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Effect of the membership function type on the fuzzy risk of allowable groundwater drawdown calculation results

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Abstract

Because of the complexity of groundwater systems and human activities, fuzzy and random uncertainties are two kinds of uncertain factors that exist widely in groundwater systems. The fuzziness of the variables is usually described by membership functions. When the variables obey different membership functions, the fuzzy risk of adverse events may be different. To explore the influence of the membership function type on the reliability of the estimation results of allowable groundwater drawdown, taking groundwater exploitation in desert oasis areas that have great dependence on groundwater as an example, a fuzzy stochastic coupling model of the allowable groundwater drawdown is established. Using the theory of the cut level λ, fuzzy variables are transformed into random variables to obtain the fuzzy risk. The results show that unlike the random risk, the fuzzy random risk is an interval. The membership functions with a normal distribution and quasi-normal distribution have little effect on the fuzzy risk in the case study. When λ < 0.67, the fuzzy risk interval of the triangle membership function is the largest, and its risk interval maximum value of 98.36% can be obtained at λ = 0.1; however, when λ > 0.8, it has the smallest risk interval of all the membership functions. If the skewness of the design parameters is taken into consideration, the lognormal membership function is a better choice, with a fuzzy random risk of 57.68% at λ = 0.5. The results of this paper can also provide references for groundwater exploitation risk assessment.

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References

  • Bickel PJ, Doksum KA (2020) Mathematical statistics. Taylor & Francis Inc, Abingdon

    Google Scholar 

  • Guo A et al (2019) Uncertainty analysis of water availability assessment through the Budyko framework. J Hydrol 576:396–407

    Article  Google Scholar 

  • Jahani E, Muhanna RL, Shayanfar MA, Barkhordari MA (2014) Reliability assessment with fuzzy random variables using interval Monte Carlo simulation. Comput-Aided Civ Inf 29(3):208–220

    Article  Google Scholar 

  • Jensen HA, Jerez DJ (2018) A stochastic framework for reliability and sensitivity analysis of large scale water distribution networks. Reliab Eng Syst Saf 176:80–92

    Article  Google Scholar 

  • Kwak BM, Lee TW (1987) Sensitivity analysis for reliability-based optimization using an AFOSM method. Comput Struct 27(3):399–406

    Article  Google Scholar 

  • Kwakernaak H (1978) Fuzzy random variables-I. Definitions and theorems. Inform Sci 15(1):1–29

    Article  Google Scholar 

  • Lal A, Datta B (2019) Multi-objective groundwater management strategy under uncertainties for sustainable control of saltwater intrusion: solution for an island country in the South Pacific. J Environ Manag 234:115–130

    Article  Google Scholar 

  • Li F, Zhu J, Deng X, Zhao Y, Li S (2018) Assessment and uncertainty analysis of groundwater risk. Environ Res 160:140–151

    Article  CAS  Google Scholar 

  • Lightfoot LA (1983) Reliability evaluation of engineering systems. Electron Power 29(11.12):814

    Article  Google Scholar 

  • Liu PG, Shu LC et al (2008) Fuzzy-stochastic method for reliability analysis of groundwater allowable withdrawal. J Hydraul Eng 39(9):1141–1145

    Google Scholar 

  • Long CS, Liu PG, Ongor BTI (2008) Environmental impact assessment using FORM and groundwater system reliability concept: case study Jining, China. Environ Geol 55(3):661–667

    Article  Google Scholar 

  • Ma JZ, Qian J, Gao QZ (2000) Groundwater evolution and its influence on the fragile ecology in the South Edge of Tarim Basin. J Desert Res 20(2):145–149

    CAS  Google Scholar 

  • Manassero M (1994) Hydraulic conductivity assessment of slurry wall using piezocone test. J Geotech Eng 120(10):1725–1746

    Article  Google Scholar 

  • Mordeson JN, Nair PS (2010) Fuzzy mathematics. Physica, Heidelberg

    Google Scholar 

  • Mouyeaux A et al (2019) Probabilistic analysis of pore water pressures of an earth dam using a random finite element approach based on field data. Eng Geol 259:105190

    Article  Google Scholar 

  • Nowak AS, Collins KR (2012) Reliability of structures. CRC Press, Boca Raton

    Book  Google Scholar 

  • Puri ML (1986) Fuzzy random variables. J Math Anal Appl 114(2):409–422

    Article  Google Scholar 

  • Rehana S, Mujumdar PP (2009) An imprecise fuzzy risk approach for water quality management of a river system. J Environ Manag 90(11):3653–3664

    Article  CAS  Google Scholar 

  • Todd DK, Mays LW (2004) Groundwater hydrology. Wiley, Hoboken

    Google Scholar 

  • Russo D, Bouton M (1992) Statistical analysis of spatial variability in unsaturated flow parameters. Water Resour Res 28(7):1911–1925

    Article  CAS  Google Scholar 

  • Smith L (1981) Spatial variability of flow parameters in a stratified sand. J Int Assoc Math Geol 13(1):1–21

    Article  Google Scholar 

  • Sreekanth J, Moore C (2018) Novel patch modelling method for efficient simulation and prediction uncertainty analysis of multi-scale groundwater flow and transport processes. J Hydrol 559:122–135

    Article  Google Scholar 

  • Su H, Wen Z (2013) Interval risk analysis for gravity dam instability. Eng Fail Anal 33:83–96

    Article  Google Scholar 

  • Sudicky AE (1986) A natural gradient experiment on solute transport in a sand aquifer: spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resour Res 22(13):2069–2082

    Article  CAS  Google Scholar 

  • Tan XH (2001) The stability analysis of slope by fuzzy probability method. J HeFei Univ Technol 24(3):442–446

    Google Scholar 

  • Wang C, Matthies HG (2020) Random model with fuzzy distribution parameters for hybrid uncertainty propagation in engineering systems. Comput Method Appl Mech 359:112673

    Article  Google Scholar 

  • Woodbury AD, Sudicky EA (1991) The geostatistical characteristics of the borden aquifer. Water Resour Res 27(4):533–546

    Article  Google Scholar 

  • Yang S et al (2018) Health risk assessment of phreatic water based on triangular fuzzy theory in Yinchuan plain. Ecotoxicol Environ Saf 164:732–738

    Article  CAS  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23(2):421–427

    Article  Google Scholar 

  • Zhang YJ et al (2014) Study of boundaries of membership function values for slope fuzzy reliability analysis. Rock Soil Mech 35(4):1157–1163

    CAS  Google Scholar 

  • Zhao GF, Li YG (1989) Reliability analysis of RC structures in serviceability limit states. In: Proceedings of ICOSSAR’89 ASCE, pp 2067–2070

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Acknowledgements

This work was supported in part by the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering No. 2018nkms06. Data used to produce this paper are available on contact of the first author.

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Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Peigui Liu & Su Zhang

  2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing, 210029, China

    Peigui Liu

  3. School of Transportation Engineering, Hefei University of Technology, Hefei, 230009, China

    Manting Shang

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  1. Peigui Liu
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  2. Su Zhang
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Correspondence to Peigui Liu.

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Liu, P., Zhang, S. & Shang, M. Effect of the membership function type on the fuzzy risk of allowable groundwater drawdown calculation results. Stoch Environ Res Risk Assess 35, 1883–1894 (2021). https://doi.org/10.1007/s00477-020-01950-6

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