Fault-related fold styles and progressionsin fold-thrust belts: Insightsfrom sandbox modelingDan-Ping Yan1, Yan-Bo Xu1, Zhou-Bin Dong1, Liang Qiu1, Sen Zhang1, and Michael Wells2

1State Key Laboratory for Geological Processes and Mineral Resources, China University of Geosciences, Beijing, China,2Department of Geoscience, University of Nevada, Las Vegas, Las Vegas, Nevada, USA

Abstract Fault-related folds of variable structural styles and assemblages commonly coexist in orogenic beltswith competent-incompetent interlayered sequences. Despite their commonality, the kinematic evolution ofthese structural styles and assemblages are often loosely constrained because multiple solutions exist in theirstructural progression during tectonic restoration. We use a sandboxmodeling instrument with a particle imagevelocimetry monitor to test four designed sandbox models with multilayer competent-incompetent materials.Test results reveal that decollement folds initiate along selected incompetent layers with decreasing velocitydifference and constant vorticity difference between the hanging wall and footwall of the initial fault tips.The decollement folds are progressively converted to fault-propagation folds and fault-bend folds throughdevelopment of fault ramps breaking across competent layers and are followed by propagation into fault flatswithin an upper incompetent layer. Thick-skinned thrust is produced by initiating a decollement fault within themetamorphic basement. Progressive thrusting and uplifting of the thick-skinned thrust trigger initiation of theuppermost incompetent decollement with formation of a decollement fold and subsequent converting tofault-propagation and fault-bend folds, which combine together to form imbricate thrust. Breakouts at the baseof the early formed fault ramps along the lowest incompetent layers, which may correspond to basement-covercontacts, domes the upmost decollement and imbricate thrusts to formpassive roof duplexes and constitute thethin-skinned thrust belt. Structural styles and assemblages in each of tectonic stages are similar to that in therepresentative orogenic belts in the South China, Southern Appalachians, and Alpine orogenic belts.

1. Introduction

Fault-related folds include decollement folds, fault-propagation folds, and fault-bend folds and are commonlyassociated with thrust assemblages including imbricate thrusts and duplexes [e.g., Boyer and Elliot, 1982; Berger,1984; Banks and Warburton, 1986; Jamison, 1987; Lacombe et al., 1999; Pfiffner, 2006; Yan et al., 2003a, 2008,2009, 2011] (Figure 1). These structural styles and assemblages coexist in orogenic belts, such as the intraplateorogenic belt in the South China Block (Figure 2a), plate marginal Appalachian orogenic belt (Figure 2b), andthe other representative orogenic belts (Figure 2c).

Decollement folds formwhen displacement along a bedding-parallel decollement fault is transferred into foldingof the hanging wall layers. Decollement folds are characterized by a decollement that defines the downward ter-mination of the fold and an incompetent, ductile basal unit thickened in the core of the fold with no visible thrustramp (Figure 1a) [Suppe and Medwedeff, 1990; Erslev, 1991; Shaw et al., 2003]. Fault-propagation folds form at thetip of flat-ramp type fault and consume slip. Fault-propagation folds tighten with depth and slip on the faultdecreases upward terminating within the fold with synclines pinned to the fault tips (Figure 1b) [Dahlstrom,1969; Suppe and Medwedeff, 1990; Erslev, 1991; Narr and Suppe, 1994; Hardy and Ford, 1997; Shaw et al., 2003](Figures 1a and 1b). Fault-bend folds, which form as hanging wall rocks move over bends in an underlying faultwith flat-ramp-flat geometry, have kinematics of forelimb rotation and axial migration along the hanging wall fold[Rich, 1934; Suppe, 1983; Srivastava and Engelder, 1990; Erickson and Jamison, 1995;Hardy and Ford, 1997;Medwedeffand Suppe, 1997; Shaw et al., 2003] (Figure 1c). Layer-parallel shortening along fault tip results in strain transfer andproduces variable fold types including decollement folds and fault-propagation folds, whereas displacementthrough flat-ramp inflections produces fold-bend folds (Figures 1a and 1c). Therefore, development of fault tipsand fault flat-ramp inflections are important in distinguishing the fold-thrust mechanisms [Storti et al., 1997].

Imbricate thrusts, formed by two or more thrusts bounding structural wedges, exhibit a variety of shapes andstyles that reflect initial fault geometries, propagation direction, and folding mechanisms [Suppe, 1983; Shaw

YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2087

PUBLICATIONSJournal of Geophysical Research: Solid Earth

RESEARCH ARTICLE10.1002/2015JB012397

Key Points:• Fault-related folds are commonelements in fold-thrust beltsthroughout the world

• The thick-skinned thrust trigger andresult in formation of the imbricatethrusts and duplex

• Imbricate thrust and duplex involvingin cover sequence constitute thethin-skinned thrust belt

Correspondence to:D.-P. Yan,yandp@cugb.edu.cn

Citation:Yan, D.-P., Y.-B. Xu, Z.-B. Dong, L. Qiu,S. Zhang, and M. Wells (2016), Fault-related fold styles and progressions infold-thrust belts: Insights from sandboxmodeling, J. Geophys. Res. Solid Earth,121, 2087–2111, doi:10.1002/2015JB012397.

Received 27 JUL 2015Accepted 19 FEB 2016Accepted article online 22 FEB 2016Published online 15 MAR 2016

©2016. American Geophysical Union.All Rights Reserved.

et al., 1999; Yan et al., 2009] (Figures 1d and 2). Kinematic interpretations have further defined the process offormation of duplexes from imbricate thrusts and structural wedges in a condition of multilayer decollementswith a roof thrust along upper fault flat [Hudec and Davis, 1989;Moore et al., 1991; Roure et al., 1991; Schellingand Arita, 1991; Decelles and Mitra, 1995; Braathen et al., 1999; Mukhopadhyay and Mishra, 2005; Yan et al.,2009] (Figures 1e, 1f, and 2).

Structural styles and assemblages of fault-related folds form in thin-skinned fold-thrust belts, involving coversequences in the foreland belt, or form in thick-skinned thrust belts involving metamorphic basement in thehinterland or foreland of orogenic belts [Boyer and Elliot, 1982; Shaw et al., 1994, 2003; Yan et al., 2003a,2003b; Pfiffner, 2006; Weil and Yonkee, 2012] (Figure 2). Therefore, these structural styles and assemblageshave been widely used to describe the fold-fault geometry, divide tectonic zones/levels, and restore defor-mational processes for the orogeny [Boyer and Elliot, 1982; Suppe, 1983; Suppe et al., 1992, 1997; Epard andGroshong, 1995; Shaw et al., 1994, 1999, 2005; Poblet and McClay, 1996; Shaw and Suppe, 1996; Medwedeffand Suppe, 1997; Mitra, 2002; Shaw et al., 2005; Pfiffner, 2006; Bernard et al., 2007; Yan et al., 2003a, 2009;Sanchez et al., 2011] (Figure 2).

When fault-fold relationships are understood, the coexisting structural styles and assemblages in orogenicbelts are commonly retrodeformed using geometric and kinematic analysis of balanced cross sections[Dahlstrom, 1969; Boyer and Elliot, 1982; Shaw et al., 1994, 2003; Yan et al., 2003a; Pfiffner, 2006]. However,ambiguity in the genetic relationships between the coexisting structural styles and assemblages, for example,transitions from separated styles to imbricate thrust and duplex (Figures 1 and 2), give a variety of possibilitiesfor restoration. Therefore, a genetic model built with development and transitions of the fault-related folds isessential for the understanding of tectonic evolution of the orogenic belt.

