Temperature-dependent resilient modulus of asphalt-rubber mixtures

Temperature-dependent resilient modulus of asphalt-rubber mixtures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Temperature-dependent resilient modulus of asphalt-rubber mixtures Raphael Lúcio Reis dos Santos, Vinícius Antônio Florentino Camargo, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9440307/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract This study investigates the temperature-dependent resilient modulus of asphalt-rubber mixtures based on resilient-modulus tests performed at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil. Eighteen laboratory-prepared asphalt mixtures were analyzed after anonymization as Mix 1 to Mix 18, comprising conventional, asphalt-rubber, and polymer-modified mixtures. The available experimental information included mixture description, binder type, summarized gradation, and resilient modulus values at 25, 35, and 45°C. To strengthen the engineering interpretation of the results, the analysis combined absolute resilient modulus, modulus-retention ratios, family-level variability, and a logarithmic thermal susceptibility index. The asphalt-rubber mixtures exhibited resilient modulus values ranging from 3938 to 4736 MPa at 25°C and from 523 to 629 MPa at 45°C. Although their family-average modulus was lower than that of the conventional family, direct comparison with the explicit conventional CAP 50/70 control showed that the selected dense asphalt-rubber mixture presented 11.1% higher resilient modulus at 25°C and 34.8% higher resilient modulus at 45°C, despite a lower value at 35°C. At family level, asphalt-rubber and conventional mixtures displayed nearly identical average thermal susceptibility, while the asphalt-rubber family also showed lower between-mixture dispersion. An exploratory internal comparison further suggested that nominal grade C asphalt-rubber mixtures had lower initial stiffness but better high-temperature retention than nominal grade B rubberized mixtures. The results demonstrate that asphalt-rubber mixtures exhibit a technically competitive temperature-dependent resilient modulus response, particularly through favorable high-temperature stiffness retention, supporting their relevance for pavement engineering applications. Asphalt-rubber resilient modulus crumb rubber temperature susceptibility viscoelasticity hot-mix asphalt pavement materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction The incorporation of crumb rubber derived from end-of-life tires into asphalt binders and asphalt mixtures has evolved from a waste-management alternative into a mature pavement-engineering strategy with important mechanical, rheological, environmental, and durability implications. Heitzman [ 1 ] documented the early consolidation of asphalt-rubber practice in the United States, whereas Lo Presti [ 2 ] systematized the technological foundations of recycled tyre rubber modified binders and highlighted the strong influence of production route, storage condition, digestion time, and compatibility between rubber particles and the asphalt phase. Bressi et al. [ 3 ], through a state-of-the-art and statistical review, showed that crumb-rubber modification has become one of the main international pathways for combining pavement performance with circular-economy objectives. In a similar vein, Picado-Santos et al. [ 4 ] argued that asphalt-rubber mixtures should be regarded as a heterogeneous technological family rather than as a single material class, because their behavior depends on whether the wet, dry, terminal-blend, or hybrid route is adopted. More recently, Li et al. [ 5 ], White and Kidd [ 6 ], and Wu et al. [ 7 ] reinforced that the current research frontier is no longer limited to demonstrating that crumb rubber can modify asphalt, but rather to understanding how swelling, degradation, digestion history, and mixture architecture jointly govern field-relevant performance. Beyond its laboratory-scale formulation, asphalt-rubber has become a consolidated pavement technology across multiple climatic and regulatory contexts. In the United States, the wet process evolved from early Arizona practice into broader adoption in states such as California, where rubberized binders have been used in chip seals, open-graded friction courses, gap-graded mixtures, and stress-absorbing interlayers, with long-term monitoring supporting their use for crack mitigation and surface durability [ 1 , 8 , 9 ]. In Europe, asphalt-rubber has also been used since the 1980s, with particular emphasis on Portugal, Spain, Italy, the Czech Republic, and Sweden. In Portugal, rubberized asphalt mixtures have been employed since the late 1990s, whereas in Sweden the technology has been applied in road sections near urban centers with emphasis on noise reduction [ 2 , 10 , 11 ]. South Africa and Australia, in turn, developed distinct implementation cultures according to local climate, logistics, and surfacing strategy, combining modified-binder practice with performance-oriented applications [ 2 ]. This international diffusion is relevant because it indicates that asphalt-rubber should be interpreted not as a niche material, but as a family of engineering solutions adapted to different performance targets, including crack control, rutting mitigation, noise reduction, and durability enhancement. Within this broader context, resilient modulus remains one of the most important descriptors of asphalt-mixture response under repeated traffic loading. Bahia and Davies [ 12 ] showed that crumb-rubber modification alters performance-related rheological properties of asphalt binders, thereby affecting how stiffness and recoverable deformation are expressed at mixture level. Lee et al. [ 13 ] further demonstrated that crumb rubber changes the performance properties of rubberized binders used in hot-mix asphalt pavements, while Xiao and Amirkhanian [ 14 ] showed that the resilient modulus of rubberized asphalt concrete is strongly dependent on mixture composition. Noura et al. [ 15 ] confirmed that the resilient modulus of rubberized stone mastic asphalt is highly sensitive to process route and truck-tire-rubber dosage, whereas White and Kidd [ 6 ] showed that even low-dosage crumb-rubber modification can substantially affect stiffness, deformation resistance, and fatigue-related behavior. Taken together, these studies indicate that resilient modulus should not be treated as a fixed intrinsic constant, but rather as a temperature-dependent response shaped by modifier technology, binder interaction, aggregate skeleton, and internal mixture structure. For asphalt-rubber mixtures, however, resilient modulus cannot be interpreted through the simplistic assumption that higher stiffness always implies better engineering performance. Abdelrahman and Carpenter [ 16 ] described the interaction between asphalt cement and crumb rubber as a complex physico-chemical process in which the rubber absorbs lighter asphalt fractions and alters the internal balance between viscosity and elasticity. Jeong et al. [ 17 ] showed that interaction effects in crumb-rubber-modified binders are substantial, while Dong et al. [ 18 ] demonstrated that rubber swelling in asphalt affects both the structure and the properties of the system. Kök and Çolak [ 19 ] also observed that crumb-rubber and SBS-modified binders may develop distinct mixture-level responses even when both are intended to improve performance. In practical terms, this means that a rubberized mixture may not maximize resilient modulus at every test temperature and still remain attractive from the standpoint of permanent deformation, cracking resistance, damping, or durability. The literature further shows that the engineering response of asphalt-rubber begins at binder level with the characteristics of the crumb rubber itself and the conditions under which interaction takes place. Ambient grinding generally produces irregular, rougher, and more porous particles, whereas cryogenic processing tends to generate smoother and more regular particles; this distinction affects interaction intensity during wet-process modification [ 2 , 20 ]. In wet-process systems, the interaction between asphalt and crumb rubber is associated with absorption of lighter fractions, particle swelling, increased viscosity, and the development of a more elastic binder network, all of which may influence mixture-level behavior through thicker binder films and modified stress relaxation [ 2 , 16 , 18 ]. Accordingly, asphalt-rubber should be viewed as a highly modified binder system whose rheological class may help explain part of the variability observed in temperature-dependent mixture response. This non-linear interpretation is consistent with mixture-level studies focused on rutting, deformation, and overall mechanical response. Palit et al. [ 21 ] reported that crumb-rubber-modified asphalt mixtures can be mechanically competitive under laboratory conditions without necessarily exhibiting universal stiffness superiority. Fontes et al. [ 22 ] showed favorable deformation-related performance of asphalt-rubber mixtures, while Moreno et al. [ 23 ] observed that crumb rubber may improve resistance to plastic deformation. Rodríguez-Fernández et al. [ 24 ] demonstrated that the microstructure and mechanical performance of dry-process crumb-rubber asphalt concrete are highly process-sensitive, and Wu et al. [ 7 ] showed that even when high-content crumb-rubber-modified asphalt displays promising binder-level performance, mixture-level validation remains essential. Accordingly, resilient modulus must be interpreted in conjunction with the broader mechanical meaning of the mixture rather than as an isolated ranking parameter. Another important issue concerns the scale at which asphalt-rubber is commonly evaluated. Many published studies rely on carefully controlled laboratory programs with relatively small factorial designs, whereas road agencies and public laboratories often accumulate resilient-modulus results from systematic testing programs that are rarely converted into publication-oriented comparative studies. This gap is significant because practical material adoption depends not only on mechanistic understanding but also on how real laboratory-prepared mixtures compare with conventional and polymer-modified alternatives under consistent internal testing frameworks. Experimental programs conducted in public laboratories therefore offer a valuable bridge between academic experimentation and engineering decision-making, provided that they are interpreted transparently and positioned within the international state of the art. The present study addresses this gap by analyzing resilient-modulus results obtained for 18 laboratory-prepared asphalt mixtures tested at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil. The main objective was to evaluate the temperature-dependent resilient modulus of asphalt-rubber mixtures and benchmark their behavior against conventional and polymer-modified mixtures. A second objective was to position the results within the international literature, emphasizing the importance of temperature-profile interpretation in mixture-level performance assessment. The central hypothesis was that asphalt-rubber mixtures would exhibit a technically competitive temperature-dependent resilient modulus response, even when not associated with the highest absolute modulus at every temperature, thereby reinforcing their relevance for pavement engineering applications under thermally demanding conditions. 2. Materials and methods 2.1 Data source and study design This study is based on resilient-modulus tests performed at the LED of a public road agency in Brazil. The experimental program comprised 18 laboratory-prepared asphalt mixtures, including conventional, asphalt-rubber, and polymer-modified formulations, evaluated at 25, 35, and 45°C. The available experimental information included mixture designation, binder type, summarized gradation, and resilient modulus values at the three test temperatures. To preserve technical anonymity and maintain consistency throughout the manuscript, the mixtures were renumbered as Mix 1 to Mix 18. This anonymization strategy allows the discussion to remain focused on material behavior and comparative performance rather than on original project-specific identification. The resilient-modulus values were preserved exactly as obtained in the laboratory program. The experimental results provide a technically meaningful basis for comparative engineering analysis, supporting a benchmark-oriented framework focused on temperature-dependent mixture response across conventional, asphalt-rubber, and polymer-modified systems. Accordingly, the present study emphasizes comparative interpretation of resilient modulus, stiffness-retention behavior, and thermal susceptibility under a consistent laboratory testing context. The resilient-modulus tests were conducted in accordance with DNIT 135/2018-ME, which prescribes the determination of the resilient modulus of asphalt mixtures by repeated-load indirect tensile diametral compression under controlled temperature conditions. Laboratory-prepared cylindrical specimens complying with the dimensional requirements of the standard were used, with nominal diameter of 101.6 ± 3.8 mm and height between 35 and 70 mm. Before testing, the specimen dimensions were measured with caliper precision as prescribed by the standard, and the specimens were stored under controlled conditions prior to testing. Although DNIT 135/2018-ME generally adopts 25 ± 0.5°C as the reference test temperature, in the present study the same test procedure was applied at 25, 35, and 45°C, with prior thermal conditioning of each specimen for at least 4 h at the target temperature in a temperature-controlled chamber operating within the precision required by the standard. In accordance with the standard, the cyclic load level was defined as a fraction of the mean indirect tensile strength of specimens with the same mixture characteristics, and the applied load during the resilient-modulus test was kept within the range of 5% to 25% of the average diametral tensile strength. During testing, the specimen was vertically aligned and centered between the loading strips, and the displacement response was monitored by LVDT sensors arranged according to the adopted measurement configuration. The loading cycle had a total duration of 1 s, consisting of a 0.1 s load pulse followed by a 0.9 s rest period under constant contact load. The standard also requires a contact load maintained during the test and real-time acquisition of load and displacement signals. Following DNIT 135/2018-ME, each specimen was first subjected to 50 conditioning cycles. Without interrupting the test, three subsequent sets of 15 load cycles were then applied, with 5% increases in load between consecutive sets. The resilient modulus was determined from the load–displacement response in accordance with the calculation procedure established by the standard, and the parameter was evaluated from the last five cycles of each load set. In accordance with the standard procedure, at least three similar specimens were used to determine the average indirect tensile strength required to define the test load, and the resilient-modulus values reported in this study correspond to the mean response adopted for comparative interpretation at mixture level. Because the objective of the present article is to discuss comparative thermomechanical behavior, only the resilient-modulus results are analyzed herein, although the test procedure also allows determination of the instantaneous modulus, total modulus, and Poisson’s ratio. Representative photographs of the experimental phase are shown in Fig. 1 . These images document the test environment, specimen positioning, instrumentation arrangement, and the temperature-controlled chamber. Their placement at the end of this subsection is appropriate because they visually support the experimental context without interrupting the subsequent analytical organization of the study. Rather than pursuing full mechanistic calibration, the study focuses on extracting scientific and engineering value from a consistent resilient-modulus experimental program through a structured comparative framework. This approach is particularly suitable for identifying material competitiveness, interpreting temperature-related response patterns, and strengthening the connection between laboratory testing and publication-oriented performance analysis. 