Research on the Hard-Rock Breaking Mechanism of Hydraulic Drilling Impact Tunneling

35 Pages·2015·11.96 MB·English

Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2015, Article ID 153648, 34 pages
http://dx.doi.org/10.1155/2015/153648
Research Article
Research on the Hard-Rock Breaking Mechanism of
Hydraulic Drilling Impact Tunneling
RishengLong,1,2ShaoniSun,3andZishengLian1,2
1CollegeofMechanicalEngineering,TaiyuanUniversityofTechnology,Taiyuan,Shanxi030024,China
2ShanxiKeyLaboratoryofFullyMechanizedCoalMiningEquipment,Taiyuan,Shanxi030024,China
3SchoolofMechanicalEngineeringandAutomation,NortheasternUniversity,Shenyang,Liaoning110004,China
CorrespondenceshouldbeaddressedtoRishengLong;[email protected]
Received19May2015;Revised21July2015;Accepted26July2015
AcademicEditor:FrancescoFranco
Copyright©2015RishengLongetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Inordertorealizetherapidhard-rocktunnelinginasafe,highlyeffective,andeconomicmanner,thehydraulicdrillingimpact
hard-rocktunneling(HDIHT)technologyandmethodwereintroducedbasedonthetheoriesofrockmechanicsandhydraulic
impact.Thekeyparameters,includingdrillingradiusandimpactdistance,wereresearchedtorevealthestressbehaviorduring
HDIHTprocess.TheVonMisesequivalentstressanditsprincipalstresscomponentswereanalyzed,andthebreakingmechanism
ofHDIHTwasalsodiscussed.Thesimulationresultsshowthat,toensuretheeffectivenessof“secondarybreaking”causedby
drillingholefreesurfaces,theimpactdistanceshouldnotexceed200mm,andtheoptimaldrillingradiuswasabout35mm.
1.Introduction on the theories of rock mechanics, when hammer impacts
hard rock directly, its impact energy will be converted into
Hard-rock rapid tunneling, especially for the rock whose the compressive wave in the depths of rock at the impact
hardnessexceedsf10(rockPlattsruggednesscoefficient),isa moment,andabrokenpitisformedinstantly.Ifsomeholes
worldwidetechnicalissue,whetherforundergroundtunnel- existedinworkingface,thecompressiveimpactwavewillbe
ing or construction. So far, drill and blast tunneling (DBT) transformedintothetensilestressafterthereflectionatfree
and heavy-duty roadheader are still the main methods for surfaces. Owing to the fact that the tensile strength of rock
hard-rocktunnelingincoalmine.However,lotsofauxiliary is only three to five percent of its compressive strength, the
equipmentandpersonsneededatworkingface,greatdamage rockneartheholesmaybebrokenagainunderthesecondary
tothesurroundingrocks,andovertunnelingandinsufficient breaking effect of “compression-tension” transformation [1,
tunneling of final sections are the major problems of DBT 2].Thus,intheproposedHDIHTprocess,manyholesshould
method. Heavy-duty roadheader also has its disadvantages bedrilledinadvancetoincreasefreesurfacearea,andthen
whichareasfollows:lowereconomiccuttinghardness(≤f8), a hydraulic breaker with large impact energy was used to
nethermoretunnelingefficiency,highercutterconsumption impactandcrushhardrockdirectly.