Previous investigations identified the influence of brittle-ductile layering in the mechanics of fold-thrust belts[e.g., Bonini, 2001; Costa and Vendeville, 2002; Couzens-Schultz et al., 2003]. Based on fold-thrust belt in theSouth China block, this paper uses a sandbox instrument with a particle image velocimetry (PIV) monitor builtin the China University of Geosciences, Beijing, to simulate the deformational process and relationships

Figure 1. Typical structural styles and assemblages of the fault-related folds. (a) Decollement fold, (b) fault-propogation fold, (c) fault-bend fold, (d) imbricate thrust,(e) passive roof duplex, and (f) active roof duplex (comprehensive sorted from Boyer and Elliot [1982] and Jamison [1987]).

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between decollement folds, fault-propagation folds, fault-bend folds, imbricate thrusts, and duplexes in anenvironment with a competent-incompetent interlayer sequence (Figures 2a and 3). We use velocity differ-ence (VED) and vorticity difference (VOD) between the hanging wall and footwall of the initial fault tips toconstraint fault initiation. The sandboxmodeling results reveal that decollement folds initiate along the lowerincompetent layers with decreasing VED and constant VOD for the following forming fault tips. The decolle-ment folds are sequentially converted to fault-propagation and fault-bend folds, which are combined intoimbricate thrusts. A passive duplex is produced by the initial decollement fault breaking through competentlayers and doming the upper decollement levels. Thus, the PIV results quantitative constraint the kinematicmodel with initial decollement folds evolving into fault-propagation folds and formation of structural assem-blages. Thick-skinned thrusts trigger imbricate thrusts and duplexes to form thin-skinned thrust belts, corre-sponding to many typical orogenic belts with a thick-skinned belt in the hinterland belt and a thin-skinnedbelt in the foreland thrust belt [Bonini, 2001].

2. Sandbox Modeling Methods

Sandbox modeling is one of the most effective means to study geometry and kinematics of progressivedeformation of layered materials [Buchanan and McClay, 1991; Zhou et al., 2007]. Materials of quartz sandand glass bead, which follow Mohr-Coulomb rupture criteria, and silicone polymer of Newtonian (viscous)rheology are commonly used for the simulation in the sandbox [Buchanan and McClay, 1991; Dominguez

Figure 2. Typical thrust belts with coexisted structural styles of fault-related folds and assemblages. (a) Multilayer decolle-ment thrusts with thick-skinned and thin-skinned thrusts within the South China Block and locations in the insert figure oftectonics outline of the South China (modified from Yan et al. [2003a, 2009] and Tang et al. [2014]). (b) Geological profileacross the Cumberland Plateau and Valley and Ridge Province of the Southern Appalachians (modified after Pfiffner [2006]and cited from Hatcher [1989]). (c) Idealized sketch of thrust belt synthesized Moine thrust zone, Appalachian, and Aplsorogenic belts (modified from Boyer and Elliot [1982]).

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et al., 2000; Ellis et al., 2004; Adam et al., 2005; Zhou et al., 2007]. We analyze the development of fold-thrustbelts in a competent-incompetent interlayer sequence with multilayer decollements using a Canon 500Dcamera to record section deformation and a PIV (particle image velocimetry) device to monitor the sand par-ticle moving velocity and vorticity during the deformation [e.g.Wolf et al., 2003; Adam et al., 2005; Cruz et al.,2008]. This study, focusing on analog forward modeling of the fault-related fold style of multilayers, buildsupon the earlier works of thrust belt systems with typical thrust style and assemblage. The thrust systemsinclude the Mesozoic fold belt within South China block [Yan et al., 2003a, 2009, 2011], the southernAppalachians [Hatcher, 1989; Pfiffner, 2006], Moine thrust zone, and Alpine orogenic belts [Boyer and Elliot,1982; Butler, 2004].

2.1. Experimental Setup and Method

The experimental apparatus used in this study to perform the sandbox experiments is similar to those used byDominguez et al. [1998] and Graveleau et al. [2012]. This apparatus has a flat basal plate bound by two lateralglass walls (see detail in Malavieille [1984], Dominguez et al. [2000], Konstantinovskaya and Malavieille [2005,2011], Bonnet et al. [2007, 2008], and Graveleau et al. [2012]). Before sand and silicon polymer deposition, ethylalcohols were used to lubricate the sidewall glass and reduce the amount of sidewall friction, because ethylalcohols offer very little resistance to forward translation of the modeling during shortening (Figures 3a–3d).This means that very little lateral shear stresses would interfere with model evolution and thus leading toformation of cylindrical structures and plane strain deformation [e.g., Costa and Vendeville, 2002].

Similar geometrical models of layer thickness and viscosity were subjected to four different boundary conditionsfor the analog experiments (Figure 3). The initial dimensions of the deformation box are 74 cm (length) × 30 cm(width)× 5 cm (height). Experiments were subjected to 15–26 cm (20 to 36%) of total shortening. A continuous

Figure 3. (a–d) Four sandbox models designed for testing. Description details are in the text. (e) Columnar section showing the major lithologies, thicknesses,compressive strengths, and incompetent layers along shale within the Sinian, Cambrian, Silurian, and Triassic (Figure 2a) in the South China Block (after F. F. Luet al., unpublished report, 1989; Sichuan Bureau of Geology and Mineral Resources (SBGMR), 1991; Yan et al., 2003a, 2006; Zhang et al., 1996].

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motor either pushes a backstop or pulls a basal canvas sheet beneath a vertical rigid backstop at one side of theboxwith rate of 0.00333mm/s (vM=12mm/h). In the case of pulling the basal canvas sheet (Model 4 in Figure 3),the rough surface of the canvas sheet allows simulation of a high basal friction at the base of the layered incom-ing sand. The stable backstop represents the upper plate against which the thrust wedge develops. A Canon500D camera was used to take photographs of the deformed section through a lateral glass wall on one sideof the experimental apparatus at time intervals of 2min. A PIV (particle image velocimetry) device with data pro-cessing software MicroVec V3.3.2, which was developed by Beijing Lifangtiandi Science and Technology LimitedCompany, is used to monitor the deformation and calculate the velocity field in the same cross sectional planeas that captured in photography, with an effective monitoring width from hinterland to foreland of ~60 cm(Figures 3a–3ad). We use this device to record the location and displacement (Δs) for each equally spaced tracerparticle of 3–5pixels every minute (Δt=1min), which allows the velocity (v) of each of the tracer particle (sandgrain or microunit for silicone polymer) to be calculated using equation (1) [Adrian, 1991]:

v ¼ limΔs s; tð ÞΔt

(1)

where Δs is the displacement of a sand grain, located at s at time t, over a short time interval Δt separatingobservations of the marker images.

We then calculate shear strain rate (dVdX,dUdY) and vorticity (Ω) using equations (2) and (3) [Meynart, 1983]:

dVdX

¼ V i þ 1; jð Þ � V i � 1; jð ÞX i þ 1; jð Þ � X i � 1; jð Þ

dUdY

¼ U i; j þ 1ð Þ � U i; j � 1ð ÞY i; j þ 1ð Þ � Y i; j � 1ð Þ (2)

Ω ¼ dVdX

� dUdY

(3)

where U and V are velocity components in the direction of X and Y of the PIV system, respectively. Based onthe invariants of the velocity gradient tensor, vorticityΩ of�1 and +1 represent simple shear, but of oppositesense, and that a value of 0 represents pure shear.

2.2. Materials, Scaling, and Tectonic Model

In order to compare sandbox models with natural examples, the experiment should be geometrically, kine-matically, and dynamically scaled [Hubbert, 1937; Ramberg, 1981; Bonini et al., 2012]. Characterizations of ana-log materials, scaling, and models used in sandbox modeling have been widely discussed [e.g., Dahlen, 1984;Dahlen et al., 1984; Davy and Cobbold, 1991; Gutscher et al., 1996, 1998; Kukowski et al., 2002; Lallemand et al.,1994; Lohrmann et al., 2003] and reviewed [Graveleau, 2008; Bonini et al., 2012]. The models described in thispaper are scaled such that 1 cm in the model simulates approximately 4 km in the field, i.e., a geometric scalefactor of

λ* ¼ 2:50�10�6

Depending on the scaling M/N ratio, the sand models of 74 cm length * 5 cm thickness represent a scale ofdeformational stratigraphy with width of ~300 km and thickness of ~15 km, which in scale corresponds toupper crustal deformation of the fold-thrust belt.

