Asphalt Pavcnllent Telnperature Prediction
Manuel
J.
C. Minhoto* -- Jorge C. Pais*": -- Paulo A. A. Pereira**
"'/IISliIllIO ['l!lill;('fli('(J de Brugllll('U - Ew,'olu Sliperior de TC'C/w/ogiu I'dI' GI'SIII(}
CuillpllS de SUIIIC! A1)()IIJlliu, ;Ijlllilildo 13-/, 5301-857 iJrogllll('l,l
il/ill/zolo (ei" ip/JPI (}jMilllI!J
j)epIII{IIII'1l1 ureil'il Ellgilleeril/g, CUII/PliS A~lIn;1I1, -IS{)(U)58 C;lIill/uUIC,I, l'oriligul
jpuis ~1\1 'i I'il. i i lllill/zU.j!1 J!IJI'I't'iru @ci1'iI.1IIIIillfIOPI
MIST/icier /\ 3 nFllile 1'11'1I'l'lIll17odel (FE'M) fi'(lS c/cI'l'lujJcd Iu (,!llclllllle Illc 11'llIjJef'{III1U' oron
mplwll /II/JIW/ l'oFc/llenl lout/cd ill lize Norlizellsl uj' PIJriligul. Tin' goul oil/Ie cllse Silie/V
/nl's(,lIll'd ill 1111'S /JU/ler is to slllJ\\' lize good II('CllnlCl' lempel'llilire plecliCiioll Ihlll CIIII be
oi7luilln/ lI'illi IIiis lIludel WllClI ('l!II/jJurl'd Il'iliz IIIC .field jJlm'lIll'lIl IIienl/ull'iJlldiliun uiJluineil
iIurillg II yeur, jl/pill dulu 10 rile Illodel ore IIII' hOllrit' ni/Il1's jill' solur /'Ili/iurioll IIllci
1I'IIIpl'I'IIIlfre lIl/c/1111' 1111'1/11 duih' I'ul{{cs Urll'illd sp~ed o/iluillfCljiol7l II 1I!~1~{)r()l(}gi('(tI SlllliOll,
nil' II/I'r/l/CII respollse (lj' if !Illilliloyered 1}[II'el71cIII slrllclurc is Illudellet! usillg 0 FElv!
I ((/11 si(,11 I rlll'nnuilillu/Y,\is Lind eucll uill//rsis Ims illiliuled Ivilli IiiI' jitll deplli cOllslunl illiliul
lelllperoilire (}bruillerl jimll peld IIICUSUrellll'lIfS, FIJI' "ueli lilli/lysed c/ur, lit" /){II'CIIICIiI
II'III/)el'llilln' II'US !lleusllu'd (/1 ({ 111'11' jlUI'elilenl sectiulI, fUCtilCd ill IP) !!luill ruad, 111'111'
Bmgul1('lI, ill IiiI' lIorlli oj' Purillgu/, 1\1 litis locutioll, SCl'i'I/ Ilicl'llIo{,(Jllplcs \I'ere illslililcd ill
Ihe uSjillUl1 1'111,/7('1' Ililci cOIlI'ell/iollul lIIi,I: 1(/\,1'1',1', (/1 S('I'C'II difF'Fel!! depills, TlICSI' /hll'eIllCllf
dliia 1I'{lS I/,\I'd 10 wi/idOl!' tliis simlilulioll model, In cOlllpC/rillg lIlodei eillclilulcd dUlo Il'illz
1I/eIlSifU'd !JiI],(!lIlclil lemperalures, lIs cOIlc/usioll, lite 3-D./i'nile-eicJllc/J1 u/Julysis I"DI'ed (o be
WI illll'l'l'Slillg lu!!1 II) sil7lullllt' IiiI' IUlllsiell1 /Jeli01'ior oj'i/,\pliull plII'ell/elllS, Till,' presellied
Silllll/llliull Illudel 1'1111 prediCi lite pUI'emenl lemperulurl' (/1 di/Terenl icTe/s Il/, hilllmil70w
111.1'1''-.1' lI'illl good ucclirucy.
IO';['lvorms: lIsllfloll }'u/J/Jer mix, 1t'lIIjil'rcrtlln: I'arililioll, lizerll1ul mixl's l,eliul'iollr, IIl1llwricu/ II/lu/vsis
19cf ;\sphall Rubber 2006
I. Introduction
Temperature variations have an important inFluencc ill.tiJe pavement thermal state. Depending on the tCl1lpcn1ture variation, stresses are induced in the overlay in two differcnt ways, which need to be distinguished: through rcstrained shrinkage of thc overlay and through the cxisting illovements of slabs, due to the thermal shrinking phenomcnon.
Tn orclcr to calculate the pavement thcrmal cffects ancl the asphalt concretc mix thermal response, it is necessary to evaluate the tcmpcratures distribution at many depths of bituminolls laycrs throughout typical twenty-four hours periods. The temperature distributions obtained for different hours, during the day, allow the
calculation of thermal cffects in the pavement, mainly in the overlay Cor
rehabilitation studies.
