Probabilistic approach on course material transport under waves: Vol. 1 Theory and experiment.

(1)

(2)

(3)

i i

-ABSTRACT

The probabilistic design method of a cover layer of pipe line under the horizontal bottom is described. By assuming that the water velocity at the bottom is Rayleigh distributed, probability of bottom shear stress was derived. With a combination of the probability func-tion of bottom shear and a simple sediment transport formula given by Madsen and Grant (1976), the expected transport rate was calculated. The results gave a warning that conventional design methods have a risk to underestimate the amount of loss.of covering material.

To confirm the e stab Li.shedrformu'las .about inception of motion of particles and sediment transport under w~ves, some experiments were carried out. As for inception of particle mqtion, comparison between steady flow condition and wave condition was, done. It turned out that the one gives lower value than the othe~, ~nd that Shields' curve gives the lower limit of the total experimental data. The data of critical velocity under waves agreed ~o Komar-Mi~ler's formula which involves the factor of wave period. The critica~ :velocityin the direction of wave propagation was found considerably higher than that against it.

Sedimen.t-transport-rateY1asmea~uredtogetherwith velocity. As had been already presented by v~nde Graaff and Tilmans (1980), the transp?rt-rate could be r~lated to the Fouri~r components of the ve-locity. It could also be related to the maximum and minimum veve-locity. The influence of a phase lag bet~een the f~rst and second terms of the Fourier components, which is closely related .to the acceleration and the deceleration.of the total vel?city, was not clear yet in that spe-cific condition. Critical velocity obtained by the visual observation, .- ~.

generally agreed to the limit line of tran~port-rate (zero line) on both

u

1 -

u

2 plane and umax - u.m~n plane.

This report consists of two volumes. The Vol. I includes the the-oretical consideration on the probability of sediment transport and the experimental consideration on the migration of coarse material under a steady flow and regular waves. The Vol. 11 contains the proce-dure of the experiment, the data and the computation programs.

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

(40)

(41)

(42)

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

(52)

(53)

(54)

(55)

(56)

(57)

(58)

(59)

(60)

(61)

(62)

(63)

(64)

(65)

(66)

(67)

(68)

(69)

(70)

(71)

(72)

(73)

(74)

(75)

(76)

(77)

(78)

(79)

(80)

(81)

(82)

(83)

(84)

(85)

(86)

(87)

(88)

(89)

(90)

(91)

(92)

(93)

(94)

(95)

(96)

(97)

(98)

(99)

(100)

(101)

(102)

(103)

(104)

(105)

(106)

(107)

(108)

(109)

(110)

(111)

(112)

(113)

(114)

(115)

(116)

(117)

(118)

(119)

(120)

(121)

(122)

(123)

(124)

(125)

(126)

(127)

(128)

(129)