vestnik Экологический вестник научных центров Черноморского экономического сотрудничества Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation 1729-5459 Кубанский государственный университет RU 1126 10.31429/vestnik-22-4-45-55 Научная статья Original article Механика Mechanics Разработка физически обоснованной модели распространения ультразвуковых волн в бетоне с частично деградированным наружным слоем Development of a physically based model of ultrasonic wave propagation in concrete with a partially degraded surface layer https://orcid.org/0000-0003-1686-5589 Чебаненко В.А. Чебаненко Валерий Александрович Chebanenko Valery A. valera.chebanenko@yandex.ru

канд. физ.-мат. наук, старший научный сотрудник лаборатории динамики неоднородных структур Южного научного центра РАН

 https://orcid.org/0000-0003-4275-6984 Шевцов С.Н. Шевцов Сергей Николаевич Shevtsov Sergei N. sergnshevtsov@gmail.com

д-р техн. наук, профессор, главный научый сотрудник, заведующий лабораторией динамики неоднородных структур Южного научного центра РАН

 https://orcid.org/0000-0002-6797-0920 Кириллова Е.В. Кириллова Евгения Вадимовна Kirillova Evgeniya V. kirillova@web.de

канд. физ.-мат. наук, профессор Университета прикладных наук Рейн-Майн в г. Висбаден

 Федеральный исследовательский центр Южный научный центр РАНFederal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences Университет прикладных наук Рейн-МайнRheinMain University of Applied Sciences in Wiesbaden 02 12 2025 22 4 45 55 20 10 2025 22 11 2025 02 12 2025 Copyright (c) 2025 Чебаненко В.А., Шевцов С.Н., Кириллова Е.В. 2025 Чебаненко В.А., Шевцов С.Н., Кириллова Е.В. Это произведение доступно по лицензии Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.

В работе представлена численная модель распространения ультразвуковых волн в бетоне с деградированным поверхностным слоем, разработанная в пакете COMSOL Multiphysics. Модель учитывает градиентное распределение упругих свойств и частотно-зависимое затухание, отражающее процесс деградации материала. Возбуждение задавалось волновым пакетом, а граничные условия типа слабого отражения позволили минимизировать отражения. Проведено моделирование при 100 кГц для различных толщин деградированного слоя. Показано, что увеличение его толщины приводит к снижению скорости и росту затухания амплитуды волны, что согласуется с экспериментальными исследованиями. Новизна заключается в создании физически обоснованной модели бетона с градиентом свойств, применимой для генерации синтетических данных при обучении систем искусственного интеллекта для неразрушающего контроля.

This paper presents a numerical model of ultrasonic wave propagation in concrete with a degraded surface layer, developed using the COMSOL Multiphysics package. The model takes into account the gradient distribution of elastic properties and frequency-dependent attenuation, reflecting the material degradation process. Excitation was specified by a wave packet, and weak-reflection boundary conditions minimized reflections. Simulations were conducted at 100 kHz for various thicknesses of the degraded layer. It was shown that increasing its thickness leads to a decrease in velocity and an increase in attenuation of the wave amplitude, which is consistent with experimental studies. The novelty lies in the creation of a physically based model of concrete with a property gradient, applicable for generating synthetic data for training artificial intelligence systems for non-destructive testing.

