Détection Des Cavitées Souterraines

8/10/2019 Dtection Des Cavites Souterraines

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tel00855987,v

ersion

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http://hal.archives-ouvertes.fr/http://tel.archives-ouvertes.fr/tel-00855987


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t

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B

H

B = 0

H ,

0= 410

7Hm1

1

= i ,

i2 = 1

tan =

r

0

r = /0 =

r i

r

0= 8, 854 10

12

r

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S/m

Jc =

E ,

Jc A/m

2

E

V /m

= + i

,

f

=

,

= 2f

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E = Bt

Jm , H = Dt

+Je , B = 0, D = qv,

E

V /m

H

A/m

D

C/m2

B

W/m2

Je

A/m2

Jm V /m

2

qv

C/m3

t

E

H

E 0

E

t 0

2E

t2 =

0

H 0

Ht

02H

t2 =

0 .

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E = (Ex, 0, 0) z

Ex = E0eitz

E0 t = 0 z = 0

2Ex

i0Ex

+20Ex

= 0.

= + i ,

=

00r

2 (

1 + tan2 1)

= 00r

2

(1 + tan2 + 1),

tan =

.

tan =

.

tan = 1

tan 1

tan


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v = c0

r,

c0 = 1

00,

299792458 ms1

c0 = 0, 3 m/ns

= v

f.

tan2


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sin iv1

=sin r

v1=

sin tv2

,

i r t v1

v2

n21

n21 = sin i

sin t=

v1v2

=

21

.

c

t 90

v2 i> c

r

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r

r = 80 r = 50

r = 50 r = 25

r = 80

r = 25

r = 25 r = 8

r = 80 r = 8

r = 3.8 r = 80

r

rTE

rTE =

1cos(i) 2cos(t)1cos(i) +

2cos(t)

.

1sin(i) = 2sin(t)

rTE =

1cos(i) 2

1 12

sin2(i)

1cos(i) +

2

1 12

sin2(i).

r =

1 21+

2

.

r =

1

r

1

+1

1r

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180

67%

c

t 90

12

sin(i) > 1

rTE

rTE =1cos(i) +i212 sin2(i) 1

1cos(i) i212

sin2(i) 1,

Re(rTE) =1cos(i) 2

12

sin2(i) 1

1 2=

1cos(2i) +21 2

.

Im(rTE) = 21cos(i)1sin2(i) 21 2 .

1

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v2 v1

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t

d

v

t = d

v.

v1

Tx a m m

t =

x2 + 4h2

v ,

x

h

c = arcsin(v/c0),

Xc

c = 2hv

c20 v2.

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t = x

c0+ 2h

1

v2 1

c20.

t

x

1/v1

1/c0

1/c0

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tf= (1, x)2d

v,

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tf d v x

tf= 1, 3

2dv

fc> 75

Z

MHz,

Z

L

fc> 30

L

MHz,

fc /4

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d1= 0, 25

h1 = 0.25 h2 = 0.5 h3 = 1 h4 = 2

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d5= 3

h1 = 0.25 h2 = 0.5 h3 = 1 h4 = 2

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h

d

d

h

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th

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i

R

R=

1cos(i)

21 12

sin2(i)

1cos(i) +

2

1 12

sin2(i),

i 1

1= 5.32 2

2= 1

2 < 1

c = sin1

12

c

Real(R) = 1cos(2i) +2

1 2.

X =2d tan i d

Xp= 2d tan(cos1( 221 ))

Xp = 0.97

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0.6

0.2

0.6

0.8

1

0

0.50 2.5

Rea(R)

Offset (m)

1 1.5 20.8

0.4

0.2

0.4

Xc Xp

X

i Xc

c Xp

Real(R) = 0

Xc

Xp

3.8 m

2.85 m

0

10

20

30

ime(ns

1 2 3Distance (m)

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3 m inside the vault

0.34v=

r=1.3 m

m/ns

Masonry ?

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0

10

20

30

Times

(ns)

1 2 3 4Offset (m)

th

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1

1

2

2

3

3

1

1

2

3

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I

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V

S

l

I

=

S

l

V

I.

R

R = l

S .

I

R

S

I

C1 C2 V

P1 P2

R

= k V

I,

k

k = 2

1

r1+ 1r2

+ 1r3

+ 1r4

,

r1 C1 P1 r2 C2 P1 r3

C1 P2 r4 C2 P2

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I V

1.6 108

107

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k

P1 P2 C1 C2

a

a

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C1

P1

P2

C2

C1

P1 P2 C2

a

a

a

2a

2a

2a

3a

4a

5a

6a

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h1 = 0.4

h2= 1

h2= 1

h1 = 0, 4

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h1 = 0.4

h2 = 1

h2 = 1

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W1

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7

Theodolite

W1P2

P

P6

P5

P4

P3

P

1

Distance(m)

