<?xml version="1.0" encoding="UTF-8"?>
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" dtd-version="1.4" article-type="research-article">
  <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 pub-id-type="doi">10.31897/PMI.2021.1.4</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-14397</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/14397</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Горное дело</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Mining</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Determination and verification of the calculated model parameters of salt rocks taking into account softening and plastic flow</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Определение и верификация параметров расчетной модели соляных пород с учетом разупрочнения и ползучести</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Kozlovskiy</surname>
            <given-names>Evgenii Ya.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Козловский</surname>
              <given-names>Е. Я.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Kozlovskiy</surname>
              <given-names>Evgenii Ya.</given-names>
            </name>
          </name-alternatives>
          <email>ekozlovskiy@outlook.com</email>
          <contrib-id contrib-id-type="orcid">0000-0001-9496-7148</contrib-id>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Белорусский государственный университет (Минск, Беларусь)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Belarusian State University (Minsk, Belarus)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Zhuravkov</surname>
            <given-names>Mikhail A.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Журавков</surname>
              <given-names>М. А.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Zhuravkov</surname>
              <given-names>Mikhail A.</given-names>
            </name>
          </name-alternatives>
          <email>zhuravkov@bsu.by</email>
          <contrib-id contrib-id-type="orcid">0000-0002-7420-5821</contrib-id>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">Белорусский государственный университет (Минск, Беларусь)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Belarusian State University (Minsk, Belarus)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2021-04-26">
        <day>26</day>
        <month>04</month>
        <year>2021</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2021</year>
      </pub-date>
      <volume>247</volume>
      <fpage>33</fpage>
      <lpage>38</lpage>
      <history>
        <date date-type="received" iso-8601-date="2020-11-16">
          <day>16</day>
          <month>11</month>
          <year>2020</year>
        </date>
        <date date-type="accepted" iso-8601-date="2021-03-02">
          <day>02</day>
          <month>03</month>
          <year>2021</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2021-04-26">
          <day>26</day>
          <month>04</month>
          <year>2021</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 2021 Е. Я. Козловский, М. А. Журавков</copyright-statement>
        <copyright-statement xml:lang="en">© 2021 Evgenii Ya. Kozlovskiy, Mikhail A. Zhuravkov</copyright-statement>
        <copyright-year>2021</copyright-year>
        <copyright-holder xml:lang="ru">Е. Я. Козловский, М. А. Журавков</copyright-holder>
        <copyright-holder xml:lang="en">Evgenii Ya. Kozlovskiy, Mikhail A. Zhuravkov</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/14397">https://pmi.spmi.ru/pmi/article/view/14397</self-uri>
      <abstract xml:lang="ru">
