Deformation of brittle-ductile thrust wedges in experiments and nature

Authors


Abstract

[1] Even though the rheology of thrust wedges is mostly frictional, a basal ductile decollement is often involved. By comparison with purely frictional wedges, such brittle-ductile wedges generally display anomalous structures such as backward vergence, widely spaced thrust units, and nonfrontward sequences of thrust development. Laboratory experiments are used here to study the deformation of brittle-ductile thrust wedges. Results are compared with natural systems in the Jura Mountains and the northern Pakistan Salt Range and Potwar Plateau. Two series of three models are used to illustrate the effects of varying the basal wedge angle (β) and shortening rate (V). These two parameters directly control variations in relative strength between brittle and ductile layers (BD coupling). Wedges with strong BD coupling (low β and high V) give almost regular frontward sequences with closely spaced thrust units and, as such, are not significantly different from purely frictional wedges. Weak BD coupling (high β and low V) gives dominantly backward thrusting sequences. Intermediate BD coupling produces frontward-backward oscillating sequences. The spacing of thrust units increases as coupling decreases. Back thrusts develop in parts of a wedge where BD coupling is weak, regardless of the thrust sequence. Wedges with weak BD coupling need large amounts of bulk shortening (more than 30%) to attain a state of equilibrium, at which stable sliding along the base occurs. On this basis, we argue that a state of equilibrium has not yet been attained in at least some parts of the Jura Mountains and eastern Salt Range and Potwar Plateau thrust systems.

1. Introduction

[2] It has long been recognized that deformation within foreland thrust wedges at the front of mountain belts strongly depends on the rheology of the geological materials involved, especially when the thrust wedge is detached from its basement along a ductile decollement level. On the other hand, since the early work of Smoluchowski [1909], mechanical theories of thrusting have required simplifications of rock rheology complexities to remain tractable, often leading to models where the entire wedge rheology is considered as either frictional [e.g., Hubbert, 1951; Hafner, 1951; Hubbert and Rubey, 1959; Davis et al., 1983] or viscous [e.g., Elliot, 1976; Ramberg, 1981]. While these types of models explain some aspects of natural thrust systems, it has been pointed out that no single rheology satisfactory explains all the observed geological variables [e.g., Platt, 2000].

[3] The most fruitful approach to thrust system mechanics of the last 20 years, the so-called “critical taper theory” [Chapple, 1978; Davis et al., 1983; Dahlen et al., 1984], explains the overall geometry of Coulomb wedges in terms of internal strength versus basal friction. It is elegantly summarized by Davis et al. [1983, p. 1153] as follows:

The overall mechanics of fold and thrust belts and accretionary wedges along compressive plate boundaries is considered to be analogous to that of a wedge of soil or snow in front of a moving bulldozer. The material within the wedge deforms until a critical taper is attained, after which it slides stably, continuing to grow as constant taper as additional material is encountered at its toe. The critical taper is the shape for which the wedge is on the verge of failure and the horizontal compression everywhere, including the basal decollement.

Various applications were made to natural thrust wedges such as accretionary prisms (e.g., Figure 1a) and foreland thrust belts (e.g., Figure 1b) [Davis et al., 1983; Dahlen et al., 1984; Jaumé and Lillie, 1988; Mitra, 1994; Boyer, 1995; Wang et al., 1996]. Experimental studies support the predictions of the critical taper theory and have also considered structural aspects of thrust kinematics and geometries for particular initial and boundary conditions applicable to natural thrust systems [Davis et al., 1983; Malavieille, 1984; Mulugeta, 1988; Storti et al., 1997; Cobbold et al., 2001]. The internal deformation of Coulomb wedges, in both nature and experiments, is characterized by dominant frontward vergent thrusts with regular narrow spacing and frontward sequences of thrust development.

Figure 1.

Examples of thrust wedge structure: (a) Nankai trough (Japan) (after Moore et al. [1990] as cited by Gutscher et al. [1998]), (b) eastern Chartreuse Massif (France) without basal evaporite layer [after Philippe, 1994], (c) Cascadia accretionary prism (northwest America) [after Gutscher et al., 2001], and (d) southern Jura (France) with basal evaporite layer [after Philippe, 1994]. White arrows indicate sense of basal shear. The Nankai trough and eastern Chartreuse illustrate “normal” structural patterns characteristic of a purely frictional behavior with narrow-spaced and frontward vergent thrusts. In the southern Jura and Cascadia accretionary prism a weak basal decollement is present; they illustrate “anomalous” structural patterns with widely spaced (Figure 1d) or backward vergent (Figure 1c) thrusts. No vertical exaggeration.

