Publicado

2019-07-01

Updating the probability of failure of rock wedges

Actualización de la probabilidad de falla en cuñas de roca

DOI:

https://doi.org/10.15446/esrj.v23n3.74779

Palabras clave:

Uncertainty, probability of failure, rock wedge, random sets, reliability (en)
Incertidumbre, probabilidad de falla, cuña de roca, conjuntos aleatorios, confiabilidad (es)

Descargas

Autores/as

  • Rodrigo Hernandez-Carrillo Universidad Nacional de Colombia – Sede Bogota – Departamento de Ingenieria Civil y Agricola - GIGUN https://orcid.org/0000-0001-7412-8902
  • Gloria Beltran Universidad Nacional de Colombia – Sede Bogota – Departamento de Ingenieria Civil y Agricola - GIGUN
In hard rock masses, discontinuities control the slope stability, rather than block matrix breakage. The relative position of joints and slope face defines the most likely mechanisms of failure. Among these mechanisms, the wedge failure is one of the most common ways of failure in which joint sets dip and dip direction, slope geometry and direction, external forces (including water pressure and earthquake) and rock and joints mechanical properties control the stability. The determination of these input parameters is not straightforward, mainly due to their variability and the limited amount of information available. Besides, in most projects, input parameters come from different sources (e.g., expert opinion, back-calculation, laboratory tests, field test or different project stages). Therefore, this limited information from different sources should be appropriately incorporated into the stability analysis to assist the design and decision-making process. In this context, random sets arise as a powerful tool to combine different sources of information and to perform a reliability assessment under limited information. This feature makes it possible to update the probability of failure as new evidence is available. With this framework, this paper presents a reliability assessment of wedge stability in a rock slope of a sandstone quarry, located in Une Cundinamarca, where information on mechanical and geometrical parameters has been collected for 20 years.
En rocas duras, las discontinuidades controlan la estabilidad de los taludes. La posición relativa entre las discontinuidades y el talud define el mecanismo de falla más probable. Entre estos mecanismos, la falla en cuña es uno de los más comunes. La estabilidad de las cuñas está controlada por la orientación de los planos de discontinuidad, la geometría y orientación del talud, las fuerzas externas (incluyendo presión de agua y sismo) y las propiedades mecánicas de las discontinuidades. La determinación de estas propiedades no es sencilla, debido a su variabilidad y cantidad limitada de información. Además, en muchos proyectos de ingeniería la información proviene de diferentes fuentes, tales como la opinión de expertos, retro-análisis, ensayos de laboratorio y pruebas de campo, en diferentes etapas de proyectos. Por lo tanto, los modelos de análisis deben ser capaces de incorporan información con estas características, para asistir el proceso de toma de decisiones en los proyectos de ingeniería. En este contexto, la teoría de los conjuntos aleatorios se constituye en una herramienta apropiada para combinar diferentes fuentes de información y efectuar análisis de confiabilidad cuando se tiene información escasa de los parámetros de entrada del modelo. Esta característica hace posible la actualización de la probabilidad de falla, a medida que aparece nueva información. Con este marco de referencia, este trabajo presenta el análisis de confiabilidad de la estabilidad de cuñas en una mina de arenisca, localizada en Une, Cundinamarca, donde se ha recolectado información durante 20 años.

Referencias

Al Machot, F., Mayr, H. C., & Ranasinghe, S. (2018). A Hybrid Reasoning Approach for Activity Recognition Based on Answer Set Programming and Dempster–Shafer Theory. Recent Advances in Nonlinear Dynamics and Synchronization, 303–318.

Bernardini, A., & Tonon, F. (2010). Bounding Uncertainty in Civil Engineering - Theoretical Background. Springer Science & Business Media.

