Click
Here
GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L23302, doi:10.1029/2009GL040684, 2009
for
Full
Article
Effects of gouge fragment shape on fault friction:
New 3D modelling results
Steffen Abe1 and Karen Mair2
Received 25 August 2009; revised 29 September 2009; accepted 8 October 2009; published 1 December 2009.
[1] The friction of granular fault gouge plays an important
role in governing the mechanical behavior and hence
earthquake potential of faults. Using numerical modelling,
significant progress has recently been made towards
understanding the micro-mechanics that drive fault gouge
evolution. Despite these insights, many previous numerical
models have predicted unrealistically low macroscopic
frictional strength. Here we describe modified 3D discrete
element simulations of fault gouge evolution. Our particlebased simulations, modelled on laboratory experiments,
include breakable bonds between individual particles (or
particle clusters) allowing fracture of aggregate grains. With
accumulated strain, grains break up, evolving in size and
shape to produce a textural signature reminiscent of natural
faults. Cluster-simulations, producing pseudo-angular
daughter fragments yield realistic frictional strength (0.6).
Non-cluster simulations, producing angular and spherical
daughter fragments, have much lower friction levels. We
therefore demonstrate that gouge fragment shape and
resulting interactions dominate the frictional strength of
faults. Citation: Abe, S., and K. Mair (2009), Effects of gouge
scopic evidence collected at the end of the experiments.
Numerical modelling provides a potentially powerful tool
with which to investigate grain scale events and interactions
that are tricky to view directly in the laboratory. Recent
modelling has made significant progress towards better
understanding micromechanical processes [e.g., Cundall
and Strack, 1979; Aharonov and Sparks, 1999; Morgan,
1998]. Despite these valuable insights however, an overriding issue is that many previous models have predicted
unrealistically low values of macroscopic frictional strength.
[4] Here we present new modified 3D simulations of
gouge evolution during shear that successfully produce
realistic values of macroscopic friction (ca. 0.6). The main
new features compared to previous work are the inclusions
of rough boundary plates and unbreakable particle clusters.
We demonstrate that gouge fragment shape (and resulting
geometric interaction) is a crucial factor controlling macroscopic frictional strength. We suggest that the implementation of more complicated grain shapes will dramatically
improve the applicability fault gouge models.
fragment shape on fault friction: New 3D modelling results,
Geophys. Res. Lett., 36, L23302, doi:10.1029/2009GL040684.
2. Method
1. Introduction
[2] The granular wear material (fault gouge) that accumulates between the walls of a fault as it slides, plays an
important role in controlling macroscopic sliding friction
and the frictional stability of the fault. Fragmentation
processes operating in this gouge material during shear,
alter grain size distributions [e.g., Sammis et al., 1987;
Blenkinsop, 1991; Rawling and Goodwin, 2003; Storti et
al., 2003; Billi, 2005], change grain shape [e.g., Storti et al.,
2007; Heilbronner and Keulen, 2006], and hence influence
local grain scale interactions. This will undoubtedly change
force chain characteristics across the layers [Hazzard and
Mair, 2003] and influence the localization state [Beeler et
al., 1996; Mair and Marone, 1999] that are both key factors
affecting macroscopic sliding behavior.
[3] Laboratory experiments have provided important
constraints and understanding of the frictional behavior of
sheared granular materials [Mair et al., 2002; Anthony and
Marone, 2005], however one limitation is that dynamic
grain scale processes must generally be inferred from
macroscopic response or determined from ‘snapshot’ micro1
Geologie-Endogene Dynamik, RWTH Aachen University, Aachen,
Germany.
2
Physics of Geological Processes, University of Oslo, Oslo, Norway.
Copyright 2009 by the American Geophysical Union.
0094-8276/09/2009GL040684$05.00
[5] To model this inherently discrete problem, we use a
3D discrete element (DEM) approach [Cundall and Strack,
1979; Mora and Place, 1994; Place and Mora, 1999].
Previous work [Hazzard and Mair, 2003] has demonstrated
that 3D simulations are essential to capture the range of
grain scale processes, e.g., out of plane motions, operating
in evolving faults. In our simulations, fault gouge grains are
modelled as aggregates [Abe and Mair, 2005] composed of
many (ca. 8000) individual spherical particles bonded
together with breakable elastic bonds (Figure 1). The
particles are either grouped together into particle clusters
(models C1, C2) or not (models SP1, SP2). When the bond
failure threshold is exceeded, aggregate grains can fracture,
permitting gouge evolution in a somewhat natural way. The
use of aggregate grains composed of particle clusters, where
bond strength is much higher inside particle clusters than
between the clusters, (see enlarged pastel grain in Figure 1)
ensures that broken daughter fragments are predominantly
pseudo-angular rather than spherical as is common when the
aggregate grains consist of bonded single particles. This
modification allows us to directly investigate the effects of
grain fragment shape on macroscopic friction. In order to
enable the simulation of sufficiently large models, the
parallel DEM simulation package ESyS-Particle [Abe et
al., 2003] (https://launchpad.net/esys-particle/) has been
used.
