<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">sibadi</journal-id><journal-title-group><journal-title xml:lang="ru">Научный рецензируемый журнал "Вестник СибАДИ"</journal-title><trans-title-group xml:lang="en"><trans-title>The Russian Automobile and Highway Industry Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2071-7296</issn><issn pub-type="epub">2658-5626</issn><publisher><publisher-name>The Siberian State Automobile and Highway University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26518/2071-7296-2025-22-6-1000-1017</article-id><article-id custom-type="edn" pub-id-type="custom">YOGPUR</article-id><article-id custom-type="elpub" pub-id-type="custom">sibadi-2124</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>СТРОИТЕЛЬСТВО И АРХИТЕКТУРА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>CONSTRUCTION AND ARCHITECTURE</subject></subj-group></article-categories><title-group><article-title>Учет влияния содержания воздушных пустот на модуль упругости асфальтобетонов для расчета дорожных одежд</article-title><trans-title-group xml:lang="en"><trans-title>The consideration of air void content effect on asphalt concrete elastic modulus in pavement design</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5765-2726</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чусов</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Chusov</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чусов Василий Владимирович – преподаватель кафедры «Строительство и эксплуатация дорог»</p><p>Author ID: 865632 </p><p>644080, г. Омск, просп. Мира, 5 </p></bio><bio xml:lang="en"><p>Chusov Vasiliy V. – Lecturer, Road Construction and Operation Department</p><p>5, Prospect Mira, Omsk, 644080</p></bio><email xlink:type="simple">chysow@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Муртазин</surname><given-names>Р. Х.</given-names></name><name name-style="western" xml:lang="en"><surname>Murtazin</surname><given-names>R. Kh.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Муртазин Раис Харисович – магистрант кафедры «Строительство и эксплуатация дорог»</p><p>644080, г. Омск, просп. Мира, 5 </p></bio><bio xml:lang="en"><p>Murtazin Rais Kh. – Master’s student, Road Construction and Operation Department</p><p>5, Prospect Mira, Omsk, 644080</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2009-5361</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Александров</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Aleksandrov</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Александров Анатолий Сергеевич – канд. техн. наук, доц., доц. кафедры «Строительство и эксплуатация дорог»</p><p>Researcher ID: I-8860-2018, Author ID (РИНЦ): 639655, Author ID (Scopus): 57191531014</p><p>644080, г. Омск, просп. Мира, 5 </p></bio><bio xml:lang="en"><p>Aleksandrov Anatoliy S. – Candidate of Technical Sciences, Associate Professor, Road Construction and Operation Department</p><p>Researcher ID: I-8860-2018, Author ID (РИНЦ): 639655, Author ID (Scopus): 57191531014</p><p>5, Prospect Mira, Omsk, 644080</p></bio><email xlink:type="simple">aleksandrov00@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский государственный автомобильно-дорожный университет (СибАДИ)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>The Siberian State Automobile and Highway University (SibADI)</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>13</day><month>01</month><year>2026</year></pub-date><volume>22</volume><issue>6</issue><fpage>1000</fpage><lpage>1017</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Чусов В.В., Муртазин Р.Х., Александров А.С., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Чусов В.В., Муртазин Р.Х., Александров А.С.</copyright-holder><copyright-holder xml:lang="en">Chusov V.V., Murtazin R.K., Aleksandrov A.