Диссертация - Российский Государственный

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25.00.08 – «
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-
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2
............................................................................................................................................ 4
.............................................. 12
1
................... 12
1.1
1.2
.......................................................... 16
,
1.3
................................................................................................. 23
1.4
................................................................................................... 33
1.5
.......................................................................................... 36
1.6
..................................................................................................... 47
: ..................................................................................................................................................... 51
.............. 52
2
2.1
.......................................................................................................................... 52
2.2
........................................................ 52
2.3
........................................................................... 54
2.4
........................................ 66
2.5
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..................... 99
3
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......................................................................................................................... 99
3.2
.......................................................................................................................... 99
3.3
......................................................................................... 100
3.4
............................................................................... 107
: ................................................................................................................................................... 111
112
4
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........................................................................................... 112
4.2
................................................................................................................ 116
4.3
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............................................ 119
4.4
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4.5
.................................................................................. 162
4.6
....................................................... 164
4.7
...................................................................................... 166
: ................................................................................................................................................... 174
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.............................................. 175
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5.3
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................................................................... 181
5.4
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: ................................................................................................................................................... 188
....... 189
6
6.1
..................................................................................... 189
6.2
................................................................ 190
6.3
...................................................................................................... 193
6.4
.......................................................................................................... 199
6.5
.................................................................... 206
: ................................................................................................................................................... 222
.............................................. 224
7
............ 224
7.1
7.2
..................................................................................................................................................... 229
7.3
............................................................................................................... 234
7.4
......................... 238
7.5
...................................................................................................... 244
7.6
....................................... 249
7.7
........................................................................ 266
: ................................................................................................................................................... 279
.................................................................................................................................. 283
: ........................................................................................................................................ 289
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.......................... 312
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,
,
,
,
)
.
(
)
1.9.
(
.
[214]).
,
,
,
,
,
,
,
,
,
-
,
,
.
,
,
,
45
:
-
,
;
3
100-200
1000
3
200
.
;
;
–
200
3
3
100-
;
-
.
[180].
[147]
:
1)
(
2)
);
–
;
3)
,
4)
;
–
2-5
,
5)
;
–
(
2-3 )
,
6)
,
,
;
–
,
.
,
,
,
(
)
.
,
,
,
(
. 1.10).
1.10.
(
(
.
[222]).
)
,
<1
<5
< 20
> 20
-
, . .
.
,
.
,
, -
46
,
.
)
(
.
,
.
.
(
),
.
.
,
.
.
[136] (
.
1.
(
,
:
),
.
)
. 1.10),
:
,
,
;
)
2.
(
).
(
)
),
(
)
:
,
,
);
(
).
. 1.10.
(
.
[136])
47
,
.
[207]
.
,
,
.
,
(
,
. 1.11).
,
.
,
.
,
.
.
[208].
(
,
,
)
(
).
,
.
1.6
(
.
[289]) «
,
,
,(
,
,
)
,
».
[209]
(
)
(
).
,
(
)
,
(
.
)
48
(
(
))
(
,
,
,
–
),
–
,
,
-
–
,
»,
-
(
)
,
–
(
)
)
–
)
.1.11.
–
,
.
–
[207],
.
.
49
,
,
.
,
–
(
)
.
,
-
(
)
(
.
,
).
.
.
[128]
. 1.12.
,
. 1.12.
(
.
,
.
.
[128]).
,
,
:
.
:
.
:
50
.
,
,
.
,
.
. 1.13.
. 1.13.
(
).
51
:
,
.
–
[136].
,
,
:
,
.
,
,
.
,
–
(
)
.
-
,
(
)
(
).
,
,
,
.
,
.
.
[128].
52
2
2.1
,
.
,
,
.
,
(
),
,
–
[106].
,
,
,
.
,
,
.
2.2
:
,
.
,
.
: )
; )
; )
[206].
,
.
,
,
,
,
,
[198].
.
,
53
.
-
.
,
.
-
.
.
-
.
-
.
.
,
,
.
,
.
:
–
,
;
–
,
.
.
.
[106].
,
,
.
,
,
,
,
,
[206] .
.
,
,
.
,
)
.
,
,
,
,
.
54
2.3
:
.
.
:
.
.
,
,
[106]:
,
(
).
,
(
).
,
.
:
= l/L
l–
(2.1)
,
;L–
.
.
:
= f/F
f -
,
(2.2)
, F–
.
:
= n/F
(2.3)
n–
;F–
,
,
.
.
(fn),
=
=
:
(2.4)
.
55
.
,
, . .
.
:
= (V1 – V2))/t
(2.5)
V1 –
, V2 –
,t–
, –
.
,
.
.
,
,
,
.
.
,
[205].
(
).
,
-
,
,
.
: )
[149], )
[137], )
[220].
)
.
:
,
,
,
,
,
56
,
.
:
,
,
,
.
,
,
,
,
,
,
,
,
.
.
,
,
.
)
,
.
,
.
,
.
,
,
,
.
.
[137]
,
1.
:
I :
L2.
, bmax -
=
(2.6)
=
(2.7)
;
I :
hmax -
,L-
;
57
3.
I :
hi -
=
(2.8)
=
(2.9)
, bi -
;
4.
I :
H-
,R-
.
)
.
.
[220]
,
.
.
:
,
,
,
,
,
.
,
-
.
.
,
[54], [151]
.,
,
,
.
. 2.1.
,
,
:
.
.
[128]
58
. 2.1.
[54].
(
n),
.
:
1.
,
(
2.
3.
;
;
);
1 2
3…
59
4.
(
5.
);
;
6.
;
7.
(
).
.
,
,
.
.
,
.
,
.
,
.
,
,
.
,
.
.
:
,
—
-
,
-
1
-
,
.
(
m
)
:
=1–
–
(1 - pji)
(2.10)
; pji –
.
0
(
),
1.
60
,
(
)
.
(2.10)
.
.
.
.
,
,
,
.
.
[245]
[128]
.
,
,
.
.
.
,
:
Wk
=
Wn
×
+
(2.11)
n
.
,
,
(i
),
(2.12),
,
i
:
=
–W–
;
,
-
(
(
)
(2.12)
)
;m-
;Pi- .
,
,
61
(2.10)
,
.
,
,
.
,
,
.
(
)
,
,
.
.
.
,
,
.
(2.10)
,
.
.
[209]
(
—
,
)
)
(
).
,
,
(
,
).
62
.
[175], [176] .
.
,
.
.
.
.
,
,
[136], [290], [103].
.
,
(
)
(
)
,
,
,
.
:
,
,
;
,
,
;
,
,
,
.
,
,
,
,
63
,
,
.
,
“
”,
.
,
[6], [50].
,
,
,
,
.
:
Wn –
Cn –
n–
= (W1C1 x W2C2 x …. x WnCn ) / 1000,
(2.13)
= (W1C1 + W2C2 + …. + WnCn),
(2.14)
n;
n;
:
Wn –
Cn –
n–
n;
n;
.
.
,
2(
«Scott Wilson»
Colin Morgan
Darryn Wise,
.
),
Gareth Hearn, Andrew Hart,
,
:
;
o
;
o
(
o
);
;
o
.
o
,
,
:
64
:
/
o
;
;
o
(
):
;
o
;
o
.
o
. 2.1
.
2.1
2(
).
.
/
1
2
3
0.1 (
.
-
10
0.333
10
0.333
7
0.233
2
0.07
1
0.03
)
0(
)
3(
)
1(
)
1
2
3
1
2
3
1
2
3
,
,
.
,
.
,
.
.
,
,
,
65
,
,
,
. 2.2).
. 2.2.
,
: —
,
, —
,b—
[54].
,
«
,
»
,
,
,
,
,
,
.,
.
[54]
,
.
,
,
,
,
,
.
,
,
.
66
2.4
.
,
(
),
.
[12],
.
,
.
,
.
,
—
,
.
(DEM).
,
,
,
:
[31];
ROC
,
(receiver operating caracteristic curve analysis) [36].
,
.
.
,
;
:
;
;
;
.
[55]
,
.
[80], [70].
,
.
,
67
.
Arcview – Sinmap
Shalstab.
SHALSTAB
Geological Sciences University of Washington, Seattle [20].
[61]:
.
SHALSTAB
,
.
,
,
,
:
-
,
,
.
.
,
.
–
,
,
«
(
»).
,
.
.
,
SHALSTAB,
,
,
,
.
.
,
,
,
,
,
.
,
SHALSTAB.
.
,
,
Shalstab
(SINMAP) [80].
68
(Stability INdex MAPping (
Terratech Consulting Ltd,
)
C.N. Goodwin Fluvial System Consulting, U.S. Forest
Service, Rocky Mountain Research Station (
Columbia (
)
)
Forest Renewal British
).
,
(stabilizing forces)
(destabilizing forces)
FS
Cr
Cs
cos2
FS –
,
,
g D Dw g
D g sin cos
(2.15) [39].
w
Dw tg
,
2; –
,
3; g –
, ; Dw –
,
.
2; Cs –
3; w –
,
(2.15)
; Cr –
,
.; –
, g = 9,81
,
D–
; –
. 2.3
,
2;
,
(2.15).
. 2.3.
(2.15)
:
FS
C–
,
.,
C
cos 1 Wr tg
sin
(2.16)
,
., = (Cr + Cs) / (h g),
, W = Dw/D = hw/h,
.; h –
, , hw = Dw cos ; r –
r= w/ .
h = D cos , ; W –
, ; hw –
w
,
.
,
SINMAP
(2.17):
69
min
W
R a
,1
T sin
=
–
; m –
,
(2.17)
, 2
;K–
; a = A/b –
,(
,
,
. 2.4); R –
,
;
:
R ( I ET ) K sr
K sr –
(2.18)
,
; I –
,
.,
,
;
–
ET
.
. 2.4.
(2.16)
(2.17),
C cos 1 min
FS
:
R a
,1 r tg
T sin
(2.19)
sin
SINMAP
:
(SI)
«
»
«
»
.
«
»
(
,
SI = FSmin =
):
-
]
(2.20)
70
FS ,min –
,
2
; –
., R1 –
,
,
,
2
,
«
.;
1
–
1
–
–
1
.
»
(
,
FS ,max –
;
.;
):
, ]
-
SI = FSmax =
(2.21)
,
2
,
,
; –
.; R2 –
,
,
2
,
, C
;
2
.;
.; 2 –
2
–
–
.
