The performance grade allows us to determine the rheological properties affected by aging for construction and service life, as well as the parameters of terrain analysis related to critical failures such as rutting, fatigue, and thermal cracking. The Dynamic Shear Rheometer (DSR) from ANTON PAAR, model PHYSICA MCR 301, was used to measure the performance grade value by varying the temperature. The primary temperature ranges (maximum and minimum) for tests at 10 rad/s are based on the specifications of the Ecuadorian technical standard NTE INEN 3030. The procedure for determining the dynamic shear modulus (G*) and the phase angle (δ) is based on the ASTM D7175-15 standard, which defines the shear deformation resistance of the asphalt binder in the viscoelastic region, with a pressure range from 100 Pa to 10 MPa ( Table 1(a) and Table 1(b) ).

The Rotating Thin Film Oven (RTFO) simulates short-term aging in asphalt cement using 35 grams of the hot sample in a rotating oven, which is then cooled to room temperature for 1 hour. At the end of the test, the residues are obtained for re-characterization using the previously mentioned methods such as the Cleveland open cup flash point, penetration, softening point, penetration index, ductility, performance grade, absolute viscosity, specific gravity, within no more than 72 hours. This procedure is based on ASTM D2872.

This method works with the residue obtained from the sample aged in a rotating thin film oven, simulating plant aging influenced by factors affecting the mixture, as indicated by ASTM D6521-19a. The experiment involves heating the sample until it becomes fluid (<150˚C) and then transferring it to the respective vessel, conditioning it for 20 hours. After that, the trays are placed in the oven for 30 minutes, and the process concludes with the execution of the dynamic shear modulus (DSR) test.

The indirect tensile strength test method, described in the UNE-EN 12697-23:2018 standard, is a technique used to determine the indirect tensile strength (ITS) of bituminous mixtures. This method is crucial for assessing the mechanical properties of paving materials and their ability to withstand stresses during their service life.

The indirect tensile strength test method is based on applying a diametral load to a cylindrical specimen of bituminous mixture until it fractures. The specimen is subjected to a continuous and constant load along its diameter, generating tensile stresses in the horizontal plane and compressive stresses in the vertical plane. The tensile strength is calculated from the maximum load the specimen can withstand before breaking.

a) Testing Press: A Marshall-type testing press or similar equipment is used, capable of applying loads with a minimum recommended capacity of 28 kN and a constant deformation rate of (50 ± 2) mm/min.

b) Testing Frame with Loading Strips: The frame should be equipped with hardened steel loading strips with a concave surface corresponding to the nominal radius of the specimen.

c) Thermal Conditioning Devices: The specimens must be thermally conditioned, either by a water bath or a controlled air chamber.

a) Specimen Preparation: Cylindrical specimens are prepared in the laboratory by compaction or extracted from an existing pavement layer. Before testing, they are stored at a temperature not exceeding 25˚C for a period ranging from 48 hours to 42 days.

b) Thermal Conditioning: The specimens are conditioned to the selected test temperature (usually 10˚C ± 2˚C) by using a water bath or an air chamber.

c) Placement in the Frame: The conditioned specimen is placed in the testing frame, aligned on the lower loading strip to ensure that the load is applied diametrically.

d) Load Application: The compression of the specimen begins, and a continuous diametral load is applied at a constant rate until the maximum load and the fracture of the specimen are reached. Both the maximum load and the type of fracture are recorded.

The indirect tensile strength (ITS) is calculated using the formula:

$\text{ITS}=\frac{2000\ast P}{\pi \ast D\ast H}$

where:

P is the maximum load applied (N).

D is the diameter of the specimen (mm).

H is the height of the specimen (mm).

An average value is obtained from the results of at least three individual specimens.

To accept the results, the difference between individual indirect tensile strength values must not exceed 17% of the average value. This method is essential for ensuring the quality and durability of bituminous mixtures used in pavements, providing critical information about their ability to withstand stresses and prolong their service life.

This method is characterized by measuring the axial deformation experienced by the specimen when respective uniform moving or static loads are applied. The universal servo-hydraulic dynamic equipment is used following the procedures of ASTM D7369 and EN12697-26 standards. The height and diameter data of the briquettes are recorded to condition them in the equipment for 24 hours at the working temperature (10, 20, and 40)˚C.

Based on the Spanish standard NLT-352/00, this method involves recording the initial weight of the sample after being submerged for 24 hours at 60˚C, denoted as P1. Subsequently, the value of P2 is obtained after passing the briquette through the drum for 300 revolutions. The wear value is determined by the difference in weights, which should not exceed 40%.

The molecular dynamics (MD) method was used to investigate the mechanical properties of asphalt, the interactions between various fractions, diffusion behaviors, and the effects of aging. Molecular simulation is a computational technique that allows the study of system behavior at the atomic and molecular levels. In this study, MD simulations were conducted using the SARA software package and the force field with 3D Navier-Stokes equations to model asphalt molecules and their interactions.

