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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B12404, doi:10.1029/2007JB005560, 2008
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Gravity influenced brittle-ductile deformation and growth faulting in
the lithosphere during collision: Results from laboratory experiments
Sylvie Schueller1,2,3 and Philippe Davy1
Received 19 December 2007; revised 12 June 2008; accepted 3 September 2008; published 10 December 2008.
[1] Because of the competition between brittle and ductile rheologies and their interplay
with tectonic and buoyancy forces, lithospheric deformation results in very contrasting
styles. In continental collision, especially with unconfined boundaries, deformation can be
either homogeneously distributed or localized on complex fault patterns, and different
deformation modes such as contraction, extension, and strike-slip interfere. Using scaled
lithospheric analog experiments made of dry sand, silicone putties, and dense honey, we
investigate the mechanical parameters that control the deformation style in colliding
systems, with a particular focus on the roles of buoyancy and brittle-ductile coupling. The
analysis of tens of experiments shows that the principal deformation features depend on
two main parameters: a brittle-to-ductile strength ratio G, which controls deformation
localization at the largest scale, and a buoyancy-to-strength ratio Ar, which fixes the
relative amount of contractional, extensional, and strike-slip structures. Strain localization
occurs only for G larger than a critical value (0.5), and the range of G values, over
which the transition from nonlocalized to localized deformation occurs, is small. The three
main deformation regimes (contraction, strike-slip, and extension), which coexist in
most of the collision experiments, occur in relative proportions that depend mainly on Ar
and on the nature of the boundary conditions.
Citation: Schueller, S., and P. Davy (2008), Gravity influenced brittle-ductile deformation and growth faulting in the lithosphere
during collision: Results from laboratory experiments, J. Geophys. Res., 113, B12404, doi:10.1029/2007JB005560.
1. Introduction
[2] Continental lithosphere is heterogeneous with varied
mineralogy, a diversity of mechanical behaviors (from
rupture to viscous flow) and inherited structures. Deformation of the lithosphere therefore leads to very contrasting
deformation styles, resulting from the interplay between
various forces, rheologies, and boundary conditions. Continental collision is emblematic of this complexity since it can
result in lithospheric thickening close to the colliding
region, large-scale lateral escape of continental blocks along
strike-slip faults, and extension in the periphery in the case
of a nonconfined lateral boundary. This is well illustrated
in some active collision zones: the India-Asia collision
[Tapponnier and Molnar, 1977], the Anatolia-Arabia collision [Dewey et al., 1986; McKenzie and Jackson, 1986;
Suzanne, 1991], and the deformation of Eastern Alps
[Ratschbacher et al., 1991; Rosenberg et al., 2007]. The
opening of the South China Sea and the Japan Sea has also
been related in some cases to the India-Asia collision
[Fournier et al., 2004; Jolivet et al., 1990, 1994; Kimura
1
Géosciences Rennes, UMR 6118, Université de Rennes 1, CNRS,
Rennes, France.
2
Centre for Integrated Petroleum Research, University of Bergen,
Bergen, Norway.
3
Now at Institut Français du Pétrole, Rueil-Malmaison, France.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2007JB005560$09.00
and Tamaki, 1986; Tapponnier et al., 1986, 1982; Worrall et
al., 1996]. But the Pacific subduction zones [Schellart et al.,
2003; Schellart and Lister, 2005] or changes in plate
convergence rate along the eastern plate boundary of
Eurasia [Northrup et al., 1995] may also be accounted
together with the collision or even independently [Morley,
2002; Searle, 2006] to produce some of the extensional
structures observed along the eastern boundary.
[3] Some basic mechanical aspects of continental lithosphere are not clear. Some, but not all of the main issues
concern: (1) the relative contribution of brittle and ductile
layers and, hence, the large-scale rheological ‘‘ductile’’ or
‘‘brittle’’ behavior [Bird and Piper, 1980; Davy et al.,
1995; England and Molnar, 1997; England and McKenzie,
1982; Handy and Brun, 2004; Jackson, 2002; Ranalli, 1997;
Tapponnier and Molnar, 1977; Tapponnier et al., 1982;
Vilotte et al., 1982, 1984, 1986], (2) the importance of
buoyancy forces [Cruden et al., 2006; England and
Houseman, 1989; Houseman and England, 1986; 1993],
(3) the link between bulk deformation and localized crustal
faulting [Avouac and Tapponnier, 1993; Bourne et al., 1998;
Peltzer and Saucier, 1996], (4) the existence of large-scale
localization processes [Davy et al., 1995; Tapponnier and
Molnar, 1976; Tapponnier et al., 1982], and (5) the emerging
organization of faults [Davy et al., 1990; Sornette et al., 1993;
Sornette and Davy, 1991; Sornette et al., 1990].
[4] Most of the debates are generated by a chickenand-egg problem: a reference model is required to obtain
the large-scale tectonic interpretation using very sparse
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geological data and a mechanical model is derived from
interpreting the data. This difficulty is particularly critical
when dealing with large-scale tectonic systems. The debate
around the Tertiary India-Asia collision is a good example
of how mechanical models and large-scale tectonic interpretations are intimately related.
[5] The supporters of a ‘‘brittle’’ lithosphere put emphasize on large lithospheric faults, both in models and interpretations [Tapponnier and Molnar, 1976; Tapponnier et
al., 1982]. The lithosphere is divided into a mosaic of large
blocks with typical horizontal dimensions of 100 –1000 km.
This kinematic and mechanical model assumes that a large
fault can propagate throughout the entire system and thus
link the system boundaries. This interpretation framework
emphasizes the role of remote boundaries controlling collision deformation; it proposes that lateral block escape can
be an alternative mechanism to thickening in accommodating continental collision [Peltzer and Tapponnier, 1988].
[6] The supporters of a ‘‘ductile’’ lithosphere argue that
the deformation revealed by earthquakes is distributed in the
continental lithosphere. Even if the largest earthquakes are
located on the previously mentioned large faults, all the
other smaller earthquakes form a distributed deformation
pattern in the crust [England and McKenzie, 1982]. This
fluid-like framework is a useful approach for examining the
importance of buoyancy on the total deformation field
[England and Houseman, 1989; Houseman and England,
1993; Vilotte et al., 1982, 1984, 1986] and the fault
expression of the bulk deformation [Bourne et al., 1998;
England and Molnar, 1990].
[7] The debate cannot be reduced to these two endmember models, or to the escape-versus-shortening problem. Since the lithosphere has a brittle-ductile layering and
deforms both under vertical gravitational stress and horizontal boundary stresses applied by plate motions, a large
effort has been made to understand the mechanical coupling
between rheologically distinct layers. Most of these studies
concern horizontal shortening or stretching on vertical
lithosphere sections, with a system size of the order of the
lithosphere thickness. It would be beyond the scope of this
paper to cite all the articles dealing with necking, buckling,
boudinage, fault coupling, and other instabilities occurring
because of the brittle-ductile layering of the continental
lithosphere. At the continental scale, the consequences of
rheological layering are much less understood. Faulting is a
key issue of this modeling problem. Fault systems appear to
have a complex multiscale geometry that results from the
deformation history [Bonnet et al., 2001; Davy et al., 1990].
Analog sandbox experiments proved to be of great help in
modeling this puzzling problem. Shear bands generated in
sand layers are very similar to natural faults (see Brun
[2002] for a review) and produce multiscale fault patterns
with statistical properties comparable to lithosphere fault
networks [Davy et al., 1995; Sornette et al., 1993]. In the
case of a collision with one free lateral boundary, the
deformation in analog experiments first results in a distributed fault pattern with fractal scaling properties and eventually ends up with large-scale localization [Davy et al.,
1995, 1990; Sornette et al., 1993]. These results were
proposed as a third way to interpret the India-Asia deformation field, following the ideas first developed by Cobbold
and Davy [1988]. The use of these rheologically layered
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experiments at lithospheric scale has also been successfully
applied to understand the deformation of the Eastern Alps
[e.g., Ratschbacher et al., 1991; Rosenberg et al., 2007],
gravity-driven deformation such as the Anatolian-Aegean
system [Gautier et al., 1999], or deformation along the East
Asian active margin [Schellart et al., 2003; Schellart and
Lister, 2005]. The evolution of the strain field as a function
of the lithospheric rheological coupling is thus worthy of
more complete investigation, in which case the question is
now to evaluate the consequences of this rheological layering in terms of potential deformation styles.
