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1. 1
1.1 1
1.2 2
1.3 3
1.4 4
1.5 6
1.6 9
1.7 11
2. 13
2.1 13
2.1.1 13
2.1.2 DIN 4125 31
2.2.1 32
2.2.2 33
2.2.3 34
2.2 35
2.3 (BS 8081:1989) 37
2.4 EC-7 (EN-1997) 41
2.4.1 41
2.4.2 44
2.4.3 - 47
2.5 50
2.6 55
3. -
57
3.1 57
3.2 PLAXIS 59
3.3 60
3.2.1 - 1 - - 64
3.2.2 - 1 - - 66
3.2.3 2 67
3.2.4 2 68
3.4 - 69
3.4.1. - E1 69
3.4.2. - 2 78
3.5 - 88
3.6 - 110
3.6.1 - 1 110
3.6.2 - 2 124
4. 140
5. 145
1
1
1.
1.1
,
.
.
.
,
, .
,
.
:
.
.
( 1997):
2
2
.
1
2
1.2
:
, ( )
( ).
(.. ).
,
, ,
.
.
.
.
.
,
,
.
,
.
,
,
.
.
(
).
.
.
, .
1
3
.
(
) 0.35 1.00
.
,
.
, (..
.
1.1. :
1.3
.
, .
1.2
1
4
1.2. :
1.4
.
: .
.
, ,
. .
,
,
.
-.
, 8m 110mm.
1
5
:
. ( 1Pa),
(
, )
. ,
.
.
,
.
C : .
(>2MPa) .
.
.
, .
.
,
.
.
.
.
,
. ,
.
.
- :
,
1
6
.
D: .
.
,
,
.
1.5
,
.
.
.
, ,
, : ( ),
, .
,
(2 ).
,
10mm.
,
( )
.
1
7
1
8
,
.
.
,
.
1537:1999.
:
:
10mm .
,
, .
:
.
,
,
,
.
,
,
.
:
.
, ,
,
.
: ,
, (
1
9
)
.
.
, ,
.
,
.
3 6.11 1537:1999.
1.6
.
.
. () ,
( ),
( )
() .
:
f < 0.75Fs,
f < 0.65Fs,
f:
:
1
10
Fs: , 15-20%
,
.
1 2Pa, ,
.
.
3m ,
2m.
,
.
.
-.
.
,
:
-
( )
-
Tu
.
Au : Au=FAf=Tu
, u
, ,
.
1
11
1.7
.
,
.
, ,
, ,
.
1.3. :
u :
- u,
.
.
m=Km=K(hicos)
K .
.
1
12
- ,
=phicos, p=(45+/2)
- W
:
u=(D2o/4) + dL dW + Wsin
.
.
.
.
2
13
2.
2.1
2.1.1
ISO/DIS 22477-5:2009
,
( 1 2)
( 3).
:
,
, .
:
:
Ra -
o
Lapp
:
Pp
Po
2
14
Lapp
:
Pp
Po
Lapp
.
.
1
/ .
. 1, 2 3,
. , 1,
2 3.
-
.
,
.
.
.
.
2
15
,
1997-1, :
Pp
2
16
2.1. : 1
2.1. :
1
1 40 15 15
2 55 15 15
3 70 30 60
4 80 30 60
5 90 30 60
6 100 60 180
(min)
(% Po)
2
17
.
.
6 ,
180 ,
60 .
:
,
.
Rc Ra.
1 .
Ra 1
2mm, Rak
.
-
, ,
.
Pp Pp
2
18
Pd =
/ Pa,
10% Pp
50 kN.
(5) ,
.
,
.
2.2. : 1
2
19
2.2. :
1
.
-
Pp,
.
,
.
Pp
:
Pp = 1.25*Pd
Pp = 1.15*Pd
Pp = 1.00*Pd Po
Pd
Pd =
/ Pa,
10% Pp
50 kN.
1 40 1 1 15 15
2 55 1 1 15 15
3 70 5 5 30 60
4 85 5 5 30 60
5 100 30 60 60 180
(% Po)
(min)
2
20
2.3. : 1
2.3. :
1
Lapp.
1 40 1 1
2 55 1 1
3 70 1 1
4 85 1 1
5 100 5 15
(% Po)
(min)
2
21
2
.
.
-
1,
,
,
1.
(7)
Pp,
.
.
1:
Pp < 0.9*Rt,d
Pp = 1.5*Re
/ Pa 10%
Pp 50 kN.
1
.
2
22
2.4. : 1
2.4. :
1
3
7
30 .
1 2 3 4 5 6 7
10 10 10 10 10 10 10 1
25 37.5 50 62.5 75 81.5 1
17.5 31 44 56 69 81 94 1
25 37.5 50 62.5 75 87.5 100 15
17.5 25 37.5 50 50 62.5 62.5 1
12.5 17.5 25 25 37.5 37.5 1
10 10 10 10 10 10 10 1
. 1.
