A-70# paving asphalt was selected as the base asphalt. Its technical properties were tested in accordance with the “Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011)”. The results, presented in Tables 1, 2, confirm that all properties meet the standard specifications.

At room temperature, Albanian Rock Asphalt (ARA) is a solid bulk material, which was pulverized into a fine powder using a crusher prior to experimentation. The macroscopic appearance of ARA is presented in Figure 1, and its technical specifications are listed in Table 2.

The nano-TiO₂ used in this study was sourced in the form of a white powder. Its physical appearance is shown in Figure 2, with the relevant technical parameters provided in Table 3.

Conventional experimental designs often employ the one-variable-at-a-time approach, which fails to account for interaction effects between factors and can be inefficient, requiring a large number of experimental runs to achieve satisfactory results. To overcome these limitations, this study utilized the Response Surface Methodology (RSM) to optimize the combination of ARA dosage, nano-TiO2 dosage, and the oil-stone ratio for the composite modified asphalt mixtures, targeting predetermined Marshall index criteria. Subsequently, pavement performance tests were conducted based on the optimized formulation to comprehensively evaluate the mixture’s performance.

The Response Surface Methodology (RSM) is a statistical technique that integrates mathematical statistics with experimental design. It employs explicit polynomial or non-polynomial models to approximate complex, implicit functional relationships. This approach enables the analysis of both the individual effects of independent variables on response indicators and the interactive effects between multiple variables.

The Response Surface Methodology (RSM) primarily comprises experimental design, model fitting, significance testing, surface model analysis, and model validation. The procedure begins with the selection of an experimental design. Tests are then conducted, and based on the results, a mathematical model is fitted to describe the relationship between the independent variables and the response. This model enables the establishment of a visualized, continuous response surface. Ultimately, the optimal combination of variables is identified by targeting desired response values, thereby addressing complex, multivariate optimization problems in practical applications. In contrast to orthogonal experimental designs, RSM provides a continuous and highly visualized surface model rather than a set of discrete data points (Obaid et al., 2024). Owing to these advantages, RSM has been extensively applied across various fields, including food science, chemical engineering, and biomedicine (Faqin et al., 2022; Zhiwei et al., 2023; Meena et al., 2024).

The response surface methodology is based on the least squares method (Obaid et al., 2024) and its optimization process is as follows:

First define a relationship equation between the response indicator y and the design variable x: y = f x 1 , x 2 , x 3 , · · · , x k + ε (1)

Where: y is the response indicator, x is the design variable, and ε is the random variable.

The equation is fitted according to the relationship between the response indicator and the design variable, firstly when there is an approximate linear relationship between the response value and the design variable, a first order Taylor function is applied to expand Equation 1: y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + · · · + β k x k + ε (2)

Where: β i is the linear effect of the design variables X i ;

The design variables are fitted to Equation 2, if the fit is successful then the equation can be used to find the best response value by selecting the appropriate design variables. If the fitting fails, transform Equation 2 into Equation 3 using a second-order transformation: y = β 0 + ∑ i = 1 k β i x i + ∑ i = 2 k β i i x i i 2 + ∑ i < j k β i j x i x j + · · · + ε (3) where: β i is the linear coefficient of the design variable X i ; β i i is the squared effect of X i i ; and β i j is the interaction between the design variables;

Expressed in matrix form as Equations 4–7: Y = β 0 + X ′ b + X ′ B X + ε (4) X = x 1 , x 2 , x 3 , · · · , x k T (5) b = β 0 , β 1 , β 2 , β 3 , · · · , β k T (6) B = β 11 β 12 2 · · · β 1 k 2 β 21 2 · · · · · · β 2 k 2 · · · · · · · · · · · · β k 1 2 β k 2 2 · · · β k k (7)

Where: b is the matrix of regression coefficients; B is a k-order symmetric matrix;

If the fit is successful, the following equation is satisfied: ∂ Y ∂ Y = b + 2 B X = 0 (8)

Defining the solution X of Equation 8 as a stabilization point, the transformation of X yields: X 0 = − 1 2 B − 1 b (9)

Substituting Equation 9 into Equation 8, the predicted response index for the stabilization point can be obtained as Equation 10: Y 0 = β 0 + 1 2 X 0 ′ b (10)

Optimized design of mix ratio for nano TiO₂/ARA composite modified asphalt mixtures using response surface method.

