Mechanism of stress reduction of compaction-induced pressure

Chen (2003) proposed the mechanism of lateral stess increase due to backfill compaction. The bearing capacity failure of a surface footing is used to interpret the mechanism of soil behavior due to vibratory compaction. Fig. 2.36 shows if the cyclic compacity stress σ_cyc applied on the surface of fill exceeded the ultimate bearing capacity q_ult of foundation soil, the loaded surface ab would settle and shear failure zone would develop in the uppermost layer of fill. In Fig. 2.36 (a), the soil element A in zone III would be in the passive Rankine zone. The soil element is compressed laterally. The moving and capacity of the tamper all over the soil surface would result in a passive soil layer near the top of the compacted fill.

In this study, with the active wall movement, the soil elements near the model wall is subjected to lateral extension. With the increasing wall movement, the soil elements in the compaction influenced zone are allowed to expand laterally, and the

48

passive state of stress no longer exists. Eventually, an active state is reached and the extra horizontal pressure induced by compaction would gradually vanish.

49

Chapter 6 Conclusions

This paper studies the reduction of compaction-induced earth pressure with active wall movement. A new KA model retaining wall facilty of National Chiao Tung University has been designed and constructed. Based on the experimental data obtained during this investigation, the following conclusions can be drawn about earth pressure acting on a rigid wall that moves toward a backfill of dry sand under translational movement.

1. The earth pressure induced by compaction vanished rapidly with the active wall movement. An active state of stress is reached at the wall movement of S/H = 0.0010.

2. The distribution of active earth pressure is slightly higher than Coulomb’s solution at the upper one-third of wall height, approximately in

agreement with Coulomb’s solution in the middle one-third, and lower than Coulomb’s solution at the lower one-third of wall surface. Stresses that was locked-in the soil element has been released with the lateral extension of the active soil wedge.

3. The horizontal earth presure coefficient Kh decreases with increasing wall movement and finally a constant total thrust is reached. The active

condition occurred at the wall movement of approximately S/H= 0.001.

50

4. The experimental Ka,h values are in good agreement with Coulomb and Rankine’s prediction.

5. The active thrust is located at about 0.55H above the base of the wall.

6. The active coefficient K_a,h values obtained with compacted dense sand from this study are in fairly good agreement with Coulomb and Rankine’s prediction.

7. The Rankine theory is suitable to predict the location of surface crack for active failure.

51

References

1. Bowles, J. E. (1988). Foundation analysis and design, 4^th Edition, McGraw-Hill Book Co., 474.

2. Brinch Hansen, J. (1953). “Earth pressure calculation.” Danish Technical Press, Copenhagen.

3. Bransby, P.L., and Smith, A.A. (1975). “Side friction in model retaining wall experiments.” Journal of the Geotechnical Engineering Division, ASCE, 101(GT7), July, 615-632.

4. Bros, B. (1972). “The influence of model retaining wall displacements on active and passive earth pressures in sand.” Proc., 5th European Conf. on Soil Mechanics, Madrid, 1, 241-249.

5. Chang, S.Y. (2000). “Effect of backfill density on active earth pressure.”

Master of Engineering Thesis, Dept. of Civil Engineering, National Chiao Tung University, Hsinchu, Taiwan.

6. Chen, N. C. (2005). “Earth pressure at-rest near a vertical rock face.” Master of Engineering Thesis, Dept. of Civil Engineering, National Chiao Tung

University, Hsinchu, Taiwan.

7. Chen, T. J. (2002). “Earth pressure due to vibratory compaction.” Ph.D.

dissertation, Department of Civil Engineering, National Chiao Tung University, Hsinchu, Taiwan.

52

8. D’Appolonia, D. J., Whitman, R. V., and D’Appolonia, E. (1969). “Sand compaction with vibratory rollers.”Journal of the Soil Mechanics and Foundations Division, ASCE, 95(SM1), 263-284.

9. Das, B. M. (1994). “Principal of geotechnical engineering.” PWS Publishing Company, Boston.

10. Fang, Y. S. (1983). “Dynamic earth pressures against rotating walls.” Ph.D.

dissertation, Department of Civil Engineering, University of Washington, Seattle, Washington.

11. Fang, Y. S., and Ishibashi, I. (1986). “Static earth pressures with various wall movements.“ Journal of Geotechnical Engineering, ASCE, 112(3), Mar., 317-333.

12. Fang, Y. S., Chen, J. M., and Chen, C. Y. (1997). “Earth pressures with sloping backfill.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(3), March, 250-259.

