Analytical contributions to offshore geotechnical … McClelland Lecture Analytical contributions to offshore geotechnical engineering Mark Randolph Centre for Offshore Foundation

2nd McClelland Lecture

Analytical contributions to offshore geotechnical engineering

Mark Randolph

Centre for Offshore Foundation Systems (COFS)The University of Western Australia

18th ICSMGE, Paris Tuesday 3rd September 2013

The University of Western Australia

Bramlette McClelland (1921-2010)

• A giant of a man – pioneer of offshore foundation engineering

• Founder and President of McClelland Engineers

– Headquartered in Houston

– 14 offices around the world

• Awards included– 9th Terzaghi Lecturer (1972)

– OTC Distinguished Achievement Award (1986)

Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 2


What passes for “analytical” ?

• True analytical solution (algebraic expression)

• Computable analytical formulation (design chart)

• Synthesis of numerical parametric study

– Appropriate non-dimensional parameter groups

– Algebraic or chart outcome

“When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.”Buckminster Fuller

Idea

lisat

ion

Realism

?



Overview

• Piled foundations– Consolidation after driving

– Axial stiffness and cyclic loading

• Shallow foundations– Rectangular foundations for subsea systems

• Full-flow penetrometers– Resistance factors

– Degree of consolidation during penetration

• Subsea pipelines– Embedment and axial resistance of deep water pipelines



Piled foundations - consolidation


• Radial consolidation solution

– Refined through strain path method

• Non-dimensional time: T = cvt/Deq2

– cv as for piezocone dissipation

(horizontal flow; soil stiffness partly swelling)

– Deq reflecting outward flow of soil

Soil flow:Piles: 0:100 D/ ~ 40Suction caissons ~ 50:50 D/ > 300

t

u

r 'r(t)

D


Development of axial pile resistance


T10 ~ T50/20 : t10 ~ 2 to 5 hours

T50 ~ 0.6 : t50 ~ 2 to 5 days

T90 ~ 20T50 : t90 ~ 1 to 3 months

Consolidation index

75.050T/T1

11~CI


Consolidation around suction caissons


T10 ~ T50/20 : t10 ~ 2 to 5 hours

T50 ~ 0.6 : t50 ~ 2 to 5 days

T90 ~ 20T50 : t90 ~ 1 to 3 months

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100

Rel

ativ

e in

crea

se in

shaf

t res

ista

nce

Time (days) - scaled for Deq = 0.3 m

Radial consolidation solution(cv = 10 m2/yr; Deq = 0.3 m)

Data from suction anchors(Colliat & Colliard 2011)

Colliat & Colliard (2011):

Diameters: 3.8 m to 8 m

Deq ~ 0.28 to 0.45 m (extremely thin-walled)

Consolidation index

75.050T/T1

11~CI


Consolidation - commentary


• Radial consolidation solution

– Adequate fit to sparse data

– Analytical framework: piles to caissons and different soil types

– Consolidation coefficient: relevant cv difficult to estimate

field data (piezocone dissipation) a vital aid

Do we need the black magic of thixotropy for this problem?


Axial stiffness of piles


Pt

wt

Pb

wb

Kb

ka ~ 1.5G D

w

LtanhKS

LtanhSKS

wP

Kb

b

t

taxial

S (for L > 2)

app

p

a kEALL

EAS and L

EAk

L

Pile shaftcompliance

Mobilisation of shaft friction initiated near pile head:

- Consequences for progressive failure and cyclic stability

a

p

shaft

slip

kEA

L1

L1~

QP

L

(EA)p


Cyclic stability diagram for axial loading of piles


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Nor

mal

ised

cyc

lic lo

ad, Q

cycl

ic/Q

shaf

t

Mean load, Qmean/Qshaft

Increasing cycles (N) to failure

Metastable

Unstable N < 10

Stable N > 10,000

N ~ 300

Common form of ‘global’ stability diagram:

Diagram applies at element level -not globally

– Cyclic degradation progresses down

pile from soil surface

– Pile shaft compliance important

– Model tests (low compliance) not

directly applicable for design of more

compliant piles used offshore


Shallow mat foundations


• Widespread use for subsea systems and pipeline terminations

• Generally rectangular: 50 to 200 m2 in plan area

• Complex 6 degree of freedom loading

Pipeline end termination (PLET) Production sled during lay(photos courtesy Subsea 7)


