Wave, Loads in the fabrication, tow-out, & installation phases

& Current load

Berlian Arswendo Adietya198608262010121005

outline

• Wave theory & loads• Functional loads:

– Loads in the fabrication, tow-out, & installation phases

• Current loads on structures:– Current drag & lift forces– Blockage factor in current

Ocean surface wave

• They are primarily by the drag of the wind on the water surface

• For engineering purposes two methods available to analyze the effect of the surface wave on structures:

1. A single design wave chosen to represent extreme storm conditions,

2. A statistical representation of the wave during extreme storm conditions.

Wave theories• We need to relate the surface-wave data

to the water:– Velocity– Acceleration, &– Pressure beneath the waves

By the use of an appropriate Wave Theory

Wave theories (cont. …)

• Airy wave theory• Stokes wave theory• Cnoidal wave theory

Each of them has specific limitation & application dependent on the characteristics of the water area

DESIGN LOADS – WAVE & CURRENT LOADS

• Two different analysis concepts:1. Design/ regular wave concept:

– A regular wave of given height and period is defined and the forces due to this wave are calculated using a high-order wave theory.

– Usually the 100-year wave is chosen. – No dynamic behavior of the structure is considered.

This static analysis is appropriate when the dominant wave periods are well above the period of the structure.

– This is the case of extreme storm waves acting on shallow water structures.

Wave & current loads (cont. …)

2. Statistical analysis: – On the basis of a wave scatter diagram for the

location of the structure. – Appropriate wave spectra are defined to perform the

analysis in the frequency domain and to generate random waves, if dynamic analyses for extreme wave loadings are required for deepwater structures.

– With statistical methods, the most probable maximum force during the lifetime of the structure is calculated using linear wave theory.

– The statistical approach has to be chosen to analyze the fatigue strength and the dynamic behavior of the structure.

Wave Statistics

Wave Spectrum

• The regular wave theories are applicable in a design where a single wave method is employed. In this case an extreme wave is represented by a regular wave of the appropriate height and period. This method provides a simple analysis in determining the extreme response of an offshore structure.

• The random ocean wave, on the other hand, is described by an energy density spectrum. The wave energy spectrum describes the energy content of an ocean wave and its distribution over a frequency range of the random wave. Therefore, the random wave method of design may be important especially in the design of floating structures. The random wave is generally described by its statistical parameters.

Wave Spectrum

Wave Spectrum

Wave Spectrum

Airy wave theory• Simple theory of wave motion G.B. Airy

(1842)• Assumption:

– a Sinusoidal wave form, – H/ & H/h small

• Valuable for preliminary calculation & revealing the basic characteristics of wave-induced water motion

• A basis for the statistical representation of waves & induced water motion during storm conditions.

Definition of wave parameters

Airy wave theory

Airy wave theory

Stokes wave theory

• G.G. Stokes (1847) an extension of Airy theory wave of finite height

• Expansion the wave solution in series form determine the coeffs. of individual terms to satisfy the appropriate hydrodynamic equations for finite-amplitude wave.

• Stokes wave theory: – Stokes third-order wave theory (Skjelbreia, 1959 &

Wiegel, 1964)– Stokes fifth-order wave theory (Skjelbreia &

Hendrickson, 1961)

Stokes wave theory (cont. …)

• Stokes fifth-order wave theory: – Widely used in ocean eng. Calculations for

finite amplitude waves.– Convergence of the series is slow shallow

water– Most nearly valid in water relative depth

(h/ > 1/10) met for storm wave conditions for the design of fixed offshore platforms.

Cnoidal wave theory

• Cnoidal wave theory Firstly presented by Korteweg & deVries (1895) developed further by Wiegel (1960) for practical application.

• More satisfactory applicable for shallow water• Expressed in term of tabulated elliptic functions

& integrals• The theory assumes H/h is sufficiently small

that its square can be neglected.

Applicability of wave theories

• H/ ?• h/ ?

