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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">KMVNOM</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-16617</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/16617</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">Geometric models of typical complex-structured bench blocks</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Геометрические модели типовых сложноструктурных блоков уступов</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Rakishev</surname>
            <given-names>Bayan R.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Ракишев</surname>
              <given-names>Б. Р.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Rakishev</surname>
              <given-names>Bayan R.</given-names>
            </name>
          </name-alternatives>
          <email>b.rakishev@satbayev.university</email>
          <contrib-id contrib-id-type="orcid">0000-0001-5445-070X</contrib-id>
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        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">НАО «Казахский национальный исследовательский технический университет имени К.И.Сатпаева» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Satbayev University (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Edilbaev</surname>
            <given-names>Abdraman I.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Едильбаев</surname>
              <given-names>А. И.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Edilbaev</surname>
              <given-names>Abdraman I.</given-names>
            </name>
          </name-alternatives>
          <email>info@gornoeburo.kz</email>
          <contrib-id contrib-id-type="orcid">0000-0001-8498-7049</contrib-id>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">ТОО «Горное бюро» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Mining Bureau LLP (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Sakabekov</surname>
            <given-names>Auzhan S.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Сакабеков</surname>
              <given-names>А. С.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Sakabekov</surname>
              <given-names>Auzhan S.</given-names>
            </name>
          </name-alternatives>
          <email>auzhani@gmail.com</email>
          <contrib-id contrib-id-type="orcid">0000-0002-3141-7373</contrib-id>
          <xref ref-type="aff" rid="aff3"/>
        </contrib>
        <aff-alternatives id="aff3">
          <aff>
            <institution xml:lang="ru">НАО «Казахский национальный исследовательский технический университет имени К.И.Сатпаева» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Satbayev University (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Orynbay</surname>
            <given-names>Asfandiyar A.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Орынбай</surname>
              <given-names>А. А.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Orynbay</surname>
              <given-names>Asfandiyar A.</given-names>
            </name>
          </name-alternatives>
          <email>a.orynbay@aues.kz</email>
          <contrib-id contrib-id-type="orcid">0000-0002-3720-7625</contrib-id>
          <xref ref-type="aff" rid="aff4"/>
        </contrib>
        <aff-alternatives id="aff4">
          <aff>
            <institution xml:lang="ru">НАО «Алматинский университет энергетики и связи имени Гумарбека Даукеева» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">NPJSC “Almaty University of Power Engineering and Telecommunications named after Gumarbek Daukeyev” (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Mekebai</surname>
            <given-names>Nazira A.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Мекебай</surname>
              <given-names>Н. А.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Mekebai</surname>
              <given-names>Nazira A.</given-names>
            </name>
          </name-alternatives>
          <email>miekiebai_79@mail.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0002-3124-2630</contrib-id>
          <xref ref-type="aff" rid="aff5"/>
        </contrib>
        <aff-alternatives id="aff5">
          <aff>
            <institution xml:lang="ru">НАО «Казахский национальный исследовательский технический университет имени К.И.Сатпаева» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Satbayev University (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Ibyrkhanov</surname>
            <given-names>Temirlan S.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Ибырханов</surname>
              <given-names>Т. С.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Ibyrkhanov</surname>
              <given-names>Temirlan S.</given-names>
            </name>
          </name-alternatives>
          <email>ibir.tem@mail.ru</email>
          <contrib-id contrib-id-type="orcid">0009-0001-6344-8270</contrib-id>
          <xref ref-type="aff" rid="aff6"/>
        </contrib>
        <aff-alternatives id="aff6">
          <aff>
            <institution xml:lang="ru">НАО «Казахский национальный исследовательский технический университет имени К.И.Сатпаева» (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Satbayev University (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2026-02-02">
        <day>02</day>
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2026</year>
      </pub-date>
      <volume>278</volume>
      <fpage>16</fpage>
      <lpage>29</lpage>
      <history>
        <date date-type="received" iso-8601-date="2024-11-25">
          <day>25</day>
          <month>11</month>
          <year>2024</year>
        </date>
        <date date-type="accepted" iso-8601-date="2025-10-09">
          <day>09</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 Б. Р. Ракишев, А. И. Едильбаев, А. С. Сакабеков, А. А. Орынбай, Н. А. Мекебай, Т. С. Ибырханов</copyright-statement>
