Abstract

This review article discusses the applications of poroelasticity to the mechanics of faulting and failure in geomaterials. Values of material parameters inferred from laboratory and field studies are summarized. Attention is focused on solutions for shear dislocations and shear cracks. A common feature is that undrained response, invoked by rapid slip or deformation, is stiffer than drained response, which occurs for slower slip or deformation. The time and spatial variation of the stress and pore pressure is different for slip on permeable and impermeable planes. These solutions are applied to interpretation of water well level changes due to slip, earthquake precursory processes, and stabilization of spreading slip zones. Inclusion models for reservoirs, aquifers, and other inhomogeneities are formulated and the results are applied to stress and strain changes caused by fluid mass injection or withdrawal.

References

1.
Kerr
RA
(
1993
),
Looking-deeply-into the Earth’s crust in Europe
,
Science
261
,
295
297
.
2.
Kerr
RA
(
1994
),
German super-deep hole hits bottom
,
Science
266
,
545
545
.
3.
Kennedy
BM
,
Kharaka
YK
,
Evans
WC
,
Ellwood
A
,
DePaolo
DJ
,
Thordsen
J
,
Ambats
G
, and
Mariner
RH
(
1997
),
Mantle fluids in the San Andreas Fault system, California
,
Science
278
,
1278
1281
.
4.
Rudnicki
JW
(
2000
),
Geomechanics
,
Int. J. Solids Struct.
37
,
349
358
.
5.
Roeloffs
EA
(
1988
),
Hydrologic precursors to earthquakes: A review
,
Pure Appl. Geophys.
126
,
177
209
.
6.
Roeloffs EA (1996), Poroelastic methods in the study of earthquake-related phenomena, in Advances in Geophysics, Dmowska R (ed), Academic Press, San Diego CA 37, 135–195.
7.
Hickman
SR
,
Sibson
R
, and
Bruhn
R
(
1995
),
Introduction to special section: Mechanical involvement of fluids in faulting
,
J. Geophys. Res.
100
,
831
12
.
8.
Ingebritsen
SE
and
Rojstaczer
SA
(
1993
),
Controls on geyser periodicity
,
Science
262
,
889
892
.
9.
Johnson CE (1979), I. CEDAR—An approach to the computer automation of short-period local seismic networks: II Seismotectonics of the Imperial Valley of sourthern California, PhD Thesis, California Inst of Tech, Pasadena CA.
10.
Elsworth
D
and
Voight
B
(
1992
),
Theory of dike intrusion in a saturated porous solid
,
J. Geophys. Res.
97
,
9105
9117
.
11.
Elsworth D, Voight B, Ouyang Z, and Piggott AR (1996), Poroelastic response resulting from magma intrusion, in Mechanics of Poroelastic Media, APS Selvadurai (ed), Kluwer Academic Publ, Netherlands, 215–233.
12.
Blakeslee S (1992), Quake theory attacks prevailing wisdom on how faults slide, New York Times, April 14, pp. B5, B8.
13.
Kerr
RA
(
1992
),
Weak faults: Breaking out all over
,
Science
255
,
1210
1212
.
14.
Zhao
D
,
Kanamori
H
,
Negishi
H
, and
Wiens
D
(
1996
),
Tomography of the source area of the 1995 Kobe earthquake: Evidence for fluids at the hypocenter?
,
Science
274
,
1891
1894
.
15.
Peltzer
G
,
Rosen
P
,
Rogez
F
, and
Hudnut
K
(
1996
),
Postseismic rebound in fault step-overs caused by pore fluid flow
,
Science
273
,
1202
1204
.
16.
King
C-Y
,
Koizumi
N
, and
Kitagawa
Y
(
1995
),
Hydrochemical anomalies and the 1995 Kobe earthquake
,
Science
269
,
38
39
.
17.
Wawersik WR, Rudnicki JW, Dove P, Harris J, Logan JM, Pyrak-Nolte L, Orr FM Jr, Ortoleva PJ, Richter F, Warpinski NR, Wilson JL, and Wong T-f (2000), Terrestrial sequestration of CO2: An assessment of research needs, in Advances in Geophysics, Dmowska R (ed), 43, 97–177.
