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OTC 20158

Re-Assessment of P-Y Curves for Soft Clays from Centrifuge Testing and Finite Element Modeling P. Jeanjean, BP America Inc.

Copyright 2009, Offshore Technology Conference This paper was prepared for presentation at the 2009 Offshore Technology Conference held in Houston, Texas, USA, 4–7 May 2009. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract The paper focuses on the results of centrifuge testing on a laterally loaded conductor. The conductor was installed to simulate jetted conditions and lateral transfer curves (so called P-Y curves) were generated for monotonic and cyclic conditions. The influence of a previous set of cyclic loads on the subsequent behavior of the pile when subjected to additional cyclic loads was investigated. The paper focuses on the determination of P-Y curves tangent and secant moduli since there are the key input parameters for structural software in determining the lateral displacements of the conductor and therefore the cyclic fatigue-generating stresses in the conductor. Results show that the P-Y curves as recommended by API RP2A (2000) can be conservative, with moduli and ultimate unit pressures less than what test data and theoretical modeling suggest. The centrifuge tests validated theoretical curves derived via Finite Element Analyses (FEA) and described by Templeton (2009). Equations are proposed to generate the backbone P-Y curves and to calculate the secant modulus to the P-Y curves to analyze the cyclic loading of interest to this paper. Introduction Roadmap for the paper The paper is divided into the following parts:

• It first describes the problem of interest and defines the jetted conductor loading conditions that were studied. • It then describes the theoretical Finite Element Analyses (FEA) that were performed and the obtained P-Y curves, • After which the centrifuge tests performed to calibrate the FEA derived P-Y curves are detailed. • An extensive comparison of the P-Y curves from the FEA analyses and the P-Y curves is presented, • And new equations to derived backbone P-Y curves for soft clays are proposed. • Last, conclusions from centrifuge pile head load displacement curves are listed, along with implications for pile

design. Loads on jetted conductor for top tension risers The study work reported herein focuses on the evaluation of lateral small-displacement soil-structure interaction for jetted conductor fatigue analysis. The conductor is assumed to be connected to a floating structure via a top-tensioned production riser. As the riser responds to the platform motions and to the sea currents, it imparts loads on the well head and the conductor. These loads are being applied simultaneously but, as a simplification, these loads are assumed to be applied independently, when calculating fatigue life.. A large fatigue safety factor covers this non-conservative assumption. The loads, which are assumed to be collinear, that induce fatigue damage in the conductor can be divided into three categories: Vessel Motions (VM), Hull Vortex Induced Hull Motion (VIM), Riser Vortex Induced Vibration (VIV) (Fig. 1):

• Vessel Motions: The platform, or vessel, motions are separated in motions caused by the wind and waves first. These are the "vessel motions or VM". A finite element model of the hull, the mooring the risers and well foundations are subjected to various sea and wind conditions for 3 hours. From these 3 hours simulations, the fatigue rate of the connector is calculated. The total VM fatigue rate is the metocean condition frequency weighted sum of these fatigue rates.

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• Hull VIM: The vessel hull will oscillate in certain current conditions and produce "hull Vortex Induced Motions” or

“hull VIM". Physical model of the hull and its mooring have been towed at various speed and orientations to determine the anticipated amplitude and period of these oscillations. These oscillations for the various expected current speeds and directions have been used to derive a vessel finite element model and the fatigue rate have been combined with the occurrence frequencies to generate fatigue rates.

• Riser (VIV): The riser, when subjected to current, will VIV in the non-strake section. The normal modes of the riser

and its foundation where determined with a finite element model of the riser and its foundation. (Beynet, 2008) For the study case, the vessel motions (VM), Hull VIM, and the riser VIV caused 20%, 32%, 48% of the total fatigue damage respectively.

Wind and waves forces cause vessel motions

Some current conditions cause hull VIM

Current forces cause riser VIV

Conductor

Wellhead

Riser

Hull

Drawing not to scale

Wind and waves forces cause vessel motions

Some current conditions cause hull VIM

Current forces cause riser VIV

Conductor

Wellhead

Riser

Hull

Drawing not to scale

Wind and waves forces cause vessel motions

Some current conditions cause hull VIM

Current forces cause riser VIV

Conductor

Wellhead

Riser

Hull

Drawing not to scale

Fig. 1: Schematic of types of loads on conductor for a top tensioned riser. Pile cyclic stresses and fatigue damage The key point of the soil-structure analysis of the conductor is to determine the cyclic stresses in the conductor caused by the above loads. It is the cyclic stress range that is of interest and not the absolute stress level. Indeed, fatigue failures in metals and other materials are mechanistically driven by the accumulation of damage to the materials as characterized by the Palmegrin-Miner Damage Rule. This rule relates the number of cycles at a specific stress range and associated plastic strain range to the total life at this same stress and strain range. Damage, as measured by the amount of unrecoverable string or plastic work on the materials creates voids or "free surfaces" internally that grow to a crack (crack initiation) under reversed plastic strain. Once the crack is large and follows continuum mechanics theory (not submicrostructural) the crack now grown by the continued cycle driving force of the stress or strain field to failure. Loading of the materials to a maximum load only will not create this failure mechanism. Sometimes failures of static loading are misnomer as "static fatigue" which refer to other failure modes such as creep or environmentally assisted crack (Burk, 2007). Most software used for riser analysis are unfortunately limited in the manner with which they can model complex soil structure interaction. Most of them are limited to linear and non-linear elastic springs. These springs are usually derived through the method recommended by API RP2A (2000) which is based on the work of Matlock (1962). The recommended method in API 2000 has remained unchanged since the 3rd Edition of RP2A in 1973. There exists however sufficient data (i.e. Reese and Cox, 1971, Stevens and Audibert, 1979, Murff and Hamilton, 1993, Randolph and Houlsby, 1984) to suggest that the API (2000) method for soft normally consolidated clays, will produce springs that underestimate the ultimate unit pressure that can be generated at the face of the pile. It was also suspected that the API spring were also too soft.

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API, the cyclic stresses in the pile will be reduced and the fatigue life will therefore be increased. A Finite Element Analysis (FEA) of a laterally loaded pile was performed for Gulf of Mexico soil and indeed generated P-Y curves stiffer than those of API and with higher ultimate unit pressure. Details of the FEA analyses can be found in Templeton (2009). The FEA curves were to be used, somewhat arbitrarily, as follows by the structural software to calculate the cyclic soil displacements (and therefore the cyclic stresses in the pile): for a given load cycle (P1 to P2 in Fig. 2), the soil-structure interaction was modeled as a linear spring that had a stiffness equal to the tangent modulus of the P-Y curve taken at the mean load of the load cycle (see Fig. 2).

