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The most famous model known in prediction of dynamic modulus for asphalt concretes
is
the Witczak and Hirsh models. These models didn’t use the mineralogical and chemical properties of aggregates. Witczak models used the passing or refusal percentage to sieve diameters and Hirsh model use
d
the volumetric analysis. All models developed until now considered that the aggregates were geotechnical conforming to standards. In this study the first mineralogical and chemical properties were considered through the percentage of silica in the rock source of aggregates and the electric aggregate particles charge zeta. Dynamic modulus values used for regression process are determined from complex modulus test on nine asphalt concretes mix designed with aggregate types (basalt of Diack, quartzite of Bakel and Limestone of Bandia). Between Twelve initial inputs
,
the statistical regression by exclusion process keeps only seven parameters as input for the model. The mineralogical model showed good accuracy with R^{2} equal to 0.09. The student test on the model parameters showed that all the parameters included in the model were meaningful with good p inferior to 0.05. The Fisher test on the model showed the same result. The analysis of the sensitivity of the mineralogical model to zet
a potential showed that the dynamic modulus increase
s
with the positive zeta-potentials and decrease
s
with the negative zeta-potentials.
The analysis of the sensitivity of the mineralogical model to the silica showed that the dynamic modulus decreases with the increase of the silica.

The principal objective of this paper is to develop a partial mineralogical and electrochemical dynamic modulus predictive model for asphalt concretes. Indeed, the impact of aggregate type has never been considered in the dynamic modulus of asphalt concrete or in the interpretations of factor which impacted the dynamic modulus test results. Only the passing and refusals percentage trough the U.S. sieve is considered in the Witczak models [

The development of mineralogical model needs results of complex modulus laboratory tests. Study was carried to “Laboratoire des Chaussées et Matériaux Bitumineux” (LCMB). Formulation of nine asphalt concretes was made with three aggregate types: basalt of Diack, quartzite of Bakel and limestone of Bandia [

For each mixture, test temperatures used during test were 0°C, 10°C, 20°C, 40°C and 55°C and for each temperature frequencies used were 0.1 Hz, 0.3 Hz, 1 Hz, 5 Hz and 10 Hz. For the development of the mineralogical model, statistical analysis is used on Statistica software. But a primary choice of parameters for the mineralogical model must be done.

For the bitumen, it was decided to keep the selection of the complex shear modulus |G*| and phase angle δ_{b} for each test temperature and frequency. Note that the viscosity related to temperature and frequency can also be used to take into account the impact of the bituminous binder on the prediction [_{2} content (TSiO_{2}). Silica is a component of almost all rock types. The granularity of the mineral structure is related to the specific surface of the aggregate mixture noted ∑. Indeed, more an aggregate mixture is coarse, more its specific surface andits binder content are also higher. Mineralogy also affects the hardness of the rock, which will be translated by the coefficients Micro Deval and Los Angeles (_{2}. Volumetric properties of the bituminous mixture are the thickness of the bitumen film (h), the effective binder content (V_{beff}) and the void percentage (V_{a}).

Pure Silica is very hard mineral which exist in several forms. It is the principal

Rock type | SiO_{2} (%) | Specific gravity | Crushability | Los Angeles | Dynamic fragmentation | Abrasi veness |
---|---|---|---|---|---|---|

Basalt | 20 - 50 | 2.7 - 3.1 | 20 - 44 | 8 - 21 | 11 - 32 | 500 - 2300 |

Diabase | 45 - 55 | 2.6 - 3.1 | 18 - 44 | 7 - 34 | 11 - 21 | 450 - 2300 |

Diorite | 55 - 70 | 2.6 - 2.9 | 20 - 36 | 14 - 30 | 13 - 24 | 400 - 1700 |

Dolomite | 0 - 10 | 2.6 - 3.0 | 30 - 56 | 15 - 55 | 20 - 38 | 20 - 250 |

Gabbro | 40 - 55 | 2.7 - 3.0 | 27 - 34 | 14 - 30 | 15 - 19 | 800 - 1700 |

Gneiss | 55/75 | 2.6 - 2.8 | 30 - 67 | 15 - 28 | 12 - 42 | 600 - 1600 |

Granit | 65 - 75 | 2.6 - 2.8 | 28 - 90 | 17 - 35 | 17 - 41 | 900 - 1900 |

Limestone | 0 - 30 | 2.4 - 2.8 | 30 - 45 | 30 - 45 | 28 - 44 | 0 - 500 |

Quartzite | 90 - 99 | 2.5 - 2.7 | 22 - 65 | 17 - 40 | 14 - 40 | 1400 - 2400 |

component of detrital sedimentary rocks. Silica represents 27% of Earth crust and 95% of silicate minerals [

Silica is represented by quartz in metamorphic and magmatic rock, and by crystalized or amorphous forms in volcanic rock [

Zeta potential is the electrical charge that a particle acquires through ion cloud surrounding when it is suspended (

When the Zeta-meter 4.0 is used, the zeta potential is calculated by the Smoluchowski equation [

ζ = 113.000 × V t D t × E M (1)

With:

EM = electrophoretic mobility at the given temperature;

V_{t} = the viscosity of the suspension liquid at the temperature t (poise);

D_{t} = the dielectric constant;

ζ = Zeta potential in millivolts (mV).

