Pageoph, Vol, 116 (1978), Birkh~tuser Verlag, Basel
The Effect of Water on Stress Relaxation of Faulted and
Unfaulted Sandstone
By E. H. RUTTER t) and D, H, MAINPRICE1) 2)
Abstract-A series of stress relaxation experiments have been carried out on faulted and intact
Tennessee sandstone to explore the influence of pore water on strength at different strain rates. Temperatures employed were 20, 300 and 400~ effective confining pressure was 1.5 kb and strain rates as low as
10- lo sec-) were achieved. Most samples were prefaulted at 2.5 kb confining pressure and room temperature. This is thought to have secured a reproducible initial microstructure.
The strength of the dry rock was almost totally insensitive to strain rate in the range 10 -4 to 10-3o
sec-1. In contrast, the strength of the wet rock decreased rapidly with strain rate at rates less than
10-6 sec 1. Brittle fracture of the quartz grains which constitute this rock is the most characteristic mode
of failure under the test conditions used.
The experimental data are discussed in terms of the possible deformation rate controlling processes,
and it is suggested that in the wet experiments at intermediate to high strain rates (10 -7 to 10 4 sec- t) the
observed deformation rate is controlled by the kinetics of water assisted stress corrosion, whilst deformatier: at low strain rates (ca. I(; -~ sec- ~) is contr~Iled by a pressure solution process.
The results have implications for the rheology of fault rocks at depths of perhaps 10 to 15 km in sialic
crust.
Key words: Strength o f rocks; Crack growth with water; Rock mechanics.
1. Introduction
This is a preliminary report on a continuing experimental programme designed
to study the effects of water on the mechanical behaviour of rocks to very low strain
rates. The experiments were initially devised to test a prediction based on a theoretical
model by RUTT~r: (1976) that rock deformation by pressure solution might be experimentally detectable at strain rates of the order of 10 .9 sec - t or less at moderate
temperatures (ca. 300~
and effective confining pressures (ca. 1.5 kb). At more
typical laboratory strain rates (ca. 10 .5 sec-i) silicate rocks are usually extremely
brittle under these environmental conditions.
In order to explore the effects of a wide range of strain rates in a practicable
period of time the stress relaxation technique was employed. The particular advantages
of this technique for long term experiments are discussed in the next section.
~) Department of Geology, Imperial College, London SW7, Great Britain.
z) Research School o f Earth Sciences, Austraiian NationaI University, Canberra, A.C.T., Australia.
Stress Relaxationof Faultedand UnfaultedSandstone
635
In this preliminary study we have had two simple objectives. Firstly, to contrast
the mechanical behaviour of a quartz sandstone (Tennessee sandstone) in the presence
and absence of pore water' (taking care to exclude any unwanted pore pressure effects)
and, secondly, by repeating these long term experiments, to show that the effects
observed are reproducible. In these respects the experiments have been entirely
successful. We will show that in the strain rate range 10 - 5 to 10 - 10 sec - ~the strength
of oven dry Tennessee sandstone is almost insensitive to strain rate changes whereas
the same rock tested with pore water but at the same effective confining pressure shows
a marked reduction in strength, particularly at the lower end of the strain rate range.
A discussion of the interpretation of these experimental results is given and it is
concluded that in the wet experiments deformation at the lowest strain rates involves
rate control by pressure solution, giving way to rate control by stress corrosion
cracking at higher strain rates. The geological implications of the results are discussed,
and particular emphasis is given to their significance for studies of earthquake
mechanisms and stable sliding on faults.
2. Experimental design
The stress relaxation testing method
Stress relaxation testing is usually used in conjunction with constant strain rate or
constant stress (creep) tests. After an arbitrary amount of strain the specimen length
is held constant, and the applied stress is allowed to relax with time. During an ideal
relaxation test (on an infinitely stiff machine), elastic strain energy in the specimen is
dissipated through permanent deformation of the specimen at a rate which is determined by the rheological characteristics of the specimen material. At any instant in
time the permanent strain rate is proportional to the stress relaxation rate, the constant of proportionality being an elastic constant of the specimen material. The
maximum amount of permanent strain which can be accumulated equals the elastic
strain.
The application of the relaxation test in studies of dislocation dynamics has been
described by GUPTA and LI (1970a and 1970b). In the rock mechanics literature, the
relaxation test has been used in rheological studies by RALEIGHand KIRBY (1970),
RUTTER and SCHMID(1975) and SCHMID(1976). EVANS(1973) has used the relaxation
method to study the kinetics of crack growth in glass plates.
In triaxial testing machines it is not usually possible to hold the length of the
specimen alone constant during stress relaxation. Rather, it is necessary to hold
constant the length of the specimen plus that of a portion of the machine. This means
that a given stress relaxation requires a longer time because the elastic strain energy
in the portion of the machine between the constant length points must also be dissipated in the specimen, therefore the permanent strain accumulated in the specimen
636
E.H. Rutter and D. H. Mainprice
(Pageoph,
during relaxation will become greater than the specimen elastic strain. Thus if the
machine stiffness is equal to the specimen stiffness the time required for a given
relaxation will be doubled. A further effect is that if there is any kind of time dependence in the machine relaxation, this will be imprinted on the total relaxation curve.
