<?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">mgssuvest</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник МГСУ</journal-title><trans-title-group xml:lang="en"><trans-title>Vestnik MGSU</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1997-0935</issn><issn pub-type="epub">2304-6600</issn><publisher><publisher-name>Moscow State University of Civil Engineering (National Research University) (MGSU)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22227/1997-0935.2025.5.718-733</article-id><article-id custom-type="elpub" pub-id-type="custom">mgssuvest-623</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>Гидравлика. Геотехника. Гидротехническое строительство</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Hydraulics. Geotechnique. Hydrotechnical construction</subject></subj-group></article-categories><title-group><article-title>Актуализация линейной телескопической модели осадки сваи</article-title><trans-title-group xml:lang="en"><trans-title>Updating the linear telescopic pile settlement model</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6020-0328</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Алексеев</surname><given-names>А. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Alekseev</surname><given-names>A. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Андрей Григорьевич Алексеев — доктор технических наук, доцент, профессор кафедры механики грунтов и геотехники; руководитель центра геокриологических и геотехнических исследований</p><p>129337, г. Москва, Ярославское шоссе, д. 26; 109428, г. Москва, Рязанский проспект, д. 59</p><p>РИНЦ AuthorID: 873091, ResearcherID: AAB-8070-2020</p></bio><bio xml:lang="en"><p>Andrej G. Alekseev — Doctor of Technical Sciences, Associate Professor, Professor of the Department of Soil Mechanics and Geotechnical Engineering; Head of the Center for Geocryological and Geotechnical Research</p><p>26 Yaroslavskoe shosse, Moscow, 129337;59 Ryazansky prospect, Moscow, 109428</p><p>RSCI AuthorID: 873091, ResearcherID: AAB-8070-2020</p></bio><email xlink:type="simple">adr-alekseev@ya.ru</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>Безволев</surname><given-names>С. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Bezvolev</surname><given-names>S. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Степан Георгиевич Безволев — кандидат технических наук, старший научный сотрудник</p><p>109428, г. Москва, Рязанский проспект, д. 59</p><p>РИНЦ AuthorID: 271303, Scopus: 6602971111</p></bio><bio xml:lang="en"><p>Stepan G. Bezvolev — Candidate of Technical Sciences, Senior Researcher</p><p>59 Ryazansky prospect, Moscow, 109428</p><p>RSCI AuthorID: 271303, Scopus: 6602971111</p></bio><email xlink:type="simple">compgeo@ya.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский Московский государственный строительный университет (НИУ МГСУ); Научно-исследовательский, проектно-изыскательский и конструкторско-технологический институт оснований и подземных сооружений им. Н.М. Герсеванова Научно-исследовательского центра «Строительство» (НИИОСП НИЦ «Строительство»)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Moscow State University of Civil Engineering (National Research University) (MGSU); Research, Design and Survey and Design and Technological Institute of Foundations and Underground Structures named after N.M. Gersevanov of the Research Center “Construction”</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Научно-исследовательский, проектно-изыскательский и конструкторско-технологический институт оснований и подземных сооружений им. Н.М. Герсеванова Научно-исследовательского центра «Строительство» (НИИОСП НИЦ «Строительство»)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Research, Design and Survey and Design and Technological Institute of Foundations and Underground Structures named after N.M. Gersevanov of the Research Center “Construction”</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>30</day><month>05</month><year>2025</year></pub-date><volume>20</volume><issue>5</issue><fpage>718</fpage><lpage>733</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Алексеев А.