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Fdc + Fb < Fedc

Fdc: Driving force (Fdc < 0)

Fedc: Lithospheric strength in contraction (Fedc < 0)

Fb: is a measure of the potential energy stored in the orogenand may be considered as the buoyancy force exerted by thedeformed lithosphere on its surrounding(Fb > 0: tension; Fb < 0: contraction)

fczc

h

flzl

zl

zc

Lithosphere thickening occurs when:

Fdc + Fb > Fedt

Lithosphere thinning occurs when:

Fedc: Lithospheric strength in tension (Fedt > 0)

fc: crustal strain factor

fl: lithospheric strain factor

MECHANICAL STABILITY OF CONTINENTAL LITHOSPHERE

LITHOSPHERIC DEFORMATION: WHY ?

Driving force

RIGDE PUSH

SLAB PULL

STRENGTH OF THE LITHOSPHERE

2α

σn

τ

σ3 σ1σi σ

ΦΦ

C

FAILURE

Coulomb's criteria

failure envelope

C : cohesion between crystalat atmospheric pressureµs : coefficient of internal friction(roughness of the shear plane),µs = tan (φ)φ : angle of internal friction

Brittle def. Ductile def.

Brittle deformation

τ = C + µs (σn - Pp)

σ n : normal stress on the failure planePp : pore pression

τ : shear stress

τ = C + µs ( )σn 1 - λλ = Pp / σn

(σ1−σ3) =2(C-µsσz(1 - λ))

µs + 12

- µs

Strength incontraction

(σ1−σ3) =2(C-µsσz(1 - λ))

µs + 12

+ µs

Strength intension

At low temperature and high strain rate, the failure mechanism is modelledas frictional sliding and is described by the Coulomb criteria.


ORIGIN OF THE TECTONIC DRIVING FORCES

TRENCH SUCTION

= β.ρ.g.z.(1-λ)

= β.ρ.g.z.(1-λ)

β=3

β=0.75

Ductile deformationAt high temperature the failure mechanism is modelled by a...

1/ ...power-law creep in the crust for all (σ1−σ3) and in the mantle for(σ1−σ3) < 200 MPa

2/ ...Dorn-law creep in the mantle for (σ1−σ3) > 200 MPa

(σ1−σ3) = εΑ

[ ] exp [ ]1/n Qp

nRT

(σ1−σ3) = εd

εln[ ] ]RTQd

[1-σd

A: material constantn: power law exponentQp: the activation energy

R: Boltzman's constantε: strain rateT: temperature

Qd: activation energyσd: threshold stressεd: pre-exponential constant for Dorn-Law creep

1 100 10000

20

40

60

80

0

2 10-15

s-1

Dep

th

∆σ: strength (MPa)

Fedt = fl.zl * ∆σ dz fl.zl

h

Strength profile

(Nm )-1

Lithospheric strength in contraction

Lithospheric strength in tension

⌡

⌡

Fedc = fl.zl * ∆σ dz fl.zl

h

(Nm )-1

⌡

⌡

c

t


STRENGTH OF THE LITHOSPHERE

2.6 2.8 3.0 3.2

50

100

150

200

0

h

zc

fczc

flzl

zlρliρlf

∆ρa

∆ρb ∆ρc

∆ρd

∆ρe

ρ(10 kg/m )3 3

z (km)

flzl

zl

zc fczc h

2.60

Fb = ρ (z).g.z dz - ρ (z).g.z dz⌡

⌡

fl.zl⌡

⌡

fl.zl

h

fi

σ = Fbfl.zl

Induced horizontal deviatoric stress

Induced horizontal buoyancy force

0

0

Reference level

Fb<0

Fb>0

Lateral heterogeneities of density induce horizontal buoyancy forces


BUOYANCY FORCES

fc: crustal strain factor

fl: lithospheric strain factor

fc= zc zco

fl= zl zlo

Lithospheric vertical strain represented in the fc-fl plane


LITHOSPHERIC DEFORMATION IN THE PLANE fc-fl

1 2 fc

1

2

00

fl

crus

tm

antle

fc.zc<fl.zl

3 Fc-Fl PLANE

R eference lithosphere

R ey and O'Halloran, 19 9 7, modified

from Sandiford and P owell (19 9 0 )