The method of treatment of machine relaxation effects has been described by GuIu
and PRATT (1964).
The stress relaxation test offers certain advantages which are particularly important for the experiments reported here. The general form of the constitutive flow law
for thermally activated deformation mechanisms is
= A exp ( - H/RT)f~(a)f2(S)
(1)
where ~ is the strain rate, A a constant, H an activation enthalpy, R the gas constant
and T is the absolute temperature, f~(o-) is a function of stress andf2(S) is a function
which describes the effect of specimen structure on strain rate. The form of the flow
law follows from the experimental fact that the relationships between strain rate and
any one of temperature, stress or structure can be determined whilst holding the other
two constant (DORN, 1957). In determining strain rate/stress relationships it is not
only necessary to ensure constant temperature but also constant specimen microstructure if extrapolation to strain rates outside the experimental range using a flow
law of the form of equation (1) is to be considered. Because the complete Stress/strain
rate relation is determined from a relaxation on a single specimen over a small range
of specimen strain, there will obviously be no scatter of results due to specimen variability and, provided there is no significant structural change (e.g., recrystallisation,
change in microcrack density, extensive recovery, etc.) the constant structure requirement will be fairly closely met. Further, if a succession of relaxations are carried out at
different strains on a material which suffers significant structural change with strain
(e.g., through work hardening), then the effects of structural change on rheology may
be studied. Finally, in tests on rocks at high pressure and temperature the stress
relaxation test permits the range of accessible strain rates to be extended about two
orders of magnitude below the normal lower limit of laboratory strain rates (10 -s
sec- 1). This is because with a force gauge inside a pressure vessel relaxed load can be
easily and accurately measured over a very small increment of specimen strain in a
reasonable period of time.
Test material
The material used for these experiments comprised 1 cm diameter by 2 cm long
cylinders of Tennessee sandstone cored perpendicular to bedding. This rock consists
of 84 percent sub-rounded quartz grains with a predominantly phyllosilicate matrix.
The quartz grains were free from discernible optical strain features and possessed a
fairly uniform grain size of 150 gin. A scanning electron microscope (SEM) study of
Vol. 116, 1978)
Stress Relaxation of Faulted and Unfaulted Sandstone
637
the undeformed material revealed that most quartz grains had quartz overgrowths
with well developed crystal faces bearing growth features such as steps and terraces
(Plate la). The overgrowths are interpreted as having developed during diagenesis.
The effective porosity of the rock is 6.7 percent and the permeability is 3.7 x 10 -*
darcy (R. HARDY,personal communication, 1972). The experimental programme called
for the rock to be tested both wet and dry. The dry samples were oven dried for at least
one week at 120~ and the wet samples were prepared by the vacuum saturation
technique (RUTTER, 1972).
Plate la
Scanning electron micrograph showing well developed diagenetic overgrowth features on quartz grains in
undeformed Tennessee sandstone, plus interstitial clay minerals.
Apparatus and experimental conditions
Three identical testing machines were used (at various times) for these experiments, and have previously been described by RUTTER (1972). A series of standard
constant strain rate tests were performed at room temperature, at various confining
pressures up to 3.0 kb and at a strain rate of 3 x 10 - 5 sec- 1 in order to determine the
basic mechanical characteristics of the material both dry and wet (zero pore pressure).
638
E, H. Rutter and D. H. Mainprice
(Pageoph,
Most of the relaxation tests were carried out at 300~ and lasted between two and
ten weeks. One relaxation was carried out at 400~ and one at room temperature on
wet rock. All of the relaxation tests were carried out at an effective confining pressure
of 1.5 kb. In the case of the wet tests a pore fluid pressure system was employed to
provide a nominal pore water pressure of 0.15 kb so that the specific gravity of the
pore water remained close to unity at all test termperatures used. Because of the low
strain rates used, the relatively high specimen porosity and permeability and low value
of pore pressure compared to confining pressure, it is believed that there could be
no significant effects due to dilatancy hardening (BRACE and MARTIN, 1968).
F r o m the preliminary constant strain rate tests it was known that at the conditions
chosen for the relaxation tests brittle fracture would be the most characteristic and
obvious mode of failure of the quartz grains comprising this rock, at least at the high
strain rate end o f each relaxation. In order to ensure comparability between the
results of relaxation tests on different specimens it was necessary to ensure that each
specimen had the same microstructure (e.g., crack density) at the start of each experiment. It was considered that for a significant interval of strain ( ~ 1 percent) in the
post shear failure sliding region of the stress/strain curve the crack density would be
Plate lb
Optical micrograph showing typical microstructure of the deformed specimens. On either side of a glass
indurated fault plane are microfractured quartz grains. The density of microfracturing falls off over about
20 grain diameters from the fault. Microfractures tend to be oriented along the applied compression
direction, parallel to the short side of the photograph (crossed polars).
