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

Abstract

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.

Investigation into Rheological Behavior of Warm-Mix Recycled Asphalt Binders with High Percentages of RAP Binder

“…The 2S2P1D model is a complex-valued model consisting of two spring elements, two parabolic elements, and a dashpot element; thus, it can analytically represent the dynamic modulus and phase angle components as well as the storage modulus and loss modulus components. Besides, its continuous relaxation and retardation spectra can also be analytically derived [ 32 ]. The 2S2P1D model has the following form: where G e is the equilibrium modulus; G g is the instantaneous modulus; α , k , h , β, and τ 0 are the model parameters.…”

Additive manufactured parts surface treatment through impinged hot air jet technique the theoretical and experimental evaluation

“…, 2019; Viviani et al. , 2022; Zhang and Sun, 2022). The values of g i and τ i are presented in Table 1.…”

“…where G(t), G 0 , g i and t i are time-dependent shear modulus (Pa), initial shear modulus (Pa), ith Prony constant, ith Prony retardation time constant, respectively (Muliana, 2022;Di Paola et al, 2021;Shojaeiarani et al, 2019;Viviani et al, 2022;Zhang and Sun, 2022). The values of g i and t i are presented in Table 1.…”

A generalized time-domain constitutive finite element approach for viscoelastic materials

“…All of the constitutive relations are similar in that they fit an analytic function to experimentally measured data by adjusting parameters. The problem of fitting parameters to these models to match real-world materials is a substantial and laborious one, with effort taking place still on finding the best fit methodologies [15]. Furthermore, matching complex behavior curves can require hundreds of series terms [16].…”