How the Airy theory can be used to obtain a reasonable accurate estimate of the wave characteristics ??

• A main feature of the more accurate Stokes & Cnoidal theory the increase of the crest amplitude of a wave over that given by Airy theory.

Applicability of wave theories

• Allowable error in the crest ampl. of 10%.

Applicability of wave theories

• The obvious question is, when is one of these theories suitable for application??

• A region of validity of the various theories that are applicable to offshore structures in relatively deeper waters is presented in fig. 3.12. The chart is taken from API RP2A Guidelines (2000),

• Since the basic wave parameters are H, T and d, the regions are shown as functions of H/(gT2) and d/(gT2)

Applicability of wave theories

An example :• Take a wave of height 30

m, period of 16 s in a water depth of 160 m.

• Then H/(g.T2) = 0.012 and d/(g.T2) =0.064.

• From the chart (in the figure), the applicable wave theory is Stokes’ third-order.

• A fifth-order Stokes wave may be applied here as well.

Applicability of wave theories• A rule of thumb for the practical application of wave

theory is presented here with recommendation for the appropriate theory in specific cases.

• The theories for the cases shown are suggestions for normal applications.

Wave force on vertical cylinders

• Morison et al. (1950)• D/ < 1/10• CD & CI = drag & inertia coeff.• u & ax = horizontal acc. & vel.

Of wave particle (from an appropriate wave theory)

• API (1980): CD = 0.6 ~ 1.0 CI = 1.5 ~ 2.0

y

xID

y

dyaCDuuDCFw

dyFiFdFw

0

2

0

41

21

Drag term Inertia term

Effects of relative motion• When the motion of the cylinder is considered:

– The drag force reduced by the relative motion– The inertia force reduced by a factor proportional

to the acc. of the cylinder– : the horizontal velocity & acc. of the cylinder

element

y

IxID dyxDCaCDxuxuDCFw0

22

4)1(

4)(

21

xx ,

Effects of cylinder diameter

• When the D/ > 1/10 the distortion of the wave due to the cylinder must be considered

• Diffraction theory (MacCamy & Fuchs, 1954 and Mogridge & Jamieson, 1976) :– Drag forces are negligible in comparison with inertia

forces.– The effect of the cylinder is to modify the value of the

inertia coeff. in Morison eq & introduce a phase angle lag

WAVE DIRECTION

1 2

A

B

1 2

A

B

Wave force on arbitrarily oriented cylinder

• The determination of wave force on cross bracing & on inclined (battered) piles of offshore platform.

• Chakrabarti et al. (1975):– Resolving the water velocity & acc. into

components normal & tangential to the cylinder axis

– Using only the normal comps. in Moriso eq. to calculate the wave force per unit length of the cylinder.

Wave lift and slamming Loads

• In addition to the forces given by Morison's equation, the lift forces FD and the slamming forces FS, typically neglected in global response computations, can be important for local member design. – FL = (1/2) ρ CL Dv2 – FS = (1/2) ρ Cs Dv2

• CL ≈1,3 CD. • Cs ≈ π For tubular members

Dropped Object & Collision Loads

• The impact Energy due to dropped object:

• E = M.go.h– E: impact (dropped) energy

(kJ)– M: mass of objects (tonnes)– go: ground acceleration

(9.81 m/s2)– h : dropped height in air (m)

• The weight of the dropped objects are normally taken as the operational hook loads in cranes

• The impact Energy due to collision:

• E = 1/2 (M+a)v2

– E: impact (collision) energy (kJ)

– M: displc. vessel (tonnes)– a: added mass of vessel,

normally assumed as 0.4 M for sideway collision and 0.1 M for bow or stern collision

– v : impact speed (m/s)

Loads in the fabrication, tow-out & installation phases

• The occurrence of welding stresses & possible extreme loads in the launching of vessels must be recognized.

