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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 .




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                                                                         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]




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ences to the sections .




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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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