Fault Permeability and Strength Evolution Related to Fracturing and Healing Episodic Processes (Years to Millennia): the Role of Pressure Solution
Oil & Gas Science and Technology - Rev. IFP Energies nouvelles, Vol.
Fault Permeability and Strength Evolution Related to Fracturing and Healing Episodic Processes (Years to Millennia): the Role of Pressure Solution
J.-P. Gratier 0
0 LGIT , Observatoire , Université Joseph Fourier - CNRS , Maison des Géosciences, rue de la Piscine, 38041 Grenoble - France
Résumé - Évolution de la perméabilité et de la résistance des failles associée à des processus épisodiques de fracturation et colmatage (années - millénaires) : le rôle de la dissolution cristallisation sous contrainte - Il est bien connu que les fluides circulent le long des failles, mais il est aussi démontré que les failles se comportent en barrières imperméables. Il faut donc considérer que les failles puissent être successivement des chemins ouverts et fermés. À l'échelle de temps des activités humaines (années à millénaires), l'étude du cycle sismique offre la possibilité de construire un modèle de telles évolutions. Selon ce modèle, la fracturation sismique (ou hydraulique) ouvre les chemins des fluides de manière quasi-instantanée le long des failles avec des processus d'amollissement et de fluage post-fracturation. La fermeture de ces chemins de fluide par cicatrisation de la faille est beaucoup plus progressive, associée à un durcissement et une reconstitution de pression des fluides. De tels comportements transitoires ont des conséquences majeures dans les études : - de l'évolution de la perméabilité le long des failles, avec application à l'exploitation de réservoirs pétroliers et aux stockages de fluides et de déchets ; - de l'évolution des flux de fluides le long des failles avec application au bilan des échanges et à l'évolution du climat à l'échelle de la terre ; - du temps de retour des séismes et de la probabilité de leur occurrence.
Le but est de comprendre et d’évaluer la cinétique des processus et donc les temps caractéristiques
spécifiques des cycles de fracturation et de colmatage. Des résultats d’expériences de laboratoire et
d’étude de failles naturelles sont présentés qui montrent comment des processus de dissolution
cristallisation sous contrainte peuvent expliquer à la fois les processus de fluage et de colmatage, et la
façon dont ils sont associés dans la nature. Les divers processus de cicatrisation des failles sont discutés,
avec leurs temps caractéristiques très variés de quelques semaines à des millénaires. On montre comment
ils peuvent être intégrés dans des lois de fluage et de colmatage. Les expériences de laboratoire en
donnent les valeurs de certains paramètres (cinétiques, thermodynamiques). D’autres paramètres de ces
lois doivent cependant toujours être évalués à partir d’études de structures naturelles (géométrie des
chemins de transfert, conditions de pression et température, nature des fluides et des minéraux). Ainsi, la
durée des cycles de fracturation et colmatage est reliée, d’une certaine façon, au contexte géologique de la
zone de faille. Finalement, comme ces processus d’évolution de perméabilité, de pression fluide et de
résistance mécanique interagissent et se produisent à différentes échelles de temps et d’espace, ils doivent
être intégrés dans des modèles numériques qui sont brièvement discutés.
– the evolution of permeability along faults with application to oil-field reservoir exploitation and fluid
and waste storage;
– the evolution of fluid fluxes along faults with application to mass balance and climate evolution on the
scale of the earth;
– the timing of earthquakes and the probability of their occurrence.
The aim is to understand and evaluate the kinetics of the processes and the specific characteristic times
of the fracturing and healing cycles. Results from laboratory experiments and natural fault studies are
presented that show how pressure solution processes can explain both creep and sealing processes and
the way they are associated in nature. The various fault-healing processes are discussed with their
various characteristics in times from weeks to millennia. It is shown how they can be integrated into
creep and sealing laws. Laboratory experiments give the values of some parameters of the laws (kinetics,
thermodynamic). Other parameters must always be evaluated from the study of natural structures
(geometry of path transfer, pressure and temperature conditions, nature of minerals and fluids).
Consequently, the duration of the fracturing and sealing cycle is related to some extent to the geological
context of a faulted area. Finally, as the mechanisms of permeability and strength evolution interact and
occur on various scales of time and space, they must be integrated into numerical models, which are
Faults are linked to a wide range of global phenomena
including opening and closure of oceans, rise and fall of
mountains ranges, and fluid transfers from solid earth to its
(Handy et al., 2007)
consequences are important, from earthquake hazard to long-term
climate change, from mineral and petroleum resource
development to waste disposal and geological fluid storage.
Moreover, it is the evolution of fault permeability and
strength with time, which is a key parameter in most of these
processes. We know that fluids flow through active faults.
Kennedy et al. (1997)
Pili et al. (1998)
showed, from 3He/4He ratio studies, that fluids flow from
depth with a mantle signature along the San Andreas fault.
Meteoric waters are also able to percolate down into active
baume et al., 2004
; Pizzino et al., 2004; Benedicto
et al., 2008). Such fluid transfers along faults have been
related to earthquake occurrence
(Sibson et al., 1988)
development of aftershocks
(Miller et al., 2004)
. However, it
is also well demonstrated that fault zones act as impermeab
barriers (Person et al., 2007
). Consequently, one must
consider that faults are successively open and closed paths for
fluids, the opening being linked to the earthquake occurrence
or to any other fracturing and associated chemical
mechanisms, and the closing being associated with post-fracturing
healing. Evidence of increase in fault permeability associated
with earthquake has been shown by
Kitagawa et al. (2002)
followed by after-slip healing and creeping processes
2007; Li et al., 2003, 2007; Brenguier et al., 2008)
question is thus to identify the mechanism that can
accommodate such fault permeability and strength evolution, and
we will see that stress-driven mass transfer processes play a
key role in such evolution; specifically, pressure solution
processes. Actually, three ranges of characteristic times must
be distinguished in fluid-rock interactions within active
– seconds to minutes are characteristic of cataclastic failure.
