Journal of Hydraulic Structures

Journal of Hydraulic Structures

Uncertainty Quantification of Steady-State Seepage Through Earth-fill Dams by Random Finite Element Method and Multivariate Adaptive Regression Splines

Document Type : Research Paper

Authors
Milad Kheiry
Farhoud Kalateh
Faculty of Civil Engineering, University of Tabriz, East Azerbaijan Province, Tabriz, Iran.
10.22055/jhs.2023.44288.1259
Abstract
This paper aims to investigate the effects of uncertainty in soil characteristics and dam geometry on seepage flow using the hybrid Multivariate Adaptive Regression Splines (MARS) and Monte Carlo Method (MCM). A computer program based on Darcy flow is developed in the Fortran language to calculate the discharge flow. After validating the numerical FORTRAN code with experimental outputs, firstly, the Deterministic Finite Element Method (DFEM) was used to obtain Seepage Exit Discharge (SED) in Steady State Condition (SSC), and MCM was used for probabilistic analysis to account for uncertainty in random parameters. The program monitored Pore Water Pressure (PWP) changes and integrated them into the time/space domains. To ensure minimal error, the results of the models were compared by Standard Error Calculation (SEC). The research also introduced a new component to compare the seepage flow resulting from the analysis of models in a dimensionless manner called the Effective Discharge MARSplines (EDM). In the present research, the combination of Machine Learning (ML) and MCM algorithms was used in an innovative way for Random Finite Element Method (RFEM) calculations. The results of the research indicate that a 17.9% increase in the Hd/Hu ratio in the deterministic analysis results in a 29.3% decrease in EDM, while in the probabilistic analysis, a similar increase leads to a 19.02% decrease in EDM. Upon comparing deterministic and stochastic models, it can be concluded that deterministic analysis is more accurate and exhibits less error when compared to the probabilistic model.
Keywords
FORTRAN Programming
Seepage Exit Discharge (SED)
Two-Phase Soil
Stochastic Analysis
Computational Fluid Dynamics
Subjects
  1. Wise, J., Hunt, S. & Al Dushaishi, M. (2023). Prediction of earth dam seepage using a transient thermal finite element model. Water15(7), p. 1423. Doi: 10.3390/w15071423.
  2. Kalateh, F., Hosseinejad, F., & Kheiry, M. (2022). Uncertainty Quantification in the analysis of liquefied soil response through Fuzzy Finite Element Method. Acta Geodynamica et Geomaterialia, 19(3).‏ Doi: 10.13168/AGG.2022.0007
  3. Kalateh, F., & Kheiry Ghoujeh-Biglou, M. (2022). Probabilistic analysis of seepage in earthen dam using Monte Carlo method and with considering permeability of materials and dam geometry. Irrigation and Drainage Structures Engineering Research, 23(86), 133-162.‏ Doi:10.22092/idser.2022.358681.1509
  4. Kalateh, F., & Kheiry, M. (2022). Finite Elements Modeling of the Seepage through Earth Dam in Isotropic and Non-Isotropic Conditions and Considering the of Downstream and Reservoir Water Level. 2 In International Conference on Architecture, Civil Engineering, Urban Development, Environment and Horizons of Islamic Art in the Second Step Statement of the RevolutionAt.‏
  5. Zhang, W.G. & Goh, A.T.C. (2013). Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Computers and Geotechnics48, pp. 82–95. Doi: 10.1016/j.compgeo.2012.09.016.
  6. Shiau, J., Lai, V.Q. & Keawsawasvong, S. (2023). Multivariate adaptive regression splines analysis for 3D slope stability in anisotropic and heterogenous clay. Journal of Rock Mechanics and Geotechnical Engineering 15(4), pp. 1052–1064. Doi: 10.1016/j.jrmge.2022.05.016.
  7. Kumar, V., Samui, P., Himanshu, N. and Burman, A. (2019). Reliability-based slope stability analysis of Durgawati earthen dam considering steady and transient state seepage conditions using MARS and RVM‏. Indian Geotechnical Journal 49(6), pp. 650-666‏.
  8. Qureshi, M.U., Mahmood, Z. & Rasool, A.M. (2022). Using multivariate adaptive regression splines to develop relationship between rock quality designation and permeability. Journal of Rock Mechanics and Geotechnical Engineering 14(4), pp. 1180–1187. Doi: 10.1016/j.jrmge.2021.06.011.
