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Physically Based Landslide Susceptibility Analysis Using a Fuzzy Monte Carlo Simulation in Sangju Area, Gyeongsangbuk-Do

Fuzzy Monte Carlo simulation을 이용한 물리 사면 모델 기반의 상주지역 산사태 취약성 분석

  • 장정윤 (세종대학교 지구정보공학과) ;
  • 박혁진 (세종대학교 지구정보공학과)
  • Received : 2017.05.18
  • Accepted : 2017.06.14
  • Published : 2017.06.28

Abstract

Physically based landslide susceptibility analysis has been recognized as an effective analysis method because it can consider the mechanism of landslide occurrence. The physically based analysis used the slope geometry and geotechnical properties of slope materials as input. However, when the physically based approach is adopted in regional scale area, the uncertainties were involved in the analysis procedure due to spatial variation and complex geological conditions, which causes inaccurate analysis results. Therefore, probabilistic method have been used to quantify these uncertainties. However, the uncertainties caused by lack of information are not dealt with the probabilistic analysis. Therefore, fuzzy set theory was adopted in this study because the fuzzy set theory is more effective to deal with uncertainties caused by lack of information. In addition, the vertex method and Monte Carlo simulation are coupled with the fuzzy approach. The proposed approach was used to evaluate the landslide susceptibility for a regional study area. In order to compare the analysis results of the proposed approach, Monte Carlo simulation as the probabilistic analysis and the deterministic analysis are used to analyze the landslide susceptibility for same study area. We found that Fuzzy Monte Carlo simulation showed the better prediction accuracy than the probabilistic analysis and the deterministic analysis.

정량적인 산사태 취약성 분석 중 물리 모델 기반의 분석(physically based approach)은 산사태의 발생 메커니즘 과정을 고려할 수 있는 장점으로 인해 다양한 취약성 분석기법 중 가장 효과적인 기법으로 알려져 있다. 물리 모델 분석은 사면의 지형학적 및 지질공학적 특성과 관련된 입력 자료들을 활용하는데, 현장으로부터 지질공학적 특성을 획득하는 과정에서 지반의 공간적 변동성과 복잡한 지질조건으로 인해 불확실성이 발생하며 이는 부정확한 결과를 초래한다. 따라서 이러한 불확실성을 정량화하기 위하여 확률론적 기법이 활용되어 왔다. 그러나 확률론적 분석을 수행하기 위해 필요한 입력변수의 확률특성은 현장 조사나 실험에서의 수량 제약으로 인하여 정확하게 파악하기 힘들다는 문제가 발생한다. 따라서 본 연구에서는 이러한 원인으로 인해 발생하는 불확실성을 다루기 위하여 퍼지집합이론(fuzzy set theory)을 활용하였다. 특히, 본 연구에서는 퍼지집합이론과 몬테카를로기법(Monte Carlo simulation)을 결합한 분석기법을 제안하였고 이를 실제 산사태가 발생한 연구지역에 적용하여 적정성을 파악하였다. 이를 위하여 1998년 8월 대규모의 산사태가 발생한 경상북도 상주시 일대를 연구지역으로 선정하고 산사태 취약성 분석을 수행하였다. 또한 퍼지몬테카를로기법(Fuzzy Monte Carlo simulation)의 예측 정확도 비교를 위해, 기존의 확률론적 기법인 몬테카를로기법(Monte Carlo simulation)과 안전율 수행 결과와 비교분석 하였다. 그 결과 퍼지몬테카를로기법(Fuzzy Monte Carlo simulation)이 다른 기법에 비해 가장 좋은 예측의 정확도를 보였다.

