Solutions for the stress and pore pressure p are derived due to sudden introduction of a plane strain shear dislocation on a leaky plane in a linear poroelastic, fluid-infiltrated solid. For a leaky plane, y=0, the fluid mass flux is proportional to the difference in pore pressure across the plane requiring that Δp=Rp/y, where R is a constant resistance. For R=0 and R, the expressions for the stress and pore pressure reduce to previous solutions for the limiting cases of a permeable or impermeable plane, respectively. Solutions for the pore pressure and shear stress on and near y=0 depend significantly on the ratio of x and R. For the leaky plane, the shear stress at y=0 initially increases from the undrained value, as it does from the impermeable plane, but the peak becomes less prominent as the distance x from the dislocation increases. The slope (σxy/t) at t=0 for the leaky plane is always equal to that of the impermeable plane for any large but finite x. In contrast, the slope σxy/t for the permeable fault is negative at t=0. The pore pressure on y=0 initially increases as it does for the impermeable plane and then decays to zero, but as for the shear stress, the increase becomes less with increasing distance x from the dislocation. The rate of increase at t=0 is equal to that for the impermeable fault.

References

References
1.
Pan
,
E.
,
1991
, “
Dislocation in an Infinite Poroelastic Medium
,”
Acta Mech.
,
87
(
1–2
), pp.
105
115
.
2.
Zheng
,
P.
, and
Ding
,
B.
,
2015
, “
Body Force and Fluid Source Equivalents for Dynamic Dislocations in Fluid-Saturated Porous Media
,”
Transport Porous Med.
,
107
(
1
), pp.
1
12
.
3.
Wang
,
Z.
, and
Hu
,
H.
,
2016
, “
Moment Tensors of a Dislocation in a Porous Medium
,”
Pure Appl. Geophys.
,
173
(
6
), pp.
2033
2045
.
4.
Booker
,
J. R.
,
1974
, “
Time-Dependent Strain Following Faulting of a Porous Medium
,”
J. Geophys. Res.
,
79
(
14
), pp.
2037
2044
.
5.
Rice
,
J. R.
, and
Cleary
,
M. P.
,
1976
, “
Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media With Compressible Constituents
,”
Rev. Geophys. Space Phys.
,
14
(
2
), pp.
227
241
.
6.
Rudnicki
,
J. W.
,
1987
, “
Plane strain Dislocations in Linear Elastic Diffusive Solids
,”
ASME J. Appl. Mech.
,
54
(
3
), pp.
545
552
.
7.
Rice
,
J. R.
, and
Simons
,
D. A.
,
1976
, “
The Stabilization of Spreading Shear Faults by Coupled Deformation-Diffusion Effects in Fluid-Infiltrated Porous Materials
,”
J. Geophys. Res.
,
81
(
29
), pp.
5322
5334
.
8.
Simons
,
D. A.
,
1977
, “
Boundary Layer Analysis of Propagating Mode II Cracks in Porous Elastic Media
,”
J. Mech. Phys. Solids
,
25
(
2
), pp.
99
115
.
9.
Rudnicki
,
J. W.
, and
Koutsibelas
,
D. A.
,
1991
, “
Steady Propagation of Plane Strain Shear Cracks on an Impermeable Plane in an Elastic Diffusive Solid
,”
Int. J. Solids Struct.
,
27
(
2
), pp.
205
225
.
10.
Rudnicki
,
J. W.
,
1991
, “
Boundary Layer Analysis of Plane Strain Shear Cracks Propagating Steadily on an Impermeable Plane in an Elastic Diffusive Solid
,”
J. Mech. Phys. Solids
,
39
(
2
), pp.
201
221
.
11.
Rudnicki
,
J. W.
, and
Roeloffs
,
E. A.
,
1990
, “
Plane-Strain Shear Dislocations Moving Steadily in Linear Elastic Diffusive Solids
,”
ASME J. Appl. Mech.
,
57
(
1
), pp.
32
39
.
12.
Rudnicki
,
J. W.
, and
Rice
,
J. R.
,
2006
, “
Effective Normal Stress Alteration Due to Pore Pressure Changes Induced by Dynamic Slip Propagation on a Plane Between Dissimilar Materials
,”
J. Geophys. Res.
,
111
(B10), p.
B10308
.
13.
Biot
,
M. A.
,
1941
, “
General Theory of Three-Dimensional Consolidation
,”
J. Appl. Phys.
,
12
(
2
), pp.
155
164
.
14.
Wang
,
H.
,
2000
,
Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrology
,
Princeton University Press
,
Princeton, NJ
.
15.
Anand
,
L.
,
2015
, “
2014 Drucker Medal Paper: A Derivation of the Theory of Linear Poroelasticity From Chemoelasticity
,”
ASME J. Appl. Mech
,
82
(
11
), p.
111005
.
16.
Detournay
,
E.
, and
Cheng
,
A. H.-D.
,
1993
, “
Fundamentals of Poroelasticity
,”
Comprehensive Rock Engineering: Principles, Practice and Projects
,
J. A.
Hudson
, ed., Vol.
2
,
Pergamon Press
,
Oxford, UK
, pp.
113
171
.
17.
Cheng
,
A. H.-D.
,
2016
,
Poroelasticity
,
Springer International Publishing
,
Heidelberg, Germany
.
18.
Erdélyi
,
A.
,
Magnus
,
W.
,
Oberhettinger
,
F.
, and
Tricomi
,
F.
,
1954
,
Tables of Integral Transforms, Vols. 1 and 2
,
McGraw-Hill
,
New York
.
19.
Abramowitz
,
M.
, and
Stegun
,
I. A.
, eds.,
1964
,
Handbook of Mathematical Functions, Appl. Math. Ser. 55
,
National Bureau of Standards
,
Washington, DC
.
20.
Chester
,
F. M.
,
Chester
,
J. S.
,
Kirschner
,
D. L.
,
Schulz
,
S. E.
, and
Evans
,
J. P.
,
2004
, “
Structure of Large-Displacement, Strike-Slip Fault Zones in the Brittle Continental Crust
,”
Rheology and Deformation in the Lithosphere at Continental Margins
,
G. D.
Karner
, ed.,
Columbia University Press
,
New York
, pp.
223
260
.
21.
Rice
,
J. R.
,
2006
, “
Heating and Weakening of Faults During Earthquake Slip
,”
J. Geophys. Res.
,
111
(
B5
), p.
B05311
.
22.
Rice
,
J. R.
,
Rudnicki
,
J. W.
, and
Platt
,
J. D.
,
2014
, “
Stability and Localization of Rapid Shear in Fluid-Saturated Fault Gouge: 1. Linearized Stability Analysis
,”
J. Geophys. Res.
,
119
(
B5
), pp.
4311
4333
.
23.
Wibberley
,
C. A. J.
, and
Shimamoto
,
T.
,
2003
, “
Internal Structure and Permeability of Major Strike-Slip Fault Zones: The Median Tectonic Line in Mie Prefecture, Southwest Japan
,”
J. Struct. Geol.
,
25
(
1
), pp.
59
78
.
24.
Mandel
,
J.
,
1953
, “
Consolidation des sols (Étude Mathématique)
,”
Geotechnique
,
3
(
7
), pp.
287
299
.
25.
Rudnicki
,
J. W.
,
1986
, “
Slip on an Impermeable Fault in a Fluid-Saturated Rock Mass
,”
Earthquake Source Mechanics
(Geophysical Monograph),
Das
,
J.
,
Boatwright
,
J.
, and
Scholz
,
C. H.
, eds, Vol.
37
,
American Geophysical Union
,
Washington, DC
, pp.
81
89
.
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