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The change in orientation of subsidiary shears near faults containing pore fluid under high pressure
295
Tectonophysics, 2 11 ( 1992) 295-303 Elsevier
Science Publishers
B.V.,
Amsterdam
The change in orientation of subsidiary shears near faults containing pore fluid under high pressure J. Byerlee U.S. Geological Sunsey, 345 Middlefield Road, Menlo Park, CA 94025, USA (Received
June 13, 1991; revised version accepted October
I, IYYI)
ABSTRACT
Byerlee, J., 1992. The change in orientation Mikumo,
K. Aki,
Precursors.
M.
Ohnaka,
of subsidiary shears near faults containing
L.J. Ruff
and P.K.P.
Spudich
(Editors),
pore fluid under high pressure. In: T.
Earthquake
Source
Physics and Earthquake
Tectonophysics, 211: 295-303.
The mechanical
effects of a fault containing
cally from
the core of the fault
mechanical
implications
stress is oriented
zone
near-lithostatic
to the adjacent
for the orientation
country
fluid pressure in which fluid pressure decreases monotonirock is considered.
This
fluid
pressure
distribution
of subsidiary shears around a fault. Analysis shows that the maximum
at a high angle to the fault in the country rock where the pore pressure is hydrostatic,
and rotates to 45” to
the fault within the fault zone where the pore pressure is much higher. This analysis suggests that on the San Andreas where
heat flow constraints
require
that the coefficient
of friction
has
principal fault,
for slip on the fault be less than 0.1, the pore fluid
pressure on the main fault is 85% of the lithostatic pressure. The observed geometry of the subsidiary shears in the creeping section of the San Andreas
are broadly consistent with this model, with differences
that may be due to the heterogeneous
nature of the fault.
Introduction
The lack of a heat flow anomaly over the San Andreas fault (Lachenbruch and Sass, 1992) and the high angle that the maximum principal stress makes with the fault (Zoback et al., 1987), can be explained if the fluid pressure at the center of the fault zone is much greater than the hydrostatic fluid pressure in the country rock (Byerlee, 1990; Rice, 1992). While this idea is not new, previous models have led to the unsatisfying prediction that the fluid pressure within the fault exceeds the magnitude of the least principal stress and, as a result, hydrofracture would occur allowing the high pressure fluids to escape (Zoback et al., 1987). This difficulty, however, is overcome in both the Byerlee model and in the Rice model by
Correspondence Middlefield
Elsevier
to: J.D. Byerlee,
Road, Menlo
Science
Publishers
U.S. Geological
Park, CA 94025, USA.
B.V
Survey, 345
assuming that the fault zone material fails in shear before the conditions for tension fracture are reached. An important result of this shear failure process is that the magnitude of the minimum principal stress increases as the main fault plane is approached. Consequently, the pore pressure at any point never exceeds the magnitude of the local minimum principal stress, so that hydrofracture cannot occur. In the continuous flow model of Rice (1992), the very high pore pressure can be maintained in the center of the fault zone if the loss of fluid into the country rock is made up by the injection of water up the center of the fault zone from the mantle. This model requires very low permeability of the fault zone so that a heat flow anomaly associated with the injection of hot fluid from below does not occur near the fault. Permeability must be lower in the country rock than in the fault zone to channel fluid up the fault zone, but the permeability must also be high enough so that
2%
hydrostatic pore pressure can be maintained in the country rock. These potential problems do not arise in the model proposed by Byerlee (1990) because it is assumed that high pore pressure is generated during compaction of the water-saturated gouge as it is sheared and the structure of the fluid channels within the fault zone prevents the escape of this overpressured water unless the pressure gradient between the center of the fault zone and the country rock exceeds a threshold value. There is experimental evidence of a threshold gradient in dense clay and there is a well-established physical mechanism for the existence of a threshold gradient in the fault zone, regardless of its composition, if the width of the channels for fluid flow are less than ten times the diameter of a water molecule (Byerlee, 1990). There is also evidence for the existence of a threshold gradient in other geological situations. For example, in studies of the structure, pore pressure distribution, and the geological histories of many deep oil reservoirs, it is found that the pressure within the fluid compartments can only be maintained for the tens of mihions of years of their existence if the permeability of the oil seals surrounding the compartments is zero (Hunt, 1990, 1991). These observations can be explained if the channelways in these dense fine-grained rocks are so small that below the threshold gradient flow does not occur and the permeability is zero. It is possible that in some regions pore pressure is maintained by the injection of fluid from the mantle as proposed by Rice (1992) and in other regions it is maintained because the threshold gradient is not exceeded, as proposed by Byerlee (1990). It may be possible to find out whiqh meehapism operates in a given region by det~~~~~~~ the origin of the fluid by isotopic studies of Ihe pore fluid within the fault zone. With the aId of a Mohr circle construction, Rice (1992) has shown that the direction of the maximum princjpal stress &ranges within the fault zone. This resulf applies to the Ryerlee model as well because mechanically both yodels are identical, even though the mechanisms for maintaining the high pore pressure at the center of the
fault zone are different in the two models. In his analysis, Rice (1992) made the reasonable assumption &hat when slip occurs on the main fault, it is the Coulomb slip plane. This is consistent with what would be predicted during simple shearing of granular materials obeying the nonassociated flow rule developed by Mandl and Fernandez Luque (1970). The theory predicts that the maximum principal stress makes an angle of @=7r/44 f tan _ ‘pi with the normal to the fault plane, where pi is the coefficient of internal friction of the material in the fault zone. In an experimental study designed to determine the (orientation of the stress directions during the formation of the subsidiary Riedel shears and the main fault Mandl et al. (19771 found. to their surprise that both the Riedel shears and the main fault were formed when the maximum principal stress made an angle of 7r/4 to the main fault pIane. These experimental results fed Mandl (1988) to the conclusion that “a final throughgoing fault which develops under tectonic simple shearing in rocks that initially were in a state of isotropic stress or transpression in the deformation plane is not of the Coulomb-type, albeit that it is formed by the cooperation of Coulomb-type precursory shears. The nonCoulomb-type fault zone, which was forced to develop parallel to moving boundary rocks, is bounded by planes of m~imum shear stress (or nearly so) and is therefore referred to as simpleshear fault.” If, in the simple shear geometry, the maximum principal stress makes an angle of 45” to the plane of the fault, then the subsidiary Riedel shears which are generally inclined at an angle of about 15” to the main fault are Coulomb shears and Mandl (1988) suggested that in the region of overlapping Riedel shears as shown in Figure 1, the local stress direction is rotated until another Coulomb shear, which is commonly known as a P shear, is developed. In this way unrestricted shear displacement can occur on the main fault plane. With large displacement an anastomosing series of R and P shears are developed in the main fault zone. Structures such as this are. commonly observed on both natural and artificial faults (Tchalenko, 1970; Moore and Byerlee, 1991;