13. Fang, Y. S., Chen, T. J., Holtz, R. D., and Lee, W. F. (2004). “Reduction of boundary friction in model tests.” ASTM Geotechnical Testing Journal, 27(1), 1-10

14. Gere, J.M., and Timoshenko, S.P. (1984). “Mechanics of materials.”

Brooks/Cole.

15. Holl, D. L. (1941). “Plane strain distribution of stress in elastic media.” Iowa Engineering Experimental Station Bulletin, 148-163.

53

16. Ichihara, M., and Matsuzawa, H. (1973). “Earth pressure during earthquake.”

Soils and Foundations, Japanese Society of Soil Mechanics and Foundation

Engineering, 13(4), 75-85.

17. Ingold, T. S. (1979). “Retaining wall performance during backfilling.” Journal of the Geotechnical Engineering Division, ASCE, 105(GT5), 613-626.

18. Ingold, T. S. (1979). “The effects of compaction on retaining walls.”

Geotechnique, 29(3), 265-283.

19. Janbu, N. (1957). “Earth pressure and bearing capacity calculation by gerneral procedure of slices.” Proceedings, 4^th Int. Conf. Soil Mechs. Found. Eng., London, 2, 207-212.

20. Lo Presti, D. C. F., Pedroni, S., and Crippa, V. (1992). “Maximum dry density of cohesionless soils by pluviation and by ASTM D 4253-83: A comparative study.” ASTM Geotechnical Testing Journal, 15(2), 180-189.

21. Mackey, R. D., and Kirk, D. P. (1967). “At rest, active and passive earth pressures.” Proc., South East Asian Conference on Soil Mechanics and Foundation Engineering, Bangkok, 187-199.

22. Matteotti, G. (1970). “Some results of quay-wall model tests on earth pressure.”

Proceeding, Institution of Civil Engineers, 47, 185-204.

23. Morgenstern, N. R., and Eisenstein, Z. (1970). “Methods of estimating lateral loads and deformations.” Proceedings, ASCE Specialty Conference on Lateral Stresses in the Ground and the Design of Earth Retaining Structures, Cornell University, 51-102.

54

24. NAVFAC. (1982). Foundations and earth retaining structures design manual, Dept. of Navy, DM 7.2, Alexandria, Va.

25. Peck, R. B., and Mesri, G. (1987). Discussion of “Compacted-induced earth pressures under K -conditions.” Journal of Geotechnical Engineering, ASCE, _o 113(11), 1406-1408.

26. Rad, N. S., and Tumay, M. T. (1987). “Factors affecting sand specimen preparation by raining.“ ASTM Geotechnical Testing Journal, 10(1), 31-37.

27. Sherif, M. A., Ishibashi, I., and Lee, C. D. (1982). ”Earth pressure against rigid retaining walls.” Journal of Geotechnical Engineering, ASCE, 108(5), May, 679-695.

28. Sowers, G. B., and Sowers, G. F. (1961). Introductory soil mechanics and foundations, New York: Macmillan, 386.

29. Terzaghi, K. (1932). “Record earth pressure testing machine.” Engineering News-Record, 109, Sep., 29, 365-369.

30. Terzaghi, K. (1934). “Large retaining-wall tests.” Engineering News-Record, 111, 136-140.

31. Terzaghi, K. (1941). “General wedge theory of earth pressure.” ASCE Transaction, 106, 68-80.

32. Wang, F. J. (2005). “Effects of adjacent rock face inclination on earth pressure at-rest.” Master of Engineering Thesis, Dept. of Civil Engineering, National Chiao Tung University, Hsinchu, Taiwan.

55

33. Wu, B. F. (1992). “Design and construction of National Chiao Tung University model retaining wall.” Master of Engineering Thesis, Dept. of Civil

Engineering, National Chiao Tung University, Hsinchu, Taiwan.

