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Effect of increased shear stress along a plate boundary fault on the formation of anout-of-sequence thrust and a break in surface slope within an accretionary wedge,based on numerical simulations

Ayumu Miyakawa ⁎, Yasuhiro Yamada, Toshifumi MatsuokaDepartment of Civil and Earth Resource Engineering, Kyoto University, Katsura, Kyoto 615-8246, Japan

⁎ Corresponding author. Tel.: +81 75 383 3206; fax:E-mail address: [email protected]

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Please cite this article as: Miyakawa, A., etsequence thrust and a break in surface..., T

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Article history:Received 31 January 2009Accepted 31 August 2009Available online xxxx

Keywords:Accretionary wedgeNumerical simulationOut-of-sequence thrustPlate boundary faultNankai Trough

We investigated the effect on accretionary wedge structure of increased shear stress, which describes thefrictional sliding resistance along a decollement arising from an increase in material friction or reduction inpore pressure. To clarify the nature of the effect, we performed numerical simulations using two models: aStable Friction model and an Increased Friction model. The Stable Friction model produced a low-angle,smooth, surface slope and an in-sequence thrust, whereas the Increased Friction model produced a break insurface slope (scarp) and an out-of-sequence thrust (OST) that cuts through the thrust sheet. The OST formedvia the connection of segments of two adjacent thrusts, and its formation resulted in a change in the thickeningmode of the wedge from thrust-sheet rotation and back-thrust activity to underplating. This contrast inthickening mode between the landward high-friction zone and seaward low-friction zone resulted in theformation of a clear break in slope, as the landward zone is steeper than the seaward zone, consistent withcritical taper theory. The subduction of a basement slice or seamount can produce similar structures arisingfrom an increase in resistance to basal shear sliding. However the distinctive structures arising in anaccretionary wedge as a result of increased shear sliding resistance include a flat basal plane and absence ofslope-failure sediments beneath the OST. These structural features are observed in accretionary wedges of theNankai Trough off Muroto (Japan), the Sunda Strait, and the Barbados Ridge.

+81 75 383 3203.p (A. Miyakawa).

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1. Introduction

The overall mechanics of accretionary wedges located alongcompressive plate boundaries is considered to be that of a Coulombwedge. The theory of a critically tapered Coulomb wedge (Davis et al.,1983; Dahlen, 1984) states that the taper angle is controlled by theinternal friction coefficientof thewedgebodyand the friction coefficientof the basal plane; however, the natural wedge shape is not that of asimple wedge.

Recent studies have investigated changes in the frictional behavior ofthe basal fault beneath an accretionarywedge, including 1) temperature-controlled transitions in clay minerals (Hyndman and Wang, 1993;Hyndmanet al.,1995,1997;Oleskevich et al.,1999), 2) a reduction influidpressure and diagenesis (Moore and Saffer, 2001), 3) a change in thelocation of the plate boundary fault within basement basalt (Matsumuraet al., 2003), and 4) reactivation of a roof thrust (Kitamura et al., 2005).These changes in frictional behavior can affect aspects of theoverall wedge structure (Kimura et al., 2007) (Fig. 1), including 1) thedevelopment of a trench slope break, 2) changes in the wedge taper andthe thickening mode of the accretionary wedge from in-sequence

thrusting to out-of-sequence thrusting, 3) a step-down of the aseismicdecollement, and 4) ramping up of a low-angle, out-of-sequence thrust(OST) above the underplated complex. However, the detailed dynamicsof the formation of the OST and the break in surface slope remain poorlyunderstood.

Geologicalmodeling is a useful technique for detailed examinations ofthe geometry and deformation processes of geological structure. Previousstudies have used analog models to investigate variations in physicalproperties within accretionary wedges and in fold-and-thrust belts (e.g.,Lohrmann et al., 2003). In the present paper, we investigate the effect onaccretionary wedge structure of increasing shear stress, which describesthe frictional sliding resistance along the decollement, which arises froman increase in material friction or reduction in pore pressure.

Numerical simulations are a suitable method for conductingexperiments in which the physical properties are changed over time;this is difficult to realize using analog materials. We employed thedistinct element method to examine the effect on wedge structure ofvarying physical properties along the decollement. By controlling theinternal friction along the basal fault, we sought to determinewhetheran increase in shear sliding resistancewould generate anOSTand slopebreak, and how these features might form. We also compared themodeled OST and slope break structures with other types of OSTs andslope breaks, and with naturally occurring accretionary wedges.

late boundary fault on the formation of an out-of-9.08.037

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Fig. 1. Generalized structure around the up-dip limit of the seismogenic zone within theNankai Trough (from Kimura et al., 2007). The wedge is divided into three segmentsbased on differences in frictional behavior along the basal fault.

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2. Background

2.1. Decollement beneath an accretionary wedge

Recent investigations have revealed that accretion at a subductionmargin generally results in the development of a sub-horizontaldetachment (i.e., a decollement) within the sedimentary sequencesaccumulated in the trench area (e.g., Moore, 1989). Such decollementzones are considered to beweak, due to either high pore-fluid pressure(e.g., Moore, 1989) or high concentrations of clay minerals with a lowcoefficient of friction (Vrolijk, 1990; Deng and Underwood, 2001). Thesediments above the decollement are typically deformed by a series ofimbricate thrusts that convergewith the decollement surface,whereassediments beneath the decollement are subducted without internaldeformation.

A typical example of an accretionary wedge with a basaldecollement is found in Nankai Trough, where the Philippine SeaPlate is subducting beneath the Eurasian Plate (toward 310–315°) at arate of 4 cm/yr (Seno et al., 1993) (Fig. 2). Extensive seismic surveys inthis area reveal a decollementwithin the accreted sediments, not at thetop of the volcanic basement (Bangs et al., 2004). The reverse polarityof the decollement suggests that the layer may have extremely highfluid pressure, even in the proto-decollement region (Tsuji et al.,2005). The proto-decollement is the extension of the decollementsurface in undeformed sediments, seaward of the deformation front.The clear depiction of the proto-decollement in seismic profilessuggests that a preferred layer for the decollement exists prior to theinitiation of displacement. Geophysical logging and core analysisat Site 1174 of Ocean Drilling Project Leg 196 revealed that the

Fig. 2. Map of the plate boundary south of Japan. The Nankai trough is located at theboundary between the Eurasia and Philippine Sea Plates. The rectangle indicates theMuroto region.

