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.

1.
Adams
,
F. D.
,
1912
, “
An Experimental Contribution to the Question of the Depth of the Zone of Flow in the Earth’s Crust
,”
J. Geol.
,
20
, pp.
97
118
.
2.
Cooling
,
L. F.
, and
Smith
,
D. B.
,
1936
, “
The Shearing Resistance of Soils
,”
J. of the Institution of the Civil Engineers
,
3
, pp.
333
343
.
3.
Ewy
,
R. T.
, and
Cook
,
N. G. W.
,
1990
, “
Deformation and Fracture Around Cylindrical Openings in Rock—I. Observations and Analysis of Deformations
,”
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
,
27
(
5
), pp.
387
407
.
4.
Sherwood
,
J. D.
, and
Bailey
,
L.
,
1994
, “
Swelling of Shale Around a Cylindrical Wellbore
,”
Proc. R. Soc. London, Ser. A
,
444
, pp.
161
184
.
5.
van den Hoek, P. J., Smit, D.-J., Kooijman, A. P., de Bree, Ph., Kenter, C. J., and Khodaverdian, M., 1994, “Size Dependency of Hollow-Cylinder Stability,” Proceedings SPE/ISRM Rock Mechanics in Petroleum Engineering Conference, SPE# 28051, Delft, The Netherlands, Aug. 29–31, pp. 191–198.
6.
Papamichos, E., and van den Hoek, P. J., 1995, “Size Dependency of Castlegate and Berea Sandstone Hollow-Cylinder Strength on the Basis of Bifurcation Theory,” Proc. of the 35th US Symp. on Rock Mech., Daemen and Schultz, eds., Reno, NV, June 5–7, pp. 301–306.
7.
Talesnick
,
M. L.
,
Haimson
,
B. C.
, and
Lee
,
M. Y.
,
1997
, “
Development of Radial Strains in Hollow Cylinders of Rock Subjected to Radial Compression
,”
Int. J. Rock Mech. Min. Sci.
,
34
(
8
), pp.
1229
1236
.
8.
Lee
,
D.-H.
,
Juang
,
C. H.
,
Chen
,
J.-W.
,
Lin
,
H.-M.
, and
Shieh
,
W.-H.
,
1999
, “
Stress Paths and Mechanical Behavior of a Sandstone in Hollow Cylinder Tests
,”
Int. J. Rock Mech. Min. Sci.
,
36
, pp.
857
870
.
9.
Papamichos, E., Skjærstein, A., and Tronvoll, J., 2000, “A Volumetric Sand Production Experiment,” 4th North Amer. Rock Mech. Symp., Seattle, WA, July 31–Aug. 3, pp. 303–310.
10.
Sugiyama
,
T.
,
Bremner
,
T. W.
, and
Holm
,
T. A.
,
1996
, “
Effect of Stress on Gas Permeability in Concrete
,”
ACI Mater. J.
,
93
(
5
), Sept.–Oct., pp.
443
450
.
11.
Subramaniam
,
K. V.
,
Popovics
,
J. S.
, and
Shah
,
S. P.
,
1998
, “
Testing Concrete in Torsion: Instability Analysis and Experiments
,”
J. Eng. Mech.
,
124
(
11
), pp.
1258
1268
.
12.
Taber, L. A., Yang, M., Keller, B. B., and Clark E. B., 1991, “Poroelastic Model for the Trabecular Embryonic Heart,” Proc. Winter Annual Meeting of the ASME, Bioengineering Division, Dec. 1–6, Atlanta, GA, ASME, New York, pp. 623–626.
13.
Lim
,
T.-H.
, and
Hong
,
J. H.
,
2000
, “
Poroelastic Properties of Bovine Vertebral Trabecular Bone
,”
J. Orthop. Res.
,
18
(
4
), pp.
671
677
.
14.
Kanj
,
M. Y.
, and
Abousleiman
,
Y.
,
2003
, “
The Generalized Lame´ Problem: Part I—Coupled Poromechanical Solutions
,”
ASME J. Appl. Mech.
,
71
, pp.
168
179
.
15.
Lame´, G., 1852, “Lec¸ons sur la The´orie Mathe´matique de l’E´lasticite´ des Corps Solides,” Gautheir-Villars, Paris.
16.
Kanj, M. Y., and Abousleiman, Y., 2003, “Porothermomechanics of Anisotropic Hollow Cylinders in Oedometric-Like Setups,” CD-Proceedings of the 16th ASCE Engineering Mechanics Conference, Seattle, WA, July 16–18.
17.
Kanj
,
M.
,
Abousleiman
,
Y.
, and
Ghanem
,
R.
,
2003
, “
Anisotropic Poromechanics Solutions for the Hollow-Cylinder
,”
J. Eng. Mech.
,
129
(
11
), pp.
1277
1287
.
18.
Kanj, M., and Abousleiman, Y., 2003. “Porothermoelastic Analyses of Anisotropic Hollow Cylinders,” Proceedings of the 39th U.S. Rock Mechanics Symposium (Soil Rock America 2003), Cambridge, MA, June 23–25, pp. 1211–1218.
19.
Abousleiman, Y., and Kanj, M., 2002, “Generalized Lame´ Solutions in Poromechanics,” Proceedings, Second Biot Conference in Poromechanics, Grenoble, France, Aug. 26–28, A.A. Balkema, Rotterdam, pp. 79–84.
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