Fuzw Logic; Its Attributes, and Application to a Discontinuity Controlled Slope Failure

Öz

This paper is concerned with the basic attributes offitzzy logic, its possible application areas in engineering geology and a simple slope stability application, Some uncertainties are inherent to many engineering geological applications. In the literature, two types of uncertainty such as ignorance and variability are described, Some approaches such as fuzzy logic, probability theory etc are used io minimize thest uncertainties. The fuzzy logic, one of these techniques, is an effective tool to define some uncertainties sourced from ignorances and variabilities, Theoretically, fuzzy rules can be constructed based either an expert knowledge or on a sei of observed or measured data. One of the most important stage of fuzzy logic approach is the construction of membership functions. The assumption underlying fuzzy logic theory* is that the transition from membership to non-membership is seldom a step function. Rather, there is a gradual but specifiable change from membership to non-membership.In crisp set theory, a membership Junction pa x has only Hvo values 0 and I . In this study, some memberhip Junctions defined in the literature were presented with their graphical illustrations. In order to demonstrate the strength and use of this approach, a conventional deterministic slope stability analysis incorporated with the fuzzy logic was performed and the results were discussed A wedge failure occurred in the andésites was analyzed and the factor of safety was found as 1.24. However, it was concluded that this result did not reflect the actual condition, This was, most probably due to the uncertainties associated with the measurement of the shear strength parameters,. Also, the stabiliiy index value was determined. According to the stability index, value the stability class of this slope is fair and the slope is prone to slide.. When performing the fuzzy logic approach, the triangular membership functions were selected,, because, a triangular members hip function can be defined bv a maximum, a minimum and a mode value, In classical geotechnical studies, if there is no statistically significant database, the use of fuzzy logic approach based on competent judgement can be accepted as an .effective way to eliminate uncertainties.. As a consequence, the fuzzy logic is attracting more and more attention in several research fields because it is able to tolerate a wide range of uncertainty

Anahtar Kelimeler

• Fuzzy logic, deterministic analysis, stability index,, slope instability,.

Bulanık Mantık: Özellikleri ve Süreksizlik Denetimli Bir Şey Duraysızhğına Uygulanması

Öz

Bilgisayar destekli tasarım amaçlı mühendislik çalışmaları bir takım mantık sistemleri ve matematiksel uıo deUeri gerektirir. Klasik sayısal analiz yöntemleri sadeleştirilmiş ve sınırlan belirli sistemlerin çözümü için uygun olmasına karşın, karmaşık ve etkileşimli sistemlerin değerlendirilmesinde zaman zaman yetersiz kalabilmektedir, özellikle mühendislik jeolojisinde kayaç ve zeminlerin dayanım parametrelerine bağlı sınıflandırılması ve bu parametreler kullanılarak bilgisayar ortamında gerçekleştirilecek bilgi temelli uzmanlık sistemi knowledgebased expert systems değerlendirmeleri için uygun nitelikte olan bulanık mantık yaklaşımı bu çalışma kapsamında incelenerek, süreksizlik denetimli bir şev duraysszlığı bulanık mantık yaklaşımı kullanılarak değerlendirilmiştir. Andezitler içerisinde gelişmiş olan kama türü şev duraysızlığmın analizi limit-denge yöntemiyle yapıldığında, güvenlik katsayısı 1.24 olarak elde edilmiş» duraysız bîr şev için Tden büyük olarak hesaplanan bu güvenlik katsayısının» şev geometrisi, süreksizlik konumları ve özellikle süreksizliklere ilişkin makaslama dayanım parametrelerinin kesin bir şekilde belirlenememesinden kaynaklandığı düşünülmüştür, Bulanık mantık: yaklaşımı île yapılan değerlendirmede ise duraylslık indeksi 0,31 olarak elde edilmiştir. Bu indeks değerine göre şevin duraylılıği "orta*1 derecede olup, kaymaya eğilimlidir. Bu iki sonuç karşılaştırıldığında, bulanık mantık yaklaşımının, yer yer olasılık yaklaşımlarının kullanımı gibi, klasik deterministik analiz yöntemlerini destekleyici biçimde kullanılmasının yararlı olacağı ortaya çıkmaktadır»

