Post on 20-Jun-2020
PROFESSOR MICHAEL C R DAVIESUniversity of Sussex
andCity, University of London
Geotechnical Centrifuge Modelling: Capturing Complexities To Enable
Analytical Solutions
Western Geotechnical Centrifuge Opening & Symposium 2-3 May 2019
• Introduction− Capturing complexity in analytical models− Centrifuge modelling to capture complexity− Geotechnical research process
• Examples − Soil nailing− Root reinforcement of slopes− Earthquake soil-foundation-structure interaction (SFSI)
• Conclusions
Scope of Presentation
• Introduction− Capturing complexity in analytical models− Centrifuge modelling to capture complexity− Geotechnical research process
• Examples − Soil nailing− Root reinforcement of slopes− Earthquake soil-foundation-structure interaction (SFSI)
• Conclusions
Scope of Presentation
• Analytical methods are particularly valuable in cases where high accuracy is not required or unachievable due to lack of data or level of risk, and where high performance computing time and costs are prohibitive.
• Focus on the development of models for analyses that capture important complexities while being simple enough to be solved analytically and implemented easily.
New construction techniques
Poorly defined geotechnical systems
Screening and assessment of geotechnical systems
Capturing complexity in analytical models
• Observations of geotechnical systems inform the development of analytical solutions for assessing stability, calculating movements and for predicting the impact of geotechnical processes.
• Correctly scaled and appropriately instrumented physical models that capture the important complexities of geotechnical systems can provide an alternative to field measurements.
• Such models allow simulation of geotechnical systems that might be too expensive, time consuming or almost impossible to monitor in the field.
Centrifuge modelling - capturing complexity
• Requirement for similitude between material properties in prototype and model.
• Stress/strain behaviour of soil is highly non-linear, stress level dependent and stress history dependent.
• Close control over material properties and well defined boundary conditions in a model enable repeatability -permitting parametric studies to be conducted.
• Instrumentation and monitoring systems provide quantitative data that may be used both to inform the development and to validate analytical solutions.
Centrifuge modelling - capturing complexity
Fundamental generic study
Field Assessment
PhysicalModelling
Site investigation
Information for numerical modelling
Information for model testing
Fundamentalgeneric analysis
Validation by experiment
Case specific analysis
Case specific tests
Numerical and Analytical Modelling
Understanding&
Design
Integrated geotechnical research process
150 g-tonne beam centrifuge (Actidyn C67-2)
Centrifuge modellingDundee Geotechnical Centrifuge
150 g-tonne beam centrifuge (Actidyn C67-2)
Centrifuge modellingDundee Geotechnical Centrifuge
• Introduction− Capturing complexity in analytical models− Centrifuge modelling to capture complexity− Geotechnical research process
• Examples − Soil nailing [New construction technique]− Root reinforcement of slopes [Poorly defined geotechnical system]
− Earthquake soil-foundation-structure interaction (SFSI) [Screening and assessment of geotechnical systems]
• Conclusions
Scope of Presentation
Soil Nailing
Construction Sequence
Soil Nailing
Construction Sequence - Excavation
Soil Nailing
Construction Sequence - Nail Installation
Soil Nailing
Construction Sequence - Facing Placed
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Soil Nailing
Construction Sequence - Completed Structure
Soil Nailing
Construction Sequence - Completed Structure
Soil Nailing
Cementation Foundations Skanska
