Double-Recycled Reclaimed Asphalt Pavement: A Laboratory Investigation at Low Temperatures Based on Different Mathematical Approaches
Abstract
:1. Introduction
2. Objective and Research Approach
3. Material Preparation
4. Experimental Work
- S(t) = time-dependent flexural creep stiffness (MPa);
- D(t) = creep compliance (1/MPa);
- σ = bending stress in the beam (MPa);
- ε(t) = time-dependent bending strain in the beam (mm/mm);
- P = applied constant load (mN);
- δ(t) = beam deflection (mm);
- L, b, h = beam dimensions (L = 102 mm, b = 12.7 mm, h = 6.25 mm);
- t = time (s);
- A1, A2, A3 = fitting constants
5. Mathematical Approaches for Computing Thermal Stress and Critical Cracking Temperature
5.1. Simple Power Law Model (Method 1)
- tc, ν and w = fitting parameters;
- aT = shift factor; this can be expressed as:
- C1, C2 = constant parameters, and
- Ts = reference temperature (°C, lowPG + 10 °C).
5.2. Hopkins and Hamming’s Algorithm (Method 2)
5.3. Laplace Transformation (Method 3)
- (1)
- (2)
- Rewrite Equation (17) as follows:
- (3)
- Generate master curve of D(ξ) in the reduced time domain using D(t) experimental data based on dual series of power law function as seen in Equation (19).A, B, C and D are fitting parameters.In this study, the average value of D(ξ) (i.e., average between D(ξ, at lowPG + 10 °C) and D(ξ, at lowPG + 10 − 12 °C) data were considered.
- (4)
- Consider Equations (17)–(19) to relate thermal stress and strain assuming an idealized scheme as:
- (5)
- With considerations of the Laplace transformation, Equation (20) can be expressed as:Based on Equations (17)–(21) parameter α and T can be reexpressed as:
- (6)
- (7)
- Compute thermal stress, (T) in the actual time domain, starting from the thermal stress: σ(ξ) in the reduced time domain using Equations (17)–(24).
6. Data Analysis
6.1. Creep Stiffness and m-Value
6.2. Thermal Stress
6.2.1. Thermal Stress Curves
6.2.2. Thermal Stress Factor (TSF)
6.3. Comparisons on Critical Cracking Temperature
7. Summary and Conclusions
- BBR mixture creep results indicate that mixtures prepared with SRRAP have almost identical low-temperature cracking performance to that of mixtures designed with DRRAP. As expected, all RAP mixtures (SRRAP or DRRAP) presented a poorer performance at low temperatures compared to the conventional asphalt mixtures;
- By applying different mathematical approaches, upper and lower bounds on thermal stress can be derived. In the case of critical cracking temperature, the different mathematical approaches did not provide clear upper and lower bounds. In this sense, the use of strength or fracture tests is recommended to verify if the three different formulations may result in a consistent critical cracking temperature;
