force (F) acting on the pile and total moment of forces (M) about the mud 

 line z = -d are of primary interest. These may be obtained by integration 

 of equation (7-20). 



= f fi dz + J f^ dz = F^ + F^ (7-27) 



■ n ^n 



M = f (z+d) f^ dz + [ (z + d) f^ dz = M^ + M^ (7-28) 

 -d -d 



In general form these quantities may be written 



F. = C^ pg ^ H K. (7-29) 



1 M '^ h % 



F^= C^lpgDH^K^ (7-30) 



•nVt 



M. = C., pg ^^ H K. d S. = F. d S. (7-31) 



M^= C^|pg Dh2 K^d S^= F^d S^ (7-32) 



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



and S^ are dimensionless. When using Airy theory (eqs. 7-25 and 7-26), the 



integration indicated in equations {1-11) and (7-28) may be performed if the 

 upper limit of integration is zero instead of n . This leads to 



K,.Itanh (^) si„ (-1?) (7-33, 



Ut\ I 



1 I / 2irt \ I / 2iit 

 4 n 1 cos 



7-111 



