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Consolidation Problems (consolidation + problem)
Selected AbstractsCoupled HM analysis using zero-thickness interface elements with double nodes,Part II: Verification and applicationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2008J. M. Segura Abstract In a companion Part I of this paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.735), a coupled hydro-mechanical (HM) formulation for geomaterials with discontinuities based on the finite element method (FEM) with double-node, zero-thickness interface elements was developed and presented. This Part II paper includes the numerical solution of basic practical problems using both the staggered and the fully coupled approaches. A first group of simulations, based on the classical consolidation problem with an added vertical discontinuity, is used to compare both the approaches in terms of accuracy and convergence. The monolithic or fully coupled scheme is also used in an application example studying the influence of a horizontal joint in the performance of a reservoir subject to fluid extraction. Results include a comparison with other numerical solutions from the literature and a sensitivity analysis of the mechanical parameters of the discontinuity. Some simulations are also run using both a full non-symmetric and a simplified symmetric Jacobian matrix. On top of verifying the model developed and its capability to reflect the conductivity changes of the interface with aperture changes, the results presented also lead to interesting observations of the numerical performance of the methods implemented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical modelling of dynamic consolidation on granular soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2008S. López-Querol Abstract The application of Pastor,Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u,w formulation), which is firstly compared with u,pw formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u,w formulation has been ascertained for this kind of dynamic problems in soils, one- and two-dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ,wave of dryness', observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd. [source] Arbitrary Lagrangian,Eulerian method for large-strain consolidation problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008Majidreza Nazem Abstract In this paper, an arbitrary Lagrangian,Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore-water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated-Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] A new mixed finite element method for poro-elasticityINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2008Maria Tchonkova Abstract Development of robust numerical solutions for poro-elasticity is an important and timely issue in modern computational geomechanics. Recently, research in this area has seen a surge in activity, not only because of increased interest in coupled problems relevant to the petroleum industry, but also due to emerging applications of poro-elasticity for modelling problems in biomedical engineering and materials science. In this paper, an original mixed least-squares method for solving Biot consolidation problems is developed. The solution is obtained via minimization of a least-squares functional, based upon the equations of equilibrium, the equations of continuity and weak forms of the constitutive relationships for elasticity and Darcy flow. The formulation involves four separate categories of unknowns: displacements, stresses, fluid pressures and velocities. Each of these unknowns is approximated by linear continuous functions. The mathematical formulation is implemented in an original computer program, written from scratch and using object-oriented logic. The performance of the method is tested on one- and two-dimensional classical problems in poro-elasticity. The numerical experiments suggest the same rates of convergence for all four types of variables, when the same interpolation spaces are used. The continuous linear triangles show the same rates of convergence for both compressible and entirely incompressible elastic solids. This mixed formulation results in non-oscillating fluid pressures over entire domain for different moments of time. The method appears to be naturally stable, without any need of additional stabilization terms with mesh-dependent parameters. Copyright © 2007 John Wiley & Sons, Ltd. [source] Direct, partitioned and projected solution to finite element consolidation modelsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2002Giuseppe Gambolati Abstract Direct, partitioned, and projected (conjugate gradient-like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi-CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi-CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two-dimensional (2-D) and three-dimensional (3-D) coupled consolidation problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Performance of Jacobi preconditioning in Krylov subspace solution of finite element equationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2002F.-H. Lee Abstract This paper examines the performance of the Jacobi preconditioner when used with two Krylov subspace iterative methods. The number of iterations needed for convergence was shown to be different for drained, undrained and consolidation problems, even for similar condition number. The differences were due to differences in the eigenvalue distribution, which cannot be completely described by the condition number alone. For drained problems involving large stiffness ratios between different material zones, ill-conditioning is caused by these large stiffness ratios. Since Jacobi preconditioning operates on degrees-of-freedom, it effectively homogenizes the different spatial sub-domains. The undrained problem, modelled as a nearly incompressible problem, is much more resistant to Jacobi preconditioning, because its ill-conditioning arises from the large stiffness ratios between volumetric and distortional deformational modes, many of which involve the similar spatial domains or sub-domains. The consolidation problem has two sets of degrees-of-freedom, namely displacement and pore pressure. Some of the eigenvalues are displacement dominated whereas others are excess pore pressure dominated. Jacobi preconditioning compresses the displacement-dominated eigenvalues in a similar manner as the drained problem, but pore-pressure-dominated eigenvalues are often over-scaled. Convergence can be accelerated if this over-scaling is recognized and corrected for. Copyright © 2002 John Wiley & Sons, Ltd. [source] Hybrid and enhanced finite element methods for problems of soil consolidationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007X. X. Zhou Abstract Hybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement-based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method can be easily extended to non-linear consolidation problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||