Tectonophysics 526–529 (2012) 196–206

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Tectonophysics

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Sensitivity analysis of numerical scaled models of fold-and-thrust belts to granularmaterial cohesion variation and comparison with analog experiments

Faramarz Nilfouroushan a,b,⁎, Russell Pysklywec b, Alexander Cruden b,c

a Department of Earth Sciences, Uppsala University, Villavägen 16, 75236 Uppsala, Swedenb Department of Geology, University of Toronto, 22 Russell Street, Toronto, ON, Canada M5S 3B1c School of Geosciences, Monash University, Melbourne, VIC 3800, Australia

⁎ Corresponding author. Tel.: +46 18 4712559.E-mail addresses: faramarz.nilfouroushan@geo.uu.se

(F. Nilfouroushan), russ@geology.utoronto.ca (R. Pysklysandy.cruden@monash.edu (A. Cruden).

0040-1951/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.tecto.2011.06.022

a b s t r a c t

a r t i c l e i n f o

Article history:Received 29 January 2011Received in revised form 23 June 2011Accepted 24 June 2011Available online 6 July 2011

Keywords:CohesionBrittle–viscousAnalog modelingNumerical modelingFold-and-thrust belts

Scaled analog and numerical brittle–viscous shortening models are employed to evaluate how fold–thruststructures evolve with changes in the cohesion of brittle materials, a rather poorly constrained physicalparameter at this scale of experiment. The shortening models are characterized by various styles of shearzones and features resembling pop-up structures. The kinematics, geometry, and number of these structuresare controlled by the viscous detachment layers in the models; the finite deformation of the model wedges isfundamentally different in model sets with one or two viscous layers. We demonstrate that the structuralevolution of the numerical models is very sensitive to small changes in cohesion value. This is especiallypronounced in the experiments that incorporate two weak viscous layers. The overall deformation of thenumerical models is most similar to analog models when cohesion values are 70–80 Pa.

, farnil@gmail.comwec),

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Granular materials with very small cohesion values (10's of Pa) areused widely in scaled analog experiments to simulate brittle rockdeformation in the upper crust (e.g. Bonini, 2001; Costa andVendeville, 2002; Cotton and Koyi, 2000; Davy and Cobbold, 1991;Mulugeta, 1988; Nilforoushan et al., 2008; Weijermars et al., 1993).The selection of materials with appropriate cohesion values in suchexperiments is important for appropriate and reproducible modelingof the dynamics of brittle rock deformation in nature. The mechanicalproperties of granular materials are typically determined by shear-box or ring-shear tests with results plotted on a shear stress versusnormal stress diagram. The cohesion is usually determined by linearextrapolation of the low normal stress part of the failure envelope tothe shear stress axis (Fig. 1a). There is considerable uncertainty in theresulting magnitude of cohesion for a given material because it isdifficult to measure shear stress values accurately under low normalstress conditions and because the linearity of the failure envelop inthis regime is debated (Mourgues and Cobbold, 2003; Schellart,2000). This is compounded by measurement errors (e.g. ±15 Pa), andthe physical handling technique (e.g. pouring or sifting of thematerials) (Fig. 1a) (e.g. Krantz, 1991; Lohrmann et al., 2003; Panienet al., 2006b; Ranalli, 1987; Schellart, 2000; Schrank et al., 2008). For

example, using a Hubbert-type shear box, Lohrmann et al. (2003,Table 1) reported that different preparation methods such assifted/poured, inhomogeneous or homogeneous sand can result inaverage cohesion variations of 40 Pa and 18 Pa for peak and stableconditions, respectively. The standard errors for their cohesionestimations range from ±8 to ±24 Pa.

Despite such uncertainties, dry granular materials (e.g. quartzsand) are employed extensively for modeling of brittle deformation inanalog experiments. One way to evaluate the possible influence of theuncertainty in cohesion values is to carry out direct comparisonsbetween analog and numerical experiments (e.g. Ellis et al., 2004;Pysklywec and Cruden, 2004).