% Pp
2
23
:
-
( )
- k1
- k1
Rc R.
-
2,
(3)
Pp,
.
.
1.
.
2.5. : 1
2
24
2.5. :
1
( ):
0515501505001500(1 )5000(3 )15000(10 )
:
-
( )
- k1
- k1
-
(2) Pp,
. ,
,
.
Pp
:
Pp = 1.25*Pd
Pp = 1.15*Pd
1 2 & 3 1 2 & 3
10 10 10 10
40 40 33 33
80 80 66 66
100 100 100 100
80 80 66 66
40 40 33 33
10 10 10 10 1
1
1
15
1
1
(min)
1
%Po
2
25
Pp = 1.00*Pd Po
Pd
Pd =
/ Pa
10% Pp
50 kN.
.
2.6. : 1
2.6. :
1
1 2 1 2
10 10 10 10
40 40 33 33
80 80 66 66
100 100 100 100
80 80 66 66
40 40 33 33
10 10 10 10
1
1
1
1
1
15
1
%Po
(min)
2
26
( ):
0515501505001500
.
,
Lapp.
3
,
.
-
3
Pp.
.
,
.
(8)
.
2
27
2.7. : 1
2.7. :
1
( ):
0123457101520304560
:
-
-
-
Pc
Ra. 3 - Pp .
1 2 3 4 5 6 7 8
10 25 40 50 60 70 80 90 100 % Pp
0 60 60 60 60 60 60 60 60
(min)
(%Pp)
2
28
2.8. : 3 - Pp
-
.
.
.
(6)
2
29
2.9. : 1
2.8. :
1
( ):
0123457101520304560
:
-
-
-
3.
1 2 3 4 5 6
10 25 40 55 70 85 100 % Pp
0 60 60 60 60 60 60
(min)
(%Pp)
2
30
-
Pp,
( , ).
Pp
.
Pp
.
5
.
2.10. : 1
2.9. :
1
1 2 3 4 5
10 25 40 55 70 85 % Pp
-
(min)
(%Pp)
2
31
2.10. :
1
01234571015
,
Lapp.
2.1.2 DIN 4125
4125 ,
.
, , ,
.
.
.
, , ,
-
. ,
.
.
1 2 3 4 5 6 7 8 9 10 11
(% Pp)10 30 50 70 90 100 90 80 70 80 90 100
(min)
15
2
32
.
,
,
.
.
2.2.1
,
.
. ,
,
.
.
, .
.
.
2
33
2.11. :
,
0.1*s*Fe.
0.15*s. 0.30*s
, ,
o,
.
.
.
2.2.2
1.20
t ( ).
( )
2
34
5 ,
15 .
o.
0.4 - 0.8 - 1.0 - 1.2,
.
.
2.2.3
, .
.
,
.
.
- ,
. ,
, .
-
,
( )
-
- (
)
2
35
2.2
,
,
.
,
. ,
.
DIN EN1537.
. CG2
CG3
.
k.
d,
.
, .
GZ 1B (GEO STR)
:
k Rd
Rd = Ra,d ( ) Ri,d
( )
Ra,d
GZ 1B (GEO-2) :
Ra,d = Ra,k / A
2
36
Ra,k =
.
GZ 1B (GEO-2)
.
M 1
DIN EN 1537: 2001-01, 9.4.
ks = 2 mm ks .
2 mm Pp
. Ra,k
.
Ri,d
GZ 1B (STR) :
Ri,d = Ri,k /
:
Ri,k =
Ri,k
:
Ri,k = As * f t,0,1,k
:
s =
f t,0,1,k = 0,1%
Ri,k.
, 1 DIN EN 1537: 2001-01, 9.4.
Pp
Ek :
2
37
Pp = 1.25 * Ek
Pp = nk * Ek
:
nk 1.5,
nk 1.33,
.
, Pp
0.80 * s * f t,k 0.95 * s * f t,0,1,k :
s =
f t,k =
f t,0,1,k = 0.1%
.
2.3 (BS
8081:1989)
.
.
.
,
(
)
( ).
, ,
.
.
2
38
2.11. :
/
/
/
1.40 2.00 2.00 1.10
1.60 2.5* 2.5* 1.25
2.00 3 3* 1.50
2
.
* 2.00
4.00
:
1.
.
2. / 2.5
4.0. ,
( ),
.
3. /
, .
6
2
39
:
- w,
- t,
- 1o,
- lt,
, ,
.
.
w
, .
.
,
,
.
,
,
.
w
wULS,
wSLS.
t
,
. 1.25
1.50
2
40
.
.
25% ,
.
,
1.25
wSLS wULS ( ).
25% .
.
lo
1.1
.
lt
lt.
:
- w
- , ,
w
- ,
.
lt.
.
wULS
2
41
wSLS.
.
lt. ,
lt. ,
.
2.4 EC-7 (EN-1997)
7 1997
(CEN)
,
.