The role of fluids during such short intervals is mostly
mechanical (fluid pressure) or catalytic (melting);
– days to thousands of years represent characteristic times
for the evolution of the rheological and transport properties
of rocks in human times;
– thousands to millions of years are characteristic times of
chemical and mechanical differentiation processes
associated with mass transfer that progressively localized
deformation and transfer.
In this paper we will mostly discuss the processes that
occur on the human-activity time scale (years to millennia),
even if processes that develop on a given time scale interact
with processes that develop on other time scales. On the
human-activity time scale most data are available from
earthquake studies. This is why most of the examples given in this
paper are related to this topic. However, the same processes
occur in other contexts and understanding the mechanisms of
fault permeability and strength evolution on this time scale
remains a major fundamental task and has important
consequences in terms of:
– the evolution of permeability along faults with application
to oil-field reservoirs and fluid and waste storage;
– the evolution of fluid fluxes along faults with application
to mass balance and climate evolution on the scale of the
– the timing of earthquakes and the probability of their
Earthquakes, especially the larger ones, occur at time
intervals that are characteristic of the geodynamic context.
Sykes and Menke (2006)
gathered data on 15 seismic fault
segments, lying at different plate boundaries, showing various
repeat times ranging from 20 to 1000 years (with a mean
value of 7 successive events of magnitude 6 to 8). Earthquake
recurrence is explained by the strain buildup and release
. The idea is that large events do not
rupture the same fault segment again until sufficient time has
elapsed to re-establish the stresses that were partially
discharged by the preceding event. This leads to the concept of
seismic cycles, which requires that active faults strengthen
(heal) between earthquakes
creep and associated porosity evolution (damage then
recovery) observed on natural faults
(Freed, 2007; Li et al., 2003,
2007; Brenguier et al., 2008)
attest to this post-seismic
healing process (Fig. 1a). Observations of seismic fault zones
naturally exhumed from depth, or cored by drill holes, show
that healing mechanisms of both the fault gouge and the
damaged zone that lies around it
(Gratier et al., 2003;
Andreani et al., 2005)
are related to stress-driven mass
transfer processes that can explain both post-seismic mechanisms
of creep and sealing. So, kinetics of healing by mass transfer
processes play a key role in determining the repeat time of
earthquakes, even if the seismic cycle timing is rather complex
since it depends on several parameters:
– the rate of stress loading imposed by boundary conditions
– the rate of strength recovery;
– the rate of fluid pressure increase;
– the role of heterogeneities on all scales;
– the possibility of earthquake triggering by external forcing.
Each parameter has at least one specific characteristic
time and the interactions between all these different times
are complex but specific to a given region. For the same
characteristic time and the same geological context, the
mechanisms and the kinetics of permeability and strength
evolution are the same for earthquake cycles and for
fracturing and healing cycles that can occur in oil-fields and
gas reservoirs that are submitted to intermittent fracturing
processes either natural (earthquake) or artificial (fracturing
promoted to increase fluid extraction, or fracturing induced
by fluid storage).
The main problem is to identify these mechanisms and
evaluate their kinetics. One problem is that such stress-driven
mass transfer processes are very slow, resulting in strain rates
ranging from 10-11 to 10-15 s-1,
. The fastest strain rates with such processes
(10-10 s-1, Gratier et al., 2009)
are found within active creeping
zones, such as along the San Andreas fault (Titus et al., 2006).
Reproducing such low strain rates on natural minerals in the
presence of a fluid in the laboratory is therefore a challenge
. Strain rates as low as 10-11 s-1 may be
registered in the lab (Gratier, 1993; Dysthe et al., 2003;
Le Guen et al., 2007
; Gratier et al., 2009), however
the strain values are very low and not necessary representative
of large finite deformation. Gaining one or two orders of
magnitude on pressure solution strain rates may be achieved by
using analogue material or by activating some parameters of
the creep and sealing laws (Eq. 2-5): see discussion in
and Gueydan (2007)
. Moreover, some parameters of the creep
and sealing laws must always be evaluated, in parallel, from
natural observations: geometry of path transfer,
pressure-temperature conditions, and the nature of minerals and fluids. As
a consequence, results are presented here which also came
from observations and measurements on natural samples that
have been recovered from drill holes through active faults
(California, Taiwan, Japan and Greece).
Finally, as the post-fracturing mechanisms of healing and
strengthening interact and develop on various characteristic
scales of time and space (times of days to thousands of years,
sizes of microns to kilometers), the various deformation laws
have to be integrated into numerical models of the
“fracturing and healing” cycles. Various methods need to be
combined: rate-and-state friction laws, weakening-strengthening
viscous models and fluid percolation, plus possible triggering
effects not developed here. The paper presents only a few
examples of such numerical methods.
