Georges Gazetas

École Polytechnique Nationale d’ Athènes

on the Verge of “Failure”

7 th COULOMB Lecture, Paris 26 June 2009

Seismic Soil–Foundation

Interaction

Topics of Presentation

PART 1

(a) Why Going to the Limit and “Beyond”

in Seismic Foundation Analysis / Design

(b) Conventional versus New Design

Concept: Bridge Pier Foundation

PART 2

The Causes of Overturning

of Buildings in Adapazari (1999)

Seismic Foundation Practice

• Analysis in terms of FORCESFORCES

• Safety through SAFETY FACTORSSAFETY FACTORS

AnalysisAnalysis––Design in terms ofDesign in terms of

DISPLACEMENTS, DISPLACEMENTS, ROTATIONSROTATIONS

“ Performance–Based Design ”

But now TIME has come for CHANGE :

Current Seismic Approach :

“Capacity” Design

(α) Plastic Deformation Allowed Only in

the (Super)Structure

(b) NO “Plastic Hinging” Below Ground:

• Piles, Cap, Footings : Structurally Elastic

• NO Mobilization of Bearing Capacity Failure Mechanisms

• NO Slippage , LIMITED Uplift

Why we need to consider Soil–Foundation Nonlinearity + Inelasticity:

Records in last 20 years: have revealed very strong seismic shaking

Examples:

1994 Northridge : 0.98 g , 1.40m/s

1995 Kobe : 0.85 g , 1.50m/s

1986 San Salvador : 0.75 g , 0.84m/s

and SA values reaching 2 g

Foundation Foundation ““Plastic HingingPlastic Hinging””:: UNAVOIDABLEUNAVOIDABLE

(a)11

(b) Retrofitting Existing/Damaged Structures

Usually Impossible

to Accomplish Elastically

(even if very conservative design required)

Must Consider Inelastic Action in

Soil + Foundation

N small

M very large

Shear Wall

Existing Retrofitted

M

N

M

Uplifting, Nonlinearity:

Significantly affect

the sharing of lateral force

among shear-wall and

frames

Retrofitted

Shear Wall

M

N

(c) Need : Determine Collapse Motion

• for Insurance Purposes

( special projects demanding estimate of

LOSS in worst case )

• for Compatibility

with Structural Design

( Push-over analysis, ductility–based design )

Can we moveCan we move BeyondBeyond

this Conventional this Conventional

““CapacityCapacity”” DesignDesign ?

Major Contribution of Alain Pecker (1998)

“Capacity design principles for shallow

foundations in seismic areas”

Previous Research /Applications

• Pecker (1998): Capacity Design for Foundations

•Paolluci (1998): Inelastic-soil SSI

• FEMA 356 (2000): Rehabilitation Code

• Kutter et al (2001): Centrifuge Experiments

•Martin & Lam (2000): Retrofit of Bridges

• El Naggar et al (2000): Elasto-plastic Winkler

• Pecker et al (2009): Inelastic Macro-element

Factors of SafetyFactors of Safety

•• StaticStatic : FS > 1

• SeismicSeismic :: min FS (t) < 1t

ExternalExternal Force P >> Pu

δ

P

PuElastoElasto--Plastic Plastic Systems :Systems :

(a) if SSTTAATT IICC :: FailureFailure

P

sσ

R

PPP

(b) ii ff SEISMICSEISMIC ::Inelastic

Deformations

(only)

Thanks to the Nature of

Seismic Excitation

K I N E M A T I K I N E M A T I CC

C Y C L I CC Y C L I C

A

m As

ACPu m=

Elastic Response : As < ACP m

u

As

mAC

A

Plastic Response: As = AC PS = Pu

AC

P m

u

Pu m=

Unloading: 0< AS < AC

A

m As P m

u

ACPu m=

Unloading: As = - AC

A

mAC P m

u

ACPu m=

AA

umax

AA >> AC max AS (structure) =AC

umax > uelast

BButut NONO FFailureailure

ACPu m =

AS

(α) Sliding (symmetric, asymmetric)

(b) Uplifting , Overturning

in Geotechnical Engineering

the implications of

Dynamic Safety FactorDynamic Safety Factor

FSFS < 11 :

(c) Bearing Capacity “Failure” ??