,
:
-
- ,
-
.
2.4.1
,
:
-
( ).
2
42
-
(
..)
7
.
QU:
GEO:
, .
STR:
.
.
UPL:
.
D: ,
, , ..
1.15 GEO
1.16 STR
(1) (2) (3)
2.12. :
(1) (
)
(2)
(3)
2
43
GEO.
(1)
( ), (2)
, (3)
.
() ()
2.13. :
(1) /
(2) ( )
1.16
STR.
(1) /
, (2)
( ).
SRT GEO
.
.
, .
2
44
2.4.2
.
:
-
-
-
-
- ..
1990 1991 .
Frep,
.
Fd
F :
Fd = F * Frep
.
.
,
,
. 7,
1,
, .
d,
, :
d = Xk /
7,
.
2
45
,
, .
:
1: ,
.
2: ,
.
.
2 , ,
, ,
..
3:
, ,
..
:
-
-
-
,
-
- ,
2
46
-
, :
1.
,
2.
.
3.
.
(1.5m).
-
.
-
.
.
-
-
1537:1999
-
-
1537:1999
-
- , ,
2
47
2.4.3 -
7
, STR GEO,
:
Ed Rd
:
d =
Rd =
d :
) F
Frep :
Ed = E (F * Frep, Xk / M, ad)
(F, )
,
) ()
: Ek = (Frep , Xk), :
Ed = (Frep, Xk / , ab)
(Frep, Xk) ()
(.. ) .
k
ad
.
Rd
k :
Rd = R (F * Frep, Xk / M, ad)
k :
Rd = R (F * Frep, Xk, ad) / R
k
:
2
48
Rd = R (F * Frep, Xk / M, ad) / R
(F)
E
1.12
2.12. : F E
:
G =
Q =
.
2.13. :
M
A1 A2
1.35 1.00
1.00 1.00
1.50 1.30
0.00 0.00
F
G
Q
M1 M2
1.00 1.25
c 1.00 1.25
cu 1.00 1.40
qu 1.00 1.40
( ) 1.00 1.00
* tan '
2
49
.
2.14. : R
R
d Rd.
F = E, M R
R .
- 1 (Design Approach 1)
:
1: 1 + 1 + R1
2: 2 + (1+2) + R4
Rd Ed
:
1: F = 1.35 1.50, = 1.00, R = 1.00
2: F = 1.00 1.30, = 1.25 1.40, R = 1.00
2, 1
Rd, 2
.
1 2.
R1 R2 R3 R4
g ,t 1.00 1.10 1.00 1.10
g a,p 1.00 1.10 1.00 1.10
2
50
- 2 (Design Approach 2)
:
1+1+R2
: F = 1.35 1.50
1.00 1.30, M = 1.00 R = 1.10.
- 3 (Design Approach 3)
:
(1 2) + 2 + R3
: F = 1.35 1.50,
M = 1.25 1.40 R = 1.00
1
2
.
7, ,
.
2.5
7
. ,
, .
()
,
. :
-
-
2
51
- (, ) ,
-
.
:
-
- ,
,
.
,
1990.
.
2.15. : R
( )
0 2
1 10
2 25
3 25
4 50
,
,
,
5 100
, ,
,
..
2
52
, 2.1 (8)P,
,
, ,
.
( 2.1 (13))
, ,
. 1
, 2
3 .
2 (DA-2) (DA-3) 3. 3:
E (F Frep, Xk / ) R (F Frep, Xk / )
F = 1.35 1.50 (), F = 1.0 1.3 (.), = 1.25 1.40
:
-
(, , , )
- (
, )
- ( )
(
F =1.00) (.. ).
(DA-2) 2
:
R (F Frep, Xk / ) / R (Frep, Xk / )
R = 1.10 1.40 = 1.35 1.50
2
53
F M 1.
2
:
- (GEO) (STR)
, ,
- (STR)
(
, )
- (GEO) (STR)
( ) (..
)
- (UPL)
(HYD)
7
.
.
,
:
-
-
-
- ,
- ,
- ,
-
2
54
-
.
.
.
7
.
,
.
,
.
.
.
(
EN 1537:1999), .
,
.
1.5m.
2
55
1537:1999.
2.6
7, d Rd, :
Pd Ra,d
Pd: .
,
Pd = F*Pk F = 1.35
- Ra,d: .
Ra,k ( )
:
Ra,d = Ra,k / R
R 2.15
Ra,k
:
-
. = 1
Ra,k = min (DLf fsu,k, Asf y,k)
:
D =
Lf =
fsu,k = -
s =
fy,k =
- (n)
(suitability tests)
2
56
: Ra,1, Ra,2, Ra,3,Ra,n.
Ra,k :
Ra,k= min {(Ra,m)mean / 1, (Ra,m)min / 2}
:
{Ra,m}min = min [Ra,1,
Ra,2,..,Ra,n] ,
(a1 a2) :
2.16. :
1 2 3
1 = 1.20 1.15 1.10
2 = 1.20 1.10 1.00
3
57
3. -
3.1
-
.
