Öz
This article aims to investigate the reliability of slopes opened in weak rocks and to provide insight into the design of rock slopes. For this purpose, a cut slope opened in the Thrace Formation on a highway route was examined with deterministic and reliability analyses. Based on the engineering geology and rock mechanics data obtained within the scope of the project, assuming that the probable slip of the highway slope examined would develop in the form of a wedge, deterministic stability analyses were performed using the Hoek-Brown and Mohr-Coulomb failure criteria and Janbu and Generalized Limit Equilibrium Method for different disturbance conditions. In the reliability analyses, stability analyses were performed with the First Order Reliability Method, First Order Second Moment Method, and Monte Carlo Simulation for the probable slip wedge considered. The probability and reliability functions used in these analyses, which were performed using an algorithm developed in Python, were obtained from the open-source OpenTURNS library. For the reliability assessment of the considered rock slope, shear strength parameters, crack water depth ratio, and horizontal earthquake acceleration were considered as stochastic variables. Probabilistic properties of shear strength parameters were obtained based on field and laboratory data of the Thrace Formation. Deterministic analyses have demonstrated that rock mass properties and calculation approaches have a significant impact on slope stability. Probabilistic stability analyses provided necessary results for design and evaluation purposes, such as failure probability or reliability index.
Anahtar Kelimeler
Rock slope stability weak rock Thrace Formation reliability-based analysis probabilistic design approach
Kaynakça
- Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek–Brown failure criterion – 2002 edition. Proceedings of the North American Rock Mechanics Symposium (NARMS-TAC), Toronto.
- Terzaghi, K., Peck, R. B., & Mesri, G. (1996). Soil Mechanics in Engineering Practice (3rd ed.). Wiley-Interscience.
- Bentley Systems Inc. (2022). PLAXIS LE – Limit Equilibrium Slope Stability Software [Computer software]. https://www.bentley.com/software/plaxis-le/
- OpenTURNS Developers. (2024). OpenTURNS: An open source initiative for the treatment of uncertainties, risks and statistics [Computer software]. GitHub.
- Duncan, J. M. (2000). Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
- Low, B. K., & Tang, W. H. (2007). Efficient spreadsheet algorithm for first-order reliability method. Journal of Engineering Mechanics, 133(12), 1378–1386. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378).
- Park, H. J., West, T. R., & Lee, J. H. (2006). Development of a slope stability probability classification system: A case study. Engineering Geology, 87(1–2), 1–15.
- Jimenez-Rodriguez, R., & Sitar, N. (2007). Seismic analysis and design of slopes using the deterministic–stochastic method. Journal of Geotechnical and Geoenvironmental Engineering, 133(6), 628–639. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(628)
- Bozkurt, S., & Akbaş, S. O., (2023). Finite element-based geotechnical risk analysis for anchor-supported deep excavations. Arabıan Journal Of Geoscıences, vol.16, no.8, 470.
- Zhu, W.-Q., Zhang, S.-H., Li, Y.-H., & Liu, J. (2023). Efficient slope reliability analysis based on representative slip surfaces: A comparative study. Frontiers in Earth Science, 11, 1100104. https://doi.org/10.3389/feart.2023.1100104.
- Hoek, E., & Bray, J. W. (1981). Rock slope engineering (3rd ed.). Institution of Mining and Metallurgy.
- Wyllie, D. C., & Mah, C. W. (2004). Rock slope engineering: Civil and mining (4th ed.). Spon Press.
- Baecher, G. B., & Christian, J. T. (2003). Reliability and statistics in geotechnical engineering. Wiley.
- Einstein, H. H., & Baecher, G. B. (1983). Probabilistic and statistical methods in engineering geology. Rock Mechanics and Rock Engineering, 16(1), 39–72. https://doi.org/10.1007/BF01030204
- Duncan, J. M. (2000). Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
- El-Ramly, H., Morgenstern, N. R., & Cruden, D. M. (2002). Probabilistic stability analysis of a tailings dam slope: A case study. Canadian Geotechnical Journal, 39(2), 315–330. https://doi.org/10.1139/t01-100
- Hasofer, A. M., & Lind, N. C. (1974). An exact and invariant first-order reliability format. Journal of the Engineering Mechanics Division, 100(1), 111–121.