THE CHANGE
IN ORIENTATION
OF SUBSIDIARY
297
SHEARS
the insert. The x and y axis are as shown and the z axis is normal to the plane of the figure. The main fault plane is parallel to the yz plane. In the country rock we assume that the pore pressure p is hydrostatic and that the maximum principal stress crlc is only slightly greater than the vertical stress a,. (We will use the convention that subscript ‘c’ denotes country rock and ‘f denotes the main fault zone.> The only place, near the San Andreas fault, where the in situ stresses have been measured as a function of depth is at Cajon Pass where Zoback and Healy (1992) found that the difference between the maximum and minimum principal stress increased with depth at a rate that is consistent with laboratory measurements of the coefficient of friction of crustal rocks, provided that the pore pressure to at least a depth of 3.5 km is not significantly greater than hydrostatic. In addition it was found that the maximum horizontal stress has a value approximately equal to, to slightly greater than the vertical stress, and increases with depth at a rate similar to that of the vertical stress. While the present paper assumes that plc is essentially equal to a,, it also has general application because if c,, > cY then p = ACT.,= (ho;/c~,,b,, and the anaiysis that foIlows should be modified by multiplying A by ~,/a,, to obtain the general solution. We assume in our model that the pore pressure p decreases linearly from
Moore and Byerlee, 1992). Near natural faults that have simple shear geometry, Hancock (1972) and Vialon (1979) observed that the angle which tension cracks, and hence (or, make with the shear plane is close to 45”. Analysis As presented here, we seek simple expressions for the orientation of the maximum principal stress, the strike of the subsidiary faults throughout the fault zone, and the apparent coefficient of friction, as a function of h,, the ratio of the pore pressure in the fault zone to the magnitude of the vertical stress. To be consistent with the laboratory and field observations, we will here assume that the main fault is the plane of maximum shear stress and that in the region between the central fault plane and the country rock, the subsidiary faults are Coulomb shears. The displacement on these subsidiary shears is very small because of the constraints on their movement by the stronger country rock. The small amount of shear that occurs on these planes accommodates a small amount of compaction of the material in the fault zone. This deformation sufficiently modifies the magnitude of the minimum principal stress to prevent hydrofracture. Figure 1 is a Mohr representation of the state of stress in the fault zone shown schematically in
0 I
PC
ff3c
p
Pf -3
03f
Olc
“1
“If
Fig. 1. Mohr representation of the state of stress during sliding in the simple shear geometry shown in the insert. P,, and r are the normal and shear stresses which for equilibrium must be the same on all planes parallel to the yz plane. In the standard nomenclature R is the R, Riedel shear and P is a thrust shear which form an anastomosing network in the main fault zone. The subscripts c and f refer to the state of stress, the failure angle .9 and A in the country rock and at the main fault, respectively.
a value of hr~~,~ at the center of the fault zone to hydrostatic pressure of hc~lc in the country rock so that at any point at a distance x from the country rock:
where D is the half-width of the fault zone. Subject to this distributi(~n of h and the assumption that the plane of maximum shear stress is parallel to the fault plane at the main fault, wc solve for the stress field everywhere invoking only continuity of stress. We further assume that the fault zone material obeys the effective stress law and that its constitutive property is such that: ‘r, = ni?;
main fault cos 2Hr = 0 and sin 28, -L I, so that WC have from eqs. 6 and 7:
Equating ey. 0 with cq. # and ry. rearranging WC have: ( 12 ” 1) .- .__. __.__(,, II.
It
wth
cq. ‘) ami
( fl --. 1) j ---‘------Acr,c. 1 60s .3ti II
(2)
where ft is a constant greater than I, (7,= ((I; -- 1~) = (u; - hfr,,), h is given by cy. 1. Equation 7 reduces to: (7’3 =
;
[a,“t
(n - l)Aa,,]
_
at any point in the fault zone. We next make use of the standard relations: (a,+cr,)+(cr,-a~)cos28=2~r;
(1)
or- it_‘(r,, -__.I1
01 ..- !i
; --~ n,tr:~j
/I
i. i i !
Dividing ~4. i 1 by eq. 10, we have after some a&bra:
and (5j
(WI - tag) sin 2@= 27
where u;, and I are the normal and the shear stresses acting on a plane parallel to the yr planc and 0 is the angle between the (r, direction and the normal to that plane. By substituting for CT,; from eq. 3 into eqs. 4 and 5 we have:
--------fJ
I
-
( t1 -- 1) -----/hJr, 17
’ COS
?t)
For equilibrium in this simple shear system it is required (see Fig. 1) that both c,, and r be the same on all the planes parallel to the yz plane. At the main fault glf makes an angle of 45” to the plane of the fault (Fig. 1). Therefore, at the
f:rorn Figure I it can be seen ttuii:
f:rom ey. 3. (rIi can be expressed I(( terms of‘ r,r,, and ft. If the density of the overtying rocks is 73iHI kg/m’ then n; =- (1.4 and h3 s~l(~~titutin~ thcsc values into eq. 13 we have:
X [cos lti, -t sin I@,].
4 141
CI,~/U,~ is a maximum when cos 2H, = sin 28, 1
I/ v’?. If n = 3 which is about the ratio of e,jif_{ for rocks close to the San Andreas (Zoback and
THE CHANCiE IN ORIENTATION
OF SUBSlDIARY
299
SHEARS
Healy, 19891, then from eq. 14 the maximum value for (T,~/o~~ is 1.08. From Figure 1 it can be seen that vlC da, ,< cif so that @,/v~~ =: au/alC = 1, and eq. 12 then reduces to the approximate solution: tan 28=
1 --A, ~ [ A,-A
1
An exact solution at the counts rock can be found by recognizing from Figure 1 that: Ulf -
03f
= h
-
r3,)
sin 28,
(16)
Then by expressing @s3fand c3C in terms of elf and glC and as before when A,= 0.4, eq. 16 reduces to: Plf
-
=0.6 sin 28,+A,
(17)
g1c
By substituting this value into eq. 12 and as before by assuming n = 3, we have after some algebra: 2 sin 20, - cos 28, = 4 - 5hf
(18)
The approximate solution for eC at the country rock from eq. 15, and the exact solution for @, from eq. 18 are plotted as a function of A, in Figure 2. For values of A, less than 0.8, the approximate solution provides an upper bound for 8,, but for values of hf greater than this it
0 i ._ _. _-.-~_-.~_..
04
05
._i.L.
0.6
i
0.7
CL?
..L-,i
=-=---J i.
ii9
-.
