Academic literature on the topic '2S2P1D model'

An experimental campaign has been carried out on five different unaged and five aged penetration grade bitumens to determine the properties of the 2S2P1D (combinations of two springs, two parabolic elements and one dashpot) model. The dynamic oscillatory test was conducted in order to obtain the rheological data using the dynamic shear rheometer (DSR). Earlier, the samples were aged following the Rolling Thin Film Oven Test (RTOFT) test procedure. It was found that the 2S2P1D model which consists of seven parameters simulates in an excellent way the linear viscoelastic properties of aged and unaged penetration grade bitumens over a wide range of temperatures and frequencies. The goodness of fit statistical analysis showed that the model had a good correlation and comparable to the measured dynamic data.

Creep compliance (D(t)) is a very important input for the thermal cracking resistance in the Mechanistic-Empirical Pavement Design Guide (MEPDG). The aim of the work presented here is to predict the results of creep compliance D(t) from the result of complex modulus E*(ω). The work plan is divided in two main parts: an experimental part consisting of creep tests, and a modeling part. Three configurations were compared together, namely direct tensile, direct compression and indirect tensile tests. The modelling part consists of using a 2S2P1D model coupled to Kopelman approximation to switch from the frequency domain to the time domain. Additionally, 2S2P1D was used to calibrate the generalized Kelvin–Voigt model and get the creep compliance directly from E* results. The experimental results show that D(t) from direct tensile and direct compression are the same in the viscoelastic domain and are greater than D(t) from the indirect tensile test. The indirect tensile test (IDT) seems to be very difficult to achieve compared to the other two variants. The converted results using the 2S2P1D model coupled to Kopelman approximation and the results from the GKV model describe the experimental points very well.

Prony series representations have been extensively applied to characterizing the time-domain linear viscoelastic (LVE) material functions for asphalt concrete. However, existing methods that can generate high-quality Prony series parameters (i.e., discrete spectra) mostly involve complicated programming algorithms, which poses a challenge for quick access of Prony series parameters. Also, very limited research has been devoted to establishing methods for simultaneously determining both retardation and relaxation spectra. To resolve these issues, this study presented a practical approach to fast acquiring high-quality Prony series parameters for both relaxation modulus and creep compliance of asphalt concrete by using the complex modulus test data. The approach adopts the analytical representations of the continuous relaxation and retardation spectra from the Havriliak-Negami (HN) and 2S2P1D complex modulus models to directly determine the discrete spectra, and the elastic constants, Ee and Dg, for both LVE modulus and compliance functions are further calculated by fitting the corresponding generalized Maxwell model representations to smoothed data from the storage modulus representations of the HN and 2S2P1D complex modulus models. In this way, all the procedures in the proposed method can be easily implemented in Microsoft Excel. The results showed that the HN and 2S2P1D models yielded slightly different continuous spectral patterns at shorter relaxation times and longer retardation times. However, at the region covered by the test data, the continuous spectra of the two complex modulus models were very close to each other. Thus, the two models can generate comparable Prony series parameters within the time or frequency range covered by the test data. Considering that the quality of the resulting Prony series parameters are closely related to the master curve models used for presmoothing, the HN and 2S2P1D models were compared with the conventional Sigmoidal model. Additionally, the Black diagram was recommended for examining the quality of the complex modulus test data before constructing the master curves.

The relationship between the various phases of asphalt materials, from asphalt binder to mastic and mixture, has received great attention over the years, with efforts being made to establish linkages among these phases. Many methods for predicting the rheology properties of asphalt mastics from those of asphalt and filler volume fractions exist. However, most prediction methods are based on an empirical formula and on the micromechanical model. Very few research studies focus on the constitutive model. In addition, relatively little research has explored the influence of asphalt–filler interaction on mastic’s rheology properties, which is believed to be an important factor. In this study, the 2S2P1D (two springs, two parabolic elements, and one dashpot) model was applied to link the behavior of asphalt binder, filler volume fraction, asphalt–filler interaction and asphalt mastic. First, the interaction between asphalt and filler was evaluated, and the interaction parameter C of the Palierne model was used as an assessment indicator to calculate the effective filler volume fraction of asphalt mastic. Then, the relation between the 2S2P1D model parameters of asphalt mastic and those of asphalt binder and the effective filler volume fraction was analyzed. Finally, a simple relationship associating the 2S2P1D model parameters h, log(τ0) of mastic and that of asphalt binder and the effective filler volume fraction was developed. The proposed expression was validated, and the result showed that it was an efficient model for the shear complex modulus prediction of virgin asphalt mastic.