. ,
,
.
- .
-
.
(, , )
.
.
.
-
.
(=150 c=40kPa),
(=400 c=10kPa).
- .
.
1.0 m,
s = 5.0 m.
3
58
. 4
D=2.00 m.
.
. ,
.
.
.
,
:
.
52.0 m
25.0 m 10.0 m
.
.
, ,
.
,
,
.
.
,
.
3
59
3.2 PLAXIS
PLAXIS .
.
PLAXIS -
(Mohr-Coulomb model),
.
,
, PLAXIS.
,
.
80%,
60%, 40% 20% .
.
,
node-to-node anchor.
2 .
( ), .
.
geogrid,
. .
.
, PLAXIS, S.F.
, phi/c reduction.
.
c .
. S.F.
. ,
,
.
3
60
3.3
.
.
,
:
1 (1):
-
=15 c=40 kPa
=20 MPa
Poisson =0.3
=20 kN / m3
2 (2):
-
=40 c=10 kPa
=50 MPa
Poisson =0.2
=22 kN / m3
1.0 m, s=5.0 m.
- 1.0 m
1.5 m .
W=14 kN/m/m.
- :
= 1.0 m x 1.0 m
= 1.5 m x 1.0 m
= 30 cm x 30 cm
= 40 cm x 40 cm
20 cm x 40 cm ( )
3
61
40 cm x 80 cm ( )
:
=29 GPa (C20/25)
EI=483333.3 kNm2 / m
EA=5800000 kN / m
:
=29 GPa
EI=1631250 kNm2 / m
EA=8700000 kN / m
:
=29 GPa
I= bh3/12=0.000675 m4
EI=3915 kNm2 / m
EA=522000 kN / m
:
=29 GPa
I= bh3/12=0.00213 m4
EI=12373.33 kNm2 / m
EA=928000 kN / m
3
62
20 cm x 40 cm:
=29 GPa
Is=bdo3=0.0004796 m4,
Beton
Kalender
EI=2781.68 kNm2 / m
EA=899000kN / m
40cm x 80 cm:
=29 GPa
Is=bdo3=0.00934 m4,
Beton Kalender
EI=54172 kNm2 / m
EA=2204000 kN / m
s = 2.0 m, =14.0 m.
0.6 Fe=5.56 cm2, d=0.1 m
.
0.6 m.
.
:
-
40.6 Fe=5.56 cm2
d=0.1 m
Es=200 GPa
EsAs= 111200 kN
Eb=25 GPa
EbAb=182350 kN
EA= EsAs + EbAb=293550 kN
3
63
:
-
s=2.0 m
d=0.1 m
EA=146775 kN / m
= 400 kPa
:
0.6 m
EA=3532500 kN / m
EI=79481.25 kNm2 / m
Poisson =0.2
3
64
3.2.1 - 1 - -
14.0 m
. 2.0 m.
- .
(EI ) .
1 (=15 c=40 kPa) .
11.0 m, 9.0 m, 6.0 m 6.0 m,
1, 2, 3 4 .
, ,
=150 c=40kPa
E=20 MPa =20kN/m3
: 20x40
3
65
45+/2
, 1.0 m - 1.5 m.
9.0 m
:
d = S1700/S1900
d =
= 400 kPa.
.
=15 .
.
.
-3.0 m
-2.0 m .
.
(m)
(m)
(m)
(m)
1 -2.0 11.0 9.0 20.0
2 -5.0 9.0 9.0 18.0
3 -8.0 6.0 9.0 15.0
4 -11.0 6.0 9.0 15.0
3
66
3.2.2 - 1 - -
14.0 m.
.
.
, , =15
.
,
.
=150 c=40kPa
E=20 MPa =20kN/m3
: 40x80
3
67
3.2.3 2
=40 c=10 kPa.
.
.
: 20x40
=400 c=10kPa
E=50 MPa =22kN/m3
3
68
3.2.4 2
,
=40 c=10 kPa,
. 20 cm x 40 cm
40 cm x 80 cm.
.
.
: 40x80
=400 c=10kPa
E=50 MPa =22kN/m3
3
69
3.4 -
.
- , .
3.4.1. - E1
-
1.