1 :,
Xf
Fig. 3. pa, the apparent coefficient of friction, calculated for the stress conditions and pore pressure in the country rock, plotted as a function of h, in the main fault zone.
becomes a lower bound. For A, > 0.7 the error in using the approximate solution is less than 2”. The heat Row constraint requires that the apparent coefficient of friction fl;, < 0.1, where: *a=
-=:- Tc CT nc --PC
Tf %f -PC
(19)
and TV,
Tf, q,,, q,, are the shear and normal stress components as illustrated in Figure 1. Then by substituting the values for rf and o;lf from eqs. 8 and 9 into eq. 19 and using A, = 0.4, we have:
If, as before, we assume that n = 3 and CY,~ = crlcr then eq. 20 reduces to: 1 -A,
iCLa=0.8+A,
3.6
08 hi
10
Fig. 2. A plot of Ba, the angle that the maximum principal stress makes with the main fault plane in the country rock against h,, the ratio of the pore pressure in the main fault zone and the maximum principal stress in the country rock which in our model is approximately equal to 0~ due to the weight of the overburden. (3, for both the approximate solution and the exact solution are given in the figure.
cw
pa is plotted as a function of A, in Figure 3. If kL, < 0.1, then from the figure A,>, 0.85, where in Figure 2 the approximate solution gives values for 8 very close to the correct values. From eq. 9, if II = 3 and cle = vlf, then TV= Co-,,/3)(1 - Af). If A, = 0.85 and a,, = a,, as it seems to be for the San Andreas fault, and if we assume that the density of the overIying rocks is 2500 kg/m3, then we have -rr = O.O.S(Z)z, where Tf is the shear stress in MPa and z is the depth in km. If the total depth of the zone where frictional heat is being generated is 15 km, then the aver-
age shear stress on the fault is 9.375 MPa, which is close to the upper bound of 10 MPa required by the heat flow constraints. This is simply another way of expressing, as we did above, that the heat flow constraints require that pLi,G 0.1. When A, = 0.4, the pore pressure is hydrostatic everywhere and from Figure 3, JA;~= 0.5. The internal coefficient of friction pi is given by the slope of the failure envelope for the subsidiary shears which from our model is given by: ui=tan[sin-‘~~~]=0577ifn=3
(22)
Thus pL, is smaller than pi in our simple shear system. In experiments to determine the constitutive properties of soils, it has been observed that the simple shear tests give shear strengths considerably less than what is found in standard triaxial experiments (Saada et al., 19831, but to date there has been no satisfactory explanation for this. In the analysis of the experimental data, it is assumed that the shear plane in the simple shear experiments is the Coulomb failure plane, but the experiments of Mandl et al. (1977) have shown that this assumption is not correct. With this system and the one analysed in this paper the main failure plane is the plane of maximum shear stress and this explains why gL, < pi in our model and in the soil mechanics experiments. In experiments designed to measure the coefficient of friction of brittle materials a layer of fault gouge is eventually developed between the stronger forcing blocks and with further displacement between the surfaces the fault gouge deforms in the simple shear mode analysed in this paper. In deriving the approximate solution (es. 21) for the case where the pore pressure is not constant throughout the fault zone, we assumed that heir= clC but in the special case where the pore pressure is constant, as it is in the usual friction experiment, the exact solution is given by:
n-i Pa = -
i-It-1
regardless of whether the rocks are dry or contain pore fluids under pressure.
Until now it has been difficult to explain why pi (eq. 22) for the bulk properties of brittle particulates varies between wide bounds, but in friction experiments where we are really studying the rheological properties of the fault gouge, pa ieq. 23) for most rocks is about 11.75 regardless of their bulk strength. From eq. 23 pi’y, = t1.75, then n = 7 which is about the value measured for the bulk strength of dense sand (Lamb and Whitman. 1979). JL;,, however, is not strongly dependent on ra, for example pL;,approaches 1 as II approaches infinity, so that the coefficient of friction can never be greater than 1 regardless of the bulk strength of the gouge. The other limiting case in our model is when A,= 1, then from Figure _i p%,‘1 0. What this means is that or = c.\ =p at rho center of the fault zone so that the fault has no strength and movement can then occur on the fault with an infinitesimally small shear stress in the plane of the fault. If the main fault is vertical, the movement can even occur in the vertical direction so that the fault acts as a high-angle reverse fault with a dip of 90°. If the main fault is horizontal, it could be called a horizontal ov~rthr~lst or a normal fault with zero dip. If we assume that the pore pressure decreases linearly from the center of the fault zone to the country rock. we have h as a fu~lcti~~ of x from eq. 1. By substituting this value into eq. 15 and by assuming that h, I= 0.4: 1 “’ A,
tan 28 =
i A,
--I
0.4 - (A, - 0.4).X,/l) i
(244
H throughout the fault zone is plotted as a function of x/D for A, = 0.85 and 0.99 in Figure 4. In both cases tl is equal to 45” at the fault plane as required in our model and at the country-rock boundary # is about 10” when A, =: 0.85 and about 1” when A, = .99. In the limiting case analyzed by Byerlee (1990), 0, = 0 when hi = 1 For geological applications a more useful figure would be a map view of the trace of the subsidiary shears within the fault zone. In laboratory experiments it has been found that R, is far better developed than its R, conjugate. The R, subsidiary shear is shown in the insert in Figure
THE CHANGE IN ORIE~AT~ON
0
0
0.2
301
OF SUBSIDIARY SHEARS
0.6
0.4
0.8
Equation 2.5has been integrated numerically and the results are shown in the map view of the main fault trace, the country rock fault zone boundaries and the subsidiary faults for A, = 0.85 in Figure 5. To obtain the results shown in Figures 4 and 5, it was assumed that the pore pressure decreased Iinearly with distance from the main fault. The results are correct if the permeabili~ in the continuous flow model of Rice or the threshold gradient in the no flow model of Byerlee are independent of the effective pressure. If these conditions are not satisfied, then the correct solution can be found by inserting the correct value for A into eq. 15 to obtain 8 as a function of x and then integrating the equation:
1.0
X/D
Fig. 4. 8, the angle that the maximum principal stress makes with the normal to the plane of the main fault, is plotted as a function of any distance x from the country rock normalized by the half-width D of the fault zone, for ht =0.85 and A, = 0.99 in the main fault.
dx 5, where from the figure we have tan4dy = dx. ff,= 7r/3 - B is the angle between the strike of the subsidiary shear and the main fault trace and 8 is given as a function of x in eq. 24. Then by integration we have:
’ =f tan(7r/3 - 0)
It should be noted that regardless of the pore pressure distribution throughout the fault zone if A, is known and the pore pressure in the country rock is hydrostatic then SC, the angle the maximum principal stress makes with the normal to the main fault, is given exactly by eq. 18. Figure 6 is a map of the fault zone in the creeping section of the San Andreas fault in
dx Y=j
tan 7r/3-
+ tan-’
Cl--Ar)
h,-0.4-(A,-0.4)x/D
Ii Country
(26)
Rock
Cou~ock x.=0.4 Fig. 5. A map view of the geometry and the sense of movement on subsidiary faults throughout the fault zone, for A, = 0.85. It is not suggested that the subsidia~ faults are continuous across the fault zone: it is simply that the geometry of these faults is as shown if the pore pressure distribution is the same on both sides of the main fault plane.