Previous studies suggest that cohesion in granular materials maydecrease towards the surface of the model (e.g. Panien et al., 2006a,2006b; Schellart, 2000). Such a phenomenon is not included in oursubsequent numerical experiments. It may be that the decreasingcohesion could lead to changes in the character of the structuralfeatures that develop in the models. However, exploration of thispossibility is beyond the scope of what we intend to consider here. Itcan be argued that any such effect will be of second order compared toother influences since the same numerical code (SOPALE, see below)has been used successfully in other comparison studies betweennumerical and analog results (e.g. Cruden et al., 2006; Ellis et al., 2004;Panien et al., 2006a; Pysklywec and Cruden, 2004; Yamada et al.,2006).

In this paper, we report a series of 2-D numerical brittle–viscousshortening experiments that investigate systematically the effect ofvarying the cohesion value. The numerical models are compared to

y = 0.5592x + 99.5

y = 0.7185x +

3.2

0

3000

6000

9000

12000

0 3000 6000 9000 12000 15000 18000

She

ar s

tres

s (P

a)

Normal stress (Pa)

Peak internal fr

iction

stable-dynamic internal friction

Normal stress (Pa)

She

ar s

tres

s (P

a)

b

a

Fig. 1. (a) Shear test results for different granular materials (after Schellart, 2000). S =sand, GM = glass microspheres, CS = caster sugar. Uncertain linear extrapolations atlow normal stresses result in uncertainties in estimated cohesion values. (b) Ring-sheartest results for dry quartz sand used in our analog experiments (J. Lohrmann,Geoforschungszentrum, Potsdam, unpublished results). Linear extrapolation givesapproximate values of 3±38 and 99±17 Pa for the cohesion of the sand for peak andstable dynamic friction conditions, respectively.

PDMS, viscous material

dry quartz sand, brittle material

5mm

fixed

wal

l

15mm/hr

400mm

140mm

30m

m

Model 1

PDMS, viscous material

PDMS, viscous material

dry quartz sand, brittle material

5mm

9mm

5mm

fixed

wal

l

15mm/hr

400mm

140mm

30m

m

Model2

free surface

no-slip

free surface

no-slip

Fig. 2. Pre-deformation vertical cross sections of both analog and numericalexperiments.

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similar 3-D analog experiments and evaluated in terms of thestructural evolution of fold-and-thrust belts. Instead of conductingtypical km-scale experiments (e.g. Ellis et al., 2004; Stockmal et al.,2007), we configured cm-scale numerical models that eliminate theneed for scaling between the analog and numerical models. As such,the gravity, length, thickness, density, viscosity of viscous layer/layers,shortening rate, angle of internal friction of brittle materials, andcohesion (the parameter under investigation) are equal in both analogand numerical models (i.e. the ratio between them is 1). Similar toprevious studies which discussed the evolution of thrust wedges withalternating the strength of materials (e.g. Ellis et al., 2004; Stockmal etal., 2007), we include one and two layers of viscous materials belowand between the brittle materials, to simulate the configurations ofmany fold–thrust belts with single or multiple ductile decollements(evaporites and shales).

We do not attempt to simulate directly any specific naturalprototypes. However, the materials, configuration and boundary

conditions used in our models have been employed previously formodeling of a variety of natural fold-and-thrust belts containingsingle or multiple decollements such as the Zagros belt, SW Iran(Sherkati et al., 2005; 2006), the Northern Apennines, Italy (Massoli etal., 2006) and the southern Canadian Rocky Mountains (Stockmal etal., 2007). To relate our model setup to a natural example, we selectthe Zagros fold–thrust-belt and focus on the effects of weakdecollements like salt or shale on the deformation history of this area.

