Lateral Earth Pressure

Lateral Earth PressureThe magnitude of lateral earth pressure depends on:

1. Shear strength characteristics of soil2. Lateral strain condition3. Pore water pressure4. State of Equilibrium of soil5. Wall and ground surface shapePrevious conditions depends mainly on:

a) Drainage conditionsb) Interaction between soil and wall

Soil state of EquilibriumThe state of Equilibrium of soil can be divided into two states :

a) State of Elastic Equilibrium When a small change in stress produces a corresponding small change

in strain.b) State of Plastic Equilibrium When irreversible strain takes place at a constant stress.

The strain state relating to earth pressure calculation fall into three categories:a) At Rest State:

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It is the case when state of elastic Equilibrium with no lateral displacementoccurs (Figure 1 ).

b) Active state: It is the case when plastic equilibrium with lateral expansion takes place

(wall moves outward from the soil). ( Figure 2 ).c) Passive state: Plastic equilibrium with lateral contraction takes place (wall moves toward the soil).

( Figure 2 )

Figure 1

Figure 2(1) Earth Pressure at rest (ko condition )

lateral strain , h = 0

ko = coefficient of lateral earth presser at rest. ko depends on :

Soil type ( sand, silt, clay)


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Loading Unloading history Relative density of soil

For normally consolidated soil (N.C.) and sand

For over consolidated soil (O.C.)

where OCR is the over consolidated ratio

and in general where is Poisson ratioIn this case ,the mohre circle is below the shear envelope of this soil (Figure 3).

Figure 3


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(2) Active Earth pressure (Rankines Active state )

Rankines theory neglects frictionbetween soil and wall .

when the wall moves outward from the soil , the lateral earth pressure starts to be reduced until it reaches its , minimum Figure 3

value ,

where , where , ka = coefficient of active earth pressure. (Figure 3)And in this case , the failure plane makes ( 45 /2 ) with the direction of the majorprincipal plane ( usually horizontal axes ) .

(3) Rankin Passive StateIf the wall moved toward the soil , the passive condition will take place.

The passive pressure will increase until it reaches its maximum value of:


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and in this case , the failure place makes ( 45 + /2 ) with the direction of the majorprincipal plane.

Earth pressure Distribution for SandIn general, the active earth pressure distribution in sand will be:

Figure (4) where = soil unit weight H = wall height

However the distribution and value of passive earth pressure in sand is, Figure(5)


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Figure 5

(b) For clay The value of active earth pressure is (Figure 6)

Figure(6)

where , c = soil cohesion The passive pressure values are (Figure 7)


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Figure(7)

Effect of Ground Water Tablea) Static water table

For static water table the water pressure should be treated separately from soil lateral pressure as shown in Figure(8)

Figure(8)


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where sub = submerged unit weight of soil = sat - w

b) Moving Water TableIn this case , the flow net and equipotential lines should be

drawn for the wall , Then the pore pressure against the wall can be determined, ( Figure 9)

Figure (9 )

Effect of Stratified Soil As an example of stratified soil shown in(Figure10)


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(Figure 10)

Effect of Sloping Ground SurfaceIn this case the active coefficient of lateral earth pressure is

and the resultant in this case will be parallel to the ground surface, (Figure 11)Coulomb's Theory for Rough Walls


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Figure(12) = angle of wall friction

for concrete wall

and

and

Strutted Trench sheeting


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Figure(13)The location of struts affects the values and distributions of lateral earth pressures

Figure(14)


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Lateral Earth Pressure