Vol. 116, 1978)
Stress Relaxationof Faulted and UnfaultedSandstone
639
fairly constant. In the pre-shear failure region the microcrack density changes
extremely rapidly with strain. Due to specimen variability it would under the latter
circumstances be impossible to produce similar microstructure conditions at the start
of relaxation tests on different specimens. The adopted experimental procedure
therefore involved prefracturing each specimen until steady sliding occurred on a
through going shear fault at room temperature and 2.5 kb confining pressure. This
resulted in a region of crushed rock in the shear fault zone, bounded by wide areas in
which most quartz grains were either partly or through fractured (Plate 1b), the
intensity of microfracturing being inversely related to distance from the main fault.
Specimens prepared thus were heated at lower pressure, and reloaded at a strain rate
of 10 -4 sec 1 until frictional sliding on the fault recurred and then relaxed. The 300~
relaxation experiments were repeated several times in order to confirm observations
of the contrasting behaviour of wet and dry rock.
In order to obtain a preliminary idea of the effects of structural variations, two
wet samples which had not been loaded to their ultimate strengths were relaxed at the
same temperature/pressure conditions as above. By loading to different fractions of
the ultimate strength, different pre-relaxation microcrack densities were produced. A
third such sample was relaxed at room temperature.
Experimental results
(i) Constant strain rate tests. Figure la shows the results of constant strain rate tests
on wet and dry rock performed at room temperature. The specimens always failed in
a brittle manner, the formation of a through going shear failure surface accompanying
the stress drop after the ultimate strength was reached.
The observed effects of water on both ultimate and residual (frictional sliding)
strengths are characteristic of many rocks (COLBACKand WIID, 1965; RUTTER, 1972;
ATKINSON, 1975). The curve relating differential stress at failure to confining pressure
is displaced downwards through wetting (at zero pore fluid pressure), the slope being
virtually unaffected. This kind of effect, due to physico-chemical action of the pore
fluid at grain boundaries, may involve several fundamental processes, and these may
be grouped together under the general descriptive term 'Rehbinder Effects' (BOOZER
et al., 1963; RUTTER, 1972; ATKINSON, 1975).
(ii) Relaxation tests on faulted samples. Figures 2a and 2b show the results of relaxation tests performed on prefaulted samples at 300~ wet and dry. The results are
presented in Fig. 2b as loglostress against loglostrain rate. Figure 2a shows typical
raw stress against log~otime data from which the log stress/log stain rate data are
derived. The data points are sampled on a logarithmic time base from the force transducer output. They are converted into stress values in the manner described by RUTTER
(1972) and the apparent relaxation rate is calculated between adjacent data points.
Fluctuations in the apparent relaxation rate therefore appear due to short term drift
E. H. Rutter and D. H. Mainprice
640
(Pageoph,
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(a) Ultimate (short term) and residual (frictional sliding on fault surface) differential stress levels (a 1 - G3)
supported by wet and dry Tennessee sandstone at 20~ at various confining pressures. Dashed lines indicate
trends in data. Results of relaxation tests on wet, unfaulted Tennessee sandstone. (b) Samples raised to
about 90~ of the ultimate (short term) strength prior to relaxation. (c) Sample TS 35, raised to only 60~ of
the ultimate strength prior to relaxation.
originating in the apparatus. The resulting scatter in the log stress/log strain rate plots
increases with decreasing strain rate (Fig. 2). Relaxation rates are converted into
displacement rates using the calibrated stiffness characteristics o f the testing machine
and specimen. Stated strain rates are nominal, and are calculated by dividing the
observed displacement rate by the specimen length.
The effects o f specimen variability and reproducibility between runs m a y be
appreciated from Fig. 2d, in which several relaxation runs at 300~ on wet and dry
prefaulted samples are plotted. The reproducibility is considered to be satisfactory.
At high strain rates at 300~ the dry samples are stronger than the wet ones by an
amount comparable to that observed at r o o m temperature. Comparing both the
ultimate and residual strengths at r o o m temperature and 300~ there is seen to be no
Vol. 116, 1978)
641
Stress Relaxation of Faulted and Unfaulted Sandstone
|
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Results of relaxation tests on pre-faulted Tennessee sandstone. All samples relaxed at 300~ except the
400~ TS 34 relaxation. (a) Log stress/log time curves for wet and dry samples. (b) Log stress/-log strain
rate data for the same samples as in (a). (c) Log stress/-log strain rate data for sample TS 34, relaxed at
400~ and 300~ Point F is that at which temperature controller failure occurred (see text). The points
labelled B were obtained by relaxation at a separately imposed reduced load. (d) Reproducibility on
different test pieces.
significant effect d u e to t e m p e r a t u r e , a n d this o b s e r v a t i o n is consistent with t h o s e
r e p o r t e d b y STESKY et al. (1974) for o t h e r silicate rocks.
W i t h d e c r e a s i n g strain rate the s t r e n g t h o f the d ~ r o c k decreases but slightly a n d
this result is closely c o m p a r a b l e with the effects o f large strain rate changes at r o o m
t e m p e r a t u r e r e p o r t e d for a s a n d s t o n e by DONATH a n d FRUXH (197t) a n d for p o l y crystalline p y r i t e b y ATKINSON (1975). A t strain rates d o w n to a b o u t 10-7 s e c - 1 at
300~ t h e r e is little effect on the s t r e n g t h o f the wet r o c k b u t at lower rates the strength
642
E.H. Rutter and D. H. Mainprice
(Pageoph,
of the wet rock begins to decrease at an accelerating rate. This kind of dramatic
weakening induced in the wet rock has not been reported in any previous study,
probably because the strain rate range which is observed-here lies outside the range
of previous studies on wet rock.