56

Table 3.1. Wall displacements required to reach active state

Note: RB = Rotation about base; RT = Rotation about top; T = Translation; and H = Wall height

Investigator Soil Type Type of Wall Movement

Max. Wall Displacement Required

Loose Sand 0.0020 H

Sowers and Sowers

(1961) Dense Sand RB mode

0.0005 H

Loose Sand 0.0040 H

Mackey and Kirk (1967)

Dense Sand T mode

Loose Sand 0.0020 H

NAVFAC DM-7.2 (1982)

Dense Sand ___

0.0005 H

Loose Sand 0.0020~0.0040 H

Bowles (1988)

Dense Sand ___

0.0010~0.0020 H Fang et al. (1997) Loose Sand T mode 0.0015 H

57

Table 4.1. Properties of Ottawa sand

Shape Rounded

emax 0.76

emin 0.50

G s 2.65

60,

D mm 0.32

10,

D mm 0.21

C u 1.78

58

Table.5.1 Active wall movement at the end of compaction

Test No. (S/H)up (S/H)down (S/H)avg

0826 0.00053 0.00050 0.00052

0827 0.00047 0.00051 0.00049

0829 0.00040 0.00053 0.00046

59

(a) Bridge Abutment

(b) Elevated Highway or Railroad

(c) Depressed Highway or Railroad

(d) Hillside Highway or Railroad

(e) Canal

(f) Retains Fill around Building

(g) Flood Wall

(h) Material Storage

Fig. 1.1 Common uses of retaining walls (after Fang, 1983)

60 Wall Displacement

Passive Pressure

Compacted Backfill

Active Pressure

Fig. 1.2 Earth pressure under active wall movement

61

Fig. 2.1 Coulomb’s theory of active earth pressure

62 B

Pa(max)

C³ C2

C1

A

θ

φ H/3

H

δ Pa

F

Backfill W

β

Wall Moves away from backfill

Soil Thrust

i

Fig. 2.2 Determination of Coulomb’s active earth pressure

63

σ^a σ^a

(b) (a)

H i i

B B A A Wall Moves away from backfill

φγ

Wall

Fig. 2.3 Rankine’s theory of active earth pressure

64

45°+φ/2

δ

45°+φ/2

c a

Ideal Rankine Zone

Log-Spiral

Rupture Surface d

b P

^a

H/3

H Wall

Fig. 2.4 Failure surface in soil by Terzaghi’s log-spiral method

65

r

r

^o

45°+φ/2

O

¹

θ

f

^{1 45°+φ/2}

δ

c

¹

a

Log-Spiral d

b P

^a H/3

H

Fig. 2.5 Evaluation of active earth pressure by trial wedge method

66

Soil

δ

δ f

¹

a

O

¹

l

²

l

¹

P

¹

b

d

¹

H

^d1

/3 P

^d1

H

^d1

l

³

W

¹

dF H/3

Fig. 2.6 Stability of soil mass abd1f1

67

3 4 1 2

Trial 4 Trial 3 Trial 2 Trial 1 f

1

P

a

d b

a

H/3

O

¹

P

a

δ H

45°+φ/2

Fig. 2.7 Active earth pressure determination with Terzaghi’s log-spiral failure surfaces

68

PERCENTAGE (Rankine Theory = 100 %)

δ = φ

PERCENTAGE (Rankine Theory = 100 %) _Rankine

Log Spiral (after Morgenstern and Eisenstein, 1970)

69

Fig. 2.9 MIT model retaining wall ( after Terzaghi, 1932 )

70

Test 1 and Test 2 Compacted Sand

0.00036h

Test 1

tilting wall Test 2 sling wall

0.00057h b 0.001hc 3hr d

71

0.00057h

0.00036h

Test 1

Compacted Sand Tilting Wall

0.001h

a 3hr

b

d c' c

0 0 0.5 1.0 1.5 2.0 2.5 0.1

0.2 0.3 0.4 0.5

Wall Movement, mm

Height of Center, h

c

/h

Fig. 2.11 Height of center of pressure in relation to yield of wall (after Terzaghi, 1934)

72

SECTIONAL ELEVATION A-A

Wall Face

Fixed Slep Drive shaff

wheel

SECTIONAL ELEVATION B-B Base Channel (after Mackey and Kirk, 1967)

73

Pressure , psi

Wall Movement , in

9"

6"

3"

0.2 0.3

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 2.13 Earth pressure with wall movement ( after Mackey and Kirk, 1967)

74

0 2 4 6 8 10

12 8 4 0

Loose Sand DISTANCE FROM WALL, in

DEPTH OF SAND, in

3 2 1

1

3 2

Coulomb δ=0

Sand 1: A uniformly graded fine sand Sand 2: A medium graded sand

Sand 3: A uniformly graded coarse sand

Fig. 2.14 Failure surfaces ( after Mackey and Kirk, 1967)

75

Fig. 2.15 College of Agriculture model retaining wall (after Bros, 1972)

76

0.0123 h

0.0076 h

0.0041 h

0.0018 h0.0006 h

S

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

K TEST NR 17/1

Fig. 2.16 Active earth pressure coefficient under T mode with wall movement (after Bros, 1972)

