Lateral E arth Earth Pressures Erizal

Transcription

1 Lateral Earth Pressures Erizal

2 Contents Geotechnical applications K 0, active & passive states Rankine s earth pressure theory Design of retaining walls 2

3 Lateral Support In geotechnical engineering, it is often necessary to prevent lateral soil movements. Tie rod Anchor Sheet pile Cantilever retaining wall Braced excavation Anchored sheet pile 3

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

5 Soil Nailing 5

6 Sheet Pile Sheet piles marked for driving 6

7 Sheet Pile Sheet pile wall 7

8 Sheet Pile During installation Sheet pile wall 8

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

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

11 Earth Pressure at Rest In a homogeneous natural soil deposit, σ h X σ v GL the ratio σ h /σ v is a constant known as coefficient of earth pressure at rest (K 0 ). Importantly, at K 0 state, there are no lateral strains. 11

12 Estimating K 0 For normally consolidated clays and granular soils, K 0 = 1 sin φ For overconsolidated clays, K 0,overconsolidated = K 0,normally consolidated OCR 0.5 From elastic analysis, K 0 υ = 1 υ Poisson s s ratio 12

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. 13

14 Active Earth Pressure -in granular soils σ v = γz σ h A σ v z Initially, there is no lateral movement. σ h = K 0 σ v = K 0 γz As the wall moves away from the soil, σ v remains the same; and σ h decreases eases till failure occurs. Active state 14

15 Active Earth Pressure -in granular soils τ As the wall moves away from the soil, Initially (K 0 state) Failure (Active state) active earth pressure decreasing σ h σ σ v σ 15

16 Active Earth Pressure -in granular soils τ φ [σ h ] active σ v σ WJM Rankine ( ) [ σ ' ] = K σ ' [ h active A v K A 1 sin φ 2 = = tan (45 φ / 2) 1+ sinφ Rankine s coefficient of active earth pressure 16

17 Active Earth Pressure -in granular soils τ Failure plane is at 45 + φ/2 to horizontal 45 + ϕ/2 σ h A σ v φ 90+ϕ [σ h ] active σ v σ 17

18 Active Earth Pressure -in granular soils As the wall moves away from the soil, σ h decreases till failure occurs. σ h σ h A σ v z σ h σ h K 0 state Active state wall movement 18

19 Active Earth Pressure -in cohesive soils Follow the same steps as for granular soils. Only difference is that c 0. [ σ h ' ] active = K Aσ v ' 2c K A Everything else the same as for granular soils. 19

20 Passive Earth Pressure -in granular soils σ h σ h B σ v Initially, soil is in K 0 state. As the wall moves towards the soil, σ v remains the same, and σ h increases till failure occurs. Passive state 20

21 Passive Earth Pressure -in granular soils τ As the wall moves towards the soil, Initially (K 0 state) Failure (Active state) passive earth pressure σ σ v σ increasing σ h 21

22 τ Passive Earth Pressure -in granular soils φ σ v [σ h ] passive σ [ σ ' ] = K σ ' [ h passive P v K P 1 + sin φ 2 = = tan (45 + φ / 2) 1 sinφ Rankine s coefficient of passive earth pressure 22

23 τ Passive Earth Pressure Failure plane is at 45 - φ/2 to horizontal 45 - ϕ/2 -in granular soils σ h A σ v φ 90+ϕ σ v [σ h ] passive σ 23

24 Passive Earth Pressure -in granular soils As the wall moves towards the soil, σ h increases till failure occurs. σ h σ h B σ v σ h σ h K 0 state Passive state wall movement 24

25 Passive Earth Pressure -in cohesive soils Follow the same steps as for granular soils. Only difference is that c 0. [ σ h ' ] passive = KPσ v ' + 2c KP Everything else the same as for granular soils. 25

26 Earth Pressure Distribution P A and P P are the resultant active and passive thrusts on the wall -in granular soils [σ h ] active [σ h ] passive H P 05K H A =0.5 A γh 2 h P =0.5 2 P K P γh K P γh K A γh 26

27 σ h Passive state Active state K 0 state Wall movement (not to scale)

28 Rankine s Earth Pressure Theory [ σ '] = K σ ' 2c h active [ σ '] = K σ ' + 2c h passive A P v v K K A P Assumes smooth wall Applicable only on vertical walls 28

29 Retaining Walls - Applications Road Train 29

30 Retaining Walls - Applications highway 30

31 Retaining Walls - Applications High-rise building basement wall 31

32 Gravity Retaining Walls cement mortar cobbles plain concrete or stone masonry They rely on their self weight to support the backfill 32

33 Cantilever Retaining Walls Reinforced; smaller section than gravity walls They act like vertical cantilever, fixed to the ground 33

34 SOAL Gambarkan distribusi tekanan tanah dan hitung total tekanan tanah yang berada dibelakang dinding penahan dengan permukaannya datar. Tanah dalam keadaan aktif dengan nilai kohesi sebesar 22.5 kn/m 2, sudut gesek dalamnya sebesar 25 o dan berat jenisnya 19.5 kn/m 3. Permukaan dinding yang bersentuhan dengan tanah dianggap licin dan tinggi dinding penahan sebesar 5 m. h = 5m Tanah: γ= 19.5 kn/m 3 c = 22.5 kn/m 2 φ= 25 o 34

35 Design of Retaining Wall -in granular soils Block no toe toe W i = weight of block i Analyse the stability of this rigid body with vertical walls ( Rankine theory valid) x i = horizontal distance of centroid of block i from toe 35

36 Safety against sliding along the base F sliding = P + {W W }. tan δ P P A i soil-concrete friction angle φ to be greater than P A 2 H P P toe 1 y S 3 R h P P 1 toe y S 3 R PA P h P = 0.5 K P γh 2 P A = 0.5 K A γh 2

37 Safety against overturning about toe F overturning = P P h / 3 + { Wi x P H/3 A i } to be greater than P A H P P toe 1 y S 3 R h P P 1 toe y S 3 R PA

38 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 K 0 state (K 0 > K A )? 38