Mediterranean Workshop on Landslides (MWL) Naples-Italy, 21-22 October 2013

Session 1 : Landslides in HSWR and Relevant Material Properties

Part 5 : Modeling of HSWR for the Investigation of Landslides

(modeling key characteristics of HSWR controlling landslides)

Michael J. Kavvadas

National Technical University of Athens, Greece

The Mediterranean Workshop on LandslidesLANDSLIDES IN HARD SOILS AND WEAK ROCKS (HSWR)

Naples, 21-22 October 2013

Introductory Reports

Part 5 : Modeling of HSWR for the Investigation of Landslides

Michael J. Kavvadas

National Technical University of Athens, Greece

CONTENTS

Modeling strength degradation wrt the initiation and evolution of landslides, i.e., :

• strain softening (strain-induced strength degradation)

• creep effects (time-dependent strength degradation)

The Mediterranean Workshop on LandslidesLANDSLIDES IN HARD SOILS AND WEAK ROCKS (HSWR)

Naples, 21-22 October 2013

Mechanics of progressive failure in stiff soils – effect of strain softening

= slope inclination

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6

Bas

e s

he

ar

T /

W

Displacement () / o

stiff

soft tano o oT C N U

tanu uT N U

o u

1sini iF W F T

Force equilibrium in slice :

cosN U W

Strain compatibility :

1 1 1

o o

i i i i i iF F F F

Slice elongation reduction of compression

Solution method : Toe force (F1 ) is gradually reduced (from initial value Fo ) and all

slice displacements () and inter-slice forces (Fi ) are calculated

δ1 > δ2 > δ3 … as F1 decreases δ1

δi

δn

Progressive failure in “soft” soils

0

0.1

0.2

0.3

0 1 2 3 4 5

Bas

e S

he

ar T

/ W

Displacement (δ) / o

o

o = 25o , U = 0.2 W

tano oT N U

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 10 20 30 40 50

Shea

r a

lon

g fa

ilure

su

rfac

e T

/ W

Slice number (left = bottom, right = top)

F/Fo = 0.94

F/Fo = 0.77

F/Fo = 0.51

F/Fo = 0.40

F/Fo = 1

F/Fo = 0.60

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Toe

Fo

rce

F /

Fo

Toe Displacement / o

Toe

force

= 30oTi

Evolution of base shear as toe

force is gradually reduced

δ

TOE

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

Bas

e S

he

ar

T /

W


Progressive failure in “stiff” soils

o

Co = 0.2 W, o = 25o

u = 18o , U = 0.2 W

tano o oT C N U

tanu uT N U

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

Toe

fo

rce

/ F

o


Toe

force

= 30oTi

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50

She

ar a

lon

g fa

ilure

su

rfac

e T

/ W

Slice number (left = bottom, right = top)

F/Fo = 0.9

F/Fo = 0.4

F/Fo = 0.2 F/Fo = 0.16 F/Fo = 0.45

F/Fo = 1

Point of slope instability

Toe force (support) cannot

be reduced furtherEvolution of base shear as toe

force is gradually reduced

TOE

δ

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6

Bas

e S

he

ar

T /

W


0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

Toe

fo

rce

F

/ F

o


Progressive failure in “stiff” soils – effect of groundwater

o Co = 0.2 W, o = 25o , u = 18o

tano o oT C N U

tanu uT N U

Toe

force

= 30oTi

Evolution as toe force is

gradually reduced

Point of slope instability

Toe force (support) cannot be reduced

further

u

U = 0.2 W

U = 0.6 W

δ

U = 0.2 W

U = 0.6 W

Initiation and evolution of landslides in HSWRKey characteristic is strength degradation due to :

1. Strain softening : loss of shear strength due to large strains2. Creep effects : loss of shear strength with time under high

shear stress (tertiary creep)

Note : The effect of water table fluctuation is not discussed

Modeling of HSWR for the Investigation of Landslides

Example : Lignite mine (130m deep excavation)

Lateral stress relief due to the deep excavation, causes appreciable (elastic) horizontal

displacements intense shearing along the base of the lower lignite stratum (usually

basal clay), with its strength reducing to residual ( = 6-10 degrees)

Creep under the large shear strain can further reduce strength ……

130m

Example : Lignite mine (130m deep excavation)

