Deep Excavation Design
Transcript of Deep Excavation Design
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DEEPEXCAV
A SOFTWARE FOR ANALYSIS AND DESIGN OF RETAINING WALLS
THEORY MANUAL
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1 I 4
2 G A M 4
3 G 4
4 UD A 5
5 A P C L E P 5
5.1 A P L E P C
A
6
5.2 A P L E P PARATIE 7
5.3 P P E 10
5.4 C E P O 115.4.1 A & P P L G 11
5.4.2 P 1969 E P E 13
5.4.3 FHWA A E P 14
5.4.4 FHWA R A E P D
S M C
16
5.4.5 FHWA L S S P 16
5.4.6 M FHWA 19
5.4.7 V E S C FHWA A 23
5.4.8 C T P D 26
5.4.9 T S R P D 26
6 E 7 28
6.1 S P E 7 ( DM08) 29
6.2 A
EC7 .
31
6.3 D W P & N W P
A (C L E
A)
33
6.4 S 34
6.5 L L S 35
6.6 S S 38
6.7 O 3D 387 A E EC7 41
8 G A C C 60
9 G S F 67
9.1 I 67
9.1.1 I 67
9.1.2 C W ( ) 68
9.1.3 W
.
69
9.1.4 W (
)
69
9.2 C P & B S I 709.3 G 73
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10 H PE.L' . 75
11 W T S C C 76
12 S P O 80
12.1 S 81
12.2 D R 82
12.3 S T O 85
12.3.1 S 85
12.3.2 MO 86
12.3.3 R S 87
12.3.4 U 88
12.3.5 W A 8912.3.6 W M 90
12.4 W B 90
12.5 W I S E 91
12.6 V E 92
13 V 10
97
14 V 20 102
15 V 30 107
A A APPENDIX: V P P C
C
111
A B APPENDIX: S P I F G N
S P
115
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1. I
T DXP ,
, . T E 7
.
2. G A M
T DXP
(.. PARATIE
). A :
) C
) P
) C CP A: 1 C
. O , P
.
3. G
T :
) H: A P . I P,
100
.
) : A P . T 1D
. I P , P
.
) F F : A P . W
2D . I PARATIE,
UTAB . T
.
) : A P . W
. I PARATIE, UTAB
.
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I AAIE,
.
4. D A
C ( ). W
U
D.
I , U. H,
D/ A . T
D/U A O:
) D: A . I ,
φ
. F , PARATIE
(φ φ ) .
) : A . I ,
U S S φ
. F , PARATIE
U S S
(φ φ ),
.
) : O
(S ) ) . A
.
I AAIE,
.
5. A C L E
T A P
(P C). A
PARATIE U D D
R S. S 5.1 5.2
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/ C P . H,
T 1 .
1: A E A L E C
M
R Y N1 N
1 N Y N
1 N
1 N
C Y Y Y N Y Y Y Y
CK T N Y Y Y N
CK T N Y Y Y NL N Y Y Y Y
N:
1. R C
.
2. S .
5.1 A L E C A
I
. O ,
. I
. I
. H
. I
/
.
T
(..
, , .).
A K/K . T
.
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5.2 A L E AAIE
P 7.0 . H,
P 7.0 K/K ,
K/K ( ,
). I , P
K/K . T
, .
I SW K/K ( φ φ )
. T PARATIE K/K (T B ).
T
. O,
, K/K
S D D. I K K
F 1.
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Options 1 2 3
Default Ka, Kp = Rankine
(RECOMMENDED)
Default engine Ka/Kp (Butee) for zero
wall friction and horizontal ground gives
same numbers as Rankine
User defined Ka/Kp
that can include slope
and wall friction (NOT
RECOMMENDED)
Default KaBase, KpBase defined for each soil type
(Performed for each stage)
1. Default Option (YES) 2. No
SW automatically determines slope angle, wall friction, and other effects KaBase
Options: A. Enable Kp changes for seismic effects (Default = Yes) KpBase
B. Enable Ka/Kp changes for slope angle (Default = Yes)
C. Enable wall friction adjustments (Default = Yes)
For each stage then Options 1.1 and 1.2 are available:
Ka= Kabase x Ka(selected method, slope angle, wall friction)
Ka Rankine (i.e. ground slope =0, wall friction = 0)
Kp= Kpbase x Kp(selected method, slope angle, wall friction, EQ)
Kp Rankine (i.e. ground slope =0, wall friction = 0)
Ka= Ka(selected method, slope angle, wall friction)
Kp= Kp(selected method, slope angle, wall friction, EQ)
IMPORTANT LIMITATIONS
A) Ka/Kp for irregular surfaces is not computed and is treated as horizontal.
B) Seismic thrusts are not included in the default Ka calculations.
Sub option 1.2: Use Actual Ka/Kp as determined from Stage Methods and Equations
(see Table 1)
3. Examine material changes. The latest Material change property will always override the above equations.
Soil Type Dialog/Base Ka-Kp
Enable automatic readjustment of Ka/Kp for slope angle, wall friction etc?
Sub option 1.1: Prorate base Ka/Kp for slope and other effects (Default)
* . H,
) , ) % , )
.
F 1: K/K
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5.3 E
T
.
) R : T
. T
.
) C : T ,
, . T D
P G E, 3
E, . 430 :
W α= S ( )
= S =
= ( )
= , + ( )
θ= W (0 )
) L: A :
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W
A
) CK (T): R P .
5.4 C E
5.4.1 A & L G
O . T
DX (. 10 )
. DX . F
, DX R, C, CK
, ( ).
F , DX
. P :
) , , )
. T
. W
C
.
T . H,
( )
. T,
( ). H,
.
I . T
.
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S
.
Figure 2.1: Active force wedge search solution according to Coulomb.
Figure 2.2: Passive force wedge search solution according to Coulomb.
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5.4.2 1969 E E
A P (1969)
:
γ
F 2.3: A E , 1969
F ( ) DX . A D. P,
( ) . F
, DX "S" "S "
"S C" . N K DX . T
K ( ),
.
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5.4.3 FHA A E
T DX FHWA
(F H A). T FHWA
.
F 2.4: FHA
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TOTAL LOAD (N// ) = 3H2 6H
2 (H )
F 2.5: FHA.
I 2.4 2.5, :
. F : = 2 L / (H +H/3)
. F : = 2 L /2 H 2(H1 + H+1)/3)
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5.4.4 FHA A E D M C
T (.. N>4)
.
P
.
F ( ), TP
2.5
. F
:
W
. W N 6, 0.4.
O, 1.0 (P, 1969). U T P =0.4
N>6 .