R/T
«
»
«
»
. 2.2 [151].
2.2
,C
R/T
«
»
«
»
–
g,
2
T3n-r hg
Q
9,81
9,81
w,
,
,
3
3
1000
1000
1982
1846
.
15,2 30,3
6,5 29,3
C
R/T
0,011 0,340
0,010 0,260
0,00190 0,00040
0,00083 0,00036
,
(2.22):
SI = Prob(FS > 1)
(2.22)
SINMAP
. 2.5.
SINMAP
.
71
. 2.5.
SINMAP.
,
,
ARCVIEW – SMORPH (slope
morphology model) [85].
.
,
.
,
.
,
,
[69].
SMORPH
,
(
)
.
,
-
72
(
),
,
,
.
,
SMORPH
.
.
,
,
,
,
,
90 %
SMORPH [85].
:
,
(DEM),
(
,
.
,
,
,
.
)
«
»
.
(
.
)
,
,
,
[93]:
Z = Ax2y2 + Bx2y + Cxy2 + Dx2 + Ey2 + Fxy + Gx +
,
–
,
+I
(2.23)
–
,
.
-
.
,
,
.
SMORPH
10 ),
,
.
,
.
73
,
,
,
[151].
,
.
(
–
)
:
;
(
–
);
;
.
,
,
.
(
.
. 2.6)
,
1,
,
2.
(
,
«
»
,
6
,
).
. 2.6.
74
wj (
.),
(n)
,
1:
wj
1
j
,
n
(2.24)
j
j 1
j
–
j-
.
. 2.3
wj
[151].
–
,
(
. 2.4).
xij
,
1:
=
(2.25)
2.3
,
–
[151]
wj,
.
0,337
(
)
–
0,230
0,254
0,180
1,000
.
H
:
n
H
w j xij
i, j 1
–
.; wj –
,
(2.26)
,
j,
.; xij –
i
j,
H.
.
(
)
.
75
2.4
,
–
,
[151]
wj
xij
.
.
.
.
.
.
1.
2.
(
),
3.
,
(Q)
(N2 tg)
(J1-2 hc)
(T3n-r hg)
(P3 bc)
(C-P3 bs)
.2-3
.3-4
.4-5
. 5 - 5,5
. 5,5 - 6
.0-3
.3-6
. 6 - 15
. 15 - 30
. 30 - 45
.
45
8
0
0
43
0
0
51
0
7
10
34
0
51
0
5
17
29
0
0
51
0.157
0.000
0.000
0.843
0.000
0.000
1.000
0.000
0.137
0.196
0.667
0.000
1.000
0.000
0.098
0.333
0.569
0.000
0.000
1.000
0
0
21
0
0
0.000
0.000
0.412
0.000
0.000
1
25
0
0.020
0.490
0.000
4
0
0.078
0.000
0
0.000
0
0
51
0.000
0.000
1.000
.
.
.
.
.
.
.
.
4.
.
.
.
.
.
,
76
2.5
–
(
–
)
–
,
.
,
,
:
.
.
.
,
.
.
,
: 1)
; 2)
,
;
–
3)
,
; 4)
; 5)
,
;
6)
.
–
(
351
2
(
2
238,5
-
).
. 2.7).
,
[153].
–
.
.
,
.
77
. 2.7.
,
.
,
,
:
,
, –
,
.
.
,
.
,
:
-
;
-
;
;
78
-
,
;
-
;
-
;
-
,
.
[153].
(
(
. 2.5).
)
:
(
) (
. 2.8).
- 1837.7
,
,
80 - 85%
.
.
95%.
1140.8
.
,
.
,
,
,
,
,
,
.
2.5
,o
,
(
),
22.5
12.6
27.2
o
-
o
(
(
),
-
268
108
),
18.7
), o
38.3
),
82.1
),
, 4.2
,
,
,
,%
82.6
1
1837.7
1140.8
82.8
79
. 2.8.
15
1989
2003
(
)
,
,
.
.
,
.
,
,
,
,
.
.
,
.
[153].
.
,
,
,
.
SPOT5 (
2,5 ),
,
,
1:50.000,
(
. 2.9).
:
80
. 2.9.
-
(
).
,
47,35%
-
(
,
;
,
,
).
2,47%
;
-
,
.
10,73%
-
.
;
6.40%,
.
.
,
20%.
[153].
,
.
,
(
[180].
. 2.10).
,
. 2.11).
.
(436
),
- 10,80
81
. 2.10.
[64]
. 2.11.
(
)
;
[153].
–
(
.
)
:
;
;
82
(
),
.
[134] (
-
. 2.12):
(C-P3 bs),
,
;
-
(P3 bc),
(J1-2 hc),
(N2 tg),
,
;
-
(T3n-r hg),
;
-
,
(Q),
,
,
,
.
. 2.12.
.
,
,
83
.
,
,
,
.
.
:
,
-
;
,
,
.
,
,
.
–2÷6
(
. 2.13).
. 2.13.
,
,
[293].
. 2.6
,
84
2.6
(kg/cm2)
1
Si Al Fe,
Fe Si Al, Si Al
T3n-r hg
2
P2 bc
3
Si Al
N2 tg
(
0.23 0.52
0.39 0.42
0.50 0.75
Si Al ,Si Al Fe
o
)
,
o
32 - 34
.
,
19º - 22º
o
.
o
11 - 28
,
4
0.04 0.86
(Q)
,
6o - 29o
,
,
.
,
5
0.08 0.18
(Q)
,
2o - 12o
.
[153].
,
,
.
,
[134]:
-
;
-
;
-
;
-
;
-
;
-
.
.
.
[153].
,
,
,
[180].
–
,
,
.
,
,
(
. 2.14),
.
,
,
85
,
,
.
. 2.14.
(
)
.
,
–
–
.
1988
= 4,8
M
H = 15
20
.
= 6,1
6,5
,
.
,
[153].
:
;
;
.
(
)
(
).
.
,
.
–
,
86
[153].
,
.
51
(
. 2.15).
. 2.15.
.
(
)
:
-
3
(> 1000
) -
,
(
).
-
.
. 2.16).
-
(100 - 1000
3
),
,
.
,
(
-
(<100
3
. 2.17).
),
,
.
,
(
. 2.18).
87
. 2.16.
. 2.17.
. 2.18.
88
:
,
,
,
,
,
.
[106].
,
[209].
.
SINMAP [151]
SINMAP
:
-
(digital elevation model - DEM);
-
;
(
,
);
-
;
-
(
)
( 1989
- (
2003
).
),
), C
= (Cr + Cs)/(h rs g) (
)
T/R (
R–
,
; T –
)
(SI)
. 2.7.
2.7.
, C
T/R
«
»
(kg/m3)
T3n-r hg
Q
1982
1846
«
(o)
15.2 30.3
6.5 29.3
»
C
0.011
0.010
T/R
0.340
0.260
SINMAP
,
.2.8.
527 2494
1212 2813
89
2.8
SI
- Stable
- Moderately Stable
- Quasi-stable
- Lower Threshold (
-
SI > 1.5
1.25 < SI 1.5
1.0 < SI 1.25
0.5 < SI 1.0
)
- Upper Threshold (
0.0 < SI
0.5
)
(SI)
(
. 2.19).
,
,
:
- 0.0 < SI
0.5;
,
SI -
(0.5 < SI
(1.0 < SI
1.0)
1.25).
(0.0 < SI
0.5)
(0.5 < SI
1.0)
(
)
. 2.19.
(
.
–
SINMAP)
90
SI.
,
,
,
.
SMORPH [152]
SINMAP,
(SMORPH).
,
,
,
.
,
,
,
«
,
»
.2.9.
,
,
,
.
"
".
:
-
;
-
;
-
.
2.9
SMORPH
(
<15%
1 < -0.5
-0.5 <=
2<= 0.5
3 > 0.5
<= 24%
-
)
<= 47%
<= 70%
-
-
> 70%
-
-
-
-
91
,
,
SMORPH (
. 2.20),
.
.
. 2.20.
(
–
SMORPH)
,
:
-
,
.
4.5%
.
,
.
5.5%
.
,
.
,
.
92
-
.
90%
.
,
(
)
.
.
-
.
8
(
MSK-64).
.
,
.
,
[51]:
=
ah –
g–
=
=
(2.27)
=
(2.28)
, av –
, kh
,W–
,
kv –
.
.
,
.
[152]
,
SMORPH.
,
.
,
[136],
,
,
6.2 (
.
6
. 4 «
»).
«
»
8
,
. 2.10.
-
93
2.10
SMORPH
-
8
(
<= 3%
1 < -0.5
-0.5 <=
-
<= 26%
<= 49%
-
-
2<= 0.5
)
> 49%
-
-
-
3 > 0.5
-
8
MSK 64,
SMORPH
. 2.21.
. 2.21.
–
(
SMORPH)
8
,
:
94
–
,
,
3%,
49%.
11,8%
.
–
,
26%)
(
19,6%
49%)
(
.
.
–
,
(
(
68,6%
49%)
26%)
.
.
,
,
49%.
. 2.21.
-
8
,
,
.
SMORPH,
8
MSK 64
.
11,8%
19,6%.
,
95
[151]
SINMAP
SMORPH,
.
H.
(
,
)
.
"
-
".
:
–
.
–
.
.
H
(
:
. 2.22).
(
= 0.600 - 0.800).
.
,
,
,
.
,
.
,
,
,
.
96
. 2.22.
–
,
(
).
(
).
.
(
= 0.400 - 0.600).
,
:
,
,
,
.
.
,
,
,
,
,
.
(
,
= 0 - 0.400).
,
97
,
,
-
.
,
(
)
),
(
,
)
(
.
,
,
.
:
,
,
,
.
,
,
.
(
),
.
,
,
:
.
.
.
,
.
,
.
-
,
,
.
:
(
)
98
1.
,
,
,
,
.
2.
SINMAP
,
,
3.
.
SMORPH
,
(
,
).
.
4.
-
.
.
-
8
MSK 64.
,
8
,
MSK 64
,
-
.
5.
,
,
.
,
.
,
.
6.
,
,
.
99
3
3.1
,
.
,
.
[209]:
(
,
,
)
;
,
,
.
:
;
-
(
),
.
