Retaining walls

Retaining Retaining WallsWalls

Introduction

IntroductionIntroduction• Retaining walls are used to retain earth (or other

material) in a vertical position at locations where an abrupt change in ground level occurs.

• The walls therefore prevents the retained earth from assuming its natural angle of repose.

BackfillBackfill & Surcharge& Surcharge• The material retained or supported by a retaining

wall is called backfill.• Backfill may have its top surface horizontal or

inclined.• The position of the backfill lying above the

horizontal plane at the elevation of top of wall is called surcharge & its inclination to the horizontal is called as Surcharge angle.

Types of Retaining Types of Retaining WallsWalls

• Gravity Wall• Counterfort Wall • Basement Wall

• Cantilever Wall• Buttress wall• Bridge Abutment

Gravity WallsGravity Walls• The “gravity wall” resist

the earth pressure exerted by backfill by its own self weight (dead load) .

• It is usually built in stone masonry, and occasionally in plain concrete.

Gravity WallsGravity Walls• The “gravity wall”

provides stability by virtue of its own weight , and therefore, is rather massive in size.

• It is usually built in stone masonry, and occasionally in plain concrete.

Gravity WallGravity Wall• The thickness of wall is also

governed by need to eliminate or limit the resulting tensile stress to its permissible limit .

• Plain concrete gravity walls are not used for heights exceeding about 3m, for obvious economic reasons.

Gravity WallGravity Wall• Stress developed is very

low.

• These walls are so proportioned that no tension is developed anywhere and the resultant of forces remain within the middle third of the base.

Cantilever WallCantilever Wall• The “Cantilever wall ”

is the most common type of retaining structure and is generally economical for heights up to about 8m.

• The structure consists of vertical stem , and a base slab, made up of two distinct regions, viz., a heel slab and a toe slab

Cantilever WallCantilever Wall• All three components

behave as one way cantilever slabs:

• “stem” acts as a vertical cantilever under the lateral earth pressure

• “heel slab” acts as a horizontal cantilever under the action of weight of the retained earth (minus soil pressure acting upwards from below)

• “toe slab ” acts as a cantilever under the action of resulting soil pressure acting upward.

Cantilever WallCantilever Wall• It resists the

horizontal earth pressure as well as other vertical pressure by way of bending of various components acting as cantilevers

• May be L shaped or T shaped

Counterfort WallCounterfort Wall• Stem and Heel slab are

strengthened by providing counterforts at some suitable intervals.

• The stability of the wall is maintained essentially by the weight of the earth on the heel slab plus the self weight of the structure.

Counterfort WallCounterfort Wall• For large heights, in a

cantilever retaining wall, the bending moments developed in the stem, heel slab and toe slab become very large and require large thickness.

• The bending moments can be considerably reduced by introducing transverse supports, called counterforts.

Counterfort WallCounterfort Wall• Counterfort wall are

placed at regular intervals of about1/3 to ½ of the wall height, interconnecting the stem with the heel slab.

• The counterforts are concealed within the retained earth on the rear side of the wall.

Counterfort WallCounterfort Wall• This wall is economical

for heights above (approximately) 7m.

• The counterforts subdivide the vertical slab (stem) into rectangular panels and support them on two sides(suspender-style), and themselves behave essentially as vertical cantilever beams of T-section and varying depth.

Buttress WallButtress Wall• It is similar to counterfort wall,

except that the transverse stem supports, Called buttress, are located in the front side, interconnecting the stem with the toe slab(and not with heel slab, as with counterforts)

Buttress WallButtress Wall• Although the buttresses are structurally

more efficient (and more economical) counterforts, the counterfort wall is generally preferred to the buttress wall as it provides free usable space (and better aesthetics)in front of the wall.

Lateral Earth pressureLateral Earth pressure• The retaining force due to earth pressure

constitutes the main force acting on the retaining wall, tending to make it bend , slide and overturn.

• Let pressure p increasing linearly with increasing depth z below the surface:

P=Cϒez

• Where ϒe is the unit weight of the earth and C is the coefficient that depends on its physical properties and also on the pressure is active or passive.

ACTIVE EARTH ACTIVE EARTH PRESSUREPRESSURE

Rankine's TheoryRankine's TheoryAssumptions

•The soil mass is semi-infinite, homogeneous, dry and cohesionless•The ground surface is plane which may be horizontal or inclined.•The back of the wall is vertical and smooth(No shearing stresses are developed between the wall and soil).•The wall yields about the base and satisfies the deformation conditions for plastic equilibrium.

Cohesionless BackfillsCohesionless Backfills• Dry or moist backfill with no surcharge• Submerged backfill• Backfill with uniform surcharge• Backfill with sloping surfaces

Dry or moist backfill Dry or moist backfill with no surchargewith no surcharge

Dry or moist backfill Dry or moist backfill with no surcharge with no surcharge

(cont.…)(cont.…)

Effect of surcharge on Effect of surcharge on a level backfilla level backfill

• Gravity loads act on a level backfill due to the construction of buildings and the movement of vehicles near the top of retaining wall.