[8] In this paper, we describe and discuss 84 experiments
carried out in the experimental tectonic laboratory of Geosciences Rennes in the University of Rennes. The purpose
of this study is not to perform a review on lithospheric
deformation produced in analog experiments but to understand the role of the rheological layering on the deformation
style and the development of fault patterns. That is why
only the experiments allowing to follow the deformation
pattern through time are presented. These lithospheric
analog experiments are built with the classical ‘‘brittle’’
sand/‘‘ductile’’ silicone layering resting upon honey. They
all display a friction-free boundary at the base and along one
or two sides of the simulated lithosphere, allowing tectonic
escape and the development of strike-slip fault pattern due
to the applied tectonic forces. Each experiment has a unique
combination of rheological parameters and boundary conditions. The combination of these experiments provides us
with broad insight into the influence of individual parameters such as the thicknesses of the layers, densities,
viscosities and shortening rates. The aim is to determine
the mechanical parameters that control the deformation style
in such colliding systems. The investigations focus particularly on the joint role of buoyancy and of brittle-ductile
coupling on deformation patterns and more particularly fault
growth. We first describe the experimental method. Then we
classify the experiments and results according to two mechanical parameters (the brittle-ductile parameter G, which is
a brittle-to-ductile strength ratio and the Argand number Ar,
which is a buoyancy-to-strength ratio), and describe the
resulting deformation styles. The discussion focuses on the
parameters controlling strain localization and on the effect of
buoyancy on deformation styles.
2. Experimental Method and Mechanical
Dimensionless Parameters
2.1. Basic Principles
[9] The justification of the sandbox experiments as an
analog for lithospheric mechanics was extensively described
by Davy and Cobbold [1991], as well as originally by
Faugère and Brun [1984] and is summarized hereafter.
Briefly, the continental lithosphere is assumed to behave
as a material composed of brittle and ductile horizontal
layers, where ‘‘brittle’’ refers to rupture and fault sliding and
‘‘ductile’’ refers to viscous creep. Both rheological mechanisms have been identified and characterized experimentally
[e.g., Brace and Kohlstedt, 1980; Goetze and Evans, 1979;
Kirby, 1983; Kohlstedt et al., 1995; Kuznir and Park, 1986;
Ord and Hobbs, 1989; Shimada and Cho, 1990]. According
to the strength profile originally developed by Goetze and
Evans [1979], the brittle-ductile organization leads to a
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Figure 1. Simplified lithospheric strength profiles for uniform shortening (with strike-slip faults in the
brittle crust) in nature (solid line) and in the experiments reported herein (dotted line) [Davy and
Cobbold, 1991]. (a) Profiles for two-layer experiments. (b) Profiles for three-layer experiments.
simplified lithospheric rheological profile, with only four
layers, namely, from the surface down, a brittle crust, a
ductile crust, a brittle mantle, and a ductile mantle. The
mechanical strength of these layers has been calculated for
different thermal and kinematic conditions [Davy and
Cobbold, 1991; Sonder et al., 1986]. The Moho temperature
was used as the main controlling factor, causing a significant rheological change at Moho temperatures above
650°C, where the ‘‘brittle mantle’’ ceases to exist. Also,
the strength of the ‘‘ductile mantle’’ decreases rapidly above
this temperature, which results in most of the differential
stress being supported by the upper crust.
[10] In the sandbox experiments based on this simple
layering, sand and silicone putties are used to model the
brittle and viscous deformation mechanisms of the lithosphere. For the brittle crust, our sand layer is a close analog
with negligible cohesion [Schellart, 2000] and an internal
friction angle of about 30° [Mandl et al., 1977] consistent
with Byerlee’s law for rock friction [Byerlee, 1978]. For the
ductile crust, our silicone layers are imperfect analogs since
silicone is a Newtonian fluid with no depth viscosity
dependency, whereas the viscous creep of rock is characterized by a nonlinear relationship between the differential
stress and applied strain rate, and has a thermal dependency.
Davy and Cobbold [1991] proposed that the model conditions were based on the total mechanical strength, that is,
the differential stress integrated over the layer thickness.
The ratio of the brittle to the ductile strength fixes the range
of admissible viscosities for silicone putties between 103
and 105 Pa s.
[11 ] Although performed under natural gravity, the
experiments are scaled for gravitational forces, meaning
that the ratio between buoyancy force and strength is
approximately similar to that of nature [Davy and Cobbold,
1988, 1991]. In the experiments, as well as in nature, the
buoyancy force is mostly generated by the density contrast
between the bulk of the brittle-ductile lithospheric layers
and the underlying asthenospheric fluid layer [England and
McKenzie, 1982]. In the experiments presented herein, the
basal fluid layer is honey of relatively high density (1.4–
1.45 g cm3). Honey allows isostatic readjustment of the
sand-silicone sandwich and plays the same role as the
asthenosphere does for the lithosphere. The chosen honey
has also a very low viscosity (on average 10 Pa s for
temperatures between 15°C and 20°C) and can thus be
regarded as a very weak material that will not exert any
traction at the base of the layers.
[12] The purpose of the presented experiments is neither
to reproduce the lithosphere with all its complexity nor to
simulate specific regional settings but to discern the
physics of brittle-ductile systems submitted to gravity
and tectonic forces. Accordingly, the 84 experiments were
performed using a simplified lithospheric stratification.
We are aware that the continental lithosphere is of a
much higher level of complexity in terms of rheology
(e.g., depth-dependent viscous creep), processes (thermal
and fluid transfers affect lithosphere mechanics), and
heterogeneity also inherited from previous deformation
episodes. However, we consider our experiments as
simplified proxies for insight into lithospheric mechanics.
The basic brittle-ductile interactions were thus determined
using simple two-layer experiments (one brittle layer
overlying one ductile layer, both floating on weak, dense
honey, Figure 1a). The case of a brittle-ductile crust
overlying a viscous upper mantle was studied using sand
overlaying two silicone layers (Figure 1b). The rheological profile in Figure 1b addresses issues about the
coupling between the brittle upper crust and deep ductile
resistant layers.
2.2. Experimental Setup
[13] The experiments consist of a layer of dry sand
superimposed on one or two layers of silicone and a basal
layer of honey (Figures 1 and 2). The sand used for the
topmost layer is naturally uncemented aeolian sandstone
(Fontainebleau sandpits). The grains (pure quartz) are well
rounded. The mean grain size lies between 150 and 212 mm.
In some experiments [Davy and Cobbold, 1988; Sornette et
al., 1993], the sand was riddled, and grains with a size
below 0.2 mm are kept. In other experiments, grain sizes up
to 500 mm are retained [Bonnet, 1997] (models M). The
sand density ranges from 1.2 to 1.5 g cm3. The density of
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SCHUELLER AND DAVY: DEFORMATION IN LITHOSPHERE ANALOGS
Figure 2. Experimental apparatus: cut-away side view
of sand-silicone-honey ‘‘squeeze-box.’’ Both sand and
silicone layers are deformed thanks to a movable wall
displaced at constant velocity. At least one border of the
sand-silicone layering remains free (no contact with the
box walls).
pure quartz sand is 1.5 g cm3 (when distributed evenly
with a sieve). Low densities of sand (1.2 g cm3) are
obtained by mixing the sand with ethyl-cellulose. The
sand density also depends on the way it is deposited
[Krantz, 1991]. Sand poured in bulk has a lower density
than sand sprinkled with a sieve. In all of the experiments, sand was distributed evenly using a sieve. Sand
deforms by developing shear bands, where progressive
dilatation causes strain softening and hence localization
[Desrues, 1984]. Silicone putties were used for the ductile
layer(s) [Faugère and Brun, 1984; Weijermars, 1986].
The silicone used in most of the experiments was
Rhodorsil Gum7007. Later experiments used PDMS
SGM 36 manufactured by Dow Corning. At experimental
strain rates below 10 4 s 1 , the silicone putty is
Newtonian. Viscosity can be decreased from 105 to 103
Pa s by adding oleic acid. Adding galena powder to the
silicone increases both the density and the viscosity. The
sand and silicone layers float on acacia honey, which has
a very low viscosity of about 10 Pa s and a density of
1.40 – 1.45 g cm3.
