IntroductionDuring flood events, rivers experience solid transport: sediment, fine organic matter, and large wood (LW). Braudrick et al. (1997) defined LW as logs thicker than 0.1 m and longer than 1 m. In mountain and piedmont rivers, during high flows, the steep channel gradients provide energy to the system. In this context, solid transport, especially of coarse elements (LW, gravel, and cobbles), can reach impressive volumes (Rickenmann et al. 2015; Ruiz-Villanueva et al. 2019). When reaching an urbanized area, LW tends to obstruct bridges and other hydraulic structures, and sediment to fill channel bed, both aggravating flood hazards (Badoux et al. 2014; Ruiz-Villanueva et al. 2014; Mazzorana et al. 2018; De Cicco et al. 2018; Friedrich et al. 2022). Relevant strategies to prevent LW stopping and sediment deposition in critical areas is usually (1) to adapt the bottleneck sections, e.g., by removing piers of bridges or of dam spillways and by increasing their section (Schmocker and Hager 2011; Gschnitzer et al. 2017; Bénet et al. 2021), and/or (2) to trap the solid transport at dedicated structures, such as the debris basins, open check dams, racks, or flexible barriers (Comiti et al. 2016; Piton and Recking 2016a,b; Mazzorana et al. 2018; Wohl et al. 2019; Bénet et al. 2021, 2022).Several recent works have focused on the effects of LW on flow levels at rigid structures as dam reservoir spillways (Furlan et al. 2019, 2020, 2021; Vaughn et al. 2021; Bénet et al. 2021, 2022), slit and slot dams (Piton et al. 2020), as well as, at racks made of piles (Shibuya et al. 2010; Schmocker and Hager 2013; Horiguchi et al. 2015; Schalko et al. 2018, 2019a; Schalko 2020). Schalko et al. (2018) notably performed a thorough analysis of the head losses related to LW accumulations. To cover a wide range of porosity, size, and number of logs and amount of fine material as branches or leaves, they prepared the accumulations manually rather than to let the flow naturally building them. In their later works, natural accumulations were studied over fixed and mobile beds and still against rigid racks.Flexible barriers made of steel nets are interesting alternative to these rigid structures. They are lighter, more discreet in the landscape, and faster and relatively easier to build. The possible use of flexible barriers in water courses has attracted a lot of interest lately, especially in a context of debris flows and regarding structural design questions as impact force and loading cases (e.g., among other Wendeler 2008; Brighenti et al. 2013; Ashwood and Hungr 2016; Leonardi et al. 2016; Ng et al. 2016; Albaba et al. 2017; Wendeler et al. 2018). Meanwhile, only a few papers have focused on functional design (see the State-of-the-Art section below). Interaction of flexible barriers with LW was, to the best of our knowledge, only studied by Rimböck and Strobl (2002) and Rimböck (2004) using both small scale and full scale physical models. We synthesize their recommendation in the State-of-the-Art section below. In essence, their pioneering work provided a first set of relevant criteria regarding (1) the kind of stream in which such flexible barriers could be used to trap LW, (2) the trapping mechanisms and phases of filling, and (3) how to compute the water depth, noted hereafter h, at a filled barrier. Meanwhile, no precise criterion was given on how exactly emerge the trapping of LW. Another question is related to high magnitude events: no previous work has described how LW stays (or not) in barriers when the flows pass over the top cable.The present paper aims at repeating and extending their work on the trapping process, as well as to better describe these two complementary phases of the trapping initiation and barrier functional overloading, i.e., structure experiencing discharge much higher than the design event. These three phases of functions are sketched in Fig. 1. (1) The bottom clearance should be defined to start trapping material for relatively routine events, i.e., events not triggering damage. (2) The barrier capacity, strongly controlled by its height, is defined according to design events, i.e., the events for which trapping of solid transport is necessary. (3) A checking of the barrier functioning when submitted to safety-check events, i.e. events reasonably higher than the design events should be performed to verify if dramatic aggravation might emerge during such functional or structural overloading. Consistent with the terminology used for dams (Royet et al. 2010), we call “danger events”, the events for which the structural stability or capacity to achieve its function—here, the trapping of LW—is no longer guaranteed. The whole range of events should be studied by designers.Piton et al. (2019, 2020) and Horiguchi et al. (2021), for instance, demonstrated that rigid structures trapping LW might release sudden and massive amounts of LW when overtopped by a sufficiently high depth. It was unclear if such a process might appear on flexible barriers as