[4] Thrust systems that are decoupled from their substratum by weak layers (e.g., salt) or high fluid pressure often display discrepancies compared with Coulomb wedges (Jura Mountains [Laubscher, 1975, 1977; Guellec et al., 1990; Philippe et al., 1996; Burkhard and Sommaruga, 1998], Pyrenees [Vergés et al., 1992; Burbank et al., 1992], Rocky mountains [Frey, 1973], Appalachians [Wiltschko and Chapple, 1977], Moroccan Rif [Morley, 1988, 1992], Arctic Canada [Harrison, 1995], Pakistan Salt Ranges [Crawford, 1974; Johnson et al., 1986; Baker et al., 1988] and the Cascades [Seely, 1977; MacKay, 1995; Gutscher et al., 2001]). The most commonly observed deviations from Coulomb wedges involve backward thrust vergence (e.g., Figure 1c), wide thrust spacing (e.g., Figure 1d) and nonfrontward sequences of thrust development [Laubscher, 1975, 1977, 1992; Davis and Engelder, 1985, 1987; Morley, 1988, 1992; Pennock et al., 1989; Boyer, 1995; Weijermars et al., 1993; Philippe, 1994; Burkhard and Sommaruga, 1998]. These specific characteristics of decoupled thrust wedges can occur separately or combined, and have also been observed in analogue experiments on brittle-ductile systems [Ballard et al., 1987; Philippe, 1994; Letouzey et al., 1995; Tondyi-Biyo, 1995; Corrado et al., 1998; Cotton and Koyi, 2000; Bonini, 2001; Costa and Vendeville, 2002; Lickorish et al., 2002]. Davis and Engelder [1985] tried to reconcile these discrepancies with the critical taper theory assuming a brittle wedge with zero basal friction. This approach explains tapers that are smaller than observed on purely frictional wedges, but does not account for the different internal deformation patterns in terms of vergence, spacing or thrusting sequence.

[5] We present a series of laboratory experiments on brittle-ductile wedge models to study the effects of varying initial wedge angles and strength profiles on internal deformation patterns and final geometry of thrust wedges. A broad spectrum of thrusting patterns is obtained, varying from geometries directly comparable with Coulomb wedges to systems where vergence, spacing and sequence of thrusting are all anomalous compared to Coulomb wedges. Stress analysis shows that thrusting patterns and final wedge geometry depend directly on variations in mechanical coupling between brittle and ductile layers. A quantitative explanation is proposed that relates deformation style to rheology and initial geometry. Results are applied to field examples from the Jura Mountains and Pakistan Salt Range and Potwar Plateau.

2. Model Construction and Deformation

[6] Brittle-ductile models consist of a sand wedge resting on a ductile basal layer made of silicone putty (Figure 2). As shown by cross sections through different fold-and-thrust belts (e.g., Canadian Rockies [Bally et al., 1966], the Appalachians [Boyer, 1995] and Jura (see Figure 1b) [Philippe, 1994; Burkhard and Sommaruga, 1998]), these belts develop from sedimentary basins that are wedge-shaped. Hence we performed our experiments on models with an initial wedge shape (Figure 2). The basal ductile layer is wedge-shaped with a maximum thickness at the backstop of 20% of the total wedge thickness. The wedge shape of the sedimentary basin implies that younger strata extend farther into the foreland. Accordingly, the sand wedge in the experiments extends further from the tip of the ductile layer.

Figure 2.

Experimental apparatus and wedge model geometry.

[7] The modeling apparatus consists of a rigid and variably inclinable table on top of which a rigid wall is pushed upslope at constant velocity by two screwjacks. Although a rigid vertical wall represents the most suitable way to apply a horizontal compressive stress to the model, we are aware of boundary effects inherent to this solution, notably vertical shear parallel to the wall.

[8] In combination with the horizontal surface, the inclined base gives an initial wedge-shape geometry to the model (basal angle β). Since all models have the same initial length of 125 cm, model thickness increases as a direct function of the initial wedge angle β.

[9] Variations in the thickness of both brittle and ductile layers, as a function of basal angle β, have direct mechanical implications. Brittle layer strength directly depends on vertical stress, which is proportional to the sedimentary column weight. Ductile layer strength, for a given viscosity, is a function of shear strain rate, which itself depends on ductile layer thickness as well as displacement rate. To analyze the relative effects of variations in thickness and strain rate, two series of three experiments are presented. The first series investigates the effects of variations in angle β at constant backstop velocity V, and the second series those of variations of backstop velocity V at constant angle β. The experimental results are quantitatively analyzed using strength profiles.

[10] Since the study by Davis et al. [1983], it has been recognized that wedge angles α and β are dynamic parameters determining thrust wedge behavior that can be directly measured from field and seismic data. The maximum β angle observed in fold-and-thrust belts with a basal ductile decollement is of the order of 3° (central Pakistan Salt Ranges [Jaumé and Lillie, 1988; Pennock et al., 1989]). On this basis, we chose β = 3.0° as the highest wedge angle, using β = 0.75° and 1.5° for the other models to cover the range of β values observed in nature. Corresponding model thicknesses at the backstop are 1.7, 3.3, and 6.6 cm, respectively. A bulk shortening of 40 cm (i.e., 32% of the total length) was applied to all models at boundary displacement rates of 1.0, 5.0, and 10 cm/h.

[11] Brittle, i.e., frictional, layers are made up of pure eolean quartz sand from Fontainebleau, France, with a mean density ρ ∼ 1300 kg m−3, negligible cohesion and a coefficient of internal friction ϕ ∼ 0.58. The ductile, i.e., viscous, layers representing potential decollements, are made up of Newtonian silicone putty (Rhodorsil Gomme GS1R RG 7009; Rhône Poulenc Paris), with a viscosity μ = 2.4 × 104 Pa s, at laboratory temperature (29° ± 2°C). Colored sand layers visualize internal deformation in the brittle layers while two colors of the same silicone putty were used as vertical passive markers in the ductile layers.

[12] During deformation, surface photographs were taken at regular time intervals to study the sequence of faulting and the changes in topography. After shortening, the models were wetted and cut parallel to the direction of shortening. Photographs of these cross sections served to analyze internal structures.