,
(
,
,
,
.)
.
[165], [267]:
;
;
.
3.2
[205].
100
[220]
[137].
.
,
,
,
,
,
.
3.3
,
,
.
.
,
,
,
.
[226].
.
1848 .
.
.
[168] "
,
,
".
)
(
,
,
,
,
.
[171]:
,
.
:
)
;
)
,
;
)
;
)
;
101
)
,
,
.
(
),
(
)
(
).
,
,
,
mL
:
L / L = mL ,
L
(3.1)
L -
.
,
(
)
,
,
,
m:
/
=m .
(3.2)
-
.
,
m :
=m .
(3.3)
-
.
,
(mL = L /L )
(
=
),
(
= ),
.
(
),
.
,
=
,
,
n,
mL.
,
mL = L / L = 1/100
100
..
,
(100
,
mL = 1/100)
,
,
102
.
1932
.
.
[212]
«
».
[212]
,
,
,
,
.
,
.
,
.
0,4—0,5
n
500
.
20
.
,
,
.
.
,
.
,
,
,
.
,
,
.
=
,
,
,
,
.
,
1936 .
. . .
[274],
.
[174]
,
,
.
,
.
103
,
,
.
,
.
.
,
,
(
) [267].
,
.
.
,
,
,
[171].
,
,
.
,
,
,
.
,
,
.
,
,
,
,
. .
,
,
.
).
[274]
,
,
104
,
.
,
,
,
,
.
.
.
,
,
,
.
,
.
,
.
[146].
,
.
[274],
,
.
.
[252].
70
.
,
1/ 2>10).
.
,
.
,
.
,
(
,
,
)
,
.
.
.
[146]
.
(
)
,
.
.
1941
[254].
105
,
(
. 3.1)
[274]:
3.1.
.
+
=0
+
=
=
=
=
=
1
1
=
=
=
=0
=
1
=
=
1
=
,
:
:
:…
=
:
:…
,
(3.4)
106
:
:…
=
:
:…
(3.5)
,
:
=
(
(
)×
(3.6)
)×
,
,
,
,
,
.
,
,
.
,
,
,
.
,
.
[274]
-
.
,
.
,
,
.
.
,
.
,
.
,
,
.
[267].
107
3.4
,
,
.
,
,
.
,
,
,
.
:
.
,
,
.
(
)
250
,
[272].
1773
:
= tg +c ,
,
-
(3.7)
-
,
-
,
.
,
.
1820 .,
[215]
,
.
.
,
1857
,
.
,
,
.
,
XIX
,
.
,
XX
(
XIX
40-
.).
,
.
,
.
,
.
,
.
.
(1903) [230]
,
,
,
.
(Resal) [243]
1910
,
.
108
,
,
:
.
.
(Frontard)
,
,
.
.
(1920),
.
,
.
(1925)
(1938)
.
.
(1927)
.
(1934),
.
.
(1939) [230].
«
,
»
,
(
)
,
,
.
«
»
,
,
,
,
:
(
0)).
,
,
.
:
,
,
,
,
).
,
.
.
,
,
1936 .
(1937) [285].
,
,
.
.
109
20
.
1916
,
,
,
.
(1936)
,
[51].
,
.
,
.
1950
(1954) [48]
(1955) [7]
.
,
1960-
,
,
,
,
.
.
(1965) [62]
,
(1967) [77].
,
.
,
.
.
[105],
.
:
.
[124],
[186],
[280],
.
.
[192],
[252],
.
[253],
[288]
.
.
[99],
[135],
.
.
[179],
[241],
.
[285],
.
.
[286],
[157].
(
–
)
,
,
,
.
:
;
(
);
[34].
1980-
,
,
.
,
110
.
,
,
.
,
,
.
,
,
,
.
.
.
(1977) [28] ,
.
.
(1971) [52].
.
.
1970
(GLE)
[30].
.
PC-
SLOPE,
1977
,
Geo-Slope.
.
,
90-
.
1997
SoilVision,
,
.
.
2007
SoilVision.
,
Geo-Slope
SoilVision
.
2003
.
.
«
».
-
,
,
,
.
,
,
,
.
,
(
(
) PLAXIS
) FLAC-Slope.
,
PHASE2 ,
111
:
,
.
.
.
:
;
.
:
;
(
)
:
;
;
.
250
.
:
:
XVIII
XIX
—
;
:
XIX
XX
—
(
;
:
1950
70-
. —
;
:
.
1970
—
),
(
40-
.)
112
4
4.1
.
,
.
200)
.
,
.
[270].
.
.
.
.
,
[252],
.
[253]
.
.
[130]
:
(
),
(
),
(
,
,
,
),
(
).
.
,
,
,
,
.
.
–
–
[204]
(
.
)
:
–
.
:
113
–
,
,
,
.
–
,
,
.
–
,
.
–
,
,
.
.
.
[281]
,
,
,
,
,
.
,
,
.
.
.
.
[246]
.
,
-
.
«
,
.
»
.
,
(
-
)
;
.
(1967
.
)
[283].
.
. [279] , Abramson, L.W. [1], Gitirana G. [35], Coggan,
J.S, Stead et al. [16].
Coggan
(1998) (
. 4.1)
Gitirana, 2005 (
. 4.1).
114
4.1
(Coggan et al., 1998,
[16])
,
,
Kulhawy(1969)
Kopaszy (1970)
Revillaand Castillo (1977)
Baker and Garber(1978)
Fellenius (1936)
Bishop's simplified (1955)
Zienklewlcz etal. (1975)
Janbu's simplified (1954)
Janbu's generalised (1956)
Lowe-Karafiath
Corps of Engineers
Spencer (1967)
Morgenstern-Prlce (1965)
Sarma(1973)
GLE (Fredlund. 1981)
. 4.1 .
Adikarl-Cummlns (1985)
Beuptrup-Levell(1980)
Celesti no-Dun can (1981)
Nguyen (1985)
Arai-Tagyo(1985)
Chen-Shae(19e8)
Greco (1996)
Kim and Lee (1997)
Baker (1980)
Yamagami-Ueta(1989)
Gitirana, 2005 [35].
.
115
,
.
,
[9]:
=
S–
(4.1)
.
,
,
:
K
,
c
cr
–
tan
n tan
n
,
,
(4.2)
r
n–
;
r–
,
r,
.
Phi-reduction (
c),
PLAXIS
.
:
=
=
(4.3)
.
,
.
.
,
.
,
:
M
F
F
.
(4.4)
.
.
[263].
116
,
.
(
,
)
.
,
,
.
,
.
.
,
,
,
.
.
,
:
;
;
;
;
;
,
(
. 4.2).
,
,
.
.
4.2
.
.
),
Fp [185].
(
),
.
(
,
n,
:
n=
(4.5)
. 4.3)
117
. 4.2 .
,
118
:
tg
p
tg
2
,
, ;
,
= tg +
(4.6)
;
-
; z-
,
-
,
3
;
-
;
.
. 4.3.
Fp
Fp
[119].
,
,
Z
:
+
(4.7)
Zi
cp
.
.
.
,
,
.
,
119
.
,
(
).
.
,
,
.
.
[186],
F
,
.
,
,
,
.
,
,
.
,
4.3
.
[248].
,
,
(Limit Equilibrium Methods – LEM).
–
.
.
(
. 4.4).
.
.
,
: )
(«
»
,
); )
.
,
: 1)
2)
.
,
,
,
,
.
120
. 4.4.
:
–
[112].
,
(
1936 .)
.
1937 .
[156].
.
.
)
(
.
[81], [239],
,
.
.
–
,
[240], .
,
.
. [283].
,
r(
. 4.5).
,
,
,
-
.,
. 4.5).
. 4.5
[283].
121
.=
(4.8),
ao —
,
(
.)
:
.=
–
;
–
);
.
:
.=
.
(4.10)
ao o = r
.
,
,
k,
.
.
[81],
,
,
,
.
.
,
.
:
=
./
.
(4.12)
.
.
,
.
,
,
(
. 4.6)
,
[51]:
,
,
,
.
,
122
. 4.6.
,
[51].
.4.2
,
,
[51].
4.2
,
.
**
**
,
(
. 4.2),
[7].
(
,
).
,
,
,
123
.
,
,
.4.7.
. 4.7.
[51].
(
)
:
=
–
; W –
(
)
(4.12),
;
;
–
;
–
-
;
-
.
,
,
.
(
,
).
,
(
. 4.3)
(1954) [48],
[84],
(Lowe-Karafiath) [58].
,
:
.
[48].
[7]
,
,
.
.4.8.
,
,
124
. 4.8.
[51].
,
,
,
,
,
.
,
.
[182],
.
[84],
[58],
[119]
.
,
(
.).
,
.
,
,
,
.
,
,
,
(
,
,
[68]).
[84].
,
.
,
.
[58]
,
,
(
(
)
).
,
,
.
,
.
[288],
,
.
125
,
,
,
(4.13):
=
(4.13)
,
:
[119].
(
[77],
[68]
. 4.2)
[62].
(GLE)
1970 [28], [29].
,
.4.2.
GLE
.
(Fm),
–
(Ff).
(1965).
. 4.9
,
,
.
4.9.
[51].
.
:
:
)=
)×
(4.14)
126
:
× ×
( )=
’ ;N; , R, x, f, d,
×
; ’ ,
(
× )×
×
×
(4.15)
; u;W-
-
;
;D-
-
.
,
,
:
=
,
f( )
(4.16)
–
;X;
E
X;
(x) –
E
X
.
.
,
(1978) [51]
,
,
«…
,
».
: «
».
,
,
.
,
,
.
[192],
,
.
,
:
,
,
.
,
:
= 0;
=0;
=0;
=0;
= 0;
= 0;
=0;
=L;
(4.17a)
(4.17b)
,
[157]:
Ey=Ex*tg
(4.17c)
127
;
-
-
;
;L–
,
–
.
,
,
,
.
K
:
K=
= c |c
(4.18)
c -
,
c -
.
. 4.10.
. 4.10.
[51]
,
.
,
Fredlund
Krahn
1977 . [28] (
. 4.11).
. 4.3.
,
,
5%,
,
,
[51],
,
128
.
,
,
5%.
