Preface i
Acknowledgments ii
1. Rock Testing
1. Instability Characteristics of a Single Sandstone
Plate 1
2. Instability Characteristics of Double-Layer Rock
Plates 11
3. Rupture and Energy Analysis of Double-Layer Rock
Plates 18
4. Double-Layer Rock Plates With Both Ends Fixed
Condition 27
5. Viscoelastic Attenuation Properties for Different
Rocks 32
6. Cutting Fracture Characteristics of Sandstone 39
7. Energy Dissipation Characteristics of Sandstone
Cutting 46
8. Fracture Properties on the Compressive Failure of
Rock 52
References 58
Further Reading 60
2. Rockbolting
1. Mathematical Derivation of Slip Face Angle 61
2. A Mechanical Model for Cone Bolts 73
3. Effect of Introducing Aggregate Into Grouting
Material 86
4. Optimizing Selection of Rebar Bolts 90
5. Poissons Ratio Effect in Push and Pull Testing 102
6. Study on Rockbolting Failure Modes 112
7. Steel Bolt Profile Influence on Bolt Load Transfer 128
8. Tensile Stress Mobilization Along a Rockbolt 141
References 146
Further Reading 149
3. Grouted Cable
1. Load Transfer Mechanism of Fully Grouted
Cable 151
2. Theoretical Analysis of Load Transfer Mechanics 159
3. Impacting Factors on the Design for Cables 168
4. Mechanical Properties of Cementitious Grout 177
5. Anchorage Performance Test of Cables 187
6. Axial Performance of a Fully Grouted Modified
Cable 196
7. Sample Dimensions on Assessing Cable Loading
Capacity 203
References 212
Further Reading 215
4. Tunnel Engineering
1. Construction Optimization for a Soft Rock
Tunnel 217
2. Water Inrush Characteristics of Roadway
Excavation 225
3. Lining Reliability Analysis for Hydraulic Tunnel 233
4. Disturbance Deformation of an Existing Tunnel 239
5. Energy Dissipation Characteristics of a Circular
Tunnel 250
6. Pressure-Arch Evolution and Control Technique 256
7. Skewed Effect of the Pressure-Arch in a
Double-Arch Tunnel 266
References 276
Further Reading 279
5. Slope Engineering
1. Three-Dimensional Deformation Effect and Optimal
Excavated Design 281
2. Stability Analysis of Three-Dimensional Slope
Engineering 289
v
Biography iii
3. Fracture Process Analysis of Key Strata in the
Slope 295
4. Parameters Optimization of the Slope
Engineering 303
5. Key Technologies in Cut-and-Cover Tunnels in Slope
Engineering 310
6. Potential Risk Analysis of a Tailings Dam 319
7. A New Landslide Forecast Method 326
References 331
Further Reading 333
6. Mining Geomechanics
1. Analytical Analysis of Roof-Bending Deflection 335
2. Analytical Solution of the Roof Safe Thickness 345
3. Catastrophe Characteristics of the Stratified Rock
Roof 350
4. Pressure-Arch Analysis in Coal Mining Field 357
5. Analysis of Accumulated Damage Effects on the
Roof 363
6. Tunnel and Bridge Crossing the Mined-Out
Regions 372
7. Pressure-Arch Analysis in Horizontal Stratified
Rocks 381
8. Pressure-Arch in a Fully Mechanized Mining
Field 392
References 400
Further Reading 402
Index 403
內容試閱：
There have been significant advances in rockmechanics and understanding of the behaviorof rock with developments in science and engineering.This has occurred at the same time asthere has been greater demand for the utilizationof underground space that has in many casespushed the limits in the engineering design ofunderground excavations while there has beenthe continual need to improve safety and reducethe cost of excavation. It is imperative, then, thatresearch continues which will provide theknowledge necessary to underpin the designand development of new excavation techniques.The book summarizes and enriches the latestresearch results on the theory of rock mechanics,analytical methods, innovative technologies,and its applications in practicalengineering. The book is divided into six chaptersincluding such features as Chapter 1： RockTesting Shuren Wang Sections 1e7; PaulHagan Section 8; Chapter 2： Rock BoltingChen Cao Sections 1e7; Paul Hagan Section8; Chapter 3： Grouted Anchor Paul Hagan;Chapter 4： Tunneling