Dimensionless critical shear stress in gravel-bed rivers

Geomorphology 250 (2015) 308–320

Contents lists available at ScienceDirect

Geomorphology journal homepage: www.elsevier.com/locate/geomorph

Dimensionless critical shear stress in gravel-bed rivers François Petit ⁎, Geoffrey Houbrechts, Alexandre Peeters, Eric Hallot, Jean Van Campenhout, Anne-Cécile Denis University of Liège, Department of Geography, Hydrography and Fluvial Geomorphology Research Centre, B-4000 Sart-Tilman, Belgium

a r t i c l e

i n f o

Article history: Received 23 April 2015 Received in revised form 14 September 2015 Accepted 15 September 2015 Available online 21 September 2015 Keywords: Critical shear stress Shields criterion Grain shear stress Shear velocity Gravel-bed rivers Meuse basin

a b s t r a c t This paper first compiles critical shear stress values from 26 studies of gravel-bed rivers (GBRs) worldwide. The most frequently proposed value of the Shields criterion (θc) is 0.045, but three major groups with θc values ranging from b0.030 to N0.100 were identified. Second, dimensionless critical shear stresses (the Shields criterion) were evaluated for 14 GBRs (18 sites) with watershed areas ranging from 12 to 3000 km2. Different approaches were used to identify the initial movement of the bed material: painted and PIT-tag pebbles, sediment traps, and bedload samplers. The Shields criterion (θc) was estimated using the total shear stress (τ) and the grain shear stress (τ′). Several shear stresses were also estimated using shear velocities. For bedload transport, we obtained an average Shields criterion (θc) of 0.040. The values were higher in small rivers (N0.050) than larger rivers (b0.030) because of more significant bedform shear stresses. The Shields criterion (θ′c) was lower when the grain shear stress (τ′) was used and only reached 0.019. Different values are also proposed in relation to the type of mobilization: the θc value for partial transport was ~0.025 and exceeded 0.040 for full transport (usually reached in association with discharges with a 10-year return period). The values based on the results of sediment traps and a bedload sampler were greater than those obtained using tracers, but these differences are smaller than those usually reported in the literature. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Although many parameters are used to estimate the mobilization of river bedloads such as critical erosion velocity (Hjulstrom, 1935; Sundborg, 1956; Costa, 1983; Williams, 1983), critical specific stream power (Gintz et al., 1996; Ferguson, 2005; Petit et al., 2005a; Gob et al., 2008, 2010; Parker et al., 2011; Houbrechts et al., 2015), and unit critical discharge (Bathurst et al., 1987; Ferguson, 1994; Lenzi et al., 1999; Rickenmann, 2001; Whitaker and Potts, 2007; Mao et al., 2008; Phillips and Deslosges, 2014), shear stress remains one of the most used parameters. Shear stress values permit the estimation of transported quantities, and this parameter is typically included in the most frequently used equations, such as the Meyer-Peter equation (Graf, 1971; Richards, 1982; Gob et al., 2005; Gao, 2011). In addition, shear stresses can explain the shapes of river beds, particularly meandering beds (Dietrich et al., 1979; Lisle, 1979; Bridge and Jarvis, 1982; Jackson and Beschta, 1982; Petit, 1987; Clifford and Richards, 1992; Sear, 1996; Robert, 1997; Thompson et al., 1999; Milan et al., 2001). This parameter has also been used to explain the formation and destruction of pebble clusters (Storm et al., 2004; Piedra et al., 2012; Heays et al., 2014), the stability of step-pool systems (Zimmermann and Church, 2001; Wohl and Wilcox, 2005) and the

⁎ Corresponding author at: ULg, Department of Geography, Clos Mercator, 3, B11, 4000 Sart-Tilman, Belgium. E-mail address: [email protected] (F. Petit).

http://dx.doi.org/10.1016/j.geomorph.2015.09.008 0169-555X/© 2015 Elsevier B.V. All rights reserved.

evolution of other bedform patterns, such as bedrock patterns and cascades (Thompson and Croke, 2008). The Shields criterion, which uses critical shear stress (the force needed to move an element of a given size), can be used to resolve protrusion and hiding effects using equations that include the relationship between the considered particle size and the median diameter of the bed (Parker et al., 1982; Andrews, 1983; Petit, 1994; Batalla and Martin-Vide, 2001). These equations lead to theories of equal mobility or, conversely, the theory of selective entrainment (Parker et al., 1982; Andrews, 1983). In addition, the Shields criterion can account for the effect of particle shape on the resistance to entrainment (Petit, 1989; Thompson and Croke, 2008). Using shear stress values, it is possible to identify changes in bed morphology and sedimentology caused by embankments or the construction of dikes (Frings et al., 2009). This parameter was also used to highlight the incision of beds and thus the formation of paving in rivers in the Southern Alps (Liébault and Piégay, 2001). Excess shear stress relative to the critical shear stress is used to assess the propagation velocity of the bedload and, consequently, the bedload discharge (Milan, 2013; Vazquez-Tarrio and Menendez-Duarte, 2014). The excess shear stress is also taken into account to estimate the longterm river bed incision rate in relation to tectonic movement (Lavé and Avouac, 2001). Shear stress permits the estimation of the effects of aquatic microorganisms on the delay in movement initiation of particles that form the bed (Statzner et al., 1999; Statzner, 2012). Shear stress is also involved in the evaluation of the stability of different bank protection methods

F. Petit et al. / Geomorphology 250 (2015) 308–320

(Frothingham, 2008) and the stability of sedimentary units colonized by vegetation (Rodrigues et al., 2007). The only limiting factor in the use of shear stress, as highlighted previously by several authors (Ferguson, 2005; Petit et al., 2005a; Parker et al., 2011), is that this parameter is more difficult to determine than the specific stream power because, in addition to knowing the width of the river, the depth of flow at the time of mobilization must be known, which may be difficult to obtain after the flow event, particularly in large rivers. Another problem occurs when shear stresses are used. Indeed, several uncertainties remain regarding the critical shear stress values that affect the Shields criterion. As presented below, a wide range of values have been proposed in the literature. These differences result mainly from methodological aspects, which raise some questions considered below (for example, the definition of motion initiation and the method used in the estimation of shear stress). This paper aims first to synthesize the values proposed in the literature and then propose Shields criterion values for 14 gravel-bed rivers (GBRs) (18 sites) mainly situated in the Ardennian massif. These values are obtained following the same methodology with a unique definition for the parameters (mobilization criterion and calculation methods for the total shear stress and the grain shear stress). For comparison, we have also included several values obtained from sediment traps and a bedload sampler (Helley-Smith). 2. Overview of the equations In a uniform flow, the total shear stress (τ), expressed in N/m2, originates from the product of the slope (s) multiplied by the hydraulic radius (Rh) and two constants (g is the acceleration caused by gravity and ρf is the density of the fluid) (Eq. (1)): τ ¼ ρ f g Rh s

ð1Þ

The total shear stress (τ) can be divided into two components: the grain shear stress (τ′) and the bedform shear stress (τ‫)״‬. The grain shear stress (τ′) is the component of the total shear stress that intervenes only in the transport and movement initiation of the bedload. This parameter can be estimated in different ways but is generally obtained from the method recommended by Richards (1982), which has been successfully tested in flumes (Petit, 1989) and in natural rivers (Petit, 1990; Garcia et al., 2000; Latapie et al., 2014). This method is based on the Manning equation (Eq. (2)), which compares the total roughness coefficient (nt) and the roughness coefficient caused by the resistance of the particles that form the river bed (no), as estimated by the Strickler equation (Eq. (2b)): τ0 ¼ ðno =nt Þ3=2 τ with no ¼ 0:048D50 1=6

ð2Þ ð2bÞ

where D50 represents the median particle diameter (expressed in m). Moreover, the shear stress can be estimated from the shear velocities (u*): τ ¼ u2 ρ f with u=u ¼ 2:5 ln ðy=y0 Þ

ð3Þ ð3bÞ

where u is the velocity measured at a distance (y) above the bottom of the bed (but less than one-fifth of the total depth, or 0.2 d), and y0 represents the roughness height, which depends on the size of the material constituting the river bed. The most commonly used descriptor of roughness height is D50. Different relationships have been proposed

309

for gravel-bed rivers (Hey, 1979; Petit, 1994), but most fall within the following range: yo ¼ 0:20D50 to 0:25D50

ð3cÞ

In medium-sized rivers, the velocities can be measured directly at the marking sites even for high flow rates, but this process is difficult in larger rivers. However, the relationship between total shear stresses (Eq. (1)) and shear stresses based on shear velocities (Eq. (3)) can be estimated using velocity measurements from different cross sections. Several relationships have been proposed to provide the critical value for movement initiation according to particle size (Miller et al., 1977). However, the most commonly used is the Shields function (θ) (Eq. (4)). The Shields function represents a dimensionless relationship among the shear stress τ (N/m2), density of the sediment ρs, (kg/m3), density of the fluid ρf (kg/m3), particle diameter D (m), kinematic viscosity ν (m2/s) and acceleration caused by gravity g (m/s2).    θ ¼ τ= ρs −ρ f gD ¼ fctðu  DÞ=ν

ð4Þ

The Shields entrainment function θ can be assigned a critical value (Shields criterion θc) to solve this equation for a given particle diameter. According to the well-known Shields diagram (Miller et al., 1977), θc varies with (u⁎ D)/ν (more commonly known as the particle shear velocity Reynolds number Re⁎). However, for hydraulically rough beds, defined as Re⁎ N 102, θc becomes independent of the roughness conditions and tends to approach a constant value of 0.060 or 0.050 based on a movement initiation probability of 0.5 (Gessler, 1971). 3. Overview of dimensionless critical shear stresses The value of the initially proposed Shields criterion is 0.060 (Shields, 1936; Miller et al., 1977), which leads to the equation τc = D, where τc is expressed in N/m2, and D, the diameter of the particles to be moved, is expressed in mm (Baker and Ritter, 1975). Most of the Shields criterion values have been estimated using total shear stress. We will clarify below how this criterion differs when grain shear stress or shear velocities are used. Furthermore, some studies propose a single value, whereas others report more or less restricted ranges with various average values. Other studies present very wide ranges for which average values are not obvious. Furthermore, some papers suggest values for partial mobilization, whereas others suggest values for total mobilization, and still others do not provide any information on this point. Select studies are presented in chronological order in Table 1 and are also illustrated in Fig. 1. Characteristics of the rivers, sediment sizes and data acquisition methods are summarized in Table 1 and sometimes developed in the text below. Neill (1968) observed that isolated grains were set in motion when the Shields criterion was equal to 0.030 and that some movement was recorded at even lower values, provided that the observation time was sufficiently long. Values lower than 0.020 were proposed by Carling (1983). Similarly, Hammond et al. (1984), who used the shear velocities of tidal channels, documented θ⁎c values ranging from 0.015 to 0.031. By contrast, Parker et al. (1982) proposed a significantly higher θc value (0.088). As a synthesis of studies performed by different laboratories, Komar (1987) proposed a θc value of 0.045, which was also recommended by Knighton (1998) and Robert (2003). Buffington and Montgomery (1997) performed a detailed synthesis of the issues and uncertainties in the assessment of movement initiation that included more than 600 values, but some of these values are also applicable to sandy beds or to Re⁎ values b102 when θc is not constant. The authors concluded that

Total shear stress Neill (1968) Parker et al. (1982)

0.030 0.088

Carling (1983)

0.020–0.080

0.015–0.031 (θ*c).

