimensionlessgeometricalparameterthatisrelatedtotheinclinations
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