Application of the Viscoelastic Continuum Damage Theory to Study the Fatigue Performance of Asphalt Mixtures—A Literature Review
Abstract
:1. Introduction
2. Theory of Viscoelastic Continuum Damage
2.1. The Work Potential Theory
2.2. Elastic–Viscoelastic Correspondence Principle
2.3. Viscoelastic Continuum Damage Model Applied to Asphalt Mixtures
2.4. Pseudo-Strain Calculation
2.5. Simplified Viscoelastic Continuum Damage Model
2.6. Mechanistic Fatigue Life Prediction Model
2.7. Fatigue Failure Criterion
2.8. Linear Viscoelasticity
3. Studies on the Application of the VECD Theory
3.1. Full Asphalt Mixture Approach
3.2. Fine Aggregate Matrix Approach
4. Analysis Protocol of Tests with FAM Using the S-VECD Approach
5. Application of the S-VECD Theory: Laboratory Tests and Discussion of Results
5.1. Experimental Method—Materials and Preparation of the FAM Specimens
5.2. Experimental Method: Fingerprint Test
5.3. Experimental Method: Damage Test
5.4. Analysis and Discussion of Results
6. Conclusions
- The findings of the experimental study with RAP and binders PG 64-22 and PG 58-16 indicated that the FAMs containing 40% of RAP (2 and 4) presented higher |G*|LVE values and higher damage evolution ratios as compared to the FAMs containing 20% of RAP (1 and 3). Out of the FAMs prepared with 20% of RAP (FAM1 and FAM3), the highest |G*|LVE was observed for the FAM containing binder PG 64-22 (FAM1), and the damage evolution ratios were the same for both FAMs, which was an expected result, once the presence of the softest binder (PG 58-16) was supposed to reduce the stiffness of the FAMs (3 and 4).
- Regarding the prediction of the fatigue lives of the materials evaluated in the experimental study, the addition of RAP increased the parameter A of the fatigue model (related to the initial stiffness of the material and how the stiffness changed with the evolution of the damage) and the parameter B (related to the damage evolution rate)—the resulting fatigue lives of the FAMs prepared with 20% RAP were longer than the ones obtained for the FAMs prepared with 40% of RAP. The fatigue performance was directly related to the specimen stiffness: the higher the stiffness, the higher its susceptibility to damage and the lower the relaxation rates (which resulted in higher damage accumulation rates). The best solution to adjust the binder content of FAMs produced with 20% and 40% of RAP was the use of the binder PG 58-16. The FAM tests combined with the S-VECD theory as a tool to analyze the results was a practical approach, and is widely used to evaluate all sorts of variables of an asphalt mixture. However, some variables, such as low temperatures and/or high percentages of RAP, turn the mixtures into overly stiff materials, and the tests can be unpractical due to the limits of the rheometer torque. Equipment with a higher torque capability could accelerate the test duration.
- The improvement of computational simulations of the test protocols is an important subject for future works, and could contribute to a better understanding of the mechanisms and variables involved in the fatigue process, and could also help overcome the rheometer limitations.
- Comparisons between fractures mechanics and continuum mechanics results could also be an interesting topic to improve the VECD model in order to account for the different types of damage: adhesive or cohesive.