Г., Безволев С.Г., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Алексеев А.Г., Безволев С.Г.</copyright-holder><copyright-holder xml:lang="en">Alekseev A.G., Bezvolev S.G.</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://www.vestnikmgsu.ru/jour/article/view/623">https://www.vestnikmgsu.ru/jour/article/view/623</self-uri><abstract><sec><title>Введение</title><p>Введение. Показана целесообразность повышения точности и общности упрощенных решений для расчета осадки одиночных свай. Такие решения рекомендованы строительными нормами РФ для оценки величины проектной осадки свай, а также применяются для определения параметров контактных моделей при разработке конструкций свайных фундаментов.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Выполнены теоретический анализ и сопоставление методов расчета, основанных на аппроксимации работы сваи в упругом полупространстве. Осуществлена проверка и разработана актуализация зависимостей основного аналитического решения, исходящего из телескопической схемы работы вмещающего сваю упругого массива.</p></sec><sec><title>Результаты</title><p>Результаты. Представлены результаты сопоставления расчетов различными методами. Анализ выявил ряд расхождений в зависимости от параметров свай и грунтового основания. Разработаны рекомендации по применению рассмотренных решений и установлена область их использования — оценка начального линейного сопротивления сваи и соответствующих параметров контактной модели, применяемой для конструирования свайного фундамента.</p></sec><sec><title>Выводы</title><p>Выводы. Упрощенные решения для расчета осадки одиночных свай востребованы строительной практикой, повышение точности и общности таких решений обеспечивает определение адекватных параметров контактных моделей для разработки надежных и рациональных конструкций свайных фундаментов. Область использования актуализированного решения — оценка начального линейного сопротивления сваи. Достоинством актуализированного решения является четко выделенная доля пяты сваи, что позволяет отдельно оценить работу ее боковой поверхности, в частности, в актуальных задачах с выдергивающей нагрузкой на сваю или по учету «выключения» пяты сваи из-за рыхлого шлама под пятой буронабивной сваи.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. The expediency of increasing the accuracy and generality of simplified solutions for calculating the settlement of single piles is shown. Such solutions are recommended by the building codes of the Russian Federation for assessing the value of the design settlement of piles, and are also used to determine the parameters of contact models in the development of pile foundation structures.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The theoretical analysis and comparison of calculation methods based on the approximation of pile work in an elastic half-space are performed. A verification and update of the dependencies of the main analytical solution based on the telescopic scheme of the elastic massif containing the pile is developed. Comparisons of the calculation results by various methods are presented.</p></sec><sec><title>Results</title><p>Results. The analysis revealed a number of discrepancies depending on the parameters of the piles and the soil base. Recommendations for the application of the considered solutions are developed and the area of their application is established — assessment of the initial linear resistance of the pile and the corresponding parameters of the contact model used to design the pile foundation.