Please cite this article as: Miyakawa, A., et al., Effect of increased shearsequence thrust and a break in surface..., Tectonophysics (2009), doi:10

decollement at Nankai is located within a hemi-pelagic mudstonesequence (Mikada and Becker, 2002).

The above features of decollement development are also observedin Barbados (DiLeonardo et al., 2002) and Cascadia (Tobin et al., 1994).The decollement in the Barbados accretionary wedge, where theAtlantic Plate is subducting beneath the Caribbean Plate, is located in aradiolarian mudstone with high porosity and low strength (Mooreet al., 1998). This horizon also forms the proto-decollement. InCascadia, a large-scale accretionary wedge has developed in associa-tion with subduction of the Juan de Fuca Plate beneath the NorthAmerican Plate. The decollement (and proto-decollement) occur at theboundary between overlying turbidities and underlying hemi-pelagicmudstones (Westbrook et al., 1994). A decollement is also clearlyobserved at the Sunda margin, where the Indo-Australian Plate iscolliding with Eurasia. Here, excess pore-fluid pressures are inhibitedby intense faulting and fracturing that is initiated in the trench and thatintensifies along the frontal accretionary wedge (Kopp and Kukowski,2003). However, low levels of stress are found along the Sundadecollement because of the intrinsically weakmaterial along this zone(Kopp and Kukowski, 2003); consequently, the decollement is themechanically weak layer in this area.

2.2. Temporal and spatial changes in pore pressure and shear strengthalong a decollement

The shear stress at the base of a wedge, which describes thefrictional sliding resistance in a general Coulomb wedge, is given by

τb = C0 + μðσn � pf Þ ð1Þ

where C0 is cohesive strength, μ is the coefficient of friction, σn istraction normal to the base, and pf is pore-fluid pressure (Davis et al.,1983). The coefficient of friction is described by the internal frictionangle ϕ:

μ = tanϕ: ð2Þ

The cohesionC0 is relatively unimportant in terms of themechanicsof an accretionary wedge composed mainly of silicate sediments(Davis et al., 1983). Therefore, the shear sliding resistance is controlledby the coefficient of friction, the normal traction, and pore-fluidpressure. However, in analog modeling and numerical simulations,normal traction is basically taken into account as overburden upon thebasal fault, based on thewedge geometry. In this paper,we focus on theeffect on wedge structure of the coefficient of friction and pore-fluidpressure.

The proto-decollement and decollement beneath the toe of awedge sustain high pore-fluid pressure (Tsuji et al., 2008), whichensures low frictional sliding resistance τb. However, Bangs et al.(2004) suggested a landward reduction in pore-fluid pressure pfalong the decollement. This view is supported by estimates ofconsolidation based on steady-state hydrogeologic models thataccount for subduction geometry, subduction rate, bulk permeability,and fluid derived from dehydration reactions (Saffer and Bekins,1998). Likewise, Matmon and Bekins (2006) reported a landwardreduction in pore pressure along the decollement beneath Peru,based on a numerical simulation. This reduction in pore pressureleads to an increase in frictional sliding resistance τb to the forearc.

Landward changes are also seen in material friction along decolle-ments. The temperature-dependent transition from smectite to illite/chlorite results in a change in material properties along the basal fault(Hyndman and Wang, 1993; Hyndman et al., 1995, 1997; Oleskevichet al., 1999). However, the nature of the overall change in materialfriction along decollements remains unknown. In our modeling, weconsidered the case that friction increases landward, although it is alsopossible that friction remains constant or decreases landward.

stress along a plate boundary fault on the formation of an out-of-.1016/j.tecto.2009.08.037


Table 1Physical and numerical parameters used in the simulations.

Particle A Particle B Particle C

Radius (m) 12–30 6–10 6–10Density(kg/m3) 2650 2650 2650Grain shape Circular Circular CircularShear drag coefficient 30 0.5 0.5–30Internal friction angle (deg) 35 25 25–35

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The aim of the present simulations is to investigate the effects onaccretionary wedge structure of increasing shear sliding resistancealong the decollement caused by an increase in material friction orreduction in pore pressure. The increase in material friction isreproduced by increasing the friction coefficient in the distinct elementmethod (DEM). However, it is difficult to directly accommodate pore-fluid pressure in the DEM, as it was originally constructed for solidgranular mechanics; a fluid–solid coupling technique remains to bedeveloped. Consequently, the increase in shear sliding resistance arisingfrom a reduction in pore pressure is replaced by an increase in thefriction coefficient in Eq. (1). In this analysis, the effects on wedgestructure of an increase in material friction and reduction in porepressure are reproduced by increasing the friction coefficient along thedecollement in the DEM. This approach enables us to simplify thenatural phenomena such that it can be represented in numericalmodeling; however, a potential limitation of this approach is difficultiesencountered in distinguishing the effects on wedge structure related tothe reduction in pore pressure from those related to the increase inmaterial friction.

3. Method

3.1. Distinct element method (DEM)

The distinct elementmethod (DEM) (Cundall and Strack,1979) hasbeen applied in a broad range of studies, including investigations ofshear zones (Morgan, 1999; Morgan and Boettcher, 1999), gravity-driven volcanic deformation (Morgan and McGovern, 2005a,b), andthe evolution of thrust systems (Benesh et al., 2007). The mostimportant advantage of DEM (Burbidge and Braun, 2002) is its abilityto express spontaneous strain localization and large-scale strainaccumulation along discontinuous surfaces,which is generally difficultto achieve using alternative approaches such as the finite elementmethod. Changes in force and displacement are calculated individuallyfor each particle in the model, from which deformation is obtainedthroughout the entire model.