Beynon, M., Curry, B., & Morgan, P. (2000). The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modelling. Omega, 28(1), 37–50. https://doi.org/10.1016/S0305-0483(99)00033-X

Couso, I., Dubois, D., & Sánchez, L. (2014). Random Sets as Ill-Perceived Random Variables. In Kacprzyk, J. (Editor). Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables, Springer International Publishing, 7-45.

Cundall, P. A. (1980). UDEC - A generalized distinct element program for modelling jointed rock. No. PCAR-1-80, Cundall (Peter) Associates Virginia Water, England.

Dempster, A. P. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. The Annals of Mathematical Statistics, 38(2), 325–339.

Dutta, P. (2018). An uncertainty measure and fusion rule for conflict evidences of big data via Dempster–Shafer theory. International Journal of Image and Data Fusion, 9(2), 152–169.

Einstein, H. H., & Low, B. K. (1992). Simplified reliability analysis for wedge mechanisms in rock slopes. 6th International Symposium on Landslides, Christchurch, New Zealand, 499–507

Environmental Protection Agency (EPA) (2002). Total Risk Integrated Methodology (TRIM) - TRIM.FaTE. Research Triangle Park, Nort Carolina, US.

Ferson, S., Kreinovich, V., Ginzburg, L., Myers, D., & Sentz, K. (2003). Constructing Probability Boxes and Dempster - Shafer Structures. Albuquerque, NM.

Fisher, R. (1953). Dispersion on a Sphere. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 217(1130), 295-305.

Goodman, R. E. (1995). Block theory and its application. 35th US Symposium on Rock Mechanics, AA Balkema. Rotterdam. 3-15.

Goodman, R. E., & Taylor, R. L. (1966). Methods Of Analysis For Rock Slopes And Abutments: A Review Of Recent Developments, 8th U.S. Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association, 303-320.

Hoek, E., Bray, J. W., & Boyd, J. M. (1973). The stability of a rock slope containing a wedge resting on two intersecting discontinuities. Quarterly Journal of Engineering Geology and Hydrogeology, 6(1), 1–55.

Jimenez-Rodriguez, R., Sitar, N., & Chacón, J. (2006). System reliability approach to rock slope stability. International Journal of Rock Mechanics and Mining Sciences, 43(6), 847–859.

Kari, T., Gao, W., Zhao, D., Zhang, Z., Mo, W., Wang, Y., & Luan, L. (2018). An integrated method of ANFIS and Dempster-Shafer theory for fault diagnosis of power transformer. IEEE Transactions on Dielectrics and Electrical Insulation, 25(1), 360–371.

Khairina, D. M., Hatta, H. R., Rustam, R., & Maharani, S. (2018). Automation Diagnosis of Skin Disease in Humans using Dempster-Shafer Method. E3S Web of Conferences, 31, 11006.

Kim, J. K., Choi, M. J., Lee, J. S., Hong, J. H., Kim, C.-S., Seo, S. Il, Jeong, C., Byun, S., Koo, K. Chung, B., Park, Y., Lee, J., & Choi, I. Y. (2018). A Deep Belief Network and Dempster-Shafer- Based Multiclassifier for the Pathology Stage of Prostate Cancer. Journal of Healthcare Engineering, 2018, 1–8.

Klapperich, H., Rafig, A., & Wu, W. (2012). Non-Deterministic Analysis of Slope Stability based on Numerical Simulation. Ph. D. Thesis, Faculty of Geosciences, Geoengineering and Mining, Technische Universität Bergakademie Freiberg, Freiberg, Germany.

Lee, Y.-F., Chi, Y.-Y., Juang, C. H. & Lee, D.-H., Hsein Juang, C. (2012). Reliability Analysis of Rock Wedge Stability: Knowledge-Based Clustered Partitioning Approach. Journal of Geotechnical and Geoenvironmental Engineering, 138(6), 700–708.

Li, D., & Zhou, C. (2009). System reliability analysis of rock slope considering multiple correlated failure modes. Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, 28(3), 541–551.