[14] The experiments are about 1 m wide with a typical
layer thickness of about 1 cm (see Tables 1 and 2 for exact
dimensions); shortening lasts between 5 and 15 h, which
gives scaling ratios with natural systems of about 106 and
1010 for length and time, respectively. The deformation is
generated by the inward displacement of a vertical wall that
pushes the full width, or in some experiments part of the
width, of the sand-silicone layers (Figures 2 and 3). We call
experiments, where the indenter is applied to 100% of the
experiment width, ‘‘uniaxial compression,’’ and experiments with a narrower indenter ‘‘indentation.’’ The indenter
is displaced at uniform velocity. Because of the low viscosity of the honey (on average 3 orders of magnitude lower
than the silicone layers), the boundary at the base of the
lower silicone layer is considered as friction-free. Experiments have also at least one (most generally two) unconfined
and friction-free lateral side, meaning that the sand-silicone
layers do not extend to the lateral wall of the box. The
presence of one or two unconfined borders makes lateral
escape possible, as well as extension parallel to the free
border. We thus expect the deformation pattern (shortening,
wrenching and/or extension) to establish as a result of
mechanical parameters rather than constricted boundary
conditions.
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2.3. General Deformation Styles Versus Physical
Parameters
2.3.1. Boundary Conditions
[15] A diversity of strain distributions and evolutions are
observed at the experiment surface for various model
parameters (thickness of layers, viscosities, densities) and
boundary conditions (boundary shape, shortening velocity).
[16] Figure 3 presents three experiments each having
unique boundary conditions (differing lengths of the moving vertical wall or indenter and different lateral boundaries). Rather different deformation styles are obtained. In
Figure 3a [Sornette et al., 1993], the contractional zone is
located immediately in front of the indenter, while in Figure 3c,
it has developed in the middle of the experiment. In the
case of one friction-free border, an asymmetrical fault
pattern develops (Figure 3a), whereas with two frictionfree borders the fault pattern is symmetrical (Figure 3b).
Deformation is distributed more homogeneously in the
case of a uniaxial compression (Figure 3c) than in the case
of indentation (Figure 3b). This demonstrates the influence
of the boundary conditions on the final deformation style.
Caution must thus be applied in interpreting experiments
in order to separate boundary condition effects from
mechanical parameter effects.
2.3.2. Brittle-Ductile Coupling and Localization
Instability
[17] Many experiments have pointed out the role of the
brittle-ductile coupling on deformation in compression
[Bonnet, 1997; Davy, 1986; Davy and Cobbold, 1988,
1991; Davy et al., 1995; Sornette et al., 1993] and in
extension [Allemand et al., 1989; Benes and Davy, 1996;
Brun, 1999; Brun and Beslier, 1996; Brun et al., 1994;
Faugère and Brun, 1984; Gautier et al., 1999; Schellart et
al., 2003; Schellart and Lister, 2005; Schellart et al., 2002;
Vendeville et al., 1987]. Variations in the silicone viscosities, in the sand thickness, or in the shortening velocity
modify the strength ratio between brittle and ductile layers.
Varying the brittle-to-ductile strength ratio results mainly in
drastic changes of the localization regime of experiments, as
illustrated in Figure 4. In brittle-like experiments (thick sand
layer or very slow shortening velocity), deformation is
localized on a few large faults (Figure 4c). In contrast, the
deformation pattern appears to be distributed into a large
number of small faults in experiments, whose strength is
dominated by the ductile layer (i.e., for high silicone
viscosity or fast shortening velocity, Figure 4a). Intermediate brittle-to-ductile strength ratio leads to intermediate
deformation styles, with a dense fault pattern localized in
two conjugate shear bands (Figure 4b).
[18] Strain localization is discussed in detail in sections 4.1
and 4.2 as a consequence of brittle-ductile coupling. First,
the concept of strain localization, as used in the experiments, must be defined as well as the manner in which
strain localization is quantified. In a broad sense, localization expresses the development of highly deformed zones
bounded by undeformed areas. Localization of deformation
can be a consequence of a heterogeneous stress field
induced by boundary conditions and can be enhanced by
rheological heterogeneities. Since we are more interested in
characterizing the material properties rather than the
boundary conditions, we focus on the dynamic localization
instability, generally associated with strain softening,
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SCHUELLER AND DAVY: DEFORMATION IN LITHOSPHERE ANALOGS
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Table 1. Characteristics of the Two-Layer Experimentsa
A1
A2
A3
A4
A5
A18
A19
A20
A21
A22
A23
A24
M1
M2
M3
M4
M7
M8
M17
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S17
S18
S19
S20
S21
S22
S23
S24
S25
S26
S27
S28
S39
S40
S41
S53
S54
Boundary
Conditions
hsi
(m)
rsi
(kg m3)
hsi
(104 Pa s)
hsa
(m)
rsa
(kg m3)
L
(m)
U
(cm h1)
G
Ar
Authorb
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
I2
I2
I2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U1
U2
U2
U2
U2
U2
0.0060
0.0090
0.0090
0.0090
0.0090
0.0125
0.0125
0.0125
0.0125
0.0125
0.0125
0.0125
0.0090
0.0090
0.0090
0.0090
0.0060
0.0050
0.0215
0.0200
0.0200
0.0200
0.0200
0.0200
0.0200
0.0200
0.0210
0.0100
0.0100
0.0200
0.0210
0.0100
0.0200
0.0200
0.0200
0.0200
0.0200
0.0200
0.0200
0.0200
0.0100
0.0200
0.0200
0.0200
0.0200
0.0100
0.0100
0.0100
0.0100
0.0200
0.0200
1200
1200
1200
1200
1200
1350
1350
1350
1350
1350
1350
1350
1340
1355
1330
1348
975
975
1350
1360
1400
1400
1400
1400
1400
1340
1350
1340
1340
1340
1350
1340
1360
1360
1360
1360
1360
1360
1360
1360
1360
1360
1360
1360
1360
1350
1240
1240
1320
1350
1190
3.00
3.00
3.00
3.00
3.00
1.75
1.75
1.75
1.75
1.75
1.75
1.75
8.00
1.50
1.60
3.50
4.00
4.00
5.50
4.00
4.00
4.00
4.00
4.00
4.00
5.50
5.50
5.50
5.50
5.50
5.50
5.50
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
1.70
1.40
1.40
3.80
5.50
2.60
0.004
0.004
0.004
0.004
0.004
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.007
0.010
0.009
0.007
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.010
0.010
0.010
0.010
0.015
0.015
0.005
0.005
0.005
0.005
0.005
0.015
0.010
0.010
0.005
0.005
0.005
1200
1200
1200
1200
1200
1400
1400
1400
1400
1400
1400
1400
1500
1500
1500
1500
1500
1500
1500
1400
1400
1400
1400
1400
1400
1230
1270
1400
1230
1230
1270
1230
1400
1400
1400
1400
1400
1400
1400
1400
1400
1400
1400
1400
1400
1400
1220
1220
1220
1270
1230
1.0
0.5
0.5
0.5
0.7
0.5
0.5
0.4
0.4
0.3
0.3
0.4
1.0
1.0
1.0
1.0
0.7
0.9
0.6
0.8
1.0
1.0
1.0
1.0
1.0
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.6
0.5
0.5
0.5
0.5
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
2.0
2.5
2.5
2.7
11.7
11.7
0.6
4.0
5.0
5.5
6.5
7.5
9.5
2.0
2.0
2.0
2.0
10.0
10.0
10.0
8.5
5.0
6.6
10.3
20.6
25.0
37.0
55.0
4.0
1.2
2.5
4.1
8.2
1.0
10.0
2.0
4.0
1.5
7.0
2.26
2.26
2.26
2.26
2.26
7.06
7.06
7.06
7.06
7.06
7.06
7.06
0.83
3.53
3.31
2.37
1.13
0.92
7.87
0.77
0.62
0.56
0.48
0.41
0.33
0.99
1.02
1.12
0.99
0.20
0.20
0.20
0.29
0.49
1.50
0.96
0.48
0.40
0.60
0.40
0.62
2.01
1.00
0.60
0.30
65.44
3.08
15.39
0.71
1.36
0.60
1.072
1.793
1.793
1.793
1.801
0.612
0.612
0.611
0.611
0.609
0.609
0.610
0.073
0.045
0.093
0.001
0.015
0.006
0.357
1.190
0.810
0.805
0.795
0.786
0.768
2.653
2.394
0.446
1.113
2.202
1.981
1.007
0.943
1.054
0.384
0.371
0.339
0.327
0.198
0.185
0.379
1.153
1.056
0.950
0.760
0.108
0.620
0.626
1.160
2.222
3.844
DC
DC
DC
DC
DC
Su
Su
Su
Su
Su
Su
Su
Sc
Sc
Sc
Sc
Sc
Sc
Sc
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Su
Bo
Bo
Bo
Bo
Bo
a
Boundary conditions (boundary conditions: I1, indentation with one friction-free border; I2, indentation with two friction-free borders; U1, uniaxial
compression with one friction-free border; U2, uniaxial compression with two friction-free borders); hsi, silicone layer thickness; rsi, silicone density; hsi,
silicone viscosity; hsa, sand layer thickness; rsa, sand layer density; L, initial length of the experiment; U, shortening velocity; G, brittle-ductile parameter;
Ar, Argand number.
b
The author list corresponds to the following references: Bo, Bonnet [1997]; DC, Davy and Cobbold [1988]; Fo, Fournier [1994]; So, Sornette [1990]
and Sornette et al. [1993]; Su, Suzanne [1991]; Sc, Schueller [2005].
which is expressed as a progressive reduction of the
actively deformed volume [Davy et al., 1995].
