Erizal - Bogor Agricultural Universityweb.ipb.ac.id/~erizal/mektan/LateralEarthPressures.pdf · Soil nailing Reinforced earth wall. ... Microsoft PowerPoint - LateralEarthPressures.ppt

Lateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth Pressures

Erizal

SIVASIVA Copyright©2001Copyright©2001

ContentsContentsContentsContentsContentsContents

• Geotechnical applications• K0 active & passive statesK0, active & passive states• Rankine’s earth pressure theory

• Design of retaining wallsDesign of retaining walls

2


Lateral SupportLateral Support

In geotechnical engineering, it is often necessary to prevent lateral soil movements.

Tie rod

Anchor

Sheet pile

3Cantilever retaining wall

Braced excavation Anchored sheet pile



We have to estimate the lateral soil pressureslateral soil pressureslateral soil pressures acting on these structures, to be able to design them.

S il ili4Gravity Retaining

wallSoil nailing

Reinforced earth wall


Soil NailingSoil Nailing

5


Sheet PileSheet Pile

Sheet piles marked for driving6



Sheet pile wall7



During installation Sheet pile wall

8



Reinforced earth wallsReinforced earth wallsReinforced earth walls are increasingly becoming popular.

geosynthetics

9



Crib wallsCrib wallsCrib walls have been used in Queensland.filled with

soil

Good drainage & allow plant growth.

Interlocking stretchers

and headers

Looks good.

and headers

10


Earth Pressure at RestEarth Pressure at Rest

GL

In a homogeneous natural soil deposit,

Xσh’σv’

X

the ratio σh’/σ ’ is a constant known as coefficientcoefficientcoefficientthe ratio σh /σv is a constant known as coefficient coefficient coefficient of earth pressure at rest (Kof earth pressure at rest (Kof earth pressure at rest (K000).).).

Importantly, at K0 state, there are no lateral strains.

11


Estimating K0Estimating K0

For normally consolidated clays and granular soils, K0 = 1 – sin φ’0 φ

For overconsolidated clays,

K0,overconsolidated = K0,normally consolidated OCR0.5

From elastic analysis,

υK Poisson’s

υ−=

10K Poisson s ratio

12


Active/Passive Earth PressuresActive/Passive Earth Pressures- in granular soils

Wall moves f ilaway from soil

Wall moves AWall moves towards soil

A

smooth wall

B

smooth wall

Let’s look at the soil elements A and B during the 13wall movement.


Active Earth PressureActive Earth Pressure- in granular soils

Initially there is no lateral movement

σv’ = γz

A

σv’σh’

zInitially, there is no lateral movement.

∴σh’ = K0 σv’ = K0 γzA

As the wall moves away from the soil,

σv’ remains the same; and

σh’ decreases till failure occurs.σh dec eases t a u e occu s.

Active state14



τAs the wall moves away from the soil,

τ

Initially (K0 state)

Failure (Active state)

σσ ’ σσv

decreasing σh’active earth

pressure15

p



τ

φ

WJM Rankine(1820-1872)

σv’[σh’]active σ

']'[ K σσ =][ vAactiveh K σσ =

sin1 2φ−Rankine’s coefficient of

active earth pressure16

)2/45(tansin1sin1 2 φ

φφ

−=+

=AK active earth pressure



τσv’

’

Failure plane is at 45 + φ/2 to horizontal

Aσh’45 + ϕ/2

φ 90+ϕ

σv’[σh’]activeσ

17



As the wall moves away from the soil,

σ ’ decreases till failure occursσh decreases till failure occurs.

σh’ K state

A

σv’σh’

zσh

Active state

K0 state

Aσh state

wall movement

18


Active Earth PressureActive Earth Pressure- in cohesive soils

Follow the same steps asFollow the same steps as for granular soils. Only difference is that c ≠ 0.

KK 2']'[ AvAactiveh KcK 2']'[ −= σσ

Everything else the same as for granular soils

19as for granular soils.


Passive Earth PressurePassive Earth Pressure- in granular soils

Initially, soil is in K0 state.