Keywords

References

  1. Avanzi, G.D.A., Falaschi, F., Giannecchini, R. and Puccinelli, A. (2009) Soil slip susceptibility assessment using mechanical-hydrological approach and GIS techniques: an application in the Apuan Alps (Italy). Natural hazards, v.50, p.591-603. https://doi.org/10.1007/s11069-009-9357-4
  2. Takara, K., Yamashiki, Y., Sassa, K., Ibrahim, A.B. and Fukuoka, H. (2010) A distributed hydrological-geotechnical model using satellite-derived rainfall estimates for shallow landslide prediction system at a catchment scale. Landslides, v.7, p.237-258. https://doi.org/10.1007/s10346-010-0214-z
  3. Beven, K.J. and Kirkby, M.J. (1979) A physically based, variable contributing area model of basin hydrology/ Un modele a base physique de zone d'appel variable de l'hydrologie du bassin versant. Hydrological Sciences Journal, v.24, p.43-69. https://doi.org/10.1080/02626667909491834
  4. Borga, M., Dalla Fontana, G., Da Ros, D. and Marchi, L. (1998) Shallow landslide hazard assessment using a physically based model and digital elevation data. Environmental geology, v.35, p.81-88. https://doi.org/10.1007/s002540050295
  5. Burrough, P.A., MacMillan, R.A. and Deursen, W.V. (1992) Fuzzy classification methods for determining land suitability from soil profile observations and topography. European Journal of Soil Science, v.43, p.193-210. https://doi.org/10.1111/j.1365-2389.1992.tb00129.x
  6. Burton, A. and Bathurst, J.C. (1998) Physically based modelling of shallow landslide sediment yield at a catchment scale. Environmental Geology, v.35, p.89-99. https://doi.org/10.1007/s002540050296
  7. Chae, B.G., Lee, J.H., Park, H.J. and Choi, J. (2015) A method for predicting the factor of safety of an infinite slope based on the depth ratio of the wetting front induced by rainfall infiltration. Natural Hazards and Earth System Sciences, v.15, p.1835-1849. https://doi.org/10.5194/nhess-15-1835-2015
  8. Chen, C.S. and Liu, Y.C. (2007) A methodology for evaluation and classification of rock mass quality on tunnel engineering. Tunnelling and Underground Space Technology, v.22, p.377-387. https://doi.org/10.1016/j.tust.2006.10.003
  9. Choi, J.G. (2007) Geostatistics. Sigmapress, 386p.
  10. Coduto, D.P., Yeung, M.R. and Kitch, W.A. (2010) Geotechnical engineering: principles and practices. 2nd edition, Pearson, 816p.
  11. Davis, T.J. and Keller, C.P. (1997) Modelling uncertainty in natural resource analysis using fuzzy sets and Monte Carlo simulation: slope stability prediction. International Journal of Geographical Information Science, v.11, p.409-434. https://doi.org/10.1080/136588197242239
  12. Dietrich, W.E., Wilson, C.J., Montgomery, D.R., McKean, J. and Bauer, R. (1992) Erosion thresholds and land surface morphology. Geology, v.20, p.675-679. https://doi.org/10.1130/0091-7613(1992)020<0675:ETALSM>2.3.CO;2
  13. Dodagoudar, G.R. and Venkatachalam, G. (2000) Reliability analysis of slopes using fuzzy sets theory, Computers and Geotechnics, v.27, p.101-115. https://doi.org/10.1016/S0266-352X(00)00009-4
  14. Egan, J.P. (1975) Signal detection theory and ROC analysis. Academic Press, 297p.
  15. Einstein, H.H. and Baecher, G.B. (1982) Probabilistic and statistical methods in engineering geology I. Problem statement and introduction to solution. In Ingenieurgeologie und Geomechanik als Grundlagen des Felsbaues / Engineering Geology and Geomechanics as Fundamentals of Rock Engineering, p.47-61.