well. It was questionable that this failure mode observed on rigid barriers would be the same on flexible barriers for two reasons: (1) flexible barriers can obviously deform. The overtopping process is thus possibly more complicated than on rigid barriers because the level of the structure crest, noted as z2, tends to decrease under loading [compare Figs. 1(a–c)], thus increasing the overflowing depth h−z2 that drives the LW overtopping process (Piton et al. 2020). Meanwhile, (2) flexible barriers are extremely porous, which decreases flow levels, increases the flow velocity, stabilizes the LW trapped against the structure (stronger drag forces push the LW against the structure), and LW tends to entangle in the mesh and cables and cannot slide against the structure as against a steel pile or a concrete wall.To study these processes with small scale modeling, the stiffness and associated deformability of the barrier should therefore be consistent with the prototype scale (Wendeler 2008). This challenge is addressed in the companion paper of Lambert et al. (2022). In essence, the flexible barrier elements (cables and net) were manufactured with a 3D printer using not only a geometry respecting the geometrical similitude, but also material defined to be in mechanical similitude to achieve a relevant barrier deformation. The mechanical behavior of the small scale barrier was validated with elementary tests. Then, using this consistently deformable structure, a comprehensive small scale modeling campaign was conducted to cover the three regimes of functioning (Fig. 1): trapping initiation, full trapping, and end of trapping. This paper presents the results of this campaign. Tests involving mixtures of LW were performed measuring flow depth and trapping efficacy until eventual release occurred by barrier overtopping. Other tests with single logs were performed to study trapping initiation by quantifying their blockage probability for varied flow conditions and bottom clearance.The paper is organized as follows: a State-of-the-Art section first recalls the main lessons learned from previous works. Material and method are presented second. Third, results are provided regarding the trapping initiation and bottom clearance, the head losses associated with LW, the release conditions, as well as the deformation measured on the barrier when loaded with LW. These results are discussed and exemplified by a case study. The conclusions ultimately close the paper.State-of-the-ArtFor the use of flexible barriers as debris-flow trapping structures, see Wendeler (2008), Volkwein et al. (2011), Volkwein (2014), and Wendeler (2016).To the best of our knowledge, only Rimböck and Strobl (2002) and Rimböck (2004) studied interactions of flexible barriers with LW [see also recommendations by Lange and Bezzola (2006, pp. 76–81)]. Regarding structural design, Rimböck and Strobl (2002) demonstrated that the dynamic impact of single logs only occurred at the onset of the trapping, when upstream flow velocity remained high along and backwater effects associated with LW trapping were low, thus not slowing down the flows. Consequently, dynamic impact forces were much lower than the pseudo-static force of the barrier obstructed by logs and filled up to the crest. Regarding functional design, Rimböck (2004) provides many relevant recommendations. He recalled that typical mesh apertures, e.g., in the range 0.3–0.5 m, are much smaller than LW, ensuring their trapping. Smaller openings tend to trap small organic matter (leaves and branches) and should thus be avoided. He also stressed that a bottom clearance below the net is necessary to prevent fast clogging even during low flows that would greatly increase maintenance efforts. No clear criterion was however provided, except that the trapping initiation should be sought for flows approaching discharges triggering first damage to elements at risk. Rimböck (2004) also recommends to install flexible barriers in reasonably wide streams (channel width bC<15 m), and relatively straight reaches to prevent uneven LW accumulation and barrier loading (radius of curve >10bC, barrier located at least 5bC downstream of the upstream curves). He also advised not to use flexible barriers in channels with unit discharge Q/bB>5 m3/s·m, with channel unit LW volume VLW/bC>20 m3/m, with channel unit sediment volume Vsed/bC>100 m3/m, with Q the water discharge (m3/s), VLW the solid volume of LW (excluding void) (m3), Vsed the sediment volume (m3), bC the channel width (m), and bB the barrier width (possibly narrower than the channel) (m). Finally, Rimböck (2004) also advised not to use flexible barriers to trap LW in channels steeper than ≈5% to ensure that the upstream deposition area has sufficient room to buffer LW and sediment deposition. In steep streams potentially supplying large amounts of sediment, the design of the flexible barrier must absolutely account for both LW, bedload transport, and debris flows. Sediment deposition notably interferes with the