Li, D., Zhou, C., Lu, W., & Jiang, Q. (2009). A system reliability approach for evaluating stability of rock wedges with correlated failure modes. Computers and Geotechnics, 36(8), 1298–1307.

Liu, F., Zhao, Q., & Yang, Y. (2018). An approach to assess the value of industrial heritage based on Dempster–Shafer theory. Journal of Cultural Heritage, 32, 210-220

Low, B. K. (1997). Reliability Analysis of Rock Wedges. Journal of Geotechnical and Geoenvironmental Engineering, 123(6), 498–505.

Low, B. K., & Einstein, H. H. (2013). Reliability analysis of roof wedges and rockbolt forces in tunnels. Tunnelling and Underground Space Technology, 38, 1–10.

Low, B. K.. (1979). Reliability of rock slopes with wedge mechanisms. Ph. D. Thesis, Massachusetts Institute of Technology, US.

Moradi, M., Chaibakhsh, A., & Ramezani, A. (2018). An intelligent hybrid technique for fault detection and condition monitoring of a thermal power plant. Applied Mathematical Modelling, 60, 34–47.

Nasekhian, Ali, & Schweiger, H. F. (2011). Random set finite element method application to tunnelling. International Journal of Reliability and Safety, 5(3-4), 299-319.

Oberguggenberger, M. (2012). Combined methods in nondeterministic mechanics. In: Elishakoff, I. (Editor), Nondeterministic Mechanics, Viena, Austria, 263–356.

Peschl, G. M. (2004). Reliability Analyses in Geotechnics with Random Set Finite Element Method. Ph.D. Thesis, Technische Universitat Graz, Graz, Austria.

Rathman, J. F., Yang, C., & Zhou, H. (2018). Dempster-Shafer theory for combining in silico evidence and estimating uncertainty in chemical risk assessment. Computational Toxicology, 16-36.

Schweiger, H. F., & Peschl, G. M. M. (2005). Reliability analysis in geotechnics with the random set finite element method. Computers and Geotechnics, 32(6), 422–435.

Schweiger, H. F., & Peschl, G. M. (2004). Numerical analysis of deep excavations utilizing random set theory. Geotechnical Innovations, Essen, 277–294.

Schweiger, H. F., & Peschl, G. M. (2005). Application of the random set finite element method (RS-FEM) in geotechnics. Plaxis Bulletin, 17, 16-21.

Sentz, K., & Ferson, S. (2002). Combination of Evidence in Dempster- Shafer Theory. Sandia, National Laboratories, Albuquerque, NM, US.

Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton Uiversity Press, New Jersey, NJ, US.

Shen, H., & Abbas, S. M. (2013). Rock slope reliability analysis based on distinct element method and random set theory. International Journal of Rock Mechanics and Mining Sciences, 61, 15–22.

Tonon, F., Bernardini, A., & Mammino, A. (2000a). Determination of parameters range in rock engineering by means of Random Set Theory. Reliability Engineering & System Safety, 70(3), 241–261.

Tonon, F., Bernardini, A., & Mammino, A. (2000b). Reliability analysis of rock mass response by means of Random Set Theory. Reliability Engineering & System Safety, 70(3), 263–282.

Tonon, F., Mammino, A., & Bernardini, A. (1996). A Random Set Approach to the Uncertainties In Rock Engineering And Tunnel Lining Design, ISRM International Symposium - EUROCK 96. Turin, Italy,

Tonon, F., & Bernardini, A. (1999). Multiobjective Optimization of Uncertain Structures Through Fuzzy Set and Random Set Theory. Computer-Aided Civil and Infrastructure Engineering, 14(2), 119–140.

Torkzadeh-Mahani, N., Dehghani, M., Mirian, M. S., Shakery, A., Taheri, K., Torkzadeh Mahani, N., Taheri, K. (2018). Expert finding by the Dempster-Shafer theory for evidence combination. Expert Systems, 35(1).

