Ratio of Dissipated Energy Change-based Failure Criteria of Asphalt Mixtures

Transcription

1 Research Journal of Appled Scences, Engneerng and Technology 6(14): , 013 ISSN: ; e-issn: Maxwell Scentfc Organzaton, 013 Submtted: November 08, 01 Accepted: December 1, 01 Publshed: August 10, 013 Rato of Dsspated Energy Change-based Falure Crtera of Asphalt Mxtures Yuan Mao-Mao, Zhang Xao-Nng, Chen We-Qang and Zhang Shun-Xan School of Cvl Engneerng and Transportaton, South Chna Unversty of Technology, Guangzhou , Guangdong, Chna Abstract: A four-pont bendng fatgue test system researched by Cooper was used to evaluate the fatgue performance for dfferent partcle sze and dfferent asphalt content of asphalt mxtures. Based on the four -pont bendng fatgue test and dsspated energy method, the Rato of Dsspated Energy Change (RC) was calculated that s ndcatve of the damage evoluton n asphalt mxtures. And then based on the correlaton of Rato of Dsspated Energy Change (RC) and load cycles, a new fatgue falure crtera was presented that s materals falure happen when RC ncrease sharply. Under these falure crtera, fatgue lfe predcton model on RC s accepted and ths model s ndependent on constant stran and constant stress modes. Keywords: Asphalt mxtures, fatgue falure crtera, four-pont bendng fatgue test, rato of dsspated energy change INTRODUCTION Fatgue damage s the manly form for the damage of asphalt concrete pavement and the mechansm nvestgaton about fatgue damage of asphalt concrete pavement have attracted extensvely attentons recently years. However, the fatgue damage mechansm of asphalt mxtures s very complcated and shows closely dependence on many factors, n whch the nteracton between these factors exsts. Therefore, t s urgent to develop a model, whch not only can gve an accurate predcton of the fatgue lfe but also to avod the lmtaton of load patterns (such as stress control and stran control), to express accurately the fatgue damage behavor of asphalt mxtures. The predcton of the fatgue lfe of the asphalt mxture manly demonstrated ndoor fatgue test through the researchng a lot of lteratures at home and abroad. Many asphalt mxture fatgue lfe predcton models, ncludng phenomenologcal method, mechancal approxmaton method and dsspated energy method were reported. Phenomenologcal method uses fatgue curves to characterze the fatgue propertes of the materal. It holds that the fatgue of asphalt mxtures s the damage phenomena nduced by the ntensty attenuaton accumulaton under the repetton load (Moghadas et al., 010; Park et al., 009; Km et al., 1997). However, ths method cannot reflect the fatgue damage accumulaton process and lack of an accurate defnton on the fatgue falure crteron. In addton, dfference test results would be ganed for dfferent test methods. Thus, the fatgue model obtaned from phenomenologcal method s dffcult to express the actual fatgue propertes for asphalt mxtures. Mechancal approxmaton method s a strategy that used the fracture mechancs to explan the fatgue crack propagaton law to determne the materal fatgue lfe. Ths method consders materal exst cracks ntally wthout consderng the stage of the formaton of cracks. Its research focus s the nvestgatons of fracture mechansm and the crack propagaton law for materals (Kua et al., 009). Addtonally, asphalt mxture s a vscoelastc materal, the stress ntensty factor K s not a constant at hgh temperature. Therefore, the applcaton scope for mechancal approxmaton method was lmted to some extent. Early n 197, Van Djk proposed dsspated energy method would be an effcent method to study the fatgue ssue of asphalt mxture (Van et al., 197). Latter, Van Djk and Vsser used stran and stress control mode to test the fatgue of asphalt mxtures at dfferent loadng frequency and dfferent temperatures (Van and Vsser, 1977). The relatonshp between cumulatve dsspated energy and fatgue lfe was gven as followng: W fat = AN Z f n whch, W fat = The cumulatve dsspated energy when fatgue falure N f = The load cycle ndex when fatgue falure A, Z = The obtaned test model parameters (1) Correspondng Author: Yuan Mao-Mao, School of Cvl Engneerng and Transportaton, South Chna Unversty of Technology, Guangzhou , Guangdong, Chna 514

