شبیه‌سازی رفتار ماسه اشباع با ترکیب روش اجزاء منفصل و هیدرودینامیک ذرات هموار

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی عمران، آب و محیط زیست، دانشگاه شهید بهشتی، تهران، ایران

چکیده

روش اجزاء منفصل (DEM) از روش‌های عددی معتبر برای تحلیل موضوعات ژئوتکنیکی، به خصوص رفتار مصالح دانه‌ای است. هیدرودینامیک ذرات هموار (SPH) نیز یکی از روش‌های نوین برای مدل‌سازی رفتار سیالات است. هر دو روش DEM و SPH دارای مزیت عدم نیاز به شبکه‌بندی هستند. هنگامی که برای تحلیل یک پدیده ژئوتکنیکی مانند روانگرایی ماسه، بررسی رفتار مصالح دانه‌ای اشباع مد نظر باشد، استفاده از مکانیک سیالات و ترکیب آن با مکانیک ذرات اجتناب‌ناپذیر خواهد بود. روش ترکیبی DEM-SPH به عنوان یک روش لاگرانژی-لاگرانژی، بهترین ترکیب برای مدل‌سازی محیط‌های چندفازی است. زیرا می‌تواند به طور کامل نیاز به شبکه‌بندی حجمی را برطرف کند. عدم نیاز به شبکه‌بندی در مسائلی که دارای هندسه پیچیده، تغییرشکل‌های بزرگ یا سطح آزاد جریان هستند، مزیت بزرگی محسوب می‌شود. با این وجود، تاکنون مدل ترکیبی رضایت‌بخشی بر پایه استفاده همزمان از DEM و SPH برای تحلیل رفتار زهکشی‌نشده مصالح دانه‌ای اشباع ارائه نشده است. در این مقاله با استفاده از روش اجزاء منفصل و ترکیب آن با هیدرودینامیک ذرات هموار، رفتار زهکشی‌نشده ماسه اشباع شبیه‌سازی شده است. مدل عددی با استفاده از نتایج آزمایش‌های سه‌محوری زهکشی‌شده و زهکشی‌نشده بر روی نمونه ماسه گردگوشه صحت‌سنجی شده است. جریان سیال و برهم‌کنش‌های سیال-ذره در مدل منظور شده است. برای اعمال شرایط مرزی ذرات جامد، از یک غشاء انعطاف‌پذیر استفاده شده و شرایط مرزی سیال نیز با استفاده از ذرات فرضی سیال متصل به غشاء پیرامونی، تعریف شده است. نتایج شبیه‌سازی‌ها نشان داد که مدل ترکیبی DEM-SPH به خوبی قادر به پیش‌بینی پاسخ زهکشی‌نشده مصالح دانه‌ای اشباع و متغیرهای محلی مانند توزیع فشار سیال است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Coupled DEM-SPH Modeling of Saturated Sand

نویسندگان [English]

  • Younes Khalili
  • Ahmad Mahboubi
  • Mohammad Haji-Sotoiudeh
Department of Civil and Environmental Engineering, Shahid Beheshti University, Tehran, Iran
چکیده [English]

DEM (Discrete Element Method) is a particle-based method for modeling the granular materials. SPH (Smoothed Particle Hydrodynamics) is also a particle-based method to analyze fluids using a limited number of integration points. These mesh-free methods are suitable to analyze geotechnical problems with large deformations or complicated geometries. Coupling DEM and SPH for simulating multi-phase media, resolves the need for the spatial mesh and prepares a more realistic understanding of the saturated granular materials. In this study by coupling both DEM and SPH methods, a novel DEM-SPH model was developed to simulate saturated granular media such as saturated sand. The particles were modeled using DEM and the inter-particle fluid was simulated using SPH. The fluid flow and the particle-fluid interactions were included in the model. The model was validated by comparing the numerical results to experimental data. The evolution of the fluid pressure distribution was investigated. Three phases were observed in fluid pressure distribution. After starting loading, a pressure wave appeared adjacent to the top wall that formed a “transient phase”. After finishing the transient phase, a “stable phase” of the fluid pressure distribution started, during which the pressure gradient changed gradually. There was an “instable phase” at large axial stains. The pressure gradient changed randomly in this phase. The results showed that the model could satisfactorily predict the undrained behavior of the saturated granular materials and capture the local parameters of the inter-particle fluid e.g. the local variations of the fluid pressure.