The objective of this study is to analyse the differences between experimental LVE properties of both a straight-run bitumen and a bituminous mixture and simulations with analogical 2S2P1D (2 Springs, 2 Parabolic elements, and 1 Dashpot) model fitted by 14 different users. Data for the bitumen consisted of isotherms of G∗ and φ obtained from DSR complex modulus tests at 12 different temperatures ranging from −29.9°C to 60.0°C and frequencies ranging from 6.3 to 40 Hz, for a total of 60 data points. Data for the bituminous mixture consisted of isotherms of E∗ and φ obtained from strain-controlled traction/compression complex modulus tests at 8 different temperatures ranging from −29.7°C to 38.8°C and frequencies ranging from 0.01 to 10 Hz, for a total of 55 data points. All users worked independently and for the same time duration of one hour to fit the 2S2P1D model on both sets of data. Successful simulations of experimental data of both bitumen and mixture were generally obtained by all the users over the whole range of frequencies and temperatures, regardless of their familiarity and experience with the model. The accuracy of the model to fit experimental data is all the more evident if the great spans of complex modulus (G∗ of the bitumen between 10−2 and 103 MPa, E∗ of the mixture between 10 and 40000 MPa) are considered. The obtained results highlight the convenience of 2S2P1D model to perform multiscale modelling of LVE behaviour of bituminous materials, from bitumens to mixtures.

In recent years, nanoparticles have been introduced into warm-mix-modified asphalt to improve asphalt performance after sustaining ultraviolet (UV) aging, yet the evaluation of aging performance is often a descriptive characterization of rheological properties. This study extends rheological characterization with viscoelastic mechanical modeling to evaluate resistance to UV aging using Sasobit and SBS compound-modified binder blended with nano-titanium dioxide (TiO2). The extended method comprises characterizations using several rheological properties and a viscoelastic mechanical model, named the 2S2P1D model, on modified asphalt after 3 days, 6 days and 9 days of ultraviolet (UV) aging. The rheological properties of the UV-aged binders were tested at high and medium temperatures in terms of viscosity, complex modulus, phase angle and fatigue factor. Rheological test results showed that nanoparticles generally had no apparent effect on the complex modulus of aged binders regardless of UV aging times. However, the aged binder with nanoparticles showed better fatigue resistance than aged binders without nanoparticles after 3 days of UV aging. As an extension, the black space diagram and 2S2P1D model were used to investigate the viscoelastic properties of these aged binders. The k and h values, as important model parameters, were almost the same and less than one for all UV-aged binders. All investigated aged asphalt binders showed characteristics of a viscoelastic solid in terms of the master curves of the complex modulus and phase angle, and the master curves of the phase angle for all UV-aged binders did not meet the time–temperature equivalence. Moreover, these observations from the 2S2P1D model revealed that aging durations did not affect the viscoelastic mechanical characteristics of warm mix asphalt in this study. The method adopted in this study may promote a comprehensive evaluation of asphalt properties after UV aging, especially considering the viscoelastic mechanical performance.

Mechanical behaviour of bituminous mixtures is characterized by the great thermal sensitivity and the large viscous effects. This paper focuses on the linear viscoelastic (LVE) behaviour of bituminous mixtures that is considered for pavement design. The studied material is a GB3 mix (GB in French is “Grave Bitume”) which is often used for base course construction in France. Complex modulus tests are performed to determine the LVE properties of bituminous mix. Sinusoidal cyclic loadings in tension and compression for small strain amplitudes (up to 10-4 m/m) are applied on cylindrical samples at different temperatures (from -23.4°C to 39.1°C) and different frequencies (from 0.03 to 10Hz). The complex modulus E* and complex Poisson’s ratio ν* are obtained for these large ranges of temperature and frequency. From all these data, it is shown that within the linear viscoelastic domain and in the 3D case, the Time Temperature Superposition Principle (TTSP) is applicable and verified. A model with a continuum spectrum called 2S2P1D (2S2P1D means two Springs, two Parabolic elements, one Dashpot), developed at the Ecole Nationale des Travaux Publics de l’Etat (ENTPE), is used to simulate the 3D LVE behaviour of tested bituminous mixture. Keywords: linear viscoelasticity; bituminous mixture; modelling; complex modulus; complex Poisson’s ratio.