  9. Kumar, R., Metya, S., & Bhattacharya, G. (2022). Probabilistic Evaluation of Liquefaction Potential Using Multivariate Adaptive Regression Splines. Department of Civil Engineering, National Institute of Technology, Jamshedpur.
  10. Wang, L., Wu, C., Gu, X., Liu, H., Mei, G. & Zhang, W. (2020). Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines. Bulletin of Engineering Geology and the Environment 79(6), pp. 2763–2775. Doi: 10.1007/s10064-020-01730-0.
  11. Zheng, G., Zhang, W., Zhou, H. & Yang, P. (2020). Multivariate adaptive regression splines model for prediction of the liquefaction-induced settlement of shallow foundations. Soil Dynamics and Earthquake Engineering 132, p. 106097. Doi: 10.1016/j.soildyn.2020.106097.
  12. Vu, D.T., Tran, X.-L., Cao, M.-T., Tran, T.C. & Hoang, N.-D. (2020). Machine learning based soil erosion susceptibility prediction using social spider algorithm optimized multivariate adaptive regression spline. Measurement 164, p. 108066. Doi: 10.1016/j.measurement.2020.108066.
  13. Deng, Z.-P., Pan, M., Niu, J.-T., Jiang, S.-H. & Qian, W.-W. (2021). Slope reliability analysis in spatially variable soils using sliced inverse regression-based multivariate adaptive regression spline. Bulletin of Engineering Geology and the Environment 80(9), pp. 7213–7226. Doi: 10.1007/s10064-021-02353-9.
  14. Selçuklu, S., Coit, D., & Felder, F. A. (2022). A Classification of Aleatory and Epistemic Uncertainties in Generation Expansion Planning. Available at SSRN 4216589.‏
  15. Zhang, W., Dai, B., Liu, Z., & Zhou, C. (2017). Unconfined seepage analysis using moving kriging mesh-free method with Monte Carlo integration. Transport in Porous Media, 116, 163-180.‏ Doi:10.1007/s11242-016-0769-9.
  16. Ahmed, S.A., Revil, A., Bolève, A., Steck, B., Vergniault, C., Courivaud, J. R. & Abbas, M. (2020). Determination of the permeability of seepage flow paths in dams from self-potential measurements. Engineering Geology, 268, 105514. Doi: 10.1016/j.enggeo.2020.105514.
  17. Fukumoto, Y., Yang, H., Hosoyamada, T. & Ohtsuka, S. (2021). 2-D coupled fluid-particle numerical analysis of seepage failure of saturated granular soils around an embedded sheet pile with no macroscopic assumptions. Computers and Geotechnics 136, p. 104234. Doi: 10.1016/j.compgeo.2021.104234.
  18. Su, H., Li, J., Wen, Z., Guo, Z., & Zhou, R. (2019). Integrated certainty and uncertainty evaluation approach for seepage control effectiveness of a gravity dam. Applied Mathematical Modelling, 65, 1-22. Doi: 10.1016/j.apm.2018.07.004.
  19. Johari, A., & Talebi, A. (2019). Stochastic analysis of rainfall-induced slope instability and steady-state seepage flow using random finite-element method. International Journal of Geomechanics, 19(8), 04019085. Doi: 10.1061/(ASCE)GM.1943-5622.0001455.
  20. Johari, A., & Hooshmand Nejad, A. (2018). An Approach to Estimate Wetting Path of Soil–Water Retention Curve from Drying Path. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 42(1), 85-89. Doi:10.1007/s40996-017-0074-z.
  21. Zhao, X., Shang, S., Yang, Y., & Hu, M. (2021). Three-Dimensional Stochastic Seepage Field Analysis of Multimedia Embankment. Advances in Civil Engineering. Doi: 10.1155/2021/1936635.
  22. Johari, A., Talebi, A. & Heydari, A. (2020). Prediction of discharge flow rate beneath sheet piles using gene expression programming based on scaled boundary finite element modelling database. Scientia Iranica0(0), pp. 0–0. Doi: 10.24200/sci.2020.53281.3158.
  23. Kalateh, F., & Kheiry, M. (2023). Stochastic analysis in the Simulation of Effective Seepage Flow through Earth dams with the Monte Carlo Simulation and Machine Learning. Water and Soil Management and Modelling, (), -. Doi: 10.22098/mmws.2023.12184.1208.
