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Article

Improvement in the Recycled Aggregate Replacement Ratio in Concrete Pavement Bricks by Incorporating Nano-Calcium Carbonate and Basalt Fibre: Model Experiment Investigation

1
School of Architecture and Civil Engineering, Qiqihar University, Qiqihar 161006, China
2
Heilongjiang Xinyu Cement Products Co., Ltd., Qiqihar 161099, China
*
Author to whom correspondence should be addressed.
Buildings 2025, 15(12), 2070; https://doi.org/10.3390/buildings15122070
Submission received: 15 May 2025 / Revised: 11 June 2025 / Accepted: 13 June 2025 / Published: 16 June 2025

Abstract

This study focuses on improving the recycled coarse aggregate (RCA) replacement ratio in recycled aggregate concrete products. First, the mix design and compressive performance of recycled aggregate concrete (RAC, RCA replacement percentages of 20%, 35%, and 50%) were evaluated using the monofactor analysis method and response surface methodology under three different conditions: single addition of nano-calcium carbonate (NC, dosages of 0.1%, 0.2%, and 0.3%), single addition of basalt fibre (BF, volume content of 0.1%, 0.2%, and 0.3%), and combined addition of both. The results show that the compressive strength of RAC at 7 and 28 days rises as the BF or NC content increases and then falls as the NC content increases. According to the sensitivity analysis, RAC’s compressive strength is significantly impacted by the replacement ratio of RCA, with NC having a more considerable effect on RAC’s 7-day compressive strength than BF, while BF affects the 28-day compressive strength more than NC does. Based on the desirability function, the ideal BF and NC content in RAC was optimised and confirmed by the compressive strength test. It demonstrates that the best compressive performance is achieved by RAC with 1% NC and 0.3% BF. Finally, concrete pavement brick models were created using the ideal mix proportion provided by the compressive strength test. The model compression test results show that RAC pavement bricks (RCA replacement ratio of 60%) with 1% NC and 0.3% BF had a 28d compressive strength of 5.7% and 15.8% higher than NAC and RAC pavement bricks, respectively.

1. Introduction

Under the combined stresses of global climate change and resource constraints, the recycling of construction and demolition waste (CDW) has become a critical avenue to accomplishing dual carbon goals [1,2]. As a major source of CDW, waste concrete generates approximately 2 billion tonnes annually [3]. It is of great significance to consume this waste concrete reasonably and efficiently [4,5,6]. Nowadays, through crushing, dust removal, and other processes, waste concrete can be processed into recycled aggregate to be used in recycled concrete products, as shown in Figure 1. However, RCA’s intrinsic drawbacks, such as high porosity, variable strength, and poor workability [7,8,9], hinder its high-volume inclusion into recycled aggregate concrete (RAC) products. This is due to the mechanical properties of RAC being usually lower than those of natural aggregate concrete (NAC), especially in the core parameter of mechanical properties, compressive strength, which is often reduced by 15–30% [10,11]. Although extensive study has been undertaken on structural elements (such as beams, slabs, and columns) composed of recycled concrete, studies concerning small-scale goods created from recycled concrete are very scarce.
Concrete pavement bricks are widely employed in urban infrastructure as non-load-bearing components with yearly production approaching 100 cubic meters [12]. Utilising RCA to replace NCA in pavement brick manufacturing offers a new route for RCA utilisation. However, compared with NAC pavement bricks, RAC pavement bricks are prone to problems such as low compressive strength, easy cracking, and insufficient durability [13,14]. Especially with a higher proportion of RCA incorporation, this problem will be more serious. Due to these disadvantages, in China, the RCA replacement ratio in RAC pavement bricks is often less than 30% [15], which is not conducive to the effective consumption and engineering application of recycled aggregate. Therefore, it is necessary to improve the mechanical properties of RAC products by introducing new materials or adopting new technologies to achieve a high RCA replacement ratio in concrete products.
As a core parameter of mechanical property evaluation, compressive strength strongly determines the safety and durability of RAC pavement bricks [16,17]. Recently, incorporating new materials such as fibre materials or nano-materials (e.g., nano-silicon dioxide (NS), nano-calcium carbonate (NC)), or new technology (e.g., accelerated carbonation) can improve the compressive properties of RAC, which has been widely proven [18,19,20]. Compared with NS, NC demonstrates extraordinary advantages in cost control, interfacial performance, and strengthening effects. NC possesses abundant raw material reserves, with its industrial production cost only 1/3 to 1/2 of NS’s [21]. Experimental studies indicate that nano-calcium carbonate (NC) exhibits a high specific surface area and a strong nucleation effect. This helps to fill the pores of recycled aggregates, promotes the formation of calcium silicate hydrate (C-S-H) gel in the hydration products, and increases the compactness of the matrix by 15–20% [22]. Adding just 1% of NC can enhance the 7-day compressive strength of RAC by 10 to 20% and improve the 28-day compressive strength by 5–15% [23,24,25,26,27]. While accelerated carbonation technology can enhance strength in the short term, it requires sealed equipment and a CO2 gas source, leading to high industrialisation costs. Moreover, excessive carbonation reduces alkalinity, increasing the risk of steel corrosion [28]. As a continuous fibre drawn from natural basalt, basalt fibre (BF) has the characteristics of high strength, corrosion resistance, and low cost, which can effectively improve concrete’s compressive and crack resistance [29,30,31]. Relevant studies have indicated that BF with a volume fraction of 0.2 to 0.3% can increase the compressive strength of RAC by 7 to 14%. However, excessively high dosages may decrease fibre dispersion and weaken the interfacial transition zone (ITZ) [32,33,34]. Adding NC to BF-reinforced concrete can further enhance the compressive performance and crack resistance of BF-reinforced concrete. This is primarily attributed to the ability of NC to accelerate the cement hydration process, which densifies the microstructure of cement-based composites and strengthens the bond between BF and the cement matrix, thereby achieving the modification and enhancement of concrete properties [35,36,37].
Many investigations have been undertaken on the mechanical properties of RAC with the single addition of NC or BF. However, the following issues need to be addressed: (i) The mechanical properties of RAC and concrete products under the synergistic effect of NC and BF are not well understood, particularly manifested in the lack of exploratory research on the optimal mix proportion for their combined addition. Current studies typically determine the dosage of one material beforehand and then perform single-factor analysis, lacking systematic coupling exploration with both NC and BF dosages treated as concurrent variables [38,39]. (ii) The impact of the source of recycled aggregates on RAC is unclear. Most existing research focuses on recycled aggregates from a single source, typically derived from laboratory waste concrete or demolition debris from the same building. There is a lack of studies using recycled aggregates obtained from the CWD recycling company, which have a diverse range of components and significant variations in primary strength, and (iii) the effect of the shape of natural coarse aggregate needs further investigation. Most research has used gravel as the natural coarse aggregate, while the use of pebbles has been infrequently explored.
Based on solid waste aggregates provided by enterprises, this study investigates the mechanical properties of recycled concrete and its pavement bricks under single addition or combined addition of NC and BF, aiming to explore their strengthening effects and determine the optimal dosages of NC and BF for high-proportion recycled aggregates. This provides experimental references for engineering applications. The detailed research design is outlined as follows: Initially, based on the monofactor analysis method (MAM), the effects of different RCA replacement percentages (30%, 45%, and 60%), BF content (with volume fractions of 0.1%, 0.2%, and 0.3%), and NC content (1%, 2%, and 3% as a substitute for cement) on the 7-day and 28-day compressive properties of RAC were analysed, respectively. Subsequently, using the response surface method (RSM), a three-factor and three-level test scheme was constructed by Box-Behnken design (BBD). Based on the regression model of the 7d and 28d compressive strength response of RAC, analysis of variance (ANOVA) was carried out, and the optimal mix proportion of RAC was obtained by the desirability function and verified by compression testing. Finally, using the optimal proportion of mix provided by MAM and RSM, RAC pavement brick models with a high replacement ratio of RCA were produced, and the compressive strength test and scheme verification were carried out. Additionally, the morphology and element distribution of the ITZ of recycled aggregate were analysed by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS), and the mechanism of NC-BF synergistic enhancement of RAC was revealed.