trapping of the LW [see additional comments on interactions between sediment deposition and LW accumulation in Rimböck (2004)].The barrier location should be reasonably easy to access to facilitate surveys and maintenance. It should also not be too far from the protected assets, otherwise LW and sediment might be recruited along the intermediate channel reach. The channel bed should additionally be protected against scouring on the bank on a length of twice the barrier height both upstream and downstream, but also below the barrier to prevent deep scouring and uncontrolled erosion below the structure. This latter recommendation is consistent with the recent works of Schalko et al. (2019b) who observed deep scouring at racks trapping LW: the accumulation of logs tend to float and to redirect flows toward the channel bed, which might result in structure scouring if the bed is mobile.Rimböck (2004) finally provides an equation to estimate h, the flow depth at the barrier. The barrier height z2 should be higher than h(1) z2>h=4.44(VLWbC)cFM0.17(1−35−K105)Q3bBwhere FM is the fine organic matter content, K is the Strickler coefficient of the upstream channel bed (m−1/6) (see Yen 1992 for the units) and, c is a coefficient depending on the channel gradient S (c=0.20 for S=1.0%; c=0.25 for S=3.0%, and c=0.26 for S=5.0%).A careful analysis of Eq. (1) shows that it is not dimensionally homogeneous. The equation is supposed to compute a length (m), while the term on the righthand side has a dimension of (m2c+1 s−0.5), i.e. (m1.4 s−0.5)–(m1.52 s−0.5) depending on c(S). The results provided by Eq. (1) are thus scale dependent. Eq. (1) provides good estimates of the measured h performed at small scale by Ceron Mayo (2020, p. 27, which were preliminary experiments to this paper). Its application to the same conditions at the prototype scale resulted in overestimations of h by a factor of about 2 for the application case performed by Ceron Mayo (2020, p. 39). This bias is on the safe side, because it results in a conservative design of an excessively high barrier, but an update of the approach would be interesting to remove this scale effect. This was one of the objectives of the present paper.ResultsInitiation of the Trapping: The Bottom ClearanceAlthough these tests were performed within the last experimental series (#8), it seems more logical to present them first as a way to study the beginning of the trapping process. The study of the bottom clearance intended to study the blockage probability Pblockage of single logs. Although Pblockage varies in the range 0 to 1, similar to the trapping efficacy ratio computed as the ratio of trapped volume to the supplied volume (D’Agostino et al. 2000; Shibuya et al. 2010; Horiguchi et al. 2015), both ratios cannot directly be compared. The latter is based on the behavior of groups of logs and encapsulates the progressive capture of key pieces and the subsequent increase of the LW stopping. Conversely, blockage probability Pblockage focuses only on single logs and intends to highlight how the blockade exactly starts, whatever happens later. As such, while high trapping efficacy must be sought (close to one ultimately), it seems sufficient in many cases to seek lower Pblockage. For instance, if Pblockage≈1/3, it means that, on average, trapping will start as soon as three logs pass. If the trapped piece is a large one, it will then likely partially obstruct the structure and trapping efficacy will increase a great deal for the next supplied LW.During the 498 measurements of Pblockage, logs were not transported on the rough bed for discharges lower than Q=2−3 l/s. Also, Pblockage was systematically null for flow depths lower than the bottom cable (h1), Pblockage is ≈50% when z1* is close to 0 and exceeds 75% for z1*>1, being even equal to one for long logs. Meanwhile, for thinner logs (DLW/z1<1), Pblockage≈50%, 25%, and 5% for z1*=1 and long, medium, and short logs, respectively. Pblockage becomes very high (>75%) only for z1*>3 for these logs of smaller diameter. This demonstrates that thick and/or long logs are intuitively much easier to trap, but also that logs might pass a flexible barrier even if the latter is submerged on more than the log diameter. Drag forces simply suck the log below the structure that may in addition deform upward.The diameter of LW pieces varies according to the type and age of riparian forests. We recommend using the criteria of Fig. 5 in an inverse approach: for a given target water discharge at which LW trapping would be necessary (or not), the user will find how much is the Pblockage for small and high values of DLW based on the mean trends of Fig. 5(c). A few iterations varying z1 enables to define an appropriate bottom clearance preventing excessively high trapping probability that would trigger high maintenance costs, while having a non-null trapping probability for flows for which trapping is necessary.As a design criteria, we suggest to select z1 considering the discharge of floods potentially