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Review

Fatigue Testing in Asphalt Mixes: Emerging Trends and Findings from an Integrated Literature Review

by
Jessé Valente de Liz
1,*,
Breno Salgado Barra
2,
Alexandre Mikowski
2,
Gary B. Hughes
3 and
Adelino Ferreira
4,*
1
Department of Civil Engineering, Federal University of Santa Catarina, Florianópolis 88037-000, Santa Catarina, Brazil
2
Department of Mobility Engineering, Federal University of Santa Catarina, Joinville 89219-600, Santa Catarina, Brazil
3
Department of Physics, University of California, Santa Barbara, CA 93106, USA
4
Research Center for Territory, Transports and Environment (CITTA), Department of Civil Engineering, University of Coimbra, 3030-790 Coimbra, Portugal
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2025, 15(18), 10220; https://doi.org/10.3390/app151810220
Submission received: 12 August 2025 / Revised: 12 September 2025 / Accepted: 15 September 2025 / Published: 19 September 2025
(This article belongs to the Special Issue Innovations in Binder and Asphalt Mixture Rheology)

Abstract

This study compiled a dataset of published works relating to fatigue testing in asphalt mixes, covering 2020–2025. The dataset was subjected to bibliometric and textual analyses, including a systematic review, to explore emerging trends and patterns in experimental protocols. Bibliometrix, VOSviewer, and IRaMuTeQ were employed to map the scientific landscape of 368 articles. Following PRISMA guidelines, the 100 most-cited articles were reviewed to identify prevailing test setups and parameters. The results showed a growing scientific production (9.1% per year), concentrated in a few high-impact journals and dominated by China, with emphasis on sustainability. A comparison between scientific output and a road quality index revealed a disconnect between academic research and field implementation. Five thematic clusters emerged: sustainable pavement management, mechanical characterization, binder modification, performance modeling, and evaluation of innovative materials. Indirect tensile and four-point bending tests were the most common loading modes. Considerable variability in protocols, frequent omissions of methodological details, and limited statistical treatment were also observed. The study highlighted the importance of standardized reporting and robust analysis, offering a reproducible framework to understand fatigue behavior and support future research.

1. Introduction

Fatigue cracking is generally regarded as a primary deterioration mechanism in asphalt pavements [1,2,3]. Fatigue damage in asphalt pavement is caused by repeated traffic loading, even when individual loads remain below the material’s resistance threshold. The cumulative effects lead to progressive deterioration, including the formation and propagation of cracks, ultimately undermining structural durability and reducing road quality [4,5,6,7,8,9]. Due to implications for user safety [10,11] and economic impact [12,13], properties related to fatigue are routinely used as key parameters in pavement design [2,14,15]. In the context of asphalt pavement design, accurate estimates of fatigue properties of asphalt mixes are essential for the development of more efficient and reliable paving projects.
Fatigue properties of asphalt mixes have generally been obtained through laboratory tests which employ cyclic loading [2,7,14,16]. Several experimental protocols have been developed to simulate and evaluate fatigue behavior of asphalt mixes, resulting in a series of test methodologies with various metrics, including loading mode, loading frequency, controlled mode, test temperature, and loading waveform, among others [17,18,19,20,21,22]. Previous studies indicated that the selection of methodological factors directly influenced the observed degradation mechanisms and derived parameters. Di Benedetto et al. [4] conducted an inter-laboratory study with different experimental setups and observed that the five investigated loading modes and the choice of controlled mode (stress/load or strain/displacement) influenced the parameters obtained using the classical fatigue approach.
Prior studies have also addressed the influence of test setup on fatigue parameters. Cheng et al. [23] compared four-point bending (4PB) and indirect tensile (ITT) test methods at different temperatures and observed that, while increasing the temperature leads to longer fatigue life in 4PB tests, the opposite occurs in ITT tests. Poulikakos et al. [24] compared two-point bending (2PB) and four-point bending (4PB) tests using aged asphalt concrete field samples and reported distinct fatigue parameters, such as strain at 10 6 cycles ( ε 6 ), which showed differences of up to 63 % between the two methods. Khalid [25] compared three-point bending (3PB) and indirect tensile (ITT) tests and, although a correlation was found at low strain levels, the author reported significant differences in fatigue life, with ITT tests underestimating this parameter. Di Benedetto et al. [26] investigated the relationship between fatigue curves obtained from uniaxial tension–compression and four-point bending (4PB) tests and emphasized that the curves reflected both true fatigue damage and biased effects for the two test types. Pintarelli and Melo [27] evaluated the influence of different loading waveforms and found performance differences between haversine and sinusoidal waveform approaches. In addition to the aforementioned factors, temperature [28,29,30] and loading frequency [31,32] have also been widely recognized in prior studies as key variables affecting fatigue performance.
In addition to the consolidated challenges related to the progressive deterioration of pavements—e.g., environmental conditions [33], traffic overload [34,35,36], performance prediction [37]—a continuous growth in the adoption of modified materials has been reported [38,39,40,41,42], particularly among asphalt formulations deemed to be ecologically responsible [42,43,44,45,46]. The movement toward ecological responsibility is reportedly driven, in large part, by global commitments established in the 2030 Agenda for sustainable development [47,48]. In the context of improving asphalt performance, fatigue tests can contribute to a better understanding of degradation mechanisms and to the development of predictive models of the mechanical behavior of mixes. Fatigue testing also serves a strategic role as a technical–scientific sieve. The application of improved testing methods can contribute to a more rigorous assessment of the viability of innovative and sustainable solutions and to evaluation of whether proposed new materials present satisfactory mechanical performance and durability that are compatible with field requirements.
Due to the inherent complexity of materials testing, the nuanced interplay between fatigue behavior and pavement design, the wide range of experimental and methodological frameworks used for pavement characterization, and the strong influence of test variables, asphalt fatigue testing remains an active and evolving area of research. A comprehensive understanding of testing context, including test administration, analysis, and dissemination of results, is crucial. In the context of evaluating research trends and synthesizing prior studies, tools such as bibliometric and textual analyses and systematic reviews have proven to be valuable [49,50,51]. Such approaches play a fundamental role in mapping the scientific output on the subject, enabling the identification of established patterns, knowledge gaps, and emerging directions in the field [49,50,51].
Bibliometric analyses have been effectively applied in the areas of construction and building [52,53,54] and, more specifically, in paving [55,56,57,58,59]. Textual analysis (also known as lexical analysis) has also been successfully employed in several areas of knowledge [60,61,62,63,64,65,66,67,68,69,70], allowing comprehensive investigations on specific topics. In a similar way, systematic reviews—which allow for the gathering, critical evaluation, and synthesis of available evidence in a rigorous and transparent manner [51]—have also been effective for exploring the discipline of infrastructure [56,71,72,73,74].
Although previous reviews—such as Cheng et al. [18] and Sudarsanan and Kim [19]—have addressed aspects related to fatigue tests on asphalt mixes, these approaches were limited to descriptive overviews, without adopting systematic methodologies or addressing emerging themes in the conduction, analysis, and application of such studies. Research performed for this study sought to carry out an integrated review of fatigue testing in asphalt mixes, focusing on emerging approaches and recent trends, thereby enabling the identification of knowledge gaps and potential research opportunities. Through bibliometric and lexical methods, this study aimed to map the state of the art of scientific production between 2020 and 2025, identifying publication patterns, international collaborations, methodologies used, terminologies employed, and thematic approaches. Moreover, the work proposed—through systematic review—to investigate and classify the fatigue test setups employed in the literature dataset in order to synthesize the current panorama of experimental practices.
Furthermore, this study introduced, in a novel way in the field of Engineering, the integrated application of three review methodologies—systematic, bibliometric, and lexical—which allowed for a comprehensive, focused, and reproducible overview of the topic. The findings derived from this approach provide new insights into research directions, test setup preferences, and methodological limitations, thereby advancing the state of the art and offering valuable contributions for the development and evaluation of fatigue testing practices in the field.