I , H .
A N>6
1.0. I ,
(P).
T N>4 N
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T
. A
. T
. T :
E
. F
.
T , 1.3. A
.
D
F 2.4.
W ,
.
T T P (1967)
. O
. F N>6,
,
, . I
, H (1971) K
(
FHWA N>6):
W =1 H (1971). T :
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F 2.6: H
F 2.7 K H /H . F
S = S. T 4
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F 2.7: C
(FHA 2004).
F :
, .
FHA, ,
D. ,
.
B , ,
FHA .
5.4.6 M FHA
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O
. U,
. H,
. H,
.
I ,
. T
. I ,
. K (2010)
, ,
. T ,
.
I
, , ,
. A, , ,
50%
( F 2.8). A ,
.
I ,
. T
. I ,
.
T
FHWA P .
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F 2.8: M FHA ( ).
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Figure 2.9: Proposed modifications to stiff clay and FHWA apparent lateral earth
pressure diagrams (Konstantakos 2010).
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5.4.7 E C FHA A
A 10 2
. T 2, 5, 8 .
A :
C 1: F 0 10 , S = 50 P γ= 20 N/3
C 2: F 10 S = 30 P γ= 20 N/3
T =10 (
, .. )
F 2.10: FHA
T :
σ=20 N/3 10 =200 P
T :
FS= 5.7 30 P/ 200 P = 0.855 ( F. 2.10)
T H K (=1):
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T : P = 0.5 K σ H = 647 N/
T :
= 2 L /2 H 2(H1 + H+1)/3) = 2 647 N/ /2 10 2 (2 +2)/3= 74.65 P
T 74.3 P
.
T 3 74,3P = 222.9 N/ (
). W
. I
, 195 . I 100
200 .
N 30 .
F 2.11: FHA
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I , : P = 0.65 K σ H = 432.9 N/
T :
= 2 L /2 H 2(H1 + H+1)/3) = 2 432.9 N/ /2 10 2 (2 +2)/3= 49.95 P
T .
N, .
S: F 0 5 , φ = 30 γ= 20 N/3
C 1: F 5 10 , S = 50 P γ= 20 N/3
C 2: F 10 S = 30 P γ= 20 N/3
I , N=6.67. A H
. T .
F 0 5 S 1 :
F = 0.5 20 N/3 5 (30 ) 5 = 144.5 N/
T C 1 : 5 50 P = 250 N/
T : 250 N/ + 144.5 N/ = 395.5 N/
T :
S.= 395.5 N/ / 10 = 39.55 P
T H K (=1):
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T : P = 0.5 K σ H = 849 N/
T :
= 2 L /2 H 2(H1 + H+1)/3) = 2 647 N/ /2 10 2 (2 +2)/3= 98 P
T 99.2 P.
F 2.12: FHA
5.4.8 C D
W
. T 1.1 1.4
. T
.
5.4.9 D
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V , US,
. T
M1 M2 .
M1 M2 . U
. T
.
F 2.10: .
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5.4.10
6. E 7
I US S
R A E . E 7 (
, EC7) D
A (DA1, DA2, DA3) . I E 7
M ,
A , R
. H, A2 + M2 + R2
A, M, R. A
. H,
. I , EC7
6.1:
D A 1, C 1: A1 + M1 + R1
D A 1, C 2: A2 + M2 + R1
D A 2: A1* + M1 + R2
D A 3: A1* + A2
+ + M2 + R3
A1*
= F , A2+=
EQK ( EC8): M2 + R1
(T I DM08 DA11, DA12, EQK ).
I P ( 7 ),
L H. T L H
D S. E D S
B D S. W ,
B D S S C O (.,
E 7, DM08 ).
I E 7, :
) STR: S /
) GEO: G
) HYD: H
) UPL: U ( )
) EQU: E ( ?)
T STR, GEO, HYD E 7 . U, E 7
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. I
( P), E 7
. H,
. S
6.1 / .
6.1 E 7 ( DM08)
T 2
EC72008. A DM08. T 4
/ (.. C 1 M1, C
2 M2).
2.1: L E 7
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γ .3.2 1.00 1.25 1.25
' γ 1.00 1.25 1.25
γ 1.00 1.40 1.4
() γ .3.1 1.50 1.30 1
() γ
.3.
130 1.35 1.00 1
() γ .3.1 0.00 0.00 1
() γ
.3.
130 1.00 1.00 1
0.00 0.00 1
γ
.3.3.4 1.10 1.10 1 1.1 1.1
γ
.12.
134 1.10 1.10 1 1.1 1.1
.. γ
.3.3.5 1.00 1.40 1 1
(
γ .3.1 1.35 1.00 1
(
)
γ .3.
130 1.00 1.00
γ .5 1.35
γ
.17.
136 0.90
γ .4 1.10
γ .15.
136 0.90
γ .3 1.35 1.00 1
1.00 1.00 1 1 1
.4 .
130
2.2: L DM 2008
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*
γ .3.2 1.00 1.25 1.25
' γ 1.00 1.25 1.25
γ 1.00 1.40 1.4
() γ .3.1 1.50 1.30 1
() γ
.3.
130 1.30 1.00 1
()
γ .3.1 0.00 0.00 1
() γ
.3.
130 1.00 1.00 1
0.00 0.00 1
γ
.3.3.4 1.10 1.10 1.10 1.1
γ
.12.
134 1.20 1.20 1.20 1.2
.. γ
.3.3.5 1.00 1.40 1
( γ .3.1 1.30 1.00 1
(
)
γ .3.
130 1.00 1.00
γ .5 1.35
γ
.17.
136 0.90
γ .4 1.10
γ .15.
136 0.90
γ .3 1.30 1.00 1
1.00 1.00 1
.4 .
130
6.2 A EC7 .
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F 3
. I ,
.
(, , )
"
&
5.1 5.2
.
11 1
. , ,
, ,
. .
. .
( 1 7, 0)
/
. . .
F 3: C K K .
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6.3 D & A
(C L E A)
T EC7
. I , .
1 (D):
I , . S,
F_WDR
. T . H,
:
W = (WW) F_WDR
2: ( .)
I , . S,
F_WDR
. T
. H, :
W= W F_WDR W F_WRES
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6.4
T . S
PARATIE, ,
P E. T 3 .
3: A
S T
P/
T
(P/T)
E
P
E
E
C
A
C A
C
S L P & T N Y
T .
C H
V .