Engineering ShurenWang; Chapter 5： Slope Engineering ShurenWang; and Chapter 6： Mining GeomechanicsShuren Wang. This book is innovative, practical,and rich in content, which can be of greatuse and interest to the researchers undertakingvarious geotechnical engineering and rock mechanics,teachers and students in the relateduniversities, as well as on-site technicians.The material presented in this book contributesto the expansion of knowledge related torock mechanics. The authors, through theirextensive fundamental and applied researchover the past decade, cover a diverse range oftopics from the microbehavior of rock and rockproperties through the interaction of large-scalerock masses and its effect on surface subsidence,mechanics of rock cutting, techniques to improvethe strength and integrity of rock structures insurface and underground excavations, andimprovement in approaches to modeling techniquesused in engineering design.Shuren Wang, PhDProfessor at School of Civil Engineering, HenanPolytechnic University, ChinaPaul C. Hagan, PhDAssociate Professor and Head of School of MiningEngineering, University of New South Wales,AustraliaChen Cao, PhDResearch Fellow at School of Civil, Mining andEnvironmental Engineering, University of Wollongong,Australia
CHAPTERCHAPTER1
RockTesting
1.INSTABILITYCHARACTERISTICSOFASINGLESANDSTONEPLATE1.1IntroductionInChina,numerousshallowmined-outareashavebeenleftduetothedisorderedminingbytheprivatecoalmines.Itisofimportanttheoreticalandpracticalvaluefortheroofstabilityevaluationanddisasterforecastingtoresearchthedeformationrupture,instabilitymechanism,andfailuremodeoftherockroofinthemined-outareas.
ThestudiesontheinstabilityoftherockroofintheminingfieldhavebeenamaintopicbothforscholarsinChinaandabroad.Forexample,accordingtoelasticthinplatetheory,Wangetal.2006analyzedthefractureinstabilitycharacteristicsoftheroofunderdifferentminingdistancesintheminingworkface.Wangetal.2008aanalyzedtherheologicalfailurecharacteristicsoftheroofinthemined-outareasthroughcombiningthethinplateandrheologytheories.Panetal.2013hadconductedtheanalyticalanalysisofthevariationtrendofthebendingmoment,thedeflection,andtheshearforceofthehardroofintheminingfield.Thisresearchisinclinedtoadopttraditionalanalyticmethodstoprobeintotheroofstability.Newtheoriesandmethodshavebeenusedinrecentyears.Zhaoetal.2010utilizedthecatastrophetheory
tosetupverticaldeformationmodeloftheoverlappingroofinthemined-outareas,andputforwardthecriteriaforevaluatingtheroofstability.Wangetal.2013canalyzedthechaosandstochasticresonancephenomenonproducedintheroofduringtheevolutionaryprocessoftherockbeamdeformation.Meanwhile,somenumericalcomputationmethodswereappliedindiscussingthemechanicalresponseofrockplateorbeam.Wangetal.2008aanalyzedtheblast-inducedstresswavepropagationandthespallingdamageinarockplatebyusingthefinite-differencecode.Nomikoetal.2002researchedthemechanicalresponseofthemultijointedroofbeamsusingtwodimensionaldistinctelementcode.Mazoretal.2009examinedthearchingmechanismoftheblockyrockmassdeformationaftertheundergroundtunnelbeingexcavatedusingthediscreteelementmethod.CraveroandIabichino2004discussedtheflexuralfailureofagneissslabfromaquarryfacebyvirtueoflinearelasticfracturemechanicsLEFMandfiniteelementmethodFEM.
Insummary,thoughmanyresearchachievementshavebeenmade,themostresultsstilllacklaboratorytestingandneedtobeverified.Inaddition,somenumericalcalculationswereconductedbasedonthecontinuummechanics,whichcouldnotreflectthespatialheterogeneityandtheanisotropiceffectoftheroofintheminingfield.Onlyafewresearchersutilizedthediscreteelementmethodstostudythemacromechanical
1
1.ROCKTESTINGresponseoftherockplate,anddidnotfurtherexplorethemicroscopicdamageoftherockplate.Therefore,anewloadingdevicewasdevelopedtostudytherock-archinstabilitycharacteristicsoftheplate,andparticleflowcodePFCwasusedtofurtherprobeintothemicroscopicdamageoftherockplateundertheconcentratedandtheuniformloading,respectively.