The limc variation of pavement thcrmal statc is controlled by: clill1atic conditions, thcrmal diffusivity of the materials, thermal conductivity, specific hcat, density and the depth below the surface (Sousa et 0/.,2(02).
The temperaturc distribution in a pavement structure can be obtained through field measurements, using temperaturc-recording equipment (Datalogger associated with thermocouples) or estimated by using mathematical models. The option of using the field mcasurement is desirable bccausc actual temperature can be reliably measurcd and usee! in stress calcLtlation models. However, lhis method is relatively slow :lIlcl only provides illformation about temperatures in the observed period. On , tbe other hand, a temperature theoretical model may suffer slightly due to lack of accural'ics but will give a tempcraturc distribution quickly and chcaply, and can he usecllCi prcdict temperaturc dislributions under a wide range of conditions, including any unusllal or extrcme conditions.
The simulation modcl proposed in this paper is bascd on Finite Element Method, involving weather data as input. The silllulation model simulation was cione by
comparing the calculated temperatures with measured pavement ternper~llures,
obtained in field since January 2004 until Deccmber 2004. The model comJlutes the pavemelll temperatures hy using measured climate delta \'~dues ;IS input.
Although this thermal approach may havc a nature or a one-dimensionill problem of thc heat cOllduction in the vertical direction, given the inrinite nature in the horizontal direction, the suggested model was devcloped in a three-dimensional helsis, having in view its future compatibility with a 3-D mechanical rcJkcti\'c crelcking model used by the authors in olher projects.
The pavement tcmperatures prediction model is based on fell basic Ixinciples. Once the hourly temperature distribution is govcrned by heat conduction principles within pavemcnt anci by energy interactiun between the pavement and its sLlITOllndings, in the following chapter the main prilll'ipics adopted in the proposed modct arc presented.
2. Thennal model
Conjugating the first law of the thcrmodynamics. which st~ltes that thermal
cnet'g.)' is conserved. and Fumier's law, that relates the heat flux with the therlllal gradicnt. the problem uf hcattransfer by cunduction withill the pavemetll is suhcd,
Fur ~1Il ts()tropic mcdiulll ~tncl
rOt"
consLlllt thcrrn~tl conductivity. thi,s ~td()ptcd[lr-incipic is expressed as follllws (Dewit, 1l)l)6 and Oiisik. 1l)85):
V2T
=L (
~2'
!
0: \ ill )where: 'I' =
la'
)+(a2/(t~')k - Thermal diflusivity: IX~ p,e k - thermal conluctivity: p - dcnsity; C - specific heat; t - timc,
III
011 a sunny day the heattranskr by energy interaction between pavement ane! its
surroundings consists of radiation balance and of exchanges by cunvection, The radiation balance (or thermal radiation) invulves the consideration uf uLltgoing longwave radiation. longwave counter radiation ami the shortwave radiatiun (or
solar radiation) (Hermctnsson. 200 I).
The earth surface is assllmed to emit longwave radiation as a black body_ Thus.
the outgoing lung wave radiation folluws the Stefan-BultzlllCln law (Dewit, 1996 ane!
}lermanssoll, lOO 1):
where: q" - outgoing radiation;
E.~ - emission coellicient:
u-
Stefan-Boltzman constant:Ts - pavement surface temperature.
[2]
As the atl1losphere absorbs radiation and emits it as long wave rae!iation lC1 the
earth, this counter radiation absorbed by tbe pavement surface is calculated as
proposed by (Dewit, 1996 and Hermansson. 200 I):
[31
where: Cj" - absorbed cOLlnter radiation;
E" - pavement surface absorptivity for longwavc racli~ltion and the amount
of clouds;
) 96 Aspl1alt r,uiJiJcr 20(J6
Several authors (Donath el al., 2002 and Picado-Santos L, 1994) consider the
longwavc radiation intensity balance (or thermal rac!i(l(ion) through thc following
expression:
Col f r I l l , .
=h(T -T)
WI'where: q, - longwave radiation intcnsity balance:
h, - thermal radiation coefficient.
The expression usee! to obtain hI is the following (Donath el al., 2002):
h,
= ECT(T,,,, +'F.'i'
)(T,~r
+'F.,~,)
where: E - emissivity of pavement surface.
1-'1
151
Part of the high frequency (shortwave) radiation emitted by the sun is diffusely scattered in the atmosphere of the earth in all directions and the diffuse radiation that reach the earth is called diffused incident radiation. The radiation from the sun
reaching the earth surface, without being rellectecl by clouds or absorbed or
scatterecl by atmosphere, is called direct incident shortwave radiation. The total incident radiation (direct and diffused) can be estimated using the following
equation (Dewil et aI., ] 996, Ozisik, 1985 and Donath et aI., 20(2):
q, = 17 s,_
f
cose
[(ijwhere: if, -thermal incident solar radiation;
'I - loss facLc'r accounting for scattering and absorption of shortw~lve
r:lciialiull by atl11osphen::
S, - solar constant asslIll1cd to bc 135.3 W/mo; ./-- LidoI' accoullting the lTCclltriCity nll:arlh nrbil;
(3 - 7cnilh angle.
