Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos
La geología estructural tiene muchos campos de aplicación, en geotecnia de rocas es fundamental el estado de fracturamiento para realizar una clasi cación geomecánica seg un metodologías establecidas como el RMR (Rock Mass Rating) y el GSI (Geological Strength Index), sin embargo la estimación cuali...
- Autores:
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Moná Graciano, Juan Esteban
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- 2019
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- 550 - Ciencias de la tierra
Fractals
Fractures
Cellular Automaton
Fractal Dimension
RMR
GSI
Fractales
Fracturamiento
Autómatas Celulares
Dimensión Fractal
RMR
GSI
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| dc.title.spa.fl_str_mv |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| dc.title.alternative.spa.fl_str_mv |
On the application of fractal theory for the geometrical behaviour of faults among rock massifs |
| title |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| spellingShingle |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos 550 - Ciencias de la tierra Fractals Fractures Cellular Automaton Fractal Dimension RMR GSI Fractales Fracturamiento Autómatas Celulares Dimensión Fractal RMR GSI |
| title_short |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| title_full |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| title_fullStr |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| title_full_unstemmed |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| title_sort |
Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos |
| dc.creator.fl_str_mv |
Moná Graciano, Juan Esteban |
| dc.contributor.advisor.spa.fl_str_mv |
Mesa Sánchez, Oscar José Echeverri Ramírez, Oscar Brasil Cavalcante, André Luis |
| dc.contributor.author.spa.fl_str_mv |
Moná Graciano, Juan Esteban |
| dc.contributor.corporatename.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Medellín |
| dc.subject.ddc.spa.fl_str_mv |
550 - Ciencias de la tierra |
| topic |
550 - Ciencias de la tierra Fractals Fractures Cellular Automaton Fractal Dimension RMR GSI Fractales Fracturamiento Autómatas Celulares Dimensión Fractal RMR GSI |
| dc.subject.proposal.eng.fl_str_mv |
Fractals Fractures Cellular Automaton Fractal Dimension RMR GSI |
| dc.subject.proposal.spa.fl_str_mv |
Fractales Fracturamiento Autómatas Celulares Dimensión Fractal RMR GSI |
| description |
La geología estructural tiene muchos campos de aplicación, en geotecnia de rocas es fundamental el estado de fracturamiento para realizar una clasi cación geomecánica seg un metodologías establecidas como el RMR (Rock Mass Rating) y el GSI (Geological Strength Index), sin embargo la estimación cualitativa de fracturas conlleva errores de metodología, interpretación y valoración en las obras subterraneas. Este aporte investigativo involucra la teoría fractal para realizar estimaciones en términos de clasi cación geomecánica y como herramienta para simular geométricamente el comportamiento de una falla. Para esto se establecen las características de los fractales y las características del fracturamiento donde la dimensión fractal es utilizada como herramienta para realizar la clasi cación geomecánica en 15 frentes de obra subterranea y en cartografía geotécnica en dos localidades del departamento de Antioquia, Colombia. Por otro lado, se lograron obtener modelos de distribución geométrica de fracturas utilizando autómatas celulares probabil ísticos programados en el lenguaje de programción Wolfram Mathematica. Ambos métodos muestran tener una buena potencialidad para ser aplicados en la ingeniería con las calibraciones e investigaciones (Tomado de la fuente) |
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2019 |
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2019-08-31 |
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2020-05-11T13:44:57Z |