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.sibadi.org/jour/article/view/2124">https://vestnik.sibadi.org/jour/article/view/2124</self-uri><abstract><sec><title>Введение</title><p>Введение. Показано, что воздушные пустоты по своей сути являются дефектами структуры асфальтобетона. Приведены сведения о математических моделях, учитывающих влияние содержания воздушных пустот как на модуль упругости асфальтобетона, так и на срок службы дорожной одежды, выраженный в суммарном числе расчетных нагрузок, которые могут быть реализованы до разрушения дорожной одежды. Поэтому учет содержания воздушных пустот при определении модуля упругости асфальтобетона, применяемого в расчете дорожной одежды, является актуальной задачей, имеющей практическую значимость.</p></sec><sec><title>Методы и материалы</title><p>Методы и материалы. Выполнен анализ методов учета эффекта накопления повреждений, применяемых к расчету асфальтобетонов и других материалов по сопротивлению усталостному разрушению. На основании этого анализа сделан вывод о возможности применения к определению модуля упругости асфальтобетона теории повреждаемости. Подчеркнута аналогия между повреждаемостью Ю.Н. Работного и содержанием воздушных пустот. При этом обоснована возможность применения к расчету модуля упругости асфальтобетона принципа деформационной эквивалентности поврежденной и сплошной среды. К расчету напряжения от растяжения при изгибе применена концепция Л.М. Качанова, состоящая в увеличении величины напряжения при возрастании количества повреждений.</p></sec><sec><title>Результаты</title><p>Результаты. Приведены результаты расчета модулей упругости асфальтобетона на битуме марок БНД при различном содержании воздушных пустот, но в пределах, допускаемых ГОСТ Р 58406.2–2020. За счет этого дополнены данные ГОСТ Р 71404–2024 о значениях модулей упругости асфальтобетонов. Целесообразность дополнения авторами данных ГОСТ Р 71404–2024 объясняется тем, что температура асфальтобетонной смеси в различных частях кузова самосвала различна, что обуславливает неодинаковые условия уплотнения смеси по ее температуре. В этом случае испытания кернов, взятых из точек отбора, расположенных друг от друга на близком расстоянии, показывают практически одинаковое содержание битума, но разное содержание воздушных пустот. Поэтому при проектировании нежестких дорожных одежд нужно ориентироваться на модули упругости асфальтобетона, соответствующие максимальному допуску по содержанию воздушных пустот.</p></sec><sec><title>Заключение</title><p>Заключение. Полученные результаты позволяют более детально производить расчет дорожной одежды.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. It has been demonstrated that air voids are inherently structural defects in asphalt concrete. The article presents information on mathematical models that take into account the influence of air void content on both the elastic modulus of asphalt concrete and the service life of the pavement, expressed as the cumulative number of design loads that the pavement can withstand before failure. Therefore, considering air void content when determining the elastic modulus of asphalt concrete used in pavement design is a relevant and practically significant task.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The analysis of methods for accounting the damage accumulation effect applied to the fatigue destruction resistance calculation of asphalt concrete and other materials has been performed. Relying on this analysis, it was concluded that the damage theory can be used to determine the elastic modulus of asphalt concrete. The analogy between Yu. N. Rabotnov’s damage parameter and air void content is emphasized. Furthermore, the possibility of applying the principle of deformational equivalence between a damaged and a homogeneous medium to the calculation of asphalt concrete elastic modulus is justified. The concept proposed by L.M. Kachanov, which involves an increase in stress magnitude with an increasing number of damages, was applied to the calculation of tensile stress in bending.