Abstract
This paper proposes a hybrid fuzzy zoning approach to compute the spatial variation and design the layout of additional samples during geotechnical investigation of an engineering structure. The geotechnical and geological data of Semilan dam site in southern Iran are utilized to evaluate this methodology. The optimal zoning of the site is found using the Fuzzy c-means (FCM) and comparison of results of various fuzzy clustering validity indices. The borehole samples are assigned to the selected zones according to their fuzzy membership degrees. In each zone, the geostatistical procedures are performed to model the 3-dimensional spatial variability and the related kriging variances. The estimated outputs of four zones are merged to generate the unit and reliable model. After fuzzifying the variables, the uncertainty index is defined as the function of rock quality designation (RQD), Lugeon, lithology index, index of dam structures, and estimation error. To model uncertainty in this site, the Mamdani fuzzy inference system (FIS) is used to establish the rule base relationship between the input and output variables. These outputs of uncertainty can be implemented as a guideline to design the layout of additional exploratory boreholes. In the studied area, five additional boreholes are suggested between the primary network.
Similar content being viewed by others
References
Acaroglu O, Ozdemir L, Asbury B (2008) A fuzzy logic model to predict specific energy requirement for TBM performance prediction. Tunnel Under Space Technol 23:600–608
Alemdag S (2015) Assessment of bearing capacity and permeability of foundation rocks at the Gumustas waste dam site, (NE Turkey) using empirical and numerical analysis. Arab J Geosci 8:1099–1110
Alemdag S, Gurocak Z, Cevik A, Cabalar AF, Gokceoglu C (2016) Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Eng Geol 203:70–82
Alvarez Grima M (2000) Neuro-fuzzy modeling in engineering geology. Taylor & Francis, Didcot (252pp)
Aydin A (2004) Fuzzy set approaches to classification of rock masses. Eng Geol 74(3):227–245
Badel M, Angorani S, Shariat Panahi M (2011) The application of median indicator kriging and neural network in modeling mixed population in an iron ore deposit. Comput Geosci 37:530–540
Balasko B, Abonyi J, Feil B (2002) Fuzzy clustering and data analysis toolbox. University of Veszprem, Veszprém (74 pp)
Bandyopadhyay S, Maulik U (2001) Nonparametric genetic clustering: comparison of validity indices. IEEE Trans Syst Man Cybern Part C Appl Rev 31:120–125
Bensaid AM, Hall LO, Bezdek JC, Clarke LP, Silbiger ML, Arrington JA, Murtagh RF (1996) Validity-guided (re) clustering with applications to image segmentation. IEEE Trans Fuzzy Syst 4:112–123
Bezdek JC (1974) Cluster validity with fuzzy sets. J Cybernetics 3:58–73
Bezdek JC (1975) Mathematical models for systematics and taxonomy. In: Estabrook G (ed) Proceedings of the 8th International Conference on Numerical Taxonomy, San Francisco, USA (143–166 pp)
Bezdek JC, Ehrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10:191–203
Bezdek JC, Hathaway RJ, Sabin MJ, Tucker WT (1987) Convergence theory for fuzzy c-means: counterexamples and repairs. IEEE Trans Syst Man Cybern 17:873–877
Caers J (2011) Modeling uncertainty in the earth sciences. Wiley-Blackwell, Chichester (229 pp)
Camastra F, Ciaramella A, Giovannelli V, Lener M, Rastelli V, Staiano A et al (2015) A fuzzy decision system for genetically modified plant environmental risk assessment using Mamdani inference. Expert Syst Appl 42(3):1710–1716
Carvalho FDAD, Tenório CP, Cavalcanti Junior NL (2006) Partitional fuzzy clustering methods based on adaptive quadratic distances. Fuzzy Sets Syst 157:2833–2857
Castillo O (2012) Type-2 fuzzy logic in intelligent control applications. Springer, Heidelberg (187 pp)
