Journal ArticleDOI
An investigation of the stability of numerical solutions of Biot's equations of consolidation
John R. Booker,John C. Small +1 more
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In this article, a finite element formulation based on approximation in the Laplace transform space, is given for Biot's Consolidation theory and conditions under which these integration schemes are stable are investigated.About:
This article is published in International Journal of Solids and Structures.The article was published on 1975-07-01. It has received 201 citations till now. The article focuses on the topics: Biot number & Numerical stability.read more
Citations
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Book ChapterDOI
Fundamentals of Poroelasticity
TL;DR: In this paper, the authors focus on the fundamentals of poroelasticity, and discuss the formulation and analysis of coupled deformation-diffusion processes, within the framework of the Biot theory of pore elasticity.
Journal ArticleDOI
Analysis of rigid rafts supported by granular piles
N. P. Balaam,John R. Booker +1 more
TL;DR: In this article, an analytic solution using the theory of elasticity is developed for the settlement of the foundation and expressions for evaluating the moment and shear distributions across the foundation are given.
Journal ArticleDOI
An accuracy condition for consolidation by finite elements
TL;DR: In this paper, a lower limit for the time steps is derived, in terms of the mesh size and the coefficient of consolidation near the draining boundary, for finite element solutions of consolidation problems.
Journal ArticleDOI
On stability and convergence of finite element approximations of biot's consolidation problem
TL;DR: In this paper, a family of decay functions, parametrized by the number of time steps, is derived for the fully discrete backward Euler-Galerkin formulation, showing that the pore-pressure oscillations, arising from an unstable approximation of the incompressibility constraint on the initial condition, decay in time.
Journal ArticleDOI
Minimization principles for the coupled problem of Darcy–Biot-type fluid transport in porous media linked to phase field modeling of fracture
TL;DR: In this paper, the authors developed new minimization and saddle point principles for the coupled problem of Darcy-Biot-type fluid transport in porous media at fracture and showed that the quasi-static problem of elastically deforming, fluid-saturated porous media is related to a minimization principle for the evolution problem.
References
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Journal ArticleDOI
General Theory of Three‐Dimensional Consolidation
TL;DR: In this article, the number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three-dimensional problems.
Journal ArticleDOI
General solutions of the equations of elasticity and consolidation for a porous material
TL;DR: In this paper, general solutions of these equations for the isotropic case are developed, giving directly the displacement field or the stress field in analogy with the Boussinesq-Papkovitch solution and the stress functions of the theory of elasticity.
Journal ArticleDOI
Theory of deformation of a porous viscoelastic anisotropic solid
TL;DR: In this article, the deformation of a viscoelastic porous solid containing a viscous fluid was studied under the most general assumptions of anisotropy, and the particular cases of transverse and complete isotropy were discussed.
Journal ArticleDOI
Consolidation Des Sols (Étude Mathématique)
TL;DR: In this article, Terzaghi has given the solution of the problem of the settlement of a stratum of clay in a particular case, i.e., that of the stratum subjected to a normal uniform pressure.