FREQUENCY DOMAIN ANALYSIS OF OFFSHORE PILES

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Frequency Domain Dynamic Analysis to
Assess the Structural Integrity of Large
Diameter Foundation Piles during Offshore
Installation using GT STRUDL and GT SELOS
Loic Faure and Dr Arash Parsa
June 2013
Offshore Pile Installation Operations
72 to 102’’ Diameter Piles with WT of 60 to 100mm – 60 to 110m Lg Piles
Pile driving with heavy hydraulic hammers (up to 550Te) in a difficult
environment (Offshore North Sea)
Pile Only
Pile + Hammer
above Wave Zone
Pile + Hammer in
Wave Zone
Pile + Hammer
below Wave Zone
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25th Annual GT STRUDL Users Group Meeting
June 2013
Pile Driven to Target
Penetration
Goal of the Analysis
Ensuring pile integrity at each stage of the installation
Minimising weather down time during offshore installation
Producing clear guidelines on the acceptable sea states (combination of
significant wave height (Hs) and period (Tz)) for driving operations
Pile Utilisation Factor (UF) > 1.0
Driving is not allowed
Pile Utilisation Factor (UF) < 1.0
Driving is allowed
Allowable Dynamic Driving Stress
is 131 MPa
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Codes of Practice Requirements
Codes of Practice: API RP2A, ISO
19902, Norsok N004..
Waves
Mean Sea Level
Pile Oscillations
Beam-Column Check at the Critical
Section(s) (Usually at the upper
shim, sometimes at sections with
changes in pile wall thickness)
P-Delta Moment to be included
Hammer
Current
Pile
Sum of Driving Stresses + Axial &
Bending Stresses < Yield Stress
Axial Force
Bending Moment
Upper Shim
Lower Shim
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Mud Line
Overview of the Analysis
Based on Frequency Domain Dynamic Analysis
Use of a GT STRUDL beam model
Dynamic Base Shear
Static Base Shear
GT SELOS
GT STRUDL / GT SELOS
Wave Induced
Bending Moment
(P-∆ Analysis)
GT STRUDL / GT SELOS
Dynamic Amplification Factor
Wave Design Spectrum
Bending Moment RAO
Bending Moment Spectral
Density
Total Bending Moment and
Axial Force
Buckling
Factor
Code Check
GT STRUDL
Operability Table
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Dynamic Driving Stress Vs.
Hammer Mechanical
Efficiency Setting
FOUNDATION DEPARTMENT
GT STRUDL and GT SELOS Facilities Used
SPREADSHEET
•Generate the Sea Spectral Density
(function of Hs and Tz)
GT STRUDL
•Eigen Value
SPREADSHEET
GT SELOS
•Added Mass due to
Entrapped Water
•Wave and Current Loading
Generation
•Wave Motion Time History
Analysis
SPREADSHEET
GT STRUDL
•P-Delta Analysis
GT SELOS
•Wave and Current Loading
Generation
SPREADSHEET
GT STRUDL
•Buckling Analysis
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Interaction with Excel
Use of the COUTPUT command to export the relevant GT STRUDL / GT
SELOS output to a text file and extracted with a spreadsheet including a
macro (using VBA)
Typical GT STRUDL Input
Data extracted and sorted
out in the required format
in a spreadsheet
automatically
Typical GT STRUDL Output
Typical VBA Macro
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Computing the DAF
Two models are run with GT SELOS to calculate the base shear
‘Pseudo’ static model: unit amplitude waves (of varying periods) are stepped
through the structure (with no modal information) and the maximum static
base shear is extracted
Dynamic model: unit amplitude waves (of varying periods) are stepped
through the structure and a time motion history analysis is used to calculate
the maximum dynamic base shear
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Calculating the Natural Period of the Pile + Hammer
First step is to calculate the entrapped water in the pile by using the added
mass generation command with GT SELOS. An output file xx.AMG is
generated.
$ EXECUTE ADDED MASS GENERATION
$ INERTIA JOINTS ADD INCLUDE MEMBER FLOOD MASS $ AXIAL MASS EXCLUDED
Second step is to calculate the eigen values. An output file (STDBX13)
containing all the modal information is created.
$$***REFERENCE INPUT FILE***
CINPUT ‘xx.AMG'
$$**************************
EIGEN PARAMETERS
SOLVE USING GTLANCZOS
NUMBER OF MODES 25
DYNAMIC ANALYSIS EIGEN
LIST DYNAMIC EIGENVALUES
LIST DYNAMIC PARTICIPATION FACTORS
WRITE REPLACE DYNAMIC DATA FOR SELOS
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25th Annual GT STRUDL Users Group Meeting
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Output File from Wave Loading
Typical GT SELOS Input
‘Static’ Base Shear for a
given wave period and a
unit wave amplitude
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25th Annual GT STRUDL Users Group Meeting
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Output File from Wave Motion Time History Analysis
GT SELOS uses of a
modified Morison’s
equation to account for
hydrodynamic damping in
addition to the structural
damping
Dynamic Base Shear for
a given wave period and
increasing wave heights
Typical GT SELOS Input
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June 2013
Calculating the DAF using GT SELOS Output
A spreadsheet including macro is used to extract the static base shear
and dynamic base shear from the output files and to calculate the DAF.
DAF = Dynamic Base Shear / Static Base Shear
Dynamic base shear is linear with the wave amplitude except for wave
periods close to the pile natural periods.
Dynamic base shear is interpolated using a polynomial equation
(typically 2nd or 3rd order) when necessary.
The DAF can then be plotted as a function of the wave period (for any
sea state).
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Non Linearity of the DAF at the natural period
Because the DAF is a function of the wave amplitude, the DAF will vary
with the sea spectral density.
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25th Annual GT STRUDL Users Group Meeting
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Wave Induced Bending Moment (including P-Delta Analysis)
The wave loadings (from GT SELOS) for a unit wave amplitude over a
range of periods are used to perform a large deflection (P-Delta)
analysis of the pile and hammer with GT STRUDL.
Typical GT STRUDL Input
Waves
Still Water
Wave Induced
Mean Deflection Deflection
Mean Deflection
Hammer
Hammer
Current
Current
Pile
Mean Axial Force
Mean Bending Moment
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Pile
Mean + Wave Induced
Axial Force
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Mean + Wave Induced
Bending Moment
Wave Induced Bending Moment (including P-Delta Analysis)
The output from the P-Delta analysis (bending moment in the critical
section(s) of the pile) is stored in a text file (using the COUTPUT
COMMAND) and extracted with a spreadsheet including a macro.
Bending Moment values for
waves of unit amplitude and
varying period
The wave induced bending moment is then plotted against the wave period
(for a unit wave amplitude).
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25th Annual GT STRUDL Users Group Meeting
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Linearity of the Wave Induced Bending Moment
The frequency domain analysis approach is only possible because the wave
induced bending moment is linear with the wave height despite the fact
that a non-linear (P-Delta) analysis is performed to calculate the wave
induced bending moment.
The bending moment in the pile is a linear function of the wave height
(because the wave only generates lateral loads on the pile) and a nonlinear function of the hammer weight (which is not a variable for the
analysis). This has been checked by performing a sensitivity analysis with
GT STRUDL varying the hammer weight and wave height for a number of
P-Delta analysis.
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25th Annual GT STRUDL Users Group Meeting
June 2013
Response Amplitude Operator (RAO) of the Bending Moment
The RAO of the bending moment is the product (squared) of the DAF
Curve and the Wave Induced Bending Moment Curve.
GT STRUDL
GT SELOS
GT STRUDL
GT SELOS
Because the RAO is built using the DAF curve, one should keep in mind
that the RAO is also a function of the sea state considered.
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Calculating the 3Hrs Maximum Bending Moment
Sea Spectral Density
(function of Hs and Tz)
Bending Moment
Spectral Density
A = Area under the Curve