  16. El-Ramly, H., Morgenstern, N.R. and Cruden, D. M. (2002) Probabilistic slope stability analysis for practice. Canadian Geotechnical Journal, v.39, p.665-683. https://doi.org/10.1139/t02-034
  17. Elton, D. J., Juang, C. H. and Lin, P. S. (2000) Vertical capacity of piles using fuzzy sets. CIVIL ENGINEERING SYSTEMS, v.17, p.237-262. https://doi.org/10.1080/02630250008970284
  18. Fawcett, T. (2006) An introduction to ROC analysis. Pattern recognition letters, v.27, p.861-874. https://doi.org/10.1016/j.patrec.2005.10.010
  19. Fell, R., Corominas, J., Bonnard, C., Cascini, L., Leroi, E. and Savage, W. Z. (2008) Guidelines for landslide susceptibility, hazard and risk zoning for land-use planning. Engineering Geology, v.102, p.99-111. https://doi.org/10.1016/j.enggeo.2008.03.014
  20. Finol, J., Guo, Y.K. and Jing, X.D. (2001) A rule based fuzzy model for the prediction of petrophysical rock parameters. Journal of Petroleum Science and Engineering, v.29, p.97-113. https://doi.org/10.1016/S0920-4105(00)00096-6
  21. Formetta, G., Capparelli, G. and Versace, P. (2016) Evaluating performance of simplified physically based models for shallow landslide susceptibility. Hydrology and Earth System Sciences, v.20, p.4585. https://doi.org/10.5194/hess-20-4585-2016
  22. Frattini, P., Crosta, G.B., Fusi, N. and Dal Negro, P. (2004) Shallow landslides in pyroclastic soils: a distributed modelling approach for hazard assessment, Engineering Geology, v.73, p.277-295. https://doi.org/10.1016/j.enggeo.2004.01.009
  23. Ghose, A.K. and Dutta, D. (1987) A rock mass classification model for caving roofs. International Journal of Mining and Geological Engineering, v.5, p.257-271. https://doi.org/10.1007/BF01560777
  24. Giasi, C.I., Masi, P. and Cherubini, C. (2003) Probabilistic and fuzzy reliability analysis of a sample slope near Aliano. Engineering Geology, v.67, p.391-402. https://doi.org/10.1016/S0013-7952(02)00222-3
  25. Godt, J.W., Baum, R.L., Savage, W.Z., Salciarini, D., Schulz, W.H. and Harp, E.L. (2008) Transient deterministic shallow landslide modeling: requirements for susceptibility and hazard assessments in a GIS framework. Engineering Geology, v.102, p.214-226. https://doi.org/10.1016/j.enggeo.2008.03.019
  26. Gokceoglu, C. (2002) A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Engineering Geology, v.66, p.39-51. https://doi.org/10.1016/S0013-7952(02)00023-6
  27. Gokceoglu, C. and Zorlu, K. (2004) A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Engineering Applications of Artificial Intelligence, v.17, p.61-72. https://doi.org/10.1016/j.engappai.2003.11.006
  28. Gorsevski, P.V., Gessler, P.E., Foltz, R.B. and Elliot, W.J. (2006) Spatial prediction of landslide hazard using logistic regression and ROC analysis. Transactions in GIS, v.10, p.395-415. https://doi.org/10.1111/j.1467-9671.2006.01004.x
  29. Griffiths, D.V., Huang, J. and Fenton, G.A. (2011) Probabilistic infinite slope analysis. Computers and Geotechnics, v.38, p.577-584. https://doi.org/10.1016/j.compgeo.2011.03.006
  30. Grima, M.A. and Babuska, R. (1999) Fuzzy model for the prediction of unconfined compressive strength of rock samples. International Journal of Rock Mechanics and Mining Sciences, v.36, p.339-349. https://doi.org/10.1016/S0148-9062(99)00007-8
  31. Haldar, A. and Mahadevan, S. (2000) Reliability assessment using stochastic finite element analysis. John Wiley & Sons, 344p.
