HSE

Health & Safety

Executive

Cyclic degradation of offshore piles

Prepared by
WS Atkins Consultants Ltd
for the Health and Safety Executive

OFFSHORE TECHNOLOGY REPORT

2000/013
 HSE
Health & Safety
Executive

Cyclic degradation of offshore piles

WS Atkins Consultants Ltd

Woodcote Grove
Ashley Road
Epsom
Surrey
KT18 5BW

HSE BOOKS
© Crown copyright 2000
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First published 2000

ISBN 0 7176 1911 7

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assume any liability for the reports nor do they
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 CONTENTS

Page

1. INTRODUCTION ............................................................................................................ 1
1.1 Experimental findings ................................................................................................. 1
1.2 Soil capacity degradation model.................................................................................. 2
1.3 Assessment of overall structural capacity loss ............................................................. 2

2. SCOPE OF WORK .......................................................................................................... 4

2.1 Soil model calibration ................................................................................................. 4
2.2 Development of storm model...................................................................................... 4
2.3 Implementation of cyclic degradation model into RASOS ............................................. 4
2.4 Pile loading for the “design” of a synthetic soil system ................................................. 4
2.5 Degradation analysis of foundation system using full degradation model......................... 4
2.6 Degradation analysis of foundation system using simplified treatment which assumes
a threshold ................................................................................................................ 5
2.7 Reliability analysis...................................................................................................... 5

3. AXIAL CAPACITY DEGRADATION ANALYSIS OF A SINGLE PILE IN

ISOLATION ..................................................................................................................... 6
3.1 Analytical background................................................................................................ 6
3.2 Definition of pile cyclic loading ................................................................................... 8
3.3 Pile shaft shear resistance degradation........................................................................ 9

4. EXAMPLE OF DEGRADATION ANALYSIS ON A PILE........................................... 11

4.1 Response to cyclic loading.........................................................................................11
4.2 Cyclic shaft resistance degradation ............................................................................13

5. CALIBRATION OF DEGRADATION MODEL............................................................ 16

6. CYCLIC FOUNDATION DEGRADATION STUDY FOR AN EXAMPLE NORTH

SEA PLATFORM ........................................................................................................... 22
6.1 Design environmental conditions ................................................................................23
6.2 Pile system capacity .................................................................................................25

7. MODELLING OF STORMS .......................................................................................... 29

7.1 Notation...................................................................................................................29
7.2 Long term storm statistics .........................................................................................30
7.3 Short term storm statistics .........................................................................................30
7.3.1 Individual wave height distribution..................................................................31
7.3.2 Distribution of maximum wave in a sea-state ..................................................31
7.3.3 Distribution of maximum wave in a storm.......................................................32

8. ANALYSIS OF FOUNDATION CAPACITY DEGRADATION FOR EXAMPLE

NORTH SEA PLATFORM............................................................................................. 33
8.1 Procedure for degradation analysis ............................................................................33
8.2 Degradation analysis results ......................................................................................35

i
9. REANALYSIS FOR DEGRADATION THRESHOLD MODEL.................................... 43

10. CALCULATION OF PROBABILITY OF COLLAPSE................................................. 49

10.1 Conditional probability of failure during a storm...........................................................49
10.2 Annual probability of failure for all possible storms ......................................................51

11. SUMMARY AND CONCLUSIONS ............................................................................. 55

11.1 Analysis procedure ...................................................................................................55
11.2 Analysis results ........................................................................................................56
11.3 Conclusions specific to the platform considered ..........................................................57
11.4 Generic Conclusions .................................................................................................58

12. RECOMMENDATIONS FOR FUTURE WORK .......................................................... 60

12.1 Soil modelling ...........................................................................................................60
12.2 Storm modelling and reliability....................................................................................60
12.3 Structural analysis.....................................................................................................61

13. REFERENCES................................................................................................................ 62

LIST OF TABLES

Table 1 100 year extreme environmental design conditions

Table 2 Maximum pile forces under extreme environmental design conditions
Table 3 Axial pile capacity
Table 4 Gumbel distribution parameters for maximum wave in storm
Table 5 100 year storm discretisation. Number of waves in each block for each sea-state
Table 6 1000 year storm discretisation. Number of waves in each block for each sea-state
Table 7 Individual pile capacity degradation
Table 8 Degradation in foundation capacity
Table 9 Threshold cyclic axial load and wave height
Table 10 Analysis with degradation threshold: wave discretisation, 100 year storm, outer skirt piles
Table 11 Analysis with degradation threshold: wave discretisation, 1000 year storm, outer skirt piles
Table 12 Analysis with degradation threshold: wave discretisation: 1000 year storm, leg piles
Table 13 Analysis with degradation threshold. Individual pile capacity degradation
Table 14 Threshold analysis: degradation in reserve strength ratio
Table 15 Conditional probabilities of component and system collapse
Table 16 Annual pile system collapse probability for threshold model
Table 17 Summary of deterministic results
Table 18 Annual probability of pile system collapse

ii
 LIST OF FIGURES

Figure 1 Pile and soil modelling

Figure 2 Definition of pile loading components
Figure 3 Synthetic pile: distribution of shaft shear resistance with depth
Figure 4 Synthetic pile: distribution of shaft shear stress with depth
Figure 5 Synthetic pile: distribution of axial pile deflection with depth
Figure 6 Synthetic pile: distribution of average and cyclic shaft shear stress with depth
Figure 7 Progressive degradation of soil resistance with depth during the course of cyclic loading.
10 Sub-Blocks of 20 Cycles
Figure 8 Summary of pile calibration analysis R3
Figure 9 Summary of pile calibration analysis, R3. Shaft shear stress results
Figure 10 Calibration analysis R3: Pile head deflection
Figure 11 Summary of pile calibration analysis, R4
Figure 12 Summary of pile calibration analysis, R4. Shaft shear stress results
Figure 13 Calibration analysis R4: Pile head deflection results
Figure 14 Model of foundation system
Figure 15 Pile layout
Figure 16 Synthetic soil profile: shaft shear resistance of skirt piles
Figure 17 Undegraded pile system: environmental load vs. lateral deflection
Figure 18 Pile system collapse mode
Figure 19 Individual pile axial load-deflection characteristic
Figure 20 Undegraded foundation system: axial pile load vs. environmental load factor
Figure 21 Undegraded foundation system: axial pile deflection vs. environmental load factor
Figure 22 Storm history
Figure 23 Short-term wave statistics in a sea-state
Figure 24 Flow chart of full storm degradation analysis
Figure 25 100 year storm, full degradation model, amplitude of cyclic pile force amplitude
Figure 26 100 year storm, full degradation model, pile axial capacity degradation history
Figure 27 1000 year storm, full degradation model, amplitude of cyclic pile force amplitude
Figure 28 1000 year storm, full degradation model, pile axial capacity degradation history
Figure 29 Pushover analysis for degradation in middle of 100 year storm
Figure 30 Pushover analysis for degradation in middle of 1000 year storm
Figure 31 Middle of 100 Year Storm: Axial Pile Load vs. Environmental Load Factor
Figure 32 Middle of 100 Year Storm: Axial Pile Deflection vs. Environmental Load Factor

iii
Figure 33 Middle of 1000 year storm: axial pile load vs. environmental load factor
Figure 34 Middle of 1000 year storm: axial pile deflection vs. environmental load factor
Figure 35 Relationship between cyclic load amplitude and degradation after 1000 cycles as
predicted by the degradation model
Figure 36 Analysis with degradation threshold: 100 year storm. Pile degradation history
Figure 37 Analysis with degradation threshold: 1000 year storm. Pile degradation history
Figure 38 Normalised degradation, force and RSR for full degradation model during 100 year storm
Figure 39 Conditional probability of system collapse, P(F|T) for storms of different return period, T
Figure 40 Conditional probability of component failure, P(F|T) for storms of different return period,
T
Figure 41 Conditional probability of system failure P(F|T) assuming foundation system degradation
equals maximum pile degradation for storms of different return period, T

iv
1. INTRODUCTION

This report presents the results of a pilot study carried out by WS Atkins Consultants Ltd
into the effects of cyclic storm loading on the degradation in the capacity and the consequent
reduction in the reliability of the foundations of offshore platforms. This work was funded by
the Health and Safety Executive under contract OSD-D3448.

The work was carried out in collaboration with Professor Richard Jardine of Imperial
College who is conducting an experimental investigation into the effects of loading history
and ageing on the capacity of piles driven into sand, and in the development of appropriate
numerical models for pile analysis.

The primary objectives of the study were:

1. To demonstrate the consequences of ignoring cyclic degradation in terms of reduced

static capacity and reliability,

2. To define the scope for a realistic set of large and small scale tests in proportion to
the extent of the problem,

3. To investigate the need for a further broad analytical study aiming at the
characterisation of typical structural forms, soil and loading conditions, with respect
to perceived risks due to cyclic loading. The full scope of this future study will be
developed in the light of the present study following discussion with the HSE.

1.1 Experimental findings

The axial strength of cylindrical piles driven into sand has been found by experiment to be
influenced by the effects of age and cyclic loading history. At the start of this study, the
degradation in strength arising from cyclic loading, and the increase in strength arising from
ageing were known, but only sparse experimental data was available. Subsequent
experimental investigation has studied both these features and their interaction [1], [2], [3].
The main results of these studies are:

a) The severe cyclic loading that eventually causes cyclic failure of the pile brings about
reductions in the static capacity that may take a long time to recover. The rate of
increase in pile capacity after failure is much slower than that shown by piles that
have not been failed. Pile failure in the context of the field studies was associated
with significant movements of the pile.

b) Low level cyclic loading that leads to relatively small local pile to soil movements can
enhance pile capacity by accelerating the ageing process.

c) Relatively high level cyclic loading leads to a progressive loss of pile capacity. The
number of cycles required to degrade the pile capacity sufficiently to lead to cyclic
pile failure decreases as the amplitude of the cyclic loading increases.

1
1.2 Soil capacity degradation model

The analyses described in this report consider a simplified model for the behaviour of a pile
subject to cyclic loading. Piles were modelled using a number of discrete beam elements.
The soil behaviour was modelled using laterally (p-y) and axially (t-z) orientated non-linear
springs. The degradation model was applied locally to the axial t-z springs.

The model for axial pile strength and degradation derived by Imperial College had the
following limitations:

1. Only sand was considered.

2. Only one soil profile was considered.

3. There was no explicit model for increases in pile capacity arising from ageing.

4. The interaction between cyclically induced enhanced ageing and cyclic degradation
was not considered.

5. Only regular constant-amplitude cyclic loading was considered.

6. Degradation in tip capacity was assumed not to occur.

1.3 Assessment of overall structural capacity loss

The assessment of the effects of cyclic degradation on the full structural capacity was
performed on an example North Sea platform. The example platform was assumed to
remain elastic throughout the analysis, and the capacity degradation was assessed in terms of
the loss in capacity of the foundation system.

An initial study was performed with the following mixture of conservative and non-
conservative assumptions and limitations

1. The effects of ageing were ignored.

2. The effects of prior storms were ignored.

3. Waves of all amplitudes contributed to the degradation.

4. Interaction between ageing and degradation was ignored.

5. Storms were discretised into blocks of constant amplitude waves.

6. The overall structural degradation considered to be representative of the storm was

assumed to occur just after half way through the storm.

