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Chapter 7: Approximation of the maximum dynamic...
added within each of the three groups defined for Approximation 2, this time depending
on the value of the riser displacement ((cid:652) ) to form Approximation 3. Cases were
2
separated into two groups at the middle of the appropriate intervals of variation of (cid:652)
2
(i.e. lower and upper half of (cid:652) depending on the range of (cid:507)z) leading to six ANNs. An
2
additional division at one-eighth of the appropriate ranges of (cid:652) was made in
2
Approximation 4, which is formed by nine ANNs and has a similar structure as the final
approximation defined for the static cases (‘9-ANNs static approximation’ in Quéau et
al. (2014b)). Approximations 3 and 4 showed that, regardless of the value of (cid:507)z, the
accuracy of the fit improved with the increase of (cid:652) , but yet the accuracy for the low
2
values of (cid:652) was insufficient. Further subdivisions on (cid:652) values where attempted but did
2 2
not lead to better results.
To explore the performance of other subdivisions, another strategy was used for
Approximations 5 and 6, which have the same structure as Approximations 3 and 4
respectively but with subdivisions based on the value of the imposed displacement
velocity ((cid:652) ) due to its fundamental role for the dynamic cases. This approach did not
4
offer better performance and led to over fitting some areas of the design space. Over
fitting happens when an ANN can accurately predict the results for the training set but
cannot interpolate correctly; it is not able to generalise from the trends given by the
training set and thus offers poor performance for the testing set. This could arise from
the use of too many neurons in the hidden layer or from poor quality of the data used for
training.
Both of the more advanced approximations using nine ANNs therefore needed further
refinements. It was chosen to try to refine Approximation 4 in order to get a similar
architecture as for the approximation developed for the static cases (Quéau et al.,
2014b).
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7.4.2(cid:3)Refinement of ANNs inherent to Approximation 4(cid:3)
In view of the performance of Approximation 4 in Table 7-5, the subspaces at the
lowest end of the riser displacement ((cid:652) ) intervals for each range of (cid:507)z were the prime
2
target for refinement as they presented the poorest performances. MATLAB (2012) was
used for refinement as it offers more freedom than modeFRONTIER in the choice of
ANN type and architecture. For instance, using MATLAB it is possible to test the effect
of an addition of one or several hidden layers to the ANN architecture, a feature not
available in modeFRONTIER. The number of neurons was varied following a trial-and-
error approach to find an optimum solution. The number of hidden layers was also
varied but it was shown not to improve the performance of the approximations.
The best results were achieved by using only one hidden layer (as used by default
originally), 50 neurons for the ANNs used for the lowest intervals of (cid:652) for the low and
2
medium range of (cid:507)z and 20 neurons for the lowest intervals of (cid:652) for the high range of
2
(cid:507)z. However, it was necessary to exclude the very low (cid:652) values (representing very
2
small motion amplitudes as a proportion of the water depth) from the range of
application of the ANNs where high discrepancies between OrcaFlex and the
approximation were found in the training and in the testing set. This was the case for
(cid:652) ≤ 6.88E-4 for the low range of (cid:507)z, (cid:652) ≤ 1.89E-4 for the medium range of (cid:507)z and for
2 2
(cid:652) ≤ 1.27E-4 for the high range of (cid:507)z. (These values correspond to the lowest 1/32nd of
2
the overall selected range of variation for (cid:652) for the low range of (cid:507)z and the lowest
2
1/64th of the overall selected range of variation for (cid:652) for the medium and high ranges of
2
(cid:507)z.) These values were however used for training the ANNs as excluding them from the
training set decreased the performances on the rest of the selected ranges of (cid:652) .
2
The refined Approximation 4 has the architecture presented in Figure 7-4 and introduces
the notations for the ANNs. ANN1 corresponds to the ANN having 50 neurons in its
hidden layer and developed for the region of the design space indicated as ‘Low (cid:507)z,
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7.4.3(cid:3)Performance of Approximation 4(cid:3)
The individual performances of each of the inherent ANNs are illustrated in Table 7-6,
using notations introduced in Figure 7-4 while the performance of the overall
approximation is presented in Table 7-7. The root mean squared errors (RMSE) and
mean absolute errors (MAE) are evaluated too as a further indication of the performance
of the ANNs. For the testing set, the RMSE and MAE are low and there are ~ 96 % and
~ 80 % of the cases within (cid:114) 15 % and (cid:114) 5 % relative difference with OrcaFlex results
respectively. The defined ANNs forming Approximation 4 therefore provide a good
basis for a first approximation as part of this pilot study since, despite some marginal
high values of relative differences within some ANNs, a large proportion of the cases of
the database are within a negligible range of error.
7.5(cid:3) REFINEMENT OF THE APPROXIMATION FOR PART OF THE
DESIGN SPACE BY EXPANDING THE DATABASE
The focus is now brought to part of the design space where some of the marginally high
relative differences between estimated and OrcaFlex stress range results were observed.
Additional cases were added to the initial database in this part of the design space to
explore the effect of refining the database on improvement of the ANN approximation,
prior to testing its accuracy on fatigue predictions. The refinement is applied only on the
part of the design space initially targeted by ANN4 (i.e. without the limit on (cid:652) ), which
2
corresponds to 950 m ≤ (cid:507)z< 1,500 m, 9° ≤ (cid:537) ≤ 17° and 6.67E-5 ≤ (cid:652) ≤ 1.05E-3. This
HO 2
is an arbitrary choice based on (a) the fact that (cid:507)z was set to 982 m in the SCR base case
used by the authors (Quéau et al., 2011, 2013), corresponding to the medium range of
selected (cid:507)z and (b) that, within this range of (cid:507)z, the area corresponding to
6.67E-5 ≤ (cid:652) ≤ 1.05E-3 presented the least accurate results. The initial database
2
comprised 2,338 cases in this part of the design space.
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Training set Testing set
1- Correlation, 1-r 1.12E-03 4.26E-03
Maximum 124.83% 143.19%
Relative difference with Minimum -47.72% -57.38%
OrcaFlex results: RMSE 0.20% 0.40%
MAE 2.14% 3.32%
±5% 90.54% 80.40%
Proportion of cases with
±10% 97.02% 93.00%
errors within:
±15% 98.60% 96.67%
Table 7-7. Performance of the final approximation of Max Δσ /E on the overall
TDZ
design space (accounting for the introduced limits on the value of π ).
2
7.5.1(cid:3)Detailed analysis of the initial database on the selected part of the
design space(cid:3)
Two strategies were implemented to select the additional cases and extend the database.
On the one hand the training set size was increased to capture the relationships better
between the input dimensionless groups and the output; on the other hand, more cases
were added to the testing set to match the statistics of the training set defined in this part
of the design space, and improve the assessment of the interpolation ability of the
trained ANN. (The statistically consistent approach was used for the overall training and
testing sets and therefore does not necessarily guarantee similar statistical consistency
for the training and testing sets formed by the subsequent divisions of the design space,
depending on the value of the riser displacement ((cid:652) ) and water depth ((cid:652) ).)
2 15
Plots shown in Figure 7-5 were used to assist the selection of the additional cases. The
blue parts of Figure 7-5 represent the cases of the current database in this reduced part
of the overall design space whereas the red parts illustrate the additional cases, as
discussed in Section 7.5.2. Plots are similar to those in Figure 7-3, with the diagrams in
Figure 7-5a representing values of either the output or a particular input dimensionless
group for each case, and in Figure 7-5b the output value for each value of the various
input dimensionless groups, or pairs of values of different input dimensionless groups,
within the reduced part of the overall design space.
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Figure 7-5a shows that the ranges of the input dimensionless groups are not always
covered homogenously, for instance more cases simulating values within the higher end
of the ranges for the riser submerged weight ((cid:652) ) and the riser tension ((cid:652) ) could be
7 9
added for a better accuracy since isolated high values of (cid:652) and (cid:652) were detected. It is
7 9
(trivially) an easier task to map the input design space appropriately than the output
space and Figure 7-5b gives a further indication on the location of the ‘gaps’ within the
part of the design space under study. For instance, the soil stiffness ((cid:652) ) is completely
11
independent from any of the other input dimensionless group, which means that, ideally,
the scatters should cover a rectangular shaped area in each of the subplots representing
the choice of soil stiffness in conjunction with another input dimensionless group.
Additional cases in the highest end of the ranges of the riser submerged weight ((cid:652) ) and
7
the riser tension ((cid:652) ) for the entire range of soil stiffness ((cid:652) ), or in the highest end of
9 11
the ranges of the riser velocity ((cid:652) ) and the riser outside diameter ((cid:652) ) for the entire
4 5
range of soil stiffness, could hence be defined to enhance performance. Similarly, the
riser velocity is independent from all the other input dimensionless groups with the
exception of the riser displacement ((cid:652) ) and therefore the subspaces formed by the level
2
of the riser velocity and any other dimensionless groups (other than (cid:652) ) should have a
2
rectangular shaped area too to improve the quality of the database; and so on by
considering the other pairs of dimensionless groups. These observations provide a first
basis for the selection of additional cases.
The quality of the training and testing set in this part of the design space was then
investigated to refine further the database and the performance of the subsequent
approximation. A detailed analysis of the cases from the training and testing databases
for the selected part of the design space is performed in Table 7-8. The table shows that
1,727 cases were selected for training and 611 for testing. The statistics of the training
and testing sets are compared, revealing target areas for improvements. For example,
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7.5.2(cid:3)Improved database characteristics(cid:3)
The original database of 2,338 cases in the selected part of the design space was
extended to 8,377 cases, with 5,797 for training and 2,580 for testing. The additional
cases were established based on the observed gaps in the design space with Figure 7-5
showing the scatter plot of the values of the input dimensionless groups and output for
the extended database. In Figure 7-5b, the cases of the initial database (in blue) are
represented on top of the cases of the extended database (in red) to highlight the gaps
that the new cases are now filling.
The allocation of cases to the training or the testing set was performed following a trial-
and-error approach aiming to obtain similar statistics between both improved sets, as
per the approach applied for the overall design space. Table 7-9 summarises the results
obtained with the larger database in the selected part of the design space. The improved
training and testing set now have similar statistics, especially for the input design space,
and have the potential to improve further the quality of the proposed approximation.
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7.5.3(cid:3)New approximation on this part of the design space(cid:3)
A new ANN, referred to as ANN4*, was trained and tested using the improved training
and testing sets. As for ANN4, it was trained in MATLAB and comprised one hidden
layer with 50 neurons. The limit on the value of the riser displacement ((cid:652) ) was re-
2
introduced at this stage to be consistent with ANN4 allowing their performances to be
compared appropriately. Only cases with values of (cid:652) higher than 1.89E-4 (and less than
2
1.05E-3) are therefore considered here. The performance of ANN4* is assessed using
the results shown in Table 7-10, where the new testing set was also used with ANN4 to
enhance comparison between ANN4 and ANN4*.
The quality of the results shown in Table 7-10 for ANN4 has decreased compared with
the results presented in Table 7-6, and Table 7-10 shows that some high differences
with OrcaFlex results on the value of Max (cid:507)(cid:305) /E were not captured when using the
TDZ
initial testing set. This emphasises the significance of the choice of cases for the testing
set.
ANN4* is indeed found to be a better approximation than ANN4, offering better
correlation, reduced interval of relative difference and higher number of cases within
low range of relative differences with OrcaFlex results, confirming that the steps
undertaken in Sections 7.5.1 and 7.5.2 have contributed to refining the quality of the
approximation in this part of the design space.
The current best approximation, namely “9-ANNs dynamic approximation”, has
therefore the structure presented in Figure 7-4 with ANN4* in place of ANN42. Even
though the accuracy of the 9-ANNs dynamic approximation does not reach the original
criterion of errors within (cid:114) 5% of errors for the entire design space, the benefits of the
approach for practical purposes (i.e. fatigue life predictions) is investigated next.
2 The 9-ANNs dynamic approximation can be provided as a standalone application by contacting the
corresponding author.
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ANN4* ANN4
Refined
Refined training set Refined testing set
testing set
1- Correlation, 1-r 1.96E-03 5.85E-03 8.54E-02
Maximum 207.86% 129.31% 314.42%
Relative
difference with Minimum -45.02% -61.48% -86.15%
OrcaFlex RMSE 0.68% 0.94% 7.07%
results:
MAE 3.96% 5.10% 15.51%
Proportion of ±5% 77.75% 71.84% 34.01%
cases with ±10% 92.40% 88.04% 56.18%
errors within: ±15% 95.99% 93.41% 68.48%
Table 7-10. Performance of ANN4* (with the same limit on the value of π than for
2
ANN4).
7.6(cid:3) APPLICATION OF THE FRAMEWORK IN FATIGUE DESIGN
CASE STUDIES
The current best approximation (9-ANNs dynamic approximation) is now applied on a
series of case studies to assess its accuracy for prediction of fatigue life using a
deterministic approach (as appropriate for structural systems presenting nonlinearities
(Patel and Seyed, 2005)). In light of the refinements performed in Section 7.5, this
section focuses on the part of the design space corresponding to the selected medium
range of water depth (i.e. 950 m ≤ (cid:507)z< 1,500 m).
7.6.1(cid:3)SCR configurations and loading conditions(cid:3)
The first case study, namely Base Case 1 (BC1), is performed with the usual SCR base
case used by the authors (as per BC1 in Quéau et al. (2013)). Its input parameters and
corresponding dimensionless groups are shown in Table 7-11. The base case is derived
from an in-service SCR connected to a semisubmersible in the Gulf of Mexico (GoM).
Four additional base cases, namely BC2, BC3, BC4 and BC5, were defined in order to
test the accuracy of the 9-ANNs dynamic approximation for different riser setups (i.e.
input data from different areas of the design space). The input parameters and
corresponding dimensionless groups of these base cases are also presented in Table
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7.6.2(cid:3)Fatigue life evaluation(cid:3)
The dynamic time history analyses were carried out using OrcaFlex to assess the value
of Max (cid:507)(cid:305) for each of the LCs. The results are compared with the estimations from
TDZ
the 9-ANNs dynamic approximation in Table 7-14. Some of the first LCs correspond to
small displacement amplitudes ((cid:652) ) which are outside the selected ranges and therefore
2
ANN4* was used in extrapolation for these LCs as indicated in Table 7-14. For the LCs
within the selected range of application of the 9-ANNs dynamic approximation, the
differences in stress range are small overall, ranging mainly from 0 % to 10 % relative
difference with marginal higher differences of up to 45% (e.g. LC4 in BC3).
Extrapolated stress range results vary in accuracy from 0% (for LC1 of BC3) relative
difference with OrcaFlex results up to 214% (for LC1 of BC4).
Based on the number of wave occurrences presented in Table 7-12, the fatigue damage
created by each of the LCs was calculated by using the D-type S-N curve for seawater
below (DNV-RP-C203, 2011)
Log (N) = 11.764 – 3 * log (Max (cid:543)(cid:592) ) for N ≤ 106 cycles
10 10 TDZ
(7-2)
Log (N) = 15.606 – 5 * log (Max (cid:543)(cid:592) ) for N > 106 cycles(cid:3)
10 10 TDZ
Due to the nonlinear relationship between the stress range and the damage introduced
by the number of occurrences of the wave and number of allowable cycles, for some
cases small relative differences on Max (cid:507)(cid:305) can lead to high differences on damage
TDZ
for an individual load case. This is observed, for instance, for LC6 in BC1 or LC5 in
BC4 where only -5% and 9% relative differences in Max (cid:507)(cid:305) respectively lead to
TDZ
-21% and 52 % relative differences in the damage. As the fatigue life is the inverse of
the sum of the individual damage contribution for each LC, small errors in the estimated
Max (cid:507)(cid:305) for a load case that has a high contribution to the global damage can have a
TDZ
high impact on the estimated fatigue life (e.g. for LC5 in BC4) and vice versa for a load
case that does not contribute much to the global damage (e.g. for LC1 in BC4).
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However, the positive and negative errors in damage contribution from each load case
tend to balance out so that the total damage estimated shows much smaller error than
the individual components. In addition, the relative accuracy for the load cases that
dominate fatigue damage (typically LC5 to LC10) is generally much better than for the
small amplitude load cases.
The fatigue lives of the five BCs are calculated and results are summarised in Table
7-15. The estimated fatigue lives using 9-ANNs dynamic approximation are all
reasonably close to those calculated using conventional time history analysis using
OrcaFlex directly, thus demonstrating the benefits and usefulness of the ANN method.
All BCs have an estimated fatigue life within 16 % relative differences with the results
derived from OrcaFlex calculations, with most BCs within 10 % relative difference.
Based on the damage calculated from OrcaFlex stress range results, LC8 and LC5
correspond to the waves having the highest contributions to the global damage for all
BCs. The damage for LC5 was not as well estimated in BC4 than in the other base cases
(with a notable overestimation), which is why the fatigue life of BC4 approximated by
the ANN approach is less than the fatigue life calculated based on OrcaFlex results by a
larger amount than for the other base cases.
Using the 9-ANNs dynamic approximation, it takes less than 1 minute of calculation to
obtain the results presented in Table 7-15 (since the time taken to develop the
approximation by training the ANNs does not impact the final application time).
Although it is hard to estimate accurately the time necessary to obtain equivalent results
from OrcaFlex, since it will vary between users and on the available computer
resources, it could take about a day to pre-process the numerical models, simulate them
and post-process the results. The ANN approach therefore provides excellent efficiency
for estimation of fatigue life for different SCR configurations.
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ANNs. The size of the database was limited by the time taken to run each of the cases in
OrcaFlex. Design of experiment methods were applied when generating the database to
capture the complex relationships between the eight selected input dimensionless groups
and the output (Max (cid:507)(cid:305) ). Different ANN configurations were tested and a
TDZ
framework comprising nine ANNs was selected since it was able to estimate the critical
stress range results for the majority of the cases of the database within (cid:114) 5 % relative
difference with numerical results. A refinement of the quality of the database was
applied for part of the design space to explore the effect of the size of training and
testing sets and the choice of cases within these sets on the performance of the
approximation. The current best ANN approximation (accounting for the refinement of
the database in part of the design space), referred to as ‘9-ANNs dynamic
approximation’, was used to assess the fatigue lives of example SCRs under a selected
small wave scatter diagram inspired from realistic GoM data. The ANN approximation
was found to predict well the fatigue results, with a maximum discrepancy of 16 % on
the predicted fatigue life.
This pilot study has demonstrated that fatigue life calculations for the touchdown zone
of SCRs may potentially be reduced to a matter of minutes using the proposed ANN
framework, without compromising much on the level of accuracy, and without the need
for advanced numerical analyses. Once ‘trained’, the ANN approximation may be used
conveniently by any external user and could represent a major improvement in
efficiency of SCR fatigue estimations, particularly for the early stages of design where
optimisation studies are needed to establish values of input parameters that provide
optimal performance.
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Estimating the fatigue damage of SCRs in the TDZ
CHAPTER 8(cid:3)SENSITIVITY STUDIES OF STEEL CATENARY
RISER FATIGUE DAMAGE IN THE TOUCHDOWN ZONE
USING AN EFFICIENT SIMPLIFIED FRAMEWORK FOR
STRESS RANGE EVALUATION
8.1(cid:3) ABSTRACT
Steel catenary risers (SCRs) are widely used in deep water. Several sources of
nonlinearities make SCR fatigue design challenging. Limited understanding of the
influence of the various input parameters on the structural response of SCRs leads to
unnecessarily high conservatism in design. Also, time consuming numerical simulations
are usually performed to assess SCR fatigue damage which is inefficient, especially for
early design stages.