  32. Hamidi, J.K., Shahriar, K., Rezai, B. and Bejari, H. (2010) Application of fuzzy set theory to rock engineering classification systems: an illustration of the rock mass excavability index. Rock mechanics and rock engineering, v.43, p.335-350. https://doi.org/10.1007/s00603-009-0029-1
  33. Hanss, M. and Turrin, S. (2010) A fuzzy-based approach to comprehensive modeling and analysis of systems with epistemic uncertainties. Structural Safety, v.32, p.433-441. https://doi.org/10.1016/j.strusafe.2010.06.003
  34. Harr, M.E. (1987) Reliability based on Design in Civil Engineering. Mcgraw-Hill, 400p.
  35. Ho, J.Y., Lee, K.T., Chang, T.C., Wang, Z.Y. and Liao, Y.H. (2012) Influences of spatial distribution of soil thickness on shallow landslide prediction. Engineering Geology, v.124, p.38-46. https://doi.org/10.1016/j.enggeo.2011.09.013
  36. Horton, R.E. (1933) The role of infiltration in the hydrologic cycle. Eos, Transactions American Geophysical Union, v.14, p.446-460. https://doi.org/10.1029/TR014i001p00446
  37. Huang, J.C., Kao, S.J., Hsu, M.L. and Lin, J.C. (2006) Stochastic procedure to extract and to integrate landslide susceptibility maps: an example of mountainous watershed in Taiwan. Natural Hazards and Earth System Science, v.6, p.803-815. https://doi.org/10.5194/nhess-6-803-2006
  38. Huang, J.C., Kao, S.J., Hsu, M.L. and Liu, Y.A. (2007) Influence of Specific Contributing Area algorithms on slope failure prediction in landslide modeling. Natural Hazards and Earth System Sciences, v.7, p.781-792. https://doi.org/10.5194/nhess-7-781-2007
  39. Jang, H.D. and Yang, H.S. (2010) An analysis of stability on rock slope by changing water level, Tunnel and Underground Space, v.20(1), p.7-14.
  40. Jang, W.S., Ryu, J.C., Kang, H.W., Kim, K.S., Lee, C., Kim, Y.S. and Lim, K.J. (2010) Application of the Technique for Determining the Most Appropriate Spot for a Check-dam in Chungju-dam Watershed. Journal of the Environment, v.7, p.19-31.
  41. Juang, C.H. and Elton, D.J. (1996) A practical approach to uncertainty modeling in geotechnical engineering. In Uncertainty in the Geologic Environment: from Theory to Practice, ASCE, p.1269-1283.
  42. Juang, C.H., Wey, J.L. and Elton, D.J. (1991) Model for capacity of single piles in sand using fuzzy sets. Journal of Geotechnical Engineering, v.117, p.1920-1931. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:12(1920)
  43. Juang, C.H., Huang, X.H. and Elton, D.J. (1992a) Modelling and analysis of non-random uncertainties-fuzzy-set approach. International journal for numerical and analytical methods in geomechanics, v.16, p.335-350. https://doi.org/10.1002/nag.1610160504
  44. Juang, C.H., Lee, D.H. and Sheu, C. (1992b) Mapping slope failure potential using fuzzy sets. Journal of geotechnical engineering, v.118, p.475-494. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:3(475)
  45. Juang, C.H., Jhi, Y.Y. and Lee, D.H. (1998) Stability analysis of existing slopes considering uncertainty. Engineering Geology, v.49, p.111-122. https://doi.org/10.1016/S0013-7952(97)00078-1
  46. Kamai, T. (1991) Slope stability assessment by using GIS. Science and Technology Agency of Japan, in Japanese.
  47. Kayabasi, A., Gokceoglu, C. and Ercanoglu, M. (2003) Estimating the deformation modulus of rock masses: a comparative study. International Journal of Rock Mechanics and Mining Sciences, v.40, p.55-63. https://doi.org/10.1016/S1365-1609(02)00112-0
  48. Kim, J.S., Kim. N.C. and Lee, H.H. (2000) Articles : Application of a Physically Based Model to Shallow landsliding. The Korea Society For Environmental Restoration And Revegetation Technology, v.3, p.62-69.