To study the behavior of fine aggregates investigated in aqueous solutions,

zeta potential measurements were performed at different pH (acidic, neutral and basic) to the laboratory of the “Experimental Station of Environmental Pilot Processes” (STEPPE) at “Ecole de Technologie Supérieure” (ETS). Aqueous solutions were prepared using stock solutions of HCl acid and base NaOH.

There are several expressions of the specific surface for aggregate skeleton for asphalt concretes. In French mix design method the specific surface is used to calculate de binder content [

In this study the expression of the specific surface is given by the Equation (2) [

Σ ( m 2 / kg ) = 1 100 ( 0.25 G + 2.30 S + 12 s + 135 f ) (2)

With:

Aggregates type | Zeta potentiel | ||
---|---|---|---|

pH = 5.02 | pH = 7.12 | pH = 9.08 | |

Basalte of Diack | 19.87 | 37.07 | 38.63 |

Quartzite of Bakel | 22.58 | 38.52 | 37.89 |

Limestone of Bandia | 13.32 | 16.41 | 18.66 |

G = gravel > 5 mm (%);

S = coarse medium sand (0.315 < S < 5 mm) (%);

Sand, s = (0.08 < s < 0.315) (%);

f = filler < 80 μ (%).

The thickness of the binder film is calculated by Equation (3) (NCHRP, 2004).

AFT = 1000 VBE Σ P s G m b (3)

With:

AFT = thickness of the binder film (μm);

VBE = effective binder content in percentage of volume (%);

Σ = specific surface area (m^{2}/kg);

P_{s} = aggregate percentage in the mixture (100-binder content) (%);

G_{mb} = bulk specific gravity of compacted asphalt.

Complex shear modulus test for asphalt binder G* are performed according to American standards (ASTM DD7552-09) [

The volumetric parameters used in the mineralogical model are the effective binder content (V_{beff}) and the void content (V_{a}).

Asphalt mixes Complex modulus tests (Dynamic modulus) were performed using the Direct Traction-Compression (DTC) test on cylindrical samples according to Canadian or European standards, respectively LC 26-700 [

Mix | T ˚C | f Hz | V_{beff} (%) | V_{a} (%) | log(δ_{b}) | ∑ m^{2}/kg | ζ basic pH | T SiO 2 (%) | log|G*| measured | log|E*| measured |
---|---|---|---|---|---|---|---|---|---|---|