The field tests showed that low amplitude cyclic loading leads to enhanced ageing obtained
after the completion of this first set of analyses. In the light of these results, it was considered
that the capacity degradation was being overestimated because the small amplitude waves

2
were contributing to the degradation in direct contradiction to the field tests which showed
enhanced ageing for cyclic loading at these amplitudes.

In the light of the field study findings, a second study on the capacity degradation was
performed using a simplified treatment of degradation in which a threshold was applied to
the amplitude of the axial cyclic pile force. Cyclic loading above this threshold amplitude was
assumed to lead to pile degradation, whereas cyclic loading below the threshold was
assumed not to give any degradation. The threshold was calibrated against the field study
results.

3
2. SCOPE OF WORK

The scope of work for this pilot study is described below

2.1 Soil model calibration

A solution method implemented in Mathcad for analysing the behaviour of single cyclically
and axially loaded cylindrical piles in sand was developed. This spreadsheet was used for
the dual purpose of providing a check for further programming work on RASOS software
and for calibration of the model against experimental results. The calculation method used
for axial pile capacity was that developed by Jardine and Chow [4].

Using the Mathcad spreadsheet the Imperial College soil degradation model was tested and
the results used for calibration of the model against Imperial College's Dunkirk pile test
results.

2.2 Development of storm model

On the basis of the data available for the example North Sea structure analysed in this study,
a wave model for storms of two different return periods was developed for use in the
calculation of the short-term degradation of a complete foundation system.

2.3 Implementation of cyclic degradation model into RASOS

The following items were implemented into the RASOS software in order to facilitate the
degradation analysis of the full foundation system.

1. Automatic generation of the loading history as a wave passes through a structure,

2. A full cyclic hysteretic model for the cyclic p-y and t-z response of individual soil
springs,

3. A facility for the automatic calculation of the degraded capacity of the t-z springs.

2.4 Pile loading for the “design” of a synthetic soil system

Axial pile loads under the extreme 100 year design storm conditions were calculated for the
purposes of “designing” a synthetic soil profile for the sand used in the degradation analysis,
as detailed in [2].

2.5 Degradation analysis of foundation system using full degradation model

The degradation in foundation capacity for storms of 100 and 1000 year return periods was
analysed. This entailed discretising the wave loading for each block of equal amplitude
waves in the discretised storm, tracing the history of local soil deformation and cumulatively
applying the degradation model.

4
 The degradation in foundation system capacity was calculated from push-over analyses at
the middle and end of the storm history using the soil degradation models developed in [1],
[2], and [3].

2.6 Degradation analysis of foundation system using simplified treatment which

assumes a threshold

The analysis using the full degradation model of Section 2.5 was carried out under the
assumption that cyclic loading of all amplitudes gives rise to some degree of degradation.
Experiments performed subsequently to this analysis showed that there is interaction
between cyclic loading and ageing. Low amplitude cycles, rather than degrading the pile
strength, can accelerate the gain in pile strength seen during ageing.

In the light of these field study results which showed considerable interaction between cyclic
degradation and cyclically induced enhanced ageing, a reanalysis of the pile system using a
simplified treatment which attempted to capture this interaction was performed. The analysis
assumed a threshold on the cyclic axial force component below which no degradation
occurs. The degradation analysis was repeated for the two storm events using this simplified
treatment of ageing-degradation interaction.

2.7 Reliability analysis

The degraded foundation system capacity and pile component capacity derived for 100 and
1000 year return period storms were used to estimate the conditional probability of
foundation system failure and pile component failure during the course of these storms.

The annual probability of system and component failure were estimated from the conditional
probability of failure for the individual storm events. This was done by obtaining an
approximate function for the conditional failure probability as a function of storm return
period and using this to account for the possibility of a storm of any size occurring in a year.

5
3. AXIAL CAPACITY DEGRADATION ANALYSIS OF A SINGLE PILE IN
ISOLATION

The analysis of the cyclic loading behaviour of a single pile in isolation was performed with
the objectives of:

1. Developing a prototype of the cyclic loading and degradation model to be

implemented in RASOS where it is used for analysis of a complete platform.

2. Providing a tool for use in validation and calibration of the degradation model against
the results of tests performed by Imperial College [1].

3. Validation and comparison of the model against the results of nonlinear geotechnic
finite element analyses performed by Imperial College [1].

3.1 Analytical background

The single axial pile model was developed in the form of a Mathcad [5] spreadsheet and
considers a single pile with a cyclically varying axial load applied at the pile head. The pile is
discretised into N elastic axial elements of equal length connecting N+1 equidistant nodes.
Attached to each node are non-linear axial t-z springs which model the relationship between
the frictional shaft stress and strain. An additional spring is added to the bottom node to
represent the pile tip load deflection relationship.

The soil spring behaviour was assumed to follow an elasto-plastic hysteretic characteristic
which is typical for the behaviour of sands as specified in the recommendations of the API
20th Edition recommendations for offshore platforms [6]. The essential features of the pile
modelling are depicted in Figure 1.

6
 P P
Cyclic T-Z Spring
Characteristic for Sand
Linear Hysteretic
Cyclic Model
T

Tcompression

Ttension

Figure 1 Pile and soil modelling

The elastic pile stiffness matrix is given by

 1 −1 
 
−1 2 −1 
EA  −1 O O 
K Pile =   (1)
L Elem  O O −1 
 − 1 2 − 1
 
 −1 1 

where E is the Young's modulus of the pile steel, A is the cross sectional pile area and LElem
is the length of a single pile element.

The stiffness matrix of the soil springs is expressed in terms of an incremental secant stiffness
in the form:

 K s1 (∆ X 1 ) 
 
 K s 2 ( ∆X 2 ) 
K Soil ( ∆X ) =  O  (2)
 
 K sn −1 ( ∆X n −1 ) 

 K sn ( ∆X n ) + K sTip (∆ X n )

7
 where Ksi is the secant stiffness of soil spring i, and KsTip is the secant stiffness of the pile tip
spring. The incremental soil secant stiffness matrix is a function of the individual soil spring
displacement increment and of the current level of force in each spring.

For a given current state of pile deflections, X0, and internal soil spring forces, F0, a new
loading increment, ∆ P, is applied at the top of the pile. The pile-soil system must satisfy the
following relationship for a single loading increment

[K Pile ]
+ K Soil (F0 , ∆X) ∆X = ∆P (3)

This solution is achieved within a load increment by iteratively deriving the displacement
vector. The soil spring cyclic force-deflection relationship is then used to derive the total
spring force corresponding to this deflection increment. The spring force and displacement
increments are used to derive an incremental soil secant stiffness matrix from which a new
displacement vector is derived. The calculations for a single iteration are given in Equations
(4), (5) and (6) where i is the current iteration number.

∆X i = [K Pile + K Soil i −1 ] ∆P
−1
(4)

Fi = F(X 0 , F0 , ∆Xi ) (5)

Fi − F0
K soili = (6)
∆X i

Iterations are repeated until convergence, measured as the difference in displacement norm
between consecutive iterations, is achieved.

3.2 Definition of pile cyclic loading

Cyclic loading applied to a pile is defined in terms of the average Pav and cyclic Pcy load
components which are given in terms of the maximum and minimum pile forces as:

P av = (P U+P L)/2

P cy = (P U-P L)/2
and are as shown in Figure 2.

8
 Pile Force

PU

Pcy

Pav

Pcy

PL

Figure 2 Definition of pile loading components

Similarly, the local shaft frictional stress is decomposed into cyclic and average components

τav = (τU + τL)/2

τcy = (τU - τL)/2

Although in reality the cyclic loading is of variable amplitude, this section concentrates on
constant amplitude cyclic loading. This is because the majority of pile tests have been
performed for constant amplitude cyclic loading conditions, and the available degradation
models have also been developed and calibrated for this case.

3.3 Pile shaft shear resistance degradation

The model for shaft shear degradation developed by Imperial College from test results is
described in [2].

This model assumes that pile strength degradation arises as a result of a local reduction in the
radial effective stress, σr′0 , of the sand. For a sequence of N cycles of constant shear stress
amplitude, τcy, the reduction in radial effective stress, ∆σrcyclic
′ , is given by

∆σrcyclic
′  τcy 
= A + B N C (7)
σr′0  τmax static 

where A, B and C are model parameters and τmax static is the shaft shear capacity.

The compressive and tensile shaft friction resistance calculated using the methodology given
in [4] are updated to account for this degradation according to the following equations:

9
 (
τcompmax static = σr′0 + ∆σrcyclic
′ )
+ ∆σrd′ tan δ (8)

( ( )
τtens max static = 0.9 0.8 σr′0 + ∆σrcyclic
′ )
+ ∆σrd′ tan δ (9)

The capacities of the t-z springs are derived from the shaft shear capacity by multiplying by
the surface area of pile which each spring represents. It is assumed that no degradation of
the pile tip resistance occurs.

10
4. EXAMPLE OF DEGRADATION ANALYSIS ON A PILE

4.1 Response to cyclic loading

This section describes cyclic analyses performed with the objective of testing the Mathcad
spreadsheet and gaining some understanding of pile behaviour under cyclic loading. The
synthetic soil profile, developed to ensure that the piles meet the design requirements, was
used for the investigation of the global structural behaviour. This profile was established by
Jardine and is fully described in [2]. The pile length is 74m, divided into 25 elements. The
cylindrical pile cross section is 2.134m in outer diameter and has a thickness of 70mm.

The stiffness of the t-z springs was derived by assuming that the compressive frictional
resistance is fully mobilised at a deflection 2.54mm. This follows the recommended practise
for platform design given in the API 20th Edition recommendations [6]. The tip spring was
also assumed to have a bilinear hysteretic characteristic. The stiffness of the tip spring
assumes that the tip resistance is fully mobilised at a tip displacement of one tenth of the pile
diameter, again in accordance with the API 20th Edition recommendations. However, the
initial tip spring stiffness was taken to be linear, whereas API 20th Edition specifies a non-
linear characteristic. The difference in response is likely to be very small, particularly if the
shaft friction resistance is not fully mobilised.

The distribution with depth of the local shaft frictional capacity for both overall compressive
pile loading and tensile (pull-out) loading is plotted as a function of depth in Figure 3. The
overall pile capacity, obtained by integrating the local shaft frictional capacity around the pile
circumference and down the pile length is:

Tensile pile capacity arising from shaft frictional resistance 34 MN

Compressive pile capacity arising from shaft frictional resistance 47 MN

Compressive tip resistance 15 MN

Total compressive capacity 62 MN

11
 0

20 Tension Compression
Depth (m)

40

60

80
300 200 100 0 100 200 300 400
Shaft Shear Resistance (kPa)

Figure 3 Synthetic pile: distribution of shaft shear resistance with depth

A cyclic loading history of five load steps was applied as follows:

P1=10 MN
P2=40 MN
P3=10 MN
P4=40 MN
P5=10 MN

In terms of cyclic and average loading components this is:

Pcy=15 MN
Pav=25 MN

The variation in shaft shear stress following the application of the sequence of five loading
steps is shown in Figure 4 whereas the vertical displacement of the pile is shown in Figure 5.
It can be seen that, after the first load step, the pile response reaches a steady state
response, with the cyclic and average stress components being constant.