A simplified framework for fatigue analysis of SCRs in the touchdown zone (TDZ) has
been developed previously, using artificial neural networks. The approach may be used
to efficiently estimate maximum static and dynamic stress ranges in the TDZ, from
which the fatigue damage can be deduced. Comparison of the maximum static and
dynamic stress changes for a given input motion allows quantification of the dynamic
amplification factor (DAF). This paper explores the sensitivity of the maximum
dynamic stress ranges and DAF to the key dimensionless groups of input parameters
and also certain individual input parameters. The study illustrates the usefulness of the
proposed framework in understanding SCR behaviour in the TDZ, providing guidance
on optimisation of SCR design from a fatigue perspective. The paper also reflects on the
potential benefits of using DAFs for SCR fatigue design.
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8.2(cid:3) INTRODUCTION
Oil and gas developments in deep water commonly use steel catenary risers (SCRs) to
transfer fluids between seabed and sea surface as they are a cost effective solution.
Under the action of environmental loading a complex interaction is created in the
touchdown zone (TDZ – the dynamic area of riser-soil interaction (Bridge, 2005)) and
fatigue damage is generated. Fatigue design is a major challenge for SCRs as there is a
lack of understanding of the influence of the various input parameters on the fatigue
damage, leading to unnecessary conservatism. Fatigue damage is usually evaluated by
running time consuming numerical simulations. This approach is inefficient, especially
for the early stages of design where optimisation studies are required to find values of
input parameters leading to the best performance. A simple approach able to provide
quantitative guidance on how the input parameters impact the static and dynamic
response of SCRs in the TDZ, thus allowing rapid evaluation of the fatigue damage in
the TDZ, would be better suited for initial design. The development of such an approach
was indeed encouraged in a recent standard for the design of offshore risers (DNV-OS-
F201, 2010).
A program of research (Chapter 2 to Chapter 7) has been undertaken by the authors with
the ultimate aim of proposing a simplified fatigue analysis and design framework for
SCRs in the TDZ. The original intention was to use the dynamic amplification factor
(DAF) approach for dynamic response of SCRs, since it is used widely for
simplification of structural dynamic analyses for linear structural systems (e.g. Barltrop
and Adams, 1991; Bea et al., 1999; Ruiz-Teran and Aparicio, 2006). DAFs quantify the
amplification of stress due to dynamic effects when compared with the static response.
The simplification relies on the ability to evaluate the static response and the DAF
values through simple methods, and hence deduce the dynamic response. However,
SCR behaviour is impacted by geometrical and material nonlinearities in the TDZ and
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Chapter 8: Sensitivity studies of SCR fatigue damage...
well suited to SCR fatigue design in the TDZ, the more substantial steps necessary to
develop the approach were pursued. The major challenge was to predict DAF values
and their sensitivity to key input parameters.
As a pre-requisite to the sensitivity studies, dimensional analysis was carried out for
SCR systems under harmonic motions to identify the dimensionless groups of input
parameters influencing the stress range, and consequently the DAF (Quéau et al., 2013).
A summary of the various dimensionless groups is given in Figure 8-2, using the
dimensionless groups notation introduced in Quéau et al. (2013). The validity of the
dimensionless groups was tested through numerical analyses and demonstrating that,
under the simplifying assumptions adopted in the study, the maximum stress ranges
occurring respectively under dynamic motions (accounting for hydrodynamic and
inertia effects as longitudinal and transverse waves travel along the riser) and static
motions (no inertia or damping effects) could be expressed as
Max (cid:507)(cid:305) H H ρ D D p T k
TDZ_dyn steel o o o s
= f( , Δθ , , , , , ν, , μ, , C , C ,
E Δz m T E Δz w E Δz E Δz2 E D A
t
(8-1)
ρ g Δz ρ
steel steel
, ,β)
ρ E
water
Max (cid:507)(cid:305) H D D p T k ρ g Δz ρ
TDZ_sta o o o s steel steel
= f( , Δθ , , , , ν, , μ, , , ,β) (8-2)
E Δz m Δz w E Δz E Δz2 E ρ E
t water
with
(cid:533) Angular position on the SCR circumference
(cid:507)z Vertical difference between hang-off point and seabed
(cid:507)(cid:537)
m
Angle of the motion relative to the hang-off angle ((cid:537) HO)
(cid:541) Soil friction coefficient
(cid:542) Poisson’s ratio
(cid:545)
steel
,(cid:545)
water
Steel and water densities
C D, C
A
Drag and added mass coefficient
D o, w
t
Riser outer diameter and wall thickness
E Young’s modulus
g Gravity acceleration
H,T Heave amplitude and period of the input motion
k
s
Soil stiffness
p Unit submerged weight
T
o
Horizontal tension component
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Throughout the study, numerical analysis of the SCR system has been carried out using
the dynamic analysis software OrcaFlex (Orcina, 2011). Approximate, but accurate,
analytical solutions can evaluate the static response (and maximum static stress range)
of an SCR (Quéau et al., 2014a). However, since it is complex to develop analytical
solutions able to accuractely evaluate the dynamic response of SCRs in time domain,
the approach has been to develop artificial neural networks (ANNs), trained using the
numerical results from OrcaFlex. This approach was validated initially for the static
response (Quéau et al., 2014b) before embarking on the dynamic response.
Extensive sensitivity studies were performed to capture SCR behaviour in the TDZ for
many thousands of different configurations, loading conditions, riser properties etc...
(Quéau et al., 2014b, 2015b). The sensitivity studies were originally intended to
increase the understanding of SCR behaviour and predict the DAF value using an
advanced mathematical tool, the artificial neural network (ANN). Since the same
amount of computational effort was required for approximating the relationships
between either Max (cid:507)(cid:305) or DAF, it was decided to use the ANN tool to capture the
TDZ_dyn
relationships between the input dimensionless groups and Max (cid:507)(cid:305) directly.
TDZ_dyn
Indeed, this is essentially more convenient for the final user in future applications (the
maximum dynamic stress range being directly linked to the fatigue damage). The
development of such a framework was performed in Chapter 5 to Chapter 7.
The main aim of this paper is to link together all of the previous steps of the study,
focusing on two distinct aspects:
(i)(cid:3) After presenting the ANN framework (Section 8.3), it is used to efficiently
explore the sensitivity of the maximum stress range in the TDZ to variations
of some of the input dimensionless groups and individual parameters
(Section 8.4); the results are then used to optimise an example SCR system
in respect of the fatigue life (Section 8.5).
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ranges are presented in Table 8-1 and Table 8-2. A series of criteria, referred to as
“design criteria” as presented in Table 8-1, were implemented between some of the
input parameters and dimensionless groups to select realistic combinations of
dimensionless groups when defining SCR configurations and loading conditions. For
instance, small hang-off angles were considered for deep water and larger for shallower
water to match with industry practices. The riser displacement characteristics were
derived from in-service conditions of a typical semisubmersible vessel under calm to
harsh seastates in the Gulf of Mexico (GoM).
For the dynamic motion, small parts of the design space had to be excluded since it was
not possible at this stage to define an approximation of the relationships between the
input dimensionless groups and the maximum normalised stress range in the TDZ with
a sufficient level of accuracy in these areas, as discussed later. These areas are
summarised in Table 8-3. Further details on the choice of ranges can be found in
Chapters 4 to 7.
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Area excluded from the design space for
Range of Δz dynamic loading
(restricting the range of π ) (for any appropriate values of π , π , π ,
15 4 5 6
π , π , π )
7 9 11
400 m ≤ (cid:507)z≤ 950 m (cid:652) ≤ 6.88E-4
2
950 m < (cid:507)z ≤ 1500 m (cid:652) ≤ 1.89E-4
2
1500 m < (cid:507)z ≤ 2000 m (cid:652) ≤ 1.27E-4
2
Table 8-3. Parts removed of the design space for dynamic loading.
8.3.2(cid:3)Framework characteristics(cid:3)
A global ANN approximation for the entire design space was developed for the static
loading cases initially, in order to ensure the usefulness of the proposed methods, and
the more complex dynamic loading cases were examined afterwards. Ultimately, two
approximations were established, namely the “9-ANNs static approximation” (Quéau et
al., 2014b) and the “9-ANNs dynamic approximation” (Quéau et al., 2015b). Both
approximations comprise a total of nine single hidden layer Levenberg-Marquardt back-
propagation neural networks, having two activation functions (a bipolar sigmoidal
function for the nodes of the hidden layer and an identity function for the output nodes)
and different number of neurons in the hidden layer (ranging from 20 for some of these
ANNs to 100 for others). Each of these ANNs were trained and tested using large
databases to find the weights and biases matrices leading to a good match between
approximated results and results from OrcaFlex simulations (Quéau et al., 2014b,
2015b).These approximations were developed as standalone MATLAB applications and
have been combined into a single standalone MATLAB application, namely “ANN
framework”, for convenience1. The flowchart for the application is given in Figure 8-2.
All the matrices of weights and biases inherent to the various ANNs are built-in the
standalone application for straightforward use. The application uses an Excel™
1 The application may be obtained through the corresponding author.
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interface so that a user can simply copy and paste a dataset (i.e. series of dimensionless
groups’ combinations defining SCR configurations and loading conditions, as per the
“Varied dimensionless groups” in Figure 8-2) and automatically obtain the maximum
stress range corresponding to the static and dynamic loading of the specified SCRs and
loading conditions (as per the “Approximated outputs” in Figure 8-2). The standalone
application performs matrix multiplications based on the input values and the built-in
matrices of weights and biases to calculate the maximum stress range results (Quéau et
al., 2014b, 2015b), and therefore the time taken to develop the approximations does not
impact the time necessary to assess the outputs with the ANN framework application.
The fatigue damage can then be evaluated directly from the dynamic results. The ANN
framework application also reports DAF values, evaluated using the static and dynamic
results obtained with the 9-ANNs static and dynamic approximations.
8.3.1(cid:3)Performance of the ANN framework
The ANN framework application is very efficient, taking about 1 minute to estimate the
outputs (Max (cid:507)(cid:305) , Max (cid:507)(cid:305) and DAF) for ~ 50,000 cases (different SCR
TDZ_sta TDZ_dyn
configurations with given static or dynamic loading conditions) and without the need for
any specialised software. It is difficult to quantify accurately the time saving impact of
the ANN framework since the time necessary to obtain stress range results from marine
analysis software (such as OrcaFlex, as used here) will vary from user to user,
depending on the experience of the user, the performance of the computer used to run
the simulations and on the efficiency of pre- and post-processing the numerical models.
The last aspect may be streamlined by the use of automation sub-routines (as shown in
Chapters 5 to 7). However, four months of calculation were necessary here to obtain the
results for the entire database using OrcaFlex running on a high performance computer.
The proposed simplified framework represents therefore a tremendous time saving in
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fatigue design studies, with only limited loss in accuracy.
The two approximations provide a good level of accuracy as summarised in Table 8-4.
Excellent accuracy was consistently reached with the 9-ANNs static approximation.
With the 9-ANNs dynamic approximation, a reasonably good level of accuracy was
obtained, although future work (outside the scope of this paper) was recommended to
improve the accuracy further in order to increase the robustness of the predictions
(Quéau et al., 2015b). There is also a restriction on minor parts of the design space for
the 9-ANNs dynamic approximation where the results might not be as accurate as for
the rest of the design space and therefore it is not recommended to apply the
approximation in these areas. This is the case for regions corresponding to low values of
imposed displacement relative to the water depth ((cid:652) ), as shown in Table 8-3; these
2
regions represent waves that are unlikely to contribute significantly to the fatigue
damage (Quéau et al., 2015b). The performances indicated in Table 8-4 are valid when
excluding the low (cid:652) values, as presented in Table 8-3, from the design space.
2
Application of the 9-ANNs dynamic approximation to a series of SCR configurations
was shown to predict the fatigue life within (cid:114) 15% of the numerical results (Quéau et
al., 2015b).
9-ANNs static 9-ANNs dynamic
approximation approximation
Database size > 50,000 > 40,000
Proportion of ±5% > 99% > 86 %
cases with
±15% 100% > 97 %
errors within:
Reference Quéau et al. (2014b) Quéau et al. (2015b)
Table 8-4. Performance of the approximations from the ANN framework.
In the rest of the paper, this simplified framework is used for convenience on a smaller
part of the design space where the 9-ANNs dynamic approximation underwent more
substantial validations (Quéau et al., 2015b). This corresponds to water depths of
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950 m < Δz ≤ 1500 m (and therefore 3.45E-4 < (cid:652) ≤ 5.45E-4), riser displacement
15
(cid:652) > 1.89E-4 (due to the comment on lower accuracy and fatigue relevance for low riser
2
displacement) and corresponding ranges for (cid:652) , (cid:652) , (cid:652) , (cid:652) , (cid:652) , (cid:652) .
4 5 6 7 9 11
8.4(cid:3) SENSITIVITY STUDIES USING THE ANN FRAMEWORK
The simplified framework is now used to shed light on the sensitivity of the maximum
stress range in SCRs in the TDZ and of the DAF to the variation of some of the key
input dimensionless groups of parameters. The resulting sensitivities are benchmarked
against results from published literature. There are many ways to vary the key input
dimensionless groups and individual parameters and this paper illustrates the usefulness
of the ANN framework by considering a selection of examples of individual and
simultaneous variations of the key input dimensionless groups and individual input
parameters. The first two examples, testing the effect of the displacement characteristics
and the soil stiffness on the maximum stress range in the TDZ, aim to demonstrate that
the ANN framework can reproduce expected and known trends to validate further its
accuracy. Building on from these two examples, two further examples derived from
published studies performed using the traditional approach (i.e. numerical simulations)
are presented to illustrate the usefulness of the ANN framework in validating published
trends for new ranges of the inputs.
Throughout this section and wherever possible based on (i) the tested variations, (ii) the
selected values for the input parameters and dimensionless groups, and (iii) the design
criteria among them, the unvaried dimensionless groups and individual parameters are
fixed to their appropriate mean value, except for (cid:652) the value of which is determined
7
based on the water depth and the riser unit submerged weight for an empty riser (for
convenience). The term ‘appropriate’ implies that the design criteria between individual
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input parameters and dimensionless groups, as shown in Table 8-2, are respected and
refers to the mean values accounting for the selected range of water depth:
950 m < (cid:507)z ≤ 1500 m (or 3.45E-4 < (cid:652) ≤ 5.45E-4). Moreover, the reported values of the
15
horizontal component of the tension (T ) is assessed by using one of the common
o
catenary equations: T = p (cid:507)z sin ((cid:537) )/(1-sin((cid:537) )).
o HO HO
8.4.1(cid:3)Effect of the imposed displacement amplitude (π ) and velocity (π )(cid:3)
2 4
The effect of the imposed riser displacement amplitude ((cid:652) ) and velocity ((cid:652) ) on SCR
2 4
behaviour in the TDZ is investigated first. For this purpose, H and T were varied within
the four selected ranges of H and corresponding T values. Table 8-5 summarises the
selected values of the individual input parameters and dimensionless groups that were
used for this example. A series of design charts showing the sensitivity of
Max (cid:507)(cid:305) /E and DAF to variations of (cid:652) and (cid:652) were established, as illustrated in
TDZ_dyn 2 4
Figure 8-3 and Figure 8-4 respectively. The range of (cid:652) was normalised in the subplots
4
for convenience, using the extreme (max) and minimum (min) values shown in Table
8-5 (so that Normalised (cid:652) = (2* (cid:652) – max – min) / (max – min)). Results are discussed
4 4
next, for the maximum stress range in the TDZ first and then for the DAF.
8.4.1.1(cid:3) Maximum stress range in the TDZ
Increasing the velocity ((cid:652) ) by keeping the displacement amplitude constant ((cid:652) ),
4 2
thereby reducing the period of the imposed displacement (T), leads to an increase of
Max (cid:507)(cid:305) /E. Also, the higher the displacement amplitude, the higher the maximum
TDZ_dyn
stress range in the TDZ (i.e. increase of fatigue damage) since it generates higher
variations of the curvature in the TDZ. These trends are observed for the four ranges of
H and corresponding T values selected and show that no resonance effects were
detected for the SCR configuration under study.
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8.4.1.2(cid:3) DAF
The values of maximum stress range found under static loading (Max (cid:507)(cid:305) /E) using
TDZ_sta
the simplified framework are shown in Table 8-6. They were used to calculate the DAF
values from Max (cid:507)(cid:305) /E results presented in Figure 8-3. Figure 8-4 indicates that
TDZ_dyn
the DAF increases with increasing velocity of the imposed displacement. Also, it tends
to confirm an interesting trend of the DAF sensitivity that was already noted at the pilot
study stage of this research (Quéau et al., 2011). For low displacement amplitudes, DAF
varies inversely with the displacement amplitude, whereas it increases with increasing
displacement amplitude for higher heave amplitude values; Figure 8-4b captures the
transition between these opposing trends.
Interestingly, DAF values do not decrease down to unity in any of the plots presented in
Figure 8-4, indicating that the SCR under study did not reach its static response for the
selected displacements and wave periods. To some extent, this is consistent with the
results obtained during the pilot study (Quéau et al., 2011). Even though the selected
values for the input parameters and dimensionless groups are not all identical in this
paper to those selected for the pilot study, DAF values of unity were only reached in the
pilot study when considering imposed displacements with a period (T) greater than 20 s.
That limit is beyond the highest limit selected for T here and also when defining the
ANN framework (see Table 8-1 and Chapters 5 to 7).
The similarity of the observed trends when using the ANN framework to those of the
pilot study, when DAF sensitivity was investigated using results from numerical
simulations, further validates the framework.
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8.4.2(cid:3)Effect of the soil stiffness (π ) for various imposed displacement
11
characteristics
This example focuses on the effect of the soil stiffness ((cid:652) ) on SCR behaviour in the
11
TDZ for various characteristics of the imposed displacement. The values of the
individual input parameters and dimensionless groups used for this purpose are
summarised in Table 8-7 and the design charts are shown in Figure 8-5 and Figure 8-6
for Max (cid:507)(cid:305) /E and DAF respectively.
TDZ_dyn
8.4.2.1(cid:3) Maximum stress range in the TDZ
The overall trend of the results presented in Figure 8-5 is for increasing values of
Max (cid:507)(cid:305) /E with increasing soil stiffness, which is consistent with other published
TDZ_dyn
work (e.g. Bridge et al., 2004; Quéau et al., 2011). The trend results from higher contact
forces and greater curvature variation in the TDZ with increasing soil stiffness. There
are minor fluctuations in Figure 8-5d where higher soil stiffness locally gives lower
values of Max (cid:507)(cid:305) /E for low values of displacement velocity. This may however
TDZ_dyn
indicate local inaccuracy of the ANN framework rather than an indication of a different
trend for the results in that area. As is true for any simplified approach (DNV-OS-F201,
2010), engineering judgement is required when interpreting results from the proposed
framework to differentiate between results indicating a change in SCR behaviour and
those affected by slight inaccuracies of the simplified framework.