BDF | −0.1 | 10.0 | 11.34 | 8.77 | 0.56 | 13.76 | 38.63 | 46.00 | 8.01E−01 | 4.19 |

BDF | −0.1 | 3.0 | 11.34 | 8.77 | 0.84 | 13.76 | 38.63 | 46.00 | 8.01E−01 | 4.15 |

BDD | 1.0 | 10.0 | 12.25 | 5.05 | 0.49 | 11.50 | 38.63 | 46.00 | 7.99E−01 | 4.05 |

BDD | 1.1 | 3.0 | 12.25 | 5.05 | 0.82 | 11.50 | 38.63 | 46.00 | 7.99E−01 | 3.99 |

BDC | 20.30 | 1.0 | 11.00 | 8.91 | 1.50 | 7.82 | 38.63 | 46.00 | 6.12E−01 | 3.43 |

BDC | 20.15 | 0.3 | 11.00 | 8.91 | 1.57 | 7.82 | 38.63 | 46.00 | 6.15E−01 | 3.24 |

GDF | 0.9 | 10.0 | 11.64 | 5.28 | 0.49 | 15.00 | 38.89 | 94.50 | 7.99E−01 | 4.12 |

GDF | 0.9 | 3.0 | 11.64 | 5.28 | 0.82 | 15.00 | 38.89 | 94.50 | 7.99E−01 | 4.06 |

GDD | 0.1 | 10.0 | 11.50 | 2.19 | 0.55 | 13.43 | 38.89 | 94.50 | 8.00E−01 | 4.25 |

GDD | 0.1 | 3.0 | 11.50 | 2.19 | 0.83 | 13.43 | 38.89 | 94.50 | 8.00E−01 | 4.20 |

GDC | 0.4 | 10.0 | 11.12 | 6.95 | 0.53 | 12.19 | 38.89 | 94.50 | 8.00E−01 | 4.04 |

GDC | 0.4 | 3.02 | 11.12 | 6.95 | 0.83 | 12.19 | 38.89 | 94.50 | 8.00E−01 | 3.98 |

CDF | 0.6 | 10.0 | 6.97 | 16.44 | 0.52 | 11.18 | 18.66 | 0.70 | 8.00E−01 | 3.01 |

CDF | 0.5 | 3.0 | 6.97 | 16.44 | 0.83 | 11.18 | 18.66 | 0.70 | 8.00E−01 | 2.99 |

CDD | 0.6 | 10.0 | 7.23 | 12.85 | 0.52 | 8.47 | 18.66 | 0.70 | 8.00E−01 | 3.89 |

CDD | 0.4 | 3.0 | 7.23 | 12.85 | 0.83 | 8.47 | 18.66 | 0.70 | 8.00E−01 | 3.86 |

CDC | −0.1 | 10.0 | 6.23 | 13.93 | 0.56 | 5.97 | 18.66 | 0.70 | 8.01E−01 | 3.91 |

CDC | −0.2 | 3.0 | 6.23 | 13.93 | 0.84 | 5.97 | 18.66 | 0.70 | 8.01E−01 | 3.88 |

|E*| = dynamic complex modulus (MPa); V_{beff} = effective binder content as a percentage of volume; V_{a} = percentage of void volume percentage; δ_{b} = phase angle of the bituminous binder (˚); ζ = Zeta potential (mV); SiO_{2} content of the source of aggregate rock; |G*| = dynamic shear modulus (MPa); Σ = surface area of the mineral skeleton of the mixes (m^{2}/kg).

Multiple linear regressions (polynomial) by descending exclusion (step by step) are used in the development of mineralogical model prediction of the dynamic modulus of asphalt concrete studied. Statistical development tool used is statistical software [

R a 2 = 1 − ( N − 1 ) × ( 1 − R 2 ) N − p − 1 (4)

With:

R a 2 = Adjusted coefficient of multiple determination;

N = number of observations;

p = number of variables;

If the data are limited to 30 samples. We must use the coefficient of determination R^{2 }(Equation (5)).

R 2 = SCR e g SCT (5)

With:

SCR_{e}g = sum of squared deviations of the model;

SCT = total sum of squared deviations.

Student’s t test is used to check whether each parameter is statistically significant before introducing it in the model. The Fisher test checks the significance model itself. These two tests are related to the p-value and a test is significant if the p-value less than 0.05. The database is composed by 271 points of dynamic complex modulus data. After several simulations process on a statistical software, the selected model is given by the Equation (6).

log | E ∗ | SILICE-ZETA = 2.88487656 + 0.366038859 V b e f f − 0.03864789 V b e f f 2 − 0.0073155 V a 2 + 2.72454806 log δ b − 1.6527836 log δ b 2 + 0.3947615 ζ − 0.8851 E − 4 T SiO 2 2 − 0.37305171 log | G ∗ | 2 + 0.002125823 Σ 2 (6)

With:

| E * | SILICE-ZETA = dynamic complex modulus (MPa);

V_{beff} = effective binder content as a percentage of volume;

V_{a} = percentage of void volume percentage;

δ_{b} = phase angle of the bituminous binder (˚);

ζ = zeta potential (mV);

SiO_{2}= content of the source of aggregate rock;

|G*| = dynamic shear modulus (MPa);

Σ = surface area of the mineral skeleton of the mixes (m^{2}/kg).

_{beff}, V_{a}, log(δ_{b}), ∑ and TSiO_{2} log|G*|) present the best significances (p = 0.000). The zeta potential seems to be the least significant variable (p = 0.000047), but very good.