77

0.0008h 0.0018h 0.0035h 0.0065h 0.0100h 0.0147h

S TEST NR 15/1

RB Mode

Fig. 2.17 Active earth pressure coefficient under both RT and RB mode with wall movement (after Bros, 1972)

78

Fig. 2.18 Shaking table, soil box, and actuator (after Sherif et al., 1982)

Aluminum Plates

79 P1, P2, P3 : Horizontal Load Cells

(Note : P3 is Behind P4)

(Note : P3 is Right Below P1)

Fig. 2.19 Shaking table with movable retaining wall (after Sherif et al., 1982)

80

kSh,(h/H)S ,tanδ

S (X 10-3 inches)

Test No.1113

Soil Specimen:Loose Ottawa Sand

γ=1.54 g/cm3 , φ = 31.5°

Speed of Wall Displacement 1.50×10-3 in/sec (after Sherif et al., 1982)

81

Fig. 2.21 Experimental KSah values at S /H=0.001 versus soil density (after Sherif et al., 1982)

1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 γ (gr/ cm

³

)

0.00 0.10 0.20 0.30 0.40

K

A, h

a t S / H = 1/ 1000

32.00 34.00 36.00 38.00 40.00 φ

Static Active

Coulomb's

82

Rotation about Top (RT mode) Test 406 (Loose Backfill)

γ = 98.8 pcf

Wall Rotation ( x10 radian)^-4

Normalize Lateral Pressure, k = σh/γz

0 1 2 3 0 5 6 7 8 9 10

Fig. 2.22 Change of normalized lateral pressure with wall rotation about top (loose backfill) (after Fang and Ishibashi, 1986)

83

Rotation about Top (RT mode)

γ

= 98.8 pcf

Lateral Earth Pressure (psf)

Depth (ft)

Fig. 2.23 Distributions of horizontal earth pressure at different wall rotation (rotation about top ) (after Fang and Ishibashi, 1986)

84 Test: 310

γ

= 97.7 pcf

Rotation about Base (RB mode)

Wall Base Line

Lateral Earth Pressure (psf)

Depth (ft)

Fig. 2.24 Distributions of horizontal earth pressure at different wall rotation (rotation about base ) (after Fang and Ishibashi, 1986)

85

Rotation about Base Test: 310

γ

= 97.7 pcf

tanδ

K

h

K

h

, h/H, tan δ h/H

0 20 40 60 80

Wall Rotation ( x10 radian)^-4

10 30 50 70

0.1 0.2 0.3 0.4 0.5 0.6

0.0

Fig. 2.25 Horizontal earth pressure coefficient Kh, relative height of resultant pressure application h/H, and coefficient of wall friction tanδ Versus wall rotation(rotation about base ) (after Fang and Ishibashi. 1986)

86

Translation (T mode) Test: 342

γ = 98.1 pcf

Normalize Lateral Pressure, k = σh/γz

0.0

Fig. 2.26 Change of normalized lateral pressure with translation wall displacement (after Fang and Ishibashi, 1986)

87

Lateral Earth Pressure (psf)100 80

Fig. 2.27 Distributions of horizontal earth pressure at different wall displacement (after Fang and Ishibashi, 1986)

88

Density (pcf)

Coefficient of Horizontal Active Thrust, KA,h

φ (degree)

Translation + Rotation about base (Ichihara & Matsuzawa, 1973) Translation

Fig. 2.28 Coefficient of horizontal active thrust as a function of soil density (after Fang and Ishibashi, 1986)

89

-25 -15 -5 5 15 25

i, (Degree) 0

0.001 0.002 0.003

(S/H)a

Loosed Sand

i

Fig. 2.29 (S/H)a versus backfill inclination (after Fang et al., 1997)

90

Rankine Terzaghi Coulomb

NCTU Data (S = 0.003H)

i, (Degree)

K

a,h

0.6 0.5 0.4 0.3 0.2

0.1

0.0 -25 -15 -5 5 15 25

Fig. 2.30 Active earth pressure coefficient Ka,h versus backfill inclination (after Fang et al., 1997)

91

Eq. 2.12

Eq. 2.13 Eq. 2.11

Eq. 2.10

σ

h

d b c

a

Depth, z

Lateral Pressure,

Fig. 2.31 Hand-calculation for estimating σ_h (after Peck and Mesri, 1987)