2. Background

Classically, the typical response of asphalt mixes has been interpreted as a function of the strain ( ε ) or stress ( σ ) amplitude and number of loading cycles (N). At a given temperature, three typical behaviors have been observed (see Figure 1): (i) nonlinear viscoelasticity; (ii) linear viscoelasticity (LVE); and (iii) fatigue damage. Fatigue has been shown to occur in low strain regimes, where load amplitudes lower than the critical strength of the material have been shown to induce the formation and propagation of cracks and progressive energy dissipation in the form of heat, resulting in failure after a certain number of repeated cycles [5,6,75,76].
Under the influence of a high number of loading cycles—ranging from tens of thousands to several million—pavement materials are known to exhibit damage phenomena often characterized by a gradual degradation of mechanical properties, ultimately leading to failure [6]. The fatigue cracking process has been characterized as occurring in two distinct degradation phases: the initiation phase and the propagation phase [4]. The first phase has been characterized by the initiation and propagation of micro-cracks accompanied by the progressive reduction in the stiffness modulus [4,6]. In the second phase, the coalescence of micro-cracks and the formation of macro-cracks are observed, ultimately leading to structural collapse [4,6]. A propagating crack preferentially follows paths that require less energy, which is particularly relevant in composite materials such as asphalt mixes, where it can propagate either through the asphalt binder (matrix) or through the aggregates [78].
In the French mix design methodology [16], for example, fatigue played a central role in the acceptance of mixes. The methodology established specific criteria for different applications (e.g., intended use, asphalt mix type, and traffic volume) and provided up to four successive levels of evaluation of the formulations (see Figure 2). Each level, from 0 (the simplest) to 4 (the most thorough), was declared to be eliminatory. Among these, the last level—considered fundamental for the validation of the mix—was deemed to correspond to the evaluation of the material’s fatigue behavior. Level 4 focuses on the estimation of two parameters, derived from the fatigue curve, that are used in pavement design: (i) ε 6 —the strain corresponding to 10 6 loading cycles—and (ii) b—the inverse of the slope of the fatigue line [7,14].
Test results related to fatigue behavior have been shown to vary depending on both the frequency and temperature conditions under which testing is conducted [4,30,79,80,81,82,83,84,85]. Fatigue tests, depending on the standard applied, have historically been conducted using different test setups and analysis methods. The selection of test factors has been observed to significantly influence test results [4,17,18,19,22,27,86]. Variables related to the experimental setup have typically included loading mode, specimen geometry, loading frequency, control mode, environmental conditions (temperature and moisture), and loading waveform [18,19]. Analysis methods have also invoked different approaches, such as fatigue life models, stiffness modulus method, energy-based method, and the viscoelastic continuum damage (VECD) method [18].
Fatigue tests have been classified according to loading mode and stress–strain distribution. The most typically used loading modes have been (i) simple flexure; (ii) diametral load tests; and (iii) direct uniaxial [19]. The resulting stress–strain distributions have then been categorized as (i) homogenous and (ii) non-homogenous [19]. Some of the most consolidated loading modes for fatigue characterization in asphalt mixes (see Figure 3) have been the following [4,18,19]: (i) two-point bending (2PB) [33]; (ii) three-point bending (3PB) [87]; (iii) four-point bending (4PB) [43]; (iv) semi-circular bending (SCB) [88]; (v) indirect tensile (ITT) [89]; and (vi) uniaxial [22]. Among these, only the uniaxial method exhibits a homogeneous stress–strain distribution [4,90,91].
Loading frequency, control mode, failure criterion, specimen geometry, and temperature control, among others, vary across different standards and directly affect the estimated performance parameters. This normative diversity complicates standardization and should be taken into account when interpreting and comparing international studies. Previous works, such as those by Sudarsanan and Kim [19] and Braham and Underwood [91], cataloged a wide range of fatigue tests, their standards, and the most common practices associated with them. As an example of such methodological variety, Sudarsanan and Kim [19] reported that the ITT can be performed at loading frequencies ranging from 0.01 Hz to 30 Hz, which directly influence the results obtained.
In addition to aspects of experimental setup, test results can display intrinsic variability due to physical characteristics of the tested material, including heterogeneity, air void distribution, aggregate structure, and self-healing, among others. Such material characteristics have been observed to contribute to different fatigue responses even under similar testing conditions [4,6,86,92,93,94,95,96,97,98,99,100,101,102]. Moreover, mechanical tests have been observed to display inherent uncertainties related to measurement procedures, equipment sensitivity, and others, which contribute to data scattering and, consequently, the need for adequate statistical treatment [19,103,104,105,106].
The following sections describe the methodologies applied and the corresponding results. In the discussion of the results, some of the topics addressed in this section are further explored.

3. Methodology

This section outlines the methodology adopted for selecting and analyzing the dataset under investigation.

3.1. Search Terms and Data Selection

A systematic search was conducted using the Scopus database. Recognized as one of the largest curated abstract and citation databases available [107,108], Scopus has been extensively employed in systematic reviews and bibliometric analyses within the field of pavement engineering [55,74,109]. The database offers broad global coverage, comprising approximately 29 thousand active journals and more than 20 million active author profiles [110].
This research was conducted according to guidelines from the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology [51]. The PRISMA methodology has previously been used effectively in systematized research in the infrastructure area [74,111,112]. Methodological adaptations were incorporated for this research in order to broaden the understanding of scientific production. Specifically, before the eligibility and inclusion stages, bibliometric and textual analyses were carried out. This approach was intended to meet all guidelines for bibliometric analysis [50,113] and for the textual analysis investigations performed [63,65]. These modifications allowed for strategic screening, without compromising the transparency and methodological rigor proposed by PRISMA.
Initially, two keywords were selected for a broad search: “asphalt mix*” and “fatigue test*”. Inserting the asterisk (*) allowed the search to be performed automatically for all endings for that word, capturing terminological variations and number inflections (singular and plural) [74,114].
The search was limited to articles published in English only. On 6 February 2025, a search with these parameters resulted in 808 documents, with a time span of 1980–2025. In order to emphasize the current state of the literature, an additional limitation was introduced: articles published after 2020 until the date of the search, i.e., 2020–2025. The definitive string used for the search was (TITLE-ABS-KEY (“asphalt mix*” AND “fatigue test*”) AND PUBYEAR > 2019 AND PUBYEAR < 2026 AND (LIMIT-TO (DOCTYPE,“ar”)) AND (LIMIT-TO (LANGUAGE,“English”))). This approach—summarized in Table 1—generated an initial dataset of 399 documents.
The steps outlined in Figure 4 were then performed. After reading the titles and abstracts of the 399 articles, 31 of them were excluded due to incompatibility with the theme, i.e., the studies did not report on fatigue tests for asphalt mixes. The pared list contained 368 articles which were used in the bibliometric and textual analyses, hereafter referred to as the dataset.
Citation count can serve as a robust measure for the influence and impact of a publication in its field. This metric has been widely used as a criterion for article selection, especially when dealing with extensive search results, contributing to a transparent method that facilitates reproducibility [54,114,115,116,117]. Accordingly, the 100 most cited articles were selected for full reading and systematic evaluation. The choice of 100 articles is a literature-supported practice that has been adopted across multiple research domains [116,117]. In this dataset, the 100-article limit represents 27.2 % of the total number of articles from the broad analysis and 72.4 % of all citations. All 100 articles were confirmed to have investigated the mechanical fatigue behavior of asphalt mixes and, therefore, met the eligibility criteria and were included in the systematic review.
The dataset was mapped according to research trends, resulting in a synthesis of the main scientific contributions in the field. Details of the analysis methods adopted were described in Section 3.2.

3.2. Dataset Analysis

Analyses of the dataset followed the structure presented in Figure 4. The bibliometric and textual analyses were carried out using the full dataset ( n = 368 ), while the systematic literature review focused on the top-100 most cited articles ( n = 100 ). This approach provided a comprehensive overview of the research topic.
Bibliometric analysis is a rigorous method which has been developed for examining large volumes of scientific data [50,113,114]. Through indicators, this approach allows for identifying emerging areas, trends, and knowledge gaps in a defined research field [50,113,114]. The bibliometric analysis (Section 4.1) of the dataset was performed using two bibliometric analysis tools: Bibliometrix [118] (version 5.0.0) and VOSviewer [119] (version 1.6.20) [50,113,120]. Applications relating to the fields of construction and infrastructure of both Bibliometrix [121,122] and VOSviewer [123,124,125] have been reported in the literature, including studies that employed both tools simultaneously [52,53].
Bibliometrix is an R-based tool for comprehensive science mapping analysis and has been used for quantitative research in scientometrics and bibliometrics [118]. In this study, quantitative data visualization was performed using OriginPro Graphing & Analysis, version 2025. VOSviewer, in turn, is a software tool used for constructing and visualizing bibliometric networks [119]. Bibliometrix and VOSviewer worked with data exported from the Scopus database.
Textual analysis (or lexical analysis), which automatically extracts relevant information, has been used to classify statements according to their lexical similarities [49]. It is described as a set of techniques that apply statistical methods to texts, using quantitative approaches on essentially qualitative variables (the texts themselves) [49].
The textual analysis described in Section 4.2 was based on the abstracts of the articles in the dataset and was conducted using IRaMuTeQ (acronym for “Interface de R pour les Analyses Multidimensionnelles de Textes et de Questionnaires”), version 0.8 alpha 7 [126]. IRaMuTeQ provided functionalities ranging from basic lexicographic processing to complex multivariate statistical analyses [127]. This software has previously been used effectively in various fields of knowledge, including transportation [60], urban resilience [61], sustainability [62,63], energy [64], education [65], health [66,67], business [68,69], and manufacturing [70].
The textual analysis stage began with the construction of the corpus, which is the name given to the set of texts to be analyzed. The corpus consisted of 368 texts (abstracts). After importing the corpus, the software recognized the texts and divided them into text segments. Text segments (TS) are excerpts of texts and considered as the environment of the words [127]. Then, analyses were performed.
Specifically, after text segmentation, the TS were classified using Reinert’s hierarchical descending classification. This procedure grouped the TS into clusters of homogeneous vocabulary, which were identified by their most significant forms through χ 2 association tests [127,128,129]. For each cluster, IRaMuTeQ provided the most representative words, their frequencies, and the corresponding χ 2 values [127,128,129]. In addition, a factorial correspondence analysis (FCA) was performed, enabling the visualization of the relative positions of clusters in a two-dimensional factorial space, thus highlighting their proximities and divergences [127,128,129]. This set of techniques implemented in IRaMuTeQ also allows for associating complete texts (i.e., abstracts, and consequently the articles) with the clusters generated by the classification, thereby strengthening the link between vocabulary structures and the distribution of research topics within the reviewed literature [127].
The systematic review process—described as a robust and appropriate approach for research in the area of infrastructure [56,72,73,74]—followed the precepts of the PRISMA methodology [51], with the systematic organization and extraction of data from the selected articles. These data were synthesized, and the main findings are presented in Section 4.3.

4. Results and Discussion

This section presents the findings from the bibliometric and textual analyses, along with the systematic literature review performed.

