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untitledσo ? Soil Backfill
Fig. 1.1. Earth pressure at-rest on the basement wall near vertical rock
faces
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σ
σσ
σ
σ
x
y
= h
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Fig. 2.3. Jaky’s formulation of the relationship between Ko on OC and φ mobilized in OAB (after Mesri and Hayat, 1993)
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O
O
Eq. 2.8
Eq. 2.9
Eq. 2.11
Eq. 2.10
Fig. 2.4. Hand-calculation for estimating σh (after Peck and Mesri, 1987)
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0 5 10 15 20 25 30 Vertical Earth Pressure, σv (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
(γ = 15.5 kN/m3)
Compacted Sand Dr = 75 %
φ = 40.8o
Fig. 2.5. Distribution of vertical earth pressure measured in soil mass
(after Chen, 2003)
Fig. 2.6. Distribution of horizontal earth pressure after compaction (after Chen, 2003)
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Silo
Hopper
(b)
Fig. 2.7. Horizontal lamina for derivation of Janssen’s equations (redrawn after Safarian and Harris, 1985)
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0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Janssen's Solution For Rectangular Silo (a x b x H)
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
(b = 1.5 m, a = 50 mm ~ 1500 mm) H = 1.5 m
a = 50 m m
a = 1500 m m
a = 100 m m
a = 700 mm
Fig. 2.8. Distribution of earth pressure for Janssen’s solution with different hydraulic radius R
62
h
max
(b) Fig. 2.9. Lamina of stored material for derivation of the Reimbert’s
equations (redrawn after Safarian and Harris, 1985)
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0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Jaky, Ko Rankine, Ka
Reimbert & Reimbert's Solution For Rectangular Silo (a x b x H)
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
(b = 1.5 m, a = 50 mm ~ 1500 mm) H = 1.5 m
a = 50 m m
a = 1500 m m
a = 100 m m
a = 200 m m
a = 400 m m
a = 700 m m
Fig. 2.10. Distribution of earth pressure for Reimbert’s solution with different hydraulic radius R
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Trench
Conduit
Fig. 2.11. Free-body diagram for a ditch conduit (after Spangler and Handy, 1982)
65
(a) (b)
Fig. 2.12. Distribution of soil pressure against fascia walls to partial
support from wall friction F (after Spangler and Handy, 1982)
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0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
B = 50 m
B = 400 mm B = 700 mm
Fig. 2.13. Distribution of earth pressure for Spangler and Handy's solution with different distance B
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0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Jaky (At-Rest) Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1984)
γ = 15.6 kN/m3
δw = 9.3o
Fig. 2.14. Comparison of earth pressure calculated with different theories
for d = 900 mm
Fig. 2.15. Model retaining wall (after Frydman and Keissar, 1987)
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15001500
70
Fig. 3.2. Locations of soil-pressure transducers mounted on the wall (after Chen and Fang, 2002)
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Adaptor
Φ = 13 mm
ducer (Kyowa PGM-0.2KG)
Dynamic Strain Amplifiers (Kyowa: DPM601A and DPM711B)
NI BNC – 2090 Adaptor Board
Fig. 3.4. Data acquisition system
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Handle
74
(Front-view)
(a) Front view of the strip soil compactor and the model wall
Model Wall
Fig. 3.6. Strip vibratory soil compactor
75
Steel Tube
Steel Tube
(d) Steel tube and compaction plate
Fig. 3.6. Strip vibratory soil compactor (cont’d)
76
50
100
150
200
No. of Acentric Plate
0 0 10 20 30 40
Fig. 3.7. Acentric force as a function of number of acentric plate