To check whether if all types of aggregates used in the study (basalt of Diack,

SC | Degree of-Liberty | MC | F | p | |
---|---|---|---|---|---|

Ord. Orig. | 1.08826 | 1 | 1.08826 | 22.6891 | 0.000003 |

V_{beff} | 0.30535 | 1 | 0.30535 | 6.3663 | 0.012228 |

V b e f f 2 | 1.30081 | 1 | 1.30081 | 27.1205 | 0 |

V_{a} | 0 | 0 | 0 | 0 | 0 |

V a 2 | 7.06054 | 1 | 7.06054 | 147.2048 | 0 |

log(δ_{b}) | 5.16039 | 1 | 5.16039 | 107.5885 | 0 |

log(δ_{b})^{2} | 13.40954 | 1 | 13.40954 | 279.5745 | 0 |

ζ | 0.8229 | 1 | 0.8229 | 17.1566 | 0.000047 |

ζ^{2} | 0 | 0 | 0 | 0 | 0 |

T SiO 2 | 0 | 0 | 0 | 0 | 0 |

T SiO 2 2 | 5.21807 | 1 | 5.21807 | 108.7911 | 0 |

log|G*| | 0 | 0 | 0 | 0 | 0 |

log|G*|^{2} | 1.99868 | 1 | 1.99868 | 41.6703 | 0 |

∑ | 0 | 0 | 0 | 0 | 0 |

∑^{2} | 1.05976 | 1 | 1.05976 | 22.0949 | 0.000004 |

Error | 12.47066 | 260 | 0.04796 | 0 | 0 |

|E*| = dynamic complex modulus (MPa); V_{beff} = effective binder content as a percentage of volume; V_{a} = percentage of void volume percentage; δ_{b} = phase angle of the bituminous binder (˚); = Zeta potential (mV); SiO_{2} content of the source of aggregate rock; |G*| = dynamic shear modulus (MPa); Σ = surface area of the mineral skeleton of the mixes (m^{2}/kg).

quartzite of Bakel and limestone of Bandia) positively participate and to what degree in the accuracy of mineralogical model, correlation studies were conducted separately with the test results of each type of aggregate.

The results of correlations show that the basalt was alone shows an accuracy of R^{2} = 0.97 (

shows good correlation of the measure modulus and predicted modulus by the mineralogical model. Its coefficient of determination is R^{2} = 0.96 (^{2} = 0.88).

To study the impact of the zeta potential on the mineralogical model and thus indirectly on the dynamic modulus of asphalt mixtures the approach consist to choose an asphalt mix for each type of aggregate. Selected options are the CDC, the BDC and the GDC. For each formula, a theoretical variation of the zeta potential will be conducted to measure its impact on the predicted dynamic modulus.

To study the influence of SiO_{2} content, the same scenario as the zeta potential was adopted. A theoretical variation of 0% to 100% SiO_{2} was considered and the effects on the dynamic modulus predicted were calculated.

_{2} content has a negative effect on the predicted dynamic modulus of asphalt mixtures, because the mineral composition of an aggregate cannot change during formulation this observation is handled with caution. However the physical interpretation of this result is difficult because it can move in several directions, as complex as the presence in quantity and quality of silica in the rock. Mechanically by lower aggregate surface properties (roughness drop) due to the increase of the silica but also the form in which it is located. Chemically by increasing electro negativity due to the silica. Dynamic shear modulus testing of bituminous mastics improvement with silica powder can verify this observation.

Simulations with other model parameters showed that:

• An increase of V_{a} in the model leads to a decrease in the dynamic modulus predicted, and an increasing of the effective binder content also leads to a lower module;

• The surface area is the effective binder content and increasing the specific surface area must always be accompanied by an increase in the V_{beff}. Increasing the surface area taken individually leads to an increase of the dynamic modulus;

• The influence of asphalt parameters (|G*| and δ_{b}) is more difficult to perform. Indeed, if we consider the module |G*| separately, its increase causes a fall of the dynamic modulus predicted. But considering also the change of the phase angle, an increase in the predicted dynamic modulus is observed;

• This verifies that the module link |G*| to δ_{b} phase angle, increasing the asphalt’s modulus as a function of the binder and the degree of susceptibility as a function of frequency and temperature module.

The development of mineralogical model allowed to indirectly study the impact of aggregate on dynamic modulus of asphalt mixtures, through the variation of the mineralogical composition (TSiO_{2}) and chemical composition (zeta potential). Unlike other developed prediction model, it allows a good prediction of the dynamic modulus for asphalt concretes mix designed with road and non-road aggregates. But with better accuracy for road aggregates with middle and high silica content, the study showed that sensitivity increases with the positive zeta potentials aggregates and aggregate decreases with negative zeta potentials, bringing to highlight the phenomena of attraction and repulsion between charged mineral particles. The “increase” of silica in the aggregate also causes a decrease of the dynamic modulus. However, the variation of the content of silica is impossible to carry out in an aggregate and its nature is not uniform in all aggregates. This phenomenon can affect aggregates at its mechanical and/or chemical properties, making it difficult the physical interpretation of the impact of silica. But this hypothesis can still be checked by dynamic shear tests on bituminous mastics or the possibility of varying the silica content is possible.

The authors would like to acknowledge the team of LCMB.

The authors declare no conflicts of interest regarding the publication of this paper.

Aidara, M.L.C., Ba, M. and Carter, A. (2020) Development of a Dynamic Modulus Prediction Model for Hot Mixture Asphalt and Study of the Impact of Aggregate Type and Its Electrochemical Properties. Open Journal of Civil Engineering, 10, 213-225. https://doi.org/10.4236/ojce.2020.103018