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1 Lateral Earth Pressure We can calculate σ v ’ Now, calculate σ h ’ which is the horizontal stress σ h ‘/ σ v ‘ = K Therefore, σ h ‘ = Kσ v ‘ (σ V ‘ is.

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Presentation on theme: "1 Lateral Earth Pressure We can calculate σ v ’ Now, calculate σ h ’ which is the horizontal stress σ h ‘/ σ v ‘ = K Therefore, σ h ‘ = Kσ v ‘ (σ V ‘ is."— Presentation transcript:

1 1 Lateral Earth Pressure We can calculate σ v ’ Now, calculate σ h ’ which is the horizontal stress σ h ‘/ σ v ‘ = K Therefore, σ h ‘ = Kσ v ‘ (σ V ‘ is what?) σv’σv’ σh’σh’ H

2 2 Lateral Earth Pressure There are 3 states of lateral earth pressure K o = At Rest K a = Active Earth Pressure (wall moves away from soil) K p = Passive Earth Pressure (wall moves into soil) Passive is more like a resistance σvσv σhσh z H

3 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) K o can be calculated as follows: K o = 1 – sin φ for coarse grained soils K o =.44 +.42 [PI / 100] for NC soils K o (oc) = K o (NC) (OCR) 1/2 for OC soils σvσv σhσh z H

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

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

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

7 7 Active Earth Pressure Active earth pressure occurs when the wall tilts away from the soil (a typical free standing retaining wall) K a can be calculated as follows: K a = tan 2 (45 – φ/2) thus: σ a ‘ = K a σ v ’ – 2 c (K a ) 1/2 45 + φ/2 Failure wedge H Soil sliding down pushing the wall

8 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) K p can be calculated as follows: K p = tan 2 (45 + φ/2) thus: σ p ‘ = K p σ v ’ + 2 c (K p ) 1/2 45 - φ/2 Failure wedge H Soil being pushed up the slope

9 9 Active Stress Distribution (c = 0) γ c = 0 Φ dry soil H σ a ‘ = K a σ v ’ – 2 c (K a ) 1/2 σ a ‘ = K a σ v ’ 0 σ a ‘ is the stress distribution P a is the force on the wall (per foot of wall) How is P a found? P a = ? ? - What is this value

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

11 11 Stress Distribution - Water Table (c = 0) H1H1 K a γ H 1 or P a = Σ areas = ½ K a γH 1 2 + Ka γH 1 H 2 + ½ K a γ’H 2 2 + 1/2γ w H 2 2 H2H2 K a γ H 1 K a γ’ H 2 K a (γ H 1 + γ’ H 2 ) Effective Stress Pore Water Pressure PaPa γ w H 2

12 12 Stress Distribution With Water Table H1H1 K a γ H 1 or H2H2 0 K a γ H 1 K a γ’ H 2 K a (γ H 1 + γ’ H 2 ) Effective Stress Pore Water Pressure PaPa γ w H 2 Why is the water pressure considered separately? (K)

13 13 Active Stress Distribution (c ≠ 0) - γ c ≠ 0 Φ dry soil H Ka γHKa γH zozo 2 c (K a ) 1/2 K a γH – 2 c (K a ) 1/2 = Find z o : K a γz o – 2 c (K a ) 1/2 = 0 Zo = 2c / γ (K a ) 1/2 Pa = ? _

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

15 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


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