The model materials were chosen to represent rocks of the upper crust. The incompetent layers are createdby introducing thin layers (0.2–0.5 cm) of silicone polymer at different levels of the sand cake. Viscous siliconepolymer is considered a good analog material for simulating viscous flow of soft layers in the upper crust[Vendeville and Cobbold, 1987]. The silicone may simulate the role of decollement layer that may be variouslycomposed of salt, evaporites, and overpressured shales [Couzens-Schultz et al., 2003]. Therefore, thin layers ofsilicone polymer could act as possible decollement levels in the competent-incompetent interlayer sequence[Bonini, 2001]. The silicone polymer used in the modeling is an unsaturated resin of S-156 (with viscosity cor-responding to Silbione silicone of Couzens-Schultz et al. [2003]) processed by Zhili company in Guangzhou,China. The silicone polymer has a Newtonian fluid behavior (exponent = 1) with a high viscosity (μ) of2.12 × 104 Pa s at 22°C and a density (ρ) of 9.60 × 102 kg/m3 (Table 1). For Newtonian ductile materials, the fol-lowing relation applies [Benes and Davy, 1996]:

ε* ¼ σ*=η*

where η* and ε* are the viscosity and strain rate ratios between model and nature, respectively. Assuming an

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average magnitude of natural viscosity of 1019 Pa s for the incompetent layers and σ* = 2.5 × 10�6 [Van Kekenet al., 1993; Cotton and Koyi, 2000; Leturmy et al., 2000; Couzens-Schultz and Wiltschko, 2000; Bonini, 2007],η* = 2.12 × 10�15, and ε* = 1.18 × 109.

Using v* = ε*λ* = 2.95 × 103, thus vN= vM/v* = 1.13 × 10�9m/s [Corti et al., 2003; Couzens-Schultz and Wiltschko,2000; Bonini et al., 2012], corresponding to a natural velocity of ~3.51 cm/yr, which is comparable with naturalrates of incompetent ductile materials (Table 2). Thus, the high-viscosity silicone polymer deformed at short-ening rates of 12mm/h in our models corresponds to either a salt or shale with moderate to no overpressure[Couzens-Schultz and Wiltschko, 2000].

The white quartz sand used in the experiments is rounded with a medium sand grain size between 0.125 and0.225mm, a mean angle of internal friction (Ф1) of ~35.5°, a density (ρ) of 1.56 × 103 kg/m3, and a cohesion (C)of 20 Pa; other related physical parameters are presented in Table 1. The colored quartz sand is dyed usingwhite sand with the same physical properties. Glass beads used in the model are rounded with a mediumsand grain size between 0.100 and 0.400mm, a mean angle of internal friction (Ф1) of 28.3–30.0°, a density(ρ) of 2.50–3.00 × 103 kg/m3, and a cohesion (C) of 10–30 Pa (Table 1).

The quartz sand layers scale to brittle sedimentary rocks such as sandstones or carbonates [Dahlen, 1984;Dahlenet al., 1984; Lohrmann et al., 2003; Bernard et al., 2007, and references therein]. The glass bead layers scale tobrittle-ductile sedimentary rocks such as siltstone and sandy mudstone [Bernard et al., 2007, and referencestherein]. Both the quartz sand and glass bead have frictional properties satisfying the Mohr-Coulomb failurecriterion with differences in angles of internal friction (Table 1).

The density ratio between the granular sand and glass bead materials and rock is ρ* = 0.62, and the gravityratio between model and nature is g* = 1, as they are subject to the same value of gravitational acceleration.The corresponding stress ratio between model and nature is

σ* ¼ ρ*g*λ* ¼ 5:00�10�6

where ρ*, g*, and λ* represent density, gravity, and length model to nature ratios, respectively [e.g., Couzens-Schultz et al., 2003; Bonini et al., 2012].

Table 2. Scaling Parameters and Ratios for Models and Nature

λ* = λM/λN = 10�2(m)/4 × 103 (m) = 2.50 × 10�6; g* = gM (m/s2)/gN (m/s2) = 1

ρ (kg/m3) σ (Pa) C (Pa) μ v (m/s)Brittle Materials (Quartz Sand and Glass Bead)

Model (M) 1.25 × 103 2.50 × 102 3.82 × 102 0.40–1.00Nature (N) 2.50 × 103 5.00 × 107 6.00 × 107 0.60–0.85

ρ* σ* C* μ*M/N 0.5 5.00 × 10�6 6.37 × 10�6 ~1.00

Silicone Polymer

Model (M) 9.60 × 102 2.12 × 104 3.33 × 10�6

Nature (N) 1.95 × 103 1019 1.13 × 10�9

ρ* σ* η* ε* v*M/N 0.49 2.5 × 10�6 2.12 × 10�15 1.18 × 109 2.95 × 103

Table 1. Physical Properties of Analog Materials (Integrated From Kranta [1991], Gutscher et al. [1996, 1998], Yagupskyet al. [2008], Reddy et al. [2013] and Our Tests)

Properties\Material White Quartz Sand Glass Bead Silicone Polymer

Grain size (mm) 0.125–0.225 0.100–0.400 —Density (ρ) (kg/m3) 1.56 × 103 2.50–3.00 × 103 9.60 × 102

Angle of internal friction (Ф1) 35.5° 28.3–30.0° —Coefficient of internal friction (μ) 0.4–1 ~0.4Angle of dynamic stable friction (Фd) 31.2° — —Cohesion (C) (Pa) 3.82 × 102 9.90 × 10Viscosity (η) (Pa s) — 2.12 × 104 (22°C)Exponent 1 (Newtonian fluid)

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For normal gravity experiments gM= gN and g* = 1. Considering ρ* = 0.5, from the above equation, the stressscaling ratio σ* can be directly obtained [Corti et al., 2003; Bonini et al., 2012]. Note that by having the samedimensions of stress, the cohesion must have a similar scaling ratio; i.e., C* =CM/CN= σ* (Table 2). In nature,the coefficient of internal friction μ varies between 0.6 and 0.85 and shares similar values of 0.40–1.00 for quartzsand and glass beads (Table 2) [Byerlee, 1978; Brace and Kohlstedt, 1980; Corti et al., 2003; Bonini et al., 2012].

The tectonic model simulates formation of themultilayer overthrust system in competent-incompetent inter-layer sequences such as in the South China Block, North America, and other representative orogenic belts(Figures 1 and 2). The sandbox model is composed of interlayers of colored sand and siliconepolymers/glass beads over a flat sheet, simulating sedimentary sequences from the basement/basementunconformity through the cover sequence. The stratigraphy for the four starting conditions for the modelsis illustrated in Figure 2 and consists of eight or more material layers from bottom to top.

The model layers include (Figure 3).

A homogeneous sand layer only incorporated inModel 1: a 1.0 cm thick colorful sand layer with identical physicalproperties, which we will refer to as the metamorphic basement.

L1, a 0.2 cm thick basal layer of silicon polymer, representing an incompetent layer at the basement unconfor-mity between the metamorphic basement and cover, has potential for development as basement-coverdecollement fault.

L2, L4, L6, and L8 are 0.6, 0.8, 1.0, and 1.3 cm thick sand layers, respectively, of various colors but identicalphysical properties, which we will refer to as a competent layer of limestone and sandstone.

