The experimental set-up is an adaptation of a former apparatus used for studying deformation mechanisms in convergent settings (oceanic and continental subduction [12,25,27]) and for analyzing erosion–transport processes [8,14,15]. It is composed of:

• • a computerized deformation device;
• • a rainfall system for erosion;
• • an optical measurement bench (Fig. 2).

Analogue materials in experimental models often consist in dry granular materials (sand [10,25,27]) or water-moisten powders (loess [23]; silica powder [3,8,34]; fly ash [14]). Our material has been selected after in-situ tests realized on a great variety of materials (glass microbeads and microspheres; silica, plastic, graphite, pumice powders; clay; talc). Its composition and characteristics have been determined to satisfy several physical criterions:

• • the material rheology must satisfy the Mohr–Coulomb failure criterion [6,9,10,22] so as to generate faults;
• • it should erode trough diffusive processes on hillslopes (landslide, solifluction) and advection in valleys (channels) so as to simulate the main erosion/transport processes that shape the morphology of natural relief and form drainage basin, crest, hillslope and riverbed features;
• • grain size distribution should be small enough and range over several orders of magnitude to ensure both varying transport distances of particles and grain sorting;
• • erosion rates should be high enough to limit experiment duration.

Thus, sedimentary deposits would be stratified and might record tectonic and stratigraphic structures (fault, fold, unconformity, cut-off, downlap…). Our tests on water-saturated materials show that deformation style, erosion/transport processes and therefore morphologies are strongly dependent on their physical properties. For instance, rounded and well-sorted materials, such as glass microbeads or PVC granules, erode rapidly by dominant landslide processes and have a limited mechanical strength. Some other angular compositions concentrated in silica powder erode slowly by incision and hardly deform due to their high cohesion. Accordingly, it appears that grain-size, grain-shape, and water-content control cohesion that is responsible for the observed erodabilities and deformation styles. The composition of our selected analogue material (median D₅₀ at 105 μm) is made up with glass microbeads (40%), silica powder (40%) and plastic powder (20%). During experiments, it is progressively sifted and moistened with water (saturation rate around 25% in weight). Its physical characteristics are synthesized in Table 1.

We used available geophysical data (DEM, seismic profiles, geodetic measurements) and field geological observations across active mountain ranges (Tian Shan, Taiwan; [5,7,29]) to determine initial boundary conditions of models (rheology, structure). We focused our study on the first 10–15 km of the continental crust and simplified the continental rheology by forming two main layers (Fig. 2). Typically, the brittle sedimentary cover is represented by 5–10 cm of composite material, whereas the deeper basement, whose mechanical behaviour is more ductile, is modelled with a viscoplastic material composed of a mixture of talc (65%) and mineral oil (35%). We used an initial model topography made of very low amplitude relief (less than 1 cm) because it fastens the development of drainage network by concentrating water flow, thus shortening the duration of experiments by several hours. This is justified because deformation at active mountain front propagates on pre-structured foreland topography where hydrographic network and inherited relief already exist.