L P & T N Y S
W L L P & T N Y S
S S
SP & T Y Y S
W S
P & T Y Y S
A S
SP & T N Y
F (3D) P N Y
B (3D) P N Y
3D P L P & T N Y
V (3D) T N Y
A L (3D) P & T N Y
T .
V D .
M/R Y N
W EC7 ( DM08) , :
) I AAIE : I D
E ,
.
I L (F 4.1),
. .
) U P F_LP
1.0.
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) U T F_LV
0.
T . S
. I ,
. M
. H,
. W P'
P .
F 4.1: S P F 4.2: E
6.5 L L
L : ) P, ) P. I
, ,
. F ,
. T =2
. H, =1.5
.
F ( ,
),
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. T L/S F 4.2 . I
, .
F : W
, B P D, 1974, E 2.7
H S
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F , ,
B (T, 1954).
F : T M P
D, 1974, E 2.10 . 27
=(1)/
H S
F : T C
P D E 2.9
H S
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F : T M
E 2.11 . 27, P & D
H S
6.6
S
. H, . S
.
T
. T 50
. O ,
.
6.7 3D
T 3 . I ,
/ 3D .
F 3D , :
) B . I
.
) B 3D .
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F : T B .
R
.
T :
T :
W :
T, :
F : T M
P D, 1974 2.4., 2.4.
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6.8 L
W EC7,
. I ,
. H,
,
. I ,
1. U
1 1.5
( . ).
W ,
.
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7. A E EC7
A EC7
. T
:
R ( ) E. +200
M ( ) E. +191
W E. +195
W E. +191
W γ= 10N/3
S : γ= 20N/3, γ= 19N/
3, = 3 P, φ= 32 ,
E : E= 15000 P, E = 45000 P, = 1 , =0
K =3.225 (R), K= 0.307 (R)
U T = 150 P
U FS G= 1.5
T D: E E. +197,
H = 2
A = 30
P = 400 N (.. 200N/)
S P: 4 /1.375 ,T A = 5.94
2
S F = 1862 MP
F L = 9
F D D = 0.15
W D: S S AZ36, F = 355 MP
W . E. +200
W 18
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M I I = 82795.6 4/
S M S = 3600 3/
S: V
P 5P E. +200 ( )
P 0P E. +195
T F 4.1 4.4. F
:
R
C : A (F )
F : A 1.3, 0 P
25% H., A .
F .
W : S
F 5.1: I ( 0, D )
F 5.2: 1, E. +196.5 ( )
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F 5.3: 2, E. +197
F 5.4: 3, E. +191
T
F 5.
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Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 m
Apparent Eart h Pressure Factor: 1.3 ( times ac ti ve)
Eurocode Safety factors 1 1 1SOIL
UNIT
WEIGHT
DRY UNIT
WEIGHT
WATER UNIT
WEIGHT
WATER
TABLE
ELEV. φ Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m
32 0.307 3.255 3 195 22 0.1818
20 19 10 195 32.00 0.307 3.255 3.000
ELEV.
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
Acive
LATERAL
SOIL STRESS
Apparent
Earth
Pressures
TOTAL
LATERAL
STRESS
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
LATERAL
SOIL
STRESS
TOTAL
LATERAL
STRESS NET
(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0.00
199.43 10.82 0.00 10.82 0.00 -7.93 -7.93 -7.93
197.75 42.75 0.00 42.75 -9.81 -31.33 -31.33 -31.33
195 95 0 95 -25.86 -31.33 -31.33 -31.33
191 175 -32.7 142.3 -40.39 -31.33 -64.06 -64.06
191 175 -32.7 142.3 -40.39 -40.39 -73.12 0 0 0 10.82 10.82429 -62.3
182 355 -106.4 248.64 -73.07 -73.07 -179.43 180 106.4 73.64 250.48 356.84 177.4
Total active earth force above subgrade:
ΔFxFrom El. 200.00 to El. 199.43 0.0 kN/m
From El. 199.43 to El. 197.75 8.2 kN/m
From El. 197.75 to El. 195.00 49.1 kN/m
From El. 195.00 to El. 191.00 132.5 kN/m
Sum= 189.8 kN/m
Factored Forc 246.7
Max. Apparent Earth Pressure= 31.3 kPa
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
Modified for calculation/Strength Reductions
Hydraulic
travel length
Hydraulic loss
gradient i
WATER
TABLE
ELEV.
180
182
184
186
188
190
192
194
196
198
200
202
-200 -100 0 100 200 300 400
E L E V A T I O N ( m )
LATERAL STRESS (kPa)
LEFT LAT SOIL
LEFT WATER
LEFT TOTAL
RIGHT LAT SOILRIGHT WATER
RIGHT TOTAL
NET
F 6: C
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A F 6 , 31.3 P
31.4 P (F 7.1). A
( ).
F 7.1: A
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F 7.2:
F 7.3:
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F 7.4: ()
F 7.5: ( )
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F 7.6: (
).
F 7.7: ( )
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N, EC7 DA3 . H, EC7
. T .
F 8.1: G EC7 DA3 A
T :FS((φ)) = 1.25
FS() = 1.25
FS(S) = 1.5 ( )
FS(A ) = 1.3
FS(A)= 1.1
FS(W D)= 1.0
FS(D_E)= 1.0
N , DA3
F 8.2. A F 8.3 8.4 ,
F 8.2.
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Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 m
Apparent Eart h P ressure Fac tor: 1. 3 ( times ac ti ve)
Eurocode Safety factors 1.25 1 1.25
SOIL
UNIT
WEIGHT
DRY UNIT
WEIGHT
WATER UNIT
WEIGHT
WATER
TABLE
ELEV. φ Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m
32 0.307 3.255 3 195 22 0.1818 1 1 1
20 19 10 195 26.56 0.382 2.618 2.400
ELEV.
TOTAL
VERTICAL
STRESS
UNFACTORED
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
Acive
LATERAL
SOIL STRESS
Apparent
Earth
Pressures
TOTAL
LATERAL
STRESS
(factored
earth)
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
LATERAL
SOIL
STRESS
TOTAL
LATERAL
STRESS
Net water
pressure
(factored) NET(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0 0.00
199.59 7.77 0.00 7.77 0.00 -7.37 -7.37 0 -7.37
197.75 42.75 0.00 42.75 -13.37 -40.60 -40.60 0 -40.60
195 95 0 95 -33.33 -40.60 -40.60 0 -40.60
191 175 -32.7 142.3 -51.39 -40.60 -73.33 -32.73 -73.3
191 175 -32.7 142.3 -51.39 -51.39 -84.11 0 0 0 7.77 7.765837 -32.73 -76.3
182 355 -106.4 248.64 -92.02 -92.02 -198.39 180 106.4 73.64 200.51 306.88 0.00 108.5
Total active earth force above subgrade:
ΔFx
From El. 200.00 to El. 199.59 0.0 kN/m
From El. 199.59 to El. 197.75 12.3 kN/m
From El. 197.75 to El. 195.00 64.2 kN/m
From El. 195.00 to El. 191.00 169.4 kN/m
Sum= 245.9 kN/m
Factored Forc 319.7
Max . Apparent Eart h P ressure= 40. 60 kPa
Modified for calculation/St rength Reductions
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
WATER
TABLE
ELEV.