8.4.2.2(cid:3) DAF
DAF increases with increasing velocity of the imposed displacement, as observed for all
selected values of soil stiffness and displacement amplitude (see Figure 8-6). Except for
high velocity values (i.e. low period of imposed displacement), DAF is almost
insensitive to the soil stiffness. This confirms the trend observed in Quéau et al. (2011)
with other values of input parameters and dimensionless groups (e.g. different values of
water depth, riser diameter and wall thickness, hang-off angle etc...).
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Figure 8-6 Sensitivity of DAF to the variation of the displacement velocity (π ) for
4
various soil stiffnesses (π ) and displacement amplitudes: (a) π = 0.44E-3;
11 2
(b) π = 1.84E-3; (c) π = 3.67E-3; and (d) π = 5.31E-3
2 2 2
8.4.3(cid:3)Effect of the water depth (π ) for various hang-off angles and
15
imposed displacement characteristics
In this example the effect of increasing water depth ((cid:652) ) for a constant value of hang-
15
off angle is investigated. Various values of hang-off angle and imposed displacement
characteristics are considered. This example was selected to compare the results found
with the simplified framework and for the selected ranges of parameters against the
results reported by Zhan (2010), established using numerical simulations. The selected
values of input parameters and dimensionless groups are presented in Table 8-8 and the
results are shown in Figure 8-7, Figure 8-8 and Figure 8-9. The hang-off angle is
measured from the vertical.
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Figure 8-8 Sensitivity of Max Δσ / E to the variation of the water depth (π )
TDZ_dyn 15
for various hang-off angles (θ ) and displacement characteristics: (a) H = 0.55 m
HO
and T = 12 s; (b) H = 2.25 m and T = 13.5 s; (c) H = 4.50 m and T = 15 s; and
(d) H = 6.50 m and T = 16.5 s
8.4.3.1(cid:3) Maximum stress range in the TDZ
The static results are presented in Figure 8-7 and indicate that increasing water depth
leads to a reduction of Max (cid:507)(cid:305) /E. Also, higher hang-off angle values result in
TDZ_sta
lower values of Max (cid:507)(cid:305) /E due to increased tension in the TDZ ((cid:652) ), thereby
TDZ_sta 9
reducing the curvature variation in the TDZ. The marked change in gradient observed
between the two lowest values of water depth (particularly for low hang-off angles) may
indicate slight inaccuracy of the ANN approximation rather than reflecting true SCR
behaviour. Indeed, estimation of the maximum stress range in the TDZ for the extreme
values of inputs may not be as accurately captured as for intermediate input values,
which is inherent to the response surface method.
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For dynamic results, Figure 8-8 shows that increasing water depth generally results in a
slight reduction of the dynamic stress range (Figure 8-8a, b, c) although an opposite
trend is found in Figure 8-8d for the highest displacement amplitude, H = 6.5 m. Also,
lower hang-off angles lead to higher values of Max (cid:507)(cid:305) /E for all the selected cases
TDZ_dyn
expect for H = 6.5 m where the opposite trend is observed. The trend illustrated in
Figure 8-8d is consistent with the results from Xia et al. (2008) who found that, for a
given water depth, increasing the hang-off angle increased the fatigue damage. Further
work is needed to ensure that the abrupt variations exhibited by the results in Figure 8-8
reflect true physical behaviour of SCRs in the TDZ and are not the result of the ANN
framework. For both static and dynamic conditions, the variation of maximum stress
range in the TDZ with water depth is quite limited, showing a rather weak sensitivity for
a given hang-off angle. These results are consistent with the results from Zhan (2010),
who worked with bending moment (which dominates the contribution to SCR stresses
in the TDZ (Shiri and Hashemi, 2012)) and found that the dynamic bending moment
envelope did not vary much with changing water depth.
8.4.3.2(cid:3) DAF
The DAF results are shown in Figure 8-9. In general, the DAF increases with increasing
water depth and smaller hang-off angles generate less dynamic amplification (Figure
8-9a, c, d); a slight opposite trend is found in Figure 8-9b, although with low sensitivity
of the DAF to the hang-off angle.
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Figure 8-9 Sensitivity of DAF to the variation of the water depth (π ) for various
15
hang-off angles (θ ) and displacement characteristics: (a) H = 0.55 m and T = 12
HO
s; (b) H = 2.25 m and T = 13.5 s; (c) H = 4.50 m and T = 15 s;
and (d) H = 6.50 m and T = 16.5 s
8.4.4(cid:3)Effect of the outside diameter (D ) for various wall thicknesses and
o
imposed displacement characteristics
This example was inspired by a parametric study performed by Xia et al. (2008) where
a SCR base case was established to test the effect of the internal diameter on SCR
behaviour in the TDZ. For this purpose, the same loading was applied to the SCR base
case for fixed values of hang-off angle ((cid:537) ) and wall thickness (w) but various values
HO t
of the internal diameter. For the constant wall thickness this resulted in varying the
outside diameter (D ), the submerged weight (p) and the horizontal tension component
o
(T ) to keep the hang-off angle unchanged. Here, the sensitivity of SCR behaviour to
o
variations of the outside diameter is investigated by considering several values of the
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wall thickness and also for various displacement characteristics (and corresponding
values of p and T ), therefore exploring wider ranges of the input parameters. The
o
values of dimensionless groups and individual input parameters used for this purpose
are shown in Table 8-9. Results are presented in Figure 8-10, Figure 8-11 and Figure
8-12 and are discussed below.
8.4.4.1(cid:3) Maximum stress range in the TDZ
In order to compare the results against the findings from Xia et al. (2008), the effect of
the variation of the outside diameter on the maximum stress range occurring in the TDZ
is illustrated for static and dynamic loading in Figure 8-10 and Figure 8-11 respectively.
In general, increasing the outside diameter for a given wall thickness tends to increase
Max (cid:507)(cid:305) /E, which is consistent with the results from Xia et al. (2008). However, it
TDZ_sta
seems that for low values of the displacement amplitude a slight opposite trend may be
found (Figure 8-10a). Greater wall thickness systematically leads to higher
Max (cid:507)(cid:305) /E in this example since it results in higher value of submerged weight ((cid:652) )
TDZ_sta 7
and therefore an increase of curvature in the TDZ.
Regarding dynamic loading, Max (cid:507)(cid:305) /E also increases with increasing outside
TDZ_dyn
diameter for most of the selected cases, although it decreases for high displacement
amplitude and low wall thickness (Figure 8-11d). In their case study, Xia et al. (2008)
found that the fatigue damage for dynamic loading decreased with increasing outside
diameter for a given wall thickness. Further work is therefore needed to validate the
observed trends and find the values of input parameters that lead to a change of trends.
Another complex behaviour is also noted depending on the value of the displacement
amplitude: for low displacement amplitude, the higher the wall thickness, the greater the
fatigue damage (Figure 8-11a, b), whereas the reverse is true for higher values of
displacement amplitude (Figure 8-11c, d). This illustrates the usefulness of the
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Figure 8-12 Sensitivity of DAF to the variation of outside diameter (D ) for various
o
wall thicknesses (w) and displacement characteristics: (a) H = 0.55 m and T = 12 s;
t
(b) H = 2.25 m and T = 13.5 s; (c) H = 4.50 m and T = 15 s; and (d) H = 6.50 m and
T = 16.5 s
The four examples selected in this section were used to compare the trends observed
when using the proposed simplified framework against published results obtained with
different methods, validating further the usefulness of the framework. It also enabled the
sensitivity of SCR behaviour in the TDZ to be explored for wider ranges of input
parameters and dimensionless groups. The examples have illustrated that conclusions
obtained from a base case or for small ranges of input parameters and dimensionless
groups cannot always be generalised, complicating general quantification of the
influence of particular dimensionless groups on the maximum stress range in the TDZ.
This reinforces the need for a simplified method that can conveniently assist screening
tasks in the early design stages, providing designers with a tool to optimise values of the
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dimensionless groups within their control (e.g. riser properties) for given values of
dimensionless groups that are outside their control (e.g. environmental conditions).
In addition, for the selected examples it was shown that DAF values could vary up to
values exceeding 16. Overall, the DAF patterns found in the design charts were no
simpler than the patterns for the maximum stress range values. This supports the choice
to develop an ANN framework to predict Max (cid:507)(cid:305) /E directly rather than to predict
TDZ_dyn
DAF values (Quéau et al., 2015b).
8.5(cid:3) OPTIMISATION OF THE FATIGUE LIFE USING THE ANN
FRAMEWORK
This section illustrates application of the ANN framework for SCR fatigue design by
performing a simple screening study typical of initial design.
The case study is based on deterministic fatigue design of an in-service SCR in the
GoM, namely ‘Base Case 1’ (BC1), characteristics of which are presented in Table
8-10. A simplified wave scatter table was used and 15 load cases (LCs) characterised by
a sinusoidal vessel motion (displacement of amplitude H and period T) were selected to
represent the loading conditions. These LCs were derived from a selection of 15 waves
from a sample wave scatter table for GoM, with wave heights, periods and number of
occurrences presented in Table 8-11, which represent over 95 % of the waves occurring
over a 20 year period. The values of the corresponding heave amplitudes were assessed
based on RAO (response amplitude operator) tables of the semisubmersible following
the procedure proposed by Kimiaei et al. (2010).It is assumed that a designer wishes to
optimise the outside diameter (D ), outside diameter over wall thickness ratio ((cid:652) ) and
o 6
hang-off angle ((cid:537) ) for the riser presented in BC1 in order to improve the fatigue life.
HO
The location of the SCR is fixed so that the loading conditions (displacement amplitude
and velocity, (cid:652) and (cid:652) respectively), the soil stiffness ((cid:652) ) and the water depth ((cid:652) ) are
2 4 11 15
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The example sensitivity studies in the previous section demonstrated that loading
conditions might lead to different choices of recommended values of (cid:537) , D and w in
HO o t
order to decrease the maximum dynamic stress range in the TDZ. The fatigue life is
based on the cumulative damage from each LC of a wave scatter diagram, and the
damage is non-linearly related to the maximum dynamic stress range in the TDZ
through the allowable number of occurrence. It is therefore necessary to find the
combination of (cid:537) D and (cid:652) values leading to the least overall damage to find the
HO, o 6
optimum fatigue life. For the sake of simplicity, it is assumed that the designer has the
choice between three values for each of the inputs, as follows:
(cid:120)(cid:3) (cid:537) can take a value of 9.8° (as for BC1), 13° or 17°.
HO
(cid:120)(cid:3) D can take a value of 0.228 m (as for BC1), 0.25 m or 0.35 m.
o
(cid:120)(cid:3) (cid:652) can take a value of 9.12 (as for BC1), 12 or 15.
6
Since there are three possible choices for each of three inputs, 27 possible designs result
for the SCR. The ANN framework is applied to investigate the fatigue lives of the SCRs
formed by the 27 combinations of inputs, with results shown in Table 8-12. Fatigue
results are assessed using the DNV S-N curve type D for seawater (DNV-RP-C203,
2011). Under those circumstances, by keeping D and (cid:652) to their values in BC1 and
o 6
increasing (cid:537) to 17° the fatigue life can be increased from 163 to 722 years, improving
HO
fatigue performance by a factor greater than 4.
This illustrates how the proposed ANN framework can assist screening design tasks in
finding combinations of input parameters that optimise fatigue performance, although
other practical considerations may affect the final selection of input parameters. In
practice, the ANN framework may be used in conjunction with optimisation software in
order to consider many more choices for the input parameters.
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8.6(cid:3) CONCLUSIONS
This paper has illustrated the usefulness of the simplified framework based on artificial
neural networks (ANNs) developed previously (Chapters 6 and 7) for SCR design with
respect to fatigue in the TDZ.
A series of sensitivity studies were performed by varying a selection of dimensionless
groups and individual input parameters to illustrate the trends in SCR behaviour.
Estimated trends were benchmarked against published results to validate further the
accuracy of the ANN framework. The sensitivity studies explored wider ranges of the
inputs and showed how misinterpretations can arise from generalising the trends
obtained from more restricted studies, since the effect of certain inputs on the maximum
stress range in the TDZ may depend on the value of other inputs. For this reason, and
because the fatigue life depends on the cumulative damage for a given wave scatter
diagram, optimisation of an SCR design with respect to fatigue must consider the
overall level of damage rather than individual load cases. The usefulness of the ANN
framework for such optimisation was illustrated by a simple example.
The sensitivity of DAF values, quantifying the dynamic amplification compared with
static results, was also investigated. It was shown that values of DAF as high as 16
could occur with the selected examples and that the DAF pattern was no easier to
predict than the pattern of the maximum dynamic stress range in the TDZ directly.
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Estimating the fatigue damage of SCRs in the TDZ
CHAPTER 9(cid:3)CONCLUDING REMARKS
The focus of this thesis has been to define a simplifying fatigue assessment approach for
the early stages of design and improve the understanding of the behaviour of steel
catenary risers in the touchdown zone. The research has combined extensive numerical
analyses with analytical work, statistical and mathematical techniques, to perform the
various incremental steps necessary to the development of a simplified framework for
the fatigue analysis of SCRs in the TDZ. The proposed framework, using artificial
neural networks, has been shown to achieve accurate prediction of fatigue life results
and fatigue damage trends on a series of examples.
The main conclusions and findings arising from this research and the directions for
future work are summarised in this final chapter.
9.1(cid:3) KEY CONCLUSIONS AND ORIGINAL CONTRIBUTION
The key conclusions resulting from this thesis are summarised in this section. As a
whole, they represent a substantial and original contribution to the knowledge of the
structural response and estimation of the fatigue damage of steel catenary risers in the
touchdown zone.
Dynamic analysis of steel catenary risers is time consuming and requires high
computational efforts due to the different sources of nonlinearity involved in their
structural response. The thesis critically examined the viability of defining a simplified
framework for the fatigue design of SCRs in the TDZ. The initial strategy for
simplification developed within this thesis was based on the use of dynamic
amplification factors (DAFs) since DAFs were successfully used to simplify the
structural dynamic analyses in other engineering fields. Chapter 2 to Chapter 6 therefore
explored various steps necessary to the implementation of the DAF approach for SCRs.
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Building on the knowledge acquired mainly from the work reported within Chapter 3,
Chapter 5 and Chapter 6, a framework using artificial neural network to efficiently
predict the critical dynamic stress range, directly, was established and is reported in
Chapter 7. Chapter 8 subsequently illustrated the usefulness of this framework and
reflected back on the original intention of using DAFs for simplification of dynamic
analyses of SCRs in the TDZ.
Since all the chapters represent incremental steps towards the main research aim of
simplifying the fatigue analysis of SCRs in the TDZ, the major findings are organised
accordingly and are summarised next, based on the findings from each individual
chapter.
9.1.1(cid:3) Investigation of the usefulness of DAF for the fatigue design of
SCRs in the TDZ
A pilot study was performed (Chapter 2) in order to get the first insights on the
usefulness of DAF for the fatigue design of SCRs in the TDZ. A definition for the DAF
was proposed, as the ratio between the critical dynamic and static stress ranges in the
TDZ. The sensitivity of DAFs to vessel motions (amplitudes and periods), and soil
stiffness were examined through numerical simulations and it was found that vessel
motions could significantly influence the DAF, while the soil stiffness had no major
effect on it. The DAF approach seemed well suited for the simplification of SCR
dynamic analysis at this stage.
9.1.2(cid:3)Clarification of the parameters impacting the fatigue damage of
SCRs in the TDZ
Fatigue design of SCRs in the TDZ is a complex challenge that is at the heart of current
research in the field of riser design. Despite the large interest in understanding the role
of design parameters in the level of stress range in the TDZ, there is still a lack of clear
guidance and of simple approaches able to conveniently produce information on SCR
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behaviour.
The study presented in Chapter 3 laid out the basis for pertinent sensitivity studies by
clarifying the dimensionless groups of input parameters influencing the dynamic and
static response of SCRs. A comprehensive set of numerical simulations was performed
to validate the proposed dimensionless groups and allow for a better control on the input
parameters, a wider scope of application of the results from numerical simulations and
easier comparison and interpretation of the results.
The input parameters related to the SCR geometry and structural properties,
environmental loading and the seabed characteristics were examined. When modelling
the seabed with a linear soil model, a final selection of 18 dimensionless groups formed
by 21 independent input parameters was established. The key dimensionless groups
influencing the response of SCRs identified among them were the normalised riser
displacement, velocity, outside diameter, unit submerged weight and tension
(accounting for the effect of the hang-off angle), the outside diameter to wall thickness
ratio, and the normalised soil stiffness and water depth.
9.1.3(cid:3)Development of an analytical model for the prediction of the stress
range in SCRs under static loading
Since it is essential for the DAF approach to have the ability to determine the critical
static stress range in the TDZ, preferably through a simple method, and since published
literature did not provide this pre-requisite with a sufficient level of accuracy, an
analytical model able to fulfil this purpose was developed. Chapter 4 therefore focused
on extending an existing analytical model, using a boundary layer solution in the
vicinity of the touchdown point and a Winkler type soil model in the riser-soil contact
area, tailoring the model to the need of this study. Numerical simulations in OrcaFlex
software were performed to validate the results of this model, namely the Extended
Three Fields Model (ETFM). A good level of accuracy was reached so that the ETFM
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provides a simple and efficient analytical tool for the evaluation of the critical static
stress range in the TDZ.
9.1.4(cid:3)Investigation of the usefulness of ANN for the fatigue design of
SCRs in the TDZ
The main challenge in the development of a simplified method using DAF was to
produce a database providing sufficient information on the relationships between the
dimensionless groups of inputs (as found in Chapter 3) and the DAF values, and to find
a way to capture these relationships. For these purposes, a series of sensitivity studies,
testing the effects of variation of the key input dimensionless groups on the structural
response of SCRs, were conducted and the ability of the response surface method in
approximating these relationships was also investigated.
Most published sensitivity studies in the field of riser design have only been carried out
for small ranges of some of the input parameters, hereby limiting their scope. The thesis
attempted to increase the knowledge of SCR behaviour for a broad range of input
parameters, encompassing most of the realistic SCR applications, in order to develop a
simplified approach with a wide range of applicability. Traditional methods applied
within published sensitivity studies were usually not suited to consider large ranges of
input parameters and to account for the effect of the interactions between the input
parameters. It was therefore necessary to investigate a suitable approach to perform the
sensitivity studies and post-process their results. This was the main concern of the pilot
study reported in Chapter 5.
The in-house automation sub-routine that was developed to generate the numerical
models providing the necessary information for the sensitivity studies, was presented in
this chapter. It was shown on a database of 4800 SCR configurations under static
loading that design of experiment techniques could conveniently assist the definition of
the database. Also, the usefulness of the artificial neural network, which is an advanced
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mathematical tool of the response surface method, was tested and seemed well suited to
the simplification of fatigue analysis of SCRs in the TDZ.
9.1.5(cid:3)Development of an ANN approximation for the critical static stress
range for SCRs in the TDZ
Based on the promising results from Chapter 5, Chapter 6 was concerned with the
expansion of the database to refine the approximation of the critical static stress range
defined within Chapter 5. Chapter 6 was another preliminary step towards the
application of the proposed ANN approach to the more complex prediction of DAF
values, or of the critical dynamic stress range in the TDZ as was decided ultimately.