کلیدواژه‌ها [English]

  • DEM
  • SPH
  • Mesh-free
  • Saturated Sand
  • particle shape

مراجع

[1] T. Mogami, A statistical approach to the mechanics of granular materials, Soils and Foundations, 5(2) (1965) 26-36.
[2] P.A. Cundall, A computer model for simulating progressive, large-scale movement in blocky rock system, in:  Proceedings of the International Symposium on Rock Mechanics, 1971, 1971.
[3] P.A. Cundall, O.D. Strack, A discrete numerical model for granular assemblies, geotechnique, 29(1) (1979) 47-65.
[4] R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly notices of the royal astronomical society, 181(3) (1977) 375-389.
[5] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, The astronomical journal, 82 (1977) 1013-1024.
[6] A.V. Potapov, M.L. Hunt, C.S. Campbell, Liquid–solid flows using smoothed particle hydrodynamics and the discrete element method, Powder Technology, 116(2–3) (2001) 204-213.
[7] P.W. Cleary, M. Sinnott, R. Morrison, Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media, Minerals Engineering, 19(15) (2006) 1517-1527.
[8] J.W. Fernandez, P.W. Cleary, M.D. Sinnott, R.D. Morrison, Using SPH one-way coupled to DEM to model wet industrial banana screens, Minerals Engineering, 24(8) (2011) 741-753.
[9] F.M. Katubilwa, M.H. Moys, Effects of filling degree and viscosity of slurry on mill load orientation, Minerals Engineering, 24(13) (2011) 1502-1512.
[10] M. Sinnott, P.W. Cleary, R.D. Morrison, Slurry flow in a tower mill, Minerals Engineering, 24(2) (2011) 152-159.
[11] P.W. Cleary, R.D. Morrison, Prediction of 3D slurry flow within the grinding chamber and discharge from a pilot scale SAG mill, Minerals Engineering, 39 (2012) 184-195.
[12] Y.J. Huang, O.J. Nydal, Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows, Theor. Appl. Mech. Lett., 2(1) (2012).
[13] X. Sun, M. Sakai, Y. Yamada, Three-dimensional simulation of a solid–liquid flow by the DEM–SPH method, Journal of Computational Physics, 248(0) (2013) 147-176.
[14] M. Robinson, S. Luding, M. Ramaioli, SPH-DEM simulations of grain dispersion by liquid injection, in:  AIP Conference Proceedings, 2013, pp. 1122-1125.
[15] M. Robinson, S. Luding, M. Ramaioli, Fluid-particle flow modelling and validation using two-way-coupled mesoscale SPH-DEM, eprint arXiv:1301.0752, 2013.
[16] M. Tak, D. Park, T. Park, Computational Coupled Method for Multiscale and Phase Analysis, Journal of Engineering Materials and Technology, 135(2) (2013).
[17] M. Robinson, M. Ramaioli, S. Luding, Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation, International journal of multiphase flow, 59 (2014) 121-134.
[18] P.W. Cleary, Prediction of coupled particle and fluid flows using DEM and SPH, Minerals Engineering, 73 (2015) 85-99.
[19] P.W. Cleary, M.D. Sinnott, Computational prediction of performance for a full scale Isamill: Part 2 – Wet models of charge and slurry transport, Minerals Engineering, 79 (2015) 239-260.
[20] T. Breinlinger, T.C. Kraft, Coupled discrete element and smoothed particle hydrodynamics simulations of the die filling process, Computational Particle Mechanics, 3(4) (2016) 505-511.
[21] D.M. Robb, S.J. Gaskin, J.-C. Marongiu, SPH-DEM model for free-surface flows containing solids applied to river ice jams, Journal of Hydraulic Research, 54(1) (2016) 27-40.
[22] M.D. Sinnott, P.W. Cleary, Particulate and water mixing in the feed box for a screen, Minerals Engineering, 109 (2017) 109-125.
[23] M.D. Sinnott, P.W. Cleary, R.D. Morrison, Combined DEM and SPH simulation of overflow ball mill discharge and trommel flow, Minerals Engineering, 108 (2017) 93-108.