4.1. Bibliometric Analysis

A descriptive analysis of parameters such as article distribution by year and growth rate can provide valuable insights into research productivity, impact, and development trends [50,113,130]. The dataset, composed of 368 documents, had a time span of 2020–2025, consisting of articles with an average age of 2.7 years. Publications were distributed as follows: (i) 2020: 60 documents; (ii) 2021: 58; (iii) 2022: 79; (iv) 2023: 73; (v) 2024: 85; and (vi) 2025 to date of search: 13. Without considering the partial-year 2025, the observed distribution indicated a growth trend (see Figure 5), with an annual growth rate of 9.1 % . The observed growth may indicate an increase in interest in the topic, investments, broader collaborations, and greater scientific productivity.
Papers in the dataset were published in 73 sources. The ten most relevant sources are listed in Table 2. A high concentration of papers were contained in relatively few scientific journals. The journal “Construction and Building Materials” (S1) is highly relevant to the field (see Figure 6), accounting for 27.2 % of the total articles. Combined with the “Journal of Materials in Civil Engineering” (S2), these two journals accounted for 37 % of papers in the dataset, suggesting a pattern of research dissemination. Particular sources were assessed to be specialized in the subject, both in the field of pavement engineering (S3, S5, S7, and S10) and in transportation (S8).
Bradford’s Law allowed for evaluation of the relevance of sources and identification of the most influential works related to a specific field of science [131,132]. By applying the concepts of this law (see Figure 6), S1 and S2 (2 sources, 136 articles) were classified as Zone 1 (core), S3 to S9 (7 sources, 116 articles) as Zone 2 (intermediate), and from S10 onwards (64 sources, 116 articles) as Zone 3 (peripheral). These results (ratio of 1:3.5:32 sources) were deemed to be broadly consistent with Bradford’s Law, whereby a few journals concentrate the majority of publications, while many others publish few articles on the topic [131,132].
Table 2 shows two journal-based metrics (JBMs): the CiteScore and the Journal Impact Factor. CiteScore is a metric developed by Elsevier (based on Scopus) which measures the impact of a journal based on the average number of citations received per document published over a period of three years. The Journal Impact Factor (JIF) is a similar metric developed by Clarivate Analytics (based on Web of Science), with a two-year evaluation window [133,134]. The correlation between these two metrics for the reported journals was r = 0.94 (see Figure 7), which can be classified as strong [135]; for comparison purposes, this correlation was higher than that reported by Okagbue and Silva [134]. Moreover, the ratio between CiteScore 2023 and JIF 2023 of Table 2 journals ranged from 1.169 to 2.382, with a mean value of 1.933 (i.e., CiteScore 1.933 × JIF ).
Construction and Building Materials” has a high journal-based metric (CiteScore of 13.8 and JIF of 7.4), ranking just behind the “Journal of Cleaner Production” (CiteScore of 20.4 and JIF of 9.8); see Figure 6. The latter focuses on sustainable materials, such as those in the dataset that address rubberized asphalt mixes [136], cold recycled mixes [137,138,139,140], and the incorporation of waste carbon fibers [141] and bamboo fiber [142].
The dataset included 1048 authors and 1707 author appearances, corresponding to 0.35 documents per author and 4.6 co-authors per document. Only 11 documents were single-authored. Following the precepts of Lotka’s Law [132,143]—which states that few authors publish a lot and many authors publish little—most authors in the dataset ( 71.7 % of the total number of authors) wrote only one article, while few wrote two articles (14%) or three articles (6.4%). As the number of documents increased, the number of authors dropped sharply. The author in the dataset who produced the most wrote 24 articles, being equivalent to 0.1 % of the total number of authors. The five most productive researchers were (i) Li, S.: 24 articles; (ii) Li, Y.: 14; (iii) Peng, X.: 12; (iv) Wang, Z.: 10; and (v) Zhang, Y.: 10.
The ten countries with the highest scientific production were (i) China: 898 appearances; (ii) United States of America (USA): 168; (iii) Iran: 93; (iv) Brazil: 78; (v) India: 74; (vi) France: 34; (vii) Pakistan: 25; (viii) Italy: 23; (ix) Australia: 20; and (x) Spain: 20. In total, 44 countries were represented, with the figures for Chinese scientific production reflecting the significant influence of China in this research domain.
Productivity by country was established by considering the country of the corresponding author, summarized in Table 3, showing the list of countries with five or more articles. The observed distribution confirms China’s leading role, being responsible for 45.1 % of the total number of articles. This dominance was reflected not only in quantity, but also in impact. When evaluating the number of citations (see Figure 8), Chinese research had a total of 2041 citations, which was approximately five times more than the second country with the most citations (Iran with 408 citations).
The average number of citations per document in the dataset was 10.4. Among the countries that produced the most (Table 3), the ranked list based on citation frequency was (i) Pakistan: 15 citations per document; (ii) Iran: 14.6; (iii) Australia: 14.4; (iv) India: 12.5; and (v) China: 12.3. The negative highlights were the USA and Turkey (see Figure 8). The USA, despite being the second-most productive country by number of publications, had a rate of 4.8 citations per document and was in fifth place in terms of number of citations. Turkey—the eleventh-most productive country by number of publications—had a rate of 3.6 citations per document, ranking fifteenth in terms of number of citations.
International collaborations have been reported to enhance the quality of research, contributing to greater scholarly impact and broader dissemination of published work [115,145]. Articles in the dataset had international co-authorships in 22.8 % of the research. Table 3 and Figure 9 show the degree of internationalization through the single-country publications (SCP) and multiple-country publications (MCP) indices. European countries, such as the United Kingdom (UK) ( 83.3 % ) and Italy ( 57.1 % ), showed high international collaboration. On the other hand, China ( 24.1 % ) and the USA ( 3.4 % ), despite being the most productive countries in the dataset, displayed a lower rate of international collaboration.
An analysis of co-authorship by country can support identification of social, scientific, and institutional affinities [50,146]. Figure 10 shows co-author relationships between countries in the dataset that have five or more documents (19 countries met this requirement). China was indicated to have influence on the structure and dynamics of the network [50,119], appearing as a central node with multiple connections, mainly with the USA, India, UK, and countries in the Middle East. The following clusters were identified as follows:
(i)
Red (Iran, Vietnam, France, Italy, Australia, and Egypt): The dataset indicated that these countries have a well-defined relationship with the USA and with each other.
(ii)
Green (Iraq, Malaysia, Pakistan, Saudi Arabia, and Spain): The dataset indicated a strong relationship with China.
(iii)
Blue (Hong Kong, Turkey, and UK): The dataset indicated that, with mutual independence, these countries have cross-collaborations with China.
(iv)
Yellow (China, Germany, and India): The dataset indicated that these countries are very productive and work closely together.
(v)
Purple (Brazil and USA): This is the only cluster in the dataset which was formed by just two countries, highlighting the two collaborations carried out.
Periodically, the World Economic Forum (WEF) publishes The Global Competitiveness Report, which has addressed various economic, social, and infrastructure pillars based on the WEF Executive Opinion Survey [144]. Road quality has been one of the components assessed under the infrastructure pillar. Respondents rated the roads on a scale from 1 to 7, where 1 = extremely poor—among the worst in the world—and 7 = extremely good—among the best in the world [144]. The road quality scores and the ranking positions of the countries with the highest levels of scientific output were presented in Table 3. The relationship between the number of articles, citation counts, and road quality indicated that there is no direct correlation between scientific productivity and road infrastructure (see Figure 11).
Countries such as China and Iran, which stood out in the dataset both in terms of volume and citations, still had a median road quality score (4.6 and 3.9, respectively). This suggests that the research environment in these two countries had not yet translated into practical improvements that were represented in the dataset. Brazil, in turn, had the worst road quality score among these countries (3.0); however, it had a high average of citations per article (10.8 citations). This behavior suggests that research was being driven by real and local needs, with good academic acceptance. Brazil has been described as being in the process of updating and improving its pavement design methodology, with potential influence on the academic environment [147,148,149,150,151].
Publications from USA produced a high road quality score (5.5) and high scientific output (29 documents). These aspects did not contribute to enhanced scientific dissemination, as the works from the country in the dataset had a low average number of citations per article (4.8 citations). Countries such as France and the UK, despite indications of high-quality roads (scores of 5.4 and 4.9, respectively), had modest scientific output in the dataset (six documents) and low relative impact (46 and 55 citations, respectively). These patterns reveal that science, although essential, did not necessarily operate in isolation: Its translation into concrete improvements could be hypothesized to depend on public policies, investments, governance, and local implementation capacity [152].
The dataset had a total of 3828 citations, with an average of 10.4 citations per document and an average of 2.3 citations per year per document. The ten most cited articles are presented in Table 4. These articles, which accounted for 2.7 % of the total number of documents, contained 15.1 % of the total citations. In line with previous analyses, the most prominent country was China, with Chinese researchers represented in 8 out of the 10 studies. Furthermore, 7 of the 10 most cited studies involved international collaboration, supporting the notion that this type of research tends to have greater impact [115,145].
Overall, the research summary presented in Table 4 indicated a convergence between material innovations, efforts to simulate real traffic conditions more accurately, and a strong focus on sustainability and durability. The most cited study in the dataset [22] investigated fatigue behavior under different loading conditions to effectively simulate real traffic. There was also a notable trend of studies with an emphasis on sustainability—such as the use of reclaimed asphalt pavement (RAP)—in combination with rejuvenators and polymers [43] and the use of alternative binders like epoxy asphalt to enable the use of 100 % RAP [44]. The use of RAP has involved several challenges, including limitations on RAP content, protocols for component characterization, mix design methodologies, the effects of material aging, the need for rejuvenation agents, and comprehensive life-cycle assessments—factors that all contributed to the high interest and impact of research in this area [154].
There were also investigations into aggregate morphologies and compaction methods on skeleton structures [89], as well as the incorporation of materials such as glass fibers with lengths of 6 mm and 12 mm in dosages of 0.3 % and 0.6 % (by %wt. of total mix), which contributed to increasing strength, resistance to rutting, reduced susceptibility to moisture damage, delayed fatigue cracking, enhanced healing capability, and mitigated adverse aging effects [40]. In addition, rubber powder from 40-mesh bias tires, incorporated at 21 % by weight of pure asphalt and tested under different conditions, allowed investigation of the influence of loading rate on the studied tests and supported the proposal of a new method for calculating the strength structure coefficient to improve design accuracy [136]. Furthermore, rock asphalt–styrene butadiene rubber with 5 % SBR (by weight of asphalt) demonstrated a significant improvement in low-temperature fatigue life ( 10   ° C) of about 15 % compared with mixes containing only Buton rock asphalt [39]. Studies examining different environmental conditions—including temperature, moisture, and aging—also demonstrated significant relevance and impact [23,87,153]. The clusters referenced in Table 4 were discussed in Section 4.2.
The dataset included a total of 1185 author’s keywords. The list of keywords with ten or more occurrences was (i) “asphalt mixture”: 80 appearances; (ii) “fatigue”: 49; (iii) “fatigue life”: 40; (iv) “fatigue cracking”: 23; (v) “fatigue performance”: 19; (vi) “asphalt mixtures”: 18; (vii) “fatigue damage”: 18; (viii) “road engineering”: 15; (ix) “asphalt pavement”: 14; (x) “fatigue test”: 12; (xi) “cracking”: 11; (xii) “rutting”: 11; (xiii) “road performance”: 10; and (xiv) “self-healing”: 10.
Wordcloud is a tool that has been commonly used to visually represent the frequency and importance of words in a research context [155]. A wordcloud composed of the thirty most frequent author’s keywords in the study dataset is presented in Figure 12, where the size of each word is proportional to its frequency.
The keyword analysis presented in Figure 12 emphasizes a central theme of this research: asphalt mixes and fatigue testing. The terms “fatigue life” (40 appearances), “fatigue cracking” (23), “cracking” (11), “fatigue performance” (19), and “fatigue resistance” (9) indicate that the research focused on evaluating the performance and fatigue life of asphalt mixes, with a central concern regarding resistance and cracking under cyclic loads. Test methods such as the “indirect tensile fatigue test” (9 appearances) and parameters such as “dynamic modulus” (8) and “dissipated energy” (9) were predominant, indicating dominant laboratory approaches.
An emerging increase in themes relating to sustainable technologies was evident through the terms “reclaimed asphalt pavement” and its variations (17 appearances), “warm mix asphalt” (7), and “crumb rubber” (6). These approaches have been characterized as representing innovative strategies to reduce environmental impacts, whether through recycling materials, reducing energy consumption or using sustainable reinforcements. Such initiatives are in line with the Sustainable Development Goals (SDG) of the 2030 Agenda, particularly SDG 9 (industry, innovation, and infrastructure), SDG 11 (sustainable cities and communities), and SDG 12 (responsible consumption and production) [47].
Terms such as “self-healing” (10 appearances), “aging” (9), “durability” (7) identified trends in research on topics associated with long-term resilience. Keywords such as “road engineering” (15 appearances), “asphalt pavement” (14), “road performance” (10), and “pavement performance” (8) provided evidence of the link between laboratory research and its relevance to real performance in road pavements.
Articles in the dataset included a total of 14,840 references. The most cited references (with five or more local citations) addressed a variety of topics, but most of the works were focused on evaluating and modeling the mechanical response of asphalt mixes under cyclic loads. More specifically, these studies addressed the influences of the test setup on different types of asphalt mixes [4,22,32,156,157,158]. Other prevalent themes included the proposal of a protocol for the evaluation of premature cracking based on principles of fracture mechanics [159], fundamental approaches of fatigue damage [4,8], and polymeric modification of the asphalt binder [160].
This bibliometric analysis employed an innovative approach by combining traditional models, such as Bradford’s and Lotka’s Laws, with modern impact and productivity indicators. This study revealed an important paradox: Although scientific production on fatigue is growing at approximately 9.1 % per year—led by Chinese production and focused on high-impact journals—its translation into practical improvements remains limited. This relationship was evident when relating the road quality index and academic relevance. These findings reinforced that technological innovation, although essential, should also be complemented by public implementation policies to transform scientific advances into practical solutions for road infrastructure. In addition, the analysis identified clusters of international collaboration and emerging themes (e.g., RAP), providing a roadmap for future research.