2.2 Mixture families and comparator groups To improve interpretability and align the nomenclature with the revised grouping, the 18 mixtures were organized into three families with sequential numbering: Mix 1 to Mix 4: Conventional mixtures Mix 5 to Mix 9: Asphalt-rubber mixtures Mix 10 to Mix 18: Polymer-modified mixtures This organization is methodologically important because resilient modulus is an emergent property that reflects the combined effect of binder technology, aggregate skeleton, fines content, nominal grading, and internal mixture architecture. As emphasized by Lo Presti [ 2 ], Bressi et al. [ 3 ], Picado-Santos et al. [ 4 ], and Li et al. [ 5 ], modifier technology changes not only binder rheology but also the way mixture stiffness is distributed across temperature and loading time scales. Consequently, comparing all 18 mixtures as though they formed a single homogeneous population would obscure the distinct design logics underlying conventional, asphalt-rubber, and polymer-modified systems. Some heterogeneity remains within each family. The conventional family includes dense asphalt concrete mixtures and one premixed hot asphalt. The asphalt-rubber family includes dense mixtures with different nominal grading categories and different aggregate/filler combinations, while the polymer-modified family includes dense mixtures and one stone mastic asphalt. This internal variability is not a drawback; rather, it reflects the practical diversity of mixture formulations typically encountered in pavement engineering. The family-based organization adopted here therefore supports a more technically meaningful interpretation of comparative trends in resilient modulus and thermal susceptibility. Because the asphalt-rubber family includes mixtures prepared with both AB-8 and AB22 binders, it is useful to position these materials within the Brazilian normative framework. According to DNIT 111/2009 [ 25 ], both are wet-process asphalt-rubber binders, but they are not equivalent in specification terms. In particular, AB22 is defined by a substantially higher Brookfield viscosity at 175°C and a slightly higher minimum elastic recovery than AB-8, while both binder classes share the same penetration range and the same post-RTFOT minimum retained penetration and elastic recovery requirements. These normative differences are relevant to the present study because part of the mixture-level variability observed among the asphalt-rubber mixtures may reflect not only differences in aggregate structure and gradation, but also differences in the rheological class of the binder employed. Selected specification limits for the Brazilian asphalt-rubber binders AB-8 and AB22 are summarized in Table 1 . Table 1 Specification limits for Brazilian asphalt-rubber binders AB-8 and AB22. Property Unit AB-8 AB22 Penetration, 100 g, 5 s, 25°C 0.1 mm 30–70 30–70 Softening point, minimum °C 55 57 Brookfield viscosity at 175°C, 20 rpm, spindle 3 cP 800–2000 2200–2400 Flash point, minimum °C 235 235 Elastic recovery, 25°C, 10 cm, minimum % 50 55 Storage stability, maximum °C 9 9 Mass change after RTFOT, maximum % 1 1 Softening-point variation after RTFOT, maximum °C 10 10 Retained penetration after RTFOT, minimum % 55 55 Retained elastic recovery after RTFOT, minimum % 100 100 Note: Adapted from DNIT 111/2009 [ 25 ]. 2.3 Analytical indicators The analytical framework adopted in this study was designed to capture not only absolute stiffness levels, but also the way each mixture preserved or lost structural response as temperature increased. For this reason, resilient modulus at 25, 35, and 45°C was used as the primary response variable, and its interpretation was complemented by normalized indicators capable of describing stiffness retention and thermal susceptibility. This combined approach is particularly appropriate for asphalt-rubber mixtures, whose engineering behavior cannot be adequately understood through single-temperature stiffness ranking alone. The first two indicators are the modulus-retention ratios at 35 and 45°C, respectively: $$\:{R}_{35}=\:\frac{{MR}_{35}}{{MR}_{25}}$$ 1 $$\:{R}_{45}=\:\frac{{MR}_{45}}{{MR}_{25}}$$ 2 Where \(\:{MR}_{25}\) , \(\:{MR}_{35}\) , and \(\:{MR}_{45}\) ​ are the resilient modulus values measured at 25, 35, and 45°C, respectively. These ratios express the extent to which a mixture retains stiffness as test temperature increases relative to its 25°C condition. The third indicator is the modulus loss between 25 and 45°C, expressed as: $$\:{Loss}_{25-45}\left(\%\right)=\:\left(1-\:\frac{{MR}_{45}}{{MR}_{25}}\right)X\:100$$ 3 This metric provides a direct measure of stiffness decay over the thermal interval investigated and is particularly useful for engineering interpretation because it expresses the magnitude of thermal degradation in percentage terms. The fourth indicator is a logarithmic thermal susceptibility index (TSI), defined as: $$\:TSI=\:\frac{\text{ln}\left({MR}_{25}\right)-\:\text{ln}\left({MR}_{45}\right)}{45-25}$$ 4 A lower TSI indicates lower temperature sensitivity of resilient modulus over the 25–45°C range. Because it is based on logarithmic variation, this index allows mixtures with different initial stiffness levels to be compared on a relative basis. Finally, family-level variability was examined through standard deviation and coefficient of variation. This step is important because a mixture family with lower between-mixture dispersion may represent a more stable mechanical envelope, even when its average modulus is not the highest. In the context of asphalt-rubber, this is especially relevant because formulation sensitivity is a recurrent theme in the literature. In addition to family-level comparisons, two complementary exploratory analyses were carried out. First, the asphalt-rubber family was subdivided according to nominal grading category to investigate whether grade B and grade C mixtures displayed distinct temperature-response trends. Second, a direct benchmark was established between the dense asphalt-rubber Mix 5 and the explicit dense conventional control Mix 1, since this comparison provides the most practically informative reference for engineering interpretation. 2.4 Literature benchmark strategy Interpretation of the experimental results was reinforced through a structured literature benchmark. The review prioritized peer-reviewed studies indexed in widely recognized databases and published in journals with strong relevance to asphalt materials, pavement engineering, and transportation infrastructure. Special attention was given to studies on asphalt-rubber binders and mixtures, resilient modulus or stiffness modulus, temperature susceptibility, rutting, fatigue, moisture damage, wet versus dry process, storage stability, and sustainability implications of crumb-rubber use in pavements. The benchmark was organized into three analytical layers. The first comprised broad state-of-the-art reviews, such as Lo Presti [ 2 ], Bressi et al. [ 3 ], Picado-Santos et al. [ 4 ], Li et al. [ 5 ], Zakerzadeh et al. [ 26 ], and Wu et al. [ 27 ]. These studies established the conceptual background regarding modifier technologies, interaction mechanisms, and current research frontiers. The second layer comprised mixture-level studies focused on resilient modulus, stiffness, rutting, fatigue, and overall mechanical response, such as Palit et al. [ 21 ], Xiao and Amirkhanian [ 14 ], Fontes et al. [ 22 ], Noura et al. [ 15 ], White and Kidd [ 6 ], and Wu et al. [ 7 ]. The third layer comprised sustainability- and field-oriented studies, such as Farina et al. [ 28 ], Wang et al. [ 29 ], Dias et al. [ 30 ], and Sol-Sánchez et al. [ 31 ], which helped interpret why a rubberized mixture with only comparable stiffness may still be attractive from a pavement-engineering standpoint. This layered strategy is important because the present article is neither a pure laboratory-report paper nor a pure review paper. Rather, it is a data-driven comparative study whose scientific contribution depends on combining experimental results with a careful interpretation of the broader literature. 2.5 Scope and robustness of the comparative framework The present study is structured as a comparative performance assessment of laboratory-prepared asphalt mixtures based on a consistent resilient-modulus experimental program. Its analytical strength lies in the integration of absolute modulus values, normalized retention indicators, and family-level benchmarking, allowing a technically grounded interpretation of temperature-dependent response across distinct mixture technologies. This framework is particularly useful for identifying comparative trends, evaluating material competitiveness, and supporting performance-oriented discussion of asphalt-rubber mixtures. While the experimental program is most suitable for comparative interpretation rather than full mechanistic calibration, it provides clear and relevant evidence for mixture-level benchmarking under controlled laboratory conditions. 3. Results 3.1 Composition of the experimental program and first-order stiffness landscape Before discussing temperature susceptibility, it is necessary to frame the experimental program in terms of mixture family, nominal type, and binder technology. Resilient modulus is not an isolated intrinsic property; it emerges from the combined effect of binder type, aggregate skeleton, fines content, and overall mixture architecture. For this reason, Table 2 presents the full mixtures and groups them by family according to the revised numbering adopted in this paper. Table 2 . Mixtures and resilient modulus values grouped by family. Table 2 A. Conventional mixtures (Mix 1 to Mix 4). Mix ID Simplified mixture description Binder Fine aggregate Coarse aggregate Filler MR25 (MPa) MR35 (MPa) MR45 (MPa) Mix 1 Dense asphalt concrete CAP 50/70 Stone chips + stone dust Gneiss Limestone dust 3989 1692 437 Mix 2 Dense asphalt concrete, grade B CAP 50/70 Washed sand Limestone Limestone dust 7060 3428 700 Mix 3 Dense asphalt concrete, grade C CAP 50/70 Washed sand Limestone Limestone dust 5069 3968 847 Mix 4 Premixed hot asphalt, grade D CAP 50/70 Washed sand Limestone Limestone dust 4492 2671 731 Table 2 B. Asphalt-rubber mixtures (Mix 5 to Mix 9). Mix ID Simplified mixture description Binder Fine aggregate Coarse aggregate Filler MR25 (MPa) MR35 (MPa) MR45 (MPa) Mix 5 Dense asphalt concrete Asphalt-rubber AB-22 Washed sand Limestone Limestone dust 4430 1496 589 Mix 6 Dense asphalt concrete, grade B Asphalt-rubber AB-8 Washed sand Arkose Limestone dust 4736 1451 523 Mix 7 Dense asphalt concrete, grade C Asphalt-rubber AB-8 Washed sand Arkose Limestone dust 4380 1478 629 Mix 8 Dense asphalt concrete, grade B Asphalt-rubber AB-8 Hydrated lime CH1 Basalt Hydrated lime CH1 4584 1741 542 Mix 9 Dense asphalt concrete, grade C Asphalt-rubber AB-8 Hydrated lime CH1 Basalt Hydrated lime CH1 3938 1344 605 Table 2 C. Polymer-modified mixtures (Mix 10 to Mix 18). Mix ID Simplified mixture description Binder Fine aggregate Coarse aggregate Filler MR25 (MPa) MR35 (MPa) MR45 (MPa) Mix 10 Dense asphalt concrete, grade C CAP Flex Pave 60/85 Stone chips + stone dust Granite gneiss Limestone dust 4122 2026 510 Mix 11 Stone mastic asphalt, grade C CAP Flex Pave 60/85 Stone chips + stone dust Gneiss Limestone dust 3546 1908 602 Mix 12 Dense asphalt concrete, grade C Polymer-modified asphalt Artificial sand + limestone dust Limestone Limestone dust 4453 2686 983 Mix 13 Dense asphalt concrete, grade B Polymer-modified asphalt Artificial sand + limestone dust Limestone Limestone dust 3580 1185 1185 Mix 14 Dense asphalt concrete, grade C Polymer-modified asphalt Artificial sand + limestone dust Limestone Limestone dust 3816 1856 811 Mix 15 Dense asphalt concrete, grade C Polymer-modified asphalt Artificial sand + limestone dust Limestone Limestone dust 4457 3011 983 Mix 16 Dense asphalt concrete, grade C Polymer-modified asphalt Artificial sand Limestone Limestone dust 4814 4240 811 Mix 17 Dense asphalt concrete, grade B CAP 50/70 Industrial sand (gneiss) Limestone Gneiss dust 4764 1442 678 Mix 18 Dense asphalt concrete, grade C CAP 50/70 Industrial sand (gneiss) Limestone Gneiss dust 4213 1486 585 A first inspection of Table 2 already reveals two important features. First, the asphalt-rubber family occupies an intermediate stiffness range within the overall experimental program: it is clearly competitive with many polymer-modified mixtures at 25°C, although it does not exceed the highest-stiffness conventional limestone mixtures represented by Mixes 2 and 3. Second, the asphalt-rubber mixtures appear less dispersed than the conventional family. Their resilient-modulus values remain confined to a comparatively narrower interval, suggesting a more compact family behavior than might be expected from the literature on highly formulation-sensitive rubberized systems. The full temperature-modulus trajectories of all mixtures are presented in Fig. 2 , which helps visualize how family membership and individual formulation influence the decay of resilient modulus with increasing temperature. 3.2 Temperature-normalized response of the asphalt-rubber mixtures Absolute modulus values are informative, but they do not fully explain how the rubberized mixtures respond to thermal loading. For this reason, Table 3 presents the normalized indicators for the five asphalt-rubber mixtures and the four conventional mixtures that serve as the most relevant baseline. Table 3 Temperature-sensitivity indicators for asphalt-rubber and conventional mixtures. Mix ID Family MR25 (MPa) MR35 (MPa) MR45 (MPa) R35 R45 25–45°C loss (%) TSI Mix 1 Conventional 3989 1692 437 0.424 0.110 89.0 0.1106 Mix 2 Conventional 7060 3428 700 0.486 0.099 90.1 0.1156 Mix 3 Conventional 5069 3968 847 0.783 0.167 83.3 0.0895 Mix 4 Conventional 4492 2671 731 0.595 0.163 83.7 0.0908 Mix 5 Asphalt-rubber 4430 1496 589 0.338 0.133 86.7 0.1009 Mix 6 Asphalt-rubber 4736 1451 523 0.306 0.110 89.0 0.1102 Mix 7 Asphalt-rubber 4380 1478 629 0.337 0.144 85.6 0.0970 Mix 8 Asphalt-rubber 4584 1741 542 0.380 0.118 88.2 0.1068 Mix 9 Asphalt-rubber 3938 1344 605 0.341 0.154 84.6 0.0937 Table 3 shows that the asphalt-rubber family does not behave as a single monotonic sequence. Mix 6 has the highest \(\:{MR}_{25}\) among the rubberized mixtures, but it also exhibits one of the highest temperature-susceptibility levels within that family. By contrast, Mix 9 has the lowest \(\:{MR}_{45}\) in the rubberized subset, yet it shows the best \(\:{R}_{45}\) and the lowest TSI among the asphalt-rubber mixtures. Mix 7 also performs favourably in high-temperature retention, with \(\:{R}_{45}=0.144\) , exceeding the explicit conventional control Mix 1 and approaching the better conventional responses. A second relevant observation is that the asphalt-rubber mixtures cluster relatively closely in \(\:{MR}_{45}\:\) ,ranging from 523 to 629 MPa, even though their 25°C values span almost 800 MPa. In engineering terms, this suggests that part of the meaningful differentiation among the rubberized mixtures occurs at intermediate temperature rather than only at the highest condition. In other words, a mixture with high initial stiffness does not necessarily preserve that advantage as temperature rises, which further underscores the value of normalized retention indicators. 