The dTective inciden! solar ralii:ltioll ail.s()rbcd
detennined by tile cqLlatioll (l-lcrl1l:1nsS0I1, :iHI 1 )
p:n'Clllcllt :;l1rf~ICC may be
(I,
=
II, - (/,\\'11('I'l' Cj, - incicicnlso/ar r;ldiatiol1 absorbeci hy p:lITIllCnl c,url-ace;
0:, --solin- radiation ;lb.sorption coefficient.
171
In thc Illude I suggested in this paper, sllOrl\VaVC r;ldi;ltilJn IS glvcn ;IS input data
obtained from measured values.
The convection heJ( transfer bet ween tbe paveillent surface and the ai I'
immediately above is given as (J-lcrmanssol1, 2001 and Donath et al., 2()02):
(/, =
ii, (T"" (S)where: Cj, --convection heat transfel-;
The eunvt:ction heZlt lr~lJlsfer cocflieiL,tll eatl be calculatcd as propll.,cLi h\'
(Ikrtlt~lnS'I)n, 20() I and D(Hl~lth ct aI., 2U()2):
Jr, = h9K.:'-f lllA-+dO' U'i), (')/Il() • (J )")J 1')1
\\Ilcrc:
T"".
i.l\·cragc tcmperature gi\'cn byl; - \\ind spcL'd,
3. Finite E1cmcnt 1\Icthod
This study is based 011 the use of the finite,elcment metilod ill the predil'lion uf tCJ1lpnatLll'c Liistrihutior;s in pavcments, In Ihe last years, this I11ctlrmlolugy lIas
revealed to he it tool of great applicability ill tile pilV('mCllls rcse;lrcll dumain, TlIus,
the thcorcticctl hasis of this l1lethmllllogy ;lIlel the ~ljlplic;iti\)11 1m pruposL'cl simultttioll
mudeL ~Irc de:.:cribed,
The I'irst 1;ltV of thermodynamics, which slates that Ihel'llwl energy is COllSCT\ecl,
was used to build the solution of pavement thermal problem through finite eIemetlls,
Considering a differcntial control volume of a pavement, ill lint methoc!ology, the
c()nserv~ltion of thermal energy is expressed by:
where:
p
density: C - specific heat; T - te11lper~ltun~=
T(x,y.z,t)): I - time: Ja /
1
~~c
l
l~/~\'
rl/()~J
- Vector operator:{cI} -
heat flux vector.() lilll
It should be noted that the term
{LY
{q}
Illay also be interpreted dSV
{q},
where1,7 represents the divergence operator, Fourier's law can be Llsed to relate the heat
flux vector to the thermal gradients through the following expression:
19R Asphalt Rubber 2006
[K
0 0 where:[Dj=
~
K"" 0 - conductivity matrix; 0 k--K", Kyy , Kzz - thermal conductivity in the element x, y and z directions, respectively.
Expanding Equation [10] to its more familiar form:
pC
~~
= : ,l
K"~:
) + :,l
K 'I~:
j
+:J
K~~)
[12]
Considering the isotropy of material (K=Kyx=Kyy=Kzz):
[13J
Three types of boundary conditions, which cover the entire model, were considered: heat flow acting over the model surface limits; surface cOllvection applied in the superior surface of model and the raLliant energy between the model superior surface and its SllITOLllldings.
Specified heat flow acting over a surface follows the general expression:
{q
Y
V7}=-Q'where: {77} - unit outward normal vector;
g* - specified heat flow.
'-[14J
Specified convection surfaces heat flows acting over a surface follows the general expression:
J 1 Gy'}T Jl 77 } - h (T - T ) - j 1/1,- 11/1- 115J
where h[-convection coefficient:
T,," - temperature at the surface of the model:
Tall - bulk temperature of the adjacent fluid.
Radiant energy exchange between a surface of the model and its surroundings is translated by the following expression, which gives the heat transfer rate between the surface and a point representing the surroundings:
-
(T' T")
Cj, - at' \III" - - OI!
where () - Stefan-Boltzman coefficient:
[ - effective emissivity:
qr -' heat flux loss of surface.
1\1\cl11cntl'cr!ilrlllanCC and Design 199
4. 3-D FEM Pavement thermal model
The 3-D Finite-Element Method was used for modelling the thermal behaviuur of pavement. The pavement structures traditionally are idealized as a set of horizontal layers of constant thickness, homogeneous. continuoLls and infinite in the horizontal dircction. resting on a subgradc, semi-infinite in the vertical direction. The thermal configuration of the pavcment model was defined in basis of thosc principles anci is presented in Figure l. This modcl considers the possibility of
thermal data transfer for a mechanical mudel wi th the same mesh.
Figure 1. Finite element meshfor thermal model
The adopted mesh was designed also for study of the reflective cracking phenomenon due to the traffic loading and represents an existing pavement, where a crack is simulated through an element with zero-stiffness, and a layer on top of the existing pavement representing an overlay. This mesh was described in other works
of the authors (Minhoto et al., 2003 and Minhoto et al., 2005).