18.
Biot
MA
(
1941
),
General theory of three dimensional consolidation
,
J. Appl. Phys.
12
,
155
164
.
19.
Detournay E and AH-D Cheng (1991), Fundamentals of poroelasticity, in Comprehensive Rock Engineering: Principles, Practice & Projects, Hudson JA (ed), Pergamon New York, Vol 2, Ch 5, 113–171.
20.
Coussy O (1995), Mechanics of Porous Continua, New York: Wiley.
21.
Wang HF (2000), Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrology, Princeton Univ Press, 276 pp.
22.
Rice
JR
and
Cleary
MP
(
1976
),
Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents
,
Rev. Geophys. Space Phys.
14
,
227
241
.
23.
Coussy
O
,
Dormieux
L
, and
Detournay
E
(
1998
),
From mixture theory to Biot’s approach for porous media
,
Int. J. Solids Struct.
35
,
4619
4635
.
24.
Biot
MA
(
1973
),
Nonlinear and semilinear rheology of porous solids
,
J. Geophys. Res.
78
,
4924
4937
.
25.
Rice
JR
(
1975
),
On the stability of dilatant hardening for saturated rock masses
,
J. Geophys. Res.
80
,
1531
1536
.
26.
Nur
A
and
Byerlee
JD
(
1971
),
An exact effective stress law for elastic deformation of rock with fluids
,
J. Geophys. Res.
76
,
6414
6419
.
27.
Cornet FH and Fairhurst C (1974), Influence of pore pressure on the deformation behavior of saturated rocks, in Proc of 3rd Congress of the Int Soc for Rock Mechanics, Vol 1, Part B, 638–644, National Academy of Sciences, Washington DC.
28.
Biot
MA
and
Willis
DG
(
1957
),
The elastic coefficients of the theory of consolidation
,
ASME J. Appl. Mech.
24
,
594
601
.
29.
Geertsma J (1966), Problems of rock mechanics in petroleum engineering, in Proc of 1st Congress Int Soc of Rock Mechanics, Lisbon: Labatorio Nacional de Engenharia Civil, National Laboratory of Civil Engineering, Lisbon, 585–594.
30.
Geertsma
J
(
1973
),
Land subsidence above compacting oil and gas reservoirs
,
J. Pet. Technol.
25
,
734
744
.
31.
Segall
P
(
1989
),
Earthquakes triggered by fluid extraction
,
Geology
17
,
942
946
.
32.
Segall
P
(
1992
),
Induced stresses due to fluid extraction from axisymmetric reservoirs
,
Pure Appl. Geophys.
139
,
535
560
.
33.
Segall
P
,
Grasso
JR
, and
Mossop
A
(
1994
),
Poroelastic stressing and induced seismicity near the Lacq gas field, southwestern France
,
J. Geophys. Res.
99
,
423
15
.
34.
Rice JR (1980), Pore fluid processes in the mechanics of earthquake rupture, in Solid Earth Geophysics and Geotechnology, Nemat-Nasser S (ed), ASME Applied Mechanics Vol. 37, 81–89.
35.
Rudnicki
JW
(
1986
),
Fluid mass sources and point forces in linear elastic diffusive solids
,
Mech. Mater.
5
,
383
393
.
36.
Rudnicki JW (1996), Moving and stationary dislocations in poroelastic solids and applications to aseismic slip in the Earth’s crust, in Mechanics of Poroelastic Media, Selvadurai APS (ed), Kluwer Academic Publ, Netherlands, 3–22.
37.
Cleary
MP
(
1977
),
Fundamental solutions for a fluid-saturated porous solid
,
Int. J. Solids Struct.
13
,
785
808
.
38.
Segall
P
(
1985
),
Stress and subsidence resulting from subsurface fluid withdrawal in the epicentral region of the 1983 Coalinga earthquake
,
J. Geophys. Res.
90
,
6801
6816
.
39.
