The primary constituents of FDR-PC are RAP, reclaimed inorganic binder stabilize aggregate (RAI) and cement. The RAP material was specifically recovered from the asphalt surface layer of the existing pavement on National Highway 110, a secondary road located in China’s Inner Mongolia Autonomous Region. The original pavement structure consisted of a 4-cm-thick AC-16 asphalt mixture surface layer overlying a 20-cm-thick cement-stabilized crushed stone base layer. During material preparation, a milling machine was used to perform layer-by-layer removal of the existing pavement. Following laboratory processing involving natural air-drying and sieving, two distinct materials were obtained: RAP and RAI, as illustrated in Figure 1. The stabilizing agent was 42.5-grade ordinary Portland cement, with all technical specifications complying with the requirements of the Technical Specifications for Highway Asphalt Pavement Recycling (JTG/T 5521-2019) (Ministry of Transport of the People’s Republic of China, 2019). Detailed technical parameters are provided in Table 1.

Based on the thickness ratio between the aged asphalt surface layer and base layer, practical construction conditions, and economic considerations relevant to China’s national road network, this study employed three representative base-to-surface ratios (mass ratios of RAI to RAP) of 10:0, 8:2, and 6:4. These predefined ratios were used to guide the blending of RAI and RAP for the preparation of recycled materials. The gradation curves of the resulting recycled materials are presented in Figure 2, with all parameters meeting the requirements specified in China’s Technical Specifications for Highway Asphalt Pavement Recycling (JTG/T 5521-2019) (Ministry of Transport of the People’s Republic of China, 2019).

In this study, three representative mechanical performance parameters—UCS, ITS, and RCS after freeze–thaw cycles—were selected as key indicators for evaluating the performance of FDR-PC cold recycled mixtures. Among these, the UCS test is widely recognized for its simplicity and cost-effectiveness, and it has been extensively adopted by numerous countries as a primary parameter in mixture design. ITS serves as a crucial basis for determining the allowable tensile stress at the bottom of semi-rigid base layers in China’s Specifications for Design of Highway Asphalt Pavements (Ministry of Transport of the People’s Republic of China, 2019). It is also a commonly used mechanical index for mixtures stabilized with inorganic binders. This method is easy to perform, has good repeatability, and is one of the most commonly used approaches for assessing tensile properties of materials. Given that Inner Mongolia belongs to a seasonal frozen soil region, the durability issues of pavement bases caused by freeze-thaw damage are one of the primary forms of distress. Therefore, this study considers the freeze-thaw resistance of FDR-PC as one of its important performance evaluation indicators.

All test specimens were prepared using a static compaction method. The specimens were cylindrical, with a diameter of 150 mm and a height of 150 mm. Curing was carried out under standard conditions at a temperature of 20°C ± 2°C and a relative humidity of 95% until the designated curing age. Some specimens underwent water immersion treatment prior to the end of the curing period. The specific procedures for each performance test are described as follows.

The UCS test was conducted in accordance with JTG E51-2009 (T0806-1994) (Ministry of Transport of the People’s Republic of China, 2009). Specimens were cured for 6 days, followed by immersion in water for 1 day. Compression loading was then applied at a constant rate and the maximum load at failure was recorded. The UCS was calculated using Equation 1. U s = 4 P π d 2 (1) where U s is the UCS of the specimen (MPa), P is the maximum load at failure (N), and D is the specimen diameter (mm).

The ITS test was performed after 90 days of specimen curing, following the procedures outlined in T0806-1994 (Ministry of Transport of the People’s Republic of China, 2009). A standardized loading apparatus was used to apply the load, and the maximum load at specimen failure was recorded. The ITS was calculated using Equation 2. R i = 0.004178 P h (2)

In the equation, R i represents the ITS of the specimen (MPa), P denotes the maximum failure load (N), and h corresponds to the specimen height after immersion (mm).