The finite element model used in numerical thermal analysis was performed
llsing a general finite elements analysis source code, ANSYS 7.0. This analysis is a
3-D transient analysis, using a standard finite element discretization, in space. In the
design of the thermal finite-element mesh, the compatibility of mesh with other mechanical models was observed.
The designed mesh has 13538 elements. For three-dimensional thennal analysis,
3-D soliel element, SOLlD70, was used. This element, applicable to a
2()O Aspllall Rubb~r 2006
conduction, according with previous explanation. The clement has eight nodes with a single degree of freedom. defined as temperature, at each node.
The thermal properties of pavement material, such as thermal conductivity, specific heat and density, for each pavement layer, were defined in the "material properties" of this element, when the model was developed.
For surface effect applications, such as radiation exchanges by convection heat transfer, the surface element SURF152 was used. The geometry, node locations, and the system coordinates for this element are shown in the Figure 2.
M(Ex!ranodo)
III
Figure 2. 3-D Slilface Thermal element (SURFJ52)
I(
The element is defined by four nodes and by material properties. An extra node (away from the base clement) is llsed for simulating the effecls of convection and radiation and represents the point where the hourly air temperature is introduced as represel1tati\'e of the atmosphere. This element was overlaid onto an area face of 3-D thermal clement SOLID70, locateel ncar top of Illudel (pavement surface) as it shows in Figure 3.
M(C:xtrAf1ode)
'"
'.
l[lad 1\[Xc ~Im! ~urLIce elfel'h, suc'h ~IS hL'~11 rIuxc·" III e\I:.;1 SlllltliLllWUlISh TbL'
sllri'~lle CiL'lllCIllS werc pl~ICL(ll)11 (illil,' SUI LIL'L' SS (1, ii,
III (he ulilducti\'I(\' 'IEtirix l'lIlcLlI~ltioll, lor Cl)l1slciL'ring Surl~ICL' U)lllCL'!IOII. lile
COIl\(c!lllll cllclIiciL'llt (or filill c(lelliciellti IIllL" be u:.;ed, 'I'-hen CXIIU IIllliL' I, II\L'd,
ils tL'lllllL'l:tture lwcul11cS thL' air tellllxTiltul'cc, This L'kll1elll allll\\, illl 1'~ldi~lIIOII
belll'eell th,' suri'ilcc ~Illd thc cxlru 1\()(1c "[Vl" Thc ,:IIIl""i\ il) (If thL: sUILIL'l' i, u:,cd lit
the comlucti\ Jl\' Ill~lll'i\ citiculilliull. Illr clll1sitil'liili' ,1Irt~IL'c lildidl!UI1. lind tlH'
')teLIIl-Bult/mull cOllstant is also (bcd tUIIIIL' cOlldul'tilitv 1I1~111'J\ l'it!Cltl~llt\lll
The SUIIlI r:tlktliUll i, l'ullSlliL'n.'d ~L, II h,,'11 iiu\ Ih~lI I, ilJ'I,!il:tI (lll "tl!'lUCl' SS, III unlerll) (krill\: Ihe huullcLlry LIJlhJIIIllllS ~I !lull hl'ilt 111I\ I', ;tl,!,ill:d 1)11 ·,uricl,('" 1,1, L,l, LJ, 14 ~(Ild S1. pleSl.'lliCd ill till' h!'IlIL' I
5.l'aVl.'lllcn( Temperature prediction - case study
The maill goal uf this study is tu show Ihe guml Cll'l'lIJ'lll'Y ternper,lIl1lC predlcti()n
llJat C!11 hI: ubtained with lhe model presenteci in this papCl' wilell 1'1lIlljl~ired to thl:
field P,I\'ell1ent [herl11all'ondilion in several reprcscntzltive clays 01 tlte year
Firstly, a FEM numerical analysis for the temperature distrihution in CI pdVel11Cllt
of a trial section was performed fur the weather conditiuns (ail' tcll1jlcr,lture, ,;ul:tr
radiation and willd speed) obtained fmm January 20(Q to December 2UWr (j'v]inhutu
ct u/., :ZOOS). The muclel y,lliclillioll WilS made by statistical analysis between the
FEM l1luncrical temperature results and the ficld .. measured temperatures alld
Ple:SClllcc\ ill Millhoto et (//. (2005),
III this study, a set of' thermal daily dala lIas selected to perforrn :l study aboL1l
the accuracy of the temperature: prediction that can be obtained with this model. This set of days was selected along the year and have: typical daily air temperatures evolution, characterized by a combination of rnaximuill and minimum [ern perature,
The adupted values for the maximum lelllper~ltures were the following: J5°C. 30D
C, 25°C, 20°C, 2SOC and ICfC. The adopte:d \'~lIues for minimum temperatures were:
2()°C, 15°e, I (Joe, SOc, oDe and _5°C. The combination DC thesc twu tempeJ'atures
al1owccito defille 24 clays which were studied in the work,
For each selectecl clay, the thermal hourly c!itld was llsed by thl: 3-D FEl\i[ IIlmlcl.