Chen Y-C, Chiang W, Yeh H-C (2008) Rainfall network design using kriging and entropy. Hydrol Process 22:340–346
Chilès J-P, Delfiner P (2012) Geostatistics: modelling spatial uncertainty. Wiley, New York (734 pp)
Chou D, Schenk DE (1983) Optimum locations for exploratory drill holes. Int J Mining Eng 1:343–355
Clayton CR, Matthews MC, Simons NE (1995) Site investigation: a handbook for engineers. Blackwell, Oxford
Cornelissen AMG, van den Berg J, Koops WJ, Grossman M, Udo HMJ (2001) Assessment of the contribution of sustainability indicators to sustainable development: a novel approach using fuzzy set theory. Agric Ecosyst Environ 86(2):173–185
Cressie N (1990) The origins of kriging. Math Geol 22:239–252
Dagdelen K, Turner AK (1996) Importance of stationarity for geostatistical assessment of environmental contamination. ASTM Spec Tech Publi 1283:117–132
Deere DU (1963) Technical description of rock cores for engineering purposes. Rock Mech Eng Geol 1(1):16–22
Deere DU, Deere DW (1989) Rock quality designation (RQD) after twenty years. In: U.S. Army Corps of Engineers contract report GL-89-1. Waterways Experiment Station, Vicksburg, MS (67) (67 pp)
Delmelle EM, Goovaerts P (2009) Second-phase sampling designs for non-stationary spatial variables. Geoderma 153:205–216
Deutsch CV, Journel AG (1998) GSLIB-geostatistical software library and User’s guide, 2nd edn. Oxford University Press, Oxford, New York
Du YG, Tyagi RD, Bhamidimarri R (1999) Use of fuzzy neural-net model for rule generation of activated sludge process. Process Biochem 35(1–2):77–83
Ertugrul S (2008) Predictive modeling of human operators using parametric and neuro-fuzzy models by means of computer-based identification experiment. Eng Appl Artif Intell 21(2):259–268
Everitt B, Landau S, Leese M, Stahl D (2011) Cluster analysis, 5th edn. Wiley Publishing, Hoboken, NJ (330 pp)
Gershon M, Allen LE, Manley F (1988) Application of a new approach for drillholes location optimization. Int J Min Reclam Environ 2:27–31
Guillaume S (2001) Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans Fuzzy Syst 9(3):426–443
Gurocak Z, Alemdag S (2012) Assessment of permeability and injection depth at the Atasu dam site (Turkey) based on experimental and numerical analyses. Bull Eng Geol Environ 71(2):221–229
Hagen-Zanker A, Jin Y (2013) Adaptive zoning for transport mode choice modeling. Trans GIS 17:706–723
Hassanipak AA, Sharafodin M (2004) GET: a function for preferential site selection of additional borehole drilling. Explor Min Geol 13:139–146
Hekmat A, Osanloo M, Moarefvand P (2013) Block size selection with the objective of minimizing the discrepancy in real and estimated block grade. Arab J Geosci 6:141–155
Hengl T, Toomanian N, Reuter HI, Malakouti MJ (2007) Methods to interpolate soil categorical variables from profile observations: lessons from Iran. Geoderma 140:417–427
Hoppner F, Klawonn F, Kruse R, Runkler T (1999) Fuzzy cluster analysis: methods for classification, data analysis and image recognition. Wiley, Chichester (289 pp)
Hossein Morshedy A, Memarian H (2015) A novel algorithm for designing the layout of additional boreholes. Ore Geol Rev 67:34–42
Hossein Morshedy A, Torabi SA, Memarian H (2015) A new method for 3D designing of complementary exploration drilling layout based on ore value and objective functions. Arab J Geosci 8(10):8175–8195
Huang YT, Siller TJ (1997) Fuzzy representation and reasoning in geotechnical site characterization. Comput Geotech 21(1):65–86
Jain AK (2010) Data clustering: 50 years beyond K-means. Pattern Recogn Lett 31:651–666
Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31:264–323
Jalalifar H, Mojedifar S, Sahebi AA, Nezamabadi-Pour H (2011) Application of the adaptive neuro-fuzzy inference system for prediction of a rock engineering classification system. Comput Geotech 38(6):783–790