15
,
1.665
Unit Weight
(kN/m3)
Strength Type
Upper Soil Layer
15
Mohr-Coulomb
5
20
Lower Soil Layer
18
Mohr-Coulomb
10
25
Color
Cohesion Phi
(kPa)
(deg)
-2.5
0
2.5
5
7.5
10
12.5
Material Name
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
27.5
30
32.5
35
37.5
40
. 4.11
.
Lowe-Karafiath
1,66
1,66
1,55
1,67
1,68
1,67
1
0.99
0.99
0.93
1.01
1.01
1.01
.1
( - )
(
)
.2
.
1,66
-
.
4.3
,
,
.
,
.
.
.
,
.
(
,
)
,
,
.
129
4.4
,
,
.
LAM (Limit analysis method).
,
LAM,
,
,
,
.
(
) [91].
.
,
LAM,
,
,
.
:
1.
;
2.
.
,
)
.
,
,
,
.
,
,
,
.
,
.
,
,
,
.
,
,
.
,
130
,
,
Druker [21]
Chen [15],
.
,
,
LAM
,
.
.
.
.
1962 .
.
[232]
,
,
,
[119].
,
,
,
(
. 4.12).
.
[232]
,
u.
,
,
,
,
,
,
.
S,
,
:
S = u /cos i.
. 4.12.
(4.19)
.
.
131
[119],
:
,
.
)
:
A
= SdQ = (u /cos ) Psin dx;
A
= u Ptg dx;
(4.20)
A = - SdR = - (u /cos )(Pcos
A = -u (Ptg
tg dx + c(dx/cos );
+ c/cos2 )dx.
(4.21)
,
,
,
,
K
,
.
:
KA
+A =0
(4.22)
K
.
,
:
=
/
×
=
)
(4.23)
×
(
),
:
A
i
= (u /cos i)(Picos itg
i
+ cili) = u (Pitg
i
+ cili/cos i),
(4.24)
:
A
i
= (u /cos i)(Pisin
i
+ Q i) = u (Pitg
i
+ Q i/cos i).
(4.25)
:
=
,
,
=
(4.26)
:
132
1969 .
=
.
,
(4.27)
[123]
.
,
,
,
,
.
,
,
(
,
,
,
),
,
,
,
,
.
,
,
.
,
.
,
,
,
.
,
,
,
,
.
,
,
.
"
"
.
.
,
.
,
.
,
–
,
,
«
,
.
,
.
.
DLO (Discontinuity layout optimization)
.
(
.
[76].
)
DLO
,
»
133
.
,
DLO
.
[76],
. 4.13.
.
(
LimitState GEO)
.
,
Fredlund
(
Krahn
1977 . [28]).
. 4.14.
)
. 4.13.
DLO
. 4.14.
.
(
= 1.7)
,
134
,
,
5%,
.
,
.
,
,
.
.
.
,
.
.
,
,
.
.
.
1942 .
. .
[231]
[122]
.
,
,
,
,
.
,
.
:
{(
=
—
,
2
)
}
1
(4.28)
-
.
:
(4.29)
135
:
=
=0),
+1
×
(4.30)
(
,
.
,
:
= ( +2
(4.32)
2 )
= +1
;
=
(4.31)
(4.32)
:
=2
(4.33)
(
)
.
—
:
=
(
)
(4.34)
,
.
,
,
,
,
,
,
.
.
,
,
,
.
. .
.
,
,
.
[97], [96].
[154].
=f(x).
: f(x)
,
const
± .
=f(x)
: f’(x), f’’(x)
=f(x).
.
.
(
f’(x)
)
,
136
,
= (x, y) = const; g –
.
[197]:
sxy
sxx
x
0,
y
syx
syy
x
y
mxz
x
syx sxy
g,
myz
(4.35)
0,
y
:
yx
sin
sin
zx
sin
xx
yy
cos
cos
0,
0,
zy
cos
0.
xy
(4.36)
arctgf ' ( x ) –
.
s
f’(x)
s (x, y) ,
(x, f (x)) –
«
»
.
,
.
m
m(x, y) ,
,
( x , f ( x ))
(
)
.
.
s yx ,
sxy
»,
«
– 0=0.
(4.35)
,
(4.36)
,
,
–
,
3
6
.
(4.35) – (4.36)
.
(
),
,
.
(4.35) – (4.36),
.
»,
.
–
.
137
».
([97], [96], [155], [223]).
,
(4.35)
m.
s
,
(4.36)
,
(4.36),
(4.35).
,
,
,
,
.
«
,
,
,
».
.
(4.35) – (4.36)
.
s
s
(4.37)
s
(4.35) s
s
».
(4.35)
[126].
(4.35).
(4.35).
:
s
s
s
s
s
s
(4.38)
.
,
«
ds
dx
g
dD
dx
»:
gf ' (x) .
(4.39)
,
s
f’(x) 0,
,
«
»
± ,
-
.
.
.
»
,
(4.36)
.
138
,
.
sp
0, m
0,
sp
0, m
0,
-
.
±
(4.40)
.
,
(4.41)
,
«
»,
sp
m.
.
[197]:
sxxp
s yxp
y
U
y
y
U
x
x
y
mzx
U
x
U( x, y) ,
, sxyp
, s yyp
, mzy
x
U
y
x
x
U
x
y
y
,
(4.42)
.
.
(4.43)
[197], [227].
( x, y)
.
(4.48)
(4.43) –
[188], [197], [227].
[188]
,
»
. «
[227].
(4.45) – (4.46) «
,
(
,
.)» [227].
[227]
«
»,
.
.
.
,
.
.
(«
,
,
[96], [129], [150].
»
:
S=S(x, y), N=N(x,y),
»),
[97],
139
S
dx
x
N
dx
x
dS
dN
,
S
dy,
y
N
dy.
y
(4.44)
(4.47)
[110],
,
,
:
S
x
N
,
y
S
y
N
.
x
(4.45)
,
.
,
,
«
,
».
.
[129], [150], [216].
S
y=f(x).
S
,
dS
dx 2 dy2
1
,
y'x 2 dx .
( ,
x+dx, y+dy:
N
,
) = (S, N)
,
z=z(x)
N
y=y(x): y’x z’x=-1.
[121], [126], [155], [223].
,
,
(4.36)
[97], [197], [227]:
S
U
y
x
S
U
x
y
N
(4.46)
0,
(4.47)
N 0
0.
N 0
0,
N 0
(4.48)
140
,
(4.35)-(4.36)
(4.49)-(4.51).
,
:
(S , N )
U
1
ln(S 2
2
U (S , N )
«
N2) ,
arctg
(4.49)
S
.
N
(4.50)
»
,
.
,
,
,
–
.
(4.50)-(4.51)
.
,
.
«
».
.
,
[110]
2
2
S2
N2
2
U
S2
0,
(4.51)
0.
(4.52)
S, N:
2
U
N2
.
:
S
, sin
R
S 2 N 2 , cos
R
N
,
R
(4.53)
.
S
N
U
S
cos
,
2
2
N S
N
R
sin
U
N
.
2
2
S
S
N
R
,
(4.56)
,
R=R(x,y)=0
(
(«
(4.54)
= (x,y)=0.
)
»).
,
(4.43):
141
=
s xxr
sin 2(
R2
)
sxyr
cos 2(
R2
)
s ryx
cos 2(
R2
)
s ryy
sin 2(
R2
)
)
R
sin(
)
R
cos(
sin
.
(4.55)
cos
.
(4.56)
)
R
cos(
)
R
)–
(s )
sin(
sin
cos
y=f(x)
d (arctgyx ' )
,
dS
d
dS
.
(4.57)
.
(4.58)
[110], [121], [155]:
d
dN
(N )
d (arctgzx ' )
dN
(4.45)
(4.59)
(4.52)-(4.53),
«
»
S, N,
, .
(4.58)-(4.67),
1/R2,
,
s
–
1/R.
,
(
R
)
.
,
R,
«
»
.
,
[129], [150],
[259]
[216]
.
(4.35)-(4.36).
2
S/ x2 ,
–
2
N / y2
2
S/ x y ,
2
.
N/ x y
.
,
(
.
,
).
,
[150], [210].
,
.
142
(4.56)-(4.59).
, 2 2–
.
s
s
cos
R
sin
R
2
sxyp syxp
2
:
,
(4.60)
.
.
,
1/R2.
1/R,
,
,
.
.
sp
,
, sp
: s
sp
,
=0,
,
,
,
d2f(x)/dx2=0.
,
,
s xx s yy / 2 ,
.
s
=0
,
,
.
,
,
.
,
.
J2
s xs
s s
1
R4
sin
R3
.
:
(4.61)
,
.
,
,
,
(
)
,
.
,
:
1.
,
,
[155].
2.
(4.35)
(4.56)-(4.59).
,
.
143
3.
(
)
,
:s
,
,
,
s .
.
4.
»,
.
5.
(
–
),
,
.
,
6.
.
(4.56)-(4.59)
,
,
.
,
.
(
(
,
,
)
),
sxx-syy
(
sxy+syx=0.
,
)
,
,
«
»,
.
(
,
)
sxx-
syy
,
.
,
,
,
.
"
,
"
,
,
.
(
).
, "
"
.
,
.
"
"
"
,
,
144
,
.
.
"
"
(
6)
.
.
.
,
.
,
,
,
.
.
,
,
,
,
,
,
.
,
,
.
.
.
.
.
,
.
,
,
.
,
,
,
,
.
,
.
,
.
,
.
,
,
,
. [166], [178], [267].
,
.
,
,
.
145
,
[166], [178], [177].
,
,
x, y, z
(
. 4.15).
,
,
.
(
)
,
,
)-
.
x,
x,
y,
z,
yz,
xy,
yx,
zx;
,
y, -
,
-
zy
xz.
,
(4.62):
(4.62)
,
,
,
,
,
.
. 4.15.
,
,
(57).
146
[267],
,
:
)
(4.63):
xy
x
x
xz
y
y
z
xy
y
yz
x
z
z
z
x
0
Y
0
(4.63)
yz
xz
X
0
Z
y
X, Y, Z -
.
)
.
,
(
-
)
(
)
.
: x, y, xy = yx
),
:
x
xy
v
,
y
(4.64)
1 u v
;
2 y x
(4.65)
u
,
x
yx
y
u, v, -
.
x
y
x
y,
.
xy = yx
,
.
(4.64-4.65)
.