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Modulus used to calculate cyclic displacement FEA derived

PY curve

Cyclic Displacement

From FEA Curve

Cyclic Displacement From API Curve

API derived PY curve

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Modulus used to calculate cyclic displacement FEA derived

PY curve

Cyclic Displacement

From FEA Curve

Cyclic Displacement From API Curve

API derived PY curve

Fig. 2: Calculation of soil-structure spring stiffness in riser analysis program

The above methodology gave stresses in the conductor that were lower than if standard API curves had been used, and therefore increased the fatigue life of the conductor. However, because these curves had not been calibrated, a series of centrifuge tests was performed to verify the theoretical curves with experimental data. In a Class A type of prediction, the FEA was performed again, but with soil properties closely matching those of the clay in the centrifuge rather than Gulf of Mexico clays and P-Y curves for kaolin were generated. This paper focuses on the comparison of the FEA and centrifuge curves for kaolin, because the comparison validates the method used to generate the P-Y curves for Gulf of Mexico clays. The paper also confirms that the method implemented in the structural analysis program to calculate cyclic stresses (see Fig. 2) is conservative for the cases of interest herein. Conclusions on cyclic modulus degradation are also included. FEA modeling of a laterally loaded conductor Geometry and soil model A Finite Element Analysis (FEA) of the lateral performance of the conductor was performed to generate P-Y curves for a kaolin clay. Details of the analysis are given in Templeton (2009) and salient points are summarized herein. A free-head 0.91m (3ft) diameter, 36.5m (120ft) long, 50.8mm (2 in.) wall thickness well conductor in clay soil was modeled with the soil properties closely matching those of the centrifuge tests. A 3D non linear total stress analysis with the ABAQUS program was performed using an elastic-plastic, work hardening model with Mises yield for the soil behavior. Soil properties were based on direct simple shear and resonant column test data for kaolin. The static loading applied to the conductor was a lateral load with no moment restraint at the load application point. This applied lateral load was increased until very large lateral displacements were achieved. The basic geometry of the model used is shown on Fig. 3. Symmetry conditions permitted use of a half-space model (180 degrees about the conductor axis). The model included finite elements out to a diameter of 36.6m (120 ft) or 40 times the conductor diameter and infinite elements beyond that diameter. The solid continuum elements used to represent the soil were 8-node brick elements. The conductor was modeled with 4-node shell elements, 50.8mm (2 in.) thick, using an elastic- perfectly plastic behavior and properties of 414 MPa (60 ksi) steel. The conductor was modeled down to a depth of 61m (200

Because stiffer P-Y curves will produce, for a given load range, less cyclic lateral displacement of the pile than predicted by

ft), at which depth its displacement was fixed.

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The soil was modeled as an elastic-plastic, work hardening material with Mises yield. The shear strength, as referenced to a Direct Simple Shear (DSS) tests was taken as the profile measured in the centrifuge tests (see Fig. 8). This shear strength profile was corrected for field conditions using the following factor:

⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ × ×+=

DSS Su T

T Logf

1.0 1.01 10 ..................................................................................................................................... (1)

Where • TDSS is the time period for peak shear strain, or 279 minutes for the Kaolin data • TRC is the time period for peak shear strain for an assumed resonance test, or 3 seconds for the data set herein.

Fig. 3: Finite Element Mesh For the modeling of the centrifuge tests.

The factor 0.1 in ⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ ×

DSS

T T 1.0

in Eqn. 1 corresponds to the approximate fraction (10%) of the strength estimated to be mobilized under small-displacement load cycles that cause most of the fatigue damage. The second 0.1 factor in front of the Log10 term in Eqn. 1 accounts for a rate of increase of shear strength of 10% per log cycle of strain rate. Therefore, for each soil layer the input rate-adjusted shear strength, Su, was calculated as:

SuDSS fSuSu ⋅= ................................................................................................................................................................(1a) With:

• DSSSu : shear strength profile obtained in the centrifuge and shown in Fig. 8. • Suf : calculated as per Eqn. (1) is equal to 1.27, for the case studied herein.

So the shear strength, as measured in a DSS test is increased by 27% to provide the input soil profile to the FEM analysis. The maximum shear modulus Gmax was taken as 550 times the shear strength, Su. The stress strain behavior was taken as elastic with slope given by this Gmax, up to the initial yield point, which was taken as 10 percent of the ultimate strength. Beyond the initial yield point, the stress strain behavior was given at each stress by additive combination of the elastic strain and a work hardening plastic strain based on the particular ultimate strength and the plastic part of the normalized stress strain curve of Fig. 4. P-Y curves were then extracted at 8 depths and verified with centrifuge testing.

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0.2

0.4

0.6

0.8

1.2

1.4

-1.00 1.00 3.00 5.00 7.00 9.00 11.00 13.00 15.00

Shear Strain, γ, %

N or

m al

iz ed

S he

ar S

tr es

s, th

/th m

1_44b_NF elastic comp linear piece fit to data

N or

m al

iz ed

s he

ar s

tr es

s, τ

/ τ m

DSS test Elastic Component Linear fit to data

Shear strain, γ (%)

0.2

0.4

0.6

0.8

1.2

1.4

-1.00 1.00 3.00 5.00 7.00 9.00 11.00 13.00 15.00

Shear Strain, γ, %

N or

m al

iz ed

S he

ar S

tr es

s, th

/th m

1_44b_NF elastic comp linear piece fit to data

N or

m al

iz ed

s he

ar s

tr es

s, τ

/ τ m

DSS test Elastic Component Linear fit to data

Shear strain, γ (%) Fig. 4: Comparison of DSS test result and elasto-plastic strain hardening model used in FEA.

Centrifuge Tests Model dimensions and test set-up The free-head conductor analyzed had a prototype outside diameter of 0.91m (3ft), and a 50.8mm (2 in.) wall thickness. In the centrifuge the length of the model conductor was limited by the depth of the sample container strongboxes. The total embedded model conductor length was 421mm, which was the maximum that could be accommodated within the existing 500mm deep test container (maximum depth of clay 450mm). The conductor tip was simply resting on the clay tub bottom. Four tests were run in a single tub container. A scale factor of 1:48 was achieved by carrying out these tests at 48 gravities (g) in C-CORE’s large geotechnical centrifuge. The embedded prototype length of the conductor was 20.2m (66ft). The model conductor had a resulting diameter of 19.05mm and a wall thickness of 1.22 mm of steel and an additional 0.35 mm from heat shrink tubing added to the exterior of the conductor to waterproof the strain gauges. The section modulus (EI) for the model was chosen as representative of the prototype conductor. Fig. 5 shows the model conductor with the string of strain gauges.

Bottom strain gauge

Load application point

Top strain gauge Bottom strain gauge

Load application point

Top strain gauge

Fig. 5: Model conductor used with its instrumentation In prototype units, the conductor was to be cyclically loaded in the 0.1 to 1 Hz range. In the model, a loading frequency of 1 Hz was used. Ideally, at 1:48 scale, the cycling should have been conducted between 4.8 and 48 Hz, but this would have introduced inertial effects into the model tests which are not present in the prototype. Instrumentation: Each conductor model was instrumented with 13 sets of strain gauges (Wheatstone bridge configuration) to measure the strains at discrete points along the conductor as well as instrumentation to measure the load, inclination, and lateral movement of the wellhead. The strain gauges were spread out along most of the length of the conductor with a higher concentration of gauges between about 6.1m and 12.2m (20 and 40 feet) below the mudline where the moments were expected to be the greatest.

