A data-driven fuzzy approach to simulate the critical shear stress of mixed cohesive/non-cohesive sediments

  • Aline Schäfer Rodrigues Silva
  • Markus Noack
  • Dirk Schlabing
  • Silke Wieprecht
Physical and Ecological Aspects of Mobile Sediments



The critical shear stress of cohesive and mixed cohesive/non-cohesive sediments is affected by multiple interacting physical, chemical and biological parameters. There are various mathematical approaches in the scientific literature for computing critical shear stress. However, processes that influence sediment stability are still not fully understood, and available formulas differ considerably. These discrepancies in the literature arise from random system behaviour (natural variability of the sediments), different definitions of the critical shear stress, different measurement techniques and different model frameworks (scope of the parameters, undisturbed versus artificial sediment samples). While analytical approaches fail to address the involved uncertainties, fuzzy logic-based models integrate uncertainty and imprecision.

Materials and methods

With this in mind, a data-driven neuro-fuzzy model (ANFIS) was used to determine the critical shear stress based on sediment characteristics such as wet bulk density and grain size distribution. In order to select model predictors systematically, an automated stepwise regression algorithm was applied. The database for this analysis consisted of 447 measurements of the critical shear stress originating from 64 undisturbed sediment samples.

Results and discussion

The study identified clay content as the primarily controlling variable for erosion resistance. Depending on the characteristics of the sampling location, the bulk density was also selected as a model predictor. In comparison to analytical models that are available in the scientific literature, the fuzzy model achieved higher correlation coefficients between measured and predicted data.


The neuro-fuzzy-model includes uncertainties of input variables and their interactions directly. Thus, it provides a reliable method for the prediction of erosion thresholds of cohesive/non-cohesive mixtures. It was also shown that this approach requires fewer measured variables as well as fewer assumptions than the models it was compared to.


ANFIS Critical shear stress Data-driven modelling Fuzzy logic Mixed cohesive/non-cohesive sediments 



The authors would like to acknowledge the German Federal Waterways and Shipping Authority in conjunction with the German Federal Institute of Hydrology and the Agency for Flood Defense and Water Management of Saxony-Anhalt for funding and their support during the measuring campaigns.