2. Model setup

2.1. Analog models

We ran two series of analog and numerical brittle–viscousexperiments (Fig. 2). Model 1 comprised a single basal viscous layeroverlain by brittle material and Model 2 included a second viscouslayer. The analog experiments were carried out in a 45 cm×40 cmPlexiglas box filled with a total thickness of 3 cm of dry sand and oneor two 0.5 cm thick layers of viscous polydimethylsiloxane (PDMS;Dow Corning Silastic 4–2901). The sand was sifted from about 20 cmheight above the model at a rate of about 250 cm3/min. Four thinlayers of colored sand were included between the lower PDMS andupper surface levels, as markers, to better visualize the internaldeformation of the models at the final stage of shortening. The overallbrittle deformation is governed bymechanical properties of bulk sand,which was uncolored in our experiments. The sidewalls were notlubricated. The viscous layers were located adjacent to the movablewall and extend 2/3 of the length of the Plexiglas box (Fig. 2). Theconfigurations of the viscous layers were designed to exemplify the socalled zero-edges (Davis and Engelder, 1985) of weak (e.g. salt)decollements and the basement-step effect (Ge et al., 1997) in naturalfold-and-thrust belts.

Transparent, viscous PDMS is frequently used in analog modelingstudies (e.g. Bonini, 2007; Nilforoushan and Koyi, 2007; Pysklywecand Cruden, 2004; Weijermars 1986). Our PDMS has a Newtonianviscosity of 2.5×104 Pa s at strain rates below 3×10−3 s−1 anddensity of 970 kg/m3 at room temperature (Cruden et al., 2006).

The sieved dry quartz sand has an average grain size of 200 μm anda bulk density of 1570 kg/m3. The mechanical properties of the sandused in our experiments were measured using a ring-shear apparatus(J. Lohrmann, GeoForschungsZentrum, Potsdam, unpublished re-sults), which provides more precise results than classical shear-boxmeasurements (Schulze, 1994; Lohrmann et al., 2003). The angles ofpeak and stable dynamic friction are measured at peak strength (faultor shear zone initiation) and stable dynamic strength (fault sliding)respectively (Panien et al., 2006b). For the sand used in our analogexperiments, the angle of internal friction is 35.7°±0.3° and29.2°±0.1° for peak and stable dynamic strengths, respectively(Fig. 1b). The minimum normal stress used in the ring-shear

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measurements was 500 Pa (Fig. 1b), which is equal to the mean valuein Schellart's (2000) measurements (Fig. 1a). However the debateremains as to whether cohesion is estimated by linear extrapolation ofthe failure envelope or if its convex-out behavior should beconsidered. Here, linear extrapolation gives approximate values of 3±38 Pa and 99±17 Pa for the cohesion of the sand for peak andstable dynamic strengths, respectively (Fig. 1b). In nature, thecohesion values for natural sedimentary rock types are about 5–10 MPa. Most studies use a length and stress ratio equal to 10−5

which means 1 cm in model is 1 km in nature and cohesion value of1 Pa is equal to 0.1 MPa in nature (e.g. Buiter et al., 2006; Ellis et al.,2004). Therefore the cohesion values of 0–100 Pa in our analogexperiments simulates rocks with a cohesion range of 0–10 MPa,which is reasonable for sedimentary rocks in geological processes.

All of thematerial in the boxwas shortened continuously from oneside by moving a vertical wall at a velocity of 1.5 cm/h and eachexperiment was stopped after 9 cm displacement (22.5% bulkshortening). After wetting the sand, vertical sections were cut parallelto the shortening direction to study internal structures (Fig. 3) and tocompare with 2D numerical experiments.

2.2. Numerical models

For the numerical experimentswe used SOPALE, a two-dimensional,thermal–mechanical finite element code that solves for the creepingdeformation of viscous-plastic materials assuming incompressibilityand no inertial accelerations. SOPALE is based on the ArbitraryLagrangian Eulerian (ALE) method and can model large finite strainsand evolving material domain boundaries, such as the top free surface(Fullsack, 1995). This code has been used in different geodynamicmodeling applications (Beaumont et al., 2009; Buiter and Torsvik, 2007;Pysklywec and Shahnas, 2003; Stockmal et al., 2007) and its agreementand compatibility with scaled physical analog models has beenevaluated by several studies (Buiter et al., 2006; Cruden et al., 2006;Ellis et al., 2004; Pysklywec and Cruden, 2004). This version of SOPALEcannot model elastic behavior, only rigid-plastic rheology in thefrictional domain, but the effect of elasticity is small with such modelset-ups and material properties (Buiter et al., 2006; Ellis et al., 2004).