An ANN approximation of the maximum static stress range in SCRs (evaluated here
through numerical simulations using the marine analysis software OrcaFlex) was
developed successfully using a database of over 50,000 SCR configurations under static
loading conditions. The proposed approximation, comprising nine ANNs, can evaluate
over 99% of the cases of the database with an accuracy of (cid:114) 5% compared with the
results from OrcaFlex. The outcomes of Chapter 6 provided sufficient confidence in the
ANN approach to examine the dynamic loading conditions using similar methods.
9.1.6(cid:3)Development of an ANN approximation for the critical dynamic
stress range for SCRs in the TDZ
Months of calculations were necessary to develop a large database of more than 40,000
SCR configurations under dynamic loading and support the training of a response
surface using ANN, and this part of the research was presented in Chapter 7. It was
found at this stage of the research that using ANNs, it was possible to capture the
relationships between the input dimensionless groups (as found in Chapter 3) and the
critical dynamic stress range of SCRs in the TDZ directly. As a consequence, the overall
strategy of this research shifted slightly since it was found more convenient for future
applications to use a framework able to predict the critical dynamic stress range in the
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TDZ in a straightforward manner (rather than obtaining an evaluation through DAF).
An approximation was defined having similar architecture to the approximation
developed to estimate the critical static stress range in the TDZ (in Chapter 6) was
defined. It is also composed of nine ANNs and is able to estimate the majority of the
cases of the database (> 80 %) within (cid:114) 5% errors with OrcaFlex results. Further
strategies aiming to further improve the accuracy of the approximation were proposed
and applied on part of the design space to confirm their beneficial effect on
performances. Using this refined approximation, the fatigue lives of a series of example
SCRs were estimated within only a few minutes of simple computational works and
were found to be within a negligible range of errors with the results derived from
OrcaFlex calculations.
The findings from this chapter proved that by using the proposed approximation and
approaches, it is possible to tremendously shorten the fatigue design calculations for
SCRs in the TDZ for the early stages of design where a minor compromise on accuracy
is acceptable.
9.1.7(cid:3)Illustration of the usefulness of the proposed ANN framework
The final technical chapter of the thesis drew all of the previous steps of this research
together by illustrating the usefulness of the proposed ANN framework. It provided
insights on the sensitivity of the structural response of SCRs in the TDZ and shed light
on how the proposed ANN framework could be used in the screening tasks aiming at
optimising the fatigue life of SCRs in the TDZ.
A series of sensitivity studies were performed using the ANN framework. The trends
obtained for the critical stress range in the TDZ compared well against published
results, although by selecting wider ranges of the input parameters it was shown how
generalising from a limited number of results, derived from sensitivity studies
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performed only on some of the input parameters or considering small ranges of the input
parameters, could sometimes lead to misinterpretations. The sensitivity of DAF to the
variation of input parameters was also investigated and results were consistent with the
preliminary results presented during the pilot study stage of this research (Chapter 2),
further validating the performance of the developed ANN framework. The obtained
trends confirmed that the DAF pattern was not simpler to predict than the pattern of the
critical dynamic stress range, reinforcing the shift of strategy that occurred in the
research (Chapter 7).
In addition, the ANN framework was applied to an example fatigue optimisation study
to illustrate how it can assist the selection of an improved setup for SCRs to improve the
fatigue life in the TDZ.
9.2(cid:3) LIMITATIONS AND FUTURE RESEARCH
9.2.1(cid:3)In-depth investigation of the accuracy of the stress range and
fatigue results from the ANN framework
The performance of the ANN framework for practical purposes was investigated by
using it to evaluate the fatigue life of example SCRs (Chapter 7) and its usefulness for
SCR design was illustrated through a series of sensitivity studies, exploring the effects
of the variation of the key input dimensionless groups or input parameters on the
structural response of SCRs (Chapter 8). It could be worth evaluating the fatigue life of
more example SCRs and using different wave scatter diagram to increase the
understanding of the performance of the ANN framework and quantify further its
accuracy. Further sensitivity studies, considering different values of the input
dimensionless groups and individual parameters, could also be performed using the
ANN framework to shed more light on the structural response of SCRs.
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9.2.2(cid:3)Extension of the existing ANN framework
A number of assumptions and simplifications were adopted in this research to render the
problem manageable. For example, the study was limited to 2 D conditions, the current,
flow rate of the content and coating were not accounted for, the floater was limited to
the case of a semisubmersible and a deterministic approach was used for the loading,
represented by an imposed displacement to the upper end of the SCRs. Also, a linear
soil model was used mostly throughout the thesis (as per common practice), whereas it
is generally agreed that this model is too simple to capture the complex seabed
interactions occurring in the TDZ. In the future, it could therefore be desirable to extend
the present work to other types of floaters, stochastic loadings, and to include the effect
of the current, using a nonlinear soil model for instance, in order to enlarge the scope of
applicability of the ANN framework.
9.2.3(cid:3)Refinement of the accuracy of the ANN framework for dynamic
loading conditions
A good level of accuracy was reached overall by the ANN framework for the estimation
of the critical dynamic stress range occurring in SCRs in the TDZ but some marginal
cases with high relative differences with numerical results were observed, signalling
margins for future improvement. It could be worth expanding the database in the future
and/or investigating the effect of using more advanced data division algorithms (e.g.
self-organising map or fuzzy clustering for instance) on the performance of the
approximated results.
Since the structure of the overall approximation (with the nine ANNs) led to good
performances overall, improvement of the inherent ANNs could be performed
separately and a statistically consistent approach could be used on each of the training
and testing sets of the ANNs, similar to what was performed for part of the design space
in Chapter 7. In turn, these recommendations might improve the robustness of the
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DECLARATION FOR THESES CONTAINING
PUBLISHED WORK AND/OR WORK PREPARED FOR
PUBLICATION
This thesis contains published work and work prepared for publication, which has
been co-authored. The bibliographical details of the work and where it appears in the
thesis are outlined below.
This thesis is presented as a series of academic papers in accordance with the
regulations of the University of Western Australia regarding higher degrees by research.
Chapter 1 and 9 comprise of the introduction and conclusions of the thesis respectively.
Chapters 2 and 3 contain the literature review. These chapters have been solely prepared
by the candidate. Chapters 4, 5, 6 and 7 are published journal papers. Chapter 8 has
been submitted to Géotechnique and was “under review” at the time of thesis
submission. Appendices I, II and III are papers published in peer reviewed conference
proceedings. The candidate is the first author on five of the eight publications arising
from this thesis and second author on the other three. Overall the candidate is
responsible for more than 80% of the content presented in this thesis. The publications
arising from this thesis are as follows:
Journal papers
Chapter 4: O’Loughlin, C. D., Blake, A. P., Richardson, M. D., Randolph, M. F.
and Gaudin, C. (2014). Installation and capacity of dynamically embedded plate
anchors as assessed through centrifuge tests. Ocean Engineering, Vol. 88, pp. 204–
213.
The centrifuge testing was carried out by the candidate along with preliminary data
processing and interpretation. The first author conducted further analyses of the data
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and was responsible for an initial draft of the paper. All co-authors reviewed and
contributed to the final draft.
Chapter 5: Blake, A. P., O’Loughlin, C. D., Morton, J. M., O’Beirne, C., Gaudin,
C. and White D. J. (2016). In situ measurement of the dynamic penetration of free-
fall projectiles in soft soils using a low cost inertial measurement unit. Geotechnical
Testing Journal, forthcoming.
This paper presents field data gathered by the candidate (dynamically embedded
plate anchor data), and the third (instrumented free-fall sphere data) and fourth
(deep penetrating anchor data) authors. All data processing was conducted by the
candidate. The interpretation framework presented by in the paper was developed
and implemented by the candidate. The candidate prepared an initial draft of the
paper and all co-authors reviewed and contributed to the final draft.
Chapter 6: Blake, A. P. and O’Loughlin, C. D. (2015). Installation of dynamically
embedded plate anchors as assessed through field tests. Canadian Geotechnical
Journal, Vol. 52, No. 9, pp. 1270–1282.
Field testing was conducted by the candidate along with data processing and
interpretation. The candidate prepared an initial draft of the paper and the co-author
all co-authors reviewed and contributed to the final draft.
Chapter 7: Blake, A. P., O’Loughlin, C. D. and Gaudin, C. (2014). Capacity of
dynamically embedded plate anchors as assessed through field tests. Canadian
Geotechnical Journal, Vol. 52, No. 1, pp. 87–95.
The field tests described in this paper and subsequent data processing and
interpretation were performed by the candidate. The candidate prepared an initial
draft of the paper and all co-authors reviewed and contributed to the final draft.
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ABSTRACT
The dynamically embedded plate anchor (DEPLA) has been proposed as a cost effective
and technically efficient anchor for deepwater mooring applications. The DEPLA is
rocket or torpedo shaped anchor that comprises a removable central shaft and a set of
four flukes. The DEPLA penetrates to a target depth in the seabed by the kinetic energy
obtained through free-fall in water. After embedment the central shaft is retrieved
leaving the anchor flukes vertically embedded in the seabed. The flukes constitute the
load bearing element as a plate anchor. The DEPLA combines the installation
advantages of dynamically installed anchors (no external energy source or mechanical
operation required during installation) and the capacity advantages of vertical loaded
anchors (sustain significant horizontal and vertical load components).
Despite these advantages there are no current geotechnical performance data for the
DEPLA, as development of the anchor is in its infancy. This thesis has focused on
assessing the geotechnical performance of DEPLAs through an experimental study
involving a centrifuge testing program and an extensive field testing campaign. The
centrifuge tests provided early stage proof of concept for the DEPLA and motivation for
subsequent field testing. The field tests were carried out on reduced scale DEPLAs at
two sites: (i) Lough Erne, which is an inland lake located in County Fermanagh,
Northern Ireland and (ii) the Firth of Clyde which is located off the West coast of
Scotland. The reduced scale anchors were instrumented with a custom-design, low cost
inertial measured unit (IMU) for measurement of anchor motion during installation. The
field tests were designed to assess the behaviour of the DEPLA during free-fall in water
and dynamic embedment in soil, and quantify the loss in embedment during keying and
the subsequent plate anchor capacity. Analytical design tools for the prediction of
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DEPLA embedment and capacity were verified, refined and calibrated using the
centrifuge and field data.
Back analysis of the IMU data showed that the fluid drag resistance acting on the
DEPLA during free-fall in water may be approximated using a constant mean drag
coefficient of 0.7. DEPLA impact velocities derived from the IMU data were in the
range 2.7 to 12.9 m/s corresponding to anchor release heights of 0.4 to 21.3 times the
anchor length. The DEPLA required a release height in the range 6.5 to 7 anchor lengths
to reach terminal velocity but then slowed slightly due to the increasing fluid drag
resistance afforded by the increasing length of mooring and follower recovery lines that
mobilised in the water. DEPLA tip embedment derived from the IMU data were in the
range 2.1 to 3.5 times the anchor length in Lough Erne and 1.4 to 2 times the anchor
length in the Firth of Clyde. These tip embedments were in good agreement with the
centrifuge data (1.6 to 2.8 times the anchor length). The shallower embedments
measured in the Firth of Clyde tests reflect the much higher strength gradient at this site.
The results indicated that anchor embedment increases with increasing impact velocity.
The appropriateness of an embedment prediction model for DEPLA based on strain rate
enhanced shear resistance and fluid mechanics drag resistance was demonstrated
through comparison with the IMU measurements. Qualitatively, the embedment depth
prediction model captures the dynamic response at both test sites adequately and is
capable of predicting the final embedments to within 10% of the measurements.
Back analysis of the IMU data indicated that a power function is capable of describing
the strain rate dependence of undrained shear strength at the very high strain rates
associated with the dynamic embedment process, although complexities associated with
initial embedment (up to one anchor length) were not captured by the model. However,
these shortcomings did not appear to unduly lessen the capability of the embedment
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model to predict the measured velocity profiles and importantly the final anchor
embedment depth.
Video captured by a remotely operated vehicle in the Firth of Clyde showed an open
crater at the anchor drop sites which suggest that the hole caused by the passage of the
anchor remains open.
The keying response in the field was qualitatively consistent with the DEPLA
centrifuge data. However, despite the geometrical similarity between the field and
centrifuge DEPLAs, the loss in embedment of 1 to 1.8 times the plate diameter in
Lough Erne (could not be determined in the Firth of Clyde), was much higher than that
in the centrifuge tests (0.5 to 0.7 times the plate diameter). This was attributed to the
soil strength ratio which was much higher in Lough Erne than in the centrifuge tests.
Field test data indicated that the end of keying coincides with the peak anchor capacity
and the plate anchor bearing capacity factor decreases with reducing load inclination for
plate embedment ratios less than four. Back analysed peak bearing capacity factors from
the centrifuge and field tests were in the range 14.2 to 15.8 (centrifuge), 14.3 to 14.6
(Lough Erne) and 4.2 to 12.9 (Firth of Clyde). These bearing capacity factors were
compared with corresponding numerically derived values. This comparison indicated
the potential for soil tension to be lost at the underside of the anchor plate at shallow
embedment, where the plate embedment is less than 2.5 times the diameter, resulting in
a lower bearing capacity factor. At deep embedment, where the plate embedment is at
least 2.5 times the diameter, the experimental bearing capacity factors reached limiting
values in good agreement with that determined numerically.
A simple design procedure, based on a design chart presented in terms of the total
energy of the anchor at impact with the mudline for a range of strength gradients and
soil sensitivities, was shown to be useful approach for preliminary sizing of a DEPLA.
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ACKNOWLEDGEMENTS
I am grateful for the financial support I received during my candidature, which included
a Scholarship for International Research Fees and a University International Stipend
from the University of Western Australia (UWA), a top-up scholarship from the Centre
for Offshore Foundation Systems (COFS), maintenance and fee grants from the Mayo
Vocational Education Committee, and a scholarship provided by the Society for
Underwater Technology through their Educational Support Fund. I am also grateful to
Enterprise Ireland for funding the centrifuge and field testing reported in this thesis,
through their Commercialisation Fund Technology Development Programme.
I would like to take this opportunity express my sincere gratitude to my supervisors
Associate Professor Conleth O’Loughlin and Professor Christophe Gaudin for their
encouragement, guidance, time and patience. It has been a great privilege to have
worked with both of you.
I appreciate the assistance provided by the COFS staff, particularly Bart Thompson,
Dave Jones, John Breen, Lisa Melvin, Monica Mackman, Keith Russell, Ivan Kenny
and Monika Mathyssek-Kilburn.
I acknowledge the professionalism, experience and skill of the individuals I have
worked with during field testing, especially John Taylor, Michael and John Patrick
McCaldin of Aghinver Boat Company, Toms Wadsworth of Hydrabotix, and Tom
Stevenson and Duncan Fraser of the University Marine Biological Station Millport.
I thank Cathal Colreavy for conducting site investigation and characterisation at both
test locations reported in this thesis.
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I thank Assistant Professor Scott Draper for helping to enhance my understanding of
fluid mechanics and being a sounding board for my ideas relating to the topic.
I thank the people whose friendship and camaraderie I enjoyed over the course of my
studies such as Tom Burke, Cathal Colreavy, John Cunningham, John Heneghan,
Richard Hughes, Paul McGarry, Simon Leckie, Neil Marshall, Gary Jennings, Keith
Jennings, Colm O’Beirne, Shane O’Doherty, Joe Phillips, Lucile Quѐau, Raffaele
Ragni, Amin Rismanchian, Sam Stanier, Yusuke Suzuki, Pauline Truong and Padraig
Varley. Special thanks to Siobhan Durkan who provided me with encouragement and
support throughout the course of my studies.
I thank my secondary school physics and chemistry Austin Egan for the excellent
foundation for learning that he provided me with, which has helped me enormously
throughout my subsequent studies. I am fortunate to have been educated by Austin.
I thank my parents Patrick and Mary Blake for their encouragement, support and
patience throughout my education. During my time in Australia, I have missed my
family (Mom, Dad, Helen, Noel, Matthew and Jamie) dearly.
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CHAPTER 1 INTRODUCTION
In the context of offshore hydrocarbon exploration and development, the advancement
of technology has changed the definition of deepwater over time. At present, waters
depths less than 300 m are considered ‘shallow’, depths ranging 300 to 1500 m are
regarded as ‘deep’ and depths varying from 1500 to 3000 m are classified as ‘ultra-
deep’ (Nixon et al. 2009). In 1947 the world’s first offshore platform out of sight of
land, Superior, was installed in the Gulf of Mexico, 30 km off the coast of Louisiana in
6 m of water (Aubeny et al. 2001). Since then the offshore oil and gas industry have
installed platforms in ever increasing water depths (Figure 1.1). During 2012 the
Pioneer FPSO was installed in the Gulf of Mexico 250 km off the coast of Louisiana in
a world record water depth of 2500 m (Figure 1.2) (Pipeline and Gas Journal 2012).
Figure 1.1. Worldwide progression of water depth capabilities for offshore drilling
and production (after FloaTEC 2012)
Global oil demand was 89.8 million barrels per day (mb/d) in 2012, with medium-term
forecasts projecting an increase of 7.6 % to 96.7 mb/d by 2018 (International Energy
Agency 2013). Long-term forecasts predict a 12.3 % increase in world oil demand to
99.7 mb/d by 2035. Over the same period global natural gas demand is expected to rise
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Brazil, such as the Tupi oil field located in the Santos Basin off the Coast of Brazil in
water depths ranging from 1500 to 3000 m. This field was discovered in 2007 with
estimated recoverable reserves in the range of 5 to 8 billion barrels of oil (Offshore
Magazine 2008). Australia’s deepwater exploration and development activities include
the Enfield and Stybarrow oil fields located in water depths of 550 and 825 m
respectively, and several substantial gas fields in waters depths of up to 1500 m such as
Dionysus (1100 m), Geryon (1232 m), Io (1350 m) and Scarborough (1500 m)
(Department of Industry and Resources 2008).
In shallow water oil and gas development systems are typically bottom-founded
structures (e.g. fixed platforms and compliant towers) that are not viable in deepwater.
Instead, floating vessels are utilised such as Tension Leg Platforms (TLPs), Semi-
submersible floating and production units (Semi-FPUs), Floating Production, Storage
and Offloading units (FPSOs) and SPARs (Figure 1.6). Floating vessels are kept on
station with mooring lines anchored to the seabed. The oil and gas industry has
traditionally used a catenary mooring system in shallow water (Figure 1.7). However, in
deepwater operations, the weight and length of the catenary mooring line become
limiting factors in the design of the platform (Vryhof Anchors 2010). Therefore it is
becoming increasingly common for deepwater platforms to be moored using taut-leg
(Figure 1.7) and vertical mooring systems. These systems are designed to have high
angles of inclination with the mud-line (up to 90° in the case of vertical mooring
systems) and require anchors that can sustain both horizontal and vertical load
components.
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years at the Browse Basin on the North West Shelf of Australia 200 km offshore in 250
m of water (Figure 1.8) (Offshore Magazine 2012). FLNG developments in deepwater
have also been proposed such as at the Carnarvon Basin on the North West Shelf of
Australia 220 km offshore in 900 m of water (Offshore Magazine 2013). Permanently
moored vessels of Prelude’s size and weight will significantly increase the loads that the
anchoring system must sustain.
