pdf, 12 MiB - Infoscience - EPFL

Index of Figures
Fig.6.17: Evolution of the sediment transport rate Qb at S0 = 0.5%, for 3 measured discharges,
without macro-roughness (B1), and with ribs spaced every 4, 2 and 1° (B2 to B4). 132
Fig.6.18: Changes of the average bed level for the preliminary tests (with and without ribs) at a constant
sediment transport rate 133
Fig.6.19: Comparison of predicted and computed armoring layer (computed with Gessler, 1965,
1670, 1990) 134
Fig.6.20: Characteristic average grain size diameter for the different test series (average over the 3
discharges) 135
Fig.6.21: Bed surface in the first scour hole (tests B1d and B2d) without (left) and with ribs (right)
137
Fig.6.22: Tangential velocities at 40° without macro-roughness (left) and with ribs spaced every 2°
(right); view in the downstream direction (see also Appendix 11.4) 138
Fig.6.23: Top: Main (1) and inner bank (2) secondary cells in the first scour hole at 40° (no MR)
Bootom: Main (1) and inner bank (2) secondary cells and outer bank secondary cell (3)
protecting the wall of the channel (rib spacing 2°) at 70° 140
Fig.6.24: Flow field after the first point bar for a rib spacing of 1° (at 85°) 146
7. Establishing an empirical formula 149
Fig.7.1: Results of the enhanced equation (eq. 7.5) of Kikkawa (see also Fig. 7.3 for explanations)
156
Fig.7.2: Results of the enhanced equation (eq. 7.6) of Bridge (see Fig. 7.1 and 7.3 for explanations)
158
Fig.7.3: Characteristic points in a cross-section profile at the (upstream) maximum scour location
on top: cross-section in the upper scour; bottom right: transversal bed slope as a function
of h/r 160
Fig.7.4: Results of the centered polynomial equation (3rd degree) without correction factor (eq.
7.10, ) (see Fig. 7.1 and 7.3 for explanations) 161
Fig.7.5: Results of the uncentered polynomial equation (3rd degree) without correction factor (eq.
7.12, ) (see Fig. 7.1 and 7.3 for explanations) 163
Fig.7.6: Results of the uncentered polynomial equation (3rd degree) with vertical correction and
horizontal bed slope at the outer bank, without correction factor (eq. 7.15) (see Fig. 7.1
and 7.3 for explanations) 164
Fig.7.7: Results of the uncentered polynomial equation (3rd degree) with vertical correction and
horizontal bed slope at the inner bank, with correction factor (eq. 7.20) (see Fig. 7.1 and
7.3 for explanations) 165
Fig.7.8: Results of the uncentered polynomial equation (3rd degree with additional terms) with
vertical correction, with correction factor (eq. 7.22) (see Fig. 7.1 and 7.3 for explanations)
167
Fig.7.9: Results of the uncentered polynomial equation (5th degree), horizontal bed slope at the
inner bank, with correction factor (eq. 7.27) (see Fig. 7.1 and 7.3 for explanations) 168
Fig.7.10: Results of the uncentered polynomial equation (5th degree), horizontal bed slope at the
outer bank, with correction factor (eq. 7.28) (see Fig. 7.1 and 7.3 for explanations) 169
Fig.7.11: Tangential forces acting on a control volume 172
Fig.7.12: Comparison of maximum relative scour depth computed with equation 7.63 with the
complete dataset (R2 = 0.876) (left) and the one without Peter’s tests (right). 181
Fig.7.13: Analysis of parameters influencing the reduction of the maximum scour depth (see also
Fig. 6.5!) 182
Fig.7.14: Schematic view of the bank protection elements upstream the Wilerbrücke (right end of
the scheme). Element 1 is the vertical side wall equiped with ribs [Kuster et al, 1992, Fig.
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 221