N. Newmark:

1965 Rankine Lecture

Ambraseys & Sarma 1967

Seed et al 1967

Richards & Elms 1979

Pecker 1998

Whitman 1964

Current Seismic Codes

• (Gravity) Retaining walls

• Embankments / Natural Slopes

Designed (indirectly) forinelastic deformation ∆ ~ 10–30 cm :

ADESIGN = 1/2 A

W

WADES∆

W

WADES

∆

A(t)

AC = µgSymmetric

sliding

D

Asymmetric

sliding

D

A (t)

AC= µ g cosβ – g sinβ

LefLef kadakada 20032003

D(t)

[m]

-0.2

-0.1

0

0.1

3 6 9 12 15

0.14 m-1

-0.5

0

3 6 9 12 15

1 m

-5

-2.5

0

2.5

5 0.42 g

A(t)

[m/s2]

-5

-2.5

0

2.5

5

AC/A=0.1

0.42 g

V(t)

[m/s]

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

Effect of ExcitationEffect of Excitation FrequencyFrequency

Dmax : cm

0

5

10

15

20

25

30

0 1 2 3 4

µ / α = 0.1

µ / α = 0.2

µ / α = 0.4

µ / α = 0.6

µ / α = 0.8

Frequency : Hz

“Factor of Safety”

Rigid Block on a Rigid Base

mAc

mg

Uplifting

Acceleration

Ac = (b/h) gg

Toppling

(under Static Conditions)

θc

b

h

Rocking of Slender Block on Rigid Base

(undergoing a one-cycle sinusoidal shaking)

f ( Hz )0 1 2 3

OVERTURNING

SAFE

AAAA ( g )

4

3

2

11,10 g

= 0,25

bh = 4 b

Static Failure ΑΑΑΑ > 0,25 g

Seismic Failure (with f = 2 Hz ) ΑΑΑΑ > 1,10 g

h A

SPLB

-0.4

0.0

0.4

0 2 4 6 8 10t : s

α : g

Duzce

-0.4

0.0

0.4

0 2 4 6 8 10t : s

α : g

Overturning οf a Slender Tombstone

in the Athens Earthquake : 7 - 9 - 99

0.35 g

0.35 g

Two Hypothetical Base Excitations :

A : g

A : g

Düzce

Overturning οf Tombstone

2 h = 1.27 m , 2 b = 0.20 m , h / b = 6.35 , Ac ≈ 0.16 g

Overturning οf Tombstone

2 h = 1.27 m , 2 b = 0.20 m , h / b = 6.35 , Ac ≈ 0.16 g

SPLB - 0.85 g

-1

-0.5

0

0.5

1

0 2 4 6 8 10

α : g

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10θ

: rad

0.85 g

0.84 g

Scaling of the Records needed

to Overturn the Tombstone

Overturning οf Tombstone

2 h = 1.27 m , 2 b = 0.20 m , h / b = 6.35 , Ac ≈ 0.16 g

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10

θ : r

ad

0.85 g

0.84 gSPLB - 0.85 g

-1

-0.5

0

0.5

1

0 2 4 6 8 10

α : g

Scaling of the Records needed

to Overturn the Tombstone overturning

at A ≈ 5.3 AC

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10

t : s

θ : r

ad0.27 g

0.26 goverturning

at A ≈ 1.7 AC

Duzce - 0.27 g

-1

-0.5

0

0.5

1

0 2 4 6 8 10

t : s

α : g

Düzce

Consequences

(α) Sliding (symmetric, asymmetric)

(b) Uplifting , Overturning

(c) Bearing Capacity “Failure”

Dynamic Safety FactorDynamic Safety Factor

FSFS << 11 :

Simple Model of Bridge Pier

N

B = 6m

Νu≈ 4000 kN

T = 1.5 sec

Su = 130 kPa

Inertial Force

Hs = 20m

h = 12m

Modelling with Finite ElementsModelling with Finite Elements

Beam

Elements

Interface

Elements

Soil and Column: Inelastic

Quadrilateral Solid

Plane–Strain

Elements

Viscous

Boundary

ρVS , ρVS

at x = 20 B

22BB

εpl

σmax

σ

σy0

0

σyσy0

σy0

a a’

