EFFECTS OF TYRE CONTACT PRESSURE DISTRIBUTION ON THE DEFORMATION RATES OF PAVEMENTS

Transcription

1 EFFECTS OF TYRE CONTACT PRESSURE DISTRIBUTION ON THE DEFORMATION RATES OF PAVEMENTS M. Costanzi**, V. Rouillard*, D. Cbon** **Enginring Dpartmnt, Univrsity of Cambridg, England *School of Architctural, Civil and Mchanical Enginring, Victoria Univrsity, Mlbourn, Australia Prsntr: M. Costanzi Rsarch Studnt Enginring Dpt., Trumpington St., Cambridg, England ABSTRACT This papr prsnt th prliminary findings of rsarch aimd at dtrmining th charactr of th contact prssur distribution of cran tyrs and stimating thir influnc on th dformation of pavmnts. Th imptus for th rsarch was: (i) th rquirmnt of th (Australian) rgulation for a minimum tyr siz of 2.5-inch (525mm) for all-trrain crans with a maximum allowabl axl load of 12 tonns; and (ii) th Australian cran industry s argumnt for th adoption of smallr tyrs with rducd inflation prssurs basd on th xpctation of incrasd contact ara, hnc rducd contact prssur. Th papr dscribs th us of prssur-snsitiv film to gnrat a digital fild proportional to contact prssur. Th rsults show that th contact prssur distributions masurd wr complx and not uniformly-distributd ovr a circular ara as is assumd in convntional pavmnt analysis. Th prssur distribution maps rvald larg localisd contact prssurs (oftn gratr that thr tims th man nt contact prssur) at th dg of individual trad blocks. Th masurd data wr usd to study th ffcts of ralistic contact prssur distributions on th dformation rats of flxibl pavmnts, using Finit Elmnt Analysis basd on a non-linar visco-plastic strain and tmpratur dpndnt constitutiv modl.

2 EFFECTS OF TYRE CONTACT PRESSURE DISTRIBUTION ON THE DEFORMATION RATES OF PAVEMENTS M. Costanzi**, V. Rouillard*, D. Cbon** **Enginring Dpartmnt, Univrsity of Cambridg, England *School of Architctural, Civil and Mchanical Enginring, Victoria Univrsity, Mlbourn, Australia 1 INTRODUCTION Most pavmnt analysts hav assumd that th normal componnt of th contact prssur btwn tyr and road surfac is uniform, acts ovr a circular ara and is nominally qual to th inflation prssur (s, for xampl [1-3]). It has bn widly acknowldgd [4, 5] that ths assumptions ar ovr-simplistic and that contact patch ara, shap and prssur distribution vary significantly dpnding on tyr typ, trad pattrn, inflation prssur and load. It has also bn shown [6] that th simplifications lad to an undrstimation of pavmnt strsss. Th localisd paks in th prssur distribution hav bn shown to rsult in incrasd ovrall rutting. Undr normal inflation and loading conditions, th maximum shouldr prssur is obsrvd to b twic th inflation prssur [7-9], although th contact prssur distribution is found to b mor uniform for highr inflation prssurs and/or lowr vrtical loads [8, 9]. A numbr of authors hav calculatd [2, 7, 1], or masurd [1-13], th influnc of tyr contact conditions on strsss and strains in th road surfac. Th gnral consnsus is clar: th dtails of th contact conditions, such as th xact ara, prssur and prssur distribution, affct strsss and strains nar to th surfac of th pavmnt, whras th rspons in th lowr layrs dpnds mainly on th ovrall load [2, 7, 1, 14]. Robrts t al [7] and Marshk t al [15] applid non-uniform, axisymmtric contact prssur distributions to lastic layr pavmnt modls. Both studis stablishd that assumptions about contact conditions can altr prdictd horizontal strains at th bottom of thin surfac layrs (lss than 5 mm) substantially, particularly for undr-inflatd tyrs which hav larg shouldr contact prssurs. Th ffcts of non-uniform loading ar much lss significant for vrtical comprssiv subgrad strains and for thickr pavmnts. Rsarch into pavmnt damag confirms th localisd influnc of contact conditions [6, 14]. Robrts t al [7] and Haas and Papagiannakis [2] stimatd rut formation by summing thortical prmannt dformations of th pavmnt layrs and both ascrtaind that rutting damag is snsitiv to contact prssur. Laboratory masurmnts by Eisnmann t al [1] on a 225 mm thick asphalt road surfac modl showd that rut dpth dvlopmnt was approximatly linarly rlatd to th avrag contact prssur, (indpndnt of load). Th aim of th rsarch in this papr is to invstigat th ffcts of tyr contact prssur distribution on surfac dformation. It has two nw faturs compard to prvious work: (i) It uss uniquly dtaild masurmnts of tyr contact prssurs gnratd by havy vhicl tyrs; (ii) it utilizs a nw nonlinar, visco-plastic modl of asphalt dformation, basd on rcnt matrials rsarch, and implmntd using finit lmnt analysis.