3. Experimental Results

3.1. Brittle Models

[13] A series of purely brittle models experiments, with basal angles β = 0.75°, 1.5°, and 3.0°, have been performed (Figure 3). Since several experimental studies have already extensively investigated thrust tectonics in Coulomb wedges [i.e., Davis et al., 1983; Malavieille, 1984; Mulugeta, 1988; Storti et al., 1997; Gutscher et al., 1998], we do not analyze or discuss these experiments in great detail here. Nevertheless, we use the brittle models to facilitate comparison with previous modeling studies and with the experiments on brittle-ductile wedges presented below.

Figure 3.

Cross sections in purely brittle Coulomb wedge models illustrating the influence of basal angle β. Master thrusts exhibit a systematically frontward vergence, with narrow spacing and frontward sequence of thrust development. Back thrusts are transient structures that accommodate internal deformation within thrust units. The size of the thrust units increases with layer thickness, i.e., with basal angle β. No vertical exaggeration.

[14] The common characteristics of these brittle wedges are (1) a systematic frontward vergence and frontward sequence of major thrust development, (2) the progressive development of a stable surface slope and (3) development of transient secondary back thrusts that accommodate internal deformation within thrust units. The models also show that the first transient back thrust associated with a new major thrust merges at the surface at the tip of the previous major thrust. Subsequently, transient back thrusts deform previous major thrusts ultimately giving rise to rather complicated fault patterns. Nonfrontward sequence thrusts are only observed close to the moving wall.

[15] The following characteristics are related to the initial wedge shape, i.e., to the initial basal angle β. These characteristics are (1) increase of basal slope β that leads to a gradual increase of size and spacing of first-order thrust units and (2) increase of β that leads to a greater development of back thrusts. For β = 0.75°, the frontward thrusts dominate with only few transient back thrusts, while for higher β values (1.5° and 3.0°) the transient back thrusts become more numerous.

3.2. Brittle-Ductile Models

[16] Brittle-ductile models give structures and sequences of thrust development that significantly differ from those observed in purely brittle models. As a framework for discussing brittle-ductile models, we first identify the basic types of elementary thrust units observed (Figure 4) and characterize their sequence of development (Figure 5).

Figure 4.

Four main types of elementary thrust structures observed in brittle-ductile models. (a) Thrust units consisting of a forward master thrust associated with conjugate transient back thrusts accommodating internal deformation within the thrust unit. (b) Master back thrust with conjugate transient forward thrusts. (c) Flip-type units in which a transient fault becomes a master fault during deformation. (d) Pop-up structure with equally important forward and back thrusts. Arrows indicate sense of slip.

Figure 5.

Three main thrust sequences observed in brittle-ductile models: (a) mainly frontward (as in purely brittle models, e.g., Figure 3), (b) initially backward, and (c) mixed frontward and backward, here referred to as oscillating. Open and solid circles indicate the first and last thrusts of the sequence, respectively.

[17] The most common thrust units consist of a forward master thrust with conjugate transient back thrusts that accommodate internal deformation within the thrust unit (Figure 4a). Master back thrusts with conjugate transient forward thrusts are common in a number of models (Figure 4b). As deformation increases, one of the transient faults may become a master thrust fault crosscutting and passively transporting the previous master thrust fault (Figure 4c). This process, here called “flip,” occurs at restricted places in models with initial wedge angle β = 0.75° and 1.5°. Finally, pop-up structures are present with equally important forward and backward thrusts (Figure 4d). Three types of thrust sequences are observed in brittle-ductile models (Figure 5). They are (1) mainly frontward (Figure 5a), similarly to sequences in purely brittle (or Coulomb-type) models, (2) initially backward (Figure 5c), or (3) a mixture of both types of sequences, here called oscillating (Figure 5b). In backward-type sequences, thrusts start at the front of the wedge and propagate toward the backstop. As shortening increases, new thrusts tend to saturate the model progressively, sometimes producing complicated patterns.

3.2.1. Effects of Variable β With Constant Backstop Velocity V = 1.0 cm/h

[18] Figures 6 and 7 illustrate the influence of initial wedge angle β at constant backstop velocity V = 1.0 cm/h. The models with the smallest initial wedge angle, β = 0.75° (Figures 6a and 7a) show deformation patterns closely resembling those of Coulomb wedges. The sequence of thrusting is dominantly frontward, as illustrated by surface views (Figure 8). Close and regular spacing of thrust units results in a clearly defined cross-sectional taper. In contrast with Coulomb wedges, master back thrusts develop close to the moving wall during the early stages of deformation. For an initial wedge angle β = 1.5° (Figures 6b and 7b), two thrusts appear at the onset of deformation, at the front and the back of the wedge. These two thrusts are rapidly followed by an oscillating thrust sequence initiating in the central part of the model, as displayed by surface views (Figure 9). Thus we consider the two early thrusts as directly related to boundary effects and not belonging to the sequence characterizing this model. Deformation is concentrated in the frontal half of the model, away from the backstop. After 15% of bulk shortening, when the model is clearly building up a frontal wedge, deformation begins to affect the part of the model close to the backstop (Figures 6c and 7c). Master back thrusts are among the first structures to occur, developing in the middle of the model at early stages (10% of bulk shortening; Figure 9). For an initial wedge angle β = 3.0°, the first thrust appears at the frontal tip of the ductile layer (Figure 10). Subsequent thrusts develop in a backward sequence, with master back thrusts located in the middle of the model, this pattern resembles that seen for β = 1.5° but at later stages of deformation (Figure 10).

Figure 6.

Cross sections in brittle-ductile wedge models illustrating the effects of varying initial basal angle β on deformation patterns at backstop velocity V = 1.0 cm/h. Sequence of thrust initiation is indicated above the cross sections.