Model scaling [18] has been defined with a semi-empirical approach. A rigorous scaling is difficult to achieve because some laws and physical properties in model and nature are not well constrained (cohesion, erosion threshold, erosion and transport laws; [23,34]). First, we performed several tests to compare the geometrical characteristics of experimental morphologies to their natural counterparts as observed from satellite pictures or field measurements. From analysis of valley, terrace and fan dimensions, a geometrical scaling ratio of 1–2 × 10⁻⁵ (1 cm ≈ 500–1000 m) has been defined (see for instance Figs. 3 and 4). This is similar to classical values used in analogue modelling [20,22]. Given the model dimensions (1.2 × 2.2 m), we reproduce a portion of piedmont that is about 100 km large. Second, writing the fundamental equation of dynamics for continuum medium in a non-dimension form [10] defines a dimensionless number that compares surface to body forces: σ/(ρ g L). The conservation of this number between model and nature leads to σ* = ρ* g* L*, with σ*, ρ*, g* and L* the model-to-nature ratios for cohesion, density, gravity, and length, respectively. Given that g* = 1 (experiment in the Earth's gravity field), ρ* ≈ 1.5 (sedimentary rocks to material mean density ratio; respectively 2400 and 1600 kg/m³) and L* = 1–2 × 10⁻⁵ (estimated geometrical scaling), σ* should be 1,5 × 10⁻⁵–3 × 10⁻⁵. If one considers that cohesion for consolidated sedimentary rocks is about 10⁷–5 × 10⁷ Pa (limestone, sandstone; [6]), analogue material cohesion should range between 150–1500 Pa. Cohesion of our moisten material has been estimated around 400–600 Pa with an apparatus similar to the Hubbert-type shear box [22]. This value is reasonable according to scaling. Further discussion of experiments and material physical properties are developed in a paper in preparation. Finally, the time ratio between model and nature has been estimated empirically with a specific set-up that calculates mean erosion rates of composite materials for various surface slopes. These measurements are performed with constant precipitation rates similar to typical experiments (around 30 mm/h). For topographic slopes ranging from 10 to 20°, mean erosion rates are respectively estimated at 2–5 mm/h. Compared to natural mean erosion rates (few mm/yr [4]), the time ratio in our model is roughly estimated between 5 × 10⁻¹⁰ and 1 × 10⁻⁰⁹ (i.e. 1 s ≈ 35–70 yr and 1 h ≈ 125–250 kyr). By considering both temporal and geometrical scaling ratios, appropriate shortening velocities in the model should be around 20–40 mm/h to simulate natural convergence rates around 10–20 mm/yr. Typically, experiments span about 10 h, which is equivalent to 20 km shortening in 2 Myr. Note that such temporal and dynamical scaling calculations are empirical and somewhat speculative, as they have been performed with mean geologic and experimental values that present uncertainties. In addition, some distortions might arise with morphological modelling as some hydraulic and hillslope characteristic times are hardly downscaled in experiments [23,34]. However, our calculation is performed at a global scale with mean shortening and erosional velocities. Therefore, it would indicate smooth discrepancies between individual characteristic times of processes and provide a reasonable approximate time scale.

We performed several experiments to compare model surface morphologies and deformation mechanisms with natural cases. To illustrate our first results, we describe some examples of structural and morphological markers issued from a typical experiment and compare them with natural morphologies and structures from the Tian Shan mountain range (Figs. 3 and 4). In this experiment, rainfall and convergence rates were kept constant during 9 h, respectively at 30 mm/h and 40 mm/h. Rainfall was almost homogeneous over the model surface (less than 20% of lateral variations) and the imposed model shortening corresponds to a frontal convergence. Based on these parameters, we model a piedmont with a rapid convergence rate (about 20–30 mm/yr) and a relatively slow erosion rate (less than 1 mm/yr). Two digital pictures framed prior to final stage are presented in Figs. 3a and b. The overall morphology is dominated by two topographic ridges trending perpendicular to the direction of convergence. These structural reliefs are controlled by several reverse faults spaced by about 10 cm and dipping toward the buttress. This deformation pattern corresponds to a tectonic accretionary wedge similar to typical active piedmont structure [9,24]. The drainage network is characterized by upstream sub-parallel patterns and ‘en treillis’ network in the frontal deformation domain. Several fan-shape sedimentary bodies lie at the base of the deformation front. They are formed by the break in slope and drop of the transport capacity of channels that widen brutally when crossing the deformation front and reach the foreland basin. All these features can be considered as the equivalent of natural river networks (Fig. 3c and d).

We present three examples of morphotectonic features formed in this experiment (Fig. 4). The first example is an alluvial fan (Fig. 4a). Its fan shape (apex localized at the channel outlet and circular front) is linked to the sweeping and divagation motion of distributary channels on its surface. This dynamics leads to the coexistence of old, preserved alluvial surfaces and active channels. Its slope is 5–6° and its surface is around 250 cm² (i.e. few hundreds of square kilometres in nature). On the field, slopes of most alluvial fans range below these experimental values (1.5 - 3̊ in Tian Shan piedmonts; Fig. 4a′). However, the morphology displays similar features as the one described above (Fig. 4a and a′). It suggests that transport processes in experiments may not be perfectly similar to natural ones [23] or that vertical and horizontal scaling may be different. Nevertheless, it does not prevent from having alluvial fans with a comparable morphological dynamics.

