Poroelastic Solution for an Inclined Borehole

1997 ◽  
Vol 64 (1) ◽  
pp. 32-38 ◽  
Author(s):  
L. Cui ◽  
A. H-D. Cheng ◽  
Y. Abousleiman
Keyword(s):  
Analytical Solution ◽  
Plane Strain ◽  
Antiplane Shear ◽  
Far Field ◽  
Poroelastic Medium ◽  
Principal Stresses ◽  
Decomposition Scheme ◽  
Shear Problem ◽  
Inclined Borehole

The analytical solution for an infinitely long borehole in an isotropic, poroelastic medium, inclined to the far-field principal stresses, is presented. The solution utilizes a loading decomposition scheme which leads to three fundamental problems: a poroelastic plane-strain, an elastic uni-axial, and an elastic antiplane shear problem.

scholarly journals A Study on Modelling the Plane Strain Behaviour of Sand and its Stability

2012 ◽  
Vol 59 (3-4) ◽  
pp. 85-100 ◽  
Author(s):  
Andrzej Sawicki ◽  
Justyna Sławinska
Keyword(s):  
Plane Strain ◽  
3D Model ◽  
Original Model ◽  
Governing Equations ◽  
Principal Stresses ◽  
Full System ◽  
Incremental Model ◽  
Strain Behaviour ◽  
Incremental Equations ◽  
Principal Strains

Abstract The plane strain behaviour of sand is studied using, previously proposed, incremental model describing its pre-failure deformations. Original model has been formulated for the tri-axial configuration, and then generalized for 3D conditions. This 3D model was subsequently adapted to study deformations of sand in the plane strain conditions, in the x1; x3 plane. There are three unknowns in such a configuration, namely the principal strains "1; "3 and the principal stress σ2. Respective equations were derived, and then applied to study deformations of sand for chosen stress paths. The governing incremental equations were integrated numerically, and it was shown, for some loading paths, that σ2 epends linearly on the other principal stresses, so introduction of apparent Poisson’s ratio is justified, as a kind of approximation. Subsequent analysis of deformations of sand was performed using this concept, as well as using full system of governing equations.

Finite plane strain

1953 ◽  
Vol 246 (910) ◽  
pp. 181-213 ◽  
Keyword(s):  
Plane Strain ◽  
Strain Energy Function ◽  
General System ◽  
Infinite Body ◽  
Approximation Process ◽  
Elastic Deformations ◽  
Circular Rigid Inclusion ◽  
Incompressible Materials ◽  
Shear Problem ◽  
Finite Elastic Deformations

A general theory of plane strain, valid for large elastic deformations of isotropic materials, is developed using a general system of co-ordinates. No restriction is imposed upon the form of the strain-energy function in the formulation of the basic theory, apart from that arising naturally from the assumption of plane strain. In applications, attention is confined to incompressible materials, and the general method of approach is illustrated by the examination of a number of problems which are capable of exact solution. These include the flexure of a cuboid, and of an initially curved cuboid, and a generalization of the shear problem. A method of successive approximation is then evolved, suitable for application to problems for which exact solutions are not readily obtainable. Attention is again confined to incompressible materials, and the approximation process is terminated when the second-order terms have been obtained. In considering problems in plane strain, complex variable techniques are employed and the stress and displacement functions are expressed in terms of complex potential functions. In dealing with finite elastic deformations, a complex co-ordinate system may be chosen which is related either to points in the deformed body or to points in the undeformed body, and in the present paper both methods are developed. The theory is applied to obtain solutions for an infinite body which contains either a circular hole or a circular rigid inclusion, and which is under a uniform tension at infinity.