Soil nailing construction problems
Soil nailing construction problems
Soil nailing Analysis of internal stability Bishop’s simplified method of slices
after: BS 8006-2:2011 Code of practice for strengthened/reinforced soils. Soil nail design
B width of slice (m)H height of slope (m)La length of nail to base of slice (m)Le length of embedment zone (m)r radius of slip circle (m)Td design tension in nail at point (kN)
α angle as defined by Bishop (1955)β angle of slopeε nail declinationη angle between normal to slip plane and
nail = 90° − α − ε
Assessment of mechanisms which are either fully
contained within the soil nailed zone or pass through some part of it the soil nailed zone or pass through some
part of it to ensure:
Mdriving ≤ Mresisting
after: CIRIA RP 674: Soil Nailing: Best practice guidance (2005)
Soil nailing Summary of factors recommended by commonly used soil nailing design codes
after: CIRIA RP 674: Soil Nailing: Best practice guidance (2005)
Soil nailing Estimating nail pullout resistance using effective stress methods
Range from empirical
data
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.0 5.0 10.0 15.0
Dep
th b
elow
cre
st z
/H
Factored unit bond Tb kN/m
Ln =5m, D=0.1m, Ks = 0.9
15°, Sh = 1m
’ = 38 deg, ’cv = 32 deg, c’=0
18.5 kN/m3ru= 0.1
z
EC7FHWA LRFDHA68/94BS8081BS8006FHWA SLD/Clouterre
Tb = πD[Kσ’v tan δ + c’]
Hh
gravel drain
PPTs/tensiometers
bund for stage 5
gravel drain
reservoir (variable head) reservoir (fixed head)
nails
Geometry of centrifuge models
Soil NailingModel soil nails
300 mm
8 mm
Soil NailingModel with flexible facing
Stage 2 and Stage 4
Stage 5
Stage 1 and Stage 3
phreatic surface
Soil NailingDrainage boundary conditions for each stage
Soil NailingNail axial force
0
5
10
15
20
25
0 1 2 3 4 5 6Distance from Facing, m
Axia
l For
ce, k
N
Stage 1Stage 2Stage 3Stage 4Stage 5
nail elevation (h/H): 0.125
slope angle: 60º
Soil NailingVertical and horizontal displacements (60˚ slope)
0
5
10
15
20
25
30
1 2 3 4 5
Slop
e di
spla
cem
tent
, mm
Experimental Stage
vertical
horizontal
Soil NailingPeak axial forces (T) at each experimental stage (60˚ slope)
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25Peak Axial Force, kN
Nai
l Ele
vatio
n (h
/H)
Stage 1Stage 2Stage 3Stage 4Stage 5
Soil NailingAxial forces (T) normalised by theoretical pullout values (Tp')
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8T/Tp'
nail
elev
atio
n (h
/H)
Stage 1Stage 2Stage 3Stage 4Stage 5
slope angle: 60º
Soil NailingPredicted utilisation factor (MR/MD)
1
2
3
4
1 2 3 4 5Experimental Stage
Util
isat
ion
Fact
or
slope angle: 60º
Soil NailingComparison of horizontal spacing
0
1
2
3
4
5
6
0 5 10 15 20 25 30Axial force, kN
Hei
ght o
f nai
l hea
d, m
spacing = 1.4 mspacing = 2.0 mspacing = 3.4 m
vertical spacing = 1.5 m
slope angle: 70º
Soil NailingMeasured axial forces in nails at different horizontal spacings, Sh
(slope angle: 70º)
Height of nail head, m
Sh = 1.4 m Sh= 2 m Sh = 3.4 m5.25 2.4 3.3 10.53.75 6.6 7.9 11.42.25 7.8 13.8 19.80.75 10.3 18.5 26.3
Tmax 27.0 43.5 68.0
Tmax/Sh, kN/m 19.3 21.8 20.0
Maximum axial force in nail, Tmax, kN
Soil NailingPressure on facing - Miniature total pressure cells attached to facing
Soil NailingPressure on facing (70º slope)
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140
Pressure on facing, kPa
Hei
ght f
rom
bas
e, m
spacing = 1.4 m excavatespacing = 2.0 m excavatespacing = 3.4 m excavateKospacing = 1.4 m testspacing = 2.0 m testspacing = 3.4 m test
Soil NailingLateral facing deformations at test stage 4 (70º slope)
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70
Facing deformation, mm
Hei
ght f
rom
bas
e, m
spacing = 3.4 mspacing = 2.0 mspacing = 1.4 m
N.B. Tree line is above top of landslide scar, landslide has occurred wherethere are no deep rooting plants.