Three zones of soil behaviour can be identified as indicated in Figure 4 by Roman numerals.
Towards the top of the pile, in zone I, the soil deformation and shaft frictional stress vary in
large amplitude alternating cycles, with the soil describing nominally stable hysteresis loops.
Local shaft frictional capacity is fully mobilised under both senses of shearing (τrz both
negative and positive). At intermediate levels, zone II, the shaft frictional capacity is fully
mobilised only for pile deflections in the downwards direction and, following the initial plastic
excursion at first loading, the behaviour in this region “shakes down” to a cyclic elastic
behaviour. In zone III the shear resistance is not mobilised fully in either sense and the soil
springs remain in their "elastic" range.

12
 0

-10 0
P1 P 3,P5
-20
Zone I P 2,P4

-20
-30

Depth (m)
Depth (m)

-40 -40
Zone II
-50
-60
-60
Zone III
-70 -80 0 0.005 0.01 0.015 0.02
P1 P3 ,P5 P2 ,P4 Displacement (m)
-80
-100 -50 0 50 100 150 200
Shaft Frictional Shear Stress (kPa)

Figure 4 Synthetic pile: distribution of Figure 5 Synthetic pile: distribution of

shaft shear stress with depth axial pile deflection with depth

4.2 Cyclic shaft resistance degradation

The degradation of shaft resistance was calculated in terms of the cyclic component of the
shaft frictional shear stress, τcy. This is plotted with depth in Figure 6 for the stable response
described above.

-20
Depth (m)

-40

-60

-80
0 50 100 150 200
Shear Stress (kPa)
Cyclic Shear Stress
Average Shear Stress

Figure 6 Synthetic pile: distribution of average and cyclic shaft shear stress
with depth

An important feature of the integrated behaviour of the pile and soil is that, given a constant
amplitude of force at the pile tip, the amplitude of the local stress cycles does not remain
constant. For constant amplitude cyclic loading of the pile, and as a result of continual soil

13
capacity degradation, the zone of two-way mobilisation of shaft frictional capacity (zone I)
penetrates further down the pile after each cycle of degradation with the limiting shaft shear
stress envelope shrinking continuously. This growth of the fully mobilised zone down the pile
and the locally increasing amplitude of stress cycles elsewhere leads to a non-uniform
pattern of degradation as the cyclic loading progresses. In order to capture this effect, a
single block of constant pile force cycles was divided into sub-blocks and an incremental
degradation accumulation law for use between sub-blocks was applied. The degradation
model for sub-blocks thus has the form:

 τcy 
r = A + B (10)
 τmax static 

∆σrcyclic
′
=
(
r N totC − ( N tot − N s )
C
)
1+ r( Ntot − N s )
(11)
σ r′0 C

where
Ntot: Total number of cycles to date in block, including the present sub-block
N s: Number of cycles in the present sub-block of cycles

Successive application of this updating scheme resulted in the same overall degradation in
those areas that are fully mobilised in both tension and compression as the application of a
single block of Ntot cycles given by Equation (7). When a new block of cyclic loading of a
different amplitude is applied, Ntot is reset to zero. This simulated the observed increase in
degradation rate when a new loading block was applied.

The example considered the following properties for the cyclic loading:

Number of Cycles = 200 divided into 10 sub blocks of 20 cycles

Pcy
= 0 .32
Pmax comp

Pav
= 0.53
Pmax comp

Here Pmax comp is the compressive pile capacity.

The cumulative degradation ratio of shaft frictional resistance with depth predicted by the
model is shown in Figure 7. Here, the degradation factor was defined as being one minus
the ratio between the degraded and original shaft strength. The increasing depth of the fully
mobilised region of shear stress cycles as the loading progresses resulted in a progressive
change in the shape of the degradation profile. The reduction in the degradation rate as the
number of cycles increases is clearly evident from the Figure.

14
 100

200
20

40

60
80
0

10

20

30
Depth (m)

40

50

60

70

80
0 0.2 0.4 0.6 0.8 1

Degradation Factor

Figure 7 Progressive degradation of soil resistance with depth during the

course of cyclic loading. 10 Sub-Blocks of 20 Cycles

15
5. CALIBRATION OF DEGRADATION MODEL

The local shaft frictional resistance degradation model was originally derived by Jardine from
a series of simple shear test results on dense sands carried out on samples from a North Sea
site [2]. Full scale cyclic pile tests carried out at Dunkirk by Imperial College were
compared with analysis results using the Mathcad spreadsheet described above. The
objective was to calibrate the pile degradation model applied to a complete pile against the
test results.

Full details of this calibration exercise are reported by Jardine [1]. A brief description of the
models and results is given below.

Two piles tests, denoted R3 and R4, were used for calibration of the soil degradation
model. Both piles had identical material and soil properties. The piles penetrated 19.37m
into the soil, had a diameter of 0.457 m and a thickness of 13.5mm. The static tensile shaft
friction capacity was taken as 2.4 MN for each pile.

The pile cyclic loading was purely tensile, the applied load cycling between its maximum
tensile value and zero. Pile R3 was subjected to two phases of cyclic loading. The first
comprised 200 cycles between a peak tension of 1.4 MN and zero, and the second of
cycles of between zero and 1.8 MN until collapse. Pile R4 was cycled between zero loading
and a maximum tension of 2 MN. These cycles were applied continuously until collapse
occurred.

Application of the original model derived from the cyclic shear tests was found to over-
predict the number of cycles required to fail the piles in tension. On the basis of these results,
it was decided to increase the factor A used in the degradation model of Equation (7) by a
factor of 1.5. The final model parameters used for all the subsequent analyses were

A = -1.245

B = -0.060

C = 0.355

Using these revised parameters, a reanalysis of the single pile calibration tests was
performed, and the results are summarised in Figure 8 to Figure 13. The results for this
revised analysis over predicted the total number of cycles required to fail pile R3, giving 50
cycles in the second phase as opposed to 13 cycles required in the experiment, and under-
predicted the number of cycles required to fail pile R4, 160 cycles being required to failure
in the analysis as opposed to 221 in the experiment. It was concluded that these revised
model parameters gave a better representation of the expected behaviour at the Dunkirk site
as well as in the North Sea, in both cases the sand being less dense than that used in the
original simple shear tests. The model was found to give realistic representations of the most
important features of the cyclic capacity degradation seen in Dunkirk tests. One weakness
was that the progressive increase in deflections observed in the experiments was not
simulated by the analyses.

16
The results of the Dunkirk calibration analyses were also used in a comparison with the
results of a series of finite element analyses performed by Imperial College. The comparison
between these results is given by Jardine [1], in which it is concluded that the two analyses
gave comparable initial shaft shear stress distributions, with both analyses predicting a two
way cyclic loading zone developing over the top 40% of the pile shaft.

It is stated in the Introduction that reliability of a platform can suffer reduction due to short-
term cyclic deterioration. To estimate the magnitude of this reduction, which is the objective
of this pilot study, a number of computational steps have to be undertaken. These steps are
defined in Section 2.

So far this report has addressed the first portion of these steps relating to the development
and calibration of the deterministic model for the degradation analysis of a single pile. In the
next part of the report, the use of this model in the context of the analysis of an overall
foundation system is considered.

17
 Pile R3: Cyclic Tension Test

Stage 1: Stage 2:
Pcy = 0.7 MN Pcy = -0.95 MN
Pav = -0.7 MN Pav = -0.95 MN
N=200 Cycle until Collapse
5 Sub-Blocks of 40 Cycles Sub-Blocks of 10 Cycles until collapse occurs
After 200 Cycles: Collapse after 50 Cycles in Stage 2

Tensile Capacity=2.15 MN
Degradation = 11.9%
0 0
Dunkirk Test: Pile R3
2.4

2.3
5
5

Tensile Capacity (MN)

2.2

Depth (m)
2.1
Depth (m)

10
10

15
15
1.9

1.8
0 50 100 150 200 250 300
20
450 400 350 300 250 200 150 100 50 0 Number of Cycles
20 Shear Capacity (MPa)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Shear Strength Degradation Factor

Degradation Factor Variation with Depth. Local Shaft Frictional Resistance with Progressive Strength Degradation
Stage 1: 5 Sub-Blocks of 40 Cycles Depth
Stage 2: 6 Sub-Blocks 0f 10 Cycles Stage 1: 5 Sub-Blocks of 40 Cycles
Stage 2: 6 Sub-Blocks 0f 10 Cycles

Figure 8 Summary of pile calibration analysis R3

18
 0
0

5
5
Depth (m)

Depth (m)
10
10

15
15

20
200 150 100 50 0 50 100 20
200 150 100 50 0 50 100
Shaft Shear Stress (kPa)
Shaft Shear Stress (kPa)

Beginning of Stage 1 End of Stage 1

0 0

5 5
Depth (m)
Depth (m)

10
10

15
15

20
400 300 200 100 0 100
20
400 300 200 100 0 100 Shaft Shear Stress (kPa)
Shaft Shear Stress (kPa)

Beginning of Stage 2 End of Stage 2

Figure 9 Summary of pile calibration analysis, R3. Shaft shear stress results
Dunkirk Test: Pile R3
10

8
Pile-Head Deflection (mm)

0
0 50 100 150 200 250 300
Number of Cycles
deflection at zero load
deflection at maximum load

Figure 10 Calibration analysis R3: Pile head deflection

19
 Pile R4: Cyclic Tension Test

Maximum Tension = 2.0 MN

Minimum Tension = 0.0 MN

Pcy = 1.0 MN
Pav = -1.0 MN

Cyclic Loading Model is Applied in sub-blocks of 20 cycles until collapse occurs after 160 cycles

0 0
Dunkirk Test: Pile R4
2.3

5 5
2.2

Tensile Capacity (MN)

Depth (m)

Depth (m)

10 10
2.1

15 15 2

20 20 1.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 450 400 350 300 250 200 150 100 50 0 0 50 100 150 200
Shear Strength Degradation Factor Shear Capacity (MPa)
Number of Cycles

Degradation Factor Variation with Depth: Local Shaft Frictional Resistance with Progressive Strength Degradation
8 Sub-Blocks of 20 Cycles Depth
8 Sub-Blocks of 20 Cycles

Figure 11 Summary of pile calibration analysis, R4

20
 0 0

5 5
Depth (m)

Depth (m)
10 10

15
15

20
20 400 300 200 100 0 100 200
400 300 200 100 0 100

Shaft Shear Stress (kPa) Shaft Shear Stress (kPa)

Beginning of Cyclic History End of Cyclic History (Just Prior to Failure)

Figure 12 Summary of pile calibration analysis, R4. Shaft shear stress results
Dunkirk Test: Pile R4
10

8
Pile-Head Deflection (mm)

0
0 50 100 150 200
Number of Cycles
deflection at zero load
deflection at maximum load

Figure 13 Calibration analysis R4: Pile head deflection results

21
6. CYCLIC FOUNDATION DEGRADATION STUDY FOR AN EXAMPLE
NORTH SEA PLATFORM

The effects of cyclic degradation in axial pile capacity on the resistance of a complete
structure were investigated using a model of an example of a central North Sea platform
shown in Figure 14. The objective of using this platform is to ensure that capacity
degradation is investigated in the context of realistic environmental loading and pile system
effects. However, for this analysis, an artificial soil profile was used.

Loading Direction

6 400 30 000 6 400

S6 S8

6 400
S5 L11 L12 S7

25 000
S2 L9 L10 S4
6 400

S1 S3
Figure 14 Model of
foundation system
Figure 15 Pile layout

The platform has twelve piles; 4 leg piles 1.829m in diameter and 0.070m thick, and 8 skirt
piles 2.134 m in diameter and 0.070 m thick, laid out in the manner illustrated in Figure 15.
The pile tip is 74m below mudline level. The platform sits in 84m of water.

