Session 11 – 12 LATERAL EARTH PRESSURE

1. Session 11 – 12 LATERAL EARTH PRESSURE Course : S0484/Foundation Engineering Year : 2007 Version : 1/0

2. LATERAL EARTH PRESSURE Topic: • General • Active earth pressure • Rankine earth pressure • Coulomb earth pressure • Lateral earth pressure due to surcharge • Passive earth pressure • Rankine earth pressure • Coulomb earth pressure • Influence of ground water table

3. GENERAL • Lateral earth pressure represents pressures that are “to the side” (horizontal) rather than vertical. • Caused by soil self weight and or external load • 3 categories: • At rest earth pressure • Active earth pressure • Passive earth pressure

4. AT REST EARTH PRESSURE The at rest pressure develops when the wall experiences no lateral movement. This typically occurs when the wall is restrained from movement such as a basement wall that is supported at the bottom by a slab and at the top by a floor framing system prior to placing soil backfill against the wall.

5. ACTIVE EARTH PRESSURE The active pressure develops when the wall is free to move outward such as a typical retaining wall and the soil mass stretches sufficiently to mobilize its shear strength.

6. PASSIVE EARTH PRESSURE If the wall moves into the soil, then the soil mass is compressed sufficiently to mobilize its shear strength and the passive pressure develops.

7. AT REST EARTH PRESSURE q Jaky, Broker and Ireland  Ko = M – sin ’ Sand, normally consolidated clay  M = 1 Clay with OCR > 2  M = 0.95 v =  . z + q Broker and Ireland z Ko = 0.40 + 0.007 PI , 0  PI  40 Ko = 0.64 + 0.001 PI , 40  PI  80 v h Sherif and Ishibashi  Ko =  +  (OCR – 1) •  = 0.54 + 0.00444 (LL – 20) • = 0.09 + 0.00111 (LL – 20) LL > 110%   = 1.0 ;  = 0.19 At rest, K = Ko

8. ACTIVE EARTH PRESSURE

9. ACTIVE EARTH PRESSURE RANKINE ACTIVE EARTH PRESSURE 1 = 3 . tan2 (45+/2)+2c.tan (45+/2) a = v . tan2(45-/2) – 2c . tan (45-/2) a = v . Ka – 2cKa Ka = tan2 (45 - /2)

10. ACTIVE EARTH PRESSURE Note : z = 0  v = 0 ; a = -2cKa z = H  v = H The tensile stress decreases with depth and becomes zero at a depth z = zc or zcKa – 2cKa = 0 and zc = depth of tensile crack

11. ACTIVE EARTH PRESSURE RANKINE ACTIVE EARTH PRESSURE FOR INCLINED BACKFILL (for granular soil, c = 0) For c- soil

12. ACTIVE EARTH PRESSURE COULOMB ACTIVE EARTH PRESSURE • Assumptions: • Fill material is granular soil • Friction of wall and fill material is considered • Soil failure shape is plane (BC1, BC2 …) Pa = ½ Ka .  . H2

13. ACTIVE EARTH PRESSURE COULOMB’S ACTIVE EARTH PRESSURE WITH A SURCHARGE ON THE BACKFILL

14. PASSIVE EARTH PRESSURE RANKINE PASSIVE EARTH PRESSURE

15. PASSIVE EARTH PRESSURE RANKINE PASSIVE EARTH PRESSURE p= v . tan2(45+/2) + 2c . tan (45+/2)

16. PASSIVE EARTH PRESSURE RANKINE PASSIVE EARTH PRESSURE Kp = tan2 (45 + /2) h = v . Kp + 2cKp

17. PASSIVE EARTH PRESSURE COULOMB PASSIVE EARTH PRESSURE Pp = ½ Kp .  . H2

18. LATERAL EARTH PRESSURE DUE TO SURCHARGE a > 0,4 a  0,4

19. LATERAL EARTH PRESSURE DUE TO SURCHARGE

20. PURPOSE OF LATERAL EARTH PRESSURE • STABILITY ANALYSIS GRAVITY WALL AGAINST • SLIDING • OVERTURNING

21. PURPOSE OF LATERAL EARTH PRESSURE

22. PURPOSE OF LATERAL EARTH PRESSURE