The DEM is calculated in incremental steps as follows: the contactpoint and amount of overlap are calculated from the particle and wallpositions; then, the force oriented normal to the contact plane (Fn) iscalculated from the overlap. Also exerted on each element is a shearforce proportional to the amount of displacement parallel to the contactplane (Fs). The shear force is limited to a value less than μsFn, where μs isthe shear drag factor between the elements at the contact point. Theparticle positions are then calculated from Newton's laws of motion,with the contact force obtained from the previous time step. Bycalculating this process every time step, the bulk deformation of themodel is simulated. Because the DEM describes only those parametersrelated to element contacts, parameter testing is necessary to measurethe bulk physical properties of the element assembly (Yamada et al.,2006). In this paper, the bulk internal friction angle of the particles isincreased to reproduce the increase in frictional sliding resistance alongthe decollement. This increase in bulk internal friction is achieved byincreasing the shear drag factor between particles. We use a 2D DEM inwhich particles are assumed to be 2D discs. The simulation is run usingthe software PFC2D (ITASCA Corp., Minneapolis, USA).

3.2. Particle parameters

The DEM simulation can reproduce accretionary wedge structuresand a decollement developed in sediments by considering particleparameters that represent sand and microbeads, respectively(Yamada et al., 2006). It is difficult to accurately simulate naturalphysical properties because of the heterogeneous nature of naturalmaterials and because of technical limitations. However, sand-microbead analog modeling has been successful in reproducing anaccretionary wedgewith a decollement, and in simplifying the natural


geometry of wedge structures and investigating relevant deformationprocesses (Kukowski et al., 2002; Yamada et al., 2005, 2006). Dry sandis an appropriate material for modeling brittle deformation (McClay,1990), and microbeads are a suitable analog material for simulating aweak layer such as a decollement, as they are a Coulomb material andtheir density and size are similar to those of dry sand, yet their near-perfect sphericity results in a smaller coefficient of internal frictionthan that of dry sand, with almost negligible cohesion (Kukowskiet al., 2002).

Following Yamada et al. (2006), we determined the parametersrelated to element contacts. Table 1 lists the physical characteristics ofthree particle types, as obtained from a series of simulated biaxialcompression tests. The properties of Particle A represent those of sand,and the properties of Particle B represent those of microbeads. Theproperties of Particle C represent those of microbeads, although thebulk internal friction angle can be increased from that of microbeads(25°) to that of sand (35°) by increasing the shear drag factor from 0.5to 30. This variation in the shear drag factor reproduces thedocumented variation in physical properties along the decollementfrom incoming to the deeper. Initial cohesion and bonding betweenelements are not introduced because of the cohesionless nature of theanalog materials. Although the sizes of the elements in this study arelarger than those of the natural materials or those used in analogexperiments, previous studies have accurately reproduced geologicalstructures using DEM particles with larger diameters (e.g., Saltzer,1992; Burbidge and Braun, 2002; Strayer and Suppe, 2002; Finch et al.,2003; Yamada et al., 2004; Benesh et al., 2007). The elements are ofvariable size to avoid the formation of a preferential weak plane in theinitial arrangement of the elements.

3.3. Model settings

Given the aim of this study (i.e., to estimate the effect on anaccretionary wedge of increasing sliding resistance along a basalfault), we performed simulations using two types of model settings: aStable Friction model and an Increased Friction model. The modelsettings are based on those used in previous studies that succeeded inreproducing accretionary wedge structures (e.g., Yamada et al., 2006).

3.4. Stable Friction model

In the Stable Friction model, we set a constantly low internalfriction angle in the bottom layer to simulate a decollement that is amechanically weak layer due to high pore pressure or the presence ofweak materials. Sediment in the models occupies an initial area of40,000 m in width and 900–1000 m in thickness (Fig. 3). The bottomlayer, up to~100 m thick, is composed of Particle B, which has a lowfriction angle as a bulk material. The upper layer consists of Particle A.

The set-up for the model is shown in Fig. 3. Rigid walls are used forthemodel boundaries. The shear drag factor between particles and thebasal wall is the same as that within the bottom layer (Particle B),whereas the shear drag factor between particles and the side walls isthe same as that within the upper layer (Particle A). The basal plate inthe simulation is set horizontally. Amovingwall with a basal slit (60 min height; see Fig. 3) shortens the sediments to represent the accretion



Fig. 3. Set-up for numerical simulations. The upper layer (100–1000 m) is composed ofParticle A, and the bottom layer (0–100 m) is composed of Particle B for the StableFriction model and Particle C for the Increased Friction model. The left side wall pushesthe particles to the right side at a small rate of displacement (0.009 m for eachcalculation cycle). The moving wall has a slit (0–60 m) to produce a detachment(decollement) within the bottom layer. The shear drag factor of Particle C increasesfrom the left-hand side in response to displacement of the moving wall.

Fig. 4. Schematic view of the increase in frictionwithin the Particle C layer. Each group ofparticles is numbered, and their shear drag factors increase according to Eqs. (3) and (4).

Fig. 5. Temporal and spatial changes in friction within the Particle C layer (the bottomlayer) in the numerical model. Darker colors represent higher friction.


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process. The slit generates a detachment horizonwithin the first layer.The displacement rate should be small enough to approximate thedeformation as quasi-static, and is therefore set to 0.009 m for eachcalculation cycle. In this study, we refer to the moving wall side as“landward” and the other side as “seaward,” reflecting the terminologyused for natural accretionary wedges.

