cive.4310 lateral earth pressures - faculty server...

Revised 01/2017

CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures

Slide 1 of 26

In a homogeneous natural soil deposit,

'h'v

the ratio 'h/'v is a constant known as

Coefficient of Earth Pressure at Rest (Ko).

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

LATERAL EARTH PRESSURES AT REST

A

v

hoK

Revised 01/2017


Slide 2 of 26

For normally consolidated clays and granular soils,

Ko = 1 – sin ' (Jaky, 1944)

Ko = 0.95 – sin ' (Brooker & Ireland, 1965)

For overconsolidated clays,

Ko,overconsolidated = Ko,normally consolidated OCR0.5

From elastic analysis:

1oK Poisson’s

ratio

ESTIMATING Ko

OCR = Overconsolidation Ratiov

vmOCR

Revised 01/2017


Slide 3 of 26

TYPICAL VALUES OF Ko and POISSON’S RATIO FOR SOILSTable 15. California Trenching and Shoring Manual

Revised 01/2017


Slide 4 of 26

ACTIVE EARTH PRESSURES - RANKINE- in granular soils (No soil slope behind wall)

Smooth Wall(i.e. no friction between wall and soil)

Wall moves away from

soilWall moves towards soil A

B

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

Revised 01/2017


Slide 5 of 26

'v'h

z

As the wall moves away from the soil,

Initially, there is no lateral movement.

'v = z

'h = Ko 'v = Ko z

'v remains the same; and

'h decreases till failure occurs.

Active state

- in granular soils (No soil slope behind wall)

ACTIVE EARTH PRESSURES - RANKINE

A

Revised 01/2017


Slide 6 of 26

'v

decreasing 'h

Initially (Ko state)Failure (Active state)

As the wall moves away from the soil,

Active Earth Pressure



Revised 01/2017


Slide 7 of 26

'v['h]active

vAactiveh K ][

)2/45(tansin1sin1 2

AK

Rankine’s Coefficient of Active Earth Pressure

- in granular soils (No soil slope behind wall)ACTIVE EARTH PRESSURES - RANKINE

Revised 01/2017


Slide 8 of 26

'v['h]active

A

'v'h45 + '/2

90+'

Failure plane is at 45 + '/2 to horizontal



Revised 01/2017


Slide 9 of 26

A

'v'h

z

Wall Movement

'h

Active State

Ko State

- in granular soils (No soil slope behind wall)ACTIVE EARTH PRESSURES - RANKINE

H

La

Soil Type La/HLoose Sand 0.001-0.002Dense Sand 0.0005-0.001

Soft Clay 0.02Stiff Clay 0.01

As wall moves away from soil,'h decreases until failure occurs

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Slide 10 of 26

- in cohesive soils (No soil slope behind wall)

AvAactiveh KcK 2][

Only difference from granular soils: Addition of Cohesion (c')


'v['h]active

'

c'

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Slide 11 of 26

B

'v'h

Initially, soil is in Ko state.

As the wall moves towards the soil,

'v remains the same, and

'h increases till failure occurs.

Passive state


PASSIVE EARTH PRESSURES - RANKINE

Revised 01/2017


Slide 12 of 26

'v

Initially (Ko state)Failure (Passive state)

As the wall moves towards the soil,

increasing 'h

Passive Earth Pressure



Revised 01/2017


Slide 13 of 26

'v ['h]passive

vPpassiveh K ][

)2/45(tansin1sin1 2

PK

Rankine’s coefficient of passive earth pressure

- in granular soils (No soil slope behind wall)PASSIVE EARTH PRESSURES - RANKINE

Revised 01/2017


Slide 14 of 26

'v ['h]passive

B

'v'h

90+'

Failure plane is at 45 - '/2 to horizontal

45 - '/2



Revised 01/2017


Slide 15 of 26

B

'v'h

Wall Movement

'h

Ko state

Passive state



As wall moves towards from soil,'h decreases until failure occurs Soil Type Lp/H

Loose Sand 0.01Dense Sand 0.005

Soft Clay 0.04Stiff Clay 0.02

Revised 01/2017


Slide 16 of 26

- in cohesive soils (No soil slope behind wall)

Only difference from granular soils: Addition of Cohesion (c')


'v ['h]passive

'

c'

PvPpassiveh KcK 2][

Revised 01/2017


Slide 17 of 26

What if a Slope Exists?Granular Soils

RANKINE EARTH PRESSURES

45°+'/2

H

= Slope of Backfill

Ka coscos cos2 cos2 0.5

cos cos2 cos2 0.5

Kp coscos cos2 cos2 0.5

cos cos2 cos2 0.5

ap K

K 1For Sloped Backfill:

H/3

Pa

Revised 01/2017


Slide 18 of 26

RANKINE EARTH PRESSURESTable 11.2 Ka vs. Slope Angle (Das, FGE, 2005)

Table 11.3 Kp vs. Slope Angle (Das, FGE, 2005)

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Slide 19 of 26

COULOMB ACTIVE EARTH PRESSURES

W = Weight of Soil WedgeF = Resultant of Shear and Normal Forces on

Soil Failure SurfacePa = Active Force (per unit length of wall) = 0.5KaH²' = Interfacial Friction Angle

Figure 11.18. Das FGE (2005).

Cohesionless Backfill

Revised 01/2017


Slide 20 of 26

COULOMB PASSIVE EARTH PRESSURES

W = Weight of Soil WedgeF = Resultant of Shear and Normal Forces on

Soil Failure SurfacePp = Passive Force (per unit length of wall) = 0.5KpH²' = Interfacial Friction Angle

Cohesionless Backfill

Revised 01/2017


Slide 21 of 26

COULOMB EARTH PRESSURE COEFFICIENTS

Ka cos2

cos2 cos 1sin sin cos cos

2

Kp cos2

cos2 cos 1sin sin cos cos

2

Where:' = Effective Soil Friction Angle' = Interfacial Friction Angle = Wall Angle from Vertical = Angle of Sloped Backfill

Revised 01/2017


Slide 22 of 26

NOTE:⅓' ' < ⅔'

INTERFACIAL FRICTION ANGLES(NAVFAC DM7.02)

Revised 01/2017


Slide 23 of 26

COULOMB EARTH PRESSURE COEFFICIENTS

Revised 01/2017


Slide 24 of 26

Rankine “State of Stress” Earth Pressure Theory:

• Does not account for wall friction.

• Requires vertical wall.

• Conservative relative to other methods.

• Fixed plane of failure.

• Favored by the transportation agencies (AASHTO andFHWA) . See AASHTO Standard Specifications for Highway Bridges.

COMMENTS ON RANKINE & COULOMB EARTH PRESSURES

Revised 01/2017


Slide 25 of 26

Coulomb “Wedge Theory”:

• Unique failure angle for each design.

• Used by National Masonry Concrete Association (NCMA) Design Manual for Segmental Retaining Walls - Second Edition and USACE TM 5-818-1.

• Inaccurate passive earth pressures w/large wall anglesor friction angle (particularly for ' > ' /2) .

• Decreased accuracy w/ depth.

• Calculates lower active earth pressure than Rankinefor level backslope.

COMMENTS ON RANKINE & COULOMB EARTH PRESSURES

Revised 01/2017


Slide 26 of 26

COMMENTS ON COULOMB EARTH PRESSURES

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