Photograph by J E Norris - Eco-Slopes Final Report ECO-SLOPES QLK5-2001-00289
Shallow landslide occurring in cutting
Eco-Slopes Final Report ECO-SLOPES QLK5-2001-00289
Exposed roots - cut slope in London Clay
Root reinforcement of slopesSoil nailing versus vegetation for slope stabilisation
Root reinforcement of slopesRoot soil interaction: tensile strength and stiffness
Axial strain calculated using particle image velocimetry (PIV)
Radial strain measurement using variation in colour intensity
Root reinforcement of slopesRoot soil interaction: tensile strength and stiffness
Relationship between (a) the tensile strength and (b) modulus of willow roots and their diameter
Root reinforcement of slopesRoot soil interaction: tensile strength and stiffness
dichotomouspattern
taproot herringbone pattern
Root reinforcement of slopesRoot soil interaction: effect of root architecture on pull-out
Pull-out resistance of representative samples of embedded willow root segments with different architectures pulled from dry sand
Root reinforcement of slopesRoot soil interaction: effect of root architecture on pull-out
Root reinforcement of slopesSlope reinforcement: centrifuge model tests
Schematic of centrifuge model of 6.0 m high slope (dimension in mm in model scale; tests conducted at 15g )
100 400 100
400
100
Root reinforcement of slopesSlope reinforcement: centrifuge model tests
Tensile strength of root analogue material and live roots (willow plant after 290 days of growth in centrifuge strong box and
control tubes)
0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
120
Root diameter [mm]
Tens
ile s
treng
th
[N/m
m2 ]
T = 15.04 * d -0.55 (R2 = 0.340)
Linden wood
Viton rubber
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (grown willow)
Willow grown for 290 days
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (grown willow)
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (fallow slope)
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (root analogue)
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (root analogue)Dichotomous wood – bending and pull-out
x [mm]
y [
mm
]
100 200 300 400 500 600
0
50
100
150
200
250
300
350
400 -60
-40
-20
0
20
40
60
Failure onslope toe
x [mm]
y [
mm
]
100 200 300 400 500 600
0
50
100
150
200
250
300
350
400 -60
-40
-20
0
20
40
60
Branches oflower root
Branches ofupper root
x [mm]
y [
mm
]
100 200 300 400 500 600
0
50
100
150
200
250
300
350
400 -60
-40
-20
0
20
40
60
Contour plots of displacement magnitude from PIV analysis as the water table in the model is raised.(a) Development of shallow slope failure across roots, (b) Start of shear plane migration, (c) Final shear plane below root influence
(a) (b)
(c)
Root reinforcement of slopesSlope reinforcement: centrifuge model tests (root analogue)
Dichotomous woody root analogues
01002003004005006007008000
100
200
300
400
500
600Summary of failure: Mid-span
x [mm]
y [m
m]
Marker: 50, 100 and 150 mm
S03 - Fallow (New Water)S05 - Taproots; Dens 2 (w. Head)S07 - Willow; Time 2S09 - Dichotomous WoodS10 - Dichotomous Viton
FallowTaproot
Branched roots
Root reinforcement of slopesSlope reinforcement: centrifuge model tests
*values predicted from element tests
Back-calculated change of c′ (Δc′) required to give FOS = 1.0 at failure using Bishop’s method (using φ′ = 24.0°, c′ = 5.5 kPa) and comparison
with results from reinforcement calculation methods
Fallow Taproot Dichotomous rootNo root head
With root head Wood Rubber
RAR 0 0.0018 0.0005 0.0005 0.0005
FOS 1 0.9 1.0 0.8 0.9
Δc’ (kPa) - 0.6 0.1 2.7 1.2Δc’ pullout* (kPa) - 1.7 0.5 1.5 1.2
