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Journal of Structural Geology.
Vol. 7. No. 6, pp. 751 to 754, 1985 0191-8141/85 $03.00 + 0.00
Printed in Great Britain © 1985 Pergamon Press Ltd.
Brevia
SHORT NOTES
A note on fault reactivation
RICHARD H. SIBSON
Department of Geological Sciences, University of California, Santa Barbara, California 93106, U.S.A.
(Received
13
November
1984;
accepted in revised form
22
January
1985)
Abstract--Reactivation of existing faults whose normal lies in the ~ri~r ~ plane of a stress field with effective
principal compressive stresses cr'~ > or;_ > cr~ is considered for the simplest frictional failure criterion, r = ~cr', =
tz(~r, - P), where ~- and or, are respectively the shear and normal stresses to the existing fault, P is the fluid pressure
and # is the static friction. For a plane oriented at 0 to gl, the stress ratio for reactivation is (crl/cr~) =
(1 + ~ cot 0)/(1 - ~ tan 0). This ratio has a minimum positive value at the optimum angle for reactivation given
by 0* = ½ tan -h (1/~) but reaches infinity when 0 = 20", beyond which cr~ < 0 is a necessary condition for
reactivation, An important consequence is that for typical rock friction coefficients, it is unlikely that normal
faults will be reactivated as high-angle reverse faults or thrusts as low-angle normal faults, unless the effective
least principal stress is tensile.
IT IS now widely recognized that much intracontinental
deformation within the frictional seismogenic regime,
which commonly extends to depths of 10-15 km (Sibson
1983), is accommodated by the reactivation of existing
discontinuities rather than by the creation of new faults
(McKenzie 1972, Sykes 1978). This is especially true of
collision belts. Given our general lack of quantitative
knowledge concerning the triaxial stress state at depth,
full three-dimensional analysis of the conditions for
frictional reactivation (Bott 1959, McKenzie 1969,
Jaeger & Cook 1979) is rarely practicable, though it has
been done successfully on occasion (Raleigh
et al.
1972).
However, in view of recent suggestions that many high-
angle reverse faults and low-angle normal faults have
developed by reactivation of normal and thrust faults
respectively (e.g. Jackson 1980, Winslow 1981, Brun &
Choukroune 1983, Smith & Bruhn 1984), it is instructive
to consider certain limitations imposed by the simplest
two-dimensional analysis for frictional reactivation of a
cohesionless fault.
CONDITIONS FOR REACTIVATION
Consider a triaxial stress state with principal compres-
sive stresses 0.~ > 0" 2 > 0"3 containing a cohesionless plane
lying at an angle, 0, to 0.t, with its normal contained in
the 0.10.3 plane (Fig. 1). If a fluid pressure, P, is present,
the effective principal stresses (Hubbert & Rubey 1959)
are
0.] = (0"1 - P) > 0"~ = (ere - P) > 0.~ = (0" 3 - P).
(1)
Byerlee (1978) has shown that nearly all rocks share the
same frictional properties with a failure criterion which
may be adequately approximated by Amonton's Law
r =/~.o-~ =/z(o-, - P), (2)
where r and 0.. are, respectively, the shear and normal
stresses to the plane, and the coefficient of friction, tz is
c. 0.75 (Sibson 1983).
In terms of the effective principal stresses, equation
(2) may be rewritten
(0.~ - o'i) sin 20 =/z[(0.~ + o-i) - (0.~ - o'i) cos 20] (3)
which reduces to
R = (0.{/o'i) = (1 +/z cot 0)/(1 -/x tan 0). (4)
15
R
lO
5
=5
-lO
~u : 0,75
[
I
I
r , , I I i~ i , ,__J
e'3o 21
"3 x
Fig. 1. Stress ratio required for frictional reactivation, R = (or'i/cry),
vs reactivation angle, 0, for a static frictional coefficient, ~z = 0.75,
751
752 R.H. SmsoN
9O
6O
i , I
I
)
0 , , , , I I 'I' i
R* 4
3
2
1
I I I I I ! I I I
0 0.5 1.0
Xl
Fig. 2. Variation of optimum reactivation angle, O*, 20" and minimum
positive stress ratio for reactivation, R*, with frictional coefficient,/z.
The stress ratio for reactivation, R, is plotted against 0
for the particular case of tz = 0.75 in Fig. 1. R has a
minimum positive value,
R* = (V1 + U -~ + /z) 2 (5)
at the optimum angle for frictional reactivation given by
0* = ½ tan -I (1//z) (Sibson 1974), but increases to infinity
for 0 = 0 and 0 = 20*. For/z = 0.75, 0* = 26.5 ° with R*
= 4, and 20* = 53 °. For 0 > 20*, R < 0 which requires o-~
< 0, that is, the effective least principal stress must be
tensile. Values of R*, O* and 20* corresponding to other
values of/z are plotted in Fig. 2.
