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**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?)

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**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

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**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

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

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

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

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**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

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**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

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**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?

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**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?

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**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

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**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)

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**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 = ?

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**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 = ?

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**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

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