4.2. Textual Analysis

Lexicographic analysis was performed based on the 368 abstracts of the articles in the dataset. This process identified and isolated text units, identified parameters, searched for vocabulary and reduced words based on their roots (reduced forms), created a dictionary of reduced forms, and identified active and supplementary forms [127]. This analysis allowed for finding the parameters exposed in Table 5. In the analysis of the 368 texts, 88,688 occurrences (words, forms, or vocabulary) were identified, of which 3988 were distinct words and 1357 had a single occurrence.
The 100 most frequent active words encountered in the dataset references are shown in Table 6. As with the keyword analysis performed in Section 4.1, these words reveal a strong thematic concentration around the mechanical behavior and durability of asphalt mixes. The most frequent terms, such as “asphalt” (1950 appearances), “fatigue” (1891), “mixture” (1611), and “test” (1485), confirmed the theme of this research: fatigue assessment in asphalt mixes through mechanical tests. Furthermore, the terms “laboratory”, “specimen”, “sample”, and “conduct” provided evidence of the experimental character of the including works.
Words such as “performance”, “resistance”, “life”, “crack”, “heal”, “damage”, and “prediction” have been deemed to reflect an emphasis on investigating deterioration mechanisms and the parameters and phenomena that influence the durability of asphalt mixes under cyclic loading. Aligned with the 2030 Agenda [47], the presence of terms such as “rap” (reclaimed asphalt pavement), “recycle”, “rubber”, “fiber”, “modify”, and “additive” highlights a trend toward the investigation of sustainable or modified materials to enhance fatigue performance, reflecting environmental concerns and the pursuit of resource efficiency.
Words such as “indirect” and “tensile” have been used to refer to the indirect tensile test (ITT), which is one of the most commonly used methods in this type of study (as discussed in Section 4.3). As with the ITT, flexural tests such as four-point bending (4PB), three-point bending (3PB), two-point bending (2PB), and semi-circular bending (SCB) have also been employed for fatigue characterization; words deemed to reflect these approaches include “beam”, “point”, and “bend”. These tests are controlled by either “strain” or “stress” at different “levels”. In stress-controlled tests, the measurement of “strength” has typically been important for determining the stress “ratio”. Given that testing terminology can vary across standards and regions, the words most frequently observed may reflect these normative influences.
Descending hierarchical classification analyses of the active forms (words) were performed using IRaMuTeQ and based on Reinert’s method [127,128,129]. Text segments were grouped into classes based on their vocabulary and the set of terms was partitioned based on the frequency of the reduced forms [127,128,129]. This technique is generally useful for synthesizing a large amount of data and has been used to verify trends in a given field of knowledge [61,63].
The corpus was segmented into 2449 text segments (TS), of which 2188 ( 89.3 % ) were retained for analysis. The analyzed content was categorized into four clusters (see Figure 13): (i) cluster 1 (red): 382 TS ( 17.5 % ); (ii) cluster 2 (gray): 281 TS ( 12.8 % ); (iii) cluster 3 (green): 274 TS ( 12.5 % ); (iv) cluster 4 (blue): 574 TS ( 26.2 % ); and (v) cluster 5 (purple): 677 ( 30.9 % ).
The five clusters formed two major branches in the corpus (see Figure 13). The upper main branch, composed of clusters 2 and 4 and responsible for approximately 39 % of the textual segments, concentrated studies on mechanical characterization and performance modeling. The lower main branch, which brings together clusters 1, 3, and 5 and corresponds to approximately 61 % of the segments, covered topics related to pavement management and sustainability, with an emphasis on performance prediction, functional evaluation, and behavior of innovative mixes.
In Table 7, the ten most representative words of each cluster are presented, along with relevant information such as the number of text segments containing the word in the cluster (Fr. TS), the total number of text segments in the corpus containing the word at least once (Total Fr.), the percentage of the word’s occurrences in the cluster relative to its occurrences in the entire corpus (%), the association between the word and the cluster ( χ 2 ), and the significance level of this association (p) [127].
As shown in Table 7, each cluster is characterized by a specific vocabulary with high χ 2 association. These clusters are represented in Figure 13 (dendrogram), which illustrates the hierarchical process that led to their formation. To complement this hierarchical representation, Figure 14 shows the factorial correspondence analysis (FCA), which projects the clusters into a two-dimensional factorial space. While the dendrogram (Figure 13) depicts the division process based on lexical similarity and Table 7 details the characteristic terms, the FCA plot highlights the relationships and proximities between clusters, helping to identify overlapping themes and divergent research directions [127,128,129].
Therefore, the distribution of clusters in Figure 14 and the importance of words were determined based on a χ 2 analysis. The clusters were separated by quadrants, and the classes exhibited well-defined relationships, consistent with the dendrogram in Figure 13. As a result, Figure 13 and Figure 14 and Table 7 should be interpreted jointly: the dendrogram depicts the partitioning process, the table details the lexical content of each class, and the FCA plot illustrates how the classes relate to one another.
Cluster 4 (blue) was located in quadrant I (see Figure 14). This cluster had a strong emphasis on fatigue modeling, prediction, and analysis. The dataset article that most closely matched cluster 4 is that of Zhang et al. [161] ( χ 2 = 22.58 ), which is entitled “Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and a fatigue-freeze-thaw damage evolution model”.
Cluster 2 (gray), densely positioned in quadrant IV, grouped shapes related to mechanical properties and mechanical tests, such as indirect tensile, bending, and uniaxial methods. Cluster 2 properties were highlighted by the dominance of laboratory protocols in fatigue characterization. The article “Correlation between stiffness and fatigue behavior at asphalt mastic and asphalt mixture level” of Steineder et al. [162] was identified as the dataset study with the greatest relationship with the cluster ( χ 2 = 21.53 ).
Cluster 1 (red) occupied the upper left corner (quadrant II) and was distantly separated from the other clusters. In addition, cluster 1 was associated with terms that refer to pavement management, as well as sustainable policies and practices. The most representative article of this class was that of Sá et al. [163] ( χ 2 = 33.20 ) entitled “Use of iron ore tailings and sediments on pavement structure”.
Cluster 5 (purple) was distributed mainly between quadrants II and III. The cluster theme was the intersection between material modification and assessments of susceptibility to environmental conditions, as well as mechanical and functional performance. The most representative article in cluster 5 was that of Yang, Zhou, and Li [164] ( χ 2 = 17.92 ), which evaluated the “Influence of fiber type and dosage on tensile property of asphalt mixture using direct tensile test”.
Cluster 3 (green) was primarily located in quadrant III and addressed articles focused on modifications of the asphalt binder, such as the use of styrene–butadiene rubber (SBR), styrene–butadiene–styrene (SBS), and polyethylene, among others. The article with the highest correspondence with cluster 3 ( χ 2 = 28.61 ) was that of Liu et al. [39]—the fourth most cited article in the dataset (see tab:top10articles).
To quantify the relevance of research topics, the 10 most-cited articles (tab:top10articles) were classified within the clusters generated for the entire dataset ( n = 368 ) through hierarchical descending classification and FCA. The classification considered the most significant association ( χ 2 ), which indicates the predominant affinity of each study with a given theme. The analysis reveals that the most influential studies are mainly concentrated in two thematic axes: evaluation of innovative materials (cluster 5, 40 % of the articles) and performance modeling (cluster 4, 30 % ). Notably, although sustainability is evident in several high-impact articles—through the use of RAP, rubber, and recycled polymers—none fall into cluster 1 (sustainable management and policies). This suggests that the most influential research in the analyzed period prioritized the validation of technical and mechanical performance of sustainable solutions (the focus of clusters 3 and 5) over management and policy aspects, which characterize cluster 1. This quantitative approach therefore weighs the importance of different factors, highlighting the scientific community’s focus on the technical feasibility of innovative materials.
In summary, the textual analysis applied to the 368 abstracts supported construction of a robust lexical–thematic overview of the state of the art on fatigue in asphalt mixes. Basic lexicography and multivariate analyses revealed a predominance of studies focused on mechanical characterization, performance modeling, and evaluation of modified materials. Descending hierarchical classification and factorial correspondence analysis highlighted the segmentation of the studies, which addressed aspects ranging from sustainability and pavement management to advanced binder modification techniques. There appeared to be a tendency to focus on improving the performance of asphalt mixes combined with environmentally friendly solutions. These results complement the trends identified in the bibliometric analysis performed in Section 4.1, consolidating a comprehensive view of the topic.