L3, L5, and L7 are 0.3, 0.5, and 0.3 cm thick layers of silicone polymer, respectively, representing incompetentlayers of shale, which have the potential for development as decollements.

3. Sandbox Modeling Results

We ran four experiments (Figures 3a–3d) designed to investigate the development and transitions between fault-related fold styles in a multilayer decollement fault system in the case of no denudation. We use various para-meters, including sand grain moving velocity, shortening, and vorticity, to constrain the changing geometry ofthe orogenic wedge. The purpose of the experiments is to examine the transitions between decollement folds,fault-propagation folds, and the assemblage of structures for the multilayer decollement fault-related fold-thrust system.

Based on previous works [Storti et al., 1997], our models are designed to examine several effects during thetransitions of fault-related folds. (1) We vary the manner in which forces are applied to the model, which con-trols the strength of the decollement (Figures 3a–3c versus Figure 3d). (2) We design four models with lengthof 74 cm and total shortening from ~20% to ~36% to investigate the relationship between the structural styleand model scales. (3) We test layer selections of the decollement fault by comparing thick basal homoge-neous sand layer in model 1 with no basal sand layers in models 2 and 3 and comparing right baffles in mod-els 1 and 2 with free right boundary. (4) In model 4, we test layer selection of the decollement fault using glassbeads to replace the silicone polymer. (5) We distinguish phases of progressive deformation based on differ-ent length changing of all layers with representative structural style or assemblage for each of the four mod-els. (6) Finally, we test model reproducibility by running two more duplicate experiments for each of the fourmodels. For all models, we do not introduce syn-shortening erosion and sedimentation into our experiments.We use the first subscript number to differentiate themodels in Figures 3a–3d and the second subscript num-ber to differentiate formational sequence of faults (F) and folds (f) in each of the model, e.g., F2-3 and f2-3represent the third forming fault and fold in the Model 2, respectively.

3.1. Model 1 Results

Model 1 contains four silicone polymer layers (L1, L3, L5, and L7) interlain with four sand layers (L2, L4, L6, andL8) and a thick basal layer of homogeneous sand under L1, which was designed to represent the basement.The pressure along the left side of the baffle is applied through the experiment with a total of 20.3% appliedshortening (15 cm shortening for an initial model length of 74 cm) (Figure 3). Ultimately, three phases ofprogressive deformation are distinguished. A fold-thrust belt is produced with four separate thrust flats along

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the homogeneous sand layer and L7, and decollement fold, fault-propagation fold, complex fold, and imbri-cate thrust (Figure 4).

Phase one has model shortening from 0% to ~5.4% (Figures 4a–4c, 5a, and 6 (a–c)). Decollement fault F1-1 initi-ates along the bottom of model 1 (equivalent to an incompetent layer within the basement) and immediatelydevelops into flat-ramp type with a fault ramp cutting upward and development of a decollement-buckle foldf1-1 in the hang wall (Figures 4a–4c). The eight layers show consistent shortening (Figure 5a). There are obviousgrain velocity differences (VED) and vorticity differences (VOD) between the hanging wall and footwalls of theinitial F1-1 tips with VED at 0.0018 s�1 and VOD at 0.2880 s�1, respectively (Figure 6 (a) and Table 3). Neitherobserved fault nor VEDs and VODs occurred along L3, L5, or L7 (Figures 4a–4c and 6 (a–c)).

Phase two has model shortening from ~5.4% to ~14.9% (Figures 4d, 4e, 5a, and 6 (d and e)). Flat-ramp typefaults F1-2 and F1-3 are sequentially formed along L7 with fault-propagation folds f1-2 and f1-3, respectively.Association of F1-2-f1-2 and F1-3-f1-3 produces forward-propagating imbricate thrusts (Figures 4d and 4e).During this phase all eight layers keep constant layer length at ~70 cm, indicating a cylindrical folding process(Figure 5a). Continued compression results in breaking out at the base of the F1-1 ramp into L1 and formationof flat fault F1-4 and decollement fold f1-4 (Figures 4e and 6 (e)). There are smaller grain VEDs and VODsbetween the hanging wall and footwall of faults F1-2 and F1-3, which have fault tip VEDs at 0.0013,0.0010mm/s, fault tip VODs at 0.2681, 0.2794 s�1, respectively (Figure 6 (d and e) and Table 3).

Phase three has model shortening from ~14.9% to ~20.3% (Figures 4f, 4g, 5a, and 6 (f and g)). The compressionresults in a transition of f1-3 from fault-propagation fold to fault-bend fold as F1-3 cuts upward and forms a new flat(Figures 4e and 4f). Subsequent formation of fault F1-5 and fault-propagation fold f1-5 along L7, together with F1-1,F1-2, and F1-3 forms an imbricate fan. Simultaneously, f1-4 is transformed from decollement fold to fault-propagation fold to produce a passive duplex with roof underthrust along L7 and floor thrust along L1(Figure 4g). During this phase there are distinctions in layer deformationwith elongation of L7-L8while shorteningof L1-L6 (Figures 4g and 5a). There are smaller grain VED of 0.0012mm/s and VODs of 0.2971 s�1 between thehanging wall and footwalls of the F1-5 fault tip, respectively (Figure 6 (f and g) and Table 3).

From Phases one to three, each of sequential five faults is initiated with decollement along incompetentlayers, followed by the thrust cutting up through a competent layer into an overlying incompetent layer,to form a flat-ramp-flat type trajectory for the advancing fault tiplines (Figures 4 and 6). The VEDs betweenhanging wall and footwall of the initial fault tip (Vdift1) reduce gradually with trend equations, which arededuced using trend line simulation in Microsoft Excel (Figure 7a and Table 3):

Figure 4. (a–g) Pictures with fault-fold interpretation of Model 1 are selected when major faults initial.

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Vdift1 ¼ 0:001N2 � 0:008Nþ 0:0025 (4)

where N is the modeling stages, corre-sponding to a, b, c, d, … in Table 3 andFigures 4 and 6. The VODs between thehanging wall and footwall keeps constantat ~0.30 for initial fault tip (Figure 8a).

From Phases one to three, the basementis gradually raised by the formationand progressive slip of F1-1 along thehomogeneous sand layer. Sequentialfault-propagation folds f1-2, f1-3, and f1-5,which are transformed from initial decol-lement folds, combine together to pro-duce an imbricate fan (Figures 4b–4e). Adeep passive duplex is produced by theformation of roof thrust along L7 andfloor thrust along L1 with structuralassemblage of f1-4–F1-4 (Figures 4e–4g).The changing of eight layer lengthsfrom uniform shortening to stablecorresponds to transition from fault-propagation fold to imbricate thrust,while from stable to differentiation ofshortening and elongation correspondsto formation of imbricate thrust and pas-sive duplex (Figures 4 and 5a).

3.2. Model 2 Results

Unlike Model 1, the Model 2 designdoes not include a basal sand layer thatrepresents the homogeneous basement.Model 2 is set with four silicon polymerlayers at L1, L3, L5, and L7 interlayeredwith sand layers L2, L4, L6, and L8,respectively. The pressure along the leftside of the baffle is applied throughoutthe experiment with total model short-

ening of 35.1% (26 cm shortening for model length of 74 cm). Ultimately, a multilayer fault-related fold withfive separate thrust flats along L1 and L7, decollement folds, fault-propagation folds, fault-bend folds, imbri-cate thrust, and duplex is produced after three phases of progressive deformation (Figure 9).