  49. Kim, J.S. (2011) Assessment of Landslide Hazard Induced by Earthquake and Groundwater Level Variation. Masters dissertation, Sejong university, Seoul.
  50. Kim, W.Y., Chae B.G., Kim, K.S., Cho, Y.C., Lee, C.O., Lee, C.W., Kim, K.Y., Kim, J.H. and Kim, J.M. (2003) Study on landslide hazard prediction. Ministry of Science and Technology, 339p.
  51. Kim, K.S., Song, Y.S., Cho, Y.C., Kim, W.Y. and Jeong, G.C. (2006) Characteristics of Rainfall and Landslides according to the Geological Condition. The journal of Engineering geology, v.16, p.201-214.
  52. Kim, M.S., Kim, J.K., Cho, Y.C. and Kim, S.W. (2011) Geomorphic-characteristics of debris flow induced by typhoon "RUSA" in 2002 using Shalstab Model and Remote Sensing: case study in Macheon region near Jiri-Mountain. Journal of the Korean geomorphological association, v.18, p.193-202.
  53. Lee, J.H. (2013) Landslide susceptibility analysis using transient infiltration model and probabilistic method in Inje area. Masters dissertation, Sejong university, Seoul.
  54. Lee, J.H. and Park, H.J. (2012) Assessment of landslide susceptibility using a coupled infinite slope model and hydrologic model in Jinbu area, Gangwon-do. Economic and Environmental Geology, v.45, p.697-707. https://doi.org/10.9719/EEG.2012.45.6.697
  55. Lee, J.H. and Park, H.J. (2016) Assessment of shallow landslide susceptibility using the transient infiltration flow model and GIS-based probabilistic approach. Landslides, v.13, p.885-903. https://doi.org/10.1007/s10346-015-0646-6
  56. Lee, S.H. (2005) Application of a physically based hydrologic model to the prediction of shallow landslide potential area using GIS. Doctor dissertation, Chungbuk university, Cheongju-si, Chungcheongbuk-do.
  57. Lee, H.W. (2011) Analysis of Landslide Susceptibility using Probabilistic Method and GIS. Masters dissertation, Sejong university, Seoul.
  58. Luo, Z., Atamturktur, S., Juang, C.H., Huang, H. and Lin, P.S. (2011) Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach. Computers and Geotechnics, v.38, p.1031-1040. https://doi.org/10.1016/j.compgeo.2011.07.009
  59. McBratney, A.B. and Moore, A.W. (1985) Application of fuzzy sets to climatic classification. Agricultural and forest meteorology, v.35, p.165-185. https://doi.org/10.1016/0168-1923(85)90082-6
  60. Michel, G.P., Kobiyama, M. and Goerl, R.F. (2014) Comparative analysis of SHALSTAB and SINMAP for landslide susceptibility mapping in the Cunha River basin, southern Brazil. Journal of soils and sediments, v.14, p.1266-1277. https://doi.org/10.1007/s11368-014-0886-4
  61. Montgomery, D.R. and Dietrich, W.E. (1994) A physically based model for the topographic control on shallow landsliding. Water resources research, v.30, p.1153-1171. https://doi.org/10.1029/93WR02979
  62. Mostyn, G.R. and Li, K.S. (1993) Probabilistic slope analysis - state of play. In Proceedings, Conference on Probabilistic Methods in Geotechnical Engineering, p.89-109.
  63. Mostyn, G.R. and Small, J.C. (1987) Methods of stability analysis. Soil Slope Instability and Stabilization, Balkema, p.71-120.
  64. National Disaster Management Institute (2000) Fundamental Issues for Landslide Hazards Avoidance or Mitigation Plans. National Disaster Management Institute, 276p.