[19] A scalar measure of localization, S2, is introduced
and defined as [Davy et al., 1995; Sornette et al., 1993]
S2 ¼
1
St
2
R
IdS
RSt
I 2 dS
St
ð1Þ
St is the total surface of the experiment. I is a scalar strain
measure, which was taken as the second invariant of the
strain tensor. If the deformation is perfectly homogeneous
(hI2i = hI i2), S2 is equal to 1. If the deformation is restricted
to a small area a, S2 is a ratio between a and St, necessarily
smaller than 1. The smaller S2, the more localized the
deformation. S2 is thus a scalar measure of the deforming
area, and the decrease, or not, of S2 with time (finite
shortening) can be used to detect the localization instability
(Figure 5).
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Table 2. Characteristics of the Three-Layer Experimentsa
A10
A11
A12
A13
A14
A15
A16
A27
A28
A29
A30
A31
M9
M10
M11
M12
M13
M14
M15
M16
S31
S32
S33
S36
S37
S38
S46
S47
S49
S50
S51
S52
S56
Boundary
Conditions
hsi1
(m)
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
I1
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U2
U1
U1
U2
U2
U2
U2
U2
0.0050
0.0050
0.0050
0.0050
0.0050
0.0050
0.0050
0.0100
0.0100
0.0100
0.0100
0.0100
0.0055
0.0060
0.0070
0.0050
0.0050
0.0055
0.0040
0.0045
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
rsi1
hsi1
(kg m3) (104 Pa s)
1200
1200
1200
1200
1200
1200
1200
1140
1140
1140
1190
1190
975
975
975
975
975
975
975
975
1310
1310
1300
1350
1340
1340
1350
1350
1310
1310
1310
1340
1320
2.30
2.30
2.30
2.30
2.30
0.60
3.00
5.00
5.00
5.00
5.00
5.00
4.20
4.20
4.20
4.00
4.00
4.00
4.00
4.70
4.90
4.90
1.00
4.10
4.60
4.60
4.00
4.00
4.90
4.90
4.90
5.50
1.50
hsi2
(m)
0.0100
0.0100
0.0100
0.0100
0.0100
0.0050
0.0050
0.0050
0.0050
0.0050
0.0050
0.0050
0.0120
0.0130
0.0160
0.0155
0.0130
0.0135
0.0135
0.0155
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
0.0100
rsi2
hsi2
(kg m3) (104 Pa s)
1400
1400
1400
1400
1400
1400
1400
1340
1340
1340
1280
1280
1380
1375
1375
1356
1335
1335
1350
1350
1350
1330
1450
1400
1370
1370
1400
1400
1400
1330
1330
1360
1430
4.50
4.50
4.50
4.50
4.50
7.00
7.00
7.00
7.00
7.00
7.00
7.00
3.45
3.32
3.32
3.70
3.60
3.60
3.90
5.00
8.90
8.90
4.00
9.50
9.50
9.50
11.50
11.50
8.90
8.90
8.90
7.20
14.00
hsa
(m)
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.008
0.0075
0.008
0.006
0.0065
0.006
0.006
0.006
0.0075
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
rsa
L
U
(kg m3) (m) (cm h1)
1200
1200
1200
1200
1200
1200
1200
1100
1100
1100
1100
1100
1500
1500
1500
1500
1500
1500
1500
1500
1230
1230
1400
1400
1380
1400
1400
1400
1230
1230
1230
1230
1400
0.7
0.7
0.7
0.7
0.7
0.7
0.7
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.6
0.6
0.9
0.6
0.8
0.8
1.0
0.7
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
1.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
6.0
6.5
5.5
7.0
20.0
4.0
2.0
2.0
5.0
5.0
10.0
3.0
1.0
2.0
10.0
8.0
2.0
10.0
2.0
10.0
10.0
2.0
4.0
10.0
3.8
4.0
G1
G2
Average G
Ar
Author
0.92
0.92
0.92
0.92
0.92
3.53
0.71
0.32
0.30
0.35
0.28
0.25
1.77
4.04
2.27
1.12
0.95
0.48
1.59
6.34
1.11
0.22
1.55
1.51
0.26
1.34
0.31
0.31
1.11
0.55
0.22
0.52
2.06
0.47
0.47
0.47
0.47
0.47
0.30
0.30
0.23
0.21
0.25
0.20
0.18
2.16
5.11
2.87
1.21
1.06
0.53
1.63
5.96
0.61
0.12
0.39
0.65
0.13
0.65
0.11
0.11
0.61
0.31
0.12
0.40
0.22
0.70
0.70
0.70
0.70
0.70
1.92
0.50
0.28
0.26
0.30
0.24
0.21
1.97
4.57
2.57
1.16
1.01
0.50
1.61
6.15
0.86
0.17
0.97
1.08
0.20
1.00
0.21
0.21
0.86
0.43
0.17
0.46
1.14
2.28
2.28
2.28
2.28
2.28
1.46
1.43
3.47
3.44
3.50
3.18
1.69
0.75
0.80
2.20
1.28
1.25
1.36
1.06
0.87
2.83
2.28
1.45
1.19
1.18
1.32
0.95
0.95
2.75
2.69
2.28
2.47
1.30
So
So
So
So
So
So
So
Fo
Fo
Fo
Fo
Fo
Sc
Sc
Sc
Sc
Sc
Sc
Sc
Sc
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
Bo
a
See Table 1 footnotes.
2.3.3. Buoyancy
[20] Buoyancy quantifies the ability of lithosphere to flow
under its own weight, and hence may impose a great
influence on deformation style [Schellart and Lister, 2005].
When the buoyancy force is small (i.e., ‘‘heavy’’ lithosphere), contractional structures are ubiquitous (Figure 6a).
In contrast, in systems with large buoyancy force (i.e.,
‘‘light’’ lithosphere), deformation tends to spread out and
extensional structures prevail (Figure 6c). For intermediate
values, strike-slip deformation is dominant. In case of a
continental collision, deformation can be expressed as a
function of the three modes: contraction, strike-slip or
extension. The buoyancy forces seem to be responsible
for the preferential expression of one mode. Following
England and McKenzie [1982], we assume that the buoyancy effects can be parameterized by the dimensionless
Argand number, which compares buoyancy forces and
material strength. The mathematical expression of Ar is
given in section 3.
3. Experimental Deformation Styles Classified by
G and Ar
[21] The experimental setup used in this article produces
a wide range of deformation patterns when varying the
experimental parameters. The origin and calculation mode
of the two mechanical parameters on which we base the
interpretation of the experiments are explained in the
following: G, the brittle-ductile parameter and Ar, the
Argand number.
3.1. Mechanical Parameters
3.1.1. Brittle-Ductile Coupling and Corresponding
Dimensionless Parameter
[22] The brittle-ductile coupling is first characterized by
the experimental strength ratio R, which is the ratio between
the brittle layer strength and the ductile layers strength,
R
R¼
ðs1 s3 Þdz
brittle:layer
R
ðs1 s3 Þdz
ð2Þ
ductile:layer
where (s1 s3) represents the differential stress and z is the
depth.
[23] The average strength of the layers is calculated
according to simple strain and strain rate assumptions, as
described by Davy and Cobbold [1991] and Davy et al.