1.2LoadingExperimentofRockPlate1.2.1SamplesofRockPlateTherocksamplesusedinthetestwereHawkesburysandstone,whichobtainedfromGosfordQuarryinSydney,Australia.Thequartzsandstoneswhichcontainedasmallquantityoffeldspars,siderite,andclaymineralswereformedinmarinesedimentarybasinofthemid-Triassic,andlocatedonthetopofcoal-bearingstrata.Thesurfaceofspecimenexhibitedlocalredratherthanwhitebecauseofthecontentanddistributionofironoxide.
Forthesingle-layerroofofthemined-outareas,itcouldbeclassifiedintotwocategoriesaccordingtothethickness：thethinplateandthethickplate.Andtheroofwasalwaysmadeupofvariouscombinationsofthethinplatesandthethickplates.Thus,accordingtothedefinitionofthethinplateandthethickplateinelasticmechanics,thespecimensizeofthethickplatewasdeignedto190mm75mm24mmlength,width,andthicknessandthatofthethinplatewasdeignedto190mm75mm14mmlength,width,andthickness.ThespecimenswereobtainedbycuttingthesamesandstoneinthelaboratoryofSchoolofMiningEngineering,UniversityofNewSouthWales.ThephysicalemechanicalparametersofrockplateswereshowninTable1.1.
1.2.2LoadingEquipmentTheMTS-851rockmechanicstestingmachinewasselectedasloadingequipment,andtheloadwascontrolledbyverticaldisplacementandloadingratewasset1102mmsPotyondyandCundall,2004.Theverticalforceanddisplacementoccurredintheprocessofthetestandwereautomaticallyrecordedinrealtimebyadataacquisitionsystem.
AsshowninFig.1.1,theconcentratedandtheuniform-loadingtestsetsmainlyconsistedofthreeparts.Thetopwasapoint-loadingfortheconcentratedloadingoranassemblyofthesteelballsfortheuniformloading.Themiddlewasaloadingframeworkwhichincludedfourboltswithnutsconnectingthesteelplatesonbothsides,andthelateralpressurecellwasplacedbetweenthedeformablesteelplateandthethicksteelplatesoastomonitorthehorizontalforce.ThecapacityofthelateralpressurecellLowPressureXTypeLPXwas1000kg.Thebottomwasarectanglesteelfoundation,therotatablehingesupportsweresetonbothsidesoftheloadingframeworktomaintainconnectingwiththesteelplates.
1.2.3AcousticEquipmentandDataAcquisitionSystemTomonitorthecracksinitiatedandidentifythefailurelocationoftherockplate,theUSBAcousticEmissionAENodeswereusedinthetest.TheUSBAENodeisasinglechannelAEdigitalsignalprocessorwithfullAEhitandtimebasedfeatures.InthetesttherewerefourUSBAEnodesbeingconnectedtoaUSBhubformultichanneloperationFig.1.2.AlltheseAEnodesweremadeinMISTRASGroup,Inc.,intheUnitedStates.
TABLE1.1PhysicalandMechanicalParametersofRockPlates
DensityElasticModulusPoissonCohesionFrictionAngleTensileStrengthCompressionNamekgm3GPaRatioMPaDegreesMPaStrengthMPaSandstone26502.70.202.8450.9513.5
1.3 Experiment Results and Analysis1.3.1 Characteristic ofForceeDisplacement CurveAs shown in Fig. 1.3, the vertical forcedisplacementcurves appeared two peaksunder both the concentrate loading and the uniformloading, and the second peak value ishigher than the first one. The thin rock plateshowed the similarity cases in the test withthe thick plate; only the peak values of the verticaland the horizontal force were lower thanthat of the thick one. In general, the curves ofA BFIGURE 1.1 Loading experiment for the rock plate. A Concentrated loading. B Uniform loading.A C D14 23BMTS loadingLateralload cellAE sensor1 2 3 4USB hubPowerAE MTSFIGURE 1.2 Mechanics Testing System MTS connectionwith acoustic emission monitoring system diagram.00.50.00.51.01.52.02.5Stage 13.0Force kN3.54.04.55.05.56.06.52Displacement mm4 6 8 10 12Stage 2Stage 3Stage 4Vertical forceHorizontal force020246 Stage 18Force kN10121416182Displacement mm4 6 8 10Stage 2Stage 3Stage 4Vertical forceHorizontal forceA BFIGURE 1.3 Forceedisplacement curves under different loading conditions. A Concentrated loading. B Uniformloading.1. INSTABILITY CHARACTERISTICS OF A SINGLE SANDSTONE PLATE 31.ROCKTESTINGtheforceedisplacementcouldbeclassifiedasfourmechanicalresponsestagesasfollowsFig.1.1A：