Jeannee N, Desnoyers Y, Lamadie F, Ioos B (2008) Geostatistical sampling optimization of contaminated premises. In: Decommissioning challenges: an industrial reality? (DEM). France, Avignon
Journel AG, Huijbregts CJ (1978) Mining Geostatistics. Academic Press, London
Kaufman L, Rousseeuw PJ (2009) Finding groups in data: an introduction to cluster analysis. Wiley, New Jersey (342 pp)
Kayabasi A, Yesiloglu-Gultekin N, Gokceoglu C (2015) Use of non-linear prediction tools to assess rock mass permeability using various discontinuity parameters. Eng Geol 185:1–9
Kim DW, Lee KH, Lee D (2004) On cluster validity index for estimation of the optimal number of fuzzy clusters. Pattern Recogn 37:2009–2025
Knödel K, Lange G, Voigt H-J (2007) Environmental geology: handbook of field methods and case studies. Springer-Verlag, Berlin (1357 pp)
Lashkaripour GR, Ghafoori M (2002) The engineering geology of the Tabarak Abad dam. Eng Geol 66(3-4):233–239
Lee GS, Lee KH (2006) Application of fuzzy representation of geographic boundary to the soil loss model. Hydrol Earth Syst Sci Discuss 3:115–133
Liao TW, Celmins AK, Hammell RJ (2003) A fuzzy c-means variant for the generation of fuzzy term sets. Fuzzy Sets Syst 135:241–257
Lin YP, Yeh MS, Deng DP, Wang YC (2008) Geostatistical approaches and optimal additional sampling schemes for spatial patterns and future sampling of bird diversity. Glob Ecol Biogeogr 17:175–188
Look BG (2014) Handbook of geotechnical investigation and design tables, 2nd edn. CRC Press, Boca Raton, Florida (393pp)
Mahab Ghodss (consulting engineers) (2009) Engineering geology report of Semilan dam site. Semilan dam Project, Ministry of Energy, Teheran (in Persian)
McNeill FM, Thro E (1994) Fuzzy logic: a practical approach. AP Professional, New York
Mojarab M, Memarian H, Zare M, Hossein Morshedy A, Pishahang MH (2014) Modeling of the seismotectonic provinces of Iran using the self-organizing map algorithm. Comput Geosci 67:150–162
Myers JC (1997) Geostatistical error management: quantifying uncertainty for environmental sampling and mapping. Van Nostrand Reinhold, New York (594 pp)
Myers DE, Journel AG (1990) Variograms and zonal Aniostropies and Noninvertable kriging systems, math. Geol 22(7):779–785
Nascimento S, Mirkin B, Moura-Pires F (2000) A fuzzy clustering model of data and fuzzy c-means. In: Proceedings of the IEEE 9th Conference on Fuzzy Systems, San Antonio, TX, USA. pp 302–307
Nefeslioglu HA, Gokceoglu C, Sonmez H (2006) Indirect determination of weighted joint density (wJd) by empirical and fuzzy models: Supren (Eskisehir, Turkey) marbles. Eng Geol 85:251–269
Olea RA (2009) A practical primer on geostatistics. U.S. Geological Survey, Open-File Report 2009-1103 (346 pp)
Remy N (2004) Geostatistical earth modeling software: User’s manual. In: Stanford Center for Reservoir Forecasting (SCRF). Stanford University, California, USA (87 pp)
Rezaee MR, Lelieveldt BPF, Reiber JHC (1998) A new cluster validity index for the fuzzy c-mean. Pattern Recogn Lett 19:237–246
Rossi ME, Deutsch CV (2014) Mineral resource estimation. Springer, Netherlands (332 pp)
Savinskii JD (1965) Probability tables for locating elliptical underground masses with a rectangular grid. Consultants Bureau, New York (109 pp)
Schejbal C (1998) Optimization of the borehole grid in mineral exploration. In: Singhal RK (ed) 7th international symposium on mine planning and equipment selection, Calgary, Canada. pp. 47–52
Selim SZ, Ismail MA (1984) Soft clustering of multidimensional data: a semi-fuzzy approach. Pattern Recogn 17:559–568
Shurygin AM (1976) The probability of finding deposits and some optimal search grids. Math Geol 8:323–330
Sinclair AJ, Blackwell GH (2002) Applied mineral inventory estimation. Cambridge University Press, London
