cost ac(on tu1208 · cost is supported by the eu framework programme horizon2020 cost ac(on tu1208...

COST is supported by the EU Framework Programme Horizon2020

COSTAc(onTU1208CivilEngineeringApplica(onsofGroundPenetra(ngRadar

Structuralevalua(onofexis(ngpavementsbasedondeflec(onandGPRmeasurementsAuthor:CarlVANGEEMBRRC,Belgium

Thispresenta(onispartoftheTU1208Educa(onPack

ThankyoutoLoredanaMateraandSantoPronteraforcontribu=ngtotheedi=ngandlayou=ngofthislecture.


Summaryofthelecture(1/2)

§  Old-fashionedway:theequivalentsinglelayermodel§  Modernway:theback-calcula=onapproach§  Mul=-layermodelofaroad§  Applica=onofloadsandmeasurementofdeflec=ons

Introduc(ontoapproachesfortheevalua(onofthestructuralproper(esofpavement

Evolu(onofmathema(calmodelsofpavement

§  Pavementmodelsbasedonthetheoryofelas=city§  Pavementmodelsbasedonthestrengthofmaterials§  ModelproposedbyBurmister(1943)


Summaryofthelecture(2/2)

§  Theequivalentsemi-infinitebody§  Deflec=onsandinterpreta=onofthesurfacemodulus§  Example:Back-calcula=onforathree-layermodelofaroad§  Sensi=vityoftheprocedure

Evalua(onofthebearingcapacityofamul(layeredroadstructure

Applica(on:Back-calcula(onandredesignofaroad

§  Measureddeflec=onsandpresentroadstructure§  Back-calcula=onandredesignwithQualidim§  Studyoftheinfluenceoflayerthicknessesontheroadlife=me

BiographyandcontactdetailsoftheAuthor


Introduc(ontoapproachesfortheevalua(onofthe

structuralproper(esofpavement


Theold-fashionedway:equivalentsinglelayermodel

§  Replaceeachlayerofthemul=-layermodeloftheroadbyonelayerwith"equivalent"thicknesshe(thickerthanthesumofthicknesseshi)

Ø Mul=-layermodel:thicknessesh1,h2,…Ø  Theso-called‘equivalentfactors’

a1,a2,…canbecalculatedbyusingthefollowingformula:

Ø  Thicknessoftheequivalentlayer:

Here, Ei is the layer elas=citymodulus, measured or takenfromatable(thisisaparameterdependingonthelayermaterial)

ai = Ei /5003

he = ai +hi∑


Equivalentsinglelayermodel:thicknessofoverlay…

§  Determinetraffic(kNc):Past,presentandfuturetraffic §  Graphsestablishedin1991(BRRCreportR56/85)

Thicknessesofcrushedstonebasecourseandasphaltlayer

Thicknessofgranularsubbase(fordifferentsoils)

Traffic(kNc) Traffic(kNc)


Equivalentsinglelayermodel:thicknessofoverlay…

§  TrafficmapsareusedtodeterminethethicknessesH1,H2,H3oftheidealmul=-layerroad.

§  Theidealequivalentthicknessis:He=Σai·Hi(fortheequivalent1-

layermodel).§  Then,dooverlay:W=(He–he)/2.7(withai=2.7forabituminous

layer)istheneededthicknessofthebituminousoverlay,inordertoachieveequivalencewiththeidealmul=-layerroadstructure.


Themodernway:back-calcula(onapproach

§  Objec=ve:DetermineE-modulesofalllayers

Ø  Computedeflec=onbowlfromamul=-layermodelØ  Comparethecomputeddeflec=onbowlwiththemeasureddeflec=onbowlØ  Ifdeflec=onbowlsarenot"iden=cal"thenmodifyE-modulesanditerate…


Themodernway:back-calcula(onapproach

§  Thenredesignthe"currentstructure+overlay"(asifyouaredesigninganewroad)withasuitablesojwareandes=matetheexpectedlife=me.

§  Ifresultsarepoor,thendochangesindeeperpartoftheroadstructure.


Back-calcula(onsoWwaretools

§  Freesojware:Ø  “Qualidim”:IntendedforBelgium,tobeusedbynon-specialists

§  Commercialsojware:

Ø  Alizé-LCPC(itech-soj)Ø  PAVERS(VIAAperta)Ø  Rosy(SWECO–carlBro)Ø  ELMOD(Dynatest)

Ø  …


Defini(onandseZngsofthedeflec(ondeviceused

Deflec(onsandsurfacemodulus

Comparisonbetweenmeasuredand

computeddeflec(ons

Computedelas(citymoduli

Proper(esofmaterialsDivers

Back-calcula(on:Qualidim


Modeloftheroad:amul(-layer


Applica(onofloadsandtheireffects

chargeof50kN,p=0,7MPa(r=150mm)

