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?)

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

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

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

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

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

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

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

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?

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?

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

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)

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 = ?

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 = ?

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