130m

0

4

8

12

16

20

0

300

600

900

1200

1500

1-1-2012 31-1-2012 1-3-2012

Rai

nfa

ll (

mm

/day

)

Ho

rizo

nta

l dis

pla

cem

en

t (m

m)

Date

1A.2

2A.2

4A.2

rain

v= 20 mm/day

v= 40 mm/day

v= 8 mm/day

2A.21A.2

4A.2

Landslide in Megalopoli lignite mine – 14 Sept 2013(rapid movement by 70m)

700m

130m

before

after

Failure surface

LIGNITE

Modeling Strength Degradation

Non-structured soils : normally consolidated (NC) clays

• Mechanical behaviour is described only via current stresses () and void ratio (e)

• Properties of non-structured soils are called “intrinsic properties”

Structured soils : all others ( HSWR are structured)

• Components of structure = stress history (hard over-consolidated clays),

cementation (calcareous marls, thixotropic-sensitive clays), diagenesis (weak rocks)

• Mechanical behaviour depends on ( , e) and “structure”

• Structured soils have high stiffness & strength, compared to NC clays at same ( , e)

• Structured soils can have high porosity (higher than NC clays) such as tuffs, or low

porosity (lower than NC clays) such as OC clays and many HSWR

• Structure degrades with strain (plastic and creep strain) at large strains

complete loss of structure : material becomes non-structured and has intrinsic

properties

• Structure degradation causes loss of strength (strain softening) and volume changes

(compaction/collapse or dilation)

Strength degradation results from loss of structure

2000 - M. Kavvadas & A. Amorosi : “A constitutive model for structured soils”,

Geotechnique, Vol 50, No 1, pp 263-273

Modeling structured soils - 1. Strain softening

1

exp expp p

v v v

p

q qq

p

v q

e

0:1

,; 22

2 KKKK

cF ssssσσBSE :

Strength

Degradation :

Volumetric

degradation

Shear

degradationVolumetric

hardening

Bond Strength Envelope (BSE) :

• Bounds “strength states”

• Oriented parallel to isotropic axis ()

• Center K :

• Center moves (SK 0 anisotropy)

• Size changes with plastic strains

Plastic Yield Envelope (PYE) :

• Encloses the “elastic domain”

,K K K sσ

pppqε ee :

32

2000 - M. Kavvadas & A. Amorosi : “A constitutive model for structured soils”,

Geotechnique, Vol 50, No 1, pp 263-273

Experiment Model Prediction

Undrained triaxial tests from Ko-consolidated states (OC clay)


σK

σ

s ΙSE

Κ*

α*σΚ*

σο* =σΚ* +α*=2α*

Κ

σΚ α

cα

cα

SSE

σο=σΚ+α

L

PYE

M΄

ξα ξα

L

σL

PYE

M

β

M΄΄

σK

σ

s

σ

s ΙSE

Κ*

α*σΚ*

σο* =σΚ* +α*=2α*

ΙSEΙSE

Κ*Κ*Κ*Κ*

α*σΚ* α*σΚ*

σο* =σΚ* +α*=2α*

Κ

σΚ α

cα

cα

SSE

σο=σΚ+α

ΚΚΚ

σΚ ασΚ α

cα

cα

cα

cα

SSESSE

σο=σΚ+ασο=σΚ+α

L

PYE

LL

PYEPYE

M΄M΄

ξα ξα

L

σL

PYE

ξα ξα

L

σL

PYELL

σLσL

PYEPYE

MM

ββ

M΄΄M΄΄

2010 - G. Belokas & M. Kavvadas : “An Anisotropic Constitutive Model for Structured

Soils”, Computers and Geotechnics, Volume 37 (6), Pages: 737-747

Structure Strength Envelope (SSE) :

• Bounds “strength states”

• Orientation (b) anisotropy

• Size changes with plastic strains

Plastic Yield Envelope (PYE) :

• Encloses the “elastic domain”

Intrinsic Strength Envelope (ISE) :

• Reference strength of intrinsic material

Size * = function of ( , e)

Orientation along consolidation path

b

0)-()-(:)-(1

; 22

2 ασσ

σ

σ

σ

σ

cα,F ΚΚ

Κ

Κ

Κ

Κ ssssσσSSE :

* * *1exp expp p

v v v q q q

p p

v q

e

Strength Degradation :