Subbase E3,µ3

Basecourse E2,µ2

Soil E4,µ4

Tensilestress

Ver(caldeforma(on

Asphaltlayer E1,µ1Tensilestress

§  Aloadisappliedtothemul=-layersystem…


h 1 E 1 Pavement

h 2 E 2 Base course

h 3 E 3

E 4

Subbase

Soil

Distribu(onoftheloadandmeasurementofdeflec(ons

Ø  Thefartherthedeflec=onismeasuredfromthecentreofimpact,thelessthedeflec=oniscausedbytheupperpartoftheroadstructure…

§  Onlythepartofthepavementthatissubjectedtostresses,willdeform…(i.e.onlytheareainsidetheredcone,inthesketch)


Evolu(onofmathema(calmodelsinpavementdesign

Seealsothebook:

FransVanCauwelaert,«Pavementdesignandevalua(on:Therequiredmathema(csandapplica(ons,»ISBN978-2-960043-00-6


Pavementmodelsbasedonthetheoryofelas(city

Ø  Thesubgradeisanisotropicbody(Boussinesq,1883)

σ z =−3P2πz2

Ø  Defini=onofastressconcentra=onfactor(Fröhlich,1934)

σ z =−νP2πz2

Concentra(on:ν>3Dispersion:ν<3

Ø  Thesubgradeisanorthotropicbody(Lekhnitskii,1963)

σ z =−1+ s+ s2s2

P2πz2

s2 = n−µ2

n2 −µ2 n=EvertEhor

§  Semi-infinitebodysubjectedtoaver=calloadP


Vertical stress vs anisotropy

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250Depth z

Stre

ss n=2n=1n=0.5

(Lekhnitskii,1963)

Pavementmodelsbasedonthetheoryofelas(city


Pavementmodelsbasedonthestrengthofmaterials

Ø  Equilibriumequa=on

∂2

∂r2+1r∂

∂r

⎛

⎝⎜⎜

⎞

⎠⎟⎟∂2w∂r2

+1r∂w∂r

⎛

⎝⎜⎜

⎞

⎠⎟⎟=

p−qD

Ø  Westergaard(1924):Thesubgradeisaseriesofver=calsprings(k)

q= kw

Ø  Pasternak (1954): The subgrade is a series of ver=cal (k) andhorizontalsprings(G)

q=−G ∂2w∂r2

+1r∂w∂r

⎛

⎝⎜⎜

⎞

⎠⎟⎟+kw

§  Slabsubjectedtoaver=calpressurep

p

q

E,I

k,G

D


Surface deflection

0

0.05

0.1

0.15

0.2

0.25

0 500 1000 1500 2000 2500

Distance from the axis

Def

lect

ion

WestergaardPasternak

Pavementmodelsbasedonthestrengthofmaterials


Ø  Hypothesesofthetheoryofelas=city:equilibrium,con=nuityandelas=cityforeachlayer

ModelproposedbyBurmister(1943)§  Mul=layeredstructure

p

E1

E2

E3

h1

h2

∞

2a

∂2

∂r2+1r∂

∂r+∂2

∂z2⎛

⎝⎜⎜

⎞

⎠⎟⎟∂2ϕi

∂r2+1r∂ϕi

∂r+∂2ϕi

∂z2⎛

⎝⎜⎜

⎞

⎠⎟⎟=0


§  Mathema=calsolu=on(here,weskipthemathema=calsteps,butyouareencouragedtocalculatethem!)

∂2

∂r2+1r∂

∂r+∂2

∂z2⎛

⎝⎜⎜

⎞

⎠⎟⎟∂2ϕi

∂r2+1r∂ϕi

∂r+∂2ϕi

∂z2⎛

⎝⎜⎜

⎞

⎠⎟⎟=0

Byintroducingintheequa=ontheexpressionφ(r,z)=J0(mr)f(z),weobtain:

∂2

∂r2+1r∂

∂r

⎛

⎝⎜⎜

⎞

⎠⎟⎟ J0(mr)=−m2 J0(mr)

J0(mr) m4 −2m2 ∂2

∂z2+∂4

∂z4⎛

⎝⎜⎜

⎞

⎠⎟⎟ f (z)=0

ϕi(r ,z)= J0(mr) Aiemz −Bie−mz + zCiemz − zDie−mz( )

ModelproposedbyBurmister(1943)


§  Stressesanddisplacements(again,weignorethemathema=calstepsleadingtotheseformulas):

σ z = f (r) Am2emz +Bm2e−mz −(1−2µ+mz)Cmemz +(1−2µ−mz)Dme−mz{ }

τ rz = f (r) Am2emz −Bm2e−mz +(2µ+mz)Cmemz +(2µ−mz)Dme−mz{ }

u= f (r)E

Am2emz +Bm2e−mz +(1+mz)Cmemz −(1−mz)Dme−mz{ }

w =f (r)E

Am2emy −Bm2e−my −(2−4µ−mz)Cmemz −(2−4µ+mz)Dme−mz{ }

ModelproposedbyBurmister(1943)