Figure 7.

Line drawings of Figure 6 showing the domains of dominant forward (shaded) and backward (white) thrust vergence.

Figure 8.

Top views of model evolution for β = 0.75° and V = 1.0 cm/h (see Figure 6a) at shortening amounts of (a) 10, (b) 20, (c) 30, and (d) 40 cm. The sequence of thrust development is dominantly frontward.

Figure 9.

Top views of model evolution at β = 1.5° and V = 1.0 cm/h (see Figure 6b), for shortening values of (a) 10, (b) 20, (c) 30, and (d) 40 cm. The sequence of thrust development is oscillating.

Figure 10.

Top views of model evolution at β = 3.0° and V = 1.0 cm/h (see Figure 6c), for shortening values of (a) 10, (b) 20, (c) 30, and (d) 40 cm. The sequence of thrust development is dominantly backward.

[19] Master back thrusts develop at various places and times throughout the wedge, depending on the initial basal angle β (Figure 6). For β = 0.75°, these structures develop at the back of the model during early stages of deformation. For β = 1.5°, they develop in the middle of the model at early stages, and a master back thrust is the first thrust to appear. For β = 3.0°, master back thrusts develop in the middle of the model, as seen for β = 1.5°, but at late stages.

3.2.2. Effects of Variable V at Constant Initial Wedge Angle β = 1.5°

[20] Figures 11 and 12 illustrate the influence of varying backstop velocity V at constant initial wedge angle β = 1.5°. Note that the model with the lowest velocity (V = 1 cm/h) is the second model discussed before (Figure 6b). Domains of dominant master back thrusts are present in all models. As seen before, for V = 1 cm/h, master back thrusts are not very numerous and develop in the center of the model. By contrast, at V = 5 and 10 cm/h, main back thrusts are more numerous and develop at the rear, while the front part of the wedge is the site of forward thrusts. In these two models, the thrust sequence develops regularly frontward, contrary to the oscillating sequence observed before for V = 1 cm/h. In the intermediate model (with V = 5 cm/h), deformation is concentrated at the rear on three master back thrusts. At the end of the experiment, deformation reaches the front and the wedge is entirely saturated by thrusts. To the contrary, at V = 10 cm/h, the frontal part remains unaffected by thrusting. In all models, master back thrusts develop at early stages of deformation.

Figure 11.

Cross sections of brittle-ductile wedge models illustrating the effects on deformation patterns of varying backstop velocity (V) at basal angle β = 1.5°. The sequence of thrust initiation is indicated above the cross sections.

Figure 12.

Line drawings of Figure 11 showing the domains of dominant forward (shaded) and backward (white) thrust vergence.

[21] The shape of the cross-sectional taper differs in the three models. At V = 1 cm/h, a clear wedge only forms at the wedge front during the first 15% of bulk shortening, while the rear remains almost horizontal. At V = 10 cm/h, the model shows a nearly perfect wedge geometry with a frontward dipping straight envelope.

3.3. Stress Analysis

[22] Previous experimental studies have analyzed the effects of brittle-ductile coupling in terms of relative strength between the brittle and ductile layers in both extensional [Nalpas and Brun, 1993; Brun, 1999, 2002] and compressional settings [Bonini, 2001]. The same approach is applied in the following stress analysis. It consists in considering the initial geometry and boundary conditions of the thrust wedge and assuming constant strain rates throughout the entire wedge. The velocity at the brittle-ductile interface, i.e., at the site of thrust initiation, is taken to be equal to the backstop velocity. This means that we ignore boundary effects related to the backstop that can produce two types of discrepancies. First, displacement rate may not always be constant between the backstop and the site of thrust initiation. Second, ductile layer thickness may change with progressive shortening close to the backstop.

[23] First, displacement rate could slightly vary between the backstop and the site of thrust initiation. Second, ductile layer thicknesses could vary as well close to the backstop with progressive shortening. Nevertheless, the analysis shows that variations in stress ratio between brittle and ductile layers, successfully account for the dynamics of thrust wedge development, particularly in terms of thrust spacing, vergence and sequence.

[24] From the Mohr circle, one can obtain the following relations:

display math
display math
display math
display math

where σ1 and σ3 are the maximum and minimum principal stresses, σf is the normal stress on the fault, τf is the shear stress on the fault, and ψ is the angle of internal friction related to the friction coefficient ϕ by

display math

From equations (2) to (5), we obtain [Jaeger and Cook, 1979]

display math

The vertical normal stress σ in the brittle layer is given by

display math

where ρ is the sand density, g is the acceleration due to gravity, and Td is the thickness of the sand layer. Because σ = σ3 in compression, the maximum differential stress is

display math

Consequently, the maximum differential stress in the brittle layer only depends on layer thickness for a given sand density (ρ).

[25] At the onset of deformation, it can reasonably be assumed that the ductile layer undergoes layer-parallel simple shear. The shear strain rate is then given by

display math

where V is the backstop velocity and Td the thickness of the ductile layer. Therefore the shear stress in the ductile layer can be written as

display math

where τ is the shear stress and μ is the viscosity.