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Druck PDCR 81 differential miniature pore pressure transducers (PPTs) were installed in the soil sample through ports in the sidewall of the strongbox to monitor pore pressure dissipation in the soil tub. In addition to the PPTs installed in the soil, consolidation was also monitored at the soil surface. The strain gauges used on the conductor models were also full Wheatstone bridge bending pairs. The strain gauge locations were chosen after consideration of the shear force profile, bending moment profiles and those from previous testing programs. Thirteen 13 gauge levels were installed with the layout shown on Fig. 6. In test 1, 2 gauges failed during soil consolidation and 4 failed in test 2. Fortunately the location of these non-functioning gauges was such that they did not impact the resolution of the bending moment in the depth of interest (top 10m). A blown fuse in Test 3 prevented all gauges from acquiring bending moments data. All gauges functioned for test 4. Conductor Installation: The centrifuge tests aimed at developing an installation method for the model pile that would be appropriate for the study of jetted conductors. It was believed that pushing the pile into virgin soil could potentially produce lateral stresses that would be higher than those along a jetted conductor. The conductor model was pushed (closed ended) into slightly undersized (15.87 mm diameter hole vs 19.05 mm conductor diameter) pre-augered hole prior to each test. The conductor was pushed into the soil such that the point where the lateral load was applied was approximately 91 mm above the mudline, or for the prototype about 4.3m (14 feet) above the mudline as shown in Figure 7.

-5

D ep

th b

el ow

m ud

lin e

(m )

-5

Pile Head

Mudline

Bottom of Conductor

x x

x x x x x

Test 1 Test 2 Test 3 Test 4

x indicates non-working

strain gauge

Location of strain gauge

-5

D ep

th b

el ow

m ud

lin e

(m )

-5

Pile Head

Mudline

Bottom of Conductor

x x

x x x x x

Test 1 Test 2 Test 3 Test 4

x indicates non-working

strain gauge

Location of strain gauge

Fig. 6: Overview of strain gauges layout

Fig. 7: View of pre-drilled undersized hole and (b) conductor after installation.

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Shear Strength The soil used in this test series was fine Alwhite kaolin processed by English China Clays, Lovering Pochrin & Co. Ltd. (ECLP) of Cornwall, England, and purchased through their US distributor Hamill & Gilespie. Alwhite was previously known as speswhite kaolin. The clay tested was designed to be lightly over consolidated to depth. Properties of the Alwhite kaolin are summarized in Table. 1 (from C-CORE, 2005)

Table 1: Summary of Alwhite Kaolin Properties (from C-CORE, 2005)

The construction method for the kaolin cake was in two lifts, separated by a 5 mm thick sand drainage layer to accelerate consolidation of the kaolin cake. This drainage layer was approximately 215 mm below the final clay surface. Clearance holes in the sand layer were placed at predesigned locations to accommodate conductor and PCPT tests. The clay was reconstituted from slurry and mixed at approximately 120% water content (twice the liquid limit) for a minimum of 3 hours under a vacuum of approximately one-half an atmosphere. In order to reduce consolidation time in the centrifuge, and because of the large starting slurry height, the clay sample was pre-consolidated to about 95% of its effective vertical stress profile prior to the centrifuge test. The pre-consolidation was conducted in two stages: (1) consolidation under a uniform effective stress, and (2) consolidation under a downward hydraulic gradient (DHG). Because of the need to keep the pile head above the water level to preserve the integrity of the strain gauges connection, little water could be added above the soil bed. The PCPT cones had to be kept saturated by being partially inserted into the sediments. A PCPT test was performed before each test and the interpreted shear strength profiles are shown on Fig. 8. The shear strength measurements near the surface show scatter and the interpreted profile was deduced from SHANSEP calculations. The PCPT profiles also show a sharp increase around the depth of the intermediate sand layer. It is believed that the PCPT measurements were affected by the presence of the sand drainage layer. The results and P-Y curves presented herein are limited to the depths above the sand drainage layer and therefore were not affected by the shear strength “bump” at 11m below surface. Tests Objectives: Four tests were performed in a single tub. Each test was designed to meet a specific set of loading conditions that included extreme events as well as events that cause the most fatigue damage to the conductor. The loading sequence for Tests 2, 3, and 4 is shown on Figures 9, 10, and 11. The purpose and loading sequence for each test is provided below:

• Test 1: The first test was a reference test. The pile was monotonically loaded until the pile head moved just over 1 conductor diameter (914mm = 36 inches). Results from the remaining 3 tests were compared to the results of this test.

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0 10 20 30 40 20−

18−

16−

14−

12−

10−

8−

6−

4−

2−

0 test 1 test 2 test 3 test 4 Interpreted Su for FEA input and data analysis depth of strain gauges

Undrained Shear Strength, Su (kPa)

Pr ot

ot yp

e D

ep th

b el

ow M

ud lin

e (m

)

Fig. 8: PCPT records and interpreted shear strength

• Test 2: The objective of this test was to understand the impact of large vessel motions on soil response. The loading sequence was as follows:

o Ten cycles of loading with an amplitude corresponding to wellhead displacements from the greatest vessel motions VM

o Soil consolidation for about three months (prototype time) o Fifty cycles of loading with amplitudes corresponding to wellhead displacements from the combined

effects of a) the greatest probability of occurring for vessel motion and hull VIM displacements and b) the maximum displacements from riser VIV.

o Soil consolidation for about three months (prototype time) o Monotonic push to failure.

1300 1400 1500 0

100

200

300

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e H

ea d

D is

pl ac

em en

t ( m

m )

Max Vessel Motion (10 cycles)

Mean Vessel Motion + Mean Hull VIM + Max Riser VIV

(50 cycles)

Monotonic Push to Failure

(a) (b)

(c)

Test 2

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100

200

300

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e H

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t ( m

m )

Max Vessel Motion (10 cycles)

Mean Vessel Motion + Mean Hull VIM + Max Riser VIV

(50 cycles)

Monotonic Push to Failure

(a) (b)

(c)

1300 1400 1500 0

100

200

300

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e H

ea d

D is

pl ac

em en

t ( m

m )

Max Vessel Motion (10 cycles)

Mean Vessel Motion + Mean Hull VIM + Max Riser VIV

(50 cycles)

Monotonic Push to Failure

1300 1400 1500 0

100

200

300

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e H

ea d

D is

pl ac

em en

t ( m

m )

Max Vessel Motion (10 cycles)

Mean Vessel Motion + Mean Hull VIM + Max Riser VIV

(50 cycles)

Monotonic Push to Failure

(a) (b)

(c)

Test 2

Fig. 9: Pile head load vs time for Test 2

• Test 3. The objective was to assess the impact of large numbers of cycles with displacements corresponding to the

most damaging VIV motions. The loading sequence was as follows. o One thousand cycles of loading with amplitudes corresponding to wellhead displacements equal to the most

damaging riser VIV case. o Soil consolidation for the equivalent of three months. o One thousand cycles of loading with amplitudes corresponding to wellhead displacements equal to the most

damaging riser VIV case. o Soil consolidation for the equivalent of three months. o Monotonic push to failure.