Hydraulic
travel length
Hydraulic loss
gradient i
Safety
factor on
net water
pressures
Safety
factor on
earth
pressures
Safety
factor on
Passive
Resistance
180
182
184
186
188
190
192
194
196
198
200
202
-300 -200 -100 0 100 200 300 400
E L E V A T I O N ( m )
LATERAL STRESS (kPa)
LEFT LAT SOIL
LEFT WATER
LEFT TOTAL
RIGHT LAT SOIL
RIGHT WATER
RIGHT TOTALNET Water
Net
F 8.2: C DA3 A
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F 8.2: A DA3 A (40.7
)
F 8.3: F DA3 A (7.5 = 5 1.5)
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F 8.4: F DA3 A
32.73 = 32.73 1.0 , 32.7 F 6.3
32.7
F 8.5: DA3 A
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N DA11 .
Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 m
A pparent E art h P res sure Fac tor: 1. 3 ( ti mes ac tive)
Eurocode Safety factors 1 1 1
SOIL
UNIT
WEIGHT
DRY UNIT
WEIGHT
WATER UNIT
WEIGHT
WATER
TABLE
ELEV. φ Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m
32 0.307 3.255 3 195 22 0.1818 1.35 1.35 1
20 19 10 195 32.00 0.307 3.255 3.000
ELEV.
TOTAL
VERTICAL
STRESS
UNFACTORED
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
Acive
LATERAL
SOIL STRESS
Apparent
Earth
Pressures
TOTAL
LATERAL
STRESS
(factored
earth)
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
LATERAL
SOIL
STRESS
TOTAL
LATERAL
STRESS
Net water
pressure
(factored) NET(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0 0.00
199.43 10.82 0.00 10.82 0.00 -7.93 -10.71 0 -10.71
197.75 42.75 0.00 42.75 -9.81 -31.33 -42.30 0 -42.30
195 95 0 95 -25.86 -31.33 -42.30 0 -42.30
191 175 -32.7 142.3 -40.39 -31.33 -75.02 -44.18 -86.5
191 175 -32.7 142.3 -40.39 -40.39 -87.25 0 0 0 10.82 10.82429 -44.18 -87.9
182 355 -106.4 248.64 -73.07 -73.07 -205.01 180 106.4 73.64 250.48 356.84 0.00 151.8
Total active earth force above subgrade:
ΔFx
From El. 200.00 to El. 199.43 0.0 kN/m
From El. 199.43 to El. 197.75 8.2 kN/m
From El. 197.75 to El. 195.00 49.1 kN/m
From El. 195.00 to El. 191.00 132.5 kN/m
Sum= 189.8 kN/m
Factored Forc 246.7
Max . A pparent Eart h P res sure= 31. 33 k Pa
Safety
factor on
earth
pressures
Safety
factor on
Passive
Resistance
WATER
TABLE
ELEV.
Hydraulic
travel length
Hydraulic loss
gradient i
Modified for calculation/Strength Reductions
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
Safety
factor on
net water
pressures
180
182
184
186
188
190
192
194
196
198
200
202
-300 -200 -100 0 100 200 300 400
E L E V A T I O N ( m )
LATERAL STRESS (kPa)
LEFT LAT SOIL
LEFT WATER
LEFT TOTAL
RIGHT LAT SOIL
RIGHT WATER
RIGHT TOTAL
NET Water
Net
F 8.6: C DA11 A
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F 8.7: A DA11 A (42.4
)
F 8.8: F DA11 A
44.18 = 32.73 1.35 , 32.7 F 6.3
44.18
I , .
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F
9.1: .
F 9.2: DA3 .
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F 9.3: DA3 ( )
F 9.4: DA11 .
IMA F DA11:
I P W U E U 1, , ,
. I ,
E U (1.35 DA11), ,
1.5/1.35=1.111 1.35/1.35=1. W
, , 1.35. T
.
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T STR & GEO C DA11:
γ = 1.1 ( )
γ = 1 (S )
FS G = 1.0 U ,
1.35 .
F L = 9
F D D = 0.15
U S = 150 P
T :
R.= L π D / (γ )
R.= 578.33 N
T ( ) :
R.= L π D / (γ γ FS G) = 578.33 N
T U S :
R.= A. F/ ( γ )
N 1/ γ = φ EC = 0.87
R.= 0.87 A. F
R.= 0.87 5.94 2 1862 MP = 961.8 N
T :
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F 9.6: I /
T GEO C DA12:
γ = 1.1 ( )
γ = 1.4 (S )FS G = 1.0 I M2 1.0
( FS=2.0).
F L = 9
F D D = 0.15U S = 150 P
T :
R.= L π D / (γ γ FS G)
R.= 578.33 N
T ( ) :
R.= L π D / (γ γ FS G) = 413.1 N
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F 9.7: I / DA12
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8. G A C C
A , . T
EC
( ). T
() . H,
(
, ( ), ). T (
) :
) U :
R.= L π D / (γ )
) T ( ) :
R.= L π D / (γ γ FS G)
W:
= U S ( )
L = F
D = F (0.09 0.15 )
FS G = 1.0 2.0 .
FS G= 1.0 M2 .
γ = 1 1.2 R
γ = 1 1.4 (S , )
N γ γ 1, E DM08
.
) T S :
P.= φ. (A T) F
φ . = M 0.9
P.= φ (A T) F
φ = M 0.6 0.9
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T
. φ.
. φ
. W E φ φ..
N φ= 1/ γ
I P ,
(W )
STR GEO . A
A T T . H, .
F 10.1 . T
, , (D).
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F 10.1: M (E )
T
. T
. A ,
. W P ,
ELPL . I, P
. T
. A :
) S . F
, DX
. F , .
F,
. E
. T .
H, :
=F1 0.5 (σ+ σ) (φ) + F2 α ( S)
I S φ=0. F
φ .
W:
F1 = F ( 1)
F2 = C ( 1)
α = A ( =1),
S. I :
α = V 1 = 0.8 S = C2
α = L S C1 C2.
