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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Structural Mechanics of Engineering Constructions and Buildings</journal-id><journal-title-group><journal-title xml:lang="en">Structural Mechanics of Engineering Constructions and Buildings</journal-title><trans-title-group xml:lang="ru"><trans-title>Строительная механика инженерных конструкций и сооружений</trans-title></trans-title-group></journal-title-group><issn publication-format="print">1815-5235</issn><issn publication-format="electronic">2587-8700</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">52520</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2026-22-3-222-234</article-id><article-id pub-id-type="edn">KKMJWA</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Analytical and numerical methods of analysis of structures</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Аналитические и численные методы расчета конструкций</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Stability of the Coastal Revetment Using 2D and 3D Simulations: A Case Study in Vinh Long, Vietnam</article-title><trans-title-group xml:lang="ru"><trans-title>Устойчивость берегового укрепления с использованием 2D- и 3D-моделирования: исследование на примере Виньлонга, Вьетнам</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0005-4578-1458</contrib-id><name-alternatives><name xml:lang="en"><surname>Tran</surname><given-names>Hoang P.</given-names></name><name xml:lang="ru"><surname>Тран</surname><given-names>Хоанг Фу</given-names></name></name-alternatives><bio xml:lang="en"><p>Master of Civil Engineering, Board Member, Department of Project Operation and Management</p></bio><bio xml:lang="ru"><p>магистр в области гражданского строительства, член совета, отдел эксплуатации и управления проектами</p></bio><email>thphu9@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4928-6236</contrib-id><name-alternatives><name xml:lang="en"><surname>Pham</surname><given-names>Ngoc T.</given-names></name><name xml:lang="ru"><surname>Фам</surname><given-names>Нгок Тхинь</given-names></name></name-alternatives><bio xml:lang="en"><p>Doctor of Civil Engineering, Lecturer, Faculty of Civil Engineering</p></bio><bio xml:lang="ru"><p>доктор в области гражданского строительства, преподаватель факультета гражданского строительства</p></bio><email>thinhtls@tlu.edu.vn</email><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0006-3545-8814</contrib-id><name-alternatives><name xml:lang="en"><surname>Le</surname><given-names>Van T</given-names></name><name xml:lang="ru"><surname>Ле</surname><given-names>Ван Туан</given-names></name></name-alternatives><bio xml:lang="en"><p>Doctor of Civil Engineering, Head of the Research Department of Oceanography</p></bio><bio xml:lang="ru"><p>доктор в области гражданского строительства, директор исследовательского отдела океанографии</p></bio><email>levantuan.vktb@gmail.com</email><xref ref-type="aff" rid="aff3"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9600-0539</contrib-id><name-alternatives><name xml:lang="en"><surname>Dang</surname><given-names>Van P.</given-names></name><name xml:lang="ru"><surname>Данг</surname><given-names>Ван Фу</given-names></name></name-alternatives><bio xml:lang="en"><p>Doctor of Civil Engineering, Lecturer, Faculty of Civil Engineering</p></bio><bio xml:lang="ru"><p>доктор в области гражданского строительства, преподаватель факультета гражданского строительства</p></bio><email>phudv@tlu.edu.vn</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Vinh Long Province Agricultural Project Management Board</institution></aff><aff><institution xml:lang="ru">Совет по управлению сельскохозяйственным проектом провинции Виньлонг</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Thuyloi University</institution></aff><aff><institution xml:lang="ru">Университет Туйлой, Тай Сон</institution></aff></aff-alternatives><aff-alternatives id="aff3"><aff><institution xml:lang="en">Institute of Coastal and Offshore Engineering</institution></aff><aff><institution xml:lang="ru">Институт прибрежной и морской инженерии</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2026-09-30" publication-format="electronic"><day>30</day><month>09</month><year>2026</year></pub-date><volume>22</volume><issue>3</issue><issue-title xml:lang="en">VOL 22, NO2 (2025)</issue-title><issue-title xml:lang="ru">ТОМ 22, №2 (2025)</issue-title><fpage>222</fpage><lpage>234</lpage><history><date date-type="received" iso-8601-date="2026-09-30"><day>30</day><month>09</month><year>2026</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2026, Tran H.P., Pham N.T., Le V.T., Dang V.P.