3.3 Family-level behavior and variability To determine whether the asphalt-rubber results represent isolated cases or a broader family trend, the data were aggregated by mixture family. The resulting summary statistics are presented in Table 4 . Table 4 Family-level summary statistics for resilient modulus and temperature-response indicators. Family n Mean MR25 (MPa) SD MR25 Mean MR35 (MPa) SD MR35 Mean MR45 (MPa) SD MR45 Mean R35 Mean R45 Mean TSI Conventional 4 5152.5 1346.0 2939.8 986.9 678.8 173.0 0.572 0.135 0.1016 Asphalt-rubber 5 4413.6 300.2 1502.0 145.1 581.6 43.9 0.341 0.132 0.1017 Polymer-modified 9 4196.1 473.1 2204.4 961.3 794.0 252.7 0.518 0.192 0.0847 At family level, the conventional mixtures display the highest mean modulus at all temperatures, largely because Mixes 2 and 3 are substantially stiffer than the rest of the experimental program. Polymer-modified mixtures exhibit the lowest mean thermal susceptibility, which is consistent with the intended role of polymer modification. The asphalt-rubber family occupies an intermediate position in absolute stiffness but an almost identical position to the conventional family in mean TSI. This is one of the central findings of the study: the rubberized mixtures are not markedly more temperature-sensitive than the conventional family, even though their average resilient modulus is lower. Equally important is the issue of dispersion. The asphalt-rubber family shows much lower standard deviation than the conventional family, particularly at 25 and 45°C. In relative terms, the coefficient of variation of the asphalt-rubber family is 6.8% at 25°C, 9.7% at 35°C, and 7.6% at 45°C, whereas the conventional family reaches 26.1%, 33.6%, and 25.5%, respectively. This lower dispersion suggests that, within the experimental program, the asphalt-rubber mixtures behaved more uniformly than the conventional family. From a practical standpoint, this may be relevant for quality control and formulation robustness. These family-level trends are illustrated in Fig. 3 , which presents the family-average modulus values with one standard deviation at the three test temperatures, and in Fig. 4 , which summarizes the normalized modulus-retention ratios. 3.4 Exploratory internal comparison within the asphalt-rubber family Because the asphalt-rubber subset includes both nominal grade B and grade C dense mixtures, an exploratory internal comparison was performed to investigate whether nominal grading category was associated with systematic response differences. Table 5 Exploratory internal comparison within the asphalt-rubber family. Asphalt-rubber subgroup n Mean MR25 (MPa) Mean MR35 (MPa) Mean MR45 (MPa) Mean R35 Mean R45 Mean TSI Grade B (Mixes 6 and 8) 2 4660.0 1596.0 532.5 0.343 0.114 0.108 Grade C (Mixes 5, 7 and 9) 3 4249.3 1439.3 607.7 0.339 0.143 0.097 The subgroup comparison shown in Table 5 reveals an informative and technically coherent pattern within the asphalt-rubber family. The nominal grade B asphalt-rubber mixtures exhibited higher average modulus at 25 and 35°C, whereas the nominal grade C asphalt-rubber mixtures showed better high-temperature retention and lower mean thermal susceptibility. This result suggests that aggregate skeleton and nominal gradation may play an important role in shaping how rubber modification is expressed across the temperature range. In practical terms, the grade C rubberized mixtures appear to provide a more stable high-temperature modulus profile despite their lower initial stiffness. This internal trend reinforces the importance of interpreting asphalt-rubber performance through the full temperature-response trajectory rather than through single-point stiffness ranking alone. 3.5 Direct benchmark against the conventional CAP 50/70 control The most practically relevant one-to-one comparison in the experimental program is the benchmark between the dense asphalt-rubber Mix 5 and the explicit dense conventional CAP 50/70 control (Mix 1). This comparison is summarized in Table 6 . Table 6 Direct benchmark between the dense asphalt-rubber mixture and the conventional CAP 50/70 control. Indicator Mix 1 (Conventional CAP 50/70) Mix 5 (Asphalt-rubber) Relative change of Mix 5 vs Mix 1 MR25 (MPa) 3989 4430 + 11.1% MR35 (MPa) 1692 1496 -11.6% MR45 (MPa) 437 589 + 34.8% R35 0.424 0.338 -20.3% R45 0.110 0.133 + 21.3% TSI 0.1106 0.1009 Lower 25–45°C loss (%) 89.0 86.7 Lower This direct comparison clarifies the engineering meaning of the experimental program more effectively than any family average. The asphalt-rubber mixture is not uniformly superior, because it shows a lower modulus at 35°C and a lower \(\:{R}_{35}\) . However, it is superior at 25°C and especially at 45°C, where it exceeds the conventional control by 34.8% in resilient modulus while also exhibiting better high-temperature retention and lower thermal susceptibility. This pattern is particularly relevant because elevated-temperature stiffness preservation is closely associated with rutting-related structural adequacy in flexible pavements. The direct comparison between Mixes 1 and 5 is illustrated in Fig. 5 . 4. Discussion 4.1 What the temperature-dependent modulus profile reveals about asphalt-rubber The results show that the asphalt-rubber mixtures in the experimental program are neither universally stiffer nor universally weaker than the comparison families. Instead, they display a characteristic response profile in which initial modulus, modulus loss, and high-temperature retention interact in a non-linear manner. This interpretation is strongly aligned with the literature. Lo Presti [ 2 ] argued that crumb-rubber-modified systems are inherently process-dependent because swelling, digestion, and compatibility evolve during production and storage. Picado-Santos et al. [ 4 ] similarly emphasized that comparing crumb-rubber mixtures without careful attention to process route and formulation history is scientifically risky. Li et al. [ 5 ] and Wu et al. [ 27 ] further explained that the dominant interaction mechanism may shift between physical swelling and chemical degradation depending on rubber characteristics, asphalt composition, and processing conditions. From this perspective, the present results are mechanically coherent. The asphalt-rubber mixtures did not achieve the highest family-average modulus, but neither did they exhibit a thermally fragile profile. On the contrary, their mean TSI was virtually identical to that of the conventional family, and their within-family dispersion was much lower. This suggests that the tested asphalt-rubber systems were not merely softer versions of conventional asphalt, but mixtures with a distinct thermomechanical balance. Such a balance is consistent with the view of Abdelrahman and Carpenter [ 16 ], Dong et al. [ 18 ], Jeong et al. [ 17 ], and Xiang et al. [ 32 ], who described rubberized binders as multi-phase systems in which enhanced elasticity, swelling-induced thickening, and altered relaxation kinetics redistribute stiffness across the temperature spectrum. 4.2 Stiffness retention, thermal susceptibility, and non-monotonic superiority One of the most relevant outcomes of this study is that mixture superiority depends on the criterion adopted. If the ranking is based solely on family-average \(\:{MR}_{35}\) , the conventional mixtures appear superior. If the ranking is based on mean TSI, asphalt-rubber and conventional mixtures are essentially equivalent. If the comparison is restricted to the direct dense-graded benchmark, the asphalt-rubber mixture outperforms the conventional control at 25 and 45°C. This non-monotonic superiority is not anomalous; rather, it reflects a well-known characteristic of crumb-rubber systems reported in the literature. Xiao and Amirkhanian [ 14 ] showed that the resilient modulus of rubberized asphalt concrete is strongly dependent on mixture composition and reclaimed material content. Noura et al. [ 15 ] demonstrated that rubberized stone mastic asphalt can present distinctly different stiffness levels depending on process route and dosage. White and Kidd [ 6 ] reported that rubber dosage and digestion time alter stiffness and broader mechanical behavior simultaneously. Wu et al. [ 7 ], working with high-content crumb-rubber-modified asphalt mixtures, concluded that favorable binder-level indicators do not necessarily translate directly into better mixture-level performance. This conclusion is particularly relevant here because it reinforces the methodological lesson of the present study: mixture performance indicators must be interpreted at the mixture scale, not merely inferred from binder modification or from a single modulus value. The direct benchmark between Mix 1 and Mix 5 illustrates this principle clearly. At 35°C, the asphalt-rubber mixture appears less stiff. At 45°C, however, the same mixture becomes clearly superior in resilient modulus and modulus retention. For pavement design and material screening, this pattern may be more meaningful than a modest difference at intermediate temperature, especially in warm climates or under slow-moving and heavy traffic loads. Fontes et al. [ 22 ], Moreno et al. [ 23 ], Shafabakhsh et al. [ 33 ], and Rodríguez-Fernández et al. [ 24 ] all reported that crumb-rubber systems can improve resistance to permanent deformation even when mechanical ranking is not straightforward under every test condition. 4.3 Role of aggregate skeleton, nominal gradation, and mixture architecture The internal variability of the asphalt-rubber family also deserves careful interpretation. The nominal grade B rubberized mixtures exhibited higher average modulus at 25 and 35°C, whereas the nominal grade C rubberized mixtures showed better \(\:{R}_{45}\) and lower TSI. Although the subgroup sizes are small, this result suggests that nominal grading category and mineral skeleton influence how rubber modification manifests at different temperatures. In other words, the performance contribution of rubber cannot be decoupled from the aggregate framework that hosts it. This interpretation is consistent with broader mixture-level research. Palit et al. [ 21 ], Cao [ 34 ], Chavez et al. [ 35 ], and White and Kidd [ 6 ] showed that the mechanical consequences of rubber modification depend not only on the binder itself but also on aggregate arrangement, void system, and the resulting internal stress distribution. Gardziejczyk et al. [ 36 ] and Rodríguez-Fernández et al. [ 24 ] also highlighted that mixture architecture strongly affects the viscoelastic and mechanical expression of rubberized systems. Therefore, when a rubberized mixture exhibits lower modulus at one temperature but better retention at another, the explanation may lie as much in mixture design as in binder chemistry. A second and somewhat unexpected result is the lower dispersion of the asphalt-rubber family relative to the conventional family. This finding may appear counterintuitive because the literature frequently highlights variability in rubberized mixtures. One plausible interpretation is that the tested rubberized formulations were developed within a relatively narrow production window, whereas the conventional family combined dense limestone-based mixtures with markedly different stiffness profiles. Even without replicate-level information, the experimental program therefore suggests that rubberized mixtures may achieve a reasonably stable modulus envelope when the technology is already consolidated. 4.4 Asphalt-rubber versus polymer-modified mixtures The polymer-modified family exhibited the lowest mean TSI and the highest mean \(\:{R}_{45}\) , which is consistent with the established role of polymers in enhancing thermal stability. Kök and Çolak [ 19 ], Lee et al. [ 13 ], Han et al. [ 37 ], and Li et al. [ 5 ] all noted that polymer-modified binders often form more effective high-temperature structural networks than conventional crumb-rubber systems. Nevertheless, the comparison should not be oversimplified. The polymer-modified family in this study is also highly dispersed, especially at 35 and 45°C, and includes distinct mixture types, as well as two records whose binder field indicates CAP 50/70 despite their classification as polymer-modified mixtures. Thus, the polymer-modified family functions here as a relevant performance benchmark, enabling a broader interpretation of how asphalt-rubber mixtures compare with other modifier technologies under the same analytical framework. More importantly, stiffness retention is only one part of the engineering response. Asphalt-rubber remains particularly attractive because of its well-documented benefits in viscoelastic accommodation, cracking resistance, fatigue-related performance, damping potential, and waste-tire reutilization. In this sense, the comparison with polymer-modified mixtures does not diminish the technical merit of asphalt-rubber; instead, it helps position rubberized mixtures within a broader performance landscape in which different modifier technologies optimize different response attributes. 4.5 Implications for pavement design, circularity, and current research frontiers The practical implication of this work is that asphalt-rubber should not be screened out simply because its mean resilient modulus is lower than that of some conventional or polymer-modified mixtures. A more defensible engineering approach is to examine the full temperature-response profile in relation to the intended pavement function. In warm regions, under slow-moving traffic, or where rutting risk is a dominant concern, the strong 45°C performance of the direct asphalt-rubber benchmark becomes particularly relevant. In contexts where cracking, fatigue, and damping are also critical, the broader literature further strengthens the case for rubberized systems. This issue becomes even more important when sustainability is considered. Farina et al. [ 28 ] showed that crumb rubber can contribute to favorable life-cycle outcomes in bituminous mixtures, while Wang et al. [ 29 ] quantified the energy and environmental implications of rubberized asphalt pavements. Khiong et al. [ 38 ] also highlighted the environmental benefits associated with using local crumb rubber in hot-mix asphalt. Sol-Sánchez et al. [ 31 ], in turn, demonstrated the viability of combining crumb-rubber technology with reduced-temperature production strategies. Thus, a rubberized mixture with only comparable stiffness may still be attractive from a broader transportation-materials perspective because it combines structural adequacy with circular-economy benefits. The current research frontier also supports this broader interpretation. White and Kidd [ 6 ] emphasized the role of dosage and digestion time in optimizing low-dosage rubberized asphalt mixtures. Wu et al. [ 7 ] advanced the field by combining laboratory evaluation with field application for high-content crumb-rubber mixtures. Wu et al. [ 27 ] reviewed asphalt-rubber interaction from macroscopic to molecular scales and showed that future progress depends on controlling swelling, degradation, viscosity, and compatibility simultaneously. In that sense, the present study contributes to the frontier not by proposing a new modifier chemistry, but by showing how resilient-modulus results obtained in a structured laboratory program can be interpreted in a way that is directly useful for performance-based benchmarking. 4.6 Scientific contribution and future research directions A central contribution of this study lies in demonstrating that results from a resilient-modulus experimental program can be converted into a scientifically meaningful comparative framework for evaluating asphalt-mixture performance. By integrating absolute modulus values, retention ratios, thermal susceptibility, and family-level variability, the study provides a consistent basis for interpreting the competitive response of asphalt-rubber mixtures relative to conventional and polymer-modified alternatives. This contribution is especially relevant because it connects laboratory testing to publication-oriented performance analysis, offering a practical pathway for extracting scientific value from structured experimental programs. The results also reinforce the importance of temperature-profile interpretation in mixture-level assessment. Rather than relying exclusively on stiffness ranking at a single temperature, the proposed framework captures how mixtures preserve or lose structural adequacy across the thermal interval, which is particularly relevant for performance-oriented discussion of asphalt-rubber systems. In this regard, the study contributes not only a set of comparative findings, but also an analytical approach that can be replicated in future evaluations of laboratory-prepared mixtures. Building on these findings, future investigations can further expand this framework by incorporating full volumetric characterization, rubber dosage and digestion history, loading frequency, wheel-tracking, fatigue, cracking resistance, and binder rheology in a controlled experimental design. Such developments would deepen mechanistic interpretation, while the present study already provides robust comparative evidence of temperature-dependent mixture behavior. 