(Mikasa KJ75)
21 00
21 00
42 2
32 0
42 7
43 0
31 5
Steel Plate (4.5 mm thick)
Steel L-Beam (65 x 65 x 8 mm)
(a) Front-view (b) Back-view
78
79
80
(a)
(b)
Walkway
Fig. 4.3. Top supporting beam
1210
1084
81
297
82
1195 × 297 × 125 mm
C-clamp
Soil Pressure Transducer
Fixing Plate
Soil Bin
(a) Side-view
Model Wall
d = 900Top Supporting Beam C-clamp
Base Spacing Plate
Base Spacing Plate
Vertical Interface Plate
Base Supporting Frame (297 x 1195 x 125 mm)
(b) Top-view
Fig. 4.6. Model retaining wall near a vertical interface plate with d = 900
mm
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85
ination of base spacing plates for d = 900 mm
300 × 200 × 17.5 mm
Plastic Sheets Lubricating
Beam
Fig. 4.9. For d = 900 mm between interface plate and model wall
87
H =
C-clamp
d = 1500 d = 1100
d = 900 d = 700
d = 500 d = 400
d = 300 d = 200
d = 100 d = 50
Fig. 4.10. Different spacing d between interface plate and model wall
88
H =
Model Wall
Fig. 4.11. For d = 1500 mm between interface plate and model wall
89
90
H =
Base Supporting Frame
Base Spacing Plate
(a)
(b)
Fig. 4.12. For d = 50 mm between interface plate and model wall
d = 50 mm Interface Plate
Model Wall
0
20
40
60
80
) Ottawa Silica Sand ASTM C-778
Fig. 5.1. Grain size distribution of Ottawa sand (after Chen, 2001)
91
(after Wu, 1992)
Unit Weight, γ (kN/m3 )
Fig. 5.3. Relationship between unit weight γ and internal friction
angle φ (after Chang, 2000)
93
Fig. 5.4. Direct shear test arrangement to determinate wall friction angle
δW (after Ho, 1999)
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15.50 15.75 16.00 16.25 16.50 16.75 17.00 17.25 Unit Weight , γ (kN/m3)
8.0
9.0
10.0
11.0
12.0
13.0
14.0
(d eg
re e)
Test Data (air-pluviation) δW = 3.41γ - 43.69 Test Data (compaction) δW = 3.08γ - 37.54
Ottawa Sand σN = 79.8 kN/m2
Fig. 5.5. Relationship between unit weight γand wall friction angleδW
(after Ho, 1999)
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96
Fig. 5.6. Plastic sheets lubrication layer hung on the side wall
Lubrication layer (1 thick + 2 thin plastic sheets)
Steel Interface Plate
Model Wall
Fig. 5.7. Schematic diagram of sliding block test. (after Fang et al., 2004)
97
δ
Standard weight↓
(after Fang et al., 2004)
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Sliding Block Test Plastic-sheet method 1 thick + 2 thin sheeting
1 10 Normal Stress, σ (
5
15
0
10
(after Fang et al., 2004)
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o
80
(b) Steel plate with Safety-Walk
Fig. 5.10. Direct shear test to determinate friction angle δi of the
interface plate with Safety-Walk
10
15
20
25
30
Ottawa Sand σn = 4.60 kN/m2
Fig. 5.11. Relationship between unit weight γ and interface plate friction
angle δi
15 16 17 18 19 20 Unit Weight, γ (kN/m3)
0
10
20
30
40
50
φair = 6.43γ - 68.99 (Chang, 2000)
φcomp = 7.25γ - 79.5 (Chang, 2000)
δi, comp = 1.97γ - 8.9
δi, air = 2.7γ - 21.39
δw, comp = 3.08γ - 37.54 (Ho, 1999)
δw, air = 3.41γ - 43.69 (Ho, 1999)
ip between unit weight γ aFig. 5.12. Relationsh nd friction angle for
different types of interfaces
Fig. 5.14. Air-pluviation of the Ottawa sand into soil bin
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0
0.3
0.6
0.9
1.2
(m )
Compacted Backfill 90k500 mm Strip Compactor No. of Acentric plates = 8 + 8 Drop Height = 1.5 m Lift Thickness = 0.5 m D
r = 70%
0.1 m
0.5 m
Fig. 5.15. Distribution of soil density with depth for sand compacted with
the 90 mm × 500 mm strip compactor
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Steel Tube
Model Wall
Fig. 5.16. Backfill compacted with 90 mm × 500 mm strip compactor
106
H =
10 0
10 0
Fig. 5.17. Backfill compacted with 90 mm × 500 mm compactor for d =
900 mm
Steel Interface Plate
90 mm x 500 mm compacting plate