We will consider rocks that are under stress in the presence
of fluid that can react with at least part of the mineral of the
rock, so we will mainly consider the role of pressure solution
mass transfer. We will not discuss here other mechanisms of
that are not time dependent. For
example, clay-rich sediment (more than 40%) deform to
produce clay smearing of fault that can significantly reduce their
(Bouvier et al., 1989; Yielding et al., 1997;
Fisher and Knipe, 2001; Bretan et al., 2003)
. Clay smearing
mostly occurs between the hanging wall and the footwall of
clay-rich horizon but it could also result in injection through
Sealing & creep S F S
Water injection 40 80
Days Natural deformation a) b)
Effect of fracturing on displacement rate 0.05 mm e) 0.05 mm
a) Schematic view of damaged zone deformation near active fault: earthquake-induced fracturing networks (black) that are progressively
sealed by self-healing and sealing (white) associated with pressure solution creep processes (Fig. 3); (below) evolution of displacement and
porosity with time during fracturing and healing cycles. b) Mechanism of fracture-induced deformation weakening: during indentation of
halite by dissolution under stress, a dramatic change in displacement rate occurs when radial fractures develop (day 71). The effect of
fractures is to reduce the mean distance of diffusion d (Fig. 1d, Eq. 4, 5 in the text), which is here the limiting process. c) Effect of water
injection on deformation displacement during flow through experiment of chalk axial deformation. d) Effect of radial fracturing that
drastically reduces the mean distance of mass transfer along fluid phase trapped under the indenter (parameter d in Eq. 4, 5 in the text).
e) Fracturing associated with pressure solution at grain contacts in natural examples. Adapted from Gratier and Gueydan, 2007 (a, b),
Brenguier et al., 2007 (a - bottom), Hellmann et al., 2002 (c), Gratier et al., 2009 (d), Labaume and Moretti, 2002 (e).
the less clay-rich sediment. Clay smearing can also changes
the rheological properties of faults as clay minerals are likely
to creep relatively easily
(Prioul et al., 2000; Bourouis and
The hydraulic structure of active faults is another important
parameter that is not very well known. Recent works on the
cored Nojima and Chelungpu active faults show relatively
weak fine-grained gouges surrounded by more resistant
damage zones of fractured rocks (Lockner et al., 2009). The
damage zones act as high permeability conduits for both
vertical and horizontal flow whereas the fine-grained gouge
acts as relatively impermeable barriers than prevent
significant fluid flow across the fault (Doan et al., 2007;
Moore et al., 2009).
In this context, we will discuss the evolution with time of
the permeability and strength of the whole fault: the gouge
and the damaged zone that lies around it, that can extend
meters to kilometers away from the main gouge, trying to
answer two major questions:
– how does fault strength evolve with time during the
turing and healing” cycle?;
– how do permeability and pore pressure evolve during the
“fracturing and healing” cycle?
1 HOW DOES FAULT STRENGTH EVOLVE WITH TIME
DURING THE “FRACTURING AND HEALING”
1.1 Weakening Processes during the Fracturing Event
A weakening process is defined here as a process that is
associated with a decrease in the strength of the rock. Here, the
strength is defined as the stress needed to accommodate
creep at a given strain rate. The weakening process
associated with a fracturing event has been observed in the lab by
pressure solution creep experiments with the indenter
(Gratier et al., 1999)
. With this experimental technique
(Fig. 1d), the driving force of dissolution is promoted by a
dead weight that presses onto an indenter that loads itself on
a crystal surface, along which stress-enhanced dissolution
occurs. Stress under the indenter increases the chemical
potential of the solid compared with the solid free surface at
zero stress far away from the indenter (Gibbs, 1877).
Δμ = Δf + Vs Δσn + ΔEs
where Δμ is the difference in chemical potential of the
dissolved component between the maximum stressed part
(under the indenter) and the free solid/fluid surface away
from the indenter, Δσn is the difference between the normal
stress component under the indenter and the fluid pressure Pf
on the solid away from the indenter, and is simply named σn
in the creep relations, Vs is the molar volume of the solid. Es
is the curvature-related potential. The molar Helmholtz free
energy, Δf, gathers various contributions
Palciauskas, 1994; Leroy and Heidug, 1994)
as the elastic
strain energy and the plastic strain energy. Creep laws
(Eq. 2-5) may be derived from the displacement rate Δx/Δt
versus stress σn relationships when the characteristic length
of the closed system is assumed to be equal to the indenter
diameter (d), Gratier et al. (2009). Pressure solution being an
in-series process: dissolution then diffusion then
precipitation, two types of creep laws are expected depending on the
limiting step of this in-series process
(Gratier et al., 2009)
Model R: Δx/Δt = α k Vs2σnn/RT
is relevant if either dissolution or precipitation kinetics is the
Spiers et al. (2004)
Model D: Δx/Δt = β D w c Vs2σnn/RTd2
or: Δx/Δt = β’ D w c Vs(e3σnVs/RT–1)/d2
applies when diffusion flux through a fluid phase under stress
below the indenter is the rate-limiting process:
Dewers and Ortoleva (1990)
In Equations (2) to (5), α, α’, β, β’ are dimensionless
constants that depend on the geometry of the interface, d is
the indenter diameter (m), t is time (s), k is the kinetics
constant for dissolution or precipitation reaction (mol.m-2.s-1),
c is the solubility of the diffusing solid (mol.m-3), Vs is the
molar volume of the stressed solid (m3.mol-1), R is the gas
constant (8.32 m3.Pa.mol-1.K-1), T is the temperature (K), D
is the diffusion constant along the stressed interface (m2.s-1)
and w is the thickness of the fluid interface (m) along which
diffusion occurs. The factor 3 in the exponential of Equation
(Dewers and Ortoleva, 1990)
reflects the fact that for
balance of forces during a constant approach of two planar
surfaces, the normal stress at the center of the contact
between the surfaces is higher than the average stress across
(Weyl, 1959; Rutter, 1976)
In the example of Figure 1b, the same dead weight was
maintained throughout the experiment. The only change was
to induce radial fractures under the indenter at day 71. The
displacement rate of the indenter was constant during the first
71 days then it showed a sudden increase at the time of this
fracturing, and it stayed constant at this new rate for the
following 77 days. We interpreted fracturing to have augmented
the rate of diffusive mass transfer along the contact between
the indenter and halite
(Gratier et al., 1999)
fracturing, the displacement rate Δx/Δt is controlled by the rate of
mass transfer out of the nanometer-thick fluid film interface
trapped beneath the indenter, and is inversely proportional to
the square of the radius, d, of the indenter (Eq. 4, 5). The
development of radial fractures, which are longer than the
diameter of the indenter and several microns wide, induce
some shortcuts for fast mass transfer away from the indenter
contact area. Along these new paths, diffusive mass transfer
occurs within the free fluid that fills the open fractures and
fluxes along such paths are several orders of magnitude
higher than along the thin-trapped fluid under stress.