3.5. Increased Friction model

In the Increased Friction model, a layer of progressively increasingfriction was placed at the bottom of the model to simulate a landwardincrease in shear stress, which describes the frictional sliding resistancealong the decollement. Although the pore pressure distribution andmaterial properties are affected by changes in temperature, overburdenthickness, porosity, and the development of faults and fractures that actas fluid conduits, it is difficult to take these factors into account in themodel. However, the distribution of pore-fluid pressure can beaccommodated in the model: it is described by the distance from thedeformation front of thewedge when thewedge grows in a self-similarmanner (Saffer and Bekins, 1998). Once the distribution of pore-fluidpressure has been determined, the increasing rate of the shear dragfactor is determined from several preliminary experimentswith the aimof setting the front of the friction-increasing area at a near-constantdistance (~5000 m) from the deformation front of the wedge, andsetting the region of the friction-increasing at a near-constant value (c3000 m). This enables the use of a simplifiedmodel compared with thecase of considering several of the factors that control pore pressure. Thebasic settings (i.e., size of the experimental apparatus and kinematics)are the same as those in the Stable Friction model, except for theparticles in thebottom layer. Thebottom layer (~100 mthick) consists ofParticle C, which has a low shear drag factor (0.5). The bottom layer isdivided into 890 groups (numbered asn) by setting vertical partitions at45 m intervals from themovingwall at the initial position. After 4500 mof initial shortening (500,000 time steps), the shear drag factor wasincrementally increased after every 90 m (10,000 time steps) ofshortening (Fig. 4). Here, t is the time step used in the calculationsand fn

T is the shear drag factor of group n at the renewal interval T:

f Tn = 0:25 × ð3T � n + 6Þ ð3Þ

T =t � 500;000

10;000

� �ð4Þ

For each group, we imposed a maximum value of 30 for the sheardrag factor. The bottom layer (Particle C) becomes highly sheared anddeformed due to the force of the moving wall, and some particles aretaken into the wedge during the simulation. Therefore, the assemblyof particles set as groups at the initial condition are also sheared and


deformed. Consequently, the friction-increasing zone shows a shearedrather than rectangular shape (Fig. 5).

4. Results

4.1. Deformation features

The Stable Friction model is able to reproduce typical structures of afold-and-thrust belt, including the wedge geometry and foreland-vergent thrusts that propagate upward from the basal decollement in aforeland-propagating (piggyback) sequence (Fig. 6). The frontal thrust isalways the most active fault in this model. During deformation, theearlier-formed thrustswere back-rotatedwith reactivation. Someminorback-thrusts were formed after approximately 9000 m of shortening.Displacement along these structures cut through and slightly steepenedthe upper part of the previously formed foreland-vergent thrusts.

The overall structure style of the Increased Frictionmodel is awedgeshape that increases in size with ongoing displacement of the wall(Fig. 7). Foreland-vergent thrusts formed at the toe of thewedge as partof a piggy-back sequence. Back-thrusts formed after 9000 m of shorten-ing. Someof the thrust sheetswerehighly deformedby theback-thrusts,especially the fourth and fifth thrust sheets from the left (Fig. 7, thosepanels showing 13,500–18,000 m of shortening). The intense deforma-tion is observed in the high-friction zone. The foreland-vergent thrustsare rotated anticlockwise as the wedge grows; in particular, the upperparts of thrusts are strongly rotated by back-thrusting. The upper part ofthefifth thrust (see Fig. 7) is strongly rotated from13,500 to 15,750 mofshortening. A small break in the surface slope—the surface inflectionpoint that separates the steep landward slope from the gentle seawardslope—is observed at the tip of the fourth thrust after 15,750 m ofshortening. The break jumps to the tip of the sixth thrust after 18,000 mof shortening. The difference in slope between the landward and



Fig. 6. Sequential simulation results and accompanying schematic drawings for theStable Friction model (2250–22,500 m of shortening). The white bar at the bottom ofeach panel represents the constant, low angle of internal friction of the bottom layer (cf.Fig. 7). The Stable Frictionmodel produces typical features of thrust wedges, including apiggyback in-sequence fold-and-thrust complex. The surface slope is a low-angle plane.

Fig. 7. Sequential simulation results and accompanying schematic drawings for theIncreased Friction model (2250–22,500 m of shortening). The gray-scale bars at thebottom of each panel show the internal friction angle of the bottom layer: black is thehighest angle of internal friction; white is the lowest. Vertical arrows indicate the breakin surface slope that occurs after 15,750 m of shortening. This model produces typicalfeatures of thrust wedges, including a piggyback in-sequence fold-and-thrust complex,although with complicated internal structure.


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seaward surfaces continues to increase with ongoing shortening. Thelower part of the fifth thrust and the upper part of the sixth thrustbecomeconnectedbyanew low-angle reverse fault, after approximately18,900 m of shortening (Fig. 7, 20,250 and 22,500 m). The connectedfaults act as a single large fault until the end of shortening (22,500 m).


The shape of the connected faults is initially slightly sigmoidal, butbecomes increasingly planar with ongoing displacement. The seawardthrust sheetwasunderplated beneath the rearof thewedge as a result ofdisplacement along the connected fault (Fig. 8).



Fig. 8. Schematic drawing of the Increased Friction model after 22,500 m of shortening.The lower part of the fifth thrust and the upper part of the sixth thrust are connected bya newly developed reverse fault to form a connected fault. A seaward thrust isunderplated beneath the connected fault. A clear break in the surface slope is observed,with the landward surface slope being steeper (19.8°) than the seaward surface (12.1°).The gray-scale bars at the bottom of each panel show the internal friction angle of thebottom layer: black is the highest angle of internal friction; white is the lowest. The solidlines are fore-thrusts and the broken lines are back-thrusts. The numbers indicate theorder of the thrust.

Fig. 9. Generation intervals of frontal thrusts. (a) Generation interval for the frontalthrust in the Stable Friction model. (b) Generation interval for the frontal thrust in theIncreased Friction model.


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4.2. Generation interval of new frontal thrusts

The generation of a new frontal thrust can be detected fromminoruplift in the undeformed foreland sediments. The average generationinterval of frontal thrusts (shortening (in meters)/number of frontalthrusts) can be calculated using a least squares approximation. Thisaverage interval represents how much shortening is required togenerate a new frontal thrust. In the Stable Friction model, thegeneration interval during the early stages of deformation (i.e., duringthe first 9000 m of shortening) is 1802.6 m; subsequent to approxi-mately 9000 m of shortening, the generation interval is 2638.3 m(Fig. 9 (a)). In the Increased Friction model, the generation intervalduring the first 9900 m of shortening is 1874.6 m; thereafter, theinterval is 3141.0 m (Fig. 9 (b)). The generation intervals are similarbetween the two models during the early stages of shortening;however, during the later stages of shortening the Increased Frictionmodel shows a longer generation interval than does the Stable Frictionmodel.

