LATERAL EARTH PRESSURE

ECG426 – SOIL MECHANICS

WEEK 11 LATERAL EARTH PRESSURES

PN. FAUZILAH ISMAIL T1-17-10C 03-55435256

SHEAR STRENGTH OF SOILS

ACTIVITY - Week 11 • Lecture ~ 39 slides • Tutorial 5 • Independent learning activities

2

SOIL MECHANICS (ECG426)

ARM/FBI 2012

LEARNING OUTCOMES Week 11 : Coverage ~ Principles of lateral pressures; at rest, active and passive pressures. Lateral pressures based on Rankine’s Theory.

Learning outcomes: At the end of this lecture/week the students would be able to: i.

Discuss the different types of lateral earth pressures.

ii. Perform analysis to determine lateral thrust based on Rankine’s Theory.

SOIL MECHANICS (ECG426)

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LATERAL EARTH PRESSURE

TOPIC 5 : LATERAL EARTH PRESSURES

Soil Mechanics (ECG426)

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LATERAL EARTH PRESSURE

OUTLINE of PRESENTATION 5.1

Introduction & Overview.

5.2

States of Equilibrium – at rest, active and passive.

5.3

Lateral Pressures Distribution based on Rankine’s Theory.

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Introduction & Overview

5.1

Introduction and overview

Retaining structures such as retaining walls, basement walls, and bulkheads are commonly encountered in foundation engineering, and they may support slopes of earth mass.

Proper design and construction of these structures require a thorough knowledge of the lateral forces that act between the retaining structures and the soil mass being retained.

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Types of Lateral Pressure

5.2 States of Equilibrium 5.2.1 Hydrostatic Pressure and Lateral Thrust 5.2.2 Earth Pressure at Rest 5.2.3 Active Earth Pressure 5.2.4 Passive Earth pressure

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Types of Lateral Pressure

5.2.1 Hydrostatic pressure and lateral thrust g.w.t

Horizontal pressure due to a liquid Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Earth Pressure at Rest

5.2.2 Earth pressure at rest A Unit weight of soil = 

 f  c   tan 

z σv σh = Ko σv

B Earth pressure at rest Soil SoilMechanics Mechanics(ECG426) (ECG413)

If wall AB remains static – soil mass will be in a state of elastic equilibrium – horizontal strain is zero.

Ratio of horizontal stress to vertical stress is called coefficient of earth pressure at rest, Ko and is given by;

h Ko  v

 h  K o  v  K o z ARM/FBI ARM 2012 2012

LATERAL EARTH PRESSURE Earth Pressure at Rest Earth pressure at rest .. Cont’d. f = c’ + ’n tan’ Shear stress, 

Normal stress, ’n

’v = ’1

’h = ’3

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Earth Pressure at Rest 5.2.2.1 Coarse-grained soils

•

For loose sand, Ko is given by;

K o  1 - sin 

(after Jaky, 1944) where  = drained friction angle.

Notes; Jaky’s equation also can be used for normally consolidated soils.

•

For dense sand backfill the above formula grossly underestimated the lateral earth pressure at rest, so use;

 d   K o  (1 - sin  )  - 1 5.5 (after Sherif et al, 1984)    d(min)  where d = actual compacted dry unit weight of the sand.

d(min) = dry unit weight at the loosest state.

•

Thus the value of Ko depends on the angle of friction (’) and the stress history (loading/unloading) of the soil.

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LATERAL EARTH PRESSURE Earth Pressure at Rest 5.2.2.2 Fine-grained soils (i) Normally consolidated

K o  1 - sin  (after Jaky, 1944)  PI(%)  K o  0.44  0.42  (after Massarch, 1979)  100  (ii) Overconsolidated soil



K o  1  sin c'



OCR thus,

K o  K o nc  OCR where OCR  Soil SoilMechanics Mechanics(ECG426) (ECG413)

(after Massarch, 1979)

preconsolidation pressure present effective overburden pressure ARM/FBI ARM 2012 2012

LATERAL EARTH PRESSURE Active Earth Pressure

5.2.3 Active earth pressure A’

A Unit weight of soil = 

 f  c'   ' tan  ' z σv σh

Plastic equilibrium in soil refers to the condition where every point in a soil mass is on the verge of failure.

If wall AB is allowed to move away from the soil mass gradually to position A’B, horizontal stress will decrease.

B

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Active Earth Pressure

•

•

• Soil Mechanics (ECG426)

At this time, the horizontal effective stress, ’h= ’a will be referred to as active pressure.

σ h' σ a' thus K  K a  '  ' σv σv

a = 45 + ’/2

Earth pressure at active

If the frictionless wall rotates sufficiently to position A’B (La), then the triangular soil mass ABC’ adjacent to wall will reach a state of plastic equilibrium and will fail sliding down the plane BC’.

Horizontal effective stress decreased and soil failed in expansion.

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Active state

•

Active lateral pressure ~ where ’ha < ’v thus the soil will fail in expansion.

•

Angle of failure surface is given by; a = 45 + ’/2

Passive State

Whitlow, R. – page 281

Soil Mechanics (ECG426)

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Shear stress, 

LATERAL EARTH PRESSURE Active Earth Pressure  f  c'   ' tan  '

Mohr’s circle representing Rankine’s active state.

D b a

A

' '

c’

O

σ'a

C Koσ’v

σ'v

Normal stress, ’n

D’

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Active Earth Pressure

Soil Mechanics (ECG426)

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Active Earth Pressure

Soil Mechanics (ECG426)

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LATERAL EARTH PRESSURE Active Earth Pressure Based on the diagram :

 'a Ratio  coefficient of Rankine' s active earth pressure  'v  K a (Ka is the ratio of the effective stresses) Therefore :

 'a  ' 1 - sin  ' 1 - sin ' 2 Ka   tan (45 - )  , thus K a   'v 2 1  sin  ' 1  sin ' It can be shown that (refer previous slide) :

'

'

2

2

 'a   z tan (45 - ) - 2c' tan (45 - ), thus 2

 'a   z K a - 2c' K a Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Active Earth Pressure Active pressure distribution for c’~’ soils.