312
central California as mapped by Rymer ( 1981) and described in more detail by Rymer et al. (1984). The northeast and southwest boundar) faults are high-angle reverse faults. It appears that the rocks between them arc being thrust up and out of the fault zone. The main fault trace i\ not straight and contains constraining and rcleasing jogs. There are some variations in the strike of the subsidiary faults along the length of the main fault trace which may be caused by variability in the constitutive properties of the material in the fault zone or it could be that the subsidiary faults belong to different populations. Our model would predict that those that make an angle 01‘ about IS” to the main fault trace, were formed when the pore pressure was hydrostatic everywhere, but those that make a maximum angle of 50” to the main fault were formed when A! was about 0.85. If this is correct. then the most recent faults should be the steepest if the present dircction of the maximum principal stress is about W to the fault as the observations of Zoback ct al. ( 1987) would suggest. Some of the subsidiary faults are concave towards the main fault trace, whereas the theoretical solution requires that they curve the other way. The significance of this is unclear but ma) be related to the local inhomogeneous stress field caused by irregularities in the geometry of the main fault. It is also possible that some of the
variation of geometry of subsidiary shcara couic! partly arise from finite rotational strain within the fault zone. It should he noted that the ahsch lute value of the pore prcssu~~~ Luridthe i;trcssch arc dependent only on h. which 14Indcpendcnt (tt depth so that the gcometr\ oi rhe suhsidiar! faults is indepcndcnt of depth. fi the map talc i\ normalized by II. the half-uidth ti! Ihe fault zone. 2s it is in Figure: 5. It has been pointed out t hilt ihr’ distribution co! aftershocks indicates that the 1:~gc-hcale \uri‘acl irregularities of the San Andrcas tault per&s: throughout the seismogenic LOW 6Eaton ct rd.. 1970: Bakun et ai., IYXO: ticascnberg and Ellsworth. I(P-2) but it is nol clc,tr ihat thus i\ ;II~s~I true for the subsidiary faults LLX 11til’n1L)dcIwould suggest. The abnormally high Ilii!!rt pressurc’k cttcountered in wells drilled for ~iii i:t~~the Mcstcrt: margin of the great valley. Icd Berry (1077) to suggest that at a depth grcatcr thar! ;I tcw kilomctcrs. the Franciscan rocks adjacent to Ihe San Andreas fault may contain pore fluids ,tt pussurcs much greater than hydro~t:.~tic, 1:‘ this i> correct. then the geometry of the subsidiary t’auits below this depth may bc yuilc diffcrcnt from what it is on the surface.
SUBSIIXAHY
N,E
B@JNDARY
FAUL’
-
Fig. 6. Map of the main fault trace. the subsidiary faults and the boundary central California.
FAULTS
modified
faults in the creeping section of thy &II
from Rymer (10x1)
Andrras
f’aulr rn
THE C’HANGE IN ORiENTATlON
OF SUBSIDIARY SHEARS
in hydraulic pressure communication with adjacent compartments nor with the overlying hydraulic regime (Hunt, 1990). If this is also true in California, then the high pore fluid pressures measured in the oil reservoirs should have little or no effect on the mechanical behavior of the San Andreas fault system. In any case, detailed mapping of the geometry of the subsidiary faults may give an indication of the pore pressure distribution in the upper crust, in and adjacent to the fault. References Bakun, W.H., Stewart, R.M., Bufe, C.C. and Marks, SM., 1980. Implication of seismicity for failure of a section of the San Andreas fault. Bull. Seismol. Sot. Am., 70: 185201. Berry, F.A.F., 1973. High fluid potentials in California Coast Ranges and their tectonic significance. Bull. Am. Assoc. Pet. Geol., 57: 1219-1249. Byerlee, J., 1990. Friction, overpressure and fault normal compression. Geophys. Res. Lett., 7: 2109-2112. Eaton, J.P., O’Neil, M.E. and Murdock, J.N., 1970. Aftershocks of the 1966 Parkfield-Cholame, California. earthquake: A detailed study. Bull. Seismol. Sot. Am., 60: 1151-1197. Hancock, P.L., 1972. The analysis of en-echelon veins. Geol. Mag., 109: 269-276. Hunt, J.M., 19YO. Generation and migration of petroleum from abnormally pressured fluid compartments. Bull. Am. Assoc. Pet. Geol.. 74: I-12. Hunt, J.M., 1991. Generation and migration of petroleum from abnormally pressured fluid compartments: reply. Bull. Am. Assoc. Pet. Geol., 75: 328-330 and 336-338. Lachenbruch, A.H. and Sass, J.H., 1992. Heat flow from Cajon Pass, fault strength and tectonic implications. J. Geophys. Res., 97: 4995-5030. Lamb, T.W. and Whitman, R.W., 1979. Soil Mechanics, SI Version. Wiley, New York. Mandl, G., 1988. Mechanics of Tectonic Faulting. Elsevier, New York., N.Y., 407 pp. Mandl, G. and Fernandez Luque, R., 1970. Fully developed plastic shear flow of granular materials. Geotechnique, 20: 277-307.
303 Mandl, Cl., deJong, L.N.J. and Maltha, A., 1977. Shear zones in granular material: an experimental study of their structure and mechanical genesis. Rock Mech., 9: 95-166. Moore, D. and Byerlee, J., 1991. Comparison of the San Andreas fault, California, and laboratory fault zones. Bull. Geol. Sot. Am., 103: 162-774. Moore, D.E. and Byerlee, J., 1992. Relationships between sliding behavior and internal geometry of laboratory fault zones and some creeping and locked strike-slip faults of California. In: T. Mikumo, K. Aki. M. Ohnaka. L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: Reasenberg, P. and Ellsworth, W.L.. 1982. Aftershocks of the Coyote Lake, California, earthquake of August 6, 1979: A detailed study. J. Geophys. Res., 87: 10637-10655. Rice, J.. 1992. Fault stress states, pore pressure distributions, and the weakness of the San Andreas fault. Fault Mechanics and Transport Properties of Rock. In: Brian Evans and Teng-Fong Wong (Editors), A Festschrift in Honor of W.F. Brace (based on June 1990 symposium at MIT). Academic Press, London, pp. 475-503. Rymer, M.J., 1981. Geologic map along a 12 kilometer segment of the San Andreas fault zone, southern Diablo Range, California. U.S. Geol. Surv. Open-File Rep. 811173, scale 1:12,000. Rymer, M.J., Lisowski, M. and Burford, R.O., 1984. Structural explanations for low creep rates on the San Andreas fault near Monarch Peak. central California. Bull. Seismol. Sot. Am., 74: 925-931. Saada. AS., Fries, G. and Ching-Chang, K., 1983. An evaluation of laboratory testing techniques in soil mechanics. Soils Found., 23: 98-l 12. Tchalenko, J.S., 1970. Similarities between shear zones of different magnitudes. Bull. Geol. Sot. Am.. 81: 1625-1640. Vialon, P., 1979. Les deformations continues-discontinues des roches anisotropes. Eclogae Geol. Helv., 72: 531-549. Zoback, M.D. and Healy, J.H., 1989. Overview of in-situ stress measurements in the Cajon Pass scientific drillhole to a depth of 3.5 km. Eos, Trans. AGU, 7: 480. Zoback, M.D. and Healy, J.H., 1992. In situ stress measurements to 3.5 km depth in the Cajon Pass scientific research borehole: implications for the mechanics of crustal faulting. J. Geophys. Res., 97: 5039-5057. Zoback. M.D., Zoback, M.L., Mount. VS., Suppe, J.. Eaton, J.P., Healy, J.H., Oppenheimer, D., Reasenberg. P., Jones, L., Raleigh, C.B., Worry. LG., Scotti. 0. and W~n~orth, C., 1987. New evidence on the state of stress of the San Andreas fault system. Science, 238: l105- I I Il.