A further limitation on allowable stress states for
frictional reactivation is that they must not induce failure
of the surrounding rock either in shear or in tension. In
Fig. 3, a composite failure envelope for intact rock is
plotted together with the envelope for frictional failure
in a series of Mohr diagrams illustrating the range of
allowable stress states for reactivation. Following Brace
(1960), the failure envelope for intact rock is taken to be
approximately of parabolic Griffith form in the tensile
field with a cohesive strength, C, equal to twice the
tensile strength, To. In the compressional field the
envelope is assumed to be of the linear Coulomb form,
r = C +/zi~r',. (6)
T
?
T 0
C
/
r
o (;~
NON-OPTIMUM O( e( • e
R°( R<•
T
?
r o
o.'
NON-OPTIMUM e'~ e~ 2e t
R*(
R~-
T
r o or.'
NON-OPTIMUM 2et~ e~ 90" -m ~ R( 0
OPTIMUM @" • ~' R - R*
T
?
r
o o'~
NON-OPTIMUM • -2e ~ R= w
T
r
o 0".'
NON-OPTIMUM e-tgo" R--~O
Fig. 3. Allowable stress states for frictional reactivation of an existing fault (see text for discussion).
Fault reactivation 753
Hoek (1965) found that the coefficient of internal fric-
tion,/z i generally lies between 0.5 and 1.0 for rocks, so
that for convenience the failure envelopes for intact rock
and fault reactivation in the compressional field are
plotted parallel with/x~ =/~ = 0.75.
The optimum condition for reactivation with R = R*
and 0 = 0* is shown in Fig. 3(b) with the stress circle
touching the frictional failure envelope. Note that
here may have any value greater than zero for reactiva-
tion to be possible. Stress conditions for reactivation
with 0 < 0 < 0* and 0* < 0 < 20* are shown in Figs. 3(a)
and (c), respectively. Clearly, the diameter of the stress
circle is constrained by the presence of the intact rock
envelope to be not too great, so that cr~ --, 0 as 0 trends
towards 0 or 20*. At 0 = 20", R = ~, requiring tr~ = 0
(Fig. 3d). Reactivation at 0 > 20* requires cr~ < 0 with a
progressively diminishing differential stress as 0--~ 90 ° in
order to prevent failure of the intact rock (Figs. 3e & f).
DISCUSSION
In the framework of simple 'Andersonian' faulting
(Anderson 1951), principal stress trajectories are either
vertical or horizontal and the three main classes of fault,
thrust, wrench and normal, develop in homogeneous
crust in accordance with the Coulomb criterion (eqn. 6),
depending on which of the three principal stresses is
vertical. For typical values of internal friction, faults
develop at c. 30 ° to or I . Thus, ideal normal faults should
dip at c. 60 ° and thrusts at c. 30 °. If or 1 and tr 3 are
interchanged, as may occur if a former rifted continental
margin becomes involved in continental collision, or
when a former thrust belt is caught up in a zone of
distension, normal faults may potentially be reactivated
as high-angle reverse faults, and thrusts as low-angle
normal faults. However, in both cases the 0 angle for
reactivation is c. 60 ° if the stress trajectories remain
horizontal and vertical. Such a high reactivation angle
requires either a friction coefficient,/x < 0.55 (Fig. 2),
significantly lower than the usual value of 0.75, or o'~
must be tensile. In fact, Bruhn
et al.
(1982) have
demonstrated reactivation of gently dipping joints as
low-angle normal faults with 0 values of 70-80 °, implying
either ~ < 0.35 or cr~ < 0. Vein systems associated with a
normal fault reactivated in high-angle reverse mode in
North Wales unequivocally demonstrate o-~ < 0 during
reactivation (Sibson 1981).
Even if the conditions described above are not met
fully, it is apparent from Fig. 3(c) that for frictional
reactivation to occur at large 0 values in preference to
the formation of a new, favourably oriented fault, o'~
must tend towards zero, implying abnormal fluid pres-
sure conditions and comparatively low differential stress
levels at the time of reactivation. Clearly, however,
listric normal faults would be more easily reactivated in
reverse mode than the ideal 'Andersonian' variant. In
contrast, flattening of thrusts with depth tends to exacer-
bate the problem if they are to undergo frictional reacti-
vation in normal slip mode. The problem is acute also in
the case of the brittle, flat-lying detachment faults
associated with regional extension in the western United
States which, in some cases at least, appear to have been
active with dips of only a few degrees (Davis
et alo
1980).