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) U ( ) .
F 10.2: A
) U .
= G
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F 10.3: G ( )
) U
.
= S (B T)
I , B (F. 10.5.1,
10.5.2) .
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F 10.4: B (>
).
) W E
( )
S. H, M2
U S FS_ . T,
E 7 NTC , FS_G
M1 .
W ,
/
M .
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F 10.5.1: E A95 B.
F 10.5.2: E FHA
F .
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9. G F9.1 E ( )
9.1.1 I
S . DX
1.0
. T
, , . T
:
1) P R S F (C A):
2) R S F (C A):
3) L (C A):
4) M (PARATIE)
T
( ).
5) Z (PARATIE)
T P .
W PARATIE ,
(E 9.1,
9.2, 9.3). S, PARATIE ,
E. 9.4. I
PARATIE .
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N 9.1 9.2 (.. )
.
9.1.2 C ( )
F , "" ""
. T
1.0 . T
.
N , . I .
I
FS= 1.0 . I ,
( ). T
, (FS=
D / ).
.
F 11.1: F E M
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9.1.3 .
F
. F ,
. H, . T
:
FS= R M / O M
F 11.2: F E M
9.1.4 ( )
F
(E. 9.1 9.2):
FS= R M / O M
O / .
F ,
:
) I B ,
. T
:
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) I ,
(..
). T :
D = +
9.2 C & B I
C (C . ., 1989)
. C
(E) (I)
(γ ) . T
: )
( 9 12 )
7 17 , ) 2 3, )
, )
.
I
. I
,
, , ,
, , . F,
C . . [1989]
.
R, J [1998]. T
, , . T : I) G (
, , ), II) S P ( ,
, OCR ), III)
S S ( , ).
J [1998] : ) U
; ) ( ); ) . S
. W
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. S
.
F 11.3: C . .
4.1: L ( T, 1943).
N __
FS= F D(¨
2 / 2) B
2
γ
¨ 2 B
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=
=
B = B
D = D
N = 5.4
S DX
. N S
.
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9.3 G B W . T
,
, . W
:
) C A
) B A
T
. B A A
.
W ( ), DX
. I , DX
. T
. T
.
I ,
( ).
F 11.4: D : ,
( B 2003).
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4.2:
.
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10. H
A , P E
. T
P :
A G:
A A: I
I , /
. T
E 7 DM08
. T , ,
, , .
. T
M G (M )
A B: (M)
F ,
(
). H,
. F , 15
1,35 :
N H = 1.35 15 = 20.25
I , 5.25 . F , M (
3 )
2.25 , .
T,
.
A C: A
I , (
) . W
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11. C C
T .
T
(.. ). T
.
5.1: A C &
(E E)
W S
H
T I
W S
P O
W S
P
C
R
C
L
S
(
)
S
T I/ .
: O
. I , . T
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. O, (
) .
5.2: A C, &
(E E)
W S
H
D= B
D
T I
C 25%
.
W S
P O
D= P
D
W S
P
C
D= P
D
R
CD=W
E
I= I/4
α=
S
(
)
D=W
T P W S
S E
.
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5.3: A C, D C
(E E)
A
R
C
SPTC W (S P
T C)
O
O . U
,
:
E C :
T
. I
.
T I T 5.1 5.3
S. T:
T
I S . H, ,
.
T .
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12.
E
. T
. I,
. T
:
) T
) T .
) I
U (.. )
. H,
. I (.. P )
. T P
.
F, , . W
. T . I
:
) D , .
) S ( ). F
).
) F , (R ).
) S .
) O .
) S ( ).
) O .
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F 12.1:
12.1
T
( ) ,
, , . T
:
W: A = M
A = B
S = S ( 1 2)
S = T (, , )
1 1.4
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I = I ( ). 1 ,
.
S (.. I)
( 12.5).
12.2 D
F (.. )
R:
) W ,
R E 8 S (2004).
F 12.2: 2004
) RE : R E (1979)
. T :
O
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W: δ = P
= M
α = M ( /2)
.
α = H ( /2)
K (1996) /α
S /α
R 0.05
D 0.15
) LW :
L W
.
) I (NTC 2008) :
T I 20087
.
ah = k h·g = α·β ·aMAX (NTC 2008 eq. 7.11.9)
amax = S ·ag = S S· S T·ag (NTC 2008 eq. 7.11.10)
The software program then determines the design acceleration with:
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The α and β parameters are determined with the aid of the following design charts where:
H = Excavation height (automatically determined during analysis)
us = design permanent wall displacement (defined by user)
F 12.3: αααα according to Italian building code NTC 2008
F 12.4: ββββ according to Italian building code NTC 2008
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12.3
12.3.1
I
( )
B. T .
W:
B = M ( 0.75, .. H S C)
σ = T
= W , , (
)
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12.3.2 M
O (1926) M M (1929)
MO (MO)
. T MO
C ( ) .
T MO
.
W α= S ( )
= S = D
I = (EC. E. E.13)
P = (EC. E. E.16)
α = ( )
α = , + ( )
θ= W (0 )
F :
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T S & W (1970)
0.6H
( ). T
:
12.3.3
T RS (1994) MO
. F :
W :
W: σΖ = (1 α) γ U ( )
σΖ0 = γ U ( )
τ = α γ
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T :
T :
T
MO . I , .
I . T
RS
.
12.3.4
I .
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12.3.5 A
I
:
W γ = A ( 12.4):
) D
) T ,
) T
.
T :
I .
T .
W P
(..
). T ( )
. D P .
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12.3.6 M
T A W M
.
12.4 B
F W
(W, 1931)
:
F
. I ( ) ,
.
D ,
. W
( , ). T
:
) A . W ,
.
) A . W ,
.
) A E 8 . S
5 104
/
.
I
(K, 2009):
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: T W .
I ,
W .
12.5 I E
T ( )
. T
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12.6 E
L 10 , .
T
:
R ( ) E. +0
M ( ) E. 10
W E. 0
W E. 0
W γ= 10N/3
H = 0.25
V = 0.125 ()
W δ= 11
S : γ= 21.55N/3, γ= 18.55N/
3, = 0 P, φ= 32 ,
P K= 0.001 /
E : E= 15000 P, E = 45000 P, = 1 , =0
K =3.225 (R), K= 0.307 (R)
N C 11 :
K =3.301, K= 0.278
A: C
MO .
