shore to a deep-water berth. However, as noted by Newmark(8.7)the solitary-wave theory is
often applied to situations beyond its strict range of validity for want of a better theory. For
deep-water structures the solitary-wave theory gives over-conservativevalues of wave force.
However, equations 8.7 to 8.9 based on this theory together with the dimensionless graphs
are simple and easy to use. It is suggested that the equations are used for all parts of a deep-
water berthing-head structure and for the shallow-water approach whenever it is necessary
to calculate wave forces. If these forces together with current drag, wind forces, and berthing
impact forces do not produce excessive bending stresses on the piles then the calculations
need not be further refined. It must be kept in mind that the cross-sectional area of a pile
may be governed by considerations of corrosion and driving stress rather than the stress
resulting from environmental forces. Where the wave forces calculated by the solitary-wave
theory are a significant factor in the design of the piles more detailed calculations should
be made taking into account the relationship between wave height, water depth, and wave
period. Methods of general application can be found in the publications of the US Army
Coastal Engineering Research Centre(8.8).
In general wave theories, the wave force on a fixed structure is taken as the sum of the
drag and inertial forces exerted by the wave. These are expressed by the commonly used
Morison equation(8.9):

(8.7)

where f,fD, and fIare the wave force, drag force, and inertial force, respectively, per unit area
of object in the path of the wave, CDis a drag coefficient, wis the density of water, gis the
gravitational acceleration, uis the horizontal particle velocity of water, CMis a coefficient
of inertia force, Dis the diameter of the cylindrical object, and du/dtis the horizontal
acceleration of a water particle.
BS6349-1, Clause 39.44, expresses the Morison equation in a somewhat different form
and includes guidance on its limitations, together with equations for calculating the velocity
of the water particles. The values for CDshown in Table 8.2, Section 8.1.4 below, can be used
in the version of the Morison equation given in equations 8.7 to 8.9. The values of C 1 in
Table 8.2 can also be used for CMin equations 8.7 to 8.9.
Newmark(8.7)reduced equation 8.7 to a simple expression given in lb-ft-sec units. By
taking the weight of sea water as 64 lb/ft^3 and the gravitational acceleration as 32.2 ft/sec
the equation becomes

f fDfI  50 CDh (8.8)

u

c

2

 50 CMD·^1 g·

du

dt^

lb/ft^2

f fDfI CD

wu^2

2 g

CM

w

g

D

4

·

du

dt

410 Piling for marine structures

Table 8.2Drag force and inertia coefficients for square section piles

Flow direction Figure no. CD CL

Perpendicular to face 8.13a 2.0 2.5
Against corner, in direction of diagonal 8.13b 1.6 2.2
Perpendicular to face, rounded corner,r/ys 0.17 8.13c 0.6 2.5
Perpendicular to face, rounded corner,r/ys 0.33 8.13c 0.5 2.5