Boundarycondi(ons(Burmister)§  Surface(load) p

Ø  Ver=calstress=-pØ  Shearstress=0

§  Interfaces(layersincontact)Ø  Ver=calstressesareallequalØ  ShearstressesareallequalØ  Deflec=onsareallequal

§  Interfaces:horizontalcondi=on,therearethreealterna=ves:Ø  Displacementsareequal:Fric=onØ  Shearforcesarenull:SlipØ  Intermediatescenario:Par=alfric=on

§  Subgrade,therearetwoalterna=vesØ  Semi-infinitebodyØ  Fixedbouom


Evalua(onofthebearingcapacityofamul(layeredroadstructure


Theequivalentsemi-infinitebody

r r

E1h1

E2h2

E0

A A

E0h1,eq

E0h2,eq

E0 B

z


Thefurtherawayfromthecentreofpressure…

)()()1()(2

20 iwir

paiE µ−=

§  Deflec=on “at the centre of impact”: is influencedby thewhole roadstructureàhence,thederivedsurfacemoduluscharacterizesthewholeroadstructure

§  Deflec=on“faraway”fromthecentreofimpact:itisinfluencedbythelowerpartoftheroadstructure,onlyà hence, the derived surface modulus characterizes the lower part of theroadstructure

h 1 E 1 Pavement

h 2 E 2 Base course

h 3 E 3

E 4

Subbase

Soil

r(0),w(0) r(600),w(600)


Iden(caldeflec(ons

2a

r

z

z1r1

A

B

w(z)= 1+µE

P2π .z (3−2µ)

w(r)= 2(1−µ2)

EP2π .r

w(r)=w(z /2→2z /3)Simpletransforma=on:


Interpre(ngthesurfacemodulus

§  ThesurfacemodulusE0(i)correspondstothedeflec=onw(i)measuredatadistancer(i)

E0(i)=2(1−µ2)r(i)w(i)

P2π = pa2 (1−µ

2)r(i)w(i)

Ø  Pressurep,radiusa,Poissoncoefficient(Poisson’sra=o)μ

Ø  Modelused:Boussinesq’stheory,computa=onoftheelas=cmodulusofahomogeneoushalf-space

§  So,fromthemeasureddeflec=onw(i)atadistancer(i),wecancomputethesurfacemodulusE0(i)


Example:ComputeE0,thendrawconclusionsontheE-moduliofthedifferentlayersofthe3-layermodel

030060090012001500180021002400

0 500 1000 1500 2000 2500

E0

Distances

030060090012001500180021002400

0 500 1000 1500 2000 2500 3000 3500

E0

Distances

030060090012001500180021002400

0 100 200 300 400 500 600 700

E0

Distances

0

300

600900

1200

1500

18002100

2400

0 500 1000 1500 2000 2500 3000 3500

E0

Disatances Athree-layerroadmodelwithanincreasing

modulusofthesubgradeoras(ffbolom

Athree-layerroadmodelwithaweakinterlayer

Athree-layerroadmodelwithas(ffinterlayer

Athree-layerroadmodelwithdecreasingmoduli

§  Input:Measureddeflec=onsatdifferentdistancesfromloadcentre


Back-calcula(onofathree-layer(1/2)

§  Letw1,w2,…wnbethedeflec=onsatthedistancesr1,r2,…,rn

§  LetusassumetheseedvaluesE10,E20,E30

§  Wecomputethetheore=caldeflec=onsz0(1),z0(2),…,z0(n)

§  WechooseE11=E10∙z0(1)/w0,E21=E20∙z0(2)/w1,E31=E30∙z0(n)/wn

§  WithE11,E20,E30,wecomputez1(1),z1(2),…z1(n)

§  WithE10,E21,E30,wecomputez2(1),z2(2),…z2(n)§  WithE10,E20,E31,wecomputez3(1),z3(2),…z3(n)


Back-calcula(onofathree-layer(2/2)

§  Weapplythe“AlBushIII”algorithm:Ø  Fork=0to3,wedefine:

zk(i)=a(i)logE1.+b(i)logE2.+c(i)logE3.+d(i)

§  Fromthis,wecomputethesolu=onfora(i),b(i),c(i),d(i)Ø  Weintroducetheseinthenequa=ons(i=1,..,n):

z0(i)=a(i)logE1+b(i)logE2+c(i)logE3+d(i)

Ø  Weminimise [ ]2)()(

10∑ −

n

iziw andobtaintheexpectedvaluesE1,E2,E3

§  Ifthissumofsquaresis“smallenough”thenwestopØ  ElseweiteratewithE1,E2,E3asnewseedvalues…