        <p>В статье предложено использование комбинации модифицированной модели Бюргерса и модели Мора – Кулона с деградацией коэффициента сцепления и возрастанием коэффициента трения для определения параметров соляных пород. Проводится сравнительный анализ длительных лабораторных испытаний и натурных наблюдений в подземных горных выработках с результатами, выполненными по расчетной модели с определенными параметрами. По статистически обработанным данным лабораторных испытаний получены параметры модели Мора – Кулона с деградацией коэффициента сцепления и возрастанием коэффициента трения, определены параметры модифицированной модели Бюргерса. С использованием численных методов выполнены виртуальные (компьютерные) осесимметричные трехосные испытания, как мгновенные, так и длительные на базе предложенной модели с подобранными параметрами. Решена модельная задача для сравнения поведения модели с данными наблюдательных станций в подземных горных выработках, полученных со скважинных стержневых экстензометров и контурных деформационных марок. Полученные аналитически коэффициенты нелинейного вязкого элемента модифицированной модели Бюргерса для всех проанализированных соляных пород не нуждались в коррекции по результатам мониторинга. В то же время для коэффициентов вязкоупругого элемента для всех рассмотренных пород требовалась оптимизация. Анализ модельных исследований показал удовлетворительную сходимость с данными по наблюдательным станциям. Проведенный на моделях сравнительный анализ по лабораторным испытаниям и наблюдениям в выработках свидетельствует о корректном определении параметров для соляных пород и верифицированности модели в целом.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>The article suggests using a combination of the modified Burgers model and the Mohr – Coulomb model with the degradation of the adhesion coefficient and the increase in the friction coefficient to determine the parameters of salt rocks. A comparative analysis of long-term laboratory tests and field observations in underground mine workings with the results obtained using a calculated model with certain parameters is carried out. The parameters of the Mohr – Coulomb model with the degradation of the adhesion coefficient and the increase in the friction coefficient were obtained from the statistically processed data of laboratory tests, and the parameters of the modified Burgers model were determined. Using numerical methods, virtual (computer) axisymmetric triaxial tests, both instantaneous and long-term, were performed on the basis of the proposed model with selected parameters. A model problem is solved for comparing the behavior of the model with the data of observation stations in underground mine workings obtained from borehole rod extensometers and contour deformation marks. The analytically obtained coefficients of the nonlinear viscous element of the modified Burgers model for all the analyzed salt rocks did not need to be corrected based on the monitoring results. At the same time, optimization was required for the viscoelastic element coefficients for all the considered rocks. The analysis of the model studies showed a satisfactory convergence with the data on the observation stations. The comparative analysis carried out on the models based on laboratory tests and observations in the workings indicates the correct determination of the parameters for salt rocks and the verification of the model in general.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>механика горных пород</kwd>
        <kwd>соляные породы</kwd>
        <kwd>обратный анализ</kwd>
        <kwd>подземные сооружения</kwd>
        <kwd>модели ползучести</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>rock mechanics</kwd>
        <kwd>salt rocks</kwd>
        <kwd>underground structures</kwd>
        <kwd>reverse analysis</kwd>
        <kwd>plastic flow models</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body/>
  <back>
    <ref-list>
      <ref id="ref1">
        <label>1</label>
        <mixed-citation xml:lang="ru">Ермашов А.О. Геомеханическое обоснование расчетов оседаний земной поверхности при добыче калийно-магниевых руд (на примере Верхнекамского месторождения калийно-магниевых солей): Автореф. дис. … канд. техн. наук. Пермь: Горный институт УрО РАН, 2015. 22 с.</mixed-citation>
        <mixed-citation xml:lang="en">Ermashov A.O. Geomechanical substantiation of calculations of the earth surface subsidence calculations for the extraction of potash-magnesium ores (on the example of the Verkhnekamskoye potash-magnesium salt deposit): Avtoref. dis. … kand. tekhn. nauk. Perm: Gornyi institut UrO RAN, 2015, p. 22 (in Russian).</mixed-citation>
      </ref>
      <ref id="ref2">
        <label>2</label>
