Abstract
Searching for the precise solution of the free surface has remained the main bottleneck in analyzing the unconfined seepage problem for earth-rock dams. This paper proposes an approach to solve classic earth-rock dams using the smoothed finite element method (S-FEM). To overcome the problems of complex calculation and accuracy loss caused by integrating the area of intersecting elements in saturated seepage, this paper optimizes the shape function calculation by reducing the area integral to a line integral along the elements. To achieve a balance between efficiency and accuracy, we investigated the distinct effects of various smooth elements on computational efficiency, which included computation time and iteration times. Moreover, we first explored the extensive effect of seepage anomalies and their positional changes on hydrological state variables, including head, free surface, overflow point, seepage velocity, and fluid pressure. This exploration presented could provide a potential for developing multi-parameter seepage inversion and serve as constraints for hydro-geophysical inversion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of Data and Materials
Available upon reasonable request.
References
Bardet JP, Tobita T (2002) A practical method for solving free-surface seepage problems. Comput Geotech 29(6):451–475. https://doi.org/10.1016/S0266-352X(02)00003-4
Bazyar MH, Talebi A (2015) Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite-element method. Int J Numer Anal Met 39(1):1–22
Butera I, Climaci M, Tanda MG (2020) Numerical analysis of phreatic levels in river embankments due to flood events. J Hydrol 590:125382. https://doi.org/10.1016/j.jhydrol.2020.125382
Dai Q, Lei Y, Zhang B, Feng D, Wang X, Yin X (2019) A practical adaptive moving-mesh algorithm for solving unconfined seepage problem with Galerkin finite element method. Sci Rep 9(1):1–15. https://doi.org/10.1038/s41598-019-43391-4
Daneshmand F, Kazemzadeh-Parsi MJ (2009) Static and dynamic analysis of 2D and 3D elastic solids using the modified FGFEM. Finite Elem Anal Des 45(11):755–765. https://doi.org/10.1016/j.finel.2009.06.003
Darbandi M, Torabi SO, Saadat M, Daghighi Y, Jarrahbashi D (2007) A moving-mesh finite-volume method to solve free-surface seepage problem in arbitrary geometries. Int J Numer Anal Met 31(14):1609–1629. https://doi.org/10.1002/nag.611
Desai CS, Li GC (1983) A residual flow procedure and application for free surface flow in porous media. Adv Water Resour 6(1):27–35. https://doi.org/10.1016/0309-1708(83)90076-3
Dou Z, Wu J, Zhang H, Huang K (2017, June) The solution of unconfined water seepage problem in saturated-unsaturated soil using Bathe algorithm and Signorini condition. IOP Conf Sers: Earth Environ Sci 69(1):012170. IOP Publishing
Dupuit JE (1863) Etudes théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et à travers les terrains perméables avec des considérations relatives au régime des grandes eaux, au débouché à leur donner, et à la marche des des alluvions dans les rivières à fond mobile. 2éme édition, Dunod, éditeur, Paris
Farzin S, Meysam N, John A (2020) Upstream cutoff and downstream filters to control of seepage in dams. Water Resour Manag 34:4271–4288. https://doi.org/10.1007/s11269-020-02674-6
He ZC, Liu GR, Zhong ZH, Zhang GY, Cheng AG (2011) A coupled ES-FEM/BEM method for fluid-structure interaction problems. Eng Anal Bound Elem 35(1):140–147
Johari A, Heydari A (2018) Reliability analysis of seepage using an applicable procedure based on stochastic scaled boundary finite element method. Eng Anal Bound Elem 94:44–59. https://doi.org/10.1016/j.enganabound.2018.05.015
Jiang QH, Deng SS, Zhou CB, Lu WB (2010) Modeling unconfined seepage flow using three-dimensional numerical manifold method. J Hydrodyn 22(4):554–561. https://doi.org/10.1016/S1001-6058(09)60088-3
Lacy SJ, Prevost JH (1987) Flow through porous media: a procedure for locating the free surface. Int J Numer Anal Met 11(6):585–601. https://doi.org/10.1002/nag.1610110605
Liu GR, Dai KY, Nguyen TT (2007) A smoothed finite element method for mechanics problems. Comput Mech 39(6):859–877. https://doi.org/10.1007/s00466-006-0075-4