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θ atanγ d Ax⋅
γ t γ w−( ) 1 Ay−( )⋅
:= for pervious soil
β 0= β 0deg= θ 24.649deg=
According to Mononobe Okabe if B < FR - THETA test1 φ θ−:= test1 7.351deg=
KAEsin ψ φ+ θ−( )( )
2
cos θ( ) sin ψ ( )( )2
⋅ sin ψ θ− δ1−( )⋅ 1sin δ1 φ+( ) sin φ β− θ−( )⋅
sin ψ θ− δ1−( ) sin ψ β+( )⋅
0.5
+
2
⋅
:=
KAE 0.756=
In the horizontal direction KAE.h KAE cosπ
2ψ − δ1+
⋅:= KAE.h 0.742=
T :
σ= γ U = 21.55 10 10 10 = 115.5 N/2
T :
F.SEQ= (K. (1) K.) σ H/2 = 214.4 N/
T :
= 8.57 P
T :
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8.57 P + 2 21.875 P= 52.33 P
T :
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F 12.5: M , A, A
( ).
B: N . I ,
:
θ atanγ t Ax⋅
γ t γ w−( ) 1 Ay−( )⋅
:= for impervious soil
β 0= β 0deg= θ 28.061deg=
According to Mononobe Okabe if B < FR - THETA test1 φ θ−:= test1 3.939deg=
KAEsin ψ φ+ θ−( )( )
2
cos θ( ) sin ψ ( )( )2
⋅ sin ψ θ− δ1−( )⋅ 1sin δ1 φ+( ) sin φ β− θ−( )⋅
sin ψ θ− δ1−( ) sin ψ β+( )⋅
0.5
+
2
⋅
:=
KAE 0.936=
In the horizontal direction KAE.h KAE cosπ
2ψ − δ1+
⋅:= KAE.h 0.919=
T :
F.SEQ= (K. (1) K.) σ H/2 = 303.8 N/
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= 12.15 P
12.15 P + 21.875 P= 34.02 P
T , (
):
F 12.6: M , B, .
C: C B=0.75
. I , :
σ= γ U = 18.55 10 0= 185.5 N/2
T , , :
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F 12.7: M , C, .
I
13. 10
T , ,
10 . P :
L S E. = 0 FT R S E.= 10 FT G. W E= 10 FT
S γ = 120 F A=30 W γ = 62.4
A = 0.333 P =3
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F 13.1: C
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F 13.2: 10 .
T DEEP F 13.2. DEEP
FS. 1 EL. 24.5 . O FS. 1 E. 24.76
. DX . T
(.. )
.
T :
FS =40/ (10 (24.5)) = 2.758
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T
. DX 4.136
FS=2.213. T
DX.
T E. 10 E. 50 :
σ10= γ U = 0.120 10 0= 1.2
σ50= σ10 + (γ−γ ) = 1.2 + (0.1200.0624) 40 = 3.504
H,
. H, .
D = 0.333 1.20 10/2 + 0.333 (1.2 + 3.504 ) 40 /2 = 33.35 /
R = 3 (0.1200.0624) 40 40/2 = 138.24 /
T :
FS= 138.24/ 33.35 = 4.145 4.136
DX 22.4 .
T
.
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14. 20
U 14.1, 20
E. 10 (10 ). T
1.0, ,
. L F 1.
F 14.1: L 20 .
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F 14.2: D 20 10 .
A F 2, DEEP FS=1.0 E. 35.75
EL. 35.9 . T,
DX.
T :
FS.= 30 / (20 (35.75)= 1.904
DX
R = 10.48 ( ).
U
. A F
14.3, 45.9 / DX
44.6 /. T, DX .
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F 14.3: C M 20 .
F . T
. DX 1.915
1.915. T DX
.
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1.915
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15. 30
T 30 , 10 , 20 . A
(14.1 14.2). F 15.1 30 . DX
F 15.1.
SOIL UNIT
WEIGHT
WATER UNIT
WEIGHT
WATER
TABLE
ELEV. Ka Kp
WATER
TABLE ELEV.
(kcf) (kcf) (FT) (FT)
0.12 0.0624 -10 0.333 3 -30
ELEV.
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
LATERAL
SOIL
STRESS
TOTAL
LATERAL
STRESS
TOTAL
VERTICAL
STRESS
WATER
PRESSURE
EFFECTIVE
VERTICAL
STRESS
LATERAL
SOIL
STRESS
TOTAL
LATERAL
STRESS NET(FT) (ksf) (ksf) (ksf) (ksf) (ksf) (ksf) (ksf) (ksf) (ksf)
0 0 0 0 0 0 0
-10 1.2 0 1.2 -0.4 -0.4 -0.4
-20 2.4 -0.624 1.776 -0.592 -1.216 -1.216
-30 3.6 -1.248 2.352 -0.784 -2.032 0 0 0 0 0 -2.032
-43.22 5.186 -2.073 3.113 -1.038 -3.111 1.586 0.825 0.761 2.284 3.109 -0.001
-50 6 -2.496 3.504 -1.168 -3.664 2.4 1.248 1.152 3.456 4.704 1.04
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES
-60
-50
-40
-30
-20
-10
0
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
E L E V A T I O N ( F
T )
LATERAL ST RESS (KSF)
LEFT LAT SOIL
LEFT WATER
LEFT TOTAL
RIGHT LAT SOIL
RIGHT WATERRIGHT TOTAL
NET
F 15.1: L 30
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F 15.2: L 30 D.
F 15.3: 30 E
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T
E 43.22 . R
F 15.3. T 72.5 / E. 20 65.0
. DX 72.6 / E. 20 65.0 /
. S DEEP 1.24 / 32.01/
(E. 20). T, DX
.
F 15.4: , , DEE 30
.
N .
Reaction at pin support at El -43.22 ftFB 9.000kip:=
Note that the pressure at El -43.22 is zero. Now calculate the net passive resistance to the
bottom of the wall.
σBOT 0.944ksf :=
Therefore, the next passive resisting force below El. -43.22 is
RNET 50ft 43.22ft−( )σBOT 1⋅ ft
2⋅:= RNET 3.2kip=
Passive force safety factor FSPASRNET
FB:= FSPAS 0.356=
DeepXcav calculates 0.36 which verifies the hand calculated safety factor.