</p></sec><sec><title>Results</title><p>Results. The results of calculating the elastic moduli of bitumen-based asphalt concrete (grades BND) with varying air void content, but within the limits permitted by GOST R 58406.2-2020, have been presented. This let the authors to supplement the data on elastic modulus values for asphalt concretes in GOST R 71404-2024. The reason to add the data in GOST R 71404-2024 is explained by the fact that the temperature of the asphalt concrete mix in different parts of the dump truck body varies, which leads to different compaction conditions for the mix based on its temperature. In this case, tests of cores taken from sampling points located close to each other show almost identical bitumen contents, but different air void contents. Therefore, when designing flexible road surfaces, it is necessary to focus on the elastic moduli of asphalt concrete that correspond to the maximum limits for the content of air voids.</p></sec><sec><title>Conclusion</title><p>Conclusion. The obtained results allow to make more detailed pavement design calculations.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>асфальтобетон</kwd><kwd>содержание воздушных пустот</kwd><kwd>модуль упругости асфальтобетона</kwd></kwd-group><kwd-group xml:lang="en"><kwd>asphalt concrete</kwd><kwd>air void content</kwd><kwd>elasticity modulus of asphalt concrete</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Косенко Н.В., Горячев М.Г. Обоснование кратковременных расчетных модулей упругости асфальтобетонов для проектирования дорожных одежд улично-дорожной сети // Наука и техника в дорожной отрасли. 2025. № 2. С. 20–22.</mixed-citation><mixed-citation xml:lang="en">Kosenko N.V., Goryachev M.G. Justification of the loading duration of the street and road network pavements. Advanced Science and Technology for Highways. 2025; 2: 20–22. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Косенко Н.В., Горячев М.Г. Обоснование расчетных характеристик асфальтобетонов по ГОСТ Р 58406.2–2020 при проектировании дорожных одежд // Наука и техника в дорожной отрасли. 2022. № 2. С. 24–27.</mixed-citation><mixed-citation xml:lang="en">Kosenko N.V., Goryachev M.G. Justification of Design Parameters of Asphalt Concrete According to GOST R 58406.22020 for Pavement Design. Advanced Science and Technology for Highways. 2022; 2: 24–27. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Экспериментальные исследования модулей упругости асфальтобетонов для проектирования дорожных одежд / Н.В. Косенко, М.Г. Горячев, С.М. Дмитриев, С.В. Яркин // Транспортные сооружения. 2024. Т. 11, № 1. URL: https://t-s.today/PDF/04SATS124.pdf. (дата обращения: 29.10.2025). Https://doi.org/10.15862/04SATS124</mixed-citation><mixed-citation xml:lang="en">Kosenko N.V., Goryachev M.G., Dmitriev S.M., Yarkin S.V. Investigational studies of asphalt concrete elastic moduli for pavement design. Russian Journal of Transport Engineering. 2024; 11(1). Available at: https://t-s.today/PDF/04SATS124.pdf (in Russ.). Https://doi.org/10.15862/04SATS124. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Углова Е.В. Прогнозирование остаточного ресурса асфальтобетонных покрытий с учетом реальных условий эксплуатации // Вестник ВолгГАСУ. Серия Строительство и архитектура. 2010. № 17(36). С.43–47.</mixed-citation><mixed-citation xml:lang="en">Uglova E.V. Forecasting of the residual resource asphalt concrete coverings with the account real working conditions. Bulletin of Volgograd state university of architecture and civil engineering. Series Construction and Architecture. 2017; 36(17): 43–47 (in Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Uglova E.V., Tiraturjan A.N., Eganyan G.V. Calibration of the prediction model for fatigue damage accumulation in asphalt courses of flexible pavements for the conditions specific to the Russian Federation // IOP Conf. Series: Materials Science and Engineering. 2019. Т. 698. Article No 077010. Https://doi.org/10.1088/1757-899X/698/7/077010</mixed-citation><mixed-citation xml:lang="en">Uglova E.V., Tiraturjan A.N., Eganyan G.V. Calibration of the prediction model for fatigue damage accumulation in asphalt courses of flexible pavements for the conditions specific to the Russian Federation. IOP Conf. Series: Materials Science and Engineering. 2019; 698: Article No 077010. https://doi.org/10.1088/1757-899X/698/7/077010</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Углова Е.В., Тиратурян А.Н., Шило О.