Fig. 5.18. Backfill compacted with 90 mm × 500 mm compactor in 10 lanes
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110
d= 900Top Supporting Beam
Fig. 5.21. Locations of soil density control cups at the same elevation
111
(b) Cup filled and Buried in Backfill
(c) Compaction of soil
V Ws
d =γ
(e) Soil mass in cup weighted (f) Calculation of dry density
Fig. 5.22. Procedure of density control test
112
100 r (%)
Dr = 72% ± 2.8% Lift = 0.1 m
Loose Sand γ = 15.6 kN/m3
Dr = 35% ± 3.1% Drop Height = 1.5 m Slot Opening = 18 mm
D r =
3 2%
D r =
D r =
7 5%
This Study
Fig. 5.23. Distribution of soil density for loose and compacted sand
113
(a)
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0128 Test 0216
Loose Sand d = 1500 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
(b)
Fig. 6.1. Distribution of horizontal earth pressure for loose sand with d =
1500 mm
114
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0616 Test 0619
Loose Sand d = 1100 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.2. Distribution of horizontal earth pressure for loose sand with d =
1100 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0503
Loose Sand d = 900 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.3. Distribution of horizontal earth pressure for loose sand with d =
900 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0428 Test 0430 Test 0503
Loose Sand d = 700 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.4. Distribution of horizontal earth pressure for loose sand with d =
700 mm
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0409 Test 0412
Loose Sand d = 500 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.5. Distribution of horizontal earth pressure for loose sand with d =
500 mm
116
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0407 Test 0413
Loose Sand d = 400 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.6. Distribution of horizontal earth pressure for loose sand with d =
400 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0324 Test 0328
Loose Sand d = 300 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.7. Distribution of horizontal earth pressure for loose sand with d =
300 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0406-1 Test 0406-2
Loose Sand d = 200 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο δw = 9.3ο, δi = 20.7ο
Fig. 6.8. Distribution of horizontal earth pressure for loose sand with d =
200 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0331 Test 0405 Test 0609
Loose Sand d = 100 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο δw = 9.3ο, δi = 20.7ο
Fig. 6.9. Distribution of horizontal earth pressure for loose sand with d =
100 mm
118
(a)
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0330 Test 0331 Test 0609
Loose Sand d = 50 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
(b)
Fig. 6.10. Distribution of horizontal earth pressure for loose sand with d
= 50 mm
Z
Water
Z Sand
(c) Filled with sand
Fig. 6.11. Distribution of horizontal pressure for water and sand with d
= 200 mm
120
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5 El
ev at
io n,
(m ) Jaky
d = 1500 mm d = 900 mm d = 500 mm d = 400 mm d = 200 mm d = 100 mm d = 50 mm
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
f horizontal earth prFig. 6.12. Distribution o essure for loose sand at different spacing d
121
0
0.2
0.4
0.6
0.8
1
h
Jaky Rankine (Ka) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.13. Distribution of Ko,h for loose sand at different spacing d
122
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
-Ko,h
Ko,h
d/H
123
0
0.2
0.4
0.6
0.8
1
h/ H
h/H = 0.33 Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
r loose sand at dif
124
0
1
2
3
4
5
6
)
Loose Sand Jaky Janssen (1895) Reimbert and Reimbert (1976) Spangler and Handy (1982) This Study
