Monotonic and Cyclic p-y Curves for Clay based on Soil Performance Observed in Laboratory Element TestsYouhu Zhang Knut H Andersen, Rasmus T. Klinkvort, Hans Petter Jostad, Nallathamby Sivasithamparam, Noel P. Boylan, Thomas Langford

Presentation at Geotechnical Input to Well Integrity Assessment Workshop , BP Helios Plaza building, Houston, Texas, 29 April 2016

Outline

• General

• The monotonic p-y model and validation

• Extension to cyclic p-y model

• Numerical procedure for calculation overall pile response

• Example case and validation

• Conclusions

Slide 2

General: p-y springs

Slide 3

http://www.findapile.com/p-y-curves/definition

Piles under lateral loading are typically designed by the beam-column approach with the lateral support represented by “p-y springs”

p-y springs for cyclic loading: current practice

Slide 4

• Developed from limited field tests with specific soil and loading conditions

• No account of site specific soil response under cyclic loading

• Either cyclic/static, with no possibility to account for storm loading make-up

• Should cyclic p-y curves applied along the whole pile?

• Implied fully smooth pile-soil interface

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20

p/p u

displacement, y/yc

yc 3yc

0.72(X/Xr)

0.72

0.5

Matlock (1970) monotonic

Matlock (1970) cyclic for X≥Xr

Matlock (1970) cyclic for X<Xr

'modified Matlock' cyclic for X<Xr

8yc

The monotonic p-y model: basic idea

Slide 5

γ

τ/su

y/D

p/pu

(y/D, p/pu)(γ, τ/su) Scaling

p/pu = τ/su

y/D = ξγ

Development of monotonic model

Slide 6

10D

20D

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10 12 14 16 18 20

τ/su

γ(%)

γpf (%) = 2, 4, 6, 8, 12, 16, 20

A comprehensive parametric study:• A wide range of stress-strain response• Different pile interface roughness

NGI-ADP soil model

A simple linear relation between scaling coefficient ξ and pile-soil interface factor α is found: ξ= 1.35 + 0.25α

Retrospective prediction

Slide 7

The p-y curves calculated from Plaxisanalyses are back-predicted by the p-y model, showing excellent match for all parametric ranges considered.

0

2

4

6

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10

12

14

0.00 0.05 0.10 0.15 0.20 0.25 0.30

p/s u

y/D

γpf (%) = 2, 4, 6, 8, 12, 16, 20

Gmax/su = 500α = 0.5

Plaxis

model prediction

0

0.2

0.4

0.6

0.8

1

1.2

0.00 0.05 0.10 0.15 0.20 0.25 0.30

p/p u

y/D

Jeanjean(2009)

Gamma = 0.10

Series5

Gmax/su = 550γp

f = 10%α = 1ε50 = 0.5% (γM=2 = 0.75%)b = 0.33

Jeanjean (2009)

Currently proposed

API, εc = 0.5%

(b)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10 12 14 16

τ/su

γ(%)

Power law fit

NGI ADP fit

Test data

NGI ADP fitGmax/su = 550γp

f = 10%Power law fitγM=2 = γ50 = 0.75%b = 0.33

(a)

Comparison with Jeanjean (2009)

For the same soil examined by Jeanjean (2009), the current model does match well.

Validation of monotonic model

Slide 8

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45

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

Dep

th [m

]

Lateral displacement [m]

Plaxis

p-y springs

0

5

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15

20

25

30

35

40

45

-15000 -10000 -5000 0 5000 10000 15000

Dep

th [m

]

Cross-sectional shear force [kN]

Plaxis

p-y springs

A 84” pile embedded 40 m in a clay profile:• su

DSS = 5.1 + 2.4z• Gmax/su

DSS = 500, and γpf = 4%

• Fully rough pile-soil interface• Plaxis: NGI-ADP nonlinear

stress-strain response

The p-y spring model offers an excellent prediction of overall pile response!

Extension to cyclic p-y response

Slide 9

τcy/su, Npcy/pu, Nequivalent to

with pcy/pu = τcy/su

Randolph and Houlsby (1984)

The postulation

How to obtain cyclic p-y curves?

Slide 10

τcy

τcy

time

τcy

time

τcy

timeTest 1

Test 2

Test 3

Test 1

Test 2

Test 3

No. of cycles

τ cy/s

u

Stress strain cross-section for Neq=100

γ (%)

τ cy/s

u

Cyclic DSS tests

Neq=100

Scale stress-strain curve to obtain p-y curve corresponding to Neq

Test results

Cyclic contour diagram

The extension to cyclic p-y curves is verified at pile slice level against finite element analyses using undrained cyclic accumulation soil model UDCAM

Numerical procedure to analyse overall pile response

Slide 11

Lateral load history

Spring 1

Spring 2

Spring 3

Spring n

y

y

y

y

y

y

pNeq_1

Neq_2

Neq_3

Neq_n

Perform accumulation for each of the springs, and calculate Neq

Construct p-y curves for each spring based on respective Neq

No. of cyclesτ c

y/su

Global beam-column model

Validation of the numerical procedure Slide 12

-5

0

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40

-0.10 0.00 0.10 0.20 0.30 0.40 0.50

Dep

th, m

Lateral displacement (m)

-5

0

5

10

15

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25

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35

40

-6000 -4000 -2000 0 2000 4000 6000

Dep

th, m

Cross-sectional shear force (kN)

-5

0

5

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15

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25

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35

40

-10000 0 10000 20000 30000 40000 50000 60000

Dep

th, m

Cross-sectional bending moment (kNm)

-5

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40

0 5 10 15 20 25 30

Dep

th, m

Neq

FEA

NGI-PILE

Parcel 1, 2, 3

End of Parcel 3, predicted by Program

Parcel No. Load, kN No. of cycles 1 2000 20 2 3000 10 3 4000 5

A 84” pile embedded 40 m in a clay profile:• su

DSS = 3.4 + 1.6z• Drammen clay, OCR =1• Cyclic pile head lateral load parcels• Symmetric load cycles• Fully rough soil-pile interface• Lateral load applied 2D above mudline

Further developmentsSlide 13

• Develop procedures for 1-way cyclic loading with non-zero average

component

• Models for sand

• Models for t-z response

• Ultimate goal: a practical tool for designing offshore piles under cyclic lateral

and axial loading

ConclusionsSlide 14

• A model for constructing site-specific monotonic p-y curves for piles in clay is

introduced

• The monotonic p-y model is successfully extended for cyclic response using

well-established cyclic accumulation procedure

• A procedure to calculate overall pile response under cyclic loading is

proposed and validated by numerical simulation

• Site-specific soil response and storm load history can be considered explicitly

Welcome to presentation at OTC:OTC-26942-MSMay 4, 9.30 - 12.00Geotechnics for well design

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