Pile Design and Construction Practice, Fifth edition

From �7.5 to �3.0 m: no increase of diameter (i.e. D � 0.61 m)
From �3.0 to �1.5 m: increase of 70 mm (D � 0.68 m)
From �1.5 m to sea bed: increase of 190 mm (D � 0.80 m)
Piling for marine structures 433
Taking Newmark’s values a drag force coefficient of 0.5 is used to calculate the current
and wave drag forces, and an inertia coefficient of 2.0 is used to calculate the wave inertia
forces. Thus in equation 8.10:
F D � 0.5 � 0.5 � � � V 2 � A n � 0.25V 2 A n kN (for � � 1 mg�m 3 )
In equation 8.9
f � 7.8 � 0.5 � 11(u�c) 2 � 8 � 2 � D� 1 g
The calculated wave and current forces are shown in Table 8.4 and Figure 8.20. The bending
moments shown in Table 8.4 have been calculated on the assumption of virtual fixity of the
pile at a point 1.5 m below the sea bed in the stiff boulder clay. Scour would not be expected
around the piles in this type of soil. From Table 8.4, the combined wave and current forces
produce a maximum bending moment at the point of fixity of 690.57 kN m.
Bending moment due to wind force on deck slab:
� 1
2 � 25 � (15.0 � 1.5) � 206.25 kN m
Total bending moment � 896.82 kNm�pile.
Moment of inertia of pile section � �(0.6100 4 � 0.5846 4 )�64 � 1.063 � 10 �3 m 4 .
Extreme fibre stress of pile �
896.82 � 0.305
1.063 � 10 �3 � 10 3 � 257 MN�m 2 .
The direct stress resulting from the dead load of the deck slab and self weight of the pile is
added to the bending stress calculated above. It is also necessary to calculate the susceptibility
of the pile to current-induced oscillations.
Assuming the pile to be filled with fresh water, the effective mass is approximately equal
to the mass of metal plus twice the mass of the displaced water. Therefore
M � 187 � (2 � 1
4��0.61 2 � 1 000) � 771.5 kg�m
When the pile is in an unsupported condition cantilevering from the sea bed, from
equation 8.13:
fN � 0.56
14 2�200 � 109 � 1.063 � 10�3 � 1.50 Hz 771.5
du
·
dt� � 42.9(u�c) 2 � 16D� 1 du
g ·
dt� .
From equation 8.12 critical velocity for onset of cross-flow oscillation � 5.5 � 1.5 � 0.61 �
5 m/sec.
Therefore cross-flow or in-line oscillations should not take place for the flow velocities
shown in Figure 8.20.