Pile Design and Construction Practice, Fifth edition

The empirical equation of Korzhavin (8.12) for calculating p is
where
p � Imk� c
I � indentation factor
m � shape factor
k � contact factor
� c � uniaxial compression strength of the ice
(8.17)
I is stated to be equal to unity for a wide pier and 2.5 for a narrow pier (t/b � 1). The shape
factor is approximately unity for a circular pier, k is also unity for perfect contact between
the ice and the structure. The compression strength is difficult to determine by laboratory
testing. It depends on the crystal structure, strain rate, temperature and sample size.
Croasdale gives an alternative calculation method based on plasticity theory. The penetration
of the pier into the ice is analogous to the failure of a soil surface under the imposed
loading of a strip foundation, when the ice sheet is displaced around the pier in the form of
wedges, similar in shape to the soil heave around the foundation.
For wedges splitting at an angle of 45� to the edge of the ice sheet the equation for
calculating the effective ice stress is
p � � c (1 � 0.304t/b) (8.18)
It appears from Croasdale’s paper that the contact factor k should be applied to the value
of p calculated from equation 8.18. A factor of 0.5 is given for continuously moving ice, and
1.0 or more for ice frozen around a structure.
The equation of Tryde (8.13) based on wedge theory is
2.1
p � 0.8�c�1 �
(0.4 � b/t)�
Piling for marine structures 415
(8.19)
The forces on the pile from the rubble have been mentioned above. Frictional forces from
loose blocks can be assumed to act as a granular material. Where the blocks are frozen
together the stresses on the pile will be lower than that of the consolidated ice sheet because
the bonds between the blocks will fracture at low strain levels.
It is evident that a single large pile or cylinder will be more effective in resisting ice forces
than a cluster of smaller piles. A more efficient structure has a conical shape as shown in
Figure 8.14. The impact force from the ice sheet is distributed in directions normal and
tangential to the sloping face. Energy is dissipated as the ice sheet is levered up and cracked
circumferentially. Further energy is dissipated as the broken blocks are pushed up the slope.
Methods of calculating ice forces on conical structures are discussed by Croasdale (8.14) and
more recently by Brown (8.15) .
The structure shown in Figure 8.14 is designed for weak ground conditions needing support
by a piled raft to resist horizontal and vertical forces. The shape is unsuitable for berthing large
ships, but it is suitable as a single point mooring, or as a foundation for a wind generator.
8.1.7 Materials for piles in jetties and dolphins
For jetties serving vessels of light to moderate displacement tonnage and of shallow draught,
timber is the ideal material for fender piles. It is light and resilient and easy to replace.