- Ditlevsen, O., & Madsen, H. O. (1996). Structural reliability methods. Wiley.
- Cornell, C. A. (1969). A probability-based structural code. ACI Journal, 66(11), 974–985.
- Benjamin, J. R., & Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers. McGraw-Hill.
- Ang, A. H.-S., & Tang, W. H. (1984). Probability concepts in engineering planning and design: Volume II – Decision, risk and reliability. John Wiley & Sons.
- Ditlevsen, O., & Madsen, H. O. (1996). Structural reliability methods. Wiley.
- ISRM (2007). The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007–2014. Compiled by the ISRM Commission on Testing Methods.
- Low, B. K. (2007). Reliability analysis of rock slopes involving correlated non-normals. Engineering Geology, 94(3–4), 137–148. https://doi.org/10.1016/j.enggeo.2007.02.004
- US Army Corps of Engineers. (1997). Engineering and Design - Slope Stability (EM 1110-2-1902). Department of the Army, U.S. Army Corps of Engineers.
- Hoek, E., & Diederichs, M. S. (2006). Empirical estimation of rock mass modulus and strength. International Journal of Rock Mechanics and Mining Sciences, 43(2), 203–215. https://doi.org/10.1016/j.ijrmms.2005.06.005
Öz
Bu makalede zayıf kayada açılan şevlerinin güvenilirliğinin incelenmesi ve kaya şevi tasarımlarına ışık tutulması amaçlanmıştır. Bunun için bir otoyol güzergâhında, Trakya Formasyonunda açılmış bir yarma şevi deterministik ve güvenilirlik analizleri ile incelenmiştir. İncelenen otoyol şevinin olası kaymasının proje kapsamında yapılan mühendislik jeolojisi ve kaya mekaniği verilerine dayalı olarak kama şeklinde gelişeceği varsayımı ile farklı örselenme durumları için Hoek-Brown ve Mohr-Coulomb kırılma kriterleri ile Janbu ve Genelleştirilmiş Limit Denge Yöntemi kullanılarak deterministik duraylılık analizleri gerçekleştirilmiştir. Güvenilirlik analizlerinde ise dikkate alınan olası kayma kaması için Birinci Mertebe Güvenilirlik Yöntemi, Birinci Mertebe İkinci Moment Yöntemi ve Monte Carlo Simülasyonu ile duraylılık analizleri yapılmıştır. Python programlama dili ile geliştirilen bir algoritma aracılığıyla gerçekleştirilen bu analizler kapsamında kullanılan olasılık ve güvenilirlik fonksiyonları açık kaynaklı OpenTURNS kütüphanesinden alınmıştır. Dikkate alınan kaya şevinin güvenilirlik değerlendirmesi için kayma dayanımı parametreleri, çatlak suyu derinlik oranı ve yatay deprem ivmesi stokastik değişkenler olarak dikkate alınmıştır. Kayma dayanımı parametrelerinin olasılıksal özellikleri, Trakya Formasyonuna ait saha ve laboratuvar verilerine dayalı olarak elde edilmiştir. Yapılan deterministik analizler, kaya kütle özelliklerinin ve hesaplama yaklaşımlarının şev duraylılığı üzerinde belirleyici etkilere sahip olduğunu göstermiştir.
Yapılan olasılıksal duraylılık analizleri, göçme olasılığı veya güvenilirlik indeksi gibi tasarım ve değerlendirme amaçları için gerekli sonuçları sağlamıştır.
Anahtar Kelimeler
Kaya şevleri zayıf kaya Trakya Formasyonu güvenilirlik analizi olasılıksal yaklaşım
Kaynakça
- Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek–Brown failure criterion – 2002 edition. Proceedings of the North American Rock Mechanics Symposium (NARMS-TAC), Toronto.
- Terzaghi, K., Peck, R. B., & Mesri, G. (1996). Soil Mechanics in Engineering Practice (3rd ed.). Wiley-Interscience.