- 2c' K a

- 2c' K a

zo

+  z Ka Soil SoilMechanics Mechanics(ECG426) (ECG413)

z

 z Ka - 2c' Ka ARM/FBI ARM 2012 2012

LATERAL EARTH PRESSURE Active Earth Pressure Active pressure distribution Based on the previous slide, using similar triangles, it can be shown that :

2c' zo   Ka

where zo is depth of tension crack

For pure cohesive soil, i.e. when ’ = 0 ;

zo 

Soil SoilMechanics Mechanics(ECG426) (ECG413)

2c'

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LATERAL EARTH PRESSURE Active Earth Pressure Active pressure distribution for cohesionless soil (c’=0)

z

For cohesionless soil, c’ = 0

 'a   ' v K a   z K a  z Ka Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Passive Earth Pressure

5.2.4 Passive earth pressure A

A” Unit weight of soil = 

 f  c'   ' tan ' z σv σh

If the wall is pushed into the soil mass to position A”B, the principal stress σh will increase. On the verge of failure the stress condition on the soil element can be expressed by Mohr’s circle b.

The lateral earth pressure, σp, which is the major principal stress, is called Rankine’s passive earth pressure .

B

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Passive Earth Pressure

•

•

• Soil Mechanics (ECG426)

At this time, the horizontal effective stress, ’h= ’p will be referred to as passive pressure. ' σ h' σ p thus K  K a  '  ' σv σv

p = 45 - ’/2

Earth pressure at passive

If the frictionless wall rotates sufficiently to position A”B (Lp), then the triangular soil mass ABC” adjacent to wall will reach a state of plastic equilibrium and will fail sliding upward the plane BC”.

Horizontal effective stress increased and soil failed in compression.

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Active state

•

Passive lateral pressure ~ where ’hp > ’v thus the soil will fail in compression.

•

Angle of failure surface is given by; p = 45 - ’/2

Passive State

Whitlow, R. – page 281

Soil Mechanics (ECG426)

ARM/FBI 2012

LATERAL EARTH PRESSURE Passive Earth Pressure Shear stres, 

 f  c'   ' tan  ' D

b

Mohr’s circle representing Rankine’s passive state.

a

A

' '

c’

Koσ’v

σ'v

C

σ'p Normal stress, ’n

O

D’

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Passive Earth Pressure

Soil Mechanics (ECG426)

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Passive Earth Pressure

Soil Mechanics (ECG426)

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LATERAL EARTH PRESSURE Passive Earth Pressure Referring to previous slide, it can be shown that :

 'p   v' tan 2 (45 

' 2

)  2c' tan (45 

' 2

), thus

 'p   z K p  2c' K p For cohesionless soil : ' '  'p  1  sin  2  K  tan (45  )  p ' v 2 1  sin  '

1  sin  ' Thus K p  1  sin  ' Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Passive Earth Pressure Passive pressure distribution

+  z Kp For cohesionless soil, Soil SoilMechanics Mechanics(ECG426) (ECG413)

z

2c' K p

2c' K p

 z Kp

 'p   v' K p   z K p ARM/FBI ARM 2012 2012

LATERAL EARTH PRESSURE Earth Pressure Earth Pressure, ’h

In conclusion;

Passive pressure, ’p

At-rest pressure, ’h

Active pressure, ’a

Wall tilt direction Soil SoilMechanics Mechanics(ECG426) (ECG413)

La H

L p H

Wall tilt direction ARM/FBI ARM 2012 2012

LATERAL EARTH PRESSURE Rankine’s Lateral Pressure

5.3 Rankine’s Theory 5.3.1 Rankine’s active pressure 5.3.2 Rankine’s passive pressure

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Rankine’s Lateral Pressure

5.3 Rankine’s Theory  Initial work done in 1857  Develop based on semi infinite “loose granular” soil mass for which the soil movement is uniform.  Used stress states of soil mass to determine lateral pressures on a frictionless wall

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Rankine’s Lateral Pressure

Assumptions by Rankine :  The earth retaining wall is vertical.  The interface between the wall and soil is frictionless.  The soil surface is horizontal and no shear stress acts on horizontal and vertical boundaries.  The wall is rigid and extends to an infinite depth in a dry, homogeneous, isotropic soil mass.  The soil is loose and initially in an at-rest state.

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE Rankine’s Lateral Pressure

Elements behind the retaining wall to be considered:  Retained soil (single or multi-layered)  Presence of water  Presence of imposed surcharge  Cohesionless or cohesive soils

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LATERAL EARTH PRESSURE 5.3.1 Rankine’s Active Pressure 5.3.1.1 Active pressure (horizontal cohesionless soil, c’=0)

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE 5.3.1 Rankineâ&#x20AC;&#x2122;s Active Pressure 5.3.1.2 Active pressure (horizontal cohesionless soil with standing water)

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE 5.3.1 Rankineâ&#x20AC;&#x2122;s Active Pressure 5.3.1.3 Active pressure (horizontal cohesionless soil with imposed surcharge,q)

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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LATERAL EARTH PRESSURE 5.3.1 Rankineâ&#x20AC;&#x2122;s Active Pressure 5.3.1.4 Active pressure (horizontal cohesionless soil with imposed surcharge,q and standing water)

Soil SoilMechanics Mechanics(ECG426) (ECG413)

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