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2026, Тран Х.Ф., Фам Н.Т., Ле В.Т., Данг В.Ф.</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="en">Tran H.P., Pham N.T., Le V.T., Dang V.P.</copyright-holder><copyright-holder xml:lang="ru">Тран Х.Ф., Фам Н.Т., Ле В.Т., Данг В.Ф.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/structural-mechanics/article/view/52520">https://journals.rudn.ru/structural-mechanics/article/view/52520</self-uri><abstract xml:lang="en"><p>Coastal erosion in the Mekong Delta has intensified due to climate change and rising sea levels, necessitating robust protective structures. This study evaluates the stability of a coastal revetment in Duyen Hai, Vinh Long province, using both two-dimensional (2D) and three-dimensional (3D) numerical simulations. Vinh Long, following its 2025 administrative merger, faces significant pressure from the East Sea’s irregular tidal regime and monsoon-driven wave energy. The stability analysis was conducted using the Simplified Bishop Method within the Limit Equilibrium Method (LEM) framework via the GeoStudio software suite (SLOPE/W and SLOPE3D). Results indicate that the safety factors (FS) for all considered load combinations, basic and extreme, comply with the Vietnamese national standard TCVN 9901:2023. Notably, the 3D simulations yielded FS values approximately 11.2% higher than the 2D counterparts, with the 3D model providing a more realistic representation of soil-structure interaction by accounting for lateral resistance and interaction forces between cross-sections. Furthermore, under an extreme loading combination representing the rainy season, where upstream discharge artificially elevates the landside water level by 1.5 m, the safety factors decrease due to increased pore water pressure within the embankment. This research demonstrates that while 2D analysis remains a conservative and safe approach for design, 3D modeling offers critical insights for cost-effective design refinement and a more accurate understanding of complex failure mechanisms in soft-soil coastal foundations.</p></abstract><trans-abstract xml:lang="ru"><p>Эрозия побережья в дельте Меконга усилилась из-за изменения климата и повышения уровня моря, что требует внедрения надежных защитных сооружений. Авторами проведена оценка устойчивости берегового укрепления в районе Дуенхай, провинция Виньлонг, с использованием двухмерного (2D) и трехмерного (3D) численного моделирования. После административной реформы 2025 г. Виньлонг испытывает значительное давление со стороны нерегулярного приливного режима Восточного моря и энергии волн, вызванных муссонами. Расчет на устойчивость выполнен упрощенным методом Бишопа в рамках метода предельного равновесия (МПР) с помощью программного комплекса GeoStudio (SLOPE/W и SLOPE3D). Результаты показывают, что коэффициенты запаса (КЗ) для всех рассматриваемых сочетаний нагрузок - как основных, так и особых - соответствуют требованиям национального стандарта Вьетнама TCVN 9901:2023. Примечательно, что значения КЗ, полученные при расчете 3D-модели, оказались примерно на 11,2 % выше, чем у 2D-модели. Трехмерная модель дает более реалистичное представление о взаимодействии грунта и сооружения за счет учета бокового сопротивления и взаимодействия сил между сечениями. Кроме того, при сочетании нагрузок с особыми воздействиями, соответствующими сезону дождей (когда сброс воды искусственно повышает уровень воды с внутренней стороны укрепления на 1,5 м), коэффициенты запаса снижаются из-за увеличения порового давления воды в теле насыпи. Исследование демонстрирует, что 2D-расчет остается подходом для безопасного проектирования с избыточным запасом прочности, однако 3D-моделирование предоставляет критически важные сведения для экономической оптимизации конструкции и более точного понимания сложных механизмов разрушения фундаментов в мягких прибрежных грунтах.