А. Прогнозирование накопления усталостных разрушений в асфальтобетонных слоях нежестких дорожных одежд // Научный журнал строительства и архитектуры. 2019. № 3 (55). С. 52–61. Https://doi.org/10.25987/VSTU.2019.55.3.006</mixed-citation><mixed-citation xml:lang="en">Uglova E.V., Tiraturyan A.N., Shilo O.A. Prediction of Failure Fatigue Accumulation in Asphalt Concrete Layers of Flexible Pavements. Russian Journal of Building Construction and Architecture. 2019; 55(3): 52–61. (In Russ.) Doi 10.25987/VSTU.2019.55.3.006</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Пегин П.А., Капский Д.В., Буртыль Ю.В. Разработка методики оценки продольной ровности при изменении прочности дорожных конструкций // Бюллетень результатов научных исследований. 2022. Вып. 4. С. 37–47. Https://doi.org/10.20295/2223-9987-2022-4-37-47</mixed-citation><mixed-citation xml:lang="en">Pegin P.A., Kapski D.V., Burtyl Yu.V. Development of Assessment Methodology for Pavement Longitudinal Evenness When Road Construction Durability Changes. Bulletin of scientific research results. 2022; 4: 37–47. (In Russ.) Https://doi.org/10.20295/2223-9987-2022-4-37-47</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Буртыль Ю.В., Капский Д.В. Моделирование взаимосвязи ровности и прочности нежестких дорожных одежд на основании теоретическо-практических исследований // Вестник СибАДИ. 2022. Т.19, № 4 (86). С. 570–583. https://doi.org/10.26518/2071-7296-2022-19-4-570-583</mixed-citation><mixed-citation xml:lang="en">Burtyl Y. V., Kapski D. V. Modelling the relationship of smoothness and resistibility in non-rigid pavements based on theoretical and practical studies. The Russian Automobile and Highway Industry Journal. 2022; 19(4): 570-583. https://doi.org/10.26518/2071-7296-2022-19-4-570-583</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Iskakbayev A.I., Teltayev B.B., Rossi C.O. Deformation and strength of asphalt concrete under static and step loadings // In book: Transport Infrastructure and Systems. 2017. С. 3-8. Https://doi.org/10.1201/9781315281896-1</mixed-citation><mixed-citation xml:lang="en">Iskakbayev A.I., Teltayev B.B. Rossi C.O. Deformation and strength of asphalt concrete under static and step loadings. In book: Transport Infrastructure and Systems. 2017; 3-8. Https://doi.org/10.1201/9781315281896-1</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Elnashar G., Bhat R.B., Sedaghati R. Modeling pavement damage and predicting fatigue cracking of fexible pavements based on a combination of deterministic method with stochastic approach using Miner’s hypothesis. // Applied Sciences. 2019. Т. 1. Article No 229. Https://doi.org/10.1007/s42452-019-0238-5</mixed-citation><mixed-citation xml:lang="en">Elnashar G., Bhat R.B., Sedaghati R. Modeling pavement damage and predicting fatigue cracking of fexible pavements based on a combination of deterministic method with stochastic approach using Miner’s hypothesis. Applied Sciences. 2019; 1: Article No 229. doi.org/10.1007/s42452-019-0238-5</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Fahad M., Nagy R. Fatigue damage analysis of pavements under autonomous truck tire passes. // Pollack Periodica. 2022. Т. 17. № (3). С 59–64. Https://doi.org/10.1556/606.2022.00588</mixed-citation><mixed-citation xml:lang="en">Fahad M., Nagy R. Fatigue damage analysis of pavements under autonomous truck tire passes. Pollack Periodica. 2022; 17(3): 59–64. Https://doi.org/10.1556/606.2022.00588</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Olexa T., Mandula J. Comparison of complex modulus and elasticity modulus of bitumen bonded materials. // Pollack Periodica. 2016; Т. 11. №3. С. 131–140. Https://doi.org//10.1556/606.2016.11.3.12</mixed-citation><mixed-citation xml:lang="en">Olexa T., Mandula J. Comparison of complex modulus and elasticity modulus of bitumen bonded materials. Pollack Periodica. 2016; Т. 11. №3. С. 131–140. Https://doi.org/10.1556/606.2016.11.3.12</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Aleksandrova N.P., Chusov V.V., Stolbov Y.V. Criteria Of Strength And Plasticity Of Asphalt Concrete With The Account Of Effect Of Accumulation Of The Damage While Influence Of Re-Load. // IOP Conference Series: Materials Science and Engineering. 