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IntroductionIntroduction• Retaining walls are used to retain earth (or othermaterial) in a vertical position at locations where anabrupt change in ground level occurs.• The walls therefore prevents the retained earth fromassuming its natural angle of repose.
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BackfillBackfill & Surcharge& Surcharge• The material retained or supported by a retainingwall is called backfill.• Backfill may have its top surface horizontal orinclined.• The position of the backfill lying above thehorizontal plane at the elevation of top of wall iscalled surcharge & its inclination to the horizontal iscalled as Surcharge angle.
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Types of Retaining WallsTypes of Retaining Walls• Gravity Wall• Counterfort Wall• Basement Wall• Cantilever Wall• Buttress wall• Bridge Abutment
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Gravity WallsGravity Walls• The “gravity wall” resistthe earth pressureexerted by backfill by itsown self weight (deadload) .• It is usually built instone masonry, andoccasionally in plainconcrete.
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Gravity WallsGravity Walls• The “gravity wall”provides stability byvirtue of its own weight ,and therefore, is rathermassive in size.• It is usually built instone masonry, andoccasionally in plainconcrete.
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Gravity WallGravity Wall• The thickness of wall is alsogoverned by need toeliminate or limit theresulting tensile stress to itspermissible limit .• Plain concrete gravity wallsare not used for heightsexceeding about 3m, forobvious economic reasons.
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Gravity WallGravity Wall• Stress developed is verylow.• These walls are soproportioned that notension is developedanywhere and theresultant of forcesremain within themiddle third of the base.
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Cantilever WallCantilever Wall• The “Cantilever wall ” isthe most common typeof retaining structureand is generallyeconomical for heightsup to about 8m.• The structure consists ofvertical stem , and abase slab, made up oftwo distinct regions,viz., a heel slab and atoe slab
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Cantilever WallCantilever Wall• All three componentsbehave as one waycantilever slabs:• “stem” acts as a verticalcantilever under the lateralearth pressure• “heel slab” acts as ahorizontal cantilever underthe action of weight of theretained earth (minus soilpressure acting upwardsfrom below)• “toe slab ” acts as acantilever under the actionof resulting soil pressureacting upward.
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Cantilever WallCantilever Wall• It resists the horizontalearth pressure as wellas other verticalpressure by way ofbending of variouscomponents acting ascantilevers• May be L shaped or Tshaped
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Counterfort WallCounterfort Wall• Stem and Heel slab arestrengthened byproviding counterforts atsome suitable intervals.• The stability of the wall ismaintained essentiallyby the weight of theearth on the heel slabplus the self weight ofthe structure.
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Counterfort WallCounterfort Wall• For large heights, in acantilever retaining wall,the bending momentsdeveloped in the stem,heel slab and toe slabbecome very large andrequire large thickness.• The bending momentscan be considerablyreduced by introducingtransverse supports,called counterforts.
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Counterfort WallCounterfort Wall• Counterfort wall areplaced at regularintervals of about1/3 to½ of the wall height,interconnecting thestem with the heel slab.• The counterforts areconcealed within theretained earth on therear side of the wall.
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Counterfort WallCounterfort Wall• This wall is economical forheights above(approximately) 7m.• The counterfortssubdivide the verticalslab (stem) intorectangular panels andsupport them on twosides(suspender-style),and themselves behaveessentially as verticalcantilever beams of T-section and varyingdepth.
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Buttress WallButtress Wall• It is similar to counterfort wall, exceptthat the transverse stem supports,Called buttress, are located in thefront side, interconnecting the stemwith the toe slab(and not with heelslab, as with counterforts)
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Buttress WallButtress Wall• Although the buttresses are structurallymore efficient (and more economical)counterforts, the counterfort wall isgenerally preferred to the buttress wall asit provides free usable space (and betteraesthetics)in front of the wall.
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Lateral Earth pressureLateral Earth pressure• The retaining force due to earth pressureconstitutes the main force acting on the retainingwall, tending to make it bend , slide andoverturn.• Let pressure p increasing linearly with increasingdepth z below the surface:P=Cϒez• Where ϒe is the unit weight of the earth and C isthe coefficient that depends on its physicalproperties and also on the pressure is active orpassive.
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Rankines TheoryRankines TheoryAssumptions•The soil mass is semi-infinite, homogeneous, dry andcohesionless•The ground surface is plane which may be horizontalor inclined.•The back of the wall is vertical and smooth(Noshearing stresses are developed between the walland soil).•The wall yields about the base and satisfies thedeformation conditions for plastic equilibrium.
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Cohesionless BackfillsCohesionless Backfills• Dry or moist backfill with no surcharge• Submerged backfill• Backfill with uniform surcharge• Backfill with sloping surfaces
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Dry or moist backfill withDry or moist backfill withno surchargeno surcharge
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Dry or moist backfill withDry or moist backfill withno surcharge (cont.…)no surcharge (cont.…)
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Effect of surcharge on aEffect of surcharge on alevel backfilllevel backfill• Gravity loads act on a level backfill due to theconstruction of buildings and the movement ofvehicles near the top of retaining wall.• These additional loads can be assumed to be staticand uniformly distributed on top of the backfill, forcalculation purpose.• This distributed load ws (kN/m2) can be treated asstatically equivalent to an additional(fictitious)height hs=ws / ϒe of soil backfill with unit weight v. thisadditional height of backfill is called surcharge, isexpressed either in terms of heights hs or in terms ofthe distributed load ws.
