Lateral Earth Pressure

1
Lateral Earth Pressure
sv
H
sh

• We can calculate sv
• Now, calculate sh which is the horizontal
  stress
• sh/ sv K
• Therefore, sh Ksv (sV is what?)

2
Lateral Earth Pressure

• There are 3 states of lateral earth pressure
• Ko At Rest
• Ka Active Earth Pressure (wall moves away from
  soil)
• Kp Passive Earth Pressure (wall moves into
  soil)
• Passive is more like a resistance

sv
z
H
sh
3
At Rest Earth Pressure
At rest earth pressure occur when there is no
wall rotation such as in a braced wall (basement
wall for example) Ko can be calculated as
follows Ko 1 sin f for coarse
grained soils Ko .44 .42 PI / 100 for
NC soils Ko (oc) Ko (NC) (OCR)1/2 for OC
soils
sv
z
H
sh
4
Active Earth Pressure
Active earth pressure occurs when the wall tilts
away from the soil (a typical free standing
retaining wall)
5
Active Earth Pressure
Active earth pressure occurs when the wall tilts
away from the soil (a typical free standing
retaining wall)
6
Active Earth Pressure
Active earth pressure occurs when the wall tilts
away from the soil (a typical free standing
retaining wall)
7
Active Earth Pressure
Active earth pressure occurs when the wall tilts
away from the soil (a typical free standing
retaining wall) Ka can be calculated as
follows Ka tan2 (45 f/2) thus sa
Ka sv 2 c (Ka)1/2
Soil sliding down pushing the wall
Failure wedge
H
45 f/2
8
Passive Earth Pressure
Passive earth pressure occurs when the wall is
pushed into the soil (typically a seismic load
pushing the wall into the soil or a foundation
pushing into the soil) Kp can be calculated as
follows Kp tan2 (45 f/2) thus sp
Kp sv 2 c (Kp)1/2
Soil being pushed up the slope
H
Failure wedge
45 - f/2
9
Active Stress Distribution (c 0)
? c 0 F dry soil
H
Pa ?
? - What is this value
sa Ka sv 2 c (Ka)1/2 sa Ka sv
0
sa is the stress distribution Pa is the force
on the wall (per foot of wall) How is Pa found?
10
Passive Stress Distribution (c 0)
? c 0 F dry soil
H
Pp ?
? - What is this value
sp Kp sv 2 c (Kp)1/2 sp Kp sv
0
sp is the stress distribution Pp is the force
on the wall (per foot of wall) How is Pp found?
11
Stress Distribution - Water Table (c 0)
Effective Stress
H1
Pore Water Pressure
Ka ? H1
H2
Pa
Ka ? H1
Ka ? H2
?w H2
or
Ka (? H1 ? H 2)
Pa S areas ½ Ka ?H12 Ka ?H1H2 ½ Ka ?H22
1/2?wH22
12
Stress Distribution With Water Table
Why is the water pressure considered separately?
(K)
Effective Stress
H1
Pore Water Pressure
0
Ka ? H1
H2
Pa
Ka ? H1
Ka ? H2
?w H2
or
Ka (? H1 ? H 2)
13
Active Stress Distribution (c ? 0)
zo
? c ? 0 F dry soil
H
_
-

Ka ?H
2 c (Ka)1/2
Ka ?H 2 c (Ka)1/2
Find zo Ka ?zo 2 c (Ka)1/2 0 Zo 2c / ?
(Ka)1/2 Pa ?
14
Passive Stress Distribution (c ? 0)
? c ? 0 F dry soil
H

-

Kp ?H
2 c (Kp)1/2
Kp ?H 2 c (Kp)1/2
Pp ?
15
Practice Problems
Chapter 12 Problems 13 15 (part c is using
equation 12.47 and part d uses equation
12.49) 25 13 and 25 are the same problem just
one is active calcs and the other is passive
calcs