Figure 2c shows the results of experiment TS34, in which the same faulted sample
was relaxed at both 300~ and 400~ Assuming the microstructure to be the same
during both relaxations, the heat of activation, H, of the rate controlling process at
various stress levels during relaxation may be calculated from this data using the
relation
H = - R(~ In ~/~ 1/T)~, s
(2)
assuming H to be constant over the temperature interval employed. This point will
be pursued further in the discussion.
(iii) Relaxation tests on unfaulted samples. Three relaxations were performed on
samples which had not been prefaulted (Figs. lb and lc). TS12 and TS13 were relaxed
at 300~ and 20~ respectively. Both samples were loaded to an estimated 90 percent
of the short term ultimate failure stress. After relaxation and thin sectioning both
samples were found to have no through going fault but a high microcrack density. It
will be seen that the relaxation behaviour of sample TS12 is very similar to that of the
prefaulted samples.
To investigate further the effects of microcrack density, sample TS35 was loaded
to only about 60 percent of the ultimate strength at 300~ and relaxed (Fig. lc). This
sample was examined in thin section after relaxation, as was a similar sample which
was loaded to a similar stress at 300~ but which was not relaxed. Both samples
exhibited virtually zero visible microcrack density. The relaxation of TS35 is also
strikingly different to that of a heavily microcracked sample. No significant relaxation
occurred until a strain rate of about 3 x 10-s sec-1 was reached, beyond which the
strength dropped abiuptly, rather like the rapid relaxation observed at low strain
rates in the cracked samples. From these observations we infer that relaxation at
moderate strain rates depends strongly upon crack density, whilst this dependence is
less marked at low strain rates.
3. Discussion of the results
Description of rheological data
Over the full range of strain rates investigated, the dry samples showed a small but
steady reduction in strength with decreasing strain rate. There is no significant change
in the slope of the data trend. In contrast, in the results for wet rock, at least one and
possibly two significant changes of slope occur, no matter whether the data be plotted
in the log stress/log strain rate or stress/log strain rate coordinate frame. As a matter
Vol. 116, 1978)
Stress Relaxation of Faulted and Unfaulted Sandstone
643
of course, we attempted to describe the relaxation data by polynomial regression
analysis, but in view of the fact that this involves making m~justified presuppositions
about the form of the constitutive flow law, and because examination of the residuals
from the analysis showed no grounds for preferring a fit in either coordinate frame,
we prefer to interpret the data from a qualitative standpoint only.
Deformation mechanisms
In thin section, the texture of all deformed samples was dominated by evidence of
brittle fracture (Plate lb). There is no significant difference in the appearance of
freshly faulted samples compared to prefaulted samples which had been relaxed. In
view of the small strains accumulated during relaxation, this is not surprising. The
same small strains also mean that it is difficult to infer which deformation mechanisms
were dominant during the various phases of stress relaxation. Possible deformation
mechanisms are discussed in the next sections.
(i) Crystal plastic flow. Plastic flow by intracrystalline processes in response to high
mean and deviatoric stresses might be expected to occur at point contacts of prefractured grains especially, perhaps, in the presence of an aqueous pore fluid. We have
observed no evidence from SEM or optical studies to support this hypothesis, however. We are also inclined to discount a significant contribution from plastic deformation because MARTINand DURHAM(1975) have shown that plastic deformation even
at crack tips in quartz deformed at 270~ in the presence of water vapour is insignificant.
A preliminary examination of some of our deformed samples by high voltage transmission electron microscopy by Dr S. H. WHITE(personal communication, 1977) has
so far failed to reveal any evidence for plastic deformation at the points of impingement of quartz grains. Nevertheless, in view of the small strains accumulated during
relaxation, we cannot be certain that crystal plastic flow has not been important,
especially at the lower strain rate ends of our stress relaxation tests, either in the quartz
framework of the rock or in the clay matrix or in both.
(ii) Stress corrosion crack 9rowth. This phenomenon has received much attention in
the materials science literature (e.g., WEIDEgI-IORN, 1968; EVANSand JOHNSON, 1975).
At low levels of the stress intensity factor, K, crack growth in silicate crystals and
glasses takes place slowly (ca. 10 -4 to 10- J0 m sec- 1) and the crack velocity depends
on the concentration of water vapour in the environment. In quartz it is believed to be
determined by the kinetics of the hydrolysis of Si-O-Si bonds at the crack tip to the
weaker, hydrogen bonded Si-OH---OH-Si group (MARTIN, 1972; SCHOLZ, 1972).
The slope of a plot of log crack velocity against log K commonly lies in the range
10 to 20 (EvANs, 1973).
At high K levels crack velocity is independent of water vapour concentration but
shows a marked sensitivity to small changes in K. Thermal fluctuations are believed
644
E, H. Rutter and D. H. Mainprice
(Pageoph,
to influence crack velocity through their effect on the rate of nucleation and
propagation of kinks in the crack tip line (LAWN, 1975).