Therefore, fracturing renders the displacement rate inversely
proportional to the square of the mean size of the small
domains bounded by the radial fractures (Fig. 1d). This
explains the sudden increase in the displacement rate, as
pressure solution indentation is here diffusion-controlled.
This effect has been seen on numerous examples of halite
(Gratier, 1993; Gratier et al., 1999)
. This effect of
fracturing that boosts the dissolution under stress may also be
recognized in natural deformation. For example, pitted
pebbles (Fig. 1e) that have long been attributed to pressure
solution (Sorby, 1865) are always broken by numerous fractures
that can be seen in cathodoluminescence
(Labaume and Moretti, 2001)
. Therefore, fracturing
weakens the rocks almost instantaneously by accelerating
pressure solution creep. However, this effect is strongly
nonlinear as fractures are progressively sealed, as seen on
samples removed from active faults
(Gratier et al., 2003)
show below that this sealing of the fracture progressively
strengthens the rocks. Another effect of the fracturing process
is linked to the fact that fluids can react with the minerals:
fluid can dissolve or help transform them, and consequently
weaken the whole aggregate. This effect, not detailed here, is
well known in natural deformation (
; Evans and
Gueydan et al., 2003
Boullier et al., 2004
Another chemical effect is the self-organization process that
leads to flow-channeling during reactive fluid flow in porous
(Ortoleva, 1994; Bazin et al., 1996; Renard et al.,
1998; Hellmann et al., 1998; Worthington and Ford, 2009)
The effect of such “free-face” chemical processes on the
evolution of strength and transfer properties must be added to
the fracturing effect on pressure solution. The effect of
chemical dissolution can be almost instantaneous in the lab: see,
for example, the evolution of the strain rate when injecting
water into dry chalk under stress, Figure 1c
(Hellmann et al.,
. However, in natural deformation, chemical reaction
effects do not usually occur at the same characteristic times
as the fracturing effect on pressure solution. They develop
much more slowly so they interact with potential
strengthening processes in a complex way that is not discussed in this
1.2 Strengthening Processes after the Fracturing Event
Strengthening is commonly assumed to be linked to:
– increase in packing density of the damaged fault rock
(Renard et al., 2004)
– contact strengthening, or;
– contact area increase (Niemeijer et al., 2008).
Strengthening may be reproduced in the lab but not
necessarily with the same mechanism as in natural deformation.
What geologists see in the field, either in the exhumed upper
crust or on samples removed from a drill hole through an
active fault, is that this strengthening is most often
accommodated by mass transfer processes. Another common
geological observation is that such sealed fractures are harder than
the initial non-fractured rocks. This appears by the so-called
(Fig. 2, Gratier and Vialon, 1980)
where in a boudinage process, the boudins become
progressively thinner than the interboudin sealed fractures. This is
a) Example of extension veins in boudinaged structures (left)
and crystallizations in pressure shadow (right) that are wider
than the initial boudins and the rigid objects, respectively.
b) Schematic evolution of extension veins in boudinaged
structures: extension veins become wider than the boudins:
this shows that sealed fractures are harder than the initial
non-fractured rocks. The vein sealing is white (soluble
species such as quartz and calcite), the initial rock is gray
with a mixing of soluble and insoluble species (such as
phyllosilicates), solution cleavage seams are black due to
passive concentration of insoluble species.
because, when pressure solution is the deformation mechanism,
it is easier to dissolve a polycrystalline rock that contains
both soluble and insoluble species (the boudin) than to
dissolve a monomineralic rock composed of only one soluble
species (the interboudin sealed fractures). The reason is that
the diffusion paths at the contact between soluble and
insoluble minerals (such as phyllosilicates) are much faster than the
diffusion paths at the contact between two soluble minerals.
This is probably due to a more efficient healing of the grain
boundary of the same species. This effect is also well
demonstrated by experiments (Hickman and Evans, 1991; Zu
et al., 2004
). So, in natural processes, sealing of fractures
strengthens the rocks, which become harder than before the
fracturing process (at least when pressure solution is the main
mechanism of deformation).
Several processes compete to seal the fractures in active
faults. Actually, the characteristic times of post-fracturing
healing vary from days to millennia (Fig. 3), depending on
the processes involved (Eq. 2-5):
(stress > diffusion)
(temp. stress fluid flow)
(stress > diffusion)
Various mechanisms of fault self-healing and sealing with characteristic times ranging from days to millennia: a) self-healing driven by
surface energy; b) dissolution of props driven by stress and pore pressure decreases; c) crack sealing with fluid advection controlled either by
free-face reaction rates in pores or by diffusion rates along solution cleavage seams; d) crack sealing driven by stress with mass transfer from
solution cleavage to fracture. Adapted from
Gratier and Gueydan (2007)
. Below, the photographs show these structures in their geological
– self-healing is driven by minimization of surface energy:
Figure 3a. It may be rather fast
(from days to months; see,
for example, Brantley et al., 1990)
. However it is only
relevant to very thin fractures (micrometer aperture) that
keep solid-solid contacts in order to promote high surface
energy sites (see enlargement Fig. 3a).
Tenthorey et al.
performed experiments at high temperature that
show how hydrothermal reactions in faulted rocks lead to
strength recovery and permeability decrease with a power
dependence in time (exponent = 0.38, Fig. 4b). Contact
strengthening was observed by Dysthe et al. (2003) with a
decrease in the interface roughness with displacement
with also a power law (exponent = 0.33).