4.3. Systematic Review

This section offers an in-depth examination of the topics previously introduced in Section 2, which is further enriched by the trends observed in the analyzed dataset.
The studies from the dataset used in the systematic review ( n = 100 ) followed the trends identified in the broader analysis conducted in Section 4.1 and Section 4.2 ( n = 368 ). It was possible to observe that the thematic areas align with the clusters in Figure 14, including (i) cluster 1, which addressed pavement management, policies, and sustainable practices (e.g., [137,165,166]); (ii) cluster 2, which focused on mechanical properties and mechanical testing (e.g., [23,136,167]); (iii) cluster 3, which focused on binder modification, had emphasis on styrene–butadiene–styrene (SBS), used in 32 studies, and rubber modifiers such as styrene–butadiene–rubber (SBR) or crumb rubber, which were used in 20 studies; (iv) cluster 4, which involved modeling, prediction, and fatigue analysis (e.g., [168,169]); and (v) cluster 5, which addressed material modification with fibers, for instance, as well as evaluations of environmental susceptibility, mechanical performance, and functional behavior (e.g., [170,171,172]).
Also consistent with the trends identified in the broader analysis, the countries most represented in the dataset included—based on the indexed Reprint Address—were China (54 articles), Iran (10), India (8), the USA (4), and Brazil (4).
Reflecting international collaborations, regulations in force in the country, or existing laboratory infrastructure, Figure 15 presents the relationship between the countries of the corresponding authors and the tests performed in the studies, noting that a single study may have included more than one type of test. The “others” category listed less conventional, poorly standardized studies, or those lacking information relating to configurations. These include two unspecified bending tests [173,174], five-point bending test (5PB) [175], different configurations of shear fatigue tests [176,177,178,179], and a characterization by small-scale accelerated pavement test [180].
In this analysis, the tests presented in Figure 3 are the predominant ones in the following order: (i) ITT; (ii) 4PB; (iii) uniaxial; (iv) SCB; (v) 3PB; and (vi) 2PB. The results demonstrated a high concentration in the ITT (35 appearances) and 4PB (31) tests, which together represented 61 % of the total. These results are comparable to Section 4.1 and Section 4.2 and with those of Cardoso et al. [74], in which the fatigue tests 4PB and ITT were predominant in the incorporation of plastic waste into road pavements, representing 75 % of the studies in the systematic literature review. However, the classification reflects methodological choices of the present study; as a dynamic research field, future reviews may identify different loading modes and distributions across categories. In this regard, Braham and Underwood [91] provide a comprehensive overview of the wide range of tests employed for fatigue evaluation.
Furthermore, China was found to possess a wide range of method occurrences: ITT (15 appearances), 4PB (14), uniaxial (12), SCB (8), 3PB (7), and others (6). All 3PB tests in the dataset occurred in China. Countries such as Iran and India focused on ITT and 4PB tests, while Iran presented ITT (5) and 4PB (5), and India featured ITT (6) and 4PB (2) tests. In this context, Brazil emphasized characterization with ITT (2) and uniaxial (2) tests.
The ITT is a repeated load test applied to a cylindrical specimen (see Figure 3e), generating tensile stresses perpendicular to the loading direction. Used in 10 of the 17 countries considered and applied across a wide range of uses aligned with the trends presented in Section 4.1 and Section 4.2, it is a simple and low-cost test that uses the same equipment as other tests (resilient modulus and indirect tensile strength) and presents a biaxial state of stress [3,17,181]. This method can be performed with both laboratory-fabricated specimens and field-extracted samples [3,17]. However, this type of test tends to underestimate fatigue life due to the significant accumulation of permanent deformation and fatigue damage, as well as the absence of stress reversal and potential—under great loadings and temperatures—for shear and compressive failures [4,17,165,181].
In the study by Di Benedetto et al. [4], which compared the ITT with 2PB, 3PB, 4PB, and uniaxial tension–compression tests, the lowest fatigue life value was obtained using the ITT. These limitations were highlighted by Ziari et al. [165]—the fourteenth most cited article in the dataset—who used the method only for comparative purposes between mixes, without recommending it for accurate fatigue life estimation. However, this test is covered by widely applicable and highly important standards, such as NF EN 12697-24 [7], and, with proper field correlation, it can, in principle, be used in pavement design [17].
Together, beam bending fatigue tests (2PB, 3PB, and 4PB—see Figure 3) were the most common in the dataset and with the most diverse applications, being consistent with the trends in Section 4.1 and Section 4.2. These tests have tended to produce higher fatigue lives than the ITT and uniaxial tests, with results influenced by the specific test configuration and specimen size [4,18,19]. Although the stress state is essentially uniaxial and the execution is more complex, involving more elaborate compaction and cutting procedures, these tests showed broad applicability within the dataset. The technique measures a fundamental property and is recommended for the evaluation of asphalt mixes and pavement design (with an appropriate shift factor) [17,18,21]. The 4PB test was reported to hold the advantage of generating a uniform stress distribution in the fracture region, which helps reduce result variability [17]. The trapezoidal 2PB test, although appearing only once in the dataset, is a classical method with historical relevance, having been employed since Huet’s pioneering studies [80]. A dearth of citations in the dataset suggests unexplored potential that merits further investigation.
The uniaxial test (see Figure 3f) was identified in the dataset, being conducted under direct tension (e.g., [136,167,182]), compression (e.g., [136,182]), and tension–compression (e.g., [22,167,183]). Uniaxial tests generally imposed direct stress on the specimen with assumed homogeneous stress field, thereby generating a damage mechanism directly in the specimen [6,18]. Uniaxial tests generally induced failure in the central part of the specimen [18]. Di Benedetto et al. [4] compared the uniaxial tension–compression with other setups and the fatigue life was higher than that of the ITT and lower than that of the beam bending (2PB, 3PB, and 4PB). Fatigue lives higher than those of the ITT were also observed in the dataset, as seen in Lv et al. [182]. Although the uniaxial test can be used to evaluate mixes and to design pavements (with shift factor), and the tension–compression test simulates the load pulse observed in the field (compression–tension–compression), this type of test does not necessarily represent actual field conditions [17].
In the dataset, tests that used the uniaxial setup stood out for investigating fatigue behavior with a focus on materials or additives [136,142,182,184,185], modeling or criteria [22,167,169,185,186], and pavement design and simulation [187], among others [183,188]. Furthermore, a link was identified between uniaxial test method and the application of advanced analysis models such as simplified viscoelastic continuum damage (S-VECD) [142,185,186,187] and analyses based on dissipated energy [22,169,186].
The connection between uniaxial tests and models such as S-VECD is enabled by the use of the Asphalt Mixture Performance Tester (AMPT), which has been employed by Jia et al. [142], Queiroz et al. [185], Keshavarzi and Kim [186], and Bueno et al. [187]. Following the AASHTO TP 107 and AASHTO TP 133 protocols and conducted in strain-controlled mode, the direct tension cyclic fatigue tests were fundamental for calibrating the S-VECD model; when performed under AASHTO TP 133, they also presented advantages in terms of testing time and resources [189,190]. The uniaxial testing methodology in the AMPT served as a link between laboratory characterization and mechanistic pavement design, enabling damage modeling and performance simulation, as it provides inputs for FlexPAVE TM cracking evaluation [19,187,191,192,193].
The SCB test (see Figure 3d), which features a loading configuration similar to that of the ITT but uses semi-circular specimens and involves a more complex stress state, has been utilized for both fatigue resistance evaluation and the investigation of fracture mechanisms [18,20,194,195,196]. SCB testing has emerged as a commonly used method in recent years [20,194,197]. In certain cases, a notch can be introduced at the center of the specimen to clearly define the onset of crack propagation [18,20]. This process can be evaluated using the digital image method, which allows for detailed assessment of both crack initiation and propagation [18,20]; this approach was also recorded in the dataset [198,199,200]. Moreover, the works that used SCB addressed different themes, such as freeze–thaw cycles [198,199], heating and self-healing [201,202], evaluation of fatigue resistance and cracking mechanisms [88,200,203,204], and alternative and sustainable materials [205].
Therefore, the selection of an appropriate fatigue test for asphalt mixes is a complex decision influenced by multiple factors. The choice is often dictated by national standards, laboratory infrastructure, research objectives, and pavement design methodologies. For instance, the ITT, despite its limitations in accurately estimating fatigue life, is frequently employed in academic settings for comparative purposes and, due to its simplicity and low cost, is also incorporated into certain pavement design contexts [17,151,165]. In contrast, methodologies aiming to reproduce field conditions and provide fundamental parameters for pavement design tend to favor beam bending tests, particularly the 4PB and 2PB configurations [17,21]. While the 4PB test has demonstrated broad applicability, the 2PB test remains a classical method of historical relevance and robustness within the well-established French methodology [14,15,21,206]. Moreover, the application of advanced damage models, such as the S-VECD, directs the selection toward uniaxial tests, which provide the parameters required for mechanistic modeling [19,192]. For investigations specifically focused on fracture mechanisms, the SCB test emerges as a suitable option [20]. Thus, bending tests—particularly 4PB and 2PB—should be considered in the classical approach [18,21], whereas in damage modeling, the uniaxial test has increasingly become the preferred choice among researchers [19,187,192]. Nevertheless, regardless of the test employed, field correlations remain essential to account for specific conditions.
Loading frequency has been described as another fundamental parameter in fatigue performance tests on asphalt mixes, with potentially direct influence on fatigue parameter estimates [31,32]. Test frequency has typically been determined from traffic-induced mechanical response pulses and has been obtained through pulse time analysis or Fourier transform methods [18,207]. Several predictive models have been developed and among the factors that can affect the frequency, vehicle speed was identified as the most influential (when compared to pavement depth, loading radius) [18]. Barra et al. [208] discussed loading frequency configuration in a test apparatus used to measure the complex stiffness modulus and fatigue of asphalt mixes.
In fatigue tests, prior research has indicated that test frequency directly affected the measured stiffness modulus and, consequently, the estimated fatigue life [3,18]. The effect of test frequency on estimated fatigue life was mitigated in studies where the fatigue failure criteria were based on the stiffness modulus [18]. In the dataset studies, test frequency values ranged from 0.01 Hz (4PB, 10   ° C) [136] to 30 Hz (4PB, 15   ° C) [209], with 59 studies using 10 Hz. Some studies investigated fatigue behavior at more than one frequency [22,39,176,179,210,211].
Fatigue tests have historically been performed in two distinct loading modes: stress- (load-) or strain- (displacement-) controlled fatigue tests [2,18,19]. Typically indicated only for specimens with thickness greater than 150 mm, in controlled stress tests, the stress is kept constant, and the strain increases following a three-phase tendency, while the modulus is expected to exhibit a tendency opposite to that of the strain [2,18,19]. In the controlled strain mode—typically indicated for thicknesses less than 50 mm—the applied stress and the modulus are decreased rapidly, while the strain is expected to remain constant throughout the test [2,18,19]. Some literature sources describe a mixed control mode, which is indicated for intermediate thicknesses and combines the two previous modes, often aiding in the monitoring of crack propagation during the fatigue damage process [2,18,19].
Prior studies have indicated that the choice of control mode can influence the material’s measured fatigue life and damage characteristics. For example, the same mix subjected to both control modes has tended to have a higher fatigue life in the controlled strain, indicating that the test under controlled stress appeared to be more severe [2,4,17,212]. Especially under strain-controlled conditions, fracture is often not visually apparent, and due to this characteristic, failure criteria such as stiffness reduction are commonly applied [6,7,17,19,213]. In the dataset, 31 articles explicitly used stiffness reduction criteria, while 27 studies applied the classical criterion of reducing the initial stiffness by 50 % (e.g., [23,28,43,214,215]).
Tests in strain-controlled mode are more representative of real pavement conditions, while those in stress-controlled mode tend to produce crack propagation at faster rates than observed in real conditions [17]. Regarding dissipated energy, tests in stress-controlled mode tended to present an increase with a fast and increasing dissipation rate, while in strain-controlled mode the opposite occurred (i.e., a decrease in dissipated energy at a slow and decreasing rate) [17]. Employing unified standards was identified as a key factor in enabling cross-study comparability, such as NF EN 12697-24 [7] or AASHTO T 321 [213], which established the experimental criteria and conditions.