Figure 1.8. Prelude FPSO and shuttle tanker (after Offshore Magazine 2012)
1.1 Anchoring systems
1.1.1 Anchor piles
Anchor piles typically comprise of a hollow steel tube with a mooring line attached at
the padeye (Figure 1.9). Installation generally involves either vibration or hammering.
Anchor piles can resist vertical and horizontal loads making them suitable for catenary,
taut-leg and vertical mooring systems. Installation costs for anchor pile are extremely
high and significantly increase as crane barges and pile driving equipment are required.
Anchor piles have been installed in water depths exceeding 1500 m (Offshore Magazine
2005).
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vertical and horizontal loads enabling them to be employed for catenary, taut-leg and
vertical mooring systems. It can be difficult for suction caissons to penetrate hard layers
of soil in the seabed. The soil plug within the anchor may fail during installation in sand
overlain by clay and thin-walled caissons may buckle due to the relatively high suction
pressures required to penetrate the sand. Installation costs are relatively high as suction
caissons require considerable deck space during transport and heavy lift vessels for
installation. These costs increase significantly with water depth (Richardson 2008).
Suction caissons have been installed in water depths exceeding 2621 m (Offshore
Magazine 2010).
Figure 1.10. Suction caissons (www.delmarus.com)
1.1.3 Drag embedment anchors
Drag embedment anchors comprise of a bearing plate (referred to as a fluke) rigidly
connected to a shank (Figure 1.11). These anchors are designed to self-embed when
dragged along the seabed by a wire rope or chain and are easily recovered making then
suitable for short to medium term mooring applications. Although drag anchors achieve
high capacity to weight ratios there is a possibility of interference with existing subsea
infrastructure during installation and it is difficult to predict the embedment (Aubeny et
al. 2001). Drag embedment anchors are only suitable for catenary mooring systems as
they cannot resist vertical load.
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Direct embedment anchors comprise of a plate anchor connected to a mooring line
installed at the end of a follower by free-fall, driving, vibrating or suction. The suction
embedded plate anchor (SEPLA) (Figure 1.13) is a direct embedment anchor which
uses a suction caisson follower to install a vertically orientated plate anchor that is
slotted into its base (Dove et al. 1998). The suction caisson enables the plate anchor to
be installed to a known penetration depth. The caisson is lowered to the seabed, where it
is allowed to penetrate under self-weight. Water is then pumped from the interior of the
caisson to allow the plate anchor to reach the design embedment depth. The plate
anchor mooring line is then disengaged from the caisson and the pump flow is reversed
with water being forced back into the caisson causing it to move upwards while leaving
the plate anchor in place at the design embedment depth. The follower is recovered to
the deck of an anchor handling vessel (AHV) for reuse in future installations. When
sufficient load develops in the mooring line the plate anchor is keyed to an orientation
that is approximately normal to the direction of loading. Sufficient load may be applied
by the bollard pull of an AHV or may develop during the life cycle of the mooring
system if the necessary environmental loading conditions occur. The installation and
keying process of the SEPLA are summarised in Figure 1.14. SEPLAs are commonly
used for the mooring of mobile offshore drilling units (MODUs) in water depths
ranging from 381 to 2195 m (Brown et al. 2010) and has recently been considered as
permanent mooring for developments in West Africa (Wong et al. 2012)
The capacity to weight ratio of VLAs is much higher than that of anchor piles and
suction caissons. VLAs can sustain significant components of horizontal and vertical
loads allowing them to be used in catenary and taut-leg mooring systems. Uncertainty
exists regarding the embedment depth loss due to the keying process and the subsequent
capacity of the plate anchor.
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Figure 1.16. Torpedo anchor (after Araujo et al. 2004)
1.1.6 Dynamically embedded plate anchor
The dynamically embedded plate anchor (DEPLA) (Figure 1.17) is a hybrid anchor
concept that combines the installation advantages of dynamically installed anchors and
the capacity advantages of VLAs (O’Loughlin et al. 2013a). The DEPLA was
conceptualised at UWA’s Centre for Offshore Foundation Systems in 2004. Further
work was undertaken to validate and refine the concept during 2008 to 2014, as detailed
in this thesis. In 2013, the intellectual property rights were assigned under contract to
Vryhof Anchors of the Netherlands.
The DEPLA is rocket or dart shaped with a removable central shaft (follower) and a set
of four flukes attached to a sleeve (plate anchor). A stop cap at the upper end of the
follower prevents the follower from falling through the DEPLA sleeve and a shear pin
connects the flukes to the follower. After release from a designated height above the
seabed (typically <100 metres), the DEPLA penetrates to a target depth in the seabed by
the kinetic energy obtained through free-fall and the self-weight of the anchor. After
embedment the follower is retrieved for the next installation leaving the flukes and
sleeve vertically embedded in the seabed. These embedded anchor flukes and sleeve
constitute the load bearing element as a plate anchor. The plate anchor remains vertical
in the seabed until sufficient load develops in the mooring line to cause the plate anchor
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to rotate or ‘key’ to an orientation that is approximately perpendicular to the direction of
loading maximising the bearing capacity of the anchor. Sufficient load may be applied
by the bollard pull of an AHV or may develop during the life cycle of the mooring
system if the necessary environmental loading conditions occur. The installation and
keying process is summarised in Figure 1.18 and Figure 1.19 respectively.
The advantages of the DEPLA are:
Installation durations and hence costs are significantly reduced as no mechanical
intervention or external energy source is required.
Installation durations and costs are independent of water depth.
Plate anchor can withstand both horizontal and vertical loads enabling use in
catenary, taut-leg and vertical mooring systems.
Fabrication is simple and economical.
Reuse of follower ˗ full anchor spread transported to site on a single vessel.
Robust and compact design makes handling and installation simple and economical
using one anchor AHV and requiring no remotely operated vehicle (ROV).
Figure 1.17. Dynamically embedded plate anchor
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components). Despite these advantages there are no current geotechnical performance
data for the DEPLA. Such data would evidently stimulate confidence in the potential of
DEPLAs as a cost effective and technically efficient anchor for deepwater applications
and FLNG vessels. Therefore, there is a clear requirement for an experimental study to
investigate the geotechnical behaviour of these anchors and provide ‘proof of concept’.
The overall objective of this thesis is to enhance the understanding of the geotechnical
behaviour of DEPLA. In order to achieve this overall objective five detailed objectives
have been identified:
Proof of concept - demonstrate feasibility through anchor deployment and retrieval.
Installation - quantifying anchor embedment for a given anchor drop height,
geometry and seabed strength profile.
Keying - quantifying the embedment depth loss of the plate anchor during keying.
Capacity - determination of anchor capacity for a given seabed strength profile.
Design tools - verification and calibration of design tools for the prediction of
anchor embedment, keying response and anchor capacity.
1.3 Research methodology
Reduced scale model DEPLAs will be modelled in UWA’s beam centrifuge.
Geotechnical field testing in an aquatic environment is generally a challenging and
expensive undertaking. Centrifuge testing offers a more convenient and economical
alternative to field testing. Testing parameters such as anchor drop height (and hence
impact velocity), anchor geometry and mass, and stress history of the soil are readily
controlled in the centrifuge environment. Centrifuge modelling provides a method for
achieving stress and strain similitude between the prototype and a reduced scale
laboratory model. Prototype body forces and stress conditions are replicated by
subjecting a model reduced in scale by a factor n , to a radial acceleration field equal
cent
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to n g (where g is the acceleration due to the Earth’s gravitational acceleration). For a
cent
given soil type, the vertical stress at a depth, z , in a model subjected to a radial
m
acceleration field of n g, will be identical to that in prototype at a depth, z = n z .
cent p cent m
This fundamental scaling law, together with dimensional analysis enables extrapolation
of model test results to prototype conditions.
The centrifuge testing program will investigate DEPLA installation, keying and
capacity, and provide early stage performance data, necessary to provide initial proof of
concept and justification for subsequent field testing. However, it is important to
validate the centrifuge findings and further qualify the DEPLA concept through reduced
scale field testing in an aquatic environment. Two test locations have been identified; (i)
Lower Lough Erne, which is an inland lake located in County Fermanagh, Northern
Ireland, and (ii) the Firth of Clyde which is located off the West coast of Scotland
between the mainland and the Isle of Cumbrae. Reduced scale model anchors will be
deployed at both locations to assess DEPLA installation, keying and capacity. These
anchors will be instrumented with a custom built six degree of freedom (6DoF) inertial
measurement unit (IMU) for measurement of anchor motion during installation. This
will represent the first reported use of a 6DoF IMU for a geotechnical application.
Hence, there is a requirement to develop a framework for interpretation of the IMU
data. The IMU data will be used to validate an embedment prediction model for
dynamically installed anchors based on strain rate enhanced shear resistance and fluid
mechanics drag resistance.
1.4 Thesis structure
The thesis is organised as a series of academic papers that have been either published or
submitted for publication in accordance with the policies of the University of Western
Australia regarding higher degrees by research. Chapters 2 and 3 comprise the literature
review. Chapters 4 to 8 are journal papers that have been published, accepted for
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publication or are under review. These chapters report the experimental development
and results of an experimental study that involved a centrifuge testing program and an
extensive field testing campaign. Details of the contents of each chapter are provided
below.
Chapter 2: This chapter reviews the literature related to dynamic penetration of
projectiles into clayey seabeds. The review details field and laboratory studies on
free-falling penetrometers and dynamically installed anchor systems. The soil
mechanics, fluid dynamics and unified frameworks for predicting the shear strain
rate dependence of soil strength are discussed. Analytical and numerical methods
developed for predicting the embedment depth of projectiles penetrating the seabed
are described.
Chapter 3: This chapter reviews the literature related to the capacity of plate
anchors in clay. Experimental and numerical studies on the keying behaviour and
capacity of plate anchors are discussed. The review considers the factors that
influence the embedment depth loss associated with the keying process and
subsequent plate anchor capacity.
Chapter 4: This chapter presents results of a centrifuge testing program on reduced
scale model anchors in kaolin clay, carried out to attain early stage anchor
performance data necessary to provide motivation for subsequent field testing
(described in Chapters 5 to 8). The tests assessed the installation and capacity of
DEPLAs. The impact velocity, initial embedment depth following dynamic
installation, follower extraction, embedment depth loss due to the keying process
and the subsequent plate anchor capacity are examined. The results are compared
with corresponding experimental and numerical results for other dynamically
installed anchors (outlined in Chapter 2) and plate anchors (outlined in Chapter 3).
The methodology and outcomes have been presented in a journal paper:
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O’Loughlin, C. D., Blake, A. P., Richardson, M. D., Randolph, M. F. and Gaudin,
C. (2014). Installation and capacity of dynamically embedded plate anchors as
assessed through centrifuge tests. Ocean Engineering, Vol. 88, pp. 204–213.
Chapter 5: This chapter describes the technical development required to enable
field testing, and presents motion data captured by an inertial measurement unit
(IMU) during field tests of DEPLAs, DPAs and an instrumented free-fall sphere. A
comprehensive framework for interpreting the motion data is described and
validated against direct measurements. The motion data is used to verify the
appropriateness of an embedment prediction model for dynamically installed
anchors (outlined in Chapter 2). The framework is subsequently adopted in the
analysis of DEPLA field data in Chapters 6 and 8. The methodology and outcomes
have been presented in a journal paper:
Blake, A. P., O’Loughlin, C. D., Morton, J. M., O’Beirne, C., Gaudin, C. and White
D. J. (2016). In situ measurement of the dynamic penetration of free-fall projectiles
in soft soils using a low cost inertial measurement unit. Geotechnical Testing
Journal, forthcoming
Chapters 6 and 7: These chapters present results from field tests on reduced scale
model DEPLAs conducted at Lough Erne, Northern Ireland, required to validate the
centrifuge findings and demonstrate DEPLA deployment and operation in an
aquatic environment. Chapter 6 focuses on the behaviour of DEPLAs during free-
fall in water and dynamic embedment in soil. The framework for interpreting
motion data captured by an IMU described and validated in Chapter 5 is applied to
the data reported in Chapter 6 to derive net resistance profiles and velocity profiles.
Theses profiles are used to determine the hydrodynamic properties of DEPLAs, and
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refine and calibrate an embedment prediction model for dynamically installed
anchors (outlined in Chapter 2).
Chapter 7 considers follower extraction, the embedment depth loss due to the keying
process and the subsequent plate anchor capacity. The results are compared with
corresponding experimental and numerical results for other plate anchors (outlined
in Chapter 3).
The methodology and outcomes of Chapters 6 and 7 have been presented in two
separate journal papers:
Blake, A. P. and O’Loughlin, C. D. (2015). Installation of dynamically embedded
plate anchors as assessed through field tests. Canadian Geotechnical Journal, Vol.
52, No. 9, pp. 1270–1282 (Chapter 6).
Blake, A. P., O’Loughlin, C. D. and Gaudin, C. (2014). Capacity of dynamically
embedded plate anchors as assessed through field tests. Canadian Geotechnical
Journal, Vol. 52, No. 1, pp. 87–95 (Chapter 7).
Chapter 8: This chapter presents results from field tests on reduced scale model
DEPLAs conducted at the Firth of Clyde, off the West coast of Scotland, required to
demonstrate DEPLA deployment and operation in an offshore environment. Chapter
8 examines: (i) DEPLA behaviour during free-fall in water and dynamic embedment
in soil and (ii) the embedment depth loss due to the keying process and the
subsequent plate anchor capacity. The results from the Firth of Clyde tests are
considered in parallel with centrifuge data (from Chapter 4) and field data (from
Chapters 6 and 7) to assess the merit of anchor embedment and capacity models. A
simple design approach for the prediction of DEPLA capacity based on these
models is developed. The methodology and outcomes have been presented in a
journal paper:
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CHAPTER 2 DYNAMIC EMBEDMENT OF
PROJECTILES INTO THE SEABED
2.1 Introduction
As offshore clay deposits are typically characterised by an increase in shear strength
with depth, the capacity of dynamically installed anchors such as the DEPLA is
dependent on the embedment depth achieved following free-fall in water. Hence
accurate prediction of the embedment depth is necessary in order to successfully
estimate the subsequent anchor capacity. The dynamic embedment of projectiles into
the seabed has previously been considered in studies of free-falling penetrometers
(FFPs) (see Section 2.2) and dynamically installed anchoring systems (see Section 2.3).
Several of these studies have adopted analytical and numerical methods to predict
embedment depth (see Section 2.5). However the accuracy of these methods is
questionable due to uncertainties regarding fluid drag resistance (see Section 2.4) and
viscous strain rate effects (see Section 2.4.3).
2.2 Free-falling penetrometers
FFPs are expendable or retrievable probes that are designed to dynamically penetrate
the seabed following free-fall through water. FFPs have been considered for seabed
strength characterisation, naval mine countermeasure research, paleolimnology
applications and the disposal of high-level nuclear waste in ocean abyssal plain
formations. FFP systems that have been developed for seabed strength characterisation
include (shown in Figure 2.1): marine impact penetrometer (MIP, Dayal 1975), marine
sediment penetrometer (MSP, Colp et al. 1975), free-fall penetrometer (Denness et al.
1981), expendable bottom probe (XBP, Akal and Stoll 1995), free-fall Cone
penetrometer (FF-CPT, Mulukutla 2009), CPT lance (Stegmann 2007), Nimrod (Stark
et al. 2009a) and lance insertion retardation meter (LIRmeter, Stephan et al. 2012).
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For naval mine countermeasure research the following FFP systems have been reported
(shown in Figure 2.2): expendable doppler penetrometer (XDP), seabed terminal impact
naval gauge (STING), electronic strength profiler (ESP), burying mock mine body
(BMMB), Australian underwater sediment strength instrument (AUSSI), FAU
Experimental penetrometer (FEP) and Proboscis (PROBOS) (Beard 1977, Lott and
Poeckert 1996, Stoll 2004). An FFP system was also developed for paleolimnology
research that involved the measurement of the relative hardness and consistency of lake-
bottom sediments (Spooner et al. 2004).
2.2.1 Field studies
Numerous field studies have been carried out to assess the feasibility of FFP systems
such as the MIP (Dayal 1975, Chari et al. 1978), MSP (Colp et al. 1975), XBP (Stoll
and Akal 1999, Strak and Wever 2009), FF-CPT (Furlong et al. 2006, Mulukutla 2009,
Mulukutla et al. 2011, Stegmann et al. 2006, Steiner et al. 2012, Steiner et al. 2014),
XDP (Beard 1977, 1981, 1985, Bowman et al. 1995, Douglas and Wapner 1996,
Thompson et al. 2002, Ortman 2008) and STING (Mulhearn et al. 1998, Mulhearn et al.
1999, Mulhearn 2003, Abelev et al. 2009a, 2009b). The field tests have taken place at
various locations including: the Baltic Sea, the Black Sea, the Gulf of Mexico, New
York Harbour and around the coasts of Italy, Spain, Germany, Turkey (Stoll and Akal
1999). The FFPs were deployed in water depths of 7 to 5430 m and achieved impact
velocities of 2.2 to 29.6 m/s. Embedment depths of 0.1 to 7.9 penetrometer lengths were
reported. Significantly lower embedment ratios were observed in sandy soil than
compared to soft clay which suggests limited applications for FFPs in granular
sediments. The results of the field studies indicated that the final embedment ratio of a
FFP was found to be dependent on impact velocity, FFP geometry, FFP mass and soil
type.
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Studies have also been carried out to assess the feasibility of using FFPs as oceanic
waste carriers for the disposal of high-level nuclear waste in ocean abyssal plain
formations (Ove Arup and Partners 1982, Freeman et al. 1984, Freeman and Burdett
1986, Freeman et al. 1988, Murray 1988). Field tests of oceanic waste carriers were
conducted at the Great Meteor East (GME) radioactive waste disposal site in the eastern
Atlantic Ocean (Freeman et al. 1984, Freeman et al. 1988) and the Nares Abyssal Plain
(NAP) in the western Atlantic Ocean (Freeman and Burdett 1986). The field tests
involved various penetrometer types including the European standard penetrator (shown
in Figure 2.3). Results indicated that impact velocities of 30 to 68 m/s were achieved
resulting in tip embedments of 29 to 58 m (8.1 to 16.4 penetrometer lengths) in the soft
seabed sediments encountered at the test sites. Tests were also conducted off the coast
of Antibes in the Mediterranean Sea where the seabed sediment was much stiffer and
stronger than encountered at the GME and NAP test sites resulting in much lower tip
embedments of 9 to 15 m (3.5 to 4.2 penetrometer lengths) (Audibert et al. 2006).
Figure 2.3. European standard penetrometer (after Freeman et al. 1984)
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2.2.2 Laboratory studies
The application of FFP systems for seabed strength characterisation is not widespread
mainly due to uncertainties regarding how to account for strain rate effects (see Section
2.4.3) which are attributed to the high penetration rates achieved by FFPs, in order to
obtain reliable estimates of undrained shear strength. Laboratory studies on model FFPs
have been carried out at 1 g to investigate the possible dependence of strain rate effects
on soil strength (Dayal 1974, Levacher 1985, Akal and Stoll 1995, Chow and Airey
2014), FFP mass (Dayal 1974, Chow and Airey 2014), tip shape (Dayal 1974, Levacher
1985, Chow and Airey 2014), tip diameter (Chow and Airey 2014) and impact velocity
(Dayal 1974, Levacher 1985, Stoll et al. 2007, Chow and Airey 2014). The results of
the studies indicated that strain rate effects are independent of FFP mass and tip
diameter. Levacher (1985) found the influence of tip shape on strain rate effects to be
negligible whereas Dayal (1974) reported results to the contrary. Test results
demonstrated that strain rate effects increase as the undrained shear strength decreases
(Dayal 1974, Chow and Airey 2014). Studies revealed that strain rate effects increase
for tests involving impact velocities of up to v = 6.1 m/s (Dayal 1974, Stoll et al. 2007)
i
and reach a limit at a critical velocity e.g. v > 6.0 m/s (Levacher 1985) or v ≈ 5 m/s
i i
Chow and Airey et al. (2014).