Hammond et al. (1984) Komar (1987) Clifford et al. (1992) Andrews (1994)

0.045 0.040 (initiation of motion) 0.021 (end of motion) 0.020–0.060 (marginal transport) N0.060 (significant movement)

Wilcock et al. (1996)

MacNamara and Borden (2004) Mueller et al. (2005) Lenzi et al. (2006) Liébault and Clément (2007) Snyder et al. (2008)

Mao et al. (2008). Turowski et al. (2009) Mao and Surian (2010)

0.052–0.086 0.030–0.073 0.054–0.104

Bunte et al. (2013) Milan (2013)

0.048 (for the small event) 0.066–0.069 (for 3 events) 0.096 (for the largest event) b0.030 bed stable 0.030–0.060 (partial transport) N0.060 (full mobility) 0.046 (0.027–0.063) 0.025–0.035 0.060–0.120 (steeper) 0.100–0.300 0.030–0.070 0.031–0.071 (average interval for all the sites) 0.048–0.127 0.040–0.050

Kociuba and Janicki (2014) May and Pryor (2014)

Field survey

20–25 mm

Bedload trap, tracers, tagged boulders

62 mm 78 mm

Underwater camera

5–40 mm

Sediment trap

D50 (bed) = 16 mm; D90 = 35 mm (From Reid and Frostick, 1984) D50 (surface bed material) = 58 mm

Trinity River (California)

D50 bedload =26 mm HS sampler Tracer gravels, gravel traps and bedload samplers

D50 (surface bed) = 29–44 mm D90 (surface bed) = 85–100 mm

0.033–0.218 (average 0.094; median 0.076) 0.052 0.023 (θ*c).

D50 (surface bed) = 23–101 mm

Allt Dubhaig (Scotland) Six reaches Desert gravel-bed streams (Negev-Israel) Torrent (Catalonia)

1460 tracers Tagged magnetically Painted tracers and samplers

D50 (bed material) = 16 mm

Sediment trap

D50 (bed) = 54 mm

6 rivers (Colorado and California)

Field survey

D50 (bed) = 11–39 mm

Torrent Idaho

Five rocks with radio transmitters (72–92 mm) Bed-load samplers (HS76 and HS152)

D50 = 84 mm

Marked pebbles and bedload traps

D b 200 mm Larger clasts D50 (bed): 19.4–36.4 mm

Cross sections, scour chains and painted tracers

D50 (bed) = 27–210 mm

Painted tracers

D50 = 51–62 (Bed material 1) D50 = 23–53 (Bed material 2) D50 = 119 mm D50 = 67 mm Motion of boulders up to 650 mm (several boulders of 1350 mm in diameter) D50 = 12.7–15.4 mm

Mameyes River (Puerto Ricco) (cobble-bedded) 22 mountain rivers

HS152 — bedload trap Marked pebbles Retention basin Geophone sensors 3500 painted tracers (GSD) Distance of transport: few cm up to 22 m (partial) 27–68 m (full mobility) 300 PIT-tags Same size than the D50 bed Bedload traps and HS

River Rede (Cheviot Hills) UK

288 painted tracers (D50 = 61 mm)

Mameyes River (Puerto Ricco) (cobble-bedded) River glacial catchment: Scott River (Spitsbergen)

300 PIT-tags Same size than the D50 bed Bedload trap samplers

D50 = 86 mm (median grain size of the surface layer) D50 (bed) = 120 mm

Coastal rivers (Maine) Narraguagus (1) Sheepscot (2) Rio Cordon (dolomites) Tres Arroyos (Chilean Andes) Erlenbach (step-pool) Switzerland Tagliamento (Italian Alpes) (Braided river)

0.023 (θ*c).

0.030 (initiation) (0.020–0.070) 0.050 (initiation) (0.030–0.090)

Gravel-bed river Oak Creek (Oregon) Great Eggleshope Beck Carl Beck (Pennine area) Gravel tidal channel West Solent (England) Review: 12 studies Turkey Brook (UK)

45 gravel bed rivers (mainly in Idaho): wide range in catchment size, channel gradient and median grain size Rio Cordon Step-pool (dolomites–Italian alps) Three small tributaries of the Drôme River (France) Barnavette River (Drôme-France)

0.071 0.071 0.040 0.100 0.044–0.085 partial transport Average 0.073 for partial transport 0.107 full mobility

Phillips et al. (2013)

Sediment size

Review more 600 values

0.030 (partial motion) 0.042 (motion of fine granules)

Phillips et al. (2013)

Instrumentation for estimation of motion and transport of sediment

Sagenen Creek (California) 0.035 (scour depth = D90) 0.031 (end of motion)

Garcia et al. (2000)

Lisle et al. (2000)

0.015 (initiation of motion) 0.017 (end of motion)

River type and localisation

Trinity River (California) 0.015 (0.005–0.023) tracers 0.034 (0.012–0.050) for D50 bed (θ*c).

36 radio-tagged particles Average size 108 mm (range 90–128 mm)

D50 (bed) = 120 mm D50 (bed) = 42–108 mm

D50 (bed) = 32 mm D50 = 47 mm

F. Petit et al. / Geomorphology 250 (2015) 308–320

Buffington and Montgomery (1997) Ferguson and Wathen (1998) Reid et al. (1998)

Grain shear stress

310

Table 1 Previously reported dimensionless critical shear stress values: Shields criterion values calculated based in the total shear stress (θc), the grain shear stress (θ′c) and the shear stress calculated from shear velocities (θ*c).

F. Petit et al. / Geomorphology 250 (2015) 308–320

311

Fig. 1. Total and grain shear stress values reported in the literature (refer to Table #1). They are represented by either a min-max range, a single value, the average or the median according to the authors. The grey zone highlights the widely agreed values of θc from 0.030 to 0.060

the data available for high Re⁎ values (typical of gravel-bed rivers) from reference-based and visual studies indicated θc values of 0.052–0.086 and 0.030–0.073, respectively. They concluded their analysis by highlighting the obvious lack of a universal value of θc in gravel-bed rivers and emphasizing that great care is required when choosing a θc value for specific applications. Wilcock (1988) defined two main methods for quantifying critical conditions for particle movement, and Bathurst (2013) performed a critical analysis of these methods: – In the so-called reference method, the two main techniques used to collect bedload are portable samplers equipped with a mesh bag, such as a Helley-Smith (HS 76 or 152 mm), and different types of sediment traps, such as those used by Reid and Frostick (1984); Bunte (1992); Habersack et al. (2001); Bunte et al. (2008), and Mao et al. (2008). – In the so-called competence method, the critical conditions are identified based on the maximum size of particles that are mobilized for a given shear stress. The first technique involves the relationship between the coarser particles in a sampler and the flow conditions (shear stress) prevailing at the sampling time, and the second involves the use of markers of different sizes and the relationship between larger particles and maximum flow that occurs between two field surveys (Mao et al., 2008). Several studies listed in Table 1 were conducted using the first approach mainly based on the sediment trap (‘reference method’ from Bathurst, 2013): Reid et al. (1998) created bed markings in a desert ephemeral stream (D50 = 16 mm) and installed a sediment trap that allowed researchers to estimate particle transport during three periods. At a θc value of 0.030, the samplers did not collect bedload; but significant movement of sand and granules occurred, suggesting conditions approaching the movement initiation threshold. During a larger

event, the samplers recorded a significant bedload accumulation (θ c = 0.042), but the bedload included only small gravel and not the D50 of the bed. Consequently, full mobilization is reached for θc values N 0.042. In a small braided river, Kociuba and Janicki (2014) used a sediment trap that allowed them to record continuous measurements during three floods within which the bedload transport significantly exceeded the average conditions. During these floods, θc varied from 0.020 to 0.070 and from 0.030 to 0.090 depending on the location. During the first two floods, the movement initiation conditions occurred for θc values between 0.030 and 0.040. The last flood showed θc values ranging from 0.040 to N 0.050. The flow during these floods was supercritical (Fr N 1), which, according to the authors, allowed effective transport of the bedload, including coarse material (N32 mm). Garcia et al. (2000) installed a sediment trap in a small torrential creek in Catalonia. The D50 was 54 mm, with local accumulations of fine sediment with sizes ranging from 1 to 20 mm. The dimensionless grain shear stress calculated for five flood events varied: 0.048 for the lowest event, between 0.066 and 0.069 for three events, and 0.096 for the largest event. These authors concluded that the presence of mobile bedforms (related to finer sediment) explains the differences in the movement initiation values. The following studies featured the second approach based on the use of tracers (‘competence method’ from Bathurst, 2013). Ferguson and Wathen (1998) placed 1460 magnetic tracers at six locations in the Allt Dubhaig River in Scotland (the reaches are near braided and wandering, succeeded by meandering). The movements of these markers were then linked with the shear stress averaged over the duration of the competent flow rates. The θc values varied from 0.054 to 0.104 depending on the location. Snyder et al. (2008) marked pebbles in five locations in two coastal rivers in Maine, USA. Most of the tracers were coarser than the D50 of the bed to facilitate their identification, but they were integrated into