92

Model Wall

Footb Wall oard

Steel Column Steel Base Plate

Sidewall

20 45

End

1500 1500

Unit : mm

1600

Fig. 2.32 National Chiao Tung Univ. non-yielding retaining wall facility

93

Fig. 2.33 Distribution of vertical earth pressure mearsured in soil mass (after Chen, 2003)

94

Fig. 2.34 Stress path of a soil element under compaction (after Chen, 2003)

0 5 10 15 20 25 30

Horizontal Earth Pressure, σh (kN/m2)

F : Fill

C : Compaction

Test C0727 Elevation : 0.15 m σ_h by SPT 2

Horizontal Earth Pressure, σh (kN/m2) F : Fill

C : Compaction Elevation : 0.55 m σ_h by SPT 6

Horizontal Earth Pressure, σh (kN/m2) F : Fill

C : Compaction Elevation : 0.65 m σ_h by SPT 7 σ_v by SPT 107 F3

95

Fig. 2.35 Distribution of horizontal earth pressure after compaction (after Chen, 2003) Horizontal Earth Pressure, σh

0 5 10 15

96

Fig. 2.36 (a) Bearing capacity failure in soil due to compaction; (b) Modes of bearing capacity failure in sand (Chen, 2003)

97 (c) (b) (a)

Fig. 3.1 Active wall movement modes, (a) Rotation about wall top (RT mode);

(b) Rotation about wall base (RB mode); (c) Translation (T mode) (after Huang, 2003)

98 Soil

Wall Top

Z nH

Smax

O^T (Center of rotation)

H H

nH

O^B (Center of rotation) Soil

S^max

Wall Base

(a) (b)

Fig. 3.2 (a) Rotation about a point above wall top (RTT mode);

(b) Rotation about a point below wall base (RBT mode) (after Huang, 2003)

99

Fig. 3.3 Steel interface plate (2100 mm × 1497mm) (after Wang, 2005)

100

Fig. 3.4 Supporting frame (after Chen, 2005)

101 Movable Wall

M2 M1

Steel Base Plate

Steel Interface Plate

Unit:mm Base Supporting Fram

Fig. 3.5 Different interface inclinations

102

Φ2

active soil 45°+

wedge

1100

45° 577

1000

1199

design length = 1500

Unit:mm

Base Movable Wall

Steel Interface Plate (2100 mm x 1497 mm)

Fig. 3.6 Critical condition for d = 0 mm and α = 45°

103

104

Fig. 3.8 Top view of NCTU KA model retaining wall

105 Steel Beam

Steel Columns Active Soil

Wedge

Acrylic Side Wall

U-Shaped Steel Beam

Steel Beam Model Wall

(End Wall)

Unit:mm Base

Fig. 3.9 Side wall reinforcment

106

Steel Column U-Shaped Steel Beam

Base

Transparent Acrylic Steel Wall

End Wall (20 mm)

unit:mm

Transparent Acrylic Wall

Fig. 3.10 End wall reinforcement

107

Fig. 3.11 Determine positions of wall driving rods(side -view)

108

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Wall displacement S in mm.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Coeff. of Earth Pressure K

Fig. 3.12 Relationship of the coefficient of earth pressure, K, and the mean wall displacement, S (after Ichihara and Matsuzawa, 1973)

109 Center Line of the Wall

Soil Pressure Transducer

Solid Steel Model Wall

Unit:mm

Fig. 3.13 Typical cross-section of the beam

110

Model Wall

Unit:mm

Fig. 3.14 Dimensions of model retaining wall

111

(a) front view

(b) rear view

Fig. 3.15 Model retaining wall

112

Steel Ball Steel

Ball

unit:mm Fixed Bed

Model Wall

Fig. 3.16 Design of roller supports and unidirectional notches

113

Fig. 3.17 roller supports and unidirectional notches

114

Ball Steel

Base Active Wall

Movement Movable Wall

30 mm 29 mm

1 mm 50 mm

Model Wall

Fig. 3.18 Gap between model wall and fixed bed

115

Fig. 3.19 Soil pressure transducer (Kyowa PGM-0.2KG)

116

(a) front view

(b) rear view

Fig. 3.20 arrangement of soil pressure transducers

117

1100

Active Wall Movement Lower Driving

Rods

Upper Driving Rods

360

168 472 430

30 1000

70

Unit:mm Base

Movable Wall

Soil

Fig. 3.21 Geometry of the wall rotation about the top

118

1100

Active Wall Movement

Lower Driving Rods

Upper Driving Rods

360

168 472 430

30 1000

70

Unit:mm Base

Movable Wall

Soil

Fig. 3.22 Geometry of the wall rotation about the base

119

Fig. 3.23 Acrylic cover to protect driving system

120

The Programmable Logic Controller (AX2n-32MR)