</p></sec><sec><title>Conclusions</title><p>Conclusions. Simplified solutions for calculating the settlement of single piles are in demand in construction practice; increasing the accuracy and generality of such solutions ensures the definition of adequate parameters of contact models for developing reliable and rational designs of pile foundations. The scope of the updated solution is the assessment of the initial linear resistance of the pile. The advantage of the updated solution is the clearly identified share of the pile heel, which allows for a separate assessment of the work of its lateral surface, in particular in current problems with a pull-out load on the pile or by taking into account the “switching off” of the pile heel due to loose slurry under the heel of a bored pile.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>свая</kwd><kwd>осадка сваи</kwd><kwd>допускаемая нагрузка на сваю</kwd><kwd>аналитическое решение</kwd><kwd>контактная модель</kwd><kwd>строительные нормы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>pile</kwd><kwd>pile settlement</kwd><kwd>permissible load on a pile</kwd><kwd>analytical solution</kwd><kwd>contact model</kwd><kwd>building codes</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">Федоровский В.Г., Левачев С.Н., Курилло С.В., Колесников Ю.М. Сваи в гидротехническом строительстве : учебное пособие. М. : Изд-во АСВ, 2003. 238 с.</mixed-citation><mixed-citation xml:lang="en">Fedorovsky V.G., Levachev S.N., Kurillo S.V., Kolesnikov Yu.M. Piles in hydraulic engineering : tutorial. Moscow, ASV Publishing House, 2003; 238. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Fleming K., Weltman A., Randolph M., Elson K. Piling Engineering. 3rd ed. CRC Press, 2020. 408 p.</mixed-citation><mixed-citation xml:lang="en">Fleming K., Weltman A., Randolph M., Elson K. Piling Engineering. 3rd ed. CRC Press, 2020; 408.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Poulos H.G., Davis E.H. Pile Foundation Analysis and Design. Sydney : Rainhom-Bridge Book Co., 1980. 398 p.</mixed-citation><mixed-citation xml:lang="en">Poulos H.G., Davis E.H. Pile Foundation Analysis and Design. Sydney, Rainhom-Bridge Book Co., 1980; 398.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Tomlinson M.J., Woodward C.J. Pile Design and Construction Practice: 6th ed. London : CRC Press Taylor &amp; Francis Group, 2015. 574 p.</mixed-citation><mixed-citation xml:lang="en">Tomlinson M.J., Woodward C.J. Pile Design and Construction Practice: 6th ed. London, CRC Press Taylor &amp; Francis Group, 2015; 574.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Бартоломей А.А., Омельчак И.М., Юшков Б.С. Прогноз осадок свайных фундаментов. М. : Стройиздат, 1994. 380 с.</mixed-citation><mixed-citation xml:lang="en">Bartolomey A.A., Omelchak I.M., Yushkov B.S. Forecast of settlement of pile foundations. Moscow, Stroyizdat, 1994; 380. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Poulos H.G., Davis E.H. The settlement behaviour of single axially loaded incompressible piles and piers // Géotechnique. 1968. Vol. 18. Issue 3. Рp. 351–371. DOI: 10.1680/geot.1968.18.3.351</mixed-citation><mixed-citation xml:lang="en">Poulos H.G., Davis E.H. The settlement behaviour of single axially loaded incompressible piles and piers. Géotechnique. 1968; 18(3):351-371. DOI: 10.1680/geot.1968.18.3.351</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Poulos H.G. Settlement of single piles in nonhomogeneous soil // Journal of the Geotechnical Engineering Division. 1979. Vol. 105. Issue 5. Pp. 627–641. DOI: 10.1061/ajgeb6.0000799</mixed-citation><mixed-citation xml:lang="en">Poulos H.G. Settlement of single piles in nonhomogeneous soil. Journal of the Geotechnical Engineering Division. 1979; 105(5):627-641. DOI: 10.1061/ajgeb6.0000799</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Федоровский В.Г. Расчет осадок свай в однородных и многослойных основаниях : дис. … канд. техн. наук. М., 1974. 198 с.</mixed-citation><mixed-citation xml:lang="en">Fedorovsky V.G. Rainfall of piles in the uniform and multilayered bases : thesis … candidate of technical sciences. Moscow, 1974; 198. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Randolph M.F., Wroth C.P. Analysis of deformation of vertically loaded piles // Journal of the Geotechnical Engineering Division. 