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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 3 of 26
TYPICAL VALUES OF Ko and POISSON’S RATIO FOR SOILSTable 15. California Trenching and Shoring Manual
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 6 of 26
'v
decreasing 'h
Initially (Ko state)Failure (Active state)
As the wall moves away from the soil,
Active Earth Pressure
- in granular soils (No soil slope behind wall)
ACTIVE EARTH PRESSURES - RANKINE
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 8 of 26
'v['h]active
A
'v'h45 + '/2
90+'
Failure plane is at 45 + '/2 to horizontal
- in granular soils (No soil slope behind wall)
ACTIVE EARTH PRESSURES - RANKINE
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 10 of 26
- in cohesive soils (No soil slope behind wall)
AvAactiveh KcK 2][
Only difference from granular soils: Addition of Cohesion (c')
ACTIVE EARTH PRESSURES - RANKINE
'v['h]active
'
c'
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
- in granular soils (No soil slope behind wall)
PASSIVE EARTH PRESSURES - RANKINE
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 12 of 26
'v
Initially (Ko state)Failure (Passive state)
As the wall moves towards the soil,
increasing 'h
Passive Earth Pressure
- in granular soils (No soil slope behind wall)
PASSIVE EARTH PRESSURES - RANKINE
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 14 of 26
'v ['h]passive
B
'v'h
90+'
Failure plane is at 45 - '/2 to horizontal
45 - '/2
- in granular soils (No soil slope behind wall)
PASSIVE EARTH PRESSURES - RANKINE
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 15 of 26
B
'v'h
Wall Movement
'h
Ko state
Passive state
- in granular soils (No soil slope behind wall)
PASSIVE EARTH PRESSURES - RANKINE
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 16 of 26
- in cohesive soils (No soil slope behind wall)
Only difference from granular soils: Addition of Cohesion (c')
PASSIVE EARTH PRESSURES - RANKINE
'v ['h]passive
'
c'
PvPpassiveh KcK 2][
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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)
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 22 of 26
NOTE:⅓' ' < ⅔'
INTERFACIAL FRICTION ANGLES(NAVFAC DM7.02)
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 23 of 26
COULOMB EARTH PRESSURE COEFFICIENTS
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
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
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 26 of 26
COMMENTS ON COULOMB EARTH PRESSURES