Niemeijer et al. (2008)
showed, in a
simulated phyllosilicate/halite fault gouge, that an
interface that has slipped seismically rapidly re-strengthens.
All these experiments that have been done at a relatively
fast strain rate (days to weeks) mostly attest to self-healing
processes controlled by reaction rates with relatively high
activation energy (70 kJ/m/°);
– dissolution of props trapped in fractures is driven by stress
and a decrease in fluid pressure: Figure 3b. It may be done
in the lab over time scales from weeks to months
and Hickmann, 2004)
. It is also a mechanism that is
relevant to very thin fractures that collapse with sealing in a
Sealing of calcite
and quartz 150°C
Mechanisms of fault strengthening: a) evolution of strength and porosity with time during fracturing and healing cycles; b) fast (hours, days)
post-fracturing strengthening (cohesion) by quartz self-healing; c) modeling of non-steady-state crack sealing: the evolution with time
depends on the nature of the minerals (quartz or calcite) and on the spacing between the fractures (parameter d in Eq. 4, 5 in the text).
Adapted from Brenguier et al., 2007 (a), Tenthorey et al., 2003 (b), Gratier et al., 2003 (c). d) Inverse evolution of pressure solution creep
strain-rates with depth (ε⋅ = Δd/dΔt) for quartz and calcite, due to the inverse evolution of their solubility with temperature, data from
et al. (2009)
, with the same small distance of mass transfer (d = 100 micrometers in fault zone) using the creep equation:
ε⋅ = Δd/dΔt = 8 D.w.c.Vs.(e3σnVs/RT–1)/d3 with, at 10 km, T = 350°C, σ = 60 MPa, at 3 km T = 120°C, σ = 18 MPa.
The sealing of large aperture cracks that constitute the
numerous veins observed in fault zones and that require an
input of matter from outside: Figures 3c and 3d is much slower:
– crack sealing driven by stress, with mass transfer by
diffusion from solution cleavage to fracture: Figure 3d is
the most commonly observed mechanism in fault zones
(Gratier et al., 2003)
. This is both a mechanism of creep
and of sealing. In natural deformation, this mechanism is
most often controlled by the diffusion step (Eq. 4, 5) or by
reaction rates that are slower than this diffusion rate due to
the effects of growth-inhibiting impurity species present in
(de Meer et al., 2000)
. Activation energy is
(10-15 kJ/m/°, Rutter, 1976)
. The characteristic
times of sealing range from years to centuries. Such a
mechanism can be only reproduced in the lab when its
kinetics is activated. This may be done by using a mineral
with high solubility in water
, such as halite
(Tada and Siever, 1986; Urai et al., 1986; Gratier, 1993;
Hickman and Evans, 1991; Karcz et al., 2006)
, or by
increasing the solubility of the solution
(with NaOH, for
example, when using quartz, Gratier and Guiguet, 1986)
The kinetics may also be activated by working at very high
(Cox and Paterson, 1991)
. Moreover, as this
sealing is associated with an increase in the surface of
contact, and thus of the distance of mass transfer, its rate
progressively decreases with time (see the effect of the
parameter d in Eq. 4, 5). This is true on a grain scale and
this rules out the possibility of steady-state compaction
rate. This aspect has been explored by
the simplest case of regular packing spheres. This is also
true for episodically fractured rock (Fig. 4c). An example
of the modeling of the evolution of the sealing rate with
time is given in Figure 4c
(Renard et al., 2000; Gratier et
. Application to the modeling of transfer
properties is discussed below. It must be noted that pressure
solution strain rates varies with depth (effect of temperature
and pressure) and minerals (effect of solubility and molar
volume). Using creep relations deduced from indenter
experiments (Gratier et al., 2009), and extending it to other
mineral such as calcite, one may compare the evolution of
the strain rate values of these two minerals with depth from
2 to 10 km (Fig. 4d) with the same constant value of the
distance of mass transfer (d = 100 micrometers). One can
see that the two minerals show opposite evolution of their
pressure solution strain rates due to the inverse evolution of
their solubility with the temperature. Calcite is more
mobile than quartz at low temperature whereas quartz is
more mobile than calcite at high temperature;
– crack sealing with fluid infiltration: Figure 3c, is controlled
either by reactions on free faces (Eq. 2, 3), or by diffusion
along solution cleavage (Eq. 4, 5). It is especially dependent
on the controlling step in the zone of dissolution.
Dissolution could occur along solution cleavage and as
dissolved species must be extracted from trapped fluid
under stress (Fig. 3c right), the controlling step is the same
as above (Fig. 3d). It is most often controlled by diffusion
or by reaction processes slower than the diffusion.
Alternatively, if dissolution occurs on free fluid faces
(Fig. 3c left) with the development of voids by the
dissolution of some mineral (for example, the
transformation of granite into episyenites), diffusion being
relatively fast in free fluids, the process may be controlled
by reaction kinetics, as is the case in the change in shape of
(Gratier and Jenatton, 1984)
characteristic times of crack sealing with fluid infiltration in
natural deformation may range from months to centuries. It
is not easy to distinguish between crack sealing with
diffusion and crack sealing with infiltration. A general rule
is that infiltration needing some open canal to occur, sealing
with infiltration cannot completely fill a vein. So most
often, this mechanism leaves some voids in veins with
euhedral growth of crystals that attests to their growth in
free fluids (Fig. 3c). Stable isotope studies can also give an
indication of the size of the closed system. One can see, for
example, the work of
Marquer and Burkard (1992)
showed that the size of the closed system evolved during
the deformation process:
• syntectonic veins with associated stylolites, within the
Helvetic carbonate cover, have δ18O compositions
depending on the adjacent wall rock compositions and
varying with respect to the initial chemical
heterogeneity of each sedimentary layer (closed systems),
• alternatively, variation profiles in major cover thrusts
show a variable increase in 87Sr/86Sr ratios combined
with a strong decrease in δ18O approaching an isotopic
equilibrium with the basement rocks, indicating that the
systems have been opened by large-scale fracturing
processes linked to the major thrusts.