S

S1

S3

S2

σmax√23

Limit

surface

Yield

surface

0adev

σy0√ 23

Limiting location

of a

af+ σy0

Nonlinear, Von-Mises Yielding,

Isotropic/Kinematic Hardening ,

Associative Flow Rule

Constitutive Cyclic Model for Soil

1-D Representation 3-D Representation

γ

tt

Calibration against G – γ curves

ττ

soil

Ishibashi & Zhang

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1 10

G/GG/G00

γγ (%)(%)(%)(%)(%)(%)(%)(%)

PI= 30σ0 = 100 kPa

0

10000

20000

30000

40000

50000

60000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Reinforced Concrete

d = 3m

C30C30

S400 :100 Ø32Ø13/8.

M : kNm

Curvature : 1/m

Simple Model of Bridge Pier

N

B = 6m

Νu≈ 4000 kN

T = 1.5 sec

Su = 130 kPa

Inertial Force

Hs = 20m

h = 12m

0

1000

2000

3000

4000

0 500 1000 1500 2000 2500

MMultult

N = 1000 kN

zcθθ

Ultimate Vertical LoadΝult

1900 kNmMMulultt

NN

Mu ≈ 1900 kN m

zcθ

N ≈ ¼ Νu

Pseudo–Static Analysis

(constant Ν = 1000 kN)

contact

Qu = Mu / h

1 250 kPa 410 kPa2

570 kPa

3

790 kPa

4

0

0.5

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2 0.25

tilt-angle [rad]

mom

ent

[MN

m]

1

2

3

4

(π + 2) Su ≈ 670kPa

6 840

-0.3

0.2

t : sec

A(t) : g

00 2

1

2

4 6

3

4T : sec

R / A

Ricker Wavelet : fo= 0.5Hz and A = 0.30 g

A

0.6 A0.6 A

Pseudo – Static Analysis:

Determine the Yield AccelerationDetermine the Yield Acceleration

AAcc

((i.e., the maximum possible i.e., the maximum possible

acceleration of the massacceleration of the mass))

h = 12m

N = 1000 kN

mAc

Mu ≈ 1900 kN m

Mu = mAch

Ac= 1900 / [(1000 :g ) x 12 ] = 0.16 g

-0.4

0

0.4

-0.4

0

0.4

Excitation: Ricker Wavelet

2 s

0.30 g

0.50 g

free field

rock

Seismic Analysis

Excitation

M N = 1000 kN

Pseudo–Static Failure : M = MuCritical Acceleration : Ac = 0.16 g

Seismic (“Apparent”)

Safety Factor :

Ac /A = 0.16 / 0.50 = 0.32 << 1

Will there be Failure ??

2.2 s

0.4 g

Contours of Plastic Strains

Maximum Acceleration :

0.50 g

Base Excitation :

Ricker TE = 2 sec, PGA = 0.30 g

h = 12 m

M [kNm]

-3000

-1500

0

1500

3000

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

tilt-angle [rad]θ [rad]

h = 12m

terminalterminal

Mzcθ

N = 1000 kN

-0.2

-0.1

0

0.1

0.2

-0.2 -0.1 0 0.1 0.2

zc [m]

θ [rad]

h = 12mM

zcθ

N = 1000 kN

Topics of Presentation

PART 1

(a) Why Going to the Limit and “Beyond”

in Seismic Foundation Analysis / Design

(b) Conventional versus New Design

Concept: Bridge Pier Foundation

PART 2

The Causes of Overturning

of Buildings in Adapazari (1999)

To demonstrate the feasibility of

designing a foundation to

undergo large deformations ,

beyond the conventional wisdom

a Comparative Example:

h = 12m

Stiff Clay

Su = 150 kPa

25m

B = 11 m

mdeck= 1200 t

d = 3 m

B = 7 m

ConventionalDesign

ExploredNew Concept

Pseudo-Static Safety Factors

for a Seismic Coefficient CS = Rd /q = 0.30

Β = 7m FSV = 2.8

FSE = 0.5 < 1

e > B/3

Β = 11m FSV = 5.8

FSE = 2.0

e < B/3

0

0.5

1

1.5

2

2.5

0 1 2 3

Kalamata, 1986

0.27 g

Takatori (Kobe, 1995)0.62 g

Lefkada, 1973

0.52 g

Τ : sec

R: g

ξ = 0.05

uθ

Aff

β

θ

utotuStr

wdyn

Am

BAΕ

Low-Intensity Shaking:

Kalamata Kalamata 19861986

RESULTSRESULTS for the for the RESPONSERESPONSE of the:of the:

((aa)) FOUNDATIONFOUNDATION

((bb)) STRUCTURE STRUCTURE –– FOUNDATION FOUNDATION

SystemSystem

M : MNm

w :m

-0.08

-0.06

-0.04

-0.02

0

-0.01 -0.005 0 0.005 0.01

-100000

-50000

0

50000

100000Β = 7m

-100000

-50000

50000

-0.08

-0.06

-0.04

-0.02

0

-0.01 -0.005 0 0.005 0.01

Β = 11m

-50

-100

100

50

0

FOUNDATION FOUNDATION (( M – θ andand w – θ ))

θ : rad θ : rad

≈ + 2 cm

≈ + 4 cm

-0.2

-0.1

0

0.1

0.2

0 5 10 15 0 5 10 15

u : m

t : sec

Β = 7m

t : sec

utotuθ u

Str

max uStr= 0.10 m

Β = 11m

max uStr= 0.02 m

STRUCTURESTRUCTURE + FOUNDATIONFOUNDATION

uθ uStr utotversus time

RESULTSRESULTS for the for the RESPONSERESPONSE of the:of the:

((aa)) FOUNDATIONFOUNDATION

((bb)) STRUCTURE STRUCTURE –– FOUNDATION FOUNDATION

SystemSystem

Very Strong Shaking:

Takatori Takatori ( ( Kobe Kobe 19951995 ))

0

0.5

1

1.5

2

2.5

0 1 2 3

Takatori (Kobe, 1995)0.62 g

Τ : sec

R: g

0.75TB=7

1.1TB=11

M :

MNm

w:m

-0.04 -0.02 0 0.02 0.04

-0.04 -0.02 0 0.02 0.04-0.3

-0.2

-0.1

0

-0.04 -0.02 0 0.02 0.04

Β = 7mΒ = 11m

-50

-100

100

50

0

θ : rad θ : rad

FOUNDATION FOUNDATION (( M – θ andand w – θ ))

≈ + 20

≈ + 8 cm

-2.5

-1.5

-0.5

0.5

1.5

2.5

0 5 10 15 20 25

-2.5

-1.5

-0.5

0.5

1.5

2.5

0 5 10 15 20 25

u : m

Β = 11m Β = 7m

utotuθ u

Str

t : sec t : sec

Collapse

STRUCTURESTRUCTURE + FOUNDATIONFOUNDATION

uθ uStr utotversus time

Β = 11m Β = 7 m

Comparison of the two Foundation Schemes

Takatori (Kobe, 1995)

Β = 11m Β = 7 m

The Final Stage

0

0.5

1

1.5

2

2.5

0 1 2 3

Takatori (Kobe, 1995)0.62 g

Τ : sec

R: g

1.7TB=7

2.1TB=11

Conventional Solution:

“Capacity” Design

Soil

Plastification

New Concept: Beyond “Capacity”

Design

Plastic “hinging”

ConclusionConclusion

The Main Conclusions

of Part 1

(α) The Dynamic behaviour of

inelastic soil–foundation systems

differs from the

Pseudo-Static response.

Sometimes dramatically

(β) New Design Approach (“Philosophy”) : Plastification

not only in the structure

but also :

at the soil–footing interface

(sliding, detachment+uplifting)

in the supporting soil

(bearing–capacity mechanism)

• Detachment–Uplifting

• Sliding at the Interface

• Mobilisation of

“Bearing–Capacity”

Mechanisms

(c) The following should NOT be a priori “forbidden” modes

FIN

Partie 1

The Overturning of Buildings The Overturning of Buildings

inin Adapazari Adapazari

1999 Izmit [Kocaeli] Earthquake

“ Even theEven the most refined theories

((before they before they can be establishedcan be established))

must be must be VALIDATED byby

COMPARISONS against the against the

REALITY that these theories that these theories

describedescribe …… ””