4.3. Slope angle

Wemeasured the surface slope angle of the wedge (along the lineslinking the tips of the thrusts) after every 900 m of shortening in bothmodels (Fig. 10). The surface slope in the Stable Friction model variesfrom 13.1 to 18.2°, and the slope in the Increased Friction model variesfrom 13.7 to 20.0°. In the Stable Friction model, fluctuations in thesurface slope gradually converge to a low angle of 14–15°. In theIncreased Friction model, the fluctuations also converge, although to awider range (14–17°). In the latter stages of shortening in the IncreasedFriction model, the surface slope is divided by a slope break (Fig. 7);subsequently, the landward surface slope increased from 17.5 to 19.8°whereas the seaward surface slope remained low (11.7–14.4°) (Fig. 8).

4.4. Length of the wedge (position of the tip of the frontal thrust)

The length of the wedge is measured as the distance from themoving wall to the tip of the frontal thrust (Fig. 11). The length of thewedge is similar between the twomodels until approximately 9000 mof shortening, from where the two models behave differently. Thewedge length shows a saw-teeth pattern that consists of abruptincreases associated with the initiation of frontal thrusts, followed bygradual decreases.


5. Discussion

5.1. Internal deformation

In our simulations, the accretionary wedge grows and deforms torelease the compressional stress imparted by the moving wall. Weidentified two types of deformation processes that act to release thecompressional stress: generation of a frontal thrust, whereby defor-mation results in the formation of a new thrust fault in the foreland,and internal deformation, representing any deformation within thewedge, except for the generation of a frontal thrust. In bothmodels, thesurface slope and wedge length vary according to the type ofdeformation. The surface slope shows an abrupt decrease followingthe generation of a new frontal thrust, and shows a gradual increaseduring periods of internal deformation (Fig. 10). The length of thewedge shows an abrupt increase following the generation of a newfrontal thrust, and a gradual decrease during periods of internaldeformation (Fig. 11). This episodic pattern of wedge accretion hasbeen reported previously in analog modeling studies (Mulugeta andKoyi,1992; Koyi, 1995; Koyi and Vendeville, 2003). The generation of anew frontal thrust accommodates compressional stress by an increasein wedge length, thereby reducing the wedge taper. In contrast,internal deformation accommodates compressional stress by increas-ing wedge thickness, thereby increasing the surface slope (MulugetaandKoyi,1992). Thewedge releases compressional stress via these twodeformation processes.

In the Stable Frictionmodel, the average generation interval of newfrontal thrusts is longer after approximately 9000 m of shortening



Fig. 10. Angle of surface slope versus shortening. Arrows indicate the timing of the generation of a new frontal thrust. For the Increased Friction model, the landward and seawardsurface slopes are plotted separately for the period after 18,000 m of shortening.


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compared with the period before 9000 m of shortening (Fig. 9). Thisfinding means that wedge lengthening was suppressed during thelater stages of shortening, even though the shortening rate of themoving wall was kept constant. The development of various internaldeformation structures (e.g., back-thrusts) became obvious during thelater stages of shortening (Fig. 6). These observations suggest thatwith ongoing shortening, less compressional stress was released bythe generation of new frontal thrusts; instead, it was increasinglyconsumed by internal deformation. This trend was also observed inthe Increased Friction model.

For theperiodafterapproximately 9000 mof shortening, theaveragegeneration interval of new frontal thrusts is larger in the IncreasedFriction model than in the Stable Friction model, whereas prior to9000 m of shortening the interval is similar between the two models.This difference between the twomodels indicates that a greater amountof compressional stress is released by internal deformation in theIncreased Frictionmodel than in the Stable Frictionmodel, even thoughthe compression rate is the same in both cases. The only physicaldifference between the twomodels during the later stages of shortening

Fig. 11. Length of the wedge versus shortening. The length was measured at the timingof generation of a new frontal thrust and prior to generation.


is the degree of friction along the basal fault. In the case of high frictionalong the basal fault, a greater amount of compressional stress isreleased by internal deformation, with less compressional stress beingconveyed to the frontal part of the wedge to generate a new frontalthrust.

During the later stages of the experimentusing the Increased Frictionmodel, internal deformation (e.g., back-thrusts) is localized in thelandward high-friction zone and the deformation is more intense thanthat in the Stable Friction model. The enhanced internal deformationacts to steepen the upper parts of pre-existing thrusts (Fig. 7). Thisrotationmeans that the thrusts are mechanically less favorable in termsof reactivation (Sibson, 1995). To release compressional stress viafaulting, new favorably oriented faults are formed in the zone ofincreased friction. The favorably oriented parts of the thrusts representreusable planes of weakness. At around 15,750 m of shortening (Fig. 7),the lower part of the fifth thrust remains at a low angle, whereas theupper part is strongly rotated. The upper part of the sixth thrust is lessstrongly steepened than is thefifth thrust, as the sixth thrustwas locatedoutside the high-friction zone prior to 15,750 m of shortening. There-fore, the lower part of the fifth thrust and the upper part of the sixththrust become connected by a new reverse fault and act as a singlesigmoidal fault. This new fault corresponds to a natural OST observed inthe accretionary wedge within the Nankai Trough, off Muroto, Japan(Fig. 12 (a)) (Park et al., 2000).

The formation of the slope break in the Increased Friction model isinterpreted to result from internal deformation. Basically, thewedgewasthickened via internal deformation such as thrust-sheet rotation andback-thrusting. With increasing friction along the basal fault, internaldeformation is enhanced in the landward high-friction zone relative tothe seaward low-friction zone. The enhanced internal deformation actsto thicken the wedge, and this contrast in thickening within differentparts of the wedge results in a corresponding contrast in surface slopeand formation of a slope break. Consequently, the slope break jumpstrenchward, following the movement of the increased-friction zone.However, the contrast in thickening is minor, as is the slope break,because prior to OST formation thickening occurs via internal deforma-tion in both the high- and low-friction zones. OST formation results in achange in thickeningmodewithin thewedge from internal deformationto underplating. The OST enables the seaward thrust sheet to subductunderneath theOST. The thickeningvia underplating is efficient in liftingthe landward segment of the wedge, and continues for a long term viaOST thrusting. The difference in thickening mode between internal



Fig. 12. Simplified profiles of accretionary wedges with slope breaks and coexistinglarge thrust faults. (a) Nankai Trough off Muroto (from Park et al., 2000). (b) SundaStrait (from Kopp and Kukowski, 2003). (c) Barbados Ridge (from Westbrook et al.,1988).


