L-Curve Based Tikhonov’s Regularization Method for Determining Relaxation Modulus From Creep Test

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Yaoting Zhu ◽  
Lu Sun ◽  
Huilin Xu
Keyword(s):  
Regularization Method ◽  
Relaxation Modulus ◽  
Asphalt Mixtures ◽  
Parameter Estimates ◽  
Noise Levels ◽  
Creep Tests ◽  
Viscoelastic Parameters ◽  
Tikhonov’S Regularization ◽  
Numerical Case Study

A numerical method for directly obtaining discrete relaxation modulus from static creep tests data is developed for linear viscoelastic asphalt mixtures. To overcome the ill-posedness of interconversion between creep compliance and relaxation modulus, Volterra integral equations of the second kind and L-curve based Tikhonov’s regularization method are used to construct the computational scheme of parameter estimation. A numerical case study is presented to demonstrate the efficiency of the regularization method, which takes into account different step lengths and noise levels. It indicates that the computed results are accurate and robust at different noise levels. Compared with other existing methods, the L-curve based Tikhonov’s regularization method provides the best parameter estimates in dealing with both the numerical case study and the experiment data. The method can be used to extract viscoelastic parameters of asphalt mixtures from creep tests effectively and robustly.

scholarly journals Influence Analysis and Optimization for Aggregate Morphological Characteristics on High- and Low-Temperature Viscoelasticity of Asphalt Mixtures

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2034 ◽  
Author(s):  
Yongchun Cheng ◽  
Wensheng Wang ◽  
Jinglin Tao ◽  
Meng Xu ◽  
Xiaoli Xu ◽  
...  
Keyword(s):  
Low Temperature ◽  
Viscoelastic Properties ◽  
Viscoelastic Model ◽  
Asphalt Mixture ◽  
Morphological Characteristics ◽  
Relaxation Modulus ◽  
Mixture Design ◽  
Asphalt Mixtures ◽  
Raw Material ◽  
Viscoelastic Parameters

Aggregate is an indispensable raw material for asphalt pavement construction. This study evaluates the influences of aggregate morphological characteristics on the high- and low-temperature viscoelasticity of asphalt mixtures. Based on simplex lattice mixture design (SLD), asphalt mix samples were designed and prepared with the same gradation but three different types of aggregates. Subsequently, three morphological characteristics of aggregate (roundness, perimeter index, and erosion-dilation area ratio) are presented to characterize fine and coarse aggregates. Then based on Burgers viscoelastic model, uniaxial compression static creep test was carried out to analyze the high-temperature viscoelastic properties for asphalt mortar and mixture. Meanwhile fitting Prony series models have been utilized to represent relaxation modulus conversed from creep compliance and the low-temperature relaxation characteristics can be also discussed. The experimental results indicated that morphological characteristics of aggregate, especially fine aggregates, are strongly correlated with the viscoelastic parameters of asphalt mixtures. However, the complex morphological characteristics of aggregates have opposite influences on the high- and low-temperature viscoelastic parameters. Therefore, when considering both high- and low-temperature viscoelastic properties, the aggregate proportion was optimized for the appropriate morphological characteristics, which will provide a reference for asphalt mixture design.

scholarly journals Comparative Analysis of Viscoelastic Properties of Open Graded Friction Course under Dynamic and Static Loads

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1250
Author(s):  
Liding Li ◽  
Chunli Wu ◽  
Yongchun Cheng ◽  
Yongming Ai ◽  
He Li ◽  
...  
Keyword(s):  
Dynamic Modulus ◽  
Viscoelastic Properties ◽  
Functional Relationship ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Creep Tests ◽  
Static Loads ◽  
Burgers Model ◽  
Viscoelastic Parameters ◽  
Open Graded Friction Course

The viscoelastic properties of open graded friction course (OGFC) are closely related to anti-permanent deformation ability, noise reduction ability and durability. To study the viscoelastic parameters of OGFC under dynamic and static loads and to establish the functional relationship between them, uniaxial compression creep tests and dynamic modulus tests were performed to obtain the creep compliance and the dynamic modulus of OGFC. In addition, the Burgers model, modified Burgers model, second-order extensive Maxwell model, Scott-Blair model and modified Sigmoid model were employed to quantitatively analyze the dynamic and static viscoelastic properties of OGFC. Subsequently, the relaxation modulus of OGFC was deduced by the viscoelastic theory. Then, the dynamic modulus of OGFC was calculated according to the deduced relaxation modulus. Based on the calculated values and the measured values of dynamic modulus, the functional relationship of viscoelastic parameters of OGFC under dynamic and static loads was established. The results show that the increase in test temperature has adverse effects on the viscoelastic indexes of OGFC, such as creep compliance, relaxation modulus, and dynamic modulus; the dynamic modulus derived from static creep compliance has a good linear correlation with that obtained by dynamic modulus tests, but the correlation of the phase angle is poor.