Istanbul Izmit Adapazari Düzce

Gölcük SapanzaYalova

Avcilar12

November Μ

= 7.2

17 August Μ = 7.5

The Geography of the The Geography of the 19991999 EarthquakesEarthquakes

ADAPAZARI : 17 – 8 – 1999

(α) Seismology; Damage distribution

(b) Soil: the disputed role of fines

(c) Soil: wave propagation analysis

(d) Seismic Analysis of Building Response

Explanation of Toppling, Settlement

12

2326

21

25

12 9

46

PGA PGA (( %% gg ))

Izmit Izmit (( KocaeliKocaeli )) 1717––88––9999

32

YPT

41

SKR

37

DUZ

41 = 0,41 g ≈≈≈≈ 4,1 m/s2

1 km

SKR

River

% ofHeavy

StructuralDamage

PLAN of

ADAPAZARI

Sagario

< 5 %

10 – 20

30 – 50

≥ 50 %

Adapazari

3 km

bedrock

1 km

Anatolian Fault

Sapanca

SW NE

SKR

Sandy SiltAlternating :

Sandy Clay

Typical Soil Profile:

Very Soft/Loose Soils

Small total thickness

of any liquefiable layers

CH / MH

Fill

SM / ML

ML

CH

ML

SM / CL

ML

CH / MH

SP / ML

CH / SM

20 400 0

qc

4

8

12

16

20

24

0.1 0.40

fs : MPa

0 5 10

Rf : %

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

.

0 2 4 6

Building Width [m ] Number of Stories

Mean

Settlement

[ cm ]

Attempts for Empirical Correlations

by other researchers: Yasuda et al, 2002

80 80

3

H / B

Overturning

00

1 2

2

4

6

Hθ

Β

θo

D [mm]

0

10

20

30

40

50

60

70

80

90

100

0,001 0,01 0,1 1 10

Adapazari

Niigata

Dagupan

Kobe

Fines Sand Gravel% Passing

0

10

20

30

10 20 30 40 50

PI

LL

The fine-grained soils

of Adapazari

SSrr or or SSu u ??

++∆∆uu

M Q

NN

SSrr

εεαα

((σσ11 –– σσ33 )) / / 22

00

SSrr ≈≈ 0.090.09 σσvv

Reinforcement for Reinforcement for

Mat FoundationMat Foundation

-0.5

-0.25

0

0.25

0.5

0 5 10 15 20

t : sec

The Sakarya Record

t : sec

A : g

0.41 g

0

1

2

0 20 40 60 80 100

u : m

-80

0

80

0 20 40 60 80 100

0.41 g-0.5

-0.25

0

0.25

0.5

0 20 40 60 80 100

81 cm/s

0.41 g

2.16md : m

A : g

V : cm /s

t : s

Teverler (Appartment Building)

0

10

20

30

40

50

60

0 100 200 300 400 500

Soil Response : Teverler

Vs : m /s

-0.5

-0.25

0

0.25

0.5

0 4 8 12

0.25 g

Excitation : SKR

-0.5

-0.25

0

0.25

0.5

0.41 g

-0.5

-0.25

0

0.25

0.5

0 4 8 12

0.23 g

Without Pore pressure rise

0.16 g

With Pore pressure rise

-0.5

-0.25

0

0.25

0.5

0 4 8 12

-0.5

-0.25

0

0.25

0.5

-0.5

-0.25

0

0.25

0.5

0.31 g

0.25 g

0.20 g

Possible Ground Motions

1D Equivalent Linear 1D Inelastic Analysis

BWGG

Excitation : SKR

0

10

20

30

40

50

0 100 200 300

Vs : m/s

Dep

th :

mNonlinear Dynamic SFSI Analysis

0

5

10

Fill

Clayey Sand

Sandy Silt

Gravely Silty Sand

Silty

Sand

W.T.

φ = 25ο c = 1 kPa

τ /σv > 0.15 : φres = 3o

φ = 25ο c = 2 kPa

φ = 28ο c = 5 kPa

φ = 30ο c = 5 kPa

P = 275 kN

MQ

0

200

400

600

0 50 100 150

M:kNm

Q : kN

he= (2/3)H

AC = 0.13 g

M = Q he

Deformation Scaling Deformation Scaling = = x 3

t = 17 s

t = 8 s

t = 4 s

This is a Critical Moment

for our Approach:

it predicts Non-Overturning

when in REALITY the building

Overturned !