Roeloffs E (1982), Elasticity of saturated porous rocks: Laboratory measurements and a crack problem, PhD thesis, Univ of Wisconsin, Madison, WI.
40.
Fatt
I
(
1958
),
The compressibility of sandstones at low to moderate pressures
,
Bull. Am Assoc. Pet. Geol.
42
,
1924
1957
.
41.
Fatt
I
(
1959
),
The Biot-Willis coefficients for a sandstone
,
ASME J. Appl. Mech.
26
,
296
297
.
42.
Mann
KL
and
Fatt
I
(
1960
),
Effects of pore fluids on the elastic properties of sandstone
,
Geophysics
25
,
433
444
.
43.
Roeloffs
EA
and
Rudnicki
JW
(
1984
/85),
Coupled deformation-diffusion effects on water-level changes due to propagating creep waves
,
Pure Appl. Geophys.
122
,
560
582
.
44.
Roeloffs
EA
(
1988
),
Fault stability changes induced beneath a reservoir with cyclic variations in water level
,
J. Geophys. Res.
93
,
2107
2124
.
45.
Mesri
G
,
Adachi
K
, and
Ullrich
CR
(
1976
),
Pore pressure response in rock to undrained change in all-round stress
,
Geotechnique
26
,
317
330
.
46.
Green
DH
and
Wang
HF
(
1986
),
Fluid pressure response to undrained compression in saturated sedimentary rock
,
Geophysics
51
,
948
956
.
47.
Brace
WF
(
1965
),
Some new measurements of the linear compressibility of rocks
,
J. Geophys. Res.
70
,
391
398
.
48.
Rice
JR
and
Rudnicki
JW
(
1979
),
Earthquake precursory effects due to pore fluid stabilization of a weakening fault zone
,
J. Geophys. Res.
84
,
2177
2193
.
49.
O’Connell
RJ
and
Budiansky
B
(
1977
),
Viscoelastic properties of fluid saturated cracked solids
,
J. Geophys. Res.
82
,
5719
5735
.
50.
Beavan
J
,
Evans
K
,
Mousa
S
, and
Simpson
DW
(
1991
),
Estimating aquifer parameters from analysis of force fluctuations in well level: an example from the Nubian Formations near Aswan, Egypt 2. Poroelastic properties
,
J. Geophys. Res.
96
,
139
12
.
51.
O’Connell
RJ
and
Budiansky
B
(
1974
),
Seismic velocities in dry and saturated cracked solids
,
J. Geophys. Res.
79
,
5412
5426
.
52.
Anderson
DL
and
Whitcomb
JH
(
1975
),
Time dependent seismology
,
J. Geophys. Res.
80
,
1497
1503
.
53.
Rice
JR
and
Simons
DA
(
1976
),
The stabilization of spreading shear faults by coupled deformation-diffusion effects in fluid-infiltrated porous materials
,
J. Geophys. Res.
81
,
5322
5344
.
54.
Kovach
RL
,
Nur
A
,
Wesson
RL
, and
Robinson
R
(
1975
),
Water level fluctuations and earthquakes on the San Andreas fault zone
,
Geology
3
,
437
440
.
55.
Fletcher
JB
and
Sykes
LR
(
1977
),
Earthquakes related to hydraulic mining and natural seismic activity in western New York state
,
J. Geophys. Res.
82
,
3767
3780
.
56.
Li
VC
(
1984
/85),
Estimation of in-situ hydraulic diffusivity of rock masses
,
Pure Appl. Geophys.
122
,
546
559
.
57.
Talwani
P
and
Acree
S
(
1984
/85),
Pore pressure diffusion and the mechanism of reservoir induced seismicity
,
Pure Appl. Geophys.
122
,
947
965
.
58.
Lippincott
DK
,
Bredehoeft
JD
, and
Moyle
WR
Jr.
, (
1985
),
Recent movement on the Garlock Faut suggested by water level fluctuations in a well in Fremont Valley, California
,
J. Geophys. Res.
90
,
1911
1924
.
59.
Rudnicki
JW
and
Hsu
T-C
(
1988
),
Pore pressure changes induced by slip on permeable and impermeable faults
,
J. Geophys. Res.
93
,
3275
3285
.