rate, and so forth. Although the hard-rock tunnels (≥f10) Manynumericalsimulationmethods,includingmechan-
are not more than 5 percent of the general amount of ics of continuous medium (MCM), mechanics of noncon-
annualtunneling,itisstillacrucialrestrictionfactorforthe tinuous medium (MNCM), and coupling analysis of con-
highly efficient production and management of coal mine. tinuous discrete (CACD), have been conducted to reveal
Therefore,itisurgenttoseekanovel,safe,andhighlyeffective the breaking and failure behavior of brittle rock. In 1995,
approach(includingtheories,technology,andequipment)for Munjiza et al. [3, 4] introduced the damage mechanics and
thehard-rockrapidtunneling,withnoexplosion. fracture mechanics into the finite element method (FEM)
Hydraulicdrillingimpacthard-rocktunneling(HDIHT) andproposedthecombinedfinite-discreteelementmethod
maybe just thepotentialmethodwe arelookingfor. Based (CF/DEM)tosimulatethebrittlefractureandfailure.Based
2 MathematicalProblemsinEngineering
P
2𝜃
h
i
h
i+1
𝜓
L
𝜃
T
𝜓
R
N
Figure1:Sketchoftherockintrusionprocessofwedgeshapedblade.
a mechanism of HDIHT method and technology have never
)
3
−m beenreportedyet.
·mc In this work, based on the relevant rock mechanics
·g theories and “element birth and death” technique, the key
k
k ( parameters, including drilling radius (dr) and impact dis-
or
w tance (di), were researched to explore the hard-rock stress
c SZ
fi behavior during HDIHT process through APDL program-
ci
pe a ming. The Von Mises equivalent stress and its principal
g s 0 stresscomponentswereanalyzedindetail,andthebreaking
elin TZ CZ mechanismofHDIHTwasalsodiscussed.
his
C
0 A0 Ac A
Impact energy (kg·m) 2.TheoreticalAnalysisandCalculation
Figure2:𝛼-𝐴curveduringimpactbreakingprocess. Onthebasisoftherelevanttheoriesofrockstaticintrusion
[1, 2], Paul simplified the rock intrusion of wedge shaped
blade into the sketch shown in Figure1. Suppose 𝑅 was the
stress component of load 𝑃 along the vertical edge-surface
on the MCM approach and deep understanding of rock’s
direction; it could be decomposed into the shear force (𝑇)
heterogeneity, Tang and his team [5–7] proposed a realistic
failureprocessanalysismodel(RFPA2D,RFPA3D),whichhad andnormalforce(𝑁)ontheshearfracturesurface.Basedon
Mohr-Coulombfailuretheory,whenshearstress𝜏exceeded
beenwidelyusedaroundtheworld.Jingetal.[8]presented
cohesion 𝐶 and internal friction 𝜇𝜎, shear-breaking would
a numerical model for coupled hydromechanical processes
occur.Thefailureconditionwasgivenby
infracturedhardrocksusingthediscontinuousdeformation
analysis (DDA) method, but their emphasis was placed on
the physical behaviour of the coupled stress/deformation 𝜏−𝜇𝜎=𝐶. (1)
and fluid flow interaction in rock fractures. Zhang et al.
[9]usedamodifieddiscontinuousdeformationalgorithmto
simulate the failure behavior of jointed rock. Using particle Assuming the load of the 𝑖th impact was 𝑃∗, the pene-
𝑖
simulationmethod,XiaandZhou[10]investigatedthefailure tration depth of the 𝑖th impact was 𝐻∗, and the edge angle
𝑖
process of brittle rock under triaxial compression through was 2𝜃 (see Figure1), there must be a relationship between
bothexperimentalandnumericalapproaches.Basedonthe the(𝑖+1)thloadanditsstress:
statisticalcontinuumdamagemechanicstheoryandthefinite
element method (FEM), Li et al. [11] developed a statistical
𝑃∗
meso-damagemechanicalmethod(SMDMM)tomodelthe 𝑅= 𝑖+1 ,
transscale progressive failure process of rock. Furthermore, 2sin𝜃
many simulations were also carried out by Min and other ℎ∗ (2)
researchers to study the failure process of brittle rock [12– 𝐿= 𝑖+1 ,
18]. However, the researches about the hard-rock breaking sin𝜓
MathematicalProblemsinEngineering 3
Impact rod of hammer (length:1200mm)
Rock (granite)
400mm
500mm 400mm
di
Symmetry planes
Figure3:SketchofFEmodelusedinthesimulations.