In an intermediate region of behaviour there is sometimes observed a range of K
which does not change the crack velocity though a sensitivity to water vapour concentration exists similar to that observed at low K values. Such characteristics are
interpreted to mean that the rate of diffusive transport of water to the moving crack
tip is velocity controlling.
In addition to slow crack growth controlled by stress corrosion, in suitable loading
configurations the propagation of fast, unstable cracks may be initiated by stress
corrosion effects. BALL and PAYNE (1976) have described the propagation of such
cracks through quartz single crystals from deliberately introduced notches in samples
tested in uniaxial tension. They showed that in the presence of water vapour nucleation
of unstable cracks occurred arlower stresses than when tested dry. They suggested that
water vapour increased the rate of sharpening of initial free surface cracks, assisted by
the applied stress. SCHOLZ(1972) similarly interpreted his experimental results on the
compression of quartz single crystals.
A load on a brktle rock such as a sandstone is transmitted through regions of point
contact between grains. This leads to the development of extension cracks oriented
predominantly at a small angle to the loading direction. It is the coalescence of a zone
of such axial microcracks along a fault plane of high resolved shear stress and the
total crushing and comminution of grains within the fault zone which leads to the
ultimate failure of a brittle rock. Microseismic emission indicates that many microcracks form rapidly (SCHOLZ, 1968; WU and THOMSEN, 1975). In their experiments on
the crushing of aggregates of glass spheres, GALLAGm~Ret al. (1974) reported small
stress drops and audible noises accompanying the formation of extension cracks
linking point contacts between grains.
Clearly, microcrack propagation between grains is often rapid and unstable, yet
brittle rocks are weaker in the presence of water than when tested dry at strain rates
of the order of 10 -4 sec- ~ (e.g., COLBACKand WIID, 1965). It seems likely therefore,
that the stress corrosion process at high strain rates controls the rate of nucleation of
microcracks rather than their rate of propagation.
(ii.a) High strain rate behaviour of Tennessee sandstone. It is clear that at high strain
rates there is a well marked effect of water on the strength of Tennessee sandstone
(Fig. la). Plate lc shows the surface features of a typical intragranular crack in this
rock. Such features are a characteristic of rapid propagation. We therefore attribute
the weakening effect of water at high strain rates to an increased overall rate of
development of fast axial cracks as a result of enhanced kinetics of sharpening of
embryonic cracks around grain to grain point contacts, We suspect that the marked
sensitivity of strain rate to small variations in the applied stress is due to the fact that
the applied stress on the specimen will be magnified many times at the small areas of
grain point contacts.
Vol. 116, 1978)
Stress Relaxation of Faulted and Unfaulted Sandstone
645
20 prn
Plate lc
Scanning electron micrograph showing typical surface features of a microcracked quartz grain.
FRIEDMAN et al. (1974) have shown that rapid (overall specimen strain rate
10 -4 sec- 1) faulting of Tennessee sandstone is accompanied by frictional melting
under experimental conditions that embrace those employed for the initial faulting of
specimens used in the present study. The glass so formed occurred in fibrous patches
tending to cement the gouge. On the fault planes of our samples we have observed
similar features with the SEM, and Wma'E (personal communication, 1977) has
observed glass in the fault gouge in his preliminary study of our samples by transmission electron microscopy. SWAINand JACKSON(1976) have reported features in a
natural fault plane which may indicate that very small amounts of frictional melting
are not uncommon in nature.
(ii.b) Behaviour o f Tennessee sandstone at intermediate to low strain rates. In the strain
rate change 10-6 to 10-8 sec-i the wet samples lose strength at a rate of about one
order of magnitude in stress to about 12 orders in strain rate. This is similar to the
rate of change of log crack velocity with respect to log K reported by EVANS(1973) for
soda-lime glass, and we suspect that the rate of stress relaxation of Tennessee sandstone is here controlled by slow tension crack growth or through frictional sliding
between particles controlled by the stress corrosion failure of adhesion bonds. From a
646
E.H. Rutter and D. H. Mainprice
(Pageoph,
comparison of the relaxation rate of the faulted samples with that of TS 12 (unfaulted
but possessing a comparable microcrack density) it seems that the presence or absence of a fault is irrelevant to the mechanical behaviour in this strain rate regime.
Therefore we conclude that at these lower stress levels most of the sample shortening
in the faulted samples is not taken up by flow of the fault gouge but by further slow
comminution of fractured grains adjacent to the gouge, with consequent widening
of the gouge zone in direct proportion to the total amount of slip in the fault zone.
Further support for this conclusion is provided by specimen TS35 (Fig. lc) which was
relaxed after loading to only 60 percent of the faulting stress, and was almost devoid
of optically visible microcracks. This sample failed to exhibit a 'slow crack growth'
regime such as inferred above, but instead exhibited an abrupt strength drop at a
strain rate of about 10 -s sec-1. The occurrence of the 'slow crack growth' regime
therefore appears to be dependent on the presence of pre-cracked grains unless the
rapid strength drop observed in TS35 is also associated with crack growth phenomena.
The question of fault slip controlled by gouge thickening as against flow within the
gouge has been discussed in the literature (e.g., EN~ELDER, 1974; JACKSONand D~JNN,
1975; ENGELDERet al., 1975).
