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
8
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
0
5
10
15
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25
30
35
40
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
10
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
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5
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25
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35
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
20
25
30
35
40
-6000 -4000 -2000 0 2000 4000 6000
Dep
th, m
Cross-sectional shear force (kN)
-5
0
5
10
15
20
25
30
35
40
-10000 0 10000 20000 30000 40000 50000 60000
Dep
th, m
Cross-sectional bending moment (kNm)
-5
0
5
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15
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25
30
35
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
@infoNGI
NORGES GEOTEKNISKE INSTITUTTNGI.NO
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