Therefore, and except for the self-healing process and for
some advection processes with free-face dissolution, sealing
processes are slow stress-driven processes linked to creep
deformation. This can explain the link observed between the
characteristic times of post-seismic strength and permeability
recovery (Fig. 1a and 4a).
1.3 Modeling Strength Evolution
Rice and Ruina, 1983
). These laws are thoroughly
discussed by Marone (1998). The concept relies on two types of
observations. The first one is that static friction between two
solids increases with time, even during stationary contact
(hold time) (Fig. 5a left). From various experiments, this
corresponds to a time-dependent strengthening effect with
logarithmic time dependence. The second observation is that
sliding (dynamic) friction decreases with velocity for most rocks,
a phenomenon known as velocity weakening (Fig. 5a right).
The rate-and-state law combines these two aspects
1998; Marone, 1998)
τ = [μo + a ln(V/Vo) + b ln(Voθ/L)]σ–
where τ is shear stress, σ– is effective normal stress, V is slip
velocity, Vo a reference velocity, μo the steady-state friction
coefficient at Vo, and a and b are material properties. L is the
critical slip distance. θ is a state variable that evolves
dθ/dt =1– (θV/L)
Other formulations of this evolution with time have been
Perrin et al. (1995)
thoroughly discussed in
. The significance of
the terms is given in Figure 5b. This law has been used in
order to model fault dynamics, such as slip instabilities
(earthquakes), earthquake triggering by stress perturbations,
post-seismic deformation, and slow earthquakes. It has been
used extensively to model earthquakes
postseismic relaxation driven by brittle creep
Avouac, 2004, 2007)
(Helmstetter et al.,
, as well as other contexts
(Heslot et al., 1994;
Helmstetter and Shaw, 2006)
. The rate-and-state law is a
conceptual approach that has only been measured for
shortterm experiments (days - weeks). It remains to be
demonstrated that it could be extended over geological time scales.
Heat flow measurements along some faults as the San
Andreas Fault constrain the coefficient of friction of the fault
in the creeping section to a value smaller than 0.2, well below
values currently expected with friction (0.6). Friction may be
linked to transitory post-seismic events
(Johnson et al.,
, however it is not likely to be a major mechanism for
1.3.2 Modeling the Competition between Weakening
and Strengthening Effects by Viscosity Evolution
Moreover, if the rate-and-state law is well adapted to the
modeling of the sliding surfaces, it is less clear how it can
model the damage induced by earthquakes that can propagate
far away from the gouge. The work of
Pili et al. (1998)
showed, from stable isotope studies that in active faults fluids
flow from depth through a 1-2-km-wide damaged zone.
Consequently, modeling the behavior of a large shear zone
requires a different approach from rate-and-state law. Such
an approach can rely on the modeling of viscosity evolution
Becler et al., 1994
Hold time (s)
a) Variations in static friction with different hold time values (left), evolution of dynamic friction with slip velocity (right); b) friction versus
normalized displacement for a rate-and-state law, see Equations 6, 7 in the text; c) modeling of strength evolution in a fault zone when
assuming a competition between weakening and strengthening processes; d) shear stress versus normalized time with various characteristic
times of strengthening: relatively fast (orange) or relatively slow (green), see Equations 8 and 9 in the text. Adapted from Marone, 1998, (a,
b) and Gratier and Gueydan, 2007, (c, d).
in which the strength of damaged zones instantaneously
decreases then slowly increases with time after an
earthquake. The characteristic time scales of weakening and
strengthening differ and this difference strongly controls the
rheology of active faults and thus influences the duration of
seismic cycles. Simple rheological models have been
proposed to account for these two effects
(Gratier and Gueydan,
. The damaged zone is modeled as a ductile material,
with constitutive rheological laws that involve
pressure-solution creep, healing processes and reaction softening. These
ductile mechanisms are assumed to be relevant within the
whole seismogenic crust, as is suggested by the occurrence
of pressure solution deformation patterns at all depths in the
upper crust. A 1D model
is used (Fig. 5c)
where an idealized damaged zone undergoes simple shear at
constant velocity. The model is composed of a layered
structure, in simple shearing (Fig. 5c),
Gratier and Gueydan
. The fault zone is the region where weakening and
strengthening will prevail, inducing a change with time in the
viscosity η(t). In contrast, the viscosity of the wall rock
remains at its initial value η0. So the viscosity η(t) within the
fault zone is changed by a competition between weakening
and strengthening (Fig. 5c) as follows:
η(t) = [w(t) + s(t)]η0
where w(t), s(t) and η0 define the amount of weakening,
strengthening and the initial viscosity, respectively, with the
0 < w(t) < 1 and 0 < s(t) <1.
The time evolution of the weakening w(t) and
strengthening s(t) are governed by the following equations:
=ϕwε[w∞ − w(t )] and
=ϕsε[s∞ − s(t )]
w∞ and s∞ define the total amount of weakening and
strengthening. ϕw and ϕs define the kinetics of weakening and
strengthening, and are free parameters that characterize the
Preliminary results of this model show that the kinetics of
the weakening and strengthening processes determine the
relative rates of shear stress decrease and increase during the
interseismic period. For example, in Figure 5d, everything
being equal, faster kinetics for the strengthening processes
induces shorter recovery times of the fault strength. The
kinetics of dissolution precipitation and mineral reactions is
therefore expected to be an important control on the healing
time of active faults and possibly on the recurrence time of
2 HOW DO PERMEABILITY AND PORE PRESSURE
EVOLVE DURING THE “FRACTURING AND
2.1 Change in Permeability
We do not discuss here what happens during the main
Zhu and Wong (1997)
studied, for example, the
evolution of porosity and permeability at the transition from
brittle faulting to cataclastic deformation. They pointed out the
various effects of both deviatoric and hydrostatic stresses.
