THE INFLUENCE OF FORM ROUGHNESS ON MODELLING OF SEDIMENT TRANSPORT AT STEEP SLOPES

THE INFLUENCE OF FORM ROUGHNESS ON MODELLING OF SEDIMENT TRANSPORT AT STEEP SLOPES Michael CHIARI 1, Dieter RICKENMANN 1, 2 1 Institute of Mountain Risk Engineering, University of Natural Resources and Applied Life Sciences, Peter-Jordan Strasse 82, 119 Vienna, Austria 2 Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Mountain Hydrology and Torrents, Zürcherstrasse 111, 893 Birmensdorf, Switzerland michael.chiari@boku.ac.at Abstract In torrents and mountain streams with irregular bed topography and low relative flow depth form roughness contributes to total friction losses. Apart from limited sediment supply, the presence of substantial bedform roughness may be an important element which reduces bedload transport efficiencies. The case study of an extreme event in the Austrian Alps shows the importance of taking into account the effect of form roughness on the bedload transport capacity. Otherwise the computed transport rates are much higher than the calculated bedload transport from field observations of morphologic changes. With a rough correction procedure a reasonable agreement between modelled and back-calculated transport was achieved. Key words: form roughness, bedload transport, steep slopes, torrents, numerical modelling INTRODUCTION In this study, sediment transport capacity formulas derived from steep experimental flumes without bed forms are taken as reference condition. Observed sediment transport in steep and small streams can be up to three orders of magnitude smaller than values predicted by these formulas (Rickenmann 21). Over prediction of sediment transport by such formulas was also observed by Rathburn & Wohl (21) and Palt (21). Apart from limited sediment supply, this discrepancy may be partly due to substantial bedform roughness reducing bedload transport efficiencies. Torrents and mountain streams with steep slopes typically have an irregular bed topography and low relative flow depths. The roughness of irregular bed profiles cannot be described sufficiently by a percentile of the grain size distribution (Aberle & Smart 23). Many authors reported about the effect of step-pool sequences contributing to flow resistance (e.g. Lee and Ferguson 22, Wohl and Thompson 2). The work from Zimmermann and Church (21) indicates that only the energy gradient within the pools may be available for bedload transport in step-pool systems. Using the total channel gradient may result in an over prediction of the streams transport capacity. FLOW RESISTANCE DUE TO FORM ROUGHNESS Rickenmann (1996) proposed equations to calculate the total roughness in terms of the Manning-Strickler coefficient n tot for torrents steeper than.8% and including slopes up to 63%:.14.19 1.97g Q = (1) n.19.64 tot S d 9 where g is the acceleration due to gravity, Q the discharge, S the slope of the energy line and d 9 is the grain size of the surface bed material for which 9% of the bed material is finer. 1 of 8

Wong and Parker (26) reanalyzed the Meyer-Peter and Müller (1948) data and showed that the grain friction k r can be expressed as: 1 23.2 = (2) n r 6 d 9 The contribution of form roughness to total roughness can be expressed by dividing eq. (1) by (2) and writing in dimensional homogenous form: n.19 r.133q = (3) n.96.19.47 tot g S d 9 Rickenmann (25) proposed a procedure to estimate flow resistance losses due to form drag as a function of slope and relative submergence.33 n r.35 h =.83S n tot d (4) 9 where h is the flow depth. The procedure assumes that grain friction losses depend on the power of a characteristic grain size (eq. 2) and these losses are compared to the total friction losses estimated from a flow velocity equation for steep streams. Using a similar procedure but direct measurements of total flow resistance, Palt (21) accounted for form losses and found much better agreement with his bedload measurements in Himalayan rivers and the bedload transport formula of Meyer-Peter and Müller (1948). Pagliara and Chiavaccini (26) experimentally investigated the flow resistance of rock chutes with slopes up to.4 and relative submergence up to 8. From this laboratory experiments they derived an equation for the Darcy-Weissbach friction factor as a function of slope and relative submergence. They also studied the effect of protruding boulders within the rock chute on the flow resistance with different boulder concentrations, dispositions and surfaces, and proposed an equation for the total friction factor. The contribution of form roughness to total roughness can be expressed by dividing the two respective equations:.1 c.17 h 3.11 ( + Γ) S f d 84 = (5) f tot 2.5 h log1 S + 2.8 d 84 where d 84 is the grain size of the surface bed material for which 84% of the bed material is finer, Γ is the boulder concentration and the exponent c depends on the disposition (random or in rows) and on the surface of the boulders (rounded or crushed). Possible values for c are given in Table 1. Table 1. Values of coefficients c from Pagliara and Chiavaccini (26) Random disposition Rows disposition Random disposition Rows disposition Coefficient rounded surface rounded surface crushed surface crushed surface c 1.6 1.8 2.4 3. A comparison of (3) and (4) is made in Figure 1 where they are applied to the data set of flow velocity measurements used by Rickenmann (1994, 1996) and extended with data from Lepp et al. (1993). Flow measurements for three cross-sections with slopes from.112 to.146 are published for different discharges by Lepp et al. (1993). A large variation of the n r /n tot values is 2 of 8