312

F. Petit et al. / Geomorphology 250 (2015) 308–320

the river bed so that they did not protrude. The mobilized elements were close to the D50 of the bed, and the θc values generally ranged from 0.040 to 0.050, with some exceeding this range. These results demonstrated that the protruding effect did not appear to play a role in this case. In a steep river in Idaho, MacNamara and Borden (2004) equipped five pebble elements with radio transmitters and obtained θc values between 0.027 and 0.063, with an average value of 0.046. The diameter of the tracers ranged from 76 to 92 mm, which was close to the D50 of the bed. Milan (2013) found a θc value of 0.052 for an upland river with pronounced riffle-pool sequence morphology and a sinuosity of 1.82. This morphology suggests energy losses and could justify a high θc value when the total shear stress is taken into account in this case. Liébault and Clément (2007) demonstrated (through topographic surveys combined with scour chains and painted pebbles) θc values varying from 0.031 to 0.071 in three tributaries of the Drôme River (French Alps). In one of these rivers (the Barnavette), the values fluctuated between 0.048 and 0.127. Using 300 PIT-tag tracers (in the Mameyes River, a minimal meandering river located in Puerto Rico) that were comparable in size to the elements of the bed (D50 = 120 mm), Phillips et al. (2013) observed a θc value of 0.023 based on shear velocities (u⁎ = 0.22 m/s). May and Pryor (2014) studied the initial movement of tracers equipped with radio transmitters (D50 = 108 mm, which corresponded to the D90 of the bed) and reported an average θc value of 0.015 (ranging from 0.005 to 0.023) for the pebbles equipped with transmitters. The θc values for material constituting the bed (D50 = 47 mm) were on average 0.034 (ranging from 0.012 to 0.050). Shear stresses were calculated using a model that included water level, flow velocities, velocity field downstream, and lateral component, which approaches the shear velocities (skin friction, considering that the drag force is negligible). The θ⁎c values for the tracers might have been slightly underestimated caused by the protrusion effect (see the D50 ratio of the tracers and the bed D50). Any underestimation was likely smaller for the mobilization because the authors were careful to place each particle within the river bed in the gap left by the removal of a particle with the same size and shape during the insertion of tracers. Other studies listed in Table 1 have focused on different transport stages (partial transport vs. total transport). On the Trinity River, Wilcock et al. (1996) demonstrated that the boundary between negligible particle movement and the movement of most of the bed surface occurs within a narrow range of local shear stresses, on the order of only 10 to 15% of the Shields criterion. Erosion equal to the bedload sheet thickness occurs for θc = 0.035. The movement initiation and transport decrease rapidly, and the bed becomes nearly motionless for a θc value of 0.031. Andrews (1994) concluded that only marginal transport occurs at θc values between 0.020 and 0.060 and that significant movement (when the majority of the bed particles are in motion) occurs at a θc value of 0.060. Mao and Surian (2010) showed that the average θc value of partial transport in a large braided gravel-bed river (the Tagliamento River in Italy) corresponds to 0.073; excluding two outliers, the observed values range from 0.044 to 0.085, whereas transport is widespread for θc N 0.107. This range of dimensionless shear stresses that result in partial transport is quite similar to the range of values documented by Lisle et al. (2000) in six rivers in Colorado and California. These authors demonstrated that bed surface is stable at θc b 0.030, partially mobile at 0.030 b θc b 0.060, and fully mobile at θc N 0.060. These results are similar to those obtained by Wilcock and McArdell (1993) in a flume using sediment with a very poorly sorted bimodal grain-size distribution. These authors demonstrated that full mobility occurs when the shear stress is approximately twice the critical shear stress, with a maximum θc value of 0.090. The formation and destruction of pebble clusters have been studied in relation to the critical shear stress. Reid and Frostick (1984) demonstrated differences in dynamic conditions between the initial motion

and end of movement in a small watercourse (Turkey Brook, UK) equipped with a sediment trap. In this experiment, the bedload transport was continuously monitored. The researchers attributed the observed difference to the fact that the mobilization required the destruction of pebble clusters (Hassan and Reid, 1990). Clifford et al. (1992) expanded upon these observations, calculating a mean θc value of 0.040 for the initial motion and a value of 0.021 at the end of the motion. When the grain shear stress was considered, the θ'c values for the initial motion and for the end of motion are very similar (0.015–0.017). Turowski et al. (2009) studied a stream with a well-developed steppool system morphology. They determined that a general θc value of 0.040 is applicable for coarse particles in a turbulent flow, as recommended by Buffington and Montgomery (1997). However, field observations and flume experiments demonstrated that the Shields criterion increases with the bed slope (Shvidchenko and Pender, 2000; Lenzi et al., 2006; Lamb et al., 2008) and suggested that a value equal to 0.100 appears to be more appropriate given the conditions present in the Erlenbach. Mueller et al. (2005) also documented slope-related differences in θc values. Rivers with a moderate slope, a common feature of GBRs, have θc values between 0.025 and 0.035. For the steepest rivers (slopes N0.020, typical of mountain rivers), the θc values are higher, exceeding 0.060 and as high as 0.120. A similar increase in the θc values related to the slope was documented by Recking (2009) and Gob et al. (2010). Furthermore, Lenzi et al. (2006) determined θc values in a step-pool Alpine torrent N 0.100 and as high as 0.300. According to these authors, such high values have never been reported for natural rivers in the literature. They are mainly related to the finest particles in the torrent (b200 mm). The researchers observed more typical values (between 0.030 and 0.070) for coarser particles, attributing the difference to the effects of submergence and the relative sizes of the particles on their mobility. The authors demonstrated that the critical shear stress decreases when the relative submergence (h/D50) increases. In summary, the values of the Shields criterion presented in this review differ markedly. Several clarifications must be made, at least partially, regarding the notion of the movement initiation of the bedload because a distinction is often made between generalized mobilization and partial mobilization. In the latter case, what percentage of the bedload is affected by the movement? A distinction is also made between movement initiation values established from marked pebbles and that established from the material collected using sediment traps or portable sediment samplers (such as the Helley-Smith device), which can differ significantly in terms of partial or full mobility and in terms of competence (Wilcock, 1988; Bathurst, 2013). Information is commonly available on the diameter of the particles used to determine initial motion, but this information is not always provided in a systematic way. For example, does the D50 correspond to the bedload or the marked tracers (or the recovered marked pebbles)? In the latter case, what is the tracer size relative to the D50 of the bedload? Even if we exclude from this analysis hiding/protrusion effects, which lead to equations involving the ratio (Di/D50), assessing the value of the Shields criterion is still difficult. Moreover, in the definition of movement initiation of the bedload, how far must the marked tracers travel to indicate that they have been mobilized? Some authors consider mobilization to have occurred when a pebble has simply been turned over, whereas others argue that the distance should be at least equal to the diameter of the particle (Mao et al., 2008), and still others argue that the movement must exceed 1 m from the marking site, given the limited accuracy of detection in natural rivers (Houbrechts et al., 2012). Another factor contributing to imprecision is that the shear stress in the majority of studies was estimated from the slope and the hydraulic radius. An average value was then obtained for the entire cross section, even though lateral variations occur in the shear stresses, although these variations are less significant in riffles (usually used as marking sites) than in pools (Petit, 1987). Moreover, in most cases, the total shear stress and not the grain shear stress was estimated.

F. Petit et al. / Geomorphology 250 (2015) 308–320

Taking into account these elements and issues, we have identified three major groups in the values listed in Table 1 and shown in Fig. 1. – The first set of data contains six studies in which the θc values are b0.030. Five other studies with lower bounds below 0.030 are also included in this first group. – The second group contains values between 0.030 and 0.060 (with a clear peak at ~0.045) and six narrow ranges with peaks of ~ 0.045. Several additional ranges are wider and feature only upper limits (i.e., three studies with values b0.050) or only lower limits (eight studies). – The third group contains values N 0.060 and some extremely large ranges. As highlighted by Bunte et al. (2013), the high θc values are present in mountain rivers, and a single value of θc cannot describe incipient motion of the bed D50 size in mountain streams. 4. Characteristics of the studied rivers Most of the rivers studied in this paper are located in the Ardennian massif (Belgium) and belong to the Meuse basin (Fig. 2 and Table 2). This massif is a low mountain area where the substratum is primarily composed of resistant Lower Devonian and Cambro-Ordovician rocks. The riverbed is composed of different types of pebbles, such as sandstone, quartzite, schist, and phyllite, and the material exhibits a noticeable flattened morphology (Houbrechts et al., 2012). This material is relatively coarse and was transported by periglacial processes during

313

the last cold period (Juvigné, 1979; Collard et al., 2012). Under the periglacial conditions, significant quantities of sediment accumulated in the valley bottoms, forming an alluvial plain that can be several meters thick. During the Holocene, only a portion of these gravel sheets were remobilized by lateral erosion, which transported only the finest pebbles, leaving a layer of coarse material and forming an armored bed (Houbrechts et al., 2012). The studied rivers are all characterized by a single channel, which follows a more or less pronounced meandering course. Mobilization of the bedload occurs on average 3–4 times per year, and the critical mobilization discharge (which is lower than the bankfull discharge) is usually reached or exceeded 5 to 20 d/y, depending on the river size (Houbrechts et al., 2006). In terms of stream energy, a sharp contrast exists between the northern and the southern parts of the Ardennian massif. In the northern part, the elevation range is higher (with elevations up to 700 m asl) with a very proximal base level (the Meuse River), which gives the rivers significant energy (e.g., a specific stream power of N 100 W/m2 at the bankfull discharge). By contrast, in the southern part, the slopes are shallower, and the base level is far more distant, which leads to lower specific stream power values (Petit, 1995; Petit et al., 2005b). Five other gravel-bed rivers located outside the Ardennian Massif were studied. First, the Berwinne River (sites 17 and 18 in Fig. 2) is located in the ‘Entre-Vesdre-et-Meuse’ region, and its course cuts through old terraces of the Meuse River. The river's bed is mainly composed of schist pebbles and rounded gravel from the highest terraces of the

Fig. 2. Localisation of the studied sites in the Meuse basin.

314

F. Petit et al. / Geomorphology 250 (2015) 308–320

Table 2 Characteristics of the studied rivers. Rivers

Number

Region

Watershed area (in km2)

Bankfull discharge (in m3/s)

D50 of the bed (in mm)

Stream power at Qb (in W/m2)

River type morphology

Rulles (Anlier Forest) Rulles (Habay la V) Semois (Laviot) Eastern Ourthe Chavanne Hoëgne Aisne (Juzaine) Lower Ourthe (Sauheid)

1 2 3 4 5 6 7 8

Ardenne Ardenne (*) Ardenne Ardenne Ardenne Ardenne Ardenne Ardenne (*)

16 98 1209 179 12 189 186 2910

1.3 11 130 21 2.9 36.8 23.8 300

15-(60) 36 70 66 41 70–200 (**) 92 54 (70)

15 27 23 56 38 140 82 49

Lesse (Eprave) Lhomme (Eprave) Lesse (Villers) Eau Blanche (Nismes) Bocq (Bauche) Bocq (Spontin) Leignon Mehaigne (Moha) Berwinne (Dalhem) Berwinne (Bombaye)

9 10 11 12 13 14 15 16 17 18

Ardenne (*) Ardenne (*) Ardenne (*) Fagne-Famenne Condroz Condroz Condroz Hesbaye Entre-Vesdre-et-Meuse Entre-Vesdre-et-Meuse

419 474 1010 254 230 170 45 345 118 123

37 60 105 29 (°) 26.3 18.3 10 18 17 17

48 58 66 28 (°°) 53 40 33 (°°) 25–70 50 49

50 83 75 31 133 93 36 41 60 72

Well-developed free meanders Well-developed free meanders Entrenched meanders Well-developed free meanders Well-developed free meanders Low sinuosity with riffle/pool sequences Low sinuosity with riffle/pool sequences Entrenched meanders and lower sinuosity with riffle/pool sequences Free meanders in large floodplain Free meanders in large floodplain Free meanders in large floodplain Well-developed free meanders Low sinuosity with riffle/pool sequences Low sinuosity with riffle/pool sequences Well-developed free meanders Well-developed free meanders Well-developed free meanders Well-developed free meanders

(*) See comments in the text regarding the regional localisation of the stations. (**) Reduction of the sediment size in relation with the gradient (see comments in the text). (°) Some reaches recalibrated and rectified river in the 1950s. (°°) Allochtonous elements composing the reconstituted spawning area (see comments in text).