</p></trans-abstract><kwd-group xml:lang="en"><kwd>Protective structure stability</kwd><kwd>Limit Equilibrium Method</kwd><kwd>2D simulation</kwd><kwd>3D simulation</kwd><kwd>Bishop Simplified Method</kwd><kwd>Mekong Delta</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>устойчивость защитных сооружений</kwd><kwd>метод предельного равновесия</kwd><kwd>2D-моделирование</kwd><kwd>3D-моделирование</kwd><kwd>упрощенный метод Бишопа</kwd><kwd>дельта Меконга</kwd></kwd-group><funding-group/></article-meta><fn-group/></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Marchesiello P, Nguyen NM, Gratiot N, Loisel H, Anthony EJ, Dinh CS, et al. Erosion of the coastal Mekong delta: Assessing natural against man induced processes. Cont Shelf Res. 2019;181:72-89. https://doi.org/10.1016/j.csr.2019.05.004</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Vietnam PwC. Snapshot on Vietnam’s administrative reform 2025. 2025. https://www.pwc.com/vn/en/publications/2025/vietnam-administrative-reform.pdf</mixed-citation></ref><ref id="B3"><label>3.</label><mixed-citation>Ty TV, Duy DV, Phat LT, Minh HVT, Thanh NT, Uyen NTN, Downes NK. Coastal erosion dynamics and protectivee measures in the Vietnamese Mekong Delta. Journal of Marine Science and Engineering. 2024;12(7):1094. https://doi.org/10.3390/jmse12071094 EDN: KVSBCK</mixed-citation></ref><ref id="B4"><label>4.</label><mixed-citation>Nordstrom KF. Living with shore protection structures: A review. Estuar Coast Shelf Sci. 2014;150:11-23. https://doi.org/10.1016/j.ecss.2013.11.003</mixed-citation></ref><ref id="B5"><label>5.</label><mixed-citation>Phan QM, Nguyen VP, Hoang TN, Vu NT. A novel approach using sustainable structures in preventing coastal erosion and forming sandy beach in Vietnam. IOP Conference Series: Materials Science and Engineering. 2020;869:072053. https://doi.org/10.1088/1757-899X/869/7/072053 EDN: BBOUSQ</mixed-citation></ref><ref id="B6"><label>6.</label><mixed-citation>Schoonees T, Gijón Mancheño A, Scheres B, Bouma TJ, Silva R, Schlurmann T, et al. Hard structures for coastal protection, towards greener designs. Estuaries and Coasts. 2019;42:1709-1729. https://doi.org/10.1007/s12237-019-00551-z EDN: DPRYUU</mixed-citation></ref><ref id="B7"><label>7.</label><mixed-citation>Angnuureng BD, Adade R, Chuku EO, Dzantor S, Brempong EK, Mattah PA. Effects of coastal protection structures in controlling erosion and livelihoods. Heliyon. 2023;9:e20633. https://doi.org/10.1016/j.heliyon.2023.e20633 EDN: KBYIGS</mixed-citation></ref><ref id="B8"><label>8.</label><mixed-citation>Le Xuan T, Ba HT, Thanh VQ, Wright DP, Hasan Tanim A, Tran Anh D, et al. Evaluation of coastal protection strategies and proposing multiple lines of defense under climate change in the Mekong Delta for sustainable shoreline protection. Ocean Coast Manag. 2022;228:106301. https://doi.org/10.1016/j.ocecoaman.2022.106301 EDN: JIDBUM</mixed-citation></ref><ref id="B9"><label>9.</label><mixed-citation>Zhechev N. Structures for permanent stabilization of the sea coast. IOP Conf Ser Mater Sci Eng. 2023;1297:012006. https://doi.org/doi:10.1088/1757-899X/1297/1/012006 EDN: ETNUBV</mixed-citation></ref><ref id="B10"><label>10.</label><mixed-citation>Fernández-Hernández M, Iglesias L, Escobar J, Ortega JJ, Pérez-Montiel JI, Paredes C, et al. The influence of hard protection structures on shoreline evolution in Riohacha, Colombia. Appl Sci. 2025;15(14):8119. https://doi.org/10.3390/app15148119 EDN: KGVFUT</mixed-citation></ref><ref id="B11"><label>11.</label><mixed-citation>Thinh PN, Van Phu D. Investigation of failure of riverbank protection structure: a case study in Long An province, Vietnam. Int J Comput Civ Struct Eng. 2025;21:62-74. https://doi.org/10.22337/2587-9618-2025-21-2-62-74 EDN: GPAIKJ</mixed-citation></ref><ref id="B12"><label>12.