where 𝐿 was the length of shear plane and 𝜓 was the shear Equation(5)couldbefurtherwrittenas
planeangle.Usingedgelengthastheunit,𝜏and𝜎couldbe
𝑃∗ 1
givenby 𝜏−𝜇𝜎= 𝑖+1 ⋅ [sin𝜓cos(𝜓+𝜃)cos𝜙
ℎ∗ 2sin𝜃cos𝜙
𝑖+1
𝑃∗
𝜏= 𝑇 = 𝑅cos(𝜓+𝜃), (3) −sin𝜓sin(𝜓+𝜃)sin𝜙]= 2ℎ𝑖+∗1 (7)
𝐿 𝐿 𝑖+1
𝑁 𝑅 sin𝜓cos(𝜓+𝜃+𝜙)
𝜎= = sin(𝜓+𝜃). (4) ⋅ ,
𝐿 𝐿 sin𝜃cos𝜙
where𝜏−𝜇𝜎wasafunctionof𝜓.Settingthefirstderivative
Substituting (3) and (4) into (1), then (1) could be of(7)equalszero,itwaseasytobefoundthatwhen
rewrittenas 𝜋 𝜃+𝜙
𝜓= − . (8)
4 2
𝑃∗ The value of 𝜏 − 𝜇𝜎 reached its maximum. Therefore, the
𝜏−𝜇𝜎= 𝑖+1 [sin𝜓cos(𝜓+𝜃)
ℎ∗ 2sin𝜃 shear-breakingsurfacewouldfirstappearintheplaneofthe
𝑖+1 (5) slopeof𝜓.When𝜃+Φ < 90∘,shear-breakingmightoccur;
−𝜇sin𝜓sin(𝜓+𝜃)]. while𝜃+Φ > 90∘,therockwasinafullycompressedstate;
theleap-forwardinvasionwouldnothappen.Substituting(8)
into(7),(7)couldbefinallywrittenas
The internal friction angle 𝜙 was used to represent the 𝜏−𝜇𝜎
internalfrictioncoefficient;thatis,
𝑃∗ sin(𝜋/4−(𝜃+𝜙)/2)cos(𝜋/4+(𝜃+𝜙)/2)
= 𝑖+1 (9)
ℎ∗ 2sin𝜃cos𝜙
sin𝜙 𝑖+1
𝜇=𝑡𝑔𝜙= .
(6)
cos𝜙 =𝐶.
4 MathematicalProblemsinEngineering
(a) (b)
(a) dr=20mm,di=200mm (b) dr=20mm,di=250mm
(c) (d)
(c) dr=20mm,di=150mm (d) dr=35mm,di=200mm
(e)
(e) dr=50mm,di=200mm
Figure4:ComparisonofdifferentFEmodels.
Solvingtheaboveformula,theratioof𝑃∗ toℎ∗ could That is, the ratio of each impact’s load to its invasion
𝑖+1 𝑖+1
begivenby depthwasaconstant.Inaddition,accordingtothecorrelation
𝑃𝑖∗+1 = 4𝐶⋅sin𝜃⋅(1−sin𝜙) =𝐾. (10) btheetw𝛼e-e𝐴ncimurpvaectoefnimerpgyacatnbdrechakisienlginpgrsopceecsisficcowuoldrkb(eCdSiWvi,d𝛼e)d,
ℎ𝑖∗+1 1−sin(𝜃+𝜙) into three zones, that is, scaring zone (SZ), transient zone
MathematicalProblemsinEngineering 5
28
7
6
.. 27
.
3
2 26
1516 25
14
24 17
18
19
23
22
21
20
1
8 9 ···1213
Figure5:SketchofnodedistributioninFEmodel.
m/s) 8.57
y (
cit ··· ···
o
Vel
0 0.3 3 100
T (ms)
Figure6:Velocity-timeloadingcurveofimpactrodinthesimulations.