carrying a significant amount of LW. The bottom clearance can be selected such that z1*≈1 on rivers where the passage of some medium and short logs, as well as a handful of long one, is acceptable. This can be relaxed to z1*≈0 if the site can accommodate some long elements. Conversely, on extremely sensitive sites, z1*≈3 is rather recommended, but such a drastic value may lead to very small bottom clearance and much heavier maintenance effort. See also the Case study section at the end of the paper for a complementary use of this criteria.Main Phases of TrappingThe following sections are based on experiments aiming to study the trapping and eventual release processes. Three main phases of accumulation were eventually observed [yet described in Lange and Bezzola (2006) and Wendeler (2008, p. 54)]: (1) trapping initiation with a few logs hitting the barrier and adopting a transverse position [Figs. 6(a, d, and g)]. A few elements might protrude under or through the net. As soon as a few logs are trapped, the subsequent single logs reaching the barrier are almost certainly trapped. (2) Accumulation phase where blockage probability is one. Logs accumulate against the barrier and progressively load it. As soon as a few logs are trapped, they obstruct the flow section and trigger a backwater effect. Flow velocities decrease drastically upstream and logs form a “floating carpet” [Figs. 6(b, e, h, and i)]. For high slope and discharge, a few elements may be sucked below the free surface and rather build a multi-layered, denser LW accumulation. (3) A release phase was observed on only a few cases [e.g., Figs. 6(c and f)]. We define a “release” by the sudden and uncontrolled transfer of many logs downstream of the barrier [criterion: cumulated mass>10% of the whole mixture for a single flow discharge, as in Piton et al. (2020)]. Flow conditions enabling releases were systematically related to high overflowing (h>z2), similar to dam spillways (Furlan et al. 2021; Bénet et al. 2021; Vaughn et al. 2021) or open check dams (Piton et al. 2020). Consequently, all overtopping were observed on the small net (series #5) and none on the 100-mm high nets.Backwater Rise Related to Large WoodThe equivalent upstream Froude number Fr0 was computed with the channel width bC and water depth without LW h0, and assuming a uniform flow, it would be equivalent to the depth out of the backwater area. Fr0=Q/gbC2h03 varies in the range 0.5–0.65 for S=2%, Fr0≈1.1 for S=4% and Fr0≈1.4 for S=6%. Upstream flow conditions are thus typical of steep, coarse gravel-bed channels. Since the flume bottom is fixed at the barrier by the Plexiglas sheet, it cannot be scoured (see sketches on Fig. 3). Our configuration is thus similar to a flexible barrier installed on a bed sill. The flexible barrier being located at the flume outlet, it was not influenced by the downstream flow level, a reasonable hypothesis regarding the relatively high Fr0 and the weir presence. It can be seen that when looking at cross-shaped dots on Figs. 7 and 8, the flow depth at the barrier, without LW, can be approximated by a weir equation (i.e., Q∝bBH01.5), providing that one uses the specific energy head H rather than the depth h in the equation, e.g., in a rectangular channel H0=h0+Q22gbC2h02=h0(1+Fr02/2)(5) Q=μbB2gH03≈μbB2gh03(1+Fr022)3with μ as the weir coefficient, calibrated at 0.45 in our case (see the agreement between black lines and cross-shaped dots in Figs. 7 and 8). Note that the upstream specific energy head is computed using the channel flow velocity, i.e., over the whole channel width bC, rather than with the weir width bB. Accounting for the inertia term Q2/(2gbC2h02) is necessary when the approximation h≈H falls in defect, e.g., if Fr>0.3 in a rectangular channel and accepting a 5% error on H: H=h+[Q2/(2gh2bC2)]=h{1+[Q2/(2gh3bC2)]}=h[1+(Fr2/2)]>1.05h. Note that the effect of the flexible barrier can be neglected when no clog it, because it is extremely porous (void ratio ≈80%). When logs begin to be trapped, they obstruct the channel section and increase the upstream flow depth. A gradually varied free surface profile then emerges: an M1-profile for the subcritical flows observed with S=2% and an S1-profile for the supercritical flows observed with S=4% and S=6% (sensu Te Chow 1959, p. 226), the transition between the supercritical and the subcritical flows occurring within a undular jump.Fig. 7 shows flow depth h against water discharge Q with and without LW. Increase of h with Q is obvious, as well as the LW-related backwater rise represented by the deviation of the measurement dots to the black lines representing the pure water depth computed with Eq. (5). The last series of experiments, performed with a rough bed and without artificial obstruction, are more plausible to compare with field sites [Figs. 7(b and c)]. Series #5 was performed to focus on the release phase. Its smooth bed is less directly comparable with field sites [Fig. 7(a)]. Depths measured during series #7 are higher because of the increased