کاربرد روش تابع پایه شعاعی به‌منظور بررسی نشت از زیر سد در حالات جریان ماندگار و غیرماندگار

نوع مقاله : علمی - پژوهشی

نویسندگان

1 دانش آموخته کارشناسی ارشد عمران آب و سازه های هیدرولیکی، دانشکده فنی و مهندسی، دانشگاه مراغه، مراغه، ایران

2 استاد، دانشکده فنی و مهندسی، دانشگاه مراغه، مراغه، ایران

3 دانشیار، گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه مراغه، مراغه، ایران

4 دانشجوی کارشناسی ارشد عمران آب و سازه های هیدرولیکی، دانشکده فنی و مهندسی، دانشگاه مراغه، مراغه، ایران

5 استادیار، گروه ریاضی، دانشکده علوم پایه، دانشگاه مراغه، مراغه، ایران

چکیده

حل مسئله به ‌روش مش‌لس بر مبنای انتخاب یک سری نقاط از داخل ناحیه محاسباتی و مرزها بدون مش‌بندی صورت می‌گیرد. در پژوهش حاضر پدیده تراوش از زیر سد در شرایط جریان ماندگار و غیرماندگار با ترکیب روش مش‌لس و تفاضل محدود انجام یافته است. حل مسئله و عملیات کالیبره کردن با کدنویسی در برنامه متلب صورت پذیرفت. روش مش لس برای جملات مکانی و روش تفاضل محدود برای گسسته سازی جملات زمانی استفاده شد. نتایج نشان داد که ضریب شکل حاصل برای نقاط کم، 0/85 و نقاط زیاد 0/52 است که بیانگر نزدیکی تقریب‌های اولیه به جواب اصلی می‌باشد. با توجه به اینکه ضریب شکل به هندسه و معادله حاکم بستگی دارد بنابراین ضریب شکل یکسانی برای جریان ماندگار و غیرماندگار برابر با 0/52 به‌دست آمد. در جریان غیرماندگار با ثابت ماندن عمق آب پشت سد، هد آبی در زیر سد به مقدار ثابتی می‌رسد. نتایج نشان داد که در حل عددی مسائل، کم بودن میزان خطا ملاک نبوده و از میان توابع پایه مختلف، برای رسم خطوط هم پتانسیل فقط تابع MQ کارایی بهتری از نظر هیدرولیکی دارد به‌طوری‌که برای تعداد نقاط 133، ضریب شکل و شاخص آماری خطای جذر میانگین مربعات خطا به‌ترتیب 0/52 و 0/0108 است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Application of Radial Base Function Method to Investigate Seepage under the Dam in Steady and Unsteady Flow Conditions

نویسندگان [English]

  • Roghayeh Adami 1
  • Rasoul Daneshfaraz 2
  • Sina Sadeghfam 3
  • , Hamidreza Abbaszadeh, 4
  • Mehdi Djahanghiri, 5
1 Graduated M.sc student of water and hydraulic structures engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran
2 Professor, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran
3 Associate Professor, Faculty of Engineering, University of Maragheh, Maragheh, Iran.
4 M.Sc. Student, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran.
5 Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, , Iran
چکیده [English]

Solving the problem with the meshless method is based on selecting a series of points from inside the computational area and boundaries without meshing. In the present study, the phenomenon of seepage below the dam under steady and unsteady flow conditions has been investigated by combining the Meshless method and the Finite Difference Method. Problem solving and calibrating operations were done by coding in MATLAB software. The Meshless method was used for spatial sentences and the Finite Difference Method was used for the discretization of temporal sentences. The results showed that the shape factor (α) for low points is 0.85 and for high points is 0.52, which indicates the proximity of the initial approximations to the main answer. Considering that, the shape factor depends on the geometry and the governing equation, so the same shape factor was obtained for the steady and unsteady conditions equal to 0.52. In the unsteady condition, with the water level behind the dam remaining constant, the water head below the dam also reaches a constant value over time. Also, examination of the results showed that in numerical problem solving, a low error is not a criterion and among the various basic functions, only the MQ function has the better hydraulic performance to draw equipotential lines, so that for 133 points, the shape factor and root mean square error index are 0.52 and 0.0108, respectively.