With 68 records ( 63 % ), stress (load) control was the most used method in the dataset, compared to strain (displacement) control, which obtained 40 records ( 37 % ). There was a strong association between the type of test and the control mode (see Figure 16). The 4PB test had a tendency to be performed with strain control, while methods such as the ITT and SCB followed the opposite tendency, with stress control dominating. The uniaxial test presented a balanced distribution (eight strain-controlled and nine stress-controlled). The 3PB test showed a strong association with the stress-controlled mode, and the test performed under 2PB used the strain-controlled mode.
It is well known that properties of asphalt mixes, being viscoelastic materials, are strongly influenced by temperature. Consequently, fatigue test results are commonly observed to be affected by test temperature [28,29,30]. Bodin et al. [216] investigated the fatigue behavior in 0 ° C, 10   ° C, 20   ° C, and 30   ° C and observed that the worst strain performance for 10 6 cycles ( ε 6 ) was at intermediate temperatures. These results suggest that standards should play a fundamental role in specifying test temperatures for asphalt mix fatigue tests.
Among dataset studies that considered test temperature, fatigue tests were performed in 10   ° C [39,202] to 60   ° C [176], with and average value of 20   ° C, standard deviation of 10.4   ° C, median of 20   ° C, and tending to a normal distribution. Figure 17 presents the test temperatures used in the studies from the dataset, the tolerance interval (mean plus three standard deviations), and the frequency histogram with a Gaussian distribution fit [217]. These data indicate that most tests were performed at intermediate temperatures (between 10   ° C and 30   ° C), although studies were also conducted at high and low temperature conditions, covering a wider range of investigation.
Some research identified in the dataset evaluated fatigue behavior under different temperatures. Cheng et al. [23] evaluated fatigue behavior at different temperatures for ITT and 4PB tests and concluded that in the case of the ITT, temperature increases decreased the fatigue life, while in the case of the 4PB, the fatigue life increased. Liu et al. [39] and Ameri et al. [218] evaluated fatigue behavior of modified asphalt at low temperatures. Cheng et al. [28] investigated the critical position of fatigue damage within asphalt layers, considering temperature and strain distribution. Chen et al. [219] investigated the influence of temperature on fatigue cracking behavior. Clark and Gallage [220] aimed to determine an equation to estimate fatigue performance at any temperature, assuming that a master curve of the complex modulus was available. The study by Zou et al. [210] concluded that temperature and strain level had a greater influence on fatigue properties than the adopted frequency. In addition, several studies have investigated fatigue behavior at more than one temperature [23,28,168,176,179,183,188,203,210,211,214,215,220,221].
The shape of loading pulses (loading waveform) applied in fatigue testing has been shown to significantly influence the response of the asphalt mix under test [22,27]. The most commonly used waveforms described in the dataset were haversine (strain of a specimen is continuously tensile) and sinusoidal (specimen exhibits tensile–compressive strain response). Reports in the literature recommended—when comparing these two approaches—the use of sinusoidal waveforms [27].
General methods permit loading waves to be applied continuously or interspersed with rest periods. Both methods seek to simulate the intervals between vehicle passages in the field—and their relationship with the self-healing phenomenon—and to reduce the severity of certain types of tests, such as ITT or stress-controlled tests [17,86,222]. Studies adopting these approaches were identified in the dataset [40,185].
Furthermore, the evaluation of loading waveforms represented a common theme in the dataset, and the most cited article in the dataset addressed this topic. Cheng et al. [22] compared haversine waveforms with in situ strain waveforms observed in the asphalt layer in the field under moving axle loads (longitudinal strain wave induced by a single axle and a tandem axle). The impact of the compression zone and the effect of superposition (strains superimposed by multiple axes) on fatigue behavior were evaluated. Three approaches were used: classical fatigue model, healing index, and dissipated energy. The assessment concluded that the application of these different waveforms resulted in distinct responses regarding fatigue life, stiffness modulus, phase angle, and dissipated energy. The compression zone was considered to attenuate the damage caused by the tensile region in the single-axle wave, whereas the superposition of strain in the tandem-axle wave was deemed to accelerate damage accumulation.
In experimental studies, increasing the sample size (total number of specimens) is generally associated with improved representativeness of results, allowing for a more robust characterization of the typical behavior of the population [135,223,224]. Standards typically require a minimum number of specimens. For instance, NF EN 12697-24 [7] requires at least 18 specimens per experimental campaign. In the case of the 2PB test, the standard mandates at least three strain levels for constructing the fatigue curve, with levels approximately regularly spaced on a logarithmic scale and a homogeneous number of specimens per level [7]. Furthermore, the standard establishes a minimum fatigue life distribution requirement, such that at least one-third of the results must have N 10 6 and one-third N 10 6 [7].
In the analyzed dataset, 40 studies did not explicitly report the number of specimens used in the tests. Among the studies that provided sample size information, the average was 8.6 ± 7.5 specimens per asphalt mix evaluated. In addition, the average number of stress levels was 2.7 ± 1.5 levels per study. In 30 studies, only one stress level was adopted during the tests (e.g., [87,225,226]). Therefore, the methodological aspects assessed by this study suggested that, in many cases, fatigue assessment was not treated as the central objective of the investigations, but rather as a complementary property among others analyzed. From the perspective of the classical fatigue approach, both the reduced sample size and the absence of fatigue curve construction may have compromised the reliability and representativeness of the results obtained. Previous research has shown that increasing the sample size directly enhances representativeness, improves data reliability, and enables a more accurate characterization of fatigue behavior [227]. Accordingly, it is recommended that future fatigue studies employ the largest feasible sample sizes to ensure the accuracy and robustness of fatigue-related test results.
Due to the inherent characteristics of asphalt mixes and fatigue-related phenomena, test specimens subjected to the same test conditions may present substantially different fatigue properties [4,29,228]. A previous study reported that the removal of high outliers in fatigue lives affected the fatigue curve parameters by up to 21.37 % , with the slope of the fatigue line changing by as much as 8.07 % [227]. In the analyzed dataset, only four studies explicitly addressed the use of techniques to manage result variability and ensure data validity. Based on Chinese regulations JTG 5210-2018, Ren et al. [229] iteratively applied tolerance intervals of three times the standard deviation, followed by removing experimental points outside the interval, until all points were within the range. Xiang et al. [230] applied the coefficient of variation (CV)—the ratio of the standard deviation to the mean [224]—as an acceptance criterion, eliminating results with CV > 15 % . Nian et al. [179] chose to remove the maximum and minimum values from five sets of parallel test specimens at each stress level, and the fatigue life results of the remaining three sets were averaged. Li et al. [231] did not clarify the method used and only reported the use of a ‘discarding treatment’.
The first two approaches [229,230] relied on metrics—mean and standard deviation—that are highly sensitive to outliers, which compromises their effectiveness in identifying and handling atypical results [135]. The third approach [179], based on the arbitrary removal of the highest and lowest values, may eliminate the material’s intrinsic variability and fail to represent its typical behavior, lacking statistical robustness. Statistically, a commonly used approach for this situation is box plot analysis, which incorporates tools to mitigate the influence of outliers and enables their identification [135,227]. In this regard, future studies are encouraged to adopt box plot analysis for outlier detection, removing atypical high values, as these may lead to an overestimation of fatigue performance [227].
Another alternative for managing data dispersion is to use Weibull distributions for characterizing experimental data. The Weibull statistic [232,233]—based on the weakest link theory—is used in different areas of engineering and materials science to model scattered datasets, including failure data [104,234,235,236,237,238]. Prior research has already reported that the Weibull distributions are suitable for the study of fatigue [239,240,241], including for asphalt materials [100,242,243].
In the investigated dataset, four studies applied Weibull distribution. In Bala and Napiah [214], Jiang et al. [244], and Yang et al. [177], Weibull distribution was used to fit fatigue life curves under different testing conditions, allowing for statistically reliable estimations. Zou et al. [210] fitted the stiffness ratio curve using Weibull equations, allowing for an adequate description of the damage behavior under different frequencies, temperatures, and strain levels. However, all these applications were made using the simplest Weibull distribution model (two parameters), without considering the complete model (three parameters), which incorporates a minimum value at which failures can occur (location parameter). Prior studies have reported better performance for the model with three parameters when compared to the two parameters [100,245] or with a normal distribution [100,240].
Beyond these statistical techniques for handling experimental data, additional approaches can contribute to statistical rigor. The application of the law of propagation of uncertainties allows for quantifying how input variable errors affect derived parameters [103,104,105,223], while the use of confidence intervals and distribution fitting models provides more robust estimates of central tendency and variability [135,224,246]. However, the application of such robust statistical tools appeared only to a limited extent in the dataset. An analysis of the ten most cited articles (see Table 4)—considered exemplars of impactful research in which methodological rigor would be expected—corroborates this observation. The results revealed a limited statistical approach: six out of ten reported only basic descriptive statistics (mean and standard deviation) for fatigue life [22,39,40,43,44,136]; none explicitly employed confidence intervals, distribution fitting, or uncertainty propagation; and only one applied the coefficient of variation [43]. This evidence indicates that the absence of advanced statistical methods may be regarded as a critical gap in the field such that reduced rigor potentially limits the reliability of the findings. Hence, future studies are encouraged to incorporate rigorous statistical methods, such as those highlighted in this review, as a standard practice in fatigue research.
The systematic analysis of the dataset confirmed trends which were identified in the bibliometric and textual analyses. The predominance of test methods—such as the ITT—reflected the widespread adoption due to practicality, standardization, and historical relevance, despite known limitations. The observed variability in test protocols (e.g., control modes, temperatures, and waveforms) reinforced the need for standardized methodologies to enhance reliability. Additionally, aspects such as frequent omission of key experimental details (e.g., sample size and statistical treatment) highlighted opportunities for improvements in methodological rigor in future studies. By addressing these gaps and by identifying and utilizing appropriate, rigorous statistics (e.g., three-parameter Weibull distribution), the research field could advance toward more robust fatigue life predictions and optimized pavement design practices, narrowing discrepancies between laboratory findings and real-world performance.
Ultimately, it is relevant that the scope of the search was restricted to English-language articles indexed in Scopus. Although Scopus is a comprehensive and widely recognized source [107,108,110], engineering practice in asphalt materials and fatigue testing is also informed by standards (e.g., NF EN 12697-24 [7]), technical reports, and conference proceedings, which were not directly captured in the dataset. As a result, the trends identified in this study may reflect a stronger representation of academic practices while under-representing applied practices or region-specific developments that are often disseminated in non-English publications or not indexed in global databases. Nevertheless, much of the academic literature builds upon or references established standards, which helps align experimental protocols with engineering practice. Future research could address this limitation by incorporating non-indexed and non-English sources, conference proceedings, and regional databases, thereby providing a more comprehensive integration of scientific, technical, and normative contributions. In addition, given the methodological variability identified, future studies should broaden the scope by assessing how such variations influence fatigue performance, particularly in asphalt mixes that reflect emerging thematic trends, such as sustainable practices with reclaimed asphalt pavement (RAP), fiber-reinforced mixes, or the use of polymer-modified binders.