[26] From equations (9) and (10), it follows that the shear stress (τ) in a ductile layer with constant viscosity (μ) is a function of the displacement rate (V) and an inverse function of the ductile layer thickness (Td). Because of the wedge shape and frontward thinning of layers, differential stress values increase frontward in the ductile layer and decrease in the brittle layer (Figures 13a and 14). The resulting frontward decrease in brittle-ductile (BD) stress ratio (Figure 15) is responsible for an increase in the BD coupling toward the wedge front. Similarly, a twofold increase in wedge angle (β) leads to a four times increase in the BD stress ratio, so that the basal ductile layer becomes a more effective décollement (Figure 15a). While brittle material is not strain rate sensitive, an increase in displacement rate V leads to an overall increase in differential stress and strength (i.e., the product of viscosity by strain rate) in the ductile layers (Figures 13b and 14b). Because in the meantime differential stress in the brittle layer strongly decreases toward the front, the decollement becomes less effective for higher displacement rates (e.g., 10 cm/h; Figure 13b). In other words, it is the relative strength between ductile and brittle layers that controls the efficiency of a decollement along a ductile layer.

Figure 13.

Variations in differential stress (σ1–σ3) as a function of distance from the initial position of backstop for model series with (a) V = 1.0 cm/h (see Figure 6) and (b) β = 1.5° (see Figure 11). From backstop to front, differential stress decreases in brittle layers and increases in ductile layers.

Figure 14.

Variations in strength profiles throughout the wedge for model series with (a) V = 1.0 cm/h (see Figure 6) and (b) β = 1.5° (see Figure 11).

Figure 15.

Relationship between brittle-ductile stress ratios and initial position of first thrust characterizing the sequence (solid circles) (a) for models with V = 1.0 cm/h (see Figure 6) and (b) for models with β = 1.5° (see Figure 11). In all models the first thrust develops at B/D stress ratios lower than 30 (shaded area).

[27] The governing role of the B/D stress ratio is documented in Figure 16. The lower line drawing represents a model with a wedge angle β = 0.75° and a velocity V = 1 cm/h, while the upper line drawing shows a model with a wedge angle β = 1.5° and a velocity V = 5 cm/h. Although the initial thicknesses of brittle and ductile layers as well as strain rate are different, the both resulting curves of brittle-ductile stress ratio and wedge structure are similar. This shows that similar thrust wedges can result from different initial and boundary conditions.

Figure 16.

Two models with different initial basal angle β and backstop velocity V, showing a comparable structure and sequence of thrusting. Although the initial and boundary conditions are different, the evolution of brittle-ductile stress ratio is similar suggesting that structural style is dominantly controlled by relative strength between brittle and ductile layers.

[28] The location of the first thrust characterizing a sequence is plotted on the curves of B/D stress ratio vs. backstop distance for each experiment in Figure 15. In all models, the location of the first thrust corresponds to a B/D stress ratio lower than 30. When this critical value is reached close to the backstop, the sequence is necessarily frontward. When this value is reached away from the backstop, the sequence necessarily involves some backward component.

4. Natural Examples

[29] The present experimental results are applied to natural thrust wedges in the Jura Mountains and in the Salt Range and Potwar Plateau of Pakistan. For both examples, geometry and deformation history are well constrained from seismic, surface, and borehole data. Both systems are young, corresponding to short-lived foreland fold-and-thrust belts with a relatively simple tectonic history. They display similar width, amount of shortening and duration of deformation, combined with variable wedge angles and decollement geometry, so that they are appropriate candidates for comparison with experimental results.

4.1. The Jura Mountains

[30] The Jura Mountains and the Swiss Molasse Basin represent a foreland fold-and-thrust belt in front of the northwestern Alps (Figure 17a). The Mesozoic and Cenozoic cover has been deformed over a weak basal decollement of Triassic evaporites and shortened by up to 30 km [Laubscher, 1965, 1992; Guellec et al., 1990; Burkhard and Sommaruga, 1998]. The evaporites reach a thickness of 1 km that decreases toward the front of the wedge [Sommaruga, 1999]. Paleontological and stratigraphic data indicate that deformation most probably took place between 9 and 4 Ma [Becker, 2000; Bolliger et al., 1993; Steininger et al., 1996]. From extensive geological and geophysical field studies, various authors have constructed crustal scale cross sections [Guellec et al., 1990; Laubscher, 1992; Burkhard and Sommaruga, 1998]. A depth to basement map, derived from depth conversion of seismic lines and borehole data, shows a rather smooth, flat basement dipping 1°–3° to the south-southeast. A flexural modeling study [Burkhard and Sommaruga, 1998] suggests that the currently observed basal angle is equal to the initial one. A similar type of analysis applied to other thrust belts might be useful in distinguishing between systems with constant and variable basal angles.

Figure 17.

Geological cross sections through (a) the Jura Mountains (redrawn from Burkhard and Sommaruga [1998]); (b) the eastern Pakistan Potwar Plateau and Salt Ranges (after Lillie et al. [1987] as cited by Pennock et al. [1989]); (c), the central Pakistan Potwar Plateau and Salt Ranges (after Lillie et al. [1987] as cited by Burbank and Beck [1989]). The sequence of thrust initiation is indicated above the Pakistan cross sections.

[31] The Jura Mountains include several strongly contrasting domains of deformation as shown in Figure 17a. From the internal zone toward the front, these are (1) the Molasse Basin, characterized by long-wavelength, low-amplitude folding, (2) the strongly deformed central High Jura with thrusts and box folds, (3) the mostly undeformed Jura Plateau, and (4) the frontal Faisceau zone made of imbricated thrusts. Most of the shortening is accommodated by thrusting in the High Jura, in the middle of the wedge [Guellec et al., 1990; Philippe, 1994; Burkhard and Sommaruga, 1998]. Box folds and major back thrusts occur in places [Laubscher, 1977; Philippe, 1994]. Because of a lack of syntectonic strata, little is known about the sequence of thrust initiation.