(
,
)
(4.64):
,
147
2
2
y
x
2
y
x
2
2
2
xy
x y
-
;
(4.66)
(
).
,
(4.66)
,
v
u
x
, . .
y.
.
,
,
.
)
.
(
,
. 4.62 -4.73)
,
,
,
.
[177]
,
,
,
.
.
Kn, Mn
.
,
Ln ,
,
(4.67):
x
cos (n,x) +
xy
cos (n,y) +
xz
cos (n,z) = Ln
xy
cos (n,x) +
y
cos (n,y) +
yz
cos (n,z) = Kn
xz
cos (n,x) +
yz
cos (n,y) +
z
cos (n,z) = Mn
(4.67)
Ln, Kn, Mn
n
,
n;
.
u*, v*, w*.
.
(4.68):
u=u*, v=v* , w=w*
(4.68)
.
,
.
(4.67),
,
,
,-
(4.68).
,
148
,
,
,
,
.
.
«
(
, BEM) -
»,
[172].
,
,
.
.
,
.
,
,
.
.
.
,
,
,
.
.
,
,
,
,
(
).
,
,
,
. [95],
[125],
. [101],
. [162],
:
. [114],
. [191],
.
. [193],
.
,
[108], [109],
[173],
,
[172],
.
, .
II,
[102],
[127]
.
,
.
(
, FDM)
.
,
-
.
.
149
)
,
;
.
,
.
,
.
,
.
[111], [120], [141], [167], [211], [225]
.,
.
,
,
,
,
,
FLAC (Itasca, 2001).
(
FLAC-Slope)
.
Fredlund
(
Krahn [28]).
. 4.16
,
4.17
,
.
. 4.18.
. 4.16.
,
.
150
. 4.17.
.
. 4.18.
,
.
(
=1.61)
,
,
,
5%.
,
,
151
,
.
.
(
, FEM)
.
,
,
-
.
,
[267].
.
,
.
,
.
, .
,
,
50-
[118].
1970
.
,
,
,
,
,
,
,
.
(
,
,
.
,
[118], [238], [250],
[139], [221], [249], [287]).
,
,
,
.
(
)
.
,
,
(
).
.
(
)
,
.
:
,
;
;
,
.
152
,
.
,
,
.
,
,
(
).
,
,
.
.
,
. 4.19
.
,
.
,
,
.
,
.
,
,
,
.
,
. 4.19.
.
,
[264].
-
153
,
(4.69)
=
+
(4.70):
cos 2 +
cos 2
sin 2
sin 2
(4.69)
(4.70)
:
= +
(4.71)
.
,
=
,
(
,
)
(4.72):
(4.72)
,
.
.
Phase2
PLAXIS.
,
,
.
(
.
.4.1)
-
PLAXIS,
(
[28]).
–
Phase2.
,
Fredlund
. 4.20-4.21
Krahn
.
,
,
,
,
(Plaxis)=1,616,
(Phaxe2)=1.62)
.
c
,
,
,
5%.
.
,
Phase2 (
.
. 4.21),
154
[274],
,
(
.
,
,
(
)
,
,
,
.
.4.20.
.4.21.
PLAXIS,
.
Phase2,
.
)
155
,
,
,
.
,
.
.
,
,
.
- DDA
(Discontinuous Deformation Analysis),
method),
- DEM (Discrete element
(distinct element method)
(DDA) -
.
,
,
[72],
[71].
.
DDA
,
,
,
,
.
.
.
.
(
)
.
,
. 4.22.
. 4.22.
UC Berkeley DDA for Windows)
156
[73].
(DEM) (Discrete element method DEM)
.
(Cundall, Strack, 1979 [17])
.
[86],
,
,
DEM
(FEM).
[66].
DEM
(generalized discrete element
method),
Williams et al., 1985 [86]
element method),
(distinct
Cundall, Strack, 1979 [17].
,
,
.
. DEM-
c
.
,
,
.
,
,
.
,
.
.
,
.
,
,
.
.
, DEM,
.
,
,
,
,
.
UDEC (Itasca, 2001).
.4.23
(DEM) [57].
157
. 4.23.
(DEM) [57]
(distinct element method) [82].
,
(
. 4.24).
(
.
1.
"
")
:
"
"
Kn,c, Ks,c
(Fn)
(Fs)
.
.
,
.
-
,
"
"
.
2.
"
"
( n)
,
( s)
.
Kn,p, Ks,p.
,
,
,
.
. 4.24.
[82].
158
PFC2D (Itasca LTD).
Costa Stend (
. 4.25
) [18]
.
. 4.25.
Costa Stend (
[18]
)
[171].
—
,
,
.
1948 .
,
,
1
,
0.
. 4.26).
,
«
».
,
.
.
159
:
;
,
;
;
.
.4.26.
(a)
(d) –
, (b)
, (e) – 16
, (c)
,
.
,
:
{0,1,2 …
N-
( + 1)
n
( )|
,
1, }
( )
(4.73)
:
(4.74),
.
:
(4.75)
(Serge, Deangeli, 1995) [171].
. 4.27.
160
,
,
:
()
, r –
()
()
, w–
, g –
( )+
, s –
()
(4.76),
.
,
(
,
,
).
.4.27.
.
. 4.28.
.4.28
60 60, (Serge,
Deangeli, 1995) [171]
161
.
.
,
.
,
.
,
.
.
1969 Kulhawy [53]
«
».
:
,
.
,
,
.
,
y
.
xy
.
. 4.29.
. 4.29. .
Kulhawy.
"
"
[51].
,
,
,
.
FEM- DEM
.
,
.
.
162
,
ELFEN (Rockflied Software, 2001),
,
.4.30 (Stead, Coggan, 2006 [79]).
.4.30.
,
ELFEN (Stead, Coggan, 2006) [79]
–
(
).
,
,
,
.
,
.
,
MCA
.
4.5
,
,
[279].
,
.
,
.
,
:
163
.
X
i
—
i-
n,
:
=
(4.77)
.
,
:
[ ]=
(4.78)
:
[ ]
=
—
(4.79)
.
,
.
.
,
,
( )=
:
×
(4.80)
:
=
,
,
(4.81)
S
,
.
,
( ),
:
=
(4.82)
fp,
:
p
–
=
(4.83)
(p),
.
–
164
p=0 (
= 1).
,
,
,
fp = 0,5.
,
,
p
0(
1),
,
(fp),
,
0,0
1,0.
4.6
,
Xie Mowen, et.al. [88], [64],
.
. 4.30.
,
,
.
.
3DSlopeGIS,
.
,
.
. 4.30.
[64].
165
,
.
,
[194],
,
.
,
,
:
)
,
,
(
)
,
,
(
)
;
)
.
–
;
)
–
,
)
GRID (
,
,
;
)
,
h,
,
S
,
(
. 4.31),
:
×
×
× ×
× ×
(4.84)
×
=
,
×
(4.85)
:
(4.86)
,
,
,
,
166
,
.
. 4.31.
.
(
)
.
,
,
,
,
.
,
[116],
,
(
.
5. 3D
).
4.7
,
.
.
[132]:
(
90
)
;
,
(
)
.
,
,
.
,
:
167
c –
(
(
(
),
),
)
(4.87)
–
,
-
(
–
).
.
,
,
. [253],
.,
.,
. [215]
. [204],
. [131],
.
,
.
,
,
.
.
,
Turner A. K.
.
Schuster, R.L., [83], Giani G.P., [33], Hoek
Bray [42].
-
,
.
,
.
,
.
1 ( .1.3),
,
:
(
. 4.32)
,
«
»(
. 4.33).
.
(
. 4.34):
20-25
.
20-25
;
-
,
;
168
.
. 4.32
. 4.33.
,
«
. 4.34
»
.
.
,
.
.
:
(
(
. 4.36).
. 4.35.)
169
oc
oc
f
p
oc
oc
f
fpfpp-
p
oc
p =ocf 200
p
f
p
p
N
0
20
0
20
p
p
f
oc
p
oc
f
. 4.34.
.
,
.
,
(FS)
:
. 4.35-4.36,
,
:
=
–
( 2); W –
(
);
( 2); U –
(4.88)
(
( );
).
-
–
3
); V –
(
(
);
–
);
–
170
. 4.35.
-
. 4.36.
(4.88)
:
( = 0):
=
(4.89)
(U=V=0)
=
(a =0):
(4.90)
171
(c=0) ,
(U=V=0)
(a =0):
=
(4.91)
1,
.
,
«
»
.
,
«
».
«
»
:
;
.
;
-
,
.
,
.
,
.
,
,
.
,
Markland’s [42].
. 4.37
.
.
,
.
,
«
»,
,
,
.
,
,
)
,
.
. 4.38.
172
oc
f
oc
i
a
oc
faoc
bfabioc
ioc
b
a
b
a
b
i
f
oc
oc
pi= f
i
f
i
N
a
oc
a
b
i
oc
i
f
oc
f
oc
b
. 4.37.
«
».
–
,
.
173
H
)
)
. 4.38.
.
),
. 4.38,
(FS)
,
:
(
=
);
:
×
–
r
× )+
+
–
(
( ); X,Y,
+
×
3
);
w
×
(4.92)
(
–
3
(
–
); H –
.
(4.92)
:
:
=
(
×
+
× )
(4.93)
(c=0) ,
:
(4.94)
),
. 4.38,
(FS),
.
,
Rocscience Inc.
);
Swedge
174
:
,
,
,
,
.
,
.
,
,
.
,
.
,
:
;
;
,
,
,
;
;
;
,
.
.
,
,
.
,
175
5
3D
5.1
[25], [258].
,
,
.
«
»
,
,
.
2D
.
.
60
,
3D
.
(SoilVisionSystems, Inc.
), TAGAsoft, Inc. (
Research, Inc. (
), Itasca International, Inc. (
)
), O.Hungr Geotechnical
.)
.
,
GEO-SLOPE International, Inc. (
)
Rocscience, Inc. (
.
,
)
3D[258].
,
,
.
,
,
.
,
[144]:
,
(
)
.
.
,
,
,
.
,
,
,
176
,
,
,
,
,
.
,
(
,
,
).
.
,
,
(
),
.
,
SVSlope® Elite 3D.
,
,
.
,
,
60
.
.
(
)
.
.
.
,
.
,
:
,
1987
S.Cavounidis [11]
,
,
.
,
.
,
,
.