d/H
Fig. 6.16. Distributio ut the base for loose sand with diff
n of overturning moments abo erent spacing d
125
H =
Base Supporting Frame
Base Spacing Plate
d = 100
Fig. 7.1. Different spacing d between interface plate and model wall
126
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0529 Test 0621
Compacted Sand d = 1500 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.2. Distribution of horizontal earth pressure for compacted sand with d = 1500 mm
127
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0706
Compacted Sand d = 1100 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.3. Distribution of horizontal earth pressure for compacted sand with d = 1100 mm
128
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0601
Compacted Sand d = 900 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.4. Distribution of horizontal earth pressure for compacted sand with d = 900 mm
129
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0603
Compacted Sand d = 700 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.5. Distribution of horizontal earth pressure for compacted sand with d = 700 mm
130
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0515
Compacted Sand d = 500 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.6. Distribution of horizontal earth pressure for compacted sand with d = 500 mm
131
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0524
Compacted Sand d = 400 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.7. Distribution of horizontal earth pressure for compacted sand with d = 400 mm
132
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0520
Compacted Sand d = 300 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.8. Distribution of horizontal earth pressure for compacted sand with d = 300 mm
133
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0524 Test 0612
Compacted Sand d = 200 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.9. Distribution of horizontal earth pressure for compacted sand with d = 200 mm
134
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0614
Compacted Sand d = 100 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.10. Distribution of horizontal earth pressure for compacted sand with d = 100 mm
135
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
(m )
Jaky Rankine (Passive) Coulomb (Passive) d = 1500 mm d = 1100 mm d = 900 mm d = 700 mm d = 400 mm d = 300 mm d = 200 mm d = 100 mm
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο, δw = 13.3ο, δi = 23.6ο
Fig. 7.11. Distribution of horizontal earth pressure for compacted sand at
different spacing d
0
0.2
0.4
0.6
0.8
1 K
o, h
Jaky Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.12. Distribution of Ko,h for compacted sand with different spacing d
137
-100
-80
-60
-40
-20
0
20
40
60
80
100
Jaky Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Line/Symbol Plot 5
Compacted Sand
138
0
0.2
0.4
0.6
0.8
H
h/H = 0.33 h/H = 0.66 Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
h/H = 0.33
h/H = 0.66
Fig. 7.14. Point of application for compacted sand with different spacing d
139
0
0.2
0.4
0.6
0.8
1 K
o, h
Jaky (Loose Sand) Jaky (Dense Sand) Janssen (1895) (Loose Sand) Janssen (1895) (Dense Sand) Reimbert & Reimbert (1976) (Loose Sand) Reimbert & Reimbert (1976) (Dense Sand) Spangler & Handy (1982) (Loose Sand) Spangler & Handy (1982) (Dense Sand) This Study (Loose Sand) This Study (Compacted Sand)
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 7.15. Comparison of Ko,h for loose and compacted sand with different spacing d
140
0
0.2
0.4
0.6
0.8
H
Janssen (1895) (Loose Sand) Janssen (1895) (Dense Sand) Reimbert & Reimbert (1976) (Loose Sand) Reimbert & Reimbert (1976) (Dense Sand) Spangler & Handy (1982) (Loose Sand) Spangler & Handy (1982) (Dense Sand) This Study (Loose Sand) This Study (Compacted Sand)