A series of centrifuge tests on oceanic waste carriers were conducted on a 60 mm long,
6 mm diameter, 13 gram projectile at 100 g (6 m long, 0.6 m diameter, 13 t at prototype
scale) in normally consolidated kaolin clay (Poorooshasb and James 1989). The tests
investigated the embedment depth, deformation pattern and degree of hole closure
associated with dynamic installation of the projectile. Results suggested that projectile
tip embedments of at least 30.5 m (at prototype scale) or 5.1 penetrometer lengths were
achievable for an impact velocity of 40 m/s.
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2.3 Dynamically installed anchors
Three types of dynamically installed anchor have been developed: the torpedo anchor
(also referred to as the torpedo pile), the Deep Penetrating Anchor (DPA) and the
OMNI-Max anchor. Each type of anchor has been developed by a different
manufacturer and has slightly different features. These anchors are released from a
designated drop height above the seabed and penetrate to a target depth in the seabed by
the kinetic energy obtained through free-fall (Figure 1.18). Resistance to loading is
predominantly provided by the skin friction developed at the anchor-soil interface.
2.3.1 Torpedo anchor
In 1996 the torpedo anchor was proposed as an efficient anchoring system for flexible
risers and floating vessels in soft seabed sediments. Torpedo anchors comprise of a
tubular steel pile, with or without fins, with a conical tip and filled with scrap chain or
concrete. A mooring line is connected to an omni-directional padeye located at the top
of the anchor (Medeiros 2001, 2002).
Full scale field tests were conducted in the Campos Basin off the east coast of Brazil in
water depths ranging from 200 to 1000 m. Tests were carried out using 12 m long
(finless) torpedo anchors with a 0.762 m diameter and a dry mass of 40.8 t. The anchors
were released from a height of 30 m (2.5 anchor lengths) above the seabed and the
following tip embedments (z ) were reported:
e
29 m (2.4 anchor lengths) in normally consolidated clay;
13.5 m (1.1 anchor lengths) in overconsolidated clay;
15 m (1.3 anchor lengths) in uncemented calcareous sand;
22 m (1.8 anchor lengths) in normally consolidated clay overlain by a 13 m thick
fine sand layer.
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Over 1000 torpedo anchors have been installed in offshore Brazil for the mooring of
flexible risers, MODUs and FPSOs (Wilde 2009). During 2005 the P-50 FPSO became
the first floating facility to be permanently moored using torpedo anchors. The P-50 is
moored with eighteen 98 t torpedo anchors in 1240 m of water at the Albacora Leste
field in the Campos Basin. The anchors were 17 m long with a 1.07 m diameter and four
10 m × 0.9 m fins. (Figure 2.4) (Brandão et al. 2006).
Figure 2.4. 98 t torpedo anchor for the Albacora Leste field in the Campos Basin
(after Brandão et al. 2006)
2.3.2 Deep penetrating anchor
In 1999 the Deep Penetrating Anchor (DPA) was conceived as a cost effective
anchoring solution for mooring floating facilities in soft seabed sediments (Lieng et al.
1999). DPAs comprise of a dart shaped, thick walled steel cylinder with fins (flukes)
attached to its upper section. A mooring line is connected to a padeye located at the top
of the anchor (Figure 2.5).
During 2003 twelve 1:3 reduced scale model DPA field tests were carried out in water
depths exceeding 300 m at the Trondheim fjord which is situated in the west central part
of Norway. The model DPA was 4.4 m long with a dry mass of 2.8 t and instrumented
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]
m
[
e
z
,h
t
p
e
d
t
n
e
m
d
e
b
m
e
p
iT
High estimate
Low estimate
Impact velocity, v [m/s]
i
Figure 2.6. Measured and predicted impact velocities and tip embedment depths
for 1:4 scale model DPA test at Troll Field – grey band denotes range of measured
values (after Strum et al. 2011)
In 2009 two full scale DPAs were installed at the Gjøa Field in the North Sea off the
west coast of Norway in 360 m of water as part of the mooring system for the
TransOcean Searcher MODU. The anchors were 13 m long with four 1 m wide flukes
and a dry mass of 80 t. The DPAs were dropped from heights of 50 m and 75 m (1.2
and 1.7 anchor lengths) achieving impact velocities of 24.5 m/s and 27 m/s respectively,
corresponding to tip embedments of 24 m and 31 m (1.9 and 2.4 anchor lengths) (Lieng
et al. 2010).
2.3.3 OMNI-Max anchor
In 2005 the OMNI-Max anchor was proposed as an anchoring solution for mooring
floating facilities in soft seabed sediments (Zimmerman and Spikula 2005). The OMNI-
Max anchor is arrow shaped with a mooring padeye located at the end of a hinged load
arm which can rotate 360º about the longitudinal axis of the anchor enabling it to be
loaded in any direction (Figure 2.7). The anchors have retractable fluke fins which
allow the anchor to be tailored to rotate into the soil and begin diving at a preferred
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tension level. Once significant load is applied to the anchor it begins to rotate into the
soil until the lateral resistance of the lower fluke fins becomes equal to the lateral
resistance of the upper fluke fins. Once this level of loading is exceeded the anchor
performance is determined by its axial capacity and begins to penetrate deeper into the
seabed mobilising stronger soil and gaining additional capacity (Shelton et al. 2011).
Figure 2.7. OMNI-Max anchor (after Zimmerman et al. 2007)
During 2006 and 2007 full scale OMNI-Max anchor field tests were carried out at
Viosca Knoll in the Gulf of Mexico in 427 m of water using a 9 m long anchor with a 3
m fin span and dry mass of 34 t. The soil at the test site was soft to medium clay and the
anchor was released from a height of 76 m (8.4 anchor lengths) above the seabed. The
test results demonstrated the stability of the anchor during free-fall (Zimmerman 2007).
Over 160 full scale OMNI-Max anchors have been installed in the Gulf of Mexico for
the mooring of MODUs (Shelton et al. 2011).
2.3.4 Laboratory studies
Massey (2000) conducted physical modelling using 1:200 reduced scale model DPAs at
1 g in kaolin clay to investigate the relationship between impact velocity, embedment
depth and holding capacity. Prototype impact velocities of 20 to 25 m/s (Lieng et al.
1999) could not be achieved at 1 g.
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Laboratory tests were conducted at The University of Texas at Austin on 1:30 reduced
scale torpedo anchors at 1 g in kaolin clay to assess the accuracy of an embedment
depth prediction model (see Section 2.5.1) (Audibert et al. 2006, Gilbert et al. 2008).
The embedment depths predicted by the model were generally within +/- 10 % of the
measured (Figure 2.11).
1500
1200
).n)m
m
i(
tn
em(
tn
em 900
d e b m e p it
d
e
tc
id
erPd e b m e p it d
etcid
erP
600
300
0
0 300 600 900 1200 1500
Measured tip embedment (mm)
Measured tip embedment (in.)
Figure 2.11. Comparison of measured and predicted tip embedment depths for
1:30 reduced scale model torpedo anchors in kaolin clay (after Gilbert et al. 2008)
Fernandes et al. (2006) conducted tests on a 1:15 reduced scale model torpedo anchor in
a water tank test to investigate anchor drag coefficient and directional stability. The test
results suggested that the anchor fins and mooring line have a positive effect on
directional stability. The anchor drag coefficient was estimated using an extrapolating
mathematical model.
Cenac Π (2011) conducted free-fall and tow tank tests in water on a 1:24 reduced scale
model OMNI-Max anchors at Texas A&M University to investigate drag coefficients
and embedment depth. The results indicated that the model anchor achieved an average
embedment depth of 1.5 times the anchor length in an artificial mud mixture following
free-fall in water and that the embedment depth increased with an increase in impact
velocity (Figure 2.12).
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Hasanloo et al. (2012) carried out tests on 1:40 reduced scale model torpedo anchors
(Figure 2.14) in a water tank to assess the influence of anchor weight, aspect ratio, scale
ratio and fin size on anchor velocity during free-fall prior to impact with the seabed.
The test results indicated that the directional stability, density ratio, aspect ratio and
scale ratio had a positive impact on the free-fall velocity of the anchors, while the
frontal area and fin length had a negative impact (Figure 2.15).
A centrifuge study was carried out at UWA on a 1:200 reduced scale OMNI-Max
anchor (Figure 2.16) in overconsolidated kaolin clay and calcareous silt from the North
West Shelf of Australia (Gaudin et al. 2013). Impact velocities of 10.4 to 23 m/s were
measured in the tests in the overconsolidated kaolin clay and corresponding embedment
depths in the range 1.18 to 2 anchor lengths (z = 10.7 to 18.1 m in prototype scale).
e
Significantly lower embedment depths of 1.14 to 1.46 anchor lengths (z = 10.3 to 13.2
e
m in prototype scale) were achieved in the calcareous silt despite higher impact
velocities of 20.5 to 29.4 m/s (Figure 2.17). Gaudin et al. (2013) suggested that this was
due to the higher undrained shear strength and potentially dilatant behaviour of the
calcareous silt.
Figure 2.14. 1:40 reduced scale model torpedo anchor (after Hasanloo et al. 2012)
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2.15) between the front and rear of the object which creates a force opposite to the
direction of motion (Hoerner 1965). The fluid drag resistance is generally expressed as
(Morison et al. 1950):
1
F C Av2 Equation 2.1
d 2 d
where C is the drag coefficient of the object, ρ is the fluid density, A is the reference
d
area (e.g. frontal area of the object) and v is the object’s velocity. The drag coefficient is
dependent on the objects geometry, surface roughness and Reynolds number of the
associated flow.
For a Newtonian fluid (e.g. water) the relationship between shear stress and shear strain
is linear and the Reynolds number is defined as (Hoerner 1965):
vD
Re Equation 2.2
where D is the projectile diameter and ν is the kinematic viscosity of the fluid.
During dynamic penetration of a projectile into the seabed, the projectile will transition
from the water into the soil. The viscosity and hence the Reynolds number of the
associated flow will vary from the water to the soil. However, it is commonly assumed
that the drag coefficient of a projectile is the same in both soil and water.
A relatively wide range of drag coefficient values have been reported for seabed
penetrating projectiles, which reflects the variation in projectile geometry and Reynolds
number:
True (1976) suggested a drag coefficient of C = 0.7 to be adopted to account for
d
fluid drag resistance in soil and water for a range of projectile velocities and
geometries.
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Back-analysis of results from field tests on oceanic waste carriers indicated drag
coefficients in the range C = 0.1 to 0.18 (Freeman et al. 1984, Freeman and Burdett
d
1986, Freeman and Murray 1988).
A Computational Fluid Dynamics (CFD) study by Øye (2000) on DPAs suggested a
drag coefficient of C = 0.63 for a four fluke anchor in water.
d
CFD analysis showed that drag coefficient decreases with increasing anchor aspect
ratio, L/d, from C = 0.35 for L/d = 1 (i.e. a sphere) to C = 0.23 for L/d ≥ 4
d d
(representing Reynolds number values of approximately 1×106 to 7×107) for
anchors with no flukes (Richardson 2008).
Fernandes et al. (2006) extrapolated a drag coefficient of C = 0.33 from results of a
d
hydrodynamic study on a 1:15 reduced scale model torpedo anchor and noted that
the mooring line increased the total drag resistance.
Free-fall and tow tank tests on 1:15 reduced scale model OMNI-Max anchors
(Cenac Π 2011) indicated drag coefficients in the ranges: C = 0.46 to 0.83 and C =
d d
0.7 to 1.12 from the free-fall and tow tank tests respectively and demonstrated the
dependence of drag coefficient on Reynolds number (Figure 2.21). Prototype scale
drag coefficients in the range C = 0.65 to 0.87 were estimated from the results. The
d
mooring line was found to increase the drag resistance by up to 13.5%. The drag
coefficient was observed to increase as the anchor fins were retracted.
Results from free-fall tests on 1:40 reduced scale model torpedo anchors (Hasanloo
et al. 2012) of various weight, aspect ratio, scale ratio and fin size indicated drag
coefficients in the range C = 0.2 to 1.2 (representing Reynolds number values of in
d
the range 4.8×105 to 2.16×106), and demonstrated the dependence of drag
coefficient on Reynolds number (Figure 2.21).
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and C is the added mass coefficient.
a
A simplified method for estimating the inertia force is to assume that a constant mass of
fluid (commonly referred to as ‘added mass’) is moving along with the object at the
same acceleration (Fernandes et al. 2006, Kunitaki et al. 2008):
F m a Equation 2.5
i a
where m is the added mass, which is a function of the object’s shape and direction of
a
motion. For slender bodies such as FFPs and dynamically installed anchors the added
mass is considered to be negligible and the inertia force is ignored in motion analysis
(e.g. Beard et al. 1981, Shelton 2011).
2.4.3 Shear strain rate effects in clay
There are two distinct frameworks for predicting the shear strain rate dependence of soil
strength: a soil mechanics framework and a fluid dynamics framework. The soil
mechanics framework generally expresses the soil shear strength using a power or semi-
logarithmic law that accounts for strain rate effects (see Section 2.4.3.1). The fluid
dynamics framework treats the soil as a non-Newtonian fluid and applies fluid
mechanics principles to estimate the soil shear strength (see Section 2.4.3.2). A ‘unified
framework’ that considers both soil mechanics and fluid mechanics principles has
recently been proposed (see Section 2.4.3.3).
2.4.3.1 Soil mechanics framework
The undrained shear strength of soil is considered to be a function of the shear strain
rate,(Casagrande and Wilson 1951, Graham et al. 1983, Sheahan et al. 1996). For
variable rate penetrometers, FFPs and dynamically installed anchors the ‘operational’
shear strain rate is usually taken as the normalised penetration rate, v/d (where v is
velocity and d is diameter, O’Loughlin et al. 2013b). At very high shear strain rates
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viscous effects dominate the undrained shear strength of soil and the undrained shear
strength increases with increasing shear strain rate (Figure 2.22) (Sheahan et al. 1996,
Lunne and Anderson 2007, Jeong et al. 2009). The dependence of the operational
undrained shear strength, s , on shear strain rate is typically accounted for using a rate
u,op
function, R:
f
s R s Equation 2.6
u,op f u
where s is the undrained shear strength at the reference shear strain-rate,γ .The rate
u ref
function is generally expressed as either a semi-logarithmic (e.g. Graham et al. 1983,
Chung et al. 2006) or power function (e.g. Biscontin and Pestana 2001, Lehane et al.
2009):
R 1log Equation 2.7
f
ref
R Equation 2.8
f
ref
where λ and β are strain-rate parameters in the respective formulations representing the
increase in undrained shear strength.
Studies of FFPs have shown that the rate effect of the shaft friction component of
penetrometer resistance is greater than that of the tip resistance component. It is
believed that the higher rate effect for the shaft friction is due to the higher strain rate at
the cylindrical shaft involving curved bands. The greater rate effects can be accounted
for in the power function by adopting a coefficient, n (Dayal and Allen 1975, Steiner et
al. 2014, Chow et al. 2014):
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R n Equation 2.9
f
ref
where n is taken as 1 for tip resistance (Zhu and Randolph 2011) and as a function of β
for estimating rate effects in shaft resistance (Einav and Randolph 2006) according to:
n
n2 1 n 12
Equation 2.10
The strain-rate parameters have been found to be dependent on strain rate range (e.g.
Sheahan et al. 1996, Jeong et al. 2009, O’Loughlin et al. 2013b), projectile geometry
(Dayal 1974, Levacher 1985, Ortman 2008) and soil properties such as: plasticity (e.g.
Bjerrum 1973, Gibson and Coyle 1968, Jeong et al. 2009), moisture content (Gibson
and Coyle 1968, Dayal 1974, Abelev and Valent 2009), stress history (Sheahan et al.
1996, Lehane et al. 2009, Chow and Airey 2013), anisotropy (Nakase and Kamei 1986,
Zhu and Yin 2000) and sensitivity (Yafrate and Dejong 2007).
Figure 2.22. Illustration of viscous effects for normally consolidated and lightly
overconsolidated soils – representative of typical deepwater seabed deposits (after
Lehane et al. 2009)
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O’Loughlin et al. (2013b) back-calculated values of λ and β from results of centrifuge
studies on dynamically installed anchors in normally consolidated kaolin clay
(O’Loughlin et al. 2004a, Richardson et al. 2006, Richardson 2008, O’Loughlin et al.
2009). The strain-rate parameters were typically in the ranges β = 0.06 to 0.17 and λ =
0.2 to 1.0 (indicating a 20 to 100% increase in soil shear strength per log cycle increase
in anchor velocity or penetration rate) (Figure 2.23). The strain rates (proportional to
v/d) in the centrifuge tests are on average 200 times equivalent strain rates in the field,
as the absolute velocities are comparable, but the anchor diameter is scaled by 1:200.
The value of v/d in the centrifuge tests were in the range 500 to 4250 s-1 compared with
v/d ≈ 25 s-1 for a typical dynamically installed anchor in the field (Randolph et al.
2011). Hence the strain-rate parameters representative of field conditions are likely to
be at the lower extreme of this range and would therefore be similar to parameters
deduced from variable rate penetrometer tests.
Gaudin et al. (2013) reported back-calculated strain rate parameters from centrifuge
tests on OMNI-Max anchors in overconsolidated kaolin clay and calcareous silt of β =
0.16 and 0.19 respectively (Figure 2.24). However a fluid drag resistance term was
excluded from the analyses.
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(Aubeny and Shi 2006, Chow and Airey 2013) in clay generally lie in the range λ = 0.05
to 0.25. Variable rate penetrometers tests in kaolin clay indicated β values in the range β
= 0.06 to 0.08 (Lehane et al. 2009). β values derived from shear vane tests (e.g.
Biscontin and Pestena 2001, Peuchan and Mayne et al. 2009, Schlue et al. 2010) in clay
are generally in the range β = 0.05 to 0.12. The power law rate function has been
reported to provide a better fit to experimental data over several log cycles of shear
strain rate than the semi-logarithmic function (Biscontin and Pestena 2001, Peuchan and
Mayne 2007, Randolph et al. 2007 and O’Loughlin et al. 2013b).
The nominal shear strain-rates of triaxial compression tests and in situ shear vane tests
are approximately 3 × 10-6 s-1 and 2 × 10-3 s-1 respectively (Einav and Randolph 2006).
These rates are four and seven orders of magnitude lower than the typical rate of 25 s-1
associated with dynamically installed anchors in the field. Therefore it is difficult to
extrapolate strain-rate parameters from laboratory and in situ tests to be adopted in the
predicting the embedment depth of dynamically installed anchors into the seabed.