        <mixed-citation xml:lang="ru">Методика прогноза напряженно-деформированного состояния крепи вертикального ствола на участке сопряжения с горизонтальной выработкой в соляных породах / М.А.Карасев, М.А.Буслова, М.А.Вильнер, Т.Т.Нгуен // Записки Горного института. 2019. Т. 240. С. 628-637. DOI: 10.31897/PMI.2019.6.628</mixed-citation>
        <mixed-citation xml:lang="en">Karasev M.A., Buslova M.A., Vilner M.A., Nguyen T.T. Method for predicting the stress-strain state of the vertical shaft lining at the drift landing section in saliferous rocks. Journal of Mining Institute. 2019. Vol. 240, p. 628-637. DOI: 10.31897/pmi.2019.6.628 (in Russian).</mixed-citation>
      </ref>
      <ref id="ref3">
        <label>3</label>
        <mixed-citation xml:lang="ru">Протосения А.Г. Прогноз нагрузок на крепы вертикальных стволов в породах склонных к развитию реологических процессов / А.Г.Протосеня, В.И.Очкуров, И.А.Откупщикова // Современные образовательные технологии в подготовке специалистов для минерально-сырьевого комплекса. Сборник научных трудов III Всероссийской научной конференции, 5-6 марта 2020, Санкт-Петербург, Россия. СПб: Санкт-Петербургский горный университет, 2020. С. 1091-1101.</mixed-citation>
        <mixed-citation xml:lang="en">Protosenya A.G., Ochkurov V.I., Otkupshikova I.A. Prediction of rock load on shaft lining in creep rock masses. Sbornik nauchnykh trudov III Vserossiiskoi nauchnoi konferentsii “Sovremennye obrazovatelnye tekhnologii v podgotovke spetsialistov dlya mineralno-syrevogo kompleksa”, 5-6 Marta, 2020, Sankt-Peterburg, Rossiya. St. Petersburg: Sankt-Peterburgskii gornyi universitet, 2020, p. 1091-1101. (in Russian)</mixed-citation>
      </ref>
      <ref id="ref4">
        <label>4</label>
        <mixed-citation xml:lang="ru">Протосения А.Г. Прогноз напряженного состояния массива на участке сопряжения ствола и горизонтальной выработки / А.Г.Протосеня, Ны Бай Нгуен // Известия высших учебных заведений. Горный журнал. 2015. № 7. С. 50-55.</mixed-citation>
        <mixed-citation xml:lang="en">Protosenia A.G., Nguen Ny Bai. The forecast of stress state of massif at the area of mine shaft and gallery junction. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2015. N 7, p. 50-55 (in Russia).</mixed-citation>
      </ref>
      <ref id="ref5">
        <label>5</label>
        <mixed-citation xml:lang="ru">A Strain-Softening Constitutive Model of Heterogeneous Rock Mass Considering Statistical Damage and Its Application in Numerical Modeling of Deep Roadways / G.Li, F.Ma, G.Liu et al. // Sustainability. 2019. Vol. 11. № 8. P. 2399. DOI: 10.3390/su11082399</mixed-citation>
        <mixed-citation xml:lang="en">LiG., MaF., Liu G. et al. A Strain-Softening Constitutive Model of Heterogeneous Rock Mass Considering Statistical Damage and Its Application in Numerical Modeling of Deep Roadways. Sustainability. 2019. Vol. 11. N 8, p. 2399. DOI: 10.3390/su11082399</mixed-citation>
      </ref>
      <ref id="ref6">
        <label>6</label>
        <mixed-citation xml:lang="ru">A visco-elasto-plastic softening model and it’s application for solving static and dynamic problems in potash mining / W.Minkley, W.Menzel, H.Konietzky, L.te Kamp // Proceedings of the 2nd International FIAC Symposium, 29-31 October, 2001, Lyon, France, 2001. P. 21-27.</mixed-citation>
        <mixed-citation xml:lang="en">MinkleyW., MenzelW., Konietzky H., Kampte L. A visco-elasto-plastic softening model and it’s application for solving static and dynamic problems in potash mining. Proceedings of the 2nd International FlAC Symposium, 29-31 October, 2001, Lyon, France, 2001, p. 21-27.</mixed-citation>
      </ref>
      <ref id="ref7">
        <label>7</label>
        <mixed-citation xml:lang="ru">Brückner D. The improved IfG gas storage cavern design concept / D.Brückner, W.Minkley, A.Lindert // Mechanical Behavior of Salt VII. London: CRC Press, 2012. P. 391-398.</mixed-citation>
        <mixed-citation xml:lang="en">Brückner D., Minkley W., Lindert A. The improved IfG gas storage cavern design concept. Mechanical Behavior of Salt VII. London: CRC Press, 2012, p. 391-398.</mixed-citation>
      </ref>
      <ref id="ref8">
        <label>8</label>
