{"id":4332,"date":"2025-09-10T22:00:24","date_gmt":"2025-09-10T21:00:24","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=4332"},"modified":"2026-04-13T08:56:10","modified_gmt":"2026-04-13T07:56:10","slug":"27-4-4-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-4-4-en\/","title":{"rendered":"27.4.4 En"},"content":{"rendered":"\n

Modeling slope stability according to various sliding curves<\/strong><\/h1>\n\n\n\n

K.N. <\/em>Anakhaev, <\/em>A.S. <\/em>Bestuzheva, <\/em>V.V. <\/em>Belikov, A.B. <\/em>Balkizov, <\/em>M.O. Mamchuev<\/strong><\/p>\n\n\n\n

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Abstract<\/strong>:<\/strong> <\/em>Landslide phenomena with loss of stability of soil slopes occur both in natural landscapes and during excavation operations with a violation of the stability of folded rocks, including during the construction and operation of soil dams and fencing dams, automobile and railway embankments, etc. The stability of slopes depends on a variety of factors, the most important of which are the physical and mechanical characteristics of the soil, which can be either homogeneous throughout the massif, or heterogeneous in the form of various layers, etc.
Aim<\/strong>. Expanding the possibilities of a comprehensive assessment of slope stability by considering additional (to the circular) families of hyperbolic sliding curves for the case of a base with different strength characteristics.
Methods<\/strong>. Methods are used to determine the outlines of the sliding curves of a landslide slope with the least margin of stability, based on a comparison of the calculated results of families of circular, lowerhyperbolic, and upper-hyperbolic curves. The calculations are performed using the Terzaghi method by dividing the proposed area of soil mass slide into vertical sections and determining the local holding and shearing forces for each section. The final result is the ratio of the total values of these forces.
Results<\/strong>. A comprehensive method for determining the outlines of the most dangerous sliding curves of soil massifs based on the Terzaghi method is proposed, considering families of circular and hyperbolic (with low and high curvature) sliding lines. The results obtained, tested for the ground slope at the specified two points on the sliding line, showed: adequacy of the proposed analytical solution for circular curves (~ 2 %) in comparison with the results of numerical calculation according to the OTKOS-22 program; the line of least stability for the case under consideration is the lower hyperbolic sliding curve with a stability coefficient 11% less than the slope stability along the circular sliding curve; the stability coefficients of slopes with relatively small differences in sliding lines can vary significantly; in the considered case, the stability coefficients for slopes with sufficiently close hyperbolic outlines of the lower and upper curvature differ by more than 19 %.
Conclusions<\/strong>. A comprehensive method for determining the outlines of the most dangerous sliding curves of soil massifs based on the Terzaghi method is proposed, considering families of circular and hyperbolic (with low and high curvature) sliding lines, which significantly expands the search area for lines of least slope stability.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/em><\/strong> slope stability, two-layer slope, stability coefficient, sliding curve, collapse area<\/p>\n\n\n\n

