Geotechnical applications K0, active & passive states Rankine’s earth pressure theory Design of retaining walls A Mini Quiz In geotechnical engineering, it is often necessary to prevent lateral soil movements.

1. www.sci-geoteknik.blogspot.com Lateral Earth Pressures N. Sivakugan Duration: 18 min

4. 4 Lateral Support We have to estimate the lateral soil pressures acting on these structures, to be able to design them. Soil nailing Gravity Retaining wall Reinforced earth wall

5. 5 Soil Nailing

6. 6 Sheet Pile Sheet piles marked for driving

7. 7 Sheet Pile Sheet pile wall

8. 8 Sheet Pile Sheet pile wall During installation

9. 9 Lateral Support geosynthetics Reinforced earth walls are increasingly becoming popular.

10. 10 Lateral Support filled with soil Crib walls have been used in Queensland. Good drainage & allow plant growth. Looks good. Interlocking stretchers and headers

11. 11 Earth Pressure at Rest GL v’ h’ In a homogeneous natural soil deposit, X the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0). Importantly, at K0 state, there are no lateral strains.

12. 12 Estimating K0 Poisson’s ratio For normally consolidated clays and granular soils, K0 = 1 – sin ’ For overconsolidated clays, K0,overconsolidated = K0,normally consolidated OCR0.5 From elastic analysis,

13. 13 Active/Passive Earth Pressures - in granular soils Wall moves away from soil Wall moves towards soil A B smooth wall Let’s look at the soil elements A and B during the wall movement.

14. 14 v’ z h’ A Active Earth Pressure - in granular soils v’ = z Initially, there is no lateral movement. h’ = K0 v’ = K0 z As the wall moves away from the soil, v’ remains the same; and h’ decreases till failure occurs. Active state

15. 15  failure envelope Initially (K0 state) Failure (Active state)  decreasing h’ Active Earth Pressure - in granular soils As the wall moves away from the soil, v’ active earth pressure

16. 16  failure envelope WJM Rankine (1820-1872)   Active Earth Pressure - in granular soils v’ [h’]active Rankine’s coefficient of active earth pressure

17. 17  v’ A 45 + /2 h’ failure envelope 90+   Active Earth Pressure - in granular soils Failure plane is at 45 + /2 to horizontal v’ [h’]active

18. 18 v’ z h’ A h’ K0 state Active state wall movement Active Earth Pressure - in granular soils As the wall moves away from the soil, h’ decreases till failure occurs.

19. 19 Macquorn Rankine

20. 20 Active Earth Pressure - in cohesive soils Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

21. 21 v’ B h’ Passive Earth Pressure - in granular soils Initially, soil is in K0 state. As the wall moves towards the soil, v’ remains the same, and h’ increases till failure occurs. Passive state

22. 22  failure envelope Initially (K0 state) Failure (Active state)  increasing h’ Passive Earth Pressure - in granular soils As the wall moves towards the soil, passive earth pressure v’

23. 23  failure envelope   Passive Earth Pressure - in granular soils v’ [h’]passive Rankine’s coefficient of passive earth pressure

24. 24  v’ A 45 - /2 h’ failure envelope 90+   Passive Earth Pressure - in granular soils Failure plane is at 45 - /2 to horizontal [h’]passive v’

25. 25 v’ B h’ h’ Passive state K0 state wall movement Passive Earth Pressure - in granular soils As the wall moves towards the soil, h’ increases till failure occurs.

26. 26 Passive Earth Pressure - in cohesive soils Follow the same steps as for granular soils. Only difference is that c  0. Everything else the same as for granular soils.

27. 27 H PA=0.5 KAH2 h PP=0.5 KPh2 Earth Pressure Distribution - in granular soils [h’]active PA and PP are the resultant active and passive thrusts on the wall [h’]passive KAH KPh

28. h’ Passive state Active state K0 state Wall movement (not to scale)

29. 29

30. 30 Macquorn Rankine

33. 33 Retaining Walls- Applications highway

34. 34 Retaining Walls- Applications basement wall High-rise building

35. 35 Gravity Retaining Walls cement mortar plain concrete or stone masonry cobbles They rely on their self weight to support the backfill

36. 36 Cantilever Retaining Walls Reinforced; smaller section than gravity walls They act like vertical cantilever, fixed to the ground

37. 37 2 2 Block no. 3 3 1 1 toe toe Analyse the stability of this rigid body with vertical walls (Rankine theory valid) Design of Retaining Wall - in granular soils Wi = weight of block i xi = horizontal distance of centroid of block i from toe

38. soil-concrete friction angle  0.5 – 0.7  2 2 PA H 3 PA 3 1 PP 1 S PP h S toe R toe R y y Safety against sliding along the base to be greater than 1.5 PP= 0.5 KPh2 PA= 0.5 KAH2

39. 2 2 PA H 3 PA 3 1 PP 1 S PP h S toe R toe R y y Safety against overturning about toe to be greater than 2.0

40. 40 Points to Ponder How does the key help in improving the stability against sliding? Shouldn’t we design retaining walls to resist at-rest (than active) earth pressures since the thrust on the wall is greater in K0 state (K0 > KA)?