- Regarding materials science and development of advanced/new materials, the FAM approach combined with the S-VECD approach offered several new possibilities in terms of material performance evaluation and material development. Some examples can be mentioned concerning the fatigue performance: (i) the evaluation of the impact of higher RAP contents added to new AC mixtures; (ii) the evaluation of the impact of recycling agents at different contents, including petroleum-based materials, vegetable-based oils, and recycled oils; (iii) the assessment of the aging impact on fatigue; (iv) the assessment of moisture damage on fatigue resistance; (v) the assessment of new asphalt modifiers, including hybrid modification using virgin and recycled materials; and (vi) the evaluation of the effect of distinct aggregate types and aggregate gradations, among others. Several doubts related to these subjects can be countered by carrying out tests at the FAM scale and using the S-VECD approach. However, one must keep in mind that such a development also depends on a larger number of experiments on the correlation between the fatigue performance at the two scales (FAM and full asphalt mixtures). Such experiments are essential for the development and popularization of these very promising techniques.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Fingerprint Test | FAM1 Sample 1 | ||
---|---|---|---|
1. Data obtained from the fingerprint | Dynamic shear modulus within the linear-viscoelastic region (|G*LVE|), relaxation rate (m) (Figure 3a,b) | - | |G*|LVE = 9.93 × 108 m = 0.476 |
2. Prony series fitted to the storage modulus values to obtain , ρi, and . | Equation (56) | , ρi, and are calculated by using Solver | |
3. Laplace transform to convert data from frequency to time domain | Equation (58) | values obtained by using the parameter of the Prony series | |
4. Model adjusted to data to obtain the material parameter, m | G(t) = G0+G1t−m (Figure 3b) | Equation (59) | G0 = 1 G1 = 2.65 × 108 m = 0.476 |
5. Equation to obtain the material parameter, α | α = (1 + 1/m) for strain-controlled tests α = 1/m for stress-controlled tests | Equation (30) Equation (31) | α = 2.10 |
Damage Test | FAM1 sample 1 k = 5 | ||
1. Data obtained from the damage tests | Complex modulus (|G*|), phase angle (φ), and strain (ε), at each cycle k | - | |G*|k = 1 = 7.87 × 108 |G*|k = 5 = 6.91 × 108 φ k = 5 = 49.5 ε k = 5 = 0.051% |
2. Peak pseudo strain during each cycle k, | Equation (45) | 5 | |
3. Pseudo stress, σR | σR = σ | Elastic-viscoelastic correspondence principle | σR = 350 kPa |
4. Initial pseudo stiffness, I | Dynamic shear modulus at the first cycle | ||
5. Normalized pseudo stiffness at each cycle k, C | Equation (47) | ||
6. Damage parameter, S | Equation (48) | ||
7. Characteristic curve, CxS | The characteristic curves, CxS, are obtained by cross-plotting the C values against the S values at each cycle k | Figure 4a | C5 = 0.88 vs. S5 = 4.71 × 107 at cycle k = 5 |
Fatigue Life Prediction Model | |||
---|---|---|---|
1. Power law fitted to the CxS curve to obtain C10, C11, and C12 | Equation (40) | Figure 4a | |
2. Calculation of the parameter A | Equation (49) | A = 7.35 × 1029 | |
3. Calculation of the parameter B | B = 2α | Equation (50) | B = 4.35 |
4. Prediction fatigue life curve | Nf = A[εR]−B | Equation (51) | Figure 4b |
5. Nf (strain = 0.005%) | Nf(0.005%) = 7.35 × 1029 [4.46 × 104]−4.35 | Equation (51) | 4.59 × 109 |