Meuse. In fact, the bed material appears to be too small relative to the competence of the river, which is able to transport considerable quantities of sediment. The gravel entrainment threshold is reached at a low recurrence interval (0.2 year), and bedload transport occurs during an average of 15.5 d/y (Houbrechts et al., 2006). The second and third rivers are the Bocq (sites 13 and 14) and the Leignon (site 15), both situated in the Condroz region. The bed material is composed of sandstone (Upper Devonian) and limestone (Carboniferous) pebbles. The fourth river, the Eau Blanche (site 12), is located in a lithological depression (the Fagne-Famenne) in soft Devonian shale at the foot of the Ardennian massif. The fifth river, the Mehaigne (site 16), is located in the silty area of Hesbaye, north of the Meuse River. In its downstream section, the Mehaigne River traverses a Paleozoic substrate, which provides a gravel load. In addition, the old terraces of the Meuse River are very close to the Mehaigne valley and may also provide pebbles to the river. Typical Ardennian rivers exhibit variable discharge regimes because their watersheds are located on impermeable bedrock and covered by relatively thin soil (Petit, 1995; Gischer et al., 2012). The same is true for the Eau Blanche River, which is located on an impermeable shale substrate. By contrast, the rivers from the Condroz, ‘Entre-Vesdre-etMeuse’ and Hesbaye regions have a less variable discharge regime because they are supplied by springs sourced from permeable rocks (Carboniferous limestone and Cretaceous chalk) covered by thick loess deposits. In terms of hydrographic characteristics (e.g., watershed area and specific stream powers), three types of rivers were studied in this research. The first two types include rivers of modest size (i.e., watershed areas of b 500 km2). The first river type features a single riverbed, and the watercourse often exhibits well-developed meanders (sinuosity index N 1.3). This category includes the Rulles (sites 1 and 2), the Chavanne (site 5), the eastern Ourthe (site 4), the Berwinne (sites 17 and 18), the Mehaigne (site 16), the Leignon (site 15), and the Eau Blanche (site 12). The specific stream power values (as defined below) of these rivers at the bankfull stage are b 70 W/m2. The second river type has greater specific stream power values at the bankfull stage (70–100 W/m2) and lower sinuosity values but still contains riffle and pool sequences. These rivers are the Aisne (site 7), the

Bocq (sites 13 and 14), and the Hoëgne (site 6), which differ in elevation by 520 m over 31 km. Larger rivers such as the lower Ourthe (site 8), the Lesse (sites 9 and 11), the Lhomme (site 10), and the Semois (site 3) were also studied. These rivers feature watershed areas N 1000 km2. Although several flow into the Famenne or Condroz regions in their downstream portions (where the measurement stations are located), they nonetheless retain the characteristics of Ardennian rivers in terms of bedload size, composition, and hydrological regime. The same is true for the Rulles River at the Habay station (site 2). 5. Methodology The oldest marked-pebble campaigns used in situ painted tracers. This approach offers two advantages. (i) The material that constitutes the bed is not dismantled and retains its own organization. (ii) The size of the marked tracers is identical to the D50 of the bed. However, the recovery rate is quite low (Hassan and Ergenzinger, 2003). To estimate the grain size characteristics of the painted pebbles (D50 and D90), we used the grid methodology proposed by Kellerhals and Bray (1971), which was successfully applied in the Canal of Miribel (Petit et al., 1996a). Topographic surveys were performed to ensure that effective mobilization occurred and that the marked pebbles were not simply buried. The marking sites were generally composed of oblique riffles, assuming that these riffles act as filters, given the reversibility of the shear stresses (Andrews, 1979; Petit, 1987; Sear, 1996; Thompson et al., 1996, 1999; Thompson, 2011). Marking sites were established using painted tracers and the grid method in the following rivers: Ourthe, Semois, Lesse, Lhomme, Hoëgne and Mehaigne (Table 3). In the Rulles River (site 1), we painted the elements that constituted the riffles as well as several lenticular pebble outcrops along the banks. The particle size analysis was based on the recovered tracers, which was possible because of the moderate size of the clasts and the low water turbidity. Since 2005, we have systematically used PIT-tag tracers, which are now the most commonly used technique in bedload transport studies (Lamarre et al., 2005; Allan et al., 2006; Rollet et al., 2008; Liébault et al., 2012; Bradley and Tucker, 2012; Houbrechts et al., 2012, 2015; Chapuis et al., 2014, 2015; Arnaud et al., 2015). Using these tracers,

F. Petit et al. / Geomorphology 250 (2015) 308–320

315

Table 3 Values of the dimensionless Shields criterion calculated based on the total shear stress (θc) and the grain shear stress (θ′c) using painted tracers. θc

θ′c

Discharge

D50 of the painted tracers (mm)

0.023–0.027

0.016

0.2–0.3 Qb

0.022–0.033 0.036–0.043 0.038 0.047 0.037 0.066 0.035–0.053 0.051 0.062 0.019 0.026–0.029 0.041

0.016 0.023–0.028 0.024 0.022 0024 0.012 0.015 0.015 0.021 0.012 0.015 0.012

0.4 Qb 2.2 Qb (Q30 yrs) 0,7 Qb Qb Qb 0.3–0.6 Qb Qb 2 Qb Qb 1.4–2.7 Qb 0.3–0.8 Qb 0.45 Qb

Partial mobilization 56–65 57–86 86 Full mobility 58 48 66 130–41 20–30 (pool) 60 (pool) 15 (riffle crossing) 70 25–70 64

the definition of initial motion met the following systematically adopted rules: (i) the marked pebbles were always placed in riffles; (ii) the size of the marked pebbles was the same as the bed grain size; (iii) mobilization was considered to have occurred when the mean distance traveled by the pebbles was at least 1 m; and (iv) at least 10% of the pebbles were mobilized (Houbrechts et al., 2012). For the Leignon River in the context of a restoration project (Peeters et al., 2013), we must use allochthonous pebbles as tracers: the PITtagged pebbles (D50 of 31 mm) were sampled in an artificial spawning area composed of pebbles with diameters between 21 and 47 mm. Similarly, for the Eau Blanche River, 100 PIT-tagged pebbles were also marked in a spawning area composed of allochthonous pebbles (with diameters between 17 and 44 mm and a D50 of 28 mm). In addition, sediments were also collected in sediment traps during floods. First, we had the opportunity to use a pit trap in the Chavanne (site 5). Indeed, during the construction of the E25 motorway, the course of the river was modified (Houbrechts et al., 2012). In summary, three rectangular pits (with an opening 2 m long and 1 m wide) were dug in the bottom of the bed. Because these pits encompassed nearly the whole width of the bed, they served as bedload traps. These pits were emptied manually on 23 occasions between May 2006 and October 2010. In the Rulles River (in Anlier Forest, site 1), a bedload trap was constructed in the 1970s. It consists of a manually over-deepened pool closed by a small dam downstream. The bottom is covered by a plastic sheet supported by a metal and wood framework. Moreover, 10 metal plates (20 by 20 cm) were installed in the trap (see illustration in Houbrechts et al., 2013). This trap was monitored each year (in terms of sediment size trapped) until the mid-1980s, when it was destroyed. We have several results from HS76 bedload samplers, but we will only present those for mobilization discharge. For a sampler with a standard opening of 76 mm, the maximum efficiency will be obtained for a load in which the elements are smaller than 16 mm (Emett in Klingemann and Emmett, 1982). Given the frequency of mobilizing floods and the modest size of bedload, samples were only taken in the Berwinne (site 17) and the Eau Blanche (site 12). As for the sediment traps, bedload samplers also collect fine elements that are particularly present in the subsurface and that are released when a rupture (even partial) occurs in the armored bed. Thus, the D90 of the elements collected in the sampler is often close to the D50 of the bed. The total shear stresses and the grain shear stresses were evaluated using the equations presented above (Eqs. (1), (2)). Field measurements conducted at different discharges provided geometrical characteristics (width, depth, slope) for calculating the total shear stress (Eq. (1)), the grain shear stress (Eq. (2)) and the Manning values. The Strickler coefficient (Eq. (2b)) is known by granulometric analysis of the bed material; observations of the movement of tracers provide the mobilization discharge and thus the geometrical characteristics during these discharges (Petit, 1990; Houbrechts et al., 2006).

Reference Lower Ourthe

Petit et al. (1996b)

Lower Ourthe Lower Ourthe Lhomme Lesse (Eprave) Lesse (Villers) Hoegne Rulles (Anlier forest) Rulles (Anlier forest) Rulles (Anlier forest) Semois Laviot Mehaigne Eastern Ourthe (1994)

Petit et al. (1996b) Petit et al. (1996b) Franchimont (1993) Franchimont (1993) Franchimont (1993) Deroanne (1995) Petit (1987) Petit (1987) Petit (1987) Gob et al. (2005) Perpinien (1998) Petit & Pauquet (1995)

In some rivers, evaluation of shear stresses using shear velocities (Eq. (3)) has been possible, including the eastern Ourthe River (site 4) based on campaigns performed in 1994 (see Table 3). Sixteen gauging measurements obtained at the limnigraphic station of Houffalize (data provided by the DCENN) permitted the calculation of flow velocity close to the bottom of the riverbed, as well as shear velocities and shear stresses using Eq. (3). A significant relationship (R2 = 0.891) was then established between the discharge and the shear stress, which permitted an estimation of the critical shear stresses at the initiation of the bedload mobilization (Petit and Pauquet, 1995). In the Rulles River (in Anlier Forest, site 1), velocities for discharges exceeding 3 Qb have been measured in more than 20 sites, whereas the mobilization discharge reaches only 0.8 Qb (Petit, 1987). The range of discharges, the study period, and the frequency of site visits relative to events are different for each river. Thus, we will consider these aspects in relation to each site in the next section. 6. Results and discussion 6.1. Marked pebbles Seven marking locations in the lower Ourthe, the largest of the studied rivers, were established in three large oblique riffle sites. Depending on the occurrence of mobilizing floods, these markings were observed up to five times. These observations were the subject of a detailed synthesis (Petit et al., 1996b) and were then linked with the total shear stresses calculated for different discharges when the bed material was mobilized. Translated into the Shields criterion, these observations yield θc values of 0.023 to 0.027 for floods that only partially mobilized the marking sites, depending on the location. When the grain shear stress is taken into account, the Shields criterion is ~ 0.016. During a 30-year flood, full mobility occurred with breaking up of the armor layer (Houbrechts et al., 2012). The shear stresses reached values ranging from 50 to 60 N/m2, corresponding to θc values between 0.036 and 0.043 and θ′c values between 0.023 and 0.028. For the Lesse and Lhomme, two medium-sized rivers, the Shields criterion values highlighted by Franchimont (1993) were between 0.037 and 0.047 when total shear stress was used and b0.025 when grain shear stress was used. Partial mobilization was likely exceeded because all marked elements were swept away even when the floods were not exceptional, close to the Qb for the Lesse and 0.7 Qb for the Lhomme. In the Semois River, the mobilization of painted pebbles was followed during two mobilizing floods (Gob et al., 2005). The θc values seem unusually low (0.019) for floods of this magnitude (2.5- and 25-year floods). By contrast, the θ'c values are closer to those observed in other rivers (Table 3). We must consider that the downstream portion of the Semois course includes incised meanders in which relatively little differentiation occurs in the bedforms (few riffle/pool alternating sequences, few convexity deposits and oblique riffles, and shallow