60.
Rudnicki
JW
,
Yin
J
, and
Roeloffs
EA
(
1993
),
Analysis of water level changes induced by fault creep at Parkfield, California
,
J. Geophys. Res.
98
,
8143
8152
.
61.
Roeloffs
EA
,
Burford
SS
,
Riley
FS
, and
Records
AW
(
1989
),
Hydrologic effects on water level changes associated with episodic fault creep near Parkfield, California
,
J. Geophys. Res.
94
,
387
12
.
62.
Cleary
MP
(
1978
),
Moving singularities in elasto-diffusive solids with applications to hydraulic fracture
,
Int. J. Solids Struct.
14
,
81
97
.
63.
Detournay
E
and
Cheng
AH-D
(
1987
),
Poroelastic solution of a plane strain point displacement discontinuity
,
ASME J. Appl. Mech.
109
,
783
787
.
64.
Vandamme
L
,
Detournay
E
, and
Cheng
AH-D
(
1989
),
A two-dimensional poroelastic displacement discontinuity method for hydraulic fracture simulation
,
Int. J. Numer. Analyt. Meth. Geomech.
13
,
215
224
.
65.
Nur
A
and
Booker
JR
(
1972
),
Aftershocks caused by fluid flow
,
Science
175
,
885
887
.
66.
Booker
JR
(
1974
),
Time-dependent strain following faulting of a porous medium
,
J. Geophys. Res.
79
,
2037
2044
.
67.
Wu
FT
,
Blatter
L
, and
Roberson
H
(
1975
),
Clay gouges in the San Andreas fault system and their possible implications
,
Pure Appl. Geophys.
113
,
87
95
.
68.
Wang
C-Y
and
Lin
W
(
1978
),
Constitution of the San Andreas fault zone at depth
,
Geophys. Res. Lett.
5
,
741
744
.
69.
Rudnicki JW (1986), Slip on an impermeable fault in a fluid-saturated rock mass, in Earthquake Source Mechanics, Das S, Boatwright J, and Scholz CH (eds), Geophys. Monogr. Ser. American Geophysical Union, Washington DC, Vol 37, 81–89.
70.
Abramowitz M and Stegun I (eds) (1967), Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55.
71.
Rudnicki
JW
(
1987
),
Plane strain dislocations in linear elastic diffusive solids
,
ASME J. Appl. Mech.
109
,
545
552
.
72.
Rudnicki
JW
and
Roeloffs
EA
(
1990
),
Plane-strain shear dislocations moving steadily in linear elastic diffusive solids
,
ASME J. Appl. Mech.
112
,
32
39
.
73.
Simons DA (1979), The analysis of propagating slip zones in porous elastic media, in Fracture Mechanics, Proc of the Symp in Applied Mathematics of AMS and SIAM, Burridge R (ed), 153–169.
74.
Johnson
AG
,
Kovach
RL
, and
Nur
A
(
1973
),
Pore pressure changes during creep events on the San Andreas fault
,
J. Geophys. Res.
78
,
851
857
.
75.
Wesson
RL
(
1981
),
Interpretation of changes in water level accompanying fault creep and implications for earthquake prediction
,
J. Geophys. Res.
86
,
9259
9267
.
76.
Rudnicki JW and Wu M (1993), Pore pressure changes induced by slip in a poroelastic half-space, in Final Technical Report to US Geological Survey for Award No 1434-92-G-2164.
77.
Rice JR (1980), The mechanics of earthquake rupture, in Physics of the Earth’s Interior (Proc of Int Sch of Physics, “Enrico Fermi,” Course 78, 1979), Dziewonski AM and Boschi E (eds), 555–649.
78.
Rudnicki
JW
(
1979
),
The stabilization of slip on a narrow weakening fault zone by coupled-deformation pore fluid diffusion
,
Bull. Seismol. Soc. Am.
69
,
1011
1026
.
79.
Koutsibelas DA (1988), Stabilization of slip in a fluid-infiltrated rock mass, PhD Thesis, Northwestern Univ, Evanston, IL.