Singer DA, Wickman FE (1969) Probability tables for locating elliptical targets with square, rectangular, and hexagonal point-nets (no. GJO-918-3). Pennsylvania State Univ., University Park (USA)
Sivanandam SN, Sumathi S, Deepa SN (2007) Introduction to fuzzy logic using Matlab. Springer, Berlin
Smith JL, Halvorson JJ, Papendick RI (1993) Using multiple-variable indicator kriging for evaluating soil quality. Soil Sci Soc Am J 57:743–749
Solberg IL, Long M, Baranwal VC, Gylland AS, Rønning JS (2016) Geophysical and geotechnical studies of geology and sediment properties at a quick-clay landslide site at Esp, Trondheim. Norway Eng Geol 208:214–230
Soltani S, Hezarkhani A (2011) Determination of realistic and statistical value of the information gathered from exploratory drilling. Nat Resour Res 20:207–216
Szidarovszky F (1983) Multiobjective observation network design for regionalized variables. Int. J. Mining Eng. 1:331–342
Taboada J, Rivas T, Saavedra MA, Araújo M, Argüelles A (2006) A fuzzy expert system application to the evaluation of ceramic- and paper-quality kaolin. Appl Clay Sci 33(3–4):287–297
Uusitalo L, Lehikoinen A, Helle I, Myrberg K (2015) An overview of methods to evaluate uncertainty of deterministic models in decision support. Environ Model Softw 63:24–31
Van Groenigen JW, Pieters G, Stein A (1999) Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma 87:239–259
Vann J, Geoval DG (2003) Beyond ordinary kriging "an overview of non-linear estimation". Geostatistical Association of Australasia (GAA), Perth (135 pp)
Webster R, Margaret A (2007) Geostatistics for environmental scientists, 2nd edn. John Wiley & Sons Ltd, Chichester (315 pp)
Wingle WL (1997) Evaluating subsurface uncertainty using modified geostatistical techniques. Degree of Doctor of Philosophy (Geological Engineer), Colorado School of Mines
Wingle WL, Poeter EP (1996) Evaluating subsurface uncertainty using zonal kriging, uncertainty '96 (ASCE). University of Wisconsin, Madison, Wisconsin
Wu KL, Yang MS (2005) A cluster validity index for fuzzy clustering, pattern Recognit. Lett 26:1275–1291
Xie LX, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841–847
Xu S, Sirieix C, Marache A, Riss J, Malaurent P (2016) 3D geostatistical modeling of Lascaux hill from ERT data. Eng Geol 213:169–178
Yagiz S, Gokceoglu C (2010) Application of fuzzy inference and non-linear regression methods for predicting rock brittleness. Expert Syst Appl 37:2265–2272
Yang Q, Zhang D, Tian F (2010) An initialization method for fuzzy C-means algorithm using subtractive clustering. In: Third international conference on intelligent networks and intelligent systems, pp 393–396
Zhao J, Bose BK (2002) Evaluation of membership functions for fuzzy logic controlled induction motor drive. In: ICON 02, IEEE 28th annual conference of the industrial electronics society, Sevilla, Spain. pp 229–234
Zhou Y, Wu X (1994) Use of neural networks in the analysis and interpretation of site investigation data. Comput Geotech 16(2):105–122
Author information
Authors and Affiliations
Corresponding author
Additional information
Highlights•We propose a hybrid fuzzy zoning approach for 3-dimensional (3D) exploration geotechnical modeling.•Using the fuzzy clustering algorithm, the site is divided into optimal zones.•The zonal geostatistical technique is performed to model the 3D spatial distribution of the geotechnical and lithological variables with corresponding variances.•Fuzzy inference system is used to model uncertainty and layout of additional boreholes.
Rights and permissions
About this article
Cite this article
Hossein Morshedy, A., Torabi, S.A. & Memarian, H. A hybrid fuzzy zoning approach for 3-dimensional exploration geotechnical modeling: a case study at Semilan dam, southern Iran. Bull Eng Geol Environ 78, 691–708 (2019). https://doi.org/10.1007/s10064-017-1133-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10064-017-1133-1