2.4.3.2 Fluid mechanics framework
In the fluid mechanics framework the soil is treated as a non-Newtonian fluid and its
stress–strain behaviour is represented by the Herschel-Bulkley model which combines
plastic and shear-thinning effects, and is expressed as (Deglo de Besses et al. 2003):
K Equation 2.11
y
where τ is the mobilised shear stress (essentially equivalent to the operative undrained
shear strength, s ), τ is the yield stress, K represents the viscosity property of the soil
u,op y
(often referred to as the consistency parameter), γ is the shear strain rate and δ is the
shear thinning index. Within this framework the resistance forces are generally
estimated using a form of Equation 2.1 with drag coefficient expressed in terms of the
non-Newtonian Reynolds number, Re (also referred to as Johnson number),
non-Newtonian
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which gives the relative magnitude of pressure drag related resistance or stagnation
pressure to the mobilised shear stress of the soil, τ, and is expressed as (Randolph and
White 2012):
v2
Re Equation 2.12
nonNewtonian
2.4.3.3 Unified framework
The power law model in the soil mechanics framework and the Herschel-Bulkley model
in fluid dynamics framework both represent the variation in mobilised shear stress with
shear strain rate. The shear strain rate effects are predicted using a multiplicative
approach within the soil mechanics framework and an additive approach within the fluid
dynamics framework. Zhu and Randolph (2011) proposed a unified formulation that
originates from the power law model but included an additive term similar to the
Herschel-Bulkley model which can be used to predict the shear strain rate effects of a
soil like material and a fluid-like material. This formulation is referred to as an ‘additive
power-law model’ and is expressed as:
s 1 s Equation 2.13
u,op u,min
ref
where s is the operative undrained shear strength, η represents the viscosity property
u,op
of the soil,γ is operational shear strain rate,γ is the reference shear strain rate, η
ref
represents the viscosity property of the soil, δ is the shear thinning index, s is the
u,min
minimum undrained shear strength at zero strain rate, while the reference undrained
shear strength is given by:
s 1s Equation 2.14
u u,min
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Equation 2.13 is essentially equivalent to the Herschel-Buckley model with s = τ , β
u,min y
= δ and s K. The ‘additive power-law model’ focuses on the viscous
u,min ref
component of resistance attributed to strain rate effects but neglects the pressure drag
component of fluid drag resistance which is independent of viscous effects and related
to the stagnation pressure, P :
stag
1
P P v2 Equation 2.15
stag stat 2
where P is the static pressure and 1/2ρv2 term is the dynamic pressure.
stat
However Zhu and Randolph (2011) noted that for high velocity, low soil strength
conditions (i.e. Re > 10) the pressure drag component starts to dominate the
non-Newtonian
fluid drag resistance and needs to be accounted for separately from the viscous
component.
Randolph and White (2012) proposed to express the forces exerted by a submarine land
slide on a pipe using the power law from the soil mechanics framework and a fluid drag
resistance term with a fixed drag coefficient (i.e. independent of strain rate effects) for
high velocity low soil strength conditions. This superposition approach treats the forces
that arise from the shear strain rate dependent strength and pressure drag separately
rather than combining them into a single term. Randolph and White (2012) expressed
the total normal force, F , acting per unit length of the pipe as:
n
1
F N s D C D v2 Equation 2.16
n p u,op p 2 d p
where C is the drag coefficient, ρ is the fluid density, v is the flow velocity, D is the
d p
pipe diameter, N is the bearing factor for the force normal to the pipeline, s is the
p u,op
operative undrained shear strength estimated using the power law. Randolph and White
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(2012) observed that the relative magnitude between the two components in Equation
2.16 are such that the fluid drag resistance term starts to dominate when the non-
Newtonian Reynolds number exceeds a boundary value of Re ≈ 10. Sahdi et
non-Newtonian
al. (2014) demonstrated that for non-Reynolds numbers higher than the boundary value
the resistance associated with the pressure drag increases linearly with non-Newtonian
Reynolds number and can be accounted for using a constant mean drag coefficient.
Studies involving assessment of the impact forces exerted by high velocity submarine
slides on pipelines (e.g. Boukpeti et al. 2012, Randolph and White 2012, Sahdi et al.
2014) and dynamically installed anchors (e.g. O’Loughlin et al. 2004a, Fernandes et al.
2006, Audibert et al. 2006, Richardson et al. 2006, Richardson 2008, O’Loughlin et al.
2009, Shelton et al. 2011, O’Loughlin et al. 2013b) have adopted the superposition
approach.
2.5 Embedment depth prediction
2.5.1 Analytical modelling
True (1976) proposed a method for predicting the dynamic embedment of projectiles
penetrating in soil after free-fall in water which considered Newton’s second law of
motion and the forces acting on the projectile during dynamic embedment. The method
considers the static forces resisting projectile embedment (Figure 2.20), remoulding of
the soil on the sides of the projectile and fluid drag resistance as the projectile passes
through the soil:
d2z
m W F F F Equation 2.17
dt2 s frict bear d
where m is the projectile mass, z is the projectile tip embedment, t is time, W is the
s
submerged weight of the projectile (in soil), F is frictional resistance and F is
frict bear
bearing resistance and F is the fluid drag resistance (see Section 2.4).
d
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The dynamic embedment of a projectile in soil is calculated using a finite difference
approximation of Equation 2.17.
The frictional and bearing resistance terms are expressed as:
F s A Equation 2.18
frict u
F N s A Equation 2.19
bear c u
where α is a friction ratio (of limiting shear stress to undrained shear strength), N is the
c
bearing capacity factor for the projectile tip or fins (front and reverse end bearing) and
s is the undrained shear strength averaged over the contact area, A. Typically, during
u
dynamic penetration of projectiles in soil, the frictional resistance generated along the
wall of the foundation is close to the remoulded shear strength of the clay and the
friction ratio is often expressed as (Andersen et al. 2005):
1 s
u,r Equation 2.20
S s
t u
where S is the soil sensitivity and s is the remoulded strength of the soil.
t u,r
The estimation of N has been influenced by the use of either shallow foundation
c
bearing capacity solutions or quasi-static cone penetrometer test interpretation methods.
Typically a constant N value is adopted for the projectile tip such as N = 12 (Beard
c c
1977, O’Loughlin et al. 2004a, Richardson 2008, O’Loughlin et al. 2009, O’Loughlin et
al. 2013b), 15 (Freeman and Schuttenhelm 1990), 10 (Mulhearn et al. 1998), 17 (Gilbert
et al. 2008) and 14 (Steiner et al. 2012, Steiner et al. 2014). N = 7.5 has been adopted
c
for the upper and lower end of dynamically installed fins (Richardson 2008, O’Loughlin
et al. 2013b) which is based on a solution for a deeply embedded strip footing
(Skempton 1951). Numerical studies tend to express N as a function of embedment
c
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ratio (e.g. Aubeny and Shi 2006, Abelev et al. 2009b). Nazem et al. (2012) expressed N
c
as a function of Rigidity Index, G/s (G is the shear modulus) in addition to the
u
embedment ratio.
Numerous studies on free-falling penetrometers (e.g. Beard 1981, Levacher 1985,
Mulhearn et al. 1998, Bowman et al. 2005, Aubeny and Shi 2006, Abelev et al. 2009b,
Strak et al. 2012, Chow 2013) and dynamically installed anchoring systems (e.g.
O’Loughlin et al. 2004a, Audibert et al. 2006, Richardson et al. 2005, Richardson et al.
2006, Gilbert et al. 2008, Richardson 2008, O’Loughlin et al. 2009, Shelton et al. 2011,
Gaudin et al. 2013, O’Loughlin et al. 2013b) have adopted True’s method for predicting
the embedment of projectiles penetrating the seabed, with slight variations on the
inclusion and formulation of forces acting on the projectile during penetration. Many
studies have included the shear strain rate function, R (see Section 2.4.3.1). Added
f
mass (see Section 2.4.2) has been considered in a limited number of studies (e.g.
Fernandes et al. 2006, Kunitaki 2008). Aubeny and Shi (2006) and O’Loughlin et al.
(2013b) assumed that a cylindrical void forms in a projectile’s wake during dynamic
embedment into soil and accounted for this with the inclusion of a soil buoyancy term,
F (included as a negative quantity on the right hand side of Equation 2.17):
b
F 'V Equation 2.21
b s
where γ' is the submerged weight of the soil and V is the volume of soil displaced by
s
the projectile. This assumption is supported by radiographs of centrifuge clay samples
by Poorooshasb and James (1989) showing open pathways in the wake of dynamically
installed cylindrical projectiles (despite closed entrance craters).
2.5.2 Numerical modelling
Einav et al. (2004) conducted finite difference numerical analyses to model dynamic
penetration of DPAs through the soil stratum. The finite difference model employed a
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rigid-deformable contact formulation in an explicit time-marching large strain
Lagrangean analysis and incorporated a separate equation of motion to solve the
incremental changes in velocity of the DPA (Einav et al. 2004). Both rate-dependent
and rate-independent models were developed. The rate dependent model adopted a
semi-logarithmic rate function (Equation 2.7). The influence of fluid drag resistance and
added mass were not considered in the model. The results of the numerical analyses
showed good agreement with experimental results from centrifuge tests on DPAs
(O’Loughlin et al. 2004b).
Raie et al. (2009) describes the development of a computational procedure to predict the
embedment depth of torpedo anchors. The procedure uses a CFD model for the
evaluation of the resistance forces acting on torpedo anchors during installation. The
soil is modelled as a non-Newtonian Bingham plastic fluid with a non-zero shear stress
at zero strain-rate. The model is capable of simulating the anchor motion during free-fall
in water and soil penetration. In addition the model also predicts the pressure and shear
distributions on the soil-anchor interface and in the soil. Good agreement was achieved
between the CFD model, results from laboratory tests of a FFP (True 1976) and field
tests of a full scale torpedo anchor (Medeiros 2002).
Strum et al. (2010) carried out large deformation finite element (LDFE) analyses to
simulate the penetration of 1:3 reduced scale DPA in clay. Anchor penetration was
modelled in a simplified manner by means of quasi-static, implicit and updated
Lagrangian analysis employing a finite-slip contact formulation along the soil anchor
interface. The LDFE model simulates the stress and excess pore water pressure
distribution during installation. The model results showed that there is an increase in
normalised mean stress and radial stress at the mid-height of the anchor following
installation which is about half the value given by cavity expansion theory for the same
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problem. Results indicated that a considerable zone of remoulded clay forms along the
anchor after installation.
The Arbitrary Lagrangian Eulerian (ALE) method of finite element analyses has been
used to model the dynamic penetration of FFPs into soil (Nazem et al. 2001, Abelev et
al. 2009b, Carter et al. 2010, Nazem et al. 2012, Carter et al. 2013). The ALE method
eliminates severe mesh distortion due to large deformations by relocating nodal points
on all material boundaries followed by a static analysis. Carter et al. (2013) adopted the
ALE method to simulate the penetration of a 1,000 kg torpedo anchor into soft seabed
sediments. The soil behaviour was represented by an elastoplastic Tresca material
model with an associative flow rule. Rate dependency of the soil was modelled using a
semi-logarithmic rate function. The influence of fluid drag resistance was not
considered in the model. The model results indicated that the forces acting on the
anchor due to soil resistance during penetration increase approximately linearly with
depth for a linear shear strength gradient. It was also observed that these forces vary
with time and hence the deceleration of the torpedo is not constant but position
dependent.
Hossain et al. (2013) conducted LDFE analyses using Coupled Eulerian-Lagrangian
(CEL) to simulate the dynamic installation of torpedo anchors. Two interesting aspects
of the soil flow mechanism during anchor installation were revealed: (i) downward soil
flow concentrating around the advancing anchor reduced gradually with reducing
penetration velocity and more rapidly with increasing number of anchor fins and anchor
projected area, and (ii) mobilisation of an end bearing mechanism at the base of the
anchor as well as the fins with the latter reduced significantly for shorter fins.
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2.6 Summary
The dynamic embedment of projectiles into the seabed has previously been considered
in studies of FFPs and dynamically installed anchoring systems. Three types of
dynamically installed anchor have been developed: the torpedo anchor, the Deep
Penetrating Anchor, DPA and the OMNI-Max anchor. Full scale dynamically installed
anchors have been installed in the Campos Basin off the coast of Brazil (torpedo
anchors), in the North Sea off the coasts of Norway (DPAs) and in the Gulf of Mexico
(OMNI-Max anchors). Extensive centrifuge and 1 g modelling has been conducted on
dynamically installed anchors. With the exception of a few limited studies there is little
published field data on dynamically installed anchors. Furthermore a wide range of drag
coefficients and strain rate parameter values have been reported for dynamically
installed anchors from physical model tests.
An analytical method often referred to as ‘True’s method’ is commonly adopted to
predict the dynamic embedment of projectiles in soil that considers Newton’s second
law of motion, the static forces resisting projectile embedment, rate effects, soil
remoulding and fluid drag resistance. However, there have been significant variations
on the inclusion and formulation of forces considered in True’s method.
Hence, there is a clear requirement for an experimental study to ascertain the drag
coefficient and strain rate parameter values that best represent DEPLA behaviour during
free-fall in water and dynamic embedment in soil. These values will facilitate
refinement and calibration of True’s method for prediction of DEPLA embedment,
which is a prerequisite for estimating anchor capacity.
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CHAPTER 3 CAPACITY OF PLATE ANCHORS
3.1 Introduction
The capacity of direct embedment plate anchors such as the DEPLA is primarily
dependent on: (i) the surrounding shear strength of the soil, acknowledging that the
embedment depth loss due to the keying process may reduce the relevant value (see
Section 3.2), and (ii) the bearing capacity factor of the plate (see Section 3.3). There
have been numerous analytical, numerical and laboratory studies on (i) and (ii).
However, there are very little reported field data on the performance of plate anchors to
verify the findings of these studies.
3.2 Keying
During the keying process the anchor embedment depth reduces as the plate rotates.
Since offshore clay deposits are typically characterised by an increase in shear strength
with depth, a reduction in anchor embedment depth will correspond to a non-
recoverable loss in potential anchor capacity (Randolph et al. 2005, Gaudin et al. 2009,
Cassidy et al. 2012). Naval Civil Engineering Laboratory guidelines (NCEL 1985)
states that the embedment depth loss, Δz , due to the keying process is
e,plate
approximately twice the anchor height, B, in cohesive soils, and is a function of anchor
geometry, soil type, soil sensitivity and duration of time between installation and
keying. However results from onshore and offshore SEPLA field tests reported by
Wilde et al. (2001) indicated embedment depth loss in the range Δz = 0.5 to 1.7B.
e,plate
The embedment depth loss of plate anchors during the keying process has been
investigated through centrifuge model tests (O’Loughlin et al. 2006, Gaudin et al. 2006,
Song et al. 2006, Song et al. 2007, Gaudin et al. 2009, Gaudin et al. 2010), LDFE,
analyses (Song et al. 2005, Song et al., 2008a, Wang et al. 2008a, Song et al. 2009, Yu
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et al. 2009, Wang et al. 2011, Wang et al. 2013a, Wang et al. 2013b), small strain finite
element analyses (Tian et al. 2013) and plastic limit analyses (Cassidy et al. 2012, Yang
et al. 2012). These studies assessed factors that may influence the keying behaviour of
plate anchors such as: installation method, padeye eccentricity ratio, pullout angle, soil
properties, anchor thickness ratio, anchor submerged unit weight, anchor aspect ratio,
anchor roughness, anchor keying flap and padeye offset. The author believes that the
most influential of these factors is padeye eccentricity ratio, and as such great
consideration should be given to this factor during design, in order to achieve optimal
anchor performance. The effect of anchor keying flap and padeye offset on keying
behaviour are not considered here as these features are incompatible with the DEPLA
geometry currently proposed.
3.2.1 Installation method
Centrifuge tests on SEPLAs in kaolin clay showed that embedment depth loss is lower
for suction embedded anchors (Δz = 0.9 to 1.3B, where B is plate width) than for
e,plate
jacked-in anchors (Δz = 1.3 to 1.5B) due to the reduced amount of soil disturbance
e,plate
during suction installation (Gaudin et al. 2006). Considerably lower embedment depth
loss was observed by Song et al. (2007) during centrifuge tests in ‘synthetic’ uniform
clay for both a suction embedded anchor (Δz = 0.23B) and a jacked-in anchor
e,plate
(Δz = 0.27B). Song et al. (2007) proposed that this is due to the difference in
e,plate
strength profiles of the kaolin clay and synthetic clay.
3.2.2 Padeye eccentricity ratio
Centrifuge tests (O’Loughlin et al. 2006) and LDFE analyses (Wang et al. 2008a, Song
et al. 2009, Yu et al. 2009, Wang et al., 2011) indicated that the embedment depth loss
of plate anchors during keying is primarily a function of the padeye eccentricity ratio,
e/B (Figure 3.1). These studies suggested that embedment depth loss may be minimised
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)
(
p
θ
,n
o
ita
to
r
e
ta
lP
Normalised embedment depth loss, Δz /B
e,plate
Figure 3.9. Influence of anchor roughness on the keying behaviour (after Song et
al. 2009)
3.2.8 Anchor geometry coefficient
Song et al. (2009) showed that the normalised embedment depth loss, Δz /B, for a
e,plate
vertical pullout may be expressed in terms of a non-dimensional anchor geometry
coefficient of the form (Figure 3.10):
z e t 0.3 M 0.1
e,plate f 0 Equation 3.1
B BB A Bs
p u0
where is the e is the padeye eccentricity, t is the anchor thickness, M is the initial
0
moment corresponding to zero net vertical load, A is the projected area of the anchor
p
perpendicular to the direction of load, B is the anchor height and s is the soil shear
u0
strength at the initial anchor embedment depth. The anchor geometry coefficient
showed good agreement with centrifuge test results (Gaudin et al. 2009) and LDFE
analyses results using the expression (Song et al. 2009):
z 0.15
e,plate Equation 3.2
B
e t
0.3
M
0.1
0
BB A Bs
p u0
Song et al. (2009) recommended an anchor geometry coefficient of at least 0.3 or
conservatively 0.4 to minimise the normalised embedment depth loss to Δz /B ≤ 0.5.
e,plate
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3.3 Capacity
The ultimate vertical pullout capacity of plate anchors is typically expressed in terms of
a bearing capacity factor or ‘break out’ factor (Das and Singh 1994, Merifield et al.
2003, Gaudin et al. 2006, Song et al. 2008b, Wang et al. 2010):
F
N v,net Equation 3.4
c A s
p u,p
where F is the ultimate vertical pullout capacity of plate anchors minus the
v,net
submerged weight of the anchor in soil, s is the undrained shear strength at the anchor
u,p
embedment depth (anchor mid-depth) corresponding with the ultimate capacity and A
p
is the projected area of the plate.
3.3.1 Failure mechanism
Plate anchors can be classified as ‘shallow’ or ‘deep’ depending on the failure
mechanism. An anchor is classified as shallow if the failure mechanism reaches the soil
surface at ultimate collapse or deep if the failure mechanism is localised shear around
the anchor and does not extend to the soil surface (see Figure 3.11). At the critical
embedment depth, z , the failure mechanism becomes localised and the bearing
cr
capacity factor of the anchor no longer increases with embedment depth (Figure 3.11,
Merifield et al. 2003, Thorne et al. 2004, Song et al. 2006, Gaudin et al. 2006), as the
undrained shear strength is assumed to be independent of the mean normal stress
(Merifield et al. 2001, 2003, 2005).
