EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES

Transcription

1 EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: Paulo A. A. Perera and Jorge C. Pas* Unversty of Mnho, umarães, Portugal E-mal: Abstract: Flexble pavements are subjected to a set of degradatons on the pavement surface, such as cracks and other specfc types of dstress whch arse from traffc and temperature varatons and whch are responsble for the users unsafety and dscomfort. The occurrence of temperature varatons n the pavement leads to a severe aggravaton of the reflectve crackng phenomenon what mples a premature dstress of the overlays. In ths way, a theoretcal study about the nfluence of temperature varaton n the reflectve crackng overlay behavour was performed. To ths end, a thermo-mechancal characterzaton of btumnous materals was made through a set of tests performed wth an asphalt rubber mx and a conventonal mx. It s ntended to study the relaxaton behavour for four dfferent temperature cases, 25ºC, 5ºC, 5ºC and -5ºC, whch s a range of temperature varatons smlar to those that occur n the pavements located n the Northeast of Portugal. Ths paper presents a study n whch the vscoelastc propertes of asphalt rubber and conventonal mxes, related wth long-tme loadng and thermal loadng, were determned through statc relaxaton tests usng dfferent test confguratons. It also descrbes the materal used, the test confguratons appled to evaluate the vscoelastc propertes and t fnally establshes a comparson between the two mxes studed. INTRODUCTION The study of the nfluence of temperature varatons n the behavour of btumnous mxes requres a smulaton of the relaxaton effect subjected to long-tme loadng, such as thermal shrnkage assocated to temperature varatons (Mnhoto et al, 25). For that purpose, a set of tests was performed n btumnous mxes samples to obtan relaxaton capablty evaluaton, expressed by relaxaton propertes estmated for a set of temperatures. A constant stran was appled to a sample durng a loadng tme under constant temperature condtons (Fgure ). The defnton of relaxaton models must be developed for ts ntegraton n fnte elements models used for calculate stress and stran states. The establshment of these models s based on the adjustment of representatve curves of the expermental results to the generalzed expressons whch descrbe ths type of behavour (Mnhoto et al, 25).

2 Fgure Relaxaton test scheme The stress functon of a vscoelastc materal s gven n an ntegral form. In the context of small stran theory, the consttutve equaton for an sotropc vscoelastc materal can be wrtten as: t t de dδ σ = 2 ( t τ ) dτ + I ( t τ ) dτ dτ () dτ The vscoelastc propertes of the materal for what respects to relaxaton, used n the numercal smulaton through fnte elements methodology, had been expressed n an ntegral form usng the kernel functon of the generalzed Maxwell elements, (t) and (t), representng the shear and bulk relaxaton modulus, respectvely, through the followng equatons: n + = n + = ( ) = ( ξ λ ) e ξ (2) ( ) = ( ξ λ ) e ξ (3) The kernel functons are represented n terms of Prony seres whch assumes the formulaton ndcated by the followng expressons: n = + = n = + = t exp τ t exp τ (4) (5) As the vscoelastc property of materals depends strongly on temperature, the so called thermorheologcal smplcty s an assumpton based on the observaton of many glass-lke materals, the relaxaton curve of whch, at hgh temperature, s dentcal to that at a low temperature f the tme s properly scaled. Thus, the characterzaton of vscoelastc propertes of the mxtures must be expressed n functon of the temperature. The consderaton of the temperature dependence n the prevous models s guaranteed through the adopton of shft factors. For ths purpose, the prncple of thermo-rheologcal smplcty s consdered as applcable and t s expressed by the shft factor X=A (T (t)), defned through the expresson of Wllam-Landel-Ferry (WLF): 2

3 log ( A( T ( τ ))) C = C 2 ( T T ) r + T T r (6) In ths work the relaxaton behavour of two btumnous mxes types were analysed: Asphalt Rubber gap-graded mx (ARHM) and conventonal dense asphalt mx (CM). The materal used to obtan the test specmens was extracted from a road pavement after constructon. TEST DESCRIPTION The relaxaton tests were performed usng prsmatc core specmens of 9 mm long by 65 mm thck by 45 mm wde. Each sample was fxed to a shear machne devce support, as shown n Fgure 2. Fgure 2 Sample used n relaxaton tests Each sample s subjected to a constant vertcal axal stran through an nduced constant dsplacement. The constant test stran appled a range from E-3 to 2E-3 and the test temperatures were -5, 5, 5 and 25 ºC. The tme loadng for each test was 72 seconds. TESTIN RESULTS For each test, the values of the three controlled parameters are obtaned perodcally: temperature, dsplacement and load. From these parameters only load presents a varaton over the tme and t s the parameter used for the characterzaton of the relaxaton behavour of the mxtures. The temperature and deformaton were kept constant durng the test. The calculaton of the bulk relaxaton modulus and the shear relaxaton modulus was obtaned wth the parameters measured n the test. The representatve curves of each observed modulus type were obtaned and were used as a bass for the adjustment to the functons kernel, n the form of Prony seres. The Prony seres obtaned must be representatve of the vscoelastc behavour of the studed mxtures. 3