Sensi(vityoftheprocedure§  GivenE1=10000,E2=3000,E3=500

Ø  Wecomputew(0)=69.6,w(1)=38.1,w(2)=26.2,w(3)=19.1,w(4)=14.3,w(5)=11.2,w(6)=9.0,w(7)=7.5,w(8)=6.5

Backcalcula(on

w(0) E1 E2 E3 Fit Loops

69.6 10036 2993 500 0.02 7

75.0 6469 3351 503 0.06 6

58.0 33840 2371 497 0.10 7


Applica(on:Back-calcula(onandredesignofaroad


Deflec(ons&presentroadstructure

Distancesri(mm) 0 300 600 900 1200 1500 1800

Deflec(onswi(µm) 91 76 59 46 36 30 26

§  Deflec=onsmeasuredwithaFWDinthemiddleofaconcreteslab:


Layer/Typeofmaterial Thickness(mm)

Modulus(N/mm2) PoissonRa(o

Concreteslabs(nodowels) 180 37000 0.20

Basecourse 500 2000 0.35

Stabilizedsubbase 350 0.50

§  Presentroadstructure,hypothe=calE-moduli(seedvalues):

Deflec(ons&presentroadstructure


Back-calcula(on



Modulus(N/mm2)

PoissonRa(o




§  Results(withsojwareQualidim©):


Modulus(N/mm2)

PoissonRa(o




§  Presentstructure,hypothe=calE-moduli(seedvalues):

Back-calcula(on


Qualidim§  Designingnewroads…


Completelynewroadstructure

Es(ma(onoftrafficandexpectedlife(me

Qualidim


§  Overlayonexis=ngroad…

Qualidim


Es(mateoftrafficandexpectedlife-(me

Exis(ngstructure,Back-calculatedE-moduli

Qualidim


Evalua(onwithatheore(calmodel


Modulus(N/mm2) PoissonRa(o

Concreteslabs(nodowels)

Between180and200 37661 0.20

Unboundbasecourse,granularmaterialTypeI 400 650 0.45

subbase(stabilizedwithchalk) 200 2000 0.50

Clayground 20 0.50

Axleload: 50kN 90kN 120kN

100trucksperday,300daysperyear

20% 60% 20%

§  Concept:Theore=calstructure:

§  Traffic:100trucks/day,300days/year,growth+2%peryear:


Studyoftheinfluenceofthicknessontheroadlife(me…


Stucturesimilartotheexis(ngone

Study:usealterna(velyback-calculatedandtheore(calE-moduli…

Es(ma(onoftrafficandexpected

life(me

Studyoftheinfluenceofthicknessontheroadlife(me…


2cmextrathicknessisimportant!§  Loweringthethicknessoftheconcreteslabinthetheore=cal

modelmakesthees=matedlife=medropdras=cally

Thicknessofconcreteslab(mm) 200 190 180

NumberofstandardaxlesNcthatcangoovertheroad

2.45*106 6.60*105 1.52*105

Es(matedlife-(me(inyears) >40 18 5

Ø  Note:thisdoesnotmeanthatthethicknessesofthelayersunderneathareofnosignificance…


AuthorDr.CarlVanGeem([email protected]) isa researcher inroadmanagement andmonitoring techniques, since 2004he is working in the Mobility, security and roadmanagement(MSM)divisionoftheBelgianRoadResearchCentre(BRRC),inBrussels,Belgium.HeisaWorkingGroupMemberoftheCOSTAc=onTU1208.In 1996, Carl Van Geem earned the doctoral degree intechnicalsciencesfromtheResearch Ins=tuteonSymbolicComputa=on (RISC-Linz), Johannes Kepler University, Linz,Austria.TheBRRChasseveraldevicesfortheevalua=onofroadsurfaceproper=es(roughness,skidresistence), for pavement management (visual inspec=on device “SAND”), and formeasuringthebearingcapacityofroads(FWD,curviameter,GPR).ThemaintopicofCarl’sresearchistheinterpreta=onofdataobtainedwiththesemonitoringdevicesforanop=malmanagementof roadmaintenance.Carl par=cipated in several na=onal and interna=onalresearchprojects,includinga“na=onalpre-norma=veresearchprojectontheindicatorsofroughness”,theCOSTAc=on354“PerformanceIndicatorsforRoadPavements”,thePIARCtechnicalcommiueeD1“ManagementofRoadInfrastructureAssets”,andtheFP7project“Tomorrow'sRoadInfrastructureMonitoringandManagement(TRIMM)”.


Thank you COSTAc(onTU1208CivilEngineeringApplica(onsofGroundPenetra(ngRadar

www.facebook.com/COSTAc(onTu1208/

[email protected]

www.cost.eu

cost ac(on tu1208 · cost is supported by the eu framework programme horizon2020 cost ac(on tu1208...

Documents