Tectonophysics, 2 11 ( 1992) 295-303 Elsevier
Science Publishers
B.V.,
Amsterdam
The change in orientation of subsidiary shears near faults containing pore fluid under high pressure J. Byerlee U.S. Geological Sunsey, 345 Middlefield Road, Menlo Park, CA 94025, USA (Received
June 13, 1991; revised version accepted October
I, IYYI)
ABSTRACT
Byerlee, J., 1992. The change in orientation Mikumo,
K. Aki,
Precursors.
M.
Ohnaka,
of subsidiary shears near faults containing
L.J. Ruff
and P.K.P.
Spudich
(Editors),
pore fluid under high pressure. In: T.
Earthquake
Source
Physics and Earthquake
Tectonophysics, 211: 295-303.
The mechanical
effects of a fault containing
cally from
the core of the fault
mechanical
implications
stress is oriented
zone
near-lithostatic
to the adjacent
for the orientation
country
fluid pressure in which fluid pressure decreases monotonirock is considered.
This
fluid
pressure
distribution
of subsidiary shears around a fault. Analysis shows that the maximum
at a high angle to the fault in the country rock where the pore pressure is hydrostatic,
and rotates to 45” to
the fault within the fault zone where the pore pressure is much higher. This analysis suggests that on the San Andreas where
heat flow constraints
require
that the coefficient
of friction
has
principal fault,
for slip on the fault be less than 0.1, the pore fluid
pressure on the main fault is 85% of the lithostatic pressure. The observed geometry of the subsidiary shears in the creeping section of the San Andreas
are broadly consistent with this model, with differences
that may be due to the heterogeneous
nature of the fault.
Introduction
The lack of a heat flow anomaly over the San Andreas fault (Lachenbruch and Sass, 1992) and the high angle that the maximum principal stress makes with the fault (Zoback et al., 1987), can be explained if the fluid pressure at the center of the fault zone is much greater than the hydrostatic fluid pressure in the country rock (Byerlee, 1990; Rice, 1992). While this idea is not new, previous models have led to the unsatisfying prediction that the fluid pressure within the fault exceeds the magnitude of the least principal stress and, as a result, hydrofracture would occur allowing the high pressure fluids to escape (Zoback et al., 1987). This difficulty, however, is overcome in both the Byerlee model and in the Rice model by
Correspondence Middlefield
Elsevier
to: J.D. Byerlee,
Road, Menlo
Science
Publishers
U.S. Geological
Park, CA 94025, USA.
B.V
Survey, 345
assuming that the fault zone material fails in shear before the conditions for tension fracture are reached. An important result of this shear failure process is that the magnitude of the minimum principal stress increases as the main fault plane is approached. Consequently, the pore pressure at any point never exceeds the magnitude of the local minimum principal stress, so that hydrofracture cannot occur. In the continuous flow model of Rice (1992), the very high pore pressure can be maintained in the center of the fault zone if the loss of fluid into the country rock is made up by the injection of water up the center of the fault zone from the mantle. This model requires very low permeability of the fault zone so that a heat flow anomaly associated with the injection of hot fluid from below does not occur near the fault. Permeability must be lower in the country rock than in the fault zone to channel fluid up the fault zone, but the permeability must also be high enough so that
2%
hydrostatic pore pressure can be maintained in the country rock. These potential problems do not arise in the model proposed by Byerlee (1990) because it is assumed that high pore pressure is generated during compaction of the water-saturated gouge as it is sheared and the structure of the fluid channels within the fault zone prevents the escape of this overpressured water unless the pressure gradient between the center of the fault zone and the country rock exceeds a threshold value. There is experimental evidence of a threshold gradient in dense clay and there is a well-established physical mechanism for the existence of a threshold gradient in the fault zone, regardless of its composition, if the width of the channels for fluid flow are less than ten times the diameter of a water molecule (Byerlee, 1990). There is also evidence for the existence of a threshold gradient in other geological situations. For example, in studies of the structure, pore pressure distribution, and the geological histories of many deep oil reservoirs, it is found that the pressure within the fluid compartments can only be maintained for the tens of mihions of years of their existence if the permeability of the oil seals surrounding the compartments is zero (Hunt, 1990, 1991). These observations can be explained if the channelways in these dense fine-grained rocks are so small that below the threshold gradient flow does not occur and the permeability is zero. It is possible that in some regions pore pressure is maintained by the injection of fluid from the mantle as proposed by Rice (1992) and in other regions it is maintained because the threshold gradient is not exceeded, as proposed by Byerlee (1990). It may be possible to find out whiqh meehapism operates in a given region by det~~~~~~~ the origin of the fluid by isotopic studies of Ihe pore fluid within the fault zone. With the aId of a Mohr circle construction, Rice (1992) has shown that the direction of the maximum princjpal stress &ranges within the fault zone. This resulf applies to the Ryerlee model as well because mechanically both yodels are identical, even though the mechanisms for maintaining the high pore pressure at the center of the
fault zone are different in the two models. In his analysis, Rice (1992) made the reasonable assumption &hat when slip occurs on the main fault, it is the Coulomb slip plane. This is consistent with what would be predicted during simple shearing of granular materials obeying the nonassociated flow rule developed by Mandl and Fernandez Luque (1970). The theory predicts that the maximum principal stress makes an angle of @=7r/44 f tan _ ‘pi with the normal to the fault plane, where pi is the coefficient of internal friction of the material in the fault zone. In an experimental study designed to determine the (orientation of the stress directions during the formation of the subsidiary Riedel shears and the main fault Mandl et al. (19771 found. to their surprise that both the Riedel shears and the main fault were formed when the maximum principal stress made an angle of 7r/4 to the main fault pIane. These experimental results fed Mandl (1988) to the conclusion that “a final throughgoing fault which develops under tectonic simple shearing in rocks that initially were in a state of isotropic stress or transpression in the deformation plane is not of the Coulomb-type, albeit that it is formed by the cooperation of Coulomb-type precursory shears. The nonCoulomb-type fault zone, which was forced to develop parallel to moving boundary rocks, is bounded by planes of m~imum shear stress (or nearly so) and is therefore referred to as simpleshear fault.” If, in the simple shear geometry, the maximum principal stress makes an angle of 45” to the plane of the fault, then the subsidiary Riedel shears which are generally inclined at an angle of about 15” to the main fault are Coulomb shears and Mandl (1988) suggested that in the region of overlapping Riedel shears as shown in Figure 1, the local stress direction is rotated until another Coulomb shear, which is commonly known as a P shear, is developed. In this way unrestricted shear displacement can occur on the main fault plane. With large displacement an anastomosing series of R and P shears are developed in the main fault zone. Structures such as this are. commonly observed on both natural and artificial faults (Tchalenko, 1970; Moore and Byerlee, 1991;