The arbitrary Lagrangian–Eulerian technique used by SOPALEswaps computations between a deforming Lagrangian mesh and anessentially undeformed (except for minor vertical dilation associatedwith the evolving free surface) Eulerian mesh. The former acts as a“tracker grid” that continues to follow the deforming materialdomains whereas the latter stable mesh performs as the “solvergrid”. We used a rectangular node resolution of 601×121 (equal to0.67 mm for horizontal and 0.25 mm for vertical resolution) for theEulerian and 1801×361 for the Lagrangian grids.

Similar to Mohr–Coulomb failure, the brittle deformation offrictional-plastic materials is specified by a pressure-dependentincompressible Drucker–Prager yield criterion (Fullsack, 1995):

J01 = 22 = P 1−λð Þ sin φð Þ + C cos φð Þ ð1Þ

where J'2 is the second invariant of deviatoric stress, P is the dynamicpressure, λ is the pore fluid factor, φ is the angle of internal frictionand C is the cohesion. The φ values can decrease linearly over a rangeof specified strains (strain softening).

The suite of scaled brittle–viscous numerical experiments has thesame initial geometry as the analog experiments. Through a series ofexperiments, the cohesion value of the sand (as a frictional plasticmaterial) layers was increased systematically from 0 to 100 Pa inincrements of 10 Pa to cover the range of apparent cohesion (3–99 Pa)

Fig. 3. Left (Model 1) and right (Model 2) are deformed analog and numerical models after 9as the analog experiments but different cohesion values, ranging from 0 to 100 Pa. Axes ar

of the sand used in the analog models. This range of cohesion values isalso similar to that reported in other analog model studies (e.g.Eisenstadt and Sims, 2005; Ellis et al., 2004). Klinkmüller et al. (2008)also characterized the mechanical parameters of 18 dry sands, fromdifferent analog modeling laboratories around the world, andreported their apparent cohesion range in the order of 10–100 Pa.No strain softening was included for cohesion but the angle of internalfriction decreased from 36° to 29° with increasing strain toapproximate the strain-softening behavior measured in granularanalog materials (Buiter et al., 2006). The softening occurs linearlyover a finite strain interval of 0.5 to 1.0. For dry sand, the pore fluidfactor, λ, is 0.

We shortened the models by moving a strong block/“indentor”from one side at the same velocity and total shortening as employedin the analog experiments (Fig. 2). A high viscosity of the indentor(2×1015 Pa s) relative to the other materials meant that the indentordid not deform as it was pushed into the solution space box. The 5 mmthick viscous layer along 2/3 of the base of all models (Fig. 2) was usedso that we could have a consistent basal boundary condition betweenthe various analog and numerical experiments (e.g. Buiter et al., 2006;Ellis et al., 2004).

3. Results and discussion

The computational models are based on a continuum assumption,i.e. the governing equations are formulated for the thermodynamicalbehavior of continuummedia (Fullsack, 1995). There is the interestingpossibility that this assumption could present problems in modelingthe granular materials, as certain details of the structural elements inthe experiments become very fine scale. However, in this study wefocus on the general structural evolution of the experiments ratherthan the details of the features, which may be more stronglyinfluenced by this issue. In this regard, we cite previous studies thatcompare numerical and analog tectonic models at similar scaleswhere the continuum assumption does not prevent a comparison (e.g.Cruden et al., 2006; Ellis et al., 2004; Panien et al., 2006a; Pysklywecand Cruden, 2004; Yamada et al., 2006). This does not preclude thelikelihood that the dynamics of granular media are not entirelyproperly captured by a continuum approach at certain smaller scalesand could be an interesting avenue for future study.

However, despite the continuum assumption and homogeneity ofthe materials in the 2-D numerical models, there are similaritiesbetween some of the numerical results and the 3-D analogexperiments (Fig. 3). For both the one and two viscous layerexperiments, the closest structural similarity between the analogand numerical models is found for cohesion values of 70 and 80 Pa(Fig. 3). It's worth mentioning that for our comparisons, we selectedvertical cross sections in the middle of the analog models to avoidboundary effects. The cohesion values of 70 and 80 Pa are closer to99 Pa (cohesion value resulting from stable dynamic strengthmeasurements) and we might infer that the bulk sand cohesion iscloser to the cohesion of stable dynamic frictional measurements. Thisis hard to prove just by a fewmodels and measurements and we needto test this with a larger suite of models.