For the freeze–thaw resistance test, a total of 18 specimens were prepared for each type of mixture and divided into two groups: the non-freeze-thaw group and the freeze–thaw group, each containing nine specimens. After 28 days of curing and water immersion on the final day, specimens underwent five freeze–thaw cycles in accordance with T0858-2009 (Ministry of Transport of the People’s Republic of China, 2009). Upon completion of the cycles, the average mass loss rate was determined. UCS tests were then conducted on both the freeze–thaw and non-freeze-thaw groups, and the strength retention ratio was calculated using Equation 3. R C S = U C S R c · 100 % (3)

Here, R C S denotes the relative compressive strength after n freeze-thaw cycles (%), UCS represents the compressive strength of specimens after n freeze-thaw cycles (MPa), and R c refers to the strength of control specimens in comparative tests (MPa).

This study employs LCA methodology to evaluate carbon emissions and energy consumption throughout the lifecycle of FDR-PC technology in highway rehabilitation. The LCA methodology follows the ISO 14040 (2006) standard (Finkbeiner et al., 2006; ISO. ISO 14040, 2006), and a process-based LCA framework is adopted. The rehabilitation process is divided into several discrete phases, with energy use and pollutant emissions quantified at each stage. By integrating activity data with corresponding carbon emission factors, a carbon emission estimation model is established, enabling the cumulative evaluation of energy consumption and carbon emissions throughout the entire life cycle.

This study is based on a real-world highway project in China, with the LCA functional unit defined as the construction of a 1-km-long, 24 cm-thick FDR-PC recycled base layer. Only the base layer construction is considered within the system boundary. The project section is located in Ulanqab City, Inner Mongolia Autonomous Region, spanning from K346 + 100 to K351 + 200. The pavement width is 10.50 m, and the subgrade width is 11.50 m.

The FDR-PC technology in highway rehabilitation can be categorized into three lifecycle phases: the raw material production phase, the transportation phase, and the construction phase.

The raw material production phase primarily involves energy consumption and carbon emissions during material processing, excluding raw material extraction and transportation. The transportation phase encompasses the delivery of processed materials from factories to construction sites, with carbon emissions predominantly resulting from transport vehicle fuel consumption. The construction phase includes processes such as existing pavement milling, material mixing, as well as paving and compaction operations, accounting only for fuel consumption and carbon emissions from construction machinery during operational activities.

Multi-objective optimization involves the simultaneous minimization of multiple objective functions subject to specified constraints, as illustrated in Equation 4. Here, F X denotes the objective function vector, f i X represents the i -th objective individual function, m is the total number of objective functions, and X corresponds to the parameter vector. minimize  F X = f 1 X , f 2 X , … , f m X (4)

In practical applications, multi-objective optimization problems often involve inherent conflicts among objectives, making it impossible to simultaneously minimize all objective functions. Therefore, the primary goal of multi-objective optimization is to identify solutions that achieve an optimal trade-off among competing objectives.

A solution X is considered to dominate another solution X ′ if X is at least as good as X ′ in all objectives and strictly better in at least one objective. The set of all non-dominated solutions constitutes the Pareto front. For any solution belonging to the Pareto front, improvement in one objective necessarily leads to deterioration in at least one other objective. As shown in Figure 3, the solid blue dots represent dominant solutions forming the Pareto front.

NSGA-II is a multi-objective genetic optimization algorithm rooted in the principle of Pareto optimality. This algorithm effectively approximates the Pareto frontier solution set while preserving population diversity through rapid non-dominated sorting and crowding distance computation. In contrast to conventional optimization methods, NSGA-II exhibits enhanced capability in managing complex trade-offs among multiple objectives. Its elitist preservation strategy promotes convergence and guarantees solution optimality, rendering it particularly effective for engineering optimization problems involving multiple constraints (Deb et al., 2002). The primary procedural steps of the NSGA-II algorithm are as follows:

1. Randomly generate an initial parent population P 0 of size N , where each individual comprises a set of decision variables, and evaluate their objective functions.