        <mixed-citation xml:lang="ru">Comparison of advanced constitutive models for the mechanical behavior of rock salt – results from a joint research project – I. Modeling of deformation processes and benchmark calculations / O.Schulze, U.Heemann, F.Zetsch et al. // The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007. P. 77-88. DOI: 10.1201/9781315106502-10</mixed-citation>
        <mixed-citation xml:lang="en">Schulze O., Heemann U., Zetsch F. et al. Comparison of advanced constitutive models for the mechanical behavior of rock salt – results from a joint research project – I. Modeling of deformation processes and benchmark calculations. The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007, p. 77-88. DOI: 10.1201/9781315106502-10</mixed-citation>
      </ref>
      <ref id="ref9">
        <label>9</label>
        <mixed-citation xml:lang="ru">Comparison of advanced constitutive models for the mechanical behavior of rock salt – results from a joint research project – II. Numerical modeling of two in situ case studies and comparison / Z.Hou, R.Wolters, R.Rokahr et al. // The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007. P. 89-98. DOI: 10.1201/9781315106502-11</mixed-citation>
        <mixed-citation xml:lang="en">Hou Z., Wolters R., RokahrR. et al. Comparison of advanced constitutive models for the mechanical behavior of rock salt – results from a joint research project – II. Numerical modeling of two in situ case studies and comparison. The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007, p. 89-98. DOI: 10.1201/9781315106502-11</mixed-citation>
      </ref>
      <ref id="ref10">
        <label>10</label>
        <mixed-citation xml:lang="ru">Dynamic back-calculation of the collapse of the Saint-Maximilien mining field during mining on rock salt in Varangéville (1873) / W.Minkley, P.Bzrest, J.P.Schleinig et al. // Mechanical Behavior of Salt VII. London: CRC Press, 2012. P. 241-252.</mixed-citation>
        <mixed-citation xml:lang="en">Minkley W., Bzrest P., Schleinig J.P. et al. Dynamic back-calculation of the collapse of the Saint-Maximilien mining field during mining on rock salt in Varangéville (1873). Mechanical Behavior of Salt VII. London: CRC Press, 2012, p. 241-252.</mixed-citation>
      </ref>
      <ref id="ref11">
        <label>11</label>
        <mixed-citation xml:lang="ru">Enhanced double-mechanism creep laws for salt rocks / P.A.L.P.Firme, N.B.Brandao, D.Roehl, C.Romane // Acta Geotechnica. 2018. Vol. 13. P. 1329-1340. DOI: 10.1007/s11440-018-0689-7</mixed-citation>
        <mixed-citation xml:lang="en">Firme P.A.L.P., Brandao N.B., Roehl D., Romanel C. Enhanced double-mechanism creep laws for salt rocks. Acta Geotechnica. 2018. Vol. 13, p. 1329-1340. DOI: 10.1007/s11440-018-0689-7</mixed-citation>
      </ref>
      <ref id="ref12">
        <label>12</label>
        <mixed-citation xml:lang="ru">Estimation of the Rock Load in Non-squeezing Ground Condition Using the Post Failure Properties of Rock Mass / M.S.Dehkordi, H.A.Lazemi, K.Shahriar, M.S.Dehkordi // Geotechnical and Geological Engineering. 2015. Vol. 33. P. 1115-1128. DOI: 10.1007/s10706-015-9891-7</mixed-citation>
        <mixed-citation xml:lang="en">Dehkordi M.S., Lazemi H.A., Shahriar K., Dehkordi M.S. Estimation of the Rock Load in Non-squeezing Ground Condition Using the Post Failure Properties of Rock Mass. Geotechnical and Geological Engineering. 2015. Vol. 33, p. 1115-1128. DOI: 10.1007/s10706-015-9891-7</mixed-citation>
      </ref>
      <ref id="ref13">
        <label>13</label>
        <mixed-citation xml:lang="ru">Hajjabdolmajid V. Modelling brittle failure of rock / V.Hajjabdolmajid, P.K.Kaiser, C.D.Martin // International Journal of Rock Mechanics and Mining Sciences. 2002. Vol. 39. Iss. 6. P. 731-741. DOI: 10.1016/S1365-1609(02)00051-5</mixed-citation>
        <mixed-citation xml:lang="en">Hajiabdolmajid V., Kaiser P.K., Martin C.D. Modelling brittle failure of rock. International Journal of Rock Mechanics and Mining Sciences. 2002. Vol. 39. Iss. 6, p. 731-741. DOI: 10.1016/S1365-1609(02)00051-5</mixed-citation>
      </ref>
      <ref id="ref14">
        <label>14</label>
        <mixed-citation xml:lang="ru">Hampel A. The Composite Dilatancy Model: A constitutive model for the mechanical behavior of rock salt / A.Hampel, O.Schulze // The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007. P. 99-108. DOI: 10.1201/9781315106502-12</mixed-citation>