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2020-05-11T13:44:57Z |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/workingPaper |
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info:eu-repo/semantics/acceptedVersion |
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Moná, J.E., Echeverri Ramírez, O., Brasil-Cavalcante, A.L., Mesa-Sánchez, O.J., (2019) Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos. Tesis de Maestría. Universidad Nacional de Colombia, Sede Medellín. Facultad de Minas. Departamento de Ingeniería Civil. |
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https://repositorio.unal.edu.co/handle/unal/77499 |
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Moná, J.E., Echeverri Ramírez, O., Brasil-Cavalcante, A.L., Mesa-Sánchez, O.J., (2019) Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos. Tesis de Maestría. Universidad Nacional de Colombia, Sede Medellín. Facultad de Minas. Departamento de Ingeniería Civil. |
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https://repositorio.unal.edu.co/handle/unal/77499 |
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spa |
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Alc arcel, F., G omez, J., and Compiladores (2019). Mapa geol ogico de colombia 2019. escala 1:2.000.000. Ayan Misra, Achyuta; Mukherjee, S. (2018). Atlas of Structural Geological Interpretation from Seismic Images. Wyley & Sons Ltd, New York. Bagde, M. N., Raina, A. K., Chakraborty, A. K., and Jethwa, J. L. (2002). Rock mass characterization by fractal dimension. Engineering Geology, 63(1-2):141{155. Barton, N. (1973). Review of a new shear-strength criterion for rock joints. Engineering Geology, 7(4):287 { 332. Barton, N., Lien, R., and Lunde, J. (1974). Engineering classi cation of rock masses for the design of tunnel support. Rock Mechanics Felsmechanik Mecanique des Roches, 6:189{236. Bieniawski, Z.T; Balkema, A. (1976). Rock mass classi cations in rock engineering. pages pp 27{32. Bieniawski, Z. T. (1989). Engineering rock mass classi cations: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons. Binglei, L., Yongtao, G., and Xiaojuan, L. (2011). Rock failure process research and analysis of fractal. 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), pages 1630{1633. de Faria Borges, L. P., de Moraes, R. M., Crestana, S., and Cavalcante, A. L. B. (2019). Geometric features and fractal nature of soil analyzed by x-ray microtomography image processing. International Journal of Geomechanics, 19(8):04019088. De Saussure, H. B. (1796). Agenda ou Tableau g en eral des observations et des recherches dont les r esultats doivent servir de base a la th eorie de la terre. de SM Ozelim, L. C., Cavalcante, A. L. B., and Baetens, J. M. (2017). On the iota-delta function: a link between cellular automata and partial di erential equations for modeling advection{dispersion from a constant source. The Journal of Supercomputing, 73(2):700{712. Dearman, W. R. (1974). Weathering classi cation in the characterisation of rock for engineering purposes in british practice. Bulletin of the International Association of Engineering Geology - Bulletin de l'Association Internationale de G eologie de l'Ing enieur, 9(1):33{42. Deere, D. (1963). Technical description of rock cores for engineering purposes. pages pp 16{22. Dixon, T. H. and Xie, S. (2018). A kinematic model for the evolution of the Eastern California Shear Zone and Garlock Fault, Mojave Desert, California. Earth and Planetary Science Letters, 494:60{68. Ehlen, J. (2000). Fractal analysis of joint patterns in granite. International Journal of Rock Mechanics and Mining Sciences, 37(6):909{922. Fernandez-Gutierrez, J.D; P erez-Acebo, H. M.