Anahtar Kelimeler

• Bulanık mantık, deterministik analiz», duraylıhk indeksi, şev duraysıziığı

Kaynakça

1. Baecher, G.B., ve Einstein, H.H., 1978, Slope stability models in pit optimisation. International Proceedings 16 Apcom Symposium.,, Tucson,, AKILSA., 501-512.
2. Bortolan, G. Ve Degani, R.,, 1985. A review of some methods, for ranking, fuzzy subsets,. Fuzzy Sets and. Systems, 15,1-20.
3. Cagnoli,, B., 1998, Fuzzy logic in volcanology. Episodes, 21 (2), 94-96.
4. Caiosso, G., DelGreco, O.., ve Giani, G.P., 1987. Some probabilistic approaches to stability analysis of open pit explorations. In Proceedings of International Symposium on Engineering Geology, Beijing, China, 881-891.
5. Chowdhuty, R.N., 1986. Geomechanics risk model for multiple failures along rock discontinuities., International Journal of Rock Mechanics Mining Science and Geomechanics Abstracts, 23 (5) 337-346.
6. Chowdhury, R.N.. ve Xu, D.W., 1995. Geotechnical system, reliability of slopes.. Reliability Engineering and System. Safety,, 4'/,, i41-151. Deere,.D.U. ve Miller, R,P,? 1966,. Engineering
7. Classification and Index Properties of Intact Rock... U.S. Air Force Laboratory, Technical Report No.AFNL-TR-65-116, Albuquerque, N.M.
8. Dim.it.ru» V. ve Luban, F.„ 1986,. ön some optimisation problems under uncertainty. Fuzzy Sets and Systems, 18, 257-272.