Phase one has a model shortening from 0 to ~4.9% (Figures 5b, 9a, and 9b). Decollement fault F2-1 initiatesalong L1 and immediately develops into a flat-ramp type with the fault ramp cutting upward and formingfault-propagation fold f2-1 at the fault tip (Figures 9a and 9b). The eight layers show consistent shorteningmagnitudes (Figure 5b). There are obvious differences in grain VED and VOD between the hanging walland footwall of the F2-1 with VEDs at 0.0014mm/s and VODs at 0.1921 s�1 for the initial fault tip, respectively(Figure 9b and Table 3). Neither observed fault nor VED and VOD occur along L3, L5, or L7 (Figures 9a, 9b, and10 (a and b)).

During Phase two, the model shortens from ~5.0% to ~20.2% (Figures 9c–9e and 5b). Flat-ramp type fault F2-2with corresponding fault-propagation folds f2-2 is formed. F2-1 and F2-2 produce a forward-propagation ofimbricate thrusts (Figures 9c–9e). Continued compression results in breaking out at the base of the F2-1 rampinto L1 and formation of backthrust in the footwall (Figures 9c and 9d). During this phase, each of layers has

Figure 5. Layer lengths variation versus model shortening in the compres-sion of Model 1, Model 2, Model 3, and Model 4.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2095

slightly shortened ~3%, indicating deformation of major cylindrical fold (Figure 5b). There are smaller grainVED and VOD between the hanging wall and footwall of fault F2-2, which have initial fault tip VEDs at0.0008mm/s, initial fault tip VODs at 0.2355 (Figure 10 (c and e) and Table 3).

Phase three has model shortening from ~20.2% to ~35.1% (Figures 9f–9h, 5b, and 10 (f and h)). The continuedcompression results in in-sequence development of imbricate thrusts with fault-propagation fold F2-3-f2-3 alongL7 (Figures 9f–9h). Simultaneously, decollement fault along L1 is forced to cut upward with flat-ramp-flat typeF2-4 and to transform to passive duplex with a roof thrust along L7 and a floor thrust along L1 (Figures 1d and9f–9h). The upward cutting F2-2 refolds the imbricate thrusts F2-2-f2-2 and F2-3-f2-3 and produces a newfault-propagation fold F2-5-f2-5 with thrust along L7 (Figures 9f–9h). During this phase there are differentialstrains to the layers with elongation of L7-L8 and shortening of the L1-L6 (Figures 9f–9h and 5b). There aremuch smaller grain VEDs at 0.0008, 0.0004, and 0.0004mm/s for initial fault F2-3, F2-4, and F2-5 tips (Figure 7b). However, the VODs remain consistent at 0.2432–0.2593 s�1 for initial fault F2-3, F2-4, and F2-5 tips (Figure 8b).

Through Phases one to three, each of the sequential five faults is initiatedwith a decollement fault along an incom-petent layer and then cuts upward through a competent layer to form a ramp by fault tips spreading (Figures 9and 10). The VEDs between the hangingwall and footwall of the initial fault tip (Vdift2) gradually reduce, fittingwithtrend equations, which is deduced using trend line simulation in Microsoft Excel (Figure 7b and Table 3):

Vdift2 ¼ 0:00006N2 � 0:0006N þ 0:0019 (5)

where N is the modeling stage, corresponding to a, b, c, d, … in Table 3 and Figure 7.

The VOD between the hanging walls and footwalls remains constant at 0.1921–0.2593 for initial faulttip (Figure 8b).

Figure 6. PIV results with fault-fold interpretation show the (left column) section distribution of grain velocity and (right column) vorticity for stages a–g of Model 1.Stages a–c, c–e, and e–g correspond to phases one, two, and three in Figure 5a, respectively.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2096

Through Phases one to three,sequential fault-propagation foldsf2-2 and f2-3, which are transformedfrom initial decollement folds, com-bine together to produce an imbri-cate thrust fan (Figures 9d–9h), anda passive duplex is produced bythe formation of a roof thrust alongL7 and floor thrust along L1 withstructural assemblage of f2-4-F2-4(Figures 9f–9h). Further deformationof the F2-4-f2-4 not only refolds butalso transfers forward the imbricatethrust fan (Figure 9). The changingof eight layer lengths from uniformshortening to stable correspondsto transition from fault-propagationfold to imbricate thrust, while fromstable to differentiation of shorten-ing and elongation corresponds toformation of imbricate thrust andpassive duplex (Figures 9 and 5b).

3.3. Model 3 Results

Model 3 is composed of four sili-cone polymer layers L1, L3, L5, andL7, interlayered with sand layersL2, L4, L6, and L8, respectively. Forcomparison with Models 1 and 2,we design a free boundary on theright side (foreland) of the modelsetup, with homogeneous sandlayers replacing the silicone poly-mer layers in the final 6 cm of themodel (Figure 3c). The pressurealong the left side of the baffle isapplied through the experimentwith a total of 35.1% shorteningapplied to the model (26 cm short-ening for model length of 74 cm).Ultimately, a multilayer fault andfault-related fold systemwith sevenfaults along L1 and L7, decollementfolds, fault-propagation folds, imbri-cate thrusts, and passive duplex areproduced after three phases of pro-gressive deformation (Figure 11).

Phase one has a model shorteningfrom 0 to ~5.4% (Figures 5c, 11a,and 11b). Decollement fault F3-1initiates along L1 and immediatelydevelops into a flat-ramp typewiththe fault ramp cutting upward andTa

ble

3.Th

eVe

locity

Differen

ces(VED

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dVo

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Differen

ces(VODs)forInitialFaultTips

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cea-velocity

a-vo

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b-velocity

b-vo

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c-velocity

c-vo

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d-vo

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e-velocity

e-vo

rticity

f-velocity

f-vo

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g-velocity

g-vo

rticity

h-velocity

h-vo

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i-velocity

i-vorticity

j-velocity

j-vorticity

Mod

el1

F 1-1

0.00

180.28

800.00

220.28

350.00

270.27

910.00

120.27

910.00

460.27

910.00

350.27

91F 1

-20.00

130.26

810.00

110.27

910.00

170.27

910.00

130.27

910.00

100.27

91F 1

-30.00

100.27

940.00

230.27

600.00

210.35

010.00

180.42

41F 1

-50.00

120.29

710.00

100.27

91Mod

el2

F 2-1

0.00

110.19

210.00

090.51

860.00

090.25

930.00

070.00

000.00

050.00

000.00

090.00

000.00

170.25

93F 2

-20.00

050.22

150.00

09(0.5186)

0.00

090.25

930.00

090.25

930.00

090.25

93F 2

-30.00

040.24

320.00

090.25

930.00

17(0.5186)

F 2-4

0.00

040.24

320.00

090.25

930.00

17(0.5186)

F 2-5

0.00

050.25

930.00

020.12

96Mod

el3

F 3-1

0.00

200.21

430.00

110.33

880.00

120.36

740.00

130.39

600.00

220.33

880.00

170.19

580.00

110.05

290.00

110.04

790.00

080.32

77F 3

-20.00

130.23

160.00

120.22

800.00

110.22

440.00

110.20

860.00

110.10

430.00

110.00

010.00

110.00

030.00

100.00

23F 3

-30.00

110.20

810.00

110.22

440.00

110.20

870.00

110.10

440.00

110.00

020.00

110.00

040.00

110.00

07F 3

-40.00

110.23

480.00

110.22

440.00

110.22

440.00

110.22

440.00

110.22

440.00

140.22

44F 3

-50.00

100.22

440.00

110.22

440.00

110.22

440.00

080.22

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060.22

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-80.00

080.24

670.00

050.22

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F 4-1

0.00

040.07

550.00

040.07

86(0.0004)

(0.0786)

(0.0004)

(0.1572)

(0.0004)

(0.1572)

(0.0008)

(0.1572)

(0.0006)

(0.0786)

(0.0004)

0.15

72(0.0000)

0.07

86F 4

-20.00

010.07

86(0.0004)

(0.1572)

(0.0004)

(0.1572)

(0.0009)

(0.1572)

(0.0007)

(0.1538)

(0.0004)

0.07

86(0.0000)

(0.0786)

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0.00

020.07

76(0.0002)

(0.1572)

(0.0003)

(0.1572)

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1)0.06

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s

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2097

forming fault-propagation fold f3-1 in the hang wall (Figures 11a and 11b). The eight layers show consistentshortening magnitudes during this stage (Figure 5c). There are obvious differences in grain VED and VODbetween the hangingwall and footwall of the F3-1 with VED at 0.0020mm/s and VOD at 0.2143 s�1 for the initialfault tip, respectively (Figure 12 (a and b) and Table 3). Neither observed fault nor VED and VOD occurred alongL3, L5, or L7 (Figures 11a, 11b, and 12 (a and b)).