3.1. Pop-up structures

Pop-up structures are observed in both analog and numerical oneviscous layer experiments (Fig. 3). These triangular structures aretypically bound by distinct shear zones resembling thrust faults(Figs. 3 and 6). Such structures are frequently developed in analogmodels when relatively strong brittle materials are shortened above aweaker viscous decollements (e.g. Ellis et al., 2004; Liu et al., 1992). In

cm displacement (22.5% bulk shortening). The numerical models had the same set-upse in mm. The undeformed 5 cm wide frontal parts of the models have been cropped.

coh=0 Pa

10 Pa

20 Pa

30 Pa

40 Pa

50 Pa

60 Pa

70 Pa

80 Pa

90 Pa

100 Pa

analogue model with one PDMS layer analogue model with two PDMS layers

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401x61

601x121

801x121

Fig. 4. Deformed one-viscous layer numerical models with different mesh resolutions and cohesion values of 70 Pa after 9 cm shortening. The undeformed 5 cmwide frontal parts ofthemodels have been cropped. The twomodels with 401×61 and 601×121 resolutions look very similar and simulate better the analog section (shown in Fig. 3) while the very highresolution model (801×121) is different in number, locations and geometry of shear zones.

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natural fold–thrust belts, similar structures are observed whensedimentary cover rocks are deformed above a viscous decollement ofsalt or shale (Bonini, 2007; Cotton and Koyi, 2000; Sherkati et al., 2006).However, in our case the number of pop-up structures and shear zonesdiffer between the analog and numerical experiments (Fig. 3).

Pop-up structures also form in two viscous layer experiments butdiffer in their size and location. Compared to one viscous layermodels,smaller pop-up structures are formed just above the lower and upperviscous layers. In the numerical experiments, the pop-up structuresare particularly prevalent above the lower viscous layer.

The development of individual fold and thrust structures in thenumerical models is clearly sensitive to the cohesion of the granularmaterial. Even in the range of a few 10s of Pa in cohesion, the number,geometry and kinematics of shear zones that develop in the modelchanges. Furthermore, these changes are not systematic withincreasing cohesion. For example, in the two viscous layer modelswith cohesion values of 80 and 90 Pa, the location and kinematics ofshear zones and surface topography are markedly different, whereasin the experiments with cohesion values of 70 and 80 Pa they arealmost identical (Fig. 3). These variations are more significant in twoviscous layer models than in experiments with only one viscous layer.The greater variability among the experiments in the two viscouslayer models is interpreted to reflect the more complex dynamicinternal state of the wedge due to the presence of a seconddetachment layer (see below).

3.2. Mesh resolution

The sensitivity of the numerical models to changing cohesion valuepersists with experiments with different mesh resolution. For

example, we tested another series of models at a lower noderesolution of 401×61 for the Eulerian grid and 1201×181 for theLagrangian grid, and a second series at a higher node resolution of801×121 for the Eulerian grid and 2401×361 for the Lagrangian grid(Fig. 4). To compare the numerical models with different meshresolutions, we selected models with a cohesion value of 70 Pa due toclosest similarity to the analog experiment. The 401×61 and601×121 resolution models look very similar and simulate betterthe analog section (Fig. 3) while the higher resolution model(801×121) is different in number, locations and geometry of shearzones. Interestingly, we observed the sensitivity of numerical modelsto cohesion changes even for different mesh resolutions. The modelswith 401×61 Eulerian mesh resolution and different cohesion valuesof 10, 20, 50 and 100 Pa are shown in Fig. 5. These models, which havedifferent mesh resolutions, are also sensitive to small cohesionchanges and the wedge geometry, location, number and geometryof shear zones do not change systematically with increasing cohesionvalues. This illustrates that the brittle–viscous experiments display asensitivity to cohesion changes that is independent of mesh resolution(Figs. 3 and 5). We show later that even purely brittle models are alsosensitive to cohesion values (see below).