[6] The initially spherical aggregate grains are constrained between rigid upper and lower boundary blocks
(or fault walls) Figure 1. Spherical grains were chosen to
L23302
1 of 4
L23302
ABE AND MAIR: GOUGE FRAGMENT SHAPE AND FAULT FRICTION
L23302
Figure 1. (left) Initial setup of a typical fault model and (right) final state of the model after engineering shear strain of ca.
4 at a normal stress of 30MPa. Aggregate grains are composed of either individual particles or particle clusters (see enlarged
grain where the pastel colors indicate the clusters) bonded together.The fractured remains of the initially spherical grains are
illustrated on right. The inset shows the (i) spherical and (ii) pseudo angular shape of the smallest fragments in single
particle (SP) and cluster (C) models respectively.
mimic laboratory experiments on spherical glass beads
[Mair et al., 2002; Anthony and Marone, 2005] and hence
allow proper model validation. The rough surface of the
driving plates, triangular saw-toothed grooves cut perpendicular to shear, has also been chosen to closely mimic the
shape of the driving plates used in laboratory experiments
[Mair et al., 2002; Anthony and Marone, 2005]. The size of
the grooves relative to the grain diameter is chosen to match
the laboratory setup. In addition, we simulate smooth, flat
boundaries as has also been done in the laboratory [Anthony
and Marone, 2005]. The model has repeating boundaries
right and left, and frictionless walls front and back. Under
constant normal stress, shear is applied to the upper and
lower boundaries. Shearing rate is increased linearly to the
chosen velocity (over the initial 0.05 shear strain) then held
constant for the duration of the simulation. Macroscopic
friction is calculated from shear force divided by normal
force acting on the upper and lower boundary blocks.
and laboratory gouge layers. The larger fluctuations in the
measured friction in the simulations (Figure 2) are also most
likely due to the smaller number of grains in the simulations
compared to the laboratory experiments. Significantly larger
simulations, using numbers of initial grains comparable to
those used in the laboratory experiments, would be needed
to confirm this.
[8] The mean steady-state friction data obtained for
different model configurations (i.e., different grain shape
3. Results
[7] Typical particle cluster model simulations (Figure 2)
show an increase in macroscopic friction level with accumulated shear strain until a steady-state friction level of
0.6 is reached. This steady-state friction level is the value
subsequently plotted in Figure 3 (from this and other
simulations). The observed ramp-up is due to the initially
spherical aggregate grains breaking down to become pseudoangular fragments. Fragmentation of the aggregate grains is
initially intense becoming less intense with accumulated
shear strain (Figure 2). Data from laboratory experiments
[Mair et al., 2002] where spherical glass beads are sheared
and broken up, shows qualitatively comparable behavior
with friction ramping up from 0.4 to 0.6. We note
however, that the steady state friction level is reached after
larger engineering shear strain (8 in experiments compared to 1 in the models). This distinction is most likely
due to the difference in number of grains across the model
Figure 2. Macroscopic friction versus shear strain for two
cluster models (Model C1, C2) where initially spherical
aggregate grains break down to become pseudo-angular
fragments with accumulated strain. Comparable laboratory
data for initially spherical glass beads being broken into
angular fragments during shear is superimposed [Mair et al.,
2002]. Data for bond breakage rate (second y-axis)
highlights the initially high fragmentation rate that decays
with shear strain. Note the different shear strain axes for
model and lab data.
2 of 4
L23302
ABE AND MAIR: GOUGE FRAGMENT SHAPE AND FAULT FRICTION
L23302
and boundary wall roughness) at a range of normal stresses
are summarized in Figure 3. Also shown are laboratory
experimental data for comparable geometries [Mair et al.,
2002; Anthony and Marone, 2005; Frye and Marone, 2002].
Macroscopic friction is systematically affected by gouge
fragment shape and boundary wall roughness. Spherical
grains with smooth boundary walls produce the lowest
friction levels in our study (0.3), spherical grains with
rough boundary walls have slightly higher friction (0.45),
and angular grains with rough boundary walls result in
friction levels of 0.6 (see Figure 3).