 неразрушающий контроль бетон ультразвуковые волны конечно-элементное моделирование comsol multiphysics градиент упругих свойств non-destructive testing concrete ultrasonic waves finite element modeling comsol multiphysics elastic gradient Публикация подготовлена в рамках реализации ГЗ ЮНЦ РАН 125011200151-9. Работа выполнена на оборудовании ЦКП ЮНЦ РАН № 501994. Участие Кирилловой Е.В. в этих исследованиях финансировалось за счет гранта 40170233 университета прикладных наук Рейн-Майн, Висбаден, Германия. This publication was prepared within the framework of the State Assignment of the Southern Scientific Center of the Russian Academy of Sciences (SSC RAS) No. 125011200151-9. The part of Evgeniya Kirillova in these research was funded by the grant 40170233 of the RheinMain University of Applied Sciences, Wiesbaden, Germany. The work was performed using equipment at the SSC RAS Common Use Center No. 501994. Aparicio Secanellas, S., Liébana Gallego, J.C., Anaya Catalán, G., Martín Navarro, R., Ortega Heras, J., García Izquierdo, M.Á., González Hernández, M., Anaya Velayos, J.J., An ultrasonic tomography system for the inspection of columns in architectural heritage. Sensors, 2022, vol. 22, iss. 17, p. 6646. DOI: 10.3390/s22176646 Lencis, U., Udris, A., Kara De Maeijer, P., Korjakins, A., Methodology for determining the correct ultrasonic pulse velocity in concrete. Buildings, 2024, vol. 14, no. 3, p. 720. DOI: 10.3390/buildings14030720 Vasanelli, E., Di Gennaro, D., Sticchi, M., Blasi, G., Capozzoli, L., Comparison of pulse-echo tomography and through-transmission ultrasonic test for UPV characterization of building materials. Infrastructures, 2025, vol. 10, p. 162. DOI: 10.3390/infrastructures10070162 Al-Neshawy, F., Ferreira, M., Puttonen, J., NDT assessment of a thick-walled reinforced concrete mock-up of NPP concrete structures. EJ. Nondestruct. Test., 2022, vol. 27, pp. 1–10. DOI: 10.58286/27190 Rucka, M., Zielińska, M., Autonomous ultrasonic imaging and crack localisation in concrete beams during the fracture process. Mechanical Systems and Signal Processing, 2025, vol. 237, p. 113105. DOI: 10.1016/j.ymssp.2025.113105 Malikov, A.K.u., Flores Cuenca, M.F., Kim, B., Cho Y., Kim Y.H., Ultrasonic tomography imaging enhancement approach based on deep convolutional neural networks. Journal of Visualization, 2023, vol. 26, iss. 5, pp. 1067–1083. DOI: 10.1007/s12650-023-00922-6 Dinh, K., Tran, K., Gucunski, N., Ferraro, C.C., Nguyen, T., Imaging concrete structures with ultrasonic shear waves–-Technology development and demonstration of capabilities. Infrastructures, 2023, vol. 8, iss. 3, p. 53. DOI: 10.3390/infrastructures8030053 Feller, V., Mielentz, F., Klewe, T., Krause, M., Orglmeister, R., Pflugradt, M., Ultrasonic phased array for investigations of concrete components. In Proc. of NDT-CE 2015 – Int. symposium non-destructive testing in civil engineering. Technische Universität Berlin/Bundesanstalt für Materialforschung und-prüfung, 2015, pp. 1–5. Larose, E., de Rosny, J., Margerin, L., Anache, D., Gouedard, P., Campillo, M., van Tiggelen, B., Observation of multiple scattering of kHz vibrations in a concrete structure and application to monitoring weak changes. Physical Review E–-Statistical, Nonlinear, and Soft Matter Physics, 2006, vol. 73, iss. 1, p. 016609. DOI: 10.1103/PhysRevE.73.016609 Larose, E., Hall S., Monitoring stress related velocity variation in concrete with a 2x105 relative resolution using diffuse ultrasound. The Journal of the Acoustical Society of America, 2009, vol. 125, iss. 4, p. 1853–1856. DOI: 10.1121/1.3079771 Zhang, L., Jiang, Z., Jia, Sh., Xie, L., Liu, Q., Li, H., Frequency-dependent reliability of ultrasonic testing based on numerical model with consideration of coarse aggregates in concrete. Case Studies in Construction Materials, 2023, vol. 19, p. e02462. DOI: 10.1016/j.cscm.2023.e02462 