Phase two has model shortening from ~5.4% to ~23.0% (Figures 5c and 11c–11f). Flat-ramp type faults F3-2,F3-3, F3-4, and F3-5 were sequentially formed with fault-propagation folds f3-2, f3-3, f3-4, and f3-5, respectively.F3-2-f3-2, F3-3-f3-3, F3-4-f3-4, and F3-5-f3-5, combined with F3-1-f3-1, produce an in-sequence imbricate thrustfan (Figures 11c–11f). During this phase, shortening of the layers is of similar magnitude with exception ofL8 which has slightly shortening of ~3%, indicating a deformation of major cylindrical fold (Figure 5c).There are gradually smaller grain VEDs for initial fault F3-2, F3-3, F3-4, and F3-5 tips at 0.0013, 0.0011, 0.0011,and 0.0010mm/s (Figure 7c and Table 3), while relatively stable VODs for initial fault tips for F3-2, F3-3, F3-4,and F3-5 of 0.2316, 0.2081, 0.2348, and 0.2244 s�1, respectively (Figure 8c and Table 3).

Phase three has model shortening from ~23.0% to 35.1% (Figures 5c, 11g–11j, and 12 (g and j)). During thisstage, a new decollement fault F3-6 breaks out in the footwall and cuts upward with flat-ramp-flat type toform a duplex, which is of passive-roof type with thrust along L7 (Figures 1e and 11g–11j). The formationof the passive roof duplex leads to faulting and folding of F3-2-f3-2, F3-3-f3-3, and F3-4-f3-4 and complexity ofthe imbricate thrust system (Figures 11g and 11h), and the forward new formation of fault-propagation

Figure 7. Velocity difference (VED) of the initial fault tips for the formation of each of the faults in Model 1, Model 2, Model3, and Model 4, respectively.

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F3-8-f3-8 along L7, and the formation of a flat-ramp thrust F3-7 along L6 with back thrusting at the free right-end side boundary (PIV is unable to monitor this area, subjecting to its effective monitoring width of ~60 cm)(Figures 11g and 11h). The formation of imbricate thrusts results in layer length differentiation with no lengthchanges of L7-L8, while L1-L6 shorten (Figure 5c). F3-8 has VED at 0.0008mm/s and VOD at 0.2467 s�1 forinitial fault tips, respectively (Figure 11j and Table 3).

From Phases one to three, each of seven sequential faults (except F7) is initiated with a decollement faultforming along an incompetent layer and then cutting upwards across a competent layer to form a flat-ramptype by propagating the fault tips (Figures 11 and 12). The VEDs between hanging wall and footwalls of theinitial fault tip (Vdift3) reduce gradually, fitting with trend equations, which is deduced using trend line simu-lation in Microsoft Excel (Figure 7c and Table 3):

Vdift3 ¼ 0:00006N2 � 0:0006N þ 0:0024 (6)

where N is the modeling stages, corresponding to a, b, c, d, … in Table 3 and Figure 6 (c). VOD between thehanging wall and footwalls remains constant at 0.21–0.24 s�1 for the initial fault tip (Figure 8c).

From Phases one to three, sequential fault-propagation folds f3-1-f3-5 and f3-8 combine together to producean imbricate thrust fan (Figures 11c–11j). A passive duplex is produced by the formation of a roof thrust alongL7 and a floor thrust along L1 with structural assemblage of f3-6-F3-6 (Figures 11e–11j). The deformationresponse of the eight layers change from uniform shortening to stable, corresponding to the transition from

Figure 8. Vorticity difference (VOD) of the initial fault tips for the formation of each of faults in Model 1, Model 2, Model 3,and Model 4, respectively.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2099

fault-propagation folding to imbricate thrusting, followed by a change from stable to differentiation of short-ening and elongation corresponds to formation of passive duplex (Figures 5c and 11).

3.4. Model 4 Results

Model 4 consists of four layers of glass beads L1, L3, L5, and L7, interlayered with sand layers L2, L4, L6, and L8,respectively. For comparison with the Models 1–3, we use glass bead layers in place of silicone polymer layersand place this model on a canvas sheet lain on the flat basal plate. Similar to Model 3, we use a free boundaryfor the right-end side of the model (Figure 3d). Hinterland-ward traction along the interface between thecanvas and the base of the analog materials produces horizontal compression resulting in sequentialdeformation of the model up to 31.1% total shortening (23 cm shortening for model length of 74 cm)(Figure 13). Ultimately, a single decollement is developed along L1 with sequential decollement folds,fault-propagation folds, imbricate thrusts, and a back thrust are produced after two phases of progressivedeformation (Figure 13).

Phase one has model shortening from 0 to 10.8% (Figures 5d and 13a–13c). Decollement fault F4-1 initiatesalong L1 immediately develops into a flat-ramp type with fault ramp cutting upward and forming fault-propagation fold f4-1, which then cuts through upward and forms the upper fault flat (Figure 13a–13c).These eight layers show a broadly similar shortening, indicating layer-parallel shortening (Figure 5d). Thereare obvious grain VED and VOD between the hanging wall and footwall of the F4-1 with VED at0.0004mm/s and VOD at 0.0755 s�1 for the initial fault tip, respectively (Figure 14 (a and c) and Table 3).

Phase two has model shortening from 10.8% to ~31.1% (Figures 5d and 13d–13j). Flat-ramp type faults F4-2,F4-3, and F4-4 and corresponding fault-propagation folds f4-2, f4-3, and f4-4 are sequentially formed by repeat-ing the forming process of F4-1-f4-1, respectively. Phases one and two faults show sequential forward imbrica-tion (Figures 13–13j). During this phase, there is differentiation in layer lengths with slight elongation ofL7-L8, fluctuating of shortening and elongation for L6, and continued shortening for L1-L5 (Figure 5d).There are grain VEDs for initial fault F4-2, F4-3, and F4-4 tips at 0.0001, 0.0002, and 0.0001mm/s (Figure 7d andTable 3), while relatively stable VODs for initial fault F4-2, F4-3, and F4-4 tips at 0.0786, 0.0776, and 0.0657 s�1

(Figure 8d and Table 3), respectively.

During Phases one and two, each of four sequential faults is initiated first as a decollement along incompe-tent layer L1, which then cuts upward through the competent layer to form flat-ramp type by propagating

Figure 9. (a–h) Pictures with fault-fold interpretation of Model 2 are selected whenmajor faults initial. Stages a–b, b–e, ande–h correspond to phases one, two, and three in Figure 5b, respectively.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2100

the fault tips (Figures 13 and 14). The VEDs of the initial fault tip (Vdift4) between hanging wall and footwallreduce gradually fitting with trend equations, which is deduced using trend line simulation in Microsoft Excel(Figure 7d and Table 3):

Vdift4 ¼ �0:000001N2 � 0:0001N þ 0:0005 (7)

N is the modeling stages, corresponding to a, b, c, d, … in Table 3 and Figures 7 and 13. VOD between thehanging wall and footwall keeps constant at 0.065–0.078 s�1 for initial fault tip (Figure 8d).