[11] A series of simulations that are identical except that
they use different values of the micro-friction parameters at
the particle level, ranging from 0.4 to 1.5, (Figure 4)
illustrate the insensitivity of the macroscopic friction measured at the boundaries of our model, to the micro-friction
parameters prescribed to individual particles. Similar observations of the saturation of the macroscopic friction for
increasing particle-level friction have previously been made
in 2D simulations of granular fault gouge [Mora and Place,
1998], however in 2D the macroscopic friction level was
limited to ca. 0.4. This demonstrates that gouge grain
geometry is a much more important factor than particle
scale friction in setting the macroscopic friction level.
[12] The comparison between friction data obtained from
models with different resolution (i.e., 190 000 and 480 000
particles) (Figure 4) also shows that the mean steady state
friction level is not significantly influenced by the model
resolution, at least for the model sizes used to date (this
resolution insensitivity may not hold for very small models).
[13] Importantly, our new results from particle cluster
models are largely consistent in terms of grain scale
processes and developing microstructures with our recent
findings on non-clustered models [Abe and Mair, 2005;
Mair and Abe, 2008]. We still observe survivor grains, i.e.,
those retaining 75% of their original equivalent diameter to
relatively large shear strains. Regions of strain localization
still appear to correspond to regions having smaller grain
size. However, we see that with rough boundaries, the
regions of localized strain are not always concentrated at
the boundary as is commonly the case for smooth boundary
runs, but are located within the layer. Additionally, for
particle cluster models with rough boundaries, the regions
of strain localization appear to be less persistent, suggesting
local strain hardening.
4. Discussion
5. Conclusions
[9] Results from the numerical models are extremely
consistent with the trends of the experimental data. Models
with pseudo-angular grains and rough boundary walls (m =
0.59 – 0.67) match the experimental data (m = 0.57 – 0.63)
very closely. As do the models having spherical grains and
rough boundary walls (m = 0.42 –0.49) with comparable
laboratory experiments conducted using spherical glass
bead gouge (m = 0.44 – 0.47) [Mair et al., 2002; Frye and
Marone, 2002; Anthony and Marone, 2005]. The fit
between numerical and experimental data for models with
smooth boundary walls is not quite so good but this can be
explained by the fact that the boundaries in the numerical
models are not perfectly smooth but are rough at the particle
scale whereas the boundary blocks used in the laboratory
experiments are mirror finished hardened steel. Notably, for
a given geometry, steady state friction shows no trend with
normal stress.
[10] The systematic increase of frictional strength with
increasing abundance of angular grains (Figures 2 and 3)
and increased wall roughness (Figure 3) in our simulations
matches the results obtained from comparable laboratory
studies very well. The likely cause is that angular grains are
essentially stuck or jammed and although they clearly
rotate, they require a larger shear force to be able to do so
whereas spheres roll much more efficiently.
[14] We show that gouge fragment angularity is crucial in
controlling macroscopic friction. By doing so, we demon-
Figure 3. Summary of mean steady state friction data for
different grain shape (spheres/angular) and boundary wall
roughness (smooth/rough) configurations. Numerical model
results (this study) and laboratory experiments [Mair et al.,
2002; Frye and Marone, 2002; Anthony and Marone, 2005]
are compared.
Figure 4. Macroscopic friction measured at boundaries of
the model versus the microscopic friction prescribed
between individual particles for two cluster models (Model
C1, C2) having different resolutions (190 000 particles and
480 000 particles respectively) but the same geometry of
angular particles and rough boundaries.
3 of 4
L23302
ABE AND MAIR: GOUGE FRAGMENT SHAPE AND FAULT FRICTION
strate the limitations of using ideal spherical indestructible
particles in simulations of fault gouge behavior. The very
good agreement between the results from our new cluster
simulations and the available laboratory data indicates that
gouge fragment angularity has been an important ‘‘missing
ingredient’’ that has, in effect, prevented previous DEM
simulations of fault gouge from reaching realistic values of
frictional strength. Due to advances in available computational resources, the implementation of more complicated
geometries into large scale simulations of faults is now
feasible. We conclude therefore that this is an important
and necessary step in order to better understanding the
mechanics of earthquake faults.
[15] Acknowledgments. Computations were made using NOTUR
(Norwegian National High Performance Computing) resources (project
nn4557k). We thank everyone who has contributed to the development of
the ESyS-Particle software, in particular, Shane Latham, Dion Weatherley,
Paul Cochrane and David Place. This work was supported by a Center of
Excellence grant from the Norwegian Research Council to PGP (Physics of
Geological Processes) at the University of Oslo.
