HUET MODEL FOR OSCILLATORY AND STATIC LOADING OF ASPHALT BINDERS AT LOW TEMPERATURE

Transcription

1 HUT MODL FOR OSCILLATORY AND STATIC LOADING OF ASPHALT BINDRS AT LOW TMPRATUR K Hoon Moon, Augusto Cannone Falcetto * and Ma Marasteanu Unversty of Mnnesota, Mnneapols, USA. *: correspondng autor. canno5@umn.edu ABSTRACT One of te smplest contnuous spectrum models used to caracterze aspalt materals was proposed by Huet n 963. Te model was furter expanded over te years Huet- Sayeg, SPD to better ft expermental data obtaned over a wde range of temperatures. Huet model as expressons for bot complex modulus and creep complance, and terefore, t s possble to use, for example, aspalt bnder Bendng Beam Reometer BBR creep complance expermental data to predct Dynamc Sear Reometer DSR complex modulus and vce versa. Ts dea s nvestgated usng BBR and DSR expermental data obtaned on a set of aspalt bnders at low and ntermedate temperatures. It s found tat Huet parameters n tme doman could be used to obtan reasonable G* predctons, f addtonal restrctons are mposed on parameter. Keywords: aspalt bnder; contnuous spectrum; creep; complex modulus 4

2 INTRODUCTION One of te smplest contnuous spectrum models used to nvestgate aspalt materals reologcal propertes was proposed by Huet n 963. Te model s composed of two parabolc elements, Jt a*t and Jt b*t, plus a sprng element stffness combned n seres as follows: Fgure. Huet model 963 A parabolc element as a contnuous spectrum and te creep complance, Dt, and complex modulus, *, functon n te parabolc element can be expressed as: t D t τ * Γ complex number -; * complex modulus;, exponents, 0 < < < ; dmensonless constant; ω *frequency; τ caracterstc tme varyng wt temperature accountng for Tme Temperature Superposton Prncple TTSP, Γ gamma functon wc can be expressed as follows: Γ n t n t e dt 0 Γ n n Γ n 3 4 n>0 or Real n>0 4

3 43 t ntegraton varable, n argument of te gamma functon. Te Huet model as expressons for creep complance, Dt, as well as for complex modulus, *: 5 6 glassy modulus. Parameter s a dmensonless number around, s an exponent around 0.3, and s an exponent between 0.3 and 0.8 for btumnous materals Huet, 999. Parameter depends on aspalt bnder agng condton; te smaller values are caracterstc of aged, oxdzed materals as a result of ar blowng or weaterng durng producton and servce lfe Huet, 999. From equaton, te real and magnary parts can be obtaned usng a metodology descrbed n Cole et al. 94 as follows: 7 8 Were: and f frequency Hz 9 Te norm of te complex modulus, *, and pase angle,, are ten obtaned as: 0 Γ Γ / / t t t D τ τ * ' sn sn " f ϖ " ' *

4 " tan ' Snce expressons 5 and 6 use te same parameters,,, and τ, teoretcally, te BBR creep complance expermental data can be used to predct te DSR complex modulus and vce versa, te DSR complex modulus expermental data can be used to predct creep complance. XPRIMNTAL INVSTIGATION DSR complex modulus tests AASHTO T 33-05, 006 and BBR creep tests AASHTO T were performed on two aspalt bnders: PG58-8 Ctgo and PG58-34 MIF. DSR frequency sweep tests were performed at seven temperatures -8ºC, -ºC, - 6ºC, 0ºC, 4ºC, 0ºC, and 6ºC BBR creep tests were performed at two temperatures - 8º and -ºC for PG -8, and -4º and -8ºC for PG 34. All tests were performed on pressure agng vessel PAV condton. xamples of G* and master curves and blac dagram curves generated from DSR expermental data are presented n Fgures and 3. Vsual nspecton of te expermental data ndcates tat tere were no obvous expermental errors and tat lnear vscoelastc condtons were present. Fgure. G* and master curves for Ctgo bnder PG

