session 11 – 12 lateral earth pressure course: s0484/foundation engineering year: 2007 version:...
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Session 11 – 12 LATERAL EARTH PRESSURE
Course : S0484/Foundation Engineering
Year : 2007
Version : 1/0
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LATERAL EARTH PRESSURE
Topic:• General • Active earth pressure
– Rankine earth pressure– Coulomb earth pressure– Lateral earth pressure due to surcharge
• Passive earth pressure– Rankine earth pressure– Coulomb earth pressure
• Influence of ground water table
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GENERAL
• Lateral earth pressure represents pressures that are “to the side” (horizontal) rather than vertical.
• Caused by soil self weight and or external load
• 3 categories:– At rest earth pressure– Active earth pressure– Passive earth pressure
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AT REST EARTH PRESSURE
The at rest pressure develops when the wall experiences no lateral movement. This typically occurs when the wall is restrained from movement such as a basement wall that is supported at the bottom by a slab and at the top by a floor framing system prior to placing soil backfill against the wall.
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ACTIVE EARTH PRESSURE
The active pressure develops when the wall is free to move outward such as a typical retaining wall and the soil mass stretches sufficiently to mobilize its shear strength.
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PASSIVE EARTH PRESSURE
If the wall moves into the soil, then the soil mass is compressedsufficiently to mobilize its shear strength and the passive pressure develops.
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AT REST EARTH PRESSURE
q
v
h
z v = . z + q
v
hK
At rest, K = Ko
Jaky, Broker and Ireland Ko = M – sin ’
Sand, normally consolidated clay M = 1
Clay with OCR > 2 M = 0.95
Sherif and Ishibashi Ko = + (OCR – 1)
= 0.54 + 0.00444 (LL – 20)
= 0.09 + 0.00111 (LL – 20)
LL > 110% = 1.0 ; = 0.19
Broker and IrelandKo = 0.40 + 0.007 PI , 0 PI 40Ko = 0.64 + 0.001 PI , 40 PI 80
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ACTIVE EARTH PRESSURE
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ACTIVE EARTH PRESSURE
Ka = tan2 (45 - /2)
1 = 3 . tan2 (45+/2)+2c.tan (45+/2)
a = v . tan2(45-/2) – 2c . tan (45-/2)
a = v . Ka – 2cKa
RANKINE ACTIVE EARTH PRESSURE
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ACTIVE EARTH PRESSURE
Note :
z = 0 v = 0 ; a = -2cKa
z = H v = H
The tensile stress decreases with depth and becomes zero at a depth z = zc or
zcKa – 2cKa = 0
and
a
cK
cz
2
zc = depth of tensile crack
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ACTIVE EARTH PRESSURE
RANKINE ACTIVE EARTH PRESSURE FOR INCLINED BACKFILL
1cossincos8cos4coscoscos4sincos2cos2cos
1'
:
22
2
22222
z
c
z
c
z
cK
where
a
22
22
coscoscos
coscoscoscosKa
Ka.H..Pa 22
1 (for granular soil, c = 0)
For c- soil
cos'aaa zKzK
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ACTIVE EARTH PRESSURE
Assumptions:
-Fill material is granular soil
- Friction of wall and fill material is considered
- Soil failure shape is plane (BC1, BC2 …)
Pa = ½ Ka . . H2
2
2
2
)sin().sin()sin().sin(
1sin.sin
)(sinKa
COULOMB ACTIVE EARTH PRESSURE
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ACTIVE EARTH PRESSURE
COULOMB’S ACTIVE EARTH PRESSURE WITH A SURCHARGE ON THE BACKFILL
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PASSIVE EARTH PRESSURE
RANKINE PASSIVE EARTH PRESSURE
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PASSIVE EARTH PRESSURE
p= v . tan2(45+/2) + 2c . tan (45+/2)
RANKINE PASSIVE EARTH PRESSURE
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PASSIVE EARTH PRESSURE
Kp = tan2 (45 + /2)
h = v . Kp + 2cKp
RANKINE PASSIVE EARTH PRESSURE
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PASSIVE EARTH PRESSURE
2
2
2
)sin().sin()sin().sin(
1sin.sin
)(sinKp
Pp = ½ Kp . . H2
COULOMB PASSIVE EARTH PRESSURE
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LATERAL EARTH PRESSURE DUE TO SURCHARGE
222
2
ba
ba.
nH
q2
222
2
ba
ba.
nH
q4
22b16,0
b203,0.
H
q
a > 0,4
a 0,4
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LATERAL EARTH PRESSURE DUE TO SURCHARGE
2cos.sinH
q
12H90
qP
12
122
H2
H'a30,57QRHz
H
'btan 1
1
H
'b'atan 1
2
22 90'b'aR
12 90'bQ
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PURPOSE OF LATERAL EARTH PRESSURE
• STABILITY ANALYSIS GRAVITY WALL AGAINST– SLIDING– OVERTURNING
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PURPOSE OF LATERAL EARTH PRESSURE
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PURPOSE OF LATERAL EARTH PRESSURE