flow specific energy on the steeper slopes (S=4% and 6%), as compared to the condition of series #6 performed with S=2% [compare Figs. 7(b and c)].In this paper, the effect of LW on water depth, i.e., the rise of the free surface level necessary for the flow to gain sufficient energy to seep through the LW accumulation, thus losing this energy gain, is called “LW-related backwater rise” or “LW-related head loss”. Since the approaching flow conditions have relatively high Froude numbers and thus non-negligible inertial terms, the LW-related head losses are analyzed with the energy head loss ΔH=H−H0, rather than just using the depths h and h0 and the associated backwater rise Δh=h−h0 used in other works (e.g., Schmocker and Hager 2013; Schalko et al. 2018). Meanwhile, flow conditions at the barrier are systematically subcritical with Fr<0.3 once clogged and the specific energy head could be approximated by the depth H≈h (it means that Q2/2gbC2h2≪h, the left term being small not because the discharge Q is small but because the water depth is high). Data analysis showed that the LW-related relative energy head losses ΔH/H0 varied in the range 0–1.75 [Fig. 8(a)]. Many small values of ΔH/H0 are observed for low discharge, i.e., for flow conditions where either, not the whole LW volume, was supplied (supply modes 1:3, 1:6 and 1:7), or some supplied pieces did not reach the barrier and were still stuck on the rough bed (for Q<3 l/s). Relative energy head loss thus tends to increase with Q during the first phase of barrier clogging but then decreases. The actual depth h increases continuously (Fig. 7), these decreases observed for the three slope trends are thus related to a relatively higher increase of the approaching specific energy head H0 as compared to the increase of h at the barrier. The difference in trends between measurements on S=2% and the similar patterns of S=4% and 6% is likely due to denser LW accumulations built by the supercritical flows of the steeper slope. On the gentler slope, LW accumulations were subjected to lower velocities and drag forces, and were thus slightly less dense.When obstructed with LW, the flexible barrier triggers a significant energy head loss. Interestingly, the general behavior was still similar to a weir equation, i.e., Q∝bBh1.5, though the equivalent weir coefficient was much lower than without LW. Two ways can be used to account for the LW-related energy head loss when computing flow depth h at the flexible barrier: (1) by assuming a relative energy head loss β=(ΔH/H0) [Eq. (6)] as proposed in (Piton et al. 2020), or (2) by assuming a reduction ratio of the discharge ΔQ* [Eq. (7)] in the line of the approach proposed by Bénet et al. (2021, 2022) for reservoir dam spillways (6) (7) The first formulation enables to directly reads the relative increase in water depth as compared with flow without wood, e.g., if β=0.2, it means that flow level increases by 20% in presence of LW. The second formulation gives a sense of the flow capacity reduction at known flow depth. Table 3 provides a selection of values of both parameters computed using ΔQ*=1−[1+(ΔH/H0)]−3/2. Fig. 8(b) shows both the measured depths and the prediction of Eq. (7) for varying discharge. It shows that using ΔQ*=0.78 (computed with β=(ΔH/H0)=1.75) provides an envelope curve of all our measurements. In essence, a heavily clogged flexible barrier has a similar behavior than a weir discharging only 22%=1−ΔQ*=1−0.78 of its full capacity. A barrier having an average clogging state might convey twice this discharge (ΔQ*≈0.65) depending on random processes related both to supply, i.e., low or high recruitment and transfer of LW to the barrier, supply of fine material or only of large pieces; and accumulation too, e.g., variably dense, evenly distributed (or not). When using Eq. (7) with ΔQ*=0.65, i.e., the mean value on our sample, the ratio between the observed depth and the predicted depth varied in the range 0.2–1.7, half of the values being in the range 0.9–1.3.Table 3. Relative energy head loss and associated discharge reduction coefficientTable 3. Relative energy head loss and associated discharge reduction coefficientβ=ΔHH0ΔQ*Value used forSource00Pure water conditions—0.250.28Lower envelope of flexible barrierThis paper0.50.46Upper range on dam spillwaysHartlieb (2017)0.60.51Upper range for slit and slot damsPiton et al. (2020)1.00.65Average behavior of flexible barrierThis paper1.10.67Upper range for racksPiton et al. (2020)1.50.75Upper range for racksSchalko et al. (2019a)1.750.78Upper envelope curve of flexible barrierThis paperIt could be possible to propose more sophisticated equations including the volume of LW, its fine matter content, and the size of the logs, e.g., mean or maximum length or diameters, as proposed by others (Schalko et al. 2018, 2019a). Such parameters, accurately known in small scale experiments, are however unknown and strongly variable in the field: VLW for instance varies over two orders of magnitude for catchments of similar