analytical contributions to offshore geotechnical … mcclelland lecture analytical contributions to...
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![Page 1: Analytical contributions to offshore geotechnical … McClelland Lecture Analytical contributions to offshore geotechnical engineering Mark Randolph Centre for Offshore Foundation](https://reader031.vdocuments.mx/reader031/viewer/2022021821/5b0805357f8b9a79538ead13/html5/thumbnails/1.jpg)
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
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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
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The University of Western Australia
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
?
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 3
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The University of Western Australia
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
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 4
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The University of Western Australia
Piled foundations - consolidation
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 5
• 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
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The University of Western Australia
Development of axial pile resistance
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 6
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
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The University of Western Australia
Consolidation around suction caissons
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 7
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
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The University of Western Australia
Consolidation - commentary
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 8
• 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?
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The University of Western Australia
Axial stiffness of piles
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 9
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
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The University of Western Australia
Cyclic stability diagram for axial loading of piles
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 10
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
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The University of Western Australia
Shallow mat foundations
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 11
• 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)
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The University of Western Australia
Design considerations for small mat foundations
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 12
• 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
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The University of Western Australia
Numerical analysis: parameterised solutions
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 13
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!
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The University of Western Australia
Design approach for small mat foundations
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 14
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
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The University of Western Australia
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
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 15
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
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The University of Western Australia
Full flow penetrometers
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 16
• 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
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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
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 17
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
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The University of Western Australia
Theoretical resistance factors – rate dependence & softening
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 18
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
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The University of Western Australia
Consolidation around penetrometers
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 19
• 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
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The University of Western Australia
Partial consolidation effects – backbone curves
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 20
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
Normalised velocity, vD/cv
Response to velocitychange (factor of 3)
Penetrationresistance
Excess porepressure
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The University of Western Australia
Partial consolidation effects – experimental study
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 21
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
Normalised velocity, vD/cv
Dissipation
tests
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The University of Western Australia
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
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 22
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
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The University of Western Australia
Pipeline geotechnical engineering
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 23
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The University of Western Australia
Deep water pipeline geotechnical design issues
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 24
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
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Pipeline geometry and key parameters
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 25
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
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The University of Western Australia
Pipeline embedment – quick estimate
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 26
• 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
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Pipeline embedment – refined approach (Westgate et al.)
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 27
• 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
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Pipeline axial friction
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 28
• 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
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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
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 29
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
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The University of Western Australia
Additional effects during axial sliding
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 30
• 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
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The University of Western Australia
Consolidation properties at shallow depth
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 31
• Near surface measurement of consolidation coefficient– Piezocone no longer practical (shallow penetration; long dissipation times)
– Introducing the ‘parkable piezoprobe’ (PPP) – offline dissipation data
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The University of Western Australia
LDFE analyses as basis for interpretation
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 32
• 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
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The University of Western Australia
Concluding remarks
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 33
• 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!
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The University of Western Australia
Acknowledgements
Mark Randolph: 2nd McClelland Lecture: Paris, September 2013 34
• 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