[24] D. Markauskas, H. Kruggel-Emden, R. Sivanesapillai, H. Steeb, Comparative study on mesh-based and mesh-less coupled CFD-DEM methods to model particle-laden flow, Powder Technology, 305 (2017) 78-88.
[25] P.W. Cleary, J.E. Hilton, M.D. Sinnott, Modelling of industrial particle and multiphase flows, Powder Technology, 314 (2017) 232-252.
[26] F.K. Mulenga, Effects of slurry hold-up on the pool volume of a batch mill, Minerals Engineering, 111 (2017) 124-130.
[27] H. Tan, S. Chen, A hybrid DEM-SPH model for deformable landslide and its generated surge waves, Advances in Water Resources, 108 (2017) 256-276.
[28] D. Markauskas, H. Kruggel-Emden, V. Scherer, Numerical analysis of wet plastic particle separation using a coupled DEM-SPH method, Powder Technology, 325 (2018) 218-227.
[29] D. Markauskas, H. Kruggel-Emden, Coupled DEM-SPH simulations of wet continuous screening, Advanced Powder Technology, 30(12) (2019) 2997-3009.
[30] M. Jahani Chegeni, Combined DEM and SPH simulation of ball milling, Journal of Mining and Environment, 10(1) (2019) 151-161.
[31] K. Tsuji, M. Asai, Flid-solid multiphase flow simulator using a SPH-DEM coupled method in consideration of liquid bridge force related to water content, in:  PARTICLES VI: proceedings of the VI International Conference on Particle-Based Methods: fundamentals and applications, CIMNE, 2019, pp. 668-679.
[32] J. Morris, S. Johnson, Dynamic simulations of geological materials using combined FEM/DEM/SPH analysis, Geomechanics and Geoengineering, 4(1) (2009) 91-101.
[33] R. Canelas, J.M. Dominguez, R.M.L. Ferreira, Coupling a Generalized DEM and an SPH Models Under a Heterogeneous Massively Parallel Framework, in:  Congreso de Metodos Numericos en Ingenieria, Lisbon, Portugal, 2013.
[34] K. Wu, D. Yang, N. Wright, A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure, Computers & Structures, 177 (2016) 141-161.
[35] M. Sarfaraz, A. Pak, An integrated SPH-polyhedral DEM algorithm to investigate hydraulic stability of rock and concrete blocks: Application to cubic armours in breakwaters, Engineering Analysis with Boundary Elements, 84 (2017) 1-18.
[36] S. Mintu, D. Molyneux, Simulation of ice-structure interactions using a coupled SPH-DEM method, in:  OTC Arctic Technology Conference, Offshore Technology Conference, 2018.
[37] W.-J. Xu, X.-Y. Dong, W.-T. Ding, Analysis of fluid-particle interaction in granular materials using coupled SPH-DEM method, Powder Technology, 353 (2019) 459-472.
[38] S. Ji, X. Chen, L. Liu, Coupled DEM-SPH method for interaction between dilated polyhedral particles and fluid, Mathematical Problems in Engineering, 2019 (2019).
[39] J.P. Morris, P.J. Fox, Y. Zhu, Modeling low Reynolds number incompressible flows using SPH, J. Comput. Phys., 136(1) (1997) 214-226.
[40] Y. Zhu, P.J. Fox, J.P. Morris, A pore-scale numerical model for flow through porous media, International Journal for Numerical and Analytical Methods in Geomechanics, 23(9) (1999) 881-904.
[41] M. Ebrahimi, P. Gupta, M. Robinson, M. Crapper, M. Ramaioli, J.Y. Ooi, Comparison of coupled DEM-CFD and SPH-DEM methods in single and multiple particle sedimentation test cases, in:  PARTICLES III: proceedings of the III International Conference on Particle-Based Methods: fundamentals and applications, CIMNE, 2013, pp. 322-334.
[42] B. Nassauer, T. Liedke, M. Kuna, Development of a coupled discrete element (DEM)–smoothed particle hydrodynamics (SPH) simulation method for polyhedral particles, Computational Particle Mechanics, 3(1) (2016) 95-106.