-A. D. (2017). Correlaci on entre el ndice RMR de Bieniawski y el ndice Q de Barton en formaciones sedimentarias de grano no. 69(547). Fossen, H. (2010). Structural Geology. Cambridge University Press. Gardener, M. (1970). The fantastic combinations of john conway's new solitaire game \life" by martin gardner. Scienti c American, 223:120{123. Ghosh, A. and Daemen, J. J. (1993). Fractal characteristics of rock discontinuities. Hall, J. (1815). Ii. on the vertical position and convolutions of certain strata, and their relation with granite. Transactions of the Royal Society of Edinburgh, 7(1):79{108. Healy, D., Rizzo, R. E., Cornwell, D. G., Farrell, N. J. C., Watkins, H., Timms, N. E., Gomez-rivas, E., and Smith, M. (2017). FracPaQ : A MATLAB TM toolbox for the quanti cation of fracture patterns. Journal of Structural Geology, 95:1{16. Hern andez Zubeldia, E., de SM Ozelim, L. C., Lu s Brasil Cavalcante, A., and Crestana, S. (2015). Cellular automata and x-ray microcomputed tomography images for generating arti cial porous media. International Journal of Geomechanics, 16(2):04015057. Hobbs, B. E. (2019). The development of structural geology and the historical context of the journal of structural geology: A re ection by bruce hobbs. Journal of Structural Geology, 125:3 { 19. Back to the future. Hoek, E. (1983). Strength of jointed rock masses. Geotechnique, 33(3):187{223. Hutton, J. (1788). X. theory of the earth; or an investigation of the laws observable in the composition, dissolution, and restoration of land upon the globe. Transactions of the Royal Society of Edinburgh, 1(2):209{304. Jiang, H. and Zhao, J. (2015). A simple three-dimensional failure criterion for rocks based on the hoek{ brown criterion. Rock Mechanics and Rock Engineering, 48(5):1807{1819. Kert esz, J. (1992). Fractal fracture. Physica A: Statistical Mechanics and its Applications, 191(1):208 { 212. Kruhl, J. H. (2013). Fractal-geometry techniques in the quanti cation of complex rock structures: A special view on scaling regimes, inhomogeneity and anisotropy. Journal of Structural Geology, 46:2{21 Lindenmayer, A. (1968). Mathematical models for cellular interactions in development i. laments with one-sided inputs. Journal of Theoretical Biology, 18(3):280 { 299. Liu, R., Jiang, Y., Li, B., and Wang, X. (2015). A fractal model for characterizing uid ow in fractured rock masses based on randomly distributed rock fracture networks. Computers and Geotechnics, 65:45{ 55. Mandelbrot, B. (1967). How long is the coast of britain? statistical self-similarity and fractional dimension. Science, 156(3775):636{638. Mandelbrot, B., Freeman, W., and Company (1983a). The Fractal Geometry of Nature. Einaudi paperbacks. Henry Holt and Company. Mandelbrot, B., Freeman, W., and Company (1983b). The Fractal Geometry of Nature. Einaudi paperbacks. Henry Holt and Company. Mukherjee, S. (2015). Atlas of Structural Geology. Number 1. Elsevier, Waltham, Massachussets. Newton, I. (1687). Philosophiae naturalis principia mathematica. J. Societatis Regiae ac Typis J. Streater. Ozelim, L. C. and Cavalcante, A. L. (2014). On the iota-delta function: Mathematical representation of two-dimensional cellular automata. Complex Systems, 22(4):405{422. Ozelim, L. C. d. S. and Cavalcante, A. L. (2017). Representative elementary volume determination for permeability and porosity using numerical three-dimensional experiments in microtomography data. International Journal of Geomechanics, 18(2):04017154. Ozelim, L. C. d. S. and Cavalcante, A. L. (2018a). 3d cellular automata as a computational tool to generate arti cial porous media. International Journal of Geomechanics, 18(9):04018096 Ozelim, L. C. d. S. and Cavalcante, A. L. (2018b). Combining microtomography, 3d printing, and numerical simulations to study scale e ects on the permeability of porous media. International Journal of Geomechanics, 19(2):04018194. Pal, S. K. and Chakravarty, D. (2003). Rock-mass Characterization using Fractals. National Conference on Nonlinear Systems & Dynamics, (January):217{220. Patton, F. and Deere, D. (1970). Signi cant geologic factors in rock slope stability. Planning Open Pit Mines: AA Balkema, Capetown, South Africa, pages 143{151. Playfair, J. (1802). Illustrations of the Huttonian Theory of the Earth. Cambridge University Press. Poincare, H. (1881). M emorie sur les courbes d e