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
h/H = 0.33
h/H = 0.66
Fig. 7.16. Comparison of h/H for loose and compacted sand with different spacing d
141
(after Fang et al., 2004)
Fig. 1.1. Earth pressure at-rest on the basement wall near vertical rock
faces
50
51
52
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
53
54
55
σ
σσ
σ
σ
x
y
= h
56
Fig. 2.3. Jaky’s formulation of the relationship between Ko on OC and φ mobilized in OAB (after Mesri and Hayat, 1993)
57
O
O
Eq. 2.8
Eq. 2.9
Eq. 2.11
Eq. 2.10
Fig. 2.4. Hand-calculation for estimating σh (after Peck and Mesri, 1987)
58
0 5 10 15 20 25 30 Vertical Earth Pressure, σv (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
(γ = 15.5 kN/m3)
Compacted Sand Dr = 75 %
φ = 40.8o
Fig. 2.5. Distribution of vertical earth pressure measured in soil mass
(after Chen, 2003)
Fig. 2.6. Distribution of horizontal earth pressure after compaction (after Chen, 2003)
60
Silo
Hopper
(b)
Fig. 2.7. Horizontal lamina for derivation of Janssen’s equations (redrawn after Safarian and Harris, 1985)
61
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Janssen's Solution For Rectangular Silo (a x b x H)
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
(b = 1.5 m, a = 50 mm ~ 1500 mm) H = 1.5 m
a = 50 m m
a = 1500 m m
a = 100 m m
a = 700 mm
Fig. 2.8. Distribution of earth pressure for Janssen’s solution with different hydraulic radius R
62
h
max
(b) Fig. 2.9. Lamina of stored material for derivation of the Reimbert’s
equations (redrawn after Safarian and Harris, 1985)
63
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Jaky, Ko Rankine, Ka
Reimbert & Reimbert's Solution For Rectangular Silo (a x b x H)
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
(b = 1.5 m, a = 50 mm ~ 1500 mm) H = 1.5 m
a = 50 m m
a = 1500 m m
a = 100 m m
a = 200 m m
a = 400 m m
a = 700 m m
Fig. 2.10. Distribution of earth pressure for Reimbert’s solution with different hydraulic radius R
64
Trench
Conduit
Fig. 2.11. Free-body diagram for a ditch conduit (after Spangler and Handy, 1982)
65
(a) (b)
Fig. 2.12. Distribution of soil pressure against fascia walls to partial
support from wall friction F (after Spangler and Handy, 1982)
66
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Ottawa Sand γ = 15.6 kN/m3
φ = 31.3o
δw = 9.3o
B = 50 m
B = 400 mm B = 700 mm
Fig. 2.13. Distribution of earth pressure for Spangler and Handy's solution with different distance B
67
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
Jaky (At-Rest) Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1984)
γ = 15.6 kN/m3
δw = 9.3o
Fig. 2.14. Comparison of earth pressure calculated with different theories
for d = 900 mm
Fig. 2.15. Model retaining wall (after Frydman and Keissar, 1987)
69
15001500
70
Fig. 3.2. Locations of soil-pressure transducers mounted on the wall (after Chen and Fang, 2002)
71
Adaptor
Φ = 13 mm
ducer (Kyowa PGM-0.2KG)
Dynamic Strain Amplifiers (Kyowa: DPM601A and DPM711B)
NI BNC – 2090 Adaptor Board
Fig. 3.4. Data acquisition system
73
Handle
74
(Front-view)
(a) Front view of the strip soil compactor and the model wall
Model Wall
Fig. 3.6. Strip vibratory soil compactor
75
Steel Tube
Steel Tube
(d) Steel tube and compaction plate
Fig. 3.6. Strip vibratory soil compactor (cont’d)
76
50
100
150
200
No. of Acentric Plate
0 0 10 20 30 40
Fig. 3.7. Acentric force as a function of number of acentric plate
(Mikasa KJ75)
21 00
21 00
42 2
32 0
42 7
43 0
31 5
Steel Plate (4.5 mm thick)
Steel L-Beam (65 x 65 x 8 mm)
(a) Front-view (b) Back-view
78
79
80
(a)
(b)
Walkway
Fig. 4.3. Top supporting beam
1210
1084
81
297
82
1195 × 297 × 125 mm
C-clamp
Soil Pressure Transducer
Fixing Plate
Soil Bin
(a) Side-view
Model Wall
d = 900Top Supporting Beam C-clamp
Base Spacing Plate