as input dat,t, amI. as result. the homly tempcr~\turc in all nodes \\',L\ computed, Then,
the obtained value: fur nocics. that represents tile p;tvelllcnt oiJ"cnc:d poi nls, \\il:,
'\
211." .c\spilait i(uhbcr 2()06
5.1. Field data coffcctioll
During it year (January 200cl to December 20()4), pavemcnt lemperatures were
measured at it newly pavelllcnt scction, located at IP4 Illain road, near Graganc,:a, in
thc northeast uf Portugal. At that locatioIl, seven thermocouples were installed in the
pavelTlent ];'yer, at seven dillerent depths: at surface, 27.5 111 III , 55 ITIlll, 125 111111, 165
IllJrl, 22() 111111 and 340 III 111, The top one was installed just at the pavement surface, The depths fur the other six were cho,,-;en to give a good representation of the whole
asphalt layers. Pavement teillperatures were recorded every hour, every clay during
the year.
With respect to short-term temperature response, it can be argued that subgradc
tCillpenlture at 2,0 m depth is reasonably constant over a given months.
From a meteorolugical station, located ncar the test pavemcnt section, it was obtained tlic Iiourly rne;lSUITlllcnts of we,lthcr parameters, such as air temperature,
:,oIar radi~11i()n intensity and wine! speee!, These measurelllt'nts were used as jllput
cl~lla in the simulation models, tu carry out temperature distribution prediction in a
3·1·()-lllill fu II-depth pavcmcn t.
5.2. Illput d([/a to sil7luhtiol/
The pa I'ement surface therlll~d cmissi vity for esti mating the longwave radiation
intensity b,i1ance was equal to Ot) and the solar absorption c()eflicicnt was equal to
()C)5. Table I presents the values for jJ~lVeJllellt I1latcrj~11 thcrlll~t! properties adoptcd
ill this study. The p,lralllt'ters were :lciaptecilll give a guocl eOITesponclellcc between
calcul~lled anci measured IX1VCI1lcnt tCl1lpCr~ltlires. The adoptee! values fullmv thc
typical v~t1Lles for those p;lraillcters suggcsled Oil bibliography by de Bondt (2J)()(]),
/\. S hdlilby cI (If. ( I 99()) aI1d HC1JnanSSOIJ (2IJU I).
Table I. /"o\cn T!/enllo! PwpL'I'lics
_()\(::rl~l)'-a"phall rubber mix _ _ _ _ _ _ _ _ L _ _ _ _ _ _
,5
OV~lJ_Clt - c()llvcnliorui lllix _____ + ____________ -:-___ -'-= ___
,c:::'E0l k
~~lxcr Sub-hasc suhgr~lde --- .. ---r----.. --.... ---,-.5 _5 1.70 23S(] 2SS0 ~U5 2370 1100 22U(),\, e\[JI·cssccl in the cOllclusion.s obtained from simulation Illacle hy HerIlldnssoil
(2()() I), thl' InfilIcnce
or
tht' therillal eonduclivitv uC the P:II'l'Illcnt is Ilwrglnal ror thejldvelnlont tCllIjlcr:llures closc to the surface. Thus, no further clTor! was madc in Ihis
5.3. AJlalysis procedllre
The tilermal res]lDIL,e (If r;Fi\1 sirllliialioll Ilwl!c'I, rcpresel1lillg d IllLlltiLlverc'd
pavellletil su'uL'lure, \\'~IS tIlodelled using ~l tr~lIlSielll thCl'Ill~t1 ~1I1~IIYSIS Il)r d Sl'vet'~i1
daily tillll"perwd, represenullg thc selectee! represcliLltlves dal's, It IS assullled Ilul
the pavcmcnt I]()urly tCl1lpcr~\llllc prufilc depcnds elltirely ()Il huml) ~Iil' killperdlllll:
value, hourly suldr raclialiull I'aluc alld wind speed dddy IllCtlil vtilue,
The allttlysis pruccdurc illvulves a tllultipk J]) l'illltc-ckrnClll rum dlld wa,
initialed with thc full depth dt CDnstant initidl teillperdlllre, ()btaiJled frolll llletlSUfed
field tClIlpCI'tllllreS, The analysis proceciure was c~lITiL'cl oul I'm a periodicity
or
ollehour,
5.4. Results
As a measure of ern'r, the differellce between calculated anclllleaSllrecl pavcmCil! temperalures werc calculated for every hour. fur every depth and fur each selected
day, ;\100 the average difference was determined fur all pavement depths ami 1'01
each computed situation uf a selel'[ed day, Table ::' presents the result
ur
thisprocedure ~ll1d prescnts the average errors and the SUllld~lrd deviation of enDrs where
aile c:ln conclude tilat the proposed model allowed to ()ht~lin excellent tempcrature
prediclion mainly in the tup layers, The presence of an asph~llt rubber mixture in the
top of the pavement analysed did not ~lffect (he temperature prediction in the other
pavement layers ,mel depths.
