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?)

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

3. At Rest Earth Pressure σv H σh
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 = [PI / 100] for NC soils
Ko (oc) = Ko (NC) (OCR)1/2 for OC soils σv z H σh

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 H
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

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

9. Active Stress Distribution (c = 0)γ
c = 0 Φ
dry soil H
Pa = ?
? - What is this value
σa‘ = Ka σv’ – 2 c (Ka)1/2
σa‘ = Ka σv’
σa‘ 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)γ
c = 0 Φ
dry soil H
Pp = ?
? - What is this value
σp‘ = Kp σv’ – 2 c (Kp)1/2
σp‘ = Kp σv’
σp‘ 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)H1
Effective Stress
Pore Water Pressure
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

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

13. Active Stress Distribution (c ≠ 0)zo γ
c ≠ 0 Φ
dry soil H _ - =
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
Pa = ?

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

15. Practice Problems Chapter 12 – Problems: 13
15 (part c is using equation 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