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Submerged BackfillSubmerged Backfill• In this case the sand fill behind the retaining wall issaturated with water.
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Submerged BackfillSubmerged BackfillLateral pressure is made of two components-•Lateral Pressure due to water at depth hPa=Kaγ’h+γwhIf the water stands to both sides of the wall, the water pressureneed not be considered & net lateral pressure is given byPa=Kaγ,H
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Backfill with UniformBackfill with UniformSurchargeSurcharge
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Backfill with UniformBackfill with UniformSurchargeSurcharge• If the backfill is horizontal and carries surcharge ofuniform intensity w per unit area, the verticalpressure increment at any depth h will increase byw. The increase in the lateral pressure at any depthh is given by,Pa=Kaγh+KawAt the base of the wall, the pressure intensity is ,Pa=KaγH+Kaw
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Backfill with UniformBackfill with UniformSurchargeSurcharge
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Backfill with slopingBackfill with slopingSurfaceSurfaceβ=inclination of sloping surface behind the wall withthe horizontal=Surcharge Angle
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Backfill with sloping SurfaceBackfill with sloping Surface• Assuming, vertical and horizontal stresses areconjugate. It can be shown that if the stress on agiven plane at a given point is parallel to anotherplane, the stress on the latter plane at the samepoint must be parallel to the first plane
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Backfill with Sloping SurfaceBackfill with Sloping Surface
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Backfill with sloping SurfaceBackfill with sloping Surface
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Passive Earth PressurePassive Earth Pressure• Passive earth pressure is exertedon a wall when it has atendency to move towards thebackfill while supporting anarch and is subjected to archthrust.• When Due to active pressurefrom the right hand side, thewall moves left. The soil to theleft is thus compressed and inturn exert passive earthpressure, resisting suchmovement .
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Stability of CantileverStability of CantileverRetaining WallRetaining Wall
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Methods of Failure ofMethods of Failure ofretaining wallsretaining walls• Overturning about the toe• Sliding• failure of soil due to excessive pressure at toe ortension at the heel• Bending failure of stem or base of slab or heel slab
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Overturning about the toeOverturning about the toe
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Overturning about the toeOverturning about the toe
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• If the wall is found to be unsafe against sliding ,shear key below the base should be provided. Sucha key develops passive pressure which resistscompletely the sliding tendency of the wall. Afactor of safety of 1.5 must be used against sliding.• In the absence of elaborate tests, the followingvalues of µ may be adopted:Soil µCoarse grained soil without silt 0.55Coarse grained soil with silt 0.45Silt 0.35
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Soil Pressure DistributionSoil Pressure Distribution
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Soil Pressure DistributionSoil Pressure Distribution
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Bending failureBending failure• The stem of T shapedcantilever retaining wall willbend as cantilever, so thattensile face will be towardsthe backfill.• The critical section will be at B,where cracks may occur atthe inner face if it is notproperly reinforced. The heelslab will have net pressureacting downwards, and willbend as cantilever, havingtensile face upwards.
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Bending failureBending failure• The critical section at B, where cracks may occur ifit is not reinforced properly at the upper face.• The net pressure on toe slab will acts upwards, andhence it must be reinforced at the bottom face.• The thickness of stem, heel slab and toe slab mustbe sufficient to withstand compressive stresses dueto bending.
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Design principles ofDesign principles ofCantilever Retaining WallCantilever Retaining Wall• The design of a cantilever retaining wall consist ofthe following –1. Fixation of base width b2. Design of stem3. Design of heel slab4. Design of toe slab
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Fixation of base width bFixation of base width b• The base width b of theretaining wall should be sochosen that the resultant ofthe forces remain withinmiddle third, and the ratioof length of toe slab to thebase width should be suchthat the stress p1 at toe doesnot exceed the safebearing capacity of soil.
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Fixation of base width (b)Fixation of base width (b)cont…cont…
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Fixation of base width (b)Fixation of base width (b)cont …cont …
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• Reinforcement is provided towards the inner face ofstem , i.e. towards side of fill. The reinforcementtowards the top of stem can curtailed since B.M.varies as h3. Distribution reinforcement is provided@0.15% of the area of cross section along thelength of retaining wall at inner face.• Similarly, at the outer face of the stem ,temperature reinforcement is provided both inhorizontal as well as in vertical direction. At the rateof 0.15% of the area of cross section.
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Design of heel slabDesign of heel slab• The heel slab is also to be designed as acantilever . It has both downward pressure(due to weight of soil and self weight )as wellas upward pressure due to soil reaction.However , the net pressure is found to actdownward and hence reinforcement isprovided at the upper face BC.
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Design of toe slabDesign of toe slab• Neglecting the weight of the soilabove it, the toe slab will bendupwards as a cantilever due toupward soil reaction. Hencereinforcement is placed at thebottom face.• Normally , the thickness of both toeslab and heel slab is kept the same,determined on the basis of greater ofthe cantilever bending moments.
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