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)