2. Materials and Experimental Program

2.1. Materials

2.1.1. Cementitious Materials

A local enterprise in Qiqihar produced Composite Portland cement (P.C 42.5 grade, containing 26.8% fly ash and 13.3% slag powder). Its chemical composition, determined by X-ray fluorescence (XRF), is listed in Table 1.
NC had an average particle size of 40 nm and a specific surface area of 20 m²/g. The morphologies of the cement clinker and NC, observed via scanning electron microscopy (SEM), are shown in Figure 2. The NC particles have a spindle-like shape, as seen in Figure 2a. The untreated nanoparticles’ high surface energy properties make them prone to agglomeration, which causes micron-scale agglomerates to form in the SEM pictures. While the slag particles have a glassy phase structure, the fly ash particles in the cement clinker are spherical and have smooth surfaces, as seen in Figure 2b. By filling the pores between the cement clinker and slag particles, fly ash reduces the overall porosity and increases the cement’s compactness, forming a particle size gradation complementarity.

2.1.2. Aggregates

This study utilised river sand with a fineness modulus of 2.85 as the natural fine aggregate (FA). The coarse aggregates consisted of two varieties: one was continuous grading NCA with a particle size of 4.75–9.5 mm; the other was RCA, primarily sourced from waste concrete resulting from road and building demolition, with negligible quantities of crushed clay bricks and glass shards, produced by Heilongjiang Xinyu Cement Products Co., Ltd., Qiqihar, China. Data in Table 2 demonstrate that RCA exhibited a high water absorption rate of 6.18%, which resulted in a 5–15% increase in actual water demand compared to the theoretical value. To solve this, a water compensation method via an Additional water approach was adopted: the aggregates were first pre-treated to a surface-dry state, and then the total water consumption was calculated based on a water-to-cement ratio of 0.38. Testing revealed that all physical parameters of fine and coarse aggregates satisfied Chinese national standard GB/T 14685-2022 [40]. Their comprehensive physical characteristics and particle size distribution graphs are presented in Table 2 and Figure 3, respectively.

2.1.3. Other Materials

BF with a length of 6 mm was employed as the shortcut type, and its physical properties are presented in Table 3. Tap water from the laboratory was used as the water source, with a water-to-cement ratio of 0.38 adopted in this study. A standard polycarboxylic acid superplasticiser with a water reduction rate of ≥25% was selected as the admixture.

2.2. Experimental Program

Concerning Refs. [41,42,43,44], three factors were selected as design variables in this study: NC (1%, 2%, and 3% by mass replacement of cement), BF (0.1%, 0.2%, and 0.3%), and RCA (30%, 45%, and 60%). Both single-factor and multivariate experimental analyses were performed. In the single-factor analysis, the effects of the RCA substitution ratio on the 7-day and 28-day compressive properties of recycled aggregate concrete were investigated, along with the influences of the BF volume fraction and NC content on compressive strength at identical RCA substitution rates (30%, 45%, and 60%). For the multivariate analysis using RSM, a three-factor, three-level experimental design was conducted. Based on the proposed test protocols and incorporating the mix proportions for pavement bricks provided by Heilongjiang Xinyu Cement Products Co., Ltd., the experimental mix ratios utilised in this study are detailed in Table 4 and Table 5.
Cubic specimens (100 mm × 100 mm × 100 mm) were created using standard moulds, with each group consisting of three specimens. A total of 74 groups were fabricated following the procedure detailed below [45,46]: First, aggregates (NCA, RCA, and FA) were placed into a forced-action mixer according to the mix proportions and blended for 60 s. Cement was then added, and mixing continued for an additional 60 s. Next, a pre-prepared mixed solution (comprising NC, superplasticiser, and water, ultrasonically dispersed for 120 s) was added in two stages: 50% of the solution was injected initially, followed by 60 s of mixing. Basalt fibres were manually sprinkled consistently into the mixer during this stage to guarantee better fibre alignment. The remaining 50% solution was gently poured, and mixing proceeded for another 60 s. This approach efficiently prevented the aggregation of nano-calcium carbonate and segregation generated by the instantaneous excess superplasticiser [22]. The mixed concrete was unloaded from the forced-action mixer and placed into a slump cone for testing. Results demonstrate that all concrete mixtures in this investigation had slump values falling within the 0–20 mm range. Notably, the concrete slump with combined NC and BF addition was much lower than that of NC-only mixtures, which was moderately lower than that of BF-only mixtures. All values fully conform to the slump requirements for plastic concrete defined in the concrete pavement brick guidelines. After mixing, fresh concrete was put into moulds, squeezed on a vibrating table for 30 s, cured in a room for 24 h, moulded, and then placed in a constant temperature and humidity curing chamber for 7 and 28 days, respectively. The specimen preparation and testing procedures are shown in Figure 4.
The compressive strength test was carried out according to the requirements of the Chinese specification GB/T50081-2019 [47]. It was carried out using a model electro-hydraulic pressure tester (model YAW-2000, accuracy 0.01 kN), loaded at a rate of 0.6 MPa/s, and some of the specimens were loaded, as shown in Figure 5.

3. Compression Test Results and Analysis of RAC

3.1. Impact of Single Factors

According to the Chinese standard GB/T 50081-2019, the median value of the compressive strength test was used as the representative value of strength when the differences between the median value and the other two values did not exceed 15% of the median value. If only one difference exceeded 15% of the median value, the median value was used as the representative value of strength; if both differences exceeded 15% of the median value, the test results of this group were not used as the basis for strength evaluation, and the test was reperformed.