Figlll'es 4 tu Figure 7 present the temperature evolution for fOLlr reprcsenullive
clays (2nd March, 24th April, 24th July ane! l6th Oetuber), each une I'm e~lch season
or
the year, and a comparison between the FEM calculatecl tcmperature and the in pavcmcnt measureel temperature is made,
These figures allow to cOilclude that the temperature mociel used lo predict the pavement temperature presents a good accuracy in the prediction uf the tcmpcrature in the first layers of the pavement where the eli Ilerences between calculated and observecllemperalures are tDO small.
As the deplh in the pavement increases, the model presents some problems in lhe
prediction of the pavement temperature. For 0,340 111 the temperature difference can
reach 4°C. S(lme important clilTerenees l'an also be founel in surfacc for hot Llays,
mainly in the summer. v'here 8 "C was fllunLl,
However, the presented model is all illtereotillg toul tll precliL'l lhe pal'Cll1ellt
temperature uillil O,lO m. The presence of an asphalt ruhher mix. layer in the tup uf
20-+ Asphalt Rubber 2()06
Table 2. A vcragc crrors Cllld stalldard dCl'iation llJ the tcmperature prediction
Average 81·ms at several pavement derths
~
'. ay-r~;On!ll Season maximum fTHlllmUm average s deviation D.DOm O.0275m 0055rn 0125m 016501 0.220m o 340m;~1::-=Ja_n_i-:-:-Wccin:::te:...f-t_':.::0:....6,-+--,.5:c.',-+--,:'..:2:::08,,--+--,:':::.':::0c-4-t-=c2:_~~~1-,1:...7.:...7:::9+:...1.:.;.7.::9:::2+:...0:::.9:.:1.::5-t_O_.2_9_5-+_0_.3...;0...;7-( 12 Feb Winlel 168 -3.7 0155 1.149 1.-402 1-"711 0830 0.517 ,-,0...;.8...;0_'+-,0...;.2_7...;6-+_0:...4.:.:8:::3-1 2 Mar Winter 9.3 -7.8 -0673 1800 1041 1.137 0.776 1391 1836 1.874 2.779 31 Mar Spring 10!J 5.2 0444 1 059 1.372 1.229 0.903 1-'0"'.3::...':...4+-'0::.;.5:.;5:.;:3-t_0.:.;.::;25:..;0'-+-'-'.::'5:::2'-1 i ___ '.:.;4-,A-,p:...r-tc-?~p:...r.:.;in~g_~_':.::5:::2,-+-~.0,-.3,-+--,.2...;.5...;'.:.;5-t __ :.::3...;.0.:.;50,-+.:.;3_4_40-l-:::3...;.2...;67-j,-:.::3...;3:.;:0.:.;0+...;3_0...;8_7+_3_6_0_7-+...;2...;._33,.,7-+_3:... . .:.;99.::9'-1 ~,,::pr Spring 18.8 -0.2 -2.324 2613 3.017 ?518 2.8313.17033092.1233.936 24 Apr Spring 22.7 2.1 -2.338 2.696 3.189 2.641 2.900 3. j 49 3.186 1.740 4.352 ~~ay Spring 15.2 5.5 ·1.261 1.547 0.983 1.276 1.115 1.992 2.447 2.433 1.901 22 May Spring 19.7 10 -2.758 2.473 3.559 3094 3.113 3633 J 630 3.805 2.276 __ ~ 1 fv18y~ _-,S",p.;..r!,I1.iCg +--=2cc5 .. 8c __ +--C.9_.7_+ __ '2".9c.c2.:.;5 --+ ___ 2...;8,0.0,-+_4 . ...;3_08'-1-,-3_. 3_01-j-,-3...;.5.4,.;..1 +_3_4...;6...;8 +_3._S4_1--+ __ 2..,.9.,.04-jr3".S.:.;S6-j '-_ ,,; J~~ Spnng 29.4 9.6 ·3.452 3.497 5.660 -1.616 4.579 4.155 3.921 3.267 4.562 30 Jun Summer 30,3 14.6 -2.8<16 3.386 5.029 4.121 3.984 3.500 3.353 2.614 4163 __ 9 Jui Summer 20.7 5.8 -3.228 2.985 5.593 4.647 4392 3.405 3.268 ~5 ~m
~-,:~)4-,J~u~i-,~S~um.:.;.:.;m=e-,r~:...3:.:4-,S~+-~15~.~5--1