2018. Т. 463. 2. С. 022021.</mixed-citation><mixed-citation xml:lang="en">Aleksandrova N.P., Chusov V.V., Stolbov Y.V. Criteria Of Strength And Plasticity Of Asphalt Concrete With The Account Of Effect Of Accumulation Of The Damage While Influence Of Re-Load. IOP Conference Series: Materials Science and Engineering. 2018; Article No. 022021.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Chusov V.V., Aleksandrova N.P., Semenova T.V. Accounting Of Damage Of Asphalt Concrete In The Criteria For Calculating The Pavement. // IOP Conference Series: Materials Science and Engineering. 2021. Т. 1079. № 5. С. 052016.</mixed-citation><mixed-citation xml:lang="en">Chusov V.V., Aleksandrova N.P., Semenova T.V. Accounting Of Damage Of Asphalt Concrete In The Criteria For Calculating The Pavement. IOP Conference Series: Materials Science and Engineering. 2021; 1079: 5: Article No. 052016.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Александров А.С., Александрова Н.П., Семенова Т.В. Применение принципа эквивалентности энергетической эквивалентности сплошных и поврежденных тел к расчету асфальтобетонных покрытий по критериям прочности и пластичности // Известия высших учебных заведений. Строительство. 2018. № 3 (711). С. 79–88.</mixed-citation><mixed-citation xml:lang="en">Aleksandrov A.S., Aleksandrova N.P., Semenova T.V. Application of the principle of energy equivalence of continuous and damaged bodies to calculation of asphalt concrete coatings by strength and plasticity criteria. News of higher educational institutions. Construction. 2018; 711(3): 79–88.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Экспериментальное исследование накапливания повреждений в асфальтобетонных покрытиях / Александрова Н.П., Александров А.С., Семенова Т.В., Чусов В.В. // Известия высших учебных заведений. Строительство. 2019. № 4. С. 114–127.</mixed-citation><mixed-citation xml:lang="en">Aleksandrova N.P., et al. Experimental investigation of damage accumulation in asphalt-concrete coatings. News of higher educational institutions. Construction. 2019; 724(4): 114–127.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Hassan N.A. et al. Effects of air voids content on the performance of porous asphalt mixtures. // Journal of Engineering and Applied Sciences. 2016. Т 20. № 11. С. 11884–11887.</mixed-citation><mixed-citation xml:lang="en">Hassan N.A. et al. Effects of air voids content on the performance of porous asphalt mixtures. Journal of Engineering and Applied Sciences. 2016; 20(11): 11884–11887.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Igwe E.A. Effects of Air Voids Variation on Stiffness Property of HMA Concrete Modified with Rubber Latex. // International Journal of Emerging Trends in Engineering Research. 2015. Т. 3. № 9. С. 86–93.</mixed-citation><mixed-citation xml:lang="en">Igwe E.A. Effects of Air Voids Variation on Stiffness Property of HMA Concrete Modified with Rubber Latex. International Journal of Emerging Trends in Engineering Research. 2015; 9(3): 86–93.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Igwe E.A., Ottos C.G. Investigating the Effect of Air Voids Content in Fatigue Life of Hot Mix Asphalt Mixtures: Case Study of Rubberized Asphalt Con crete. // International Journal of Innovative Science, Engineering &amp; Technology. 2016. Т. 3. № 5. С. 56–64.</mixed-citation><mixed-citation xml:lang="en">Igwe E.A., Ottos C.G. Investigating the Effect of Air Voids Content in Fatigue Life of Hot Mix Asphalt Mixtures: Case Study of Rubberized Asphalt Concrete. International Journal of Innovative Science, Engineering &amp; Technology. 2016; 3(5): 56–64.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Salini R., Lenngren C., High air-void volume implications for asphalt concrete service-life and price penalty. // The Civil Engineering Journal. 2022. Т. 1, article No 5. С. 1–8.</mixed-citation><mixed-citation xml:lang="en">Salini R., Lenngren C., High air-void volume implications for asphalt concrete service-life and price penalty. The Civil Engineering Journal. 