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1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

) Most Damaging

Riser VIV (1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

Test 3

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100

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Arbitrary Elapsed Time (Prototype Units) (days)

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ot yp

e he

ad d

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ac em

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m m

) Most Damaging

Riser VIV (1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

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100

150

Arbitrary Elapsed Time (Prototype Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

) Most Damaging

Riser VIV (1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

Test 3

Fig. 10: Pile head load vs time for Test 3

• Test 4. The objective was to understand the effect displacements corresponding to the maximum hull VIV will have

on the lateral response of the soil. The cyclic loadings performed in Test 3 were repeated here do to a data acquisition problems with Test 3. The loading sequence for Test 4 was as follows.

o One thousand cycles of loading with amplitude corresponding to wellhead displacements equal to the maximum hull VIV case.

o Soil consolidation for the equivalent of three months. o One thousand cycles of loading with amplitude corresponding to wellhead displacements equal to the most

damaging riser VIV case. o Soil consolidation for the equivalent of three months. o One thousand cycles of loading with amplitude corresponding to wellhead displacements equal to the

maximum hull VIV case. o One thousand cycles of loading with amplitude corresponding to wellhead displacements equal to the most

damaging riser VIV case. o Soil consolidation for the equivalent of three months. o One thousand cycles of loading with amplitude corresponding to wellhead displacements equal to the

maximum hull VIV case. o Monotonically pushed to failure immediately after the cyclic loading.

500 600 700 800 900 1000 100−

50−

100

Arbitrary Elapsed Time (Prototype Units), (Days)

Pr ot

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ad d

is pl

ac em

en t (

m m

)

Max Hull VIM

(1000 cycles)

Max Hull VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Max Hull VIM

(1000 cycles)

Monotonic Push to Failure

(a)

(b)

(c)

(d)

(e)

Test 4

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)

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(1000 cycles)

Max Hull VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Max Hull VIM

(1000 cycles)

Monotonic Push to Failure

(a)

(b)

(c)

(d)

(e)

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(1000 cycles)

Max Hull VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Max Hull VIM

(1000 cycles)

Monotonic Push to Failure

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100

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ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Max Hull VIM

(1000 cycles)

Max Hull VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Max Hull VIM

(1000 cycles)

Monotonic Push to Failure

Max Hull VIM

(1000 cycles)

Max Hull VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Max Hull VIM

(1000 cycles)

Monotonic Push to Failure

(a)

(b)

(c)

(d)

(e)

Test 4

Fig. 11: Pile head load vs time for Test 4

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Test Results: Data Processing: At a given depth, x, the relationships between the variables of interest are, with y being the lateral deflection of the pile:

P: soil resistance: 4

dx yd

EIP =

V: Shear force in conductor: 3

dx yd

EIV =

M: Bending moment in conductor: 2

dx yd

EIM = ................................................................................................... (2)

S: slope of pile deflection: dx dy

S =

Where: E = conductor Young Modulus I = conductor moment of inertia

The pressure, P, is therefore obtained by a double differentiation of the bending moments and the deflection, Y, is obtained by a double integration of the bending moment profiles, which must be obtained from the discrete measurements along the pile. A key step in the processing of the data is therefore the interpolation of the bending moments data recorded at discrete depths. The recorded data was processed with the Mathcad® software using the various interpolation functions to derive a continuous bending moment profile along the pile length:

• 6th order polynomial: a single 6th order polynomial curve was used to fit the entire bending moment profile along the conductor. The interpolated curve does not necessarily passes through the actual data points.

• Cubic spline function: a cubic spline interpolation passes a curve through a set of points in such a way that the first and second derivatives of the curves are continuous across each point. The curve is assembled by taking three adjacent points and constructing a cubic polynomial passing through those points. It should be noted that the generated moment diagram will pass through all the actual data points and is therefore most sensitive to uncertainties in the data acquired.

• Loess function: the loess function interpolates the data by generating a second order polynomial at a given depth by examining the data in a small user-specified neighborhood around the depth of interest. The larger the user-specified neighborhood, the smoother the interpolated curve will be. The generated curve does not necessarily passes through the actual data. (Mathcad 2002).

The above curve fitting was performed on the moment diagram and on the obtained shear diagram. The above functions are precoded in Mathcad® and can be implemented in a spreadsheet with minimum effort. P-Y curves were generated for each of the three above method of generating bending moments profiles. All the P-Y curves presented herein are the average of the three P-Y curves obtained by interpolating the recorded bending moments with a 6th order polynomial, a series a cubic splines, a series of loess functions. Monotonic Backbone P-Y curves: Monotonic backbone P-Y curves were obtained from the reference test Test 1, at 8 depths. Figure 12 shows plots of the lateral unit pressure, P, divided by the shear strength, Su, as a function of the lateral displacement, Y, over the conductor diameter, D. The agreement between the FEA curves and the centrifuge curves is considered very good, both in terms of initial modulus and ultimate pressure at large displacements. The centrifuge curves are stiffer than the API RP2A (2000) curves and the ultimate pressure also exceeds the value of 9 times Su given by API. The average value of the ultimate unit pressure P is 12.7 times Su for the eight FEA curves considered and 13.4 for the centrifuge curves. The value of the ultimate pressure P is plotted as a function of normalized lateral displacement in Fig. 13.

OTC 20158 11

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

Lateral Displacement / Diameter, Y/D Lateral Displacement / Diameter, Y/D

Depth = 3.7m = 4 D

Depth = 5.5 m = 6 D Depth = 6.4 m = 7 D

Depth = 7.3 m = 8 D Depth = 8.2 m = 9 D

Depth = 9.1 m = 10 D Depth = 10.5 m = 11.5 D

Depth = 1.4m = 1.5 D

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16 18 20

0 0.1 0.2 0 2 4 6 8

10 12 14 16 18 20

API WSD 21st API WSD 21st Errata

FEA Centrifuge

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

Lateral Displacement / Diameter, Y/D Lateral Displacement / Diameter, Y/D

Depth = 3.7m = 4 D

Depth = 5.5 m = 6 D Depth = 6.4 m = 7 D

Depth = 7.3 m = 8 D Depth = 8.2 m = 9 D

Depth = 9.1 m = 10 D Depth = 10.5 m = 11.5 D

Depth = 1.4m = 1.5 D

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16

0 0.1 0.2 0 2 4 6 8

10 12 14 16 18 20

0 0.1 0.2 0 2 4 6 8

10 12 14 16 18 20

API WSD 21st API WSD 21st Errata

FEA Centrifuge

Fig. 12: Comparison of monotonic P-Y curves from centrifuge Test 1, FEA analysis, and API RP2A 21st Ed. (2000) method.

12 OTC 20158

calculate the ultimate unit pressure, Pmax, as follows, for shear strength profiles approximately linearly increasing with depth:

up SNP ⋅=max ........................................................................................................................................... (3)

With: ⎟ ⎟ ⎟

⎠

⎞

⎜ ⎜ ⎜

⎝

⎛ ⋅−

⋅−= D

eN p

412 .............................................................................................. (4) λξ ⋅+= 05.025.0 for λ < 6 55.0=ξ for 6≥λ

⋅ =

0λ

:0uS shear strength intercept at seafloor :1uS rate of increase of shear strength with depth

:D pile diameter Z: depth of interest

The value of Np at depth has been limited to 12 for use in actual design, despite the fact that higher values have been measured in the centrifuge and calculated in the FEA analysis, in order to be consistent with the exact plasticity solutions proposed by Randolph and Houlsby (1984), for a rough pile. In Fig. 13, in order to compute the ultimate pressure by Eqn. 3, the above equation, the shear strength profile of Fig. 8 was approximated to a best-fit linearly increasing profile in the zone of interest. The values of ultimate pressures for the FEA analysis and the centrifuge tests were measured at a normalized displacement y/D of 0.2 because this is the displacement at which the pressure would reach a maximum according to the Matlock (1962) criteria.