The simulations were carried out under the following conditions:

Simulations were performed for both unaged and aged asphalt to understand how aging affects the properties of asphalt at the molecular level. Additionally, diffusion properties and the translational mobility of asphalt molecules were evaluated to study the effects of aging on the dynamic behavior of asphalt.

The three-dimensional Navier-Stokes equations are fundamental to understanding the behavior of all fluids. In this context, chemical reactions are deeply connected with fluid dynamics, highlighting the complexity of these systems. Rewriting equation [11] taken from reference [12] .

$P=\frac{1}{1+e^{kt-\mu {(x^2+y^2+z^2)}^{\frac{1}{2}}}}=\frac{2}{\mu {(x^2+y^2+z^2)}^{\frac{1}{2}}}\left(\left(x,y,z\right)\in {ℝ}^3,t\ge 0\right)$(1)

where:

r = (x² + y² + z²)^1/2, attenuation coefficient, μ, [1/m]; growth coefficient, $k=\frac{p_0}{2p_{0}v}$, [1/s] and concentration $C=C_0\frac{1-P}{P}$.

Starting from Equation (1) from reference [12] , which probabilistically describes the solution of the 3D Navier-Stokes equations, we can find the fundamental values of the model, which is k, the growth or decay constant of the reaction, and μ, the absorption coefficient. Given that, experimentally, through a thermogravimetric analyzer (TGA), we know the variable P(x, y, z, t), which depends on space (x, y, z) and time t, we can write:

$P\left(x,y,z,t\right)=\frac{C_0}{C\left(x,y,z,t\right)+C_0}$ (2)

where CCC, representing the concentration of the analyzed asphalt, is its mass and depends on space and time (x, y, z, t). Analogously, using Equation (1), we obtain k, μ and b through two regressions.

$P=\frac{2}{\mu }\frac{1}{r}$ (3)

$\ln \left(\frac{1-P}{P}\right)+\frac{2}{P}=kt+b$ (4)

The following presents the results of the physicochemical characterization of natural Allophane ( Table 2 ).

1) Surface Area Analysis

The determination of specific surface area through nitrogen adsorption capacity is a fundamental technique for characterizing porous materials such as Allophane. The surface area, influenced by factors such as porosity and particle size, is directly proportional to the adsorption capacity of the material. The results obtained for Allophane, with a surface area exceeding 300 m²/g, confirm its highly porous nature and its potential for applications in adsorption processes [37] .

Additionally, these results align with the values reported in the literature by Kaufhold Stephan for this mineral.

2) Fourier Transform Infrared Spectroscopy (FT-IR)

FT-IR analysis was employed to characterize the molecular structure of Allophane. This technique is based on the absorption of infrared radiation by molecules, producing a characteristic spectrum.

The results showed the presence of absorption bands characteristic of aluminum-rich Allophane, particularly in the regions of 975 - 1020 cm⁻¹, with an intense band centered at 1013.7 cm⁻¹ attributed to Si-O-Al stretching vibrations, typical of this clay mineral. The presence of a broad band in the region of 3452 cm⁻¹ corresponds to O-H stretching vibrations, indicating the presence of adsorbed water and structural hydroxyl groups. These results confirm the hydrophilic nature of Allophane and its amorphous structure, characterized by a high density of hydroxyl groups.

3) X-Ray Diffraction (XRD)

X-ray diffraction (XRD) is an analytical technique that exploits the interaction of X-rays with crystalline matter. The information obtained from the diffractograms allows for determining the crystalline structure and mineralogical composition of a sample. In the case of Allophane, the diffraction patterns obtained showed a diffuse and low-intensity character, typical of amorphous materials or those with a high degree of structural disorder. Despite these limitations, the presence of the minerals listed in Table 2 was identified, indicating a complex mineralogical composition.

4) Chemisorption

Chemisorption, a technique involving the formation of chemical bonds between the adsorbate and the adsorbent, was employed to characterize the acidic sites of Allophane. Using the temperature-programmed desorption (TPD) technique with ammonia, the distribution of acidic strength of the active sites was determined. The results showed two main desorption peaks at 420 K and 680 K, suggesting the presence of at least two types of acidic sites with different strengths. The determination of the acidic sites was carried out by acid-base titration with ammonia, assuming a stoichiometric relationship of one ammonia molecule per acidic site. The results obtained are summarized in Table 2 .

5) X-Ray Fluorescence (XRF)

It is an analytical technique that allows for the non-destructive determination of the elemental composition of a sample. When X-rays strike the sample, the atoms emit characteristic radiation, with energy unique to each element. In this study, wavelength-dispersive XRF (WD-XRF) was used to determine the Si/Al molar ratio in clay minerals. This parameter is fundamental for characterizing the tetrahedral-octahedral structure of these minerals.