3.1.1. Effect of RCA Substitution Rate on Compressive Strength

The 7-day and 28-day compressive strengths of RAC under varied RCA replacement ratios are exhibited in Figure 6a. Results indicate that at the 7-day age, compressive strength decreases continuously with increasing RCA replacement ratio: the NAC with a 0% replacement ratio has a compressive strength of 37.28 MPa, which drops to 30.37 MPa at a 60% replacement ratio, indicating that higher RCA replacement significantly inhibits the early-age strength of concrete [48,49,50]. This is because the cement hydration reaction has not been fully finished at the early stage, and the internal structure is still in the formation phase, leading to decreased bonding performance at the interface transition zone between the aggregate and cement paste. As the RCA replacement ratio increases, the defect accumulation effect is further exacerbated, leading to a continuous decrease in compressive strength. At the 28-day age, compressive strength first increases and then decreases with increasing RCA replacement ratio: when the replacement ratio increases from 0% to 30%, strength rises from 46.12 MPa to a peak of 48.78 MPa; beyond 30%, strength gradually decreases with higher replacement ratios, dropping to 42.5 MPa at 60%. The superior mechanical performance of RAC at a 30% RCA replacement ratio arises from two primary mechanisms: First, this replacement level optimises the balance between RCA strength and gradation, delivering stable skeletal support for the concrete matrix. Second, RCA exhibits more surface roughness than NCA, promoting stronger mechanical interaction with the cement matrix. This significantly improves bond performance in the ITZ, thereby synergistically improving the concrete’s overall mechanical strength. These findings are consistent with the results reported by Bai G et al. [10] and Zaetang Y et al. [14].

3.1.2. Effect of BF Substitution Rate on RAC Compressive Strength

With fixed RCA replacement ratios (30%, 45%, and 60%), the 7-day and 28-day compressive strengths of RAC and their growth rates under varying BF volume fractions are presented in Figure 6b,c,f. For each RCA replacement ratio, RAC’s early and late compressive strengths generally increase with higher BF content. At a 30% RCA replacement ratio, increasing the BF volume fraction from 0% to 0.3% raises the 7-day strength from 35.46 MPa to 39.31 MPa (a 10.86% increase) and the 28-day strength from 48.78 MPa to 52.88 MPa (an 8.41% increase). For replacement ratios of 45% and 60%, the maximum 7-day strengths (36.75 MPa and 37.86 MPa, respectively) occur at a BF dosage of 0.2%, representing increases of 10.63% and 16.35% compared to BF-free control mixes (the 0-additive group). The maximum 28-day strengths (48.34 MPa and 48.72 MPa, respectively) are achieved at a BF concentration of 0.3%.
The primary explanation for the abovementioned strength change patterns is that BF can be uniformly disseminated in the concrete matrix to establish a three-dimensional support network. It dramatically increases the concrete’s strength by preventing the production and propagation of early microcracks and enhancing the structure of the ITZ. When the BF content approaches 0.3%, the 7-day compressive strength is lower than that at a 0.2% BF level. A more substantial BF reduces fibre dispersibility, leading to agglomeration and increasing the internal porosity of the matrix and the number of weak surfaces. As a result, the synergistic effect between the fibres and the matrix is weakened, causing a decline in recycled concrete’s early-age strength. However, as the curing age advances, the continuous cement hydration progressively improves the interfacial connection between BF and the cement matrix. Even at a relatively high dosage of 0.3%—commonly linked with potential fibre aggregation in composites—BF effectively mitigates late-stage crack propagation through sustained fracture-bridging mechanisms and promotes concrete compactness by homogenising internal stress distribution. These synergistic actions cumulatively contribute to the improvement in compressive strength. These findings are compatible with the earlier research results of Lv J et al. [51], Zhang S et al. [52], and Wang Y et al. [53].

3.1.3. Effect of NC Substitution Rate on RAC Compressive Strength

The 7-day and 28-day compressive strengths and their growth rates in RAC under different NC dosages are presented in Figure 6d–f. For RCA replacement ratios of 30%, 45%, and 60%, compressive strength initially improves and then declines with increasing NC content. Specifically, at a 30% RCA replacement ratio, the maximum 7-day and 28-day strengths (40.06 MPa and 52.23 MPa, respectively) occur at a 1% NC dosage, representing increases of 12.97% and 7.07% compared to the control RAC mixture (0-additive group). For 45% and 60% RCA replacements, the highest 7-day strengths (37.85 MPa and 36.96 MPa) are achieved with 2% NC, while the highest 28-day strengths (48.82 MPa and 48.56 MPa) occur with 1% NC, corresponding to improvements of 11.1% and 14.26%, respectively. Notably, adding 1% NC delivers the largest 28-day strength gain across all RCA replacement ratios, with an average increase of 12.78%.
The observed strength evolution can be attributed to the following mechanisms: C3S hydrolysis releases substantial Ca2+ and OH ions during the initial cement hydration. Given the higher mobility of Ca2+, these ions preferentially adsorb onto calcium carbonate surfaces, using NC particles as nucleation sites. This reduces the local Ca2+ concentration around C3S grains, accelerating their hydration kinetics and increasing the cumulative heat release, thereby enhancing the early-age strength of recycled concrete [54]. With prolonged curing, NC particles promote hydration via the nucleation effect and improve matrix compactness through micro-aggregate filling, reducing porosity. However, exceeding 1% NC content induces particle agglomeration, creating stress concentration points that compromise matrix homogeneity and introduce internal defects. Additionally, excessive calcium carbonate may undergo secondary reactions with hydration products, impeding long-term structural development and leading to a discernible strength reduction [55].

3.2. Influence of Multiple Factors

To explore the impacts of BF content, NC dosage, and RCA replacement ratio on the compressive performance of RAC, Design Expert 13 software was used to build multifactorial experimental schemes and analyse findings. This technique explained RAC’s 7-day and 28-day compressive strength responses to alterations in BF content, NC dosage, and RCA replacement ratio. Based on the regression model design, the desirability function optimisation method was utilised to produce the best mix proportion for the BF-NC-RAC system, which was proven by experiments.