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u30 1.248ksf :=
Moment for water from El. -20 to El. -30ft
M1w10 ft⋅ u20⋅ 10⋅ ft⋅
2
u30 u20−( ) 10⋅ ft⋅
2
10 ft⋅ 2⋅
3⋅+
1⋅ ft:= M1w 52kip ft⋅=
Below El. -30 the net water pressure has a rectangular distribution
unet u30:= unet 1.248ksf = and the moment contribution is
M2w unet 20⋅ ft 10ft20ft
2+
⋅ 1⋅ ft:= M2w 499.2kip ft⋅=
The driving moment is then: MDR
MDRs
M1w
+ M2w
+:=
Resisting moment comes from a triangular pressure distribution pressure at bottom 3.456 ksf
onky due to soil contribution as water moment is added as a net moment on the driving side
FR 3.456ksf 20⋅ ft 1⋅ft
2:= MR FR 10ft 20ft
2
3⋅+
⋅:= MR 806.4kip ft⋅=
Now we can calculate the rotational safety factor FSROTMR
MDR:= FSROT 0.814=
Now calculate rotational safety factor about lowest support. In this method, driving and resisting
moments below the lowest support are calculated. The safety factor is then calculated at the
ratio of resistring to driving moments. Note that moments above the lowest support are ignored.
Soil pressure at El- 20 σDRs20 0.592ksf :=
σDRsbot 1.168ksf :=Soil pressure at bottom of left wall side El- 50ft
From the rectangular portion of the driving soil pressures
FDRrectS 30ft 1⋅ ft σDRs20( )⋅:= FDRrectS 17.76kip=
MDRrectS FDRrectS 30⋅ft
2:= MDRrectS 266.4kip ft⋅=
From the triangular portion of the driving pressures
FDRtriS σDRsbot σDRs20−( ) 30⋅ ft 1⋅ft
2:= FDRtriS 8.64kip=
MDRtriS FDRtriS 30⋅ ft2
3⋅:= MDRtriS 172.8kip ft⋅=
And total driving moment due
to soil pressures on left sideMDRs MDRrectS MDRtriS+:= MDRs 439.2kip ft⋅=
Now calculate the net driving moment due to water below El. -20ft
u20 0.624ksf :=
A F 15.4 , DX .
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A. AEDI: C C
KP1cos φ θ+ β−( )( )
2
cos θ( )( )
2
cos β( )( )
2
⋅ cos δ1 θ− β+( )⋅ 1sin δ1 φ+( ) sin φ α+ β−( )⋅
cos δ1 θ− β+( ) cos α θ−( )⋅
0.5
−
2
⋅
:=
KP KP1 1 Ay−( )⋅:= KP 15.976=
KPH KP cos δ1 θ−( )⋅:= KPH 15.734=
3. Calculate Kp according to Lancellotta 2007, note equation does not account for wall inclination
Θ2 asinsin δ1( )
sin φ( )
asin
sin α β−( )
sin φ( )
+ δ1+ α β−( )+ 2 β⋅+:= Θ2 1.029=
Θ2 58.981deg=γ 1 1 Ay−( )
2Ax
2+
0.5
:= γ 1 1.013=
KPE cos δ1( )cos δ1( ) sin φ( )( )
2sin δ1( )( )
2−
0.5
+
cos α β−( ) sin φ( )( )2
sin α β−( )( )2
−
0.5
−
⋅
eΘ2 tan φ( )⋅
⋅:= KPE 10.401=
KPH.Lancellotta KPE γ 1⋅ cos α β−( )⋅:= KPH.Lancellotta 10.477=
KP.Lancellotta
KPH.Lancellotta
cos δ1( ):= KP.Lancellotta 10.639=
1. Calculate Kp according to various equations, define basic parameters
Soil friction angle φ 40deg:=
Slope angle α 15deg:= Note that positive slope angle is upwards
δ1 10deg:=Wall friction
Wall inclination θ 0deg:= Note vertical face angle theta is 0
Seismic accelerations
Ax 0.16:= Ay 0:=
β atanAx
1 Ay−
:= β 0.159= β 9.09deg=
2. Calculate Kp according to Coulomb, DAS pg. 430, Principles of Geotechnical Engineering
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I , .
T K ) F S D P
, ) K E
.
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B. AEDI: I F G
**
* AAIE AALI F DEIG ECI:EC7, 2007: DA1, C 2: A2 + 2 + 1
*1: D G C
0.2
200
*2. ADD GEEAL ALL & DIEI
L 0 182 200
*3.1 DEFIE FACE F LEF ALL
0L L 182 200 1 0
0 L 182 200 2 180
*4: DEFIE IL LAE ELEAI & EGH
* BIG B 1
*DAA F LAE: 1, IL E= 1, F
L L1 200
19 10 10
3 32 0.307 3.255
0.47 0.5 1
15000 3 0 1 100 0.5
0.03048
E
*5.1: DEFIE CAL AEIAL
*A GEEAL AEIAL
* GEEAL CCEE AEIAL CEED CIE I IH FCE/LEGH2
*C : 0 = 3 C, E= 21541.9
CC03 21541900
*C : 1 = 4 C, E= 24874.5
CC14 24874500
*C : 2 = 5 C, E= 27810.5
CC25 27810500
* GEEAL EEL EBE AEIAL CEED CIE I IH FCE/LEGH2
* : 0 = F510, E= 206000
EEL0 206000000
* : 1 = A50, E= 200100
EEL1 200100000
* GEEAL EBA AEIAL CEED CIE I IH FCE/LEGH2, ED F ACH
* : 0 = G 60, E= 200100
EB0G 200100000
* : 1 = G 75, E= 200100
EB1G 200100000
* : 2 = G 80, E= 200100
EB2G 200100000
* : 3 = G 150, E= 200100
EB3G 200100000
* : 4 = 270 , E= 200100
EB4 200100000
* E DEFIED AEIAL CEED CIE I IH FCE/LEGH2, ED F ACH
* : 0 = 0, E= 1
E0 1000
* ED GEEAL AEIAL
* 5.2 D
A 100000000000
* 6.1 LEF ALL CAL EIE
*C I.
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* E= 206000 , I= 82795.6 4/ 1 = 82795.6 4
* I= E I CEI / (E CEL ) =>
* I= 206000 82795.6 4/ 1 = 82795.6 4 1E08/ (206000 1 1)= 0.00083 (4/)
* E I/L
* = (12 I/L)(1/3) = (12 0.00083)(1/3) = 0.21498 ()
BEA LBEA L 182 200 EEL0 0.214979 00 00
*7.1: GEEAE F LEF ALL
*C : /L= (A/CA) / (F L + F L / 100 =>
* /L= (5.942/100002 /2) /2 (7 + 50 9 /100 = 2.58261E05
IE L0 L 197 EB4 2.58261E05 200 30 0 0
*8.1: ADD ALL LAD & ECIBED CDII F LEF ALL
DE 0 L 195
* ED F DE ADDII
* 9.A 1 . 0
* 9.A 1 . 1
* 9.A 1 . 2
* 9.A 1 . 3
* : 3, 0 1 E. 200, = 0, = 5, = 0
* 2 E. 195, = 0, = 0, = 0
* A : E , . L LF=1.3
***** ED 0
****************************************************************
* 10: GEEAE ALL E/AGE
*****************************************************************
*A DAA F AGE: 0 : 0
0 : 0
*10.: DECIBE K, K C D F, C C
* LAE 1 0
* C : EC7, 2007, C:DA1, C. 2: A2 + 2 + 1*FF = 1.25, F'= 1.25, FDE= 1, F= 0.9, FE= 1
*FL = 1.3, FL= 1, F = 0, FA= 1.1, FA= 1.1
* KH= KHB FDE K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KDH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 3.255 /1 2.618/3.255 = 2.618
* ED LAE 1 : 0
* I 10. .