(ii.c) Change of temperature experiment. Only in the 'slow crack growth' strain rate
regime have we so far been able to perform a change of temperature experiment in
order to estimate an apparent heat of activation. Sample TS34 was relaxed at both
300 and 400~ (Fig. 2c). From an inspection of the separation of the isotherms at
constant stress the heat of activation is about 21 500 cal mo1-1 over most of the
observed stress range. Other studies have reported figures of this order from experiments on quartz and silicate glasses where it has been suggested that the mechanical
behaviour is controlled by the kinetics of hydrolysis of Si-O-Si bonds (e.g., SCHOLZ,
1972; CHARLES,1959 ; WE~DERHORN,1968).
Sample TS34 was first relaxed at 400~ but a temperature controller failure led
to the specimen cooling to room temperature for several hours, at the point indicated
by F in Fig. 2c. After reheating without changing the stress it was noted that the
relaxation rate had abruptly decreased by at least two further orders of magnitude,
below the limits of significant resolution. It was inferred that the cooling had resulted
in the deposition of dissolved silica from the pore fluid into the cracks and pores,
partially cementing the rock. When this cessation of creep had been established, the
temperature was changed to 300~ but the rock was also otttoaded and then reloaded,
so that any cement would become fractured. It is possible that the unwanted cooling
episode may have affected the activation enthalpy determination, but it has also
brought to our attention the idea that slight changes in the 'metamorphic' history of
a rock, such as a slight change in the structure through cementation, may strongly
affect the creep behaviour. DE BOER et al. (1977) have made a qualitatively similar
observation in their experiments on the compaction of quartz sand at high temperature
in the presence of a pore fluid,
Vol. 116, 1978)
Stress Relaxation of Faulted and Unfaulted Sandstone
647
(iii) Deformation by pressure solution. The characteristic rock textures attributed to
pressure solution processes are familiar to most geologists, e.g., interpenetration of
grains with the removed material being redeposited as grain overgrowth or in pores,
etc. Pressure solution as a deformation mechanism appears to be restricted to low
grades of dynamothermal metamorphism, and gives way to crystal plastic flow with
increasing grade. RUTXER (1976) presented a model to estimate the kinetics of this
process, assuming diffusion through a supposed intergranular fluid film to be rate
controlling. It was further assumed that the grain boundaries were everywhere parallel
or perpendicular to the principal stresses, so that grain boundary sliding would not
be important. Pressure solution processes are usually taken by geologists to result in
the elimination of any existing pore space (compaction). If there is no flux of mineralised fluids the characteristic intergranular diffusion distance for pressure solution will
be of the order of the grain diameter, d, in which case it may be shown that strain rate
by pressure solution is proportional to 1/d 3.
For more general granular aggregates creep by diffusive mass transfer requires
grain boundary sliding to occur concurrently, so that intergranular voids need not be
created. RaJ and ASHBY (1971) have developed a theoretical model of sliding on a
serrated grain boundary, accommodated by diffusive mass transfer (Fig. 3). This
~ra~n A
Local fliffusive flux
,.~,d
\ ~'~.,~.~ T
.~/. solution
4
/
Region~ of precipll~lllon
T
Figure 3
(a) Schematic illustration of sliding of a serrated grain boundary at a rate controlled by grain boundary
diffusion away from interfaces with relatively high normal stress and towards regions of potential dilation,
where repreeipltation occurs (after RAJ and ASHBY, 1971). (b) On the larger scale of grain to grain relationships sliding between grains (A and B) and/or interpenetration by pressure solution (B and C) may lead to
porosity fluctuations.
model may be of relevance to the deformation of rocks at low strain rates in the
presence of pore fluids, involving sliding between grains with local accommodation by
grain boundary diffusion through an ~ntergranutar fluid film. However, even though
it is assumed that there is no dilatancy in the stressed interface, on a larger scale there
may be local porosity fluctuatior~s as grains slip from one local packing configuration
to another (sand pile dilatancy of NuH, 1975) (see Fig. 3). In this adaptation of the
RAJ and ASHBY(1971) model, the characteristic diffusion distance is much less than
648
E.H. Rutter and D. H. Mainprice
(Pageoph,
one grain diameter, being of the order of the wavelength of the grain boundary
asperities. Pressure solution processes producing dilatancy on the one hand and
compaction through indentation on the other may be expected to compete, depending
on the instantaneous rock texture and the strain history. Pressure solution sliding and
indentation are possible processes at the low strain rate ends of our experiments.
ELLIOTT (1976) has appealed to Raj and Ashby's model to describe the development
of large scale striated hydrothermal vein minerals in dilatant natural shear faults.
7-
.o
theory
5"
3000C
%:: j
IBO ~
9
I
b-"
2.5'
2'
1"5'
!
3
-tog,estrain
rate
(sec")
Figure 4
Comparison of typical relaxation behaviour for wet Tennessee sandstone at 300~ (TS 33) with isotherms
predicted from the pressure solution sliding theory (see text).
Given the assumptions set out by Rtn'xv_g (1976), it is possible to obtain theoretically an estimate for the rate of serrated grain boundary sliding controlled by diffusion
through a thin liquid film, by adapting the analysis of RAT and AsI-IBV(1971). The
derivation will be given in a further paper.