3.2.1. Test Results of the Compressive Strength of RAC Based on the RSM

Through polynomial regression equations, RSM establishes a functional mapping between factor variables and response values. Its implementation approach covers five critical stages [56]: experimental data collecting, response surface model creation, model significance testing, parameter optimisation, and validation of optimal parameters. The experimental and anticipated 7-day and 28-day compressive strength values for RAC with combined BF-NC addition are shown in Table 6.
According to theoretical Equation (1) in Table 7, regression fitting analysis of the experimental data in Table 6 revealed response surface regression equations (Y1, Y2) for the 7-day and 28-day compressive strengths of recycled aggregate concrete, considering the components of NC dose, BF content, and RCA replacement ratio.
Analysis of variance (ANOVA) and reliability evaluation of the regression models were performed, with findings reported in Table 8 and Table 9. The p-values for the 7-day and 28-day compressive strength equations (Y1 and Y2) are 0.0001 and 0.0004, respectively, with F-values of 108.93 and 38.61, showing high model significance. The coefficient of determination R2, adjusted R2a, coefficient of variation CV, and signal-to-noise ratio are 0.995, 0.986, 0.74%, and 32.30 for 7-day strength and 0.986, 0.960, 1.22%, and 17.623 for 28-day strength, all supporting substantial model dependability.
Factor sensitivity analysis finds that single variables (A, B, and C) and interaction terms (AB and BC) in both the 7-day and 28-day models have p-values < 0.05, indicating substantial effects on compressive strength. For the 7-day strength, the factor significance is scored as C > B > A > AB > BC, and the AC interaction (p > 0.05) is inconsequential. For the 28-day strength, the ranking is A > C > B > AB, and both the AC and BC interactions exhibit non-significant effects (p > 0.05).
Besides ANOVA and fitting statistics, diagnostic plots were constructed to check the normal distribution of experimental and predicted data. The performance of the model for compressive strength is displayed in Figure 7 and Figure 8. It can be noticed that the diagnostic plots for 7-day and 28-day compressive strengths all fall within the specified confidence ranges. The applicability and relevance of the quadratic models of the nano-micro mixed concrete can be verified using these figures [57]. The residual normal probability plots in Figure 7a and Figure 8a indicate that all test points are equally distributed around the reference line, with residual absolute values ranging from −1.85 to 2.35, meeting the statistical condition |SR| < 3. This suggests no outliers in the dataset and a fair random distribution of residuals without clear patterns or periodicity [58]. The plots of residuals against the expected responses of the compressive strength models in Figure 7b and Figure 8b indicate the accuracy of the predictive models, as points are evenly distributed within the range of the top and bottom red lines. Additionally, as demonstrated in Figure 7c and Figure 8c, where residuals are plotted against the number of runs, the sinusoidal distribution of data points within the red border lines demonstrates no major model drift during the process.
The regression model created in this study has been verified to have good validity and reliability based on the diagnostic findings and analysis above. A literature comparison approach was used for further verification of the model’s interpretability and generalisation capacity; the outcomes are displayed in Table 10. With relative error percentages ranging from 2% to 4%, data analysis shows that the model’s projected 28-day compressive strength of recycled concrete shows excellent agreement with experimental values published in the literature. This finding implies that the model has a favourable prediction accuracy and may be applied successfully to forecast the recycled concrete’s 28-day compressive strength when NC and BF are added together.

3.2.2. Response Surface Analysis

Using the developed quadratic polynomial regression models, three-dimensional response surface plots and accompanying contour maps for RAC’s 7-day and 28-day compressive strengths were generated, considering the factors of NC dosage, BF content, and RCA replacement ratio. Visual analytic approaches were applied to intuitively reveal the influence of two-factor interactions on RAC’s compressive strength.
For the 7-day compressive strength of RAC with combined BF-NC addition, the contour plots and response surface are presented in Figure 9. Strength is significantly impacted by the interaction between NC and RCA, as shown in Figure 9a, where the RCA replacement ratio has a more pronounced effect: growing the RCA replacement ratio from 30% to 60% at 1% NC reduces compressive strength from 42.21 MPa to 38.52 MPa, while increasing NC content from 1% to 3% at a fixed 30% RCA replacement ratio decreases strength from 42.41 MPa to 40.40 MPa.
The greater contour density on the vertical axis as opposed to the horizontal axis in Figure 9b shows that the RCA has a more significant impact on strength than the BF. Because moderate BF inhibits the formation and propagation of early-age shrinkage, enhances ITZ bond performance, and creates a uniform support network to reduce internal structural flaws, increasing BF concentration consistently results in a strength gain [62].
At a fixed 45% RCA replacement ratio, Figure 9c demonstrates that at a fixed RCA substitution rate of 45%, the compressive strength decreases with increasing NC content while increasing with increasing BF content, and the influence of NC content is more significant than that of BF volume fraction. Notably, the combination of 0.3% BF volume fraction and 1% NC content achieves a strength peak of 40.15 MPa. BF inhibits crack propagation through its physical bridging effect, whereas NC accelerates early-stage cement hydration, generating more C-S-H gel and refining the pore structure of the ITZ. These two factors jointly enhance the early compressive strength of recycled concrete [63].
Figure 10 displays the response surface and contour analysis for the 28-day compressive strength of RAC with combined BF and NC addition. NC and RCA have a significant effect on strength, as shown by the abrupt curve in Figure 10a, with RCA having a more noticeable effect: increasing RCA replacement from 30% to 60% at a fixed 1% NC, compressive strength values of 53.79 MPa, 48.37 MPa, and 51.48 MPa are produced by NC dosage; while RCA replacement is fixed at 30%, increasing NC dosage from 1% to 3% results in a reduction in strength from 53.79 MPa to 50.09 MPa. Greater contour density along the horizontal axis in Figure 10b suggests that the BF substantially impacts strength more than the RCA. The likelihood of fibre bridging over microcracks improves with increasing BF concentration, which promotes energy dissipation to thwart crack progression and postpone failure, hence increasing strength [64]. Strength increases with rising BF volume fraction but decreases with rising NC dosage at a fixed 45% RCA replacement ratio, as shown in Figure 10c, where NC dosage is more significant than BF content. According to contour distributions, a high-strength region is created by a combination of 1% NC and 0.3% BF, whereas a low-strength region is produced by a combination of 2–3% NC and 0.1% BF. This is because NC improves the ITZ microstructure between old mortar and fresh paste, synergising with the physical bridging of basalt fibres to boost interfacial bond strength. This coordination between recycled aggregates and the new matrix mitigates strength deterioration induced by interfacial debonding.
According to the research above, with low RCA replacement rates, imperfections such as attached old mortar and microcracks on recycled aggregate impair the ITZ of concrete, diminishing its strength. When RCA content approaches a threshold, its particle gradation may improve the concrete’s internal structure, compensating for flaws and boosting strength. At low BF levels, uneven fibre dispersion generates stress concentrations or weak zones due to poor bonding and declining strength. As BF grows to an optimal level, fibres bridge cracks and resist fracture, limiting crack development and greatly enhancing compressive strength. Increasing BF and NC dosages at high RCA concentrations mitigates strength decline: BF restrains fracture channels by physical confinement, whereas NC plugs interfacial flaws in recycled aggregate, limiting strength loss from RCA inclusion. The synergistic process of NC and BF enhancing recycled concrete compressive strength is depicted in Figure 11. However, surpassing the appropriate dosage range for both components accelerates strength loss due to the combined impacts of RCA’s high defect rate and BF agglomeration, demonstrating the delicate interplay of several variables in regulating concrete mechanical properties.