The structural layout accurately reflects that of a realistic North Sea platform. Similarly the
environmental conditions have been chosen to accurately reflect those likely to be prevailing
upon a platform in the Central North Sea.

22
6.1 Design environmental conditions

The design loading in the piles was obtained following the requirements of the API 20th
Edition [3] recommended practice. The loading direction being considered in this study is
the wave from North direction. The extreme 100 year environmental loading conditions,
typical for the Central North sea are given in Table 1.

Table 1 100 year extreme environmental design conditions

Maximum Wave Height [m] 24.8

Wave Period [s] 14.0

Surface Current Velocity [m/s] 0.61

Wind Speed [m/s] 37.0

Water Depth [m] 86.2

A non-linear analysis of the pile-structure system, in which the soil is modelled using non-
linear p-y and t-z springs and the structure is taken to be fully elastic, was carried out for the
extreme 100 year loading plus vertical dead and live loads. The axial forces in the most
loaded skirt and leg piles under this combination are tabulated in Table 2.

Table 2 Maximum pile forces under extreme environmental design

conditions

Compression Tension
Skirt Piles 41.3 15.4
(2134∅x70)
Leg Piles 25.1 0
(1829∅x70)

The forces in the piles arising from the extreme environmental loading were multiplied by a
factor of 1.5 to give the required design capacity according to the API recommendations.
The critical design condition was for the skirt pile acting in compression.

On the basis of the calculated pile forces, a synthetic soil profile was evaluated by Jardine
[2] using the Imperial College model for axial pile capacity in sand [4] with the objective of
ensuring that the above design criteria were satisfied.

23
 0

20 Tension Compression
Depth (m)

40

60

80
300 200 100 0 100 200 300 400

Shaft Shear Resistance (kPa)

Figure 16 Synthetic soil profile: shaft shear resistance of skirt piles

The axial capacity of the two types of pile for the synthetic soil profile are given in Table 3.
The distribution of shaft skin friction capacity with depth for the skirt piles is shown in Figure
16.

Table 3 Axial pile capacity

Tensile
Compressive Capacity
Capacity
Shaft Tip Capacity Total Total
Capacity [MN] Capacity Capacity
[MN] [MN] [MN]
Skirt Pile 47 15 62 34

Leg Piles 39 13 52 29

The critical soil profile has been "designed" to lead to the compressive capacity of the skirt
pile being the critical design criterion. The tensile skirt pile capacity, and the leg pile capacity,
not being design-critical, will have reserve capacity. This, combined with the overall
foundation system redundancy, ensures that the foundation system will resist loading
considerably greater than the design loading.

24
6.2 Pile system capacity

The capacity of the pile system was determined by performing a non-linear pushover
analysis of the platform in which the dead and live loads were applied to the structure and
the 100 year extreme design environmental loading was incremented until collapse of the pile
system occurred. The factor on the 100 year extreme loading at the point of collapse
provides the measure of Reserve Strength Ratio (RSR). Failure of structural elements was
assumed not to occur, the jacket being modelled as elastic. However the non-linear p-y and
t-z soil spring characteristics were used, and plastic behaviour of the pile steel was
modelled. The capacity calculation was carried out for unaged piles that are nominally 50
days old.

The relationship between the environmental load factor and the lateral deflection at the top
of the platform and at the pile head is shown in Figure 17. The final collapse mode of the
platform is shown, to an exaggerated scale, in Figure 18. Figure 19 shows the individual pile
axial force vs. axial deflection relationship. The RSR of the undegraded pile system can be
seen to be 2.95.

3
Pile Head
Top of Platform

2.5

2
Environmental Load Factor

1.5

0.5

0 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Total Deflection (m)

Figure 17 Undegraded pile system: environmental Figure 18 Pile system

load vs. lateral deflection collapse mode

25
 Figure 19 Individual pile axial load-deflection characteristic

The axial pile behaviour, shown in Figure 19, was characterised by four distinct modes. The
stiffest part of the behaviour occurred in the region where the shaft friction resistance was
being mobilised. This behaviour was the integrated effect of the mobilisation of shaft
resistance down the pile. Once the shaft resistance had been fully mobilised in compression,
additional resistance to axial loading was offered by the pile tip. This portion of the axial
load-deflection behaviour was considerably less stiff than before the shaft resistance had
been fully mobilised. Once the tensile or compressive capacity was fully mobilised, axial
deflections could increase with no change in axial loading.

Figure 20 shows the relationship between the axial forces in the piles and the environmental
load factor. Figure 21 shows the axial pile-head deflections. At zero environmental load, the
axial loading in the piles arose from the dead and live vertical loading. There was some
eccentricity in this loading which can be seen from the higher compressive axial forces in the
eastern-most piles compared to the western piles. The environmental loading resulted in
lateral and overturning forces on the foundation system. The overturning was resisted by
increased compressive loading in the eight southern-most piles and increased tensile forces
in the eight northern-most piles. At an environmental load factor of about 1.4, the shaft
resistance in the outer-most compressive skirt pile, S3 was fully mobilised. At this point the
axial stiffness of pile S3 was significantly reduced. The additional loading, which would
otherwise be taken by pile S3, was redistributed amongst the other piles which showed a
relative increase in loading, most notable in piles S4 and L10. Pile S3 showed a significant
decrease in the rate at which its axial load increased. Similar behaviour was seen for pile S4
whose shaft resistance was fully mobilised at an environmental load factor of 1.6.

The first pile to actually reach its full capacity was the outermost tensile skirt pile, S6 at an
environmental load factor of 1.9, closely followed by the failure of its companion pile S8 at a

26
load factor of 2.05. At this point all the compressive piles had fully mobilised shaft
resistance. The resulting increase in over-turning angle and reduction in over-turning stiffness
can be clearly seen from the environmental load factor vs. top of platform displacement plot
of Figure 17 and the individual axial pile displacement plot of Figure 21.

Final collapse of the foundation system was reached once the axial capacity of the inner
compressive skirt piles S2 was reached. At this point the platform was free to rotate around
piles S7, L11, L12 and S5. However a small amount of further capacity was available from
the rotational capacity of the piles. The final failure mode, shown in Figure 18, comprised an
overall overturning mode of the platform which required for kinematic consistency, full
mobilisation of the axial deformation of the piles and the rotation capacity of the pile heads.
The pile head rotation arose as a result of the combined effects of plastic hinge formation at
some distance down the pile, and the lateral failure of the soil above this hinge.

27
 Compression Tension Compression Tension
3 3 S4 S5
S3 L10 L9 S2 S7 L11L12
S8 S6
S1
L11 L12
2.5 L9 S7 S5 2.5

L10
Environmental Load Factor

Environmental Load Factor

2 S2 2
S8
S6
S4

1.5 S1
S3 1.5

1 1

0.5 0.5

0-60 -50 -40 -30 -20 -10 0 10 20 30 40 0-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Pile Axial Force (MN) Pile Axial Displacement (m)

Figure 20 Undegraded foundation system: axial pile load vs. Figure 21 Undegraded foundation system: axial pile deflection
environmental load factor vs. environmental load factor

Pile Arrangement
S6 S8

S5 L11 L12 S7
Loading Direction

S2 L9 L10 S4

S1 S3

28
7. MODELLING OF STORMS

The modelling of the long-term storm characteristics requires models for long term statistics
and short term statistics.

The short term storm model describes the wave statistics given that the storm is of a given
peak intensity. A storm is characterised by its peak intensity (peak significant wave height)
Hsmax, and by the storm profile given in the draft ISO recommendations [7].

The long term statistics describe the annual probability that storms of a given peak intensity
are exceeded. The long term statistics are defined in terms of a probability distribution for
peak storm intensity.

7.1 Notation

H Individual wave height

Hs Significant wave height, Sea-State Intensity

Hmax Maximum wave height in a sea state

Hsmax Maximum sea-state intensity of largest annual storm.

T Individual wave period

Tz Mean Up-Crossing Period

Tp Period corresponding to spectral peak

Tm Mean Wave Period

Tstate Duration of sea state

N Number of waves in a particular sea-state

The following relationships between sea state intensity Hs, and peak spectral period, Tp, and
mean upcrossing period, Tz, are used:

Tp = 0.4392Hs + 6.0192

Tz = 0.3988Hs + 9.5341

The intensity of a sea state is expressed in terms of the significant wave height, Hs. As a
storm progresses, the instantaneous value of Hs changes, reaching a peak and then decaying.
The Draft ISO [7] recommends the profile for storm build-up in the North Sea shown in
Figure 22.

29
 Assumed Storm Build-Up in North Sea
1

0.9

0.8

0.7
Hs/Peak Storm Hs

0.6

0.5

0.4

0.3

0.2

0.1

0
0 5 10 15 20 25 30 35
Time (Hours)

Figure 22 Storm history

In the present study, the full storm history was divided into a series of individual sea states of
constant Hs within which the sea statistics were assumed to be stationary.

7.2 Long term storm statistics

The long term storm statistics define the probability of occurrence of the largest storm within
a given time period, normally one year. The storm peak intensity may be used as the random
parameter, with all other parameters being dependent on this value. For the wave from
North condition at the Central North Sea site, the probability distribution for peak storm Hs
was inferred from the data provided which gave maximum 1 year, 10 year 50 year and 100
year Hs values. Assuming these to be representative of maximum storm Hs, the distribution
of the peak Hs of the largest storm can be taken to be a Gumbel distribution with
parameters:

α = 1.143 m-1

u = 7.425 m

7.3 Short term storm statistics

The storm was divided into a number of constant sea-state blocks, each of duration Tstate.
The mean up-crossing period, Tz was used to estimate the number of waves in the sea-state:

N = Tstate / Tz

30
7.3.1 Individual wave height distribution

For the type of narrow-banded sea state to be expected in the central North Sea. The
probability density function of individual wave height, H, for a given sea state characterised
by Hs, the wave height was modelled using a Rayleigh distribution, given by:

 1416
. 
2
  h  
2

f H | Hs ( h|hs ) = 2  
 h exp − 1416
.  (12)
 hs    hs  


The period associated with a particular wave height was estimated from the modal value of
the Longuet-Higgins joint wave height/wave period distribution.

7.3.2 Distribution of maximum wave in a sea-state

The maximum wave height occurring in a given sea state is denoted Hmax. It is a function of
the number of waves occurring in the sea state, and has a cumulative distribution function
given by

FH max ( hmax ) = [FH ( h) ]

N
(13)

where N is the expected number of waves in the seastate. The most common measure of the
extreme wave is the modal value of the distribution of the maximum wave, Hmax. The typical
relationship between the individual wave distribution and distribution of the maximum wave
in the sea-state is shown in Figure 23.

2
Probability Density

Extreme Wave
Distribution

Individual Wave
Distribution
0
0 0.5 1 1.5 2 2.5 3
h/hmax

Figure 23 Short-term wave statistics in a sea-state

31
7.3.3 Distribution of maximum wave in a storm

The distribution of the maximum wave in a storm is the product of the distributions of the
maximum wave within each sea-state.

( )
7

FH max ( hmax ) = ∏ FH | H si (h)

Ni
(14)
i =1

The distribution of the maximum wave in a storm calculated according to Equation (14) has
been fitted to a Gumbel distribution and is tabulated, for storms of different return periods, in
Table 4.