nies par une equation di erentielle (i). Journal des Math ematiques Pures et Appliqu ees 3 S erie 7, pages 375{422. Poincare, H. (1882). M emorie sur les courbes d e nies par une equation di erentielle (ii). Journal des Math ematiques Pures et Appliqu ees 3 S erie 8, pages 251{296. Poincare, H. (1885). M emorie sur les courbes d e nies par une equation di erentielle (iii). Journal des Math ematiques Pures et Appliqu ees 4 S erie 1, pages 167{244. Poincare, H. (1905). La science et l'hypothese, ammarion, paris 1902. CR Acad. Sci. Paris, 140:1504. Pointe, P. R. L. A. (1988). A Method to Characterize Fracture Density and Connectivity Through Fractal Geometry. 25(6):421{429. 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Soldo, L., Vendramini, M., and Eusebio, A. (2019). Tunnels design and geological studies. Tunnelling and Underground Space Technology, 84(June 2018):82{98. T Chelidze; Y, G. (1990). Technical Note Evidence of Fractal Fracture. Earth, 27(3):223{225. Tarbuck, E. (2005). Ciencias de la tierra: Una Introducci on a la geolog a F sica. Fuera de colecci on Out of series. Pearson Educaci on. Terzaghi, K. (1946). Rock defects and loads on tunnel supports. page 95 p. : ill. ; 27 cm. Trouw, R. A., Passchier, C. W., and Wiersma, D. J. (2009). Atlas of Mylonites-and related microstructures. Springer Science & Business Media. Turcotte, D. (1997). Fractals and chaos in geology and geophysics. Cambridge University Press, second edi edition. Vernon, R. H. (2004). A Practical Guide to Rock Microstructure. Cambridge University Press, Cambridge. Von Neumann, J. and Burks, A. (1966). Theory of self-reproducing automata. University of Illinois Press. Wang, W. D., Su, Y. L., Zhang, Q., Xiang, G., and Cui, S. M. (2018). Performance-based fractal fracture model for complex fracture network simulation. Petroleum Science, 15(1):126{134. Wolfram, S. (2002). A New Kind of Science. Wolfram Media Inc, Illinois, USA. Yangsheng, Z., Zengchao, F., Dong, Y., Weiguo, L., and Zijun, F. (2015). Three-dimensional fractal distribution of the number of rock-mass fracture surfaces and its simulation technology. Computers and Geotechnics, 65:136{146. Zhang, L. and Ding, X. (2010). Variance of non-parametric rock fracture mean trace length estimator. International Journal of Rock Mechanics and Mining Sciences, 47(7):1222{1228. Zhao, Y., Feng, Z., Liang, W., Yang, D., Hu, Y., and Kang, T. (2009). Investigation of fractal distribution law for the trace number of random and grouped fractures in a geological mass. Engineering Geology, 109(3-4):224{229. Zhou, Z., Su, Y., Wang, W., and Yan, Y. (2017). Application of the fractal geometry theory on fracture network simulation. 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Atribución-NoComercial-CompartirIgual 4.0 Internacional Atribución-NoComercial-CompartirIgual 4.0 Internacional |
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Atribución-NoComercial-CompartirIgual 4.0 InternacionalAtribución-NoComercial-CompartirIgual 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Mesa Sánchez, Oscar José97c38ca7-8fa0-4233-995c-da3827a8a047Echeverri Ramírez, Oscar0928f8aa-ba75-4924-bd37-33acd0040346Brasil Cavalcante, André Luisfa4ffc23-d4a0-48d0-ad5c-277cd7b9c108Moná Graciano, Juan Esteban1f8650ea-45fc-4310-abb6-41f2f9d4bfc1Universidad Nacional de Colombia - Sede Medellín2020-05-11T13:44:57Z2020-05-11T13:44:57Z2019-08-31Moná, J.E., Echeverri Ramírez, O., Brasil-Cavalcante, A.L., Mesa-Sánchez, O.J., (2019) Aplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocosos. Tesis de Maestría. Universidad Nacional de Colombia, Sede Medellín. Facultad de Minas. Departamento de Ingeniería Civil.https://repositorio.unal.edu.co/handle/unal/77499La geología estructural tiene muchos campos de aplicación, en geotecnia de rocas es fundamental el estado de fracturamiento para realizar una clasi cación geomecánica seg un metodologías establecidas como el RMR (Rock Mass Rating) y el GSI (Geological Strength Index), sin embargo la estimación