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ENCE 461
Foundation Analysis andDesign
Retaining Walls
Lateral Earth Pressure Theory
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RetainingWalls
Necessary in situations where gradual transitionseither take up too much space or are impracticalfor other reasons
Retaining walls are analysed for both resistanceto overturning and structural integrity
Two categories of retaining walls
Gravity Walls (Masonry, Stone, Gabion, etc.)
In-Situ Walls (Sheet Piling, cast in-situ, etc.)
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Lateral Earth PressureCoefficient
K = lateral earth pressure coefficient
x = horizontal effective stress
K
x '
z '
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Mohrs Circle
and LateralEarth
Pressures
=z 'x '=
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Development of Lateral EarthPressure
Po
b1z1
2Ko
2
Note Pore Water Effect! subtract vertically add horizontally
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Groundwater Effects
Steps to properly compute horizontal stresses
including groundwater effects:
Compute total vertical stress
Compute effective vertical stress by removinggroundwater effect through submerged unit weight;plot on P
odiagram
Compute effective horizontal stress by multiplyingeffective vertical stress by K
Compute total horizontal stress by directly adding
effect of groundwater unit weight to effectivehorizontal stress
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Groundwater
Effects
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Conditions of Lateral EarthPressure Coefficient
At-Rest Condition
Condition where wall movement is zero or minimal
Ideal condition of wall, but seldom achieved in reality
Active Condition Condition where wall moves away from the backfill
The lower state of lateral earth pressure
Passive Condition
Condition where wall moves toward the backfill
The higher state of lateral earth pressure
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Effect of Wall Movement
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Wall Movements Necessary to
Achieve Active or PassiveStates
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Estimates of At Rest LateralEarth Pressure Coefficient
Jakys Equation
Modified for Overconsolidated Soils
Applicable only when ground surface is level In spite of theoretical weaknesses, Jakys
equation is as good an estimate of the coefficient
of lateral earth pressure as we have
Ko1sin '
Ko1sin 'OCRsin '
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Relationship of Poissons Ratio
with Lateral Earth PressureCoefficient
Ko 1
211
tan1
tan2(Normally Consolidated Soils)
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At Rest Pressure Example Compute at rest earth pressure coefficient
Compute Effective Wall Force
Ko1sin 'Ko1sin 300.5
Po
b1z1
2Ko
2
Po
b
1202020.52
Po
b
12000lbs
ft
12kips
ft
hPA
20
3 6.67 ft.
(valid for all theories)
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Development of Active Earth
Pressure
D l f P i E h
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Development of Passive EarthPressure
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Earth Pressure Theories
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Rankine Earth Pressure Equations
Level Backfills
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Rankine Theory with Inclined
Backfills
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Rankine Coefficients with
Inclined Backfills
Inclined and level backfill equations are identical when = 0
E l f R ki A i W ll
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Example of Rankine Active Wall
Pressure Given
Retaining Wall as Shown
Find
PA,
from At Rest Conditions
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Rankine Active Pressure
Example Compute at rest earth pressure coefficient
Compute Effective Wall Force
Po
b
1z1
2Ka
2Po
b
1202020.3332
Po
b 8000lbs
ft8kips
ft
KAtan245
2
KAtan24515
1
3
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Rankine Passive Pressure
Example
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Rankine Passive Pressure
Example Compute at rest earth pressure coefficient
Compute Effective Wall Force
Po
b
1z1
2Kp
2Po
b
12020232
Po
b 72000lbs
ft72kips
ft
KPtan245
2
KPtan245153
Summary of Rankine and At
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Summary of Rankine and AtRest Wall Pressures
72,000 lbs.
12,000 lbs. 8000 lbs.