316

F. Petit et al. / Geomorphology 250 (2015) 308–320

Table 4 Values of the dimensionless Shields criterion calculated based on the total shear stress (θc) and the grain shear stress (θ'c) using PIT-tag tracers. θc

θ′c

Discharge

D50 or M10 mobilized PIT-tag tracers (mm)

Number of marked pebbles recovered (in %)

0.043 0.050 0.042 0.032 0.035 0.042 0.036 0.030 0.049

0.023 0.023 0.013 0.012 0.012 – – 0.023 0.028

1.5 Qb (11 years) 1.5 Qb (11 years) 0.8 Qb (0.5 years) 0.9 Qb (0.58 year) 0.6 Qb (0.29 year) Q = 10 years 2.2 Qb (7 years) 1.4 Qb (2 years) Qb

56 (D50) (M10 = 115) 48 (D50) (M10 = 68) 58 68 51 90 36 28 (D50) 31

84 75 90 93 92 78 86 77 67

Bocq (Bauche) Bocq (Spontin) Eastern Ourthe (*) Eastern Ourthe Eastern Ourthe Aisne Rulles H-l-V Eau Blanche (Nismes) Leignon

(*) natural site (upstream of the town of Houffalize) under conditions close to those affecting the Eastern Ourthe in Table 3.

pools limited by bedrock outcrops; Gob et al., 2005). Thus, the difference between total shear stress and grain shear stress is smaller than in other rivers. Six marking sites were established in the Mehaigne River by Perpinien (1998). The D50 varied from 25 to 70 mm, depending on the location. Two mobilizing floods occurred with discharges lower than the bankfull discharge (0.3 and 0.8 Qb), corresponding to movement initiation conditions, which could explain the relatively low values of θc (between 0.026 and 0.029) and θ′c (0.015). Perpinien (1998) also noted that the shear stress estimated based on the shear velocities (using y0 = 0.20 D50 in Eq. (3b)) is very close to the grain shear stress estimated based on the method employing Eqs. (2) and (2b). In the eastern Ourthe River, seven locations were marked in areas with meandering morphology. More than 100 marked pebbles were mobilized during a flood that reached only 0.42 Qb (Petit and Pauquet, 1995). Seven locations on the Hoëgne River uniformly distributed along its course were marked. The slope of this river is steep, and a drastic reduction in the size of the material is observed: the D50 of the bed exceeds 200 mm in the upstream part but is on the order of 70 mm in the downstream part of the watercourse (Deroanne and Petit, 1999). Mobilization was recorded during two floods that were less than the bankfull discharge (0.3 and 0.6 Qb). These events were partial mobilization (b50% of the markers were transported), even if the θc values were high (0.066). This pattern caused by the high bed roughness (bedform shear stress), which is related to the presence of coarse elements. This hypothesis was confirmed by the θ'c value; the results were significantly lower (0.012) than the θc values and of the same order of magnitude as those of rivers with similar characteristics in terms of bedform shear stress (but not necessarily in terms of fluvial patterns), such as the Rulles River. A detailed analysis of the Rulles River (site 1) monitoring has been presented (Petit, 1987, 1990; Petit et al., 2005a). The marked pebbles (more than 250 elements) were eroded in the pools during floods close to the bankfull discharge and during much more intense floods. These results yielded θc values between 0.035 and 0.053. For floods near the bankfull discharge, 15-mm marked pebbles were transported across several riffles, which allowed us to define a θc value of 0.062. These values are generally higher than those measured in larger rivers. However, the θ'c values are fairly similar (between 0.015 and 0.021). This result can be explained by the fact that the Rulles is a mediumsized river with pronounced sinuosity, a close succession of riffles and pools, counter-current flow cells in the meanders, and many logjams. A significant proportion of the river's energy is lost because of bedform resistance. Thus, given the importance of the bedform shear stresses, a higher total shear stress is required to mobilize elements of a given size. By contrast, when we take into account only the grain shear stress, we observe values consistent with the other measurements (Petit, 1987, 1990). From Table 3, we can finally estimate an average θc value of 0.040 and an average θ'c value of 0.018.

The values obtained using pebbles equipped with PIT-tag tracers are presented in Table 4. Note that these observations relate only to medium-sized rivers because of the marking technique limitations. The equipped sites have at least 100 tracers. In our case, the recovery rate is on the order of 80 to 90%, even after several years. We obtained θc values close to those reported in painted tracer campaigns (θc = 0.040 and θ'c = 0.019 on average). As we observed for the lower Ourthe, the values are slightly higher during larger floods. The values for the Aisne and the Bocq were measured during a 10-year flood, which suggests total mobility rather than partial mobility or movement initiation. These results may explain the relatively high θc values: 0.042 for the Aisne River and between 0.043 and 0.050 for the Bocq (and θ′c values close to 0.023). The analysis of the Eau Blanche marking site revealed that most of the elements were mobilized after a series of floods, the largest of which reached a 2-year discharge, and the mobilized D50 was identical to the injection D50. However, the shear stress of the large flood was only 14 N/m2, which explains the low θc value (0.030). The Eau Blanche River was rectified and recalibrated in the 1950s, which may explain the low bedform shear stress values and the consequently low total shear stress of the initial motion. Moreover, the PIT tag size (28 mm) is larger than the bed D50 (19 mm), and a small protrusion effect is not out of the question. For the Leignon River, the particle size distribution marking site has a relatively small extent (21–47 mm), and every marked pebble was mobilized by the bankfull discharge. This situation explains the relatively high values of θc (0.049) and θ′c (0.028) because we have full mobility. Indeed, partial mobility was observed for lower discharge (0.25 Qb). For the eastern Ourthe (site 4), the observations are closer to the conditions of early mobilization (floods lower than the bankfull discharge), which may explain the relatively low values of θc (between 0.032 and 0.042) and θ′c (0.012) (Peeters et al., 2009). In addition, two measurements were obtained under artificial conditions (e.g., channels with regular geometric cross sections) through the town of Houffalize, whereas one measurement was obtained under natural conditions (upstream from Houffalize) similar to those in the eastern Ourthe in 1994 (Table 3). These location differences may explain the low θc values compared with the values obtained where the meandering system was more developed in the natural sector. By contrast, the θ′c values were more comparable. Few marked pebbles were mobilized on the Rulles River (site 2) and only over relatively short distances, even though the river experienced a significant flood with a return period exceeding a 5-year discharge (Levecq et al., 2014). The shear stress was slightly N20 N/m2 and was not able to mobilize elements coarser than 40 mm, resulting in a θc value of 0.036. This river, like most rivers in the southern part of the Ardennian massif, has a relatively low energy (Petit et al., 2005b). Our θc values based on marked pebbles (painted and PIT-tag tracers) range from 0.020 to 0.066, with an average value of 0.037. The θ′c values range from 0.012 to 0.028, with an average value of 0.019. The average θ′c/θc ratio is equal to 0.5, with some variations depending on the type of

F. Petit et al. / Geomorphology 250 (2015) 308–320

317

Table 5 Values of the dimensionless Shields criterion calculated based on the total shear stress (θc) and the grain shear stress (θ'c) using sediment traps. θc

θ′c

Q

M10 or D90 of sediment trap samples (mm)

0.035 0.074

0.013 0.027

0.3–2 Qb 2.5–3.5 Qb

5–60 (M10) 11.5–26 (D90)

river; the average is higher than 0.6 for large rivers (such as the Ourthe, Lesse, and Semois) and ~0.3–0.4 for medium-sized rivers (such as the Rulles, Mehaigne, Bocq, and Aisne). 6.2. Elements collected in sediment traps In the Chavanne River, the θc value is 0.035, which is an average value calculated for 12 different floods ranging from 0.3 to 2 Qb (Table 5). The size of the mobilized elements varies from 5 to 60 mm. Individual values deviate slightly from this proposed average. However, a clear differentiation in θc is observed because of the flattened shape of the particles (i.e., phyllite vs. arkose). When using the equivalent diameter, this differentiation is diminished, and the θc value reaches 0.045. This value corresponds to the expected values of rivers with high bedform shear stress. Similarly, the calculated average θ′c value during these different floods was 0.013. The sediment trap installed in the Rulles River in the Anlier Forest (site 1) was emptied four times. Between any two measurements, the sediment trap integrated the mobilized sediment and recorded several floods well above the bankfull discharge. During the period when the least significant floods occurred (max. 2.5 Qb), the D90 of the trapped sediment (11.5 mm) was slightly lower than the D50 of the riverbed (15 mm, the average value for six riffles located just upstream of the sediment trap). However, following a 5-year flood, the D90 of the sediment trap was significantly higher (26 mm), and the D50 of the trapped material (16.5 mm) exhibited a closer correspondence with the D50 of the riverbed. We computed the shear stresses in the six upstream riffles for the corresponding discharges. The θc values varied from 0.048 to 0.091, depending on the magnitude of the flood, with an average value of 0.074; and the θ′c values varied from 0.019 to 0.032, with an average value of 0.027. These results suggest that a wide gap exists between total shear stress and grain shear stress, as already observed in the results based on marked pebbles. The values recorded in the Rulles are higher than those highlighted in the Chavanne. In the latter case, we took into account the 10 coarsest elements collected in the trap (M10), whereas we used the D90 value for the Rulles. This artifact results from a conceptual evolution based on different tests (Sluse and Petit, 1998; Houbrechts et al., 2011) of the representative size of the coarse elements.