3.2.3. Multi-Objective Optimisation and Validation of the Model

Based on the regression model, multi-objective optimisation of BF-NC-RAC was conducted by incorporating the desirability function, with the aim of seeking optimal BF volume fraction (factor A) and recycled aggregate replacement ratio (factor B) under three different RCA substitution rates (factor C) to simultaneously maximise the compressive strength predicted by the BF-NC-RAC regression model. The optimisation design objectives are presented in Table 11.
The objectives defined in Table 11 were input into Design-Expert 13 software to obtain the optimal mix proportions and maximum compressive strength values for RCA substitution rates of 30%, 45%, and 60%, as shown in Table 12. It can be observed that the combined addition of 0.3% BF and 1% NC exhibits the best modification effect on RAC. When the RCA substitution rates are 30% and 60%, the compressive performance of RAC is optimal, with predicted compressive strength values of 58.45 MPa and 55.46 MPa, respectively.
To validate the model’s prediction accuracy, strength tests were conducted for three mix proportions (numbered as I, II, and III) in Table 12. The results show that the absolute values of relative errors E between the measured and predicted compressive strengths are 2.8%, 2.9%, and 3.4% in sequence, indicating that the established compressive strength regression model exhibits high prediction accuracy [65,66]. Thus, it can be concluded that using RSM for the optimal design of BF-NC-RAC mix proportions is reasonable and feasible, with statistical reliability.

4. Microscopic Analysis

Depending on the experimental design and results, specimens containing recycled aggregate—labelled RAC60, N1RAC60, B1RAC60, and III (N1B0.3RCA60)—were selected for SEM and EDS analysis. The microscopic examination focused on the aggregate ITZ shape and element distribution to clarify how NC and BF enhance RAC.
The SEM micrograph of RAC60 (Figure 12a) exhibits the recycled aggregate surface as rough and porous, coated with residual old mortar debris, and incompletely removed hardened cement paste. The ITZ-3 between old and new mortar is approximately 50–80 μm wide, featuring a continuous microcrack network. In ITZ-1, plate-like CH crystals accumulate, with flocculent C-S-H gel forming a loose, porous network that fails to fill voids effectively. Crack propagation along ITZ-1 connects pre-existing fractures in old and new mortars, creating dominant failure pathways that weaken paste cohesion and reduce mechanical properties in RAC.
In Figure 12b, NC in N1RAC60 uniformly disperses throughout the matrix, filling ITZ pores, reducing pore width, and increasing microporosity. Ca2+ adsorption on NC surfaces promotes C-S-H gel nucleation, transforming the gel from a porous network into a dense, layered structure. Finely dispersed CH crystals enhance paste binding capacity. Additionally, NC participates in carbonation reactions to form calcium carboaluminate (C3A·CaCO3·11H2O), which fills voids and strengthens interfacial bonding.
Figure 12c shows that in B1RAC60, BF forms a mechanically interlocking interface with the cement matrix, accompanied by about a 5–10 μm thick C-S-H gel layer. Fibre adsorption of mixing water improves hydration in the interfacial zone, creating a “stress-release region” that reduces local porosity. When cracks reach BF, their propagation path deflects; the fibre’s bridging effect effectively prevents microcrack linkage, enhancing RAC compressive strength [67,68].
In Figure 12d, specimen III (N1B0.3RCA60) demonstrates that combined NC and BF addition significantly reduces ITZ pore number and width, densifying the recycled concrete matrix: NC fills microvoids around aggregates and BF, while BF inhibits macropore formation, collectively reducing porosity and refining pore size. Well-crystallised CH crystals enhance the microstructural density of the cement matrix, and an interpenetrating fibre-gel-nanoparticle network develops, encapsulating the matrix to restrict secondary crack propagation through mechanical confinement. This cooperation between NC and BF promotes thorough cement hydration, improving recycled concrete density and strength.
Furthermore, SEM observations in this study revealed fibre bridging and agglomeration phenomena, as shown in Figure 13, which has been reported in [30,31,32,33]. This indicates that the optimal dosage of BF (≤0.3%) can enhance the strength of RAC in practical engineering applications.
EDS surface scanning and energy-dispersive spectroscopy analysis were performed on the samples to evaluate cement hydration degree via the distribution patterns and concentration gradients of Ca and Si elements. As shown in Figure 14, B0N1RAC60, B0.3N0RAC60, and III (N1B0.3RCA60) exhibit significantly more pronounced hydration reactions than RAC60. This observation aligns well with the macroscopic mechanical property results of the concretes.
According to Taylor’s study [69], the Ca/Si atomic ratio in hydration products reflects the degree of hydration reaction, with C-S-H gel content decreasing as the Ca/Si value increases. Figure 15 depicts the atomic percentages of C, O, Mg, Al, Si, Ca, and Fe elements in RAC60, B0N1RAC60, B0.3N0RAC60, and III (N1B0.3RCA60) samples. The Ca/Si values are 0.86, 0.34, 0.36, and 0.28 for the four groups, with the III group displaying the lowest ratio. This shows the III group exhibits the most advanced hydration process and maximum C-S-H gel formation. These findings demonstrate that combined NC and BF addition effectively accelerates cement hydration, greatly boosts C-S-H gel formation, and consequently improves the densification of recycled concrete structures.

5. Model Test and Analysis of Concrete Pavement Bricks

Based on the above research results and via comprehensive examination from the perspectives of economy and environmental protection, a high RCA replacement ratio of 60% is recommended for RAC pavement bricks. Concrete pavement bricks were fabricated using five mix designs: NAC, RAC60, B0.3RAC60, N1RAC60, and III (NC1, BF0.3, RCA60). Following Chinese standard GB/T 28635-2012 [70], specimens were cast in 200 mm × 100 mm × 80 mm moulds, with three replicates prepared per mix proportion. To align laboratory procedures with industrial production, the fabrication process referenced [71]: fresh mixtures were first vibrated in moulds on a laboratory shaking table for 60 s, then subjected to 25 MPa pressure for 30 s using a YAW-2000 electro-hydraulic testing machine to simulate the vibration-pressure process. A 10-mm-thick iron-red iron oxide dye layer was applied to the specimen surface to match the traditional pavement brick colour, formulated at a mass ratio of cement/fine sand/water/iron oxide/water reducer = 1:2.3:0.38:0.08:0.015. The detailed manufacturing process is illustrated in Figure 16, with curing conditions consistent with those of the recycled aggregate concrete described earlier.
The 28-day compressive strength test findings for concrete pavement brick specimens (stress-strain curve depicted in Figure 17) reveal that RAC60 achieves a compressive strength of 41.62 MPa at 28 days, reflecting a 10.07% drop compared to NAC. Monolithic inclusion of BF or NC significantly enhances the compressive strength: 1% NC integration boosts strength by 11.03% to 46.21 MPa (0.4 MPa higher than NAC), while 0.3% BF addition increases it by 7.28% to 44.65 MPa. This suggests that 1% NC surpasses 0.3% BF in strengthening efficiency during vibration-pressure processing. When using a combined addition of 0.3% BF and 1% NC, the compressive strength of concrete pavement bricks increases significantly, reaching a maximum value of 48.21 MPa. Compared to RAC and NAC, this indicates a 15.8% and 5.76% increase, respectively. The mechanism is that NC optimises recycled concrete’s ITZ structure through high reactivity and micro-filling effects, lowering porosity. At the same time, BF reinforces the matrix integrity through bridging and crack-arresting mechanisms, which prevent crack propagation. Physical reinforcing and chemical modification work together to improve pavement brick products’ compactness and mechanical qualities by successfully compensating for the flaws in recycled aggregates [39]. This study offers a guide for enhancing the functionality of goods made from recycled concrete pavement bricks.