Stage1：Therockplatewasinthesmalldeformationelasticstage.Withtheverticalforceslowlyincreasing,theverticaldisplacementgrewgradually.Onthecontrary,thehorizontalforceshowedaslightdecrease,whichwasmainlycausedbytheslighthorizontalshrinkoftherockplateduringtheloadingprocess.Stage2：Therockplateproducedabrittleruptureandformedtherock-archstructure.Astheverticaldisplacementwenttoabout
2.5mm,theverticalforceappearedtofirstincreaseabruptlyandthendropsharplyinasmallinterval,whichindicatedtherockplateproducingabrittlerupture.Subsequently,therock-archstructurewasformedundertheverticalandthehorizontalreactionforces,andthehorizontalforcestartedtoincrease.Stage3：Therock-archstructurebegantobearloadsandproduceddeformation.Withtheverticalforceincreasing,themiddlehingepointoftherock-archstructuremoveddown,andthetwoflanksoftherock-archrotatedaroundthehingepoint,respectively.Suchkindsofmotionwouldstretchtherock-archstructureinthehorizontaldirectionandsqueezedtheplateintwosides,andthehorizontalforceshowedasignificantgrowth.Stage4：Thehingedrock-archstructurebecameunstable.Withtheverticalforcecontinuouslyincreasing,themiddlehingedpointoftherock-archstructuremoveddownconstantly,andwhenthehingedpointexceededthehorizontallineformedbythehingedpointandtwoendsoftheplate,therock-archstructurebecamethoroughlyunstable.Undertheuniformloading,thedamageandfractureextentoftherockplatewasmoreserious
thanthatundertheconcentratedloading,especiallyatthetwoendsoftherockplateFig.1.1B.AsshowninFig.1.3,theloadedisplacementcurveshowedsimilaritywiththeconcentratedloading,andthepeakvalueoftheverticalforcewasgreaterthanthatundertheconcentratedloading.
1.3.2AcousticCharacteristicoftheRock-PlateFailureAsshowninFig.1.4,inthebeginningofthestagetwo,theAEhitsundertheuniformloadingweregreaterthanthatundertheconcentratedloading,whichwasabout5000and4500,respectively.InStage3andStage4,theAEhitswerealsogreaterandmoreevenlydistributedundertheuniformloadingcomparedwiththeconcentratedloading,whichwasabout5000and3000,respectively.
AsshownintheAElocationmapFigs.1.5and1.6,theresultsshowedobviousdifferencesintheinitialcrackpositionandthecracksdistributionoftherockplateunderdifferentloadingconditions.Whentherock-archstructurewentintoinstability,therealsoshowedthedifferencesinthedamageextentandscopebetweenthetwoloadingmethods.Allinall,theresultsofAEhitsandlocationshowedtheover-damageextentandscopeoftherockplatecausedbytheuniformloadingweremoreseriousthanthatundertheconcentratedloadingcondition.
1.4NumericalSimulationsoftheLoadingTest1.4.1ParametersCalibrationoftheRockPlateTherockplatewastreatedastheporousandsolidmaterialthatconsistedofparticlesandcementbodies.Theforceedisplacementcurvewassimulatedundertheconcentratedloadingusingthethree-dimensionalparticleflowcodePFC3D.
1.INSTABILITYCHARACTERISTICSOFASINGLESANDSTONEPLATEABB, Vetical force
18
5000
5000
16
4000 14
B, Lateral forceC, AE hitsA,Vetical forceACStage 1BStage 4Stage 2Stage 3ABStage 1Stage 4A, Lateral forceC, AE hitsStage 2Stage 32000
6
4000
Force kN
12
3000
2000
AE hitsForce kN
2
AE hits
10
3000
8
1000 4
1000
2
0
0
0
0 200 400 600 800 1000 1200
0 200 400 600 800 1000
Time s
Time Sec
FIGURE1.4Acousticemissionhitsandforceedisplacementcurvesunderdifferentloadingconditions.AConcentrated
loading.BUniformloading.