- The TSF values support the trends obtained from the experimentation and provide a simple tool that could be potentially used on a routine basis from practitioners to compare the response of mixtures against low-temperature cracking. In this view, the three mathematical models provide the link between the experimental measurements and the practical information obtained from the TSF.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Mix ID | Recycling Level | Asphalt Binder (PG) | RAP (%) | RAP Origin Mixture | NMAS (mm) | Aggregate Gradation Size (mm)/Passing (%) | Target Air Voids (%) |
---|---|---|---|---|---|---|---|
A | Reference (virgin) | 64–22 | 0 | – | 12.5 | (13/91), (10/82), (5/60), (2.5/41), (0.6/22), (0.3/16), (0.15/10), (0.08/6) | 4.2–4.9 |
B | SRRAP 1 | 64–22 | 25 | A | 12.5 | (13/92), (10/78), (5/55), (2.5/35), (0.6/20), (0.3/15), (0.15/11), (0.08/5) | 4.2–4.9 |
C | SRRAP | 64–22 | 40 | A | 12.5 | (13/91), (10/77), (5/54), (2.5/37), (0.6/22), (0.3/17), (0.15/12), (0.08/6) | 4.2–4.9 |
D | DRRAP 2 | 64–22 | 25 | B | 12.5 | (13/92), (10/79), (5/53), (2.5/35), (0.6/23), (0.3/16), (0.15/11), (0.08/5) | 4.2–4.9 |
E | DRRAP | 64–22 | 40 | C | 12.5 | (13/91), (10/81), (5/50), (2.5/34), (0.6/24), (0.3/15), (0.15/11), (0.08/5) | 4.2–4.9 |
Test | Mix ID | Asphalt Binder PG | Testing Temperature (°C) (Number of Replicates) | Applied Load (mN) (Testing Temperature °C) |
---|---|---|---|---|
BBR | A, B, C, D, E | PG 64–22 | low(PG + 10 °C) = −12 °C (10) low(PG + 10 °C) – 12 °C = −24 °C (10) | 4000-mN (−12 °C) 6000-mN (−24 °C) |
Mix ID | RAP (%) | Creep Stiffness: S(t) (GPa), Coefficient of Variation, (%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
60 s | 120 s | 240 s | 480 s | 960 s | |||||||
−12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | ||
A | Control (0%) | 4.19 (9.4%) | 7.39 (10.2%) | 3.72 (8.8%) | 6.87 (8.2%) | 3.25 (9.6%) | 6.32 (9.5%) | 2.78 (9.4%) | 5.52 (10.1%) | 2.27 (7.6%) | 4.84 (7.2%) |
B | SRRAP (25%) | 5.69 (8.2%) | 8.16 (9.5%) | 5.20 (9.8%) | 7.60 (10.1%) | 4.69 (8.7%) | 7.07 (8.8%) | 4.17 (10.5%) | 6.40 (9.2%) | 3.65 (9.1%) | 5.78 (8.1%) |
C | SRRAP (40%) | 6.09 (9.9%) | 10.57 (8.5%) | 5.49 (8.1%) | 9.78 (9.5%) | 5.03 (7.4%) | 8.69 (9.3%) | 4.56 (9.6%) | 7.82 (9.8%) | 4.12 (9.2%) | 6.86 (7.9%) |
D | DRRAP (25%) | 5.85 (8.5%) | 8.29 (9.2%) | 5.33 (8.4%) | 7.80 (9.5%) | 4.86 (9.1%) | 7.26 (8.8%) | 4.36 (7.8%) | 6.65 (8.4%) | 3.86 (8.3%) | 5.99 (8.7%) |
E | DRRAP (40%) | 6.13 (9.5%) | 10.65 (8.8%) | 5.55 (9.3%) | 9.85 (9.2%) | 5.15 (8.7%) | 8.75 (9.4%) | 4.68 (8.4%) | 7.91 (9.9%) | 4.25 (8.6%) | 6.92 (8.2%) |
Mix ID | RAP (%) | m-Value: m(t) = dS(t)/dt, Coefficient of Variation (%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
60 s | 120 s | 240 s | 480 s | 960 s | |||||||
−12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | −12 °C | −24 °C | ||
A | Control (0%) | 0.190 (9.7%) | 0.146 (10.6%) | 0.220 (8.5%) | 0.168 (8.7%) | 0.249 (9.7%) | 0.189 (8.5%) | 0.279 (10.0%) | 0.210 (9.5%) | 0.309 (7.9%) | 0.232 (8.6%) |
B | SRRAP (25%) | 0.161 (9.9%) | 0.120 (9.8%) | 0.190 (9.3%) | 0.139 (9.1%) | 0.218 (9.4%) | 0.159 (8.8%) | 0.247 (10.5%) | 0.178 (9.1%) | 0.275 (7.7%) | 0.198 (9.5%) |