Table 4 Gumbel distribution parameters for maximum wave in storm

Maximum
Storm Return
Storm Distribution of Maximum Wave In Storm (Hmax|ST)
Period
Intensity
T Hsmax α Hs |S T uH s |ST µH s |ST cov Hs|ST
[Years] [m] [m ] -1
[m] [m]
1 8.5 0.98 15.9 16.5 0.08
10 11.1 0.75 20.6 21.4 0.08
50 12.9 0.64 23.9 24.8 0.08
100 13.8 0.60 25.5 26.5 0.08
500 15.6 0.53 28.8 29.9 0.08
1000 16.4 0.51 30.2 31.4 0.08
5000 18.2 0.46 33.4 34.7 0.08
10000 19.0 0.44 34.9 36.2 0.08
50000 20.8 0.40 38.1 39.5 0.08

32
8. ANALYSIS OF FOUNDATION CAPACITY DEGRADATION FOR EXAMPLE
NORTH SEA PLATFORM

8.1 Procedure for degradation analysis

The procedure that was used for the analysis of the degradation arising in the platform during
a given storm history is depicted in the flow chart of Figure 24. The method adopted
accounts for both the effects of the redistribution in soil strength within a pile and the
progressive redistribution in loading between piles as the storm history progresses and
changes in relative pile stiffness occurs. The structural capacity calculations are based on the
unaged 50 day soil strength. This contrasts with the calibration check which allowed
implicitly for ageing in the field tests.

The model for cyclic t-z spring response and degradation developed for the isolated pile
analysis, described in Section 4, above was adopted for the axial pile response. In addition
to this, a model for the lateral response was used according to the API 20th Edition [6]
recommendations for p-y soil springs. The parameters used for the soil model were

φ' = 37o in dense sand at depths greater than 10m below mudline
φ' = 34o in medium dense sand at depths less than 10m below mudline
γ' = 9.7 kN/m 3

A hysteretic behaviour was adopted for the p-y curves. The initial non-linear p-y response
given in the API 20th Edition recommendations was assumed until first unloading was
encountered. Following the first unloading event, each p-y curve was assumed to take on a
bi-linear hysteretic characteristic similar to that of the t-z curves. The p-y and t-z hysteretic
cyclic spring formulation, and the degradation model were programmed into the RASOS
software which was used for the analysis of the degradation of the pile system.

The analysis procedure for a storm started with the initial undegraded soil properties.
Starting from the first sea-state and the smallest wave block amplitude within the sea state,
the wave was passed through the platform and the sequence of structural loading as the
wave travels through the platform was obtained. This loading was applied incrementally in a
non-linear analysis of the complete pile system. The structure was assumed to remain elastic
throughout the process. A total of three wave cycles were passed through the structure to
ensure that the cyclic response reached a steady state. The maximum and minimum forces
arising in the t-z springs were extracted and used to evaluate the cyclic and average
components of the shaft shear stress, which were then used along with the number of waves
of that amplitude to evaluate the degraded capacity. The capacity and stiffness of each t-z
spring was then updated accordingly and the next block of waves applied to the structure.
The procedure was repeated until the complete storm had been analysed.

33
 Initialise Axial Cyclic
Spring properties:

Select Sea State, Istate

Select Wave Block Within

Sea State, Iblock

Wave Height
Wave Period
Number of Waves

Pass Three Full Wave

Cycles Through Structure

For Each Axial t-z Spring

on Each Pile Obtain
Maximum, Minimum,
Average and Cyclic Spring
Forces

Update capacity of each

Axial t-z spring at the end
of each block

Go To next
Wave Height Block
in Sea- State
(If Any)

Go To next
Sea- State
(If Any)

End Storm

Figure 24 Flow chart of full storm degradation analysis

34
 The analysis of degradation for these storms assumed that the storm history was divided into
seven constant intensity sea-states each of 5 hours duration. The Rayleigh distribution for
individual wave height was used to evaluate 5 blocks of waves per sea-state. These are
given in Table 5 for the 100 year storm and Table 6 for the 1000 year storm.

In this analysis, the cyclic degradation model was assumed to be acting irrespective of the
amplitude of the wave. The interaction between cyclic degradation and ageing is thus being
ignored. This effect is considered in the simplified treatment using the loading threshold in the
subsequent analysis. The applied range of cyclic loading are not necessarily very severe in
relation to the static capacity.

Table 5 100 year storm discretisation. Number of waves in each block for
each sea-state
Wave Wave
Sea State Number
Height Period
(m) (s) 1 2 3 4 5 6 7
2.6 8.3 805 534 375 295 375 534 805
7.8 13.7 560 621 573 516 573 621 560
13 15 47 154 248 291 248 154 47
18.2 15.4 0 12 45 80 45 12 0
23.4 15.6 0 0 3 11 3 0 0

Table 6 1000 year storm discretisation. Number of waves in each block for
each sea-state
Wave Wave
Sea State Number
Height Period
(m) (s) 1 2 3 4 5 6 7
3.1 8.9 764 502 349 274 349 502 764
9.2 14.6 538 588 538 481 538 588 538
15.4 16 47 148 235 274 235 148 47
21.5 16.5 0 12 44 76 44 12 0
27.7 16.7 0 0 3 11 3 0 0

8.2 Degradation analysis results

The full model for degradation of the pile system was used to estimate the loss in structural
capacity during the 100 and 1000 year return period storms. The collapse event during a
storm was assumed to be the result of degradation in capacity followed by an extreme wave
event sufficiently large to collapse the platform. The capacity halfway through the storm was

35
 considered to provide a measure of the resistance of the platform to the collapse wave
event.

For the 100 year storm, the amplitude of the total axial force down the pile is shown in
Figure 25. The progressive degradation throughout the history of the 100 year return period
storm is shown in Figure 26. Similarly the axial cyclic force amplitude and the progressive
pile deterioration during the 1000 year return period storm are illustrated in Figure 27 and
Figure 28 respectively.

It can be seen from the plots of axial cyclic amplitude that the outer-most skirt piles attracted
the greatest loading. For the largest waves in the 100 year storm this was 9.5 MN,
corresponding to 22% of the compressive shaft capacity and 28% of the tensile shaft
capacity. In the 1000 year storm, the largest waves transferred a cyclic load amplitude of 13
MN to the outer skirt piles, corresponding to 28% of the original compressive shaft capacity
and 38% of the original tensile shaft capacity. This was superimposed onto the compressive
vertical loading condition which ranged between 18 MN and 10 MN for the outer skirt
piles.

The pile axial loading arising from waves of the same height can be seen to have decreased
in the outer skirt piles and increased in the inner skirt and leg piles as the storm progressed.
This behaviour arose as a result of the relative changes in pile stiffness with degradation. For
the largest wave in the three most intense sea-states, the cyclic force amplitude in the
outermost piles decreased by 6%.

100 Year Storm Cyclic Pile Force Amplitude

10
9
8 Outer Skirt Piles
7 Inner Skirt Piles
Leg Piles
Force [MN]

6
5
4
3
2
1
0
1 2 3 4 5 6 7
Sea State

Figure 25 100 year storm, full degradation model, amplitude of cyclic pile force
amplitude

36
 100 Year Storm Pile Capacity Degradation Ratio
1
S1
0.9 S3
0.8 S6
0.7 S3 S8
Degradation ratio

S2
0.6 S1
S8 S4
0.5
S6 S5
0.4 S7
0.3 L9
0.2 L10
L11
0.1
L12
0
1 2 3 4 5 6 7
Sea State

Figure 26 100 year storm, full degradation model, pile axial capacity
degradation history

1000 Year Storm Cyclic Pile Force Amplitude

14

12
Outer Skirt Piles
10 Inner Skirt Piles
Leg Piles
Force [MN]

0
1 2 3 4 5 6 7
Sea State

Figure 27 1000 year storm, full degradation model, amplitude of cyclic pile
force amplitude

37
 1000 Year Storm Pile Capacity Degradation Ratio
1
S1
0.9 S3
0.8 S6
0.7 S8
Degradation ratio

S2
0.6
S4
0.5
S5
S3
0.4 S7
S1
0.3 L9
S8 L10
0.2
S6 L11
0.1
L12
0
1 2 3 4 5 6 7
Sea State

Figure 28 1000 year storm, full degradation model, pile axial capacity
degradation history

A summary of the pile degradation during the storm is presented in Table 7. The degradation
at the end of the storm and at the middle of the storm is given for the three pile types. The
greatest degradation occurred in the outer skirt piles, which lost 32% of their tensile capacity
at the middle of the 100 year storm and 50% of their capacity by the end of the 100 year
storm. In the 1000 year storm, the same piles lost 50% of their tensile capacity by the
middle of the storm and 82% by the end of the storm. The compressive capacity
degradation was less pronounced since the tip capacity, originally some 25% of the total,
did not degrade. The capacity of the other piles degraded by considerably less.

Table 7 Individual pile capacity degradation

100 Year Storm 1000 Year Storm

Middle of Storm End of Storm Middle of Storm End of Storm
Comp. Tens. Comp. Tens. Comp. Tens. Comp. Tens.

Outer Skirt Pile 25% 32% 39% 50% 38% 50% 63% 82%
Inner Skirt Pile 5% 6% 9% 12% 10% 12% 18% 21%
Leg Piles 7% 9% 13% 16% 13% 16% 22% 28%

38
 The degradation in the capacity of the foundation system was assessed by performing
pushover analyses using the approach described in Section 6. The 100 year return period
environmental load was used as the reference design loading for determining the RSR for the
full foundation system. Load-deflection plots are shown for the degraded system in the
middle of the 100 and 1000 year return period storms in Figure 29 and Figure 30
respectively. The individual pile axial forces and pile-head axial deflections computed during
the course of the pushover analyses are shown in Figure 31 and Figure 32 respectively for
the middle of the 100 year return period storm, and in Figure 33 and Figure 34 for the
middle of the 1000 year storm.

In both cases, the overall pattern of failure is similar to that for the undegraded system. The
main differences are that the outer skirt piles have a considerably reduced shaft friction
capacity.

Table 8 gives the environmental load factor for first pile component failure and the system-
based RSR at the middle and at the end of the two storms. It can be seen that the system
capacity at the middle of the 100 year storm reduced by 17%, whereas the component
failure load factor reduced by 24%.

The reduction in component failure load factor was less than the degradation in the actual
capacity of the pile; 24% compared with 32%. This is because the critical failure
component, pile S6 failing in tension, was initially in compression due to the initial vertical
loading. Part of the environmental loading was required to overcome this dead loading.