5. Conclusions This study evaluated the temperature-dependent resilient modulus of 18 anonymized laboratory-prepared asphalt mixtures tested at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil, with emphasis on five asphalt-rubber mixtures and comparison against conventional and polymer-modified mixtures. The results confirm that the engineering interpretation of asphalt-rubber cannot be reduced to a one-dimensional ranking based only on absolute modulus at a single temperature. The asphalt-rubber mixtures exhibited resilient modulus values between 3938 and 4736 MPa at 25°C and between 523 and 629 MPa at 45°C, which places them within a technically relevant range for pavement applications. At family level, the asphalt-rubber mixtures showed lower average modulus than the conventional family, but their average thermal susceptibility was practically identical. Therefore, lower mean stiffness did not correspond to greater thermal fragility. The direct benchmark against the explicit dense conventional CAP 50/70 control was especially revealing. The selected dense asphalt-rubber mixture was 11.1% stiffer at 25°C and 34.8% stiffer at 45°C, although it was 11.6% lower at 35°C. It also showed better 45°C retention and lower thermal susceptibility. Accordingly, the most informative way to evaluate asphalt-rubber is through the full temperature-response profile rather than through a single modulus value. A second relevant finding is that the asphalt-rubber family displayed lower between-mixture dispersion than the conventional family in the experimental program. This suggests that, under the laboratory conditions represented in this study, rubberized mixtures may provide a comparatively stable mechanical envelope. The exploratory internal comparison further indicated that nominal grade C asphalt-rubber mixtures, despite lower initial stiffness, may retain more high-temperature modulus than nominal grade B rubberized mixtures. This internal trend further highlights the influence of aggregate skeleton and mixture architecture on the temperature-dependent response of asphalt-rubber systems. From the standpoint of current international research, the present results align well with the broader literature, which increasingly emphasizes mixture-level validation, temperature-profile interpretation, and control of asphalt-rubber interaction as key elements in the advancement of rubberized asphalt technology. In this sense, the study contributes by demonstrating that results from a structured resilient-modulus experimental program can be transformed into a publication-ready benchmarking framework with clear relevance for pavement design practice and sustainable transportation materials research. Building on these findings, future studies can expand the proposed framework by combining resilient modulus with full volumetric characterization, rubber dosage and digestion history, frequency-dependent stiffness, wheel tracking, fatigue, cracking resistance, and binder rheology in a controlled experimental design. Such an approach would further strengthen performance-based recommendations, while the present study already establishes a robust comparative basis for evaluating the temperature-dependent response of asphalt-rubber mixtures. Declarations Authors and Affiliations Federal Center for Technological Education of Minas Gerais (CEFET-MG), Belo Horizonte, MG, 30421-169, Brazil. Raphael Lúcio Reis dos Santos State Secretariats of Infrastructure, Mobility and Partnerships (SEINFRA), Rod. Pref. Américo Renê Gianeti, 4143, Belo Horizonte, MG, 31630-902, Brazil. Vinícius Antônio Florentino Camargo Ministry of Transport (MT), Esplanada dos Ministérios, Bloco R, Brasília, DF, 70044-900, Brazil. George Yun Contributions R.L.R.d.S.: Conceptualization, data collection, data analysis, writing-original draft preparation, writing-review and editing, project administration. V.A.F.C.: Conceptualization, writing-review and editing. G.Y.: data collection, data analysis. Corresponding author Correspondence to Raphael Lúcio Reis dos Santos ( [email protected] ) Ethics declarations Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Competing interests The authors declare no competing interests. Funding No funds or other support were received for the preparation of this manuscript. References Heitzman MA. State of the practice: Design and construction of asphalt paving materials with crumb-rubber modifier. Final report. Federal Highway Administration, Washington,DC (United States). Office of …. Presti D, Lo. Recycled tyre rubber modified bitumens for road asphalt mixtures: A literature review. Constr Build Mater. 2013;49:863–81. Bressi S, Fiorentini N, Huang J, Losa M. Crumb rubber modifier in road asphalt pavements: State of the art and statistics. Coatings. 2019;9(6):384. Picado-Santos LG, Capitão SD, Neves JMC. Crumb rubber asphalt mixtures: A literature review. Constr Build Mater. 2020;247:118577. 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Palit SK, Reddy KS, Pandey BB. Laboratory evaluation of crumb rubber modified asphalt mixes. J Mater Civ Eng. 2004;16(1):45–53. Fontes LPTL, Triches G, Pais JC, Pereira PAA. Evaluating permanent deformation in asphalt rubber mixtures. Constr Build Mater. 2010;24(7):1193–200. Moreno F, Sol M, Martín J, Pérez M, Rubio MC. The effect of crumb rubber modifier on the resistance of asphalt mixes to plastic deformation. Mater Des. 2013;47:274–80. Rodríguez-Fernández I, Cavalli MC, Poulikakos L, Bueno M. Recyclability of asphalt mixtures with crumb rubber incorporated by dry process: A laboratory investigation. Materials. 2020;13(12):2870. Transportes DN, de I de. DNIT 111: 2009-EM: Pavimentação flexível-Cimento asfáltico modificado por borracha de pneus inservíveis pelo processo via úmida, do tipo Terminal Blending-Especificação de material. 2009. Zakerzadeh M, Shahbodagh B, Ng J, Khalili N. The use of waste tyre rubber in Stone Mastic Asphalt mixtures: A critical review. Constr Build Mater. 2024;418:135420. Wu M, Li M, Yin L, You Z. Asphalt-rubber interaction in crumb rubber modified asphalt: a review. J Clean Prod. 2026;546:147766. Farina A, Zanetti MC, Santagata E, Blengini GA. Life cycle assessment applied to bituminous mixtures containing recycled materials: Crumb rubber and reclaimed asphalt pavement. Resour Conserv Recycl. 2017;117:204–12. Wang T, Xiao F, Zhu X, Huang B, Wang J, Amirkhanian S. Energy consumption and environmental impact of rubberized asphalt pavement. J Clean Prod. 2018;180:139–58. Dias JLF, Picado-Santos LG, Capitão SD. Mechanical performance of dry process fine crumb rubber asphalt mixtures placed on the Portuguese road network. Constr Build Mater. 2014;73:247–54. Sol-Sánchez M, del Barco Carrión AJ, Hidalgo-Arroyo A, Moreno-Navarro F, Saiz L. del Carmen Rubio-Gámez M. Viability of producing sustainable asphalt mixtures with crumb rubber bitumen at reduced temperatures. Constr Build Mater. 2020;265:120154. Xiang L, Cheng J, Que G. Microstructure and performance of crumb rubber modified asphalt. Constr Build Mater. 2009;23(12):3586–90. Shafabakhsh GH, Sadeghnejad M, Sajed Y. Case study of rutting performance of HMA modified with waste rubber powder. Case Stud Constr Mater. 2014;1:69–76. Cao W. Study on properties of recycled tire rubber modified asphalt mixtures using dry process. Constr Build Mater. 2007;21(5):1011–5. Chavez F, Marcobal J, Gallego J. Laboratory evaluation of the mechanical properties of asphalt mixtures with rubber incorporated by the wet, dry, and semi-wet process. Constr Build Mater. 2019;205:164–74. Gardziejczyk W, Plewa A, Pakholak R. Effect of addition of rubber granulate and type of modified binder on the viscoelastic properties of stone mastic asphalt reducing tire/road noise (SMA LA). Materials. 2020;13(16):3446. Han L, Zheng M, Wang C. Current status and development of terminal blend tyre rubber modified asphalt. Constr Build Mater. 2016;128:399–409. Khiong LM, Safiuddin M, Mannan MA, Resdiansyah. Material properties and environmental benefits of hot-mix asphalt mixes including local crumb rubber obtained from scrap tires. Environments. 2021;8(6):47. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2026 Editor assigned by journal 24 Apr, 2026 Submission checks completed at journal 24 Apr, 2026 First submitted to journal 16 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9440307","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624442289,"identity":"53998ea5-fd60-4475-95b1-51b19b3dfcc0","order_by":0,"name":"Raphael Lúcio Reis dos 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5.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9440307/v1/76a731abcd46b697e257a5af.png"},{"id":107488440,"identity":"7d59acf1-6fe5-416d-a4b1-156f86bcd4bd","added_by":"auto","created_at":"2026-04-22 02:44:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2253928,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9440307/v1/42ceaa42-160d-40bc-8ce1-8ca57ef28673.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Temperature-dependent resilient modulus of asphalt-rubber mixtures","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe incorporation of crumb rubber derived from end-of-life tires into asphalt binders and asphalt mixtures has evolved from a waste-management alternative into a mature pavement-engineering strategy with important mechanical, rheological, environmental, and durability implications. Heitzman [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] documented the early consolidation of asphalt-rubber practice in the United States, whereas Lo Presti [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] systematized the technological foundations of recycled tyre rubber modified binders and highlighted the strong influence of production route, storage condition, digestion time, and compatibility between rubber particles and the asphalt phase. Bressi et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], through a state-of-the-art and statistical review, showed that crumb-rubber modification has become one of the main international pathways for combining pavement performance with circular-economy objectives. In a similar vein, Picado-Santos et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] argued that asphalt-rubber mixtures should be regarded as a heterogeneous technological family rather than as a single material class, because their behavior depends on whether the wet, dry, terminal-blend, or hybrid route is adopted. More recently, Li et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], and Wu et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] reinforced that the current research frontier is no longer limited to demonstrating that crumb rubber can modify asphalt, but rather to understanding how swelling, degradation, digestion history, and mixture architecture jointly govern field-relevant performance.\u003c/p\u003e \u003cp\u003eBeyond its laboratory-scale formulation, asphalt-rubber has become a consolidated pavement technology across multiple climatic and regulatory contexts. In the United States, the wet process evolved from early Arizona practice into broader adoption in states such as California, where rubberized binders have been used in chip seals, open-graded friction courses, gap-graded mixtures, and stress-absorbing interlayers, with long-term monitoring supporting their use for crack mitigation and surface durability [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. In Europe, asphalt-rubber has also been used since the 1980s, with particular emphasis on Portugal, Spain, Italy, the Czech Republic, and Sweden. In Portugal, rubberized asphalt mixtures have been employed since the late 1990s, whereas in Sweden the technology has been applied in road sections near urban centers with emphasis on noise reduction [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. South Africa and Australia, in turn, developed distinct implementation cultures according to local climate, logistics, and surfacing strategy, combining modified-binder practice with performance-oriented applications [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. This international diffusion is relevant because it indicates that asphalt-rubber should be interpreted not as a niche material, but as a family of engineering solutions adapted to different performance targets, including crack control, rutting mitigation, noise reduction, and durability enhancement.\u003c/p\u003e \u003cp\u003eWithin this broader context, resilient modulus remains one of the most important descriptors of asphalt-mixture response under repeated traffic loading. Bahia and Davies [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] showed that crumb-rubber modification alters performance-related rheological properties of asphalt binders, thereby affecting how stiffness and recoverable deformation are expressed at mixture level. Lee et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] further demonstrated that crumb rubber changes the performance properties of rubberized binders used in hot-mix asphalt pavements, while Xiao and Amirkhanian [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] showed that the resilient modulus of rubberized asphalt concrete is strongly dependent on mixture composition. Noura et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] confirmed that the resilient modulus of rubberized stone mastic asphalt is highly sensitive to process route and truck-tire-rubber dosage, whereas White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] showed that even low-dosage crumb-rubber modification can substantially affect stiffness, deformation resistance, and fatigue-related behavior. Taken together, these studies indicate that resilient modulus should not be treated as a fixed intrinsic constant, but rather as a temperature-dependent response shaped by modifier technology, binder interaction, aggregate skeleton, and internal mixture structure.\u003c/p\u003e \u003cp\u003eFor asphalt-rubber mixtures, however, resilient modulus cannot be interpreted through the simplistic assumption that higher stiffness always implies better engineering performance. Abdelrahman and Carpenter [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] described the interaction between asphalt cement and crumb rubber as a complex physico-chemical process in which the rubber absorbs lighter asphalt fractions and alters the internal balance between viscosity and elasticity. Jeong et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] showed that interaction effects in crumb-rubber-modified binders are substantial, while Dong et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] demonstrated that rubber swelling in asphalt affects both the structure and the properties of the system. K\u0026ouml;k and \u0026Ccedil;olak [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] also observed that crumb-rubber and SBS-modified binders may develop distinct mixture-level responses even when both are intended to improve performance. In practical terms, this means that a rubberized mixture may not maximize resilient modulus at every test temperature and still remain attractive from the standpoint of permanent deformation, cracking resistance, damping, or durability.\u003c/p\u003e \u003cp\u003eThe literature further shows that the engineering response of asphalt-rubber begins at binder level with the characteristics of the crumb rubber itself and the conditions under which interaction takes place. Ambient grinding generally produces irregular, rougher, and more porous particles, whereas cryogenic processing tends to generate smoother and more regular particles; this distinction affects interaction intensity during wet-process modification [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In wet-process systems, the interaction between asphalt and crumb rubber is associated with absorption of lighter fractions, particle swelling, increased viscosity, and the development of a more elastic binder network, all of which may influence mixture-level behavior through thicker binder films and modified stress relaxation [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Accordingly, asphalt-rubber should be viewed as a highly modified binder system whose rheological class may help explain part of the variability observed in temperature-dependent mixture response.