scholarly journals Research of Method for Solving Relaxation Modulus Based on Three-Point Bending Creep Test

Materials ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2021 ◽  
Author(s):  
Yazhen Sun ◽  
Zhangyi Gu ◽  
Jinchang Wang ◽  
Xuezhong Yuan
Keyword(s):  
Creep Test ◽  
Relaxation Modulus ◽  
High Viscosity ◽  
Transcendental Equation ◽  
Creep Tests ◽  
Three Point Bending ◽  
Viscoelastic Parameters ◽  
Relaxation Experiments ◽  
Laboratory Investigations ◽  
Relaxation Characteristics

A method was developed for solving the relaxation modulus of high viscosity asphalt sand (HVAS) based on the three-point bending creep test, and was verified by comparison with experimental results. In this method, firstly, a transcendental equation was obtained by the convolution, and then equations were obtained by Taylor’s formula, which were solved by Mathmatica to obtain the relaxation modulus by Newton’s method. Subsequently, the laboratory investigations of the viscoelastic parameters of the Burgers model for the HVAS by three-point bending creep tests were carried out. In addition, the method was verified by comparing the relaxation moduli with the indoor relaxation experiments. Results showed that the numerical calculation and the test data were in good agreement, and the relaxation characteristics of the HVAS were reflected more accurately. The method can be used to study the relaxation characteristics of the asphalt mixtures effectively. In addition, this study provides a research basis for road crack prevention.

Viscoelastic Analysis of the Low-Temperature Anti-Cracking Performance of SBR Modified Asphalt Mixtures

2011 ◽  
Vol 239-242 ◽  
pp. 2919-2925 ◽  
Author(s):  
Min Jiang Zhang ◽  
Xing Hua Jiao ◽  
Wen Bo Zhang ◽  
Li Ping Zhang
Keyword(s):  
Low Temperature ◽  
Temperature Stress ◽  
Asphalt Pavement ◽  
Asphalt Mixture ◽  
Relaxation Modulus ◽  
Asphalt Mixtures ◽  
Viscoplastic Material ◽  
Modified Asphalt ◽  
Viscoelastic Parameters ◽  
Environment Temperature

Asphalt mixture is a kind of typical elastic-viscoplastic material. Environment temperature and loading condition will greatly affect its performance. As the temperature falls, asphalt pavement will engender a shrinkage deformation under the action of temperature stress. When the accumulated temperature stress exceeds tensile strength, the asphalt pavement will be cracked. Based on the results of the bending creep test in low temperature, the Burgers model was established and the viscoelastic parameters in the model were given, and the relaxation modulus of asphalt mixture was also determined in this paper. The study indicated that SBR modified asphalt mixtures have the advantage over common asphalt mixture in low-temperature performance.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Development of a predictive model for the compressive relaxation modulus of asphalt mixtures

2015 ◽  
Vol 16 (3) ◽  
pp. 674-695 ◽  
Author(s):  
Seyed Arash Forough ◽  
Fereidoon Moghadas Nejad ◽  
Ali Khodaii
Keyword(s):  
Predictive Model ◽  
Relaxation Modulus ◽  
Asphalt Mixtures

Effect of Cure State on Stress Relaxation in 3501-6 Epoxy Resin

1997 ◽  
Vol 119 (3) ◽  
pp. 262-265 ◽  
Author(s):  
S. R. White ◽  
A. B. Hartman
Keyword(s):  
Stress Relaxation ◽  
Epoxy Resin ◽  
Creep Compliance ◽  
Numerical Technique ◽  
Matrix Material ◽  
Relaxation Modulus ◽  
Master Curves ◽  
Creep Tests ◽  
Three Point Bending ◽  
Direct Inversion

Little experimental work has been done to characterize how the viscoelastic properties of composite material matrix resins develop during cure. In this paper, the results of a series of creep tests carried out on 3501–6 epoxy resin, a common epoxy matrix material for graphite/epoxy composites, at several different cure states is reported. Beam specimens were isothermally cured at increasing cure temperatures to obtain a range of degrees of cure from 0.66 to 0.99. These specimens were then tested in three-point bending to obtain creep compliance over a wide temperature range. The master curves and shift functions for each degree of cure case were obtained by time-temperature superposition. A numerical technique and direct inversion were used to calculate the stress relaxation modulus master curves from the creep compliance master curves. Direct inversion was shown to be adequate for fully cured specimens, however it underpredicts the relaxation modulus and the transition for partially cured specimens. Correlations with experimental stress relaxation data from Kim and White (1996) showed that reasonably accurate results can be obtained by creep testing followed by numerical conversion using the Hopkins-Hamming method.

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