C | SRRAP (40%) | 0.132 (9.1%) | 0.102 (8.1%) | 0.166 (9.9%) | 0.124 (7.5%) | 0.181 (8.4%) | 0.144 (9.2%) | 0.222 (10.1%) | 0.152 (9.5%) | 0.241 (8.4%) | 0.181 (9.2%) |
D | DRRAP (25%) | 0.158 (8.4%) | 0.118 (8.6%) | 0.182 (9.4%) | 0.133 (8.4%) | 0.205 (8.1%) | 0.153 (8.4%) | 0.241 (7.1%) | 0.169 (9.5%) | 0.269 (7.4%) | 0.192 (8.5%) |
E | DRRAP (40%) | 0.125 (8.8%) | 0.101 (8.3%) | 0.158 (9.8%) | 0.122 (8.9%) | 0.174 (9.5%) | 0.141 (8.8%) | 0.215 (8.4%) | 0.146 (9.9%) | 0.232 (8.6%) | 0.175 (9.2%) |
ID | Mixture | Approach | Area (MPa·°C) | TFS (%) [MixReference] − [MixInterest] | ||
---|---|---|---|---|---|---|
2 °C/h | 20 °C/h | 2 °C/h | 20 °C/h | |||
A | Control | PL | 58.0 | 92.5 | – – | – – |
HH | 50.9 | 78.6 | – – | – – | ||
LA | 62.9 | 115.4 | – – | – – | ||
B | SRRAP 25% | PL | 72.7 | 114.8 | 25.3 PL: [B] − [A] | 24.1 PL: [B] − [A] |
HH | 62.5 | 101.6 | 22.8 HH: [B] − [A] | 29.3 HH: [B] − [A] | ||
LA | 69.5 | 119.4 | 10.5 LA: [B] − [A] | 3.5 LA: [B] − [A] | ||
D | DRRAP 25% | PL | 78.8 | 124.3 | 8.4 PL: [C] − [B] | 8.3 PL: [C] − [B] |
HH | 64.7 | 104.6 | 3.5 HH: [C] − [B] | 3.0 HH: [C] − [B] | ||
LA | 73.9 | 124.6 | 6.3 LA: [3] − [2] | 4.4 LA: [3] − [2] | ||
C | SRRAP 40% | PL | 95.0 | 156.8 | 63.8 PL: [D] − [A] | 69.5 PL: [D] − [A] |
HH | 93.3 | 136.4 | 83.3 HH: [D] − [A] | 73.5 HH: [D] − [A] | ||
LA | 95.6 | 154.9 | 52.0 LA: [D] − [A] | 34.2 LA: [D] − [A] | ||
E | DRRAP 40% | PL | 98.4 | 161.2 | 3.6 PL: [E] − [D] | 2.8 PL: [E] − [D] |
HH | 99.2 | 144.2 | 6.3 HH: [E] − [D] | 5.7 HH: [E] − [D] | ||
LA | 99.7 | 160.5 | 4.3 LA: [E] − [D] | 3.6 LA: [E] − [D] |
Mixture | TCR (°C) | TCR Ranking | ||
---|---|---|---|---|
PL | HH | LA | ||
Control | −27.7 | −27.3 | −27.2 | LA > HH > PL |
SRRAP 25% | −26.9 | −28.2 | −27.7 | PL > LA > HH |
SRRAP 40% | −26.6 | −25.3 | −26.7 | HH > PL > LA |
DRRAP 25% | −26.7 | −28.1 | −27.5 | PL > LA > HH |
DRRAP 40% | −26.5 | −25.0 | −26.5 | HH > PL = LA |
Mixture | TCR (°C) | TCR Ranking | ||
---|---|---|---|---|
PL | HH | LA | ||
Control | −25.9 | −25.8 | −25.9 | HH > LA = PL |
SRRAP 25% | −24.5 | −25.8 | −24.5 | PL = LA > HH |
SRRAP 40% | −23.3 | −22.8 | −23.3 | HH > PL = LA |
DRRAP 25% | −24.2 | −25.7 | −24.2 | PL = LA > HH |
DRRAP 40% | −23.1 | −22.5 | −23.1 | HH > PL = LA |
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Moon, K.H.; Cannone Falchetto, A. Double-Recycled Reclaimed Asphalt Pavement: A Laboratory Investigation at Low Temperatures Based on Different Mathematical Approaches. Materials 2020, 13, 3032. https://doi.org/10.3390/ma13133032
Moon KH, Cannone Falchetto A. Double-Recycled Reclaimed Asphalt Pavement: A Laboratory Investigation at Low Temperatures Based on Different Mathematical Approaches. Materials. 2020; 13(13):3032. https://doi.org/10.3390/ma13133032
Chicago/Turabian StyleMoon, Ki Hoon, and Augusto Cannone Falchetto. 2020. "Double-Recycled Reclaimed Asphalt Pavement: A Laboratory Investigation at Low Temperatures Based on Different Mathematical Approaches" Materials 13, no. 13: 3032. https://doi.org/10.3390/ma13133032