,
177
,
,
,
,
.
,
,
,
.
:
,
,
[2].
3D
,
.
.
5.2
,
(Anagnosti).
1969
[3]
.
[63],
.
,
.
,
50%.
,
,
,
,
.
,
,
,
,
.
(Hovland).
,
[44],
.
.
,
,
,
,
.
.
.
,
178
.
. 5.1.
. 5.1.
,
.( )-
,( )–
,( )-
[44].
,
,
X
Z-
(
,
).
.
,
),
:
Z
=
YZ
[
(
)
]
(5.1)
Z
Z :
(5.2)
cos(
)= 1+
(5.3)
(5.4)
,
.
,
,
179
.
,
,
,
,
,
,
,
.
(Chen)
Chen R.H.
.
Chen and Chameau.
Chameau [14]
,
,
,
[77]:
. 5.2.
,
,
. 5.3.
. 5.2.
. 5.3.
. [13]
.
:
180
-
;
,
,
;
;
-
;
-
«
»
1;
.
R.H.Chen (1981) [13]
,
-
:
;
;
;
-
.
(Hungr). Hungr
1987
[46]
,
[7],
:
-
,
,
;
-
.
N,
(
. 5.4)
.
1989 [45]
.
,
.
,
–
,
,
,
.
181
. 5.4.
,
[46].
. (Duncan J.M.) [22]
,
,
.
,
,
[44],
Chen
,
Chameau [14],
,
.
,
,
,
,
,
.
5.3
,
,
,
,
(FLAC3D (Itasca, 2001))
(PLAXIS3D),
,
.
. 5.5.
PLAXIS.
182
(sliding body)
-
,
(
-
).
(
-
) [89].
.
.
-
[187]
[181].
. 5.5.
5.4
(
)
[89]
3D
[25], [258]
,
SVSlope 3D,
SoilVisionSystems, Ltd (
,
).
. 5.6.
,
,
. 5.1.
:
-
,
-
,
,
;
,
;
-
,
,
.
«
» (Entry and Exit).
. 5.7
. 5.8.
183
. 5.2
. 5.9
. 5.10.
.
5.1
,
.
(kPa)
1
80
25
(kH/m3)
20
2
60
35
20
. 5.6.
)
(
–
).
. 5.7.
.
184
. 5.8.
(
).
FOS = 1.272
Calculation Method: Spencer’s
Search Method: Entry and Exit
FOS: 1.272
Total Mass: 2.250E+004 kPa
Total Volume: 1.125E+003 m^3
Total Activating Moment: 2.104E+006 kNm
Total Resisting Moment: 2.676E+006 kNm
Total Activating Force: 1.078E+004 kN
Total Resisting Force: 1.372E+004 kN
100
80
60
Y (m)
40
20
0
-14
-22
0
20
40
60
80
100
120
140
160
X (m)
. 5.9.
2D
(
)
185
Calculation Method: Spencer’s
Search Method: Entry and Exit
FOS: 1.339
Total Mass: 2.837E+006 kPa
Total Volume: 1.419E+005 m^3
Total Activating Moment: 1.558E+008 kNm
Total Resisting Moment: 2.086E+008 kNm
Total Activating Force: 1.303E+006 kN
Total Resisting Force: 1.741E+006 kN
Total Active Columns: 270
Total Sliding Surface Area: 1.22E+04 m^2
Center Point: X: 115.895 Y: 150.000 Z: 119.477
FOS = 1.339
90
80
70
60
50
40
30
20
10
0
-22
0
20
40
60
80
100
120
140
160
X (m)
. 5 10.
3D
2D
(
)
5.2
3D
3D
2D
2D
1.34
1.27
1.05
3D/2D
1.29
1.25
1.03
1.25
1.22
1.03
:
-
,
,
,
;
,
.
,
.
(A.W. Skempton) [75]
,
,
186
,
:
(3D)=1.05×
(3D),
(2D)
(5.5)
(2D) –
,
3D
2D
.
(5.5)
,
5%.
.
.
-
,
,
-
20-30% [78], [34].
,
,
[271]:
,
.
. 5.11
3D
«Grid and Radius».
,
,
,
Exit»
«Entry and
. 5.12).
90
80
70
60
50
Z (m) 40
FOS = 0.858
30
20
10
0
-22
0
20
40
60
80
100
120
140
160
X (m)
. 5.11.
(
: 3D
2D
– «Grid and Radius»),
(
).
187
. 5.12.
(
– «Entry and Exit»),
(
).
,
,
.
,
,
,
,
.
,
,
,
[62]:
X = E× ×f(x)
(5.6)
f(x) –
,
;
.; ,
–
, .
,
,
f(x)
,
,
,
,
.
,
2D
–
188
3D
,
.
:
,
,
,
,
.
,
.
,
,
:
,
.
:
,
.
(
)
.
;
,
,
,
,
.
2D
,
3D
.
-
.
,
,
,
,
.
189
6
6.1
.
,
,
,
[271]:
;
;
;
;
;
.
(
)(
)
.
.
.
,
.
.
(
.
[176]).
(Greco V.R., [38]; Malkawi, Hassan and Sarma,
[60]),
,
,
.
[51].
:
(Greco);
(SA);
.
190
,
,
.
6.2
,
,
(
)
,
[236].
,
,
,
,
,
,
,
.
,
,
,
,
(
)
.
,
.
.
,
.
,
,
,
.
,
= 1,5
= 0,5,
= 1,2
( ),
,
= 0,1.
[51]:
191
-
K
=
–
(6.1)
(K ).
,
,
( )
.
K,
[51].
. 6.1
( )
.
. 6.1.
.
,
.
,
. 6.1
. 6.2
.
6.1
,
(
)
( )
50
30
20
10
(%)
74.65
89,11
91,7
95,55
99,2
100
192
. 6.2.
(%)
,
,
,
.
,
,
,
.
.
,
,
,
,
,
,
.
,
.
,
,
.
,
:
.
(
)
.
,
.
193
(
).
.
«
»
«
» [236].
,
.
.
[218], [200]
,
.
,
,
.
,
(
,
)
.
,
.
,
,
(
)
.
6.3
,
,
[119].
,
.
:
,
,
,
,
;
;
.
(
[282],
.
.
.
[276]
.).
.
[217],
[189],
.
.
[239],
[274],
,
.
., [119],
194
.
,
,
,
.
,
,
,
,
.
,
,
,
,
,
.
,
.
,
,
[32].
.
(
)
[119].
,
:
,
,
,
.
,
,
.
[284] -
(
)
.
[274].
40.
,
.
1953
.
[229],
,
,
,
.
,
.
:
195
;
;
(
,
)
.
,
[274],
,
:
-
,
,
;
-
,
,
:
1)
;
2)
,
,
.
,
.
,
:
u ) tg
(
; –
c
,u–
.
;
[279]: c-f
(c-f
(6.2)
su
-
; –
.
)
.
,
:
1.
.
,
[51].
:
.
,
(
. 6.3).
:
196
: u-
;
w
=
-
(6.3)
×
; h; Hu -
.
a
h
. 6.3.
.
Hu,
0
(
1,
: Hu=0
); Hu=1
.
,
, Hu
1,
(
).
2.
Ru,
1960 . [8],
:
Ru=u/ h
u–
;
(6.4)
-
;h–
.
:
u = Ru h
(6.5)
Ru
,
[8].
,
Ru
,
.
3.
-bar,
1954 . [74],
.
,
( u)
(
v):
u= B
v
(6.6)
197
(su
)
(
) [279].
,
0.
,
,
0.
,
,
( -u)
(6.2)
0
.
(6.2),
,
,
,
c-f
=
,
su
:
c-f
– u=0,
»
(
su
– u= ,
);
=0.
,
, u=1/2 , tg
«
»
[259].
,
,
-
.
,
,
.
.
1923 . [274].
,
.
,
,
.
.
[184].
.
,
,
,
.
-
,
.
,
198
,
,
,
,
.
(
).
(
)
[183]:
=
–
× ×
, l –
(6.7)
, I –
.
,
,
)
(
).
.
,
,
-
[274], [165].
,
,
,
,
.
,
–
(
) –
.
,
,
.
,
,
.
,
,
—
.
,
,
,
,
199
.
,
,
—
.
6.4
,
.
.
,
,
,
[233]:
=
: jo -
+
(6.8)
; m-
,
,
.
:
;
;
.
:
-
;
-
.
[283], [165]
,
.
,
,
,
.
.
,
,
( )
,
.6.2 [152].
–
) [152].
(
–
200
6.2
,
MSK 64
0,05
3
0,1
6
0,2
12
0,4
24
,
Fp
[233]:
(
=
: Fps -
; =
; Ps -
= (1 + ); P -
)+
(6.9)
2; -
-
,
;
=
-
; .
:
,
,
. 6.3;
-
(P),
(6.9),
( )
,
,
.
6.3
0,05
3
0,1
6
0,2
12
0,4
24
201
.
,
[51]:
F =
W=k
F =
ah –
, g –
W=k
W
W
(6.10)
(6.11)
, av –
, W –
, kh
kv –
.
,
[160].
(
)
MSK-64,
,
,
.
(
)
.
12-
MSK-64
,
. 6.4:
6.4
(
MSK-64)
(
6
7
8
9
10
0,05
0,1
0,2
0,4
0,8
MSK-64)
(
)
(
, g)
,
—
V/H (Vertical / Horizontal)
.
,
.
.
,
[143].
,
202
,
,
,
V/H
.
V/H
,
(V/H=2/3)
(
,
: 2/3, 1/2, 0.
,
. .11.
10-249-98),
(V/H=1/2) -
2000
(
,
.3.5
-5-006-87 ),
(V/H=0) (
.
.2.2-2.4
II-7-81).
,
1,
,
II-7-81*),
5
14.13330-2011 (
1,0 (
,
,
),
.
.
.
,
.
,
A` =
1×
.
[160]
.
Eurocode [24]
:
k = 0.5
a
k = ±0.33 k
–
)
(6.12)
(6.13)
(
, S –
, g –
.
,
.
,
7
.
Fredlund
Krahn [28],
. 6.5
. 6.4-6.6.
,
203
6.5.
.
1,41
.
1,38
1,38
,
,
,
.
. 6.4.
. 6.5
204
. 6.6.
.
.
,
.