1978. Vol. 104. Issue 12. Рp. 1465–1488. DOI: 10.1061/ajgeb6.0000729</mixed-citation><mixed-citation xml:lang="en">Randolph M.F., Wroth C.P. Analysis of deformation of vertically loaded piles. Journal of the Geotetchnical Engineering Division/ASCE. 1978; 104(12):1465-1488.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Randolph M.F., Wroth C.P. An analysis of the vertical deformation of pile groups // Geotechnique. 1979. Vol. 29. Issue 4. Pp. 423–439. DOI: 10.1680/geot.1979.29.4.423</mixed-citation><mixed-citation xml:lang="en">Randolph M.F., Wroth C.P. An analysis of the vertical deformation of pile groups. Geotechnique. 1979; 29(4):423-439. DOI: 10.1680/geot.1979.29.4.423</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Randolph M.F. Design Methods for Pile Groups and Piled Rafts // Proceeding of the 13th International Conference on Soil Mechanics and Foundation Engineering (ICSMFE). 1994. Vol. 5. Pp. 61–82.</mixed-citation><mixed-citation xml:lang="en">Randolph M.F. Design Methods for Pile Groups and Piled Rafts. Proceeding of the 13th International Conference on Soil Mechanics and Foundation Engineering (ICSMFE). 1994; 5:61-82.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Mylonakis G., Gazetas G. Settlement and additional internal forces of grouped piles in layered soil // Geotechnique. 1998. Vol. 48. Issue 1. Рp. 55–72. DOI: 10.1680/geot.1998.48.1.55</mixed-citation><mixed-citation xml:lang="en">Mylonakis G., Gazetas G. Settlement and additional internal forces of grouped piles in layered soil. Geotechnique. 1998; 48(1):55-72. DOI: 10.1680/geot.1998.48.1.55</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Боков И.А., Федоровский В.Г. Об учете неоднородности грунта по глубине в расчетах осадки свай // Основания, фундаменты и механика грунтов. 2021. № 4. С. 2–6. EDN QIVGYU.</mixed-citation><mixed-citation xml:lang="en">Bokov I.A., Fedorovskii V.G. Taking into account the soil depth inhomogeneity in calculation of the piles settlement. Soil Mechanics and Foundation Engineering. 2021; 4:2-6. EDN QIVGYU. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Тер-Мартиросян З.Г., Тер-Мартиросян А.З., Ермошина Л.Ю. Осадка и длительная несущая способность сваи // Промышленное и гражданское строительство. 2021. № 9. С. 18–23. DOI: 10.33622/0869-7019.2021.09.18-23. EDN HEIXNL.</mixed-citation><mixed-citation xml:lang="en">Ter-Martirosyan Z.G., Ter-Martirosyan A.Z., Ermoshina L.Yu. Settlement and long-term bearing capacity of the pile. Industrial and Civil Engineering. 2021; 9:18-23. DOI: 10.33622/0869-7019.2021.09.18-23. EDN HEIXNL. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Безволев С.Г. Аналитическое решение для расчета дополнительных осадок свайных полей // Строительная механика и расчет сооружений. 2012. № 4 (243). С. 58–65. EDN PCOHRJ.</mixed-citation><mixed-citation xml:lang="en">Bezvolev S.G. Analytical solution for calculating additional settlements of pile fields. Structural Mechanics and Calculation of Structures. 2012; 4(243):58-65. EDN PCOHRJ. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Федоровский В.Г., Безволев С.Г. Метод расчета свайных полей и других вертикально армированных грунтовых массивов // Основания, фундаменты и механика грунтов. 1994. № 3. С. 11–15. EDN KSYPMF.</mixed-citation><mixed-citation xml:lang="en">Fedorovsky V.G., Bezvolev S.G. Method of calculation of pile fields and other vertical reinforced soil masses. Soil Mechanics and Foundation Engineering. 1994; 3:11-15. EDN KSYPMF. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Banerjee P.K., Davies T.G. The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils // Geotechnique. 1978. Vol. 28. Issue 3. Рp. 309–326. DOI: 10.1680/geot.1978.28.3.309</mixed-citation><mixed-citation xml:lang="en">Banerjee P.K., Davies T.G. The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils. Geotechnique. 1978; 28(3):309-326. DOI: 10.1680/geot.1978.28.3.309</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Butterfield R., Banerjee P.K. The elastic analysis of compressible piles and pile groups // Geotechnique. 