The second example illustrates the drainage network that forms in piedmont catchments (Fig. 4b). It has a general subparallel geometrical pattern with crests and preserved alluvial surfaces between channel branches. Several knickpoints, about 1 mm in amplitude (i.e. ±50–100 m in nature), are present along channel beds. These features form in response to channel incision and headward erosion that accompany internal catchment uplift. In nature (Fig. 4b′), drainage basins in piedmont display similar sub-parallel drainage patterns, channel characteristic dimensions (width, length) and landforms (crests). It suggests that erosion–transport processes in model respect the average proportion of land sculpting processes, i.e. diffusive processes on hillslopes and advective transport in channels.

Finally, the last example corresponds to a set of stair-step surfaces located above two active thrusts (Fig. 4c). They are linked to the drainage network dynamics (divagation, piracy, incision) that entails variations in hydraulic flows and a global migration of channels rightward (terracing T₂, T₃ and T₄ on right edge; steep banks on left edge). A topographic profile perpendicular to the flowing direction indicates that the differential elevation between these surfaces is around 1 mm, i.e. more or less 50–100 m in nature. These relative heights can be correlated to the deformation front's uplift rate and to the dip of the frontal thrust. Such stair-step values and geometries compare well in amplitude and morphology to natural uplifted fluvial terraces deformed on active faults or propagation folds (see Fig. 4c′ framed on the Kuitun fold in the northern Tian-Shan piedmont [7,29]).

To illustrate the morphostructural analysis that can be performed during experiments (Fig. 5), we present three steps of the deformation front evolution at the level of the major alluvial fan framed in Fig. 3b. These stages correspond respectively to 20, 22.5 and 25 cm of total shortening (that is, a picture every 1250–2500 m of shortening in reality). During the first 20 cm, three successive thrusts appear in sequence (Thrust 1, 2, 3). The branching of Thrust 2 on Thrust 1 has channelized the drainage network parallel to the trending direction of the range and left one single outlet that fed the large alluvial fan. The sedimentary history of this period is not differentiated and appears in blue in Fig. 5a. At the next stage (Fig. 5b), the river embanks in response to frontal thrust activity and three stair-step terraces form on the right riverbank. Different alluvial surfaces appear on the fan and can be time-correlated to the fluvial terraces. Their geometry corresponds to the sweeping motion of distributary channels: firstly clockwise (phase I) and secondly counterclockwise (phase II). This sweeping motion is partly due to the natural fan dynamics, but is also clearly influenced by the activity of thrust 3 that forces channel incision and fix outlet position. A fourth thrust forms about 10 cm in front of the previous one and forms a major virgation in front of the channel outlet. Such a curvature may be the result of a focused incision effect on deformation [26,32]. In unloading continuously the hanging wall, incision would decrease local vertical stress and favour fault dip increase. In 3D, along-strike variations in fault dip would be responsible for the observed arcuate fault scarp. Finally, at the last stage, shortening is mainly accommodated on the frontal thrust (Fig. 5c) and the older thrusts are only slightly active. The scarp associated with the new thrust localizes erosion that rises upward in reworking previously deposited sediments. A new generation of alluvial fan forms at the base of the growing relief. Future similar works will provide insights into the timing of alluvial fan growth and terrace nucleation in relation to thrust activity and deformation propagation.

At the end of the experiment, serial sections are cut across the model to study its internal structure, determine the deformation style, and analyze syntectonic sedimentation. Fig. 6 shows one of these cross-sections located in Fig. 3b. The model displays a typical accretionary wedge structure with hinterlandward dipping thrusts that propagate in sequence toward the foreland. The most frontal thrusts display a flat and ramp geometry that generates low-amplitude box-shaped anticlines. Finely stratified syntectonic deposits fill piggyback and foreland basin. The laminations underline prograding (downlap) and tectonic structures (cut-off). A sharp change in the sedimentary composition occurs in the foreland sequence (Fig. 6). Based on the analysis of video movies taken during the experiment, this evolution is linked either to the progradation of proximal facies or to changes in alluvial fan hydraulics. Additional experiments are required to better characterize this diachronism and correlate its occurrence to foreland deformation history and hydraulics. This is a critical field issue, as natural equivalents are generally interpreted for identifying thrust reactivation or propagation.