Beforethenumericalsimulationmodelcouldbebuilt,themicroparametersneededtobeadjustedrepeatedlyandfinalizeduntilthemacromechanicalparameterscalculatedwereconsistentwiththephysicalmacromechanicalparameters.
Themicroparametersrequiredtobeadjustedwereasfollows：risballdensity,Rminisminimumballradius,Rratioisballsizeratio,lisparallel-bondradiusmultiplier,Ecisballeballcontactmodulus,Ecisparallel-bondmodulus,
knksisballstiffnessratio,knksisparallel-bondstiffnessratio,misballfrictioncoefficient,scisparallel-bondnormalstrength,andscisparallel-bondshearstrength.ThemicroparametersrequiredtobeadjustedarelistedinTable1.2.
1.4.2TheComputationalModelTakethethickplate190mm75mm24mmlength,width,andthicknessasanexampletoshowhowtobuildthenumericalcalculationmodel.
First,aparallelepipedspecimenconsistingofarbitraryparticlesconfinedbysixfrictionlesswallswasgeneratedbytheradiusexpansion
method.Second,theradiiofallparticleswerechangeduniformlytoachieveaspecifiedisotropicstresssoastoreducethemagnitudeoflocked-instressesthatwoulddevelopafterthesubsequentbondinstallation.Inthispapertheisotropicstresswassetto0.1MPa.Third,thefloatingparticlesthathadlessthanthreecontactswereeliminated.Fourth,theparallelbondswereinstalledthroughouttheassemblybetweenallparticlesthatwereinnearproximitytofinalizethespecimen.Finally,theloadingdeviceswereinstalledontherockplateasshowninFig.1.7.
Asquarewallwithsides10mmwasmadeonthetopoftherockplateastheconcentratedloading,andtheloadingratewassetto
0.01msTheloadingratecouldberegardedasthequasistaticloading.Thetwocylinderwallswereplacedontherightandleftatthebottomrespectivelyassupportingbase.Thetwowallslocatedonbothsidescouldinstalltheinitialhorizontalforceatthespecifiedvalue.Duringtheloading,thecracksgeneratedintherockplateweremonitoredinrealtime.Theredcracksrepresentedthetensilefracture,andtheblackonesrepresentedtheshearfracture.1.ROCKTESTINGFIGURE1.5Acousticemissionlocationofrockplateunderconcentratedloading.AInitialcracks.BUltimatecracks.
1.4.3AnalysisofNumericalSimulationResultsAsshowninFig.1.8,sincetheinteractionforcesamongtheparticlesweresimplifiedinPFC3D,thereweresomedifferencesintheverticalforceehorizontalforceedisplacementsimulatedcurvescomparedwiththephysicalexperimentalresults,butthevariationtrendof
thecurveswasbasicallythesamefortwocases,sothephysicalexperimentalresultsconfirmedthenumericalcredibility.
IntheelasticdeformationstageFig.1.9A,thedisplacementvectorfielddescribedthataslightelasticdeformationproducedintherockplate,andatthesametimetherewasnocrackgeneratedinthisstage.Inthebrittlerupture
1.INSTABILITYCHARACTERISTICSOFASINGLESANDSTONEPLATE71.INSTABILITYCHARACTERISTICSOFASINGLESANDSTONEPLATE7FIGURE1.6Acousticemissionlocationofrockplateunderuniformloading.AInitialcracks.BUltimatecracks.
TABLE1.2MicroparametersoftheModelinPFC3D
rkgm3RminmmRratiomlEcGPaEcGPaknksknksscMPascMPa
26501.21.660.51.02.72.81.81.816
1.ROCKTESTINGFIGURE1.7Computationalmodelanditsboundaries.
stageFig.1.9B,therewasmanytensilecracksproducedintherockplate,andthesetensilecracksformedatensilefailureplaneintherockplate.Intherock-archbearingloadstageFig.1.9C,theshearingandtensioncracksemergedinthehingedplaneandbothendsoftherockplate.Intherock-archinstabilitystageFig.1.9D,therock-archstructurehadalargedeformation,andpartsoftheparticlesinthehingedplaneofbothsideshadescapedfromtherockplatemainlyduetothesqueezingfracture.