0 5 10 15 20 Depth along pile / Diameter, z/D

N o

rm al

iz ed

L at

er al

U lti

m at

e U

n it

P re

ss u

re ,

P /S

Proposed Equation, modified from Murff and Hamilton (1993)

Centrifuge

FEA Kaolin

FEA GoM soil

Fig. 13: Ultimate Normalized Unit Pressure from FEA analysis, Centrifuge test 1, and Equations 3 and 4.

Despite the large monotonic displacement (i.e. up to 1 diameter) experienced by the conductor in the 4 tests, no gapping on the back side of the conductors was observed in any of the tests, except in the top 1 diameter (Fig. 14). Surface cracks in the active failure zone were clearly visible around the pile and indicate full adhesion of the soil to the pile for depths greater than one diameter. Overall, Test 1 constitutes a strong validation of the FEA analysis for the derivation of monotonic backbone P-Y curves.

The framework proposed by Murff and Hamilton (1993) for a linearly increasing shear strength profile was used, albeit with a modified expression for the calculation of Np, to calculate the ultimate lateral unit pressure. It is therefore proposed to

OTC 20158 13

Direction of loading

Fig. 14: Pile after large monotonic lateral push at the end of Test 4. Cracks in active failure zone clearly visible. Soil depression on active (back) side less than one pile diameter. The FEA derived curves are shown in Figure 15, where they have been normalized. The resistance P has been divided by the value of the resistance P at a normalized displacement of 0.2D. The curves from Matlock (1962) are also presented, with the P value normalized by the maximum P value which occurred at a normalized displacement of 0.2. Fig. 16 shows the centrifuge P-Y curves from Test 1, normalized the same way. The shape of the FEA-generated backbone curve has also been fitted with the following empirical equation, inspired from the equation proposed by O’Neill et al (1990) for P-Y curves in stiff clays:

⎥ ⎥ ⎦

⎤

⎢ ⎢ ⎣

⎡ ⎟ ⎠ ⎞

⎜ ⎝ ⎛⋅

⋅ =

5.0 max

max 100

tanh D y

S G

P P

u ............................................................................................................ (5)

With up SNP ⋅=max as per Eqn. 3 and 4 :maxG maximum shear modulus :uS shear strength

: D y

lateral displacement, y, over pile diameter, D

Fig. 16 shows good agreement between the FEA curves, the curves derived from the centrifuge tests, and the curves derived according to Eqn.5. The Matlock curves shown have been derived as per Matlock (1962):

3/1

max

5.0 ⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ ⋅=

cy y

P P

and Dyc ⋅⋅= 505.2 ε , with 50ε equal to 1%.

with all variables as previously defined.

14 OTC 20158

0 0.1 0.2 0.3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

1.2

API 21st Ed - e50 = 1% Matlock (1962) curve FEA - Depth = 1.5D FEA - Depth = 4D FEA - Depth = 6D FEA - Depth = 7D FEA - Depth = 8D FEA - Depth = 9D FEA - Depth = 10D FEA - Depth = 11.5D Proposed curve - Gmax/Su = 550

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

R es

is ta

nc e,

P /

(P a

t Y /D

= 0.

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

U ni

t P re

ss ur

e, P

/ (P

a t Y

/D =0

.2 )

0 0.1 0.2 0.3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

1.2

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

R es

is ta

nc e,

P /

(P a

t Y /D

= 0.

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

U ni

t P re

ss ur

e, P

/ (P

a t Y

/D =0

.2 )

Fig. 15: Normalized P-Y curves from Finite Element Analyses and Eqn. 5. The resistances P are normalized by the values of the Resistance P at a displacement Y/D of 0.2 Fig. 17 shows examples of P-Y curve calculated with Eqn. 5 for large embedment depths (i.e. Np ~ 12) for a range of Gmax/Su ratios, along with the Matlock 1962 curve. Curves of ultimate pressure over shear strength. P/Su, for shallow depths are given in Fig.18 with Np calculated as per Eqn. 4, along with the FEA and centrifuge curves and demonstrates the good fit. At depth where the value of Np is close to 12, a similar comparison is shown in Fig. 19 where the proposed curve gives a lower bound of the measured curves.

0 0.1 0.2 0.3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

1.2

API 21st Ed - e50 = 1% Matlock parabola FEA - Depth = 1.5D Centrifuge - Depth = 1.5D FEA - Depth = 4D Centrifuge - Depth = 4D FEA - Depth = 6D Centrifuge - Depth = 6D FEA - Depth = 7D Centrifuge - Depth = 7D FEA - Depth = 8D Centrifuge - Depth = 8D FEA - Depth = 9D Centrifuge - Depth = 9D Proposed curve - Gmax/Su = 550

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

R es

is ta

nc e,

P /

(P a

t Y /D

= 0.

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

U ni

t P re

ss ur

e, P

/ (P

a t Y

/D =0

.2 )

Fig. 16: Normalized P-Y curves from Finite Element Analyses, Centrifuge Test 1, and Eqn. 5. The resistances P are normalized by the values of the Resistance P at a displacement Y/D of 0.2

OTC 20158 15

0 0.1 0.2 0.3 0

API RP2A 21st Ed - e50 = 1% Matlock (1962) curve Proposed curve - Gmax/Su=550 Proposed curve - Gmax/Su=400

Lateral Displacement / Diameter, Y/D

R es

is ta

nc e

/ S he

ar S

tr en

gt h,

P /S

Lateral Displacement / Diameter, Y/D

API RP2A 21st Ed - e50 = 1% Matlock (1962) curve Proposed curve - Gmax/Su=550 Proposed curve - Gmax/Su=400

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/ S

u ⎥ ⎥ ⎦

⎤

⎢ ⎢ ⎣

⎡ ⎟ ⎠ ⎞

⎜ ⎝ ⎛ ⋅

⋅ ⋅⋅=

5.0 max

100 tanh

D y

S G

SNP u

Proposed PY curve:

0 0.1 0.2 0.3 0

API RP2A 21st Ed - e50 = 1% Matlock (1962) curve Proposed curve - Gmax/Su=550 Proposed curve - Gmax/Su=400

Lateral Displacement / Diameter, Y/D

R es

is ta

nc e

/ S he

ar S

tr en

gt h,

P /S

Lateral Displacement / Diameter, Y/D

API RP2A 21st Ed - e50 = 1% Matlock (1962) curve Proposed curve - Gmax/Su=550 Proposed curve - Gmax/Su=400

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/ S

u ⎥ ⎥ ⎦

⎤

⎢ ⎢ ⎣

⎡ ⎟ ⎠ ⎞

⎜ ⎝ ⎛ ⋅

⋅ ⋅⋅=

5.0 max

100 tanh

D y

S G

SNP u

Proposed PY curve:

Fig. 17: P-Y curves as per Eqn.5, compared with API and Matlock curves for large embedment depths. The ultimate value of P is 12 Su instead of 9 Su for the API curve.