On an Integral Solution of the Antiplane Shear Problem

1998 ◽  
Vol 3 (3) ◽  
pp. 319-330
Author(s):  
Peter Schiavone ◽  
Xiaofeng Shen
Keyword(s):  
Integral Solution ◽  
Antiplane Shear ◽  
Shear Problem

scholarly journals The Path-Independent M Integral Implies the Creep Closure of Englacial and Subglacial Channels

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Colin R. Meyer ◽  
John W. Hutchinson ◽  
James R. Rice
Keyword(s):  
Antiplane Shear ◽  
Far Field ◽  
Overburden Pressure ◽  
Hydrologic Systems ◽  
Path Independence ◽  
Essential Components ◽  
Drainage Channels ◽  
Stress States ◽  
Independent Integral ◽  
M Integral

Drainage channels are essential components of englacial and subglacial hydrologic systems. Here, we use the M integral, a path-independent integral of the equations of continuum mechanics for a class of media, to unify descriptions of creep closure under a variety of stress states surrounding drainage channels. The advantage of this approach is that the M integral around the hydrologic channels is identical to same integral evaluated in the far field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g., involving antiplane shear as well as overburden pressure. We start by analyzing the axisymmetric case and show that the Nye solution for the creep closure of the channels is implied by the path independence of the M integral. We then examine the effects of superimposing antiplane shear. We show that the creep closure of the channels acts as a perturbation in the far field, which we explore analytically and numerically. In this way, the creep closure of channels can be succinctly written in terms of the path-independent M integral, and understanding the variation with applied shear is useful for glacial hydrology models.

Analytical solution for active pressure of narrow backfills considering arching effect

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sahar Ghobadi ◽  
Hadi Shahir
Keyword(s):  
Analytical Solution ◽  
Retaining Wall ◽  
Earth Pressure ◽  
Back Surface ◽  
Active Earth Pressure ◽  
Soil Pressure ◽  
Principal Stresses ◽  
Content Type ◽  
Arching Effect ◽  
Lateral Earth Pressure

Purpose The purpose of this paper is to study the distribution of active earth pressure in retaining walls with narrow cohesion less backfill considering arching effects. Design/methodology/approach To this end, the approach of principal stresses rotation was used to consider the arching effects. Findings According to the presented formulation, the active soil pressure distribution is nonlinear with zero value at the wall base. The proposed formulation implies that by increasing the frictional forces at both sides of the backfill, the arching effect is increased and so, the lateral earth pressure on the retaining wall is decreased. Also, by narrowing the backfill space, the lateral earth pressure is extremely decreased. Originality/value A comprehensive analytical solution for the active earth pressure of narrow backfills is presented, such that the effects of the surcharge and the characteristics of the stable back surface are considered. The magnitude and height of the application of lateral active force are also derived.

scholarly journals 2D Plane Strain Consolidation Process of Unsaturated Soil with Vertical Impeded Drainage Boundaries

Processes ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 5 ◽  
Author(s):  
Minghua Huang ◽  
Dun Li
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Plane Strain ◽  
Unsaturated Soil ◽  
Analytical Solutions ◽  
Soil Layer ◽  
Permeability Ratio ◽  
Consolidation Process ◽  
The Time Domain ◽  
Excess Pore Pressures

The consolidation process of soil stratum is a common issue in geotechnical engineering. In this paper, the two-dimensional (2D) plane strain consolidation process of unsaturated soil was studied by incorporating vertical impeded drainage boundaries. The eigenfunction expansion and Laplace transform techniques were adopted to transform the partial differential equations for both the air and water phases into two ordinary equations, which can be easily solved. Then, the semi-analytical solutions for the excess pore-pressures and the soil layer settlement were derived in the Laplace domain. The final results in the time domain could be computed by performing the numerical inversion of Laplace transform. Furthermore, two comparisons were presented to verify the accuracy of the proposed semi-analytical solutions. It was found that the semi-analytical solution agreed well with the finite difference solution and the previous analytical solution from the literature. Finally, the 2D plane strain consolidation process of unsaturated soil under different drainage efficiencies of the vertical boundaries was illustrated, and the influences of the air-water permeability ratio, the anisotropic permeability ratio and the spacing-depth ratio were investigated.

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