Many Plausible Causes

(1) Actual Base Motion Stronger

missing NS comp. : “Fault Normal” (FN),

used EW comp. : “Fault Parallel” (FP) :

FN > FP

(2) Soil at D > 20m : Detrimental Roledue to larger soil amplification

(3) 2-D and 3-D wave focusingdue to irregular bedrock geometry

But what about

Out–of–Phase Response of

Adjacent Buildings,

and hence IMPACT Forces ??

Did this Play any ROLE in

Adapazari ??

(4 )

NO Sign of IMPACT between the NO Sign of IMPACT between the 22 buildingsbuildings

impact region

Impact Velocity very small

Insignificant Damage to the Insignificant Damage to the ““HostHost”” BuildingsBuildings

Now what about

the very Presence of Adjacent

Buildings ?

(5 )

MMultult+ >> MM ult

- : due to greater

confinement of the soil

Reversal of Plastic Rotation : Reversal of Plastic Rotation :

inhibitedinhibited

Analysis of 2 Buildings

Buildings Buildings 22 ,, 33

Deformation Scaling : Deformation Scaling : x 3

1Building

2Buildings

t = 4 s t = 4 s

t = 8 s t = 8 s

t = 17 s

v = 17 cm/sv = 12 cm/s

t = 17 s

Let us further explore Let us further explore

this possible role this possible role

by replacing the adjacent building

by its Vertical Pressure

2 Buildings Side by Side

t = 4 s

t = 8 s

v = 17 cm/sv = 12 cm/s

t = 17 s

Teverlelr+Equivalent Load

for the 2ndBuilding

t = 4 s

t = 8 s

t = 17 s

v = 10 cm/s

Any EVIDENCE ??

The Role of the Adjacent Building :

One–Directional Accumulation of Tilt

NO Reversal of PLASTIC Deformation,

Asymmetric Yielding

Here is a

Mechanical

Analogue

0 0.2 0.4 0.6 0.8 1.0

1000

100

10

1

0.1

α / α

∆(cm)

αmax

αmax

∆

∆

0 0.2 0.4 0.6 0.8 1.0

1000

100

10

1

0.1

α / α

∆(cm)

0 0.2 0.4 0.6 0.8 1.0

1000

100

10

1

0.1

α / α

∆(cm)

αmax

αmax

∆

∆

One-Directional vs. Two-DirectionalSLIPPAGE

∆

(cm)

AC /Amax

∆

(cm)

“Lonely” Buildings

did not fail

Buildings surrounded by others

did not fail

… even if they were very

slender !

Any EVIDENCE ??Here is some ( further)evidence :

3

H / B

Overturning

00

1 2

2

4

6

Hθ

Β

θo

Aspect

Ratio

H/B ≈ 3

25 m

15 m

77 77 77 7755 55

11 22 33 44 55 66

2–D Seismic Response of Adapazari

Buildings : Buildings : 11, , 22 + + 33, , 44 + + 55 ++ 66

Deformation ScaleDeformation Scale : : xx 33

11 22 + + 33 44 + + 55 ++ 66

Buildings : Buildings : 44 + + 55 ++ 66

44 66

55

CONCLUSION:

The MAIN CAUSES of FAILURES

1. Large Overturning Moment+ Very Soft Soils :

Bearing Capacity Failure

Lateral Soil Displacement

(squeezing out)

Volumetric Compression

2. Large Periods (T ≥≥≥≥ 2 sec)

of ground oscillation with

A ≈≈≈≈ 0.20 g— 0.30 g

But causes But causes ((11)) and and ((22)) areare

(at least in some of the cases)

notnot sufficientsufficient

to explain the overturning even to explain the overturning even

of very slender buildingsof very slender buildings

3. A key culprit appears to be

the PRESENCE of ADJACENT

Buildings !One–Directional Accumulation of Tilt

- as with downward sliding on INCLINED plane,

- in contrast to the symmetric sliding

on HORIZONTAL plane.

Ioannis Anastasopoulos

Nikos Gerolymos

Marios Apostolou

Marianna Loli

Evangelia Garini

This presentation was possible only

thanks to my co-workers at NTUA:

Merci Beaucoup

Pour votre attention

F I N