We simply consider that permeability in the gouge and
damaged zone decreases during an earthquake, assuming that the
post-seismic decrease in wave velocity attests to this effect
(Fig. 1a). We know that fluids flow through faults in the
upper crust, as shown, for example, by isotope studies or by
the evidence of fluid-related aftershock sequences
. The fluids come either from depth
(i.e., from the
mantle or lower crust along the San Andreas, Kennedy et al.,
or from the surface
(i.e., from meteoric water along the
Aegion Fault, Benedicto et al., 2008; Pizzino et al., 2004)
The pathways of the fluids localized along the fault are
revealed by isotope studies of fluid inclusions trapped in
(Pili et al., 1998, 2002)
. From these results, the fault
gouge and the whole damaged zone (up to 1-2 km away from
the principle slip surface near the San Andreas fault, for
example) are infiltrated several times, in connection with
several earthquakes. In contrast, each fracture is mostly opened
and sealed once (in connection with a single earthquake). As
seen above (Fig. 3), characteristic times of healing processes
by mass transfer range from days to millennia, mostly
depending on the aperture of the fractures (from microns to
cm). Consequently, modeling the post-seismic evolution of
the permeability along the whole fault must integrate the
effect of all the healing mechanisms. However, for each set
of fractures associated with a specific mechanism of sealing,
the sealing rate evolves with time. So, it is difficult to model
the evolution of various sets of fractures with various
characteristics times of sealing that evolve with time.
A first step is to try to evaluate a simple porosity versus
time relation for each type of mechanism of fracture sealing.
Renard et al. (2000)
modeled the evolution
that the sealing rate achieves by pressure solution with mass
transfer from solution cleavage to cracks. This mechanism
appears to be one of the most important mechanisms for
crack sealing and creep during post-seismic deformation
Figure 3d. The sealing rate decreases with time due to two
combined effects (Fig. 6b): the progressive increase in
the distance of mass transfer (parameter d in Eq. 4, 5) and the
increase in dissolution surface under stress that reduces the
driving forces (parameter σn in Eq. 4, 5). Taking into
account this geometric evolution the porosity φ is modeled
to decay exponentially with time and space (Fig. 4c),
et al. (2003)
φ = φ0e–x/Le–t/τ(z)
L is the characteristic distance for the exponential decrease in
the porosity after each earthquake (distance for which the
maximum porosity φ0 along the fault is divided by 2.72). τ(z)
is the characteristic time of the sealing process (time during
which the porosity is divided by 2.72). With such a very
simple relation, the characteristic time of the sealing process
expresses the sealing rate evolution with time for a given
geological context. Evolution of such a parameter with depth
may be derived from both experiments and observations of
natural samples. Examples are given in Figure 6 of the τ(z)
evolution with depth for a stratified crust near the San
Andreas Fault with different rates of compaction depending
on both the main soluble species (calcite or quartz) and the
PT evolution. Following Lockner and
relation between permeability k and porosity φ is expressed as
k ≈ φ3 . Such an evolution was used to model the evolution of
pore pressure within the fault; see Figure 6.
A second step is to find a way to integrate the various
scales of time and space during the fault healing process. The
Sealing rate with depth
Evolution of fluid pressure with time
100I 0 m
a) Fluids in fault zone (blue) with associated evolution of porosity (below); b) modeling of pressure solution crack sealing rate in the
damaged zone when considering the effect of the progressive sealing of fracture network by pressure solution: dissolution surfaces
(stylolites) are red, initial fractures filled with fluid are black, sealing is white; c) modeling of pore pressure evolution in a fault zone during
the inter-seismic period, when integrating over the upper crust the difference in sealing kinetics between quartz and calcite. Adapted from
Gratier et al., 2003, (a, c) and Renard et al., 2000, (b).
use of the percolation theory and the simulation of random
networks are possibilities that have been successfully
Zhu et al. (1995)
in order to analyze the
evolution of permeability with a random shrinkage model and a
connectivity loss model in a three-dimensional cubic
network. Their simulations predict the changes in permeability
and porosity obtained from hot-pressed calcite and quartz
experiments. It is a step toward a general model of
permeability evolution within the whole natural fault zone.
Finally, one may consider another question: does fracturing
develop during the interseismic period? It is not easy to
answer such a question because it is not easy to distinguish
co-seismic fracture from subcritical fracture that could
develop during the interseismic period.
Olson et al. (2009)
showed that it is possible to sustain opening-mode fracture
growth with sub-lithostatic pore pressure, leading to
competition between mineral precipitation and the fracture opening
rate that determines how the fracture network is
2.2 Change in Pore Pressure
Another problem arises in natural fault zones. If fluid inflow
is significant, this can increase pore fluid pressure and reduce
effective shear strength, at least locally within the fault.
During the interseismic period, the combined effect of the
strengthening linked to the sealing process and of the
increasing pore pressure sets the stage for stress building and
seismicity. The characteristic time of pore fluid change is even
more difficult to estimate than the characteristic time of the
sealing since it relies on both the flux of fluid from depth
and on the possible compaction of the whole
fault (Sleep and Blanpied, 1992), or on both the flux of fluid
from depth and the sealing rate
(Gratier et al., 2003)
Modeling the permeability evolution in gouges and damaged
zones shows that gouges must seal faster than damaged
zones due to the thinner aperture and lower size of their
fractures. An example is given in Figure 6 where the limiting
process of the rate of permeability change is considered to be
the slowest sealing rate within the damaged zone around the
gouge. The sealing rate is modeled to decay exponentially
with time (after the earthquake) and space (away from the
main seismic slip zone), relation 10 (Fig. 6a).