        <mixed-citation xml:lang="en">Hampel A., Schulze O. The Composite Dilatancy Model: A constitutive model for the mechanical behavior of rock salt. The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007, p. 99-108. DOI: 10.1201/9781315106502-12</mixed-citation>
      </ref>
      <ref id="ref15">
        <label>15</label>
        <mixed-citation xml:lang="ru">Microscopic investigations on the healing and softening of damaged salt by uniaxial deformation from CT, SEM and NMR: effect of fluids (brine and oil) / J.Chen, H.Peng, J.Fan et al. // RSC Advances. 2020. Vol. 10. P. 2877-2886. DOI: 10.1039/C9RA05866D</mixed-citation>
        <mixed-citation xml:lang="en">Chen J., Peng H., Fan J. et al. Microscopic investigations on the healing and softening of damaged salt by uniaxial deformation from CT, SEM and NMR: effect of fluids (brine and oil). RSC Advances. 2020. Vol. 10, p. 2877-2886. DOI: 10.1039/C9RA05866D</mixed-citation>
      </ref>
      <ref id="ref16">
        <label>16</label>
        <mixed-citation xml:lang="ru">Minkley W. Constitutive models to describe the mechanical behavior of salt rocks and the imbedded weakness planes / W.Minkley, J. Mühlbauer // The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007. P. 119-127. DOI: 10.1201/9781315106502-14</mixed-citation>
        <mixed-citation xml:lang="en">Minkley W., Mühlbauer J. Constitutive models to describe the mechanical behavior of salt rocks and the imbedded weakness planes. The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007, p. 119-127. DOI: 10.1201/9781315106502-14</mixed-citation>
      </ref>
      <ref id="ref17">
        <label>17</label>
        <mixed-citation xml:lang="ru">Missal C. Ein thermisch-mechanisches Stoffmodell für Steinsalz mit Berücksichtigung von Schädigung, Bruch und Verheilung / C.Missal, A.Gährken, J.Stahlmann // Geotechnik. 2016. Vol. 39. № 1. P. 2-17. DOI: 10.1002/gete.201500010</mixed-citation>
        <mixed-citation xml:lang="en">Missal C., Gährken A., Stahlmann J. Ein thermisch‐mechanisches Stoffmodell für Steinsalz mit Berücksichtigung von Schädigung, Bruch und Verheilung. Geotechnik. 2016. Vol. 39. N 1, p. 2-17. DOI: 10.1002/gete.201500010</mixed-citation>
      </ref>
      <ref id="ref18">
        <label>18</label>
        <mixed-citation xml:lang="ru">Nonlinear volumetric deformation behavior of rock salt using the concept of mobilized dilatancy angle / Y.Chen, L.Ma, P.Fan et al. // The Open Civil Engineering Journal. 2016. Vol. 10. P. 524-531. DOI: 10.2174/1874149501610010524</mixed-citation>
        <mixed-citation xml:lang="en">Chen Y., Ma L., Fan P. et al. Nonlinear volumetric deformation behavior of rock salt using the concept of mobilized dilatancy angle. The Open Civil Engineering Journal. 2016. Vol. 10, p. 524-531. DOI: 10.2174/1874149501610010524</mixed-citation>
      </ref>
      <ref id="ref19">
        <label>19</label>
        <mixed-citation xml:lang="ru">Poiate E.Jr. Mecánica das rochas e mecánica computacional para projeto de poços de petróleo em zonas de sal: DSc Thesis. Rio de Janeiro: Pontificia Universidade Católica do Rio de Janeiro, 2012. 462 p. DOI: 10.17771/PUCRio.acad.34904</mixed-citation>
        <mixed-citation xml:lang="en">Poiate E.Jr. Mecânica das rochas e mecânica computacional para projeto de poços de petróleoem zonas de sal: DSc Thesis. Rio de Janeiro: Pontifícia Universidade Católica do Rio de Janeiro, 2012, p. 462. DOI: 10.17771/PUCRio.acad.34904</mixed-citation>
      </ref>
      <ref id="ref20">
        <label>20</label>
        <mixed-citation xml:lang="ru">Post-Yield Properties of Rock Salt Using the Concept of Mobilized Strength Components and the Dilation Angle / L.Ma, F.Yang, H.Xu, Z.Xie // Geotechnical and Geological Engineering. 2017. Vol. 35. P. 2841-2849. DOI: 10.1007/s10706-017-0283-z</mixed-citation>
        <mixed-citation xml:lang="en">Ma L., Yang F., Xu H., Xie Z. Post-Yield Properties of Rock Salt Using the Concept of Mobilized Strength Components and the Dilation Angle. Geotechnical and Geological Engineering. 2017. Vol. 35, p. 2841-2849. DOI: 10.1007/s10706-017-0283-z</mixed-citation>