  1. Aberle J (2008) Measurement techniques for the estimation of cohesive sediment erosion. In: Rowiński, P.M. (ed), Hydraulic methods for catastrophes: floods, droughts, environmental disasters, 10th edn. Publs. Inst. Geophys. Pol. Acad. Sc., pp 5–20Google Scholar
  2. Ahmad MF, Dong P, Mamat M, Wan Nik WB, Mohd MH (2011) The critical shear stresses for sand and mud mixture. Appl Math Sci 5:53–71Google Scholar
  3. Debnath K, Nikora V, Aberle J, Westrich B, Muste M (2007) Erosion of cohesive sediments: resuspension, bed load, and erosion patterns from field experiments. J Hydraul Eng 133:5(508)Google Scholar
  4. Gerbersdorf SU, Jancke T, Westrich B (2007) Sediment properties for assessing the erosion risk of contaminated riverine sites. An approach to evaluate sediment properties and their covariance patterns over depth in relation to erosion resistance. First investigations in natural sediments. J Soils Sediments 7:25–35CrossRefGoogle Scholar
  5. Gerbersdorf SU, Wieprecht S (2015) Biostabilization of cohesive sediments: revisiting the role of abiotic conditions, physiology and diversity of microbes, polymeric secretion, and biofilm architecture. Geobiology 13:68–97CrossRefGoogle Scholar
  6. Grabowski RC, Droppo IG, Wharton G (2011) Erodibility of cohesive sediment: the importance of sediment properties. Earth-Sci Rev 105:101–120CrossRefGoogle Scholar
  7. Guillaume S (2001) Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans Fuzzy Syst 9:426–443CrossRefGoogle Scholar
  8. Haag I, Kern U, Westrich B (2001) Erosion investigation and sediment quality measurements for a comprehensive risk assessment of contaminated aquatic sediments. Sci Total Environ 266:249–257CrossRefGoogle Scholar
  9. Haun S, Olsen NRB (2012) Three-dimensional numerical modelling of the flushing process of the Kali Gandaki hydropower reservoir: 3D modelling of reservoir flushing. Lakes Reserv Res Manag 17:25–33CrossRefGoogle Scholar
  10. Hawkins DM (2004) The problem of overfitting. J Chem Inf Comp Sci 44:1–12CrossRefGoogle Scholar
  11. Houwing EJ (1999) Determination of the critical erosion threshold of cohesive sediments on intertidal mudflats along the Dutch Wadden Sea coast. Estuar Coast Shelf S 49:545–555CrossRefGoogle Scholar
  12. Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Sys Man Cybern 23:665–685CrossRefGoogle Scholar
  13. Kamphuis JW, Hall KR (1983) Cohesive material erosion by unidirectional current. J Hydraul Eng 109:49–61CrossRefGoogle Scholar
  14. Kern U, Haag I, Schürlein V, Holzwarth M, Westrich B (1999) Ein Strömungskanal zur Ermittlung der tiefenabhängigen Erosionsstabilität von Gewässersedimenten: das SETEG-System. WasserWirtschaft 89(2):72–77Google Scholar
  15. Kothyari UC, Jain RK (2008) Influence of cohesion on the incipient motion condition of sediment mixtures. Water Resour Res 44,
  16. Kruse R, Gebhardt J, Klawonn F (1994) Foundations of fuzzy systems. Wiley & Sons, Chichester, West Sussex, England, New YorkGoogle Scholar
  17. MathWorks, Inc. (2015a) MATLAB statistics and machine learning ToolboxTM – User’s guide. Version 10.1 (Release 2015b)Google Scholar
  18. MathWorks, Inc. (2015b) MATLAB fuzzy logic ToolboxTM – User’s Guide. Version 10.1 (Release 2015b)Google Scholar
  19. Mitchener H, Torfs H, Whitehouse R (1996) Erosion of mud/sand mixtures [Coastal Eng., 29 (1996) 1–25]. Coast Eng 30(3–4):319.
  20. Mouton AM, De Baets B, Goethals PLM (2009) Knowledge-based versus data-driven fuzzy habitat suitability models for river management. Environ Model Softw 24:982–993CrossRefGoogle Scholar
  21. Noack M, Gerbersdorf SU, Hillebrand G, Wieprecht S (2015) Combining field and laboratory measurements to determine the erosion risk of cohesive sediments best. Water 7:5061–5077CrossRefGoogle Scholar
  22. Panagiotopoulos I, Voulgaris G, Collins MB (1997) The influence of clay on the threshold of movement of fine sandy beds. Coast Eng.
  23. Sanford LP, Maa JPY (2001) A unified erosion formulation for fine sediments. Mar Geol 179:9–23CrossRefGoogle Scholar
  24. Sarma KGS (2015) Siltation and coastal erosion at shoreline harbours. Procedia Eng 116:12–19CrossRefGoogle Scholar
  25. Tolossa HG (2012) Sediment transport computation using a data-driven adaptive neuro-fuzzy modelling approach. Universität Stuttgart, Stuttgart, Mitteilungen Institut für Wasser- und UmweltsystemmodellierungGoogle Scholar
  26. van Ledden M (2003) Sand-mud segregation in estuaries and tidal basins. TU DelftGoogle Scholar
  27. Wilks DS (2006) Statistical methods in the atmospheric sciences, 2nd edn. Academic Press, Amsterdam, Boston, International geophysics seriesGoogle Scholar
  28. Witt O, Westrich B (2003) Quantification of erosion rates for undisturbed contaminated cohesive sediment cores by image analysis. Hydrobiologia 494:271–276CrossRefGoogle Scholar
  29. Wu W (2016) Mixed cohesive and noncohesive sediment transport: a state of the art review. In: River sedimentation. CRC Press Taylor & Francis Group, London, pp 9–18Google Scholar
  30. Xiao X, Cai Z (1997) Quantification of uncertainty and training of fuzzy logic systems, in: intelligent processing systems. 1997 I.E. international conference on intelligent processing systems. IEEE, pp 312–316Google Scholar
  31. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefGoogle Scholar
  32. Zhu Y, Lu J, Liao H, Wang J, Fan B, Yao S (2008) Research on cohesive sediment erosion by flow: an overview. Sci China Ser E: Technol Sci 51:2001–2012CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute for Modelling Hydraulic and Environmental SystemsUniversity of StuttgartStuttgartGermany

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