[43] S. Natsui, A. Sawada, K. Terui, Y. Kashihara, T. Kikuchi, R.O. Suzuki, DEM-SPH study of molten slag trickle flow in coke bed, Chemical Engineering Science, 175 (2018) 25-39.
[44] J. Chen, O. Orozovic, K. Williams, J. Meng, C. Li, A coupled DEM-SPH model for moisture migration in unsaturated granular material under oscillation, International Journal of Mechanical Sciences, 169 (2020) 105313.
[45] X. Li, X. Chu, D. Sheng, A saturated discrete particle model and characteristic‐based SPH method in granular materials, International journal for numerical methods in engineering, 72(7) (2007) 858-882.
[46] U. El Shamy, S.F. Sizkow, Coupled smoothed particle hydrodynamics-discrete element method simulations of soil liquefaction and its mitigation using gravel drains, Soil Dynamics and Earthquake Engineering, 140 (2021) 106460.
[47] U. El Shamy, S.F. Sizkow, Coupled SPH-DEM simulations of liquefaction-induced flow failure, Soil Dynamics and Earthquake Engineering, 144 (2021) 106683.
[48] S.F. Sizkow, U. El Shamy, SPH-DEM simulations of saturated granular soils liquefaction incorporating particles of irregular shape, Computers and Geotechnics, 134 (2021) 104060.
[49] C.P.K. Helambage, W. Senadeera, Y. Gu, R.J. Brown, B.W. Pearce, A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying, in:  Proceedings of the Eighteenth Australasian Fluid Mechanics Conference, 2012.
[50] H. Karunasena, W. Senadeera, Y. Gu, R.J. Brown, A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying, Applied Mathematical Modelling, 38(15-16) (2014) 3781-3801.
[51] A. Fakhimi, M. Lanari, DEM–SPH simulation of rock blasting, Computers and Geotechnics, 55(0) (2014) 158-164.
[52] P.W. Cleary, G.G. Pereira, V. Lemiale, C. Delle Piane, M. Ben Clennell Multiscale model for predicting shear zone structure and permeability in deforming rock, Computational Particle Mechanics, 3(2) (2016) 179-199.
[53] H.-N. Polwaththe-Gallage, S.C. Saha, E. Sauret, R. Flower, W. Senadeera, Y. Gu, SPH-DEM approach to numerically simulate the deformation of three-dimensional RBCs in non-uniform capillaries, Biomedical engineering online, 15(2) (2016) 349-370.
[54] M.D. Sinnott, P.W. Cleary, S.M. Harrison, Peristaltic transport of a particulate suspension in the small intestine, Applied Mathematical Modelling, 44 (2017) 143-159.
[55] P.A. Cundall, Distinct element models of rock and soil structure, Analytical and Computational Methods in Engineering Rock Mechanics,  (1987) 129-163.
[56] T.B. Anderson, R. Jackson, Fluid mechanical description of fluidized beds. Equations of motion, Industrial & Engineering Chemistry Fundamentals, 6(4) (1967) 527-539.
[57] J.J. Monaghan, Smoothed particle hydrodynamics, Annual review of astronomy and astrophysics, 30 (1992) 543-574.
[58] M. Kelager, Lagrangian fluid dynamics using smoothed particle hydrodynamics, University of Copenhagen: Department of Computer Science, 2 (2006).
[59] H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Advances in computational Mathematics, 4(1) (1995) 389-396.
[60] S. Ergun, Fluid flow through packed columns, Chem. Eng. Prog., 48 (1952) 89-94.
[61] C.Y. Wen, Mechanics of fluidization, in:  Chem. Eng. Prog., Symp. Ser., 1966, pp. 100-111.
[62] P.C. Rouse, Characterisation and modelling of a uniformly graded, well-rounded coarse sand, University of British Columbia, 2005.
نشریه مهندسی عمران امیرکبیر
دوره 55، شماره 11
بهمن 1402
صفحه 2207-2226

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