\u003c/p\u003e \u003cp\u003eThis non-linear interpretation is consistent with mixture-level studies focused on rutting, deformation, and overall mechanical response. Palit et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] reported that crumb-rubber-modified asphalt mixtures can be mechanically competitive under laboratory conditions without necessarily exhibiting universal stiffness superiority. Fontes et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] showed favorable deformation-related performance of asphalt-rubber mixtures, while Moreno et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] observed that crumb rubber may improve resistance to plastic deformation. Rodr\u0026iacute;guez-Fern\u0026aacute;ndez et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] demonstrated that the microstructure and mechanical performance of dry-process crumb-rubber asphalt concrete are highly process-sensitive, and Wu et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] showed that even when high-content crumb-rubber-modified asphalt displays promising binder-level performance, mixture-level validation remains essential. Accordingly, resilient modulus must be interpreted in conjunction with the broader mechanical meaning of the mixture rather than as an isolated ranking parameter.\u003c/p\u003e \u003cp\u003eAnother important issue concerns the scale at which asphalt-rubber is commonly evaluated. Many published studies rely on carefully controlled laboratory programs with relatively small factorial designs, whereas road agencies and public laboratories often accumulate resilient-modulus results from systematic testing programs that are rarely converted into publication-oriented comparative studies. This gap is significant because practical material adoption depends not only on mechanistic understanding but also on how real laboratory-prepared mixtures compare with conventional and polymer-modified alternatives under consistent internal testing frameworks. Experimental programs conducted in public laboratories therefore offer a valuable bridge between academic experimentation and engineering decision-making, provided that they are interpreted transparently and positioned within the international state of the art.\u003c/p\u003e \u003cp\u003eThe present study addresses this gap by analyzing resilient-modulus results obtained for 18 laboratory-prepared asphalt mixtures tested at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil. The main objective was to evaluate the temperature-dependent resilient modulus of asphalt-rubber mixtures and benchmark their behavior against conventional and polymer-modified mixtures. A second objective was to position the results within the international literature, emphasizing the importance of temperature-profile interpretation in mixture-level performance assessment. The central hypothesis was that asphalt-rubber mixtures would exhibit a technically competitive temperature-dependent resilient modulus response, even when not associated with the highest absolute modulus at every temperature, thereby reinforcing their relevance for pavement engineering applications under thermally demanding conditions.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Data source and study design\u003c/h2\u003e \u003cp\u003eThis study is based on resilient-modulus tests performed at the LED of a public road agency in Brazil. The experimental program comprised 18 laboratory-prepared asphalt mixtures, including conventional, asphalt-rubber, and polymer-modified formulations, evaluated at 25, 35, and 45\u0026deg;C. The available experimental information included mixture designation, binder type, summarized gradation, and resilient modulus values at the three test temperatures.\u003c/p\u003e \u003cp\u003eTo preserve technical anonymity and maintain consistency throughout the manuscript, the mixtures were renumbered as Mix 1 to Mix 18. This anonymization strategy allows the discussion to remain focused on material behavior and comparative performance rather than on original project-specific identification. The resilient-modulus values were preserved exactly as obtained in the laboratory program.\u003c/p\u003e \u003cp\u003eThe experimental results provide a technically meaningful basis for comparative engineering analysis, supporting a benchmark-oriented framework focused on temperature-dependent mixture response across conventional, asphalt-rubber, and polymer-modified systems. Accordingly, the present study emphasizes comparative interpretation of resilient modulus, stiffness-retention behavior, and thermal susceptibility under a consistent laboratory testing context.\u003c/p\u003e \u003cp\u003eThe resilient-modulus tests were conducted in accordance with DNIT 135/2018-ME, which prescribes the determination of the resilient modulus of asphalt mixtures by repeated-load indirect tensile diametral compression under controlled temperature conditions. Laboratory-prepared cylindrical specimens complying with the dimensional requirements of the standard were used, with nominal diameter of 101.6\u0026thinsp;\u0026plusmn;\u0026thinsp;3.8 mm and height between 35 and 70 mm. Before testing, the specimen dimensions were measured with caliper precision as prescribed by the standard, and the specimens were stored under controlled conditions prior to testing. Although DNIT 135/2018-ME generally adopts 25\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u0026deg;C as the reference test temperature, in the present study the same test procedure was applied at 25, 35, and 45\u0026deg;C, with prior thermal conditioning of each specimen for at least 4 h at the target temperature in a temperature-controlled chamber operating within the precision required by the standard.\u003c/p\u003e \u003cp\u003eIn accordance with the standard, the cyclic load level was defined as a fraction of the mean indirect tensile strength of specimens with the same mixture characteristics, and the applied load during the resilient-modulus test was kept within the range of 5% to 25% of the average diametral tensile strength. During testing, the specimen was vertically aligned and centered between the loading strips, and the displacement response was monitored by LVDT sensors arranged according to the adopted measurement configuration. The loading cycle had a total duration of 1 s, consisting of a 0.1 s load pulse followed by a 0.9 s rest period under constant contact load. The standard also requires a contact load maintained during the test and real-time acquisition of load and displacement signals.\u003c/p\u003e \u003cp\u003eFollowing DNIT 135/2018-ME, each specimen was first subjected to 50 conditioning cycles. Without interrupting the test, three subsequent sets of 15 load cycles were then applied, with 5% increases in load between consecutive sets. The resilient modulus was determined from the load\u0026ndash;displacement response in accordance with the calculation procedure established by the standard, and the parameter was evaluated from the last five cycles of each load set. In accordance with the standard procedure, at least three similar specimens were used to determine the average indirect tensile strength required to define the test load, and the resilient-modulus values reported in this study correspond to the mean response adopted for comparative interpretation at mixture level. Because the objective of the present article is to discuss comparative thermomechanical behavior, only the resilient-modulus results are analyzed herein, although the test procedure also allows determination of the instantaneous modulus, total modulus, and Poisson\u0026rsquo;s ratio.\u003c/p\u003e \u003cp\u003eRepresentative photographs of the experimental phase are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These images document the test environment, specimen positioning, instrumentation arrangement, and the temperature-controlled chamber. Their placement at the end of this subsection is appropriate because they visually support the experimental context without interrupting the subsequent analytical organization of the study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRather than pursuing full mechanistic calibration, the study focuses on extracting scientific and engineering value from a consistent resilient-modulus experimental program through a structured comparative framework. This approach is particularly suitable for identifying material competitiveness, interpreting temperature-related response patterns, and strengthening the connection between laboratory testing and publication-oriented performance analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Mixture families and comparator groups\u003c/h2\u003e \u003cp\u003eTo improve interpretability and align the nomenclature with the revised grouping, the 18 mixtures were organized into three families with sequential numbering:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eMix 1 to Mix 4: Conventional mixtures\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMix 5 to Mix 9: Asphalt-rubber mixtures\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMix 10 to Mix 18: Polymer-modified mixtures\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis organization is methodologically important because resilient modulus is an emergent property that reflects the combined effect of binder technology, aggregate skeleton, fines content, nominal grading, and internal mixture architecture. As emphasized by Lo Presti [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], Bressi et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], Picado-Santos et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and Li et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], modifier technology changes not only binder rheology but also the way mixture stiffness is distributed across temperature and loading time scales. Consequently, comparing all 18 mixtures as though they formed a single homogeneous population would obscure the distinct design logics underlying conventional, asphalt-rubber, and polymer-modified systems.\u003c/p\u003e \u003cp\u003eSome heterogeneity remains within each family. The conventional family includes dense asphalt concrete mixtures and one premixed hot asphalt. The asphalt-rubber family includes dense mixtures with different nominal grading categories and different aggregate/filler combinations, while the polymer-modified family includes dense mixtures and one stone mastic asphalt. This internal variability is not a drawback; rather, it reflects the practical diversity of mixture formulations typically encountered in pavement engineering. The family-based organization adopted here therefore supports a more technically meaningful interpretation of comparative trends in resilient modulus and thermal susceptibility.\u003c/p\u003e \u003cp\u003eBecause the asphalt-rubber family includes mixtures prepared with both AB-8 and AB22 binders, it is useful to position these materials within the Brazilian normative framework. According to DNIT 111/2009 [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], both are wet-process asphalt-rubber binders, but they are not equivalent in specification terms. In particular, AB22 is defined by a substantially higher Brookfield viscosity at 175\u0026deg;C and a slightly higher minimum elastic recovery than AB-8, while both binder classes share the same penetration range and the same post-RTFOT minimum retained penetration and elastic recovery requirements. These normative differences are relevant to the present study because part of the mixture-level variability observed among the asphalt-rubber mixtures may reflect not only differences in aggregate structure and gradation, but also differences in the rheological class of the binder employed. Selected specification limits for the Brazilian asphalt-rubber binders AB-8 and AB22 are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpecification limits for Brazilian asphalt-rubber binders AB-8 and AB22.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProperty\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAB-8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAB22\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePenetration, 100 g, 5 s, 25\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30\u0026ndash;70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u0026ndash;70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoftening point, minimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e57\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBrookfield viscosity at 175\u0026deg;C, 20 rpm, spindle 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e800\u0026ndash;2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2200\u0026ndash;2400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFlash point, minimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e235\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElastic recovery, 25\u0026deg;C, 10 cm, minimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStorage stability, maximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMass change after RTFOT, maximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoftening-point variation after RTFOT, maximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRetained penetration after RTFOT, minimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRetained elastic recovery after RTFOT, minimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: Adapted from DNIT 111/2009 [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Analytical indicators\u003c/h2\u003e \u003cp\u003eThe analytical framework adopted in this study was designed to capture not only absolute stiffness levels, but also the way each mixture preserved or lost structural response as temperature increased. For this reason, resilient modulus at 25, 35, and 45\u0026deg;C was used as the primary response variable, and its interpretation was complemented by normalized indicators capable of describing stiffness retention and thermal susceptibility. This combined approach is particularly appropriate for asphalt-rubber mixtures, whose engineering behavior cannot be adequately understood through single-temperature stiffness ranking alone.\u003c/p\u003e \u003cp\u003eThe first two indicators are the modulus-retention ratios at 35 and 45\u0026deg;C, respectively:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{R}_{35}=\\:\\frac{{MR}_{35}}{{MR}_{25}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{R}_{45}=\\:\\frac{{MR}_{45}}{{MR}_{25}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{25}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{35}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{45}\\)\u003c/span\u003e\u003c/span\u003e​ are the resilient modulus values measured at 25, 35, and 45\u0026deg;C, respectively. These ratios express the extent to which a mixture retains stiffness as test temperature increases relative to its 25\u0026deg;C condition.\u003c/p\u003e \u003cp\u003eThe third indicator is the modulus loss between 25 and 45\u0026deg;C, expressed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{Loss}_{25-45}\\left(\\%\\right)=\\:\\left(1-\\:\\frac{{MR}_{45}}{{MR}_{25}}\\right)X\\:100$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis metric provides a direct measure of stiffness decay over the thermal interval investigated and is particularly useful for engineering interpretation because it expresses the magnitude of thermal degradation in percentage terms.\u003c/p\u003e \u003cp\u003eThe fourth indicator is a logarithmic thermal susceptibility index (TSI), defined as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:TSI=\\:\\frac{\\text{ln}\\left({MR}_{25}\\right)-\\:\\text{ln}\\left({MR}_{45}\\right)}{45-25}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eA lower TSI indicates lower temperature sensitivity of resilient modulus over the 25\u0026ndash;45\u0026deg;C range. Because it is based on logarithmic variation, this index allows mixtures with different initial stiffness levels to be compared on a relative basis.\u003c/p\u003e \u003cp\u003eFinally, family-level variability was examined through standard deviation and coefficient of variation. This step is important because a mixture family with lower between-mixture dispersion may represent a more stable mechanical envelope, even when its average modulus is not the highest. In the context of asphalt-rubber, this is especially relevant because formulation sensitivity is a recurrent theme in the literature.