AsshowninFig.1.10,thenumberofshearcracksobeyedtheS-figurecurveduringthewholemechanicalresponseprocess,whichwas
0123 Stage 1Force kN456Stage 2Stage 3Stage 4Vertical forceHorizontal force0 2 4 6 810Displacement mm
FIGURE1.8Forceedisplacementrelationshipcurves.
alsoapplicabletothetensilecracksonlyafterthebrittlerupture.Whentheverticaldisplacementreachedaround1.0mm,thenumberofthetensilecrackssurgedto300.Asthedisplacementvariedintheinterval1.0e2.5mm,thecrackdevelopmentkeptalmostunchanged.However,withthedisplacementcontinuouslyincreasing,thenumberofbothshearingandtensioncrackskeptincreasing,thehingedplanesandbothendsoftherockplateshowedthemixtureofshearingandtensilecracks.Asrock-archstructurewentintoinstability,thenumberofcracksstillkeptsignificantincreasinguntilthedisplacementreachedto6mm.
1.5FactorsSensitiveAnalysisofRock-ArchInstability1.5.1MaterialParameterEffectAsshowninFig.1.11,withthefrictioncoefficientoftheparticlesincreasing,thepeakvaluesoftheverticalforceandthehorizontalforceoftherock-archstructurealsoincreased.Thiswasmainlybecausethefrictiongrowthenhancedthepeakstrengthoftherockmaterial,namelyafterbreakageoftheparallelbond,thestrengthoftherockmaterialoftencontributedtothecontactfrictionoftheparticles.
1.5.2GeometrySizeEffectAsshowninFig.1.12,thelength,width,andthicknessoftherockplatechanged,respectively,torevealthesizeeffectontheinstabilityoftherock-archstructure.Withthelengthoftherockplateincreasing,thepeakvaluesoftheverticalandthehorizontalforceweregraduallydecreased,andthewholevariationintervalwassmall.Withthewidthandthethicknessoftherockplateincreasing,thepeakvaluesoftheverticalandthehorizontalforceshowedobviousgrowth.Inshort,theresponseoftherock-archstructureinstabilitywasmoresensitivetothewidthandthicknesscomparedwiththelength.
1.INSTABILITYCHARACTERISTICSOFASINGLESANDSTONEPLATEA BDCFIGURE1.9Rock-archinstabilityprocessundertheconcentratedloading.AElasticstage.BBrittlerupturestage.
CBearingloadingstage.DRock-archinstabilitystage.0200400600Crack8001000Shear crackTension crack12007
6
Compressive strength MPaVertical force kNHorizontal force kN
Compressive strength MPa
Force kN
5
4
3
14
2
13
0 2 4 6 810
0.0 0.2 0.4 0.6 0.8 1.0Displacement mm Friction coefficientFIGURE1.10Crack-displacementcurves.FIGURE1.11Force-frictioncoefficientcurves.
101.ROCKTESTINGAVertical ForceHorizontal ForceB6.5
9
6.0
8
5.5
7
Force kN
Vertical ForceHorizontal ForceForce kN
5.0
4.5
4.0
3.5
6
5
4
3.0
3
2.5
2180 190 200 210 220 60 70 80 90 100 110
Length mmWidth mm
C123456Force kN789Vertical ForceHorizontal Force10 1520 25 30 35Thickness mm
FIGURE1.12Theforcesvariationwiththerockplategeometryparameters.ALengtheffect.BWidtheffect.
CThicknesseffect.1.5.3LoadingRateandInitialHorizontalForceEffectAsshowninFig.1.13A,whentheloadingrateexceeded10mms,withtheloadingrateincreasing,thepeakvaluesoftheverticalandthehorizontalforceshowedthelineargrowthtrend,andtheamplitudeofthatvariationwassmall.Whentheloadingratewasintheintervalof1.0e10mms,thepeakvalueswerealmost
unchanged,thereforesuchloadingratecouldberegardedasthequasistaticloading.
AsshowninFig.1.13B,whentheinitialhorizontalforcewaslessthan2.0kN,withtheinitialhorizontalforceincreasing,theverticalandthehorizontalforceoftherockplateshowedthenonlinearfluctuatinggrowthtrend.Whentheinitialhorizontalforcewaslargerthan2.0kN,withtheinitialhorizontalforce
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