[265]
[51]:
[K] {d} + [D] {v} + [ ] {a} = {F)
: d–
;v–
; ]–
;a–
(6.14)
; [K] –
; {F} –
; [D] –
.
[65].
,
,
,
.
,
,
,
,
.
.
.
,
,
,
,
,
.
205
[257]:
(
),
,
;
(
) .
,
,
.
.
,
.
ac,
[37]:
:
(
=
-
–
×
×
(
) ×
× ×
);
× ×
×
(6.15)
-
, -
(
3); m
,
,
-
, z –
( ).
,
[190], [115], [161].
,
.
[292],
Q.
,
Qcr
,
1300
2- .
(Q > Qa)
.
0,5
t05
×
,
,
,
:
.
(6.16)
(6.16),
[98],
[90],
.
206
,
CSR (Cyclic
Stress Ratio),
,
CRR (Cyclic Resistance Ratio).
,
FS (Factor of Safety),
FS=CRR/CSR,
.
,
,
,
15
.
CSR
,
.
,
[190]:
:
=
g —
×
= 0.65
,
g;
vo
×
×
(6.17)
(g = 9,81
2);
ma
—
—
; ’vo —
,
,
;
av,
—
ma
;rd —
.
CRR
.
,
.
,
,
[51].
,
–
-
,
.
,
.
6.5
,
.
:
207
(
),
(
)
(
) [103].
,
.
:
,
;
,
.
(
)
:
;
;
;
Cam-clay.
.
,
.
,
(
6.7).
. 6.7.
( ),
(v).
[32]:
=(
)(
)
0
0
0
0
0
0
(6.18)
z
.
208
,
v
,
0.5,
(1 – v)
(1 – 2v)/2
v.
,
,
.
,
,
(1 – 2v)
E/[(1 + v)(1 – 2v)]
.
,
,
0.5.
,
(v)
,
,
. 6.6.
6.6
-
E
v
c
.
.
,
,
,
.
–
.
.
,
.
.
«
» [43].
,
,
[43], [56]:
ci
–
;
mi –
(
:
GSI –
,
,
,
:
,
,
.);
,
.);
209
D–
.
( i, mi, GSI, D)
–
.
[43]:
, ’1
a –
+
=
’3 –
+s
,
(6.19)
ci
–
, mb ,s
,
:
=
(6.20)
= +
(6.22)
=
(6.21)
.
L
n
L
Lmin
Lmax.
,
k
= Lmax / Lmin
[267].
:
(
.
)
.
(
),
.
,
.
,
,
,
,
,
[267]:
x = a11 x + a12 y + a13 z + a14 yz + a15 xz + a16 xy ,
y = a21 x + a22 y + .................................... + a26 xy ,
(6.23):
xy = a61 x + a62 y + .................................... + a66 xy .
36
-
.
210
,
,
,
,
,
,
.
.
,
:
(n= ),
.
,
,
,
,
,
.
,
-
.
(
. 6.8).
:
': Ex’, vx’
': E
’,
'
': G ’, v
’.
[67]:
1<
<1
>0
>2
(6.24)
(6.25)
(6.26)
. 6.8.
[32].
[C']
[10]:
211
[ ]=
0 0 0
:
0
0
0
(6.27),
=
(6.28)
=
(6.29)
(1 +
=
=
+
=
)
(6.30)
(6.31)
(6.32)
=1
(6.33)
=
(6.34)
=
(6.35)
=
(6.36)
=
(6.37)
=
,
(6.38)
,
0,
(
)
(
)
) [267],
[C']
.
x'-y'
.
[C']
[C]
[94]:
:
[ ] = [ ][ ][ ]
cos
sin
[ ]=
0
sin cos
sin
cos
0
sin cos
(6.39)
2sin cos
0
0 2sin cos
1
0
0 cos
sin
(6.40)
212
,
,
.6.7.
6.7
Ex
x'
,
Vx
(
x')
Ey
'
,
Vxy
(
x'),
(
y')
Gxy
.
.
,
[23],
,
.
,
.
,
-
-
t
. 6.9.
,
ur
(
-
. 6.9).
[32].
i,
213
[23]
,
i
,
:
:
i
=
=
;
);
3
(6.41)
,
=
=
3;
KL =
(
; n =
,
.
n
(6.41)
,
½.
,
[23],
,
,
:
i
3,
–
1
3)
:
(
=
-
, (
(
)
, Et , Rf -
)(
)
(6.42)
,
-
,
;
1.0,
0.75
1-
,
3-
.
(6.42)
,
–
(
).
.
,
,
1.0.
(6.42)
:
=
(1)
Et
Rf - 0.8,
(6.43)
Rf.
Et
,
0.04 Ei
Et
,
4%
,
Ei.
,
(Pa).
.
–
( i)
.
( 3 < 0),
Et
[23]
10%
:
(
) =
-
(
)
(6.44)
[32].
214
,
1
–
3)ult,
,
-
.
1
–
3 )f
–
.
,
:
(
)
(
)
Rf
sin
cos
(6.45)
,
:
(
)
(
)
sin
cos
–
(6.46)
.
. 6.10 [32].
,
,
,
,
,
.
,
.
. 6.10.
-
.
,
[41].
,
:
{
{
}={
}={
}+{
}
(6.47)
}+{
}
(6.48)
215
,
(
.
e)
,
:
} = [ ]{
{
} = [ ]({
{
,
}
}
{
(6.49)
})
(6.50)
.
,
:
=
,
,
,
(6.51)
(6.51)
:
=
,
+
+
+
{
=
}
(6.52)
:
(6.53)
,
F < 0,
.
,
:
{
=
}=0
=
: G -
(6.54)
:
(6.55)
;
-
.
(6.55)
(6.50)
:
{
} = [ ]{
{
},
[ ]
}
(6.56)
,
, :
=
[
[
]
]
{
}
(6.57)
:
:
{
} = ([ ]
{
}
(6.58)
216
=
[
]
[
[
]
]
(6.59)
, [ ],
F
G.
,
,
. F= G.
,
.
.
.
1
3
F
,
:
F
3
1
3
1
sin
2c cos
(6.60)
:
(
-
,u–
; –
u ) tg
(6.61)
c
;
-
; –
.
. 6.11.
. 6.11.
,
,
. 6.8.
6.8
E
v
c
217
,
,
.
,
-
-
w –
.
.
[183]
);
:
(
)
(
(
-
).
.
0,
.
:
tg
cc
(6.62)
:
tg
w
w
cc
w
(6.63)
w
.
:
tg
w
w
(6.64)
:
w
(6.65)
(6.65),
0.
.
.
[51].
. 6.12
.
(
)
218
,
,
[51].
. 6.12.
.
,
,
,
Phi2
(computed)
.
-
.
[51].
,
.
,
,
),
,
. 6.13.
. 6.13.
.
,
[279],
su
.
219
Cam-clay.
Cam-clay
. 6.14).
[5],
[10].
. 6.14.
Cam-clay.
Cam-clay
.
(').
. 6.15 ( )
.
. 6.15 ( ).
Cam-clay
. 6.9:
. 6.16.
p' – q
,
.
( ),
.
( )
,
=
:
(6.66)
(v),
),
: v = 1 + e.
. 6.15.
( )
( )
Cam-clay
220
6.9
Cam-clay
M
p' – q
p'=1.0 (
ln(p')=0)
V
. 6.16.
Cam-clay.
(
)
Cam-clay
. 6.17),
p'
=
: p’x =
1
q [5]:
(6.67)
p'
t.
. 6.17.
Cam-clay
221
,
, p’ ,
p’x,
:
– 1
=
p'
q
2.7183
(6.68)
(6.69)
,
,
:
,
=
=
(6.70)
,
:
=
. 6.18.
=
(6.71)
, J2,
+
+(
:
,
)
(6.72)
.
. 6.18.
(
) Cam-clay.
222
:
.
:
;
;
;
.
,
,
.
.
,
.
,
,
,
–
.
,
,
.
,
(
)
.
(
).
223
:
;
;
.
.
,
,
,
.
,
,
,
,
,
,
,
.
,
,
.
,
,
:
,
.
.
,
.
,
–
-
,
.
,
.
,
.
:
,
;
,
.
,
(
)
.
.
224
7
7.1
:
;
;
.
:
-
,
,
(
,
)
,
;
;
-
;
-
.
(
-
)
:
;
-
;
-
;
-
;
-
;
-
;
-
;
-
;
-
.
.
.
,
,
,
.
225
.
.
,
,
,
,
,
, ,
,
,
,
[267], [143].
(
)
,
,
.
:
.
.
.
:
,
,
,
,
,
-
,
,
.
:
a)
;
b)
.
)
,
,
,
.
b)
,
,
.
,
)
(
)
(
);
,
I
,
.
:
.
226
).
.
(
)
,
(
),
.
,
,
.
,
,
:
-
(
,
,
,
»
.);
-
:
(
,
,
.),
,
,
),
,
(
«
»
);
-
(
,
,
,
.);
E
( , ,
v)
;
-
(
,
),
(
),
-
;
(
);
-
(
(
,
,
.);
,
.)
,
227
-
(
);
-
(
)
.
,
:
-
,
,
,
,
(
);
-
,
;
-
,
;
-
–
(
),
(
),
(
);
-
(
)
.
,
,
(
)
,
(
,
)
.
,
.
,
,
.
,
,
.
228
:
)
;
)
(
)
)
;
(
);
)
(
)
)
;
(
)
(
)
;
)
(
)
(
)
;
)
;
)
(
)
;
)
(
)
(
)
;
)
(
)
(
)
.
,
,
.
)
(
).
(
,
,
.)
,
. 7.1.
229
7.1
)
<1,0
1,0-1,2
1,2-1,5
>1,5
(
)
1,5,
.
7.2
.
.
(
.
.
(
II»,
).
U-
30
«
.
15 .
. 7.1).
(Greco)
(SA).
.
,
,
. 7.2.
,
,
:«
».
230
. 7.1.
.
,
,
«
. 7.2.-
2».
. 7.5.
. 7.3.
7.2
,
.
.
(kN/m3)
(kPa)
11w
18.5
1
4
15w
19.3
15
12
23
18.9
1
32
28
19.9
10
35
29
21.2
11
31
231
1.312
. 7.2.
(
)
,
).
1.233
. 7.3.
(
(
)
),
(
).
232
1.237
. 7.4.
