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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="edn" pub-id-type="custom">GEFLLF</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-16631</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/16631</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Геотехнология и инженерная геология</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Geotechnical Engineering and Engineering Geology</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Three-dimensional modeling of stress-strain state and rock massif stability analysis during the construction of an underground research laboratory</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Трехмерное моделирование напряженно-деформированного состояния  и анализ стабильности породного массива при строительстве подземной исследовательской лаборатории</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Tatarinov</surname>
            <given-names>Viktor N.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Татаринов</surname>
              <given-names>В. Н.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Tatarinov</surname>
              <given-names>Viktor N.</given-names>
            </name>
          </name-alternatives>
          <email>victat@wdcb.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0001-7546-2072</contrib-id>
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        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Геофизический центр РАН, Москва, Россия (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Gupalo</surname>
            <given-names>Vladimir S.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Гупало</surname>
              <given-names>В. С.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Gupalo</surname>
              <given-names>Vladimir S.</given-names>
            </name>
          </name-alternatives>
          <email>gupalo@ibrae.ac.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0002-2228-1275</contrib-id>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">Институт проблем безопасного развития атомной энергетики РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Nuclear Safety Institute RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Akmatov</surname>
            <given-names>Dastan Zh.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Акматов</surname>
              <given-names>Д. Ж.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Akmatov</surname>
              <given-names>Dastan Zh.</given-names>
            </name>
          </name-alternatives>
          <email>d.akmatov@gcras.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0001-6435-464X</contrib-id>
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        </contrib>
        <aff-alternatives id="aff3">
          <aff>
            <institution xml:lang="ru">Геофизический центр РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Manevich</surname>
            <given-names>Aleksandr I.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Маневич</surname>
              <given-names>А. И.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Manevich</surname>
              <given-names>Aleksandr I.</given-names>
            </name>
          </name-alternatives>
          <email>v.manevich@gcras.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0001-7486-6104</contrib-id>
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          <aff>
            <institution xml:lang="ru">Геофизический центр РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Shevchuk</surname>
            <given-names>Roman V.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Шевчук</surname>
              <given-names>Р. В.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Shevchuk</surname>
              <given-names>Roman V.</given-names>
            </name>
          </name-alternatives>
          <email>v.shevshuk@gcras.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0003-3461-6383</contrib-id>
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          <aff>
            <institution xml:lang="ru">Геофизический центр РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Losev</surname>
            <given-names>Ilya V.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Лосев</surname>
              <given-names>И. В.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Losev</surname>
              <given-names>Ilya V.</given-names>
            </name>
          </name-alternatives>
          <email>v.losev@gcras.ru</email>
          <contrib-id contrib-id-type="orcid">0009-0005-0785-4986</contrib-id>
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        </contrib>
        <aff-alternatives id="aff6">
          <aff>
            <institution xml:lang="ru">Геофизический центр РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Kamaev</surname>
            <given-names>Artem A.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Камаев</surname>
              <given-names>А. А.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Kamaev</surname>
              <given-names>Artem A.</given-names>
            </name>
          </name-alternatives>
          <email>v.kamaev@gcras.ru</email>
          <contrib-id contrib-id-type="orcid">0009-0008-5139-8086</contrib-id>
          <xref ref-type="aff" rid="aff7"/>
        </contrib>
        <aff-alternatives id="aff7">
          <aff>
            <institution xml:lang="ru">Геофизический центр РАН (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Geophysical Center RAS (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2026-01-30">
        <day>30</day>
        <month>01</month>
        <year>2026</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2026</year>
      </pub-date>
      <volume>278</volume>
      <fpage>3</fpage>
      <lpage>15</lpage>
      <history>
        <date date-type="received" iso-8601-date="2024-12-24">
          <day>24</day>
          <month>12</month>
          <year>2024</year>
        </date>
        <date date-type="accepted" iso-8601-date="2025-10-13">
