For force calculations, an appropriate wave theory should be used to 

 calculate u and du/dt. Skjelbria, et al . (1960) have prepared tables 

 based on Stokes' fifth-order wave theory. For a wide variety of given 

 wave conditions, i.e., water depth, wave period and wave height, these 

 tables may be used to obtain the variation of f^ and f^ with time 

 (values are given for time intervals of 2TTt/T = 20°) and position along 

 the pile (values given at intervals of 0.1 d) . Similar tables based on 

 Dean's numerical stream-function theory (Dean, 1965) are to be published 

 by CERC in 1973. (Dean, 1973.) 



For structural design of a single vertical pile, it is often unneces- 

 sary to know in detail the distribution of forces along the pile. Total 

 horizontal foi'ce acting on the pile and total moment of forces about the 

 mudline z = -d are of primary interest. These may be obtained by inte- 

 gration of Equation 7-13. 



F = 



-d -d 



j f. dz + I fi) dz = F. + F^ , (7-20) 



M 



d -d 



/ (z + d)f. dz + / (z + d)f^ dz = M,. + M^. (7-21) 



In general form these quantities may be written 



F.- = Cm Pg^H K,., (7-22) 



Fd = C^ ^ Pg D H^ K^ , (7-23) 



M,- = Cm Pg ^ H K,. d S. = F,. d S,., (7-24) 



Md ^ C^ 7 Pg D H2 K^ d S^ = F^ d S^ . (7-25) 



in which C^ and C>^ have been assumed constant, and where K^, K^, S^ 

 and S£j are dimensionless. When using Airy theory (Equations 7-18 and 



7-74 