Chavanne Rulles (Anlier Forest)

not during larger floods. Thus, the proposed values are close to those of movement initiation. The D90 value (22 mm) in the Eau Blanche River using the sampler HS76 is close to the D50 value of the bed (19 mm, Table 6). The θc value (0.040) is low for a Helley-Smith sampler because the sampling site was located in a reach of the river that was rectified in the 1950s. In the Berwinne River, we have several observations of bedload transport (Table 6). However, these values were obtained for discharges significantly more important than the mobilization discharge (0.3 Qb in Houbrechts et al., 2006), which explains the larger θc values (~0.060). In general, the movement initiation values based on the bedload sampler appear to be slightly (but not excessively) higher than those obtained based on marked pebbles. The values range between 0.040 and 0.067 when total shear stress is used and between 0.017 and 0.027 when grain shear stress is used. Furthermore, the average ratio between θ′c/θc is close to 0.4, which is similar to the ratio observed in association with the sediment traps. 6.4. Shear velocities The θ⁎c values for the eastern Ourthe based on campaigns performed in 1994 reach 0.023 on average (Table 7), whereas the θc and θ'c values are 0.041 and 0.012, respectively (see Table 3). The Shields criteria obtained from shear velocities (Eq. (3)) and grain shear stresses (Eq. (2)) are not clearly equivalent but are closer than that achieved from total shear stress (Eq. (1)). This adequation is better for the Rulles River. Marked pebbles were eroded in pools during different floods and yielded θ⁎c values ranging from 0.025 to 0.031 (Table 7). Identical values were obtained for the elements that were able to travel beyond the riffles. Note that the flow velocities near the bottom of the bed were measured at these sites during different hydrological events (Petit, 1987, 1990). The θ⁎c values are closer to those obtained using grain shear stress 0.017 (0.015–0.021), whereas the θc values reach 0.050 on average. The values obtained from other gravel-bed rivers, such as the Ruisseau de la Mer in the Ardennian massif (Mercenier, 1973) and in a gravel-bed reach of the Rouge Eau in the Lorraine (Petit, 1990), are very similar (respectively 0.031 and 0.023). 7. Synthesis and conclusions

6.3. Elements collected in a bedload sampler For reasons given in the methodology, θc values from bedload samplers are only proposed for the Berwinne and Eau Blanche (Table 6). Sampling performed with a bedload sampler (HS76) does not necessarily correspond to the discharge associated with movement initiation. If the flood significantly exceeds this threshold, the Shields criterion may be overestimated. However, the measurement in the Eau Blanche River was obtained during floods close to the bankfull discharge and

The objectives of this paper were first to make a synthesis of the Shields criterion values proposed in the literature and second to propose values obtained from 14 gravel-bed rivers (18 sites) from the Ardennian massif. The Shields criterion is considered in a large field of research, and having some values reliable is necessary. Previous analyses have demonstrated that the values of the Shields criterion are extremely variable (see Table 1 and Fig. 1). When total shear stress was considered, we attempted to group these values into

Table 6 Values of the dimensionless Shields criterion calculated based on the total shear stress (θc) and the grain shear stress (θ'c) using a portable bedload samplers (HS76). θc

θ'c

Q

D90 of bedload samplers (mm)

0.054 0.067 0.058 0.040

0.017 0.021 0.018 0.027

1.3 Qb 0.65 Qb 1.07 Qb 0.95 Qb (1.1 year)

46 27 40.7 22

Berwinne (19/01/2007) Berwinne (7/12/2007) Berwinne (17/02/2009) Eau Blanche (Nismes)

318

F. Petit et al. / Geomorphology 250 (2015) 308–320

Table 7 Values of the dimensionless Shields criterion using the shear stresses calculated using the shear velocities (u⁎). θ*c 0.023 0.025–0.031 0.031 0.031

Size of tracers (in mm) 0.42 Qb 2 Qb Qb Qb

64 40–50 20 15

Eastern Ourthe Rulles (Anlier Forest) Rulles (Anlier Forest) Rulles (Anlier Forest)

three data sets: θc values of ~0.030, θc values between 0.030 and 0.060 (with an average value close to 0.045), and θc values N0.060 (in some cases exceeding 0.100). In our case, we obtained an average Shields criterion (computed using total shear stress) of 0.040, with some small deviations. Lower values (0.025) were observed in large rivers, and higher values (more than 0.050) were observed in small rivers or rivers with a significantly meandering course because of huge bedform shear stresses, such as in the Rulles (Anlier Forest, site 1), the Chavanne (site 5), and the Hoëgne (site 6). Of course, with grain shear stress (Table 1), the literature gives θ′c values that are lower (0.015–0.035) than the θc values. Using grain shear stress, we obtained Shields criterion values ranging from 0.012 to 0.028, with an average value of 0.019. Our results correspond reasonably well to those in the literature. However, these values are significantly lower than those proposed by Garcia et al. (2000). In that study, the values were calculated based on sediment trap results (which led to higher Shields criterion values because the sediment trap results represent widespread mobilization of the bedload), and microforms on the bed can ‘consume’ part of the shear stress. More generally, we believe it is important to keep in mind that the values of critical grain shear stress are essential because this parameter is involved in the bedload transport equations, such as the Meyer-Peter and Mueller equations. With a lower value of critical shear stress, the bedload transport equation will give higher transport rates. However, transport equations may already overestimate measured transport rates. Remember that the sediment transport equations give a potential value of sediment discharge, assuming a sufficient quantity of movable material (Gob et al., 2005). It is not always the case for the Ardennian rivers, where the availability of movable sediment seems limited, as attested by the low annual specific bedload discharge of b 3 t/km2/y (Houbrechts et al., 2006). Few reports on the Shields criterion based on the shear velocities measured in natural rivers are present in the literature. We proposed seven values with an average of 0.023 for the Ourthe River and a range between 0.021 and 0.031 for the Rulles River. These values are close to those proposed in other studies: 0.015 to 0.030 (Hammond et al., 1984), 0.015 (Clifford et al., 1992), 0.015 (May and Pryor, 2014), and 0.023 (Phillips et al., 2013). We also observed different values depending on the type of mobilization (partial and total). For instance, the θc values varied from ~0.025 for partial transport to 0.040 for the widespread mobilization of the riverbed (cf. observations made during floods with a return period N10 years, particularly in the lower Ourthe, the Aisne, and the Bocq). These results correspond to the observations of Wilcock et al. (1996), who demonstrated that negligible particle movement and the mobilization of the majority of the riverbed surface occurred over a narrow shear on the order of only 10 to 15% of the Shields criterion. Our results only partially correspond to those of Andrews (1994), who suggested that the transport that occurs for θc values between 0.020 and 0.040 is marginal and that the values must exceed 0.060 to produce widespread transport. The values proposed by Andrews are similar to those of Mao and Surian (2010); Lisle et al. (2000), and Wilcock and McArdell (1993), who suggested values significantly higher than those identified in our study. The values obtained from sediment traps and from a portable bedload sampler are greater than those obtained from tracers, similar

to the pattern observed in the literature but with less pronounced differences. The equivalence between shear stresses calculated with shear velocities and grain shear stress (from marked pebbles) has been highlighted previously in the literature (Petit, 1989; Assani and Petit, 1995). The present study demonstrates that the values of the Shields criterion obtained using the shear velocities (from 0.023 to 0.031) are closer to those obtained using an average θ′c value of 0.019 (varying from 0.012 to 0.028) than are those obtained using an average θc value of 0.040 (from 0.019 to 0.066). Acknowledgments This paper is based on results obtained from several research projects financed by the DCENN (Direction Générale des Cours d'Eau non navigables, Service Public de Wallonie) and by the European Union through a LIFE + Project (Walphy). The hydrological data was kindly made available by the DCENN and by the SETHY (Service d'Etudes hydrologiques de la Région Wallonne). The authors thank the reviewers and the editor for their constructive comments and suggestions that significantly improved this paper. References Allan, J.C., Haert, R., Tranquili, J.V., 2006. The use of passive integrated transponder (PIT) tags to trace coble transport in a mixed sans-and-gravel beach on the high-energy Oregon coast, USA. Mar. Geol. 232, 63–86. Andrews, E.D., 1979. Scour and fill in a stream channel, East Fork River, Western Wyoming. U.S. Geological Survey Professional Paper, 1117 (49 pp.). Andrews, E.D., 1983. Entrainment of gravel from naturally sorted river bed material. Geol. Soc. Am. Bull. 94, 1225–1231. Andrews, E.D., 1994. Marginal bed load transport in a gravel bed stream, Sagehen Creek, California. Water Resour. Res. 30, 2241–2250. Arnaud, F., Piégeay, H., Vaudor, L., Bultingaire, L., Fantino, G., 2015. Technical specifications of low-frequency ratio identification bedload tracking from fields experiments: differences in antennas, tags and operators. Geomorphology 238, 37–46. Assani, A.A., Petit, F., 1995. Log-jams effect on bed-load mobility from experiments conducted in a small gravel-bed forest ditch. Catena 25, 117–126. Baker, V.R., Ritter, D.F., 1975. Competence of rivers to transport coarse bedload material. Geol. Soc. Am. Bull. 86, 975–978. Batalla, R.J., Martin-Vide, J.P., 2001. Thresholds of particles entrainment in poorly sorted sandy gravel-bed river. Catena 44, 223–243. Bathurst, J.C., 2013. Critical conditions for particle motion in coarse bed materials of nonuniform size distribution. Geomorphology 197, 170–184. Bathurst, J.C., Graf, W.H., Cao, H.H., 1987. Bed load discharge equations for steep mountain rivers. In: Thorne, C.R., Bathurst, J.C., Hey, R.D. (Eds.), Sediment Transport in Gravelbed Rivers. John Wiley, Chichester, UK, pp. 453–477. Bradley, D.N., Tucker, G.E., 2012. Measuring gravel transport and dispersion in a mountain river using passive radio tracers. Earth Surf. Process. Landf. 37, 1034–1045. Bridge, J.S., Jarvis, J., 1982. The dynamic of a river bend: a study in flow and sedimentary processes. Sedimentology 29, 499–541. Buffington, J.M., Montgomery, D.R., 1997. A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers. Water Resour. Res. 33, 1993–2029. Bunte, K., 1992. Particle number grain-size composition of bedload. In: Billi, P., Hey, R.D., Thorne, C.R., Tacconi, P. (Eds.), A Mountain Stream. Wiley, Dynamics of Gravel-bed Rivers, pp. 55–72. Bunte, K., Steven, R.A., Potyondy, J.P., Swingle, K.W., 2008. A comparison of coarse bedload transport measured with bedload traps and Helley-Smith samplers. Geodin. Acta 21, 53–66. Bunte, K., Abt, S.R., Swingle, K.W., Cenderelli, D.A., Schneider, J.M., 2013. Critical Shields values in coarse-bedded steep streams. Water Resour. Res. 49, 7427–7447. Carling, P.A., 1983. Threshold of coarse sediment transport in broad and narrow natural streams. Earth Surf. Process. Landf. 8, 135–138. Chapuis, M., Bright, C.J., Hufnagel, J., MacVicar, B., 2014. Detection ranges and uncertainly of passive radio frequency identification (RFID) transponders for sediment tracking in gravel rivers and coastal environments. Earth Surf. Process. Landf. 2109-2120. Chapuis, M., Dufour, S., Provansal, M., Couvert, B., de Linares, M., 2015. Coupling channel evolution monitoring and RFID tracking in a large, wandering, gravel-bed river: insights into sediment routing on geomorphic continuity through a riffle-pool sequence. Geomorphology 231, 258–269. Clifford, N.J., Richards, K.S., 1992. The reversal hypothesis and the maintenance of rifflepool sequences. In: Carling, P.A., Petts, G.E. (Eds.), Lowland Rivers: Geomorphological Perspectives. Wiley, Chichester, pp. 43–70. Clifford, N.J., Richards, K., Robert, A., 1992. The influence of microforms bed roughness elements on flow and sediment transport in gravel bed rivers: comment on a paper by Marwan, A., Hassan, M., Reid, J. Earth Surf. Process. Landf. 17, 529–534. Collard, S., Juvigné, E., Marion, J.M., Mottequin, B., Petit, F., 2012. L'origine des mégalithes du Fond de Quarreux (Ardenne, Belgique). Bull. Soc. Géogr. Liège 58, 33–52.