Base Spacing Plate
Vertical Interface Plate
Base Supporting Frame (297 x 1195 x 125 mm)
(b) Top-view
Fig. 4.6. Model retaining wall near a vertical interface plate with d = 900
mm
84
85
ination of base spacing plates for d = 900 mm
300 × 200 × 17.5 mm
Plastic Sheets Lubricating
Beam
Fig. 4.9. For d = 900 mm between interface plate and model wall
87
H =
C-clamp
d = 1500 d = 1100
d = 900 d = 700
d = 500 d = 400
d = 300 d = 200
d = 100 d = 50
Fig. 4.10. Different spacing d between interface plate and model wall
88
H =
Model Wall
Fig. 4.11. For d = 1500 mm between interface plate and model wall
89
90
H =
Base Supporting Frame
Base Spacing Plate
(a)
(b)
Fig. 4.12. For d = 50 mm between interface plate and model wall
d = 50 mm Interface Plate
Model Wall
0
20
40
60
80
) Ottawa Silica Sand ASTM C-778
Fig. 5.1. Grain size distribution of Ottawa sand (after Chen, 2001)
91
(after Wu, 1992)
Unit Weight, γ (kN/m3 )
Fig. 5.3. Relationship between unit weight γ and internal friction
angle φ (after Chang, 2000)
93
Fig. 5.4. Direct shear test arrangement to determinate wall friction angle
δW (after Ho, 1999)
94
15.50 15.75 16.00 16.25 16.50 16.75 17.00 17.25 Unit Weight , γ (kN/m3)
8.0
9.0
10.0
11.0
12.0
13.0
14.0
(d eg
re e)
Test Data (air-pluviation) δW = 3.41γ - 43.69 Test Data (compaction) δW = 3.08γ - 37.54
Ottawa Sand σN = 79.8 kN/m2
Fig. 5.5. Relationship between unit weight γand wall friction angleδW
(after Ho, 1999)
95
96
Fig. 5.6. Plastic sheets lubrication layer hung on the side wall
Lubrication layer (1 thick + 2 thin plastic sheets)
Steel Interface Plate
Model Wall
Fig. 5.7. Schematic diagram of sliding block test. (after Fang et al., 2004)
97
δ
Standard weight↓
(after Fang et al., 2004)
98
Sliding Block Test Plastic-sheet method 1 thick + 2 thin sheeting
1 10 Normal Stress, σ (
5
15
0
10
(after Fang et al., 2004)
99
o
80
(b) Steel plate with Safety-Walk
Fig. 5.10. Direct shear test to determinate friction angle δi of the
interface plate with Safety-Walk
10
15
20
25
30
Ottawa Sand σn = 4.60 kN/m2
Fig. 5.11. Relationship between unit weight γ and interface plate friction
angle δi
15 16 17 18 19 20 Unit Weight, γ (kN/m3)
0
10
20
30
40
50
φair = 6.43γ - 68.99 (Chang, 2000)
φcomp = 7.25γ - 79.5 (Chang, 2000)
δi, comp = 1.97γ - 8.9
δi, air = 2.7γ - 21.39
δw, comp = 3.08γ - 37.54 (Ho, 1999)
δw, air = 3.41γ - 43.69 (Ho, 1999)
ip between unit weight γ aFig. 5.12. Relationsh nd friction angle for
different types of interfaces
Fig. 5.14. Air-pluviation of the Ottawa sand into soil bin
104
0
0.3
0.6
0.9
1.2
(m )
Compacted Backfill 90k500 mm Strip Compactor No. of Acentric plates = 8 + 8 Drop Height = 1.5 m Lift Thickness = 0.5 m D
r = 70%
0.1 m
0.5 m
Fig. 5.15. Distribution of soil density with depth for sand compacted with
the 90 mm × 500 mm strip compactor
105
Steel Tube
Model Wall
Fig. 5.16. Backfill compacted with 90 mm × 500 mm strip compactor
106
H =
10 0
10 0
Fig. 5.17. Backfill compacted with 90 mm × 500 mm compactor for d =
900 mm
Steel Interface Plate
90 mm x 500 mm compacting plate
Fig. 5.18. Backfill compacted with 90 mm × 500 mm compactor in 10 lanes
108
109
110
d= 900Top Supporting Beam
Fig. 5.21. Locations of soil density control cups at the same elevation
111
(b) Cup filled and Buried in Backfill
(c) Compaction of soil
V Ws
d =γ
(e) Soil mass in cup weighted (f) Calculation of dry density
Fig. 5.22. Procedure of density control test
112
100 r (%)
Dr = 72% ± 2.8% Lift = 0.1 m
Loose Sand γ = 15.6 kN/m3
Dr = 35% ± 3.1% Drop Height = 1.5 m Slot Opening = 18 mm
D r =
3 2%
D r =
D r =
7 5%
This Study
Fig. 5.23. Distribution of soil density for loose and compacted sand
113
(a)
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0128 Test 0216
Loose Sand d = 1500 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
(b)