[1995]. The strength of the brittle layer is calculated for a
horizontal strike-slip deformation, assuming that the mean
stress (s1 + s3)/2 is the lithostatic pressure rgz. The
strengths of the ductile layers
is calculated as the product
of viscosity and strain rate e. The average shortening rate is
defined as e = U/L, with U the indenter velocity and L the
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Figure 3. Top views of experiments with different boundary conditions. (a) Indentation of an
experiment with only one friction-free border. (b) bIndentation of an experiment with two friction-free
borders. (c) Uniaxial compression.
model length parallel to the indenter displacement direction.
So, the ratio R becomes
R¼
1
2P
rgh2brittle
ductile layers i
h i hi e
The average strain rate does not describe the high rates
occurring in localized deformed zones, and thus represents a
lower bound on the actual resistance of the ductile layers.
Some authors [Bonnet, 1997] have studied the scaling issues
linked to the size of the experiments by performing
experiments with varying lengths. Following Davy et al.
[1995], the transition between nonlocalizing and localizing
experiments has been investigated for different system sizes
(i.e., different L) by calculating the parameter S2 while
deforming the experiment. They found that R scales with L
at the localizing/nonlocalizing transition, meaning that this
parameter cannot unequivocally characterize this transition.
They defined a dimensionless parameter G that remains
constant at the localizing/nonlocalizing transition, whatever
the system size, the layer thicknesses, the densities, and the
viscosities. G depends on the brittle layer thickness h and
Figure 4. Influence of relative strengths of both sand and silicone layers on deformation. A relatively
high ductile strength is obtained for a relatively high shortening velocity. A higher brittle strength is
obtained for a thicker sand layer. (a) High shortening velocity. (b) Moderate shortening velocity. (c) Low
shortening velocity and thick sand layer.
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which the mechanics of continuous media can be applied
[England and McKenzie, 1982]. The Argand number was
defined to quantify the relative contribution of buoyancy
with respect to the lithosphere strength:
Ar ¼
Figure 5. Evolution of S2 as a function of the shortening
for experiments resulting in diffuse strain (nonlocalizing
experiment; experiment M14) or localized strain (localizing
experiment; experiment M16).
density r, the ductile layer viscosity h, the shortening
velocity U, and the gravitational acceleration g:
G¼
rgh2
hU
G1 ¼
rgh2
rgh2
and G2 ¼
h1 U
h2 U
ð4Þ
ZhL
ðs1 s3 Þ dz
Fs ¼
ð6Þ
0
where hL is the total thickness of brittle and ductile layers and
z is the depth. In the experiments presented herein, Fs is
calculated according to the assumption developed previously:
Z
for the upper silicone layer and for the lower layer,
respectively. The arithmetic mean of both values G1 and
G2 was calculated to compare the three-layer with the twolayer experiments.
3.1.2. Buoyancy Effect and Corresponding
Dimensionless Mechanical Parameter
[25] The influence of buoyancy forces on lithospheric
deformation was first studied in thin viscous sheets, in
ð5Þ
where Fg is the buoyancy force exerted on the lithosphere/
model and Fs is the total strength of the lithosphere/model.
The Ar number was successfully used to parameterize
numerical simulations of continental collision based on the
thin sheet approximation [Bird and Piper, 1980; England
and McKenzie, 1982; Houseman and England, 1986; 1993;
Vilotte et al., 1982, 1986] or in sandbox experiments [Benes
and Davy, 1996; Cruden et al., 2006; Faccenna et al.,
1999]. If the buoyancy force Fg is larger than the lithosphere
strength (Fg > Fs), the lithosphere flows toward zones of
low gravity potential (e.g., free boundaries). In the case of
continental collision, a large Argand number will promote
lateral spreading and prevent high crustal thickening
[26] Fs is the mechanical resistance, which is the integral
of the differential stress over the layer thickness,
ð3Þ
Localization instabilities appear to develop only for G > 0.5
(Figure 7).
[24] For the three-layer experiments (one brittle layer
overlying two silicone layers of viscosities h1 and h2), two
brittle-ductile parameters were defined:
Fg
Fs
FS ¼
Z
ðs1 s3 Þdz þ
brittle
layer
ductile
layer
Z
Z
rgzdz þ
¼
brittle
layer
h e dz
h e dz
ductile
layer
Figure 6. Influence of the buoyancy force. (a) High silicone density, ‘‘heavy experiment.’’ (b)
Intermediate buoyancy force. (c) Very low silicone density, ‘‘light experiment.’’
8 of 21
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Figure 7. Evolution of the S2 value as a function of the brittle-ductile dimensionless parameter G.
Experiment sizes are 1 m [Bonnet, 1997] and 60– 90 cm (experiments M). The slight discrepancy
between the two series of experiments is probably due to a difference in calculating the strain. Bonnet
[1997] calculated strain for shortening increments of 1 – 2%, whereas we were able to calculate strain for
shortening increments of 0.5%. Experiments S5 (25% shortening) and S4 (28% shortening) illustrate the
transition from nonlocalizing to localizing experiments. Prolongation of the S2 fit (dashed line) toward
lower value of G is assumed to flatten out. Even if theoretically it should tend to 100%, the existence of
stress shadow zones in front of the moving and fixed walls of the experiment forces S2 to be lower than 1.
where r is the brittle material
density, h is the Newtonian
silicone viscosity, and e is the deformation rate.
[27] Fg corresponds to the buoyancy force exerted by the
‘‘heavy asthenosphere’’ on the ‘‘light lithosphere.’’ It can be
calculated as the total (i.e., integrated over thickness)
difference between the lithostatic stress of the lithosphere
on the one hand and the stress of a reference asthenosphere
column on the other hand:
Z
Fg ¼
Z
rL gz dz hL
rM gz dz
ð8Þ
hM
hL and rL are the thickness and density of the lithosphere
(i.e., including both brittle and ductile layers), hM is the
height of the asthenosphere column above the isostatic
level, and rM is the asthenosphere density. The isostatic
condition implies that rLghL = rMghM, which eventually
gives the following expression for Fg [England and
McKenzie, 1982]:
Fg ¼
rL gh2L
r
1 L
2
rM
ð9Þ
In the experiments, the Argand number varies between 0
and 3.5. In contrast to G, the Argand number depends on the
experiment length (L). However, for the range of tested
lengths (0.2– 1 m), the variation of Ar due to the variation in
the experiment length does not exceed ±0.05. This variation
was calculated by taking average values for the different
experimental parameters and varying the length between 0.2
and 1 m. This variation is thus small compared to the
uncertainty related to the measurement of layer thickness
and density (as discussed in section 3.2).
3.2. Compilation and Classification of Experiments
[28] Tables 1 and 2 as well as Figures 8 and 9 present the
experiments used for this study. Each experiment is characterized by a letter and a number. The two-layer experiments
are presented in Table 1 and Figure 8, and the three-layer
experiments are presented in Table 2 and Figure 9, respectively. Indentation was performed in experiments A, M1,
M2, and M3, whereas experiments S, M4 to M17 were
submitted to a uniaxial compression. The physical and
mechanical parameters of each experiment are given in
Tables 1 and 2. A deformed stage of each experiment
(between 20% and 30% of shortening) is presented in
Figures 8 and 9.
[29] Concerning the values reported in Tables 1 and 2, the
uncertainty on silicone densities is generally about 0.05 g cm3.
The density of sand depends on the degree of compaction.
For all the experiments carried out by the same author, the
sand density does not vary more than 0.1 g cm3. The
silicone viscosity registered in Tables 1 and 2 is the value
recorded at the beginning of the experiment. The silicone
layers were molded individually in a separate frame and then
placed in position. Their thickness is thus known with an
uncertainty less than 0.5 mm over the whole experiment
surface. The thickness of the sand layer is much more
difficult to control. It is known with an uncertainty of about
0.5 mm.
[30] The two parameters G and Ar offer a framework for
classifying the experiments with respect to the degree of
deformation localization and the deformation mode (short-
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Figure 8. Top views of the two-layer experiments presented in Table 1 (finite deformation between
20% and 30% of shortening).
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Figure 9. Top views of the three-layer experiments presented in Table 2 (finite deformation between
20% and 30% of shortening).