Bat. 300Batiment 301

N

W1

P7 P7

P2

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P2

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X0

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%

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%

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0.9%

0.80%

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E

N

S

O

12

20

28

29

30

19

11

10

13

14

15

24

23

25

26

98

7

56

422

1, 17 et 18

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Dalle

Joints

0,2m

0,1

5m

1m

2,5 m

Air

Milieu homogene uniforme

0

10Temps(ns)

0.5 1.0 1.5 2.0Distance (m)

Hyperboles de diffraction

sur les joints

Onde directe

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Air

1,5 m

0,8m

0,2m

0,6 m

0,5m

Air

Calcaire

0

10emps

ns

0.5 1.0Distance (m)

Reflections sur le fond

Reflections multiples

Onde directe

Reflection sur le toit de la cavite Diffraction sur les

coins de la cavite

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0

5

10

15

emps

ns

2 4 6 8 10 12 14 16 18 20 22 24 26stance m

Zone suspecte

Hyperboles dues aux

joints des dalles

Ondes directes

Reflections sur bases

des dalles

T

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0

5

10emps

ns

2 4 6 8 10 12 14 16 18 20 22 24 26stance m

Ondes directes

Zone suspecte

Zones suspectes

T

0

0.5

1.0

1.5

2.0

roon

eurm

2 4 6 8 10 12 14 16stance m

Queues dhyperboles

sur les joints de dalle

Fondations?

Fondations ?

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0

0.5

1.0

1.5

2.0

Profondeur(m

)

2 4 6 8Distance (m)

AlleeProfil4 (6,9 m)

0

0.5

1.0

1.5

2.0

Profondeur(m

)

2 4 6 8Distance (m)Profil5 (6,4 m)

Allee

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6Distance (m)

Allee

Profil6 (5,9 m)

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6 8Distance (m)Profil7 (5,4 m)

Allee

1 m ?

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6 8Distance (m)

Profil8 (4,9 m)Allee

?

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6 8Distance (m)

Allee

Profil9 (4,5 m)

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6 8

Distance (m)

AlleeProfil10 (4 m)

0

0.5

1.0

1.5

2.0

Profondeur(m)

2 4 6 8 10

Distance (m)

Allee

Profil11 (1 m)

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marquise 9

marquise 6 marquise11

marquise12

marquise 10

longitucentre1

NS10

NS11

NS12

NS13

NS14

NS15

ch12

ch1

ch3

ch4

ch5

ch2

ch6

ch7

ch9

ch8

ch10

marquise8

NS8

NS7

NS6

NS5

NS4

NS3

NS2

NS1NS16

NS9

EST

SiegesSieges

S

ieges

Sieges

1 m1m

marquise 3

marquise 4

marquise 5

marquise 2

marquise 1

Estrade Estrade

Air

1,5 m

0,8m

0,2m

0,6 m

0,5m

Air

Calcaire

0

10emps

ns

0.5 1.0stance m

Reflections sur le fond

Reflections multiples

Onde directe

Reflection sur le toit de la cavite Diffraction sur lescoins de la cavite

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Air

Air

Sol

3,8 m

3,5 m

0

20

40

60

80

100

emps

ns

1 2 3 4 5 6istance m

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0

20

40

60

Time(ns)

0 0.5 1.0 1.5 2.0 2.5Distance (m)

0

20

40

60

Time(ns)

0 0.5 1.0 1.5 2.0 2.5Distance (m)

0

20

40

60

Time(ns)

0 0.5 1.0 1.5 2.0 2.5s ance m

0

20

40

60

Time(ns)

0 0.5 1.0 1.5 2.0 2.5Distance (m)

0

20

40

60

me

ns

0 0.5 1.0 1.5 2.0 2.5 3.0Distance (m)

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0

20

40

60

Time(ns)

0 2 4Distance (m)

Marche

Reflexion sur le toit dune cavite

Reflexion sur le fond dune cavite

0

20

40

60

Time(ns)

0 1 2 3Distance (m)



0

20

40

60

Time(ns)

0 2 4 6 8Distance (m)



0

20

40

60

Time(ns)

0 0.5 1.0 1.5Distance (m)

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0

20

40

60

Time(ns)

0 1 2 3Distance (m)

0

20

40

60

Time(ns)

0 1 2 3Distance (m)

0

20

40

60

Time(ns)

0 1 2 3 4Distance (m)

0

20

40

60

Time(ns)

0 1 2 3Distance (m)

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???

marquise 9

marquise 6 marquise11

marquise12

marquise 10

longitucentre1

NS10

NS11

NS12

NS13

NS14

NS15

ch12

ch1

ch3

ch4

ch5

ch2

ch6

ch7

ch9

ch8

ch10

marquise8

NS8

NS7

NS6

NS5

NS4

NS3

NS2

NS1NS16

NS9

EST

SiegesSieges

Sieges

Sieges

1 m1m

marquise 3

marquise 4

marquise 5

marquise 2

marquise 1

Estrade Estrade

version

1

30Aug

2013

Documents

Détection Des Cavitées Souterraines