fc = thickness of the crust after deformation

thickness of the crust before deformation

fl =

th

ickn

ess

of

the

lith

osp

her

e a

fter

d

efor

ma

tion

thic

knes

s of

th

e

lith

osp

her

e b

efor

e d

efor

ma

tion

thickness of the crust after deformation

thickness of the crust before deformation

fl =

th

ickn

ess

of

the

lith

osp

her

e a

fter

d

efor

ma

tion

thic

knes

s of

th

e

lith

osp

her

e b

efor

e d

efor

ma

tion

Externally applied forceNo externally applied force

Resulting force: Σ F = Fb+Fdc

Lithospheric deformation occurs in Extension if Σ F > Fedt Contraction if Σ F < Fedc

The lithosphere is stable whenFedc <Σ F < Fedt



"Stable"

Thinning

Thickening

0.5 1 1.5 2 2.5

0.5

1

1.5

2

2.5

fl

fcFd=0 Nm-1 Fd=-12.10 Nm

-112

0.5 1 1.5 2 2.5

0.5

1

1.5

2

2.5

fl

fc

-16

-15

-14

-13

-12

-10

-16

-15

-14

-13

-12

-10

-17

-17

Ψ=0.35

zc =35zl =100

O

O Ψ=0.35

zc =35zl =100

O

O

Fedt

Fedc

AB C

ε < effective strain rate (3.10 s )-17 -1

STABLE=

-16

-15

-14

-13

-12

-10

-16

-15

-14

-13

-12

-10

1 2 fc0

1

2

0

fl

3

"Stable"

Thinning

Thickening

Fc-Fl PLANE CONTOURED FOR STRAIN RATE

A

-17

-17

C

B

D

D

E

E

1000 m/ 100 km/ year

10 m/ 100 km/ year

1 m/ 100 km/ year

10 cm/ 100 km/ year

1 cm/ 100 km/ year

1 mm/ 100 km/ year

0.1 mm/ 100 km/ year

Strain rate

3. 10x s-1





0.5 1 1.5 2 2.5 3

0.5

1

1.5

2

2.5

3

2

4

1

6 8 10 12 14

16

18-1

-2

-4

-6

-8

-10

0.5 1 1.5 2 2.5 3

0.5

1

1.5

2

2.5

3

-0.05

-0.8

-0.6-0.4

-0.2

-2

-1

-4

-6

-8

-10

-12

-14

-16

-18

-20

0

fl

fc

-12

fl

fcBUOYANCY FORCE

STRENGTH IN COMPRESSION

STRENGTH IN TENSION0.5 1 1.5 2 2.5 3

0.5

1

1.5

2

2.5

3

fl

fc

1

2

3

4

5

67

89

0.8

0.60.4

0.2

x10 Nm12 -1

Intraplate plateau

50 km

N

S

EW

FdFb

0º

1330º


SHORTENING VERSUS LATERAL SPREAD

N

S

EW

1

2

21 3

1

2

21 3

Direction // tectonic force (N-S)Direction tectonic force (E-W)T

Fd=-8.10 Nm12 -1

B

C

A

fc

fl

fc

fl-17

-16

-15

-14

-13

-12

-10

-17

-16

-15

-14

-13

-12

-10

-17-16

-15

-14

-13

-12

-10

A A'Thickening

Thickening

Thinning

-10

-12

-14

-16

Thinning



1

2

21

A

C

B

fl

fc

-16

-17

-15

-17

-16

-15

-14

-10 B'

-17

-16

-15

-14

-13

-12

-10

A'

Thickening

Thinning

Netthinning

Netthickening

-13

-12

-17

-16

-15

-14

-13

A B' B

NS contraction

EW extension

3.10

-123.10

3.10

3.10

3.10

3.10Str

ain

rate

(s

)-1

Strain rate along the path A-B

A'

-113.10

-103.10

Netthinning

Netthickening




EFFECT OF THE ECLOGITIZATION OF THE LOWER CRUST

0 1 2 3 4 50

1

2

3

4

5

Moho50

100

150

200

0

Depth (km)

2.8 3.0 3.2

Partially eclogitizedlower crust

Fd=-12.10 Nm-112

Fd=-25.10 Nm-112

Density profiles (g.cm )-3

0 1 2 3 4 50

1

2

3

4

5

Partially eclogitizedlower crust

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