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deformation and underplating means that the slope break becomesevident after OST formation.

5.2. Correspondence of the simulation results to the theory of anon-cohesive Coulomb wedge

The basic theory of a non-cohesive critical Coulomb wedges statesthat a criticalwedge taper is dependent on the internal andbasal frictioncoefficients, internal and basal fluid pressure ratios, and the dip of thebasal detachment (Davis et al., 1983; Dahlen, 1984; Dahlen et al., 1984).Because these factors (except for basal friction) are constant in thepresent analysis, the theory predicts that increased basal friction resultsin a steeper critical taper, and vice versa.

In the Increased Friction model, after approximately 15,750 m ofshortening, there exist two wedge segments separated by the slopebreak. The landward surface slope is steeper than the seaward slope.The slope break is located above the friction-increasing zone, and itjumps trenchward with migration of the increased-friction zone(Fig. 7). The difference between the landward and seaward segmentsis the friction along the basal fault; therefore, the difference in surfaceslope within an individual wedge results from a difference in basalfriction. These observations are consistent with critical taper theory.

Tomaintain a critical taper, internal deformation is required withinthe pre-deformed wedge (Davis et al., 1983). Hence, OSTs and fore-thrusting, which act to maintain the critical wedge taper, are anintegral part of thrust belt formation (Platt, 1986). Morley (1988)reported two end-member types of OST: (1) pre-existing in-sequencethrusts that are reactivated along their entire length, and (2) completelynew thrusts that propagate through a pre-deformed thrust sheet.Intermediate between the two end-members are thrusts that consist in


part of a reactivated in-sequence thrust and in part of a new thrust(Morley 1988). According this classification, the OST observed in thepresent simulation is an intermediate type.

5.3. Comparison of the simulation results with other types of slope breaksand out-of-sequence thrusts

Here we consider other mechanisms that generate OSTs and slopebreaks, and examine the structural features of accretionary wedges toclarify how to distinguish between the different mechanisms.

5.3.1. Surface erosion and sedimentationA reduction in surface slope by syntectonic erosion favors cycling

between accretion and underthrustingmodes (Fig.13 (a)). In contrast,a sudden syntectonic sediment load in the pro-wedge regionpromotesa prolonged phase of underthrusting, retarding the accretion of newimbricates thrusts at the pro-wedge toe (Del Castello et al., 2004)(Fig. 13 (b)). This observation suggests that surface erosion andsedimentation can generate OSTs and accompanying underthrusting.In fact, a thrust-cuttingOST is observed in the case of syntectonic erosion(Fig. 13 (a)); however, a break in surface slope was not observed.Deformation features such as OSTs in the pro-wedge force thewedge toregain its characteristic minimum critical taper, as predicted by thetheory of a critically tapered Coulombwedge (Del Castello et al., 2004).

5.3.2. Increase in bulk wedge strengthThe bulk strength of a wedge increases toward its rear as a

consequence of pervasive deformation and bulk compaction; in such acase, the taper shows a steady decrease toward the rear of the wedge,resulting in a convex geometry (Lohrmann et al., 2003) (Fig. 13 (c)).These observations are consistent with the theory of a critical taperedCoulomb wedge (Davis et al., 1983). The experiments performed byLohrmann et al. (2003) produced back-thrusts and OSTs that representthe reactivation of pre-existing in-sequence thrusts, but did not producethrust-cutting OSTs. In the case that a slope break is generated, itaccompanies the gentler slope as it migrates landward. These structuralfeatures are observed in the Nankai Trough, off Muroto (Moore et al.,1990; Lohrmann et al., 2003).

5.3.3. Differences in basal friction between coseismic and inter-seismicperiods

The dynamic Coulomb wedge theory, as proposed by Wang andHu (2006), consists of two key components: (1) it postulates that theactively deforming, most seaward part of an accretionary wedge (theouter wedge) overlies the up-dip velocity-strengthening part ofthe subduction fault, and that the less-deformed inner wedge overliesthe velocity-weakeningpart (the seismogenic zone); and (2) it states anexact stress solution for a elastic-perfectly Coulomb plastic wedge. Thetheory provides a first-order explanation for the sharp contrast instructural style between the inner and outer wedges, which iscommonly accompanied by a break in surface slope, and for thecoexistence of a relatively steep surface slope in the outerwedge (Fig.13(d)). These types of structures are seen, for example, atNankai off the KiiPeninsula (Park et al., 2002) and in Alaska between the Kenai Peninsulaand Kodiak Island (von Huene and Klaeschen, 1999; Wang and Hu,2006).

5.3.4. Subduction of a basement thrust sliceLallemand et al. (1992) modeled the effects on wedge structure of

an active basement thrust slice (e.g., Tsuji et al., 2009) as it enters asubduction zone. The subduction of the slice resulted in a change intopographic slope, and thickening of the wedge above the basementslice generated a break in topographic slope. These changes resulted inthe development of a deeply propagating accretionary wedgecharacterized by a small taper (Lallemand et al., 1992) (Fig. 13 (e)).A flattened thrust develops from the top of the edge of the slice to the



Fig. 13. Schematic models of accretionary wedges under various conditions. (a) Surfaceerosion model (from Del Castello et al., 2004). (b) Sedimentation model (from DelCastello et al., 2004). (c) Increasing bulk strength of the wedge (from Lohrmann et al.,2003). (d) Difference in basal friction between coseismic and inter-seismic periods(fromWang and Hu, 2006). (e) Subduction of a basement thrust slice (from Lallemandet al., 1992). (f) Subduction of a seamount (from Dominguez et al., 2000).


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base of the scarp. These structures are observed in the Eastern NankaiTrench (Lallemand et al., 1992).