Fig. 6.1. Distribution of horizontal earth pressure for loose sand with d =
1500 mm
114
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0616 Test 0619
Loose Sand d = 1100 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.2. Distribution of horizontal earth pressure for loose sand with d =
1100 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0503
Loose Sand d = 900 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.3. Distribution of horizontal earth pressure for loose sand with d =
900 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0428 Test 0430 Test 0503
Loose Sand d = 700 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.4. Distribution of horizontal earth pressure for loose sand with d =
700 mm
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0409 Test 0412
Loose Sand d = 500 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.5. Distribution of horizontal earth pressure for loose sand with d =
500 mm
116
0 4 8 12 16 20 Horizontal Earth Pressure, σh (kN/m2)
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0407 Test 0413
Loose Sand d = 400 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.6. Distribution of horizontal earth pressure for loose sand with d =
400 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0324 Test 0328
Loose Sand d = 300 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.7. Distribution of horizontal earth pressure for loose sand with d =
300 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0406-1 Test 0406-2
Loose Sand d = 200 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο δw = 9.3ο, δi = 20.7ο
Fig. 6.8. Distribution of horizontal earth pressure for loose sand with d =
200 mm
0 4 8 12 16 Horizontal Earth Pressure, σh (kN/m2)
20
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0331 Test 0405 Test 0609
Loose Sand d = 100 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο δw = 9.3ο, δi = 20.7ο
Fig. 6.9. Distribution of horizontal earth pressure for loose sand with d =
100 mm
118
(a)
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5
Jaky Rankine (Active) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0330 Test 0331 Test 0609
Loose Sand d = 50 mm γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
(b)
Fig. 6.10. Distribution of horizontal earth pressure for loose sand with d
= 50 mm
Z
Water
Z Sand
(c) Filled with sand
Fig. 6.11. Distribution of horizontal pressure for water and sand with d
= 200 mm
120
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
1.5 El
ev at
io n,
(m ) Jaky
d = 1500 mm d = 900 mm d = 500 mm d = 400 mm d = 200 mm d = 100 mm d = 50 mm
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
f horizontal earth prFig. 6.12. Distribution o essure for loose sand at different spacing d
121
0
0.2
0.4
0.6
0.8
1
h
Jaky Rankine (Ka) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 6.13. Distribution of Ko,h for loose sand at different spacing d
122
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
-Ko,h
Ko,h
d/H
123
0
0.2
0.4
0.6
0.8
1
h/ H
h/H = 0.33 Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Loose Sand γ = 15.6 kN/m3
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
r loose sand at dif
124
0
1
2
3
4
5
6
)
Loose Sand Jaky Janssen (1895) Reimbert and Reimbert (1976) Spangler and Handy (1982) This Study
d/H
Fig. 6.16. Distributio ut the base for loose sand with diff
n of overturning moments abo erent spacing d
125
H =
Base Supporting Frame
Base Spacing Plate
d = 100
Fig. 7.1. Different spacing d between interface plate and model wall
126
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0529 Test 0621
Compacted Sand d = 1500 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.2. Distribution of horizontal earth pressure for compacted sand with d = 1500 mm
127
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0706