  24. Smith, L. & Griffiths, D. (2004). Programming the finite element method. John Wiley & Sons.
  25. Hassanzadeh, Y., & Abbaszadeh, H. (2023). Investigating Discharge Coefficient of Slide Gate-Sill Combination Using Expert Soft Computing Models. Journal of Hydraulic Structures, 9(1), 63-80.‏
  26. Daneshfaraz, R., Norouzi, R., Abbaszadeh, H., & Azamathulla, H. M. (2022). Theoretical and experimental analysis of applicability of sill with different widths on the gate discharge coefficients. Water Supply, 22(10), 7767-7781.‏
  27. Kalateh, F., Hosseinejad, F., & Kheiry, M. (2022). UNCERTAINTY QUANTIFICATION IN THE ANALYSIS OF LIQUEFIED SOIL RESPONSE THROUGH FUZZY FINITE ELEMENT METHOD. Acta Geodynamica et Geomaterialia, 19(3).‏
  28. Emami, S., Choopan, Y., Kheiry Goje Biglo, M., & Hesam, M. (2020). Optimal and Economic Water Allocation in Irrigation and Drainage Network Using ICA Algorithm (Case Study: Sofi-Chay Network). Irrigation and Water Engineering, 10(3).‏
  29. Abbaszadeh, H., Daneshfaraz, R., & Norouzi, R. (2023). Experimental Investigation of Hydraulic Jump Parameters in Sill Application Mode with Various Synthesis. Journal of Hydraulic Structures, 9(1), 18-42.‏
  30. Ghojeh-biglou, M. K., & Pilpayeh, A. (2019). Effect of geometric specifications of ogee spillway on the volume variation of concrete consumption using genetic algorithm. Revista INGENIERÍA UC, 26(2), 145-153.‏
  31. Abbaszadeh, H., Norouzi, R., Süme, V., Daneshfaraz, R., & Tarinejad, R. (2023). Discharge coefficient of combined rectangular-triangular weirs using soft computing models. Journal of Hydraulic Structures, 9(1), 98-110.‏
  32. Daneshfaraz, R., Norouzi, R., Abbaszadeh, H., Kuriqi, A., & Di Francesco, S. (2022). Influence of sill on the hydraulic regime in sluice gates: an experimental and numerical analysis. Fluids, 7(7), 244.‏
  33. Friedman, J.H. (1991). Multivariate adaptive regression splines. The Annals of Statistics19(1), pp. 1–67. Doi: 10.1214/aos/1176347963.
  34. Ju, X., Chen, V.C.P., Rosenberger, J.M. & Liu, F. (2021). Fast knot optimization for multivariate adaptive regression splines using hill climbing methods. Expert systems with applications171, p. 114565. Doi: 10.1016/j.eswa.2021.114565.
  35. Hodson, T. O. (2022). Root-mean-square error (RMSE) or mean absolute error (MAE): When to use them or not. Geoscientific Model Development, 15(14), 5481-5487.‏
  36. Daneshfaraz, R., Norouzi, R., Abbaszadeh, H., & Azamathulla, H. M. (2022). Theoretical and experimental analysis of applicability of sill with different widths on the gate discharge coefficients. Water Supply, 22(10), 7767-7781.‏ https://doi.org/10.2166/ws.2022.354
  37. Kouhpeyma, A., Kilanehei, F., Hassanlourad, M. & Ziaie-Moayed, R. (2022). Numerical and experimental modelling of seepage in homogeneous earth dam with combined drain. ISH Journal of Hydraulic Engineering28(3), pp. 292–302. Doi: 10.1080/09715010.2021.1891469.
  38. Silva, A.V., Neto, S.A.D. and de Sousa Filho, F.D.A. (2016). A Simplified Method for Risk Assessment in Slope Stability Analysis of Earth Dams Using Fuzzy Numbers. Elecronic Journal of Geotechnical Engineering, 21(10), 3607–3624. Doi: 10.1016/j.jrmge.2022.05.016
  39. Kalateh, F. & Hosseinejad, F. (2020). Uncertainty assessment in hydro-mechanical-coupled analysis of saturated porous medium applying fuzzy finite element method. Frontiers of Structural and Civil Engineering14(2), pp. 387–410. Doi: 10.1007/s11709-019-0601-z.
  40. Gui, S., Zhang, R., Turner, J.P. & Xue, X. (2000). Probabilistic Slope Stability Analysis with Stochastic Soil Hydraulic Conductivity. Journal of Geotechnical and Geoenvironmental Engineering126(1), pp. 1–9. Doi: 10.1061/(ASCE)1090-0241(2000)126:1(1).