For reactivation of such faults to occur, either fluid
pressures must be high with ~ < 0, at least intermit-
tently, or the frictional coefficient must be abnormally
low, or stress trajectories must deviate markedly from
the horizontal and vertical. When fault reactivation at
high 0 values is suspected, evidence in the form of
fault-related hydraulic extension fractures (e.g. Sibson
1981) should be sought in support of the hypothesis for
an effectively tensile least principal compressive stress
accompanying reactivation.
Acknowledgements--Special thanks to Barbara John and Bill Power
for steadily eroding my air of detachment regarding low-angle normal
faults, to Art Sylvester for constructive criticism, and to Mrs. Ellie
Dzuro for typing the manuscript. This work was supported by National
Science Foundation grant number EAR83-05876.
REFERENCES
Anderson, E. M. 1951. The Dynamics of Faulting. (2nd Edn) Oliver &
Boyd, Edinburgh.
Bott, M. H. P. 1959. The mechanics of oblique-slip faulting. Geol.
Mag. 96,109-117.
Brace, W. F. 1960. An extension of the Griffith theory of fracture to
rocks. J. geophys. Res. 65, 3477-3480.
Bruhn, R. L., Yusas, M. R. & Huertas, F. 1982. Mechanics of
low-angle normal faulting: an example from Roosevelt Hot Springs
geothermal area, Utah. Tectonophysics 86,343-361.
Brun, J-P. & Choukroune, P. 1983. Normal faulting, block tilting and
d6collement in a stretched crust. Tectonics 2,345-356.
Byerlee, J. D. 1978. Friction of rocks, Pure appl. Geophys. 116,
615-626.
Davis, G. A., Anderson, J. L., Frost, E. G. & Shackelford, T. J. 1980.
Mylonitization and detachment faulting in the Whipple-Buckskin-
Rawhide Mountains terrane, south-eastern California and western
Arizona. In: Cordilleran Metamorphic Core Complexes (edited by
Crittenden, M. D., Coney, P. J. & Davis, G. H.). Mere. geol. Soc.
Am. 153, 79-129.
Hock, E. 1965. Rock fracture under static stress conditions. Natl.
Mech. Engng Res. Inst., C.S.1.R., Pretoria, Report MEG 383.
Hubbert, M. K. & Rubey, W. W. 1959. Role of fluid pressure in the
mechanics of overthrust faulting. Bull. geol. Soc. Am. 70, 115-205~
Jackson, J. A. 1980. Reactivation of basement faults and crustal
shortening in orogenic belts. Nature, Lond. 283,343-346.
Jaeger, J. C. & Cook, N. G. W. 1979. Fundamentals of Rock
Mechanics. (3rd Edn) Chapman & Hall, London.
McKenzie, D. P. 1969. The relation between fault plane solutions for
earthquakes and the directions of the principal stresses. Bull. seism.
Soc. Am. 59,591-601.
McKenzie, D. P. 1972. Active tectonics of the Mediterranean region.
Geophys. J. R. astr. Soc. 30,109-185.
Raleigh, C. B., Healy, J. H. & Bredehoeft, J, D. 1972. Faulting and
crustal stress at Rangely, Colorado. Mon. Am. Geophys. Union 16,
275-284.
Sibson, R. H. 1974. Frictional constraints on thrust, wrench and
normal faults. Nature, Lond. 249,542-544.
Sibson, R. H. 1981. Fluid flow accompanying faulting: field evidence
and models. In: Earthquake Prediction: an International Review
(edited by Simpson, D. W. & Richards, P. G.). Am. Geophys.
Union, Maurice Ewing Series 4, 593-603.
Sibson, R. H. 1983. Continental fault structure and the shallow
earthquake source. J. geol. Soc. Lond. 140,741-767.
754 R.H. SIBSON
Smith, R. B. & Bruhn, R. L. 1984. Intraplate extensional tectonics of
the eastern Basin-Range: inferences on structural style from seismic
reflection data, regional tectonics, and thermal-mechanical models
of brittle-ductile deformation. J. geophys. Res. 89, 5733-5762.
Sykes, L. R. 1978. Intraplate seismicity, reactivation of preexisting
zones of weakness, alkaline magmatism, and other tectonism post-
dating continental fragmentation. Rev. Geophys. Space Phys. 16.
621-687,
Winslow, M. A. 1981. Mechanism for basement shortening in the
Andean foreland fold belt of southern South America. In: Thrust
and Nappe Tectonics (edited by McClay, K. & Price, N. J.). Spec.
Publs geol. Soc. Lond. 9,513-528.