g. l. σ γz z v › bitstream › 11536 › 72935 › 21 › 658421.pdf · fig. 2.5. locations of...
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59
Fig. 2.1 Development of in-situ stresses
Z
A
G. L.
σv = γz
σhσh
σv
A
G. L.
σ1
σ1
σ3 σ3
(a)
(b)
60
Fig. 2.2. Jaky’s formulation of the relationship between Ko on OC and φ mobilized in OAB (after Mesri and Hayat, 1993)
φτφ
φ
Principal Stress Trajectories
90-
45+ 2
A B C D
O
z
z
r
r
z
Parabolic Interpolationof between OB and OC
O
O
61
Fig. 2.3. Shaking table, soil box, and actuator (after Sherif et al., 1981)
Aluminum Plates
Actuator
Actuator Mounting
Coupling
Movable Retaining Wall
2.4 m
Soil Box
1.8 m
1.2 m
Shaking Table
62
Fig. 2.4. Shaking table with movable retaining wall (after Sherif et al., 1984)
Soil
M1M2
P1
P2
P4
Shaking Table Foundation
Section
DynamicExcitation
Worm GearSystem
Center Wall
Side Wall
ExcitationDynamic
P1
P4
P3
PlexiglasWall
Plan
M1
M2
P4 : Vertical Load CellM1, M2 : Variable Speed Motors
P1, P2, P3 : Horizontal Load Cells
(Note : P3 is Behind P4)
(Note : P3 is Right Below P1)
63
Fig. 2.5. Locations of soil-pressure transducers (after Sherif et al., 1984)
Movable Wall
SP1
SP2
SP3
SP4
Wall Base
Backfill MaterialSP5
SP6
H = 1.0
0.1520.305
0.4660.628
0.7920.957
0.152
Unit : m
Top of Backfill
0.043
64
Fig. 2.6. Distribution of at-rest stresses for loose sand (after Sherif et al., 1984)
0 50 100 150 200Horizontal Earth Pressure (lb/ft2)
3.0
2.5
2.0
1.5
1.0
0.5
0.0D
epth
(ft)
Experimental At-Rest Earth Pressure Jaky's Solution (At Loosest Density)
Soil Specimen : Loose Ottawa SandTest No : TST334γ = 96.85 pcfφ = 32.3 Degrees
65
Fig. 2.7. Distribution of at-rest stresses for medium-dense sand (after Sherif et al., 1984)
0 50 100 150 200Horizontal Earth Pressure (lb/ft2)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Dep
th (f
t)
Experimental At-Rest Earth Pressure Jaky's Solution (At Loosest Density)
Soil Specimen : Medium-Dense Ottawa SandTest No : TST328γ = 98.87 pcfφ = 35.0 Degrees
Jaky's Solution (At In-Situ Density)
At-Rest (Experimental)
66
Fig. 2.8. Distribution of at-rest stresses for dense sand (after Sherif et al., 1984)
0 50 100 150 200Horizontal Earth Pressure (lb/ft2)
3.0
2.5
2.0
1.5
1.0
0.5
0.0D
epth
(ft)
Experimental At-Rest Earth Pressure Jaky's Solution (At Loosest Density)
Soil Specimen : Dense Ottawa SandTest No : TST322γ = 101.80 pcfφ = 39.0 Degrees
Jaky's Solution (At In-Situ Density)
At-Rest (Experimental)
67
Fig. 2.9. Lock-in at-rest pressure due to soil densification (after Sherif et al., 1984)
1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07γactual / γloose
0.0
0.1
0.2
0.3
0.4K
ol (E
xtra
Ko D
ue to
Loc
ked-
in S
tress
es)
Soil Specimen : Ottawa Sand
Average
68
Fig. 2.10. Broms’s simplified compaction pressure theory (after Broms, 1971)
Hor
izo n
tal E
ffe c
tive
Pre s
sure
hm
hf
hi
vi
Vertical Effective Pressure
vm
A
B
C
D
σσ
σσ
σ
σ
σ
h = K vo
rhσ = K σv
σhf
σhiσvi z
Point A
z
Point B
vmσσhm
σvi z
Vertical Effective Pressure
Hor
i zon
tal E
ffec
tive
Pre s
sure
hσ = Koσv
= Kσh r vσ
σvi vmσ
