B-bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media
Summary The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and...
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| Published in | International journal for numerical and analytical methods in geomechanics Vol. 40; no. 6; pp. 962 - 984 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Bognor Regis
Blackwell Publishing Ltd
25.04.2016
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0363-9061 1096-9853 |
| DOI | 10.1002/nag.2472 |
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| Abstract | Summary
The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. |
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| AbstractList | Summary The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u - w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B-bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. Summary The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u - w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B-bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. |
| Author | Navas, Pedro Li, Bo Yu, Rena C. López-Querol, Susana |
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| Notes | Consejería de Educación, Cultura y Deportes de la Junta de Comunidades de Castilla-La Mancha, Fondo Europeo de Desarrollo Regional - No. PEII-2014-016-P; No. BES2013-0639 ark:/67375/WNG-G30LNMGX-D Ministerio de Ciencia e Innovación - No. BIA2012-31678; No. MAT2012-35416 ArticleID:NAG2472 istex:0E9DDF35648EE64673FB34ABD690CFE8B4783E0B ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
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| PublicationTitle | International journal for numerical and analytical methods in geomechanics |
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| Publisher | Blackwell Publishing Ltd Wiley Subscription Services, Inc |
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| References_xml | – reference: Li G, Ge J, Jie Y. Free surface seepage analysis based on the element-free method. Mechanics Research Communications 2003; 30:9-19. – reference: Ganapathi M, Patel BP, Boisse P, Touratier M. Non-linear dynamic stability characteristics of elastic plates subjected to periodic in-plane load. International Journal of Non-Linear Mechanics 2000; 35:467-480. – reference: Artioli E, Castellazzi G, Krysl P. Assumed strain nodally integrated hexahedral finite element formulations for elastoplastic applications. International Journal for Numerical Methods in Engineering 2014; 99(11):844-866. – reference: Simo JC, Hughes TJR. On the variational foundations of assumed strain methods. Journal of Applied Mechanics 1986; 53(1):51-54. – reference: Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering 1990; 29:1595-1638. – reference: Bonet J, Burton AJ. A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. Communications in Numerical Methods in Engineering 1998; 14(5):437-449. – reference: Simo JC, Tarnow N, Wong KK. Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering 1992; 100:63-116. – reference: Harr ME. Groundwater and Seepage. McGraw-Hill, Inc.: New York, 1962. – reference: Nelder JA, Mead R. A simplex method for function minimization. Computer Journal 1965; 7:308-313. – reference: Bazyar MH, Talebi A. Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite-element method. International Journal for Numerical and Analytical Methods in Geomechanics 2015; 39:1-22. – reference: Ibrahimbegovic A, Al Mikdad M. Finite rotations in dynamics of beams and implicit time-stepping schemes. International Journal for Numerical Methods in Engineering 1998; 41:781-814. – reference: Wang Y, Hu M, Zhou Q, Rutqvist J. Energy-work-based numerical manifold seepage analysis with an efficient scheme to locate the phreatic surface. International Journal for Numerical and Analytical Methods in Geomechanics 2014; 38:1633-1650. – reference: Blanc Thomas, Hydrodynamics ManuelPastor. AstablizedSmoothedParticle. Taylor-Galerkin algorithm for soil dynamics problems. International Journal for Numerical and Analytical Methods in Geomechanics 2013; 37:1-30. – reference: Newmark NM. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division - ASCE 1959; 85:67-94. – reference: Kim J, Wang W, Regueiro RA. Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain. International Journal for Numerical and Analytical Methods in Geomechanics 2015; 39:1073-1103. – reference: Sulsky D, Chen Z, Schreyer HL. A particle method for history-dependent materials. Computer Methods in Applied Mechanics and Engineering 1994; 118:179-196. – reference: Navas P, López-Querol S. Generalized unconfined seepage flow model using displacement based formulation. Engineering Geology 2013; 166:140-141. – reference: Casagrande A. Seepage through dams. New England Water Works 1937; 51(2):131-172. – reference: Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-Frequency range. Journal of the Acoustical Society of America 1956; 28(2):168-178. – reference: Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics - theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 1977; 181:375-389. – reference: Biot MA. General solutions of the equations of elasticity and consolidation for a porous material. Journal of Applied Mechanics 1956: 91-96. – reference: Arroyo M, Ortiz M. Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. International Journal for Numerical Methods in Engineering 2006; 65(13):2167-2202. – reference: Terzaghi KV. Principles of soil mechanics. Engineering News-Record 1925; 95:19-27. – reference: Pastor M, Blanc T, Haddad B, Petrone S, Sanchez Morales M, Drempetic V, Issler D, Crosta GB, Cascini L, Sorbino G, Cuomo S. Application of an SPH depth-integrated model to landslide run-out analysis. Landslides 2014; 11(5):793-812. – reference: Hauret P, Kuhl E, Ortiz M. Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. International Journal for Numerical Methods in Engineering 2007; 73:253-294. – reference: López-Querol S, Navas P, Peco J, Arias-Trujillo J. 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The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous... Summary The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous... The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media.... |
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| SubjectTerms | Algorithms Earth dams free surface Free surfaces Joining Mathematical analysis Mathematical models Maximum entropy Media meshfree Meshless methods Pore water Porous media Seepage Soil columns u − w formulation |
| Title | B-bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media |
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