2 Res. J. Appl. Sc. Eng. Technol., 6(14): , 013 Van Djk ntended to verfy cumulatve dsspated energy s the only ndependent factor to predct the fatgue lfe through the fatgue test. That to say W fat s ndependent on the load mode, materal style and other factors. However, the Unted States Strategc Hghway Research Program Report SHRP A404 ponted out that ths fatgue lfe predcton model depends on the load control mode (SHRP, 1994). In vew of the lmtaton of the above mentoned methods, a four-pont bendng fatgue test system researched by Cooper was used to evaluate the fatgue performance for dfferent partcle sze and dfferent asphalt content of asphalt mxtures n ths study. Based on the four-pont bendng fatgue test and dsspated energy method, the Rato of Dsspated Energy Change (RC) was calculated that s ndcatve of the damage evoluton n asphalt mxtures. And then based on the correlaton of Rato of Dsspated Energy Change (RC) and load cycles, a new fatgue falure crtera was presented that s materals falure happen when RC ncrease sharply. Under ths falure crteron, fatgue lfe predcton model on RC s accepted and ths model s ndependent on constant stran and constant stress modes. THE FUNDAMENTAL OF DISSIPATED ENERGY Hysteress loop equaton: Assumng a snusodal stran or stress α sn ωt s appled to the asphalt mxture specmen, the specmen wll generate a stress or stran response b sn (ωt + φ) at the same frequency, n whch ϕ s the lag phase angle. Suppose: x = a snωt y = bsn t ( ω +ϕ) () (3) Substtutng Eq. () nto (3) to get the Eq. (4), as expressed as followng: y x cosϕ cosωt = - bsnϕ a snϕ (4) Fg. 1: Schematc dagram of stress-stran hysteress loop Table 1: Proporton of mneral aggregate Mass percentage/% Seve/mm AC10 AC vscoelastc materal s an energy dsspaton process, whch s a process of damage evoluton. The energy dsspated by each one stran cycle W can be determned by the area of stress-stran curve hysteress loop, as shown n Fg. 1. W can be calculated by the followng formula accordng to others research results (Zhang et al., 1998): W = ydx = πσ ε snϕ (6) W, σ, ε, φ s the dsspated energy, stress ampltude, stran ampltude and phase angle for the -th load cycle. In the whole process of fatgue lfe, cumulatve dsspated energy W fat s the sum of all the loop area, the calculaton formula s expressed as followng: W fat = nn =1 WW (7) Combnng Eq. () and (4), we can get the hysteress loop equaton, the stress-stran response equaton of asphalt mxture sample for each load cycle, as expressed n followng equaton: x a y + b xy cosϕ snϕ - = snϕ ab (5) The schematc dagram of hysteress loop equaton was shown n Fg. 1. The calculaton of dsspated energy: Asphalt mxture s a vscoelastc materal and the destructon of 515 FOUR-POINT BENDING FATIGUE TEST Trabecular specmen preparaton: The domnatng steps to prepare rectangular beam four-pont bendng fatgue specmen ncludes mxture mxng, rollng and cuttng. In ths study, the content of AC-10, AC-0 asphalt s selected about 4 and 6% for the asphalt mxture, respectvely. The porosty s desgned about %. Dabase produced from Heyuan Yu Feng quarry s used as aggregate. Lmestone slag produced form Guandong Yunfu s selected as slag. Asphalt s Tpco 70 # asphalt, the proporton of mneral aggregate s shown n Table 1.