K cos
2
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Coulomb Theory
Kpcos
2
cos2cos1
sin sin
coscos
2
Ka
cos2cos1
sin sin
coscos
2
Typical
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TypicalValues
of WallFriction
E l f C l b Th
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Example of Coulomb Theory
Given
Wall as shown above
Find
KA, K
P, P
A
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Solution for Coulomb Active
Pressures Compute Coulomb Active Pressure
KA = 0.3465
Compute Total Wall Force
PA
= 8316 lb/ft of wall
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Solution for Coulomb Passive
Pressures Compute Coulomb Passive Pressure
KP = 4.0196
Compute Total Wall Force
PA
= 96,470 lb/ft of wall
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Walls with Cohesive Backfill Retaining walls should generally have
cohesionless backfill, but in some cases cohesivebackfill is unavoidable
Cohesive soils present the following weaknesses as
backfill:
Poor drainage
Creep
Expansiveness
Most lateral earth pressure theory was firstdeveloped for purely cohesionless soils (c = 0)
and has been extended to cohesive soils afterward
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Rankine Pressures with
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a e essu es tCohesion (Level Backfill)
31 tan2
4
22 c tan
4
2
1H
KA3
1tan2
4
2
2 c
H
tan
4
2
Active
Passive
13 tan2
4
2
2 c tan
4
2
3H
KP13
tan2
4
2 2 c
H tan
4
2
Overburden Driving
Wall Driving
Comments on Valid if wall-soil
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Comments on
RankineEquations
friction is not taken in
to account Do not take into
consideration soil
above critical height
Do not take intoconsideration sloping
walls
For practical problems,
should use equations asthey appear in the book
Hc2c
Ka
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Equivalent Fluid Method Simplification used to guide the calculations of
lateral earth pressures on retaining walls Can be used for Rankine and Coulomb lateral
earth pressures
Can be used for at rest, active and passive earthpressures
Transforms the soil acting on the retaining wallinto an equivalent fluid
Example of Equivalent Fluid Method
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Example of Equivalent Fluid Method
Given
Wall as shown above
KA
= 0.3465
KP
= 4.0196
w = 3 degrees
Find
Forces acting on the
wall (both horizontaland vertical)
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Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Active
Case)
GhKa coswGh1200.3465cos3
Gh41.52 pcf
GvKa sinwG v1200.3465sin 3
Gv2.18 pcf
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Example of Equivalent Fluid Compute Wall Load (Active Case)
PabGh H
2
2
Pa
b 41.52202
2 8304 lb/ft
Va
b
Gv H2
2
Va
b
2.18202
2436 lb/ft
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Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Passive
Case)
GhKp coswGh1204.0196cos3
Gh481.69 pcf
G vKp sinwG v1204.0196sin 3
G v25.24 pcf
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Example of Equivalent Fluid Compute Wall Load (Passive Case)
PpbGh H
2
2
Pp
b 481.69202
2 96338lb/ft
Vp
b
G v H2
2Vp
b
25.24202
2
5048 lb/ft
T hi
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Terzaghi
Model Assumes log spiral
failure surface behindwall
Requires use of
suitable chart for KA
and KP
Not directly used inthis course, but optionin SPW 911
P ti L t l E th
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Presumptive Lateral Earth
Pressures Based on Terzaghi theory
Suitable for relatively simple retaining walls inhomogeneous soils
Classifies soils into five types:1. Clean coarse grained soils
2. Coarse grained soils of low permeability; mixed with
fine grained soils3. Residual soils with granular materials and clay content
4. Very soft clay, organic silts, or silty clays
5. Medium or stiff clay, very low permeability
P ti L t l E th
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Presumptive Lateral Earth
Pressures
Presumptive
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p
LateralEarthPressures
Effects of
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SurfaceLoading
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Homework Set 5 Reading
McCarthy: Chapter 16
Coduto: Chapters 22, 23, 24 & 25
Homework Problems McCarthy: 16-1, 16-8, 16-12a, 16-17
Coduto: 25.3 (Hand and Chart Solutions); 25.5 (SPW
911)
Due Date: 17 April 2002
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Questions