*ED 10.
*10: A GEEAE IL E CHAGE CAD F AGE
* E 7
* .
L1 26.56 L
L1 26.56 L L1 2.4 L
L1 2.4 L
L1 0.381719868280688 L
L1 0.381719868280688 L
L1 2.61784906429131 L
L1 2.61784906429131 L
*10: ED GEEAIG CHAGE F AGE.
* DAA F LEF ALL
L
*10.1 G 0
200 200
195 0 3830
*11: ADD LEF ALL
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*13.1: ADD LEF ALL CHAGE F LAD DIECL LADIG HE ALL
*13.2.1: ADD LEF ALL CHAGE CALCLAED IDE F AAIE EGIE
*13.3: ADD ALL CHAGE HA AE DIECL HE LEF ALL
*13.3: ED ADDIG ALL CHAGE LEF ALL
* ED DAA F LEF ALL
*19.1 EAIE IF AE EED F LEF ALL
* 19: ED EAL
*20: ADD LAEAL LIE LAD LACED DIECL ALL
EDE
*ED DAA F AGE 0 AE: 0
***************************************************************
*****************************************************************
*A DAA F AGE: 1 : 1
1 : 1
*10.: DECIBE K, K C D F, C C
* LAE 1 1
* C : EC7, 2007, C:DA1, C. 2: A2 + 2 + 1
*FF = 1.25, F'= 1.25, FDE= 1, F= 0.9, FE= 1
*FL = 1.3, FL= 1, F = 0, FA= 1.1, FA= 1.1
* KH= KHB FDE K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KDH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 3.255 /1 2.618/3.255 = 2.618
* KDH= KHB FD K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KH = 3.255 /1 2.618/3.255 = 2.618
* '= / (F FDE) = 3/(1.25 1) = 2.4* 'D= / (F F) = 3/(1.25 1) = 2.4
* ED LAE 1 : 1
* I 10. .
*ED 10.
* DAA F LEF ALL
L
*10.1 G 1
200 196.5
195 0 3830
*11: ADD LEF ALL
*13.1: ADD LEF ALL CHAGE F LAD DIECL LADIG HE ALL*13.2.1: ADD LEF ALL CHAGE CALCLAED IDE F AAIE EGIE
*13.3: ADD ALL CHAGE HA AE DIECL HE LEF ALL
*13.3: ED ADDIG ALL CHAGE LEF ALL
* ED DAA F LEF ALL
*19.1 EAIE IF AE EED F LEF ALL
* 19: ED EAL
*20: ADD LAEAL LIE LAD LACED DIECL ALL
EDE
*ED DAA F AGE 1 AE: 1
***************************************************************
*****************************************************************
*A DAA F AGE: 2 : 2
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2 : 2
*10.: DECIBE K, K C D F, C C
* LAE 1 2
* C : EC7, 2007, C:DA1, C. 2: A2 + 2 + 1
*FF = 1.25, F'= 1.25, FDE= 1, F= 0.9, FE= 1
*FL = 1.3, FL= 1, F = 0, FA= 1.1, FA= 1.1
* KH= KHB FDE K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KDH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 3.255 /1 2.618/3.255 = 2.618
* KDH= KHB FD K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KH = 3.255 /1 2.618/3.255 = 2.618
* DAA F LEF ALL
L
*10.1 G 2
200 196.5
195 0 3830
*11: ADD LEF ALL
ADD L0
*13.1: ADD LEF ALL CHAGE F LAD DIECL LADIG HE ALL
*13.2.1: ADD LEF ALL CHAGE CALCLAED IDE F AAIE EGIE
*13.3: ADD ALL CHAGE HA AE DIECL HE LEF ALL
*13.3: ED ADDIG ALL CHAGE LEF ALL
* ED DAA F LEF ALL
*19.1 EAIE IF AE EED F LEF ALL
* 19: ED EAL
*20: ADD LAEAL LIE LAD LACED DIECL ALL
EDE
*ED DAA F AGE 2 AE: 2
***************************************************************
*****************************************************************
*A DAA F AGE: 3 : 3
3 : 3
*10.: DECIBE K, K C D F, C C
* LAE 1 3
* C : EC7, 2007, C:DA1, C. 2: A2 + 2 + 1
*FF = 1.25, F'= 1.25, FDE= 1, F= 0.9, FE= 1*FL = 1.3, FL= 1, F = 0, FA= 1.1, FA= 1.1
* KH= KHB FDE K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KDH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 3.255 /1 2.618/3.255 = 2.618
* KDH= KHB FD K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KDH = 0.307 1 0.382/0.307 = 0.382
* KH= KHB /F K( F= 26.56, DF= 0, A= 0) / K( F= 32, DF= 0, A= 0)=>
* KH = 3.255 /1 2.618/3.255 = 2.618
* DAA F LEF ALL
L
*10.1 G 3
200 191
195 4
*11: ADD LEF ALL
-
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D C.A.S. , I D E LLC, U.S.A.
*13.1: ADD LEF ALL CHAGE F LAD DIECL LADIG HE ALL
*13.2.1: ADD LEF ALL CHAGE CALCLAED IDE F AAIE EGIE
*13.3: ADD ALL CHAGE HA AE DIECL HE LEF ALL
* : 3, 0 1 E. 200, = 0, = 5, = 0
* 2 E. 195, = 0, = 0, = 0
* A : E , . L LF=1.3
***** ED 0
L 195 0 200 6.5
*13.3: ED ADDIG ALL CHAGE LEF ALL
* ED DAA F LEF ALL
*19.1 EAIE IF AE EED F LEF ALL
* 19: ED EAL
*20: ADD LAEAL LIE LAD LACED DIECL ALL
EDE
*ED DAA F AGE 3 AE: 3
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*