sizes or other features (e.g., FOEN 2019, pp. 27–28). We thus chose to provide a simple approach to compute an average case (ΔQ*=0.65, computed with (ΔH/H0)=1.0), a high obstruction case (ΔQ*=0.78), and a low obstruction case (ΔQ*=0.28) as shown in Fig. 8(a) and Table 3. We trust the users to define the “what if” scenarios they want to address and to chose the associated dimensionless numbers.Release Condition of Large Wood OvertoppingSimilar to previous works, release conditions were first analyzed in the light of the dimensionless overflowing depth h*(8) The release of LW over dam spillways occurs for h*>1.5–2 (Pfister et al. 2013; Furlan et al. 2021; Bénet et al. 2021; Vaughn et al. 2021). Upstream of such structures, LW accumulates as extended floating carpets made of a single layer of LW. Conversely, LW tends to get stuck at open check dams as denser, multi-layered accumulations thanks to the higher approaching velocities allowed by the higher structure porosity. Piton et al. (2020) and Horiguchi et al. (2021) demonstrated that these thicker accumulations are more stable than on closed structures and their releases occur for h*>3–8 (also because some logs get entangled in the openings and form sort of random anchors, increasing the structure’s retention capacity).Flexible barriers are even more porous than open check dams. Consistently, natural releases of LW were difficult to obtain during the experiments. The size of dots on Fig. 7 varies with the volume of LW released. Significant releases, i.e., >10% of the mixture volume, only occurred during series #5 (net height of 50 mm). The releases occurred in a range of h*>3–8, similar to open check dams. It is worth noting that specifically low flexible barriers were manufactured to observe the LW release: the 50-mm high barrier would be a small scale model of a 2-m high barrier at scale 1:40.To get a more precise picture of the effect of the approaching flow conditions building dense accumulation or, on the contrary, lousy floating carpet, the dimensionless ratio of buoyancy to drag force introduced by Piton et al. (2020) on rigid barriers was also computed (9) Π/FD≈π2CDρ−ρLWρgDLWbC2h2Q2with the buoyancy force Π=(π/4)g(ρ−ρLW)DLW2LLW, the drag force FD=(1/2)ρCDDLWLLWvf2, the fluid density ρ, the log density ρLW, the fluid velocity vf, and the log drag coeffient CD taken as 1.2 (following Merten et al. 2010). These formulations rely on the following hypotheses (Piton et al. 2020) : (1) logs have a transverse position as compared to flow direction, (2) they are nearly fully submerged, thus their whole volume is considered in Π and their whole projected area in FD, (3) LW are stopped by the barrier and experience the drag force of the full flow velocity, (4) the mean section velocity is a good approximation of the fluid velocity near the log vf≈QbC·h, and (5) the channel is rectangular (otherwise, the mean flow velocity estimation and the Froude number equation must be adjusted). Considering these hypotheses, Π/FD, as many other dimensionless numbers, is not meant to give an accurate estimation of whether or not a given log will sink. It only gives a general sense of the balance between drag force and buoyancy. It has notably the following limits: it ignores inter-logs effects, antecedent flows, or 3D flow patterns (Piton et al. 2020).Fig. 9 shows h* versus Π/FD with the size of dots increasing with the amount of LW released. The study of release conditions requires to understand the distribution of large dots. It appears clearly that in slow flow conditions, i.e., Π/FD≫1, depths leading to overtopping are similar to the known value for dam spillways (h*≈2). On average, depths triggering releases progressively increase to h*≈5 and even higher when flow conditions become prone to creating dense, multi-layered accumulation, namely when drag force gets close to buoyancy (Π/FD≈1), though random variations appear. For fast flow conditions (Π/FD<1), LW piles up. Large parts of these thick accumulations might be released for randomly varying overflowing depths in the range h*≈4–8.While the method proposed to compute flow depth [Eq. (7)] did not account for parameters related to LW, release conditions are strongly controlled by their diameter (mean diameter in the mixture DLW) which appear in both dimensionless numbers, Π/FD and h*.In steep slope streams, LW is mostly composed of single logs without branches or rootwads (Rickli et al. 2018). However, the presence of a few of them would likely increase the stability of the LW accumulation and increase values of h* leading to releases as observed by Pfister et al. (2013) on PK-weirs. The threshold values of h* we highlight in this work are thus conservative regarding this effect.Loading MeasurementThe elongation along the horizontal direction of the flexible barrier was measured at three locations: (1) along the upper cable, (2) at the middle of the net where no supporting cable was installed to maximize deformation, and (3) along the bottom cable (Fig. 10). With the