3.3. Surface topography and deformation front

In both of the sets of models, increasing the cohesion of frictionalmaterials does not change the surface topography systematically(Fig. 3). For example, the surface topographies are very different in thetwo layer viscous models with cohesion values of 80 and 100 Pa, butexperiments with lower cohesion show intermediate topographies.The surface topography plots in Fig. 3 clearly illustrate the folding of

coh=10 Pa

coh=20 Pa

coh=50 Pa

coh=100 Pa

Fig. 5. Deformed numerical models after 9 cm shortening with different cohesion values of 10, 20, 50 and 100 Pa. These models, which have different mesh resolutions (401×61Eulerian node resolutions), are also sensitive to small cohesion changes and the wedge geometry, and the location, number and geometry of shear zones do not changesystematically with increasing the cohesion values. Axes are in mm.

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thrust sheets in most of the two viscous layer models. These generallyoccur in the frontal part of the models, about 12 to 20 cm away from themovingwall. Folds are less prevalent inmodelswith one viscous layer, inwhichpop-up structures aremostly formedabove thebasal viscous layer.

In our models, the location of the deformation front, defined by thedistal end of the deformed upper surface, depends on the extents ofthe basal and upper viscous layers, on the dip of the frontal thrust, andon the ability of the material to over thrust. The deformation front inboth analog and numerical experiments of the two series ofexperiments formed at about 22–25 cm away from moving wall atthe final stage of shortening (Fig. 3). However, it shifts slightly backand forth as the cohesion value is increased in numerical models (Fig.3). For example the deformation front is located about 23.5 cm awayfrom the moving wall in the one viscous layer model withcohesion=00 Pa, whereas the deformation front is shifted backabout 2 cm in the model with cohesion =20 Pa (Fig. 3). By increasingthe cohesion to 40 Pa, the deformation front returns to almost thesame location as the model with cohesion=00 Pa (about 23.5 cm

away from moving wall). However, the deformation fronts in twoviscous layer models are closer and vary in position by just a few mmas the cohesion is increased.

3.4. Velocity discontinuity

In all analog and numerical one viscous layer models (Fig. 3), thebasal velocity discontinuity defined by the distal end of the basalviscous layer is an important controlling parameter for straindistribution and localization of the frontal structures (Bahroudi andKoyi, 2003; Bonini, 2001; Costa and Vendeville, 2002; Ellis et al., 2004;Nilforoushan and Koyi, 2007). In these experiments, a forelandverging shear zone is localized at the terminal PDMS–sand boundary.In models with two viscous layers, the frontal foreland-verging shearzone is shifted backward, about 2 cm behind this boundary towardthe indentor (Fig. 3). With further shortening nomore shear zones areinitiated at the distal boundary of the basal viscous layer. This suggests

Fig. 6. Plots of logarithmic strain-rate (s−1) after 0.8, 1.7, 3.3, 5, 6.7 and 9 cm shortening (22.5% bulk shortening) for a one viscous layer model with cohesion=80 Pa. Axes are in cm.The undeformed 5 cmwide frontal parts of themodels have been cropped. The rectangular box in the right indicates the location of themoving wall. The color scale is the same for allimages.

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that the upper viscous layer plays an important role in the localizationand distribution of deformation in the two viscous layer models.

3.5. Deformation localization and distribution

Strain-rate plots for the two sets of numerical models withcohesion=80 Pa (chosen due to their similarity with the analogexperiments) show the localization and development of shear zonesabove the viscous layers (Figs. 6 and 7). A comparison of these plotsfor one and two viscous layer models suggest that the developmentand size of pop-ups above the basal viscous layer is restricted by thesecond layer of viscous layer, which acts as a deformation decouplinglayer. However, the basal viscous layer shows higher strain-rates,indicating that the basal decollement is more active than the upperdecollement.