3.1. : , o=0.5 o=1.0
3.2. : , o=0.5 o=1.0
3.3. : , o=0.5 o=1.0
320 0,961 0,767 0,963 0,873
240 0,971 0,835 0,974 0,944
160 0,982 0,912 0,985 1,018
80 0,993 0,995 0,996 1,092
o=0.5 o=1.0
(kN/m)
maxM / maxMo
' ( A)
(E1) =15 & c=40 kPa
320 1,001 0,834 1,022 1,040
240 1,009 0,918 1,031 1,124
160 1,018 1,003 1,040 1,214
80 1,027 1,099 1,050 1,303
o=0.5 o=1.0
(k/m)
maxM / maxMo
' ( B)
(E1) =15 & c=40 kPa
320 1,006 0,927 1,040 1,019
240 1,014 0,959 1,049 1,047
160 1,023 0,992 1,058 1,073
80 1,033 1,026 1,068 1,099
(kN/m)
maxM / maxMo
' ( )
(E1) =15 & c=40 kPa
o=0.5 o=1.0
3
70
3.1: - =0.5
3.2: - =1.0
3
71
3.3: - ,
3.4: - ,
3
72
3.5: - ,
3.6: =0.5 =1.0
3
73
3.7: - =0.5
3.8: - =1.0
3
74
3.9: - ,
3.10: - ,
3
75
3.11: - ,
3.12: =0.5 =1.0
3
76
-
-
. -
=0.5 ,
.
. ,
,
. 5%.
3.1. : =0.5 F=320 kN / m
Deformed Mesh
Extreme total displacement 122.03*10-3
m
(displacements scaled up 20.00 times)
3
77
,
, ,
. , ,
,
.
,
. ,
, =0.5 ,
.
320 kN / m, 0.767 0.834 .
- -
-
.
. ,
,
- .
.
-
1
. =0.5
=1.0. , -
, ,
.
0.1% - 4.0%.
, =160 kN / m T=80 kN / m.
, -
, 21%
80 kN / m. ,
3
78
. ,
,
. ,
- ,
,
.
3.4.2. - 2
-
2.
, 2
1, =40 c=10 kPa.
3.4. : =0.3 =0.5
3.5. : =0.3 =0.5
320 0,995 0,842 0,992 0,912
240 0,996 0,877 0,996 0,945
160 1,001 0,907 1,001 0,976
80 1,006 0,946 1,006 1,008
o=0.3 o=0.5
(kN/m)
maxM / maxMo
' ( A)
(E2) =40 & c=10 kPa
320 0,996 0,717 0,997 0,916
240 1,000 0,780 1,001 0,951
160 1,004 0,830 1,006 0,984
80 1,011 0,914 1,012 1,037
(kN/m)
maxM / maxMo
' ( B)
(E2) =40 & c=10 kPa
o=0.3 o=0.5
3
79
3.6. : =0.3 =0.5
3.13: - =0.3
320 0,998 0,853 1,000 0,991
240 1,005 0,883 1,005 0,999
160 1,010 0,902 1,010 1,000
80 1,015 0,954 1,015 1,015
(kN/m)
maxM / maxMo
' ( )
(E2) =40 & c=10 kPa
o=0.3 o=0.5
3
80
3.14: - =0.5
3.15: - ,
3
81
3.16: - ,
3.17: - ,
3
82
3.18: =0.3 =0.5
3.19: - =0.3
3
83
3.20: - =0.5
3.21: - ,
3
84
3.22: - ,
3.23: - ,
3
85
3.24: =0.3 =0.5
-
-
- =0.3
,
.
. 2
, 0.1% - 1.5%.
, 1,
.
,
, ,
. , ,
,
.
3
86
3.2. : =1.0
F=320 kN/m
- =0.3,
.
.
30%.
- -
-
. ,
.
, ,
- .
.
-
.
Deformed Mesh
Extreme total displacement 151.25*10-3
m
(displacements scaled up 20.00 times)
3
87
-
1, 2,
. =0.3
=0.5. ,
- , ,
.
0.0% - 0.2%.
, -
, 20%
80 kN / m. ,
. ,
. , -
,
,
.
1 2 -
,
- .
,
=0.5.
,
, ,
.
, -
.
80 kN / m.
,
.
,
3
88
. , 2,
,
=0.5.
3.5 -
.
- , .
, ,
.
3.5.1 - E1
-
1.
3.7. : =0.5 =1.0
320 0,933 0,893 0,973 0,971
240 0,941 0,894 0,978 0,961
160 0,950 0,898 0,984 0,955
80 0,965 0,910 0,990 0,948
maxM / maxMo
' (A)
(E1) =15 & c=40 kPa
o=0.5 o=1.0
(kN/m)
3
89
3.8. : =0.5 =1.0
3.9. : =0.5 =1.0
3.10. : =0.5 =1.0
320 0,997 1,312 0,919 1,673
240 0,976 1,033 0,900 1,419
160 0,955 0,752 0,879 1,338
80 0,929 0,440 0,858 1,615
(E1) =15 & c=40 kPa
o=0.5 o=1.0
(kN/m)
maxM / maxMo
B' (A)
320 1,002 1,255 1,059 1,476
240 1,015 1,248 1,069 1,472
160 1,027 1,235 1,082 1,495
80 1,045 1,242 1,094 1,512
(kN/m)
maxM / maxMo
' (A)
(E1) =15 & c=40 kPa
o=0.5 o=1.0
320 0,918 0,768 0,895 0,606
240 0,916 0,741 0,893 0,574
160 0,914 0,720 0,890 0,535
80 0,912 0,696 0,888 0,497
(kN/m)
maxM / maxMo
' (A)
(E1) =15 & c=40 kPa
o=0.5 o=1.0
3
90
3.25: - =0.5
3.26: - =1.0
3
91
3.27: - A
=0.5 =1.0
3.28: - A
=0.5 =1.0
3
92
3.29: - A
=0.5 =1.0
3.30: - A
=0.5 =1.0
3
93
3.31: -
A =0.5 =1.0
3.32: - =0.5
3
94
3.33: - =1.0
3.34: - A
=0.5 =1.0
3
95
3.35: - A
=0.5 =1.0
3.36: - A
=0.5 =1.0
3
96
3.37: - A
=0.5 =1.0
3.38:
- A =0.5 =1.0
3
97
-
-
,
. ,
,
.