0 0.1 0.2 0.3 0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

API 21st Ed - e50 = 1% - Depth = 1.5 D Matlock parabola - Depth = 1.5 D FEA - Depth = 1.5D Centrifuge - Depth = 1.5D FEA - Depth = 4D Centrifuge - Depth = 4D Proposed curve - Depth = 1.5D Proposed curve - Depth = 4D

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/ S

Lateral Displacement / Diameter, Y/D 0 0.1 0.2 0.3

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/ S

Lateral Displacement / Diameter, Y/D Fig. 18: Normalized resistance curves, P/Su from FEA, centrifuge Test 1, and Eqn. 5 for shallow depths.

0 0.1 0.2 0.3 0

API 21st Ed - e50 = 1% Matlock parabola FEA - Depth = 6D Centrifuge - Depth = 6D FEA - Depth = 7D Centrifuge - Depth = 7D FEA - Depth = 8D Centrifuge - Depth = 8D FEA - Depth = 9D Centrifuge - Depth = 9D Proposed curve - Np = 12 - Gmax/Su = 550

Lateral Displacement / Diameter, Y/D

N or

m al

iz ed

R es

is ta

nc e,

P /

(P a

t Y /D

= 0.

2) U

ni t P

re ss

ur e

/ S he

ar S

tr en

gt h,

P /

S u

Lateral Displacement / Diameter, Y/D Fig. 19: Normalized resistance curves, P/Su from FEA, centrifuge Test 1, and Eqn. 5 for depth where Np ~ 12

16 OTC 20158

Because the tangent modulus of the P-Y curve is of particular interest to calculate the cyclic displacements, Fig. 20 shows the comparison of the tangent modulus calculated from the proposed method and from the Matlock (1963) parabola.

0 0.05 0.1 0.15 0.2 0

Matlock (1962) curve - e50=1% Proposed curve - Gmax/Su=550 Tangent Modulus Proposed curve / Tangent Modulus Matlock curve

Lateral Displacement / Diameter, Y/D

R es

is ta

nc e

/ S he

ar S

tr en

gt h,

P /

S u

T an

ge nt

M od

ul us

P ro

po se

d C

ur ve

T an

ge nt

M od

ul us

M at

lo ck

C ur

0 0.05 0.1 0.15 0.2 0

Matlock (1962) curve - e50=1% Proposed curve - Gmax/Su=550 Tangent Modulus Proposed curve / Tangent Modulus Matlock curve

Lateral Displacement / Diameter, Y/D

R es

is ta

nc e

/ S he

ar S

tr en

gt h,

P /

S u

T an

ge nt

M od

ul us

P ro

po se

d C

ur ve

T an

ge nt

M od

ul us

M at

lo ck

C ur

Fig. 20: Ratio of Moduli from Matlock (1962) equation and Eqn.5

Cyclic Testing

Test 2: The cyclic P-Y curves obtained for Test 2 are shown on Figure 21, along with the monotonic P-Y curves obtained for the last monotonic test at the end of the test series. The backbone P-Y curves, except for those at a depth of 8D, generally agree well with the backbone curves of Test 1.

Test 4: P-Y curves were also derived for Test 4. However, because the imposed displacements at the conductor head were so small, reliable curves could only be obtained at a depth of 1 diameter below the soil surface. Results are shown in Fig. 22. Secant Modulus Degradation The cyclic tests were then analyzed to look at the degradation of the secant modulus as a function of the number of load cycles. The secant modulus of cyclic load cycles was extracted from Fig.21 and 22. Ratios of the secant modulus of each unload –reload cycle over the tangent modulus on backbone curves at mid-range load are shown on Fig. 23. The numbers greater than 1.0 confirm that the assumptions in the structural riser software (see Fig. 2) are conservative for the load cases analyzed (i.e. they give modulus lower than measured in the centrifuge). The secant modulus of each load cycle is then normalized by the secant modulus of the first cycle. Curves are shown on Fig. 24. It is proposed that the degradation of the secant modulus can be estimated conservatively by the following lower bound:

))log(7.0tanh(5.29.0 9.0

1 nM M n

⋅⋅+ = ................................................................................................................... (6)

With:

nM : secant modulus of n th cycle

1M : secant modulus of 1 st cycle

n : number of cycle

OTC 20158 17

0 0.1 0.2 6− 4− 2− 0 2 4 6 8

10 12 14 16 18 20

API FEA Test 1 Test 2a - 10 cycles Test 2b - 20 cycles Test 2c - monotonic

0 0.05 0.1 0.15 0.2 6− 4− 2− 0 2 4 6 8

10 12 14 16 18 20

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0. 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - Monotonic

Depth = 1.4m = 1.5 D Depth = 3.7m = 4 D

Depth = 5.5 m = 6 D Depth = 6.4 m = 7 D

Depth = 7.3 m = 8 D Depth = 8.2 m = 9 D

Depth = 9.1 m = 10 D Depth = 10.5 m = 11.5 D

Lateral Displacement / Diameter, Y/D Lateral Displacement / Diameter, Y/D

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

6−

4−

2−

6−

4−

2−

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0. 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6− 4− 2− 0 2 4 6 8

10 12 14 16 18 20

API FEA Test 1 Test 2a - 10 cycles Test 2b - 20 cycles Test 2c - monotonic

0 0.05 0.1 0.15 0.2 6− 4− 2− 0 2 4 6 8

10 12 14 16 18 20

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0. 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - Monotonic

Depth = 1.4m = 1.5 D Depth = 3.7m = 4 D

Depth = 5.5 m = 6 D Depth = 6.4 m = 7 D

Depth = 7.3 m = 8 D Depth = 8.2 m = 9 D

Depth = 9.1 m = 10 D Depth = 10.5 m = 11.5 D

Lateral Displacement / Diameter, Y/D Lateral Displacement / Diameter, Y/D

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

6−

4−

2−

6−

4−

2−

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/S u

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0. 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

0 0.1 0.2 6−

4−

2−

API FEA Test 1 Test 2a - 10 cycles Test 2b - 50 cycles Test 2c - monotonic

Fig. 21: Normalized P-Y curves, P/Su vs y/D, from FEA, from centrifuge Test 1, Test 2a, 2b, and 2c.

18 OTC 20158

0 0.05 0.1

10−

API FEA Test 1 - monotonic Test 2a - first loading - 1st load cycle Test 2b - second loading - 1st load cycle Test 2c monotonic after cyclic loading Test 4a - cycles 1-10-50-100-250-500-700-1000 Test 4b - cycles 1-10-50-100-250-500-700-1000

U ni

t P re

ss ur

e / S

he ar

S tr

en gt

h, P

/ S

Lateral Displacement / Diameter, Y/D

Fig. 22: Normalized resistance curves P/Su from FEA, from centrifuge Test 1, Test 2a,b,c and Tests 4a, and 4b at a depth of one (1) diameter.