6. Conclusions

In this study, a multidimensional approach combining MAM and RSM was used to carry out the mix design of RAC considering the factors of NC content, BF volume content, and RCA replacement ratio, and the compressive strength tests of RAC at 7d and 28d were conducted. The compressive performance of RAC under a single addition of BF, NC, and a combined addition of BF and NC was clarified. Based on the optimal mix proportion scheme provided by MAM and RSM, concrete pavement brick models were prepared, and scheme verification was carried out. The main conclusions are as follows:
(1) The compressive strength of RAC grows as the volume content of BF increases, whereas it initially increases and then decreases as the NC content increases. The greatest significant enhancement in 7-day and 28-day compressive strength of RAC was observed at BF volume levels of 0.2% and 0.3%, respectively. The use of 0.3% BF can improve the 28-day compressive strength of RAC with recycled aggregate replacement ratios of 30%, 45%, and 60% by 8.41%, 11.38%, and 10.23%, respectively. The addition of 2% and 1% NC significantly improved the compressive strength of RAC at 7 days and 28 days, respectively. Upon substituting 1% NC for cement, the 28-day compressive strength of RAC, with recycled aggregate replacement ratios of 30%, 45%, and 60%, exhibits improvements of 7.07%, 12.49%, and 14.26%, respectively.
(2) A regression model for the compressive strength of RAC, incorporating the volume content of BF, the content of NC, and the replacement ratio of recycled aggregate, was developed using Box-Behnken design based on the RSM. The ideal proportions of BF and NC in RAC, with replacement ratios of 30%, 45%, and 60%, are determined using the desirability function; specifically, the volume content of BF is 0.3% and the NC content is 1%. The experimental findings indicate that the regression model is accurate and reliable. SEM image analysis indicated that the synergistic effect of NC and BF was substantial. NC can infiltrate the microcracks of aggregate and facilitate the synthesis of C-S-H gel, hence enhancing the early strength of RAC. BF impedes crack propagation in a three-dimensional random distribution and enhances the subsequent strength of concrete. EDS results indicated that the synergistic interaction of NC and BF diminished the Ca-to-Si ratio and facilitated the development of C-S-H gel, hence enhancing the density of the concrete structure.
(3) Concrete pavement brick models were prepared according to the optimal mix proportion provided by the results of MAM and RSM. The findings of the model compression test indicate that the 28-day compressive strength of RAC pavement brick, with a recycled aggregate replacement rate of 60%, is 41.62 MPa. Upon the incorporation of 1% NC and 0.3% BF, the compressive strength attains 46.21 MPa and 44.65 MPa, reflecting increases of 11.03% and 7.28%, respectively. The combination of 1% NC and 0.3% BF results in a compressive strength of 48.21 MPa, representing an increase of 15.83%. The experimental results further demonstrate that the synergistic effect of NC and BF is substantial. Based on the research results, the highest limit of BF dose in field applications is advised to be restricted to 0.3%. This should be paired with mechanical vibration technology (vibration frequency ≥ 50 Hz) to achieve uniform dispersion of fibres, hence enhancing the composite strengthening effect.
Beyond compressive strength, future research should integrate cost–benefit analysis and life cycle assessment to optimise the NC/BF dosage combination (e.g., the recommended mix proportion: 1% NC and 0.3% BF in this study) while exploring low-cost nano-material substitutes or composite utilisation technologies for industrial waste slags. Further investigations are necessary to characterise mechanical properties, including splitting tensile strength, impact resistance, and flexural strength of RAC with the consideration of potential variability due to differences in RCA source quality. Meanwhile, systematic studies on the durability of RAC with single or combined BF/NC under environmental factors (freeze-thaw cycles, wet-dry cycles, chloride ion erosion, and carbonation) and physical properties of RAC products (e.g., abrasion resistance and water absorption of pavement bricks) are essential to reveal the synergistic effects and action mechanisms of BF-NC hybrid modification. Extending the research to structural components (beams, slabs, and columns) and non-structural elements (pavement bricks and concrete curbs) will facilitate a multidimensional evaluation of the modification strategy’s effectiveness and applicability across the full spectrum of recycled concrete applications.

Author Contributions

Conceptualization, investigation, methodology, writing—original draft, B.Z.; investigation, methodology, resources, writing—review & editing, X.Z.; conceptualization, investigation, validation, M.W.; project administration, resources, supervision, D.Z.; project administration, supervision, D.W.; funding acquisition, resources, X.M. All authors have read and agreed to the published version of the manuscript.

Funding

The study presented in this paper was supported by the Central Guidance for Local Technology Development Projects (Grant No. ZY23QY12) and the Fundamental Research Funds for Heilongjiang Provincial Universities (Grant No. 145309209). This financial support is gratefully acknowledged.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