net structure being more flexible than the supporting cable, the deformation at the middle was larger. An additional test (repeated twice) was performed with a plastic sheet obstructing the net to compare the loading and associated deformation related to LW with full hydrostatic loading [Fig. 10(e)]. The plastic sheet was pleated to make sure that it did not hold part of the pressure. The blue lines in Figs. 10(a–c) show the associated deformation. Fig. 10(d) shows the ratio between the measured deformation with LW and mean value of deformation for full hydrostatic loading at the same flow level. For low flow level h/z2<0.7 only, both the net and the bottom cable experience higher deformation with LW than full hydrostatic load. It might be an artifact of the measurement accuracy (the deformations are on average less than 1% in this range). It could also be that part of the drag force applied by the flow on the logs is transferred on the net through force chains between logs. Conversely, it is clear that when flow levels reach the barrier crest (h≥z2), the deformations measured with LW are systematically lower than with full hydrostatic loading (ratio of elongation with LW/hydrostatic elongation, mean±standard deviation: 0.59±0.12, 0.32±0.04, 0.21±0.07 for the lower cable, middle of the net, and upper cable, respectively). The potential drag force transfer from logs to the barrier was likely negligible at this stage because the high backwater rise reduces flow velocity to low values. In addition, LW accumulation was dense and partially held and transferred forces to the rigid side wings of the barrier, so equivalent effects would appear on rough banks (Rimböck 2004).In case more fine material than in our experiences are supplied, it might build denser and less porous and permeable LW accumulations that would eventually transfer a higher loading than in our measurement. We however demonstrated that the accumulated drag forces and the flow pressure on the logs located against the barrier remained lower than a full hydrostatic load. For the structural design of a flexible barrier intending to trap LW (and not sediment), as yet suggested by Rimböck (2004), it seems that a reasonable first order assumption is to apply a full hydrostatic loading.DiscussionInsights, Limitations, and Remaining Open QuestionsThis work pushed further the pioneering work of Rimböck and Strobl (2002) and Rimböck (2004) by using a flexible barrier capable of deforming in a realistic way, and by addressing both the initiation of the trapping and its limits leading to releases by overtopping. It shows that a very dense accumulation of LW can form at flexible barriers based on their high permeability allowing flow to seep through and stick the logs on the entire flow section. The associated increases in flow depth were high, higher than what was typically observed on the rigid barrier as reported in Table 3 (see also Piton et al. 2020, for a more comprehensive analysis of data reported in the literature).Although this work explores the aforesaid scientific gaps, it has obvious limitations. As in any hydraulic small scale model, it was impossible to meet full dynamic similitude (Heller 2011). The Reynolds number similitude was relaxed because the flows were fully turbulent (Re=Q/bB/ν>2,600 for all measurements, with ν as water kinematic viscosity). The surface tension σ might have an effect on measurements at shallow depths, 95% of measurements had Weber number We=ρgh2/σ>24 (the threshold value is given between 10 and 120 according to Peakall and Warburton 1996). Consequently, data with flow depth h lower than a certain threshold should be considered with caution. Peakall and Warburton (1996), Erpicum et al. (2016), and Fritz and Hager (1998) suggest minimum depths of 1.5 cm, 3.0 cm, and 4.0 cm in different types of studies, respectively, i.e., 6%, 13%, and 22% of our measurements might be doubtful, respectively. They were mostly the values measured without LW. Thus, we are more confident in our data with high discharge and water depth, i.e., the most interesting data anyway.In addition, it is worth stressing that sediment transport was ignored in this experimental work, which is an extremely important limitation. On steeper slopes, and more generally if significant bedload transport is involved, the whole question of interaction between water, LW, sediment, and flexible barriers becomes certainly much more complicated. This would deserve new experiments and further research (see the State-of-the-Art section for the available guidelines).Although we believe that the manufactured flexible barrier used in this work is a step forward in hydraulic small scale modeling, it is true that real wood pieces were used to model logs. Their stiffness is thus not down-scaled. As compared to reality, they are abnormally stiff, as well as resistant to breakage. We believe that the high stiffness of our logs is not a big issue. Relaxing this similitude would be a problem if, in the field, LW trapped against