A New Framework to Model Hydraulic Bank Erosion Considering the Effects of Roots

13 Abstract ： Floods and subsequent bank erosion are recurring hazards that pose threats to 14 and can cause damage to buildings and infrastructure. While numerous approaches exist on 15 modeling bank erosion, very few consider the stabilizing effects of vegetation (i.e., roots) for 16 hydraulic bank erosion at catchment scale. Taking root reinforcement into account enables the 17 assessment of the efficiency of vegetation to decrease hydraulic bank erosion rates and thus improve 18 risk management strategies along forested channels. A new framework (BankforNET) was 19 developed to model hydraulic bank erosion that considers the mechanical effects of roots and 20 randomness in the Shields entrainment parameter to calculate probabilistic scenario-based erosion 21 events. The one-dimensional, probabilistic model uses the empirical excess shear stress equation 22 where bank erodibility parameters are randomly updated from an empirical distribution based on 23 data found in the literature. The mechanical effects of roots are implemented by considering the root 24 area ratio (RAR) affecting the material dependent critical shear stress. The framework was validated 25 for the Selwyn/Waikirikiri River catchment in New Zealand, the Thur River catchment and the 26 Sulzigraben catchment, both in Switzerland. Predicted bank erosion deviates from the observed 27 bank erosion by 7% up to 19%. A sensitivity analysis based on data of vertically stable river reaches 28 also suggests that the mechanical effects of roots can reduce hydraulic bank erosion up to 100% for 29 channels with widths < 15.00 m, longitudinal slopes < 0.05 m m -1 and a RAR of 1% to 2%. The results 30 show that hydraulic bank erosion can be significantly decreased by the presence of roots under 31 certain conditions and its contribution can be quantified considering different conditions of channel 32 geometry, forest structure and discharge scenarios. function or to define permissible 𝐷 50 values. Quantitative information on how roots stabilizes streambanks is important for civil engineering, geomorphology, ecology as well as forest and channel management. Modeling hydraulic bank erosion for vegetated and non-vegetated streambanks helps to define criteria on how to manage mountain and riparian forests. Results of modeled erosion show that the effects of roots mitigating hydraulic bank erosion range between 0% up to 100% under specific channel and root conditions. Based on the results of the 37 study reaches, a susceptibility matrix to hydraulic bank erosion in relation to channel width and channel slope was proposed showing the stabilizing effects of roots. The results suggest that the stabilizing effects of roots are highest for channels with widths < 15.00 m and slopes < 0.05 m m -1 . Based on a GIS analysis using the ecological morphology data provided by the Swiss Federal Office for the Environment, these criteria correspond approximately to 42% of all Swiss torrents and streams. Considering the effects of roots (RAR in vertical direction) was validated at the Sulzigraben catchment. A sycamore maple with a DBH of 36 cm had a measured RAR of max. 2.3% at 30 cm depth and 1% at 60 cm depth - the point where erosion occurred and was modeled – standing 2.50 m away from the streambank/water interface. Considering a RAR of 1% at a radial 569 distance of 2.50 m away from the tree stem, the ideal riparian forest conditions for the Sulzigraben catchment to decrease the susceptibility of hydraulic bank erosion can be reached with a forest stand 571 of 510 trees per hectare and a mean DBH of 36 cm. With continuous erosion, RAR increases subsequently reducing hydraulic bank erosion. As such, the reduction of hydraulic bank erosion is dependent on RAR, rooting depth, the difference and modification of critical and applied shear stress and streambank height. As long as channel incision is not greater than rooting depth, roots have a stabilizing (positive) effect. If no roots are present at the area affected by the flow, roots have no or

It is usually assumed that takes values close to 1 [27,59]. can be estimated as: where is a coefficient usually ranging between 0.1 and 0.2 for cohesive material. Since BankforNET 114 uses the excess shear stress equation to calculate erosion rates not only for cohesive but also for non-115 cohesive material, is adapted empirically based on and median particle diameter 50

193
Reported RAR values range from 0.0002% up to 6.64% depending on tree species, site-specific

206
Hydraulic bank erosion at the streambank toe decreases the resisting forces that prevents the 207 streambank from failure. Assuming that the undercutting of streambanks eventually leads to failure, 208 this framework allows practitioners to assess the susceptibility of hydraulic bank erosion and 209 subsequently areas at risk of streambank retreat.  retreat. Based on a pre-and post-flood digital elevation model (DTM), the models were tested (Table   240 2). The duration of the modeled hydrograph was reduced to 38.9 h, during this time the river was 241 morphologically active. BankforNET needs few input parameters which are provided by Stecca et al.

242
[28] except for mean bank angle. Mean bank angle is assumed to be 85° based on the pre-flood survey 243 terrain analysis. Based on the information provided by Stecca (Table 4). Since no event lasted longer than one day, the discharge duration was modeled 258 to be 24 hours. For each erosion event, we assumed that the input parameters remained the same

268
The effects of roots for different discharge scenarios were also modeled for the Thur River. Based

310
The catchment area is 2.2 km 2 at the studied cross section. Discharge for both events were 311 estimated using BankforNET considering the precipitation intensities of 2012 and 2015. Other input 312 parameters (Table 5) (Figures 10 and 11). The results suggest that roots have 445 a more significant stabilizing effect for channels with widths < 15.00 m and longitudinal slopes < 0.05 446 m m -1 . The cumulative erosion reduction varies between 0% and 60% with a RAR of 0.1%, between 447 0% and 100% with a RAR of 1.0%, and between 2% and 100% with a RAR of 2% under specific channel 448 conditions. The distance of the tree stem to the streambank/water interface was placed at 1.00 m.

471
where roots can significantly reduce hydraulic bank erosion through mechanical root reinforcement.

472
The susceptibility of hydraulic bank erosion can be reduced up to 100% with a RAR of 1% and 2%,

473
representing somewhat best forest conditions for cross sections with specific channel geometries.

474
Yellow areas represent channel conditions where the stabilizing effects of roots are variable, that is 475 the susceptibility of hydraulic bank erosion can be reduced up to 32% with a RAR of 2%. The red area 476 represents the channel conditions where roots has a low or no effect on reducing the susceptibility of 477 hydraulic bank erosion. The grey area is not defined as it is assumed that channels with widths >

504
The excess shear stress equation is used to estimate hydraulic bank erosion for cohesive material.

525
The sensitivity analysis shows that the modeling framework is most sensitive to changes in 50 526 and channel slope. While the sensitivity to changes in mean channel width and mean streambank 527 angle are rather small, changes in mean bend radius have a smaller influence on the modeled results.

528
The range of modeled erosion by varying the input parameters with +/-10% depends on the absolute 529 value of the input parameter. For the Selwyn/Waikirikiri River catchment, mean channel slope is

604
preliminary results suggest that the framework predicts hydraulic bank erosion reasonably accurate.

605
Considering the effects of roots, the results also suggest that hydraulic bank erosion is significantly