3 2 TYRE CONTACT PRESSURE MEASUREMENTS Vrtical contact prssurs wr masurd with prssur snsitiv film, Prssurx, manufacturd by Fuji Prscal. Prssurx is a Mylar film containing a layr of dy - filld microcapsuls which, upon application of forc, ruptur producing an immdiat and prmannt high-rsolution topographical imag of prssur variation across th contact ara. Although th maximum ratd prssur of th film usd was spcifid at 2.5 MPa, calibration, undrtakn at various nvironmntal conditions, rvald a significantly largr dynamic rang (Figur 1). Figur 1 - Calibration data for prssur snsitiv film 5 sconds xposur. Figur 2 - Photographs of masurmnt st up. Th distribution of contact prssur normal to th pavmnt surfac was masurd by slowly lowring on whl of a loadd cran (adjustd to 6 tonns pr whl) onto a sht of prssur snsitiv film placd btwn th tyr and a whl scal as shown in Figur 2. Th load was maintaind for 5 sconds bfor bing rmovd by activating th cran s stabilisr jacks. This was don for various tyr inflation prssurs. Each imprint, g Figur 3(a), was scannd at 2 dpi with an optical scannr using an 8 bit, gry scal, bit-map format for computr analysis. This includd application of a Gaussian

4 blur algorithm to smooth-out th data and minimis th ffcts of localisd prssur variations (nois) producd by th vry high spatial rsolution of th film as shown in Figur 3(b). Th imag was calibratd (using Figur 1) and th rsult was a contour map of th prssur distribution as pr Figur 4. A sction through such a contour map givs th prssur distribution along a lin through th contact patch, s, for xampl, Figur 5. It can b sn that th prssurs at th dgs of ach trad block can b mor than doubl th prssur in th middl of th block. (a) Figur 3 (a) Exampl of an imprint from th prssur snsitiv film; (b) ffct of a 3.2mm Gaussian blur filtr on digitisd an 8BGS imag. (b) (a) Figur 4 - Exampls of prssur distributions from scannd pictur of th imprint for a Michlin XGC 16 R25 tyr, width 16. (a): inflation prssur 6 bar, (b): inflation prssur 9 bar. (b)

5 5 5 prssur [MPa] EXPERIMENTAL IDEALIZED SITUATION prssur [MPa] EXPERIMENTAL IDEALIZED SITUATION spac [mm] (a) spac [mm] Figur 5 - Transvrs sctions of th prssur distribution across th contact patch of a Michlin XGC 16 R25 tyr, width 16", along th blu lins in Figur 4. (a) inflation prssur 6 bar, (b) inflation prssur 9 bar 3 ASPHALT DEFORMATION MODEL Th mchanical bhaviour of asphalt mixturs dpnds on th quantity, siz, shap, grading and proprtis of th aggrgat, th bhaviour of th bituminous bindr and th prsnc of additivs [16]. Basd on th work of Chung [17] and Dshpand [18, 19], Ossa [2] showd that th transint triaxial dformation bhaviour of bitumn can b xprssd using an xtndd vrsion of th Modifid Cross Modl, givn by: σ & ε & ε = 1 + σ & ε ( ε ) ε ( ε ) & m 1 (b), (1) whr th quivalnt strss and strain ar givn (in tnsor notation) by σ = 3 2 s s, ε = 2 3 ε ε ( s ij ar th dviatoric strsss). Ossa dmonstratd that th xprimntal paramtrs ( ε ) ij ij & ε c, σ, m and k, can b masurd to rasonabl accuracy with a minimum of four ordinary comprssiv or tnsil tsts [2]. & ε, which is a function of strain ε, can b Th rfrnc strain-rat mastr curv ( ) masurd in a crp tst at a constant strss σ at th absolut tmpratur T rf. At any othr absolut tmpratur ( ) ( ) c ε T Trf th rfrnc strain rat is givn by: 1 1 k T Trf & ε ε = & ε ε, (2) whr k is th Arrhnius xprimntal constant. Not that if ( ) & ε & ε ε << (small strain-rat), quation (1) rvrts to linar viscous bhaviour: 1 ij ij σ & ε = σ & ε ε ( ) (3)