Fig. 3.24 Wall-driving system

121

Fig. 3.25 Hinge-and-slider

122

Fig. 3.26 Servo motor of driving system

123

Fig. 3.27 Speed reducer and worm gear linear actuators of driving system

124

(a) Outward appearance

(b) Instrumentation inside the control panel Fig. 3.28 Control panel of wall driving system

125

Fig. 3.29 Touch control LCD display

126

Fig. 3.30 Inductive proximity switch and limit switch

127

Dynamic Strain Amplifiers (Kyowa: DPM601A and DPM711B)

NI BNC – 2090 Adaptor Board

NI – DAQ PCI – 6024E LabVIEW Program

Pentium 4, PC

Fig. 3.31 Data acquisition system

128

10 1 0.1 0.01

Particle Diameter in mm

0

20 40 60 80 100

Percent Finer by Weight (%)

Ottawa Silica Sand (ASTM C-778)

Fig. 4.1 Grain size distribution of Ottwa sand

129

Fig. 4.2 Shear box of direct shear test device (after Wu, 1992)

130

φ = 6.43γ -68.99 Air-Pluviation

Compaction

φ = 7.25γ -79.51

15.00 15.50 16.00 16.50 17.00 17.50 Unit Weight, γ (kN/m

³

)

25 30 35 40 45

φ (D eg re e)

20 40 60 80 100

D

_r

( % )

Fig. 4.3 Relationship between unit weight γ and internal friction angle φ (after Chang, 2000)

131

Fig 4.4 Pluviation of the Ottawa sand into soil bin

132

Ottawa Sand

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Drop Height, (m)

0 20 40 60 80 100 120

Relative Density, Dr (%)

Opening = 5 mm Opening = 7 mm Opening = 10 mm Opening = 15 mm

Fig. 4.5 Relationship between relation density and drop height (after Ho, 1999)

133

Fig. 4.6 Side-view of vibratory soil compactor

225 48

48

40

15

10 27

360

1000

Extension cord (5 m-long)

Handle

Switch

Motor

unit :mm

20

20

134

Acentric Motor

Square Compaction Plate (225 mm × 225 mm)

Fig. 4.7 Square vibratory soil compactor

135

Driving Rod 6

5 4 3

2 250 mm

Lane 1

Soil Compactor

Wall Gear System Ottawa Sand

Soil Pressure Transducer Movable Wall

Steel Base Plate Transparent Acrylic

Side-Wall

Fig. 4.8 Backfill compacted with square compactor in 6 lanes

136

(a) Compaction at H = 0.2 m

(b) Compaction at H= 1 m

Fig. 4.9 Compaction of backfill with square compactor

137

Fig. 4.10 Soil-density control cup

unit : mm Top-view Side-view

Acrylic Tube

Acrylic Base Plate

30

5 43

3.5

70

70

70 43

50

138

Fig. 4.11 Soil-density cup

139 Movable Wall

M2 M1

Ottawa Sand

Steel Base Plate

Density cups

Unit: mm

Fig. 4.12 Soil density cups buried at the different elevations

140

Driving Rod Wall Gear

System Density cups

Ottawa Sand

Soil Pressure Transducer Movable Wall

Steel Base Plate Transparent Acrylic

Side-Wall

Fig 4.13 Locations of soil density cups at the elevation

141

0 20 40 60 80 100

Relative Density, Dr (%)

1 0.8 0.6 0.4 0.2 0

Depth (m)

Compacted Sand Lift=0.2 m

Test 0826 Test 0829

Fig. 4.14 Distribution of soil density compacted with square compactor

142

Fig. 4.15 Relative density vs. Depth relation for vibratory roller compaction (after D’Appolonia et al., 1969)

143

Fig. 4.16 Lubrication layer on the side wall

144 600 mm

900 mm

Steel Plate

10 mm20 mm

Acrylic Plate

60 mm

27 mm

F T

N Horizontal Line

Worm Gear Uplift Rod

Soil Box Standard Weight

Handle

Lubrication Layer

δ

Fig. 4.17 Schematic diagram of sliding block test (after Fang et al., 2004)