(TZ),andcrushedzone(CZ).Whenimpactenergywasquite 26kg⋅m⋅cm−3, the crushed granite volume of each impact
small, the 𝛼-𝐴 curve would fallinto its left side, which was couldbecalculatedasfollows:
SaZb.roInketnhipsitr,eagniodnt,htehderiompppaecdtrpoockweprowwdasertowoassmvearlylfitonefo,rfomr 𝑉 = 𝐴 = 7500(N⋅m) = 7500 m3
theCSWwasquitelarge.Theshadedregionin𝛼-𝐴curvewas break 𝛼 26(kg⋅m/cm3) 26×10/10−6 (12)
TZ. In this domain, the impact breaking data and behavior =2.885×10−5m3.
wereunpredictable.Asimpactenergywaslargerthan𝐴𝑐,the
𝛼-𝐴 curve would eventually enter a relatively stable region, Based on the crushed granite volume of each impact, if
CZ. hammerimpactedafixedpointrepeatedly,thefinalradiusof
Withregardtotherelationshipbetweenbrokenrockvol- brokenpit(𝑟pit)shouldmeetthefollowing:
ume(𝑉break)andimpactenergy(𝐴),thefollowingempirical
ℎ
formulawaswidelyusedandexpressedasfollows[1]: 𝜋𝑟 2⋅ =2.885×10−5×𝑛 ,
pit 3 imp
𝑟 (13)
𝑉break =𝐶1(𝐴−𝐴0)𝑎, (11) ℎpit =0.375,
pit
where𝐴0 =0,𝑎=1,𝐶1 =1/𝛼,inunitsofkg−1⋅m−1⋅cm3. wdehpetrheo𝑛fimbprwokaesnthpeiti,mapnadct0t.3im75eswaatsaaficxoendsptaonint,t,dℎepciitdwedasatnhde
Supposing the impact energy of hydraulic impact ham- given by the end-shape of impact rod. Therefore, in theory,
meris7500J,roddiameter,150mm,andtheCSWofgranite, hydraulicimpacttunnelingwasfeasible.
6 MathematicalProblemsinEngineering
0
0.250E+07
0.750E+07
0.125E+08
a)
P
0.175E+08g) (
v
a
0.225E+08V (
Q
0.275E+08SE
0.325E+08
0.375E+08
0.400E+08
(a) The0.003ths (b) The0.203ths (c) The0.403ths
0
0.250E+07
0.750E+07
0.125E+08
a)
P
0.175E+08g) (
v
a
0.225E+08V (
Q
0.275E+08SE
0.325E+08
0.375E+08
0.400E+08
(d) The0.603ths (e) The0.803ths
Figure7:TheVonMisesequivalentstresscontoursofmodelAatdifferenttime.
3.FiniteElementModelingandConfiguration and the “element birth and death” technique was
realizedthroughAPDLprogramming.
Takingthegranite,whosePlattsruggednesscoefficientvaried
from f10 to f15, as the research object, the mechanical and (3)The compressive and shear strength were used as
physicalpropertiesparameterswerelistedasfollows:elastic the failure criterion of granite elements. Program
modulus,3.58×104MPa;Poisson’sratio,0.28;ratiooftensile could automatically calculates the stress status of
each cell after one load step or substep. For the
strengthtocompressivestrength,0.03.Foralmostallcrushed
cells,whoseVonMisesequivalentstressexceededthe
granite was powdery detritus in actual impact breaking
compressiveorshearstrengthofgranite,theywould
process,andtheobjectiveofthisworkwasmainlyfocusedon
be deemed invalid and would be removed from the
thestressvariationbehaviorofbrokenpit,drillingholes,and
model immediately. In the meantime, system would
theirsurroundingarea,thecrackgenerationandpropagation
also automatically redefine the contact relationship
ofgraniteduringHDIHTprocesswouldnotbeconsidered.
betweenrod-endandbrokenpit.