observed for channel gradients up to about.1. For steeper channels form roughness appears to be much more important than grain roughness, based on the limited data available. Figure 2 shows the behaviour of eq. (3), (4) and (5) for a synthetic cross-section (width 5 m) and varying specific unit discharge from.5 to 2.5 m³/s/m. The relative submergence (h/d 9 ) is in the range from.37 to 6.5. A boulder concentration of 2% disposed in rows with crushed surface was assumed for a step pool system. Equation (5) could be regarded as upper and eq. (4) as lower boundary. 1.9.8.7 Equation (3) Equation (4) potential Equation (3) potential Equation (4).6 n r /n tot.5.4.3 Lepp et al. (1993) data.2.1.1.2.3.4.5.6.7 S Figure 1. Comparison of (3) and (4) for published data and measurements done by Rickenmann and completed with data from Lepp et al. (1993). Power law regressions have been fitted to illustrate a mean trend for each equation (f/f tot )^.5 or n r /n tot 1.9.8.7.6.5.4 Equation (3) Equation (4) Equation (5) potential Equation (3) potential Equation (4) potential Equation (5).3.2.1.1.2.3.4.5.6.7.8 S Figure 2. Comparison of (3), (4) and (5) for varying slope and discharge. Power law regressions have been fitted to illustrate a mean trend for each equation 3 of 8

To use the form roughness approaches in combination with bedload transport capacity formulas, the slope of the energy line S can now be partitioned into a fraction S red associated with skin friction only: a nr Sred = S n (6) tot where plausible values of a are probably in the range from 1 to 2. An exponent of 2 can be derived from the Manning-Strickler equation. Meyer-Peter & Müller (1948) determined a value of 1.5 from their experiments, as is also discussed by Wong & Parker (26). SIMULATION MODEL A one-dimensional sediment transport model for steep torrent channel networks called SETRAC (Rickenmann et al. 26) has been developed at the University of Natural Resources and Applied Life Sciences, Vienna. SETRAC is the acronym for SEdiment TRansport in Alpine Catchments. The model applies a kinematic flow routing of the flood hydrograph trough a channel network. Reach wise sediment stock can be considered. Three different flow resistance approaches and four transport capacity formulas appropriate for steep slopes can be combined with two approaches to take into account the effect of losses due to form roughness. The model has been applied to extreme flood events in Austria, Switzerland and France. Case study at Schnannerbach In August 25 an extreme flood event occurred in the Austrian Alps. For several torrents an event documentation was established including a sediment budget along the main channel (Hübl et al. 25). One of these torrents is the Schnannerbach in Tyrol (Austria). The sediment erosion and deposition was mapped in the field after the event in order to be compared with SETRAC calculations. The longitudinal profile and representative cross-sections were also surveyed. Grain size analyses were made with line by number sampling and evaluated after Fehr (1987). The Schnannerbach has a catchment area of 6.3 km² and a mean channel gradient of.24. No stream flow measurements are available for this torrent. The input hydrographs were modelled based on observed rainfall data, and calibrated with estimated peak discharges in measured cross-sections. The event duration was about 24 hours with a peak discharge of 24 m³/s. About 3 m³ of bedload were mobilised during the extreme event. Simulations Depending on the field investigations, different cases can be computed with SETRAC. If information about sediment stock is available, it is possible to model a so-called supply limited case. That means that sediment can only be eroded if the stock has not been depleted. If there is no information about reach wise sediment availability, a uniform sediment stock can be assumed as possible erosion depth. If the possible erosion depth is set at a high value, the so-called transport limited case can be modelled. The formula set used for the simulations with SETRAC is presented in Table 2. The Manning-Strickler coefficient is calculated for each time step with eq. (1). Form roughness effects were taken into account with eq. (4) and eq. (6) with an exponent a=1. and were also neglected for comparison. 4 of 8