During Phases one and two, sequential fault-propagation folds f4-1-f4-4, which are transformed from initialdecollement folds, combined together to produce an imbricate thrust (Figures 13d–13j). The lengths of theeight layers gradually change from shortening to differentiation of shortening and lengthening, correspond-ing to the formation of fault-propagation folds to imbricate thrusts, respectively (Figures 13 and 5d). A lot ofthe layer-parallel shortening, which is converted by the gradients in velocity within a layer and within a singlethrust sheet, takes place not in front of the propagating thrust as the dislocationmodel for thrust propagationsuggests but rather once the thrust ramp is established (Figure 14).

Figure 10. PIV results with fault-fold interpretation show the section distribution of (left column) grain velocity and (rightcolumn) vorticity for stages a–h of Model 2.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2101

4. Discussion4.1. Incompetent Layer and the Formation of Multilayer Decollement Fault

Decollement faults develop along incompetent layers within a sequence of competent-incompetent inter-layers [Miller, 1973; Chester, 2003; Yan et al., 2003a, 2003b, 2011]. Incompetent ductile layers, interlayered withcompetent layers, can form multiple levels of decollement and accommodate it to the interspaces deter-mined by the more competent layers [Williams, 1961; Byerlee, 1978]. Incompetent layers can be identifiedby differences in their structural styles to those of competent layers in nature, as well as by recognition oflithologies that show weak rock strength parameters during experimental rock mechanic analysis [Dominicand McConnell, 1994; Chester, 2003; Yan et al., 2003a, 2009]. Therefore, the study of alternating incompetentand competent layers could uncover the significant role of the weak layers in providing multiple decollementhorizons and thus providing a solution for such structural complexities [e.g., Bonini, 2001; Costa andVendeville, 2002; Couzens-Schultz et al., 2003].

Scaled stratigraphic sequences have been constructed of anisotropic multilayers with individual layers ofsand serving as analog materials of competent carbonates or sandstones and silicone polymer or glass beadserving as incompetent pelites, respectively [Dixon and Tirrul, 1991; Bonini, 2001; Couzens-Schultz et al., 2003](Figure 2). Themodels, deformed by layer-parallel shortening, folding, and thrust faultingmechanisms, repro-duced a number of fold-thrust and strain relationships between incompetent and competent layers found innature [Dixon and Tirrul, 1991]. The models suggested a mechanism of thrust-ramp nucleation followingdecollement folding: long-wavelength buckling of a competent unit can initiate localized strain (foldingand layer-parallel shear) in an underlying incompetent unit, and thrust faults propagate up section fromthese high-strain zones through the foreland-dipping limbs of buckle folds in the competent unit [Dixonand Tirrul, 1991; Bonini, 2001; Couzens-Schultz et al., 2003].

Our four models are designed based on well-studied fold-thrust belt in the South China Block [Yan et al.,2003a, 2009, 2011; Zhou et al., 2002, 2008]. The results reveal the different roles of the incompetent layersin a multilayer system with sequentially formed decollement faults F1, F2, F3, and F4. The first forming fault(F1) initiates along the lowest incompetent layer followed by growth of a steep fault ramp, regardless ofthe thickness, depth, and physical properties of the weak layer (Figures 4, 9, 11, and 13). The subsequent

Figure 11. (a–j) Pictures with fault-fold interpretation of Model 3 are selected whenmajor faults initial. Stages a–b, b–f, andf–j correspond to phases one, two, and three in Figure 5c, respectively.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2102

decollements form either along the uppermost incompetent layer as in Models 1–3, where this layer has alinear viscous rheology (silicone polymer), or along the lowest incompetent layer in Model 4 representedby a glass bead layer, which behaves as a Mohr-Coulomb material (Table 1). Therefore, the development ofthe decollement fault depends on the rheological difference between incompetent and competent layers.

In each of the models, the VED of the initial fault tip between the hanging wall and footwall has the highestvalues for the first produced flat-ramp type faults and then gradually reduce for the subsequent fault formationwith a quadratic power function (equations (4), (5), (6), and (7) associated with the modeling stage, while theVOD of the initial fault tip is relatively stable at 0.2–0.3 s�1 for all of the fault formation (Figures 7 and 8 andTable 3). Therefore, as the decollement faults successively propagate, the VED follow a regressive quadraticpower function, while the VOD values remain relatively constant at 0.2–0.3 s�1 (except VOD for Model 4 stablesat 0.06–0.08 s�1); this suggests that the successive faults are developedmore easily through time in amultilayerdecollement fault system. We interpret this to indicate that the system is evolving toward a greater componentof gravitational force relative to horizontal “end-load” compression, which ismanifest in a lesser amount of earlylayer-parallel shortening prior to formation of a new thrust imbricate.

4.2. Genetic Affiliation of Fault-Related Fold Structural Style in Multilayer Thrust Belt

In all four models, each of decollement faults is initially produced as a thrust flat with a decollement foldalong an incompetent layer, followed by upward propagation of the fault as a ramp cutting through the

Figure 12. PIV results with fault-fold interpretation show the section distribution of (left column) grain velocity and (right column) vorticity for stages a–j of Model 3.

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YAN ET AL. SANDBOX MODELING THE FOLD-THRUST BELTS 2103

competent layer and the evolving hanging wall fault-propagation fold [Storti et al., 1997]. Further deforma-tion produces a fault-bend fold as the fault tip cuts through the competent layer and flattens into a higherincompetent layer and redeforms the older fault-propagation fold, forming a compound anticline. This tran-sition of structural style is similar to that described by Storti et al. [1997] and Costa and Vendeville [2002].Simultaneously, forward deformation forms younger decollement folds and fault-propagation folds insequence (Figures 4, 9, 11, and 13). Therefore, the initial decollement fold and fault-propagation fold, subse-quent fault-bend fold, and in-sequence younger fault-propagation folds are progressively produced by akinematic sequence in a multilayer decollement fault system (Figures 15a–15f).

The in-sequence formed flat-ramp type faults constitute an imbricate thrust with redeformed fault-bend foldsuperposing over new formed fault-propagation fold in all four models (Figures 4, 9, 11, and 13). ComparingFigures 4, 9, and 11 with Figure 13, structural assemblages are essential different. In the case of bigger visc-osity differences between competent and incompetent layers, a passive duplex is produced with roof under-thrust formed by forward developing decollement flat fault of the imbricate thrust along the upmostincompetent layer (L7) and floor thrust formed by the breaking out at the base ramp into L1 (Figures 4, 9,11, and 15g). These results were previously proved and described by Bonini [2001] and Couzens-Schultzet al. [2003]. However, progressive footwall imbrications keep the decollement fault along the basal weaklayer (L1) resulting in in-sequence development of imbricate thrusts, and thus, no duplex is produced inthe case of similar brittle materials to scale the competent and incompetent layers in model 4 (Figure 13).Therefore, the assemblage of the decollement fold, fault-propagation fold, and fault-bend fold producesimbricate thrust, and the breaking out along deep incompetent layer results in formation of passive duplexfor multiinterlayer competent and incompetent layers (Figures 4, 9, 11, and 15g).

In Model 1 the homogeneous sand layer representing the basement is uplifted and potentially denuded alongthe first decollement fault F1-1, which is then overprinted by subsequent deformationwith complicated structuralstyle (Figure 4), indicating the formation of thick-skinned thrust. Subsequent decollement faults, which are pro-duced along the uppermost incompetent layer, are sequentially formed in a manner of forward-propagation,indicating the formation of thin-skinned thrust (Figure 15). Thus, the progressive deformation of the thick-skinned thrust results in the formation of a thin-skinned thrust, most likely along the upper weakest incompetentlayer with bigger viscosity difference between competent and incompetent layer.

