The Generalized Lame´ Problem—Part II: Applications in Poromechanics

2004 ◽  
Vol 71 (2) ◽  
pp. 180-189 ◽  
Author(s):  
Younane N. Abousleiman ◽  
Mazen Y. Kanj
Keyword(s):  
Plane Strain ◽  
Laboratory Testing ◽  
Infinite Medium ◽  
Time Dependent ◽  
Solid Cylinder ◽  
Testing Procedures ◽  
Lamé Problem ◽  
Essential Problem ◽  
Generalized Plane Strain ◽  
Borehole Core

The cylinder is the geometry most widely used in laboratory testing procedures for rocks and other geomaterials. This paper applies a unified and universal Lame´ solution to all the three recognized right-cylindrical problems in poromechanics. As such, the solution of the hollow-cylinder features itself converging asymptotically to the exact values predicted by the solutions of the two other essential problem setups in geomechanics; namely, the finite solid cylinder case and the borehole core in an infinite medium. The time-dependent response derivations were “scripted” within the frameworks of the Biot’s theory of linear poroelasticity and facilitated by the governing generalized plane-strain (GPS) principle.

The Generalized Lame´ Problem—Part I: Coupled Poromechanical Solutions

2004 ◽  
Vol 71 (2) ◽  
pp. 168-179 ◽  
Author(s):  
Mazen Y. Kanj ◽  
Younane N. Abousleiman
Keyword(s):  
Plane Strain ◽  
Hollow Cylinder ◽  
Closed Form Solution ◽  
Confining Pressure ◽  
Special Problem ◽  
Form Solution ◽  
Geomechanical Properties ◽  
Lamé Problem ◽  
Loading Modes ◽  
Generalized Plane Strain

Cylindrical geometries are known to present special problem simulation capabilities in engineering design. (For example, solid and hollow cylinder tests are routinely studied in soil and rock mechanics to gain insights into the geomechanical properties and to assess the stability of boreholes and cylindrical openings in the project design geomedia.) This paper identifies a unified and universal solution to all the three recognized right-cylindrical problem objects in poromechanics. A closed-form solution to the problem of the finite, homogeneous, isotropic, fully saturated, thick-walled hollow cylinder subjected to various loading modes is readily presented and described. The assumed loading modes encompass arbitrary temporal functions of uniformly distributed inner/outer pore pressure, inner/outer confining pressure, inner/outer deviatoric stress, and end axial compaction or extension. The time-dependent response derivations are outlined within the frameworks of the Biot’s theory of linear poroelasticity and facilitated by the governing generalized plane-strain (GPS) principle. The (as presented) solution is shown to converge asymptotically to those of the two essential problem setups in geomechanics: the finite solid cylinder and the borehole core in an infinite medium. As such, a complete/explicit solution to a generalized statement of the Lame´ problem is presented. The solution utilizes a fairly simple loading decomposition scheme which leads to two basic problem forms: a generalized poroelastic axisymmetric problem and a generalized, plane-strain, poroelastic deviatoric problem.

Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Vinh X. Nguyen ◽  
Younane N. Abousleiman
Keyword(s):  
Plane Strain ◽  
Laboratory Testing ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Dual Porosity ◽  
External Loading ◽  
Two Dimensional ◽  
Loading Conditions ◽  
Type Problem ◽  
Secondary Porosity

The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.

scholarly journals Effect of Static Stress on Plane Strain Vibrations in Poroelastic Solid Cylinder

2015 ◽  
Vol 127 ◽  
pp. 727-734
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Plane Strain ◽  
Static Stress ◽  
Solid Cylinder

The Snow Ski as a Dynamic System

1972 ◽  
Vol 94 (2) ◽  
pp. 133-138 ◽  
Author(s):  
R. L. Piziali ◽  
C. D. Mote
Keyword(s):  
Dynamic System ◽  
Laboratory Testing ◽  
Research Laboratory ◽  
Field Measurements ◽  
Static System ◽  
Testing Procedures ◽  
Future Design ◽  
Meaningful Information ◽  
Physical Information ◽  
System Characteristics

Paper reports research on dynamic system characteristics of snow skis. Laboratory and field measurements of frequency response, running surface pressure excitation, and static system characteristics are intended to provide a data base of physical information to guide future design and research. Laboratory testing procedures used give meaningful information for “straight running” but not for “turning.” In general, the turning and straight running maneuvers must be examined independently. This paper summarizes the general research observations with a minimum of detail included.

scholarly journals Generalized Plane Strain Elasticity Problems

1995 ◽  
Author(s):  
A.H.-D. Cheng ◽  
J.J. Rencis ◽  
Y. Abousleiman
Keyword(s):  
Plane Strain ◽  
Elasticity Problems ◽  
Generalized Plane Strain

A note on disturbances in a layered medium containing a magnetic field

1964 ◽  
Vol 54 (6A) ◽  
pp. 1771-1777
Author(s):  
D. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Layered Medium ◽  
Present Note ◽  
Infinite Medium ◽  
The Other ◽  
Time Dependent ◽  
The Earth ◽  
Propagation Of Waves ◽  
Initial Magnetic Field

abstract In recent years, Kaliski has contributed a series of papers on the interaction of elastic and magnetic fields and some of them, [1], [2], [3] are concerned with the propagation of waves in a semi-infinite medium either loaded or conditioned otherwise, at its free surface. Such problems, as Kaliski [1] has remarked, may have relevance in the practical seismic problem of detecting the mechanical explosions inside the earth. Moreover, their geophysical implications have also been examined by Knopoff [4[, Cagniard [5], Banos [6], and Rikitake [7]. The present note seeks to investigate disturbances in a medium consisting of two layers (one finite and the other infinite) of elastic medium intervened by a thin layer of vacuum. The vacuum is traversed by an initial magnetic field. The disturbances in the medium are assumed to have been produced by a time-dependent load on the free surface of the medium. The method of Laplace transform has been used to facilitate the solution of the problem.

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