This document discusses lateral earth pressures, including the calculation of at-rest (Ko), active (Ka), and passive (Kp) pressure coefficients. It provides equations to calculate these coefficients based on soil properties like internal friction angle (φ). Graphs show the stress distributions for different cases, such as with and without cohesion (c) and the influence of a water table. Practice problems are recommended from Chapter 12 involving calculating active and passive pressures using the provided equations.

1. Lateral Earth Pressure
σv’
H
σh’
• We can calculate σv’
• Now, calculate σh’ which is the horizontal stress
• σh‘/ σv‘ = K
• Therefore, σh‘ = Kσv‘ (σV‘ is what?) 1

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
σv z
H
σh
2

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 φ for coarse grained soils
Ko = .44 + .42 [PI / 100] for NC soils
Ko (oc) = Ko (NC) (OCR)1/2 for OC soils
σv z
H
σh
3

4. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)
4

5. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)
5

6. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)
6

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 – φ/2)
thus: σa‘ = Ka σv’ – 2 c (Ka)1/2
Soil sliding down
pushing the wall
Failure wedge
H
45 + φ/2
7

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 + φ/2)
thus: σp‘ = Kp σv’ + 2 c (Kp)1/2
Soil being pushed
up the slope
H Failure wedge
45 - φ/2 8

9. Active Stress Distribution (c = 0)
γ
c=0
Φ
H dry soil
Pa = ?
? - What is this value
σa‘ = Ka σv’ – 2 c (Ka)1/2
0
σa‘ = Ka σv’
σa‘ is the stress distribution
Pa is the force on the wall (per foot of wall)
How is Pa found? 9

10. Passive Stress Distribution (c = 0)
γ
c=0
Φ
H dry soil
Pp = ?
? - What is this value
σp‘ = Kp σv’ – 2 c (Kp)1/2
0
σp ‘ = K p σv ’
σp‘ is the stress distribution
Pp is the force on the wall (per foot of wall)
10
How is Pp found?

11. Stress Distribution - Water Table (c = 0)
Effective Stress Pore Water Pressure
H1
Ka γ H1
H2
Pa
Ka γ H1 Ka γ’ H2 γw H2
or
Ka (γ H1 + γ’ H 2)
Pa = Σ areas = ½ Ka γH12 + Ka γH1H2 + ½ Ka γ’H22 + 1/2γwH22
11

12. Stress Distribution With Water Table
Why is the water pressure considered separately? (K)
Effective Stress Pore Water Pressure
H1 0
Ka γ H1
H2
Pa
Ka γ H1 Ka γ’ H2 γw H2
or
Ka (γ H1 + γ’ H 2)
12

13. Active Stress Distribution (c ≠ 0)
γ
zo
c≠0
Φ
H dry soil
_- =
Ka γH 2 c (Ka)1/2 Ka γH – 2 c (Ka)1/2
Find zo:
Ka γzo – 2 c (Ka)1/2 = 0
Zo = 2c / γ (Ka)1/2 13
Pa = ?

14. Passive Stress Distribution (c ≠ 0)
γ
c≠0
Φ
H dry soil +- =
Kp γH 2 c (Kp)1/2 Kp γH + 2 c (Kp)1/2
Pp = ?
14

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
15