The Box-Behnken experimental design using the Response Surface Methodology exhibits high experimental efficiency. It not only avoids extreme corner points, making operations safer and more feasible, but also possesses excellent predictive capability. The design variables were the dosage of nano-titanium dioxide, the dosage of Albanian Rock Asphalt (ARA), and the oil-stone ratio. The response variables were Marshall mixture parameters: density, stability, flow value, voids percentage, voids filled with asphalt (VFA), and voids in the mineral aggregate (VMA). Experimental studies revealed that the ARA dosage should not be less than 5%. Furthermore, the nano-TiO₂/ARA composite modified asphalt exhibited optimal performance when the ARA dosage was 15% and the nano-TiO₂ dosage was 1%. Therefore, based on a review of literature concerning the compatibility of nano-modified asphalt mixtures and natural rock asphalt mixtures (Ke and Dawei, 2020; Zhaohui et al., 2019), and considering both technical and economic factors, the dosage ranges were determined as 0%–2% for nano-TiO₂ and 5%–25% for ARA. balancing technical performance and economic feasibility. These design variables were coded into levels using the Response Surface Software, Design-Expert (Version 10.0.3), as detailed in Table 8.

In the Box-Behnken test program, the three design variables required 17 test sets to be conducted, as shown in Table 9.

The Design-Expert 10.0.3 software was employed to fit regression models for the six response variables and to identify the most appropriate model for each. The goodness-of-fit analysis for the density response is presented in Table 12 as an illustrative example.

Table 12 shows that the quadratic model provided a superior fit compared to the linear and two-factor interaction (2FI) models. Subsequently, F-tests were performed on the variance and the lack-of-fit term for the selected quadratic regression model; the results of these analyses are presented in Tables 13, 14, respectively.

Based on the model comparison for density summarized in Table 15, the quadratic model demonstrated the best fit. Similarly, the quadratic model also provided a satisfactory fit for the other five response variables. It was therefore selected for the analysis of all response indicators in this study.

The variables A, B, and C represent the dosage of ARA, nano-TiO₂, and the oil-stone ratio, respectively. A multivariate quadratic regression model was fitted to the density data from Table 10 using Design-Expert software. The resulting Analysis of Variance (ANOVA) is presented in Table 16, confirming the model’s high statistical significance.

The model regression coefficient R 2 = 0.9890 and adjusted R 2 = 0.9749, indicating that 97.49% of the data can be explained by the model, which means that the equations are highly reliable. The primary term of nano-TiO₂ doping and oil-rock ratio had a highly significant effect on density (P < 0.01), and ARA doping had a significant effect on density (P < 0.05), and the main effect relationship of each factor was analyzed as B>C>A, i.e., nano-TiO₂ doping > oil-rock ratio > ARA doping. The secondary term interactions AC and BC had a significant effect on density and AB had a non-significant effect on density.

Combining the results of the above analysis, the regression equation for density was obtained after removing the non-significant terms as: Y 1 = 2.61 + 0.00325 × A − 0.013 × B + 0.006 × C − 0.00475 × A C + 0.00825 × B C − 0.02 × A 2 − 0.008875 × B 2 − 0.005875 × C 2

The relationship between the predicted and actual values of density is shown in Figure 4, if the points are closer to the straight line then it indicates a better fit, while the points are more deviated from the straight line indicating a larger error. From Figure 4, it can be seen that the model has a high degree of confidence.

The response surface model and contour plot of the design variables versus density are shown in Figure 6. Since the three-dimensional coordinates can only characterize the relationship between the two design variables and the response index at the same time, the third design quantity is taken to be the median of its range of values when analyzing the interaction of the two variables.

From Figure 5, it can be seen that the density tends to increase and then decrease with the increase in ARA doping. In the case of nano-TiO₂ taken as 1% and fixed: when ARA doping is 5%, the density shows a tendency to increase and then flatten out with the oil-rock ratio, and when ARA doping is 25%, the density shows a tendency to flatten out and remain unchanged with the oil-rock ratio, which shows that there is a more significant interaction between the ARA doping and the oil-rock ratio. When the ARA doping was fixed at 15%, the density gradually decreased with the increase of oil-rock ratio when the nano-TiO₂ doping was 0%, when the nano-TiO₂ doping was 2%, the density tended to slowly increase with the doping of oil-rock ratio, which can be seen that the interaction between nano-TiO₂ doping and oil-rock ratio was more significant. The interaction between A and B was not significant, which was in line with the results of the analysis of variance (ANOVA).

A second-order fit to the void ratio yielded the void ratio ANOVA test table shown in Table 17.

Table 17 shows that this void ratio regression model is well fitted. Further analysis of the data 18shows that the primary term ARA doping has a highly significant effect on the void ratio (P < 0.01), the oil-rock ratio and nano TiO₂ doping have a significant effect on the void ratio (P < 0.05), and the main effect relationship between the factors analyzed is A > B > C, i.e., ARA doping > nano TiO₂ doping > oil-rock ratio. Its secondary term interaction BC had a highly significant effect on void ratio (P < 0.01), and AB and AC had insignificant effects on void ratio (P > 0.05).