Thus,thefollowingassumptionscouldbemade:
(4)Toconsidertheeffectofsurroundingrocksinactual
(1)Basedonthecontinuoushomogeneousmediumthe-
impactbreakingprocess,thesideandbottomsurfaces
ory and the characteristics of granite, the isotropic
ofFEmodelwereallsetastheunlimitedboundaries.
bilinear kinematics hardening model was used. But
thejointdevelopmentandtectonicchangesofgranite
Themainparametersofhydraulichammerwerelistedin
wasnottakenintoaccountinthesimulations.
Table1. In order to reduce the computational workload, as
(2)InvirtueofANSYS/LS-DYNAmodule,the“surfaceto depictedinFigure3,FEmodelwiththerocksizeof400mm×
surface”contacttypeofESTSalgorithmwaschosen, 400mm × 500mm (length × width × thickness) was only
MathematicalProblemsinEngineering 7
Time=0.002s
0
(a) (b) (c)
0.125E+07
0.250E+07
a)
0.375E+07 P
0.500E+07 vg) (
a
0.625E+07 V (
Q
E
0.750E+07 S
0.875E+07
0.100E+08
Time=0.002s
0
(d) (e)
0.125E+07
0.250E+07
a)
0.375E+07 P
0.500E+07 vg) (
a
0.625E+07 V (
Q
E
0.750E+07 S
0.875E+07
0.100E+08
Figure8:TheVonMisesequivalentstresstop-viewcontoursofdifferentmodelsatthe0.002ths.
1.0E+06 1.0E+06 1.0E+06
8.0E+05 8.0E+05 8.0E+05
6.0E+05 6.0E+05 6.0E+05
a) 4.0E+05 a) 4.0E+05 a) 4.0E+05
P P P
( 2.0E+05 ( 2.0E+05 ( 2.0E+05
0.0E+00 0.0E+00 0.0E+00
−2.0E+05 A −2.0E+05 B −2.0E+05 C
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(a) TheVonMisesequivalentstresscurves
1.0E+06 1.0E+06 1.0E+06
5.0E+05 5.0E+05 5.0E+05
a) 0.0E+00 a) 0.0E+00 a) 0.0E+00
P P P
( ( (
−5.0E+05 −5.0E+05 −5.0E+05
−1.0E+06 A −1.0E+06 B −1.0E+06 C
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(b) The1stprincipalstresscurves
1.0E+06 1.0E+06 1.0E+06
5.0E+05 5.0E+05 5.0E+05
0.0E+00 0.0E+00 0.0E+00
a) a) a)
P −5.0E+05 P −5.0E+05 P −5.0E+05
( ( (
−1.0E+06 −1.0E+06 −1.0E+06
−1.5E+06 A −1.5E+06 B −1.5E+06 C
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(c) The3rdprincipalstresscurves
Figure9:StressvariationcurvesofbottomnodeinmodelsA,B,andC.
8 MathematicalProblemsinEngineering
1.0E+06 1.0E+06 1.0E+06
8.0E+05 8.0E+05 8.0E+05
6.0E+05 6.0E+05 6.0E+05
a) 4.0E+05 a) 4.0E+05 a) 4.0E+05
P P P
( 2.0E+05 ( 2.0E+05 ( 2.0E+05
0.0E+00 0.0E+00 0.0E+00
−2.0E+05 A −2.0E+05 D −2.0E+05 E
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(a) TheVonMisesequivalentstresscurves
1.0E+06 1.0E+06 1.0E+06
5.0E+05 5.0E+05 5.0E+05
Pa) 0.0E+00 Pa) 0.0E+00 Pa) 0.0E+00
( ( (
−5.0E+05 −5.0E+05 −5.0E+05
−1.0E+06 A −1.0E+06 D −1.0E+06 E
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(b) The1stprincipalstresscurves
1.0E+06 1.0E+06 1.0E+06
5.0E+05 5.0E+05 5.0E+05
0.0E+00 0.0E+00 0.0E+00
a) a) a)
P −5.0E+05 P −5.0E+05 P −5.0E+05
( ( (
−1.0E+06 −1.0E+06 −1.0E+06
−1.5E+06 A −1.5E+06 D −1.5E+06 E
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
T (s) T (s) T (s)
(c) The3rdprincipalstresscurves
Figure10:StressvariationcurvesofbottomnodeinmodelsA,D,andE.