Over-pressuring (lithostatic pressure) develops at two different depth
intervals (Fig. 6c). Firstly, at depth (bottom of the seismic
crust) due to the combined effects of localized inflow of fluid
from the lower crust and the presence of quartz that sealed
the veins, increasing the pore pressure. Secondly, in the
upper part of the crust, where the high solubility of calcite
renders this mineral available for mass transfer and relatively
fast sealing of the veins. A comparison of the evolution of the
pressure solution rates with depth for the two minerals is
given in Figure 4d. One may finally notice that the time of
significant pore pressure change (time to reach local
sublithostatic pressure of significant size) is of the order of
magnitude of the time intervals between earthquakes (tens
to hundreds years).
CONCLUSIONS, WHAT TO DO NEXT
Fault permeability and strength evolve with time during
fracturing and healing cycles related to post-fracturing creep and
sealing processes. Laboratory experiments and observations
of natural faults show how non-steady-state pressure solution
processes explain both creep and sealing processes.
Consequently, the duration of the fracturing and sealing cycle
should be related to some extent to the geological context of
a faulted area. Some leads are presented here that could be
followed or developed in the future in order to model best the
characteristic times of fracturing and sealing cycles
depending on the geological context.
Reproducing the Right Mechanism in the Lab
The need for reproducing the actual transfer mechanism is
very important since the various mechanisms of mass
transfer (self-healing or sealing) have neither the same
characteristic times nor the same sensitivity to thermodynamic
parameters. For example, kinetics of self-healing processes that
are fast enough to be reproduced easily in the lab (hours
days) are most often controlled by reaction rates with high
activation energy (high dependence on the temperature).
Conversely, sealing processes, that are always very slow and
difficult to reproduce in the lab (months or years), are mostly
controlled by diffusion, with low activation energy. Both
must be reproduced in the lab and the relative part of each
mechanism must be evaluated from the observation of
natural systems and integrated in modeling.
Evaluating the Parameters of the Creep and Sealing Laws
Modeling the evolution of transfer and rheological properties
implies knowing both the fundamental mechanism of creep
and sealing and the values of the parameters of the creep and
sealing laws. For example, investigating the pressure solution
mechanism with diffusion as the limiting process (Eq. 4, 5)
implies first choosing a model of evolution (Fig. 6b) then
evaluating two types of parameters:
– some parameters must be evaluated from experiments as
kinetics parameters (Dw = diffusion coefficient time
thickness of the diffusion path) or the effect of stress (power or
exponential effect), and;
– other parameters must be evaluated from the observations
of natural samples such as the effect of the nature of fluid
and minerals (solubility, molar volume) and the effect of
the geometry of the path of mass transfer (for example,
d = mean distance of mass transfer along the thin fluid
paths trapped under stress).
Evaluating the Duration of the Fracturing and Sealing
Process in the Field
Evaluating such duration in the field is also a major task.
Piper et al. (2007)
successfully demonstrated the potential of
travertine that precipitated over a fault, as fossil records of
geomagnetic paleo-secular variations, environmental change
and earthquake activity. Coupled U/Th dating and magnetic
studies could give both the duration of inter-seismic periods
and the evolution of the fluid flux with time, at least for
earthquakes of magnitude higher than 6-7. The problem is to
be sure that the evolution of the travertine deposition is well
connected with the evolution of fluid flow through faults at
depth. This could rely on stable isotope measurements that
help to evaluate the origin and the path of the fluids.
Evaluating the Evolution of Transfer Properties
on the Scale of an Oil Reservoir
Earthquakes have been observed to affect regional
(Rojstaczer and Wolf, 1992; Muir-Wood and King,
. Elkhoury et al. (2006) used the response of water well
level to tidal-induced deformation to show that seismic
waves increase the permeability. The change is shown to be
proportional to the peak ground velocity and the effect may
last several years. It could be interesting to collect data from
oil reservoir exploitation in order to test this idea of
permeability change within reservoirs affected by earthquakes, and
especially to evaluate the characteristic times of healing that,
according to our idea, must depend on the geological
characteristics of the reservoir.
Modeling the Complexity of the Evolution
As stated above, modeling the evolution of the transfer and
rheological properties from creep and sealing laws is only part
of the problem. One also needs to integrate the slow evolution
of fluid flux and pore fluid pressure along and near the fault.
So the modeling must integrate mechanical, geochemical and
hydrological aspects. The results predict the post-fracturing
characteristic time scales of strength and transfer recovery in
active faults, depending on the conditions of the deformation
(nature of fluid and rocks, temperature, stress, strain rate, etc.).
We expect that the complex interactions among these
recovery time scales have a strong effect on the fracturing and
healing cycle durations and on earthquake recurrence time, and
that these time scales are characteristic of the geological and
geodynamical context of a given region.
I would like to thank two anonymous reviewers for their
interesting suggestions and J. Richard, E. Frery, S. Mittempergher,
F. Renard, F. Gueydan, D. Amitrano, D. Bernard, A-M.
Boullier, G. Di Toro, H. Perfettini, C. Aubourg, M-L. Doan,
A. Helmstetter, M. Bouchon, N. Ellouz-Zimmermann,
V. Gardien, L. Jenatton, E. Larose, B. Vial, for helpful
discussions. The project has been supported by the INSU-CNRS
(aléas, risques et catastrophes naturels) and the LGIT lab.
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