The strain-rate data show how weak viscous layers facilitate rapidtransfer of deformation towards the frontal part of the model (Figs. 6

and 7). For example at 3.3 cm bulk shortening in the one viscous layermodel, shear zones are developing at the edge of the basal viscouslayer (Fig. 6). Similarly, at the same distance from the moving wall(~23 cm), shear zones are developed at the edge of the upper viscouslayer in the two viscous layer model (Fig. 7). Other studies have alsoreported rapid forward propagation of deformation in analogexperiments of fold–thrust belts deforming above a weak viscouslayer like salt or shale (e.g. Costa and Vendeville, 2002; Nilforoushanand Koyi, 2007).

In both sets of experiments, deformation initiates in various partsof the wedge, but these sites do not always subsequently develop intoshear zones (Figs. 6 and 7). This is especially pronounced for the two-viscous layer model. For example, consider the series of partiallydeveloped structures at 3.3 cm of shortening—approximately six pop-up structures have the potential to develop in the top layer of sand(Fig. 7). With progressive shortening, the brittle rheology of thematerials in the models results in localization of only a selected

Fig. 7. Plots of logarithmic strain-rate (s−1) after 0.8, 1.7, 3.3, 5, 6.7 and 9 cm shortening (22.5% bulk shortening) for a two viscous layer model with cohesion=80 Pa. Axes are in cm.The undeformed 5 cm wide frontal parts of the models have been cropped. The rectangular box on the right indicates the location of the moving wall. The color scale is the same forall images.

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number of these structures. Once localized, these shear zones definethe finite evolution of the wedge. It seems that among the modelswith varying cohesion, the early deformational sites do not subse-quently localize in a systematic manner (Fig. 3). Small perturbationsto the initial dynamic state of the wedge with varying materialcohesion may (unpredictably) trigger localization at different sitesand lead to the variable finite evolution of the wedge. Only the shearzones at the front of the wedge and at the indentor develop in allmodels (Figs. 6 and 7). The greater variability among the experimentsin the two viscous layer models reflects the more complex dynamicinternal state of the wedge with the second detachment layer.

3.6. Shortening velocity

The effect of changing the shortening velocity in the one-viscouslayer model compared to the other models is illustrated in Fig. 8.Specifically, we doubled the shortening rate to 30 mm/h in this

experiment. We observe again the change in wedge deformation evenwith cohesion changes in the range of 20 Pa. In both series ofexperiments with different shortening velocities (15 mm/h and30 mm/h), the 20 Pa change in cohesion results in different wedgedeformation patterns (Fig. 8).

3.7. Sensitivity of brittle numerical models to cohesion

Although this paper addresses the evolution of cm-scaled brittle–viscous experiments of fold–thrust-belts, we also demonstrate howcohesion affects the deformation of purely brittle numerical models.We ran a set of numerical models with the same initial configuration(Fig. 2) as the brittle–viscous models except that we used only brittlematerials and varied the cohesion from 0 to 250 Pa (in a wider rangethan our brittle–viscous models). If we consider a stress scale ratio of10−5 betweenmodel and nature (similar to, for example, Buiter et al.,2006; Ellis et al., 2004), 0–250 Pa is equal to 0 to 25 MPa in nature.We

coh=60 Pa

coh=80 Pa

coh=80 Pa

coh=60 Pa

15 mm/hr

15 mm/hr

30 mm/hr

30 mm/hr

Fig. 8. Effect of driving velocity and cohesion changes on deformation of one-viscous layer models. The shortening rate has been doubled to 30 mm/h in the two lower panels.Changes in wedge deformation are observed, even for a cohesion change of 20 Pa. The sensitivity of model deformation to cohesion is observed for both 15 and 30 mm/h drivingvelocities.

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still observe in these purely brittle models that the cohesion variationchanges thewedge taper and increases the number of small structuresnear the top surface (Fig. 9). As we illustrated previously, the effect ofcohesion is more pronounced when models contain viscous layer(s),which implies that viscous layers determine the leading-order controlon localization and development of shear zones, as opposed to thebrittle materials. We infer that with more complex brittle–viscousrheology, there is more sensitivity to small variations in cohesionvalues.