Since all solutions on the Pareto front are mutually non-dominated and cannot be directly compared in terms of superiority, they present significant decision-making challenges. In such cases, the TOPSIS algorithm can be employed to evaluate the solutions on the Pareto front. By measuring distances to both the ideal best and ideal worst solutions, TOPSIS establishes a comparable ranking system for these non-dominated solutions. This approach effectively prioritizes points on the Pareto front while preserving the diversity inherent in multi-objective optimization (Behzadian et al., 2012). The basic procedure of the algorithm is as follows (Tzeng and Huang, 2011):

1. Calculate the vector-normalized objective function values x i j for the Pareto frontier points to eliminate dimensional differences. Here, i denotes the index of the Pareto frontier solution, j represents the index of the objective function.

The experimental data of FDR-PC cold recycled mixtures with varying cement contents and RAP contents are presented as follows: Table 2 shows the 7-day UCS test results, Table 3 provides the ITS test results, and Table 4 summarizes the RCS test results.

Using cement content and RAP content as independent variables, and the mean UCS and ITS values together with the measured RCS value as dependent variables, predictive models were developed via bivariate quadratic polynomial regression. Model parameters were estimated via the least square method, with the polynomial degree fixed at two to prevent overfitting. As shown in Table 5, all fitted equations yielded coefficients of determination greater than 0.98, indicating strong model performance.

To evaluate material performance, UCS, ITS, and RCS are used as primary indicators, and a weighted aggregation method is applied to construct the material performance objective function. Since these indicators have different physical dimensions, normalization is performed to eliminate dimensional inconsistency. Normalized values are denoted with an asterisk (*), and the normalization is performed according to Equation 6: f * = f − f min f max − f min   (6) where f max and f min represent the maximum and minimum function values within the parameter range, respectively.

Using the weighted aggregation method, the performance objective function for FDR-PC cold recycled mixtures is formulated as shown in Equation 7. F 1 = w 1 · U C S * + w 2 · I T S * + w 3 · R C S * (7) ∑ i = 1 3 w i = 1

Here, U C S * , I T S * , and R C S * represent the normalized functions of UCS, ITS, and RCS, respectively, while w 1 , w 2 and w 3 denote their corresponding weights, which sum to 1. In this study, each weight is assigned an equal value of 1 3 , reflecting an assumption of equal importance among the three mechanical performance indicators. These weights can be adjusted based on the relative importance of each indicator in specific application scenarios.

When calculating carbon emissions and economic costs, the mass of the FDR-PC cold recycled mixture must be determined. The laboratory calculation formula for the FDR-PC cold recycled mixture is presented in Equation 8: m 0 = V · ρ max   · 1 + w o p t · 98 % (8) where m 0 is the mass of a single specimen (g), ρ max is the maximum dry density (g/cm³), w o p t is the optimum moisture content (%), and 98% represents the compaction degree.

The evaluation of mass requires two key parameters: maximum dry density and optimum moisture content. Table 6 presents the experimental data for these parameters in FDR-PC mixtures with varying cement contents and base-to-surface ratios. Using cement and RAP contents as independent variables, and maximum dry density and optimum moisture content as dependent variables, bivariate quadratic polynomial regression was performed on the experimental data. As shown in Table 7, all fitted models achieved coefficients of determination greater than 0.95, indicating excellent goodness of fit.

Based on Equation 8, the mass of each material within the functional unit in the LCA can be calculated. Specifically, the total mass of the mixture is determined by Equation 9, the cement mass by Equation 10, and the water mass by Equation 11. M = L · W · D · ρ max · 1 + w o p t · 0.98 (9) M c = M 1 + w o p t · w o p t (10) M w = M 1 + w o p t + c · c (11)

Here, M represents the total mass of the pavement in the functional unit, L denotes the pavement length, W the pavement width, D the base layer thickness, ρ max the maximum dry density, w o p t the optimum moisture content, and c the cement content.