145 Standard weight↓

↙ Sliding plate

↙ Soil box Plastic sheet ↘

←

Ball bearing

Handle

Worm gear Uplift rod

Fig.4.18 Sliding block test apparatus (after Fang et al., 2004)

146

1 10 100

Normal Stress, σ (kN/m2)

0 5 10 15 20 25

Fricti on Angle,

δ sw

(degree)

Sliding Block Test Plastic-Sheet Method 1 Thick + 2 Thin Sheeting

δsw = 7.5o

Fig. 4.19 Variation of interface friction angle with normal stress (after Fang et al., 2004)

147

Lower Shear Box

Unit : mm

Upper Shear Box

5 N

Smooth Steel Plate Dry Ottawa Sand

63

20

120

Fig. 4.20 Direct shear test arrangement to determine wall friction angle

148

15.0 15.5 16.0 16.5 17.0 17.5

Unit Weight, γ (kN/m³) 0

10 20 30 40

Wall Friction Angle, δ (Degree)

Test Data

δw =3.02γ − 29.49

20 30 40 50 60 70 80 90 100

D_r(%)

δ = 1/2 φ δ = 2/3 φ

Fig. 4.21 Relationship between unit weight γ and wall friction angle δ_w

149

15 15.5 16 16.5 17 17.5

Unit Weight , γ(kN/m³)

0

5 10 15 20 25 30 35 40 45

Friction Angle (degree)

Internal Friction Angle, φ φ = 7.25γ − 79.51

Model Wall Friction Angle, δw δw = 3.02γ − 29.49

Sidewall Friction Angle, δsw δsw = 7.5o

Fig. 4.22 Relationship between unit weight γ and different friction angles

150

Fig. 5.1 Variation of wall movements during compaction of backfill

151

30 34 38 42

Internal Friction Angle, φ (degree)

0.000 0.001 0.002 0.003

(S/H) a

This study (Compaction) Chang, 2000 (Air-Pluviation) Chang, 2000 (Compaction) Terzaghi, 1934

Bros, 1972 Sherif, et al.,1982 Fang, et al., 1997

Fig. 5.2 Variation of (S/H)a for backfill with different internal friction angle

152

S/H=0.003 S/H=0.0025 S/H=0.002 S/H=0.0015 S/H=0.001

Test No. 0827

Driving Rod

Movable Wall

1

0

H=1.0 m

Wall Movements (mm) Base Depth

(m)

3.5 0

Fig. 5.3 Wall movement for T mode (Test 0827)

153

0 4 8 12

Horizontal Earth Pressure σ_h, (kN/m²)

1

Fig. 5.4 Distribution of horizontal earth pressure (Test 0826)

154

0 4 8 12

Horizontal Earth Pressure σ

_h

, (kN/m

²

)

1

Fig. 5.5 Distribution of horizontal earth pressure (Test 0827)

155

0 4 8 12

Horizontal Earth Pressure σ

_h

, (kN/m

²

)

1

Fig. 5.6 Distribution of horizontal earth pressure (Test 0829)

156

0 2 4 6 8 10

Horizontal Earth Pressure σ

_h

, (kN/m

²

)

1 0.8 0.6 0.4 0.2 0

De p th , (m )

Jaky

Coulomb (active) Test: 0826 Test: 0827 Test: 0829

Dense Sand

(Compacted Method) S/H=0.001

Fig. 5.7 Distribution of lateral earth pressure from different tests at S/H = 0.001

157

0 2 4 6 8 10

Horizontal Earth Pressure σ

_h

, (kN/m

²

)

1 0.8 0.6 0.4 0.2 0

De p th , (m )

Jaky

Coulomb (active) Test: 0826 Test: 0827 Test: 0829

Dense Sand

(Compacted Method) S/H=0.002

Fig. 5.8 Distribution of lateral earth pressure from different tests at S/H = 0.002

158

0 2 4 6 8 10

Horizontal Earth Pressure σ

_h

, (kN/m

²

)

1 0.8 0.6 0.4 0.2 0

De p th , (m )

Jaky

Coulomb (active) Test: 0827 Test: 0829

Dense Sand

(Compacted Method) S/H=0.003

Fig. 5.9 Distribution of lateral earth pressure from different tests at S/H = 0.003

159

0 0.001 0.002 0.003

S/H

0 0.2 0.4 0.6 0.8 1

Kh

Dense Sand (Compaction Method)

Test 0826 Test 0827 Test 0829 Chen, 2000 Coulomb Rankine

Fig. 5.10 Variation of Kh as a function of wall movement

160

0 0.001 0.002 0.003

S/H

0 0.2 0.4 0.6 0.8

h/ H

Dense Sand (Compaction Method)