• These additional loads can be assumed to be static and uniformly distributed on top of the backfill, for calculation purpose.

• This distributed load ws (kN/m2) can be treated as statically equivalent to an additional(fictitious) height hs=ws / ϒe of soil backfill with unit weight v. this additional height of backfill is called surcharge, is expressed either in terms of heights hs or in terms of the distributed load ws.

Submerged BackfillSubmerged Backfill• In this case the sand fill behind the retaining wall

is saturated with water.

Submerged BackfillSubmerged BackfillLateral pressure is made of two components-•Lateral Pressure due to water at depth h

Pa=Kaγ’h+γwh

If the water stands to both sides of the wall, the water pressure need not be considered & net lateral pressure is given by

Pa=Kaγ,H

Submerged BackfillSubmerged Backfill

Backfill with Uniform Backfill with Uniform SurchargeSurcharge


• If the backfill is horizontal and carries surcharge of uniform intensity w per unit area, the vertical pressure increment at any depth h will increase by w. The increase in the lateral pressure at any depth h is given by,

Pa=Kaγh+Kaw

At the base of the wall, the pressure intensity is ,Pa=KaγH+Kaw


Backfill with sloping Backfill with sloping SurfaceSurface

β=inclination of sloping surface behind the wall with the horizontal

=Surcharge Angle


• Assuming, vertical and horizontal stresses are conjugate. It can be shown that if the stress on a given plane at a given point is parallel to another plane, the stress on the latter plane at the same point must be parallel to the first plane

Backfill with Sloping Backfill with Sloping SurfaceSurface


Passive Earth Passive Earth PressurePressure

• Passive earth pressure is exerted on a wall when it has a tendency to move towards the backfill while supporting an arch and is subjected to arch thrust.

• When Due to active pressure from the right hand side, the wall moves left. The soil to the left is thus compressed and in turn exert passive earth pressure, resisting such movement .



Stability of Cantilever Stability of Cantilever Retaining WallRetaining Wall

Methods of Failure of Methods of Failure of retaining wallsretaining walls

• Overturning about the toe• Sliding • failure of soil due to excessive pressure at toe or

tension at the heel• Bending failure of stem or base of slab or heel

slab

Overturning about the Overturning about the toetoe

Overturning about the Overturning about the toetoe

SlidingSliding

• If the wall is found to be unsafe against sliding , shear key below the base should be provided. Such a key develops passive pressure which resists completely the sliding tendency of the wall. A factor of safety of 1.5 must be used against sliding.

• In the absence of elaborate tests, the following values of µ may be adopted:Soil µ

Coarse grained soil without silt 0.55

Coarse grained soil with silt 0.45

Silt 0.35

Soil Pressure Soil Pressure DistributionDistribution

Soil Pressure Soil Pressure DistributionDistribution

Bending failureBending failure• The stem of T shaped

cantilever retaining wall will bend as cantilever, so that tensile face will be towards the backfill.

• The critical section will be at B, where cracks may occur at the inner face if it is not properly reinforced. The heel slab will have net pressure acting downwards, and will bend as cantilever, having tensile face upwards.

Bending failureBending failure• The critical section at B, where cracks may occur

if it is not reinforced properly at the upper face. • The net pressure on toe slab will acts upwards,

and hence it must be reinforced at the bottom face.

• The thickness of stem, heel slab and toe slab must be sufficient to withstand compressive stresses due to bending.

Design principles of Design principles of Cantilever Retaining Cantilever Retaining

WallWall• The design of a cantilever retaining wall consist

of the following –1. Fixation of base width b2. Design of stem 3. Design of heel slab4. Design of toe slab

Fixation of base width Fixation of base width bb

• The base width b of the retaining wall should be so chosen that the resultant of the forces remain within middle third, and the ratio of length of toe slab to the base width should be such that the stress p1 at toe does not exceed the safe bearing capacity of soil.

Fixation of base width Fixation of base width (b)(b)cont…cont…

Fixation of base width Fixation of base width (b)(b)cont …cont …

Design of StemDesign of Stem

• Reinforcement is provided towards the inner face of stem , i.e. towards side of fill. The reinforcement towards 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 the length of retaining wall at inner face.

• Similarly, at the outer face of the stem , temperature reinforcement is provided both in horizontal as well as in vertical direction. At the rate of 0.15% of the area of cross section.

Design of heel slabDesign of heel slab

• The heel slab is also to be designed as a cantilever . It has both downward pressure (due to weight of soil and self weight )as well as upward pressure due to soil reaction. However , the net pressure is found to act downward and hence reinforcement is provided at the upper face BC.

Design of toe slabDesign of toe slab

• Neglecting the weight of the soil above it, the toe slab will bend upwards as a cantilever due to upward soil reaction. Hence reinforcement is placed at the bottom face.

• Normally , the thickness of both toe slab and heel slab is kept the same, determined on the basis of greater of the cantilever bending moments.

Depth of foundationDepth of foundation

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Retaining walls