Sections 1.1-1.3 Lateral Earth Pressure

Priyantha Jayawickrama, Ph.D.Associate ProfessorSection I:Lateral Earth PressureTexas Tech UniversityDepartment of Civil and Environmental Engineering

CE 5331-013: Design of Earth Retaining Structures

Lateral Earth Pressure TheoriesOutline:Earth pressure at restRankines theory for active and passive earth pressuresCoulombs theory for active and passive earth pressures


Earth Pressure at Rest Coefficient of earth pressure at rest, Ko

Whereso = gzsh = Ko(gz)Note:Ko for most soils ranges between 0.5 and 1.0


Earth Pressure at Rest (Cont.)For coarse-grained soilsK0 = 1 sin f (f - drained friction angle) (Jaky, 1944)For fine-grained, normally consolidated soils (Massarch, 1979)


Earth Pressure at Rest (Cont.)

For overconsolidated claysWhere

pc is pre-consolidation pressure


Earth Pressure at Rest (Cont.)Distribution of earth pressure at rest is shown belowTotal force per unit length, P0


Earth Pressure at Rest (Cont.)Partially submerged soilPressure on the wall can be found from effective stress & pore water pressure components

z H1:

Variation of h with depth is shown by triangle ACE No pore water pressure component since water table is below z


Earth Pressure at Rest (Cont.)


Earth Pressure at Rest (Cont.)z H1:

Lateral pressure from water

- Variation of h with depth is shown by CEGB- Variation of U with depth is shown by IJK

Total Lateral pressure is


Rankines Active Earth Pressure Frictionless wall Before the wall move the, stress condition is given by circle aState of Plastic equilibrium represented by circle b. This is the Rankines active stateRankines active earth pressure is given by


Rankines Active Earth Pressure (Cont.)With geometrical manipulations we get:For cohesionless soil, c=0


Rankines Active Earth Pressure (Cont.)Rankines Active Pressure Coefficient, Ka

The Rankines active pressure coefficient is given by:

The angle between the failure planes /slip planes and major principal plane (horizontal) is:


Rankines Active Earth Pressure (Cont.)The variation of with depth:The slip planes:


Rankines Passive Earth PressureFrictionless wallCircle a gives initial state stress conditionRankines passive state is represented by circle bRankines passive earth pressure is given by


Rankines Passive Earth Pressure (Cont.)Rankines passive pressure is given by:For cohesionless soil, c=0


Rankines Passive Earth Pressure (Cont.)Rankines Passive Pressure Coefficient Kp

The Rankines passive pressure coefficient is given by:

The angle between the failure planes /slip planes and major principal plane (horizontal) is:


Rankines Passive Earth Pressure (Cont.)The variation of with depth:The slip planes:


Lateral Earth Pressure Distribution Against Retaining Walls There are three different cases considered:Horizontal backfillCohesionless soilPartially submerged cohesionless soil with surchargeCohesive soilSloping backfillCohesionless soilCohesive soilWalls with Friction


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Horizontal backfill with Cohesionless soil

Active Case


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Horizontal backfill with Cohesionless soil

Passive Case


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Horizontal backfill with Cohesionless, partially submerged soil

1. Active Case


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Horizontal backfill with Cohesionless, partially submerged soil

1. Passive Case


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Horizontal backfill with Cohesive soil

Active Case



The depth at which the active pressure becomes equal to zero (depth of tension crack) isFor the undrained condition, = 0, then ka becomes 1 (tan245 = 1) and c=cu . Therefore, Tensile crack is taken into account when finding the total active force. I.e., consider only the pressure distribution below the crack



Active total pressure force will beActive total pressure force when = 0



Passive Case

Pressure

Passive force

Passive force when = 0


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Sloping backfill, cohesionless soil

Earth pressure acts an angle of to the horizontal

Active case (c=0)

This force acts H/3 from bottom and inclines to the horizontal(Table 11.2 in page 359 gives ka values for various combinations of and )


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Sloping backfill, cohesionless soilPassive case (c=0)

This force acts H/3 from bottom and inclines to the horizontal(Table 11.3 in page 360 gives kp values for various combinations of and )


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Sloping backfill, cohesive soilActive case

Depth to the tensile crack is given by


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Sloping backfill, cohesive soilPassive case

(Table 11.4 in page 361 gives variation of and with , and )


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Friction wallsRough retaining walls with granular backfill. Angle of friction between the wall and the backfill is

Active caseCase 1: Positive wall friction in the active case (+)


Lateral Earth Pressure Distribution Against Retaining Walls (Cont.)Friction walls

Downward motion of soil

Wall AB AB causes a downward motion of soil relative to wall. Causes downward shear on the wall (fig. b)

Pa will be inclined to the normal drawn to the back face of the retaining wall

Failure surface is BCD (advanced studies): BC curve & CD straight

Rankines active state exists in the zone ACD



Case 2: Negative wall friction in the active case (-)- Wall is forced to a downward motion relative to the backfill



Passive caseCase 1: Positive wall friction in the passive case (+)



Downward motion of wall

Wall AB AB causes a upward motion of soil relative to wall. Causes upward shear on the wall (fig. e)

Pp will be inclined to the normal drawn to the back face of the retaining wall

Failure surface is BCD: BC curve & CD straight

Rankines passive state exists in the zone ACD



Case 2: Negative wall friction in the passive case (-)- The wall is forced to a upward motion relative to the backfill


Coulombs Earth Pressure TheoryFailure surface is assumed to be plane. Also, wall friction is taken into accountActive case


Coulombs Earth Pressure Theory (Cont.)BC is a trial failure surface and the probable failure wedge is ABCForces acting: W - effective weight of the soil wedge; F resultant of the shear and normal force on the surface of failure BC; Pa active force per unit lengthAngle of friction between soil and wall is The force triangle for wedge is shown in figure bFrom the law of sines,


Coulombs Earth Pressure Theory (Cont.)or, H, , , , and are constants and is the only variable. To determine the critical value of for maximum Pa


Coulombs Earth Pressure Theory (Cont.)After solvingKa Coulombs active earth pressure coefficient and given byNote: =0, =0, =0 thenSame as Rankines earth pressure coefficient


Coulombs Earth Pressure Theory (Cont.)The variation of ka for retaining walls with vertical back (=0) and horizontal backfill (=0) is given in table 11.5 in page 367

Tables 11.6 (pages 368 & 369) and 11.7 (pages 370 & 371) give the values of ka for = and = /2 respectively (useful in retaining wall design)


Coulombs Earth Pressure Theory (Cont.)Passive case


Coulombs Earth Pressure Theory (Cont.)Similarly in the active caseKp Coulombs passive earth pressure coefficient and given byNote: =0, =0, =0 thenSame as Rankines earth pressure coefficientTable 11.8 in page 373 gives variation of kp with and (for =0 & =0)

Sections 1.1-1.3 Lateral Earth Pressure

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