Table1:Mainparametersofhydraulichammerwithlargeimpact Figure4), including model A (dr = 20mm, di = 200mm),
energy. modelB(dr=20mm,di=250mm),modelC(dr=20mm,di
=150mm),modelD(dr=35mm,di=200mm),andmodel
Parametername Value
E (dr = 50mm, di = 200mm). As shown in Figure5, there
Impactenergy 7500J
were 28 typical nodes researched in each model, including
Pistonweightofhammer 200kg bottom node (node 1), nodes along the diagonal (nodes 20
Roddiameter 150mm to28),nodesarounddrillinghole(nodes14to19),andnodes
Pistonenergytransferefficiency 98% alongsideline(nodes8to13).
Elasticmodulusofrodmaterial 1.02𝐸11Pa The impact frequency of rod was 10Hz, and its loading
Densityofrodmaterial 7800kg⋅m−3 curvewasdemonstratedinFigure6,whichlastedonesecond.
In accordance with the impact energy and energy transfer
Impactfrequency 10Hz
Rodweight 200kg efficiency𝜂𝑆 (betweenthepistonofhammerandrod)listed
RRooddtleipngdtihameter 122000mmmm i2n00Ta×bleVr1o,dt2h/e2v;enloacmiteylyo,frVorodd(V=ro8d).5s7hmou⋅sld−1m. Feeutr7th5e0r0m×o9r8e%, t=o
ensure the efficiency of HDIHT method, a pressing force
Rodtiplength 200mm
wouldbeappliedontherodtooffsetitsreboundaftereach
Poisson’sratioofrodmaterial 0.3
impactandkeepitincontactwithbrokenpitallthetime.The
valueofpressingforcecouldbecalculatedby[1]
a quarter of the actual one and the symmetry boundary 𝐹=2𝑓𝑀𝑉𝑃 =0.015𝑁𝑓√𝐺𝐴, (14)
conditionswereappliedonitssymmetryplanes.
There were five different models developed to explore where 𝑁𝑓 was the impact frequency of hammer (BPM), 𝐺
the stress variation behavior during HDIHT process (see wastheweightofhammer’spiston(kg),and𝐴wastheimpact
MathematicalProblemsinEngineering 9
3.0E+06 3.0E+06
2.0E+06 2.0E+06
a) a)
P P
( 1.0E+06 ( 1.0E+06
0.0E+00 0.0E+00
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
T (s) T (s)
A A
B B
C C
(a) Node28 (b) Node27
3.0E+06 3.0E+06
a) 2.0E+06 2.0E+06
(P Pa)
1.0E+06 ( 1.0E+06
0.0E+00 0.0E+00
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
T (s) T (s)
A A
B B
C C
(c) Node26 (d) Node25
3.0E+06
3.0E+06
2.0E+06 2.0E+06
(Pa) 1.0E+06 (Pa) 1.0E+06
0.0E+00 0.0E+00
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
T (s) T (s)
A A
B B
C C
(e) Node24 (f) Node23
5.0E+06 5.0E+06
4.0E+06 4.0E+06
3.0E+06 3.0E+06
Pa) Pa)
( 2.0E+06 ( 2.0E+06
1.0E+06 1.0E+06
0.0E+00 0.0E+00
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
T (s) T (s)
A A
B B
C C
(g) Node22 (h) Node21
Figure11:Continued.