Δc’ tension* (kPa) - 184 51 51 4.4
Root reinforcement of slopesSlope reinforcement: centrifuge model tests
Slope stability calculations
Earthquake soil-foundation-structure interaction - field data
Surface ruptures during the 1999 Chi-Chi earthquake
Earthquake soil-foundation-structure interaction - field data
Surface ruptures during the 1999 Chi-Chi earthquake
Earthquake soil-foundation-structure interaction - field data
No Damage Partial Collapse Collapse
Building1
Building 2 Building 3
Mosque
2.1 m
2.3 m
Fault Rupture
Fault Rupture at the area east of Gölcük, Turkey (1999)
Earthquake soil-foundation-structure interaction - field data
Building 1: 4-storeys + Basement – No Damage
after Gazetas and Anastasopoulos (2007)
Earthquake soil-foundation-structure interaction - field data
Building 3: 2-stories + attic – No Damage
after Gazetas and Anastasopoulos (2007)
Earthquake soil-foundation-structure interaction – model testing
Centrifuge apparatus – normal fault
Test12_R2_022 (Initial)
slip=0.000 m
Throw=0.000 m
slip=0.000 mm
Throw=0.000 mm
<Model scale> <Prototype scale>
Hsoil=25.0 m
Test12_R2_028 (Throw=0.496m, slip=0.572m)
slip=0.572 m
Throw=0.496 mThrow=4.309 mm
<Model scale> <Prototype scale>
slip=4.976 mm
Test12_R2_033 (Throw=0.993m, slip=1.147m)
slip=1.147 m
Throw=0.993 mThrow=8.639 mm
<Model scale> <Prototype scale>
slip=9.975 mm
Test12_R2_036 (Throw=1.462m, slip=1.688m)
Throw=12.709 mm
<Model scale> <Prototype scale>
slip=14.675 mm slip=1.688 m
Throw=1.462 m
Test12_R2_040 (Throw=2.017m, slip=2.329m)
Throw=17.539 mm
<Model scale> <Prototype scale>
slip=20.252 mm slip=2.329 m
Throw=2.017 m
Test12_R2_045 (Throw=2.497m, slip=2.883m)
Throw=21.709 mm
<Model scale> <Prototype scale>
slip=25.067 mm slip=2.883 m
Throw=2.497 m
Hsoil=25.0 m
Test14_R_022 (Throw=0.000m, slip=0.000m)
slip=0.000 mm
Throw=0.000 mm
<Model Scale>
slip=0.000 m
Throw=0.000 m
Test14_R (Normal fault, Standard footing, Centre)
<Prototype Scale>
Free-field shear plane(Test12_R2)
Centre-line
slip
0
Throw0
Wfooting=10.12m, 88mm q=91 kPaHsoil=213.6 mm<Model>
Hsoil=24.56 m<Prototype>
Test14_R_028 (Throw=0.517m, slip=0.597m)
slip=0.597 m
Throw=0.517 m
<Prototype Scale>
Test14_R_031 (Throw=0.939m, slip=1.085m)
slip=1.085 m
Throw=0.939 m
<Prototype Scale>
Test14_R_036 (Throw=1.637m, slip=1.891m)
slip=1.891 m
Throw=1.637 m
<Prototype Scale>
Test14_R_039 (Throw=2.019m, slip=2.331m)
slip=2.331 m
Throw=2.019 m
<Prototype Scale>
Test14_R_044 (Throw=2.794m, slip=3.226m)
slip=3.226 m
Throw=2.794 m
<Prototype Scale>
Hsoil=213.6 mm<Model>
Hsoil=24.56 m<Prototype>
slip=32.58 mm
Throw=28.21 mm
<Model Scale>slip
0
Throw0
Centrifuge model of normal faultDisplacement vectors
15 20 25 30 35 40 45 50 55
-30
-25
-20
-15
-10
-5
0
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.8
1
1.2
1.5
2
2.2
2.4
2.6
2.8
3
0.05
3
2.4
0.05
distance (m)
dept
h (m
)
Centrifuge model of normal faultShear strains
15 20 25 30 35 40 45 50 55
-22
-20
-18
-16
-14
-12
-10
-8
-6
distance (m)
dept
h (m
)
shear strain, %
2
2
22
2
22
2
2
22
2
2
2
2
2
2
2
2
2
2
4
4
4
4
4
4
44
4
4
6
6
66
6
6
6
6 8
8
8
8
8
8
8
8
10
10
10
10
10
10 12
12
12
12
12
14
14
14
14
14
14
16
16
16
16
16
16
18
18
18
18
18
1820
20
20
20
20
2025
25
25
25
25
2530
30
30
30
30
3040
40
4040
4040
50
50
5050
5050
80
80
8080
80
8080
4
4 4
4
6
6
6 6
8
8
6
6
44
22
4
10
62
6
1012
8
8
1214
10
14
12
16
414
16
10
18
16
2
4 18
18 8
20
20
20
62530
2
6
2
40
25
50
6
25
8
2
8
2
2
22
10
30
10
80
2
30
84
4 14
2
16
6
4
4
18
8
20106
212
10
25
8
4
42
12
840
1214
8
2
30
2
2
2
4
2
8
8
50
2
10
44
40
50
8
4
2
40
24
2
404
6
2
6 2
2
8
254
2
4 4
2
Centrifuge model of normal faultRotation of foundation