Mata, R., Ruiz, R.O., Nuñez E., Correlation between compressive strength of concrete and ultrasonic pulse velocity: A case of study and a new correlation method. Construction and Building Materials, 2023, vol. 369, p. 130569. DOI: 10.1016/j.conbuildmat.2023.130569 Cannas, B., Carcangiu, S., Concu, G., Fanni, A., Usai, M., Numerical simulations of ultrasonic non destructive techniques of masonry buildings. In Proc. of the 2011 COMSOL Conference in Stuttgart, 2011. Jamal Mohamad, F.A., Anita, A., Ruzairi A.R., Sallehuddin, I., Juliza J., Noorhazirah, S., The identification of optimal frequency for ultrasonic transducers in concrete-defect detection using COMSOL® simulator. ELEKTRIKA – Journal of Electrical Engineering, 2025, vol. 24, iss. 2, pp. 104–110. DOI: 10.11113/elektrika.v24n2.589 Jain, H., Patankar, V.H., Simulations and experimentation of ultrasonic wave propagation and flaw characterisation for underwater concrete structures. Nondestructive Testing and Evaluation, 2024, vol. 39, iss. 6, pp. 1581–1598. DOI: 10.1080/10589759.2023.2274006 Marković, N., Stojić, D., Cvetković, R., Radojičić, V., Conić Stefan Numerical modeling of ultrasonic wave propagation-by using of explicit fem in abaqus. Facta universitatis-series: Architecture and Civil Engineering, 2018, vol. 16, iss. 1, pp. 135–147. DOI: 10.2298/FUACE170830011M Zhang, W., Yang, J., Ren, L., Dou, H., Chen, X., Jia, H., Mao, Y., Zhang, J., Xu, W., Zhou, H., Mu, X., High-performance capacitive ultrasonic transducer for non-destructive testing of concrete compressive strength. Sensors, 2025, vol. 25, iss. 16, p. 4903. DOI: 10.3390/s25164903 Tian, X., Ao, J., Ma, C., Shi, J., Guo, H., A hybrid strategy two-dimensional concrete aggregate filling algorithm. Engineering Reports, 2025, vol. 7, iss. 1, p. e13029. DOI: 10.1002/eng2.13029 Zhang, X., Yu, Y., Yu, Z., Qiao, F., Du, J., Yao, H., A scoping review: applications of deep learning in non-destructive building tests. Electronics, 2025, vol. 14, iss. 6, p. 1124. DOI: 10.3390/electronics14061124 McKnight, S., Gareth Pierce, S., Mohseni, E., MacKinnon, C., MacLeod, C., O'Hare, T., Loukas, C., A comparison of methods for generating synthetic training data for domain adaption of deep learning models in ultrasonic non-destructive evaluation. NDT & E International, 2024, vol. 141, p. 102978. DOI: 10.1016/j.ndteint.2023.102978 Jiang, J., Zhang, D., Gong, F., Zhi, D., Prediction of ultrasonic pulse velocity for cement, mortar, and concrete through a multiscale homogenization approach. Materials, 2022, vol. 15, iss. 9, p. 3241. DOI: 10.3390/ma15093241 Sun, W., Hou, S., Wu, G., Wu Z., Xiong, W., Zhang, J., Phased array ultrasonic and deep learning based internal defect detection in underwater concrete bridge structures. Case Studies in Construction Materials, 2025, p. e04946. DOI: 10.1016/j.cscm.2025.e04946 Kirillova, E., Tatarinov, A., Kovalenko, S., Shahmenko, G., Prediction of degradation of concrete surface layer using neural networks applied to ultrasound propagation signals. Acoustics, 2025, vol. 7, iss. 2, p. 19. DOI: 10.3390/acoustics7020019 Guo, J., Sun, W., Xu, Y., Lin, W., Jing, W., Damage mechanism and modeling of concrete in freeze–thaw cycles: a review. Buildings, 2022, vol. 12, iss. 9, p. 1317. DOI: 10.3390/buildings12091317 Ikumapayi, C.M., Adeniji, A.A., Obisesan, A.A., Odeyemi, O., Ajayi, J.A., Effects of carbonation on the properties of concrete. Sci. Rev., 2019, vol. 5, iss. 12, pp. 205–214. DOI: 10.32861/sr.512.205.214 Tatarinov, A., Sisojevs, A., Chaplinska, A., Shahmenko, G., Kurtenoks, V., An approach for assessment of concrete deterioration by surface waves. Procedia Structural Integrity, 2022, vol. 37, pp. 453–461. DOI: 10.1016/j.prostr.2022.01.109 Philippidis, T.P., Aggelis, D.G., Experimental study of wave dispersion and attenuation in concrete. Ultrasonics, 2005, vol. 43, iss. 7, pp. 584–595. DOI: 10.1016/j.ultras.2004.12.001