4-earth pressure theories.pdf

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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.

GL

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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.

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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

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EarthRetainingStructures


EarthRetainingStructures


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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):


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


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LateralEarthPressureLateralearthpressuresareafunctionoftypeandamountofwallmovement,shearstrengthproperties,weightofsoilanddrainage


ActiveCondition PassiveConditionAtRestCondition

SlipPlanesforActiveandPassiveFailure

ActiveConditionPassiveCondition

Horizontalmovementrequired


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AtRestCondition


AtRestCondition


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AtRestCondition


Rankines Theory


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Assumptions


ActiveFailureCondition


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)2/45(tansin1sin1 2

AK


Initially (K0 state)

Failure (Active state)


vdecreasing hactive earth pressure @A

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ActiveEarthPressure

Withoutconsideringtensilecrack:

Consideringtensilecrack:


PassiveFailureCondition

SincethewallismovedtowardsB,itseffectivehorizontalstresswillincreasebuttheeffectiveverticalstresswillremainconstant.

Initially (K0 state)

Failure (Active state)

passive earth pressure @B

']'[ vPpassiveh K


v

increasing h)2/45(tan

sin1sin1 2

PK

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PassiveEarthpressure




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Specialcases


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Specialcases


CoulombsTheory


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CoulombsEarthPressureTheory




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d


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CoulombsEarthPressureTheory GeneralCase

Coulombs Active earth pressure


Coulomb sActiveearthpressure

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CoulombsEarthPressureTheory GeneralCaseCoulombsActiveearthpressure


CoulombsEarthPressureTheory GeneralCaseCoulombsActiveearthpressure


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CoulombsActiveearthpressure


Foragivenvalueof,theeffectofwallfrictionistoreducetheactiveearthpressurecoefficient.


CoulombsPassiveearthpressure


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CoulombsPassiveearthpressure


CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureCulmannssolutioncanbeusedforanywallfriction,regardlessofirregularityofbackfillandsurcharges.Hence,itprovidesapowerfultechniqueforestimatinglateralearthpressure.

Construction procedure for c = 0 soilConstructionprocedureforc=0soil


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CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureCulmannssolutioncanbeusedforanywallfriction,regardlessofirregularityofbackfillandsurcharges.Hence,itprovidesapowerfultechniqueforestimatinglateralearthpressure.

Construction procedure for c = 0 soilConstructionprocedureforc=0soil


Trialwedge:ABCa

CoulombsEarthPressureTheory GraphicalMethodCulmann(1875)developedagraphicalsolutionofCoulombsPassiveearthpressureTheCulmannsolutionprovidesuswithonlythemagnitudeoftheactiveforceperunitlengthoftheretainingwallnotwiththepointofapplicationoftheresultant

Construction procedure for c = 0 soilConstructionprocedureforc=0soilTofindthepointofapplicationoftheresultant

ABCisthefailurewedgedeterminedbyCulmannsmethod.

OisthecenterofgravityofthewedgeABC. IfalineOOisdrawnparalleltothesurfaceofsliding,BC,thepointofintersectionofthislinewiththebackfaceofthewallwillgivethepointofapplicationofPa.


pp Thus,PaactsatOinclinedatangle withthenormaldrawntothebackfaceofthewall.

4-earth pressure theories.pdf

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