6) Atomic Force Microscopy (AFM)

It is a scanning probe microscopy technique that allows for obtaining images of surfaces with nanometric resolution. Using AFM, the surface morphology of Allophane was characterized, obtaining high-resolution images that revealed a maximum pore size of 50 nm. Additionally, the average particle heights were quantified, finding values in the nanometer range. These results confirm the nanometric nature of Allophane and provide valuable information about its surface structure.

7) Moisture Content

The moisture content of the sample was determined using the conventional gravimetric oven-drying method. The obtained value was 47%, which falls within the range of 20% - 50%, as reported by Stephan Kaufhold for similar samples [37] .

8) Apparent Density

The apparent density of the Allophane was determined using the pycnometer method, yielding a value of 1.9 g/cm³. This value is crucial for designing compaction and molding processes for Allophane. This property directly influences the mechanical strength and dimensional stability of materials based on this mineral.

9) Particle Size Analysis

The particle size distribution of the sample was characterized using an image analysis technique based on Stokes’ Law. By recording the trajectory of particles in a light beam, a real-time particle size distribution curve was obtained. The results reveal that the sample is primarily composed of particles larger than 80 micrometers.

For this purpose, penetration tests, softening point, penetration index, ductility, Cleveland open cup flash point, performance grade, absolute viscosity, and specific gravity tests were conducted according to NTE INEN or ASTM standards, depending on the test, for conventional AC-20 asphalt and asphalt modified with various percentages of Allophane, as shown in Table 3(a) and Table 3(b) .

In the case of the performance grade (PG) test with the complex modulus, it was performed at various temperatures. However, the results were compared at a maximum temperature of 64˚C, in accordance with the INEN 3030:2017 standard, which means (PG 64, max. 22 min.). “PG” stands for Performance Grade, and the 22-minute period indicates the duration for which the asphalt is expected to maintain certain properties at this maximum temperature, as shown in Table 1 .

This method allowed simulating short-term aging in asphalt cement. It was executed using the residues obtained to recharacterize with the following methods: Cleveland open cup flash point, penetration, softening point, penetration index, ductility, performance grade with dynamic shear modulus, absolute viscosity, and specific gravity. For the absolute viscosity test, it was conducted at a temperature

*54% of original penetration.

of 60˚C, as the NTE INEN 2515:2014 standard classifies semi-solid asphalt cements in Ecuador under this temperature condition. The absolute viscosity results of the AC-20 asphalt are 238 Pa*s, a value that falls within the requirement range of the NTE INEN 2515:2014 standard.

For this method, the residue obtained from the sample aged in the rotating oven was used to determine a higher performance grade with a dynamic shear modulus, indicating an asphalt with better mechanical and thermal properties, capable of providing superior performance under adverse conditions and extending the pavement’s lifespan.

This test evaluates the resistance of the asphalt mixture to tensile forces occurring in the lower fiber of the asphalt mat during operation. It is also an indicator of the cohesion within the mixture, as once the specimen breaks, it is observed whether the aggregates or the cohesion failed. In this case, almost all tested specimens showed intact aggregates, indicating a failure of cohesion.

The mixture modified with 5% Allophane produces greater resistance compared to AC-20 asphalt, as shown in Table 4 .

The indirect tensile stiffness modulus test enables the characterization of the mixture’s behavior when subjected to traffic loads, which induce tensile stresses in the inner fiber of the asphalt pavement. Generally, high stiffness moduli are sought in asphalt mixtures; however, excessively high stiffness moduli values are counterproductive, as they make the mixture more prone to cracking. The asphalt mixture was successfully characterized at different temperatures: (10, 20, and 40)˚C. The stiffness modulus of the asphalt modified with 5% Allophane is higher than the values obtained for AC-20 asphalt, as shown in Table 5 .

The Cantabrian Abrasion test simulates the deterioration conditions of the mixture once it is in service. Thus, the lower the percentage of wear, the better the cohesion between the aggregates and the asphalt, which would prevent the action of vertical traffic loads and atmospheric agents due to wear of the pavement surface. The value of the wear loss result is lower in the case of AC-20 asphalt modified with 5% Allophane, as can be seen in Table 6 .

The results obtained using the SARA method, a tool that allows analyzing the structure of modified asphalt to understand the strategic variables influencing its aging, are presented below. Additionally, by applying the three-dimensional Navier-Stokes equations, the dynamics of asphalt additives in the presence of Allophane were simulated, revealing a significant relationship between pressure, velocity, and the concentration of various components. It was determined that the optimal concentration of 5% Allophane improves the properties of the asphalt, suggesting its viability for industrial applications, as shown in Figure 1 and Figure 2 .