100

1 10 100 1000

Load Cycle number

Test 2a - Depth = 1.5D Test 2a - Depth = 4D Test 2a - Depth = 6D Test 2a - Depth = 7D Test 2a - Depth = 8D Test 2a - Depth = 9D Test 2a - Depth = 10D Test 2a - Depth = 11.5 D test 2b - Depth = 1.5 D Test 4a - Depth = 1.5 D Test 4a - Depth = 4D

S ec

an t M

od ul

us o

f u nl

oa d-

re lo

ad c

yc le

T an

ge nt

M od

ul us

o n

ba ck

bo ne

c ur

ve a

t m id

-r an

ge lo

ad P1

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of unload re-load cycle

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of unload re-load cycle

100

1 10 100 1000

Load Cycle number

S ec

an t M

od ul

us o

f u nl

oa d-

re lo

ad c

yc le

T an

ge nt

M od

ul us

o n

ba ck

bo ne

c ur

ve a

t m id

-r an

ge lo

ad P1

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of unload re-load cycle

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of unload re-load cycle

Fig. 23 Ratio of Secant Modulus of unload-reload cycle over tangent modulus on backbone curve at mid-range load. Numbers above one (1) confirm that the structural software assumptions are conservative for the problem of interest herein.

OTC 20158 19

0.2

0.4

0.6

0.8

1.2

1.4

1 10 100 1000

Load Cycle Number

Test 2a - Depth = 1.5D Test 2a - Depth = 4D

Test 2a - Depth = 6D Test 2a - Depth = 7D

Test 2a - Depth = 9D Test 2a - Depth = 10D

Test 2a - Depth = 11.5 D test 2b - Depth = 1.5 D

Test 4a - Depth = 1.5 D Test 4a - Depth = 4D

Proposed lower bound

S ec

an t M

od ul

us o

f u nl

oa d-

re lo

ad c

yc le

S ec

an t M

od ul

us o

f F IR

S T

u nl

oa d

cy cl

e P1

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of 1st unload re-load cycle

Secant modulus of nth unload re-load cycle

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of 1st unload re-load cycle

Secant modulus of nth unload re-load cycle

0.2

0.4

0.6

0.8

1.2

1.4

1 10 100 1000

Load Cycle Number

Test 2a - Depth = 1.5D Test 2a - Depth = 4D

Test 2a - Depth = 6D Test 2a - Depth = 7D

Test 2a - Depth = 9D Test 2a - Depth = 10D

Test 2a - Depth = 11.5 D test 2b - Depth = 1.5 D

Test 4a - Depth = 1.5 D Test 4a - Depth = 4D

Proposed lower bound

S ec

an t M

od ul

us o

f u nl

oa d-

re lo

ad c

yc le

S ec

an t M

od ul

us o

f F IR

S T

u nl

oa d

cy cl

e P1

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of 1st unload re-load cycle

Secant modulus of nth unload re-load cycle

P2 (P1+P2)/2

Lateral Displacement, Y

P re

ss ur

e, P

Tangent Modulus at mid-range load

FEA derived backbone PY curve

Secant modulus of 1st unload re-load cycle

Secant modulus of nth unload re-load cycle

Fig. 24 Ratio of the secant modulus of unload-reload cycles over the secant modulus of the first unload-reload cycle. Proposed lower bound, as per Eqn. 6 is also shown Conductor Head Load-Displacement curves. Next the overall conductor head-displacement curves were analyzed because, thanks to their higher resolution, they can provide additional insight into soil behavior. First, the load-displacement curve for Test 2 (a,b,c) are shown on Fig. 25. It can be seen that the ultimate monotonic push provides a curve that is stiffer than the reference test 1. This confirms that one-way small-displacement cycles have little effect on subsequent large displacement behavior, if enough time is allowed for soil consolidation. The same data is shown for Test 3 on Figs. 26 and 27 and the same conclusions can be drawn. Additionally, Fig. 27 suggests that little global stiffness reduction is experienced beyond 200 cycles, which is consistent with the P-Y curve secant modulus degradation curve of Fig. 24.

0 200 400 600 800 1000 1200 200−

200

400

600

800

1000

Monotonic push - test 1 test 2a - 10 cycles test 2b - 50 cycles test 2c - final monotonic push to failure

Prototype conductor head displacement (mm)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Monotonic push - test 1 test 2a - 10 cycles test 2b - 50 cycles test 2c - final monotonic push to failure

0 200 400 600 800 1000 1200 200−

200

400

600

800

1000

Monotonic push - test 1 test 2a - 10 cycles test 2b - 50 cycles test 2c - final monotonic push to failure

Prototype conductor head displacement (mm)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Monotonic push - test 1 test 2a - 10 cycles test 2b - 50 cycles test 2c - final monotonic push to failure

Fig. 25 Conductor pile head load-displacement curves. Tests 1 and 2.

20 OTC 20158

0 100 200

200

400

backbone - test 1 test 3a - cycles 1 to 1000 test 3b - cycles 1 to 1000 test 3c - final monotonic push

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

(3a) (3b) (3c)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm) 0 100 200

200

400

backbone - test 1 test 3a - cycles 1 to 1000 test 3b - cycles 1 to 1000 test 3c - final monotonic push

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

(3a) (3b) (3c)

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

1500 1600 1700 1800 1900 0

100

150

Arbitrary Elapsed Time (Proto type Units) (days)

Pr ot

ot yp

e he

ad d

is pl

ac em

en t (

m m

)

Most Damaging Riser VIV

(1000 cycles)

Most Damaging Riser VIV

(1000 cycles)

Monotonic Push to Failure

(3a) (3b) (3c)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm) Fig. 26 Conductor pile head load-displacement curves. Tests 1 and 3.

0 20 40 60 80

100

200

300

Prototype head displacement (mm)

Pr ot

ot yp

e he

ad lo

ad , (

kN )

backbone - test 1 cycles 1 to 10 cycles 10 to 50 cycles 50 to 200 cycles 200 to 500 cycles 500 to 750 cycles 750 to 1000

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm)

0 20 40 60 80

100

200

300

Prototype head displacement (mm)

Pr ot

ot yp

e he

ad lo

ad , (

kN )

backbone - test 1 cycles 1 to 10 cycles 10 to 50 cycles 50 to 200 cycles 200 to 500 cycles 500 to 750 cycles 750 to 1000

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm) Fig. 27: Conductor pile head load-displacement backbone curves. Tests 1 and 3a with cycle batches highlighted.

The global conductor head load-displacement curve for Test 4a is shown on Fig. 28. Because the loading for this test is two- way around the origin, the global response does soften but quickly reaches equilibrium after about 50 cycles.

20− 0 20

100−

100

backbone curve - test 1 test 4 - cycles 1 to 10 test 4 - cycles 10 to 50 test 4 - cycles 50 to 200 test 4 - cycles 200 to 500 test 4 - cycles 500 to 750 test 4 - cycles 750 to 1000

20− 0 20

100−

100

backbone curve - test 1 test 4 - cycles 1 to 10 test 4 - cycles 10 to 50 test 4 - cycles 50 to 200 test 4 - cycles 200 to 500 test 4 - cycles 500 to 750 test 4 - cycles 750 to 1000

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm)

Fig. 28: Conductor pile head load-displacement curves. Tests 1 and 4a with cycle batches highlighted.

OTC 20158 21

Finally, all the conductor head-displacement backbone curves for all tests are plotted on Fig. 29. It is interesting to note on Fig. 29 that the response for the last monotonic push is stiffer than that of the reference test, even for Test 4 where soil consolidation was not allowed after the last batch of two-way cyclic loading. This confirms that small amplitude load cycles do not seem to have any negative influence on subsequent large amplitude loads displacement behavior. Fig. 29 demonstrates that all the small displacement backbone curves follow closely the same loading path. Again, small amplitude load cycles do not seem to have any negative influence on subsequent small amplitude loads displacement behavior if reasonable soil consolidation is allowed. This is an important confirmation that each fatigue-inducing load event can be treated independently from the other, if they occur sufficiently apart from one another.