3 Res. J. Appl. Sc. Eng. Technol., 6(14): , 013 Fg. : Four-ponts bendng fatgue test setup Test process and parameters: The four-pont bendng fatgue test was demonstrated on pneumatc servo test system developed by Brtsh Cooper equpped wth asphalt mxture quartle pont bendng fatgue test fxture launched by U.S. hghway development strategy research program, the test apparatus s shown n Fg.. The data control and acquston system s the CRT- SA4PT-BB test software developed by Cooper. The dates of σ, ε, φ are acheved synchronously on ths test software. Accordng to the number of repeated load, samplng frequency s set as 1 (the number of repeated load <500), 100 (500<the number of repeated load<1000) and 500 (the number of repeated load>10000)), respectvely. The prepared specmen s conserved on an envronmental chamber for four hours to get the test temperature of 0 C for the specmen, before the fatgue test s demonstrated. Both the stress control (750, 1000 and 1500 Kpa, respectvely) and stran control (00, 400 and 600 µε, respectvely) load modes are appled on the specmen. The load s appled n the form of sne wave wth a frequency n 10 Hz. Fnally, the dsspated energy of asphalt mxtures trabecular specmens calculated by Eq. (6) and (7) for the dfferent test condtons. EXPERIMENTAL RESULTS AND DISCUSSION The dependence curve of dsspated energy and the number of load cycles s exhbted n Fg. 3. In ths study, the Rate of Dsspated Energy Change (RC) s employed to descrbe the fatgue behavor of asphalt mxtures. The applcaton of the rate of dsspated energy change n quantfyng the fatgue of materals was frstly proposed by Carpenter and Jansen (1997). In hs research, he found a close relaton between Rate of Dsspated Energy Change (RC) (the rato of the absolute dfference of dsspated energy between the -th and the +1-th load and the dsspated energy of the -th load, durng the repeated loadng) and materal fatgue lfe. The Dsspated Energy Change Rate (RC) can be calculated as followng: RC = (8) 516 Fg. 3: Dsspated energy vs number of load cycles to falure usng two modes of loadng, constant stress and constant stran where, and +1 s the dsspated energy of -th and +1-th repeated load, respectvely. However, the number of load cycles for some materals may larger than 0 mllon, owng to the varaton of fatgue lfe of materals. Thus, t s hard to acheve fatgue test data gradually. In vew of ths, the above formula about the calculaton of Rate of Dsspated Energy Change (RC) can be corrected, as expressed n Eq. (9): j - RC = ( j -) (9) In whch, and j s the dsspated energy of -th and j-th repeated load (j>), respectvely. The number of ntervals between and j s determned by the samplng frequency. Basng ths correcton, not only the calculaton effcency can be mproved, but also applcaton n the longer lfe asphalt mxtures specmens developed. Accordng to Eq. (9), the dependence of dsspated energy rato on the number of load cycles wth the mode of stran control and that wth the mode of stress control are shown n Fg. 4 and 5, respectvely. As shown n Fg. 4 and 5, the dependence curves for dsspated energy rato on the number of load cycles can be dvded nto three stages no matter wth the mode of stran control or the mode of stress control. Stage one (REEC 1 ): the rate of dsspated energy change n a chaotc state due to asphalt mxture specmen resst the deformaton nduced by the load, under the repeated loadng. Nevertheless, a gradually decreasng trend can be observed. Stage (RC ): wth the ncrease for the number of load cycles, RC mantan a low and stable Value (PV). At ths tme, the rate of dsspated energy change s a stable state, ndctng specmen damage evoluton occurs at a steady rate; Stage 3 (RC 3 ): wth the further ncrease for the number of load cycles, RC ncrease dramatcally,

4 Res. J. Appl. Sc. Eng. Technol., 6(14): , 013 (a) 00 με (b) 400 με (c) 600 με Fg. 4: The dsspated energy rato versus number of load cycles n dfferent stran level llustratng the damage s enhanced sharply and the resultng fatgue falure occurs for specmen. Furthermore, there s no obvous ncrease for the Rate of Dsspated Energy Change (RC) for both the modes of stran control and stress control and the dfferent control levels basng on the presented fatgue falure crtera, whch was defned as the stffness modulus decreased to 50% of the ntal value under repeated loadng. Therefore, damage evoluton of materal stll n a stable state, there stll exsts some resdual strength to resst the repeated loadng. Heren, the number of load cycles (N tf ) correspondng to the mutaton of RC ~RC 3 s selected to descrbe the fatgue lfe. Fatgue lfe predcton model proposed by Shen s used to ft the fatgue test date for the two control modes (stran control and stress control), Shen and Carpenter (005) as expressed n followng: d PV = cn f (10) 517 n whch, PV = The average value of RC c and d = The fttng parameters N f = The number of load cycles for fatgue falure In ths study N f s recognzed as the number of load cycles for fatgue falure as shown n Fg. 4 and 5. The fatgue lfe fttng curves for two dfferent materals wth vared load control mode and control levels are shown n Fg. 6, basng on the above mentoned fatgue lfe predcton model. From the dagram n a double logarthmc coordnates, we can see that there s a strong correlaton (R = 0.97 or 0.99) between PV and fatgue lfe for both of fne-graned (AC10) and medum-graned (AC0) asphalt mxture, no matter what knd of load patterns s demonstrated. In can also be seen than from the dagram, ths fatgue lfe predcton model based on Rate of Dsspatve Energy Change (RC) s ndependent of the load control