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Figure 10.
the Argand
extensional)
corresponds
B12404
Distribution of the two-layer experiments according to the brittle-ductile parameter G and
number Ar. The range of greens indicates the deformation regime (contractional or
encountered in association with the strike-slip structures. The middle of this range
to a pure strike-slip deformation regime.
ening, wrenching, or extension). Figure 10 shows the twolayer experiments plotted as a function of the brittle-ductile
parameter G and the Argand number Ar. Experiments M9 to
M16 are also included in Figure 10 since the difference in
viscosity between the two silicone layers is very small and
they behave as two-layer experiments. In these experiments
the upper silicone layer is used only to reduce the density of
the simulated lithosphere.
[31] The interpretation of Figure 10 is based on the
localization efficiency as expressed by the evolution of S2
(equation (1)) and on an analysis of the stress regime
deduced from the deformation structures (thrusts, strike-slip
faults, or normal faults). In Figure 10, the dotted domain
corresponds to a nonlocalizing regime of deformation. In
this region (G 0.5), the deformation remains homogeneously distributed in the experiment. The domain to the
right in Figure 10 (G > 0.5) corresponds to experiments
where the localization instability has developed. The density
of faults, the occurrence of large faults, and so the degree of
deformation localization depend on G. The range of colors
in Figure 10 indicates the main deformation regimes:
predominantly contractional structures (folds and thrusts)
in the dark green region, strike-slip faults in the intermediate
green regions, and extensional structures in the light green
region. Strike-slip faults are common in all regimes in the
‘‘localization’’ domain. The white domain of Figure 10, in
the top right corner, is void of experiments because of
technical difficulties with achieving high values of G and Ar
concurrently.
[32] Two examples illustrate the classification reported in
Figure 10: experiment M9 is a localizing experiment with
nearly pure strike-slip structures; its Argand number is close
to one and G (= 1.97) is larger than 0.5. Experiment M2 is a
localizing experiment (G = 3.53), with imbricate thrusts and
strike-slip faults (Ar = 0.045).
[33] The transition between nonlocalization and localization in our results is independent of the Argand number and
occurs close to G 0.5 (see Figure 7). The deformation
regime (contraction, strike-slip, and extension) depends
mainly on the Ar number and slightly on the brittle-toductile ratio G. The boundary conditions also induce minor
differences that are not expressed in Figure 10; boundary
effects are discussed in section 5.3.
[34] Sections 4 and 5 describe more precisely the role of
each parameter on the deformation style.
4. Localization Instability
4.1. Description of the Two-Layer Experiments
[35] The localization instability develops when the brittleductile parameter G is larger than 0.5 (Figures 7 and 8). The
transition from nonlocalization to localization is particularly
visible for large experiments (1 m long; Figure 7). For G <
0.5, the deformation is distributed more or less homogeneously in the experiment, except in the ‘‘dead triangles’’
close to the indenter and the opposite wall. These areas are
largely free of deformation in all the experiments. This implies
that S2 cannot be equal to one even for very small values of G.
For G > 0.5, two conjugate deformed zones develop with a
dense fault pattern inside the bands (Figure 11).
[36] In the localization domain (G > 0.5), strain localization
is increased when increasing the brittle-ductile parameter G.
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Figure 11. Top views of a suite of experiments and associated strike-slip fault pattern showing an
increasing localization of deformation with progressive increase of the brittle-ductile parameter G (0 <
Ar < 1).
This strain localization increase goes together with the
decrease of the localization parameter S2 (Figure 7). The
large-scale localization pattern is observed through the fault
system developed, whose geometrical pattern is highly
dependent on the brittle-ductile coupling ratio (Figure 11).
For large G (>4), the deformation concentrates into a few
large faults (i.e., fault length 10 cm). Each fault accommodates a nonnegligible part of the boundary displacement.
In contrast, for low values of G (0.5 < G < 2), fault patterns are
very dense, and the faults are typically much smaller (<2 cm
length). The number of faults is not completely controlled by
G; it may depend also on heterogeneities within the system.
[37] The statistical properties of fault patterns have been
analyzed for some experiments [Davy et al., 1995, 1990].
The experimental faults typically have similar scaling laws
as observed in natural systems [Bonnet et al., 2001; Bour
and Davy, 1999], with a power law length distribution and a
fractal organization. The power law length distribution is
truncated at large length, with a characteristic length scale lF
that is directly proportional to G. The larger the G, the larger
the lF. The fractal dimension of the fault network decreases
with G, which is consistent with the observed simplification
of the fault pattern structure [Bonnet, 1997].
4.2. Nature of the Localization Instability
[38] The experimental ‘‘S’’ series (Table 1) focuses on the
transition from nonlocalized to localized strain [Bonnet,
1997]. All these experiments use the same layer thickness
but different widths and lengths. The objective was to reveal
some finite size effects in the localization process that could
add to the description of the nature of the localization
instability. In all the experiments, the localization factor S2
(the final percentage of deformed area) remains constant
after 5% shortening (Figure 5). Figure 12 shows that as G
increases, S2 decreases with a slope change around G = 0.5,
irrespective of the system size. The sharpness of the
transition depends on the initial experiment length. The
transition is narrow (0.4 < G < 0.6) for the 1-m-long
experiments and much wider for the short experiments
(Figure 12).
[39] This scale dependency occurs also in the percolation
threshold in classical percolation theory. In percolation
theory, the system ‘‘size’’ is defined by the ratio of the
elementary element (link or crack) to the size of the entire
physical system. In the brittle-ductile experiments, the layer
thicknesses, and especially the brittle thickness, are basic
length scales of the localization process, since most of the
faults break the entire brittle layer. The ratio of the system
length to the brittle crust thickness ranges from about 10 for
the smallest experiment (20 cm long) to 200 for the largest.
A ratio of 10 significantly increases the range of the
transition zone.
[40] The ratio between the length of the experiment and
the width of the indenter may also have effects on the
eventual deformation and the orientation of the fault zones
[Ratschbacher et al., 1991]. If the length of the experiment
is narrow compared to the indenter width, the deformation
Figure 12. Influence of experiment length on the values of
S2 [Bonnet, 1997]. The fitting curves toward lower values of
G are assumed to flatten out. Because of the existence of
stress shadow zones in front of the moving and fixed walls
of the experiment, S2 cannot experimentally tend to 1.
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Figure 13. Top views of experiments showing the influence of preexisting heterogeneities. Top row
(S33, A18, and M2) are experiments without preexisting heterogeneities. Bottom row (S56, A19, and
M13) are identical experiments but with preexisting heterogeneities. Preexisting heterogeneities are
indicated by circles and ovals. For experiments S56 and M3, only the heterogeneities positioned on faults
are represented.
structures accommodating lateral escape cannot propagate
at 30° of the compression axis because they may hit the
facing wall before reaching the lateral free boundary. A very
low aspect ratio can thus reduce lateral escape and produce
extra compressive deformation structures, as described by
Sornette et al. [1993] and Suzanne [1991]. The shape and
the convergence obliquity can also affect the deformation
pattern [Ratschbacher et al., 1991; Rosenberg et al., 2007].
But it does not affect the localization degree in the experiment or the amount of lateral displacement [Rosenberg et
al., 2007].
4.3. Role of Preexisting Fractures
[41] Preexisting heterogeneities in the brittle layer have
little effect on deformation style and on the degree of
localization. They principally influence the position of
new faults in the experiment. Preexisting heterogeneities
are represented as weak zones, where deformation can
concentrate. In the experiments, heterogeneities were introduced in sand by plunging a needle or a spatula in the sand
layer. These heterogeneities simulate faults that could have
formed during previous tectonic events.
[42] Figure 13 illustrates the effect of these heterogeneities for three combinations of G and Ar. In experiment S56,
the sand defects are small holes regularly spaced; faults are
slightly less numerous than in the reference experiment
without heterogeneity (S33). Thus localization was enhanced by the defects. Heterogeneities in experiments
A19 and M3 have a ‘‘crack’’ shape and random orientations.
In contrast to experiment S56, the deformation is less
localized in A19 and M3 than in the reference experiments
A18 and M2. The numbers of faults are similar in experiments A19 and A18, but the fault pattern is more distributed
in A19 than in A18. In experiment M3, the fault number is
slightly larger than in M2, and the fault positions are
strongly correlated to the initial heterogeneity locations.