We obtain, for a sinusoidal grain boundary:
= 8 Co(p, r)
hZP
(0 In
\ ~P
,Jr
(3)
Vol. 116, 1978)
Stress Relaxationof Faultedand UnfaultedSandstone
649
in which D is the sliding rate, z the shear stress along the grain boundary, h is the
amplitude of the grain boundary asperities and D b is the grain boundary diffusion
coefficient, p is the density of the solid phase and 6 is the width of the grain boundary.
Co(p, T) is the temperature, T, and pore fluid pressure, p, dependent solubility of the
solid. The temperature dependence of the sliding rate is contained in the Co(P, T) and
Db terms. Together, it is expected that the apparent heat of activation for pressure
solution sliding will be of the order of 7000 cal mol- i. This is very low compared with
activation enthalpies usually associated with solid state diffusion processes. It means
that even at low temperatures (< 300~ a substantial temperature change will
produce a relatively small sliding rate change.
In equation (3) the shear stress, v, is that which is applied to a particular grain
boundary, and not that applied to the aggregate as a whole. For the purposes of
rough calculation, however, they will be taken to be equal.
Specifically with respect to quartz, using the data given by RUTTEP, (1976),
equation (3) can be rewritten in the form
0 = 3.0 x 10 -9 "c6h -z p-1 exp (-7460/RT) exp (0.415p)
(4)
in which h and 6 are in cm, ~ and p are in kb, R is in cal. deg- l tool- 1 and 7?is in ~
The strain rate for the aggregate cannot be obtained directly from the sliding rate.
We might assume that there is a given increment of strain, e, associated with each
increment of sliding, and this will introduce a dependence upon grain size,
e = kU/d,
hence d = kU/d
(5)
where d is the grain diameter, and k is a constant, perhaps of order unity. This is a
much weaker grain size dependence than the lid 3 dependence usually associated with
creep controlled by grain boundary diffusion (Coble creep). This difference arises
because h is taken to be generally much smaller than d.
We have calculated strain rates using equations (4) and (5), assmrning h to be
1.0 ~un,k is unity and sliding is presumed to occur on all grain boundaries. The results
are displayed graphically on Fig. 4, together with one of the sets of experimental data.
Bearing in mind the crudeness of the model and the guesses as to the values of the
various parameters, the agreement with the low stress end of the relaxation data is
remarkable. The model predicts a linear viscous types of stress/strain rate relation and
the experimental data, though possessing a considerable scatter, all lie within one
decade of the predicted strain rate over a substantial stress range.
The model also predicts no pronounced grain size effects. It was anticipated that
if there was to be a marked grain size effect then the prefaulted samples, due to their
possessing a fine grained gouge, might be expected to deform faster than the microcracked but unfaulted counterpart. As Figs. I and 2 show, there is no significant
difference between faulted and unfaulted samples in the low stress regime.
The pressure solution sliding model predicts that deformation rate should increase
as pore fluid pressure is increased, all other factors remaining constant. We have not
explored this point but SPRUNT and NuR (1976), reporting slow compaction tests on
650
E.H. Rutter and D. H. Mainprice
(Pageoph,
St Peters sand in the presence of pore fluids at 270~ showed that the compaction
rate is increased by increased pore pressure (at a constant effective confining pressure
of 0.5 kb). They ascribe the observed compaction (measured from reduction in
porosity) to pressure solution. They also showed that the compaction rate is enhanced
by the application of shear stress, which is also predicted by our model
From our experimental results it appears that flow produced by pressure solution
may occur at about 2 kb differential stress and below at 1.5 kb effective confining
pressure. This stress level is rather higher than might have been expected, for although
an increase in applied stress should increase the rate of pressure solution, we anticipate
that it might also decrease the intergranular diffusivity at some presently unknown
rate. However, in a stressed porous aggregate we might expect some spectrum of
normal stress across grain boundaries, the more highly stressed grains being on the
point of brittle failure whilst the less heavily stressed grains may be able to undergo
grain boundary sliding accommodated by pressure solution. The latter process will
tend to relieve load on the less heavily stressed grains, thereby transferring it to the
more heavily stressed grains which may fail by slow or fast brittle fracture, thus
redistributing the loading yet again. We might therefore envisage a dynamic balance
between pressure solution sliding and cracking, with the overall rate at low stress
levels being controlled by intercrystalline diffusion.
It is to be expected that sliding on grain boundaries should leave a fibrous film of
recrystallised material. We have looked for such a feature using SEM, but have failed
to find features which we consider to be totally convincing. However, assuming a
sliding rate of 10- lo cm sec- 1, if such sliding occurs during the last 10 6 sec of a
relaxation test, then recrystallised fibres will be at most 10 -4 cm in length, and would
therefore be difficult to recognise. Using the results from these stress relaxation tests
as a guide, further testing using the constant strain rate technique is planned with a
view to accumulating larger strains at low strain rates, so that the operative deformation mechanisms may be more clearly identified.