5. Conclusions

This study sought to survey and evaluate the broad scientific findings relating to fatigue tests on asphalt mixes, utilizing combined bibliometric, textual, and systematic approaches in innovative ways. The key findings are summarized below:
(i)
Trends identified in the literature survey indicate that scientific production grew at a rate of 9.1 % per year (2020–2024), which presumably has been driven by technical and sustainable demands.
(ii)
The literature survey found that China leads the scientific field in volume and impact of publications. Highlighting that science does not operate in isolation, overall, there is a mismatch between scientific production, scientific impact, and the WEF road quality index.
(iii)
Five thematic clusters were identified in the textual analysis: pavement management and sustainable policies, mechanical characterization and test protocols, binder modification techniques, performance modeling and prediction, and functional and environmental evaluation of innovative mixes.
(iv)
Consistent with the 2030 Agenda, a trend was identified toward themes focusing on sustainable solutions such as reclaimed asphalt pavement (RAP), warm mix asphalt, and crumb rubber, among others.
(v)
Polymeric modifiers, such as styrene–butadiene–styrene (SBS), and modification with different fibers were highlighted in the dataset.
(vi)
The systematic review revealed a tendency to omit methodological information in the studies analyzed, in addition to confirming the existence of significant variability in the experimental procedures adopted.
(vii)
Despite known limitations, the indirect tensile (ITT) fatigue test was the most used in the dataset, followed by the four-point bending (4PB).
(viii)
Given the dispersion of results intrinsic to fatigue and asphalt mixes, rigorous statistical approaches should be further explored in future work, contributing to more robust fatigue performance predictions and optimized pavement design practices.
Finally, it is acknowledged that the integrated review process carried out has inherent limitations related to the methodological choices adopted. The scope of this study was restricted to articles published in English and located in a single database and within a specific time interval. It is recommended that future research which seeks to replicate or expand this approach consider a broader coverage—including regional databases or studies in other languages—in order to enrich and complement the results presented here. To assist future researchers in applying the adopted methodology and utilizing the related software tools, Supplementary Materials has been made available in the back matter.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/app151810220/s1.

Author Contributions

Conceptualization, J.V.d.L., B.S.B. and A.M.; Data curation, J.V.d.L.; Formal analysis, J.V.d.L., B.S.B. and A.M.; Methodology, J.V.d.L.; Validation, J.V.d.L.; Visualization, J.V.d.L.; Writing—original draft, J.V.d.L.; Writing—review & editing, J.V.d.L., B.S.B., A.M., G.B.H. and A.F.; Supervision, B.S.B. and A.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Brazilian Federal Agency for Support and Evaluation of Graduate Education—CAPES (Finance Code 001), and by the Research Center for Territory, Transports, and Environment—CITTA (UID/04427/2023).

Acknowledgments

Jessé Valente de Liz would like to acknowledge the financial support from the Brazilian Federal Agency for Support and Evaluation of Graduate Education—CAPES. Adelino Ferreira would like to acknowledge the financial support provided by the Research Center for Territory, Transports, and Environment—CITTA. The authors would like to acknowledge the valuable suggestions of the anonymous referees, which have contributed to improving the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
2PBTwo-point bending
3PBThree-point bending
4PBFour-point bending
5PBFive-point bending
AASHTOAmerican Association of State and Highway Transportation Officials
AMPTAsphalt Mixture Performance Tester
CVCoefficient of variation
FCAFactorial correspondence analysis
IRaMuTeQInterface de R pour les Analyses Multidimensionnelles de Textes et de Questionnaires
ITTIndirect tensile
JIFJournal Impact Factor
LVELinear viscoelasticity
MCPMultiple-country publications
PRISMAPreferred Reporting Items for Systematic Reviews and Meta-Analyses
RAPReclaimed asphalt pavement
S-VECDSimplified viscoelastic continuum damage
SBRStyrene–butadiene rubber
SBSStyrene–butadiene–styrene
SCBSemi-circular bending
SCPSingle-country publications
SDGSustainable Development Goals
TCTotal of citations
TSText segments
UKUnited Kingdom
USAUnited States of America
VECDViscoelastic continuum damage
WEFWorld Economic Forum