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm)

0 500 1000 1500 0

500

1000

backbone curve - test 1 test 2 - 1st cycle of 1st set of 10 cycles test 2 - 1st cycle of 2nd set of 50 cycles test 2 - last push to failure after cyclic loads test 3 - 1st cycle of 1st set of 1000 cycles test 3 - 1st cycle of 2nd set of 1000 cycles test 3 - last monotonic push to failure after cyclic loads test 4 - 1st cycle of 1st set test 4 - 1st cycle of 2nd set test 4 - 1st cycle of 3rd set test 4 - 1st cycle of 4th set test 4 - 1st cycle of 5th set test 4 - last monotonic push to failure after cyclic loads

0 50 100 150 0

100

200

300

400

Prototype conductor head displacement (mm)

P ro

to ty

pe h

ea d

lo ad

( kN

)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Prototype conductor head displacement (mm)

0 500 1000 1500 0

500

1000

0 50 100 150 0

100

200

300

400

Prototype conductor head displacement (mm)

P ro

to ty

pe h

ea d

lo ad

( kN

)

Fig. 29: Conductor pile head load-displacement backbone curves for all tests.

22 OTC 20158

Another important observation is that , at large displacements, the monotonic curves after cyclic loads in Tests 2, 3, and 4 give higher ultimate pile head resistances than the reference monotonic curve of Test 1. The difference in resistances at large displacements is interpreted to be due to an increase in soil shear strength through hardening because of the small-amplitude loads. Test 4, with the most small amplitude load cycles (and therefore the most potential hardening), does show the most increase in ultimate pile head load on Fig. 29. The consequences of soil hardening under cyclic loads could be of critical importance when re-assessing the foundation ultimate capacity of offshore structures that have been in service for many years. Conclusions: The paper investigated the lateral soil-structure interaction for loads transferred from a top tensioned riser to a jetted conductor. Comparisons were made between P-Y curves generated from Finite Element Analyses and centrifuge testing. Insight into cyclic loading soil-structure interaction was also provided. The work herein:

• Validates the FEA methodology used by Templeton (2009) to generate P-Y curves for Gulf of Mexico clays (Fig. 12).

• demonstrates that, for the loads of interest herein, the lateral P-Y curves provided by API RP2A (2000) are too soft and underestimate the ultimate unit pressure acting on the conductor. A general equation (Eqn. 5) has been proposed to generate P-Y curves for soft clays. It should be noted that the shear strength used in the derivation of the P-Y curves should account for rate effects.

• Confirms that the methodology used by the structural riser software (and described in Fig. 2) to derive the unload- reload cyclic stiffness from the monotonic FEA P-Y curves is conservative for the problem of interest herein(Fig. 23), except for two-way loading such as in Test 4 (Fig. 28) which represented Hull VIM. Fortunately, this type of loading only caused 20% of the overall fatigue damage at the depth of interest along the conductor.

• Quantified the cyclic P-Y curve secant modulus degradation as a function of load cycles (Eqn. 6). Little modulus degradation is seen to occur after 200 load cycles.

• Confirms that small amplitude load cycles do not seem to have any negative influence on subsequent large amplitude loads displacement behavior, even if no soil consolidation is allowed (Fig. 29).

• Suggests that small amplitude load cycles do not seem to have any negative influence on subsequent small amplitude loads displacement behavior if reasonable soil consolidation is allowed (Fig. 29).. This is an important confirmation that each fatigue-inducing load event can be treated independently from the other, is sufficiently spaced in time.

The paper also suggests that, when re-assessing the lateral behavior of piled offshore structures that have been in service for many years, the pile lateral load-deflection behavior will benefit from the following modification to API RP2A recommended practice:

• increasing the ultimate unit pressure from 9 times the shear strength to 12 times the shear strength • adjusting the input shear strength for rate effects, as appropriate for the loading of interest • accounting for potential soil hardening and increase in shear strength due to many previous cycles of small

amplitude loads. Last, it should be recognized that, although the use of API P-Y curves are conservative to determine the stresses in structural members below the mudline, the use of API P-Y curves will be unconservative to estimate stresses in structural members above the mudline (i.e. wellhead connectors, Blow Out Preventers, etc…). Acknowledgement The author acknowledges the owners of the data herein, BP America Inc. and Shell Exploration & Production Co., and is grateful for their permission to publish. The author would also like to acknowledge the contributions and assistance of the following people. Ed Clukey was the centrifuge program initiator and, along with Eric Liedtke, developed the original testing program. Ed and Eric also reviewed a draft of this paper and provided valuable feedback. The centrifuge tests were performed at the C-CORE facility in St John’s, Newfoundland, under the direction of Ryan Phillips. Laboratory tests on kaolin were performed at the Fugro South laboratory in Houston under the direction of Bill DeGroff. The author is also grateful to Ed Clukey and J. S. (Jack) Templeton for insightful conversations and guidance on the topic of laterally loaded piles and advanced soil constitutive modeling.

OTC 20158 23

References API RP2A (2000): “Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms – Working Stresses

Design”, 21st Edition, December 2000. API RP2A-WSD Errata (2007): “Errata and Supplement 3 to API Recommended Practice 2A-WSD, Recommended Practice for Planning,

Designing and Constructing Fixed Offshore Platforms – Working Stresses Design”, 21st Edition, December 2000.”, October 2007. Beynet, P. (2008): personal communication Burk, J. (2007): personal communication C-CORE (2005):”Centrifuge Modeling of Cyclically loaded Conductors In Clay: Tests 1-4”, Report R-04-100-293, March Mathcad (2002): User manual for the Mathcad software, Mathsoft Engineering and Education, Inc. Matlock, H. (1962): “Correlations for design of laterally loaded piles in soft clay”. Report to Shell Development Company, September Murff, J.D., and Hamilton, J.M. (1993): P-Ultimate for undrained analysis of laterally loaded piles”, Journal of Geotechnical Engineering,

Vol. 119, No.1, January. O’Neill, M.W., Reese L.C., and Cox, W.R. (1990): “Soil Behavior for Piles Under Lateral Loading”. Proceedings, Offshore Technology

Conference, Houston, TX, Paper number 6377 Randolph, M.F., and Houlsby, G.T. (1984): “The limiting pressure on a circular pile loaded laterally in cohesive soil.” Geotechnique,

London, England, 34(4), 613-623 Reese, L., and Cox, W.R. (1975): “Field Testing and Analysis of Laterally Loaded Piles in Stiff Clays”, Proceedings, Offshore Technology

Conference, Houston, TX, Paper number 2312 Stevens, J. B. and Audibert J.M.E, (1979): “Re-examination of P-Y curve formulations”, Proceedings, Offshore Technology Conference,

Houston, TX, Paper number 3402 Templeton, J.S. (2009): “Finite element analysis of conductor-seafloor interaction”, Proceedings, Offshore Technology Conference,

Houston, TX, Paper number 20197.