Volumetric degradation Shear degradationVolumetric hardening


0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

She

ar s

tre

ss -

q (

kPa)

Mean stress - p (kPa)

0

100

200

300

400

500

600

700

0.00 0.10 0.20 0.30 0.40

She

ar s

tre

ss -

q (

kPa)

Shear strain - εq

Increasing rate ofstructure degradation

( q = q = 0.5 , 1 , 1.5 )

Ko - consolidation

Undrained shearing



Bond strength : p = 1000 kPa

Initial consolidation to p = 600 kPa and then undrained shearing


SSE

Data provided by Dr. G. Belokas

0

100

200

300

400

500

600

700

0.00 0.10 0.20 0.30 0.40

She

ar s

tre

ss -

q (

kPa)

Shear strain - εq

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

She

ar s

tre

ss -

q (

kPa)

Mean stress - p (kPa)

Ko - consolidation

Undrained shearing



Increasing rate ofstructure degradation

( q = q = 0.5 , 1 , 1.5 )

Bond strength : p = 1000 kPa

Initial consolidation to p = 100 kPa and then undrained shearing


SSE

Data provided by Dr. G. Belokas

Modeling structured soils - 2. Creep-induced strength degradation

2012 – A. Kalos “Investigation of long-term creep deformations on soil strength”,

Proceedings, European Young Geotechnical Engineers Conference (EYGEC),

Gothenburg - Sweden

Time (t)

qA

Creep strain (ε)

secondary

primary

tertiary

creep failure

q B

q C

q A < q B < q C

Strain (ε)

Shear Stress (q)

q A

q B

q C

Objective : Investigate initiation and evolution of landslides via tertiary creep

Short-term strength

Long-term strength

α*

α

σ

cα

sShort-term CSL

Short-term SSE

Long-term CSL

2 2

2

1F : σ α α

c s s

ISE

2. State leading to

long-term failure

1. State not leading

to long-term failure


* * *1exp expp p

v v v q q q

p p

v q

e

1. Strength degradation with plastic strains :

Volumetric degradation Shear degradationVolumetric hardening

Simple model with both plastic strain and creep destructuring

PYE

Initial state

t

ε

1

2

0

500

1000

1500

0 500 1000 1500

σ1

-σ

3(k

Pa)

mean stress p (kPa)

CSLCU stress pathinitial SSEfinal SSE

0

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4

σ1

-σ

3(k

Pa)

axial strain ε1

0

500

1000

1500

0 500 1000 1500 2000 2500

σ1

-σ

3(k

Pa)

mean stress p (kPa)

CSLCD stress pathinitial SSEfinal SSE

0

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4

σ1

-σ

3(k

Pa)

axial strain ε1

1. Strength degradation with plastic strains - CU and CD tests

CU test on

low OCR

clay

CD test on

high OCR

clay

1

0

11

tqt

q m

mtq

ε 2A sinh a Dε

tm

ε2A sinh a D t

Shear creep strain-rate :

Singh-Mitchell type creep

= q / qf = shear stress ratio


tLT qc c c ε a

2. Strength degradation with creep strains :

D

m A a, , = creep parameters

α σ

C α

s Short-term CSL (co)

Long-term CSL (cLT)2. State leading to

long-term failure

1. State not leading

to long-term failure

Time dependent strength degradation :

reduction of the “friction angle” with time

t

ε

1

2

0

500

1000

1500

0 0.1 0.2 0.3 0.4

She

ar

q =

σ1

-σ

3(k

Pa)

Shear strain q

primary creep

secondary creep

tertiary creep

0.0

0.2

0.4

0.6

0 5 10 15

She

ar s

trai

n

q

time (months)

primary creep

secondary creep

tertiary creep

0

500

1000

1500

0 500 1000 1500 2000 2500

She

ar s

ress

q =

σ1

-σ

3(k

Pa)

Mean stress p (kPa)

Short-term CSL Long-term CSL

Initial SSE

Final SSE

Model predictions

Drained shear test

with creep

1

3

2

1

32

1

2

3

Landslide Example : Excavation at the toe of a slope (FE analysis)

H=40m

Slope = 20o

H=10m

Toe slope = 45o

Initial condition

After toe excavation

Cases studied :

1. Only strain softening (no Creep) – Wet slope (consolidation)

2. Strain softening and Creep – Wet slope (consolidation)

3. Strain softening and Creep – Dry slope


Displacements shortly after toe excavation

(undrained toe excavation)

U = 17cm

Displacements at failure

(during consolidation)

Umax > 50cm

Localised failure surface does not develop …..