10 MathematicalProblemsinEngineering
4.0E+07
3.2E+07
2.4E+07
a)
P
(
1.6E+07
8.0E+06
0.0E+00
0.1 0.3 0.5 0.7 0.9
T (s)
A
B
C
(i) Node20
Figure11:TheVonMisesequivalentstresspeak-curvesofnodesalongthediagonalinmodelsA,B,andC.
energy(kg⋅m).Thus,thefinalpressingforceshouldnotbeless pointofHDIHTprocess;(2)whendikeptconstant,withthe
than increaseofdrillingradius,theVonMisesstressofhole-nodes
𝐹=0.015×600×√200×750×10=34850𝑁. (15) wouldascendsimultaneously.Thatis,thebiggerthedrilling
radiuswas,thelargerthemaximumVonMisesstressofhole-
nodeswas.
4.SimulationResultsandDiscussion
4.1. Von Mises Equivalent Stress Contours. Figure7 showed 4.2. Stress Behavior of Bottom Node (Node 1). In terms of
the Von Mises equivalent stress contours of model A at thethreeprincipalcomponentsoftheVonMisesequivalent
differenttime.Obviously,therodcouldbepenetrateddeep stress, because of the symmetry of FE model, only the 1st
intothegranitegradually.Inthemeantime,theelementsin principalstressandthe3rdprincipalstresswerediscussedin
brokenpitwere“killed”andremoved,fortheirstresseshad thesimulations.Thelocationofbottomnode(seeFigure5)
exceededthecompressiveorshearstrengthofgranite.Itwas wasjustbelowthedrillrodandcoulddirectlyreflectthestress
consistentwiththeconclusionoftheoreticalcalculation. behavior of the rock under impact rod. Figure9 revealed
Figure8depictedtheVonMisesstresstop-viewcontours the stress variation curves of bottom node in models A,
ofdifferentmodelsatthe0.002ths.Asdemonstratedinthe B, and C, including the Von Mises equivalent stress, the
figure, when dr was fixed (20mm), there was a significant 1st principal stress, and the 3rd principal stress. Obviously,
stressconcentrationphenomenonaroundtheholeinmodel whendrwasfixed(20mm),amongthosethreemodels,the
A, and the maximum Von Mises stress of hole-nodes (14 stressofbottomnodeinmodelCwasthelargest,whilethat
to 19; see Figure5) in model A was 2.69MPa. Instead, as in model B was the smallest, whether for the Von Mises
di was larger or less than 200mm, the stress concentration equivalent,the1stprincipalstress,orthe3rdprincipalstress.
phenomena around the holes both were weakened and Likewise,Figure10demonstratedthestressvariationcurves
became no longer obvious. In this case, the maximum Von of bottom node in models A, D, and E. It was evident that
Misesstressesofhole-nodesinmodelsBandCwere1.72MPa whendikeptconstant(200mm),amongthosethreemodels,
and 2.29MPa, respectively. Likewise, for models A, D, and theVonMisesequivalentstressofbottomnodeinmodelE
E, when di was constant (200mm), there were significant wasthesmallest,whilethatinmodelDwasthelargest.The
stressconcentrationphenomenaaroundtheholeforallthree 1stprincipalstressofbottomnodeinmodelEwasrelatively
models. The maximum Von Mises stress of hole-nodes in large,butits3rdprincipalstresswasquitesmall.
model D was 3.14MPa and that of hole-nodes in model E Comparing Figure9 with Figure10, the following was
was3.24MPa.Oncethestressreachedorexceededthetensile evident.(1)Forthe1stprincipalstressandthe3rdprincipal
strength of granite, which was only three to five percent of stressofbottomnode,therewereobvious“compress-tensile
its compressive strength, it might result in the secondary stress”transformationphenomena,whichcouldbeattributed
crushingoftherocknearthehole. to the existence of drilling hole free surface. (2) When dr
Therefore,thefollowingresultscouldbegained:(1)inthis remainedunchanged,thestressesofbottomnodeinmodelC
work, the impact distance of 200mm might be the critical weredistinctlylargerthanthoseinmodelsAandB,regardless