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04-02-2016
1
LATERAL EARTH PRESSURE
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
EarthRetainingStructuresEarth retaining structures are common in a manmade environment.
These structures were amongst the first to be analyzed using the concepts of mechanics.
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analyzed using the concepts of mechanics.
One of the most popular earth retaining structure is a retaining wall.
In this lecture, well learn the theory of earth pressure that is used to analyze the stability of retaining walls.
Xh
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
It will help you a great deal if you revised the following important concepts:
- Static equilibrium, Effective Stress, Mohrs Stress Circle and Shear Strength of Soils
04-02-2016
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EarthRetainingStructures
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
EarthRetainingStructures
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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EarthPressureCoefficients
Active earth pressure coefficient (Ka):
It is the ratio of horizontal and vertical principal effective stresses when
The ratio of horizontal and vertical principal effective stresses is termed as Coefficient of Earth pressure
It is the ratio of horizontal and vertical principal effective stresses when a retaining wall moves away (by a small amount) from the retained soil.
Passive earth pressure coefficient (Kp):
It is the ratio of horizontal and vertical principal effective stresses when a retaining wall is forced against a soil mass.
Coefficient of earth pressure at rest (K0):
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Coefficient of earth pressure at rest (K0):
It is the ratio of horizontal and vertical principal effective stresses when the retaining wall does not move at all, i.e. it is at rest.
LateralEarthPressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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LateralEarthPressureLateralearthpressuresareafunctionoftypeandamountofwallmovement,shearstrengthproperties,weightofsoilanddrainage
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
ActiveCondition PassiveConditionAtRestCondition
SlipPlanesforActiveandPassiveFailure
ActiveConditionPassiveCondition
Horizontalmovementrequired
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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AtRestCondition
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
AtRestCondition
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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AtRestCondition
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Rankines Theory
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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Assumptions
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
ActiveFailureCondition
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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ActiveFailureCondition
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
)2/45(tansin1sin1 2
AK
ActiveFailureCondition
Initially (K0 state)
Failure (Active state)
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
vdecreasing hactive earth pressure @A
04-02-2016
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ActiveEarthPressure
Withoutconsideringtensilecrack:
Consideringtensilecrack:
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
PassiveFailureCondition
SincethewallismovedtowardsB,itseffectivehorizontalstresswillincreasebuttheeffectiveverticalstresswillremainconstant.
Initially (K0 state)
Failure (Active state)
passive earth pressure @B
']'[ vPpassiveh K
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
v
increasing h)2/45(tan
sin1sin1 2
PK
04-02-2016
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PassiveEarthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
SlipPlanesforActiveandPassiveFailure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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SlipPlanesforActiveandPassiveFailure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Specialcases
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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Specialcases
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
CoulombsTheory
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
CoulombsEarthPressureTheory
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
d
CoulombsEarthPressureTheory
____________________________________________
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory
______________________________
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
CoulombsEarthPressureTheory GeneralCase
Coulombs Active earth pressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Coulomb sActiveearthpressure
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CoulombsEarthPressureTheory GeneralCaseCoulombsActiveearthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
CoulombsEarthPressureTheory GeneralCaseCoulombsActiveearthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory GeneralCase
CoulombsActiveearthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Foragivenvalueof,theeffectofwallfrictionistoreducetheactiveearthpressurecoefficient.
CoulombsEarthPressureTheory GeneralCase
CoulombsPassiveearthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory GeneralCase
CoulombsPassiveearthpressure
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureCulmannssolutioncanbeusedforanywallfriction,regardlessofirregularityofbackfillandsurcharges.Hence,itprovidesapowerfultechniqueforestimatinglateralearthpressure.
Construction procedure for c = 0 soilConstructionprocedureforc=0soil
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
04-02-2016
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CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureCulmannssolutioncanbeusedforanywallfriction,regardlessofirregularityofbackfillandsurcharges.Hence,itprovidesapowerfultechniqueforestimatinglateralearthpressure.
Construction procedure for c = 0 soilConstructionprocedureforc=0soil
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
Trialwedge:ABCa
CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureTheCulmannsolutionprovidesuswithonlythemagnitudeoftheactiveforceperunitlengthoftheretainingwallnotwiththepointofapplicationoftheresultant
Construction procedure for c = 0 soilConstructionprocedureforc=0soilTofindthepointofapplicationoftheresultant
ABCisthefailurewedgedeterminedbyCulmannsmethod.
OisthecenterofgravityofthewedgeABC. IfalineOOisdrawnparalleltothesurfaceofsliding,BC,thepointofintersectionofthislinewiththebackfaceofthewallwillgivethepointofapplicationofPa.
CE352A Dr. Rajesh Sathiyamoorthy, IIT Kanpur
pp Thus,PaactsatOinclinedatangle withthenormaldrawntothebackfaceofthewall.