Design considerations for small mat foundations


• Industry design guidelines limited

– Strip or circular geometries only

– Oriented towards bearing capacity, with allowance for H, M

• Operational loads for subsea foundation systems

– Vertical load (V) constant; low proportion of bearing capacity

– Thermally induced variations of horizontal (Hx, Hy), moment (Mx,

My) and torsion (T) from eccentric pipeline and spool connections

– Critical failure mode: combined sliding and torsion

Holy grail: analytical failure envelope for general 3-D loading


Numerical analysis: parameterised solutions


y

V

Hx

Hy

Mx

My

LRP

B

T

z

xL

mudline

z

susum

su0d

k

Simplified soilprofile

• Identify non-dimensional groups:

B/L, d/B, kB/su0, Hx/Hy, My/Mx, V/Asu0, Hres/Asu0 etc

• Evaluate ‘uniaxial’ ultimate capacities for each loading component

• Adjust ultimate horizontal and moment capacities for V/Vult, T/Tult

• ‘Collapse’ 6-dimensional failure envelope into 2 dimensions!


Design approach for small mat foundations


Parameter Value Units Design loads Value Units RatiosWidth, B 8 m Vert. load, V 1200 kN 0.17Length, L 16 m Load, Hx 200 kN 0.21Skirt, d 0.6 m Load, Hy 300 kN 0.34Strength, sum 5 kPa Moment, Mx 1500 kNm 0.07su gradient, k 2 kPa/m Moment, My -2400 kNm 0.30Skirt friction 0 Torsion, T 2100 kNm 0.45

Mobilisation

Failure envelopes

1hhh1m 22qd

fd M

HdMm

fHHh

0100020003000400050006000700080009000

10000

-1000-750 -500 -250 0 250 500 750 1000

Res

ulta

nt m

omen

t, M

(kN

m)

Resultant horizontal load, H (kN)

V = 1200 kN

Failure envelopesUnfactored

su

Zero torsion

T = 2100 kNm

Design point


0100020003000400050006000700080009000

10000

-1000-750 -500 -250 0 250 500 750 1000

Res

ulta

nt m

omen

t, M

(kN

m)

Resultant horizontal load, H (kN)

Design approach for small mat foundations


Parameter Value Units Design loads Value Units RatiosWidth, B 8 m Vert. load, V 1200 kN 0.17Length, L 16 m Load, Hx 200 kN 0.21Skirt, d 0.6 m Load, Hy 300 kN 0.34Strength, sum 5 kPa Moment, Mx 1500 kNm 0.07su gradient, k 2 kPa/m Moment, My -2400 kNm 0.30Skirt friction 0 Torsion, T 2100 kNm 0.45

Mobilisation

0.270.330.540.110.480.72

Factored su(by 0.63)

Failure envelopes

1hhh1m 22qd

fd M

HdMm

fHHh

V = 1200 kN

Unfactored su

Zerotorsion

T = 2100 kNm

Factored su

Design point


Full flow penetrometers


• Penetrometer shapes amenable to analysis– Resistance independent of soil stiffness or in situ stresses

• Sufficient projected area ratio for minimal correction for overburden stress

– Shaft area < 15 % of projected area

• Soil sensitivity measured directly: cyclic testing

• Reduced reliance on ad hoc correlations for shear strength from penetration resistance

– Variations in resistance factors arise from differences in sensitivity (and brittleness), and strain rate dependence

Motivations for introduction, targeting soft soils

T-bar: 100 cm2

ball: 30 to 50 cm2

Pore water pressure filter

Push rod and anti-friction sleeve

Spherical ball

Pore water pressure filter

Push rod and anti-friction sleeve

Spherical ball


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1 2 3 4 5 6 7 8 9 10

Deg

rada

tion

Fact

or

Cycle Number

2.30

2.40

2.50

2.60

2.70

2.80

2.90

3.00

-0.20 -0.10 0.00 0.10 0.20 0.30

Dep

th (m

)

Net ball resistance qball,net (MPa)

Cyclic degradation of soil strength


Penetro-meter

0

0.5

1

0.25

0.75

penetration

extraction

Cycle No.