THE CHANGE
IN ORIENTATION
OF SUBSIDIARY
297
SHEARS
the insert. The x and y axis are as shown and the z axis is normal to the plane of the figure. The main fault plane is parallel to the yz plane. In the country rock we assume that the pore pressure p is hydrostatic and that the maximum principal stress crlc is only slightly greater than the vertical stress a,. (We will use the convention that subscript ‘c’ denotes country rock and ‘f denotes the main fault zone.> The only place, near the San Andreas fault, where the in situ stresses have been measured as a function of depth is at Cajon Pass where Zoback and Healy (1992) found that the difference between the maximum and minimum principal stress increased with depth at a rate that is consistent with laboratory measurements of the coefficient of friction of crustal rocks, provided that the pore pressure to at least a depth of 3.5 km is not significantly greater than hydrostatic. In addition it was found that the maximum horizontal stress has a value approximately equal to, to slightly greater than the vertical stress, and increases with depth at a rate similar to that of the vertical stress. While the present paper assumes that plc is essentially equal to a,, it also has general application because if c,, > cY then p = ACT.,= (ho;/c~,,b,, and the anaiysis that foIlows should be modified by multiplying A by ~,/a,, to obtain the general solution. We assume in our model that the pore pressure p decreases linearly from
Moore and Byerlee, 1992). Near natural faults that have simple shear geometry, Hancock (1972) and Vialon (1979) observed that the angle which tension cracks, and hence (or, make with the shear plane is close to 45”. Analysis As presented here, we seek simple expressions for the orientation of the maximum principal stress, the strike of the subsidiary faults throughout the fault zone, and the apparent coefficient of friction, as a function of h,, the ratio of the pore pressure in the fault zone to the magnitude of the vertical stress. To be consistent with the laboratory and field observations, we will here assume that the main fault is the plane of maximum shear stress and that in the region between the central fault plane and the country rock, the subsidiary faults are Coulomb shears. The displacement on these subsidiary shears is very small because of the constraints on their movement by the stronger country rock. The small amount of shear that occurs on these planes accommodates a small amount of compaction of the material in the fault zone. This deformation sufficiently modifies the magnitude of the minimum principal stress to prevent hydrofracture. Figure 1 is a Mohr representation of the state of stress in the fault zone shown schematically in
0 I
PC
ff3c
p
Pf -3
03f
Olc
“1
“If
Fig. 1. Mohr representation of the state of stress during sliding in the simple shear geometry shown in the insert. P,, and r are the normal and shear stresses which for equilibrium must be the same on all planes parallel to the yz plane. In the standard nomenclature R is the R, Riedel shear and P is a thrust shear which form an anastomosing network in the main fault zone. The subscripts c and f refer to the state of stress, the failure angle .9 and A in the country rock and at the main fault, respectively.
a value of hr~~,~ at the center of the fault zone to hydrostatic pressure of hc~lc in the country rock so that at any point at a distance x from the country rock:
where D is the half-width of the fault zone. Subject to this distributi(~n of h and the assumption that the plane of maximum shear stress is parallel to the fault plane at the main fault, wc solve for the stress field everywhere invoking only continuity of stress. We further assume that the fault zone material obeys the effective stress law and that its constitutive property is such that: ‘r, = ni?;
main fault cos 2Hr = 0 and sin 28, -L I, so that WC have from eqs. 6 and 7:
Equating ey. 0 with cq. # and ry. rearranging WC have: ( 12 ” 1) .- .__. __.__(,, II.
It
wth
cq. ‘) ami
( fl --. 1) j ---‘------Acr,c. 1 60s .3ti II
(2)
where ft is a constant greater than I, (7,= ((I; -- 1~) = (u; - hfr,,), h is given by cy. 1. Equation 7 reduces to: (7’3 =
;
[a,“t
(n - l)Aa,,]
_
at any point in the fault zone. We next make use of the standard relations: (a,+cr,)+(cr,-a~)cos28=2~r;
(1)
or- it_‘(r,, -__.I1
01 ..- !i
; --~ n,tr:~j
/I
i. i i !
Dividing ~4. i 1 by eq. 10, we have after some a&bra:
and (5j
(WI - tag) sin 2@= 27
where u;, and I are the normal and the shear stresses acting on a plane parallel to the yr planc and 0 is the angle between the (r, direction and the normal to that plane. By substituting for CT,; from eq. 3 into eqs. 4 and 5 we have:
--------fJ
I
-
( t1 -- 1) -----/hJr, 17
’ COS
?t)
For equilibrium in this simple shear system it is required (see Fig. 1) that both c,, and r be the same on all the planes parallel to the yz plane. At the main fault glf makes an angle of 45” to the plane of the fault (Fig. 1). Therefore, at the
f:rorn Figure I it can be seen ttuii:
f:rom ey. 3. (rIi can be expressed I(( terms of‘ r,r,, and ft. If the density of the overtying rocks is 73iHI kg/m’ then n; =- (1.4 and h3 s~l(~~titutin~ thcsc values into eq. 13 we have:
X [cos lti, -t sin I@,].
4 141
CI,~/U,~ is a maximum when cos 2H, = sin 28, 1
I/ v’?. If n = 3 which is about the ratio of e,jif_{ for rocks close to the San Andreas (Zoback and
THE CHANCiE IN ORIENTATION
OF SUBSlDIARY
299
SHEARS
Healy, 19891, then from eq. 14 the maximum value for (T,~/o~~ is 1.08. From Figure 1 it can be seen that vlC da, ,< cif so that @,/v~~ =: au/alC = 1, and eq. 12 then reduces to the approximate solution: tan 28=
1 --A, ~ [ A,-A
1
An exact solution at the counts rock can be found by recognizing from Figure 1 that: Ulf -
03f
= h
-
r3,)
sin 28,
(16)
Then by expressing @s3fand c3C in terms of elf and glC and as before when A,= 0.4, eq. 16 reduces to: Plf
-
=0.6 sin 28,+A,
(17)
g1c
By substituting this value into eq. 12 and as before by assuming n = 3, we have after some algebra: 2 sin 20, - cos 28, = 4 - 5hf
(18)
The approximate solution for eC at the country rock from eq. 15, and the exact solution for @, from eq. 18 are plotted as a function of A, in Figure 2. For values of A, less than 0.8, the approximate solution provides an upper bound for 8,, but for values of hf greater than this it
0 i ._ _. _-.-~_-.~_..
04
05
._i.L.
0.6
i
0.7
CL?
..L-,i
=-=---J i.
ii9
-.
