Page 1
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
Page 2
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
Page 3
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
Page 4
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.
Page 5
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
Page 6
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
Page 7
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
Page 8
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
Page 9
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
Page 10
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'
Page 11
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
Page 12
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
Page 13
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
Page 14
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
Page 15
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
Page 16
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][
Page 17
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
Page 18
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)
Page 19
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
Page 20
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
Page 21
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
Page 22
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 22 of 26
NOTE:⅓' ' < ⅔'
INTERFACIAL FRICTION ANGLES(NAVFAC DM7.02)
Page 23
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 23 of 26
COULOMB EARTH PRESSURE COEFFICIENTS
Page 24
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
Page 25
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
Page 26
Revised 01/2017
CIVE.4310 FOUNDATION & SOIL ENGINEERINGLateral Earth Pressures
Slide 26 of 26
COMMENTS ON COULOMB EARTH PRESSURES