[43] Point-like heterogeneities favor the localization of
deformation in space and time [Bonnet, 1997]. Since they
have no specific orientation, they can be easily reactivated
in a direction fitting the boundary conditions. The contribution of point-like heterogeneities to deformation is thus
an enhancement of localization. In contrast, randomly
oriented crack-like heterogeneities delay localization, and
the final pattern is more distributed. If the oriented cracks
are about parallel to the eventual localization shear zone,
they can enhance localization by being reactivated more
easily. But where cracks are orthogonal to the eventual shear
zones, the localization is hindered. In fact, either the
reactivation does not happen, or if the cracks are reactivated
because of their weakness, their shear generates deformation
and stress fields that avoid faults to develop in their
surroundings [Suzanne, 1991]. This leads to spread more
the developing fault pattern. The contribution of a randomly
oriented crack set appears to be dominated by the hindrance
effect on localization.
[44] None of the heterogeneities studied modified the
global deformation style significantly. A transpressive deformation remains transpressive with preexisting heterogeneities (M2 – M3, Figure 13). Experiments A18 and A19 are
both dominated by pure strike-slip structures (discarding the
thrusts around the indenter, formed because of the indentation). The experiment-scale fault pattern is thus negligibly
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Figure 14. Distribution of the three-layer experiments according to the brittle-ductile parameter G and
the Argand number Ar.
affected by heterogeneities, although local fault patterns
within deformation belts are affected.
4.4. Three-Layer Experiments and Coupling Between
Deep Viscous and Upper Brittle Layers
[45] Adding a second silicone layer beneath the so-called
‘‘ductile crust’’ simulates a resistant ductile lithospheric
mantle, thereby allowing us to study the coupling between
this deep ductile layer and the upper brittle crust. The deeper
silicone layer is thus the most viscous. The boundary
conditions are the same as for the two-layer experiments.
[46] In order to parameterize the mechanical system, two
brittle-ductile ratios are defined: G1 for the silicone layer
representing the ductile crust and G2 for the ‘‘lithospheric
mantle.’’ We use the arithmetical mean of G1 and G2, G, for
comparison with two-layer experiments (Figure 14). The
same deformation style domains defined in Figure 10 were
used in Figure 14. As in two-layer experiments, the localization intensity increases with G, and Ar predicts the
dominant deformation modes (contractional, extensional,
or strike slip).
[47] We discuss here only the three-layer experiments that
lie in the localization regime (G > 0.5) and for which the
viscosity contrast between the two silicone layers is large
enough to depart from the two-layer case (that is, G1 > 2 G2).
This corresponds to experiments S33, S36, and S38
(Figure 9). S11 (a two-layer experiment), whose parameters
G and Ar are similar to the S33, S36, and S38 ones, is used to
compare the two-layer and three-layer responses (Figure 15).
[48] Whereas S11 exhibits a network of smaller faults that
develop into conjugate shear bands, in the three-layer
experiment (S38), the deformation is localized in a few large
strike-slip faults. The faults are, however, widely distributed
on the whole surface of the experiment (Figure 15). They are
interconnected and form a mosaic of large fault-bounded
blocks.
[49] The fault pattern characterized by a mosaic of large
fault-bounded blocks is specific to three-layer experiments
and never encountered in two-layer experiments. The largefault pattern is consistent with a high degree of localization
represented by a high value of G (controlled by the value of
G1). This indicates that fault propagation is directly related
to the coupling between the brittle layer and the lowviscosity ductile layer just in contact with it. On the other
hand, the wide spatial distribution of the faults is consistent
with a less localized deformation, represented by a lower
value of G (G2), which corresponds to the interaction
between the high-viscosity ductile layer (lithospheric upper
mantle) and the brittle crust. Further experiments are required to fully explore the consequence of this complex but
more realistic brittle-ductile coupling.
5. Buoyancy Effect: Relationship Between
Contractional, Extensional, and Strike-Slip
Domains and Structures
5.1. Spatial Relationships
[50 ] Buoyancy forces, which are quantified by the
Argand number, are the primary control on the deformation
modes, that is, the relative amount of contraction, strike-slip
or extension within the experiments. The effect of buoyancy
on deformation is illustrated in Figure 16 for localizing twolayer experiments. For Ar smaller than 0.4, the deformation
is concentrated in broad zones of folding and thrusting,
generally associated with strike-slip faults. For Ar in the
range [0.4, 2.5], the deformation is mainly accommodated
by pure strike-slip faults (tectonic escape) with local zones
of folding, thrusting and extension. For Ar 0.45, strikeslip faults are associated with local, well-defined, elongate
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Figure 15. Top views of two experiments showing the
influence of a second silicone layer in case G1 > 2* G2. Note
that G and Ar are almost similar. In the three-layer
experiment S38, G1 = 1.34 and G2 = 0.65.
zones of en echelon folds and thrusts that merge into the
main shear zones. These en echelon folds and thrusts form a
shear zone in a direction subparallel to strike-slip faults
(Figure 16). For larger Ar numbers, the fold and thrusts
act as relay structures between strike-slip fault networks.
For Ar 1.1, the deformation pattern consists principally of
strike-slip faults (experiment S11 in Figure 16). For Ar larger
than 2 – 3, the contribution of extensional faults in the
extruded blocks becomes predominant. The extension is
first expressed as transtensional structures associated with
strike-slip faults (Ar 2.39; Figure 16). For higher values
of Ar (2.65 in Figure 16), pure extensional zones develop,
independently of the position of strike-slip faults. These
zones are oriented parallel to the compression axis. Extensional structures tend to be distributed over the whole
experiment, giving the impression that the deformation is
less localized than in experiments with the same G but
smaller Ar.
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5.2. Temporal Relationships
[51] The temporal evolution of deformation structures
sheds light on the basic mechanisms responsible for the
interplay between structure formation and localization.
Figure 17 shows the first appearance of thrusts, strike-slip,
and extensional faults as a function of Ar for three ranges of
G: 0.9 –1.5 (Figure 17, top), 2 – 3 (Figure 17, middle), 3 – 7
(Figure 17, bottom). We estimate the uncertainty to be 2 –
3% of shortening because of the difficulty of identifying the
very first structures from photographic records.
[52] The first visible structures typically appear at about
5% of shortening whatever Ar and G, within the precision of
this study. The trajectories, with respect to Ar, are similar
for all ranges of G. Thrusts appear first for experiments with
no buoyancy (very low values of Ar); but in most of the
other cases, the first structures are strike-slip faults. We
consider that folds and thrusts associated to the indenter
(around small indenters) or at the meeting point between the
two ‘‘dead triangles’’ are artifacts due to the boundary
conditions and are not significant for the description of
the stress regimes. Increasing buoyancy delays the appearance of thrusts and advances extensional faults, but has
almost no effect on strike-slip fault development. Furthermore, primary structures, those that significantly contribute
to the total deformation, develop sooner than secondary
structures.
[53] The locations of the first appearing structures are
shown for four experiments in Figure 18, also indicated in
Figure 17. For experiment M1, thrusts perpendicular to the
principal compression axis first develop. Strike-slip faults
develop later and overprint the thrust pattern (Figure 18).
Both thrusts and strike-slip faults appear to be mechanically
independent. This is clearly not the case for experiment M2,
in which strike-slip faults develop first and control the later
location of thrusts. Thrusts form either within relay zones
between two strike-slip faults or with an arc shape as a splay
off of a strike-slip fault (Figure 18). In both cases the
displacement on strike-slip faults and thrusts are kinematically linked. For experiment M9, strike-slip faults prevail
(Figure 18) and develop into two conjugate wrench zones.
Both contractional and extensional structures form later.
Thrusts develop at the intersection of both shear zones, and
Figure 16. Effect of the Argand number on the distribution of deformation modes in localizing twolayer experiments.
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extension develops as a transtensive component on existing
strike-slip faults. For experiment M11 (large Ar), extension
and strike-slip faults develop initially simultaneously as independent structures, and eventually form an interconnected
pattern (Figure 18).
[54 ] The transition from ‘‘M1’’-like experiments to
‘‘M11’’-like is observed for all values of G. However, the
range of buoyancy forces (Ar) over which the transition
occurs is larger for small G.
Figure 17. Effect of the Argand number on the appearance
of major contractional, strike-slip, and extensional structures for three ranges of G values (0.8 –1.2; 2 – 3; and 3– 7).
Pictures of experiments M1, M2, M9, and M11 are shown
in Figure 18. The lines indicate our best estimate of the
trajectories between the points of measurement. The lines
represent the first appearance (in terms of shortening) of the
different structure types (contractional, strike slip, or
extensional). The strike-slip faults appear first in most of
the cases.