cualitativa de fracturas conlleva errores de metodología, interpretación y valoración en las obras subterraneas. Este aporte investigativo involucra la teoría fractal para realizar estimaciones en términos de clasi cación geomecánica y como herramienta para simular geométricamente el comportamiento de una falla. Para esto se establecen las características de los fractales y las características del fracturamiento donde la dimensión fractal es utilizada como herramienta para realizar la clasi cación geomecánica en 15 frentes de obra subterranea y en cartografía geotécnica en dos localidades del departamento de Antioquia, Colombia. Por otro lado, se lograron obtener modelos de distribución geométrica de fracturas utilizando autómatas celulares probabil ísticos programados en el lenguaje de programción Wolfram Mathematica. Ambos métodos muestran tener una buena potencialidad para ser aplicados en la ingeniería con las calibraciones e investigaciones (Tomado de la fuente)The structural geology have lots of applications, in rock geomechanics for example, the geotechnical classi cation depends on how much fractured is the massif is, that classi cation is made upon some metodologies which the most common ones are the (Rock Mass Rating) and the GSI (Geological Strength Index ), however, the cualitative approximation of the fracture networks carries on common mistakes on the intrepretation and construction of underground excavations. This works implies the fractal theory to make geotechnical classi cations and to estimate the geometrical behaviour of a fault. Some relationships between the fractals and the fracture networks are established where the fractal dimension are used as tool to make geotechnical clasi cation of 15 massifs in one underground excavation and also used in geotechnical cartography in 2 locations in Antioquia, Colombia. On the other side, one model for the geometrical distribution of fractures are proposed using probabilistic cellular automatons on the Wolfram Mathematica language. Both methods shows a good potenciality to be applied to the engineer work eld with some precitions and some more research to improve the limitants to the methods which are also proposed in the research work.necesarias (tomado de la fuente)Universidad Nacional de Colombia - Sede MedellínMaestríaMagister en Ingeniería - Geotecnia95application/pdfspa550 - Ciencias de la tierraFractalsFracturesCellular AutomatonFractal DimensionRMRGSIFractalesFracturamientoAutómatas CelularesDimensión FractalRMRGSIAplicación de la teoría fractal para la estimación de la distribución geométrica de fallas en macizos rocososOn the application of fractal theory for the geometrical behaviour of faults among rock massifsTrabajo de grado - Maestríainfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_8042Texthttp://purl.org/redcol/resource_type/WPMedellín - Minas - Maestría en Ingeniería - GeotecniaDepartamento de Ingeniería CivilUniversidad Nacional de Colombia - Sede MedellínMedellínAlc arcel, F., G omez, J., and Compiladores (2019). Mapa geol ogico de colombia 2019. escala 1:2.000.000.Ayan Misra, Achyuta; Mukherjee, S. (2018). Atlas of Structural Geological Interpretation from Seismic Images. Wyley & Sons Ltd, New York.Bagde, M. N., Raina, A. K., Chakraborty, A. K., and Jethwa, J. L. (2002). Rock mass characterization by fractal dimension. Engineering Geology, 63(1-2):141{155.Barton, N. (1973). Review of a new shear-strength criterion for rock joints. Engineering Geology, 7(4):287 { 332.Barton, N., Lien, R., and Lunde, J. (1974). Engineering classi cation of rock masses for the design of tunnel support. Rock Mechanics Felsmechanik Mecanique des Roches, 6:189{236.Bieniawski, Z.T; Balkema, A. (1976). Rock mass classi cations in rock engineering. pages pp 27{32.Bieniawski, Z. T. (1989). Engineering rock mass classi cations: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons.Binglei, L., Yongtao, G., and Xiaojuan, L. (2011). 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