• During the joining of large structural components geometrical mismatch additional stresses can be build into the structure

Forces due to geometrical mismatch• During installation in the case of deck columns

stabbing into the jacket legs.

Loads in installation sequence

• Tow-out:– In open ocean area no shelter + severe

environmental significant response in some structural components.

• Launching the jacket from a barge: – Severe load CG of the jacket passes

over the tilt beam (Fig. 3.7a)– Large axial loads must be carried by a few

bracing members lead to extra braces (Fig. 3.7b)

Loads in installation sequence

Loads in installation sequence

• Up-righting ballasting the jacket ~ a vertical orientation

• Design conditions to be investigated: – Launching– Up-righting– Setting

Current loads on structures• In design of offshore structures current

time-invariant represented by the mean value• The current strength vary with water depth• Current varying pressure distribution around

a member steady drag force on the structure in the direction of flow

• Pressure distribution not symmetric about the flow direction generate a transverse force on the structural member.

Current drag & lift force• If a 2-D structure is

placed in a uniform flow:f = current force = fluid densityA = structure projected area

normal to the flowU = uniform flow velocityCD = a constant (drag coeff.)

CD a function of the Reynolds number (Re) Re = UD/ D = diameter of structure = kinematics viscosity

The drag coefficient• A smooth stationary circular cylinder• In uniform flow• Obtained through laboratory testing

Current loads on structures

• Roughness of the structure surface:– Appendages attached to a structural component (e.g.

in ship & submarine)– Marine growth (e.g. in the floating buoys &

submerged cylindrical structural members)• The roughness is quantified by the value of the

roughness coefficient, e = KID; K = surface roughness parameter.

• API guideline a 1.5 in. growth on members for depths from 0 to 150 ft below the surface.

Marine Growth• Marine growth is accumulated on submerged

members. • Its main effect is to increase the wave forces on the

members by increasing not only exposed areas and volumes, but also the drag coefficient due to higher surface roughness.

• It increases the unit mass of the member, resulting in higher gravity loads and in lower member frequencies.

• Depending upon geographic location, the thickness of marine growth can reach 0,3m or more.

• It is accounted for in design through appropriate increases in the diameters and masses of the submerged members.

Marine Growth• The drag coefficients for a rough cylinder for a

roughness coefficient value of up to 0.02 are shown in fig. 4.2 as a function of Re and the roughness coefficient, K/D.

CD at high Reynolds number with various roughness

• In a recent experiment, the drag coefficients on a cylinder were obtained at high Reynolds number with various roughness, which is shown in fig. 4.3.

Marine Growth data

The Transverse (or Lift) force• Pressure distribution not symmetric about the flow direction

generate a transverse force (or Lift) on the structural member.

• This force is generated from the asymmetric pressure distribution due to the uneven formation of the vortices behind the member.

• The force generated in the transverse direction is irregular.• This force is written in a form similar to the inline drag force as:• This form of the lift force requires that the lift coefficient, CL in

the equation is time varying.

The Transverse (or Lift) force• Therefore, the lift coefficients are expressed either as rms

values over one measured cycle or maximum values corresponding to the maximum lift force.

• The two curves in the figure provides the upper and lower ranges of experimental CL and its value in a particular case can only be determined approximately.

Blockage factor in current• A practical structure is often

composed of relatively closely spaced small members connected in various orientations.

• The current blockage factor to account for the presence of the structure in the current flow field enables one to compute the true global load on the structure.

• The blockage factor is applied to the undisturbed current (i.e. steady flow) value in order to obtain an equivalent current velocity that accounts for the blockage by the structure.

Taylor (1991):• The summation of the drag

forces is computed from each member in the dense structure including the horizontal members in the flow,

• Ā is the perimeter area of the projected structure normal to the flow.

Current Blockage factor for jacket platform

API (2000):• In practice, such as, a

group of drilling conductors or risers of a jacket-type structure

• S is the centre to centre distance of the conductors of diameter D, which includes any marine growth on the surface of the conductors