The quadratic multinomial regression equation is obtained from Table 17: Y 2 = 4.5 − 0.54 × A − 0.2 × B + 0.19 × C − 0.76 × B C + 0.4 × B 2 + 0.42 × C 2

The relationship between the predicted and actual values of the void ratio model is shown in Figure 6, from which it can be seen that the void ratio model has a high degree of confidence.

The response surface model and contour plots of the design variables versus void fraction are shown in Figure 7.

The effect of interaction between factors on void ratio is known from Figure 8. With the increase of ARA dosage, the void ratio tends to decrease linearly, while with the incorporation of nano TiO₂, the void ratio of composite modified asphalt mixtures increases. When the ARA dosage was fixed at 15% and the oil-rock ratio was 4%, the void ratio showed an increasing trend with the increase of nano TiO2 dosage, and when the oil-rock ratio was 5%, the void ratio showed a decreasing trend with the increase of nano TiO2 dosage; when the nano TiO₂ dosage was 0%, the void ratio showed an increasing trend with the oil-rock ratio of doping, and when the nano TiO₂ dosage was 2%, the void ratio showed a decreasing trend with the increase of the oil-rock ratio of doping, the void ratio showed a trend of slowly decreasing and then leveling off, it can be seen that the interaction between nano-TiO₂ dosage and oil-rock ratio is more significant. The interaction between AB and AC is not significant, which is in line with the results of the analysis of variance (ANOVA).

The stability ANOVA results obtained by fitting and combining the stability test results using the second-order model are shown in Table 18.

From Table 18, it can be seen that the stability regression model is well fitted, and the main effect relationship of the analyzed variables is B>C>A, i.e., nano TiO₂ doping > oil-rock ratio > ARA doping, and the quadratic multinomial regression equation for stability is obtained as: Y 3 = 13.87 + 0.16 × A + 0.28 × B + 0.26 × C − 0.17 × A B + 0.31 × B C − 0.62 × A 2 − 0.63 × B 2 − 0.33 × C 2

The graph of the relationship between the predicted and actual values of the stability model is shown in Figure 8, and the model predictions of stability are highly credible.

The response surface model and contour plots of the design variables versus stability are shown in Figure 9.

According to Figure 9, with the increase of ARA doping, the stabilization tends to increase first and then decrease, and when the ARA doping takes different values, the stabilization changes differently with the increase of TiO₂ doping, which indicates that there is a significant interaction between ARA doping and nano-TiO₂ doping. When the oil-rock ratio is 4%, the stability tends to increase and then decrease with the incorporation of nano-TiO₂, and when the oil-rock ratio is 5%, the stability tends to increase gradually with the incorporation of nano-TiO₂ doping, which shows that there is a more significant interaction between nano-TiO₂ doping and oil-rock ratio. The interaction between AC is not significant, which is in line with the results of the analysis of variance (ANOVA).

Density, stability, and void ratio were analyzed above, and the other response metrics were analyzed in a similar process, and their fitting equations are presented here directly: Y 4 = 2.87 + 0.14 × A + 0.21 × C − 0.30 × A 2 − 0.13 × B 2 Y 5 = 16.80 + 0.47 × A − 0.12 × C − 0.12 × A B − 0.24 × A C − 0.19 × B 2 − 0.26 × C 2 Y 6 = 73.21 + 4.05 × A − 1.23 × B − 1.39 × C + 4.72 × B C − 2.06 × B 2 − 3.00 × C 2

The best mix ratio was optimized by setting the corresponding expectation values for each response index through Design Expert 10.0.3. Xueyuan and Lijun (2010) found that the degree of stability is linearly correlated with the splitting strength of asphalt mixtures, and the greater the degree of stability, the higher the splitting strength. Therefore, according to JTG F40-2004 construction specification, there is no requirement for the density, and the void ratio in the range of 4%∼6%, the stability takes the maximum value, the flow value is in the range of 1.5∼4 mm, the VMA ≥14%, and the VFA is in the range of 65%∼75% as the optimization objectives, in which the expected value of the stability is the highest level of importance, in order to get the high temperature performance and the water stability performance better mixes, the optimal solutions were obtained through software calculations as shown in Table 19.