4 In Fgure 3 a representatve graph of the curves obtaned for each test (or for each sample) s presented, nvolvng the asphalt rubber hot mx. In Fgure 4 the same type of representaton s presented for the conventonal mxture. Fgure 3 Relaxaton bulk modulus for AR-HMA mx ºC -5ºC -5ºC -5ºC 5ºC 5ºC 5ºC 5ºC 5ºC 5ºC 5ºC 5ºC 25ºC 25ºC 25ºC 25ºC Fgure 4 Relaxaton bulk modulus for conventonal mx 4

5 FITTIN BEHAVIOUR CURVES The adjustment of curves to the expermental results s made through the establshment of the Prony s seres constants (of Bulk and shear) and of the order of the seres, whch characterze the models of no-lnear materals. These constants were establshed to guarantee the best approach to the expermental results. Three elements of the Prony seres to represent the behavor of the studed mxtures were adopted. Thus 7 parameters of the Prony-seres were defned, seven related to the shear expresson, (t), seven related to the bulk expresson, (t), and three related to the WLF expresson. The Prony constants for a representatve relaxaton curve, relatve to a reference temperature, Tr, and assocated to the functon WLF parameters, were defned from the curves establshed for the four test temperatures, establshng a relaxaton law whch shows a temperature dependence (Table ). The obtaned parameters consttute a behavour data set of the studed mxtures whch can be consdered as nput data for the numercal modellng of the overlays behavour, under thermal loadng condtons. Table Mxes Prony parameters for WLF functon Parameters AR-HMA CM Parameters AR-HMA CM.38E+ 2.8E+ 5.62E E E E+2 4.3E+ 9.45E+ 2.2E+2 2.6E E+.3E E+ 3.7E+ τ 6.3E E- τ 6.5E E- τ 2.47E+ 9.49E+ τ 2.47E+ 9.6E+ τ E+3.E+4 τ E E+3 T r.38e+.3e+ 5.E+.4E+ C 2.23E E+7 C 2.44E+8.39E+8 In Fgure 5 the relaxaton modulus curves for the asphalt rubber mx are presented, compared wth the representatve ponts of the laboratoral tests results n whch the testng results and the developed models largely match. CONCLUSIONS The characterzaton of the relaxaton modulus was made for an asphalt rubber mxture and for a conventonal dense hot mxture, through a set of one cycle long duraton load. The tests results were ftted n the kernel functon of the generalzed Maxwell elements, (t) and (t), representng the shear and bulk relaxaton modulus, respectvely. The kernel functons were represented n terms of Prony seres resultng four relaxaton modulus relatonshps for the consdered temperatures. 5

6 35 Relaxaton Modulus vs temperature - AR-HMA Prony Seres values and observed tests values 3 Relaxaton Modulus (MPa) ºC- Prony S. 25ºC - Observed 5ºC - Prony S. 5ºC - Observed 5ºC - Prony S. 5ºC - Observed -5ºC - Prony S. -5ºC - Observed tme (sec) Fgure 5 Asphalt Rubber mx Relaxaton curves vs expermental data, for each adopted temperature The curves obtaned were used as the bass for the defnton of the Prony constants for a representatve relaxaton curve, relatve to a temperature of reference and assocated to the functon WLF parameters. Thus, a relaxaton law whch shows temperature dependence can be establshed. It was observed that, the asphalt rubber mxture shows a relaxaton modulus less than the conventonal mxture. The relaxaton modulus n an asphalt rubber mxture, for a loadng tme of 72 seconds and for a temperature of -5ºC, s 2 tmes less than the relaxaton modulus of conventonal mxtures. Thus, the resdual thermal stresses n asphalt rubber mxtures at low temperatures are lesser than n conventonal mxture. REFERENCES Mnhoto, M.J.C., Pas, J.C., Perera, P.A.A. & Pcado-Santos, L.. (25). Predctng Asphalt Pavement Temperature wth a Three-Dmensonal Fnte Element Method, Transportaton Research Board, nº 99, pp Mnhoto, M.J.C., Pas, J.C., Perera, P.A.A. & Pcado-Santos, L.. (25). Low-Temperature Influence n the Predcted of Pavement Overlay, Road Materals and Pavement Desgn, nº 3, vol 6, pp