6. Nf (strain = 0.2%) | Nf(0.2%) = 7.35 × 1029 [1.78 × 106]−4.35 | Equation (51) | 500.25 |
Basalt Rock | |||
---|---|---|---|
Quarry identification | Bandeirantes | ||
Specific gravity of coarse aggregates (g/cm³) | 2.904 | AASHTO T 85 | |
Specific gravity of fine aggregates (g/cm³) | 2.999 | AASHTO T 84 | |
Specific gravity of filler (g/cm³) | 2.769 | ASTM D7928 | |
Absorption (%) | 0.6 | ASTM C128 | |
RAP Material | |||
Quarry location | São Carlos/SP | ||
Maximum specific gravity (g/cm³) | 2.596 | AASHTO T209 | |
Asphalt Binders | |||
Performance grade (PG) | PG 58-16 | PG 64-22 | ASTM D6373 |
Specific gravity (g/dm³) | 1.015 | 1.004 | ASTM D70 |
Continuous grade—virgin (°C) | 61.07 | 66.84 | ASTM D7175 |
Continuous grade—short-term aged (°C) | 65.52 | 66.94 | ASTM D7175 |
Continuous grade—long-term aged (S [60]1) | −20.7 | −26.9 | ASTM D6648 |
Continuous grade—long-term aged (m [60]2) | −20.2 | −27.4 | ASTM D6648 |
Material | Sample | Air Voids | Linear-Viscoelastic Properties | CxS Parameters | ||||||
---|---|---|---|---|---|---|---|---|---|---|
m | M (av) | cv (%) | |G*|LVE (kPa) | |G*|LVE (av) (kPa) | cv (%) | Shape Factor | DR | |||
FAM1 | s1 | 5.15 | 0.476 | 0.461 | 3.2 | 9.93 × 108 | 8.92 × 108 | 11.3 | 1.05 | 0.382 |
s2 | 5.28 | 0.490 | 6.2 | 7.53 × 108 | −15.6 | 0.92 | 0.373 | |||
s3 | 4.96 | 0.422 | −8.6 | 9.46 × 108 | 6.1 | 0.97 | 0.350 | |||
s4 | 4.99 | 0.467 | 1.2 | 8.82 × 108 | −1.1 | 0.94 | 0.345 | |||
s5 | 4.99 | 0.452 | −2.0 | 8.85 × 108 | −0.8 | 1.08 | 0.394 | |||
FAM2 | s1 | 5.19 | 0.342 | 0.375 | −8.7 | 1.57 × 109 | 1.70 × 109 | −7.6 | 0.8 | - |
s2 | 5.05 | 0.386 | 2.9 | 1.61 × 109 | −5.3 | 0.99 | 0.332 | |||
s3 | 5.09 | 0.380 | 1.3 | 1.96 × 108 | 15.3 | 1.03 | 0.332 | |||
s4 | 5.05 | 0.392 | 4.5 | 1.66 × 109 | −2.4 | 0.98 | 0.325 | |||
FAM3 | s1 | 5.16 | 0.463 | 0.460 | 0.7 | 5.04 × 108 | 5.95 × 108 | −15.3 | 1.04 | 0.395 |
s2 | 4.67 | 0.465 | 1.1 | 5.90 × 108 | −0.8 | 0.96 | 0.415 | |||
s3 | 5.47 | 0.448 | −2.5 | 6.61 × 108 | 11.1 | 0.99 | 0.406 | |||
s4 | 5.09 | 0.463 | 0.7 | 6.24 × 108 | 4.9 | 0.91 | 0.360 | |||
FAM4 | s1 | 4.57 | 0.398 | 0.406 | −1.8 | 1.54 × 109 | 1.57 × 109 | −2.1 | 1.03 | 0.455 |
s2 | 4.68 | 0.402 | −1.0 | 1.63 × 109 | 3.6 | 1.00 | 0.448 | |||
s3 | 4.89 | 0.417 | 2.7 | 1.55 × 109 | −1.5 | 0.97 | 0.423 |
FAM | A | B | Nf (0.005%) | Rank Order | Nf (0.20%) | Rank Order | FFFAM | Rank Order |
---|---|---|---|---|---|---|---|---|
FAM1 | 7.35 × 1029 | 4.35 | 4.59 × 109 | 4 | 500.25 | 2 | 2.32 | 3 |
FAM2 | 2.68 × 1036 | 5.35 | 1.17 × 1010 | 3 | 31.80 | 4 | 2.30 | 4 |
FAM3 | 5.25 × 1029 | 4.35 | 1.77 × 1010 | 1 | 1885.85 | 1 | 2.49 | 1 |
FAM4 | 2.16 × 1034 | 4.93 | 1.52 × 1010 | 2 | 189.63 | 3 | 2.39 | 2 |
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Klug, A.; Ng, A.; Faxina, A. Application of the Viscoelastic Continuum Damage Theory to Study the Fatigue Performance of Asphalt Mixtures—A Literature Review. Sustainability 2022, 14, 4973. https://doi.org/10.3390/su14094973
Klug A, Ng A, Faxina A. Application of the Viscoelastic Continuum Damage Theory to Study the Fatigue Performance of Asphalt Mixtures—A Literature Review. Sustainability. 2022; 14(9):4973. https://doi.org/10.3390/su14094973
Chicago/Turabian StyleKlug, Andrise, Andressa Ng, and Adalberto Faxina. 2022. "Application of the Viscoelastic Continuum Damage Theory to Study the Fatigue Performance of Asphalt Mixtures—A Literature Review" Sustainability 14, no. 9: 4973. https://doi.org/10.3390/su14094973