Zargar, A., Sadiq, R., Naser, G., Khan, F. I., & Neumann, N. N. (2012). Dempster-Shafer Theory for Handling Conflict in Hydrological Data: Case of Snow Water Equivalent. Journal of Computing in Civil Engineering, 26(3), 434–447.

Cómo citar

APA

Hernandez-Carrillo, R. y Beltran, G. (2019). Updating the probability of failure of rock wedges. Earth Sciences Research Journal, 23(3), 225–236. https://doi.org/10.15446/esrj.v23n3.74779

ACM

[1]
Hernandez-Carrillo, R. y Beltran, G. 2019. Updating the probability of failure of rock wedges. Earth Sciences Research Journal. 23, 3 (jul. 2019), 225–236. DOI:https://doi.org/10.15446/esrj.v23n3.74779.

ACS

(1)
Hernandez-Carrillo, R.; Beltran, G. Updating the probability of failure of rock wedges. Earth sci. res. j. 2019, 23, 225-236.

ABNT

HERNANDEZ-CARRILLO, R.; BELTRAN, G. Updating the probability of failure of rock wedges. Earth Sciences Research Journal, [S. l.], v. 23, n. 3, p. 225–236, 2019. DOI: 10.15446/esrj.v23n3.74779. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/74779. Acesso em: 26 jul. 2024.

Chicago

Hernandez-Carrillo, Rodrigo, y Gloria Beltran. 2019. «Updating the probability of failure of rock wedges». Earth Sciences Research Journal 23 (3):225-36. https://doi.org/10.15446/esrj.v23n3.74779.

Harvard

Hernandez-Carrillo, R. y Beltran, G. (2019) «Updating the probability of failure of rock wedges», Earth Sciences Research Journal, 23(3), pp. 225–236. doi: 10.15446/esrj.v23n3.74779.

IEEE

[1]
R. Hernandez-Carrillo y G. Beltran, «Updating the probability of failure of rock wedges», Earth sci. res. j., vol. 23, n.º 3, pp. 225–236, jul. 2019.

MLA

Hernandez-Carrillo, R., y G. Beltran. «Updating the probability of failure of rock wedges». Earth Sciences Research Journal, vol. 23, n.º 3, julio de 2019, pp. 225-36, doi:10.15446/esrj.v23n3.74779.

Turabian

Hernandez-Carrillo, Rodrigo, y Gloria Beltran. «Updating the probability of failure of rock wedges». Earth Sciences Research Journal 23, no. 3 (julio 1, 2019): 225–236. Accedido julio 26, 2024. https://revistas.unal.edu.co/index.php/esrj/article/view/74779.

Vancouver

1.
Hernandez-Carrillo R, Beltran G. Updating the probability of failure of rock wedges. Earth sci. res. j. [Internet]. 1 de julio de 2019 [citado 26 de julio de 2024];23(3):225-36. Disponible en: https://revistas.unal.edu.co/index.php/esrj/article/view/74779

Descargar cita

CrossRef Cited-by

CrossRef citations1

1. Lin Yang, Shaocheng Ge, Zhihui Huang, Deji Jing, Xi Chen. (2021). The influence of surfactant on the wettability of coal dust and dust reduction efficiency. Arabian Journal of Geosciences, 14(14) https://doi.org/10.1007/s12517-021-07570-w.

Dimensions

PlumX

Visitas a la página del resumen del artículo

667

Descargas

Los datos de descargas todavía no están disponibles.

Licencia

Derechos de autor 2019 Earth Sciences Research Journal

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.

Earth Sciences Research Journal posee una licencia Creative Commons Attribution.

Usted es libre de: Compartir: copie y redistribuya el material en cualquier medio o formato. Adaptar: remezclar, transformar y ampliar el material para cualquier propósito, incluso comercialmente. El licenciante no puede revocar estas libertades mientras siga los términos de la licencia.