6 Dsphand and Cbon [18, 19] found that adding aggrgat to bitumn has two main ffcts on th mchanical bhaviour of th matrial: (i) Undr a uniaxial (comprssiv) strss fild, th aggrgat strngthns th bitumn by a constant factor, indpndnt of strain rat and tmpratur. (ii) Undr triaxial strss conditions, high volum fractions of aggrgat gnrat dilation in th mix whn it is subjctd to dviatoric strsss. Sinc th dilation acts against any applid hydrostatic strsss, th ffct is prssur snsitivity. Consquntly, lik soils, asphalt mixs ffctivly strngthn as th hydrostatic prssur incrass. Ossa [21] showd that th dformation modl for bitumn can b xtndd to asphalts by introducing a strngthning function q ( η), which is th ratio of th stady-stat strain rat of a spcimn of asphalt to th stady-stat strain rat in a spcimn mad of pur bitumn. It is a function of th strss ratio η : q asphalt bitumn ( η ) & ε & ε = (4) ss ss η σ σ m = =. (5) man strss dviatoric strss Thn quation (1) can b writtn: σ & ε & ε = 1 + σ q( η ) & ε ( ε ) q( η ) ε ( ε ) & m 1 In th paramtric study that follows a modl of pur bitumn (quation 1) is usd as a first attmpt to undrstand th ffcts of th matrial nonlinarity on surfac dformation. Sinc th constitutiv laws for bitumn and asphalt hav xactly th sam form for th cas of zro hydrostatic prssur, th rlativ ffcts of th paramtrs lucidatd with th bitumn modl ar xpctd to b similar for asphalt mixs. A finit-lmnt modl of th dformation bhaviour of asphalt is currntly undr dvlopmnt and will b usd to obtain a mor accurat undrstanding of th influnc of aggrgat dilation (paramtr q(η) in quation (6) )on th dformation rspons. Th modl dscribd in quation (1) was applid to a 5 pntration grad pur bitumn. It was calibratd as pr [2], using a dumbbll spcimn lik th on in Figur 6. Th rsults of calibration wr th mastr curv for & ε c ( ε ) in Figur 7. A matrial dformation modl, suitabl for finit lmnt analysis, was cratd for pur bitumn, according to quation (1), using th ABAQUS FEA programm. This subroutin was validatd against xprimntal rsult from tnsil tsts on dumbbll bitumn spcimns. Th agrmnt of xprimnts, FEA and analytical solution was found to b good, as shown in Figurs 8 and 9. (6)

7 Figur 6 - Dumbbll spcimn usd in th charactrization of bitumn. Th cntral gag sction is 8 mm long and 2 mm in diamtr. In light blu th sction of th axi-symmtric modl usd in FEA simulations. 7.E-4 6.E-4 Rfrnc strain rat [1/s] 5.E-4 4.E-4 3.E-4 2.E-4 rfrnc strain rat, xprimntal data running avrag 1.E-4.E Strain [non dimnsional] Figur 7 - Mastr curv for a 5 pn bitumn at 273K (from xprimnts prformd by Ossa [2]). Pntration grad = 53 dmm; Softning point = 53.5 C; k= K; m=.615; σ =.2 MPa strain [non dimnsional] tim [s] FEA, strss:.64 Mpa.127 Mpa EXPERIMENTAL, strss:.64 Mpa.127 Mpa ANALYTICAL, strss:.64 Mpa.127 Mpa Figur 8 - Constant strss tnsil tsts on a dumbbll spcimn mad from 5 pn bitumn at 283K. Comparison btwn sprimntal rsults [2], FEA rsults and analytical solution.