9. Di Mola, A., Sessa, S., Pedrycz, W., ve Sanchez, E,, 1989., Fuzzy Relation Equations and Their Applications Knowledge Engineering. Klüver Academic Publishers, London, 278s.
10. Dombi, J.,1990. Membership function as an evaluation. Fuzzy Sets and Systems., 35, 1-21.
11. Ercanoğlu, M, 1997. Altındağ (Ankara) yerleşim. bölgesindeki andezitlerde olası şev duraysızlık modellerinin incelenmesi ve duraysızlık haritasının oluşturulması. Yük.. Müh,. Tezi, Hacettepe Üniversitesi,,, Ankara, 83 s., (yayınlanmamış).
12. Gopal, S,;ve Woodcock, C, 1994., Theory and. methods for accuracy assessment of thematic maps using fuzzy sets. Photogrammetric Engineering and Remote Sensing. 60 (2), 181-188
13. Gökçeoğlu, C, 1997,. Killi, yoğun süreksizlik içeren ve .zayıf kaya kütlelerinin mühendislik sınıflamalarında karşılaşılan güçlüklerin giderilmesine yönelik yaklaşımlar. Doktora Tezi, Hacettepe Üniversitesi, Ankara, 214s.(yayınlanmamış).
14. Gökçeoğlu, C, Sönmez, H. ve Ercanoğlu, M.,, 2000. Discontinuity controlled probabilistic slope failure risk maps of the Altındağ (settlement) region in Turkey.. Engineering Geology, 55, 277-296. ^
15. Grima, NLA. ve Babuska, R., 1999. Fuzzy model for the prediction of unconfined compressive strength of rock samples.. International Journal of Rock Mechanics and Mining Science,,. 36, 339-349.
16. Grima, M.A. ve Verhoef, N.W., 1997, Forecasting of rock trencher performance using a fozzy logic approach. International Journal of Rock Mechanics and Mining Science, 34 (3-4), 707.
17. Hammah, R...E ve Curran, J.H,» 1996, Optimal delineation of joint sets using: a fiizzy clustering algorithm., International Journal of Rock Mechanics, and Mining Science, 35 (4-5), 495- 496,.
18. Heshmaty, B... ve Kandel, A.,, 1985. Fuzzy linear regression and its application to forecasting in uncertain environment Fuzzy Sets and Systems, 15, 159-182.
19. Hoek, E, ve Bray,, X, 1981. Rock Slope Engineering, Inst. Min. Metal., London, 353s.
20. Hoerger, S.F., ve Young, D..S,, 1987. Predicting loca! rock mass behavior using geostatistics,. In Proceedings of 28th Symposium in Rock Mechanics, Rotterdam, Balkema, 99-106..
21. loang, C.a, Lee,, D.H.. ve Sheu, C, 1992. Mapping slope 'failure potential using fuzzy sets., Journal of Geotechnical Engineering,. 118 (3), 475-494.
22. Juang, C.H.., Jhi, Y.Y. ve Lee, D.H., 1998, .Stability analysis of existing slopes considering uncertainly. Engineering Geology, 49,. 111-122,'
23. Kalamaras, G.S., 1.997,, A computer based system for supporting decisions for tunneling in rock under conditions of uncertainty. International Journal of Rock Mechanics and. Mining Science, 34 (3- 4), 588,.
24. Kaufmann-» A, ve Gupta, MM,, 1988. Fuzzy Mathematical Models In Engineering and Management Science, North-Holland Book Co',,, Amsterdam, 338s.
25. Krasinska, E. ve Liebhart, A,, 1986. A. note on the precision of linguistic variables for differentiating between some respiratory diseases. Fuzzy Sets and. Systems, 18, 131-142.
26. Leventhal, A.R., Barker, C.S. ve Am.bro.sis, L.P., 1992, Malanjkhve copper project-overview of the geotechnical investigation for optimum mining exploration,. Regional Symposium on Rock Slopes, India, 69-78.
27. Marek, J.M. ve Savely, J.P., 1.978., Probabilistic analysis of plane shear failure mode.. International Proceedings of 19 th US Symposium, on Rock Mechanics, 40-44
28. Matternicht, G., 1999,. Change detection assessment using fiizzy sets and remotely sensed data: an application of topographic map revision,. ISPRS Journal of Photogrammetry and Remote Sensing. 54,221-233.
29. Miller, S.M., 1983. A statistical method to evaluate homogenity of structural populations. Mathematical Geology, 15(2), 317-328.
30. Moore, D.S., 1.997,, Statistics, Concepts and ' Controversies., W.H. Freeman and Co., New York, 526s.
31. Nguyen, V.U., 1985. Some fiizzy set applications in mining geomechanics. International Journal of Rock Mechanics and Mining Science and Geomechanic Abstracts, 22 (6), 369-379.
32. Sakurai, S. ve Shimizu, N., 1987. Assessment of rock slope stability by fiizzy set theory. ISRM Symposium on Rock Mechanics, A.A. Balkema, 503-506,.
33. Svarovski S.G., 1.987.. Usage of linguistic variable concept for human operator modelling,. Fuzzy Sets and. Systems, 22,107-114.
34. Wang, F., 1990. Improving remote sensing image analysis 'through fuzzy information representation. Pbotogrammetric Engineering and Remote ' Sensing.. 56 (8), 1163-1169.
35. Yao, J... ve Farata5 H., 1986,. Probabilistic, treatment of fuzzy events in civil engineering. Journal of Probabilistic Engineering Mechanics, 1(1), 58- 64,.
36. Zadeh, L.A,, 1965. Fuzzy sets., Information and Control,, 8, 338-353.
37. Zadeh, LA., 1971. Quantitative fuzzy semantics. Information of Science, 3, 159-176,.
38. Zadeh,, LA., 1984. Making; computers think like people, IEEE Spectrum, 8, 26-32.
39. Zçttkr, AH., Poisel, R. s Lakovits, B, ve Kastner, W., 1996. Control system, for tunnel boring machines (IBM): A first investigation towards a hybrid control system, International Journal of Rock Mechanics and Mining Science,, 35 (4- . 5), 674...
40. Zimmerman,, HJ., .1978., Fuzzy programming and linear1 programming with several objective functions,. Fuzzy Sets and Systems, 1,44-55.