According to the actual operating conditions of the experiment, the design variable dosage was modified to 16.0% ARA dosage, 1.3% nano TiO₂ dosage, 4.4% oil/gravel ratio, and the results of measured and predicted values obtained by three parallel tests under these conditions are shown in Table 20, with the error within 2%, which indicates that there is a good correlation between the predicted values and measured values of the response surface method, and that it is reasonable to optimize the mixing ratio of composite asphalt mixes with the response surface method. It is reasonable to optimize the mix ratio of nano TiO₂/ARA composite modified asphalt mixture. Therefore, it can be concluded that the optimum dosage for nano TiO₂/ARA composite modified asphalt is 1.3% TiO₂+16.0% ARA, and the optimum oil/gravel ratio of the mixture is 4.4%.

Rutting is one of the common diseases of asphalt pavement, which is a cumulative permanent deformation produced under the repeated action of high temperature and vehicle loading. Rutting test is easy to operate, it can more accurately simulate the deformation state of asphalt pavement subjected to vehicle loading, and the test can be carried out several times, the test results of good reproducibility, so it is widely used to evaluate the high-temperature performance of asphalt mixtures, and related studies have shown that there is a good positive correlation between the degree of dynamic stability and high-temperature performance of asphalt mixtures (Yongjun et al., 2010), i.e., the higher the dynamic stability, the higher the high-temperature performance of asphalt mixtures. Performance. The test results are shown in Table 21 and Figure 10.

According to the specification of natural asphalt requires that the dynamic stability (DS) of natural modified asphalt mixtures is not less than 3,000 (times/mm), as shown in Table 21, the incorporation of ARA and composite modified asphalt makes the DS of asphalt mixtures still have a substantial increase on the basis of meeting the requirements. The DS of nano TiO₂/ARA composite modified asphalt mixtures, ARA modified asphalt mixtures and nano TiO₂ modified asphalt mixtures were improved by 207%, 120% and 30%, respectively, compared with that of matrix asphalt, indicating that TiO₂ and ARA can significantly improve the high temperature performance of asphalt mixtures, of which composite modified asphalt has the best improvement effect, followed by ARA, and lastly, TiO₂, which It may be due to the large specific surface area and high surface free energy of nano TiO₂, which is easy to adsorb the light components of asphalt to increase the proportion of structural asphalt, so that the asphalt mixture has a stronger high-temperature deformation resistance. ARA contains more asphaltene and colloidal, when ARA and nano TiO₂ are mixed into the matrix asphalt mixture at the same time, under the collision of temperature and nano-particles, the macromolecular micelles of ARA are ruptured and immediately filled by polar nano TiO₂ and matrix asphalt tightly to form a stabilized system centered on the macromolecular micelles and filled with small molecules of nano and matrix asphalt, which makes the nano-TiO₂/ARA The anti-temperature deformation performance of composite modified asphalt mixtures is significantly enhanced.

Pavement water damage is one of the common diseases in high temperature and rainy areas. Moisture accumulates on the road surface or enters the surface layer through cracks under the action of dynamic water pressure, and the moisture adheres to the aggregate surface, weakening the adhesion between asphalt binder and aggregate, leading to asphalt film detachment from the aggregate surface and a series of diseases such as loosening, chipping, spalling, etc., which seriously affects the use of the quality of asphalt pavements. The water stability of the modified asphalt mixture was evaluated by the water-immersion Marshall test and freeze-thaw split test, and the residual stability and freeze-thaw split strength ratio were used as the evaluation indexes.

According to the specification T0702–2011, T0709-2011 to carry out immersion Marshall test, the test results are shown in Table 22.

As can be seen from Table 22, the incorporation of nano TiO₂and ARA made the residual stability of asphalt mixtures increased significantly compared with that of matrix asphalt, indicating that nano TiO₂ and ARA effectively improved the ability of asphalt mixtures to resist water damage, in which the residual stability of nano TiO₂/ARA composite modified asphalt mixtures was the highest of 97%, which was 12.2% higher than that of matrix asphalt, indicating that nano TiO₂/ARA further enhanced the adhesion and spalling resistance of asphalt and aggregate with excellent water stability performance.

Freeze-thaw splitting test was carried out according to specification T0729-2000, and the test results are shown in Table 23.