8 strss [MPa] strain [non dimnsional] FEA, strain rat:.5 1/s.7 1/s.15 1/s.2 1/s EXPERIMENTAL, strain rat:.5 1/s.7 1/s.15 1/s.2 1/s ANALYTICAL, strain rat:.5 1/s.7 1/s.15 1/s.2 1/s Figur 9 - Constant strain-rat tnsil tsts on a dumbbll spcimn mad from 5 pn bitumn at 273K. Comparison btwn xprimntal rsults [2], FEA rsults and analytical solution. PARAMETRIC STUDY It is vidnt from Figur 4, that th prssur in th contact patch is a function of th inflation prssur. Whn inflation prssur is highr, th contact patch bcoms smallr and mor roundd, and th avrag contact prssur incrass. It is also vidnt that ach trad lug has a significantly highr prssur all around its primtr than its intrior. In Figur 5 th prssur distribution in th most highly strssd lug was idalizd by a symmtric distribution (in rd) with a flat middl ara and paks at ithr sid. Th width of th lug in this particular in this cross sction is about 65 mm. A paramtric study was prformd, simulating th ffct of th contact prssur distribution of on lug, using an axi-symmtric FE modl (s Figur 1), with th bitumn crp modl dscribd abov. Th prssur fild was approximatd by a cntral circular ara S with a uniform prssur p cntr, surroundd by a concntric primtr ring with ara S pr and uniform prssur p pr. Th shap of th prssur fild is compltly dscribd by two nondimnsional paramtrs: a = p pr p cntr (7) cntr b = D (8) whr D is th diamtr and is th width of th outr primtr rgion of th trad lmnt (figur 1). Th valus of paramtrs a and b wr varid within likly practical limits: a was varid from to 3. (a= corrsponds to a uniform prssur distribution, whil in xprimntal masurmnts it was obsrvd to vary in th rang a=2 to a=3.) Paramtr b was varid btwn and.23. (In th xprimnts b. 1). Th outr diamtr was D = 65mm in all simulations. Th load was rampd from zro to th nominal valu in 1 sc, thn kpt constant for an additional 19 sc. Dformation profils at th nd of th 2s of loading, for an avrag prssur of 1.8 MPa ar givn in Figur 11. It can b sn that concntrating th load in th cntr of th trad lmnt significantly incrass th dformation.

9 Figur 1 - Th axi - symmtric modl usd for FEA. Elmnts ar linar full intgration, axisymmtric in th ara of maximum msh rfinmnt (approx. 1 1 mm) and linar rducd intgration, axisymmtric lswhr. Two xampls of th prssur distribution ar shown on th right: (a): a > 1, (b): a < 1 Figur 12 quantifis th volumtric displacmnt rats obtaind for a = (a uniform prssur distribution), as a function of paramtr b, for two diffrnt matrial modls: th nonlinar modl of 5pn bitumn, as pr quation (1) with m =.615, and a simplifid linar viscous modl in which paramtr m in is st to. For small b, th contact ara is larg and th prssur is corrspondingly small. For larg b th contact ara is small and th prssur is larg. For th linar viscous cas, th volumtric displacmnt rat is practically insnsitiv to th valu of b (hnc th valu of p cntr ). This is a dirct consqunc of th linar viscous modl. Th ovrall volumtric displacmnt rat in th vicinity of th lug is only a function of th total forc on th lug. If th ara incrass, th prssur and hnc local displacmnt rat dcras proportionatly (to kp th sam load) so that th product of ara and displacmnt rat rmains constant. This is far from tru for th nonlinar modl. In this cas, th ffct of th powr m is to amplify th dformation du to high strsss so that th dformation rat incrass dramatically for high valus of b. Figur 13 shows th volumtric displacmnt rats as a function of a for svral valus of b. Th rd icons indicat th wid rang of prssur profils considrd. Th volumtric displacmnt rat is normalizd with rspct to th cas whr b = (uniform prssur). It can b sn that for th rang of paramtrs a and b considrd, th high shouldr prssurs hav littl ffct on th ovrall dformation rat for larg valus of a. Convrsly, dcrasing th ovrall contact ara and incrasing th contact prssur ovr th cntral ara (small valus of a) substantially incrass th volumtric dformation rat.