4.2. Pakistan Salt Range and Potwar Plateau

[32] The Northern Pakistan Salt Range and Potwar Plateau (SRPP) are part of the active fold-and-thrust belt at the southern margin of the western Himalayas. The geometry of the basin and decollement layers vary strongly along strike with basal angle β ranging from less than 1° (Figure 17b) in the eastern profile to 3° in the central profile (Figure 17c) [Jaumé and Lillie, 1988; Pennock et al., 1989]. Late Precambrian to Late Cambrian evaporites, mainly composed of halite, form a basal decollement with a maximum thickness of about 2 km [Pennock et al., 1989]. They are overlain by 2 to 8 km of Paleozoic to Holocene sediments [Johnson et al., 1986; Burbank et al., 1986; Baker et al., 1988; Jaumé and Lillie, 1988; Burbank and Beck, 1989].

[33] Deformation of the wedge started about 5 Ma and is still going on [Johnson et al., 1986; Burbank and Beck, 1989; Pennock et al., 1989]. The 25–30 km of shortening has led to a present-day wedge width of ∼100 km [Johnson et al., 1986; Baker et al., 1988; Jaumé and Lillie, 1988; Pennock et al., 1989; Burbank and Beck, 1989].

[34] Along the eastern Pakistan SRPP profile (Figure 17b), the basement dips rather gently (β ∼ 1°). Shortening is accommodated along forward and back thrusts as well as pop-up structures, distributed throughout the wedge [Jaumé and Lillie, 1988; Pennock et al., 1989]. The tip of the salt layer is marked by a small thrust along which little displacement has occurred, indicating the absence of basal sliding along this profile. Although a number of structures along the profile remain undated, the overall sequence of thrust initiation is mainly frontward (for details and discussion, see Pennock et al. [1989]).

[35] Along the profile across the central SRPP, the basement dips at 3° (Figure 17c). Shortening is mainly accommodated in the frontal Salt Range by sliding over a ramp near the wedge front, at the tip of the salt layer. Little internal deformation has affected the wedge and the Potwar Plateau remains largely undeformed. Chronologic and stratigraphic studies indicate that along this profile started in the frontal Salt range and was followed by a dominantly backward sequence of thrusting affecting the whole wedge throughout its 5 Myr history (for details and discussion, see Burbank and Beck [1989]). The sequence of thrusting for both Salt Ranges profiles is given in Figures 17b and 17c, in the same way as for the experiments (Figures 6 and 11).

4.3. Comparison of the Natural Examples

[36] Both the Jura Mountains and Pakistan SRPP are young mountain belts with weak (incompetent) evaporites acting as a basal decollement. These systems involve previously undeformed foreland basins with rather smooth basements. They are similar in length and amounts and duration of deformation. By contrast, they differ in their wedge geometry with a mean basal angle of β ∼ 2° for the Jura and 1° and 3° for the central and the eastern Pakistan SRPP profile, respectively. The eastern SRPP profile has the lowest basal angle (β = 1°), and therefore presumably the strongest BD coupling. Thrusting distributed throughout the wedge in a mainly frontward sequence accommodates shortening along this profile. Structures include pop-ups and back thrusts. The front of the wedge is only slightly deformed. In the Jura Mountains, where β is intermediate (∼2°), shortening is strongly localized at the middle of the wedge (High Jura) and moderately at the front (Faisceau zone). A mostly undeformed area (Jura Plateau) separates these two domains. At the rear (Molasse Basin), long-wavelength and low-amplitude folding accommodates only minor shortening. The central Pakistan SRPP, with β = 3° the largest initial wedge, shows deformation starting at the wedge front with the formation of the Salt ranges sliding along a frontal ramp, followed by a backward thrust sequence.

5. Discussion

[37] The present work combines laboratory experiments, theoretical analysis and field applications to present a new approach of thrust systems dynamics that involve a basal ductile decollement. We are aware that some parameters not taken into account in our experiments such as temperature, fluid pressure, erosion, and sedimentation may also play a role in thrust system development.

[38] We focused our attention on the role of coupling between brittle and ductile layers at variable initial wedge angles, since this aspect has never been considered up to now. Results are presented that allow us to compare the Coulomb wedge theory and its implications. Experimental results on thrust spacing and vergence are commonly used to characterize thrust belts in map and cross sections. Thrust sequence appears to be sensitive to rheological and geometrical properties of the initial wedge. Despite the inherent limitations of the present study, the methods and results described here may provide a new framework in the study of thrust wedge dynamics.

5.1. Role of BD Coupling

[39] The patterns of progressive deformation observed in fold-and-thrust belts with a basal ductile decollement layer are much more complex than in pure Coulomb wedges. Structural differences between systems such as the Jura Mountains and the Pakistan SRPP, and changes along strike in these systems, largely depend on the efficiency of the decollement. As demonstrated by experiments, this can be explained by coupling between the ductile decollement layer and the brittle overburden. BD coupling is a function of the magnitude and ratio of differential stresses in the brittle and ductile layers. In nature, the differential stresses depend principally on the initial geometry of the brittle and ductile layers, as well as fluid pressure, strain rate and viscosity. Wedges with strong BD coupling (low β and high V) give almost regular frontward sequences with narrow spacing of thrust units and, as such, are not significantly different from purely frictional wedges. Weak BD coupling (high β and low V) gives dominantly backward thrusting sequences, and intermediate BD coupling produces frontward-backward oscillating sequences. The spacing of thrust units increases with decreasing coupling. Back thrusts develop in those parts of the wedge where BD coupling is weakest, regardless of thrust sequence. It is noteworthy that models differing in terms of β and V, but with very close variations of brittle-ductile stress ratio from back to front, give similar structural patterns at the scale of the whole thrust wedge (Figure 16).