        <copyright-statement xml:lang="en">© 2026 Bayan R. Rakishev, Abdraman I. Edilbaev, Auzhan S. Sakabekov, Asfandiyar A. Orynbay, Nazira A. Mekebai, Temirlan S. Ibyrkhanov</copyright-statement>
        <copyright-year>2026</copyright-year>
        <copyright-holder xml:lang="ru">Б. Р. Ракишев, А. И. Едильбаев, А. С. Сакабеков, А. А. Орынбай, Н. А. Мекебай, Т. С. Ибырханов</copyright-holder>
        <copyright-holder xml:lang="en">Bayan R. Rakishev, Abdraman I. Edilbaev, Auzhan S. Sakabekov, Asfandiyar A. Orynbay, Nazira A. Mekebai, Temirlan S. Ibyrkhanov</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/16617">https://pmi.spmi.ru/pmi/article/view/16617</self-uri>
      <abstract xml:lang="ru">
        <p>Более полное извлечение полезных ископаемых из недр путем снижения их потерь актуализирует задачи совершенствования математических моделей объектов разработки. Цель данной работы – создание геометрических моделей типовых сложноструктурных блоков (ССБ), которые можно распространить на реальные ССБ. Они базируются на горно-геологических моделях виртуальных (типовых) сложноструктурных рудных блоков уступа, состоящих из разрозненных сплошных (первый тип) и рассредоточенных (второй тип) рудных тел. Ключевыми параметрами этих блоков являются координаты характерных точек разрозненных сплошных и рассредоточенных рудных тел, длины отрезков контактных линий рудных тел с вмещающими породами, площади рудных тел на разрезах ССБ. Они определяют горно-геологические характеристики этих объектов – рудонасыщенность, сложность геолого-морфологического строения блока. Эти характеристики аналитически взаимосвязаны с геометрическими параметрами разрозненных рудных тел и размерами слоя примешиваемой породы или теряемой руды, положены в основу методики расчета численных значений геометрических моделей ССБ и горно-геологических характеристик рудных тел и блока в целом. Создана компьютерная программа для автоматизированного определения геометрических характеристик ССБ по заданным начальным ключевым параметрам сложноструктурных блоков. Рассмотрен пример расчета этих характеристик для типовых сложноструктурных блоков, показана значимость результатов исследований при разработке ССБ. Предлагаемая методика расчета ключевых характеристик геометрических моделей ССБ является информационной основой для принятия решений по экономичной и экологичной разработке сложноструктурных блоков уступов. Результаты исследований можно использовать при эксплуатации реальных сложноструктурных месторождений для существенного уменьшения потерь и разубоживания полезных ископаемых.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>More complete extraction of minerals from subsurface by reducing their losses even more actualizes tasks of improving mathematical models of mining objects. Purpose of this work is to create geometric models of typical complex-structured blocks (CSB), which could be extended to real CSB. They are based on mining and geological models of virtual (typical) complex-structured ore blocks of bench, consisting of discontinuous continuous (first type) and dispersed ore bodies (second type). These blocks key parameters are isolated continuous and dispersed ore bodies characteristic points coordinates, ore bodies with host rocks contact line segments length, and ore bodies areas in CSB sections. They determine these objects mining and geological characteristics (ore saturation, block geological and morphological structure complexity). These characteristics are analytically interconnected with disparate ore bodies geometric parameters and admixed rock or lost ore layer size. They are the basis for CSB geometric models numerical values calculation methodology and mining and geological characteristics of ore bodies and whole block. Computer program for automated determination of geometrical characteristics of CSB by given initial key parameters of complex-structured blocks has been created. Example of calculation of these characteristics for typical complex-structured blocks is considered, and significance of research results in CSB development is shown. Proposed methodology of calculation of key characteristics of geometrical models of CSB is an information basis for making decisions on economical and ecological development of CSB of benches. Results of research can be used in exploitation of real complex-structured deposits to significantly reduce loss and dilution of minerals.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>сложноструктурные блоки</kwd>
        <kwd>коэффициент рудонасыщенности</kwd>
        <kwd>показатель сложности геологического строения блока</kwd>
        <kwd>горно-геологические характеристики</kwd>
        <kwd>геометрическое моделирование</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>complex-structured blocks</kwd>
        <kwd>ore saturation coefficient</kwd>
        <kwd>index of complexity of geological structure of the block</kwd>
        <kwd>mining and geological characteristics</kwd>
        <kwd>geometric modeling</kwd>
      </kwd-group>
      <funding-group>
        <funding-statement xml:lang="ru">Статья подготовлена в рамках проекта, финансируемого Министерством науки и высшего образования  Республики Казахстан, 2023/AP19676591 «Разработка инновационных технологий полного извлечения разрозненных кондиционных руд из сложноструктурных блоков уступов».</funding-statement>
        <funding-statement xml:lang="en">The article was prepared as part of a project funded by the Ministry of Science and Higher Education of the Republic of Kazakhstan 2023/AP19676591 “Development of innovative technologies for the complete extraction of scattered conditioned ores from complex-structural blocks of benches”.</funding-statement>
      </funding-group>
    </article-meta>
  </front>
  <body/>
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