(
)
(
),
(
25
Maximum
Shear Strain
5.00e-005
).
Critical SRF: 1.21
20
5.95e-004
1.14e-003
15
1.68e-003
2.23e-003
10
2.78e-003
3.32e-003
5.50e-003
5
3.86e-003
4.41e-003
0
4.96e-003
-5
0
5
10
15
20
25
30
35
40
45
50
55
. 7.5.
60
,
.
233
7.3
(
1
2
,
)
1,31
1,32
1,27
1,08
1,23
1,22
1,18
1,02
1,21
3
,
1/ 2
(
1,24
1,23
1,19
1,06
1,08
1,075
1,02
. 7.3)
:
,
(
,
>1.2).
,
(
10%,
<1.2).
—
30%
[263].
,
,
,
.
,
,
,
-
.
,
.
,
—
)
(
) [271].
234
7.3
,
.
,
– «
-2» (
. 7.6).
«
-1»
2004
-1» [271], [236].
. 7.6.
.
:1–
,3–
,2–
«
–
1», 4 –
,6–
,5
.
,
.
:
;
-
–
(
(
)
);
),
(
235
-
,
,
;
;
-
,
(
,
);
-
.
.
,
.
1 ( )
. 7.7. (
2 ( )).
1( )
(
.
2( )
. 7.8.
. 7.4)
,
.
. 7.8,
,
(
)
(
>1),
ó
(
,
=2,75)
,
,
.
,
1
,
.
.
,
2
,
.
1,
2(
<1)
7%.
?
,
,
,
(
3
),
,
?
236
. . 7.7.
1( )
2( )
. 7.8.
1( )
2( )
7.4
*
,
)
1
2
*
1,29
2,75
1,08
0,11
–
K
1,58
7,38
; K
;
–
5,01
1,47
f k, %
0,00
6,97
–
; fk –
.
,
,
[236].
,
,
,
237
,
,
.
,
,
,
.
,
.
,
,
,
,
.
.
,
–
,
(
) –
.
,
,
.
,
,
(
)
,
.
,
,
,
,
,
,
,
,
.
. 7.5,
,
,
,
,
.
,
,
.
238
7.5
,
:
(
> 10 %
–
5 – 10 %
>5%
5 – 10 %
1–5%
>1%
1–5%
0–1%
. 7.5)
.
,
.
7.4
.
2
1200
«
»-
:«
«
-
» [261].
.
30 ,
.
210 ,
8°.
,
. 7.9).
-
200 200
,
,
(
. 7.10).
,
,
.
,
,
,
,
.
(
)
:
;
. 7.6.
,
239
-
,
(
).
. 7.9.
. 7.10.
2(
.
2(
).
.
).
240
7.6
(kN/m3)
(kN/m2)
4
18.3
Mohr-Coulomb
17
7
34
17.6
Mohr-Coulomb
7
6
34
17.7
Mohr-Coulomb
21
10
10
19
Mohr-Coulomb
16
20
13c
17.8
Mohr-Coulomb
21
10
.
. 7.11
,
. 7.12.
,
. 7.7.
. 7.13
. 7.14
.
( - )
–
7.7
1
,
,
2
)
)
1,16
1,17
1,14
1,015
1,02
0,99
)
80
100
241
34
34
-20
0
20
40
60
4
0
20
40
60
80
100
120
140
160
. 7.11.
180
200
220
240
(
).
260
280
100
242
80
1.015
1.015
34
60
34
-20
0
20
40
4
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
. 7.12.
(
).
–
(
)
,
–
.
:
243
(
. 7.7)
-
(
),
,
(
2
–
,
).
0,6
,
.
.
0.004
)
G(
.
,
0,5
,
6
MSK 64.
. 7.13.
. 7.14.
.
.
244
7.5
.
,
,
:
-
;
-
;
-
su
)
,
.
,
(
)
,
.
.
,
(
)
(
1
= 10-5
2=10
-10
).
,
,
. 7.15. -
,,
. 7.18.
. 7.8.
7.8
.
1,89
(
)
0,616
0,921
(
10-5
1=
)
0,835
2=10-10
)
100
245
0
20
40
60
80
1.891
0
20
40
60
80
100
120
140
160
180
200
220
240
. 7.15.
.
–
,
. 7.6.
260
280
80
100
246
Pore Pressure
Safety
Factor
[kPa] 0.000
-20.000
0.500
20.000
1.000
60.000
1.500
100.000
2.000
140.000
2.500
180.000
0.921
60
3.000
220.000
3.500
260.000
4.000
300.000
40
4.500
340.000
5.000
380.000
5.500
420.000
-20
0
20
6.000+
460.000
0
20
40
60
80
100
120
140
160
180
200
220
240
260
. 7.16.
(
-5
1=10
).
-
.
280
80
100
247
Pore Pressure
Safety
Factor
[kPa] 0.000
0.000
0.500
40.000
1.000
80.000
1.500
120.000
2.000
160.000
2.500
200.000
0.835
60
3.000
240.000
3.500
280.000
4.000
320.000
40
4.500
360.000
5.000
400.000
5.500
440.000
-20
0
20
6.000+
480.000
0
20
40
60
80
100
120
140
160
180
200
220
240
260
. 7.17.
(
2=10-10
).
.
280
248
0
20
40
60
80
100
120
0.616
0
20
40
60
80
100
120
140
160
180
. 7.18.
(su
).
–
,
. 7.6.
200
220
240
260
280
249
(
. 7.8)
:
,
.
,
,
,
.
,
,
.
,
,
,
.
,
.
,
,
.
su
(
)
,
,
.
= 0,616
,
.
,
,
,
.
7.6
.
.
,
)(
,
.
(
. 7.19) [257].
,
.
–
.
250
.
.
,
.
.
.
(0.5 ).
.
6
22
,
.
. 7.20.
,
,
. 7.9.
7.9
,
,
.
3
(
)
(
)
(
[42]
(http://www.rocscience.com).
)
,
,
2.04
27.02
21.71
26.85
1.94
1.98
2.00
1.97
2.00
2.05
2.10
13.41
17.43
21.59
18.54
24.35
28.23
30.46
9.41
20.61
20.63
11.64
19.89
21.92
24.03
17.49
17.25
12.80
19.86
30.24
23.63
13.70
2.28
46.86
2.46
64
2.16
35.00
26.53
10.55
2.33
46.86
2.46
64
2.53
583.66
12.8
575
RockLab
251
. 7.19.
.
,
.
.
252
. 7.20.
.
253
:
-
;
-
;
-
.
,
,
.
.
. 7.21,
. 7.23
. 7.22 ,
. 7.24.
. 7.10.
-
7.10
1
1.773
1.788
1.719
2
2.583
2.47
2.375
3
2.263
2.216
2.115
1.6
.
s=6.9, Mw=6.8,
=5
),
29.04.1991 .
,
.
Akhalkalaki (
– 115
).
,
. 7.25.
,
,
. 7.24
. 7.26.
254
2.583
2.263
1.773
0
100
200
300
400
500
. 7.21.
600
700
(
)
800
255
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
0
100
200
300
400
500
(x
. 7.22.
)
600
700
800
900
256
Maximum
Shear Strain
4.80e-001
Critical SRF: 1.6
4.48e-001
4.16e-001
3.84e-001
3.52e-001
3.20e-001
2.88e-001
2.56e-001
2.24e-001
1.92e-001
1.60e-001
1.28e-001
9.60e-002
6.40e-002
3.20e-002
0.00e+000
0
100
7.23.
200
300
400
,
500
600
700
800
.
257
. 7.24.
. 7.25.
. 7.26.
. 7.27,
. 7.28.,
. 7.29.
258
)
1.587
0
100
200
300
400
500
600
700
800
)
. 7.27. )
.
,
–
; )
,
.
–
,
–
.
259
. 7.28.
. 7.29.
.
.
:
8
(
MSK 64,
g)
:
– 0.2g;
- -0.1g.
. 7.30,
. 7.31,
. 7.32.
. 7.11.
260
0.822
0.827
0.2
0.1
1.162
1.247
0.608
0.603
0
100
200
300
400
500
600
700
. 7.30.
800
(
8
)
261
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0
100
200
300
400
500
(x
. 7.31.
)
600
700
800
900
262
Maximum
Shear Strain
3.60e+000
Critical SRF: 0.58
3.36e+000
3.12e+000
2.88e+000
0.2
2.64e+000
2.40e+000
2.16e+000
0.1
1.92e+000
1.68e+000
1.44e+000
1.20e+000
9.60e-001
7.20e-001
4.80e-001
2.40e-001
0.00e+000
0
100
. 7.32
200
300
400
500
600
,
8
700
800
263
-
7.11
1
0.603
0.608
0.579
2
1.247
1.162
1.113
3
0.827
0.822
0.794
0.58
,
.
[271].
. 7.33
. 7.34.
. 7.33.
( )
,
).
(
).
264
. 7.34.
( )
,
( ).
,
,
,
.
,
,
.
,
,
,
.
,
:
,
.
(
(
750 ,
40 )
500
(
. 7.21).
(
310 ).
750 ).
,
,
.
,
265
.
,
.
,
.
«
»(
7.19)
,
.
(
– 0.2g;
- -0.1g.)
,
.
(
. 7.31).
40 )
500
(
780 ,
210 ),
.
(
780 ).
,
.
,
,
,
.
,
:
,
,
.
,
,
,
,
.
,
.
40 .
266
7.7
,
,
,
,
,
,
,
.
(
,
,
.).
,
-
,
.
,
,
.
,
,
-
,
,
.
,
,
,
,
,
.
,
,
.
,
,
,
.
,
,
,
,
,
,
[267].
,
,
,
.
,
.
[143].
–
267
,
,
,
-
[267].
(
)
.
,
.
)
-
(
)
(
,
.
,
(
,
),
[143].
,
,
,
,
.
,
(
),
[143]:
- I
–
(
)
- II
;
-
(
).
(
,
,
,
,
, II
)
–
.
,
,
.
II
,
(
)
(
),
.
II
(
,
.
)
268
(II
)
.
,
(I
),
,
.
(I
)
,
,
[51].
(
2
c = chcos
=
2
hcos
2
+ cvsin
(7.1)
2
+
vsin
–
, ):
(7.2)
;
h
v
(
)
.
.
.
I
,
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