The critical component was pile S6 failing in tension, whereas the design was critical for pile
S1 failing in compression. As a result of the redistribution that occurred once the
compressive shaft friction resistance was overcome, pile S6 attracted less load and was
thus, in a way, “protected” against complete tip failure by its sudden loss in stiffness. This
was a feature of the pile system, and for non-redundant foundation systems, for example
four legged Jackets, redistribution cannot occur, and failure will most likely be governed by
the compressive pile failure. In such a case the RSR is likely to be very close to the first
component failure load factor. Degradation is expected to have an effect on the RSR close
to that on the individual pile capacity, i.e., of 15% at the middle of the storm.
Table 8 Degradation in foundation capacity

Middle of Storm End of Storm

Component System Component System
Failure Factor RSR Failure Factor RSR
Undegraded Structure 1.90 2.95 1.90 2.95
1.45 2.45 1.10 2.20
100 Year Storm
24% 17% 42% 25%
1.20 2.20 0.70 1.75
1000 Year Storm
37% 25% 63% 41%

39
 3 3

Pile Head

ad
2.5 2.5

He
le
Pi
Top of Platform

Environmental Load Factor

Environmental Load Factor

2 Top of Platform
2

1.5 1.5

1 1

0.5 0.5

0-0.5 0 0.5 1 1.5 2 2.5 3 0-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Deflection (m) Deflection (m)

Figure 29 Pushover analysis for Figure 30 Pushover analysis for

degradation in middle of 100 year storm degradation in middle of 1000 year storm

40
 Compression Tension Compression Tension
3 3

L10 L9 L10 L9 S2 S1 S7 L11 L12 S5

2.5 S7 L11 L12 2.5
S2 S1 S3 S5
S4 S4 S3

Environmental Load Factor

Environmental Load Factor

2 S8
2 S6

1.5 S8 S6 1.5

1 1

0.5 0.5

0 -60 0-0.7
-50 -40 -30 -20 -10 0 10 20 30 40 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
Pile Axial Force (MN)
Pile Axial Displacement (m)

Figure 31 Middle of 100 Year Storm: Axial Pile Load vs. Figure 32 Middle of 100 Year Storm: Axial Pile Deflection vs.
Environmental Load Factor Environmental Load Factor

Pile Arrangement S6 S8

S5 L11 L12 S7
Loading Direction

S2 L9 L10 S4

S1 S3

41
 Compression Tension Compression Tension
3 3

2.5 2.5
S4 S2 L10 L9 S3 S1 L11 L12 S5
S7
L10 L9 S7 L11 L12 S5
S2 S1

Environmental Load Factor

2 2
Environmental Load Factor

S4 S3 S8 S6

1.5 S8 1.5
S6

1 1

0.5 0.5

0 -60 0-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
-50 -40 -30 -20 -10 0 10 20 30 40
Pile Axial Force (MN) Pile Axial Displacement (m)

Figure 33 Middle of 1000 year storm: axial pile load vs. Figure 34 Middle of 1000 year storm: axial pile deflection vs.
environmental load factor environmental load factor
S6 S8
Pile Arrangement
S5 L11 L12 S7
Loading Direction

S2 L9 L10 S4

S1 S3

42
9. REANALYSIS FOR DEGRADATION THRESHOLD MODEL

The full degradation model used for the above analyses assumed that all the waves impinging
the structure during a storm contributed to the degradation of the shaft frictional resistance.
The experiments by Jardine [1] showed that small amplitude cycles have the effect of
increasing the rate of ageing resulting in an increase in the shaft capacity. Changes in pile skin
friction capacity are therefore a combination of gain in strength in those parts of the pile
subjected to low amplitude cycling, and degradation in strength in those parts of the pile
where the local cyclic shear stress amplitude is high. In the absence of an appropriate model
for local increase and degradation of pile strength, it was decided, after discussion with
Jardine, to obtain an approximate threshold for the cyclic component of the total pile axial
force below which no capacity degradation occurs and above which the full degradation
model used above was to be implemented.

The threshold for the cyclic axial loading component was determined by considering an
equivalent threshold obtained from the full scale experiments at Dunkirk. An analysis was
performed on the test pile using the Mathcad spreadsheet.

Jardine's experiments showed that the static capacity of a 19.4 m long Dunkirk pile
degraded when Pcyc/Pmax was above 0.3 times of the original tensile shaft capacity, but
showed enhanced ageing when Pcyc/Pmax was below 0.2 times the original tensile shaft
capacity. Here Pcyc is the axial cyclic loading component and Pmax is the total tensile pile
capacity. On the basis of these results it was decided that, for the Dunkirk pile, the value of
Pcyc/Pmax below which no degradation occurs was 0.25 times the original tensile capacity.

The percentage of tensile capacity degradation predicted by the Mathcad spreadsheet is

plotted as a function of Pcyc/Pmax for the Dunkirk test pile and for the synthetic leg and skirt
piles in Figure 35. All piles where subjected to 1000 constant amplitude cycles. The
threshold value of Pcyc/Pmax for the synthetic piles was derived on the assumption that the
percentage degradation predicted by the Mathcad spreadsheet for the threshold value of
Pcyc/Pmax for Dunkirk pile is equal to that predicted for the Skirt and Leg piles at their
threshold values of Pcyc/Pmax. It can be seen from Figure 35 that the model predicted 22%
degradation for the Dunkirk pile at the end of the 1000 cycles at the threshold value of
Pcyc/Pmax of 0.25. The synthetic piles both gave this level of degradation for Pcyc/Pmax equal
to 0.2. Thus, the threshold value of Pcyc/Pmax below which it was assumed that no
degradation would take place, was taken to be 0.2.

43
 50.0%

45.0%

40.0%
Skirt Pile Leg Pile
35.0%
% Degradation

30.0%

25.0%

20.0% Dunkirk Pile

15.0%

10.0%

5.0%

0.0%
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Pcy/Pmax

Figure 35 Relationship between cyclic load amplitude and degradation after

1000 cycles as predicted by the degradation model

It was seen from the full degradation analysis that the axial cyclic load component of the
force attracted by the piles changed for the same wave height as the cyclic load history
progressed. The outer skirt piles attracted smaller load and the inner skirt piles and leg piles
attracted greater load as the outer piles lost stiffness relative to the inner piles as the storm
progressed. For the maximum wave occurring in sea-states 3, 4 and 5, this reduction was of
the order of 6% for the 100 year wave history. For the reanalysis of the system using the
threshold model, it was assumed that this redistribution does not occur, and that the pile
forces induced by a given wave height do not change as a consequence of pile degradation.
On this basis, the threshold cyclic force component and wave heights for the outer and inner
leg piles, and the leg piles were calculated and are tabulated in Table 9 below.

Table 9 Threshold cyclic axial load and wave height

Threshold Cyclic Axial Force Threshold Wave

Component Height
[MN] [m]
Outer Skirt Piles 6.8 19.2
Inner Skirt Piles 6.8 29.2
Leg Piles 5.8 27.1

44
A rediscretisation of the 100 year and 1000 year storms was carried out in order to ensure
that the waves above the threshold wave height were sufficiently well represented. The
selected wave blocks for the 100 year storm are tabulated in Table 10. The modal value of
the maximum wave in the 100 year storm does not exceed the degradation threshold for the
leg and skirt piles. The wave blocks for the outer skirt pile wave blocks of the 1000 year
storm are given in Table 11, and those for the leg piles in Table 12. The modal maximum
wave in the 1000 year storm will not cause degradation in the inner skirt piles.

The degradation in pile capacity calculated using this approach are depicted in Figure 36
and Figure 37.

Table 10 Analysis with degradation threshold: wave discretisation, 100 year

storm, outer skirt piles

Sea State Number

Wave Height Cyclic Axial Force
2 3 4 5 6
(m) (MN)
19.5 7.0 1 11 24 11 1
22.1 8.7 0 3 8 3 0
25.0 10.6 0 0 2 0 0

Table 11 Analysis with degradation threshold: wave discretisation, 1000 year

storm, outer skirt piles

Sea State Number

Wave Height Cyclic Axial Force
2 3 4 5 6
(m) (MN)
20.6 7.7 6 25 43 25 6
23.5 9.7 1 8 19 8 1
26.4 11.9 0 2 7 2 0
29.2 14.3 0 0 2 0 0

45
 Table 12 Analysis with degradation threshold: wave discretisation: 1000 year
storm, leg piles

Sea State Number

Wave Height Cyclic Axial Force
2 3 4 5 6
(m) (MN)
28.9 7.0 0 1 4 1 0

100 Year Storm: Reanalysis

1.00

0.90 S1, S3
Degradation Ratio

0.80
S6, S8
0.70

0.60

0.50

0.40
1 2 3 4 5 6 7
End of Sea State Number:

Figure 36 Analysis with degradation threshold: 100 year storm. Pile

degradation history

46
 1000 Year Storm: Reanalysis
1.00 L9, L10
L11, L12
0.90
Degradation Ratio

0.80

0.70
S1, S3
0.60

0.50
S6, S8
0.40
1 2 3 4 5 6 7
End of Sea State Number:

Figure 37 Analysis with degradation threshold: 1000 year storm. Pile

degradation history

Table 13 Analysis with degradation threshold. Individual pile capacity degradation

100 Year Storm 1000 Year Storm

Middle of Storm End of Storm Middle of Storm End of Storm
Comp. Tens. Comp. Tens. Comp. Tens. Comp. Tens.
Outer 12% 15% 16% 21% 25% 33% 39% 49%
Skirt Pile
Inner Skirt 0% 0% 0% 0% 3% 4% 4% 5%
Pile

Leg Piles 0% 0% 0% 0% 0% 0% 0% 0%

Individual pile capacity degradation for the analysis with the degradation threshold is given in
Table 13. The outer skirt piles suffered the most significant degradation, with a maximum
15% loss in tensile shaft capacity after sea-state 4 for the 100 year storm, and 33% loss in
tensile capacity for the 1000 year storm.

Individual degraded soil t-z spring capacity and stiffness parameters were output by the
Mathcad spreadsheet at the end of sea-state four and at the end of the storm. These were
then read in by the RASOS program and used for pushover analyses in order to obtain the

47
foundation system RSR. The RSR and environmental factor at first pile failure obtained from
these analyses are tabulated in Table 14.

Table 14 Threshold analysis: degradation in reserve strength ratio

Middle of Storm End of Storm

Component Component
System System
Failure Failure
RSR RSR
Factor Factor
Undegraded Structure 1.90 2.95 1.90 2.95

1.75 2.80 1.65 2.70

100 Year Storm
8% 5% 13% 9%
1.50 2.55 1.25 2.40
1000 Year Storm
21% 14% 34% 19%

The results for the analysis with the degradation threshold obviously showed considerably
less overall degradation than the full degradation model. At the middle of the 100 year
storm, i.e. after sea-state 4, the worst degradation of 15% was seen in the outer skirt pile.
For the 1000 year storm the degradation in the outer skirt pile at the middle of the storm
was 33%.

The degradation in component failure capacity was 8% at the middle of the 100 year storm
and 21% at the middle of the 1000 year storm. This is considerably lower than the individual
pile capacity degradation, and was a result of the initial compressive dead loading and the
redistribution following exhaustion of the compressive shaft friction capacity, factors already
described in the discussion on the full degradation model results.

The degradation in system capacity was 5% for the 100 year storm and 14% for the 1000
year storm. The degradation in system capacity observed in the 100 year storm is thus small.
Again this is a reflection of the enhanced strength of the platform arising from system effects.
The inner skirt piles and the leg piles showed no degradation at all during the 100 year
storm, and very little degradation during the 1000 year storm. However their strength
needed to be mobilised for full foundation collapse.

48
10. CALCULATION OF PROBABILITY OF COLLAPSE

10.1 Conditional probability of failure during a storm

During a storm a platform is subjected to a sequence of waves of varying amplitude, period

and direction. Moreover other environmental parameters such as current and wind also
affect the platform and also vary in magnitude and direction.