      </ref>
      <ref id="ref21">
        <label>21</label>
        <mixed-citation xml:lang="ru">Rafiei Renani H. Cohesion degradation and friction mobilization in brittle failure of rocks / H.Rafiei Renani, C.D.Martin // International Journal of Rock Mechanics and Mining Sciences. 2018. Vol. 106. P. 1-13. DOI: 10.1016/j.ijrmms.2018.04.003</mixed-citation>
        <mixed-citation xml:lang="en">Rafiei Renani H., Martin C.D. Cohesion degradation and friction mobilization in brittle failure of rocks. International Journal of Rock Mechanics and Mining Sciences. 2018. Vol. 106, p. 1-13. DOI: 10.1016/j.ijrmms.2018.04.003</mixed-citation>
      </ref>
      <ref id="ref22">
        <label>22</label>
        <mixed-citation xml:lang="ru">Self-Healing Characteristics of Damaged Rock Salt under Different Healing Conditions / J.Chen, S.Ren, C.Yang et al. // Materials (Basel). 2013. Vol. 6. № 8. P. 3438-3450. DOI: 10.3390/ma6083438</mixed-citation>
        <mixed-citation xml:lang="en">Chen J., Ren S., Yang C.et al. Self-Healing Characteristics of Damaged Rock Salt under Different Healing Conditions. Materials (Basel). 2013. Vol. 6. N 8, p. 3438-3450. DOI: 10.3390/ma6083438</mixed-citation>
      </ref>
      <ref id="ref23">
        <label>23</label>
        <mixed-citation xml:lang="ru">Šlizowski J. Influence of effective stress on strain rate around the gas storing cavern / J. Šlizowski, K.M. Urbanczyk // The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007. P. 363-368. DOI: 10.1201/9781315106502-42</mixed-citation>
        <mixed-citation xml:lang="en">Ślizowski J., Urbańczyk K.M. Influence of effective stress on strain rate around the gas storing cavern. The Mechanical Behavior of Salt – Understanding of THMC Processes in Salt: Proceedings of the 6th Conference (SaltMech6), 22-25 May, 2007, Hannover, Germany, 2007, p. 363-368. DOI: 10.1201/9781315106502-42</mixed-citation>
      </ref>
      <ref id="ref24">
        <label>24</label>
        <mixed-citation xml:lang="ru">Vergleich aktueller Stoffgesetze und Vorgehensweisen anhand von Modellberechnungen zum thermo-mechanischen Verhalten und zur Verheulung von Steinsalz. Teilvorhaben 2 / R.-M.Günther, C.Lüdeling, T.Popp et al. Leipzig: IfG. 2016. 184 p. (in German).</mixed-citation>
        <mixed-citation xml:lang="en">Günther R.-M., Lüdeling C., Popp T. et al. Vergleich aktueller Stoffgesetze und Vorgehensweisen anhand von Modellberechnungen zum thermo-mechanischen Verhalten und zur Verheilung von Steinsalz. Teilvorhaben 2. Leipzig: IfG, 2016, p. 184 (in German).</mixed-citation>
      </ref>
      <ref id="ref25">
        <label>25</label>
        <mixed-citation xml:lang="ru">Vermeer P.A. Non-Associated Plasticity for Soils, Concrete and Rock / P.A.Vermeer, R.de Borst // Heron. 1984. Vol. 29. № 3. P. 1-64. DOI: 10.1007/978-94-017-2653-5_10</mixed-citation>
        <mixed-citation xml:lang="en">Vermeer P.A., de Borst R. Non-Associated Plasticity for Soils, Concrete and Rock. Heron. 1984. Vol. 29. N 3, p. 1-64. DOI: 10.1007/978-94-017-2653-5_10</mixed-citation>
      </ref>
      <ref id="ref26">
        <label>26</label>
        <mixed-citation xml:lang="ru">Very Slow Creep Tests on Salt Samples / P. Bérest, H. Gharbi, B. Brouard et al. // Rock Mechanics and Rock Engineering. 2019. Vol. 52. P. 2917-2934. DOI: 10.1007/s00603-019-01778-9</mixed-citation>
        <mixed-citation xml:lang="en">Bérest P., Gharbi H., Brouard B. et al. Very Slow Creep Tests on Salt Samples. Rock Mechanics and Rock Engineering. 2019. Vol. 52, p. 2917-2934. DOI: 10.1007/s00603-019-01778-9</mixed-citation>
      </ref>
      <ref id="ref27">
        <label>27</label>
        <mixed-citation xml:lang="ru">Wittek W. Rock Mechanics Based on an Anisotropic Jointed Rock Model (AJRM). Berlin: Wilhelm Ernst &amp; Sohn; Verlag für Architektur und technische Wissenschaften GmbH &amp; Co, 2014. 900 p. DOI: 10.1002/9783433604281</mixed-citation>
        <mixed-citation xml:lang="en">Wittke W. Rock Mechanics Based on an Anisotropic Jointed Rock Model (AJRM). Berlin: Wilhelm Ernst &amp; Sohn; Verlag für Architektur und technische Wissenschaften GmbH &amp; Co, 2014, p. 900. DOI: 10.1002/9783433604281</mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