In the presented research, conventional cyclic tension–compression tests and dynamic tests were performed on two types of asphalt mixes (AM). For the tension–compression tests, the complex modulus was obtained from the measurements of the axial stress and axial strain. For the dynamic tests, an automated impact hammer equipped with a load cell and an accelerometer were used to obtain the frequency response functions (FRFs) of the specimens at different temperatures. Two methods were proposed to back-calculate the complex modulus from the FRFs at each temperature: one using the 2S2P1D (two springs, two parabolic elements and one dashpot) model and the other considering a constant complex modulus. Then, a 2S2P1D linear viscoelastic model was calibrated to simulate the global linear viscoelastic behaviour back calculated from each of the proposed methods of analysis for the dynamic tests, and obtained from the tension–compression test results. The two methods of analysis of dynamic tests gave similar results. Calibrations from the tension–compression and dynamic tests also show an overall good agreement. However, the dynamic tests back analysis gave a slightly higher value of the norm of the complex modulus and a lower value of the phase angle compared to the tension–compression test data. This result may be explained by the nonlinearity of AM (strain amplitude is at least 100 times smaller for dynamic tests) and/or by ageing of the materials during the period between the tension–compression and the dynamic tests.

The main objective of this paper was to develop a mesostructure-based finite element model of rubber modified asphalt mixture to predict both the dynamic modulus master curve and phase angle master curve under a large frequency range. The asphalt mixture is considered as a three-phase material consisting of aggregate, asphalt mortar, and air void. The mesostructure of the asphalt mixture was digitized by a computed tomography (CT) scan and implemented into finite element software. The 2S2P1D model was used to obtain the viscoelastic information of an asphalt mortar under a large range of frequencies and temperatures. The continuous spectrum of the 2S2P1D model was converted to a discrete spectrum and characterized by the generalized Maxwell model for numerical simulation. The Prony series parameters of the generalized Maxwell model and the elastic modulus of the aggregates were inputted into the finite element analysis as material properties. The dynamic modulus tests of a rubber modified asphalt mortar and asphalt mixture were conducted under different temperatures and loading frequencies. The dynamic modulus master curve and phase angle master curve of both asphalt mortar and asphalt mixture were constructed. The frequency of the finite element simulations of the dynamic modulus tests ranged from 10−6 to 104. The dynamic modulus and phase angle of the asphalt mixture was calculated and the master curves were compared with the master curves obtained from the experimental data. Furthermore, the effect of the elastic modulus of aggregates on the master curves was analyzed. Acceptable agreement between dynamic modulus master curves obtained from experimental data and simulation results was achieved. However, large errors between phase angle master curves appeared at low frequencies. A method was proposed to improve the prediction of the phase angle master curve by adjusting the equilibrium modulus of the asphalt mortar.

This thesis evaluates the rheological behaviour of asphalt mixtures and the corresponding extracted binders from the mixtures containing different amounts of Reclaimed Asphalt (RA). Generally, the use of RA is limited to certain amounts. The study materials are Stone Mastic Asphalts including a control sample with 0% RA, and other samples with RA rates of 30%, 60% and 100%. Another set of studied mixtures are Asphalt Concretes (AC) types with again a control mix having 0% RA rate and the other mixtures designs containing 30%, 60% and 90% of reclaimed asphalt which also contain additives. In addition to the bitumen samples extracted from asphalt mixes, there are bitumen samples directly extracted from the original RA. To characterize the viscoelastic behaviour of the binders, Dynamic Shear Rheometer (DSR) tests were conducted on bitumen specimens. The resulting influence of the RA content in the bituminous binders are illustrated through master curves, black diagrams and Cole-Cole plots with regressing these experimental data by the application of the analogical 2S2P1D and the analytical CA model. The advantage of the CA model is in its limited number of parameters and thus is a simple model to use. The 2S2P1D model is an analogical rheological model for the prediction of the linear viscoelastic properties of both asphalt binders and mixtures. In order to study the influence of RA on mixtures, the Indirect Tensile Test (ITT) has been conducted. The master curves of different mixture samples are evaluated by regressing the test data points to a sigmoidal function and subsequently by comparing the master curves, the influence of RA materials is studied. The thesis also focusses on the applicability and also differences of CA model and 2S2P1D model for bitumen samples and the sigmoid function for the mixtures and presents the influence of the RA rate on the investigated model parameters.