F. Petit et al. / Geomorphology 250 (2015) 308–320 Costa, J.E., 1983. Paleohydraulic reconstruction of flash-flood peaks from boulder deposits in the Colorado front range. Geol. Soc. Am. Bull. 94, 986–1004. Deroanne, C., 1995. Dynamique fluviale de la Hoëgne. Évaluation longitudinale des caractéristiques sédimentologiques du lit et des paramètres de mobilisation de la charge de fond. Mémoire de licence en Sciences Géogr.University of Liège, Belgium (155 pages) Deroanne, C., Petit, F., 1999. Longitudinal evaluation of the bed load size and of its mobilisation in a gravel bed river. In: Casale, R., Margottini, C. (Eds.), Floods and Landslides, Integrated Risk Assesment. Springer-Verlag, Berlin, pp. 335–342 (Chap. 22). Dietrich, W.E., Smith, J.D., Dunne, T., 1979. Flow and sediment transport in a sand bedded meander. J. Geol. 87, 305–315. Ferguson, R.I., 1994. Critical discharge for entrainment of poorly sorted gravel. Earth Surf. Process. Landf. 19, 179–186. Ferguson, R.I., 2005. Estimating critical stream power for bedload calculations in gravelbed rivers. Geomorphology 70, 33–41. Ferguson, R.I., Wathen, S.J., 1998. Tracer-pebble movement along a concave river profile: virtual velocity in relation to grain size and shear stress. Water Resour. Res. 34, 2031–2038. Franchimont, C., 1993. Dynamique fluviale de La Lesse: fréquence des inondations, morphométrie des méandres et sédimentologie du lit. Mémoire de licence en Sciences Géogr. University of Liège, Belgium (121 pp.). Frings, R.M., Berbee, B.M., Erkens, G., Kleinhans, M.G., Gouw, M.J.P., 2009. Human-induced changes in bed shear stress and bed grain size in the river Waal (The Netherlands) during the past 900 years. Earth Surf. Process. Landf. 34, 503–514. Frothingham, K.M., 2008. Evaluation of stability threshold analysis as a cursory of screening potential streambank stabilization techniques. Appl. Geogr. 28 (2), 124–133. Gao, P., 2011. An equation for bed-load transport capacities in gravel-bed rivers. J. Hydrol. 402, 297–305. Garcia, C., Laronne, J.B., Sala, M., 2000. Continuous monitoring of bedload flux in a mountain gravel-bed river. Geomorphology 34, 23–31. Gessler, J., 1971. Beginning and ceasing of sediment motion. In: Shen, H.W. (Ed.), River Mechanics. Colorado State University, Fort Collins (Ch 7, 22 pp.). Gintz, D., Hassan, M.A., Schmidt, K.H., 1996. Frequency and magnitude of bedload transport in a mountain stream. Earth Surf. Process. Landf. 21, 433–445. Gischer, L., Hallot, E., Houbrechts, G., Van Campenhout, J., Petit, F., 2012. Analyse des débits en période de tarissement: Essai d'une typologie régionale appliquée à des rivières du bassin de la Meuse (Belgique). Bull. Soc. Géogr. Liège 59, 59–80. Gob, F., Houbrechts, G., Hiver, J.M., Petit, F., 2005. River dredging, channel dynamics and bedload transport in an incised meandering river (the River Semois, Belgium). River Res. Appl. 21, 791–804. Gob, F., Jacob, N., Bravard, J.P., Petit, F., 2008. The value of lichenometry in assessing the incision of submediterranean rivers from little ice age, the Ardeche and the upper Loire (France). Geomorphology 94, 170–183. Gob, F., Bravard, J.P., Petit, F., 2010. The influence of sediment size, relative grain size and channel slope on initiation of sediment motion in boulder bed rivers. Earth Surf. Process. Landf. 35, 1535–1547. Graf, W.H., 1971. Hydraulics of Sediment Transport. Mc Graw Hill (513 pp.). Habersack, H.M., Nachtnebel, H.P., Laronne, J.B., 2001. The continuous measurement of bedload discharge in a large alpine gravel bed river. J. Hydraul. Res. 39, 125–133. Hammond, F.D.C., Heathershaw, A.D., Langhorne, D.N., 1984. A comparison between Shields' threshold criterion and the movement of loosely packed gravel in tidal channel. Sedimentology 31, 51–62. Hassan, M.A., Ergenzinger, P., 2003. Use of tracers in fluvial geomorphology. In: Kondolf, G.M., Piégay, H. (Eds.), Tools in Fluvial Geomorphology. Wiley, Chichester, pp. 397–423. Hassan, M.A., Reid, I., 1990. The influence of microform bed roughness elements on flow and sediment transport in gravel bed rivers. Earth Surf. Process. Landf. 15, 739–750. Heays, K.G., Friedrich, H., Melville, B.W., 2014. Laboratory study of gravel-bed cluster formation and disintegration. Water Resour. Res. 50, 2227–2241. Hey, R.D., 1979. Flow resistance in gravel bed rivers. Am. Soc. Civ. Eng. Hydr: Div. 105, 365–379. Hjulstrom, F., 1935. Studies of morphological activity of rivers as illustrated by the River Fyris. Bulletin of the Geological Institute 25. University of Uppsala, pp. 221–527. Houbrechts, G., Hallot, E., Gob, F., Mols, J., Defechereux, O., Petit, F., 2006. Fréquence et importance du charriage dans les rivières du massif ardennais. Géog. Phys. Quatern. 60, 247–258. Houbrechts, G., Levecq, Y., Vanderheyden, V., Petit, F., 2011. Long-term bedload mobility in gravel-beds rivers using iron slag as a tracer. Geomorphology 126, 233–244. Houbrechts, G., Van Campenhout, J., Levecq, Y., Hallot, E., Peeters, A., Petit, F., 2012. Comparison of methods for quantifying active layer dynamics and bedload discharge in armoured gravel-bed rivers. Earth Surf. Process. Landf. 37, 1501–1517. Houbrechts, G., Hallot, E., Levecq, Y., Denis, A.-C., Van Campenhout, J., Peeters, A., Petit, F., 2013. Images CM de Passega des rivières ardennaises. Bull. Soc. Géogr. Liège 61, 37–68. Houbrechts, G., Levecq, Y., Van Campenhout, J., Hallot, E., Peeters, A., Petit, F., 2015. Evaluation of bedload travel rates in gravel-bed rivers. Geomorphology http://dx. doi.org/10.1016/j.geomorph.2015.05.012. Jackson, W.L., Beschta, R.L., 1982. A model of two phase bedload transport in an Oregon coast range stream. Earth Surf. Process. Landf. 7, 517–527. Juvigné, E., 1979. L'encaissement des rivières ardennaises depuis le début de la dernière glaciation. Z. Geomorphol. 23, 291–300. Kellerhals, R., Bray, D.I., 1971. Sampling procedures for coarse fluvial sediments. J. Hydraul. Div. ASCE 97 (HY 8), 1165–1180. Klingemann, P.C., Emmett, W.W., 1982. Gravel bedload transport processes. In: Hey, R.D., Bathurst, J.C., Thorne, C.R. (Eds.), Gravel-bed Rivers: Fluvial Processes, Engineering and Management. Willey, Chichester, pp. 141–169.

319

Knighton, D., 1998. Fluvial Forms and Processes: A New Perspective. Arnold, London (383 pp.). Kociuba, W., Janicki, G., 2014. Continuous measurements of bedload transport rates in a small glacial river catchment in the summer season (Spitzbzegen). Geomorphology 212, 58–71. Komar, P.D., 1987. Selective grain entrainment by a current from a bed mixed sizes: a reanalysis. J. Sediment. Petrol. 57, 203–211. Lamarre, H., MacVicar, B., Roy, A., 2005. Using passive integrated transponder (PIT) tags to investigate sediment transport in gravel-bed rivers. J. Sediment. Res. 75, 736–741. Lamb, M.P., Dietrich, W.E., Venditti, J.G., 2008. Is the critical Shields stress for incipient sediment motion dependent on channel-slope? J. Geophys. Res. 113, F02008. http://dx.doi.org/10.1029/2007JF000831. Latapie, A., Camenen, B., Rodrigues, S., Paquier, A., Bouchard, J.P., Moatar, F., 2014. Assessing channel response of a long river influenced by human disturbance. Catena 121, 1–12. Lavé, J., Avouac, J.P., 2001. Fluvial incision and tectonic uplift across the Himalayas of central Nepal. J. Geophys. Res. 106 (11), 26,561–26,591. Lenzi, M.A., D'Agostino, V., Billi, P., 1999. Bedload transport in the instrumented catchment of the Rio Cordon. Part 1: analysis of bedload records, conditions and threshold of bedload entrainment. Catena 36, 171–190. Lenzi, M.A., Mao, L., Comiti, F., 2006. When does bedload transport begin in steep boulderbed streams? Hydrol. Process. 20, 3517–3533. Levecq, Y., Houbrechts, G., Peeters, A., Petit, F., 2014. Caractérisation et quantification des sédiments en rivières en relation avec une différenciation régionale (phase 3). Rapport Final, Direction Générale des Cours d’Eau Non Navigables. Ministère de la Région Wallonne (91 pp.). Liébault, F., Clément, P., 2007. La mobilité de la charge de fond des rivières torrentielles méditerranéennes. Géog. Phys. Quatern. 61, 7–20. Liébault, F., Piégay, H., 2001. Assessment of channel changes due to long-term bedload supply decrease, Roubion River, France. Geomorphology 36, 167–186. Liébault, F., Bellot, H., Chapuis, M., Klotz, S., Deschatres, M., 2012. Bedload tracing in a high-sediment-load mountain stream. Earth Surf. Process. Landf. 37, 385–399. Lisle, T.E., 1979. A sorting mechanism for a riffle-pool sequence. Geol. Soc. Am. Bull. 90, 1142–1157. Lisle, T.E., Nelson, J.M., Pitlick, J., Madej, J.M., Barkett, B.L., 2000. Variability of bed mobility in naturel, gravel-bed channels and adjustments to sediment load at local and reach scales. Water Resour. Res. 36, 3743–3755. MacNamara, J.P., Borden, C., 2004. Observations on the movement of coarse gravel using implanted motion-sensing radio transmitters. Hydrol. Process. 18, 1871–1884. Mao, L., Surian, N., 2010. Observations on sediment mobility in a large-bed river. Geomorphology 114, 326–337. Mao, L., Uyttendaele, G.P., Iroumé, A., Lenzi, M.A., 2008. Field based analysis of sediment entrainment in two high gradient streams located in alpine and andine environments. Geomorphology 368-383. May, C.L., Pryor, B.S., 2014. Initial motion and bedload transport distance determined by particle tracking in a large regulated river. River Res. Appl. 30, 508–520. Mercenier, J., 1973. Dynamique fluviale dans un petit bassin du rebord méridional du Plateau des Tailles. Mémoire de licence en Sciences Géogr. University of Liège, Belgium (148 pp.). Milan, D.J., 2013. Virtual velocity of tracers in a gravel-bed river using size-based competence duration. Geomorphology 198, 107–114. Milan, D.J., Heritage, G.L., Large, A.R.G., Charlton, M.E., 2001. Stage dependent variability in tractive force distribution through a riffle-pool sequence. Catena 44, 85–109. Miller, M.C., Mc Cave, I.N., Komar, P.D., 1977. Threshold of sediment motion under unidirectional currents. Sedimentology 24, 507–527. Mueller, E.R., Pitlick, J., Nelson, J.M., 2005. Variation in the reference Shields stress for bed load transport in gravel-bed streams and rivers. Water Resour. Res. 41, W04006. http://dx.doi.org/10.1029/2004WR003692. Neill, C.R., 1968. Note on initial movement of coarse uniform bed material. J. Hydraul. Res. 6, 173–176. Parker, G., Klingeman, P.C., McLean, D.G., 1982. Bed load and size distribution in paved gravel-bed stream. J. Hydraul. Div. ASCE 108 (4), 544–571. Parker, G., Clifford, N.J., Thorne, C.R., 2011. Understanding the influence of slope on the threshold of coarse grain motion: revisiting critical stream power. Geomorphology 126, 51–65. Peeters, A., Mols, J., Houbrechts, G., Levecq, Y., Petit, F., 2009. L’Ourthe orientale dans la traversée d’Houffalize. Etude de l'évolution morphologique. Direction des Cours d'Eau Non navigables. Ministère de la Région wallonne (94 pp.). Peeters, A., Hallot, E., Houbrechts, G., Levecq, Y., Van Campenhout, J., Denis, A.C., Petit, F., 2013. Conception d'un outil d'aide à la décision pour la restauration hydromorphologique des masses d'eau en Région Wallonne. Rapport scientifique. Suivi géomorphologique (action 7). WALPHY LIFE-Environnement (LIFE 07 ENV/B/ 000038). Direction des Cours d'Eau non navigable, Ministère de la Région Wallonne (132 pp.). Perpinien, G., 1998. Dynamique fluviale de la Mehaigne: morphométrie, transports en solution et suspension, mobilisation de la charge de fond. Mém. de licence en Sciences Géogr.University of Liège, Belgium (128 pp.) Petit, F., 1987. The relationship between shear stress and the shaping of the bed of a pebble-loaded river. La Rulles, Ardennes. Catena 14, 453–468. Petit, F., 1989. The evaluation of grain shear stress from experiments in a pebble-bedded flume. Earth Surf. Process. Landf. 14, 499–508. Petit, F., 1990. Evaluation of grain shear stress required to initiate movement of particles in natural rivers. Earth Surf. Process. Landf. 15, 135–148. Petit, F., 1994. Dimensionless critical shear stress evaluation from flume experiments using different gravel beds. Earth Surf. Process. Landf. 19, 565–576.