80.
Tse
ST
and
Rice
JR
(
1986
),
Crustal earthquake instability in relation to the depth variation of frictional slip properties
,
J. Geophys. Res.
91
,
9452
9472
.
81.
Rice JR (1968), Mathematical analysis in the mechanics of fracture, in Fracture: An Advanced Treatise 2, Liebowitz H (ed), Academic Press, New York, 191–311.
82.
Rudnicki
JW
and
Koutsibelas
DA
(
1991
),
Steady propagation of plane strain shear cracks on an impermeable plane in an elastic diffusive solid
,
Int. J. Solids Struct.
27
,
205
225
.
83.
Paterson MS (1978), Experimental Rock Deformation The Brittle Field, Springer-Verlag, New York.
84.
Rice JR (1977), Pore pressure effects in inelastic constitutive formations for fissured rock masses, in Advances in Civil Engineering through Engineering Mechanics, ASCE, 360–363.
85.
Simons
DA
(
1977
),
Boundary-layer analysis of propagating Mode II cracks in porous elastic solids
,
J. Mech. Phys. Solids
25
,
99
116
.
86.
Rudnicki
JW
(
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
,
201
221
.
87.
Craster
RV
and
Atkinson
C
(
1992
),
Shear cracks in thermoelastic and poroelastic media
,
J. Mech. Phys. Solids
40
,
887
924
.
88.
Craster
RV
and
Atkinson
C
(
1994
),
Crack problems in a poroelastic material: an asymptotic approach
,
Philos. Trans. R. Soc. London
A346
,
387
428
.
89.
Ruina A (1978), Influence of coupled deformation-diffusion effects on retardation of hydraulic fracture, in Proc of 19th US Symp on Rock Mechanics, Kim YS (ed), University of Nevada-Reno, 274–282.
90.
Atkinson
C
and
Craster
RV
(
1991
),
Plane strain fracture in poroelastic media
,
Proc. Roy. Soc.
A434
,
605
633
.
91.
Craster
RV
and
Atkinson
C
(
1992
),
Interfacial fracture in diffusive elastic media
,
Int. J. Solids Struct.
29
,
1463
1498
.
92.
Craster RV and Atkinson C (1996), Theoretical aspects of fracture in porous elastic media, in Mechanics of Poroelastic Media, Selvadurai APS (ed), Kluwer Academic Publ, Netherlands, 23–45.
93.
Eshelby
JD
(
1957
),
The determination of the elastic field of an ellipsoidal inclusion and related problems
,
Proc. Roy. Soc. London
A241
,
376
396
.
94.
Rice
JR
,
Rudnicki
JW
, and
Simons
DA
(
1978
),
Deformation of spherical cavities and inclusions in fluid-infiltrated elastic materials
,
Int. J. Solids Struct.
14
,
289
303
.
95.
Rudnicki
JW
(
1977
),
The inception of faulting in a rock mass with a weakened zone
,
J. Geophys. Res.
82
,
844
854
.
96.
Rudnicki JW (1999), Alteration of regional stress by reservoirs and other inhomogeneities, in Proc 9th Intl Congress on Rock Mechanics, Vouille G and Berest P (eds), Paris, Vol. 3, Balkema, Rotterdam.
97.
Rudnicki JW (1985), Effect of pore fluid diffusion on deformation and failure of rock, in Mechanics of Geomaterials, Bazˇant ZP (ed), John Wiley & Sons, New York, 315–347.
98.
Rudnicki
JW
and
Rice
JR
(
1975
),
Conditions for the localization of deformation in pressure-sensitive dilatant materials
,
J. Mech. Phys. Solids
23
,
371
394
.
99.
Rudnicki JW (2000), Diffusive instabilities in dilating and compacting geomaterials, in Multiscale Deformation and Fracture in Materials and Structures, Chuang T-J and Rudnicki JW (eds), Kluwer Academic Publ, 159–182.
100.
Rudnicki
JW
(
1984
),
Effects of dilatant hardening on the development of concentrated shear deformation in fissured rock masses
,
J. Geophys. Res.
89
,
9259
9270
.