,
.
7% .
- -
,
. -
,
. 15%
= 1.0. ,
50%
-
.
-
,
.
3
98
. -
,
- .
-
. ,
= 1.0,
50% .
,
50%.
.
-
,
-
.
= 0.5,
,
. = 1.0,
. = 0.5
F = 80 kN / m, F =
320 kN/m.
3
99
3.5.2 - E2
-
2.
3.11. : =0.3 =0.5
3.12. : =0.3 =0.5
3.13. : =0.3 =0.5
320 0,923 0,667 0,989 0,945
240 0,986 0,682 0,983 0,920
160 0,979 0,664 0,976 0,880
80 0,969 0,647 0,967 0,851
o=0.3 o=0.5
(E2) =40 & c=10 kPa
(kN/m)
maxM / maxMo
' (A)
320 1,006 1,312 1,013 1,191
240 1,005 1,218 1,003 1,092
160 0,994 1,139 0,993 0,989
80 0,985 1,049 0,984 0,904
o=0.3 o=0.5
(kN/m)
maxM / maxMo
B' (A)
(E2) =40 & c=10 kPa
320 1,024 1,225 0,990 0,965
240 0,996 1,201 0,996 0,999
160 1,001 1,184 1,001 1,042
80 1,004 1,115 1,004 1,027
o=0.3 o=0.5
(kN/m)
maxM / maxMo
' (A)
(E2) =40 & c=10 kPa
3
100
3.14. : =0.3 =0.5
3.39: - =0.3
320 0,898 0,647 0,992 0,949
240 0,982 0,649 0,980 0,895
160 0,971 0,626 0,969 0,828
80 0,964 0,595 0,962 0,795
(kN/m)
maxM / maxMo
' (A)
(E2) =40 & c=10 kPa
o=0.3 o=0.5
3
101
3.40: - =0.5
3.41: -
=0.3 =0.5
3
102
3.42: -
=0.3 =0.5
3.43: -
=0.3 =0.5
3
103
3.44: -
=0.3 =0.5
3.45: -
=0.3 =0.5
3
104
3.46: -
=0.3
3.47: -
=0.5
3
105
3.48: -
=0.3 =0.5
3.49: -
=0.3 =0.5
3
106
3.50: -
=0.3 =0.5
3.51: -
=0.3 =0.5
3
107
3.52:
- =0.3 =0.5
-
-
1, 2,
,
, 7%.
,
.
. ,
.
,
.
3
108
,
=0.5 .
3.3. : =0.3 F=320 kN/m
3.4. : =0.5 F=320 kN/m
Deformed Mesh
Extreme total displacement 62.11*10-3
m
(displacements scaled up 50.00 times)
Deformed Mesh
Extreme total displacement 62.35*10-3
m
(displacements scaled up 50.00 times)
3
109
- -
,
. -
, ,
. 10%
= 0.3 F = 320 kN / m.
,
30% -
. ,
F = 80 kN / m = 0.3.
-
-
,
. ,
,
. ( 3.41 -
3.44)
30%, 20%
.
,
.
, ,
.
3
110
3.6 -
.
(..) - ,
.
-
, .
,
. ,
1 2.
3.6.1 - 1
.
(..)
, 1 4
.
.. 1,2 3,4, .. 2,3
,
.. 2 3 .
1= 20 MPa 1 2= 50 Pa 2.
. ,
,
.
.
1.0 m .
- .
,
3
111
- .
3.15. :
1,2
3.53: =0.5 =1.0
.. 2 .. 1,
= 0.5 F=320 kN / m.
.. 1,
= 0.5 = 1.0
320 0,0001 -0,0054
240 -0,0014 -0,0069
160 -0,0030 -0,0083
80 -0,0047 -0,0098
(E1) =15 & c=40
s1,2 (S2-S1)
(kN/m)
3
112
.
, , .
3.16. :
2,3
3.54: =0.5 =1.0
.. 2,3.
. ..