10 CONCLUSIONS (i) (ii) (iii) (iv) Th prssur fild undr a stationary tyr can b masurd simply and rliably using a prssur snsitiv film. Th systm has bn dmonstratd on a cran tyr but it can b xtndd on any typ of tyr. Th prssur fild undr a tyr shows a complx larg-scal distribution that dpnds on th applid load and th inflation prssur, and a small-scal distribution du to individual trad lmnts. Th prssur snsitiv film can masur both. It is clar that idalising th cran tyr as a circular contact patch with a uniform contact prssur distribution is vry inaccurat. Th non-linar modifid cross modl (MCM) was implmntd in a finit lmnt cod and dmonstratd to b accurat for modlling th bhaviour of pur bitumn in tnsion. It is thought that th broad rsults should xtnd to modls of asphalt pavmnt surfacs, although with much lowr dformation rats. Not howvr that th ffct of dilation of th aggrgat may caus an ffct of intraction btwn adjacnt trad blocks. This is th subjct of on-going rsarch. Th FEA simulations of th ffct of prssur on dformation of a bitumn pavmnt show that th small-scal paks at th dg of th tyr lugs hav littl ffct on th ovrall pavmnt dformation for th rang of paramtrs considrd. Convrsly, th ovrall contact ara and prssur hav a significant ffct on dformation bcaus of th nonlinarity of matrial rspons. REFERENCES 1. DBr, M. and C. Fishr, Contact strsss of pnumatic tyrs masurd with th vhiclroad surfac prssur transducr array. 1997, CSIR: Prtoria, South Africa 2. Haas, R.C.G. and A.T. Papagiannakis. Undrstanding pavmnt rutting. in Spcial workshop on rutting in asphalt pavmnts Toronto: Roads and Transport Association of Canada. 3. Brown, S.F., A.F. Stock, and P.S. Pll, Th structural dsign of asphalt pavmnts by computr. Th Highway Enginr, (2-1). 4. DPont, J., Th impact of small diamtr tyrs on pavmnt war. 2, Transfund Nw Zaland 5. Anon, National Cran Rviw Projct. 2, National Road Transport Commission, Australia, Estill & Associats Pty Ltd 6. Wissman, S.L., Influnc of tyr-pavmnt contact strss distribution on dvlopmnt of strss mchanisms in pavmnts. Transport Rsarch Rcord, (99-774): p Robrts, F.L., t al., Effcts of tir prssurs on flxibl pavmnts. 1986, Txas Transportation Institut Rsarch. p Tilking, J.T. Finit lmnt tir modl. in FHWA Load Equivalnc Workshop Washington D.C. 9. Yap, P. A comparativ study of th ffcts of truck tir typs on road contact prssurs. in SAE Confrnc on Vhicl/Pavmnt Intraction, SAE SP765, SAE Trans Indianapolis. 1. Eisnmann, J., D. Birman, and A. Hilmr, Effcts of commrcial vhicl dsign on road strss - rsarch rsults rlating to th roads. Strass und Autobahn, (Translatd by TRRL as WP/V&ED/87/29), (6): p

11 11. Christison, J.T., K.O. Andrson, and B.P. Shilds, In situ masurmnts of strains and dflctions in a full-dpth asphaltic concrt pavmnt. Proc. Assoc. Asphalt Paving Tchnology, : p Zub, E. and R. Forsyth, An invstigation of th dstructiv ffct of floatation tirs on flxibl pavmnt. Highway Rs. Rc., HRB, N71: p Addis, R.R. Th ffct of whl loads on road pavmnts. in IMchE confrnc on road war: Th intraction btwn vhicl suspnsions and th road London. 14. Chan, G.P., t al. Laboratory masurd tir-pavmnt contact prssurs. in FHWA Load Equivalnc Workshop Washington D.C.: FHWA. 15. Marshk, K.M., t al., Effct of truck tir inflation prssur and axl load on flxibl and rigid pavmnt prformanc. Transp. Rs. Rc. TRB, : p Dshpand, V.S. and D. Cbon, Micro-mchanical modlling of stady-stat dformation in asphalt. Journal of Matrials in Civil Enginring, (2). 17. Chung, C.Y. and D. Cbon, Dformation mchanisms of pur bitumn. ASCE Journal of Matrials in Civil Enginring, (3): p Dshpand, V.S. and D. Cbon, Stady-stat constitutiv rlationship for idalisd asphalt mixs. Mchanics of Matrials, : p Dshpand, V.S. and D. Cbon, Uniaxial xprimnts on idalisd asphalt mixs. Journal of Matrials in Civil Enginring, 2. 12(3): p Ossa, E.A., V.S. Dshpand, and D. Cbon, Phnomnological modl for th monotonic and cyclic bhaviour of pur bitumn. Journal of Matrials in Civil Enginring, (2): p Ossa, E.A., V.S. Dshpand, and D. Cbon, Triaxial dformation bhaviour of bituminous mixs. Submittd to J. Matrials in Civil Enginring, 26. Figur 11 - Exampls of rsults of FEA simulations (final tim: 2 sc) on th ffct of various prssur distributions on a 5 pn bitumn half spac at C. Avrag contact prssur 1.8MPa. Th rd icons show th prssur distribution to scal.

12 2.75 Normalizd volum displacmnt rat [non dimnsional] MODIFIED CROSS MODEL LINEAR VISCOSITY paramtr b [non dimnsional] Figur 12 - Rsults of FEA simulations on th ffct of various prssur distributions with a = on a 5 pn bitumn half spac only at C. Avrag contact prssur 1.8MPa. Figur 13 - Rsults of FEA simulations on th ffct of various prssur distributions on a 5 pn bitumn half spac at C. Avrag contact prssur 1.8MPa. Th rd icons show a sction through th prssur distribution.