σhm
σvo
(a)
(b) (c)
(d) (e)
Point D
A'
B'C' E'
69
Fig. 2.11. Lateral pressure distribution due to compaction of fill (after Broms, 1971)
00
Azc
(a) (b)
Lateral Earth Pressure,
CriticalDepth, zc
Depth BelowSurface of Fill
Depth BelowSurface of Fill
Lateral Earth Pressure,
Locus of Point A
hσ σhO σ σ
σh = Kr σv
σ vh = K σoσ= Kσh o v
σ vrh = K σ
σ= Khσ vmom
mh mh
Curve 3
Curve 2Curve 1
70
Eq. 2.11
Dep
th, z
Eq. 2.8 d
Eq. 2.9
bEq. 2.10 c
Lateral Pressure,a hσ
Fig. 2.12. Hand-calculation for estimating σh (after Peck and Mesri, 1987)
71
Fig. 2.13. Distribution of vertical earth pressure measured in soil mass (after Chen, 2002)
0 5 10 15 20 25 30Vertical Earth Pressure, σv (kN/m2)
0
0.3
0.6
0.9
1.2
1.5El
evat
ion
(m)
σv = γz(γ = 16.6 kN/m3)σv = γz
(γ = 15.5 kN/m3)
, Test C0807 (Compacted Sand)* Test C0808 (Compacted Sand)
? Test A0806 (Loose Sand)’ Test A0907 (Loose Sand)
Compacted SandDr = 75 %
γ = 16.6 kN/m3
φ = 40.8o
72
Fig. 2.14. Distribution of horizontal earth pressure after compaction
(after Chen, 2002)
Horizontal Earth Pressure, σh 2
0 5 10 15
Rankine (Passive)
Jaky
(b)
+ Test C0903, Test C1141
0 5 10 15
Rankine (Passive)
Jaky
(c)
+ Test C0903, Test C1141
0 5 10 15
Rankine (Passive)
JakyCompaction-Influenced Zone
(d)
+ Test C0903, Test C1141
∆σh,ci
0 5 10 15
Rankine (Passive)Jaky
(e)
+ Test C0903, Test C1141
0 5 10 15
0
0.3
0.6
0.9
1.2
1.5
Elev
atio
n (m
)
Rankine (Passive)Jaky
Compacted Sand
+ Test C0903, Test C1141
(a)
73
(a) (b) (c)
Fig. 2.15. Stress path of a soil element under compaction (after Chen, 2002)
0 5 10 15 20 25 30
Vertical Earth Pressure, σv (kN/m2)
0
2
4
6
8
10
12
Hor
izon
tal E
arth
Pre
ssur
e, σ
h (kN
/m2 )
F : FillC : Compaction
Test C0727Elevation : 0.15 mσh by SPT 2σv by SPT 102
Jaky
Ran
kine
(Pas
sive
)
C1
F1
C2F2
C3
F3
C4F4C5
F5
0 5 10 15 20 25 30
Vertical Earth Pressure, σv (kN/m2)
0
2
4
6
8
10
12
Hor
izon
tal E
arth
Pre
ssur
e, σ
h (kN
/m2 )
F : FillC : Compaction
Jaky
Ran
kine
(Pas
sive
)
C2
C3
F3
C4
F4
C5
F5
Test C0727Elevation : 0.55 mσh by SPT 6σv by SPT 106
F2
0 5 10 15 20 25 30
Vertical Earth Pressure, σv (kN/m2)
0
2
4
6
8
10
12
Hor
izon
tal E
arth
Pre
ssur
e, σ
h (kN
/m2 ) F : Fill
C : Compaction
Jaky
Ran
kine
(Pas
sive
)
C3
C4F4
C5
F5
Test C0727Elevation : 0.65 mσh by SPT 7σv by SPT 107F3
74
Silo
Hopper
Top of fill
Y
dy
Granular Material
(a)
dyp p
γAdy
q
q + (dq/dy)dy
(b)
Fig. 2.16. Horizontal lamina for derivation of Janssen’s equations (redrawn after Safarian and Harris, 1985)
75
h
D (diameter)
pdy
Y
maxp
(a)
Weight
fric
tion
fric
tion
Equal pressures qmax
(b)
Fig. 2.17. Lamina of stored material for derivation of the Reimbert’s
equations (after Reimbert and Reimbert, 1895)
76
Natural ground
Hdh
h
Bd
Bc
V
V + dV
γBddhKVdh/Bd Kµ'Vdh/Bd
Trench
Conduit
Fig. 2.18. Free-body diagram for ditch conduit (after Spangler and Handy, 1984)
77
(a) (b)
Fig. 2.19. Distribution of soil pressure against fascia walls to partial
support from wall friction F (after Spangler and Handy, 1984)
78
(a)
(b)
Fig. 2.20. Model retaining wall (after Frydman and Keissar, 1987)