Authors Daoming Zhang and Xinwu Ma were employed by the company Heilongjiang Xinyu Cement Products Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Production and application of RCA.
Figure 1. Production and application of RCA.
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Figure 2. SEM images: (a) NC and (b) PC.
Figure 2. SEM images: (a) NC and (b) PC.
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Figure 3. Grain size distributions: (a) coarse aggregate, and (b) fine aggregate.
Figure 3. Grain size distributions: (a) coarse aggregate, and (b) fine aggregate.
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Figure 4. The specimen preparation and testing procedures.
Figure 4. The specimen preparation and testing procedures.
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Figure 5. Specimens used to obtain compressive strength: (a) pre-loading specimen, (b) under-loading specimen, and (c) post-loading specimen.
Figure 5. Specimens used to obtain compressive strength: (a) pre-loading specimen, (b) under-loading specimen, and (c) post-loading specimen.
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Figure 6. Compressive strength results of univariate analysis (a) RCA substitution rate analysis group, (b,c) BF volume content analysis group, (d,e) NC dosage analysis group, and (f) growth rate by group.
Figure 6. Compressive strength results of univariate analysis (a) RCA substitution rate analysis group, (b,c) BF volume content analysis group, (d,e) NC dosage analysis group, and (f) growth rate by group.
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Figure 7. Diagnostic diagram of 7-day compressive strength for BF-NC-RAC: (a) normal probability plot, (b) residual vs. predicted plot, and (c) residual vs. run plot.
Figure 7. Diagnostic diagram of 7-day compressive strength for BF-NC-RAC: (a) normal probability plot, (b) residual vs. predicted plot, and (c) residual vs. run plot.
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Figure 8. Diagnostic diagram of 28-day compressive strength for BF-NC-RAC: (a) normal probability plot, (b) residual vs. predicted plot, and (c) residual vs. run plot.
Figure 8. Diagnostic diagram of 28-day compressive strength for BF-NC-RAC: (a) normal probability plot, (b) residual vs. predicted plot, and (c) residual vs. run plot.
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Figure 9. Response surface plot and contour plot of 7-day compressive strength: (a) interaction between RCA and NC, (b) interaction between RCA and BF, and (c) interaction between NC and BF.
Figure 9. Response surface plot and contour plot of 7-day compressive strength: (a) interaction between RCA and NC, (b) interaction between RCA and BF, and (c) interaction between NC and BF.
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Figure 10. Response surface plot and contour plot of 28-day compressive strength: (a) interaction between RCA and NC, (b) interaction between RCA and BF, and (c) interaction between NC and BF.
Figure 10. Response surface plot and contour plot of 28-day compressive strength: (a) interaction between RCA and NC, (b) interaction between RCA and BF, and (c) interaction between NC and BF.
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Figure 11. Mechanism diagram of NC and BF synergistically enhancing the compressive strength of RAC.
Figure 11. Mechanism diagram of NC and BF synergistically enhancing the compressive strength of RAC.
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Figure 12. Microscopic topography by SEM: (a) RAC60, (b) N1RAC, (c) B0.3RAC, and (d) III (N1B0.3RCA60).
Figure 12. Microscopic topography by SEM: (a) RAC60, (b) N1RAC, (c) B0.3RAC, and (d) III (N1B0.3RCA60).
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Figure 13. Representative distribution patterns of BF in BF-RAC observed by SEM: (a) BF bridging effect and (b) BF agglomeration effect.
Figure 13. Representative distribution patterns of BF in BF-RAC observed by SEM: (a) BF bridging effect and (b) BF agglomeration effect.
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Figure 14. EDS surface scanning: (a) B0N0RAC, (b) B0N1RAC, (c) B0.3N0RAC, and (d) III (N1B0.3RCA60).
Figure 14. EDS surface scanning: (a) B0N0RAC, (b) B0N1RAC, (c) B0.3N0RAC, and (d) III (N1B0.3RCA60).
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Figure 15. EDS spectrogram: (a) B0N0RAC, (b) B0N1RAC, (c) B0.3N0RAC, and (d) III (N1B0.3RCA60).
Figure 15. EDS spectrogram: (a) B0N0RAC, (b) B0N1RAC, (c) B0.3N0RAC, and (d) III (N1B0.3RCA60).
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Figure 16. Concrete pavement block preparation process.
Figure 16. Concrete pavement block preparation process.
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Figure 17. Pavement brick compressive strength: (a) stress-strain curves, and (b) stress growth rate compared to the RAC60 group.
Figure 17. Pavement brick compressive strength: (a) stress-strain curves, and (b) stress growth rate compared to the RAC60 group.
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Table 1. Chemical composition list of cement (%).
Table 1. Chemical composition list of cement (%).
Chemical CompositionCaOSiO2Al2O3Fe2O3MgOK2ONa2OTiO2SO3
Cement44.2331.6010.953.852.631.190.720.613.67
Table 2. NCA and RCA physical properties.
Table 2. NCA and RCA physical properties.
Coarse AggregatesPacking Density/(kg·m−3)Crushing Value/%Moisture Content/%24 h Water Absorption/%Clay Content (%)
RCA129523.42.486.181.85
NCA145517.71.783.370.45
Table 3. Physical properties of BF.
Table 3. Physical properties of BF.
Calibre/μmTensile Strength/MPaUltimate Elongation/%Relative Density (g/cm3)Elastic Modulus/MPa
1715503.62.6235.8
Table 4. Mix ratio of single-factor experimental analyses.
Table 4. Mix ratio of single-factor experimental analyses.
Mix LabelNCA
(kg)
RCA
(kg)
FA
(kg)
Cement
(kg)
BF
(kg)
NC
(kg)
Water
(kg)
PCA
(kg)
Additional
Water (kg)
NAC730.240.001095.36380.000.000.00144.404.350.00
RCA30511.17219.071095.36380.000.000.00144.404.3513.53
RCA45401.63328.611095.36380.000.000.00144.404.3520.30
RCA60292.10438.141095.36380.000.000.00144.404.3527.07
N1RAC30511.17219.071095.36376.200.003.80144.404.3513.53
N2RAC30511.17219.071095.36372.400.007.60144.404.3513.53
N3RAC30511.17219.071095.36368.600.0011.40144.404.3513.53
B0.1RAC30511.17219.071095.36380.002.620.00144.404.3513.53
B0.2RAC30511.17219.071095.36380.005.240.00144.404.3513.53
B0.3RAC30511.17219.071095.36380.007.860.00144.404.3513.53
N1RAC45401.63328.611095.36376.200.003.80144.404.3520.30
N2RAC45401.63328.611095.36372.400.007.60144.404.3520.30
N3RAC45401.63328.611095.36368.600.0011.40144.404.3520.30
B0.1RAC45401.63328.611095.36380.002.620.00144.404.3520.30
B0.2RAC45401.63328.611095.36380.005.240.00144.404.3520.30
B0.3RAC45401.63328.611095.36380.007.860.00144.404.3520.30
N1RAC60292.10438.141095.36376.200.003.80144.404.3527.07
N2RAC60292.10438.141095.36372.400.007.60144.404.3527.07
N3RAC60292.10438.141095.36368.600.0011.40144.404.3527.07
B0.1RAC60292.10438.141095.36380.002.620.00144.404.3527.07
B0.2RAC60292.10438.141095.36380.005.240.00144.404.3527.07
B0.3RAC60292.10438.141095.36380.007.860.00144.404.3527.07
Note: RCA30 denotes concrete with an RCA replacement ratio of 30%; N1RAC30 refers to concrete with an NC dosage of 1% and an RCA replacement ratio of 30%; B0.1RAC30 signifies concrete with a BF content of 0.1% and an RCA replacement ratio of 30%. PCA is a polycarboxylic acid water-reducing agent, and the dosage is 1.14% of cementitious material.
Table 5. Mix ratio of the RSM test.
Table 5. Mix ratio of the RSM test.
Mix LabelBF
(%)
NC
(%)
RCA
(%)
NCA
(kg)
RCA
(kg)
FA
(kg)
Cement
(kg)
BF
(kg)
NC
(kg)
Water
(kg)
PCA
(kg)
Additional
Water (kg)
Z-10.1145401.63328.611095.36376.202.623.80144.404.3520.30
Z-20.3145401.63328.611095.36376.207.863.80144.404.3520.30
Z-30.1345401.63328.611095.36368.602.6211.40144.404.3520.30
Z-40.3345401.63328.611095.36368.607.8611.40144.404.3520.30
Z-50.1230511.17219.071095.36372.402.627.60144.404.3513.53
Z-60.3230511.17219.071095.36372.407.867.60144.404.3513.53
Z-70.1260292.10438.141095.36372.402.627.60144.404.3527.07
Z-80.3260292.10438.141095.36372.407.867.60144.404.3527.07
Z-90.2130511.17219.071095.36376.205.243.80144.404.3513.53
Z-100.2330511.17219.071095.36368.605.2411.40144.404.3513.53
Z-110.2160292.10438.141095.36376.205.243.80144.404.3527.07
Z-120.2360292.10438.141095.36368.605.2411.40144.404.3527.07
Z-130.2245401.63328.611095.36372.405.247.60144.404.3520.30
Note: Z-13 was set as the central experimental group and repeated three times.
Table 6. Experimental design and results.
Table 6. Experimental design and results.
Mix LabelFC7/MPaFC28/MPa
Measured ValueProjected ValueMeasured ValueProjected Value
Z-137.5437.5847.247.08
Z-240.2840.1553.0752.69
Z-335.8235.9545.946.28
Z-436.2336.1946.846.92
Z-540.2340.0351.0551.18
Z-641.7541.7254.654.98
Z-735.6236.6550.3749.98
Z-836.5636.7652.5552.42
Z-942.2542.4153.853.79
Z-1040.3340.4050.650.09
Z-1138.5938.5250.9751.48
Z-1235.1234.9648.648.61
Z-1336.536.544746.37
Z-1336.2436.5445.946.37
Z-1336.8936.5446.246.37
Table 7. Establishment of the response surface equation.
Table 7. Establishment of the response surface equation.
Response Surface Equation Model Y = β 0 + i = 1 n β i x i + i = 1 n β i i x i 2 + i = 1 n β i j j = 1 n x i x j + ε (1)
Compressive strength response surface equation (7d) Y 1 = 36.54 + 0.70 A     1.40 B     2.33 C     0.58 A B     0.15 A C     0.39 B C + 0.20 A 2 + 0.73 B 2 + 1.80 C 2 (2)
Compressive strength response surface equation (28d) Y 2 = 46.37 + 1.56 A     1.64 B     0.95 C     1.24 A B     0.34 A C + 0.21 B C + 1.51 A 2 + 0.36 B 2 + 4.26 C 2 (3)
Note: Y is the response value; β0 is the constant term; xi and xj are the independent variables; βi is the primary term coefficient; βii is the secondary term coefficient; βij is the interaction term coefficient; ε is the random error; n is the number of variables. A: BF content (%), B: NC dosage (%), and C: RCA replacement ratio (%).
Table 8. Analysis of variance of compressive strength regression model (7d|28d).
Table 8. Analysis of variance of compressive strength regression model (7d|28d).
SourceSum of SquaresDfMean SquareF-Valuep-ValueSignificance
Y78.38|127.409|98.71|14.16108.93|38.61<0.0001|0.0004Significant|Significant
A3.93|19.531/13.93|19.5349.21|53.270.0009|0.0008Significant|Significant
B15.57|21.581/115.57|21.58194.73|58.87<0.0001|0.0006Significant|Significant
C43.57|7.141/143.57|7.14544.99|19.49<0.0001|0.0069Significant|Significant
AB1.36|6.181/11.36|6.1816.98|16.840.0092|0.0093Significant|Significant
AC0.08|0.46921/10.08|0.46921.05|1.280.35|0.3092Not significant|Not significant
BC0.60|0.17221/10.60|0.17227.51|0.470.04|0.5236Significant|Not Significant
0.14|8.451|10.14|8.451.77|23.050.24|0.0049Not significant|Significant
1.96|0.48631|11.96|0.486324.50|1.330.004|0.3015Significant|Not Significant
11.97|67.101|111.97|67.10149.77|183.02<0.0001|<0.0001Significant|Significant
Residual0.40|1.835|50.14|0.3666
Lack of fit0.19|1.193|31.96|0.39550.58|1.220.24|0.4793Not significant|Not significant
Cor total78.78|129.2314|14
Table 9. Model credibility test and analysis (7d|28d).
Table 9. Model credibility test and analysis (7d|28d).
Std.Dev.Mean ValueC.V./%Adequate PrecisionR2Adjusted R a 2 Predicted R2
0.28|0.6138.00|49.640.74|1.2232.30|17.620.995|0.9860.986|0.9600.956|0.842
R 2 = 1 S t / ( S n + S t ) R a 2 = ( S t / D r ) / ( S n + S t D n + D t )
Note: R2 is the coefficient of determination; R a 2 is the adjusted coefficient of determination; St is the sum of squares of the residuals; Sn is the sum of squares of the regressions; Dt is the residuals degrees of freedom; Dn is the regression degrees of freedom; Std.Dev. is the standard deviation; C.V. is the coefficient of variation.
Table 10. Model verification based on the literature.
Table 10. Model verification based on the literature.
Literature BF(%)NC(%)RCA(%)Test Value (MPa)Predicted Value (MPa)Difference Ratio (%)
Lian et al. [39]0.21054.5352.593.6
Long et al. [59]0.32.55044.6245.832.7
Diao et al. [60]0.22053.0651.572.8
Khan et al. [61]0.12.5049.8850.952.1
Zheng et al. [20]0.203052.1553.793.1
Table 11. Optimisation design objectives of BF-NC-RAC.
Table 11. Optimisation design objectives of BF-NC-RAC.
Parameters to Be OptimisedRange of ValuesTarget Value
Minimum ValueMaximum Value
A/%0.10.30.1~0.3
B/%131~3
C/%306030, 45, 60
Y/MPa45.954.6Maximum value
Table 12. Optimal design results for responsive surface design.
Table 12. Optimal design results for responsive surface design.
Serial
Number
BF/%NC/%RCA/%Projected
Value/MPa
Experimental
Value/MPa
E/%Thirsty Function
Values
I0.313058.4556.812.81
II0.314552.6951.162.90.780
III0.316055.4653.573.41
Note: E is the absolute value of the relative error.
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MDPI and ACS Style