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Figure 1. Domains of behavior for asphalt mix, based on [75,77].
Figure 1. Domains of behavior for asphalt mix, based on [75,77].
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Figure 2. Formulation levels of asphalt mixes according to the French methodology.
Figure 2. Formulation levels of asphalt mixes according to the French methodology.
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Figure 3. Schematic diagrams of different loading modes (not to scale).
Figure 3. Schematic diagrams of different loading modes (not to scale).
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Figure 4. Workflow of the dataset selection process and analyses conducted.
Figure 4. Workflow of the dataset selection process and analyses conducted.
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Figure 5. Annual scientific productions, where “*” refers to the partial year 2025.
Figure 5. Annual scientific productions, where “*” refers to the partial year 2025.
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Figure 6. Most relevant sources of the dataset.
Figure 6. Most relevant sources of the dataset.
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Figure 7. Linear regression between CiteScore 2023 and Journal Impact Factor 2023.
Figure 7. Linear regression between CiteScore 2023 and Journal Impact Factor 2023.
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Figure 8. Countries with the highest citation counts in the dataset.
Figure 8. Countries with the highest citation counts in the dataset.
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Figure 9. International collaboration among the top-10 publishing countries.
Figure 9. International collaboration among the top-10 publishing countries.
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Figure 10. Co-authorship network analysis.
Figure 10. Co-authorship network analysis.
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Figure 11. Relationship between countries, scientific production and relevance, and quality of highways.
Figure 11. Relationship between countries, scientific production and relevance, and quality of highways.
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Figure 12. Wordcloud of author’s keywords.
Figure 12. Wordcloud of author’s keywords.
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Figure 13. Dendrogram using Reinert’s method.
Figure 13. Dendrogram using Reinert’s method.
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Figure 14. Factorial correspondence analysis (FCA).
Figure 14. Factorial correspondence analysis (FCA).
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Figure 15. Relationship between corresponding authors’ countries and the fatigue testing methods used.
Figure 15. Relationship between corresponding authors’ countries and the fatigue testing methods used.
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Figure 16. Relationship between controlled modes and fatigue tests performed.
Figure 16. Relationship between controlled modes and fatigue tests performed.
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Figure 17. Testing temperatures with normal distribution and tolerance interval of three standard deviations, where the solid red line represents the mean and the dashed lines represent the lower and upper limits of the tolerance interval.
Figure 17. Testing temperatures with normal distribution and tolerance interval of three standard deviations, where the solid red line represents the mean and the dashed lines represent the lower and upper limits of the tolerance interval.
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Table 1. Search strategy applied in the Scopus database.
Table 1. Search strategy applied in the Scopus database.
Search KeywordsFieldFilters
“Asphalt mix*”Article titleYear range: 2020–2025
“Fatigue test*”AbstractDocument type: article
KeywordsLanguage: English
Table 2. Most relevant sources.
Table 2. Most relevant sources.
IDSourceArticlesShare of Total
Articles (%)
CiteScore
2023
Journal Impact
Factor 2023
S1Construction and Building Materials10027.213.87.4
S2Journal of Materials in Civil Engineering369.85.83.1
S3International Journal of Pavement Engineering267.17.13.4
S4Materials256.85.83.1
S5Road Materials and Pavement Design226.08.13.4
S6Case Studies in Construction Materials143.87.66.5
S7International Journal of Pavement Research and Technology123.34.93.0
S8Transportation Research Record102.73.21.6
S9Journal of Cleaner Production71.920.49.8
S10Journal of Transportation Engineering Part B: Pavements71.94.51.9
Table 3. Research productivity and road quality rankings by corresponding author country.
Table 3. Research productivity and road quality rankings by corresponding author country.
CountryArticlesShare of
Total Articles (%)
SCP  1MCP  2MCP
(%)
TC  3Quality
of Roads [144]
ValueRanking
China16645.11264024.120414.645th
USA297.92813.41385.517th
Iran287.623517.94083.979th
India195.217210.52384.548th
Brazil133.511215.41413.0116th
Australia71.96114.31014.934th
Italy71.93457.1594.453rd
France61.65116.7465.418th
UK61.61583.3554.936th
Pakistan51.43240.0754.067th
Turkey51.44120.0185.031st
1 Single-country publications. 2 Multiple-country publications. 3 Total of citations.
Table 4. Ten most cited articles identified in the dataset.
Table 4. Ten most cited articles identified in the dataset.
Ord.ClusterAuthorsTitleYearSourceTC 1Ref.
14Cheng, H.; Sun, L.; Wang, Y.; Chen, X.Effects of actual loading waveforms on the fatigue behaviours of asphalt mixtures2021International Journal of Fatigue104[22]
23Daryaee, D.; Ameri, M.; Mansourkhaki, A.Utilizing of waste polymer modified bitumen in combination with rejuvenator in high reclaimed asphalt pavement mixtures2020Construction and Building Materials69[43]
35Wang, F.; Xiao, Y.; Cui, P.; Ma, T.; Kuang, D.Effect of aggregate morphologies and compaction methods on the skeleton structures in
asphalt mixtures
2020Construction and Building Materials61[89]
43Liu, C.; Lv, S.; Jin, D.; Qu, F.Laboratory investigation for the road performance of asphalt mixtures modified by rock asphalt-styrene butadiene rubber2021Journal of Materials in Civil Engineering58[39]
54Xia, C.; Lv, S.; Cabrera, M.B.; Wang, X.; Zhang, C.; You, L.Unified characterizing fatigue performance of rubberized asphalt mixtures subjected to different loading modes2021Journal of Cleaner Production50[136]
62Cheng, H.; Liu, J.; Sun, L.; Liu, L.; Zhang, Y.Fatigue behaviours of asphalt mixture at different temperatures in four-point bending and indirect tensile fatigue tests2021Construction and Building Materials48[23]
75Enieb, M.; Diab, A.; Yang, X.Short- and long-term properties of glass fiber reinforced asphalt mixtures2021International Journal of Pavement Engineering48[40]
84Fan, Z.; Xu, H.; Xiao, J.; Tan, Y.Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and development of fatigue-freeze-thaw (FFT) uniform equation2020Construction and Building Materials48[153]
95Yi, X.; Chen, H.; Wang, H.; Shi, C.; Yang, J.The feasibility of using epoxy asphalt to recycle a mixture containing 100% reclaimed asphalt pavement (RAP)2022Construction and Building Materials47[44]
105Wu, J.; Wang, Y.; Liu, Q.; Wang, Y.; Ago, C.; Oeser, M.Investigation on mechanical performance of porous asphalt mixtures treated with laboratory aging and moisture actions2020Construction and Building Materials44[87]
1 Total of citations.
Table 5. Summary of textual statistics.
Table 5. Summary of textual statistics.
ParameterTotal Number
Number of texts (abstracts)368
Number of occurrences88,688
Mean of occurrences by text241
Number of lexical forms (words)3988
Number of hapax legomenon 11357 ( 1.53 % of occurrences and 34.03 % of forms)
Active forms3415
Supplementary forms348
1 Words with frequency = 1.
Table 6. The 100 highest-frequency active words.
Table 6. The 100 highest-frequency active words.
Ord.Active FormsFreq.Ord.Active FormsFreq.Ord.Active FormsFreq.Ord.Active FormsFreq.
1asphalt195026strength25951indirect15776layer107
2fatigue189127evaluate25652time15777sample106
3mixture161128fiber25553analysis15078include105
4test148529low25454investigate14779find105
5performance73530stress24555failure14780beam104
6pavement56131material24456mechanical14681characteristic104
7temperature52532content24457cycle14582shear102
8result52133rap23958laboratory14083road102
9binder47134bend23759dynamic13984frequency101
10life46635heal23360rate13785index100
11crack43436method23261reduce13786additive100
12resistance43037strain23062moisture13387analyze99
13study42338modulus23063specimen13288freeze99
14load41439improve22264stability13289prediction98
15damage40640design21665type13090creep98
16high39941age21366decrease12991long98
17mix38542level20467term12792propose98
18modify38443aggregate19568parameter12593obtain97
19increase31144rut18269conduct12494surface96
20base31045recycle17970energy12195paper95
21property30546point17371addition12096significant95
22show29447ratio17272influence11697rubber94
23effect26348condition16373research11598structure93
24tensile26349compare16174control11599perform93
25model26350stiffness15975bitumen110100fracture93
Table 7. Most representative words per cluster and their statistical associations.
Table 7. Most representative words per cluster and their statistical associations.
Cluster 1Cluster 2
Ord.Fr.
TS
Total
fr.
% χ 2 Forms p Ord.Fr.
TS
Total
fr.
% χ 2 Forms p
119335554.37400.55pavement<0.000118813167.18367.49indirect<0.0001
2496180.33172.11environmental<0.0001224177731.02355.53test<0.0001
39418151.93162.74material<0.0001310320450.49284.87tensile<0.0001
4374484.09138.34construction<0.000149919151.83284.21bend<0.0001
5354283.33128.95cost<0.00015262892.86162.23uniaxial<0.0001
6569360.22123.21road<0.000165811450.88155.43conduct<0.0001
72323100.00109.89sustainable<0.000176714645.89152.64point<0.0001
8242596.00108.25maintenance<0.000186112648.41151.12dynamic<0.0001
9335263.4678.22application<0.00019385865.52147.68carry<0.0001
10273871.0577.08engineer<0.0001107418340.44135.85modulus<0.0001
Cluster 3Cluster 4
Ord.Fr.
TS
Total
fr.
% χ 2 Forms p Ord.Fr.
TS
Total
fr.
% χ 2 Forms p
112929344.03306.52modify<0.0001114216884.52319.50model<0.0001
212733038.48239.11binder<0.0001218228962.98232.28load<0.0001
3486969.57211.62sbs<0.0001312518467.93180.52stress<0.0001
4466669.70203.07grade<0.00014718088.75167.70establish<0.0001
5313393.94202.74styrene<0.0001511216368.71164.21strain<0.0001
6293096.67196.59butadiene<0.00016667588.00153.10prediction<0.0001
7375271.15167.15polymer<0.0001718235551.27137.23life<0.0001
8457361.64166.34rubber<0.00018535792.98134.74equation<0.0001
9314175.61151.80modifier<0.0001913824356.79131.89damage<0.0001
10457956.96147.75bitumen<0.000110393109735.82104.58fatigue<0.0001
Cluster 5
Ord.Fr.
TS
Total
fr.
% χ 2 Forms p
110815370.59121.01fiber<0.0001
217833353.4593.16resistance<0.0001
326057245.4576.34performance<0.0001
48713863.0471.04aggregate<0.0001
59215459.7464.30rut<0.0001
610618956.0861.20content<0.0001
717838446.3551.78temperature<0.0001
86410362.1449.224addition<0.0001
96711060.9148.68stability<0.0001
107012058.3344.58moisture<0.0001
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Valente de Liz, J.; Salgado Barra, B.; Mikowski, A.; Hughes, G.B.; Ferreira, A. Fatigue Testing in Asphalt Mixes: Emerging Trends and Findings from an Integrated Literature Review. Appl. Sci. 2025, 15, 10220. https://doi.org/10.3390/app151810220

AMA Style

Valente de Liz J, Salgado Barra B, Mikowski A, Hughes GB, Ferreira A. Fatigue Testing in Asphalt Mixes: Emerging Trends and Findings from an Integrated Literature Review. Applied Sciences. 2025; 15(18):10220. https://doi.org/10.3390/app151810220

Chicago/Turabian Style

Valente de Liz, Jessé, Breno Salgado Barra, Alexandre Mikowski, Gary B. Hughes, and Adelino Ferreira. 2025. "Fatigue Testing in Asphalt Mixes: Emerging Trends and Findings from an Integrated Literature Review" Applied Sciences 15, no. 18: 10220. https://doi.org/10.3390/app151810220

APA Style

Valente de Liz, J., Salgado Barra, B., Mikowski, A., Hughes, G. B., & Ferreira, A. (2025). Fatigue Testing in Asphalt Mixes: Emerging Trends and Findings from an Integrated Literature Review. Applied Sciences, 15(18), 10220. https://doi.org/10.3390/app151810220

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