Davies - Capturing Complexities To Enable Analytical Solutions · PROFESSOR MICHAEL C R DAVIES...

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

• 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


• 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


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

Construction Sequence - Completed Structure

Soil Nailing

Cementation Foundations Skanska

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)


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)


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


Relationship between (a) the tensile strength and (b) modulus of willow roots and their diameter


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


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


*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


Slope stability calculations

Earthquake soil-foundation-structure interaction - field data

Surface ruptures during the 1999 Chi-Chi earthquake


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)


Building 1: 4-storeys + Basement – No Damage

after Gazetas and Anastasopoulos (2007)


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


slip=4.976 mm


slip=1.147 m

Throw=0.993 mThrow=8.639 mm


slip=9.975 mm


Throw=12.709 mm


slip=14.675 mm slip=1.688 m

Throw=1.462 m


Throw=17.539 mm



Throw=2.017 m


Throw=21.709 mm



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>


slip=0.597 m

Throw=0.517 m

<Prototype Scale>


slip=1.085 m

Throw=0.939 m

<Prototype Scale>


slip=1.891 m

Throw=1.637 m

<Prototype Scale>


slip=2.331 m

Throw=2.019 m

<Prototype Scale>


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)



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



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)


• Examples − Soil nailing− Root reinforcement of slopes− Earthquake soil-foundation-structure interaction (SFSI)

• Conclusions


• 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

Davies - Capturing Complexities To Enable Analytical Solutions · PROFESSOR MICHAEL C R DAVIES...

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