 10800
3hr Maximum Bending Moment = 2 *  0.5 ln

 Tz

Total Bending Moment (used for code check)
= Mean Bending Moment + 3hr Maximum Bending Moment
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 
 * A

Buckling Analysis
Applicable K-Factor for a straight cantilever is 2. For pile installation,
most codes recommend to use a value varying from 2.1 to 2.4.
This is correct when self weight of the column is negligible compared to
the applied compressive load. However the pile can be as heavy as the
hammer during the initial stages of driving (leading to a K-factor < 2)
The applicable K-factor can be assessed by performing a linear buckling
analysis with GT STRUDL.
Typical GT STRUDL Input
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Buckling Analysis Vs P-Delta Analysis
The load multiplier obtained from the linear buckling analysis was
checked by calibrating the buckling analysis against text book cases and
by performing an additional P-Delta Analysis.
P-Delta analysis is carried out for increased loads and the deflection at
the tip of the pile is plotted against the applied load. When the critical
load is reached the P-Delta analysis can not converge anymore.
The buckling and P-Delta analyses give the same k-factor
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Final Step : Code Check of the Pile
The code check of the pile is performed using a spreadsheet including a
macro which iterate the code check for all the sea states (combination of
significant wave height (Hs) and period (Tz)) to be considered (typically
about 60 combinations).
The spreadsheet also derives the hammer energy setting not to be
exceeded to ensure pile integrity.
This analysis has to be repeated for each pile penetration deemed critical
and for the different hammers that could be used for the operations.
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Example
Key Parameters
Key GT STRUDL / SELOS Outputs
Demonstration of spreadsheets
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25th Annual GT STRUDL Users Group Meeting
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Further Points and Possible Improvements
In addition to the internal forces and moments, a number of variables
can be calculated using the same approach: pile tip deflection and
acceleration, lateral reaction on the pile sleeve.
The spreadsheet allows to use a number of sea spectral density
formulations, including multi-directional spectrums.
The analysis could be fully automated by writing a macro generating the
input files for GT STRUDL and GT SELOS and making use of the batch
run option offered by GT STRUDL.
The frequency domain analysis approach relies entirely on the linearity of
the system and therefore this has some limitations. Problems with nonlinear boundary conditions can not be analysed using a frequency
domain analysis (gap of the pile sleeve, or pin piles being driven directly
into the soil without a pile sleeve).
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Questions
Any Questions?
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25th Annual GT STRUDL Users Group Meeting
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