Zhang, B.; Zhang, X.; Wang, M.; Zhang, D.; Wang, D.; Ma, X. Improvement in the Recycled Aggregate Replacement Ratio in Concrete Pavement Bricks by Incorporating Nano-Calcium Carbonate and Basalt Fibre: Model Experiment Investigation. Buildings 2025, 15, 2070. https://doi.org/10.3390/buildings15122070

AMA Style

Zhang B, Zhang X, Wang M, Zhang D, Wang D, Ma X. Improvement in the Recycled Aggregate Replacement Ratio in Concrete Pavement Bricks by Incorporating Nano-Calcium Carbonate and Basalt Fibre: Model Experiment Investigation. Buildings. 2025; 15(12):2070. https://doi.org/10.3390/buildings15122070

Chicago/Turabian Style

Zhang, Biao, Xueyuan Zhang, Mengyao Wang, Daoming Zhang, Dandan Wang, and Xinwu Ma. 2025. "Improvement in the Recycled Aggregate Replacement Ratio in Concrete Pavement Bricks by Incorporating Nano-Calcium Carbonate and Basalt Fibre: Model Experiment Investigation" Buildings 15, no. 12: 2070. https://doi.org/10.3390/buildings15122070

APA Style

Zhang, B., Zhang, X., Wang, M., Zhang, D., Wang, D., & Ma, X. (2025). Improvement in the Recycled Aggregate Replacement Ratio in Concrete Pavement Bricks by Incorporating Nano-Calcium Carbonate and Basalt Fibre: Model Experiment Investigation. Buildings, 15(12), 2070. https://doi.org/10.3390/buildings15122070

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