\u003c/p\u003e \u003cp\u003eIn addition to family-level comparisons, two complementary exploratory analyses were carried out. First, the asphalt-rubber family was subdivided according to nominal grading category to investigate whether grade B and grade C mixtures displayed distinct temperature-response trends. Second, a direct benchmark was established between the dense asphalt-rubber Mix 5 and the explicit dense conventional control Mix 1, since this comparison provides the most practically informative reference for engineering interpretation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Literature benchmark strategy\u003c/h2\u003e \u003cp\u003eInterpretation of the experimental results was reinforced through a structured literature benchmark. The review prioritized peer-reviewed studies indexed in widely recognized databases and published in journals with strong relevance to asphalt materials, pavement engineering, and transportation infrastructure. Special attention was given to studies on asphalt-rubber binders and mixtures, resilient modulus or stiffness modulus, temperature susceptibility, rutting, fatigue, moisture damage, wet versus dry process, storage stability, and sustainability implications of crumb-rubber use in pavements.\u003c/p\u003e \u003cp\u003eThe benchmark was organized into three analytical layers. The first comprised broad state-of-the-art reviews, such as Lo Presti [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], Bressi et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], Picado-Santos et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], Li et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], Zakerzadeh et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], and Wu et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. These studies established the conceptual background regarding modifier technologies, interaction mechanisms, and current research frontiers. The second layer comprised mixture-level studies focused on resilient modulus, stiffness, rutting, fatigue, and overall mechanical response, such as Palit et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], Xiao and Amirkhanian [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], Fontes et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], Noura et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], and Wu et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The third layer comprised sustainability- and field-oriented studies, such as Farina et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], Wang et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], Dias et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], and Sol-S\u0026aacute;nchez et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], which helped interpret why a rubberized mixture with only comparable stiffness may still be attractive from a pavement-engineering standpoint.\u003c/p\u003e \u003cp\u003eThis layered strategy is important because the present article is neither a pure laboratory-report paper nor a pure review paper. Rather, it is a data-driven comparative study whose scientific contribution depends on combining experimental results with a careful interpretation of the broader literature.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Scope and robustness of the comparative framework\u003c/h2\u003e \u003cp\u003eThe present study is structured as a comparative performance assessment of laboratory-prepared asphalt mixtures based on a consistent resilient-modulus experimental program. Its analytical strength lies in the integration of absolute modulus values, normalized retention indicators, and family-level benchmarking, allowing a technically grounded interpretation of temperature-dependent response across distinct mixture technologies. This framework is particularly useful for identifying comparative trends, evaluating material competitiveness, and supporting performance-oriented discussion of asphalt-rubber mixtures. While the experimental program is most suitable for comparative interpretation rather than full mechanistic calibration, it provides clear and relevant evidence for mixture-level benchmarking under controlled laboratory conditions.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Composition of the experimental program and first-order stiffness landscape\u003c/h2\u003e \u003cp\u003eBefore discussing temperature susceptibility, it is necessary to frame the experimental program in terms of mixture family, nominal type, and binder technology. Resilient modulus is not an isolated intrinsic property; it emerges from the combined effect of binder type, aggregate skeleton, fines content, and overall mixture architecture. For this reason, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the full mixtures and groups them by family according to the revised numbering adopted in this paper.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Mixtures and resilient modulus values grouped by family.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eA.\u003c/b\u003e Conventional mixtures (Mix 1 to Mix 4).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSimplified mixture description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBinder\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFine aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCoarse aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFiller\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStone chips\u0026thinsp;+\u0026thinsp;stone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGneiss\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e3428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e3968\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e847\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePremixed hot asphalt, grade D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e2671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e731\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eB.\u003c/b\u003e Asphalt-rubber mixtures (Mix 5 to Mix 9).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSimplified mixture description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBinder\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFine aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCoarse aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFiller\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsphalt-rubber AB-22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e589\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsphalt-rubber AB-8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eArkose\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e523\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsphalt-rubber AB-8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWashed sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eArkose\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1478\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e629\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsphalt-rubber AB-8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHydrated lime CH1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBasalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHydrated lime CH1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1741\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e542\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsphalt-rubber AB-8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHydrated lime CH1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBasalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHydrated lime CH1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e605\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eC.\u003c/b\u003e Polymer-modified mixtures (Mix 10 to Mix 18).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSimplified mixture description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBinder\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFine aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCoarse aggregate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFiller\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP Flex Pave 60/85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStone chips\u0026thinsp;+\u0026thinsp;stone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGranite gneiss\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e2026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e510\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStone mastic asphalt, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP Flex Pave 60/85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStone chips\u0026thinsp;+\u0026thinsp;stone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGneiss\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3546\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1908\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e602\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePolymer-modified asphalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial sand\u0026thinsp;+\u0026thinsp;limestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4453\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e2686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e983\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePolymer-modified asphalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial sand\u0026thinsp;+\u0026thinsp;limestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1185\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1185\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePolymer-modified asphalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial sand\u0026thinsp;+\u0026thinsp;limestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1856\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e811\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePolymer-modified asphalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial sand\u0026thinsp;+\u0026thinsp;limestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e3011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e983\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePolymer-modified asphalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial sand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimestone dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4814\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e4240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e811\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIndustrial sand (gneiss)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGneiss dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4764\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1442\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e678\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDense asphalt concrete, grade C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCAP 50/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIndustrial sand (gneiss)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGneiss dust\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e585\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA first inspection of Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e2\u003c/span\u003e already reveals two important features. First, the asphalt-rubber family occupies an intermediate stiffness range within the overall experimental program: it is clearly competitive with many polymer-modified mixtures at 25\u0026deg;C, although it does not exceed the highest-stiffness conventional limestone mixtures represented by Mixes 2 and 3. Second, the asphalt-rubber mixtures appear less dispersed than the conventional family. Their resilient-modulus values remain confined to a comparatively narrower interval, suggesting a more compact family behavior than might be expected from the literature on highly formulation-sensitive rubberized systems.\u003c/p\u003e \u003cp\u003eThe full temperature-modulus trajectories of all mixtures are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, which helps visualize how family membership and individual formulation influence the decay of resilient modulus with increasing temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Temperature-normalized response of the asphalt-rubber mixtures\u003c/h2\u003e \u003cp\u003eAbsolute modulus values are informative, but they do not fully explain how the rubberized mixtures respond to thermal loading. For this reason, Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the normalized indicators for the five asphalt-rubber mixtures and the four conventional mixtures that serve as the most relevant baseline.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTemperature-sensitivity indicators for asphalt-rubber and conventional mixtures.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFamily\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR35\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eR45\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e25\u0026ndash;45\u0026deg;C loss (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eTSI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConventional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e89.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.1106\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConventional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e90.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.1156\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConventional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3968\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e847\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.783\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e83.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0895\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConventional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.595\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e83.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0908\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.133\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e86.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.1009\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.306\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e89.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.1102\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1478\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e629\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.337\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e85.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0970\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1741\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e88.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.1068\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMix 9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e605\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.154\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e84.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0937\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that the asphalt-rubber family does not behave as a single monotonic sequence. Mix 6 has the highest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{25}\\)\u003c/span\u003e\u003c/span\u003e among the rubberized mixtures, but it also exhibits one of the highest temperature-susceptibility levels within that family. By contrast, Mix 9 has the lowest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{45}\\)\u003c/span\u003e\u003c/span\u003e in the rubberized subset, yet it shows the best \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{45}\\)\u003c/span\u003e\u003c/span\u003e and the lowest TSI among the asphalt-rubber mixtures. Mix 7 also performs favourably in high-temperature retention, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{45}=0.144\\)\u003c/span\u003e\u003c/span\u003e, exceeding the explicit conventional control Mix 1 and approaching the better conventional responses.\u003c/p\u003e \u003cp\u003eA second relevant observation is that the asphalt-rubber mixtures cluster relatively closely in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{45}\\:\\)\u003c/span\u003e\u003c/span\u003e,ranging from 523 to 629 MPa, even though their 25\u0026deg;C values span almost 800 MPa. In engineering terms, this suggests that part of the meaningful differentiation among the rubberized mixtures occurs at intermediate temperature rather than only at the highest condition. In other words, a mixture with high initial stiffness does not necessarily preserve that advantage as temperature rises, which further underscores the value of normalized retention indicators.