0

Nk or q

Cycle number0.25 0.75

Undisturbed

Fullyremoulded

In

Out


Theoretical resistance factors – rate dependence & softening


Typical parameters:NTbar ~ 10 to 13Nball ~ 12 to 175

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25Rate parameter

NTbar

95 = 5095 = 2595 = 15

Parameters = rem = 0.2Tbar = 3.7

95 = 10

No strain softeninggradient = 4.8

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25Rate parameter

Nball 95 = 5095 = 2595 = 15

Parameters = rem = 0.2ball = 3.3

95 = 10

No strain softeninggradient = 4.8

Strain to 95 % remoulded

FE results

Gradient of 4.8 implies 'operative' shear strain

rate of 20 %/s or approximately 0.5v/D

u

netk s

qN T-bar

Ball


Consolidation around penetrometers


• In situ assessment of consolidation coefficient– Typically 3 to 10 times greater than from laboratory oedometer testing

– Essential for estimating set-up times around piles, caissons etc

– Pipeline-soil interaction (e.g. buckling, walking) sensitive to degree of consolidation during movement

• Penetrometer testing in intermediate soils (silt-sized)– Partial consolidation during penetration – how best to quantify?

– Requires independent measurements – multiple pore pressure sensors?

– Or varying penetration rate

Ideal: continuous sensing during penetration to detect both degree of consolidation and cv


Partial consolidation effects – backbone curves


Effect on resistance, q, and excess

pore pressure, u

• Function of relative velocity, vD/cv

• Probe by changing penetration rate

• Ideally need prior knowledge of cv -

but at least measure it

Catch 22:

• What is effect of partial

consolidation on subsequent

dissipation test?

0.5

1

1.5

2

2.5

3

0.1 1 10 100 1000

Nor

mal

ised

res

ista

nce,

q/q

un

Normalised velocity, vD/cv

Response to velocitychange (factor of 3)

0

0.2

0.4

0.6

0.8

1

1.2

0.1 1 10 100 1000

Nor

mal

ised

exc

ess p

ore

pres

sure

, Δu/Δu

ref


Response to velocitychange (factor of 3)

Penetrationresistance

Excess porepressure


Partial consolidation effects – experimental study


One soil type; varying velocity

• Dissipation testing after penetration

phase at normalised velocity, vD/cv

• Reduced initial excess pore pressure

• Gradual increase in t50 times

Simple analytical assumption

• Reduced excess pore pressure

corresponds to initial phase of

dissipation test

• Post-penetration dissipation leads to

increased T50

• Consequent under estimation of cv 0102030405060708090

100

0.001 0.01 0.1 1 10 100

Nor

mal

ised

exc

ess p

ore

pres

sure

(Δ

u/Δu

initi

al)

Normalised time factor, T (cvt/D2)

Teh & Houlsby (1991)

Typical data

Hypothetical dissipationduring penetration phase

Subsequentdissipation test

ApparentT50

0

0.2

0.4

0.6

0.8

1

1.2

0.1 1 10 100 1000

Nor

mal

ised

exc

ess p

ore

pres

sure

, Δu/Δu

ref


Dissipation

tests


1

10

100

1000

1 10 100 1000 10000cv

(mm2/s)

t50 (s)

Assuming undrained penetration

Allowing for partial consolidation

during penetration

Partial consolidation effects – theory & experiment


Theoretical approach

• Ignoring partial consolidation effects

gives cv inversely proportional to t50

• Assuming all dissipation part of same

theoretical curve gives apparent lower

limit to t50

Experimental data

• Observed (up to) 3-fold increase in t50

• Experimental data fall between above

two assumptions

• Need revised theory!

0

20

40

60

80

100

120

140

160

0.1 1 10 100 1000 10000

Exc

ess p

ore

pres

sure

(kPa

)

Time (sec)

280 s

600 s400 s

200 s

t50 times

1

10

100

1000

1 10 100 1000 10000cv

(mm2/s)

t50 (s)

Assuming undrained penetration

Allowing for partial consolidation

during penetration

Experimental data


Pipeline geotechnical engineering



Deep water pipeline geotechnical design issues


Infrastructure• Pipeline: laid directly on seabed, possibly with concrete weight coating

• Pipeline initiation, anchoring and manifold systems

Embedment in seabed• Pivotal for lateral stability, lateral buckling analysis, axial sliding

• Pipe lay dynamics has major impact on embedment

• Need combination of analytical solutions and empirical adjustments

Lateral stability• Breakout resistance, post-breakout residual resistance

Axial friction• Large range depending on drainage conditions, hence velocity and time

scale of movement


Pipeline geometry and key parameters


t

zw

Pipeline:Diameter, D Bending rigidity, EISubmerged weight, W'

Tension, T0Seabed (stiff)

Sea surface

Touch down point (TDP)

z

x

s (arc length)

T0

T W'.s

From equilibrium:

Tx constant (T0)

Tz = W'.s

(cumulative pipe weight)

Characteristic length


Pipeline embedment – quick estimate


• Linear seabed strength gradient (upper 0.5 m): su = z kPa

– Seabed plastic ‘stiffness’ (V/w): k ~ 4D

– Dynamic lay motions remould soil: need rem = /St

– Allowance for buoyancy effects as pipe embeds in soil (consider '/rem)

w/D ranges from 0.065 to 0.9

Force concentrationin touchdown zone:V/W' ~ 1.4 to 2.7


Pipeline embedment – refined approach (Westgate et al.)