__ -,.3c..1=5:.;:6--1 __.::2-,8,,4~;--I-=~4j.6~2~3j~~3~7~6~2:t~3~.8~7~7:t~3t.6~2~2:t:3t.7~0~3:!:2~'.~75t6t·1::4~49t7:j
26 Jul Summer 321 12.8 "1 466 3.:126 5.360 4.605 4490 4.092 4.123 3.251 4.689 ~"';:";2-.:":Ag'-o-lrS'::'ur'-n--rn..:cer-+-:'::2"';9 - + - - ' , 7"-. 3'-+--~~:806 3.035 3.3.-:18 2.790 2.583 2.57.::8+...;2:::.0.:.;7:...7-t:...:::' .::.2.1:....:.;5 I 4.095 r __ .. d_AC290::"-I~S.:::ur:.:;11"mc:.e-,r ~.:2:.:5.:::.2,-+--'.14".8.:...+--=.3.::.5:.:6.;.6-t __ :::3.::.1.::2.:.;9 - t 3.998 3.540 3 794 4.293 4.68:..;0--+_4...;. 8_41-j-,-3...;G,6.6--t ~ .. ,._8.A:~go __ , __ s_ul_n_m.;..er-+ __ 20_._9 __ r-_'_5_.2 __ +-_-?~ ___ 2.-:6-:27 __ .t--:1 . .,.73-:8--t __ 1._7-:S5_·~.~1.:...'9~9:..+--:'.::3::9',-+---,'.::.3:..77~.:.:;'-,.8~9~'-+.:..5:...'.::0~2-1 ,_.:":::'6 .. , s=ep::"-j..c.!Ic:;U:..:lu:::rn::.:n+-,2,,4:::9:....+---,4.=.S:....+_.-2.S45 . 1.896 _~ 2A51 ~...;:3:::.0..:.46:'-I...::.3.::Ac::8.:.;5+...:3:.:..S:..:I'..:.O.+_3::..3:..4.:c2-1~:=~=. 6'i:~~~~=~== AA~UUI 1~!'uu=nnlll=1rl:~::~=:=:~==t===:".,-~==1===~=:~.~:.,_~~~ ~.~~~ ~.~~~ ~~: ~ ~~:: ~::~ +:"~~:~::':::::::-+:"'~::':::~::'::~-':~--1
f __ ':::.:9N..:.o.:.;v-t-,-A:::,,!:::u.:.:lll::.:n+ __ ..:.5 . .:.6 __ +-~.O..:.A,--+--=-O 7-'13 0.811 1.425 1.222 O.9.'::l1 0.719 0.783 0.656 0.791
~ __ 2 .... 07cNCno_O, .• V-j---:A_U!_U_Ill_n+_' .... o_.3_+-_.0:3 ·0.682 ..,'.:,.4:.::2::5_1-".::.6-,:'.:.0+.::0,".7.::5::.2+1 -c':..:.::'9,-7-t..:O:::.9~3::::3-t_'::... . .:.:'5::.:4--t-",0.-:77,-9,-+....:.:0.93.2... L_,_:,.::.::uc':"_L.:.A",""!U,,,n:::.,P:. .. L.--,4c:..3 __ -,-~·3:..:.S=--..L_..:.'O.:.:.7.:2=2...J,--:::0.::.6:::2.:.8_LC0:..7::.::5_7.J.-'0.:.:.5.::~~_1 O.G39 ~_ ,_, . ..:._,':.::3--'.-'.1.:..0_13--< __ 0_.59_9--,
20 - SiliculiJled Sur/iKe _. Calculated "01;:'5m \ ~ Ob"rrvn·j lb 10 [l ,: 10 12 15 20 22 12 1-1 16 18 :!() 22 24 Hours -- Cdlcviate,j Ji)';"rVeu 10 16
PaVement Performance and Design 205 ,j{J 0 15 / j ~ () ',0 10 12 ;G 18 2:' il) I!OcJfS 30 2d 2G 30 20 HJ , 16 10 J2 JO 10 I? 1,1 16 18 20 22 2·, 0 '0 12 14 1 i3 18 20 ~'l
Figure
5.
COli/parison hctl\'CCIl utlelilated and observcd tempera/lIrc fi)}' 241h Ajiril50 GO l-Sl,rid-c~ " Cillculaled 1 '5 ---Clliculi!!eu 50 _=-OIJserved "OtlSf,rvecl G 4~ ~40 35 ~ 35 :;.0 r 30 I" 25 25 20 20 15 15 10 0 10 12 14
"
18 2;) 22 24 0 10 12 14 12: 20 22 2..1 HOL1fS Hours 50 39 Caicuia(sd 37 --Calculated 45 -b-OlJsprvnd . ., QbserJed 2:40 Ei
35 E I" 30 29 25 27 20 25 10 12 16 10 20 22 2' 11) 12 I" 16 1B 20 24 Hours Hours206 Asphalt Rubber 2006 23 21 -- Calculated 19 --Observod Fl' ~ 15
'"
ill 13 E ~ 11 ~/~~ _________ " 16 16 15 ~15 ~ ~ 14 ~ ~ 14 13 13 12 ---Calculated -J-Obsef'led 10 12 Hours 10 12 Hours 14 16 10 14 16 18 19 , Surface 18 -Calculated 17 --<-Observed 16"
14 13 12 11 10 20 22 24 10 12 14 16 18 20 22 24 Hours 16 16 -Calculated 15 --<:~Observed ~15 S 15 ;; ~ 15 E 1'=15 14 14 20 22 24 10 12 14 16 18 20 22 24 HoursFigure 7. Comparison between calculated and observed temperature for 161h
October
6. Conclusion
The 3-D finite~element analysis has proved to be an interesting tool to simulate
the transient behaviour of asphalt concrete pavement temperature. According to comparisons performed with field measurements, the suggested simulation model can model the pavement temperature at different levels of bituminous layers with good accuracy. At close to the surface depths the measured and calculated temperatures presents better correlation than far to from the surface.
