A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

Sun, Yiren; Huang, Baoshan; Chen, Jingyun

doi:10.1016/j.conbuildmat.2015.04.055

Cited by 56 publications

(14 citation statements)

References 37 publications

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“…Once the discrete spectra are given, other material functions either in the time or frequency domain (relaxation function, creep compliance and complex modulus) will be immediately determined. Additionally, numerous finite element software packages have incorporated the Prony series as basic material input in the numerical simulation of viscoelastic behaviors [37]. Thus accurate discrete relaxation spectrum and retardation spectrum are indispensable to better characterize and numerically simulate LVE material behaviors.…”

Section: Prony Series Represented Relaxation Modulus and Discrete Relaxation Spectrummentioning

confidence: 99%

Mechanism behind Time Dependent Elasticity of Crumb Rubber-Nano-Asphalt Hybrids Using Discrete Relaxation Spectrum

Han¹,

Zheng²,

Hong-bing³

et al. 2022

Journal of Renewable Materials

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Crumb rubber powder is a successfully used renewable material obtained from waste tire rubber, which has been incorporated into paving asphalt since the 1930s due to its good resistance to deformation and fatigue as well as its eco-friendly performance. In this study, carbon nanotubes and nano silica were incorporated into the terminal blend crumb rubber modified asphalt technology to remedy the issues of excessive desulfurization and degradation of ground tyre rubber with this technology. The mechanism behind the high temperature delayed elastic properties of the crumb rubber-nano-asphalt hybrids was experimentally investigated based on discrete relaxation spectrum. Development of the discrete relaxation spectra was accomplished by fitting on the 60°C storage modulus data tested by the dynamic shear rheometer using the generalized Maxwell model. Subsequently, the feasibility of characterizing delayed asphalt elasticity using main relaxation time was verified by test results from the 60°C creep and recovery test. Results indicated that the crumb rubber-nano-asphalt hybrids exhibited arrheodictic behavior and the asphalt elasticity was strengthened by two nano agents. Moreover, the elasticity reinforcement with carbon nanotubes was greater than with nano silica. Additionally, a good correlation was observed between the 60°C zero shear viscosity and main relaxation time, and greater 60°C zero shear viscosity was correlated to longer main relaxation times. Furthermore, longer main relaxation time of the asphalt was related to greater average recovery rate in the creep and recovery test. This research is expected to shed some light on the mechanism behind time-dependent elasticity of crumb rubber modified asphalt from the perspective of polymer physics.

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Section: Prony Series Represented Relaxation Modulus and Discrete Relaxation Spectrummentioning

confidence: 99%

Mechanism behind Time Dependent Elasticity of Crumb Rubber-Nano-Asphalt Hybrids Using Discrete Relaxation Spectrum

Han¹,

Zheng²,

Hong-bing³

et al. 2022

Journal of Renewable Materials

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“…It has been concluded that the viscoelastic properties of AC can be accurately characterized using the modified Havriliak-Negami (MHN) model (15)(16)(17). In this study, the MHN model is adopted to represent the engineering property of AC in the LVET analysis.…”

Section: Response Analysis Approach Based On Lvetmentioning

confidence: 99%

Evaluation of the Response Analysis Approach Used in the Mechanistic-Empirical Pavement Design Guide

Zhao

Liu

et al. 2020

Transportation Research Record: Journal of the Transportation R

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Asphalt concrete (AC) is a typical viscoelastic material exhibiting rate-dependent behavior. The rate-dependency of AC should be properly taken into consideration in pavement response analysis to accurately evaluate pavement performance and life. In the Mechanistic-Empirical Pavement Design Guide (MEPDG), the dynamic modulus master curve is used to account for the rate-dependency of the dynamic modulus of AC. However, the rate-dependent phase angle is ignored and a constant phase angle of 0 is assumed. The partial characterization of rate-dependent properties of AC in the MEPDG may lead to inaccurate results. This study compares the pavement responses computed using the MEPDG approach and the layered viscoelastic theory (LVET) which utilizes the complex modulus master curve to fully characterize the rate-dependent properties of AC. Typical three-layer pavement structures were analyzed at three temperatures (−10°C, 20°C and 50°C) and four speeds (10, 40, 80 and 120 km/h). The results show that the horizontal tensile stresses at the bottom of cement-treated base layer obtained from the two approaches are almost the same, and for other responses analyzed, the results obtained from the MEPDG approach are larger than those from the LVET approach, especially for the responses in the AC layer. The normalized difference of the vertical compressive strain at the mid-depth of the AC layer between the two approaches can be up to 100% and that for the horizontal tensile strain at the bottom of the AC layer can be more than 50%.

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“…This can be primarily attributed to their high computational efficiency and wide applicability [3,12,13]. The two models are composed of linear springs and dashpots linked in different configurations, and mathematically yield the so-called Prony series expressions for the relaxation modulus and creep compliance in time domain [3,12,14]. The Prony series expressions are not only very convenient to be converted analytically into the frequency-domain complex modulus and compliance, but also can considerably facilitate the computation of the convolution integrals for the LVE constitutive equations due to the presence of decaying exponential terms.…”

Section: Introductionmentioning

confidence: 99%

“…Two major issues, namely negative spectrum strengths and local spectrum oscillations, occur frequently due to the narrowband nature of the Prony series terms and significant scatters in test data. To address these problems, presmoothing techniques have been introduced by using broadband functions, like the Sigmoidal model [2], power-law series [3], Huet-Sayegh model [18], Havriliak-Negami (HN) model [14] and 2S2P1D model [19,20]. The use of these broadband functions not only improves the quality of the test data, but facilitates the data shift in accordance with the time-temperature superposition principle (TTSP) during the construction of master curves.…”

Section: Introductionmentioning

confidence: 99%

Fast-Acquiring High-Quality Prony Series Parameters of Asphalt Concrete through Viscoelastic Continuous Spectral Models

Zhang

Sun

2022

Materials

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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.

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A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

Cited by 56 publications

References 37 publications

Mechanism behind Time Dependent Elasticity of Crumb Rubber-Nano-Asphalt Hybrids Using Discrete Relaxation Spectrum

Mechanism behind Time Dependent Elasticity of Crumb Rubber-Nano-Asphalt Hybrids Using Discrete Relaxation Spectrum

Evaluation of the Response Analysis Approach Used in the Mechanistic-Empirical Pavement Design Guide

Fast-Acquiring High-Quality Prony Series Parameters of Asphalt Concrete through Viscoelastic Continuous Spectral Models

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