• Detailed assessment of lay-induced vertical and horizontal motions

– Estimated lay rate, metocean conditions – hence number of exposure cycles

– Pipeline configuration in touchdown zone (maximum dynamic vertical loads)

– Cyclic soil degradation model from cumulative pipeline motions

Non-deterministic estimates

consistent with modern

pipeline design approaches


Pipeline axial friction


• Axial friction controlled by normal effective stress and pipe-soil roughness

– Low effective stress level (< 5 kPa), so enhanced roughness coefficient

– Rapid shearing results in excess pore pressures, reducing normal effective stress

– Consolidation leads to hardening, and local reduction in soil water content

Pipediameter D

w

m

p

n' cos

W'

Average normal stress, n, enhancedby wedging factor, ≤ 1.3

ln 'n

e

emax

q

e0umax

u

e

critical state line

n


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0001 0.001 0.01 0.1 1 10

Nor

mal

ised

fric

tion,

/

n

Normalised time, T = cvt/D2

0.31

10 330

vD/cv = 0.1Backbone curve

Drained Undrained

Time scale for consolidation during axial sliding


Critical state framework

• Rapid shearing leads to ‘undrained’ friction values

• Sustained sliding results in consolidation towards ‘drained’ friction

00.10.20.30.40.50.60.70.80.9

1

0.01 0.1 1 10

Nor

mal

ised

fric

tion,

/ n

Normalised axial displacement, /D

31 10

vD/cv = 30

vD/cv ≤ 0.3

T50 = 0.05 Design range

Initial excess pore pressure & friction• Mobilisation time:

slip/v cv /vD × slip/D

• Consolidation time: T10 ~ 0.001; T50 ~ 0.05; T90 ~ 1


Additional effects during axial sliding


• High strain rates (v/D) enhance shearing resistance

• Sustained volumetric collapse of soil (‘damage’) – source of further u

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.001 0.01 0.1 1 10 100

Normalise

d frictio

n, /

n

Normalised displacement, /D

vd/cv ≤ 0.3

1

10

3

vd/cv = 30

ndamagev Dv


Consolidation properties at shallow depth


• Near surface measurement of consolidation coefficient– Piezocone no longer practical (shallow penetration; long dissipation times)

– Introducing the ‘parkable piezoprobe’ (PPP) – offline dissipation data


LDFE analyses as basis for interpretation


• Couple Modified Cam clay large deformation FE analyses– Assessment of excess pore pressure field

– Backbone consolidation curves

0

0.2

0.4

0.6

0.8

1

1.2

0.0001 0.001 0.01 0.1 1 10 100

u/

u i

T = cvt/D2

CPT (using DCPT)CPT (using DPPP)

Pipeline

PPP, w/D = 0.5

CPT (using DCPT)CPT (using DPPP)

Pipeline (w/D = 0.5)

PPP, w/D = 1


Concluding remarks


• Analysis underpins day to day design

– Direct application of solutions

– Planning of studies based on physical or numerical modelling

– Empirical correlations: a challenge to capture analytically

• Simplicity a guiding light

– Dimensional analysis

– Idealisation of analytical models and input

– Synthesis of outcomes – especially from numerical studies

– Field and laboratory data vital: validation and adjustment of models

All is worthless without understanding!


Acknowledgements


• Colleagues and collaborators throughout the world, but particularly at

– Centre for Offshore Foundation Systems at UWA

– Advanced Geomechanics

– ISSMGE Technical Committee 209 on Offshore Geotechnics

• Generous funding support from

– Australian Research Council

– Lloyds Register Foundation

– Industry

• Mentors throughout my career

Documents

Analytical contributions to offshore geotechnical … McClelland Lecture Analytical contributions to offshore geotechnical engineering Mark Randolph Centre for Offshore Foundation