5.2. Forward and Back Thrusts

[40] Major back thrusts develop in experiments with different initial geometries and strain rates, and have been described in other experimental studies of brittle-ductile wedges [Corrado et al., 1998; Bonini, 2001; Gutscher et al., 2001; Costa and Vendeville, 2002]. In our experiments, back thrusts always develop in the strongly decoupled parts of the wedge.

[41] In brittle-ductile models, the rear and front of the wedge are always characterized by forward thrusts. At the rear, this is due to the presence of the vertical wall pushing the model. At the front, the forward thrusts develop as a result of the downward rotation of the principal stress axis σ1 [Hafner, 1951].

[42] Davis and Engelder [1987] have proposed that major back thrusts would form as a result of nonfrontward sequence thrusting. A thrust-related increase in topography would lead to the backward rotation of the principal stress axis σ1, thus favoring backward vergence. Back thrusts would therefore be the direct consequence of a nonfrontward thrusting sequence. This however contrasts with experiments which show back thrusts occurring in both purely frontward and backward sequences. The development and location of back thrusts in all experiments therefore indicate that neither strain rate nor backward sequence is determinant for thrust vergence.

5.3. Sequence of Thrusting

[43] Nonfrontward sequence thrusting has been described near the front of several fold-and-thrust belts, such as in the Appalachians [Wiltschko and Dorr, 1983] and Pyrenees [Martínez et al., 1988; Burbank et al., 1992; Meigs, 1997], and is commonly ascribed to a plunging of the σ1 stress axis due to an increase of basal friction at the tip of the ductile layer. However, experimental results together with field examples (Pakistan Salt Ranges and Potwar Plateau [Burbank and Beck, 1989], Moroccan Rif [Morley, 1988, 1992]), that nonfrontward sequence thrusting can affect the whole wedge during its entire history.

[44] Unfortunately, in many natural cases, the evidence for spatiotemporal evolution of deformation has been removed by subsequent erosion. Experimental results show that the thrust sequence strongly depends on initial and boundary conditions, including layer geometry and displacement rates [see also Ballard et al., 1987; Bonini, 2001; Corrado et al., 1998; Costa and Vendeville, 2002]. Analysis of stress variations in experiments moreover shows that the location of the first thrust in a sequence corresponds to a B/D stress ratio lower than 30 (Figure 15), and thus controls the subsequent thrust sequence. If the critical value of 30 is close to the backstop, the sequence is necessarily frontward. If it is located away from the backstop, the sequence necessarily involves some backward component.

[45] In the two models with weak BD coupling and oscillating or backward sequences (V = 1.0 cm/h, β = 1.5° and 3.0°), much of the wedge at the rear remains undeformed even for large amounts of shortening (see Figures 9 and 10). This suggests that the distribution of deformation throughout the wedge reflects nonfrontward thrusting. Where a thrust sequence is not recorded in the stratigraphy, this may be an additional criterion to recognize nonfrontward sequence thrusting, e.g., Jura Mountains (Figure 17a) and southern Pyrenees, as displayed by the ECORS profile [Choukroune and ECORS Team, 1989; Vergés and Munoz, 1990].

5.4. Relationship Between Surface and Basal Slopes

[46] On a diagram of surface slope α versus basal slope β, after Davis et al. [1983] (Figure 18), the upper dashed line marks the theoretical prediction for a cohesionless Coulomb wedge, while the horizontal axis marks the other end of the spectrum, i.e., a purely viscous wedge with a horizontal surface (α = 0°). The grey shaded area between these two lines represents intermediate cases for which the surface angle α depends on the amount of BD coupling. Modeling results obtained for brittle-ductile wedges (Figures 6 and 11) are plotted for comparison. For V = 1.0 cm/h (Figure 6), the data points plot away from a classical cohesionless Coulomb wedge. It should be noted that two of these surface slope values are measured in the frontal parts of wedges with weak BD coupling that have not yet reached equilibrium. For β = 1.5°, α values closely approach the cohesionless Coulomb wedge values with increasing V and BD coupling. From this point of view, Coulomb-type wedges represent end-member cases for the mechanics of fold-and-thrust belts.

Figure 18.

Plot of mean surface slope angle α versus initial basal slope angle β. The top line and solid circles correspond to Coulomb wedges [Davis et al., 1983]. The horizontal axis corresponds to purely viscous wedges. The grey shaded area is the domain of brittle-ductile wedges. Open circles correspond to the two series of models presented here (see Figures 6 and 11). Note that when backstop velocity increases, purely brittle and brittle-ductile wedges become similar in terms of surface angle α.

5.5. Comparison of Models and Natural Examples

[47] The overall geometry depicted on the Jura cross section (including layer wedging and basal slope angle β of 1–3°, Figure 17a) [Burkhard and Sommaruga, 1998] suggests a comparison with the results from the model with β = 1.5° and V = 1 cm/h (Figure 6b). The thrust distribution along this cross section compares with that at the intermediate deformation stage of the model (20 cm bulk shortening; Figure 8), when deformation is concentrated in the center and minor structures develop at the back and front of the wedge. Further shortening leads to further internal deformation, implying that the system is in subcritical condition.