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Family-level behavior and variability\u003c/h2\u003e \u003cp\u003eTo determine whether the asphalt-rubber results represent isolated cases or a broader family trend, the data were aggregated by mixture family. The resulting summary statistics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFamily-level summary statistics for resilient modulus and temperature-response indicators.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFamily\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003en\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean MR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD MR25\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean MR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSD MR35\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMean MR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSD MR45\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMean R35\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMean R45\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eMean TSI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConventional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5152.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1346.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2939.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e986.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e678.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e173.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.572\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.1016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAsphalt-rubber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4413.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e300.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1502.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e145.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e581.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e43.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.1017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolymer-modified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4196.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e473.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2204.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e961.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e794.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e252.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.0847\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAt family level, the conventional mixtures display the highest mean modulus at all temperatures, largely because Mixes 2 and 3 are substantially stiffer than the rest of the experimental program. Polymer-modified mixtures exhibit the lowest mean thermal susceptibility, which is consistent with the intended role of polymer modification. The asphalt-rubber family occupies an intermediate position in absolute stiffness but an almost identical position to the conventional family in mean TSI. This is one of the central findings of the study: the rubberized mixtures are not markedly more temperature-sensitive than the conventional family, even though their average resilient modulus is lower.\u003c/p\u003e \u003cp\u003eEqually important is the issue of dispersion. The asphalt-rubber family shows much lower standard deviation than the conventional family, particularly at 25 and 45\u0026deg;C. In relative terms, the coefficient of variation of the asphalt-rubber family is 6.8% at 25\u0026deg;C, 9.7% at 35\u0026deg;C, and 7.6% at 45\u0026deg;C, whereas the conventional family reaches 26.1%, 33.6%, and 25.5%, respectively. This lower dispersion suggests that, within the experimental program, the asphalt-rubber mixtures behaved more uniformly than the conventional family. From a practical standpoint, this may be relevant for quality control and formulation robustness.\u003c/p\u003e \u003cp\u003eThese family-level trends are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, which presents the family-average modulus values with one standard deviation at the three test temperatures, and in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which summarizes the normalized modulus-retention ratios.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Exploratory internal comparison within the asphalt-rubber family\u003c/h2\u003e \u003cp\u003eBecause the asphalt-rubber subset includes both nominal grade B and grade C dense mixtures, an exploratory internal comparison was performed to investigate whether nominal grading category was associated with systematic response differences.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExploratory internal comparison within the asphalt-rubber family.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAsphalt-rubber subgroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003en\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean MR25 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean MR35 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean MR45 (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMean R35\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMean R45\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMean TSI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGrade B (Mixes 6 and 8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4660.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1596.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e532.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.108\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGrade C (Mixes 5, 7 and 9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4249.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1439.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e607.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.097\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe subgroup comparison shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e5\u003c/span\u003e reveals an informative and technically coherent pattern within the asphalt-rubber family. The nominal grade B asphalt-rubber mixtures exhibited higher average modulus at 25 and 35\u0026deg;C, whereas the nominal grade C asphalt-rubber mixtures showed better high-temperature retention and lower mean thermal susceptibility. This result suggests that aggregate skeleton and nominal gradation may play an important role in shaping how rubber modification is expressed across the temperature range.\u003c/p\u003e \u003cp\u003eIn practical terms, the grade C rubberized mixtures appear to provide a more stable high-temperature modulus profile despite their lower initial stiffness. This internal trend reinforces the importance of interpreting asphalt-rubber performance through the full temperature-response trajectory rather than through single-point stiffness ranking alone.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Direct benchmark against the conventional CAP 50/70 control\u003c/h2\u003e \u003cp\u003eThe most practically relevant one-to-one comparison in the experimental program is the benchmark between the dense asphalt-rubber Mix 5 and the explicit dense conventional CAP 50/70 control (Mix 1). This comparison is summarized in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDirect benchmark between the dense asphalt-rubber mixture and the conventional CAP 50/70 control.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndicator\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMix 1 (Conventional CAP 50/70)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMix 5 (Asphalt-rubber)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRelative change of Mix 5 vs Mix 1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMR25 (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;11.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMR35 (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-11.6%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMR45 (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;34.8%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-20.3%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.133\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;21.3%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLower\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u0026ndash;45\u0026deg;C loss (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e89.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e86.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLower\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis direct comparison clarifies the engineering meaning of the experimental program more effectively than any family average. The asphalt-rubber mixture is not uniformly superior, because it shows a lower modulus at 35\u0026deg;C and a lower \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{35}\\)\u003c/span\u003e\u003c/span\u003e. However, it is superior at 25\u0026deg;C and especially at 45\u0026deg;C, where it exceeds the conventional control by 34.8% in resilient modulus while also exhibiting better high-temperature retention and lower thermal susceptibility. This pattern is particularly relevant because elevated-temperature stiffness preservation is closely associated with rutting-related structural adequacy in flexible pavements.\u003c/p\u003e \u003cp\u003eThe direct comparison between Mixes 1 and 5 is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.1 What the temperature-dependent modulus profile reveals about asphalt-rubber\u003c/h2\u003e \u003cp\u003eThe results show that the asphalt-rubber mixtures in the experimental program are neither universally stiffer nor universally weaker than the comparison families. Instead, they display a characteristic response profile in which initial modulus, modulus loss, and high-temperature retention interact in a non-linear manner. This interpretation is strongly aligned with the literature. Lo Presti [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] argued that crumb-rubber-modified systems are inherently process-dependent because swelling, digestion, and compatibility evolve during production and storage. Picado-Santos et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] similarly emphasized that comparing crumb-rubber mixtures without careful attention to process route and formulation history is scientifically risky. Li et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] and Wu et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] further explained that the dominant interaction mechanism may shift between physical swelling and chemical degradation depending on rubber characteristics, asphalt composition, and processing conditions.\u003c/p\u003e \u003cp\u003eFrom this perspective, the present results are mechanically coherent. The asphalt-rubber mixtures did not achieve the highest family-average modulus, but neither did they exhibit a thermally fragile profile. On the contrary, their mean TSI was virtually identical to that of the conventional family, and their within-family dispersion was much lower. This suggests that the tested asphalt-rubber systems were not merely softer versions of conventional asphalt, but mixtures with a distinct thermomechanical balance. Such a balance is consistent with the view of Abdelrahman and Carpenter [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], Dong et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], Jeong et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], and Xiang et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], who described rubberized binders as multi-phase systems in which enhanced elasticity, swelling-induced thickening, and altered relaxation kinetics redistribute stiffness across the temperature spectrum.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Stiffness retention, thermal susceptibility, and non-monotonic superiority\u003c/h2\u003e \u003cp\u003eOne of the most relevant outcomes of this study is that mixture superiority depends on the criterion adopted. If the ranking is based solely on family-average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MR}_{35}\\)\u003c/span\u003e\u003c/span\u003e, the conventional mixtures appear superior. If the ranking is based on mean TSI, asphalt-rubber and conventional mixtures are essentially equivalent. If the comparison is restricted to the direct dense-graded benchmark, the asphalt-rubber mixture outperforms the conventional control at 25 and 45\u0026deg;C. This non-monotonic superiority is not anomalous; rather, it reflects a well-known characteristic of crumb-rubber systems reported in the literature.\u003c/p\u003e \u003cp\u003eXiao and Amirkhanian [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] showed that the resilient modulus of rubberized asphalt concrete is strongly dependent on mixture composition and reclaimed material content. Noura et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] demonstrated that rubberized stone mastic asphalt can present distinctly different stiffness levels depending on process route and dosage. White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] reported that rubber dosage and digestion time alter stiffness and broader mechanical behavior simultaneously. Wu et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], working with high-content crumb-rubber-modified asphalt mixtures, concluded that favorable binder-level indicators do not necessarily translate directly into better mixture-level performance. This conclusion is particularly relevant here because it reinforces the methodological lesson of the present study: mixture performance indicators must be interpreted at the mixture scale, not merely inferred from binder modification or from a single modulus value.\u003c/p\u003e \u003cp\u003eThe direct benchmark between Mix 1 and Mix 5 illustrates this principle clearly. At 35\u0026deg;C, the asphalt-rubber mixture appears less stiff. At 45\u0026deg;C, however, the same mixture becomes clearly superior in resilient modulus and modulus retention. For pavement design and material screening, this pattern may be more meaningful than a modest difference at intermediate temperature, especially in warm climates or under slow-moving and heavy traffic loads. Fontes et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], Moreno et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], Shafabakhsh et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], and Rodr\u0026iacute;guez-Fern\u0026aacute;ndez et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] all reported that crumb-rubber systems can improve resistance to permanent deformation even when mechanical ranking is not straightforward under every test condition.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Role of aggregate skeleton, nominal gradation, and mixture architecture\u003c/h2\u003e \u003cp\u003eThe internal variability of the asphalt-rubber family also deserves careful interpretation. The nominal grade B rubberized mixtures exhibited higher average modulus at 25 and 35\u0026deg;C, whereas the nominal grade C rubberized mixtures showed better \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{45}\\)\u003c/span\u003e\u003c/span\u003e and lower TSI. Although the subgroup sizes are small, this result suggests that nominal grading category and mineral skeleton influence how rubber modification manifests at different temperatures. In other words, the performance contribution of rubber cannot be decoupled from the aggregate framework that hosts it.\u003c/p\u003e \u003cp\u003eThis interpretation is consistent with broader mixture-level research. Palit et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], Cao [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], Chavez et al. [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], and White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] showed that the mechanical consequences of rubber modification depend not only on the binder itself but also on aggregate arrangement, void system, and the resulting internal stress distribution. Gardziejczyk et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] and Rodr\u0026iacute;guez-Fern\u0026aacute;ndez et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] also highlighted that mixture architecture strongly affects the viscoelastic and mechanical expression of rubberized systems. Therefore, when a rubberized mixture exhibits lower modulus at one temperature but better retention at another, the explanation may lie as much in mixture design as in binder chemistry. A second and somewhat unexpected result is the lower dispersion of the asphalt-rubber family relative to the conventional family. This finding may appear counterintuitive because the literature frequently highlights variability in rubberized mixtures. One plausible interpretation is that the tested rubberized formulations were developed within a relatively narrow production window, whereas the conventional family combined dense limestone-based mixtures with markedly different stiffness profiles. Even without replicate-level information, the experimental program therefore suggests that rubberized mixtures may achieve a reasonably stable modulus envelope when the technology is already consolidated.