References
Abe, S., and K. Mair (2005), Grain fracture in 3D numerical simulations of
granular shear, Geophys. Res. Lett., 32, L05305, doi:10.1029/
2004GL022123.
Abe, S., D. Place, and P. Mora (2003), A parallel implementation of the
lattice solid model for the simulation of rock mechanics and earthquake
dynamics, Pure. Appl. Geophys., 161, 2265 – 2277.
Aharonov, E., and D. Sparks (1999), Rigidity phase transition in granular
packings, Phys. Rev. E, 60, 6890 – 6896.
Anthony, J. L., and C. Marone (2005), Influence of particle characteristics
on granular friction, J. Geophys. Res., 110, B08409, doi:10.1029/
2004JB003399.
Beeler, N. M., T. Tullis, M. Blanpied, and W. Weeks (1996), Frictional
behavior of large displacement experiment faults, Pure Appl. Geophys.,
144, 251 – 276.
Billi, A. (2005), Grain size distribution and thickness of breccia and gouge
zobes from thin (<1 m) strike-slip fault cores in limestone, J. Struct.
Geol., 27, 1823 – 1837.
Blenkinsop, T. G. (1991), Cataclasis and processes of particle size reduction, Pure Appl Geophys., 136, 59 – 86.
L23302
Cundall, P. A., and O. Strack (1979), A discrete numerical model for
granular assemblies, Geotechnique, 29, 47 – 65.
Frye, K. M., and C. Marone (2002), The effect of particle dimensionality on
Granular friction in laboratory shear zones, Geophys. Res. Lett., 29(19),
1916, doi:10.1029/2002GL015709.
Hazzard, J. F., and K. Mair (2003), The importance of the third dimension
in granular shear, Geophys. Res. Lett., 30(13), 1708, doi:10.1029/
2003GL017534.
Heilbronner, R., and N. Keulen (2006), Grain size and grain shape analysis
of fault rocks, Tectonophysics, 427, 199 – 216.
Mair, K., and S. Abe (2008), 3D numerical simulations of fault gouge
evolution during shear: Grain size reduction and strain localization, Earth
Planet. Sci. Lett., 274, 72 – 81.
Mair, K., and C. Marone (1999), Friction of simulated fault gouge for a
wide range of velocities and normal stresses, J. Geophys. Res., 104,
28,899 – 28,914.
Mair, K., K. M. Frye, and C. Marone (2002), Influence of grain characteristics on the friction of granular shear zones, J. Geophys. Res., 107(B10),
2219, doi:10.1029/2001JB000516.
Mora, P., and D. Place (1994), Simulation of the frictional stick-slip instability,
Pure Appl. Geophys., 143, 61 – 87.
Mora, P., and D. Place (1998), Numerical simulation of earthquake faults
with gouge: Towards a comprehensive explanation for the heat flow
paradox, J. Geophys. Res., 103, 21,067 – 21,089.
Morgan, J. K. (1998), Numerical simulations of granular shear zones using
the distinct element method: 1. Shear zone kinematics and the micromechanics of localization, J. Geophys. Res., 104, 2703 – 2718.
Place, D., and P. Mora (1999), The lattice solid model: Incorporation of
intrinsic friction, J. Int. Comp. Phys., 150, 332 – 372.
Rawling, G. C., and L. B. Goodwin (2003), Cataclasis and particulate flow
in faulted, poorly lithified sediments, J. Struct. Geol., 25, 317 – 331.
Sammis, C., G. King, and R. Biegel (1987), The kinematics of gouge
deformation, Pure Appl. Geophys., 125, 777 – 812.
Storti, F., A. Billi, and F. Salvini (2003), Particle size distributions in natural
carbonate fault rocks: Insights for non-self-similar cataclasis, Earth
Planet. Sci. Lett., 206, 173 – 186.
Storti, F., F. Balsamo, and F. Salvini (2007), Particle shape evolution in
natural carbonate granular wear material, Terra Nova, 19, 344 – 352.
S. Abe, Geologie-Endogene Dynamik, RWTH Aachen University,
Lochnerstrasse 4-20, D-52056 Aachen, Germany. (s.abe@ged.rwthaachen.de)
K. Mair, Physics of Geological Processes, University of Oslo, PO Box
1048 Blindern, N-0316 Oslo, Norway. (karen.mair@fys.uio.no)
4 of 4