1 :,
Xf
Fig. 3. pa, the apparent coefficient of friction, calculated for the stress conditions and pore pressure in the country rock, plotted as a function of h, in the main fault zone.
becomes a lower bound. For A, > 0.7 the error in using the approximate solution is less than 2”. The heat Row constraint requires that the apparent coefficient of friction fl;, < 0.1, where: *a=
-=:- Tc CT nc --PC
Tf %f -PC
(19)
and TV,
Tf, q,,, q,, are the shear and normal stress components as illustrated in Figure 1. Then by substituting the values for rf and o;lf from eqs. 8 and 9 into eq. 19 and using A, = 0.4, we have:
If, as before, we assume that n = 3 and CY,~ = crlcr then eq. 20 reduces to: 1 -A,
iCLa=0.8+A,
3.6
08 hi
10
Fig. 2. A plot of Ba, the angle that the maximum principal stress makes with the main fault plane in the country rock against h,, the ratio of the pore pressure in the main fault zone and the maximum principal stress in the country rock which in our model is approximately equal to 0~ due to the weight of the overburden. (3, for both the approximate solution and the exact solution are given in the figure.
cw
pa is plotted as a function of A, in Figure 3. If kL, < 0.1, then from the figure A,>, 0.85, where in Figure 2 the approximate solution gives values for 8 very close to the correct values. From eq. 9, if II = 3 and cle = vlf, then TV= Co-,,/3)(1 - Af). If A, = 0.85 and a,, = a,, as it seems to be for the San Andreas fault, and if we assume that the density of the overIying rocks is 2500 kg/m3, then we have -rr = O.O.S(Z)z, where Tf is the shear stress in MPa and z is the depth in km. If the total depth of the zone where frictional heat is being generated is 15 km, then the aver-
age shear stress on the fault is 9.375 MPa, which is close to the upper bound of 10 MPa required by the heat flow constraints. This is simply another way of expressing, as we did above, that the heat flow constraints require that pLi,G 0.1. When A, = 0.4, the pore pressure is hydrostatic everywhere and from Figure 3, JA;~= 0.5. The internal coefficient of friction pi is given by the slope of the failure envelope for the subsidiary shears which from our model is given by: ui=tan[sin-‘~~~]=0577ifn=3
(22)
Thus pL, is smaller than pi in our simple shear system. In experiments to determine the constitutive properties of soils, it has been observed that the simple shear tests give shear strengths considerably less than what is found in standard triaxial experiments (Saada et al., 19831, but to date there has been no satisfactory explanation for this. In the analysis of the experimental data, it is assumed that the shear plane in the simple shear experiments is the Coulomb failure plane, but the experiments of Mandl et al. (1977) have shown that this assumption is not correct. With this system and the one analysed in this paper the main failure plane is the plane of maximum shear stress and this explains why gL, < pi in our model and in the soil mechanics experiments. In experiments designed to measure the coefficient of friction of brittle materials a layer of fault gouge is eventually developed between the stronger forcing blocks and with further displacement between the surfaces the fault gouge deforms in the simple shear mode analysed in this paper. In deriving the approximate solution (es. 21) for the case where the pore pressure is not constant throughout the fault zone, we assumed that heir= clC but in the special case where the pore pressure is constant, as it is in the usual friction experiment, the exact solution is given by:
n-i Pa = -
i-It-1
regardless of whether the rocks are dry or contain pore fluids under pressure.
Until now it has been difficult to explain why pi (eq. 22) for the bulk properties of brittle particulates varies between wide bounds, but in friction experiments where we are really studying the rheological properties of the fault gouge, pa ieq. 23) for most rocks is about 11.75 regardless of their bulk strength. From eq. 23 pi’y, = t1.75, then n = 7 which is about the value measured for the bulk strength of dense sand (Lamb and Whitman. 1979). JL;,, however, is not strongly dependent on ra, for example pL;,approaches 1 as II approaches infinity, so that the coefficient of friction can never be greater than 1 regardless of the bulk strength of the gouge. The other limiting case in our model is when A,= 1, then from Figure _i p%,‘1 0. What this means is that or = c.\ =p at rho center of the fault zone so that the fault has no strength and movement can then occur on the fault with an infinitesimally small shear stress in the plane of the fault. If the main fault is vertical, the movement can even occur in the vertical direction so that the fault acts as a high-angle reverse fault with a dip of 90°. If the main fault is horizontal, it could be called a horizontal ov~rthr~lst or a normal fault with zero dip. If we assume that the pore pressure decreases linearly from the center of the fault zone to the country rock. we have h as a fu~lcti~~ of x from eq. 1. By substituting this value into eq. 15 and by assuming that h, I= 0.4: 1 “’ A,
tan 28 =
i A,
--I
0.4 - (A, - 0.4).X,/l) i
(244
H throughout the fault zone is plotted as a function of x/D for A, = 0.85 and 0.99 in Figure 4. In both cases tl is equal to 45” at the fault plane as required in our model and at the country-rock boundary # is about 10” when A, =: 0.85 and about 1” when A, = .99. In the limiting case analyzed by Byerlee (1990), 0, = 0 when hi = 1 For geological applications a more useful figure would be a map view of the trace of the subsidiary shears within the fault zone. In laboratory experiments it has been found that R, is far better developed than its R, conjugate. The R, subsidiary shear is shown in the insert in Figure
THE CHANGE IN ORIE~AT~ON
0
0
0.2
301
OF SUBSIDIARY SHEARS
0.6
0.4
0.8
Equation 2.5has been integrated numerically and the results are shown in the map view of the main fault trace, the country rock fault zone boundaries and the subsidiary faults for A, = 0.85 in Figure 5. To obtain the results shown in Figures 4 and 5, it was assumed that the pore pressure decreased Iinearly with distance from the main fault. The results are correct if the permeabili~ in the continuous flow model of Rice or the threshold gradient in the no flow model of Byerlee are independent of the effective pressure. If these conditions are not satisfied, then the correct solution can be found by inserting the correct value for A into eq. 15 to obtain 8 as a function of x and then integrating the equation:
1.0
X/D
Fig. 4. 8, the angle that the maximum principal stress makes with the normal to the plane of the main fault, is plotted as a function of any distance x from the country rock normalized by the half-width D of the fault zone, for ht =0.85 and A, = 0.99 in the main fault.
dx 5, where from the figure we have tan4dy = dx. ff,= 7r/3 - B is the angle between the strike of the subsidiary shear and the main fault trace and 8 is given as a function of x in eq. 24. Then by integration we have:
’ =f tan(7r/3 - 0)
It should be noted that regardless of the pore pressure distribution throughout the fault zone if A, is known and the pore pressure in the country rock is hydrostatic then SC, the angle the maximum principal stress makes with the normal to the main fault, is given exactly by eq. 18. Figure 6 is a map of the fault zone in the creeping section of the San Andreas fault in
dx Y=j
tan 7r/3-
+ tan-’
Cl--Ar)
h,-0.4-(A,-0.4)x/D
Ii Country
(26)
Rock
Cou~ock x.=0.4 Fig. 5. A map view of the geometry and the sense of movement on subsidiary faults throughout the fault zone, for A, = 0.85. It is not suggested that the subsidia~ faults are continuous across the fault zone: it is simply that the geometry of these faults is as shown if the pore pressure distribution is the same on both sides of the main fault plane.