To obtain this distribution, a series of climatic clata is needed as input to the model. The use of the results for other FEM mechanical models constitutes a great advantage of the proposedmoclel.
When comparing measured and calculated temperature data for every hour for every day, one has concluded that in cole! 1110nths. the average error is less than in hot months. Thus. in the cold months, the developed model presents better performance than in hot l11onths.
The presence of an asphalt rubber mix layer in the top of the pavement seems to have no influence in the pavement temperature prediction and this type of material can be modelled with the specific heat and thermal conductivity coefficient identical to the ones used for conventional mixtures.
7. Hel'ere nces
Sousa. Jurge B .. Pais . .Jurgc
c.,
S'lim. Rachili. \\',1.1'. (it'urge &. StuiJstad. Riel1:lrli N. "DCI'clo[llllcnt ul <1 iVkchanlstic-[lllpiric:ti I~ascli Ovcrlay Design !'vkthocl lor Relketi\'(~ Cracking" Tnills/)ol'lcilioll Rc.\('urcit /?('('(}ul: JOllrnal of lit" Tnllls/}()riO/wlI Res('orch Record. N° I SOL) - p,lpcr numiJer U2-:'Scl·6. TRll. Natlollal Rcsc,llch CUUl1CII. \Vasilin"lUl1. D.C 2()()2. pp 2()L)-217.de B()lIcll. .\li'lll. "[,Ilect 01' RcinCmL'clllcnt Properties". f'1'iJ(eeilings f'NO I/, -Irll
!Il/CJ'/l({/i(}lllli HILJ.'M CUII/in'lIe!' UII He//cuin' C'mcking ill !'ill'elllt'll/S Re.\cL/n!I ill
I'ruc/iu'. hilled by /I. U. ;\!Jd EI H,tii1l1. D. 5. i\. Taylor and
"I
H. H. i\luhalllcd. Rllri\l. Ollaw,1. Ontario. CIJ1lld,1. March. 2 ()()() , PP 13-22.A. Shal:lby. ,·\bel cl I-Ltlilll AU :llllJ O.J. SITe. "LOll tClllpl?r:ltmc stresses ,Int! fracture
analysis of asphalt overlays". PI·ocecclings. TrUIlS/lul'Il/liun Rcseurc/i l\c(,()l'd: JUl/m([1 oj'
the Trt/llS/}(})'((/lioll Researcll Record. 1'\" 153'!, TRB. N~1tiunal Rl'sclll-ch Council.
Wa:shingtoll. D.C. 1'!9CJ. pp 132-139.
Donath tvl.. lVlrawirl.1 and Joseph Luca. "Thermal Pmpcrties and Tr~lnsient Temperature Response of Full-Depth Asphalt Pavcmt'nts". Trull.\j!OI'flllioll lI.escurcll Rec(}rd: J(llIf'Ilul of I//(' Trcrll.\j!IJl'lalio/l Rl'se((J'(-/( /(I'('()rri, N° ISO') -papel' number 0::'-4100. TRI3. National Research COLlllcil. Washington. D.C. 2002, pp 160-169.
Dewit D. P. :md F. P. Inc()per~l. FlIlld(((IIClIllI/S oj' Hcul ({lid Muss rroll.\In. Edited by John Wiley and Sons. Toronto. Canada. 1996.
Ozisik M. N. !lelll T],((lIs/<'I'.· A BIIsir' Appruuch. Edited by McGraw-Hill. New York. USA. I '!85.
j-jerlTlansson A.. "i\ Mathematical Muclcl I'm Calculating Pavement Temperatures. COl11parisons bel ween C:liculated and Measured Temperatures". Tm!1spor/({/ioll Rcseurch
/(ec(}ril: Journa/ of the TmllSpOriatioll Rescorch Record, N° 1764 - paper number () 1-3543. National Research Council. Washington. D.C .. 2001.
Picaclo-Santos L.. Co((siderarc7o cia Tfllllh'railira 110 DimclIsi(}{lCIlJlen/o de PuvilJlCII/os
Rodoviiirios FlnIveis. Ph. D. Tesis. University 01' Coimbra. Lisbon. 191)4.
Minhoto, Manuel J.C., Pais, Jorge
c.,
Pereira, Paulo A.A. & Picaclo-Santos, Luis G .. "Low-Temperature Influence' ill the Predicted of Pavement Overlay". A.lp/lllit Rubl)('/' 2()(}3Conference. Brasilia. Brasil, 2003. p. 167-180.
Millhoto, Manuel J.
c.,
Pais, Jorgec..
Pereira, Paulo ;\.A & Picado-Santos, Luis C .. "Predicting Asphalt Pavement Temperature with a Three-Dimensional Finite Element Model". Trw1jj)()ri(ftio/l Resc!lrch /?fcord: ]ouJ'Ilul oj'the Trollsportuti(JI1 Reseurch Bourdn° II) 19 - Rigid and Flexible Pavement Design 2005 - A peer reviewed publicatiun. p. 96-110. TRE. Washington DC. 2005.