flexible barriers were strongly deformed and bent by flows. We demonstrated that the structure, and thus the logs stuck against it, are subjected to an effort of more or less a hydrostatic loading and that flow velocities near the barrier are very low. Tree trunks and large branches are not significantly deformed by such a loading. For instance, standing trees in the floodplain regularly trap LW and act as a barrier (e.g., Abbe and Montgomery 2003). If a hydrostatic loading would bend and break them, we hypothesize that this trapping process would not be observed as often in the field. Meanwhile, in rapidly flowing river reaches, when trees are scoured and recruited by flows, they get broken when falling or when blocked against obstacles and being impacted by fast flows, other LW, and boulders (FOEN 2019, pp. 52–54). This second effect was accounted for by using logs with reduced lengths as compared with actual tree heights.Applicability to Gentler SlopesThis experimental campaign was performed with relatively steep slopes (2%, 4%, and 6%) and Froude numbers ranging from 0.5 to 1.4 for flow without barrier. Use of the results on cases with significantly different conditions should be careful. For cases of gentler slope, flow velocities are usually lower, and thus drag forces too, and Π/FD is higher. Thus, flows progressively lose their ability to pile-up logs and to suck them below water and the barrier. We suspect that for flow conditions where only floating carpets can form (Fr≪1 and Π/FD≫1), the trapping initiation would then be better captured by Eq. (3) rather than Eq. (4). Regarding LW-related head losses, it can be anticipated that in such flow conditions, logs would more likely stay at the surface and would less likely obstruct the bottom of the structure, thus with reduced head losses. Hartlieb (2012, 2017), for instance, studied LW-related head losses on dam spillways strongly overflowing before the logs were supplied. Accumulations were sometime multi-layered but did not obstruct the whole structure height. In approaching Froude numbers ranging from 0.05–0.35, the associated relative head losses varied in the range Δh/h0=0.05–0.5, i.e., much less than in our experiments. Regarding release conditions, the h* versus Π/FD criteria already accounts for possible low velocities, and was shown to be consistent with other references coming from dam spillway experiments, i.e., with quieter flows.Case Study Example: The Torrent Des GlaciersAn example of application of the criteria developed in the present paper is proposed here below on the Torrent des Glaciers. At this location, the catchment area is 114 km2. Peak discharges with return periods of 10 years, 100 years, and 1,000 years are Q10=47 m3/s, Q100=102 m3/s, and Q1000=203 m3/s, respectively (Arnaud et al. 2014). The mean diameter of the LW supplied by the catchment is assumed to be 0.25 m. The flexible barrier is intended to be fully functional for Q100, potential trapping needing maintenance operation is acceptable for Q>Q10. The structure would be installed in gorges with strong bedrock sidewalls. In these gorges, the channel is heavily armored with large boulders and sediment transport is assumed marginal. The channel width is 15 m and the slope 5%.In pure water conditions, the flow depth is approximated by a critical flow depth (continuous line in Fig. 11). The bottom cable is initially suggested to be set at the flow depth for Q10: z1=1 m≈h(Q10). Eq. (4) is used to define the discharge for which trapping might start (z1*=0), becomes probable (z1*=1), and finally is certain (z1*=3). As can be seen in Fig. 11, trapping is probable for a discharge in between Q10 and Q100 and is certain near Q100. Considering that these criteria describe the trapping of single, isolated logs and that, once a few logs are trapped, the trapping efficacy becomes almost total, this analysis validate the choice of setting the bottom cable at Q10.Flow depth in the presence of trapped LW is computed using Eq. (7) and various hypotheses of ΔQ*. The hypothesis of high obstruction (ΔQ*=0.78) leads to a flow depth of 6.2 m for Q100. Using a net height of 6 m enables us to set the top cable at z2=(z1+6)=7 m, i.e., reasonably above the maximum depth for the project design flood of Q100. For the whole range of discharge possibly involving LW trapping (Q>Q10) and every hypotheses of obstructions, applying Eq. (9) shows that Π/FD<1, i.e., that the LW accumulation is likely dense and piling up. A reasonable result regarding the steepness of the site.Neglecting the top cable lowering (this should be refined in a further step when structural design is defined), it is possible to compute the flow depth at which LW release become plausible (h*=4), probable (h*=6) and very probable (h*=8) using Eq. (8). These values are selected in the light of the Π/FD range. One can see on Fig. 11 that such flow depths are reached in between 150 and 175 m3/s, i.e., well above Q100 in the worst case of high obstruction, and are not reached for Q
