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Pile Design and Construction Practice, Fifth edition

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412 Piling for marine structures<br />

C D is related to the Reynolds number, which for cylindrical members <strong>and</strong> normal water<br />

temperatures is given by the equation:<br />

R e � 9.3VD � 10 5 in sec/m �2 units (8.11)<br />

Section 5 of BS 6349 includes graphs relating C D for cylindrical members to their surface<br />

roughness <strong>and</strong> Reynolds number. They show that C D for rough members is in the range of<br />

0.4 to 0.6 for Reynolds numbers between 10 5 <strong>and</strong> 10 6 . The code gives values for C D <strong>and</strong> C 1<br />

(C M in equation 8.7) for square section piles as shown in Figure 8.13 <strong>and</strong> Table 8.2.<br />

If piles or other submerged members are placed in closely spaced groups, shielding of current<br />

forces in the lee of the leading member will occur. Shielding can be allowed for by modifying<br />

the drag coefficient. Values of the shielding coefficient have been established by Chappelaar (8.11) .<br />

Where currents are associated with waves it may be necessary to add the current velocity<br />

vectorially to the water-particle velocity u to arrive at the total force on a member. Also, the<br />

possibility of an increase in the effective diameter <strong>and</strong> roughness of a submerged member<br />

due to barnacle growth must be considered.<br />

Having calculated the current force on a pile it is necessary to check that oscillation will<br />

not take place as a result of vortex shedding induced by the current flow. This oscillation<br />

occurs transversely to the direction of current flow when the frequency of shedding pairs of<br />

vortices coincides with the natural frequency of the pile.<br />

Determination of the critical velocity for the various forms of flow-induced oscillation of<br />

cylindrical members is given in BS 6349-1, Clause 38.3, by the equation:<br />

V crit � Kf N W s<br />

where K is a constant equal to<br />

1.2 for onset of in-line motion<br />

2.0 for maximum amplitude of in-line motion<br />

3.5 for onset of cross-flow motion<br />

5.5 for maximum amplitude of cross-flow motion<br />

fN � natural frequency of the cylinder<br />

Ws � diameter of the cylinder.<br />

(a) (c)<br />

(b)<br />

Flow direction<br />

Figure 8.13 Flow conditions for determining drag conditions.<br />

R<br />

y s<br />

(8.12)

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