U = 20cm

U = 28cm


Localised failure surface

does not develop …..

1

2

3

0.0

0.1

0.2

0.3

0.4

0.5

900 950 1000 1050

Um

agn

(m)

time (days)

1

2

3

Toe excavation

Failure

Evolution of slope displacement

during consolidation

(after toe excavation)


Displacements shortly after toe excavation

Umax = 36cm

Displacements at failure (during creep)

Umax = 80cm

Localised failure surface appears to develop …..

U = 18cm

U = 18.5cm

Mises shear stress (q)

shortly after toe excavation


at failure (during creep)

Small q on

“failure” surface


Localised failure surface appears to develop …

Large q on

“failure” surface

Shear creep strain at failure

(during creep)

0.00

0.20

0.40

0.60

0.80

0 50 100

Um

agn

-to

e(m

)

time (days)

toe

Evolution of toe displacement :

• Toe excavation (rapid)

• Creep (after toe excavation)

Toe excavation

(rapid)

Creep



appears to develop …

High shear strain

3

0.00

0.03

0.06

0.09

0.12

0 50 100

She

ar s

trai

n

εq

time (days)

0

100

200

300

400

500

0 100 200 300 400 500 600

She

ar s

tre

ss

q (

kPa)

Mean stress p (kPa)

EL. 1135

Toe excavation

creep Stress path during :

• Toe excavation (rapid)

• Creep (after toe excavation)

During creep the soil “friction

angle" drops from 20o to 8o

1

2

3

12

EL. 1135

2. Strain softening and

Creep – Dry slope

0

100

200

300

400

500

0 50 100

She

ar s

tre

ss q

(kP

a)

time (days)

EL. 1135

1

3

2

ST-CSL

LT-CSL

3. Strain softening and Creep – Wet slope (consolidation)Displacements shortly after toe excavation

U = 17cm

Displacements at failure (during creep)

Umax = 87cm

Localised failure surface clearly develops …..

U = 19cm

U = 50cm


Localised failure surface clearly develops …..


shortly after toe excavation


at failure (during creep)

Small q on

failure surface

Shear creep strain at failure

Evolution of displacements at

points along the failure surface

during creep


develops …..

High shear strain


0.0

0.2

0.4

0.6

0.8

600 620 640 660 680 700

Um

agn

(m)

time (days)

1

3

2

2

1

3

Red : Plastic domain at failure

Blue = elastic domain


Video : Evolution of plastic domain in slope during consolidation + creep


Video : Evolution of pore pressures in slope during consolidation + creep


Video : Evolution of displacements in slope during consolidation + creep


0

100

200

300

400

0 100 200 300 400

she

ar s

tre

ss q

(kP

a)

mean stress p (kPa)

EL. 846

0

100

200

300

400

600 650 700

she

ar s

tre

ss q

(kP

a)time (days)

Toe excavation

Consolidation and creep

Evolution of shear stress with time :

Retrogressive failure surface reaches EL 846 at

peak q point.

Then creep + strain softening reduce q drastically as

intense shear strains accumulate along the failure

surface

EL. 846 EL. 846

Toe excavation


Red : Plastic domain at failure (end of creep)


(during creep)

Umax = 87cm

Fast creep strength degradation (a = 1.5) < Time for consolidation

Creep strains cause excess pore pressures

Blue = elastic domain (due to creep)


Red : Plastic domain at failure (end of creep)


(during creep)

Umax = 11m

Slower creep strength degradation (a = 1.2) Time for consolidation

Creep strains cause smaller excess pore pressures

Blue = elastic domain (due to creep)

Conclusions• Strength degradation with plastic strains (strain softening) and

creep (tertiary creep) are key parameters in the initiation and

evolution of landslides

• Modelling :

• strength reduction due to creep via “friction angle drop” and

• a combination of consolidation and creep

appears to be effective for studying retrogressive landslides

• The ratio of the characteristic times of consolidation and creep

appears to control the shape of the failure surface

Acknowledgments : My PhD student Alex Kalos for performing the FE analyses

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Mediterranean Workshop on Landslides (MWL) Naples-Italy, 21-22 October 2013

Documents