101.
Martin
RJ
III
(
1980
),
Pore fluid stabilization of failure in Westerly granite
,
Geophys. Res. Lett.
7
,
404
406
.
102.
Rudnicki
JW
and
Chen
C-H
(
1988
),
Stabilization of rapid frictional slip on a weakening fault by dilatant hardening
,
J. Geophys. Res.
93
,
4745
4757
.
103.
Segall
P
and
Rice
JR
(
1995
),
Dilatancy, compaction, and slip instability of a fluid-infiltrated fault
,
J. Geophys. Res.
100
,
155
22
.
104.
Dieterich
JH
(
1978
),
Time-dependent friction and the mechanics of stick-slip
,
Pure Appl. Geophys.
143
,
425
456
.
105.
Dieterich
JH
(
1979
),
Modeling of rock friction, 1, Experimental results and constitutive equations
,
J. Geophys. Res.
84
,
2161
2168
.
106.
Ruina
A
(
1983
),
Slip instability and state variable friction laws
,
J. Geophys. Res.
88
,
359
10
.
107.
Marone
C
,
Raleigh
CB
, and
Scholz
CH
(
1990
),
Frictional behavior and constitutive modeling of simulated fault gouge
,
J. Geophys. Res.
95
,
7007
7025
.
108.
Chambon
G
and
Rudnicki
JW
(
2001
),
Effects of normal stress variations on frictional stability of a fluid-infiltrated fault
,
J. Geophys. Res.
106
,
353
11
.
109.
Pietruszczak
S
(
1995
),
Undrained response of granular soil involving localized deformation
,
J. Eng. Mech.
121
,
1292
1297
.
110.
Han
C
and
Vardoulakis
I
(
1991
),
Plane strain compression experiments on water-saturated fine grained sand
,
Geotechnique
41
,
49
78
.
111.
Rudnicki
JW
and
Smith
K
(
1997
),
Shear heating of a fluid-saturated slip-weakening fault zone
,
Trans. Geophys. Union
78
,
F477
F477
.
112.
Garagash
D
and
Rudnicki
JW
(
1999
),
Shear heating and slip instability of a fluid-saturated dilatant fault
,
Trans. Am. Geophys. Union
80
,
F682
F682
.
113.
Vardoulakis
I
(
1985
),
Stability and bifurcation of undrained, plane rectilinear deformations on water-saturated granular soils
,
Int. J. Numer. Analyt. Meth. Geomech.
9
,
399
414
.
114.
Olsson
WA
(
1999
),
Theoretical and experimental investigation of compaction bands
,
J. Geophys. Res.
104
,
7219
7228
.
115.
Dimaggio
FL
and
Sandler
IS
(
1971
),
Material model for granular soils
,
J. Eng. Mech.
47
,
149
165
.
116.
Marone
C
and
Kilgore
B
(
1993
),
Scaling of the critical slip distance for seismic faulting with shear strain in fault zones
,
Nature (London)
362
,
618
621
.
117.
Finno
RJ
,
Harris
WW
,
Mooney
MA
, and
Viggiani
G
(
1996
),
Shear bands in plane strain compression of loose sand
,
Geotechnique
47
,
149
165
.
118.
Finno
RJ
,
Harris
WW
,
Mooney
MA
, and
Viggiani
G
(
1996
),
Strain localization and undrained steady state of sand
,
J. Geotech. Eng.
122
,
462
473
.
119.
Rudnicki JW (1996), Development of localization in undrained deformation, in Proc of 11th Conf. Eng. Mech. Div., Lin YK and Su TC (ed), ASCE, New York, 939–942.
120.
Rudnicki JW, Finno RJ, Alarcon MA, Viggiani G, and Mooney MA (1996), Coupled deformation-pore fluid diffusion effects on the development of localized deformation in fault gouge, in Prediction and Performance in Rock Mechanics and Rock Engineering, EUROCK’96, Turin, Italy, Barla G (ed), Rotterdam: Balkema, 1261–1268.
You do not currently have access to this content.