- Bentley Systems Inc. (2022). PLAXIS LE – Limit Equilibrium Slope Stability Software [Computer software]. https://www.bentley.com/software/plaxis-le/
- OpenTURNS Developers. (2024). OpenTURNS: An open source initiative for the treatment of uncertainties, risks and statistics [Computer software]. GitHub.
- Duncan, J. M. (2000). Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
- Low, B. K., & Tang, W. H. (2007). Efficient spreadsheet algorithm for first-order reliability method. Journal of Engineering Mechanics, 133(12), 1378–1386. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378).
- Park, H. J., West, T. R., & Lee, J. H. (2006). Development of a slope stability probability classification system: A case study. Engineering Geology, 87(1–2), 1–15.
- Jimenez-Rodriguez, R., & Sitar, N. (2007). Seismic analysis and design of slopes using the deterministic–stochastic method. Journal of Geotechnical and Geoenvironmental Engineering, 133(6), 628–639. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(628)
- Bozkurt, S., & Akbaş, S. O., (2023). Finite element-based geotechnical risk analysis for anchor-supported deep excavations. Arabıan Journal Of Geoscıences, vol.16, no.8, 470.
- Zhu, W.-Q., Zhang, S.-H., Li, Y.-H., & Liu, J. (2023). Efficient slope reliability analysis based on representative slip surfaces: A comparative study. Frontiers in Earth Science, 11, 1100104. https://doi.org/10.3389/feart.2023.1100104.
- Hoek, E., & Bray, J. W. (1981). Rock slope engineering (3rd ed.). Institution of Mining and Metallurgy.
- Wyllie, D. C., & Mah, C. W. (2004). Rock slope engineering: Civil and mining (4th ed.). Spon Press.
- Baecher, G. B., & Christian, J. T. (2003). Reliability and statistics in geotechnical engineering. Wiley.
- Einstein, H. H., & Baecher, G. B. (1983). Probabilistic and statistical methods in engineering geology. Rock Mechanics and Rock Engineering, 16(1), 39–72. https://doi.org/10.1007/BF01030204
- Duncan, J. M. (2000). Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
- El-Ramly, H., Morgenstern, N. R., & Cruden, D. M. (2002). Probabilistic stability analysis of a tailings dam slope: A case study. Canadian Geotechnical Journal, 39(2), 315–330. https://doi.org/10.1139/t01-100
- Hasofer, A. M., & Lind, N. C. (1974). An exact and invariant first-order reliability format. Journal of the Engineering Mechanics Division, 100(1), 111–121.
- Ditlevsen, O., & Madsen, H. O. (1996). Structural reliability methods. Wiley.
- Cornell, C. A. (1969). A probability-based structural code. ACI Journal, 66(11), 974–985.
- Benjamin, J. R., & Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers. McGraw-Hill.
- Ang, A. H.-S., & Tang, W. H. (1984). Probability concepts in engineering planning and design: Volume II – Decision, risk and reliability. John Wiley & Sons.
- Ditlevsen, O., & Madsen, H. O. (1996). Structural reliability methods. Wiley.
- ISRM (2007). The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007–2014. Compiled by the ISRM Commission on Testing Methods.
- Low, B. K. (2007). Reliability analysis of rock slopes involving correlated non-normals. Engineering Geology, 94(3–4), 137–148. https://doi.org/10.1016/j.enggeo.2007.02.004
- US Army Corps of Engineers. (1997). Engineering and Design - Slope Stability (EM 1110-2-1902). Department of the Army, U.S. Army Corps of Engineers.
- Hoek, E., & Diederichs, M. S. (2006). Empirical estimation of rock mass modulus and strength. International Journal of Rock Mechanics and Mining Sciences, 43(2), 203–215. https://doi.org/10.1016/j.ijrmms.2005.06.005
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | İnşaat Geoteknik Mühendisliği |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Erken Görünüm Tarihi | 19 Haziran 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 17 Nisan 2025 |
| Kabul Tarihi | 13 Haziran 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 36 Sayı: 6 |