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N N N
c1 c2 c
z
1
z
2
z
cr
B
(a) B
(b)
‘Deep’
N
c (c)
N
c
N
c2
N
c1
Figure 3.11. Shallow and(d )deep anchor behaviour
3.3.2 Suction
Negative pore water pressure will usually develop below a plate anchor during loading
due to the low permeability of clays coupled with a high loading rate. This generates a
tensile force known as suction on the back face of the plate. Suction increases with the
differential pressure on the top and bottom faces of the plate (Shin et al. 1994). The
suction force developed between the anchor and soil is a function of the embedment
depth, soil permeability, undrained shear strength and loading rate (Merifield et al.
2001, Thorne et al. 2004, Song et al. 2008b). Following Rowe and Davis (1982) most
studies into the capacity of plate anchors in clay consider two distinct cases:
‘breakaway’ or ‘no breakaway’. For the breakaway or ‘vented’ case it is assumed that
interface between the soil and the back face of the plate cannot sustain sufficient suction
and either the soil separates from the anchor at the start of pullout (immediate
breakaway) if no initial stresses are considered or separates during pullout if initial
compressive stresses are considered. For the no breakaway or ‘attached’ case it is
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assumed that the interface between the soil and the back face of the plate can sustain
sufficient suction and the soil remains attached to the back of the plate throughout
pullout. The depth at which the anchor becomes vented is known as the ‘separation
depth’, z .
s
3.3.3 Previous studies
A number of studies have proposed simple approximate methods to estimate the bearing
capacity factors of plate anchors in clay (Adam and Hayes 1967, Ali 1968, Meyerhof
and Adams 1968, Vesic 1971, Meyerhof 1973, David and Sunderland 1977,
Kupferman, 1971, Das 1978, Das 1980, Ranjan and Arora 1980, Das 1985a, Das 1985b,
Das and Puri 1989, Das et al. 1994). The majority of these studies estimate anchor
capacity through simple analytical solutions or empirical correlations based on
laboratory model test conducted under normal gravity (1 g). However small-scale 1 g
laboratory models cannot replicate the effect of in situ overburden pressure.
Rowe and Davis (1982) carried out small strain elasto-plastic finite element analyses to
estimate the bearing capacity factors of strip anchors in homogeneous clay. However no
ultimate capacity was achieved; instead, truncated capacities were derived using elastic
reasoning. The lower and upper bound bearing capacity factors for the no breakaway
condition were found to be N = 10.28 and 11.42 respectively.
c
Yu (2000) derived an expression for N based on accurate analytical solutions for cavity
c
expansion in cohesive-frictional soil. It was assumed that breakout occurs if the
boundary of the plastic zone predicted by cavity expansion theory was sufficiently close
to or on the ground surface (when the plastic flow was not confined by the outer elastic
zone).
Martin and Randolph (2001) carried out plasticity limit analysis of deep ultra-thin
circular plates in clay assuming no breakaway which produced exact solutions for
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bearing capacity factors of N = 13.11 and 12.42 for fully rough and smooth plates
c
respectively.
The bearing capacity factors of strip, circular and square anchors in homogeneous and
nonhomogeneous soils assuming no breakaway condition were investigated by
Merifield et al. (2001, 2003, 2005) through finite element formulations of limit analyses
based on rigid plastic soil response. Limiting bearing capacity factors for rough strip
anchors were found to be N = 10.47 (lower bound) and 11.16 (upper bound) with lower
c
bound values for rough circular and square anchors reported as N = 12.56 and 11.9
c
respectively. Results suggest that the N increases linearly with overburden pressure up
c
to a limiting value that corresponds with the transition from shallow to deep anchor
behaviour and that this value can be expressed as a function of overburden stress ratio,
γz/s (Figure 3.12).
u
Song et al. (2005) investigated the bearing capacity factors of strip anchors in uniform
clay through LDFE. For the attached condition the anchor reached a limiting bearing
capacity factor of N = 12 at a critical embedment ratio of z /B =3. No limiting bearing
c cr
capacity was reached for the vented condition even for z /B = 10 albeit in weightless
cr
soil. The influence of plate angle, θ , was only found to be significant for embedment
p
ratio z/B ≤ 3 where N decreased with increasing pullout angle (measured relative to the
c
horizontal) (Figure 3.13). In Figure 3.12 and Figure 3.13 the point at which N starts to
c
reduce represents z .
cr
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k = 1, θ = 90
p
k = 1, θ = 45
p
k = 1, θ = 0
p
Uniform, s /γ'B = 0.36, θ = 90
u p
Uniform, s /γ'B = 0.36, θ = 45
u p
Uniform, s /γ'B = 0.36, θ = 0
u p
Uniform, s /γ'B = 0.89, θ = 90
u p
Uniform, s /γ'B = 0.89, θ = 45
u p
Uniform, s /γ'B = 0.89, θ = 0
u p
z/B
Figure 3.16. Influence of normalised strength ratio on bearing capacity factor
(after Song et al. 2008a)
Song et al. (2008b) investigated the bearing capacity factors of strip and circular plates
in uniform and normally consolidated through small strain and large strain deformation
finite element analyses. The bearing capacity factors assuming no breakaway condition
were found to be N = 11.6 (smooth) and 11.7 (rough) for deep strip anchors and N =
c c
13.1 (smooth) and 13.7 (rough) for deep circular anchors. When the breakaway
condition was considered the soil remained attached to the back face of the plate for
deep anchors and the bearing capacity was the same as for the no breakaway condition
(Figure 3.17). The separation depth was found to be dependent on s /γ'B (Figure 3.18).
u
Wang et al. (2008b) showed through LDFE analyses that the bearing capacity of strip
anchors in normally consolidated clay decreases with increased loading rate for a given
initial embedment depth (Figure 3.19), until the loading rate approaches a critical value
which represents the undrained condition.
Yu et al. (2009) conducted 3-D LDFE analyses to assess the bearing capacity factor of
strip and square anchors in normally consolidated and uniform clay assuming the
attached condition. Results of the study showed that N increased with increased e/B
c
(Figure 3.20) and that θ has minimal effect on N (Figure 3.21).
pull c
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Yang et al. (2012) conducted plastic limit analyses to examine the effect of the keying
flap on the capacity of rectangular SEPLAs in normally consolidated clay. The
theoretical bearing capacity factor achieved by a SEPLA with a flap (N = 12.79) was
c
higher than a SEPLA without a flap (N = 11.67) as the flap increases the bearing area.
c
Cassidy et al. (2012) implemented plastic limit analyses to predict the bearing capacity
factors of plate anchors using a plasticity model termed ‘chain and SEPLA plasticity
analysis’ (CASPA). The CASPA results showed good agreement with comparable
LDFE analyses and centrifuge tests. The study investigated the optimal vertical position
of the padeye to maximise N . Results indicated that the padeye offset results in two
c
opposing phenomenon: (i) A gain in capacity resulting from a reduced loss of
embedment (ii) A reduction in capacity due to the inclination of the anchor in respect of
the pullout direction. Cassidy et al. (2012) concluded that the extent to which the gain
resulting from the first aspect compensates the loss from the second aspect is a function
of the shear strength gradient and the initial embedment depth.
Zhang et al. (2012) carried out a parametric study to assess the undrained bearing
capacity of deeply embedded flat circular footings under general loading. The study
showed that N significantly increases with thickness ratio, with N for t/D = 1 being
c c
58% greater than for t/D =0.05 (Figure 3.29). Zhang et al. (2012) suggests that this trend
is due to the increased friction along the vertical footing-soil interface as t/D increases
and that the increased t/D deters the soil from flowing around from below the footing
through the footing edge to the top forcing the soil to take a deeper and longer route to
flow around thus mobilising more soil in the mechanism which increases foundation
capacity.
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3.4 DEPLA capacity
Wang and O’Loughlin (2014) assessed the bearing capacity factors of circular,
diamond, square and rectangular DEPLAs in normally consolidated clay through 3-D
LDFE. Results of the numerical analyses were validated by benchmarking with existing
numerical and analytical solution for circular and rectangular plate anchors. The effect
of anchor embedment depth, anchor roughness, fluke thickness, plate inclination and
anchor geometry on N were investigated assuming the attached condition. Results
c
indicated that the limiting bearing capacity factor associated with deep behaviour
occurred at a normalised embedment depth, z/D = 2.5 for circular, diamond, square and
rectangular DEPLAs under the attached condition and subject to vertical load (Figure
3.34). The limiting bearing capacity factors were found to be N =14.9 for square and
c
circular DEPLAs, N = 15 for a diamond geometry and N = 15.4 to 13.6 for rectangular
c c
DEPLAs with L/B = 0.5 and 2 respectively. The N for the rectangular DEPLA with
c
L/B = 0.5 was attributed to the geometrical difference related to the direction of the
sleeve and the relative height of the plate. Plate roughness (Figure 3.35) and fluke
thickness (Figure 3.36) were found to have a relatively small effect on N . Result
c
showed that plate inclination has a considerable effect on N (Figure 3.37), particularly
c
for shallow embedment ratios. N for a circular DEPLA at z/D = 1 (shallow) reduced by
c
23.4% as the plate inclination changed from vertical to horizontal, compared with a
1.3% reduction for z/D = 4 (deep). Analyses were also conducted where soil separation
was permitted, the results of which suggested that the bearing capacity factors of
DEPLAs approach the no breakaway values when z/D increases and s (relative to the
u
unit weight of the soil) decreases (Figure 3.38).
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CHAPTER 4 INSTALLATION AND CAPACITY OF
DYNAMICALLY EMBEDDED PLATE
ANCHORS AS ASSESSED THROUGH
CENTRIFUGE TESTS
4.1 Abstract
The dynamically embedded plate anchor (DEPLA) is a rocket or dart shaped anchor that
comprises a removable central shaft and a set of four flukes. Similar to other
dynamically installed anchors, the DEPLA penetrates to a target depth in soft seabed
sediments by the kinetic energy obtained through free-fall in water and the self-weight
of the anchor. In this chapter DEPLA performance was assessed through a series of
beam centrifuge tests conducted at 200 times earth’s gravity. The results show that the
DEPLA exhibits similar behaviour to other dynamically installed anchors during
installation, with tip embedments of 1.6 to 2.8 times the anchor length. After anchor
installation the central shaft of the DEPLA, termed a follower, is retrieved and reused
for the next installation, leaving the DEPLA flukes vertically embedded in the soil. The
load-displacement response during follower retrieval is of interest, with mobilisation of
frictional and bearing resistance occurring at different rates. The load required to extract
the DEPLA follower is typically less than three times its dry weight. The vertically
embedded DEPLA flukes constitute the load bearing element as a circular or square
plate. The keying and pullout response of this anchor plate is similar to other vertically
embedded plate anchors, with an initial stiff response as the anchor begins to rotate,
followed by a softer response as the rotation angle increases, and a final stiff response as
the effective eccentricity of the padeye reduces and anchor capacity is fully mobilised.
For the padeye eccentricity ratios considered (0.38 to 0.63 times the plate breadth or
diameter), the loss in plate anchor embedment is between 0.50 and 0.66 times the
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corresponding plate breadth or diameter. Finally, the bearing capacity factors
determined experimentally are typically in the range 14.2 to 15.8 and are higher than
numerical solutions for flat circular and square plates. This is considered to be due to
the cruciform fluke arrangement which ensures that the failure surface extends to the
edge of the orthogonal flukes and mobilises more soil in the failure mechanism.
4.2 Introduction
Floating oil and gas installations in deep water require anchoring systems that can
withstand high components of vertical load, whilst being economical to install. Deep
water installations are typically moored using either (drag embedded) vertically loaded
plate anchors (VLAs) or suction caissons, although a number of other anchoring
systems such as suction embedded plate anchors and dynamically installed anchors
(Brandão et al. 2006, Zimmerman et al. 2009) have been used with effect in recent
years. Predicting plate anchor capacity for a given embedment is generally
straightforward as it is a function of the local undrained shear strength, the projected
area of the plate and a dimensionless bearing capacity factor, which for deeply
embedded plates is typically in the range 11.7 to 14.3 depending on plate geometry and
roughness (Merifield et al. 2003, Song et al. 2005, Song et al. 2008b). However
predicting the anchor installation trajectory and hence final embedment depth is more
challenging and requires accurate shear strength data over a wide seabed footprint
(Ehlers et al. 2004). Suction caissons are advantageous in this regard as embedment is
monitored and controlled, although successful prediction of the ultimate holding
capacity must account for a number of factors including the caisson geometry and
padeye location, loading angle, time effects and the integrity of the internal seal
provided by the soil plug (Randolph et al. 2011). Several of the disadvantages of these
two anchor types have been mitigated by the suction embedded plate anchor (SEPLA)
described by Wilde et al. (2001). The SEPLA employs a suction caisson to install a
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vertically oriented plate anchor. After installation the follower is removed (and reused)
and the embedded plate is rotated or keyed so that it becomes normal or near normal to
the load applied by the mooring chain.
Anchor installation operations become increasingly more complex, time-consuming and
hence costly as water depth increases. However, this is not the case with dynamically
installed anchors as no external energy source or mechanical operation is required
during installation. Dynamically installed anchors are rocket or torpedo shaped and are
designed so that, after release from a designated height above the seafloor, they will
penetrate to a target depth in the seabed by the kinetic energy gained during free-fall.
Centrifuge model tests indicate that in normally consolidated clay, expected penetration
depths are 2 to 3 times the anchor length and expected anchoring capacities are 3 to 5
times the anchor dry weight (O’Loughlin et al. 2004b). In contrast, expected anchoring
capacities for vertically loaded plate anchors are typically 30 to 40 times the anchor dry
weight in very soft clay.
A new anchoring system, termed the dynamically embedded plate anchor (DEPLA)
combines the advantages of dynamically installed anchors and vertically loaded anchors
in much the same way as the SEPLA combines the advantages of suction caissons with
VLAs. The DEPLA is a rocket or dart shaped anchor that comprises a removable central
shaft or ‘follower’ that may be fully or partially solid and a set of four flukes (see Figure
1.17). A stop cap at the upper end of the follower prevents it from falling through the
DEPLA sleeve and a shear pin connects the flukes to the follower. As with other
dynamically installed anchors the DEPLA penetrates to a target depth in the seabed by
the kinetic energy obtained through free-fall. After embedment the follower line is
tensioned, which causes the shear pin to part allowing the follower to be retrieved for
the next installation, whilst leaving the anchor flukes vertically embedded in the seabed.
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The embedded anchor flukes constitute the load bearing element as a plate anchor. A
mooring line attached to the embedded flukes is then tensioned, causing the flukes to
rotate or ‘key’ to an orientation that is normal or near normal to the direction of loading.
In this way, the maximum projected area is presented to the direction of loading,
ensuring that maximum anchor capacity is achievable through bearing resistance. The
installation and keying processes are shown schematically on Figure 1.18 and Figure
1.19 respectively.
This chapter provides DEPLA performance data through a series of centrifuge tests that
were designed to quantify expected embedment depths and plate anchor capacities.
4.3 Centrifuge testing program
The centrifuge tests were carried out at 200 g using the fixed beam centrifuge at UWA.
The UWA beam centrifuge is a 1.8 m radius Acutronic centrifuge with a maximum
payload of 200 kg at 200 g (Randolph et al. 1991). All parameters presented in this
chapter are expressed in model scale. Table 4.1 presents the scaling laws required for
conversion from model scale to prototype scale.
Table 4.1. Centrifuge scaling laws (after Scholfield 1980, Taylor 1995)
Parameter Scaling relationship
(model/prototype)
Acceleration n
cent
Length 1/n
cent
Area 1/n 2
cent
Volume 1/n 3
cent
Mass 1/n 3
cent
Stress 1
Strain 1
Force 1/n 2
cent
Velocity 1
Density 1
Time (consolidation) 1/n 2
cent
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4.3.1 Model anchors
The model DEPLAs used in the centrifuge tests comprised a set of DEPLA flukes
(which form the plate anchor after the follower is retrieved), a DEPLA follower and
anchor lines connected to the follower and plate anchor padeyes. An interchangeable
modular design for the follower (ellipsoidal tip, shaft, padeye) allowed various steel and
aluminium sections to be combined to form different overall follower lengths and
masses, although the follower diameter and ellipsoidal tip length remained constant at
D = 6.0 mm and L = 11.4 mm (Figure 4.1). The overall length of the follower (and
f tip
hence height of the anchor) used in the centrifuge tests was either 51.5 mm, 76.0 mm or
101.5 mm, which at 200 g corresponds to equivalent prototype heights of 10.3 m, 15.2
m and 20.3 m respectively.
The flukes were fabricated from 0.8 mm thick steel and the sleeve from 0.75 mm thick
copper (rather than steel) to permit soldering of the flukes to the sleeve without
inducing high temperatures. The outer diameter of the sleeve is 7.8 mm, which, together
with the sleeve wall thickness of 0.75 mm, gave a nominal clearance of 0.15 mm
between the 6.0 mm diameter follower and the sleeve. The DEPLA flukes that formed
the plate anchor element were either circular or square, with the latter oriented in a
diamond shape on the DEPLA sleeve (Figure 4.1), so as to reduce drag and to increase
the eccentricity of the anchor padeye (load attachment point). The diameter, D, or
breadth, B, of the DEPLA flukes varied between 16 mm and 37.6 mm, which
correspond to 3.2 m to 7.5 m in equivalent prototype scale. The plate anchor padeye
was located at an eccentricity, e, from the central axis of the plate, such that the
eccentricity ratio was in the range e/D = 0.38 to 0.46 for the circular plates and e/B =
0.63 for the square plate. Details of the six model anchors employed for the centrifuge
tests are summarised in Table 4.2 and shown on Figure 4.1.
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Figure 4.1. 1:200 reduced scale DEPLAs
Both the follower and plate anchor lines were modelled using uncoated stainless steel
wire of 0.90 mm diameter (180 mm in prototype scale) and a tensile capacity of 660 N.
This line was selected due to its flexibility, high tensile strength and resistance to
stretching. The follower line was attached to the padeye located at the top of the
follower, whereas the plate anchor line was connected to the plate anchor padeye
located on one of the anchor flukes. The other extremity of each anchor line was
connected via a 1.7 kN load cell to the actuator that effected the follower recovery and
the plate anchor pullout.
Table 4.2. Model anchors
Ref. Flukes L L/D H D or D/L e e/B Mass
f f f s f
(mm) (mm) B or (mm) or (g)
(mm) B/L e/D
f
Follo- Flukes Total
-wer (plate)
A1 Circular 76.00 12.67 28.97 30.00 0.39 13.50 0.45 10.46 11.00 21.46
A2 Circular 76.00 12.67 21.21 22.60 0.35 9.80 0.43 10.46 6.09 16.55
A3 Circular 76.00 12.67 36.78 37.60 0.49 17.30 0.46 10.46 16.12 26.58
A4 Circular 51.50 8.58 12.81 16.00 0.31 6.00 0.38 9.29 2.91 12.20
A5 Circular 101.5 16.92 28.97 30.00 0.30 13.50 0.45 12.04 11.00 23.04
A6 Square 76.00 12.67 30.00 26.73 0.35 16.78 0.63 10.46 10.75 21.21
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