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Landslide generated impulse waves in reservoirs - Basics and computation Spread sheets Project name - Operator - Computational point - Date - Governing parameters Wave generation (Subsection 3.2.2) Slide impact velocity V s [m/s] - Bulk slide density r s [kg/m3] - 3 Bulk slide volume V s [m ] - Bulk slide porosity n [%] - Slide thickness s [m] - Slide impact angle a [°] - Slide or reservoir width b [m] - Still water depth h [m] - Wave propagation (3D or 2D) (Subsection 3.2.2) Wave basin (3D) Wave channel (2D) Radial distance r [m] - Streamwise distance x [m] - Wave propagation angle g [°] - Wave run-up and overtopping (Subsection 3.3.2) Still water depth h [m] - Freeboard f [m] - Run-up angle b [°] - Crest width b K [m] - - Main results Wave heigth H (H M ) [m] - Wave amplitude a (a M ) [m] - Wave period T (T M ) [s] - Wave length L (L M ) [m] - Run-up height R [m] - Overtopping volume V 0 per unit length dam crest for f = 0 [m3/m] - Duration of overtopping t 0 for f = 0 [s] - Average discharge q 0m per unit length dam crest for f = 0 [m2/s] - Maximum discharge q 0M per unit length dam crest for f = 0 [m2/s] - Overtopping volume per unit length dam crest V [m3/m] - Hor. force comp. p.u.l. dam crest resulting only from hydrostatic pressure K RW ,h [N/m] - Ver. force comp. p.u.l. dam crest resulting only from hydrostatic pressure K RW ,v [N/m] - Wave type (Stokes-like wave 3.4.3 or remaining wave types 3.4.4) - Remaining: total horizontal force component per unit length dam crest resulting from an - impulse wave and hydrostatic pressure K tot ,h [N/m] Remaining: reduced total horizontal force component per unit length dam crest resulting - from an impulse wave and hydrostatic pressure K tot ,h ,abg [N/m] Remaining: elevation z K ,tot ,h ,abg of the resultant of K tot ,h ,abg [m] - S/r: additional hor. force comp. p.u.l. dam crest resulting from impulse wave DK h [N/m] - Stokes: elevation z DK ,h of the resultant of DK h [m] - S/r: ad. vertical force component p.u.l. dam crest resulting from impulse wave DK v [N/m] - Limitations Number of not satisfied limitations out of 23 (2D) or 24 (3D), respectively - Spread sheets Input and output 1 Computation procedure Figure 3-1 Computation procedure of landslide generated impulse waves with the phases of the impulse wave, computation methods and references to the sections . Spread sheets Computation 2 Results Values dependent on 2D or 3D (Subsection 3.2.3.1) Impulse product parameter P [-] (Eq. 3.5) 2D: Heller (2007a) based on Zweifel (2004) and Fritz (2002) (Subsection 3.2.3.2) Eq. (3.7) Streamwise distance of the maximum wave amplitude from the impact location x M [m] Eq. (3.10) or Eq. (3.6) Wave height H (H M ) [m] Eq. (3.4) Wave amplitude a (a M ) [m] Eq. (3.11) or Eq. (3.8) Wave period T (T M ) [s] Eq. (3.3) Wave celerity c [m/s] Eq. (3.12) or Eq. (3.9) Wave length L (L M ) [m] 3D: Heller (2007a) with conversion-method of Huber and Hager (1997) (Subsection 3.2.3.3) Eq. (3.7) Streamwise distance of the maximum wave amplitude from the impact location x M [m] Eq. (3.13) or (Eq. 3.6) Wave height H (H M ) [m] Eq. (3.4) Wave amplitude a (a M ) [m] Eq. (3.14) or Eq. (3.8) Wave period T (T M ) [s] Eq. (3.3) Wave celerity c [m/s] Eq. (3.15) or Eq. (3.9) Wave length L (L M ) [m] Müller (1995) (Subsection 3.3.3) Eq. (3.16) Run-up height R [m] Figure 3-6(a) Overfall coefficient for the crest width k b [-] Subsection (3.3.3) Overfall coefficient for the steady case k q [-] Eq. (3.17) Overtopping volume V 0 per unit length dam crest for f = 0 [m3/m] Eq. (3.19) Duration of overtopping t 0 for f = 0 [s] Eq. (3.20) Average discharge q 0m per unit length dam crest for f = 0 [m2/s] Figure B-4(b) Maximum discharge q 0M per unit length dam crest for f = 0 [m2/s] Eq. (3.18) Overtopping volume per unit length dam crest V [m3/m] Spread sheets Computation 3 Classification of wave types with Eq. (3.23) after Heller (2007a) (Subsection 3.4.3) Eq. (3.23) or Eq. (3.29) Wave type product Eq. (3.23) or Eq. (3.29) Term on the right hand side Eq. (3.23) or Eq. (3.29) Wave type b = 90°: Stokes-like waves with Sainflou (1928) (Subsection 3.4.3) Eq. (3.21) Horizontal force component per unit length dam crest resulting only from hydrostatic pressure K RW ,h [N/m] Eq. (3.22) Vertical force component per unit length dam crest resulting only from hydrostatic pressure K RW ,v [N/m] Eq. (3.24) Pressure on dam foundation according to Sainflou (1928) p 1 [N/m2] Eq. (3.25) Average water level rise according to Sainflou (1928) Dh [m] Eq. (3.26) Pressure at still water level according to Sainflou (1928) p 2 [N/m2] Eq. (3.27) Additional horizontal force component per unit length dam crest resulting from impulse wave DK h [N/m] Eq. (3.28) Elevation z DK ,h of the resultant of DK h [m] After Eq. (3.22) Additional vertical force component per unit length dam crest resulting from impulse wave DK v [N/m] b = 90°: remaining wave types with Ramsden (1996) (Subsection 3.4.4) Eq. (3.21) Horizontal force component per unit length dam crest resulting only from hydrostatic pressure K RW ,h [N/m] After Eq. (3.22) Vertical force component per unit length dam crest resulting only from hydrostatic pressure K RW ,v [N/m] Eq. (3.30) Total hor. force comp. p.u.l. dam crest resulting from an impulse wave and hydrostatic pressure K tot ,h [N/m] Reduction of force effect if wave overtops (Subsection 3.4.4) 2 Eq. (3.32) Pressure at dam crest p K [N/m ] Eq. (3.33) Reduced total horizontal force component per unit length dam crest resulting from an impulse wave and hydrostatic pressure K tot ,h ,abg [N/m] Eq. (3.34) Elevation z K ,tot ,h ,abg of the resultant of K tot ,h ,abg [m] Eq. (3.33) − Eq. (3.21) Additional horizontal force component per unit length dam crest resulting from impulse wave DK h [N/m] After Eq. (3.22) Additional vertical force component per unit length dam crest resulting from impulse wave DK v [N/m] Spread sheets Computation 4 ences to the sections . Spread sheets Computation 5 - - - - - - - - - - - - - - - - - - - - - Spread sheets Computation 6 - - - - - - - - - - - - - - - - - - - Spread sheets Computation 7 Parameter limitations control Limitations for the impulse wave generation Table 3-2 Limitations for the calculation of the impulse waves generation. Slide Froude number - Relative slide thickness - Relative slide mass - Relative slide density - Relative grain density - Relative slide volume - Bulk slide porosity - Slide impact angle - Relative slide width - Relative radial distance - Wave propagation angle - Relative distance - Impulse product parameter - Limitations for the wave run-up Table 3-3 Limitations for the calculation of the wave run-up. Relative wave height - Wave steepness - Relative angle - Spread sheets Limitations 8

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posted: | 3/4/2010 |

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