1971. Vol. 21. Issue 1. Рp. 43–60. DOI: 10.1680/geot.1971.21.1.43</mixed-citation><mixed-citation xml:lang="en">Butterfield R., Banerjee P.K. The elastic analysis of compressible piles and pile groups. Geotechnique. 1971; 21(1):43-60. DOI: 10.1680/geot.1971.21.1.43</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Слепак М.Э. Осадки и НДС пластично-мерзлого грунта в основании центрально-нагруженной сваи // Реология грунтов и инженерное мерзлото­ведение. 1982. С. 154–158.</mixed-citation><mixed-citation xml:lang="en">Slepak M.E. Rainfall and the VAT of plastic and frozen soil in the basis of the central loaded pile. Soil Rheology and Engineering Permafrost Science. 1982; 154-158. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Rajapakse R.K.N.D. Response of an axially loaded elastic pile in a Gibson soil // Geotechnique. 1990. Vol. 40. Issue 2. Рp. 237–249. DOI: 10.1680/geot.1990.40.2.237</mixed-citation><mixed-citation xml:lang="en">Rajapakse R.K.N.D. Response of an axially loaded elastic pile in a Gibson soil. Geotechnique. 1990; 40(2):237-249. DOI: 10.1680/geot.1990.40.2.237</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Lee C.Y., Small J.C. Finite-Layer Analysis of Axially Loaded Piles // Journal of Geotechnical Engineering. 1990. Vol. 117. Issue 11. Рp. 1706–1722. DOI: 10.1061/(asce)0733-9410(1991)117:11(1706)</mixed-citation><mixed-citation xml:lang="en">Lee C.Y., Small J.C. Finite-Layer Analysis of Axially Loaded Piles. Journal of Geotechnical Engineering. 1990; 117(11):1706-1722. DOI: 10.1061/(asce)0733-9410(1991)117:11(1706)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Viggiani C., Mandolini A., Russo G. Piles and Pile Foundations. UK : Spon Press, 2012. 278 p.</mixed-citation><mixed-citation xml:lang="en">Viggiani C., Mandolini A., Russo G. Piles and Pile Foundations. UK, Spon Press, 2012; 278.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Готман А.Л., Гавриков М.Д. Расчет длинномерных буронабивных свай на вертикальную нагрузку // Основания, фундаменты и механика грунтов. 2024. № 4. С. 2–8. EDN MSBJDN.</mixed-citation><mixed-citation xml:lang="en">Gotman A.L., Gavrikov M.D. Calculation of long bored piles for vertical loading. Soil Mechanics and Foundation Engineering. 2024; 4:2-8. EDN MSBJDN. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Шарафутдинов Р.Ф., Разводовский Д.Е., Закатов Т.С. Инженерный метод прогноза осадки одиночных свай с учетом упругопластического поведения грунта // Основания, фундаменты и механика грунтов. 2024. № 3. С. 7–15. EDN OFOAVE.</mixed-citation><mixed-citation xml:lang="en">Sharafutdinov R.F., Razvodovskii D.E., Zakatov D.S. Single bored pile settlement prediction taking into account the elastic-plastic behavior of the soil. Soil Mechanics and Foundation Engineering. 2024; 3:7-15. EDN OFOAVE. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Савинов А.В. Применение свай, погружаемых вдавливанием, при реконструкции исторической застройки городов : автореф. дис. ... д-ра техн. наук. Волгоград, 2008. 34 с. EDN NKJRJL.</mixed-citation><mixed-citation xml:lang="en">Savinov A.V. Application of piles driven by pressing in the reconstruction of historical urban development : abstract of dis. ... doctor of technical sciences. Volgograd, 2008; 34. EDN NKJRJL. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Geddes J.D. Stresses in foundation soils due to vertical subsurface loading // Geotechnique. 1966. Vol. 16. Issue 3. Pp. 231–255. DOI: 10.1680/geot.1966.16.3.231</mixed-citation><mixed-citation xml:lang="en">Geddes J.D. Stresses in foundation soils due to vertical subsurface loading. Geotechnique. 1966; 16(3):231-255. DOI: 10.1680/geot.1966.16.3.231</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Барвашов В.А. Расчет на ЭЦВМ осадки свай от вертикальной нагрузки и определение перемещений грунта вокруг свай // Труды 3-й науч.-техн. конф. молодых научных работников НИИ оснований. 1967. С. 20–23.