According to the test results in Table 23, it can be found that the addition of nano TiO₂, ARA and nano TiO₂/ARA can improve the freeze-thaw splitting strength ratio (TSR) of matrix asphalt mixtures by 2.9%, 8.8% and 13.8%, respectively, which suggests that the addition of nano TiO₂ and ARA improves the resistance of mixtures to water damage, and the nano TiO₂/ARA composite modifier had the best enhancement effect. This may be due to the fact that nano TiO₂ has good adsorption properties and increases the proportion of structural asphalt, which improves the water damage resistance of asphalt mixtures, while ARA makes the viscosity of modified asphalt increase and improves the adhesion between modified asphalt slurry and aggregate, and at the same time in the nanoparticles of the size effect of the filling of the nanoparticles, the nano TiO₂/ARA modified asphalt slurry and aggregate to form a tightly cemented At the same time, under the filling of nanoparticle size effect, the nano-TiO₂/ARA modified asphalt mastic and aggregate form a tightly bonded “asphalt-mineral” blending system, which makes the interface between asphalt and aggregate of the composite modified asphalt mixture not easy to be damaged by water molecules, and it has excellent water stability performance.

Low-temperature cracking asphalt pavement damage in one of the forms of expression, and moisture along the cracks penetrate into the asphalt surface layer will exacerbate the water damage of the pavement, and when serious, it will affect the structural function of the pavement and reduce its level of service. In this paper, the low-temperature bending test is used to evaluate the low-temperature cracking resistance of each group of modified asphalt mixtures, the specific test operation is carried out in accordance with the specification, during the period of the specimen recorded in the destruction of the mid-span deflection and the maximum load is used to calculate the bending and tensile strength and bending and tensile strains, and in this way to evaluate the low-temperature cracking resistance of its mixtures, the results of the test are shown in Table 24.

Table 24 shows that the nano TiO₂ modified asphalt mixture has the largest bending and tensile strain value and the smallest modulus of strength, which indicates that the nano TiO₂ modified asphalt mixture has a better low-temperature cracking resistance, which may be due to the fact that the nano TiO₂, as a kind of inorganic rigid powder, can play a better size and interface effect with the asphalt to combine with asphalt, and it is not easy to deform under the action of the stress. The incorporation of ARA makes the bending and tensile strains of matrix asphalt mixtures decreased by 6.2% and the modulus of strength increased by 2.93%, indicating that the incorporation of ARA slightly reduces the asphalt mixtures in the low-temperature cracking resistance, but it still complies with the requirement of the specification that the bending and tensile strains should not be less than 2500με. The bending strain and modulus of strength of nano TiO₂/ARA composite modified asphalt mixtures are better than the indexes of ARA modified asphalt mixtures and are closer to the matrix asphalt mixtures, which indicates that TiO₂ can ARA modified asphalt mixtures’ low-temperature performance to some extent.

Previous studies have shown that nano-TiO₂/ARA composite modified asphalt exhibits excellent high-temperature performance and water stability. Since the macroscopic performance of asphalt is closely related to its microstructure, fluorescence microscopy was employed to observe the micro-phase changes before and after asphalt modification, aiming to elucidate the micro-modification mechanism of the nano-TiO₂/ARA composite modified asphalt.

In this study, a Zeiss IMAGER Z2 fluorescence microscope (Figure 11) was used to capture images of modified asphalt with different dosage combinations. The resulting fluorescence micrographs are presented in Figure 12.

From Figure 12, it can be observed that the micrograph of the base asphalt (a) shows no luminescence and exhibits no fluorescence response. From images (b) to (d), it is evident that after high-temperature shearing, the particle size of Albanian rock asphalt (ARA) is significantly reduced. Its asphalt components blend with the base asphalt and appear non-fluorescent in the images, while minerals such as SiO2 are suspended as particles of varying sizes in the asphalt, appearing as brighter spots in the images. When the nano-TiO2 dosage is 1%, as the ARA dosage increases from 5% to 15%, the fluorescent particles significantly increase in number and decrease in spacing, with no obvious agglomeration observed. This indicates that ARA effectively blends with the base asphalt under high-temperature shearing, nano-TiO2 disperses uniformly in the base asphalt through high-speed shearing and swelling development, combining with ARA macromolecular micelles to form a stable cross-linked network structure, which also mitigates the potential agglomeration effect caused by increased viscosity due to higher ARA content. A comparative analysis of images (b) to (d) clearly shows that the 1% T + 15% A composite modified asphalt forms a uniformly dispersed and well-stabilized cross-linked network structure. This microscopically explains why, in the performance study of asphalt mastic, the 1% T + 15% A dosage combination consistently outperforms others. From images (e) to (g), it can be seen that when 5% nano-TiO2 is combined with different ARA dosages, obvious agglomeration occurs, and the agglomeration becomes more severe with higher ARA content. This is because nano-TiO2, due to its unique nano-effects, possesses high surface energy and strong adsorption capacity; thus, a higher dosage of nano-TiO2 inherently exhibits some agglomeration tendency. Moreover, increased ARA content exacerbates the agglomeration of nano-TiO2, affecting the compatibility among nano-TiO2, ARA, and the base asphalt.