0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Rot
atio
n, d
egre
es
Throw, m
Test14_R (rigid, w=10m, q=91kPa, Centre)
Test15 (rigid, w=10m, q=37kPa, Centre)
Test22 (Flexible, w=10m, q=91kPa, Centre)
Analysis of fault diversionKinematic limit analysis approach after Paolucci and Yilmaz (2008)
Problem statement for a shallow strip foundation resting on drained soil, subject to normal or reverse fault rupture
after R. Paolucci and M.T. Yilmaz Simplified theoretical approaches to earthquake fault rupture–shallow foundation interaction (2008)
Analysis of fault diversionKinematic limit analysis approach after Paolucci and Yilmaz (2008)
after R. Paolucci and M.T. Yilmaz Simplified theoretical approaches to earthquake fault rupture–shallow foundation interaction (2008)
Analysis of fault diversionKinematic limit analysis approach after Paolucci and Yilmaz (2008)
after R. Paolucci and M.T. Yilmaz Simplified theoretical approaches to earthquake fault rupture–shallow foundation interaction (2008)
Conditions for the diversion of surface breakage of fault rupture for various dip angles (Ψ) of reverse or normal fault, and different friction
angle (φ) of drained soil, obtained by the kinematic approach
Analysis of fault diversionKinematic limit analysis approach after Paolucci and Yilmaz (2008)
after R. Paolucci and M.T. Yilmaz Simplified theoretical approaches to earthquake fault rupture–shallow foundation interaction (2008)
Comparison of centrifuge model tests with diversion criteria (φ = 30° and ψ = 60°)(a) reverse fault case and (b) normal fault case
N.B. Foundation tilting greater than 3° at 3m fault throw is denoted as excessive
Normal fault – comparison of displacement vectors
-5
0
5
10
15
20
25
0 10 20 30 40 50 60 70 80
'norm_dundee.txt' using 2:3:4:5
-5
0
5
10
15
20
25
0 10 20 30 40 50 60 70 80
'norm_sgi.txt' using 2:3:4:5
60° normal fault
Experimental results(Dundee centrifuge)
Numerical analysis(SGI)
Normal fault – final imposed dip displacement
Shear strains from numerical analysis(NTUA)
Experimental results(Dundee centrifuge)
60° normal fault
Analysis of fault diversionSemi-analytical method approach
after Anastasopoulos, Gerolymos, Gazetas & Bransby (2008)
after Anastasopoulos et al Simplified approach for design of raft foundations against fault rupture. Part I : Free-field (2008)
• Introduction− Capturing complexity in analytical models− Centrifuge modelling to capture complexity− Geotechnical research process
• Examples − Soil nailing− Root reinforcement of slopes− Earthquake soil-foundation-structure interaction (SFSI)
• Conclusions
Scope of Presentation
• Geotechnical centrifuge modelling permits repeatability associated with laboratory testing combined with the ability to conduct parametric studies.
• Correctly scaled centrifuge models capture the complexities of prototype systems.
• Centrifuge models allow the observation of mechanisms and the capture of qualitative data that can be used both to understand mechanisms and inform the development of analytical solutions.
• Centrifuge models provide quantitative data for developing and validating analytical solutions.
Conclusions
• Professor A.G. Bengough, James Hutton Institute, Dundee and University of Dundee
• Professor M.F. Bransby, University of Western Australia (formerly University of Dundee)
• Professor P.D. Hallett, University of Aberdeen (formerly James Hutton Institute, Dundee)
• Dr Omar Hamza, Civil-Stones Geotech, UK (formerly University of Dundee)
• Professor S. Mickovski, Glasgow Caledonian University (formerly University of Dundee)
Acknowledgments