          <day>13</day>
          <month>10</month>
          <year>2025</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2026-03-25">
          <day>25</day>
          <month>03</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 2026 В. Н. Татаринов, В. С. Гупало, Д. Ж. Акматов, А. И. Маневич, Р. В. Шевчук, И. В. Лосев, А. А. Камаев</copyright-statement>
        <copyright-statement xml:lang="en">© 2026 Viktor N. Tatarinov, Vladimir S. Gupalo, Dastan Zh. Akmatov, Aleksandr I. Manevich, Roman V. Shevchuk, Ilya V. Losev, Artem A. Kamaev</copyright-statement>
        <copyright-year>2026</copyright-year>
        <copyright-holder xml:lang="ru">В. Н. Татаринов, В. С. Гупало, Д. Ж. Акматов, А. И. Маневич, Р. В. Шевчук, И. В. Лосев, А. А. Камаев</copyright-holder>
        <copyright-holder xml:lang="en">Viktor N. Tatarinov, Vladimir S. Gupalo, Dastan Zh. Akmatov, Aleksandr I. Manevich, Roman V. Shevchuk, Ilya V. Losev, Artem A. Kamaev</copyright-holder>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="ru">
          <license-p>Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0)</license-p>
        </license>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="en">
          <license-p>This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/16631">https://pmi.spmi.ru/pmi/article/view/16631</self-uri>
      <abstract xml:lang="ru">
        <p>Представлены результаты моделирования полей напряжений и анализа прочности породного массива на участке Енисейский (Красноярский край), выбранного для строительства подземной исследовательской лаборатории. Обоснованы варианты граничных условий нагружения моделей по ее границам, результаты моделирования распределения компонент тензора напряжений для четырех вариантов нагружения и оценка стабильности массива с использованием известных моделей прочностного анализа Хука – Брауна, Кулона – Мора, Мизеса и др. Определены закономерности распределения полей напряжений в массиве и отличия, связанные с тектоническими условиями района. Установлено, что локализация зон концентрации интенсивности напряжений зависит от соотношения компонент главных действующих напряжений. Ориентация сжатия в субмеридиональном направлении приводит к росту интенсивности напряжений на 10-15 % относительно иных вариантов моделирования. Зоны аномальных значений интенсивности напряжений расположены внутри блоков, а также в лежачих крыльях тектонических разломов. Модели характеризуются высокими значениями потенциальной энергии формоизменения в зонах разломов (как участков массива, наиболее легко поддающихся деформированию) и их пересечений. Трехмерное моделирование позволяет обнаружить эффекты, которые слабо проявляются в моделях плоского деформированного состояния. Результаты геомеханического моделирования необходимы при планировании экспериментов в подземной исследовательской лаборатории для уточнения изоляционных свойств породного массива при захоронении высокоактивных радиоактивных отходов. Методические подходы трехмерного моделирования применяются геомеханическими и геотехническими службами промышленных предприятий и других опасных производственных объектов (подземные хранилища газа, месторождения полезных ископаемых и др.).</p>
      </abstract>
      <abstract xml:lang="en">
        <p>The paper presents the results of modeling stress fields and analyzing the strength of the rock mass at the Yeniseiskiy site (Krasnoyarsk Region), selected for the construction of an underground research laboratory. Variants of boundary loading conditions along the model boundaries are substantiated, and the results of modeling the distribution of stress tensor components for four loading scenarios are presented, along with an assessment of rock mass stability using well-known strength criteria, including Hoek – Brown, Mohr – Coulomb, von Mises, and others. Regularities in the distribution of stress fields within the rock mass and differences associated with the tectonic conditions of the area are identified. It is established that the localization of zones of stress intensity concentration depends on the ratio of the principal stress components. Orientation of compression in the submeridional direction leads to an increase in stress intensity by 10-15 % relative to other modeling variants. Zones of anomalous stress intensity values are located within blocks as well as in the footwalls of tectonic faults. The models are characterized by high values of the potential energy of distortion in fault zones (as parts of the rock mass most susceptible to deformation) and at their intersections. Three-dimensional modeling makes it possible to identify effects that are weakly expressed in plane strain models. The results of geomechanical modeling are required for planning experiments in the underground research laboratory in order to refine the isolation properties of the rock mass during the disposal of high-level radioactive waste. Methodological approaches of three-dimensional modeling are applied by geomechanical and geotechnical services of industrial enterprises and other hazardous facilities (underground gas storage facilities, mineral deposits, etc.).</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>высокоактивные радиоактивные отходы</kwd>
        <kwd>подземная исследовательская лаборатория</kwd>
        <kwd>численное моделирование</kwd>
        <kwd>породный массив</kwd>
        <kwd>напряженно-деформированное состояние</kwd>
        <kwd>критерии прочности</kwd>
      </kwd-group>
      <funding-group>
        <funding-statement xml:lang="ru">Работа выполнена в рамках Государственного задания ГЦ РАН, утвержденного Минобрнауки России.</funding-statement>
        <funding-statement xml:lang="en">The work was carried out under the state assignment of the Geophysical Center of the Russian Academy of Sciences and the Institute for Safe Development of Nuclear Energy of the Russian Academy of Sciences, approved by the Ministry of Education and Science of Russia.</funding-statement>
      </funding-group>
    </article-meta>
  </front>
  <body/>
  <back>
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