312
central California as mapped by Rymer ( 1981) and described in more detail by Rymer et al. (1984). The northeast and southwest boundar) faults are high-angle reverse faults. It appears that the rocks between them arc being thrust up and out of the fault zone. The main fault trace i\ not straight and contains constraining and rcleasing jogs. There are some variations in the strike of the subsidiary faults along the length of the main fault trace which may be caused by variability in the constitutive properties of the material in the fault zone or it could be that the subsidiary faults belong to different populations. Our model would predict that those that make an angle 01‘ about IS” to the main fault trace, were formed when the pore pressure was hydrostatic everywhere, but those that make a maximum angle of 50” to the main fault were formed when A! was about 0.85. If this is correct. then the most recent faults should be the steepest if the present dircction of the maximum principal stress is about W to the fault as the observations of Zoback ct al. ( 1987) would suggest. Some of the subsidiary faults are concave towards the main fault trace, whereas the theoretical solution requires that they curve the other way. The significance of this is unclear but ma) be related to the local inhomogeneous stress field caused by irregularities in the geometry of the main fault. It is also possible that some of the
variation of geometry of subsidiary shcara couic! partly arise from finite rotational strain within the fault zone. It should he noted that the ahsch lute value of the pore prcssu~~~ Luridthe i;trcssch arc dependent only on h. which 14Indcpendcnt (tt depth so that the gcometr\ oi rhe suhsidiar! faults is indepcndcnt of depth. fi the map talc i\ normalized by II. the half-uidth ti! Ihe fault zone. 2s it is in Figure: 5. It has been pointed out t hilt ihr’ distribution co! aftershocks indicates that the 1:~gc-hcale \uri‘acl irregularities of the San Andrcas tault per&s: throughout the seismogenic LOW 6Eaton ct rd.. 1970: Bakun et ai., IYXO: ticascnberg and Ellsworth. I(P-2) but it is nol clc,tr ihat thus i\ ;II~s~I true for the subsidiary faults LLX 11til’n1L)dcIwould suggest. The abnormally high Ilii!!rt pressurc’k cttcountered in wells drilled for ~iii i:t~~the Mcstcrt: margin of the great valley. Icd Berry (1077) to suggest that at a depth grcatcr thar! ;I tcw kilomctcrs. the Franciscan rocks adjacent to Ihe San Andreas fault may contain pore fluids ,tt pussurcs much greater than hydro~t:.~tic, 1:‘ this i> correct. then the geometry of the subsidiary t’auits below this depth may bc yuilc diffcrcnt from what it is on the surface.
SUBSIIXAHY
N,E
B@JNDARY
FAUL’
-
Fig. 6. Map of the main fault trace. the subsidiary faults and the boundary central California.
FAULTS
modified
faults in the creeping section of thy &II
from Rymer (10x1)
Andrras
f’aulr rn
THE C’HANGE IN ORiENTATlON
OF SUBSIDIARY SHEARS
in hydraulic pressure communication with adjacent compartments nor with the overlying hydraulic regime (Hunt, 1990). If this is also true in California, then the high pore fluid pressures measured in the oil reservoirs should have little or no effect on the mechanical behavior of the San Andreas fault system. In any case, detailed mapping of the geometry of the subsidiary faults may give an indication of the pore pressure distribution in the upper crust, in and adjacent to the fault. References Bakun, W.H., Stewart, R.M., Bufe, C.C. and Marks, SM., 1980. Implication of seismicity for failure of a section of the San Andreas fault. Bull. Seismol. Sot. Am., 70: 185201. Berry, F.A.F., 1973. High fluid potentials in California Coast Ranges and their tectonic significance. Bull. Am. Assoc. Pet. Geol., 57: 1219-1249. Byerlee, J., 1990. Friction, overpressure and fault normal compression. Geophys. Res. Lett., 7: 2109-2112. Eaton, J.P., O’Neil, M.E. and Murdock, J.N., 1970. Aftershocks of the 1966 Parkfield-Cholame, California. earthquake: A detailed study. Bull. Seismol. Sot. Am., 60: 1151-1197. Hancock, P.L., 1972. The analysis of en-echelon veins. Geol. Mag., 109: 269-276. Hunt, J.M., 19YO. Generation and migration of petroleum from abnormally pressured fluid compartments. Bull. Am. Assoc. Pet. Geol.. 74: I-12. Hunt, J.M., 1991. Generation and migration of petroleum from abnormally pressured fluid compartments: reply. Bull. Am. Assoc. Pet. Geol., 75: 328-330 and 336-338. Lachenbruch, A.H. and Sass, J.H., 1992. Heat flow from Cajon Pass, fault strength and tectonic implications. J. Geophys. Res., 97: 4995-5030. Lamb, T.W. and Whitman, R.W., 1979. Soil Mechanics, SI Version. Wiley, New York. Mandl, G., 1988. Mechanics of Tectonic Faulting. Elsevier, New York., N.Y., 407 pp. Mandl, G. and Fernandez Luque, R., 1970. Fully developed plastic shear flow of granular materials. Geotechnique, 20: 277-307.
303 Mandl, Cl., deJong, L.N.J. and Maltha, A., 1977. Shear zones in granular material: an experimental study of their structure and mechanical genesis. Rock Mech., 9: 95-166. Moore, D. and Byerlee, J., 1991. Comparison of the San Andreas fault, California, and laboratory fault zones. Bull. Geol. Sot. Am., 103: 162-774. Moore, D.E. and Byerlee, J., 1992. Relationships between sliding behavior and internal geometry of laboratory fault zones and some creeping and locked strike-slip faults of California. In: T. Mikumo, K. Aki. M. Ohnaka. L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: Reasenberg, P. and Ellsworth, W.L.. 1982. Aftershocks of the Coyote Lake, California, earthquake of August 6, 1979: A detailed study. J. Geophys. Res., 87: 10637-10655. Rice, J.. 1992. Fault stress states, pore pressure distributions, and the weakness of the San Andreas fault. Fault Mechanics and Transport Properties of Rock. In: Brian Evans and Teng-Fong Wong (Editors), A Festschrift in Honor of W.F. Brace (based on June 1990 symposium at MIT). Academic Press, London, pp. 475-503. Rymer, M.J., 1981. Geologic map along a 12 kilometer segment of the San Andreas fault zone, southern Diablo Range, California. U.S. Geol. Surv. Open-File Rep. 811173, scale 1:12,000. Rymer, M.J., Lisowski, M. and Burford, R.O., 1984. Structural explanations for low creep rates on the San Andreas fault near Monarch Peak. central California. Bull. Seismol. Sot. Am., 74: 925-931. Saada. AS., Fries, G. and Ching-Chang, K., 1983. An evaluation of laboratory testing techniques in soil mechanics. Soils Found., 23: 98-l 12. Tchalenko, J.S., 1970. Similarities between shear zones of different magnitudes. Bull. Geol. Sot. Am.. 81: 1625-1640. Vialon, P., 1979. Les deformations continues-discontinues des roches anisotropes. Eclogae Geol. Helv., 72: 531-549. Zoback, M.D. and Healy, J.H., 1989. Overview of in-situ stress measurements in the Cajon Pass scientific drillhole to a depth of 3.5 km. Eos, Trans. AGU, 7: 480. Zoback, M.D. and Healy, J.H., 1992. In situ stress measurements to 3.5 km depth in the Cajon Pass scientific research borehole: implications for the mechanics of crustal faulting. J. Geophys. Res., 97: 5039-5057. Zoback. M.D., Zoback, M.L., Mount. VS., Suppe, J.. Eaton, J.P., Healy, J.H., Oppenheimer, D., Reasenberg. P., Jones, L., Raleigh, C.B., Worry. LG., Scotti. 0. and W~n~orth, C., 1987. New evidence on the state of stress of the San Andreas fault system. Science, 238: l105- I I Il.