</mixed-citation><mixed-citation xml:lang="en">Barvashov V.A. Calculation on ETsVM of draft of piles from vertical loading and definition of movements of soil around piles. Proceedings of the 3rd scientific and technical conference of young researchers of the Research Institute of Foundations. 1967; 20-23. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Frank R. Etude theorique du comportement des pieux sous charge vertical; introduction de la dilatance. Paris : France, 1974. 238 p.</mixed-citation><mixed-citation xml:lang="en">Frank R. Etude theorique du comportement des pieux sous charge vertical; introduction de la dilatance. Paris, France, 1974; 238.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Cooke R.W. Settlement of friction pile foundations // Proceeding Conference on Toll Buildings. 1974. Рp. 7–19.</mixed-citation><mixed-citation xml:lang="en">Cooke R.W. Settlement of friction pile foundations. Proceeding Conference on Toll Buildings. 1974; 7-19.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Coyle H.M., Reese L.C. Load transfer for axially loaded piles in clay // Journal of the Soil Mechanics and Foundations Division. 1966. Vol. 92. Issue 2. Рp. 1–26.</mixed-citation><mixed-citation xml:lang="en">Coyle H.M., Reese L.C. Load transfer for axially loaded piles in clay. Journal of the Soil Mechanics and Foundations Division. 1966; 92(2):1-26.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Пискунов Н.С. Дифференциальное и интегральное исчисление. Т. 2. М. : Наука, 1985. 576 с.</mixed-citation><mixed-citation xml:lang="en">Piskunov N.S. Differential and integral calculus. Vol. 2. Moscow, Science, 1985; 576. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Boussinesq J. Applications des Potentiels a l’Etitude de l’Equilibre et du Mouvement des Solides Elastiques. Paris : Gauthier-Villiars, Imprimeur-Libraire, 1885.</mixed-citation><mixed-citation xml:lang="en">Boussinesq J. Applications des Potentiels a l’Etitude de l’Equilibre et du Mouvement des Solides Elastiques. Paris, Gauthier-Villiars, Imprimeur-Libraire, 1885.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Scott R.F. Foundation analysis. New Jersey, USA : Prentice Hall, 1981. 545 p.</mixed-citation><mixed-citation xml:lang="en">Scott R.F. Foundation analysis. New Jersey, USA, Prentice Hall, 1981; 545.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Schleicher F. Zur Theorie des Baugrundes // Zeitschrift für Angewandte Mathematik und Mechanik. 1925. No. 5. P. 199; Bauingenieur. 1926. Vol. 48. No. 7. Pp. 931–935; Vol. 49. Pp. 949–952.</mixed-citation><mixed-citation xml:lang="en">Schleicher F. Zur Theorie des Baugrundes. Zeitschrift für Angewandte Mathematik und Mechanik. 1925; 5:199; Bauingenieur, 1926; 48(7):931-935; 49:949-952.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Giroud J.P. Таbles pour 1е са1cul des fondations. Vol. 1: Tassement. Paris : Dunod, 1972. 383 p.</mixed-citation><mixed-citation xml:lang="en">Giroud J.P. Таbles pour 1е са1cul des fondations. Vol. 1: Tassement. Paris, Dunod, 1972; 383.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Ильичев В.А., Аникьев А.В. Система с полутора степенями свободы как динамическая модель неоднородного основания // Труды института НИИОСП им. Н.М. Герсеванова. 1987. № 85. С. 30–32.</mixed-citation><mixed-citation xml:lang="en">Ilyichev V.A., Anikiev A.V. A system with one and a half degrees of freedom as a dynamic model of a heterogeneous foundation. Proceedings of the Institute NIIOSP named after N.M. Gersevanov. 1987; 85:30-32. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Mindlin R.D. Force at a Point in the Interior of a Semi-Infinite Solid // Physics. 1936. Vol. 7. Issue 5. Pp. 195–202. DOI: 10.1063/1.1745385</mixed-citation><mixed-citation xml:lang="en">Mindlin R.D. Force at a Point in the Interior of a Semi-Infinite Solid. Physics. 1936; 7(5):195-202. DOI: 10.1063/1.1745385</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Nishida Y. Vertical stress and vertical deformations of ground under a deep circular uniform pressure in the semi-infinite // Proceedings of the 1st International Society for Rock Mechanics Congress. 