</label><mixed-citation>Duncan JM, Wright SG, Brandon TL. Soil Strength and Slope Stability. Hoboken, New Jersey: John Wiley &amp; Sons, Inc.; 2014.</mixed-citation></ref><ref id="B13"><label>13.</label><mixed-citation>Janbu N. Slope stability computations: In: Embankment-dam Engineering. Textbook. Wiley Publ.; 1973;12(4):47-86. https://doi.org/10.1016/0148-9062(75)90139-4.</mixed-citation></ref><ref id="B14"><label>14.</label><mixed-citation>Nguyen HPT, Pham NTP, Nguyen TMS, Ngo VL, Dang VP. Seepage and stability of an earth dam under the condition of rainfall infiltration. Struct Mech Eng Constr Buildings. 2025;21:207-215. https://doi.org/10.22363/1815-5235-2025-21-3-207-215 EDN: SUEUSV</mixed-citation></ref><ref id="B15"><label>15.</label><mixed-citation>Dang VP, Nguyen TMS, Le XB, Pham NT. Slope stability at the Bau Trang area using deterministic, upper and lower bounds, and reliability analyses. Inzynieria Mineralna. 2025;2:129-143. https://doi.org/10.29227/IM-2025-01-02-012</mixed-citation></ref><ref id="B16"><label>16.</label><mixed-citation>Zhang F, Jia S, Gao Y. Recent advances in stability analysis and design of 3D slopes. Front Built Environ. 2024;10:1410474. https://doi.org/10.3389/fbuil.2024.1410474 EDN: XNGABW</mixed-citation></ref><ref id="B17"><label>17.</label><mixed-citation>GEOSTUDIO. Stability Modeling with GeoStudio; 2022. Available from: https://studylib.net/doc/28240904/geostudio-stability-modeling-oct2022?ysclid=mr2fa9i3nq994287640&amp;p=2 (accessed: 17.01.2026).</mixed-citation></ref><ref id="B18"><label>18.</label><mixed-citation>Kumar S, Rao B, Choudhary SS, Burman A, Roy LB. Comparison of 2D and 3D slope stability analysis using limit equilibrium method. In: Proceedings of the Indian Geotechnical Conference; 2022. https://www.igs.org.in/storage/proceedings-uploads/TH-6-44-291223025834.pdf</mixed-citation></ref><ref id="B19"><label>19.</label><mixed-citation>Kumar S, Kumar A, Rao B, Choudhary SS, Burman A. Analysis of 2D and 3D slope stability using the Bishop simplified method. In: IOP Conf Ser Earth Environ Sci. 2024;1326:012117. https://doi.org/10.1088/1755-1315/1326/1/012117 EDN: TNBNZS</mixed-citation></ref><ref id="B20"><label>20.</label><mixed-citation>2GEOSTUDIO. Slope stability analysis with GeoStudio and PLAXIS; 2023.</mixed-citation></ref><ref id="B21"><label>21.</label><mixed-citation>Chen J, Zhu D, Zhu Y. A simplified method for effective calculation of 3D slope reliability. Water (Switzerland). 2023;15(17):3139. https://doi.org/10.3390/w15173139 EDN: KQWFEI</mixed-citation></ref><ref id="B22"><label>22.</label><mixed-citation>Reid ME, Christian SB, Brien DL, Henderson ST. Scoops3D: software to analyze 3D slope stability throughout a digital landscape; U.S. Geological Survey Techniques and Methods. 2015. https://doi.org/10.3133/tm14A1</mixed-citation></ref><ref id="B23"><label>23.</label><mixed-citation>TCVN 9901: TCVN 9901:2023 Sea dike structures - Requirements for design. Ha Noi: [publisher]; 2023.</mixed-citation></ref><ref id="B24"><label>24.</label><mixed-citation>Shoffiana A, Lastiasih Y, Rendy Satrya T. Comparison of embankment reinforcement requirements with geotextile on soft soil with 2D and 3D slope stability analysis methods. Journal of Infrastructure &amp; Facility Asset Management. 2022;4. https://doi.org/10.12962/jifam.v4i2.14369 EDN: TVFHGR</mixed-citation></ref><ref id="B25"><label>25.</label><mixed-citation>Bahsan E, Fakhriyyanti R. Comparison of 2D and 3D stability analyses for natural slope. International Journal of Engineering and Technology. 2018;7(4.35):662-667. https://doi.org/10.14419/ijet.v7i4.35.23085</mixed-citation></ref><ref id="B26"><label>26.</label><mixed-citation>Xue W, Qian W, Lin S, Chen Q, Li X. A case study of stability analysis and treatment measures for a river bank slope considering the action of a heaped load. Water (Switzerland). 2025;17(21):3068. https://doi.org/10.3390/w17213068 EDN: DZDBYW</mixed-citation></ref></ref-list></back></article>