Based on the LCA methodology and carbon emission factor approach, the total carbon emissions of FDR-PC technology during highway rehabilitation can be calculated using Equation 12: m = ∑ Q m a t · F E m a t + ∑ F E v e h · n · D + ∑ Q e q p · F E e q p (12)

Here, the three terms represent the raw material production, transportation, and construction phases, respectively. Q m a t denotes the mass of raw materials, while F E m a t is the corresponding carbon emission factor, expressed in tons per unit of usage. n represents the workload of transport machinery, D is the transport distance in kilometers, and F E v e h is the carbon emission factor of transport machinery, expressed in kilograms per ton-kilometer. Finally, Q e q p indicates the workload of construction machinery, and F E e q p is its carbon emission factor, expressed in tons per unit workload.

Similarly, the total energy consumption of FDR-PC is calculated using Equation 13: E = ∑ Q m a t · F C m a t + ∑ F C v e h · n · D + ∑ Q eqp · F C eqp (13)

Analogous to Equation 12, F C m a t corresponds to the energy consumption factor associated with raw materials, expressed in MJ per unit usage. F C v e h to that of transportation machinery, expressed in MJ per ton-kilometer. And F C e q p to that of construction machinery, expressed in MJ per unit workload.

During the raw material production phase, the primary materials consist of cement and water. In the transportation phase, cement and water are transported to the construction site by lorry. During the construction phase, a cold recycling machine mills the existing pavement, mixes the reclaimed material with cement, and forms a new surface, which is subsequently leveled by a motor grader and compacted by a road roller.

In the calculation of carbon emissions and energy consumption, conventional approaches typically consider only explicit emissions and energy use, primarily attributed to cement utilization, while overlooking the potential environmental benefits associated with the utilization of RAP and RAI. RAI and RAP contain substantial amounts of aggregate, which can significantly reduce the demand for virgin aggregate. Furthermore, RAP incorporates a certain proportion of aged asphalt binder, enabling the partial substitution of virgin asphalt materials.

Therefore, this study considers the equivalent aggregate and asphalt savings achieved through the incorporation of RAI and RAP as their inherent carbon emission and energy consumption advantages. These advantages are subsequently integrated into the environmental impact objective function for evaluation, as detailed in the following Equations 14, 15: m e q = m R A I · F E a g g + 1 − α · m R A P · F E a g g + α · β · m R A P · F E a s p h (14) E e q = m R A I · F C a g g + 1 − α   · m R A P · F C a g g + α · β · m R A P · F C a s p h (15) where m R A I and m R A P denote the mass of RAI and RAP, respectively, F E a g g and F E a s p h represent the carbon emission factors for aggregate and asphalt, respectively, F C a g g and F C a s p h denote the energy consumption factors for aggregate and asphalt, respectively. The proportion of aged asphalt binder in RAP is denoted by α , set at 5%, and the effective substitution efficiency of aged binder for virgin asphalt is denoted by β , set at 70%.

The carbon emission and energy consumption factors are listed in Table 8. The factors for cement, aggregate and asphalt were obtained from Pan (Pan, 2011), while the fuel consumption and operational efficiency data for lorry, cold recycling machine, motor graders, and road rollers were sourced from Highway Engineering Machinery Shift Cost Quota (Ministry of Transport of the Peo ple’s Republic of China, 2018) and China Energy Statistical Yearbook (National Bureau of Statistics of China, 2022).

Based on the weighted Equation 6, the environmental impact objective function is formulated by integrating the carbon emission models (Equations 12, 14) and the energy consumption models (Equations 13, 15), each with their associated weighting coefficients, as presented in Equation 16: F 2 = w 3 · m − m e q * + w 4 · E − E e q * (16) ∑ i = 3 4 w i = 1 where m − m e q * and E − E e q * represent the normalized carbon emission function and energy consumption function, respectively. w 3 and w 4 denote the weight coefficients assigned to each function. In this analysis, both weights are set to 0.5, indicating equal emphasis on carbon emissions and energy consumption in the environmental evaluation.