Examination of rocks naturally deformed by pressure solution processes usually
reveals that the characteristic textural features are best developed in rocks relatively
rich in phyllosilicate minerals, particularly clays. It may be inferred that the rate of
intergranular diffusive transfer is enhanced by the presence of phyllosilicates (Rm'TER,
1976). The presence of ca. 10 percent clay in Tennessee sandstone was one of the
reasons for choosing this rock for the experiments reported here. It will be necessary
to perform experiments like these on clay free sandstone in order to evaluate the
potential role of clays in producing the observed weakening at low strain rates.
4. Geological discussion
We have described a set of experiments which show that a brittle rock tested at
300~ in the presence of water becomes markedly weakened at low strain rates. In
addition we have presented an interpretation of the data, though much of the dis-
Vol. 116, 1978)
Stress Relaxation of Faulted and Unfaulted Sandstone
651
cussion is at this time rather speculative. Perhaps the most important geological
implications of the data and the speculations are with respect to the mechanisms of
deformation of rocks in fault zones.
The rate of heat production in fault zones depends on the shear stress and the
average rate of sliding. The lack of a sharply peaked heat flow anomaly along the
San Andreas fault zone is taken to mean that a time averaged shear stress of the order
of only 100 bars exists (STESKY and BRACE, 1973; BRUNE, 1974). This stress level must
therefore be consistent with the observed slip rate. For many years it has been difficult
to reconcile the high strengths of brittle rocks tested in the laboratory with the very
much lower strengths attributed to rocks in nature. However, it is clear that the facts
of our results hold a promise of such a reconciliation, quite irrespective of our
interpretation.
In addition to seismic fault slip it has been found that sections of active faults
sometimes exhibit aseimic slip, or creep, measurable at the trace of the fault on the
earth's surface (e.g., the straight portion of the San Andreas fault in central California,
SCHOLZ et al., 1969). The surface creep usually takes the form of discrete 'creep
events', periods of relativeiy rapid slip separated by much longer periods of quiescence,
and these events propagate along the fault trace as dislocations (NASON and WEERTMAN, 1973). The episodic nature of the creep probably reflects the rheological characteristics of the fault rock close to the Earth's surface.
In the case of the Californian active strike slip faults the seismicity is concentrated
at depths less than ca. 15 km (SCHOLZ e t al., 1969; WESSOY et at., 1973). Below this
depth range slip is totally aseismic and at lesser depths partly aseismic. Although our
experimental conditions are not precisely what would be expected at ca. 15 km depth,
let us assume them to represent a first order approximation. If we can extrapolate our
observed stress/strain rate relation linearly and to large strains, or alternatively,
employ our pressure solution sliding flow model, a fault zone I m to 10 m wide with an
effective grain size of 10 .2 cm at 300~ would slip at a rate of the order of 1 cm yr- 1
under a shear stress level of about 100 bars. The inferred slip rate is commensurate
with observed slip rates, and provided the proposed linear viscous flow law can be
extrapolated linearly to zero stress, so that slip/no slip transients will not normally
develop, we would infer that the slip rate would be fairly uniform over large areas of
the fault, without any tendency for discrete creep events.
Because the kind of flow which we envisage involves direct componental movements of rigid grains relative to one another, we regard 'flow controlled by pressure
solution sliding' as a variety of cataclastic flow. Such flow can potentially lead to
porosity and hence pore fluid pressure variations over long time periods at constant
stress. Whether such fluctuations really occur, and their potential importance, remains
to be seen. It must be pointed out that such a mechanism for producing time dependent
porosity variations contrasts with the dilatancy which occurs as rocks are progressively
loaded over a stress increment when close to failure (e.g., NtrR, 1975; BRACE and
MARTIN, 1968).
652
E.H. Rutter and D. H. Mainprice
(Pageoph,
Under the higher pressure/temperature conditions of the greenschist facies of
regional metamorphism it is reasonable to suppose that brittle fault zones pass into
mylonitic shear zones (SmsoN, 1977) which are characterised by intense plastic
deformation and recrystallisation, particularly of quartz (WHITE, 1976). Studies of
deep levels of ancient fault zones, now exposed at the earth's surface, should reveal the
various deformation mechanisms which characterise fault zones at various depths.
If the proposed process of cataclastic flow controlled by pressure solution sliding is
important in nature, we would expect it to be particularly so in the intermediate depth
range, between the regimes dominated by seismicity on the one hand and plastic
deformation on the other. On the experimental front, the effects of total confining
pressure variation, pore water pressure variation, microstructural and mineralogical
variations and the accumulation of large strains remain to be investigated, so the
present extrapolations from a limited amount of factual data must be treated with
great caution.
Acknowledgements
This work was funded initially under the U.K. Natural Environment Research
Council grant No. GR.3/2048 and the continuation under the U.S. Geological
Survey National Earthquake Hazards Reduction Program contract No. 14-08-0001G-377. For part of this project period one of us (Mainprice) was supported by a
NERC advanced course studentship.
The block of Tennessee sandstone used for these experiments, plus relevant
geotechnical information, was provided by Dr R. Hardy of the Pennsylvania State
University.
Mr R. F. Holloway assisted with the experiments and the maintenance of the
apparatus. We are grateful for discussions with and critical comment from Drs
B. K. Atkinson, S. A. F. Murrell, M. S. Paterson, R. H. Sibson and S. H. White.
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