For the platform to collapse during the course of a storm it must, at some point, experience
environmental forces sufficiently high to exceed its capacity. If wave-induced degradation of
the foundation capacity occurs, then the platform capacity at a given instant in time is a non-
stationary stochastic process which is a function of the random wave history up to that
instant. Similarly, the platform loading is also a non-stationary random process. The safety
margin M(t) at any instant in time t is:

M ( t ) = λR R( t ) − B F F ( t ) (15)

where R(t) is the random platform base-shear capacity at time t during the storm, λR is a
time-independent random variable representing the resistance uncertainty, F(t) is the total
force on the platform at time t and BF is a time-independent random variable representing
the uncertainty in modelling the environmental loading on the jacket. The probability of
failure during a storm is thus the probability that the safety margin M(t) is smaller than zero at
any instant during the storm. This may be written as:

 
Pf = P  U (λR R( t ) − BF F( t ) < 0)  (16)
0 < t <t Storm 
The task of evaluating this expression is not trivial and considering the nature of the physical
degradation model, a simplified approach was adopted.

If the foundation capacity degrades continuously throughout the storm (i.e. R(t) is a
monotonically decreasing function of t), then Equation (16) is equivalent to:

( )
   
Pf = P  U  λR R(t ) − B F F max( H(τ) ) < 0  = P  U ( M ′( t ) < 0)  (17)
τ >t
0 < t < t Storm  0 < t <t Storm 
where the force component is now that induced by the wave of maximum height following
instant t.

The probability of failure given by Equation (17) is expressed in terms of the union of an
infinite number of failure events given in terms of a continuous variable t. However the safety
margin M'(t) is expected to have high autocorrelation over a long period of time. Under
these conditions, an appropriate approximation for the failure probability in a given storm is:

0 <t < t storm

([ ( τ >t
) ])
Pf ≈ max P λ R R (t ) − BF F max (H (τ)) < 0 = max ( P[M ′( t ) < 0])
0 < t <t storm
(18)

49
The instant at which the maximum probability value of Equation (18) occurs is approximately
the same point at which the safety margin M'(t) takes on its minimum value. Figure 38 shows
the system capacity degradation, the most likely maximum force and the safety margin M'(t)
at the end of each sea state of the 100 year storm. All three quantities have been normalised
to unity at the start of the storm. The safety margin can be seen to reach a minimum value in
sea state 4.

1.4
Normalised Maximum Force Following Sea State
1.3
Normalised System Capacity
1.2
Normalised Measure

Normalised Safety Margin

1.1
1.0
0.9
0.8
0.7
0.6
0.5
0 1 2 3 4 5 6 7
End of Sea State

Figure 38 Normalised degradation, force and RSR for full degradation model
during 100 year storm

On the basis of this analysis, the point in the storm which is most critical with regards to the
safety of the platform was taken to be at the end of sea-state 4. In calculating the conditional
probability of failure for a given storm, the wave height distribution was taken to be that of
the maximum wave in the whole storm. Gumbel fit parameters for the complete storm Hmax
have been given in Table 4. The force model uncertainty parameter BF was taken to be
lognormal with a median of 1 and a cov of 0.15. The random resistance parameter λR was
taken to be lognormal with a median of 1 and a cov of 0.25.

The conditional probability of failure given a storm is calculated using the conditional short-
term Hmax distribution parameters given in Table 4 and using the First Order Reliability
Method implemented in RASOS.

The conditional probability of platform failure probability for the 100 and 1000 year storms
is tabulated in Table 15. Three failure criteria were considered: First component failure,
system failure and failure assuming that the system degradation was equal to the degradation
in the most degraded pile. This last criterion gives an indication of the effects of degradation
on the reliability of non-redundant foundations where the environmental loading is large
compared with the dead load effects, and for which foundation failure is governed by tensile
pile failure. It has been included here in order to estimate the influence of degradation on
platforms with non-redundant foundation systems.

50
 Table 15 Conditional probabilities of component and system collapse

Deterministic Environmental Load Factor Conditional Failure Probability

System System
Degradation degradation degradation
Model Type Component System equals Component System equals
maximum pile maximum pile
degradation degradation

100 Year Undegraded 1.90 2.95 2.95 1.8 × 10 -2 3.5 × 10 - 3.5 × 10 -4

Storm Structure 4

Full 1.45 2.45 2.00 1.0 × 10 -1 2.1 × 10 - 2.5 × 10 -2

Degradation 3

Analysis with 1.75 2.80 2.51 3.1 × 10 -2 5.8 × 10 - 6.0 × 10 -3

Threshold 4

1000 Year Undegraded 1.90 2.95 2.95 1.4 × 10 -1 7.3 × 10 - 7.3 × 10 -3

Storm Structure 3

Full 1.20 2.20 1.48 6.8 × 10 -1 6.7 × 10 - 5.3 × 10 -1

Degradation 2

Analysis with 1.50 2.60 1.98 3.8 × 10 -1 2.0 × 10 - 2.5 × 10 -1

Threshold 2

10.2 Annual probability of failure for all possible storms

In order to estimate the total annual probability of failure, it is necessary to consider the
possibility of failure over all possible storms. The annual probability of collapse may be
calculated from conditional probabilities of collapse for storms of given return period T from
the following expression:

1
∞ 1 −T
P(F ) = ∫ P(F | S T ) e dT (19)
0 T2
where P(F) is the probability of failure and P(F|ST) is the conditional probability of failure
during the storm of return period T. It is assumed that between storms the piles recover
their initial capacity.

The conditional failure probability P(F|ST), was expressed as a function of storm return
period using a relationship of the form

− ln ( − ln ( P[F | ST ])) = a0 + a1 ln (T ) + a 2 (ln (T ) )2 (20)

51
 The parameters a0, a1 and a2 were derived in each case from a curve fit of the conditional
probabilities obtained from the analyses for the 100 and 1000 year storms. The expression
of the conditional probability as a function of return period given by Equation (20) were then
substituted into Equation (19) and the required integration performed numerically.

The conditional probabilities of system and component failure for the case where no
degradation takes place have been calculated for storms of seven different return periods.
This involved little analysis since only the loading model changes with storm return period
and not the strength model.

For the degraded cases only two data points are available, corresponding to the 100 and
1000 year return period storms. A quadratic fit was made by noting that, for low return
periods, the curves are asymptotic to the zero degradation curve. The curve fits for the three
failure criteria are shown in Figure 39, Figure 40, and Figure 41.

An examination of the integrand of Equation (19) showed that the most significant
contribution was for values of return period between 10 and 5000 years. Thus the range
over which the curve fit was carried out seems appropriate for calculating the total failure
probability. However the accuracy of these estimates would be greater if more storms had
been analysed.

Conditional Probability of Failure Given A Storm of Return Period T Conditional Probability of Failure Given A Storm of Return Period T

1 6

0.5 5

4
0
Full Model Full Model
3
-Ln(-Ln(P[F|T]))

-Ln(-Ln(P[F|T]))

-0.5 Threshold Model Threshold Model

No Degradation 2 No Degradation
-1
1
-1.5
0
-2
-1

-2.5 -2

-3 -3
0 2 4 6 8 10 12 0 2 4 6 8 10 12
Ln(T) Ln(T)

Figure 39 Conditional probability of Figure 40 Conditional probability of

system collapse, P(F|T) for storms of component failure, P(F|T) for storms of
different return period, T different return period, T

52
 Conditional Probability of Failure Given A Storm of Return Period T

3
Full Model

-Ln(-Ln(P[F|T]))
2 Threshold Model
No Degradation
1

-1

-2

-3
0 2 4 6 8 10 12
Ln(T)

Figure 41 Conditional probability of system failure P(F|T) assuming foundation

system degradation equals maximum pile degradation for storms of different return
period, T

The total annual reliability against component failure and overall collapse for the two
degradation models are given in Table 16.

Table 16 Annual pile system collapse probability for threshold model

System Failure
assuming uniform
Component Failure System Failure
maximum pile
degradation
Annual Annual Annual Annual Annual Annual
Reliability Failure Reliability Failure Reliability Failure
Index Probability Index Probability Index Probability

No
3.1 9.3 × 10-4 3.9 4.7 × 10-5 3.9 4.7 × 10-5
Degradation

Full Degradation
2.6 4.2 × 10-3 3.4 3.1 × 10-4 2.9 2.1 × 10-3
Analysis

Analysis with
2.9 1.9 × 10-3 3.7 1.1 × 10-4 3.1 9.2 × 10-4
Threshold

The results show that the full degradation model gives failure probability estimates
approximately twice those obtained using the threshold model. Since the threshold model is
considered to be the currently available best estimate of the degradation process, it will be
used for assessing the relative effects of degradation on annual failure probability. A full
discussion of the implications of these results is given in Section 11 below.

The annual reliability index against collapse for no degradation is 3.9 corresponding to an
annual probability of failure of 4.7 × 10-5. The annual reliability index against collapse

53
accounting for degradation using the threshold model is 3.7, giving a failure probability of
just over twice that for the undegraded structure of 1.1 × 10-4. The annual reliability index
against component failure is 3.1 corresponding to an annual probability of 9.3 × 10-4.

The annual reliability estimated assuming that all piles have the same amount of degradation
as the most degraded pile reduces from 3.9 to 3.1 when the threshold model is used. This
corresponds to an increase in annual failure probability from 4.7 × 10-5 to 9.2 × 10-4, a
twenty-fold increase in failure probability.

54
11. SUMMARY AND CONCLUSIONS

11.1 Analysis procedure

This study considered the effects of cyclic degradation in the axial capacity of cylindrical
driven piles in sand.

A local model for the degradation of shaft frictional shear resistance was implemented into a
discretised t-z model of a single pile subject to cyclic axial loading. The local model,
originally based on the results of cyclic simple shear tests on sand from a North Sea site,
was modified on the basis of a comparison between single pile analysis and full-scale cyclic
pile test results. This calibration did not account for the ageing to which the piles in the
experiment had been subjected.

The degradation model has the following limitations

• The soil comprises a single layer of sand.

• There is no explicit model for ageing.

• Only regular constant-amplitude cyclic loading is considered.

• Degradation in tip capacity and lateral capacity has not been considered.

Following the initial single pile calibration, the response of an example central North Sea
platform was considered. The structural form, foundation layout and loading of the platform
were taken from a real structure, but an artificial soil profile was used. The synthetic soil
profile was derived to ensure that the design criteria under extreme wave loading for the
most stressed pile were just met. The loss in platform capacity during storms of return
period 100 years and 1000 years was considered. These storms were discretised into
blocks of constant-amplitude waves.

A full degradation analysis of the platform was performed for both storms in which the
degradation model was applied regardless of the wave amplitude. The analysis was carried
out for storms of 100 and 1000 year return period.

The field work at the Dunkirk site revealed new information regarding the interaction
between the ageing and degradation processes which was not known when the analytical
work was started. In particular it was seen that low levels of pile cyclic loading can enhance
the ageing process and lead to a gain in strength. To account for this, an approximate
treatment was applied in which the interaction between degradation and ageing was
accounted for using a threshold level of pile cyclic loading below which no cyclic
degradation was assumed to occur. The threshold was calibrated against the field test
results. Analyses using the degradation threshold were performed for the 100 and 1000 year
return period storms.

55
 The structural analysis made the following assumptions

• The effects of long term ageing were ignored.

• The effects of cyclically enhanced ageing were modelled using a threshold on cyclic
load amplitude

• The jacket structure remains elastic and, consequently, the interaction between pile
and structural failure was not considered.

• The storms were modelled as discrete blocks of constant amplitude waves.