5.3.5. Subduction of a seamountThe subduction of a seamount can lead to the formation of an OST

and break in surface slope within a Coulomb wedge (Lallemand et al.,1992; Dominguez et al., 2000). Seamount subduction results in large-scale tectonic erosion of the frontalmargin of thewedge and thickeningof the rear part of the margin (Dominguez et al., 2000) (Fig. 13 (f)). Thebulk of the margin and trench-fill sediments, dragged into the sub-


duction zone behind the seamount, are underplated beneath theaccretionary wedge (Dominguez et al., 2000); consequently, the rearpart of the wedge becomes thicker than the frontal part, and a typicalslope break (suture) separates those parts of the accretionary wedgedeveloped before and after subduction of the seamount. OSTs developfrom above the top of the seamount and propagate seaward, connectingwith pre-existing thrusts within the accretionary wedge (Dominguezet al., 2000). A large part of the frontal margin is therefore underthrustbeneath the rear part of the accretionary wedge. In the wake of thesubducted seamount, a strongly deformed seaward-dipping thrust unitis observed.

Based on the above descriptions, the subduction of a basementthrust slice or seamount has the potential to generate OSTs with acoexisting slope break; however, these structures are less likely to bedeveloped in response to an increase in the bulk strength of thewedge, surface erosion and sedimentation, or differences in basalfriction between coseismic and inter-seismic periods in a perfectlyelastic Coulomb wedge.

Coulomb wedge theory states that the slope angle maintains acritical taper as long as the bulk strength of the wedge and basalfriction remain constant. Therefore, internal deformation, includingOSTs, occurs after disturbance of the taper by syntectonic erosion orsedimentation, and the flat surface slope adjusts to its critical statefollowing such deformation. Even in the case of a change in the bulkstrength of the wedge, the surface slope becomes small toward therear of the wedge, as the bulk strength of the wedge generallyincreases toward its rear. The style of deformation according todynamic Coulomb theory also results in a smaller slope angle in therear part of the wedge.

With the subduction of a basement thrust slice or seamount,trenchward sediments or sediments upon the seamount are under-plated beneath the rear part of the wedge. The underplated sedimentsact to thicken the rear of the wedge and disturb the critical state of theCoulomb wedge. The local thickening in the rear part of the wedgeresults in the formation of a slope break (scarp), and the roof thrust ofthe underplated sediments acts as an OST. The following features canbe used to distinguish between the structures originating fromsubduction of a basement slice, subduction of a seamount, and anincrease in basal friction: (1) subduction of a basement slice results in aflattened OST and the occurrence of a basement slice at the root of theOST (Fig. 13 (e)), (2) subduction of a seamount results in a seamountlocated behind the slope break and the deposition of margin- andtrench-fill sediments beneath the slope break (Fig. 13 (f)), and (3) anincrease in basal friction is not accompanied by the existence of abasement slice or seamount, but may produce a flat decollementbeneath the slope break and OSTs that cut through pre-existing thrustsheets (Fig. 8).

5.4. Comparison of the simulation results with natural wedges

The above discussion concluded that in the case of OSTs with acoexisting scarp, the absence of a subducted seamount or a basementslice indicates an increase in basal shear stress, which describes thefrictional sliding resistance. We found three sites that match theseconditions: the Nankai Trough off Muroto, Sunda Strait, and theBarbados Ridge. Each of these is now considered in detail.

The Muroto accretionary wedge is subdivided into seven tectonic/structural domains: the Shikoku Basin, axial zone of the Nankai TroughTrench, protothrust zone, imbricate thrust zone (ITZ), out-of-sequencethrust zone (OTZ), large thrust-slice zone, and landward-dippingreflector zone (Moore et al., 2001). Structural features of the StableFriction model (e.g., the low-angle slope and in-sequence folds andthrusts) correspond well to the structural features in the ITZ of theMuroto accretionary wedge, at the deformation front. The structuralfeatures of the Increased Friction model (e.g., the break in surface slopeand OST) correspond well to the structural features in the Muroto




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accretionary wedge within the transition area between the ITZ and theOTZ. This region corresponds to the area in which the pore pressurealong the basal fault shows a reduction toward the forearc (Saffer andBekins,1998; Bangs et al., 2004). A reduction in pore pressure can resultin an increase inmaterial strength (Hubbert andRubey,1959). Park et al.(2000) reported the details of OSTs in the transition area between theITZ and the OTZ (Fig. 12 (a)). In a seismic profile across the Murotowedge, the landward surface slope, fromthe tip ofOST2, shows a steeperslope (8°) than that of the seaward surface (2.1°). In the IncreasedFrictionmodel of the present study, the landward surface slope from thetip of theOSTalso shows a steeper slope (19.8°) than that of the seawardslope (12.1°). The sigmoidal OST2 shows a gentler fault slope (10°) thanthe other seaward thrusts, and is connected to two thrusts: one in thehanging wall and another in the footwall. In the Increased Frictionmodel, the OST also shows a gentler fault slope than the other thrusts,and again, it appears to be connected to two thrusts (Fig. 14).

Based on the present simulation results, we reconstructed thedeformation history of the Muroto wedge in the transition areabetween the ITZ and the OTZ (Fig. 14). In the landward ITZ, shearstress along the decollement, which describes the frictional slidingresistance, increases due to a decrease in pore-fluid pressure as thePhilippine Sea Plate is subducted. In the zone of increased frictionalresistance, internal deformation (e.g., back-thrusts) intensifies, anduplift associated with the increase in surface slope is enhanced byinternal deformation. During this stage, a small break in the surfaceslope may develop in response to the contrast in internal deformationbetween the zones of high and low frictional resistance. As the upperparts of the thrusts became cut and steepened by internal deforma-tion, they became inactive. To release the horizontal compressionalstress, a new thrust formed via the connection of favorably orientedsegments of adjacent faults: the lower part of the landward thrust andthe upper part of the seaward thrust. The development of an OSTresults in a change in the thickeningmode, which becomes dominatedby underplating; in addition, a surface break becomes clear. Duringthis stage, we observe OST2 in the Muroto region and a surface breakat the tip of OST2. As the plate subducts, the shear stress along thebasal fault increases in a seaward direction. The position of the breakin surface slope jumps seaward, following the high-friction zone. Thegeometry of OST2 changes from sigmoidal to planar with ongoingdeformation, as observed in the Increased Friction model. A landward,planar OST1 in the Muroto region may represent an earlier OST thatonce had a sigmoidal geometry (Fig. 12 (a)).