Liu GR, Trung N (2016) Smoothed finite element methods. CRC Press. https://doi.org/10.1201/EBK1439820278
Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J Sound Vib 320(4–5):1100–1130. https://doi.org/10.1016/j.jsv.2008.08.027
Nafiseh K, Mehdi V, Mohammad RN, Somayeh PR (2018) Multi-objective hydraulic optimization of diversion dam’s cut-off. Water Resour Manag 32:3723–3736. https://doi.org/10.1007/s11269-018-2015-4
Kazemzadeh-Parsi MJ, Daneshmand F (2012) Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method. Int J Numer Anal Met 36(6):780–797. https://doi.org/10.1002/nag.1029
Kazemzadeh-Parsi MJ, Daneshmand F (2013) Three dimensional smoothed fixed grid finite element method for the solution of unconfined seepage problems. Finite Elem Anal Des 64:24–35. https://doi.org/10.1016/j.finel.2012.09.001
Oden JT, Kikuchi N (1980) Theory of variational inequalities with applications to problems of flow through porous media. Int J Eng Sci 18(10):1173–1284
Rehamnia I, Benlaoukli B, Heddam S (2020) Modeling of seepage flow through concrete face rockfill and embankment dams using three heuristic artificial intelligence approaches: a comparative study. Environ Process 7(1):367–381. https://doi.org/10.1007/s40710-019-00414-6
Shahrokhabadi S, Toufigh MM (2013) The solution of unconfined seepage problem using Natural Element Method (NEM) coupled with Genetic Algorithm (GA). Appl Math Model 37(5):2775–2786. https://doi.org/10.1016/j.apm.2012.06.030
Sharma V, Fujisawa K, Murakami A (2021) Space-time finite element method for transient and unconfined seepage flow analysis. Finite Elem Anal Des 197:103632
Xue BY, Wu SC, Zhang WH, Liu GR (2013) A smoothed FEM (S-FEM) for heat transfer problems. Int J Comp Meth 10(01):1340001. https://doi.org/10.1142/S021987621340001X
Yang Y, Sun G, Zheng H (2019) Modeling unconfined seepage flow in soil-rock mixtures using the numerical manifold method. Eng Anal Bound Elem 108:60–70
Zhang W, Dai B, Liu Z, Zhou C (2017) Unconfined seepage analysis using moving kriging mesh-free method with Monte Carlo integration. Transport Porous Med 116(1):163–180. https://doi.org/10.1007/s11242-016-0769-9
Zheng H, Liu DF, Lee CF, Tham LG (2005) A new formulation of Signorini’s type for seepage problems with free surfaces. Int J Numer Meth Eng 64(1):1–16. https://doi.org/10.1002/nme.1345
Zheng H, Liu F, Li C (2015) Primal mixed solution to unconfined seepage flow in porous media with numerical manifold method. Appl Math Model 39(2):794–808. https://doi.org/10.1016/j.apm.2014.07.007
Acknowledgements
The authors acknowledge Prof. G.R. Liu and Dr. T. Nguyen-Thoi from National University of Singapore for providing a valuable guidance to this work.
Funding
National Natural Science Foundation of China, 42374180, Qianwei Dai, 42174178, Bin Zhang, U1934211, Junsheng Yang, Key Technologies Research and Development Program, 2018YFC0603903, Qianwei Dai,Postdoctoral Science Foundation of Central South University, 22021133, Yi Lei.
Author information
Authors and Affiliations
Contributions
Conceptualization: Q.-W. Dai, B. Zhang; Methodology: Y. Lei, B. Zhang; Model simulation, visualization: Y. Lei, C.-Y. Kong, B. Zhang; Analysis and investigation: Y. Lei, B. Zhang; Writing—original draft preparation: Y. Lei, C.-Y. Kong; Writing—review and editing: B. Zhang, J.-S. Yang; Funding acquisition: Q.-W. Dai, B. Zhang, J.-S. Yang; Resources: Q.-W. Dai; Supervision: J.-S. Yang.
Corresponding author
Ethics declarations
Ethical Approval
This paper has not been published or is being considered for publication elsewhere.
Consent to Participate
All authors declare that they are aware and consent to their participation in this paper.
Consent to Publish
All authors declare that they consent to the publication of this paper.
Competing Interests
All authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Lei, Y., Dai, Q., Zhang, B. et al. A Gradient Smoothing Technique-Based S-FEM for Simulating the Full Impacts of Anomalies on Seepage Solutions and its Application in Multi-Parameter Seepage Inversion. Water Resour Manage 38, 753–773 (2024). https://doi.org/10.1007/s11269-023-03697-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-023-03697-5