1966. Vol. 2. Pp. 493–498.</mixed-citation><mixed-citation xml:lang="en">Nishida Y. Vertical stress and vertical deformations of ground under a deep circular uniform pressure in the semi-infinite. Proceedings of the 1-st International Society for Rock Mechanics Congress. 1966; 2:493-498.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Нгуен Занг Нам. Определение осадки круглого штампа с учетом его заглубления // Строительство — формирование среды жизнедеятельности : сб. тр. 4-й Междунар. науч.-практ. конф. молодых ученых, аспирантов и докторантов. 2006. С. 40–43.</mixed-citation><mixed-citation xml:lang="en">Nguyen Giang Nam. Determination of the settlement of a round stamp taking into account its depth. Construction — formation of the living environment : collection of works of the 4th International scientific and practical conference of young scientists, postgraduates and doctoral students. 2006; 40-43. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Знаменский В.В. Работа свайного фундамента в глинистых грунтах и расчет их по деформациям основания : автореф. дис. … канд. техн. наук. М., 1971. 14 с.</mixed-citation><mixed-citation xml:lang="en">Znamensky V.V. Work of pile foundation in clay soils and their calculation based on deformations of the base : abstract of dis.… cand. of technical sciences. Moscow, 1971; 14. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">PLAXIS 2D-v.9 Finite Element Code for Soil and Rock Analyses: User Manual. Rotterdam : Balkema, 2008.</mixed-citation><mixed-citation xml:lang="en">PLAXIS 2D-v.9 Finite Element Code for Soil and Rock Analyses: User Manual. Rotterdam, Balkema, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Моссаковский В.И. Основная смешанная задача теории упругости для полупространства с круговой линией раздела граничных условий // Прикладная математика и механика. 1954. Т. 18. № 2. С. 187–196.</mixed-citation><mixed-citation xml:lang="en">Mossakovsky V.I. The main mixed problem of elasticity theory for a half-space with a circular line of separation of boundary conditions. Applied Mathematics and Mechanics. 1954; 18(2):187-196. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Ефремов М.Г., Коновалов П.А., Михеев В.В. К вопросу о распределении послойных деформаций грунта в сжимаемой толще глинистых и песчаных оснований (по материалам полевых испытаний) // Основания, фундаменты и механика грунтов. 1963. № 6. С. 5–7. EDN XYWMZF.</mixed-citation><mixed-citation xml:lang="en">Efremov M.G., Konovalov P.A., Mikheev V.V. On the distribution of layer-by-layer soil deformations in the compressible thickness of clay and sandy foundations (based on field test materials). Soil Mechanics and Foundation Engineering. 1963; 6:5-7. EDN XYWMZF. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Федоровский В.Г., Безволев С.Г. Прогноз осадок фундаментов мелкого заложения и выбор модели основания для расчета плит // Основания, фундаменты и механика грунтов. 2000. № 4. С. 10–18. EDN WESCFN.</mixed-citation><mixed-citation xml:lang="en">Fedorovskii V.G., Bezvolev S.G. Prediction of shallow-foundation settlements and selection of bed models for slab analysis. Soil Mechanics and Foundation Engineering. 2000; 4:10-18. EDN WESCFN. (rus.).</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Шарафутдинов Р.Ф., Безволев С.Г. Определение сдвиговой ползучести глинистых грунтов полевыми и лабораторными методами при изысканиях под свайные фундаменты // Российский форум изыскателей : сб. докл. III Междунар. науч.-практ. конф. 2022. С. 271–275. EDN TGREAF.</mixed-citation><mixed-citation xml:lang="en">Sharafutdinov R.F., Bezvolev S.G. Determination of shear creep of clay soils by field and laboratory methods during surveys under pile foundations. Russian Surveyors Forum : collection of reports of the III International Scientific and Practical Conference. 2022; 271-275. EDN TGREAF. (rus.).</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>