As the wall moves towards the soil,

σ ’ remains the same and

B

σv’σh’

σv remains the same, and

σh’ increases till failure occurs.Bσh

Passive state

20



τAs the wall moves towards the soil,

τInitially (K0 state)

Failure (Active state)

passive earth pressure

σσ ’ σσv

increasing σ ’21

increasing σh



τ

φσv’ [σh’]passive σ

']'[ K σσ =][ vPpassiveh K σσ =

sin1 2φ+Rankine’s coefficient of passive earth pressure

22)2/45(tan

sin1sin1 2 φ

φφ

+=−+

=PK passive earth pressure



τσv’

’

Failure plane is at 45 - φ/2 to horizontal

Aσh’45 - ϕ/2

φ 90+ϕ

σv’ [σh’]passiveσ

23



As the wall moves towards the soil,

σ ’ increases till failure occursσh increases till failure occurs.

σh’ Passive state

B

σv’σh’

σh Passive state

Bσh

K0 state

wall movement

24


Passive Earth PressurePassive Earth Pressure- in cohesive soils

Follow the same steps asFollow the same steps as for granular soils. Only difference is that c ≠ 0.

KK 2']'[ + PvPpassiveh KcK 2']'[ += σσ

Everything else the same as for granular soils

25as for granular soils.


Earth Pressure DistributionEarth Pressure Distribution- in granular soils

’][σh’]active

PA and PP are the l i dresultant active and

passive thrusts on the wall

[σh’]passive H

P 0 5 K H2

h

PA=0.5 KAγH2

PP=0.5 KPγh2PP 0.5 KPγh

26KAγHKPγh


σh’σh

Passive state

Active stateK0 state

Wall movement (not to scale)


Rankine’s Earth Pressure TheoryRankine s Earth Pressure Theory

AvAactiveh KcK 2']'[ −= σσ

PvPpassiveh KcK 2']'[ += σσ

Assumes smooth wall

Applicable only on vertical walls

28


Retaining Walls - ApplicationsRetaining Walls - Applications

Road

Train

29



highway

30



High rise buildingHigh-rise building

basement wall

31


Gravity Retaining WallsGravity Retaining Walls

cement mortarl i t

cobbles

plain concrete or stone masonry

They rely on their self weight to support the backfillThey rely on their self weight to support the backfill

32


Cantilever Retaining WallsCantilever Retaining Walls

Reinforced; smaller section

than gravity allswalls

They act like vertical cantilever, They act like vertical cantilever, 33fixed to the groundfixed to the ground


SOALSOAL• 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/m2, sudut gesek dalamnya sebesar 25o dan berat jenisnya 19.5 kN/m3. Permukaan dinding yang bersentuhan dengan tanah dianggap licin dan tinggi dinding penahan sebesar 5 m.

Tanah:

γ= 19.5 kN/m3h = 5 m γ

c = 22.5 kN/m2

φ= 25o

h 5 m

34


Design of Retaining WallDesign of Retaining Wall- in granular soils

2 2

1

2

3 3

Block no.

11

toetoe

Wi = weight of block iAnalyse the stability of this rigid body with 35

xi = horizontal distance of centroid of block i from toey y g y

vertical walls (∴Rankine theory valid)

Safety against sliding along the base

}{WP ∑ δ soil-concrete frictiontan}.{

A

iPsliding P

WPF ∑+=

δ soil concrete friction angle ≈ 0.5 – 0.7 φ

A

to be greater

2 2

gthan 1.5

1

2

3 3

PA

PA

H

11PP

PPS

StoeR

h

toeR

Ryy

h2 2PP= 0.5 KPγh2 PA= 0.5 KAγH2

Safety against overturning about toe

}{3/ WhP ∑H/3

}{3/

A

iiPgoverturnin P

xWhPF ∑+=

A

to be greater

2 2

gthan 2.0

1

2

3 3

PA

PA

H

11PP

PPS

StoeR

h

toeR

Ryy


Points to PonderPoints to Ponder

How does the key help in improving the stability against sliding?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)?

38

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Erizal - Bogor Agricultural Universityweb.ipb.ac.id/~erizal/mektan/LateralEarthPressures.pdf · Soil nailing Reinforced earth wall. ... Microsoft PowerPoint - LateralEarthPressures.ppt