5.3. Role of Boundary Conditions
[55] The nature of boundary conditions is an important
parameter governing final deformation pattern. An indenter
corresponding to a vertical moving wall is the common
boundary for the whole set of experiments, but the number
of friction-free borders, as well as the indenter width, differ
from one experiment to another. We especially examine the
consequences of changing these boundary conditions.
[ 56 ] Different authors [Davy and Cobbold, 1991;
Ratschbacher et al., 1991] explored the consequences of
a variable stress confinement of the lateral border (see
experiments A3 and A4 in Figure 8). The partitioning
between thickening, lateral escape and spreading is a direct
consequence of this lateral confinement, as it is of buoyancy
forces. In nature, completely unconfined boundaries are
geologically unrealistic. In experiments, they are used to
simulate a lack of constraints [Ratschbacher et al., 1991].
They might be represented by subduction zones, which
retreat because of slab roll back [Schellart and Lister,
2005], even if in this case, back-arc extension may also
happen, leading to transmit constraints to the overriding
plate. In our experiments, we do not address the issue of
subduction zones, which are likely to play a key role in
defining the nature of the continental boundaries [Faccenna
et al., 2007]. Considering no lateral confinement allows us
to focus entirely on the role of the buoyancy forces.
[57] The number of lateral free boundaries (one or two)
has no real influence on the deformation localization and
style. The major effect of a single lateral free boundary is to
enhance the deformation asymmetry by developing only
one of the large wrench zones that eventually produce
lateral escape. Asymmetric boundaries conditions tend thus
to simplify the deformation mechanism. Experiments with
two lateral-free boundaries develop generally two large
wrench zones, but may also be asymmetrical because of
complex interactions between these wrench zones [Sornette
et al., 1993]. As shown in experiment S8 (Figure 19), where
the blocks are extruded faster westward than eastward, some
shear zones accommodate more deformation. Differences in
the widths of the shear zones are also observed (Figure 19).
[58] The indenter width influences the spatial distribution
of the deformation modes (Figure 19). The first effect is to
control the size of the nondeformed zones (‘‘dead triangles’’)
located in front of the indenter [Peltzer and Tapponnier,
1988]. A small indenter (A2 in Figure 19) induces a rotational
component of the bulk deformation; the main consequence
is to yield a well-defined spatial partitioning of the deformation into a contraction zone close to the dead triangle, an
extensional zone close to the lateral boundary, and a wrench
zone in between. In contrast, wide indenters generate a
much more homogeneous stress pattern, and thrusts, strikeslip faults, and normal faults are more distributed and
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Figure 18. Interpretative sketch on temporal appearance of contractional, strike-slip, and extensive
structures as a function of the Argand number for experiments M1, M2, M9, and M11 indicated in
Figure 17.
spatially overlapping (S8, Figure 19). Indenter rotation,
which has not been tested in these experiments, may also
be important by concentrating deformation around syntaxes
[see, e.g., Robl and Stüwe, 2005].
6. Conclusion
[59] The main conclusion of this compilation of experiments is that the deformation styles of brittle-ductile media
can be described by two main dimensionless parameters: a
brittle-ductile parameter G, which quantifies the relative
strength between the upper brittle ‘‘crustal’’ layer and the
lower ductile ‘‘crustal’’ or ‘‘mantle’’ layer(s), and the
Argand number Ar, which quantifies the ability of gravity
to deform the layered media.
[60] The brittle-ductile parameter G controls the largescale localization of deformation, and associated fault
patterns (both density and fault length distribution [Davy
et al., 1995]). Localization occurs for G larger than 0.5. For
smaller G, the large-scale deformation, although heterogeneous, never localizes. G = 0.5 can be considered as a
rheological transition between ductile-like macroscale rheology and brittle-like one. The range of G values over which
the transition occurs is dependent on the experiment size,
i.e., the ratio between the horizontal dimensions and the
thickness. In the limit of infinitely thin experiments, we can
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Figure 19. Influence of the number of friction-free borders and the length of the indenter on the
distribution of deformation modes (here transtensive mode). S8 has two friction-free borders, large
indenter. A2 has one friction-free border, small indenter.
expect the transition to occur over small variations of
viscosity, brittle thickness, or indenter velocity.
[61] The Ar number, and to a lesser extent G, controls the
relative amount of contraction, strike slip, and extension.
Except for some extreme values of Ar (no buoyancy or
conversely very large buoyancy), contraction, strike-slip,
and extension domains coexist with varying intensity. The
macroscopic evolution from a contractional regime to an
extensional regime appears rather continuous. In most
experiments, strike-slip faults and wrenching domains are
prevalent. This is likely to be a direct consequence of the
free lateral boundary.
[62] Other conclusions are as follows:
[63] 1. Preexisting heterogeneities in the brittle layer
control the initial location of faults, but they do not seem
to affect the general deformation style defined by G and Ar.
However, only three experiments were performed with
preexisting faults, which makes this conclusion still debatable.
[64] 2. The shape of the indenter plays a role on the
spatial distribution of the different deformation modes
(contraction, strike slip, and extension). A narrow indenter
yields a heterogeneous stress field with a strong rotational
component, which leads to a well-defined partitioning of the
deformation modes. With a large indenter, the general
deformation is more homogeneous; the deformation
domains are more widespread and overlap.
[65] 3. The three-layer experiments with two silicone
layers (the deepest being the strongest) are macroscopically
similar to the two-layer experiments, but the fault pattern is
slightly different.
[66] The results summarized above thus shed light on the
mechanics of these complex brittle-ductile systems. Some
of the presented experiments have been designed for studying lithospheric systems: the India/Asia collision [Cobbold
and Davy, 1988; Davy and Cobbold, 1988; Sornette et al.,
1993], the opening of the Japan Sea [Fournier et al., 2004],
and the Arabia/Anatolia collision [Suzanne, 1991]. However,
the geological conclusions are not straightforward because
the experiments are designed with some crude assumptions
about lithosphere rheology: a Newtonian viscosity with no
depth dependency, no coupling with some thermal evolution, a material brittle-ductile interface, no erosion. Despite
these limitations, the experiments can be considered as the
closest analog model to lithospheric deformation. The
complexity of the fault patterns produced during deformation has not yet been achieved by numerical simulations.
[67] For the lithosphere, the numbers G and Ar are not
easily calculated. Since the rheology is temperature- and
depth-dependent, the thickness of the ductile crust to be
taken into account in the rheological coupling for example
is unclear. Considering that the largest differential stress in
the brittle crust is the same as that in the ductile crust, we
expect G to be close to 1. This places the crust in the
localizing regime, which is consistent with the observation
that large faults accommodate a large part of continental
deformation [Avouac and Tapponnier, 1993; Peltzer and
Saucier, 1996]. With a stiff ductile mantle, the bulk lithospheric G could be even smaller meaning that the issue of a
macroscopically ‘‘viscous’’ or ‘‘brittle’’ (or both) lithosphere is still open [Jackson, 2002]. The Ar number is
somewhere around unity [England et al., 1985; Sonder et
al., 1986]. In wide hot orogens such as the Himalaya, the
estimated Ar values range between 1 and 10 [Cruden et al.,
2006]. The values of Ar and G expected in nature lead thus
to complex deformation regimes with contraction, strike
slip, and extension (providing that at least one boundary
presents a lack of constraint).
[68] The physics of fault growth and fault interaction, and
of brittle-ductile interactions, remain not fully understood.
Some results of this paper such as the nature of the
transition toward localization, or the detailed interaction
between faults are key observations to understand the
physics of such complex systems.
[69] The rapid development of computing methods will
soon make it possible to produce deformation pattern as
complex as those observed in these experiments [Bird,
1998; Braun, 1994; Braun et al., 2008; Kong and Bird,
1995; Vernant, 2006] making easier the understanding of
the mechanical coupling between faults and different rheologies. The experiments presented in this paper could be
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used as benchmarks for validating such future numerical
models.
[70] Acknowledgments. We would like to thank Walter Wheeler for
his useful comments, which have helped to improve the quality of an early
version of the manuscript. We are grateful to Jean-Jacques Kermarrec for
help with apparatus in the tectonic modeling laboratory at Géosciences
Rennes. We acknowledge the reviewers A. Cruden and L. Ratschbacher, the
Associate Editor W. Schellart, and the journal Editor J. Mutter for their
constructive comments, which improved the content and clarity of the
manuscript.
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