5 Fgure 4. Blac dagram curve for Ctgo bnder PG 58-8 Predctng aspalt bnder creep complance from aspalt bnder complex modulus expermental data and vce versa Te model parameters obtaned from fttng G* data at seven temperatures were used to predct te bendng creep data. Te values obtaned usng equaton 5 matced very well te creep complance data obtaned wt BBR at two temperatures, wc s not surprsng snce te model parameters were obtaned by fttng a large set of data. Te more callengng case s usng Huet parameters obtaned from fttng te relatvely small set of creep complance expermental data to predct complex modulus over a wde range of frequences or temperatures. Wen tese parameters were used n equatons 7 and 8 to calculate G and G, uneven sapes of Cole-Cole plots G vs. G were obtaned, as sown n Fgures 5 and 6. Te fgures sow plots of te expermental DSR data, of Huet model predctons based on te model parameters obtaned from fttng te DRS expermental data, and of Huet model predctons based on model parameters obtaned from fttng te BBR expermental data. Fgure 5: Cole-Cole plot, Ctgo bnder 45

6 Fgure 6: Cole-Cole plot, MIF bnder Based on several computaton trals, t was determned tat applyng strcter lmts n te calculaton of parameter could solve te problem. As a consequence, te followng lmts were placed for te two bnders: Bnder type Ctgo PG 58-8: 0.5 < < 0.4 Bnder type MIF PG 58-34: 0.0 < < 0.4 By mposng tese restrctons of te parameter, slgtly dfferent values were obtaned from fttng te BBR expermental data for te and parameters compared to te values obtaned wt no restrctons. Usng tese new values, Cole-Cole and blac-dagram plots for two bnder types were generated and examples are presented n Fgures 7 to 9. Fgure 7: Cole-Cole usng new parameters, Ctgo bnder 46

7 Fgure 8: Cole-Cole usng new parameters, MIF bnder Fgure 9: Blac dagram plot of MIF bnder By mposng restrcton on te Huet model parameter, t appears tat BBR creep data can be used wt reasonable degree of success to predct te beavor of bnders n te frequency doman. Drect comparson of te expermental and predcted norm of complex modulus s sown n fgure for Ctgo bnder. CONCLUSIONS In ts paper, DSR complex modulus tests and BBR creep tests were performed on two aspalt bnders n PAV condton. By fttng te Huet model expressons to te two sets of expermental data, t was found out tat oscllatory data obtaned over a wder range of temperatures could be successfully used to predct bendng creep complance. However, for te reverse scenaro, t was found tat Huet parameters obtaned from creep experments could be successfully used to predct complex modulus only f addtonal restrctons were mposed on parameter. Ts ndcates 47

8 tat addtonal wor s requred to understand te pyscal meanng of te Huet model parameters to determne a range of values tat would not collapse te sape of Cole- Cole plots. Fgure : Bnder expermental and predcted G* for Ctgo LIST OF RFRNCS. Huet, C., tude par une métode d mpédance du comportement vscoélastque des matéraux ydrocarbonés. Tèse de doctorat d ngéneur, Faculté des Scences de l Unversté de Pars, October p. [In Frenc].. Olard F., and D Benedetto H., General SPD model and relaton between te lnear vscoelastc beavors of btumnous bnders and mxes, Road Materal and Pavement Desgn, Volume 4/, Specal Issue, pp.85-4, AASHTO T 33-05, Determnng te Reologcal Propertes of Aspalt Bnder Usng a Dynamc Sear Reometer DSR, Amercan Assocaton of State Hgway and Transportaton Offcals, AASHTO T 33-06, Determnng te flexural creep stffness of aspalt bnder usng te Bendng Beam Reometer BBR, Amercan Assocaton of State Hgway and Transportaton Offcals, Cannone Falcetto, A., Marasteanu, M. O., D Benedetto, H., Analogcal Based Approac to Forward and Inverse Problems for Aspalt Materals Caracterzaton at Low Temperatures, Journal of te Assocaton of Aspalt Pavng Tecnologsts, Vol. 80, pp , Moon, K.H., Investgaton of Aspalt Bnder and Aspalt Mxture Low Temperature Propertes Usng Analogcal Models, PD tess, Unversty of Mnnesota, Mnneapols, June 0 48