Nell’ultimo ventennio si è assistito a un rapido incremento dell’utilizzo di materiale fresato nelle pavimentazioni stradali dovuto in parte al risparmio economico derivante dall’utilizzo di questo materiale e in parte ai vantaggi ambientali. Tuttavia, esistono ancora due importanti problematiche alle quali non è stata data una risposta efficace: la prima riguarda la caratterizzazione del bitume invecchiato contenuto nel fresato; la seconda riguarda la possibilità di prevedere le prestazioni delle miscele confezionate utilizzando elevate quantità di fresato. Con riferimento alla prima problematica, i metodi attualmente disponibili sono basati sull’estrazione e sul recupero del bitume contenuto nel fresato per mezzo di solventi. Tali metodi presentano però vari problemi connessi al fatto che l’estrazione e il recupero del bitume può alterarne le proprietà reologiche. Per questo motivo, nel presente lavoro, si è sviluppata una nuova procedura che permette di eseguire un retrocalcolo delle proprietà reologiche del bitume invecchiato e dei blends, composti da bitume invecchiato e bitume vergine, partendo da test su malte composte miscelando la parte fine degli aggregati del fresato e il bitume vergine; utilizzando il modello di Nielsen, appositamente adattato al caso di materiali bituminosi, e il modello di Voigt si riesce a determinare le suddette proprietà reologiche utilizzando i risultati dei test eseguiti sulle malte. Ciò ha un duplice beneficio: da una parte è possibile caratterizzare il bitume invecchiato contenuto nel fresato nelle stesse condizioni di lavoro in cui si trova all’interno della pavimentazione, evitando che subisca ulteriori trattamenti, dall’altra si possono eseguire le prove di caratterizzazione su una delle fasi che maggiormente governano le proprietà delle miscele in conglomerato bituminoso e che quindi regolano le performance delle pavimentazioni. Con riferimento alla seconda problematica, è stata sviluppata una procedura di modellazione multiscala, basata sia su modelli reologici (2 Spring, 2 Parabolic Elements, 1 Dashpot, 2S2P1D model) sia su modelli empirici (Hirsh e Witczak models), che permette di prevedere il comportamento reologico delle miscele in conglomerato bituminoso, contenenti materiale fresato, partendo direttamente dai risultati di prove eseguite sulle malte e tenendo conto della composizione granulometrica degli aggregati e di quella volumetrica delle miscele. La metodologia messa a punto consente di ottenere previsioni affidabili per entrambe le problematiche affrontate, come dimostrato dai risultati delle prove di validazione eseguite nell’ambito della tesi, e di fornire una soluzione innovativa ad alcune questioni che risultano attualmente di particolare rilievo ai fini della estesa utilizzazione del fresato per il confezionamento dei conglomerati bituminosi. In last decades the use of Reclaimed Asphalt Pavement (RAP) materials in asphalt mixtures has seen a significant expansion for economical and environmental reasons. Nevertheless, there are still two important issues which have not been effectively solved: the first regards the characterization of the aged binder contained in RAP; the second concerns the ability to predict the performance of asphalt mixture composed with high RAP content. Regarding the first problem, the current methods are based on extraction and recovery of the RAP binder using solvents; however, these methods are not fully accurate since they can alter the rheological properties of the binder. For this reason, in the present work, a new procedure to back-calculate the rheological properties of the aged binder contained in RAP materials and of the blends composed with fresh and RAP binder, was developed. This is based on DSR tests performed on mortars, composed by mixing the fine fraction of the RAP aggregate with virgin binder. Using the Nielsen model, specifically adapted to asphalt mortars’ case and the Voigt model, the rheological properties of RAP binder can be back-calculated from mortars tests. The present procedure has two advantages: the aged binder contained in RAP is tested as it is after the milling process, avoiding any further treatments, while the testing campaign is centered on the mortar phase, which is one of the most important phases governing the properties of the mixtures and, therefore, the performance of asphalt pavements. Regarding the second problem, a multi-scale approach based on rheological model (2 Spring, 2 Parabolic Elements, 1 Dashpot, 2S2P1D model) and on empirical models (Hirsh e Witczak models) was developed to predict the rheological properties of asphalt mixture containing RAP materials, starting from tests on asphalt mortars and taking into account the grading of the aggregates and the volumetric composition of the mixtures. This methodology allows to make reliable previsions for both the problems addressed, as demonstrated by the results of the validation tests carried out in this doctoral thesis. In addition, the present research provides innovative solutions to address some of the issues which are currently of particular importance for the purposes of extending the use of RAP material in the production of asphalt mixture.