This study utilizes the NSGA-II algorithm for multi-objective optimization, with the optimization model detailed in Equation 17. minimize  F = − F 1 , F 2 (17) s . t .   c L < c < c U r L < r < r U U C S L < U C S < U C S U I T S L < I T S < I T S U R C S L < R C S (18)

Here, F 1 represents the performance objective function, which is maximized and thus assigned a negative sign; F 2 represent the environmental impact objective function, which is minimized.

Equation 18 defines the constraints for the multi-objective optimization. The cement content is limited to a range of 4%–6%, corresponding to c L and c U in Equation 18. Similarly, the RAP content is constrained between 0% and 40%, denoted as r L and r U . In compliance with China’s Specifications for Design of Highway Asphalt Pavements (Ministry of Transport of the People’s Republic of China, 2019) for heavy-traffic base layers, the 7-day UCS must range between 4.0 MPa and 6.0 MPa, which correspond to U C S L and U C S U . Similarly, the ITS should be maintained between 0.4 MPa and 0.6 MPa, corresponding to I T S L and I T S U . Furthermore, this study constrains the RCS to a minimum of 90%, as denoted by R C S L in the equation.

The multi-objective optimization results are illustrated in Figure 4. Figures 4a,b depict the distribution of the Pareto front in the objective function space and parameter space, respectively. Additionally, under the condition of equal weighting between the performance and environmental objectives, where each objective was assigned a weight of 0.5, the TOPSIS scores of the Pareto optimal points were calculated and visualized using a colormap, as presented in Figure 4.

Figure 4a reveals a significant negative correlation between the performance and environmental objective functions. In the environmental impact assessment, the carbon emission factor of cement is remarkably higher than other factors, exceeding them by nearly two orders of magnitude. Given that cement enhances various aspects of the material’s performance, improvements in material properties typically stem from an increased cement content. This relationship directly leads to a substantial increase in carbon emissions and energy consumption, thus manifesting as a trade-off between the performance and environmental objective functions.

Figure 4b demonstrates the characteristic parameter combinations corresponding to the non-dominated solutions of the Pareto front. The RAP content ranges from 0% to 34%, and the cement content ranges from 4.4% to 6%. Based on the parameter distribution characteristics, three distinct regions can be roughly identified. The first region corresponds to cement content approaching its upper constraint limit, while RAP content varies from 0% to 20%, approximately the minimum to the midpoint of its constraint range. As indicated by the corresponding colormap in Figure 4a, this region is associated with high material performance and high environmental impact. In the second region, the cement content gradually decreases from 6% to 4.8%, and the RAP content gradually increases from 20% to 34%, representing a balance between moderate material performance and moderate environmental impact for both objective functions. The third region shows a decrease in cement content from 4.8% to 4.4% and a decrease in RAP content from 34% to 28%, corresponding to low material performance and low environmental impact.

In addition to the equal-weighted case, we also evaluated TOPSIS scores under performance-priority and environment-priority weighting schemes. For performance-priority, weights were set as 0.8 (performance) and 0.2 (environment); for environment-priority, the weights were reversed. Figure 5 presents the spatial distribution of the TOPSIS evaluation results under different weights using colormaps, and Table 10 summarizes the parameter combinations with the highest TOPSIS scores for the three weighting schemes. Figure 5a shows that under performance priority, high-scoring parameter combinations are concentrated in region 1, with the highest-scoring combination being 6% cement content and 5% RAP content. Figure 5b indicates that under environment priority, high-scoring parameter combinations are concentrated in region 3, with the highest-scoring combination being 4.6% cement content and 32% RAP content. As shown in Figure 4b, under balanced performance and environmental weights, high-scoring parameter combinations are concentrated in region 2, with the highest-scoring combination being 5.2% cement content and 27% RAP content.