True Non-Linear Spring Modelfor Lateral Support of Conductors

Charles AubenyTexas A&M University

Geotechnical Input to Well Integrity AssessmentHouston

April 29, 2016

OutlineOverview of soil spring models

P-y curvesSecant stiffnessTrue nonlinear analysis

Centrifuge test program

General nonlinear model

FormulationParameters

Performance

Load

Equivalent

Soil

SpringsConductor

or Pile

1. Initial Monotonic‘Backbone’

2. SecantStiffness

3. TrueNonlinear

Description of P-y Springs

P-y Description of Backbone Curve

• Strictly applicable to monotonic loading

• Adjustments for cyclic

• Superficial similarity between tangent modulus and degraded cyclic curves

• Jeanjean (2009) secant stiffness typically greater than backbone tangent stiffness

Soil

Res

ista

nce

, P

Monotonic

P-y Curve

Steady State

Displacement, y

Transient: Cycle 1 to

Steady State

Secant Stiffness

• Better representation of effects of unload-reload cycles

• Easily understandable framework for loading involving uniform load cycles

• Ambiguity for random & transient loading

P

y

Ksec = DP / Dy

Dy

Cycle N

Backbone

yhead

Conductor

or Pile

Non-Uniform & Transient Loading

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 2 4 6 8 10 12P

ile H

ead

Dis

pla

cem

ent

Load Cycle

Soil Spring Response under General Loading

Centrifuge Test Program in NC Clay

Length = 35.5 mEmbedment = 25.8 m

DiameterD = 0.914 m

Imposed yheadOffset

Cyclic

Kaolinsu (kPa) = 1.55 + 1.06 z

P

y

Lightly to Normally Consolidated Clay Test Series(partial listing)

Test Type Load Sequence Offset y/D Cyclic

C1 Pushover

C2 Harmonic M1M2M3

000

0.0250.050.1

C3 Harmonic M1M2M3M4M5

00.050.050.050.1

0.0250.050.10.0250.025

Notes: 1. C4 involved a random sequence of loading2. Similar test series conducted in stiff clay & sand3. Example fits today for Test C2, Sequence M2

Backbone Curve Comparisons

Bending Moment Profile

Force Fh = 334 kNDisplacement yh = 0.046m

Empirical Nonlinear P-y Model

3. Degradation

P

y

2. Unload-reload

1. Backbone

1a. The Backbone Curve

D D

max ( / )1 ( / )

b

ult

P Ky D

P f y D

Kmax: controls: initial stiffnessf: controls curvature: back-analysis calibration

(not fundamental parameter)Pult in normalization is a measured valuefrom monotonic test data

1b. Computation of Pult

1

1 2

1

1 2

'

exp( / )

'deep' bearing factor (9-12)

surface bearing factor (2-3)

controls transition from shallow to deep

ult p u

p

P N s D zD N

N N N z D

N

N N

Gapping in Active Zone

1

1 2

1 2

2

exp( / )

as above

ult p u

p

P N s D N

N N N z D

N N

No Gapping

D D

max ( / )1 ( / )

b

ult

P Ky D

P f y D

2. Unload-Reload Behavior

D D

0( / ) n

ref

PK y D

P

K0 n = power law coefficientsPref = reference soil resistance

D D

0( / ) n

ref

PK y D

P

After Idriss et al. (OTC, 1971)

Cyclic Degradation Model

y

P P1 (backbone)

Pn

Pm

Displacementcontrolledcyclic test

Cycle 1

n

m Pm / Pn = (m/n)-t

t = experimentallydeterminedfunction of Dycyc

Dycyc

a. The t-parameter b. The Rf-parameter

• K0 & n constant during cycling• Pref updated during cycling

Reverse Analysis & Calibration

Load

Equivalent

Soil

SpringsConductor

or Pile

Model Parameter Summary

• Ultimate Resistance Pult: N1, N2,

• Backbone Curve: Kmax, f• f varies with depth

• Kmax insensitive to depth

• Cyclic Loading: K0 , n• Both vary with depth

• Constant during cycling

• Degradation function: t(Dycyc/D)

Parameter Sets to be Developed for:• Soft vs Stiff Clay• Symmetric vs Asymmetric Loading• Load magnitudes M1, M2 & M3

Future Work

• Validate model for random loading

• Correlating model parameters to single element test data

• Interpretation of centrifuge test data in sands

• Alternative model formulation (e.g., bounding surface plasticity models)• McCaron (2015) for clays• Choi et al (2015) for sands