5 Res. J. Appl. Sc. Eng. Technol., 6(14): , 013 (a) 750 KPa (b) 1000 KPa (c) 1500 KPa Fg. 5: The dsspated energy rato versus number of load cycles n dfferent stress level (a) AC10, content of asphalt s 4% (b) AC0, content of asphalt s 6% Fg. 6: Correlaton between PV and number of cycles to fatgue falure n dfferent load modes (N tf as the falure crtera) 518

6 Res. J. Appl. Sc. Eng. Technol., 6(14): , 013 mode. In another words, one fttng curve would be obtaned for both the modes of stran control and stress control. In summary, t s rratonal to demonstrate the ndoor fatgue test of asphalt mxture usng the tradtonal falure crtera, whch was defned as the stffness modulus decreased to 50% of the ntal value. Applcaton of Rate of Energy Dsspaton Change (REDC) to descrbe fatgue falure crteron shows a clear physcal meanng. In addton, the ndependence of fatgue lfe predcton based Rate of Dsspated Energy Change (REDC) model on load control modes s verfed. CONCLUSION The relaton between Rate of Dsspated Energy Change (REDC) and fatgue lfe was exploted through a four-pont bendng fatgue test wth dfferent asphalt mxture and vared load control modes and a new fatgue falure crtera was proposed. Under ths falure crteron, the feasblty of the Rate of Dsspated Energy Change (REDC) to predct fatgue was confrmed and the ndependence of load control modes was demonstrated. The man conclusons of ths study are as follows: It s rratonal to demonstrate the ndoor fatgue test of asphalt mxture usng the tradtonal falure crtera, whch was defned as the stffness modulus decreased to 50% of the ntal value. At ths tme, the Rate of Dsspated Energy Change (RC) keeps a lower stable level, ndcatng the damage evoluton of materal s stable. In other words, there stll exsts some resdual strength to resst the repeated loadng; a qute resdual lfe should not be neglected. Fatgue evoluton ncreases dramatcally as the Rate of Dsspated Energy Change (RC) gets mutaton, the asphalt mxture specmen fatgue falure occurs. Applcaton of Rate of Energy Dsspaton Change (REDC) to descrbe fatgue falure crteron shows a clear physcal meanng. The feasblty of the Rate of Dsspated Energy Change (REDC) to predct fatgue was confrmed and the ndependence of load control modes was demonstrated through usng the fatgue falure crtera proposed n ths study. REFERENCES Carpenter, S.H. and M. Jansen, Fatgue behavor under new arcraft loadng condtons. Proceedng of Arcraft/Pavement Technology n the Mdst of Chang, pp: Km, Y.R., H.J. Lee and D.N. Lttle, Fatgue characterzaton of asphalt concrete usng vscoelastcty and contnuum damage theory. J. Assoc. Asphalt Pavng Techn: Assoc. Asphalt Pavng Technol., 66: Kua, H.D., H.J. Lee and S. Mun, 009. Applcaton of generalzed J-Integral to crack propagaton modelng of asphalt concrete under repeated loadng. Transp. Res. Record, 17: Moghadas, N.F., E. Aflak and M.A. Mohammad, 010. Fatgue behavor of SMA and HMA mxtures. Constr. Buld. Mater., 4(7): Park, H.M., J.Y. Cho and H.J. Lee, 009. Performance evaluaton of a hgh durablty asphalt bnder and a hgh durablty asphalt mxture for brdge deck pavements. Constr. Buld. Mater., 3(1): Shen, S.H. and S.H. Carpenter, 005. Applcaton of the dsspated energy concept n fatgue endurance lmt testng. Transp. Res. Record: J. Transp. Res. Board, 199: SHRP, A-404. Natonal Research Councl. Van, D.W. and W. Vsser, The energy approach to fatgue for pavement desgn. Proceedngs of the Assocaton of Asphalt Pavng Technologsts, 46: Van, D.W., H. Moreaud, A. Quedevlle and P. Uge, 197. The fatgue of btumen and btumnous mxes. Proceedng of 3rd Internatonal Conference on the Structural Desgn of Asphalt Pavements, Ann Arbor, Mchgan, USA, pp: Zhang, J.N., Y.Q. Tan and X.N. Zhang, Predctng fatgue falure of btumnous mxture usng energy dsspaton. Chna J. Hghway Transport, 11(4):