کلیدواژه‌ها [English]

  • Radial Base Function
  • Finite Element
  • Seepage from the dam body
  • Steady Flow
  • Unsteady Flow
[1] Huang, T., & Rudnicki, J. W. (2006). A mathematical model for seepage of deeply buried groundwater under higher pressure and temperature. Journal of hydrology, 327(1-2), 42-54.
[2] Honjo, Y., Giao, P. H., & Naushahi, P. A. (1995). Seepage analysis of Tarbela dam (Pakistan) using finite element method. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 32(3), 131A.
[3] Brebbia, C. A., & Chang, O. V. (1979). Boundary elements applied to seepage problems in zoned anisotropic soils. Advances in Engineering Software, 1(3), 95-105.
[4] Darbandi, M., Torabi, S. O., Saadat, M., Daghighi, Y., & Jarrabashi, D. (2007). A moving-mesh finite volume method to solve free-surface seepage problem in arbitrary geometries. Numerical and analytical methods in Geomechanics, (31)41, 1609-1629.
[5] Daneshfaraz, R., & Kaya, B. (2008). Solution of the propagation of the waves in open channels by the transfer matrix method. Ocean Engineering, 35(11–12), 1075-1079.
[6] Daneshfaraz, R., Aminvash, E., & Abbaszadeh, H. (2021). Numerical Simulation of Energy Dissipation in Crescent-Shaped Contraction of the Flow Path. Iranian Journal of Soil and Water Research, 52(5), 1299-1314. Doi: 10.22059/ijswr.2021.318989.668895.
[7] Kansa, E. J. (1990). Multiquadrics-A scattered data approximation scheme with application to computational fluid dynamics. Solution to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications, (19)8-9, 147-161.
[8] Boztosun, I., Charafi, A., Zerroukat, M., & Djidjeli, K. (2002). Thin-plate spline radial basis function scheme for advection-diffusion problems. Electric Journal of Boundary Elements, 2, 889-895.
[9] Sarler, B., Perko, J., & Chen, C.S. (2004). Radial basis function collocation method solution of natural convection in porous media. International Journal of Numerical Methods for Heat & Fluid Flow, (14)2, 187-212.
[10] Durmus, A., Boztosun, I., & Yasuk, F. (2006). Comparative study of the multiquadratic and thin-plate spline radial basis function for the transient-convection diffusion problem. International Journal of Modern Physics C, 17(8), 1151-1169.
[11] Hashemi, M. R., & Hatam, F. (2011). Unsteady seepage analysis using local radial basis function-based differential quadrature method. Applied Mathematical Modeling, 35, 4934-4950.
[12] Arshad, E. I., & Babar, M. M. (2014). Comparison of SEEP/W Simulations with Field Observations for Seepage Analysis through an Earthen Dam (Case Study: Hub Dam-Pakistan). International Journal of Research (IJR), (1)7, 57-70.
[13] Hedayati Talouki, H., Lashkaripour, G. R., Ghafoori, M., & Saba, A. A. (2015). Assessment and presentation of a treatment method to seepage problems of the alluvial foundation of Ghordanloo dam, NE Iran. Journal of the Geological Society of India, (85)3, 377-384.
[14] Nourani, V., & Mousavi, Sh. (2016). Spatiotemporal groundwater level modeling using hybrid artificial intelligence-meshless method. Journal of Hydrology, 536, 10-25.
[15] Nourani, V., & Babakhani, A. (2013). Integration of artificial neural networks with radial basis unction interpolation in earth dam seepage modeling. Computing in civil engineering, (27)2, 183-195.
[16] Bazyar, M. H., & Talebi, A. (2015). Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method. International Journal for Numerical and Analytical Methods in Geomechanics, (39)1, 1-22.
[17] Talouki, H. H., Lashkaripour, G. R., Ghafoori, M., & Saba, A. A. (2015). Assessment and presentation of a treatment method to seepage problems of the alluvial foundation of Ghordanloo dam, NE Iran. Journal of the Geological Society of India, (85)3, 377-384.
[18] Awwad, T., Donia, M., & Awwad, L. (2017). Effect of a Stiff Thin Foundation Soil Layer's Depth on Dynamic Response of an Embankment Dam. Procedia Engineering, (189), 525-532.
[19] Fazli Malidareh, B., & Hosseini, S. A. (2019). Collocated discrete subdomain meshless method for dam-break and dam-breaching modelling. Water Management, 172(2), 68-85.
[20] Deymevar, S., Akbarpour, A. (2019). Modeling of dam Break Using the Meshless Local Petrov-Galerkin Method and Shallow Water Equations. Irrigation and Water Engineering, 10(2), 62-75.
[21] Kahid Basiri, H., Babaee, R., Fallah, A., & Jabbari, E. (2020). Development of multiquadric method for solving dam break problem. Journal of Hydraulics, 14(4), 83-98.
[22] Ouria, A., Toufigh, M.M., & Nakhani, A. (2007). An investigation on the effect of the coupled and un coupled formulation on transient seepage by the finite element method. American Journal of Applied Sciences, (4)12, 950-956.
[23] Cooley, R. L. (1983). Some new procedures for numerical solution of variably saturated flow problems. Water Resources Research, (19)5, 1271-1285.
[24] Bear, J., & Verruijt, A. (1987). Modeling Two-Dimensional Flow in Aquifers. In: Modeling Groundwater Flow and Pollution. Theory and Applications of Transport in Porous Media, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3379-8_4
[25] Das, B. M., & Sobhan, K. (2013). Principles of geotechnical engineering. eighth Ed. Cengage Learning, Stamford, USA.
[26] 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. https://doi.org/10.3390/fluids7070244.