Compacted Sand d = 1100 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.3. Distribution of horizontal earth pressure for compacted sand with d = 1100 mm
128
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0601
Compacted Sand d = 900 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.4. Distribution of horizontal earth pressure for compacted sand with d = 900 mm
129
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0603
Compacted Sand d = 700 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.5. Distribution of horizontal earth pressure for compacted sand with d = 700 mm
130
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0515
Compacted Sand d = 500 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.6. Distribution of horizontal earth pressure for compacted sand with d = 500 mm
131
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0524
Compacted Sand d = 400 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.7. Distribution of horizontal earth pressure for compacted sand with d = 400 mm
132
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0520
Compacted Sand d = 300 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.8. Distribution of horizontal earth pressure for compacted sand with d = 300 mm
133
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0524 Test 0612
Compacted Sand d = 200 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.9. Distribution of horizontal earth pressure for compacted sand with d = 200 mm
134
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
Jaky Rankine (Passive) Coulomb (Passive) Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Test 0614
Compacted Sand d = 100 mm γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.10. Distribution of horizontal earth pressure for compacted sand with d = 100 mm
135
0 4 8 12 16 2 Horizontal Earth Pressure, σh (kN/m2)
0
0
0.3
0.6
0.9
1.2
(m )
Jaky Rankine (Passive) Coulomb (Passive) d = 1500 mm d = 1100 mm d = 900 mm d = 700 mm d = 400 mm d = 300 mm d = 200 mm d = 100 mm
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο, δw = 13.3ο, δi = 23.6ο
Fig. 7.11. Distribution of horizontal earth pressure for compacted sand at
different spacing d
0
0.2
0.4
0.6
0.8
1 K
o, h
Jaky Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Fig. 7.12. Distribution of Ko,h for compacted sand with different spacing d
137
-100
-80
-60
-40
-20
0
20
40
60
80
100
Jaky Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) Line/Symbol Plot 5
Compacted Sand
138
0
0.2
0.4
0.6
0.8
H
h/H = 0.33 h/H = 0.66 Janssen (1895) Reimbert & Reimbert (1976) Spangler & Handy (1982) This Study
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
h/H = 0.33
h/H = 0.66
Fig. 7.14. Point of application for compacted sand with different spacing d
139
0
0.2
0.4
0.6
0.8
1 K
o, h
Jaky (Loose Sand) Jaky (Dense Sand) Janssen (1895) (Loose Sand) Janssen (1895) (Dense Sand) Reimbert & Reimbert (1976) (Loose Sand) Reimbert & Reimbert (1976) (Dense Sand) Spangler & Handy (1982) (Loose Sand) Spangler & Handy (1982) (Dense Sand) This Study (Loose Sand) This Study (Compacted Sand)
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
Fig. 7.15. Comparison of Ko,h for loose and compacted sand with different spacing d
140
0
0.2
0.4
0.6
0.8
H
Janssen (1895) (Loose Sand) Janssen (1895) (Dense Sand) Reimbert & Reimbert (1976) (Loose Sand) Reimbert & Reimbert (1976) (Dense Sand) Spangler & Handy (1982) (Loose Sand) Spangler & Handy (1982) (Dense Sand) This Study (Loose Sand) This Study (Compacted Sand)
Compacted Sand γ = 16.5 kN/m3
Dr = 72 % φ = 40.1ο
δw = 13.3ο, δi = 23.6ο
Dr = 35 % φ = 31.3ο
δw = 9.3ο, δi = 20.7ο
h/H = 0.33
h/H = 0.66
Fig. 7.16. Comparison of h/H for loose and compacted sand with different spacing d
141
(after Fang et al., 2004)