Test 0826 Test 0829 Test 0830 Chen, 2000 h/H= 0.33

Fig. 5.11 Location of total soil thrust as a function of wall movement

161

30 34 38 42

Angle of Internal Friction φ, ( degree )

0.0 0.1 0.2 0.3 0.4 0.5

K

a,h

This study

Chang, 2000 (Compaction) Coulomb

Rankine

Terzaghi, 1934 Mackey and Kirk, 1967 Bros, 1972

Sherif et al.,1982 Fang et al.,1997

Fig. 5.12 Activeearth pressure coefficient K_a,h for soils with different internal frction angles

162

Fig. 5.13 Surface crack of active failure (S/H=0.016)

163

Fig. 5.14 Surface crack of active failure (S/H=0.016)

164

Appendix A:

Calibration of Soil Pressure Transducers

To investigate the lateral earth pressure acting on the model retaining wall, ten strain-gage type soil pressure transducers (SPT) were used. The transducers PGM-02KG manufactured by KYOWA are installed on the surface of model retaining wall to measure the lateral earth pressure against the retaining wall. The pressure acts between soil particles and the transducer is quite different from the pressure that acts between liquid and transducer. It is necessary to calibrate the soil pressure transducer in an environment similar to that of the actual testing condition. A special system was designed for the calibration of the strain-gage type soil-pressure transducers. The system consists of the calibration device, the controlled air-pressure system, signal conditioner, and the sensor data acquisition system, as indicated in Fig.A1and Fig. A2.

The calibration device is a shallow cylindrical chamber with an inner diameter of 400 mm and a height of 30 mm. The chamber is made of a solid steel plate, which is the same material as the model retaining wall. The soil-pressure transducer was inserted through the bottom of the chamber. It is important that the surface of the sensor was installed flush with the upper face of the chamber. To simulate the interface between the sand particle and soil pressure transducer, 10 mm-thick sand layer was poured into the calibration device over the transducer.

Then a 0.2 mm-thick rubber membrane was placed over the sandy layer, as shown

165

in Fig.A.1. A uniformly distributed air-pressure was applied on the membrane, over the soil particles, and transmitted to the transducer. The output voltage of the transducer was found to increase linearly with the increase of applied pressure.

A rubber O-ring was arranged to prevent air leakage between the chamber and the cap. It should be noted that the air pressure applied for the calibration of transducer should be consistent with the operating pressure range for model wall experiments. For this study, the transducers were calibrated for the pressure range of 0 to 9.81 kPa. To reduce the effect of sidewall friction, the thickness of sand layer in the chamber should be limited, so that the side-friction between the sand the sidewall of the chamber could be minimized. Fig.A.3 to Fig.A.10 shows the test results of the soil pressure transducers calibrated without the compressible layer. Table A.1 is a summary of the calibration factors of each soil pressure transducer.

166

Table A1. Soil Pressure Transducer Calibration Factors

Dynamic Strain Amplifier Transducer No.

No. Range Selector

(*100µξ) Calibration Setter(µξ) Capacity(kN/m²) Calibration Factor[(kN/m²)/volt]

EX3270003 1 5 1981 19.62 3.621

EG6210026 2 5 1906 19.62 3.481

EZ0660029 3 5 2090 19.62 2.860

YT4030029 4 5 2465 19.62 4.417

YT4030042 5 5 2510 19.62 2.977

EE2450023 6 5 1984 19.62 2.643

EZ0660017 7 5 2014 19.62 3.179

EG6210005 8 5 2005 19.62 3.771

YT4030032 9 5 2220 19.62 3.539

EX3270002 10 5 2014 19.62 3.824

167

Fig. A1 Schematic diagram of the soil pressure transducer calibration system.

168 Pressure Gauge

Pressure Regulator

Calibration Device

Air Leakage Check

Transducer

Fig. A2. Soil pressure transducer calibration system

169

Fig. A3. Applied pressure versus voltage output for soil pressure transducer SPT01 and SPT02

170

Fig. A4. Applied pressure versus voltage output for soil pressure transducer SPT03 and SPT04

171

Fig. A5. Applied pressure versus voltage output for soil pressure transducer SPT05 and SPT06

172

Fig. A6. Applied pressure versus voltage output for soil pressure transducer SPT07 and SPT08

173

Fig. A7. Applied pressure versus voltage output for soil pressure transducer SPT09 and SPT10

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