In the last decades, the multi-scale approach has gained wide attention for studying and understanding the mechanisms affecting the performance of asphalt mixtures. According to such approach, the asphalt mixture could be seen as an assemblage of components of different length scales, each with its own mechanical properties, and thanks to the investigation on these lower scales a scale-wise insight can be gained and used to capture phenomena not considered in continuum approaches. This Thesis is focused on the interrelation between the Fine Aggregate Matrix (FAM) the asphalt mixtures. Fine aggregates, filler, binder and air voids compose the FAM, which represents the intermediate scale between mastic and asphalt mixture. This phase has a critical role in the overall performance evaluation of asphalt mixture and the simplicity, efficiency and the lower costs/times required to study the FAM make it a very attractive specification-type approach. However, despite the growing interest on FAM testing, there are some concerns about proper FAM mix design. Moreover, there are many lacks in predicting the performances of asphalt mixtures from the FAM phase. The primary objective of this Thesis was the identification of a design method for FAM, which allows recreating the FAM phase, as it exists within the asphalt mixture. The selected design method has shown promising results and seems quite accurate in reproducing the FAM within the asphalt mixture. The second issue which is pursued in this Thesis, is a multi-scale approach based on the rheological 2S2P1D model, allowing to interrelate the four material scales (from binder to asphalt mixture). Firstly, it was verified that the 2S2P1D model remains valid for FAM in the Linear ViscoElastic (LVE) range and that it could adequately fit experimental data of FAM. Then, it was possible to relate the different phases thanks to the definition of interrelationships between one model parameter. The interrelation between the asphalt mixture and the corresponding FAM could be used to predict the rheological properties of the asphalt mixtures starting from FAM tests. This methodology allows making reliable forecasts of the LVE behaviour of the asphalt mixtures, as demonstrated by the results of validation tests. Future developments will investigate other volumetric compositions of mixes, to study the influence of microstructural and volumetric characteristics on the model parameters.

The article presents the results of dynamic modulus tests carried on the asphalt concrete (AC16W). The sinusoidal load was applied to the samples in accordance with DTC-CY method. The neat bituminous binder (penetration grade 35/50) was modified by means two synthetic waxes, coming from the Fischer-Tropsch raction, with various molecular weights and softening point temperature results (hard and softer). The relaxation phenomenon in terms of changes in complex modulus and phase angle was evaluated using the modified Huet-Sayegh (2S2P1D). Estimated model parameters pointed out that the addition of the synthetic wax with the high (hard wax) and the low (softer wax) molecular weight raised the stiffness of the bituminous binder in relation to the reference bitumen 35/50. The application of the modified Huet-Sayegh model showed that the presence of the synthetic wax in the bitumen significantly affected the stiffness modulus of considered asphalt concretes. Basing analysis on Cole-Cole diagram it was found significant differences in the viscoelastic behaviour between the reference asphalt concrete and the asphalt concretes with synthetic waxes. In contrast, there were no significant differences between viscoelastic properties of tested asphalt concretes modified, used in the experiment, synthetic waxes. Furthermore, the sensitivity to the loading time of asphalt concretes containing both synthetic waxes was marginal.