Fig. 14. Schematic drawing of an accretionary wedge with a progressive increase infriction along the basal fault, based on simulation results. The arrowed lines at the top ofthe figure show different tectonic/structural domains: out-of-sequence thrust zone(OTZ) and imbricate thrust zone (ITZ). The dotted line at the top and the gray shadedzone in the wedge represent the transition between the ITZ and OTZ. The vertical arrowshows the break in surface slope. The bold line is the OST, and the dotted area beneaththe OST is an underplated thrust sheet. The gray-scale bar at the bottom of the figureshows the internal friction angle of the decollement: black is the highest angle ofinternal friction; white is the lowest.


In the Sunda Strait accretionary wedge, OSTs are found at the base ofthe scarp (Koppet al., 2001, 2002;KoppandKukowski, 2003) (Fig.12 (b)),consistent with the Increased Friction model. The decollement in theSunda Strait accretionary wedge is characterized by weak materialrather than excess pore-fluid pressure; therefore, it is possible that areduction in pore-fluid pressure has not occurred. Instead, materialfriction may have increased over time, resulting in an increase in basalshear stress in this region.

A break in the surface slope is also observed across the BarbadosRidge complex at latitude 16°12'N (Westbrook et al., 1988) (Fig. 12 (c)).Large thrusts are observed beneath the slope break, possibly represent-ing OSTs that cut the thrust sheet. These structures are also assumed tobe the products of an increase in basal shear stress.

Relatively planar and gentle slopes are observed toward the rear partof the wedges in the Nankai Trough off Muroto and in the Sunda Strait.These gentle slopeswere not observed in the Increased Frictionmodel. Ifthe basal friction had decreased in response to the decollement steppingdown to a lower planewith high fluid pressure or low-friction material,the decreased basal frictionmay have resulted in a decrease in the taperangle, as described in critical taper theory. Such a convex slope breakmay have resulted from an increase in the bulk strength of the wedge(Kopp and Kukowski, 2003; Lohrmann et al., 2003) or a difference inbasal friction between coseismic and inter-seismic periods (Wang andHu, 2006), as described above.

The Increased Friction model reproduces the structural featuresgenerated by an increase in shear sliding resistance. However, theeffects of a reduction in pore pressure and increase in material frictionalong the decollement are restricted to the friction coefficient.Therefore, we are unable to estimate the magnitudes of these effects.Because the internal friction angle in the simulation is set to reproducethe properties of sand and microbead analog materials, it is difficult toquantitatively assess the effect on structure of variations in friction innatural accretionarywedge. In the present analysis, the increasing rateof the friction coefficient was set to reproduce a fixed distributionfrom the deformation front. The pore-fluid pressure and properties ofthe material are controlled by several factors, including overburdenpressure, existence of permeable faults and fractures, and thermaleffects. To make advances in this regard and to perform more realisticsimulations, it would be necessary to develop a more advancedsimulation technique that is able to simulate fluid–solid interactions.

6. Conclusion

We performed numerical simulations using two models, the StableFriction model and the Increased Friction model, to clarify the effect onwedge structure of increasing shear stress,whichdescribes the frictionalsliding resistance beneath the accretionary wedge. The Stable Frictionmodel produces a smooth, low-angle surface slope and an in-sequencethrust,whereas the Increased Frictionmodel produces a break in surfaceslope (scarp) and an OST that cuts through the thrust sheet. An increasein the shear stress along the basal fault induces strong internal defor-mation (e.g., back-thrusts). The back-thrusts cut through and steepenthe upper parts of pre-existing thrusts, making them inactive. To releaselandward compressional stress, OSTs are formed when low-angle andfavorably oriented segments of two adjacent thrusts become connected(i.e., the lower part of the landward thrust and the upper part of theseaward thrust). The development of an OST results in a change in thethickening mode of the wedge from thrust-sheet rotation and back-thrust activity tounderplating (Fig.14). This contrast in thickeningmodebetween the landward high-friction zone and the seaward low-frictionzone results in a clear break in surface slope, with the landward partbeing steeper than the seaward part. This observation is consistent withcritical taper theory.

In the two models, an increase in basal shear sliding resistancegenerates OSTs and a coexisting scarp. These structural features areobserved in the cases of subduction of a basement slice or a seamount,




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but the origin of the OSTs and scarp can be determined based on adetailed analysis of the structures in the wedge. The subduction ofa basement slice results in a flattened OST and the occurrence of abasement slice at the root of the OST. The subduction of a seamountresults in a seamount located behind the slope break and thedeposition of margin- and trench-fill sediments beneath the slopebreak. An increase in shear sliding resistance produces a flat basalplane, without slope-failure sediments beneath the OST.

The structural features observed in the above numerical simula-tions are also observed in natural accretionary wedges. Scarps andsigmoidal OSTs cutting thrust sheets are observed in the Nankaitrough, off Muroto, as well as in the Sunda Strait and Barbados Ridgecomplexes. Although there exists little information regarding basalshear sliding resistance in these complexes, these structures mightreflect an increase in basal shear stress.

The simulations reproduced the structural features expected to begenerated by an increase in shear sliding resistance. However, thepore-fluid pressure and the properties of the material are likely to becontrolled by several factors. To advance our understanding in thisregard and to perform more realistic simulations, it would benecessary to develop a more advanced simulation technique that isable to simulate fluid–solid interactions.

Acknowledgments

This work was supported by a Grant-in-Aid for Fellows awarded bythe Japan Society for the Promotion of Science (20-5034). We thankTakeshi Tsuji, Yuzuru Yamamoto, Yoshitaka Hashimoto, and GakuKimura for helpful discussions.We appreciate the critical comments oftwo anonymous reviewers, which greatly improved the manuscript.

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