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Asphalt-rubber versus polymer-modified mixtures\u003c/h2\u003e \u003cp\u003eThe polymer-modified family exhibited the lowest mean TSI and the highest mean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{45}\\)\u003c/span\u003e\u003c/span\u003e, which is consistent with the established role of polymers in enhancing thermal stability. K\u0026ouml;k and \u0026Ccedil;olak [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], Lee et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], Han et al. [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], and Li et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] all noted that polymer-modified binders often form more effective high-temperature structural networks than conventional crumb-rubber systems. Nevertheless, the comparison should not be oversimplified. The polymer-modified family in this study is also highly dispersed, especially at 35 and 45\u0026deg;C, and includes distinct mixture types, as well as two records whose binder field indicates CAP 50/70 despite their classification as polymer-modified mixtures.\u003c/p\u003e \u003cp\u003eThus, the polymer-modified family functions here as a relevant performance benchmark, enabling a broader interpretation of how asphalt-rubber mixtures compare with other modifier technologies under the same analytical framework. More importantly, stiffness retention is only one part of the engineering response. Asphalt-rubber remains particularly attractive because of its well-documented benefits in viscoelastic accommodation, cracking resistance, fatigue-related performance, damping potential, and waste-tire reutilization. In this sense, the comparison with polymer-modified mixtures does not diminish the technical merit of asphalt-rubber; instead, it helps position rubberized mixtures within a broader performance landscape in which different modifier technologies optimize different response attributes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Implications for pavement design, circularity, and current research frontiers\u003c/h2\u003e \u003cp\u003eThe practical implication of this work is that asphalt-rubber should not be screened out simply because its mean resilient modulus is lower than that of some conventional or polymer-modified mixtures. A more defensible engineering approach is to examine the full temperature-response profile in relation to the intended pavement function. In warm regions, under slow-moving traffic, or where rutting risk is a dominant concern, the strong 45\u0026deg;C performance of the direct asphalt-rubber benchmark becomes particularly relevant. In contexts where cracking, fatigue, and damping are also critical, the broader literature further strengthens the case for rubberized systems.\u003c/p\u003e \u003cp\u003eThis issue becomes even more important when sustainability is considered. Farina et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] showed that crumb rubber can contribute to favorable life-cycle outcomes in bituminous mixtures, while Wang et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] quantified the energy and environmental implications of rubberized asphalt pavements. Khiong et al. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] also highlighted the environmental benefits associated with using local crumb rubber in hot-mix asphalt. Sol-S\u0026aacute;nchez et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], in turn, demonstrated the viability of combining crumb-rubber technology with reduced-temperature production strategies. Thus, a rubberized mixture with only comparable stiffness may still be attractive from a broader transportation-materials perspective because it combines structural adequacy with circular-economy benefits.\u003c/p\u003e \u003cp\u003eThe current research frontier also supports this broader interpretation. White and Kidd [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] emphasized the role of dosage and digestion time in optimizing low-dosage rubberized asphalt mixtures. Wu et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] advanced the field by combining laboratory evaluation with field application for high-content crumb-rubber mixtures. Wu et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] reviewed asphalt-rubber interaction from macroscopic to molecular scales and showed that future progress depends on controlling swelling, degradation, viscosity, and compatibility simultaneously. In that sense, the present study contributes to the frontier not by proposing a new modifier chemistry, but by showing how resilient-modulus results obtained in a structured laboratory program can be interpreted in a way that is directly useful for performance-based benchmarking.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.6 Scientific contribution and future research directions\u003c/h2\u003e \u003cp\u003eA central contribution of this study lies in demonstrating that results from a resilient-modulus experimental program can be converted into a scientifically meaningful comparative framework for evaluating asphalt-mixture performance. By integrating absolute modulus values, retention ratios, thermal susceptibility, and family-level variability, the study provides a consistent basis for interpreting the competitive response of asphalt-rubber mixtures relative to conventional and polymer-modified alternatives. This contribution is especially relevant because it connects laboratory testing to publication-oriented performance analysis, offering a practical pathway for extracting scientific value from structured experimental programs.\u003c/p\u003e \u003cp\u003eThe results also reinforce the importance of temperature-profile interpretation in mixture-level assessment. Rather than relying exclusively on stiffness ranking at a single temperature, the proposed framework captures how mixtures preserve or lose structural adequacy across the thermal interval, which is particularly relevant for performance-oriented discussion of asphalt-rubber systems. In this regard, the study contributes not only a set of comparative findings, but also an analytical approach that can be replicated in future evaluations of laboratory-prepared mixtures.\u003c/p\u003e \u003cp\u003eBuilding on these findings, future investigations can further expand this framework by incorporating full volumetric characterization, rubber dosage and digestion history, loading frequency, wheel-tracking, fatigue, cracking resistance, and binder rheology in a controlled experimental design. Such developments would deepen mechanistic interpretation, while the present study already provides robust comparative evidence of temperature-dependent mixture behavior.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study evaluated the temperature-dependent resilient modulus of 18 anonymized laboratory-prepared asphalt mixtures tested at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil, with emphasis on five asphalt-rubber mixtures and comparison against conventional and polymer-modified mixtures. The results confirm that the engineering interpretation of asphalt-rubber cannot be reduced to a one-dimensional ranking based only on absolute modulus at a single temperature.\u003c/p\u003e \u003cp\u003eThe asphalt-rubber mixtures exhibited resilient modulus values between 3938 and 4736 MPa at 25\u0026deg;C and between 523 and 629 MPa at 45\u0026deg;C, which places them within a technically relevant range for pavement applications. At family level, the asphalt-rubber mixtures showed lower average modulus than the conventional family, but their average thermal susceptibility was practically identical. Therefore, lower mean stiffness did not correspond to greater thermal fragility.\u003c/p\u003e \u003cp\u003eThe direct benchmark against the explicit dense conventional CAP 50/70 control was especially revealing. The selected dense asphalt-rubber mixture was 11.1% stiffer at 25\u0026deg;C and 34.8% stiffer at 45\u0026deg;C, although it was 11.6% lower at 35\u0026deg;C. It also showed better 45\u0026deg;C retention and lower thermal susceptibility. Accordingly, the most informative way to evaluate asphalt-rubber is through the full temperature-response profile rather than through a single modulus value.\u003c/p\u003e \u003cp\u003eA second relevant finding is that the asphalt-rubber family displayed lower between-mixture dispersion than the conventional family in the experimental program. This suggests that, under the laboratory conditions represented in this study, rubberized mixtures may provide a comparatively stable mechanical envelope. The exploratory internal comparison further indicated that nominal grade C asphalt-rubber mixtures, despite lower initial stiffness, may retain more high-temperature modulus than nominal grade B rubberized mixtures. This internal trend further highlights the influence of aggregate skeleton and mixture architecture on the temperature-dependent response of asphalt-rubber systems.\u003c/p\u003e \u003cp\u003eFrom the standpoint of current international research, the present results align well with the broader literature, which increasingly emphasizes mixture-level validation, temperature-profile interpretation, and control of asphalt-rubber interaction as key elements in the advancement of rubberized asphalt technology. In this sense, the study contributes by demonstrating that results from a structured resilient-modulus experimental program can be transformed into a publication-ready benchmarking framework with clear relevance for pavement design practice and sustainable transportation materials research.\u003c/p\u003e \u003cp\u003eBuilding on these findings, future studies can expand the proposed framework by combining resilient modulus with full volumetric characterization, rubber dosage and digestion history, frequency-dependent stiffness, wheel tracking, fatigue, cracking resistance, and binder rheology in a controlled experimental design. Such an approach would further strengthen performance-based recommendations, while the present study already establishes a robust comparative basis for evaluating the temperature-dependent response of asphalt-rubber mixtures.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003e \u003cb\u003eAuthors and Affiliations\u003c/b\u003e \u003c/h2\u003e \u003cp\u003e \u003cstrong\u003eFederal Center for Technological Education of Minas Gerais (CEFET-MG), Belo Horizonte, MG, 30421-169, Brazil.\u003c/strong\u003e \u003cp\u003eRaphael L\u0026uacute;cio Reis dos Santos\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eState Secretariats of Infrastructure, Mobility and Partnerships (SEINFRA), Rod. Pref. Am\u0026eacute;rico Ren\u0026ecirc; Gianeti, 4143, Belo Horizonte, MG, 31630-902, Brazil.\u003c/strong\u003e \u003cp\u003eVin\u0026iacute;cius Ant\u0026ocirc;nio Florentino Camargo\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eMinistry of Transport (MT), Esplanada dos Minist\u0026eacute;rios, Bloco R, Bras\u0026iacute;lia, DF, 70044-900, Brazil.\u003c/strong\u003e \u003cp\u003eGeorge Yun\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eContributions\u003c/strong\u003e \u003cp\u003eR.L.R.d.S.: Conceptualization, data collection, data analysis, writing-original draft preparation, writing-review and editing, project administration. V.A.F.C.: Conceptualization, writing-review and editing. G.Y.: data collection, data analysis.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eCorresponding author\u003c/strong\u003e \u003cp\u003eCorrespondence to Raphael L\u0026uacute;cio Reis dos Santos ([email protected])\u003c/p\u003e \u003c/p\u003e\u003ch2\u003e \u003cb\u003eEthics declarations\u003c/b\u003e \u003c/h2\u003e \u003cp\u003e \u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eCompeting interests\u003c/strong\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eNo funds or other support were received for the preparation of this manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHeitzman MA. 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Environments. 2021;8(6):47.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Civil Engineering](https://www.springer.com/journal/44290)","snPcode":"44290","submissionUrl":"https://submission.nature.com/new-submission/44290","title":"Discover Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Asphalt-rubber, resilient modulus, crumb rubber, temperature susceptibility, viscoelasticity, hot-mix asphalt, pavement materials","lastPublishedDoi":"10.21203/rs.3.rs-9440307/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9440307/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the temperature-dependent resilient modulus of asphalt-rubber mixtures based on resilient-modulus tests performed at the Dynamic Testing Laboratory (LED) of a public road agency in Brazil. Eighteen laboratory-prepared asphalt mixtures were analyzed after anonymization as Mix 1 to Mix 18, comprising conventional, asphalt-rubber, and polymer-modified mixtures. The available experimental information included mixture description, binder type, summarized gradation, and resilient modulus values at 25, 35, and 45\u0026deg;C. To strengthen the engineering interpretation of the results, the analysis combined absolute resilient modulus, modulus-retention ratios, family-level variability, and a logarithmic thermal susceptibility index. The asphalt-rubber mixtures exhibited resilient modulus values ranging from 3938 to 4736 MPa at 25\u0026deg;C and from 523 to 629 MPa at 45\u0026deg;C. Although their family-average modulus was lower than that of the conventional family, direct comparison with the explicit conventional CAP 50/70 control showed that the selected dense asphalt-rubber mixture presented 11.1% higher resilient modulus at 25\u0026deg;C and 34.8% higher resilient modulus at 45\u0026deg;C, despite a lower value at 35\u0026deg;C. At family level, asphalt-rubber and conventional mixtures displayed nearly identical average thermal susceptibility, while the asphalt-rubber family also showed lower between-mixture dispersion. An exploratory internal comparison further suggested that nominal grade C asphalt-rubber mixtures had lower initial stiffness but better high-temperature retention than nominal grade B rubberized mixtures. The results demonstrate that asphalt-rubber mixtures exhibit a technically competitive temperature-dependent resilient modulus response, particularly through favorable high-temperature stiffness retention, supporting their relevance for pavement engineering applications.\u003c/p\u003e","manuscriptTitle":"Temperature-dependent resilient modulus of asphalt-rubber mixtures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-20 07:03:15","doi":"10.21203/rs.3.rs-9440307/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-28T16:16:49+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-24T12:54:37+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-24T12:53:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Civil Engineering","date":"2026-04-16T15:45:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Civil Engineering](https://www.springer.com/journal/44290)","snPcode":"44290","submissionUrl":"https://submission.nature.com/new-submission/44290","title":"Discover Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d7fad155-d9f4-4743-b39b-14eb2e5e909c","owner":[],"postedDate":"April 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-07T16:38:31+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-20 07:03:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9440307","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9440307","identity":"rs-9440307","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}