=0.5 =1.0
320 -0,00454 -0,0027
240 -0,0033 -0,0014
160 -0,0019 -0,00004
80 -0,0004 0,0013
(kN/m)
s2,3 (S3-S2)
(E1) =15 & c=40
3
113
2
.. 3.
3.17. :
3,4
3.55: =0.5 =1.0
.. 3,4
. .
, =0.5,
=1.0.
=0.5 =1.0
320 0,0057 0,0037
240 0,0040 0,0021
160 0,0023 0,0004
80 0,0005 -0,0014
(E1) =15 & c=40
s3,4 (S3-S4)
(kN/m)
3
114
-
3.18. :
1,2
3.56: .. 1,2 =0.5 =1.0
-
1,2,
.
0.10 1.60.
-
-
-
-
320 0,35 1,13 0,10 0,59
240 0,58 1,31 0,17 0,68
160 0,61 1,44 0,21 0,77
80 1,17 1,60 0,29 0,87
(kN/m)
(E1) =15 & c=40 kPa
o=0.5 o=1.0
s1,2 / so1,2
3
115
=0.5.
,
.
3.19. :
3,4
3.57: 3,4 =0.5
=1.0 -
.. 3,4
. ,
320 0,70 1,18 0,37 0,56
240 2,07 1,30 0,46 0,60
160 2,90 1,43 0,58 0,66
80 3,76 1,68 0,90 0,73
(kN/m)
(E1) =15 & c=40 kPa
o=0.5 o=1.0
s3,4 / so3,4
3
116
- =0.5,
.
.
-
-
(..) 1,2
.
.
3,4.
=0.5
.
.
.. 1,2
- =0.5.
F=320 kN/m F=80 kN/m
=0.5 =1.0.
- -
-
.. (1,2 2,3). .. 1,2
- .
.. 3,4
F=80 kN/m. - ,
3
117
, ..
.
-
.
(vertical displacements)
PLAXIS
.
3.58: -
=0.5, F=320 kN/m
3.59:
- =0.5, F=320 kN/m
3.60: -
=0.5, F=240 kN/m
3
118
3.61:
- =0.5, F=240 kN/m
3.62: -
=0.5, F=160 kN/m
3.63:
- =0.5, F=160 kN/m
3.64: -
=0.5, F=80 kN/m
3
119
3.65:
- =0.5, F=80 kN/m
(vertical displacements)
( ),
.
-
1
.. 1,2 = 0.5.
.
F =80 kN/m, =0.5
1.17 =1.0 0.29,
- . -
F =80 kN/m.
.. 3,4
=0.5 =1.0.
3
120
3.66:
- =0.5 =1.0
3.67:
- =0.5 =1.0
3
121
3.68:
- =0.5 =1.0
3.69:
- =0.5 =1.0
3
122
Ko.
,
.
3.70: =0.5
3.71: =1.0
3
123
3.72: =0.5
3.73: =1.0
.
..1,2
3
124
=0.5 =1.0.
0.5 -
.
.
1.0.
-
.
.. 3,4 =0.5
. 1,2.
- .
F= 80 kN/m =0.5
.
=1.0
(320 kN/m 240 kN/m) ,
- ,
.
F=80 kN/m -
F=320 kN/m
1 mm.
3.6.2 - 2
1
2
- .
1m .
- .
3
125
3.20. :
1,2
3.74: =0.3 =0.5
,
.
.. 2 . 1.
.
.. 1
..2.
o=0.3 o=0.5
320 -0,0013 -0,0035
240 -0,0018 -0,0040
160 -0,0021 -0,0044
80 -0,0026 -0,0049
(kN/m) (E2) =40 & c=10
s1,2
3
126
3.21. :
2,3
3.75: =0.5 =1.0
=0.3 =0.5
320 -0,0032 -0,0041
240 -0,0028 -0,0037
160 -0,0022 -0,0032
80 -0,0018 -0,0028
(E1) =15 & c=40
s2,3
(kN/m)
3
127
3.22. :
3,4
3.76: =0.5 =1.0
.. 3,4
.
. 1,2.
=0.3 =0.5
320 0,0027 0,0032
240 0,0022 0,0028
160 0,0018 0,0023
80 0,0013 0,0018
(kN/m)(E2) =40 & c=10
s3,4
3
128
-
.
(..)
, 1 .. 4
.
3.23. :
1,2
3.77: .. 1,2 =0.3 =0.5
-
320 0,68 1,16 0,41 0,94
240 0,58 1,29 0,41 0,98
160 0,87 1,37 0,53 1,01
80 0,95 1,51 0,60 1,09
s1,2 / so1,2
(kN/m)
(E2) =40 & c=10 kPa
=0.3 =0.5
3
129
1,2
. =0.3
.
3.24. :
3,4
3.78: .. 3,4 =0.3 =0.5
-
320 0,55 0,52 0,23 0,19
240 0,57 0,59 0,30 0,26
160 0,68 0,68 0,36 0,33
80 0,79 0,78 0,44 0,40
(E2) =40 & c=10 kPa
=0.3 =0.5
s3,4 / so3,4
(kN/m)
3
130
. 3,4
,
.