Table 2. Formulas used fort he SETRAC simulations Flow velocity 1.67. 5 v = R S Manning-Strickler (1924) n.2 d Bedload transport 9 2. 1. 6 q b = 12.6 ( q q c ) S ( s 1) d Rickenmann (199) 3 Critical discharge 1.67.5 1.5 1. 12 q c =.65( s 1) g d S Modified from Bathurst (1987) 5 Figure 3 shows the specific discharge (q) for a cross-section (5 m width, 19.2% slope) of the Schnannerbach and the related sedigraphs representing the transport capacity calculated with (qb Sred) and without taking form roughness into account (qb) after eq. (4) and eq. (6) with an exponent a=1. The diagram also shows the accumulated transported bedload volume for this cross-section. According to the field investigations about 18 m³ were transported through this reach. The bedload volumes calculated with the reduced energy slope (16, m³) show a much better agreement with the field survey than the calculations without form roughness losses (365, m³). A comparison of the observed transported bedload volume and the simulated volumes for the supply limited case is shown in Figure 4. The maximum erosion depth was estimated in the field for each channel reach. The availability varied between.1 m for channel reaches mainly in bedrock and up 3 m for channel reaches where intensive erosion was observed. Due to the higher availability of sediment the simulation without form roughness losses overestimates the observed transport, whereas the simulation considering these losses underestimates the bedload transport in some reaches. For the simulations presented in Figure 5 a constant possible erosion depth of 5 m was considered. Neglecting the influence of eq. (4) on the transport capacity leads to a massive overestimation of the observed transport, whereas the simulation considering form drag is closer to the observations. q, qb [m³/s/m] 5 4.5 4 3.5 3 2.5 2 1.5 1 q qb qb Sred Sum Qb Sum Qb Sred 4 36 32 28 24 2 16 12 8 transported bedload volume [m³].5 4 12 24 36 48 6 72 84 96 18 12 132 144 156 168 18 192 time [min] Figure 3. Specific discharge and related sedigraphs for a cross-section at the Schnannerbach 5 of 8

transported bedload volume [m³] 7 6 5 4 3 2 reconstructed bedload volume simulation without reduced energy slope simulation with reduced energy slope 1.5 1 1.5 2 2.5 3 3.5 distance from outlet [km] Figure 4. Observed versus simulated bedload transport for the supply limited case 2 transported bedload volume [m³] 18 16 14 12 1 8 6 4 reconstructed bedload volume simulation without reduced energy slope simulation with reduced energy slope 2.5 1 1.5 2 2.5 3 3.5 distance from outlet [km] Figure 5: Observed versus simulated bedload transport for the transport limited case DISCUSSION The application of sediment transport models in torrents without consideration of losses due to form roughness show the expected effect of massive overestimation of the transported sediment volumes. The observations on bedload transport in steep experimental flumes are taken as a reference condition. These conditions define maximum transport rates for the idealized case of rather uniform bed material. No morphological features and no significant form roughness effects were present in these experiments. The introduction of an 6 of 8