320

F. Petit et al. / Geomorphology 250 (2015) 308–320

Petit, F., 1995. Régime hydrologique et dynamique fluviale des rivières ardennaises. In: Demoulin, A. (Ed.), L'Ardenne: Essai de Géographie Physique. Hommage au Professeur A. Pissart, University of Liège, Belgium, pp. 194–223. Petit, F., Pauquet, A., 1995. Etude d’évaluation des incidences sur l’environnement du projet de bassins écrêteurs de crues sur l’Ourthe orientale en amont d’Houffalize, partim Géomorphologie. Ministère de la Région Wallonne, Direction Générale des Ressources Naturelles et de l'Environnement-Division de l'Eau et Groupe Interuniversitaire de Recherches en Ecologie Appliquée, pp. 39–60. Petit, F., Poinsart, D., Bravard, J.P., 1996a. Channel incision, gravel mining and bedload transport in the Rhône River upstream of Lyon, France (“canal de Miribel”). Catena 26, 209–226. Petit, F., Pauquet, A., Pissart, A., 1996b. Fréquence et importance du charriage dans des rivières à charge de fond graveleuse. Géomorphologie 2, 3–12. Petit, F., Gob, F., Houbrechts, G., Assani, A.A., 2005a. Critical unit stream power in gravelbed rivers. Geomorphology 69, 92–101. Petit, F., Hallot, E., Houbrechts, G., Mols, J., 2005b. Evaluation des puissances spécifiques de rivières de moyenne et de haute Belgique. Bull. Soc. Géogr. Liège 46, 37–50. Phillips, R.T.J., Deslosges, J.R., 2014. Glacially conditioned specific stream powers in lowrelief catchments of the southern Laurentian Great Lakes. Geomorphology 206, 271–287. Phillips, C.B., Martin, R.L., Jerolmack, D.J., 2013. Impulse framework for unsteady flows reveals superdiffusive bed load transport. Geophys. Res. Lett. 40, 1328–1333. Piedra, M.M., Haynes, H., Hoey, T.B., 2012. The spatial distribution of coarse surface grains and the stability of gravel river beds. Sedimentology 59, 1014–1029. Recking, A., 2009. Theoretical development on the effects of changing flow hydraulics on incipient bed load movement. Water Resour. Res. 45, W04401. http://dx.doi.org/10. 1029/2008WR006826. Reid, J., Frostick, L.E., 1984. Particle interaction and its effect on the thresholds of initial and final motion in coarse alluvial channels. In: Koster, E.H., Steel, R.J. (Eds.), Sedimentology of Gravels and Conglomerates. Canadian Society of Petroleum Geologists, Memoir 10, pp. 61–68. Reid, J., Laronne, J.B., Powell, D.M., 1998. Flash-flood and bedload dynamics of desert gravel streams. Hydrol. Process. 12, 543–557. Richards, K., 1982. Rivers, Form and Process in Alluvial Channels. Methuen, London (358 pp.). Rickenmann, D., 2001. Comparison of bed-load transport in torrents and gravel bed streams. Water Resour. Res. 37 (12), 3295–3305. Robert, A., 1997. Characteristics of velocity profiles along riffle-pool sequences and estimates of bed shear stress. Geomorphology 19, 89–98. Robert, A., 2003. River Processes: An Introduction to Fluvial Dynamics. Arnold, London (214 pp.). Rodrigues, S., Breheret, J.G., Macaire, J.J., Greulich, S., Villar, M., 2007. In-channel woody vegetation controls on sedimentary processes and the sedimentary record within alluvial environments: a modern example of an anabranch of the River Loire, France. Sedimentology 54, 223–242. Rollet, A.J., MacVicar, B., Piegay, H., Roy, A., 2008. L'utilisation de transpondeurs passifs pour l'estimation du transport sédimentaire: premiers retours d'expérience. La Houille Blanche 4, 110–116. Sear, D.A., 1996. Sediment transport processes in pool-riffle sequences. Earth Surf. Process. Landf. 21, 241–262. Shields, A., 1936. Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der preussischen Versuchsanstalt für Wesserbau und Schiffbau, Berlin, p. 26.

Shvidchenko, A.B., Pender, G., 2000. Flume study of the effect of relative depth on the incipient motion of coarse uniform sediments. Water Resour. Res. 36, 619–628. Sluse, P., Petit, F., 1998. Evaluation de la vitesse de déplacement de la charge de fond caillouteuse dans le lit des rivières ardennaises au cours des trois derniers siècles, à partir de l'étude des scories métallurgiques. Géog. Phys. Quatern. 52, 373–380. Snyder, N.P., Castele, M.R., Wright, J.R., 2008. Bedload entrainment in low-gradient paraglacial coastal rivers of Maine, USA: implications for habitat restoration. Geomorphology 103, 430–446. Statzner, B., 2012. Geomorphological implications of engineering bed sediments by lotic animals. Geomorphology 157-158, 49–65. Statzner, B., Arens, M.F., Champagne, J.Y., Morel, R., Herouin, E., 1999. Silk-producing stream insects and gravel erosion: significant biological effects on critical shear stress. Water Resour. Res. 35 (11), 3495–3506. Storm, K., Papanicolaou, A.N., Evangelopoulos, N., Odeh, M., 2004. Microforms in gravel bed rivers: formation, disintegration and effects of bedload transport. J. Hydraul. Eng. 130, 554–567. Sundborg, A., 1956. The River Klarälven: a study of fluvial processes. Geogr. Ann. Ser. A 115, 127–316. Thompson, D.M., 2011. The velocity reversal hypothesis revisited. Prog. Phys. Geogr. 35, 123–132. Thompson, C., Croke, J., 2008. Channel flow competence and sediment transport in upland streams in southeast Australia. Earth Surf. Process. Landf. 33, 329–352. Thompson, D.M., Wohl, E.E., Jarett, R.D., 1996. A revised velocity-reversal and sedimentsorting model for a high gradient, pool-riffle stream. Phys. Geogr. 17, 142–156. Thompson, D.M., Wohl, E.E., Jarett, R.D., 1999. Velocity reversals and sediment sorting in pools sediment sorting in pools and riffles controlled by channel constrictions. Geomorphology 27, 229–241. Turowski, J., Yager, E.M., Badoux, A., Rickenmann, D., Molnar, P., 2009. The impact of exceptional events on erosion, bedload transport and channel stability in a step-pool channel. Earth Surf. Process. Landf. 34, 1661–1673. Vazquez-Tarrio, D., Menendez-Duarte, R., 2014. Bedload transport rates for coarse-bed streams in an Atlantic region (Narcea River, NW Iberian Peninsula). Geomorphology 217, 1–14. Whitaker, A., Potts, D.F., 2007. Coarse bed load transport in an alluvial gravel bed stream, Dupuyer Creek, Montana. Earth Surf. Process. Landf. 32, 1984–2004. Wilcock, P.R., 1988. Methods for estimating the critical shear stress of individual fractions in mixed-sediment. Water Resour. Res. 24, 1127–1135. Wilcock, P.R., McArdell, B.W., 1993. Surface-based fractional transport rates: mobilisation thresholds and partial transport of sand-gravel sediments. Water Resour. Res. 29, 1297–1312. Wilcock, P.R., Barta, A., Shea, C.C., Kondolf, G.M., Matthews, W.V.G., Pitlick, J.C., 1996. Observations of flow and sediment entrainment on a large gravel-bed river. Water Resour. Res. 32, 2897–2909. Williams, G.P., 1983. Paleohydrological methods and some examples from Swedish fluvial environments. Geogr. Ann. 65, 227–243. Wohl, H.H., Wilcox, A., 2005. Channel geometry of mountains streams in New Zealand. J. Hydrol. 300, 252–266. Zimmermann, A., Church, M., 2001. Channel morphology, gradient profiles and bed stresses during flood in a step-pool channel. Geomorphology 40, 311–327.