  65. Nilsen, B. (2000) New trends in rock slope stability analyses. Bulletin of Engineering Geology and the Environment, v.58, p.173-178. https://doi.org/10.1007/s100640050072
  66. O'loughlin, E.M. (1986) Prediction of surface saturation zones in natural catchments by topographic analysis. Water Resources Research, v.22, p.794-804. https://doi.org/10.1029/WR022i005p00794
  67. Pack, R.T., Tarboton, D.G. and Goodwin, C.N. (1998) The SINMAP approach to terrain stability mapping. In 8th congress of the international association of engineering geology, Vancouver, British Columbia, Canada, p.1157-1165.
  68. Park, H.J. (2007) The Evaluation of Failure Probability for Rock Slope Based on Fuzzy Set Theory and Monte Carlo Simulation. Journal of the Korean Geotechnical Society, v.23, p.109-117.
  69. Park, H.J. and West, T.R. (2001) Development of a probabilistic approach for rock wedge failure. Engineering Geology, v.59, p.233-251. https://doi.org/10.1016/S0013-7952(00)00076-4
  70. Park, H.J., Lee, J.H. and Woo, I. (2013) Assessment of rainfall-induced shallow landslide susceptibility using a GIS-based probabilistic approach. Engineering Geology, v.161, p.1-15. https://doi.org/10.1016/j.enggeo.2013.04.011
  71. Park, H.J., Lee, S.R. and Kim, J.W. (2003) Analysis and Verification of Slope Disaster Hazard Using Infinite Slope Model and GIS. Economic and environmental geology, v.36, p.313-320.
  72. Park, H.J., Um, J.G. and Woo, I. (2008) The evaluation of failure probability for rock slope based on fuzzy set theory and Monte Carlo simulation. In Proceedings of the 10th international symposium on landslides and engineered slopes, p.1943-1949.
  73. Park, H.J., Um, J.G., Woo, I. and Kim, J.W. (2012) Application of fuzzy set theory to evaluate the probability of failure in rock slopes. Engineering Geology, v.125, p.92-101. https://doi.org/10.1016/j.enggeo.2011.11.008
  74. Park, H.J., West, T.R. and Woo, I. (2005) Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA. Engineering Geology, v.79, p.230-250. https://doi.org/10.1016/j.enggeo.2005.02.001
  75. Pathak, S. and Nilsen, B. (2004) Probabilistic rock slope stability analysis for Himalayan conditions. Bulletin of Engineering Geology and the Environment, v.63, p.25-32. https://doi.org/10.1007/s10064-003-0226-1
  76. Pradhan, A.M.S. and Kim, Y.T. (2015) Application and comparison of shallow landslide susceptibility models in weathered granite soil under extreme rainfall events. Environmental Earth Sciences, v.73, p.5761-5771. https://doi.org/10.1007/s12665-014-3829-x
  77. Pradhan, A.M.S. and Kim, Y.T. (2016) Evaluation of a combined spatial multi-criteria evaluation model and deterministic model for landslide susceptibility mapping. Catena, v.140, p.125-139. https://doi.org/10.1016/j.catena.2016.01.022
  78. Rosso, R., Rulli, M.C. and Vannucchi, G. (2006) A physically based model for the hydrologic control on shallow landsliding. Water Resources Research, v.42, p.W06410.