Figure 13. (a–j) Pictures with fault-fold interpretation of Model 4 are selected when major faults initial. Stages a–c and c–jcorrespond to phases one and two in Figure 5d, respectively.

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In summary, four sandbox modeling experiments consistently reveal a progressive genetic and kinematicconnection between different structural styles and assemblage types in a multilayer decollement system inthe South China block. Formation of the thick-skinned thrust depends on initial basement involvement,and progressive deformation involves a special decollement fault along selected incompetent layers withan in-sequence thin-skinned thrust progression showing a structural sequence of decollement fold, fault-propagation fold, fault-bend fold, and imbricate thrust. A passive duplex is produced in the case of breakingout of deep incompetent layer (Figures 15f and 15g).

The manner in which the load is applied to the sandbox has a significant influence on the way in which themodel deforms. For the cases with the end load (Models 1 to 3), there is a concentration of deformation at theedge of the model, with much layer-parallel shortening. This is likely required in order to transfer the stressthrough the analog model by developing a significant forward dipping topographic slope.

The coexisted structural styles and assemblages, which were identified in fold-thrust belts in Appalachianorogenic belt and the other representative orogenic belts, are similar to the fold-thrust belt in the South

Figure 14. P PIV result with fault-fold interpretation show the section distribution of (left column) grain velocity and (right column) vorticity for stages a–j of Model 4.

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Figure 15. Proposed kinematic model with initial decollement fold and following converting, thick-skinned thrust trigger-ing imbricate thrust and duplex to form the thin-skinned thrust. (a and b) Deformational phase one, (d and f) phase two,and (g) phase three in Models 1–3. (c and e) Seismic profiles with corresponded structural styles in the kinematic model andlocations in Figure 2a and the insert in Figure 2 of tectonics outline of the South China (modified from Yan et al., 2003a, 2009and Dong et al. [2015]; see text for discussion).

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China block (Figure 2) [Miller, 1973; Boyer and Elliot, 1982; Chester, 2003; Yan et al., 2003a, 2003b, 2008, 2009,2011; Zhou et al., 2002, 2008]. Thus, the modeling results in this paper have implications for the quantitativeunderstanding of the progressive genetic and kinematic connection between structural styles and assem-blages within these representative fold-thrust belts.

4.3. Proposed Kinematic Model for Transition of the Fault-Related Folds

The structural styles or assemblages of fault-related folds in fold-thrust belts are variable [Boyer and Elliot,1982; Yan et al., 2003a, 2009; Pfiffner, 2006]. However, the multilayer decollement thrust system generallyincludes both a thick-skinned thrust belt and a thin-skinned thrust belt, which include in-sequence imbricatethrusts and passive duplexes with variable styles of fault-related folds (Figure 2). Our sandbox modelingresults reveal the genetic relationship between different deformational phases with structural styles andassemblages during progressive horizontal compression (Figures 4, 9, 11, and 13). Comparing the sandboxmodeling results in this study and representative geological sections of orogenic belts in Figure 2, wepropose a progressive kinematic model (Figure 15).

1. Interlayer of competent and incompetent layers above metamorphic basement. Based on strata columnin fold-thrust belt in the South China [Yan et al., 2003a, 2009], the Cumberland Plateau and Valley andRidge Province of the Southern Appalachians [Hatcher, 1989; Pfiffner, 2006] and Moine and Aplsorogenic belts [Boyer and Elliot, 1982] (Figure 2), sedimentary or metasedimentary rocks overlie crystallinebasement; i.e., basement-cover sequences are established (Figure 15a). During deformation, thebasement with crystalline metamorphic rocks is treated as heterogeneity, while the cover sequences,which are represented by the interlayer of competent and incompetent layers, are characterized byinteraction change of rock mechanical properties (Figure 15a).

2. Initial decollement and fault-propagation fold. The horizontal compression initiates decollement fault F1along a weak layer within the basement with formation of fold f1, which is immediately converted intofault-propagation fold f1 by upward breaking the basement of the F1 (Figure 15b). The involvement ofthe metamorphic basement of the Neoproterozoic Banxi Group implies formation of thick-skinned thrust,which include typical decollement fold and converted fault-propagation fold in the South China intraplateorogenic belt [Yan et al., 2003a; Dong et al., 2015] (Figure 15c).

3. Initial imbricate thrust. Progressive development of the F1 results in (1) upward fault ramp cutting throughthe cover layers and uplifting basement by tightening and thrusting over the initial fault-propagation foldf1 (comparing with Figure 15c), (2) formation of a new flat-ramp fault F2 along the upmost incompetentlayer with decollement fold f2, which is immediately converted to fault-propagation fold f2 by fault tipupward cutting to the competent layer, and (3) initial imbricate thrust by combining F1-f1 and F2-f2together (Figures 15d and 15e).

4. Initial fault-bend fold and deep propagation fold. Continued compression results in (1) forwardformation of fault-propagation fold f3 and transiting f2 to fault-bend fold, (2) breaking out at the baseof the F1 ramp into the lowest incompetent layer (L1) with formation of fault-propagation fold f4, and(3) formation of thin-skinned thrust belt with multilayer decollement faults (Figure 15f). Thus,forward formation of fault-propagation fold and following transiting of fault-bend fold are properlyinterpreted the coexisting of both structural styles in seismic profiles in the South China intraplateorogenic belt (Figure 15e).

5. Initial duplex and forward the imbricate thrust. Continued compression facilitates, (1) forward propaga-tion fold f5, (2) developing of the imbricate thrust with combination of F1-f1, F2-f2, F3-f3, and F5-f5, and(3) formation of the duplex by F4 upward cutting through competent layers and detaching along incom-petent layers with flat-ramp type (Figure 15g). This duplex has passive roof thrust and in-sequence kine-matic process and thus belongs to passive roof or in-sequence duplex (Figures 1e, 15e, and 15g).

Although the effects of syn-shortening erosion and sedimentation are not considered [Bonnet et al., 2007,2008; Graveleau, 2008], kinematic model with initial decollement fold and following converting is quantitativeproved by the sandbox modeling. The converting includes thick-skinned thrust triggering imbricate thrustand duplex to form the thin-skinned thrust. This kinematic model has essential implications to understandthe forming process for the coexist structural styles and assemblages in representative fold-thrust belts inthe Southern Appalachians, Moine, thrust zone, and Alpine orogenic belts [Boyer and Elliot, 1982; Hatcher,1989; Butler, 2004; Pfiffner, 2006] (Figures 2d and 2e).

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5. Conclusions

Fault-related folds including decollement folds, fault-propagation folds, and fault-bend folds, together withthrust assemblages of imbricate thrusts and duplexes, are common elements in fold-thrust belts throughoutthe representative orogenic belts. Sandbox modeling experiments designed to represent deformation ofa cover sequence of competent-incompetent interlayers overlying a crystalline basement improve ourunderstanding of the sequential development of fault-related folds and associated thrust assemblages. Anew kinematic model with initial decollement fold and its following converting is established in this paper.Decollement folds always initiate along an incompetent layer and are progressively converted to fault-propagation folds and to fault-bend folds by decollements breaking and ramping through competent layersand flattening into upper decollement fault flats, respectively. Thick-skinned thrust F1-f1 is produced byinvolving in the following thrust sequence of initiating decollement fault. Progressive thrusting and upliftingof the thick-skinned thrust trigger the uppermost incompetent decollement with formation and followingconverting of F2-f2, F3-f3, and F5-f5. Passive duplex is formed by formation of decollement fold and followingconverting to fault-propagation and fault-bend folds along the lowest incompetent layer. Imbricate thrustand passive duplex, which involve in cover sequence, constitute the thin-skinned thrust belt. Therefore,the converting of thick-skinned thrust triggering imbricate thrust and duplex to form the thin-skinned thrustis representative for the orogenic belts.

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