3.8. Single or multiple decollements in Zagros fold–thrust-belt

In addition to the investigation of the cohesion uncertainty effecton models of fold–thrust belts we can consider again the role of weakdecollements on the deformationmechanism in natural examples likethe Zagros fold–thrust-belt. In our models, we observe that the brittlelayers above or between weak viscous layers deform differently(Fig. 3). The upper viscous decollement decouples the deformationand the size and kinematics of structures above and below thatdecollement are different. A similar deformation mechanism was

reported by Sherkati et al. (2006) who used surface data, seismicprofiles, and well information to construct interpreted cross sectionsof the Zagros. They concluded that the internal and surfacedeformation across and along the Zagros belt varies due to the spatialdistribution of evaporitic or shale layers. These authors also conductedanalog experiments that they related to different parts of the Zagros(Fig. 7 in Sherkati et al., 2006). Although the model setup andmaterials are slightly different, the structures developed in A and B inFig. 7a in Sherkati et al. (2006) are similar to our one- or two-viscouslayer experiments (Figs. 3, 6 and 7). We clearly see in their two-viscous layer models that the intermediate viscous decollementinfluences strongly the deformation mechanism of the entire belt.

4. Conclusions

Using analog and numerical experiments, we investigated the roleof cohesion uncertainty on the kinematics and geometry of modelfold-and-thrust belts. In our numerical experiments we found that forthese rheologically complex brittle-viscous models, there is no directcorrelation between cohesion changes and changes in geometry and

coh=00

coh=50

coh=100

coh=150

coh=200

coh=250

Fig. 9. Effect of cohesion on deformation of purely brittle models after 9 cm shortening.Compared to previous models, we only used frictional materials and considered thecohesion over a wider range from 0 to 250 Pa. The small structures near the surfacedevelop by increasing the cohesion.

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kinematics of structures. This was particularly pronounced inexperiments with two viscous layers. The numerical modeling resultssuggest that since we cannot measure cohesion values of granularmaterials used in analog experiments sufficiently accurately, acomparison between the results of these two approaches should beconsidered carefully. This is particularly the case as the initialconfiguration of the experiment becomes increasingly complex. Forexample, although there may not be appreciable variability betweensimple sand wedge shortening experiments, the addition of just oneor two viscous layers introduces significant differences amongmodelswith changing cohesion. For benchmarking purposes and modeling ofgeological processes in nature, the uncertainty in cohesion values andthe sensitivity of numerical results to cohesion variations canpotentially lead to misinterpretations of model results.

We interpret that the variability of the numerical experimentswith changing cohesion is due to the formation of numerous potentialdeformational sites in the early stages in the development of thewedges.With progressive shortening, perturbations to the stress stateof the wedge and the localizing rheology of the materials results inonly a selected few sites being involved in the finite deformation. Inthe numerical models, the perturbation/localization and finitedevelopment of the structures happens in a non-systematic wayamongst models with varying cohesion. With the added dynamiccomplexity of the two layer viscous model, there is an increasednumber of these initial localization sites and, as a result, additionalvariability of the finite deformation of the wedge.

Repeatability of analog experimental results can be achieved whenthey are run with the same boundary conditions, using the samematerials and the same handling techniques (Schreurs et al., 2006). Inthis work, we did not run repeated analog experiments as the focuswas to consider systematic variations in material cohesion—some-thing that could be explored best with a computational approach. Wealso did not attempt to merely simulate the analog results withnumerical experiments. However, comparisons between our analogand numerical results did find some similarities in the structuralevolution of the wedge. For both the one layer viscous and two layerviscous models, we found the most similarity for the models forcohesion values of 70–80 Pa, which is within the range of uncertaintyof the values determined for the granular materials in the laboratory.From this we infer that the fitting of both model typologies at 70–80 Pa indicates that this value most closely represents the bulkaverage magnitude for the cohesion of the sand used in our analogexperiments.

Acknowledgements

FN is funded by the Research Council of Sweden (VR). RP and ACacknowledge funding from the Natural Sciences and EngineeringResearch Council of Canada. We would like to thank Susanne Buiterand an anonymous reviewer for their helpful and constructivereviews. Christoph Schrank is thanked for assistance in the laboratoryand helpful discussions.

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