  79. Sadeghi, N., Fayek, A.R. and Pedrycz, W. (2010) Fuzzy Monte Carlo simulation and risk assessment in construction. Computer-Aided Civil and Infrastructure Engineering, v.25, p.238-252. https://doi.org/10.1111/j.1467-8667.2009.00632.x
  80. Santoso, A.M., Phoon, K.K. and Quek, S.T. (2011) Effects of soil spatial variability on rainfall-induced landslides. Computers & Structures, v.89, p.893-900. https://doi.org/10.1016/j.compstruc.2011.02.016
  81. Saulnier, G.M., Beven, K. and Obled, C. (1997) Including spatially variable effective soil depths in TOPMODEL. Journal of hydrology, v.202, p.158-172. https://doi.org/10.1016/S0022-1694(97)00059-0
  82. Song, Y.S. and Hong, W.P. (2011) Analysis of slope stability with consideration of the wetting front and groundwater level during rainfall. The Journal of Engineering Geology, v.21, p.25-34. https://doi.org/10.9720/kseg.2011.21.1.025
  83. Swets, J.A. (1988) Measuring the accuracy of diagnostic systems. Science, v.240, p.1285. https://doi.org/10.1126/science.3287615
  84. Terlien, M.T.J. (1996) Modelling spatial and temporal variations in rainfall-triggered landslides: the integration of hydrologic models, slope stability models and geographic information systems for the hazard zonation of rainfall-triggered landslides with examples from Manizales (Colombia). International Institute for Aerial Survey and Earth Sciences , ITC, 254p.
  85. venkatachalam, G. (2006) Reliability and Risk analysis of slopes. indian geotechnical journal, v.35. p.1-67.
  86. Westen, C.V. and Terlien, M.J.T. (1996) An approach towards deterministic landslide hazard analysis in GIS. A case study from Manizales (Colombia), Earth Surface Processes and Landforms, v.21, p.853-868. https://doi.org/10.1002/(SICI)1096-9837(199609)21:9<853::AID-ESP676>3.0.CO;2-C
  87. Whittle, A.J. and Hashash, Y.M.A. (1994) Soil modeling and prediction of deep excavation behavior. Pre-failure deformation of geomaterials: Rotterdam, AA Balkema, p.589-594.
  88. Williams, C.J., Lee, S.S., Fisher, R.A. and Dickerman, L.H. (1999) A comparison of statistical methods for prenatal screening for Down syndrome. Applied Stochastic Models in Business and Industry, v.15, p.89-101. https://doi.org/10.1002/(SICI)1526-4025(199904/06)15:2<89::AID-ASMB366>3.0.CO;2-K
  89. Witt, A.C. (2005) Using a GIS (Geographic Information System) to model slope instability and debris flow hazards in the French Broad River watershed. The degree of Master of Science, North Carolina State University, North Carolina.
  90. Wu, W. and Sidle, R.C. (1995) A distributed slope stability model for steep forested basins. Water resources research, v.31, p.2097-2110. https://doi.org/10.1029/95WR01136
  91. Xie, M., Esaki, T. and Zhou, G. (2004) GIS-based probabilistic mapping of landslide hazard using a threedimensional deterministic model. Natural Hazards, v.33, p.265-282. https://doi.org/10.1023/B:NHAZ.0000037036.01850.0d
  92. Xu, C., Wang, L., Tien, Y.M., Chen, J.M. and Juang, C.H. (2014) Robust design of rock slopes with multiple failure modes: modeling uncertainty of estimated parameter statistics with fuzzy number. Environmental earth sciences, v.72, p.2957-2969. https://doi.org/10.1007/s12665-014-3201-1
  93. Yao, Y., Li, X. and Yuan, Z. (1999) Tool wear detection with fuzzy classification and wavelet fuzzy neural network. International Journal of Machine Tools and Manufacture, v.39, p.1525-1538. https://doi.org/10.1016/S0890-6955(99)00018-8
  94. Zadeh, L.A. (1965) Fuzzy sets. Information and control, v.8, p.338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  95. Zhou, G., Esaki, T., Mitani, Y., Xie, M. and Mori, J. (2003) Spatial probabilistic modeling of slope failure using an integrated GIS Monte Carlo simulation approach. Engineering Geology, v.68, p.373-386. https://doi.org/10.1016/S0013-7952(02)00241-7
  96. Zimmermann, H.J. (1991) Fuzzy Set Theory and Its Applications. 2nd edition, Springer, 399p.