adaptable approach allows adjustment of the sediment transport capacity formulas to different roughness types. With these modifications the available energy slope can be corrected for friction losses due to form roughness, and the prediction of the transported bedload volumes is in the same order of magnitude as the reconstructed erosion and deposition volumes. This approach used within SETRAC corresponds to a reduction of the available energy for bedload transport. For steep slopes the reduction of the energy slope according to eq. (4) may be somewhat too strong (compare Figure 1 and 2) and represent a lower boundary. Because of the limited data of flow measurements for higher discharges at steep slopes in natural rivers it is still difficult to assess the influence of form resistance on bedload transport. CONCLUSION Modelling bedload transport in torrents is a challenging task. Neglecting the influence of form roughness on the transport capacity may lead to significant overestimation of bedload transport at steep slopes. Apart from limited sediment supply this may be an important reason for the tendency to overpredict sediment transport at steep slopes. Using a rough correction procedure to account for friction losses due to form roughness, a reasonable agreement has been obtained between simulated and observed sediment loads for the presented case study of an extreme flood event in a mountain torrent in Austria. REFERENCES Aberle, J. & Smart, G.M. (23): The influence of roughness structure on flow resistance on steep slopes. J. Hydraul. Res., 41(3); pp. 259 269. Bathurst, J.C. (1987): Measuring and modelling bedload transport in channels with coarse bed materials. In K. Richards (ed.), River Channels Environment and Process; pp. 272-294, Blackwell, Oxford. Fehr, R. 1987: Geschiebeanalysen in Gebirgsflüssen. Mitteilung 92, Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zurich. Hübl, J., Ganahl, E., Bacher, M., Chiari, M., Holub, M., Kaitna, R., Prokop, A., Dunwoody, G., Forster, A., Kerschbaumer, M., Schneiderbauer, S. (25): Ereignisdokumentation 22./23. August 25, Tirol, Band 1: Generelle Aufnahme (5W-Standard). IAN Report 19, im Auftrag von: BMLFUW, Abt. IV/5 Lee, A. J., and Ferguson R. I. (22), Velocity and flow resistance in step-pool streams, Geomorphology, Vol 46; pp.59-71. Lepp, L. R., Koger C. J. and Wheeler J, A. (1993): Channel erosion in steep gradient, gravel-paved streams, Bulletin of the Association of Engeneering Geologists, Vol. XXX, No. 4; pp.443-454 Meyer-Peter, E. and Müller R. (1948): Formulas for bedload transport. In Proc. 2ndmeeting Int. Assoc. Hydraulic Structures Research, Stockholm, Sweden; pp. 39 64.Appendix 2. Pagliara, S. and Chiavaccini P. (26): Flow resistance of rock chutes with protruding boulders. Journal of Hydraulic Engineering Vol. 132(6); pp. 545 552. doi:1.161/(asce)733-9429(26)132:6(545). Palt, S. (21). Sedimenttransporte im Himalaya-Karakorum und ihre Bedeutung für Wasserkraftanlagen. Mitteilung 29 des Instituts für Wasserwirtschaft und Kulturtechnik, Universität Karlsruhe. Rathburn, S.L. & Wohl, E.E. (21):. One-dimensional sediment transport modeling of pool recovery along a mountain channel after a reservoir sediment release. Regulated Rivers: Research & Management, 17(3): 251-273. Rickenmann, D. (199): Bedload transport capacity of slurry flows at steep slopes, Mitteilung 13 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zurich. Rickenmann, D. (1994): An alternative equation for the mean velocity in gravel-bed rivers and mountain torrents. In G.V. Cotroneo & R.R. Rumer (eds), Proceedings ASCE 1994 National Conference on Hydraulic Engineering, Vol. 1; pp. 672-676, Buffalo N.Y., USA. Rickenmann, D. (1996): Fliessgeschwindigkeit in Wildbächen und Gebirgsflüssen. Wasser, Energie, Luft, Vol. 88(11/12); pp.298 34. Rickenmann, D. (21): Comparison of bed load transport in torrents and gravel bed streams. Water Resources Research, Vol. 37, No. 12; pp. 3295-335. Rickenmann, D. (25): Geschiebetransport bei steilen Gefällen. Mitteilung 19 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zurich: 17-119. 7 of 8

Rickenmann, D., Chiari, M., Friedl, K. (26): SETRAC A sediment routing model for steep torrent channels. In: Ferreira, R.M.L., Alves, E., Leal, J., Cardoso, A. (Eds.), River Flows 26, proceedings of the on Fluvial Hydraulics, Lisbon, Portugal, 6-8 September 26 1, Taylor & Francis, London, Riverflow 26, on Fluvial Hydraulics, September 6-8, 26, Lisabon, Volume 1, pp. 843-852. Wohl, E. E., and Thompson D. M. (2): Velocity characteristics along a small step-pool channel, Earth Surface Processes and Landforms, Vol.25, pp. 353-367. Wong, M. and Parker G. 26): Re-analysis and correction of bedload relation of Meyer Peter and Müller using their own database. Journal of Hydraulic Engineering, Vol 132, pp. 1159-1168 Zimmermann, A., and Church M. (21): Channel morphology, gradient profiles and bed stresses during flood in a step-pool channel, Geomorphology, Vol. 4, pp. 311-327. 8 of 8