1 . Forces on Piles . 



a. Introduction. Frequent use of pile-supported coastal and offshore 

 structures makes the interaction of waves and piles of significant practical 

 importance. The basic problem is to predict forces on a pile due to the wave- 

 associated flow field. Because wave-induced flows are complex, even in the 

 absence of structures, solution of the complex problem of wave forces on piles 

 relies on empirical coefficients to augment theoretical formulations of the 

 problem. 



Variables important in determining forces on circular piles subjected to 

 wave action are shown in Figure 7-67. Variables describing nonbreaking, 

 monochromatic waves are the wave height H , water depth d , and either wave 

 period T , or wavelength L . Water particle velocities and accelerations 

 in wave-induced flows directly cause the forces. For vertical piles, the 

 horizontal fluid velocity u and acceleration du/dt and their variation 

 with distance below the free surface are important. The pile diameter D and 

 a dimension describing pile roughness elements £ are important variables 

 describing the pile. In this discussion, the effect of the pile on the wave- 

 induced flow is assumed negligible. Intuitively, this assumption implies that 

 the pile diameter D must be small with respect to the wavelength L . 

 Significant fluid properties include the fluid density p and the kinematic 

 viscosity v . In dimensionless terms, the important variables can be 

 expressed as follows: 



H 



2 

 gT 



d 



2 

 gT 



= dimensionless wave steepness 



= dimensionless water depth 



— = ratio of pile diameter to wavelength (assumed small) 



— = relative pile roughness 



D 



and 



HD 



— = a form of the Reynolds' number 



Given the orientation of a pile in the flow field, the total wave force 

 acting on the pile can be expressed as a function of these variables. The 

 variation of force with distance along the pile depends on the mechanism by 

 which the forces arise; that is, how the water particle velocities and 

 accelerations cause the forces. The following analysis relates the local 

 force, acting on a section of pile element of length dz , to the local fluid 

 velocity and acceleration that would exist at the center of the pile if the 

 pile were not present. Two dimensionless force coefficients, an inertia or 

 mass coefficient C and a drag coefficient C^ , are used to establish the 

 wave-force relationsnips. These coefficients are determined by experimental 



7-101 