For citation<\/strong>.<\/strong> Anakhaev K.N., Bestuzheva A.S., Belikov V.V. Balkizov A.B., Mamchuev M.O. Modeling slope stability according to various sliding curves. News of the Kabardino-Balkarian Scientific Center of RAS. 2025. Vol. 27. No. 4. Pp. 55\u201369. DOI: 10.35330\/1991-6639-2025-27-4-55-69<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Kropotkin M.P. Slope stability calculations using stability coefficient minimizing algorithms. Engineering Survey. 2017. No. 1. Pp. 20\u201330. EDN: XXRLRN. (In Russian)<\/li>\n\n\n\n
  2. Anakhaev K.N., Belikov V.V., Anakhaev K.K. et al. On the calculation of the sliding surfaces of coastal slopes based on remote data. Processy v geosredah [Processes in Geomedia]. No. 3. Pp. 1655\u20131663. EDN: MHLHXH. (In Russian)<\/li>\n\n\n\n
  3. Bukhartsev V.N., Nguen T.Kh. Assessment of the stability of soil massifs. Magazine of Civil Engineering. 2012. No. 9. Pp. 41\u201348. EDN: PQNQMR. (In Russian)<\/li>\n\n\n\n
  4. Dvoryashin V.I. Voyennaya gidrotekhnika (vodnyye zagrazhdeniya) [Military hydraulic engineering (water barriers)]. Moscow: IVIA, 1940. 360 p. (In Russian)<\/li>\n\n\n\n
  5. Gidrotekhnicheskiye sooruzheniya<\/em> [Hydraulic engineering structures]. Edited by Rozanova N.P. Moscow: Agropromizdat, 1985. 432 p. (In Russian)<\/li>\n\n\n\n
  6. Anakhaev K.N., Bestuzheva A.S., Belikov V.V., Anakhaev K.K. Stability of an inhomogeneous slope with specified points of sliding curves. Modern Problems of Hydraulics and Hydraulic Engineering. Collection of reports of the VIII-th All-Russian Scientific and Practical Seminar, May 21, 2025. Moscow: NRU MGSU IGES, 2025. (In Russian)<\/li>\n\n\n\n
  7. Bestuzheva A.S. Computational program «SLOPE-22» for calculating the stability of slopes and slopes under seismic impacts. Modern Problems of Hydraulics and Hydraulic Engineering. Collection of reports of the VI All-Russian Scientific and Practical Seminar, May 24, 2023. Moscow: NRU MGSU IGES, 2023. Pp. 79\u201380. EDN: TRWVRH. (In Russian)<\/li>\n\n\n\n
  8. Anakhaev K.N., Belikov V.V., Anakhaev K.K. On hyperbolic surfaces in calculations of coastal slopes based on remote data. Modern Problems of Applied Mathematics, Computer Science and Mechanics. Proceedings of the International Scientific Conference. Vol. 1. Nalchik: KBSU, 2022. Pp. 6\u20138. EDN: KYKECL. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong>s<\/summary>\n
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    Koshkinbai N. Anakhaev<\/strong>, Doctor of Technical Sciences, Professor, Chief Researcher, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    360000, Russia, Nalchik, 89 A Shortanov street;
    Leading Researcher, Institute of Water Problems of the Russian Academy of Sciences;
    119333, Russia, Moscow, 3 Gubkin street;
    anaha13@mail.ru, ORCID: https:\/\/orcid.org\/0000-0003-4357-4349, SPIN-code: 5974-4403
    Alexandra S. Bestuzheva<\/strong>, Candidate of Technical Sciences, Associate Professor of the Department of Hydraulics and Hydraulic Engineering, Institute of Hydraulic Engineering and Energy Construction of the Moscow State University of Civil Engineering (National Research University);
    129337, Russia, Moscow, 26 Yaroslavskoye highway, building ULB;
    alex_bestu@mail.ru, ORCID: https:\/\/orcid.org\/0000-0002-0821-4922, SPIN-code: 7762-8776
    Vitaly V. Belikov<\/strong>, Doctor of Technical Sciences, Professor, Chief Researcher, Institute of Water Problems of the Russian Academy of Sciences;
    119333, Russia, Moscow, 3 Gubkin street;
    belvv@bk.ru, ORCID: https:\/\/orcid.org\/0000-0002-1760-4498, SPIN-code: 6174-7895
    Afrasim B. Balkizov<\/strong>, Candidate of Technical Sciences, Associate Professor of the Department of Environmental Management, Kabardino-Balkarian State Agrarian University named after V.M. Kokov;
    360030, Russia, Nalchik, 1v Lenin avenue;
    afrasim_1960@mail.ru, ORCID: https:\/\/orcid.org\/0000-0002-4220-9107, SPIN-code: 4015-8381
    Mukhtar O. Mamchuev<\/strong>, Candidate of Physico-Mathematical Sciences, Researcher, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    360000, Russia, Nalchik, 89 A Shortanov street;
    mamchuevmc@yandex.ru, ORCID: https:\/\/orcid.org\/0000-0002-3830-7804, SPIN-code: 1074-2232<\/p>\n\n\n\n

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    Modeling slope stability according to various sliding curves K.N. Anakhaev, A.S. Bestuzheva, V.V. Belikov, A.B. Balkizov, M.O. Mamchuev Upload the full text Abstract: Landslide phenomena with loss of stability of soil slopes occur both in natural landscapes and during excavation operations with a violation of the stability of folded rocks, including during the construction and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-4332","page","type-page","status-publish","hentry"],"yoast_head":"\n27.4.4 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-4-4-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"27.4.4 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Modeling slope stability according to various sliding curves K.N. 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