[48] The eastern Pakistan SRPP, with a small basal angle (β ∼ 1°) (Figure 17b), shares some characteristics with both experiments. The distributed deformation and generally frontward thrust sequence compares well with the experiment showing strong BD coupling (β = 0.75°, V = 1.0 cm/h) presented in Figure 6a. Thrust spacing along this profile compares more closely with the model showing intermediate BD coupling, β = 1.5° and V = 1.0 cm/h.

[49] With most of the shortening accommodated at the front of the wedge and relatively little internal deformation, the evaporites of the central SRPP (Figure 17c) seem to form an effective decollement likely to be responsible for a weak BD coupling throughout the wedge. This resembles the model with β = 3.0° and V = 1.0 cm/h (Figure 6c). The comparison is further strengthened by the high wedge angle and the initially backward thrust sequence.

[50] Box folds are common in the Pakistan SRPP and in the Jura, similar folds develop in experiments where the base is regular and the cover homogeneous. This indicates that neither basal nor cover irregularities are necessary to explain the initiation and irregular spacing of box folds and other structures in thrust belts, as suggested by Laubscher [1975, 1977].

6. Conclusions

[51] The present study provides new insights to understand the mechanisms of thrust wedge formation involving a potential ductile basal decollement. Laboratory experiments display a broad spectrum of thrusting patterns, ranging from those directly comparable with Coulomb wedges to systems with anomalous vergence, spacing and sequence of thrusting. Stress analysis suggests that these different thrusting patterns result from variations in mechanical coupling between brittle and ductile layers. At any given point in a wedge, BD coupling is a function of the thickness and frictional properties of the brittle layer, as well as of viscosity and shear strain rate in the ductile layer. For a given wedge angle β and backstop displacement velocity V, BD coupling increases toward the wedge front because of a decrease in the brittle strength and an increase in the ductile strength caused by the frontward thinning of brittle and ductile layers. Despite the inherent limitations of laboratory experiments, the application of results to natural examples sheds new light to the mechanics and geometry of brittle-ductile wedges as well as to some structural patterns usually considered as “anomalous”.

[52] 1. Thrusting sequences in wedges with strong overall BD coupling (low β and high V) are rather regular frontward and are, as such, not significantly different from classical Coulomb type wedges [Davis et al., 1983]. Wedges with weak overall BD coupling (high β and low V) display dominant backward thrusting sequences. Wedges with intermediate overall BD coupling are characterized by frontward-backward oscillating sequences. In others words, when BD coupling decreases, the sequence of thrusting changes from frontward to backward, via a pattern of oscillations. Stress analysis shows that the first thrust develop in all models where the B/D stress ratio is lower than 30. If this critical value is located close to the backstop, the sequence is necessarily frontward. If, on the contrary, this critical value is attained away from the backstop, the sequence necessarily involves some backward component. Some models showing backward thrust sequences display a large undeformed domain at the rear of the wedge. In natural systems, this could be used as an indication of nonfrontward thrust sequence.

[53] 2. Back thrusts observed in the experiments are always located in the more strongly decoupled parts of the wedge. They occur in both frontward and backward types of thrusting sequence, suggesting that they are inappropriate for indicating non-frontward sequences of thrusting.

[54] 3. As already stated by Davis and Engelder [1985], brittle-ductile thrust systems display tapers that are lower than purely frictional wedges. Assuming zero basal friction, these authors predicted an almost tabular critical taper. In contrast with this prediction, our experiments involved different strength values for the basal decollement and yield a variety of final wedge angles that seems to be in better agreement with field observations. In terms of surface slope α versus basal slope β, brittle-ductile wedges define a broad spectrum between purely viscous wedges and Coulomb type wedges.

[55] 4. Wedges with weak BD coupling need large amounts of bulk shortening (more than 30%) to attain a state in which stable sliding along the base occurs, i.e., state of critical taper. Thus the amount of shortening and the distribution of deformation are no indication of a state of critical taper. Comparison with experimental results suggests that at least some parts of the Jura and eastern Pakistan SRPP have not yet reached a state of equilibrium enabling stable basal sliding, i.e., a state of critical taper [Davis et al., 1983]. More broadly, it should be taken into account in the study of natural examples of brittle-ductile thrust wedges that even strongly shortened wedges are not necessarily in a state of critical taper.

Acknowledgments

[56] The experiments were carried out in the experimental laboratory of Géosciences Rennes in 1998 and 1999. The authors would like to thank J.-J. Kermarrec for technical help during the experiments. J. Smit acknowledges a study grant from the Netherlands Ministry of Education and Research. This work was financed by Netherlands Centre for Integrated Solid Earth Science (ISES) (J.S., D.S.), Netherlands Organization for Scientific Research (NWO) (D.S.) and the Institut Universitaire de France (J.-P. B.). The authors would like to thank S. A. P. L. Cloetingh (Vrije Universiteit Amsterdam) for initiating the present study and his continuous support, as well as L. Barrier, G. Bertotti, P. R. Cobbold, P. Davy, C. Faccena, D. Gapais, J. Van Den Driessche, and R. Zoetemeijer for discussions and comments at various stages of the work. We are deeply grateful to G. Mulugeta for valuable remarks on an earlier version of the manuscript. Constructive reviews by M. Bonini, R. Lacassin, and Associate Editor I. Manighetti helped to improve the manuscript. M. S. N. Carpenter postedited the English style. This is Netherlands Research School of Sedimentary Geology (NSG) publication 2003.06.04.

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