- =0.3 =0.5.
-
-
.. 1,2
.
.
.. 3,4.
F=320 kN/m
F=80 kN/m
.
.
.
- -
-
3,4,
. .. 1,2
-
50%. ,
,
.
(vertical displacements)
PLAXIS
.
3
131
3.79: -
=0.3, F=320 kN/m
3.80: -
=0.3, F=320 kN/m
3.81: -
=0.3, F=240 kN/m
3.82: -
=0.5, F=240 kN/m
3
132
3.83: -
=0.5, F=160 kN/m
3.84: -
=0.5, F=160 kN/m
3.85: -
=0.5, F=80 kN/m
3.86: -
=0.5, F=80 kN/m
3
133
-
2 .. 1,2
=0.5 - ,
=0.3.
.
3.87:
- =0.3 =0.5
3.88:
- =0.3 =0.5
3
134
3.89:
- =0.3 =0.5
3.90:
- =0.3 =0.5
.. 3,4 =0.5
.
3
135
. 1
.
3.25. : =0.3
3.91: =0.3
-
-
320 -0,0039 -0,0060 -0,0013
240 -0,0033 -0,0066 -0,0018
160 -0,0050 -0,0070 -0,0021
80 -0,0054 -0,0077 -0,0026
o=0.3
(kN/m)
s1,2
(E2) =40 & c=10 kPa
3
136
3.26. : =0.5
3.92: =0.5
-
-
320 -0,0024 -0,0048 -0,0035
240 -0,0024 -0,0050 -0,0040
160 -0,0030 -0,0052 -0,0044
80 -0,0035 -0,0056 -0,0049
o=0.5
(kN/m)
s1,2
(E2) =40 & c=10 kPa
3
137
3.27. : =0.3
3.93: =0.3
-
-
320 0,0032 0,0027 0,0027
240 0,0033 0,0030 0,0022
160 0,0039 0,0035 0,0018
80 0,0045 0,0040 0,0013
o=0.3
(kN/m)
s3,4
(E2) =40 & c=10 kPa
3
138
3.28. : =0.5
3.94: =0.5
..1,2
=0.3 =0.5 .
0.3 -
. 2
-
-
320 0,0013 0,0010 0,0032
240 0,0017 0,0013 0,0028
160 0,0021 0,0017 0,0023
80 0,0025 0,0020 0,0018
o=0.5
(kN/m)
s3,4
(E2) =40 & c=10 kPa
3
139
. 1.
- -
.
0.5 -
.
- .
-
=0.3.
.
.. 3,4
- =0.3 =0.5
.
.
, -
.
=0.3
F=320 kN/m =0.5 F=80 kN/m.
4
140
4.
4.1
, .
.
-
c, . 1 ,
2 .
(4) ,
Rd,
.
-
, .
.
4.2
4.2.1.
- .
- .
- .
, ,
- 0 - 7%
4
141
- 0 - 30% .
1, -
.
2 , -
, ,
-
.
-
- ,
.
- .
-
() , .
- ().
-
. -
4%.
-
20%.
1 2.
4.2.2.
-
,
. -
0 - 15%.
- 0 67%.
4
142
.
.
-
,
- ,
.
.
1 2
, ,
.
,
,
- .
0 8%. -
3%
.
4.2.3.
- . . 1,2
,
=0.5 =0.3 1 2 .
4
143
.. 3,4
. 2
1 =1.0. =0.5
.
. 1,2 -
= 0.5, = 1.0
.
2. = 0.3
,
-
. =0.5
1,
- -
.
. 3,4 2
. 1,2. =0.3
- =0.5
.
.. 3,4
1 -
.
.
-
-
.
- ,
-
. .. 1,2
,
, .. 3,4
.
4
144
- .
1 -
50%.
, ,
1
2.
5
145
5.
. (2000), ,
., ., (2004),
, , ...
. (2001), , ...
., , 2009
. (2008),
,
. (2003), , ,
, ..
, ., , ., , .
-
Eurocode 7 (2007), Geotechnical DePart 1General rules, EN 1997
European Committee for Standarisation, EN1537:1996, Execution of special
geotechnical workGround anchors, February 1996
British Standards Institution, British Standard Code of practice for Ground
Anchorages, (1989)
DIN4125, , 19971, 2
European Standard, Geotechnical Investigation and testingTesting of
geotechnical structures: Testing of anchorages, 2005
Organisation for Standardisation, Tentative Final Draft of ISO TC 182/SC 1 ,
ISO 22477Geotechnical Investigation and testing Testing of geotechnical
structures : Testing of anchorages, 2009
Merrifield, Barrley, Von matt, The execution of Ground Anchor Works: The
European Standard EN 1537
Plaxis V8
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