2022; 1: article No 5: 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Baimukhametov G., Gayfutdinov R., Khafizov E. Calculation of the influence of various compaction on the wear resistance of asphalt concrete using material loss calculation approach. // Magazine of Civil Engineering. 2024. Т. 17. № 1. Article no. 12505. Https://doi.org/10.34910/MCE.125.5</mixed-citation><mixed-citation xml:lang="en">Baimukhametov G., Gayfutdinov R., Khafizov E. Calculation of the influence of various compaction on the wear resistance of asphalt concrete using material loss calculation approach. Magazine of Civil Engineering. 2024; 17(1): Article no. 12505. Https://doi.org/10.34910/MCE.125.5</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Ekwulo E.O., Eme D.B. Expected traffic, pavement thickness, fatigue and rutting strain relationship for low volume asphalt pavement // The International Journal Of Engineering And Science. 2013. Т. 2. № 8. С. 62–77.</mixed-citation><mixed-citation xml:lang="en">Ekwulo, E.O., Eme, D.B. Expected traffic, pavement thickness, fatigue and rutting strain relationship for low volume asphalt pavement. The International Journal Of Engineering And Science. 2013; 2(8): 62–77.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Owais M. Analysing Witczak 1-37A, Witczak 1-40D and Modified Hirsch Models for asphalt dynamic modulus prediction using global sensitivity analysis. // International Journal of Pavement Engineering. 2023. Т. 24. № 1. Article No 2268808. Https://doi.org/10.1080/10298436.2023.2268808</mixed-citation><mixed-citation xml:lang="en">Owais M. Analysing Witczak 1-37A, Witczak 1-40D and Modified Hirsch Models for asphalt dynamic modulus prediction using global sensitivity analysis. International Journal of Pavement Engineering. 2023; 24(1): Article No 2268808. Https://doi.org/10.1080/10298436.2023.2268808</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Asadi B., Hajj R., Al-Qadi I.L. Asphalt concrete dynamic modulus prediction: Bayesian neural network approach. // International Journal of Pavement Engineering. 2023. Т. 24. No 2. Article № 2270569, Https://doi.org/10.1080/10298436.2023.2270569</mixed-citation><mixed-citation xml:lang="en">Asadi B., Hajj R., Al-Qadi I.L. Asphalt concrete dynamic modulus prediction: Bayesian neural network approach. International Journal of Pavement Engineering. 2023; 24(2):. Article No 2270569, Https://doi.org/10.1080/10298436.2023.2270569</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Belhaj M., et al. Evaluating Factors Influencing Dynamic Modulus Prediction: GRA-MLR Compared with Sigmoidal Modelling for Asphalt Mixtures with Reclaimed Asphalt. // Infrastructures. 2025. №. 10. Article № 269. https://doi.org/10.3390/infrastructures10100269</mixed-citation><mixed-citation xml:lang="en">Belhaj M., et al. Evaluating Factors Influencing Dynamic Modulus Prediction: GRA-MLR Compared with Sigmoidal Modelling for Asphalt Mixtures with Reclaimed Asphalt. Infrastructures. 2025; 10: Article No 269. https://doi.org/10.3390/infrastructures10100269</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Hanandeh S., et al. Prediction the Dynamic Modulus of Hot Asphalt Mix Using Genetic Algorithms and Neural Network Modeling. // Civil Engineering Journal. 2025. Т. 11(7): 2765–2781. Https://doi.org/10.28991/CEJ-2025-011-07-08</mixed-citation><mixed-citation xml:lang="en">Hanandeh S., et al. Prediction the Dynamic Modulus of Hot Asphalt Mix Using Genetic Algorithms and Neural Network Modeling. Civil Engineering Journal. 2025; 11(7): 2765–2781. Https://doi.org/10.28991/CEJ-2025-011-07-08</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Симчук Е.Н., Жданов К.А., Дедковский И.А. Совершенствование подходов и методов оценки физических и эксплуатационных свойств дорожного асфальтобетона в России // Дороги и мосты. 2021. Вып. 45. № 1. С. 181–221.</mixed-citation><mixed-citation xml:lang="en">Simchuk E. N., Zhdanov K. A., Dedkovsky I. A. Improving approaches and methods for assessing physical and operational properties of road asphalt concrete in Russia. Roads and Bridges. 2021; 45(1): 181–221.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