• Waves approached the platform from the broadside direction only.

• The effects of previous storms were ignored.

These limiting assumptions were, for the main part, dictated by the nature of the degradation
model. It is considered that the results here obtained represent a reasonable estimate of the
amount of degradation to be expected during the analysed storms in the light of the field
studies.

11.2 Analysis results

The model with the cyclic loading threshold is considered to be a better model than that
which calculates degradation for all wave amplitudes, and the following results and
discussion refer to this analysis. Degradation in the capacity of the foundation system was
calculated in terms of the following quantities:

1. The degradation in individual pile capacity half way through the storm.

2. The load factor required to cause failure of the first pile, defined in terms of the
factor on the extreme 100 year design environmental loading calculated half way
through the storm.

3. The Reserve Strength Ratio defined in terms of the factor on the extreme 100 year
design environmental loading required to cause collapse of the complete foundation
system calculated half way through the storm.

4. Annual probability of failure of a single pile.

5. Annual probability of failure of the foundation system.

6. Annual probability of system failure assuming that the percentage degradation of the
overall foundation system capacity equals that of the most severely degraded pile.

The deterministic capacity measures 1, 2 and 3 above are given in Table 17. The reliability-
based quantities, 4, 5 and 6 above are given in Table 18 where they are compared with the
reliability of the undegraded foundation system.

56
 Table 17 Summary of deterministic results

1 2 3
Maximum
Reduction in
Reduction in Reduction in
First Pile
Outer Skirt RSR
Failure Load
Pile Capacity

100 Year Storm 15% 8% 5%

1000 Year Storm 25% 21% 14%

Table 18 Annual probability of pile system collapse

4 5 6
System Failure
assuming pile system
Component Failure System Failure degradation equals that
of the most degraded
pile
Annual Annual Annual Annual Annual Annual
Reliability Failure Reliability Failure Reliability Failure
Index Probability Index Probability Index Probability

No Degradation 3.1 9.3 × 10-4 3.9 4.7 × 10-5 3.9 4.7 × 10-5

With Degradation 2.9 1.9 × 10-3 3.7 1.1 × 10-4 3.1 9.2 × 10-4

11.3 Conclusions specific to the platform considered

Taking into account that, for recently driven piles, the threshold treatment represents the
current best estimate for cyclic degradation of pile shaft capacity in sands, the following
conclusions specific to this analysis may be made.

A. The high degree of redundancy of the pile system led to a considerable increase in
capacity above that assumed in design, which is based on a component approach.
For the undegraded foundation system, the component failure load factor was 1.9
and the system RSR was 2.95. Specifically, system collapse required mobilisation of
the majority of the piles in the system plus mobilisation of the pile head bending
resistance before the foundation system failed by overturning. Furthermore, it was
found that the design-critical compressive skirt piles attracted little load compared to
the other piles once their shaft capacity had been exhausted. This behaviour, which
arose from the high redundancy of the foundation system, meant that the analysed

57
 platform had considerable reserves of strength above the levels for which it was
designed.

B. The greatest degradation was seen to occur in the tensile capacity of the outer-most
skirt piles. This was 15% for the 100 year storm and 25% for the 1000 year storm.

C. The reduction in environmental load factor at first pile failure was 8% for the 100
year storm and 21% for the 1000 year storm. The load factor at first pile failure was
influenced by structure-specific system effects, and its value showed a smaller
decrease than the individual pile capacity. In particular the presence of constant
vertical loading and the redistribution of forces away from the outer-most
compressive skirt pile following full mobilisation of its shaft capacity contributed
towards making the degradation in the load factor at first component failure lower
than the degradation in individual pile capacity.

D. The reduction in system-collapse-based RSR from the threshold analysis was 5%

for the 100 year storm and 14% for the 1000 year storm. The reduction in RSR
was calculated half way through the storm.

E. A considerable difference between the degradation in individual pile capacity and

the degradation in the system-based RSR measure was observed. This difference
was primarily governed by the redundancy of the foundation system.

F. The estimated annual probability of both system and component failure of the
degraded structure was twice that of the undegraded structure. The effect of
degradation was a reasonably small effect in terms of overall probability of failure.
However this is a structure-specific measure and is dependent on the overall system
redundancy and the extent to which environmental load governs the design.

G. Assuming that the degradation of the complete pile system equals that of the most
degraded pile, the annual reliability index was estimated to reduce from 3.9 for the
undegraded foundation system to 3.1 for the degraded foundation system,
corresponding to a twenty-fold increase in annual failure probability from 4.7 × 10-5
to 9.2 × 10-4. This relative increase would be expected for platforms with minimal
redundancy in the foundation system and for which the pile design is governed by
the overturning effects arising from the extreme environmental load case. For such
structures, overall collapse is governed by the first pull-out or tensile pile failure.

11.4 Generic Conclusions

These conclusions are based on the results of the analysis with the degradation threshold and
relate to sands with no long-term ageing.

As has been seen, the platform considered in this study was not critical with respect to the
effects of degradation on its overall foundation capacity. The system RSR was seen to be
reduced by 5% as a consequence of degradation in the 100 year return period storm. The
maximum degradation in a single pile was 15% for the tensile capacity of the outer-most

58
skirt pile. For platforms with few piles for which system failure is governed by the first pile
failure, this figure of 15% can be assumed to be an appropriate measure of the degradation
in total structural capacity. This would correspond to a twenty-fold increase in annual failure
probability arising from degradation. This is a quite significant increase in failure probability,
and could very well have implications for the integrity of platforms with non-redundant
foundation systems.

On the basis of this study, a number of factors have been identified as having a possible
impact on the overall effects of wave-induced pile capacity degradation. These are listed in
the following:

A. Foundation system redundancy. This is the major contributor to the difference

between individual pile degradation and foundation system degradation observed in
this analysis. Reduction of the pile system redundancy could result in the
proportional degradation of the complete pile system which is the same as that for
an individual pile.

B. Increased criticality of environmental load in pile design. For some platforms,

the relative proportion between dead and environmental loading may be higher than
for the example platform analysed here. This will result in a foundation system in
which the pile is designed to resist a higher proportion of wave loading to dead
loading than in this example. Waves passing through the platform will lead to cyclic
loading which is a higher proportion of the pile capacity than in this example. This
will lead to a greater amount of degradation as a proportion of capacity than for the
example platform.

C. Decrease in shaft capacity relative to tip capacity. This will lead to complete
load reversals over the whole pile length at a lower level of cyclic loading than for
the example platform. This may lead to a relative increase in shaft degradation. The
effect could, however, be offset by the increase in tip capacity which does not
degrade.

D. Design-criticality of piles in tension. Increased design criticality of tension piles,

for which shaft friction degrades over the whole length, could lead to greater cyclic
loading down the pile and thus greater individual degradation.

59
12. RECOMMENDATIONS FOR FUTURE WORK

This pilot study has highlighted a number of areas which indicate significant effects of short-
term degradation on a foundation system. Although the system considered was by no means
critical as regards its sensitivity to degradation induced by cyclic loading, a number of
important features were highlighted.

12.1 Soil modelling

During the course of the study, and as more experimental results were obtained, it became
clear that there is considerable complexity in the interaction between long-term ageing of
piles and their response to cyclic loading events. These effects require considerably more
study for them to become fully understood.

The soil model considered in this study was developed for blocks of constant amplitude
cyclic loading. In a realistic storm scenario, a platform is subject to a variable amplitude
loading which could lead to a different degradation ratio. This effect should be further
studied.

The present model is applicable only to sand. The effects of cyclic loading on clays and
layers of mixed sands and clays should also be considered.

12.2 Storm modelling and reliability

The capacity of the foundation system has been found to depend on a complex interaction
between ageing and degradation. Storm events can give rise to degradation or enhanced
ageing, with ageing also occurring between storms. The full nature of this behaviour is not yet
fully understood, and work should be directed first towards a deeper understanding of these
phenomena, and then towards how this understanding can be combined with the random
environmental models. This will then provide a means of calculating the foundation system
failure rate expressed in terms of the probability of foundation system failure.

The following aspects are important for the derivation of the annual failure probability given
appropriate models for pile capacity ageing and degradation interaction:

1. Storm history. The random storm history will influence the capacity of the foundation
system given that prior storms will give rise to an interaction between degradation and
ageing and that ageing will occur between storms.

2. Age of the platform. The annual failure probability (failure rate) is a function of the age
of the platform, given that the foundation capacity is dependent on storm history and
time. An assessment of annual failure probability at different times in the platform lifetime
is required. This will entail the investigation of the probabilities of collapse given
alternative scenarios of prior storms and collapse storms, and the derivation of the
probability of occurrence of these scenarios.

60
12.3 Structural analysis

There is a wide variety of loading conditions, structural types, foundation systems and soil
types present in the North Sea, each combination of which may show a different sensitivity
to degradation effects. It was seen that the structural system considered in this study was by
no means critical. It possessed a high degree of redundancy in the foundation system which
led to a considerably higher value in the undegraded foundation capacity over and above the
design criteria. It was found that, because of this redundancy, only the outermost piles
significantly lost capacity. The result was a small loss in overall pile system capacity.

For other foundation systems this loss could be much more prominent and thus and
improved understanding of the degradation of a variety of different foundation systems is
urgently needed. It is important to study a wider variety of structural types and soil profiles.
In particular the following aspects are important:

1. Redundancy of the pile system. Many platforms have very little pile system
redundancy. This makes foundation failure more design-critical and also results in a
larger effect of the overall degradation.

2. Criticality of the environmental loading on pile design. The relative proportions

of dead and environmental load influence the ratio between cyclic load amplitude
and pile capacity. This will influence the amount of pile degradation.

3. Soil profile. The effects of different soil layering is important in influencing the
spread of the high amplitude cyclic load reversals down the pile.

4. Pile geometry. The effect of pile geometry influences the relative stiffness between
pile and soil and the consequently the spread of skin friction capacity mobilisation
down the pile. Piles with low D/t ratios will be relatively stiffer and will experience
full cyclic reversal over a greater proportion of their length.

5. Lateral soil behaviour. The effect of variations in the lateral soil stiffness and
capacity may affect the cyclic axial loading down the pile, and the degree of
degradation. Furthermore, the discrete spring models do not take account of any
local interaction between axial and lateral pile capacity, stiffness, degradation and
ageing.

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13. REFERENCES

[1] Jardine, R.J. and Standing, J.R, “Final report on HSE funded cyclic loading study”, for
Imperial College Consultants (ICON), March 1999.

[2] Jardine, R.J., “Interim Report on Cyclic Loading Model and Synthetic Soil Profile for HSE
Funded Pile Cyclic Loading Study”, for Imperial College Consultants (ICON), October
1998.

[3] Jardine, R.J. and Standing J.R., “Report on pile testing performed for HSE cyclic loading
study and EU funded GOPAL project at Dunkirk, France,. Phase 3, April-May 1999”, for
Imperial College Consultants (ICON).

[4] Jardine R.J. and Chow F.C., “New Design Methods for Offshore Piles”, Marine
Technology Directorate, 1996.

[5] “Mathcad 8 User's Guide”, Mathsoft 1998.

[6] “API Recommended practice for Planning, Designing and Constructing Fixed Offshore
Platforms-Working Stress Design”, 20th Edition, American Petroleum Institute, 1993.

[7] ISO TC 67/SC7/WG3 Annex 1.”Metocean Criteria” Draft.

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