Design of Cantilevered Design of Cantilevered Retaining WallsRetaining Walls

CE A433 – RC DesignCE A433 – RC Design

T. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.

Spring 2009Spring 2009

IntroductionIntroduction

A cantilever retaining wall is a A cantilever retaining wall is a system of cantilever slabs (i.e. system of cantilever slabs (i.e. beams) that retain soil.beams) that retain soil.

The key is to draw the appropriate The key is to draw the appropriate FBDs so that you can determine the FBDs so that you can determine the internal forces.internal forces.

Cantilever Retaining WallCantilever Retaining Wall

Shear Key

Toe

Stem

Heel

Forces ACTING ON the WallForces ACTING ON the Wall

Wall

FootingShear Key

Soil on Toe

Soil on Heel

Active Lateral Soil Pressure

ReactionsReactions

Passive Lateral Soil Pressure

Vertical Reaction

Friction

ACTUAL FRICTION is not the same as

FRICTION CAPACITY!

Computing Soil Bearing Computing Soil Bearing StressStress

Resolve applied Resolve applied forces into a forces into a concentric vertical concentric vertical force and moment on force and moment on the contact area.the contact area.

IIxx = bL = bL33/12/12 A = bLA = bL c = L/2c = L/2 maxmax = P/A + Mc/I = P/A + Mc/Ixx

minmin = P/A – Mc/I = P/A – Mc/Ixx

P

M

SlidingSliding

Driving Force

Resisting Capacity

Vslide = Driving Force = Demand

Vresist = sum(Resisting Forces) = Capacity

FS = Vresist / Vslide

Design for FS > 1.5

Friction CAPACITY = NNot Actual Friction Reaction

OverturningOverturning

Driving Force

Point of Rotation

Resisting Forces

MOT = Driving Force*arm = Demand

MROT = sum(Resisting Moments) = Capacity

FS = MROT / MOT

Design for FS > 2.0

Draw FBDsDraw FBDs

Stem

ToeHeel

Stem DiagramsStem DiagramsFBD

Shear Moment

Dem

an

d

Cap

acity

Dem

an

d

Cap

acity

Make stem thick

enough for

shear

Select Steel to provide flexural capacity

Add T&S Steel

ToeToe

Shear

Moment

Design Shear

Design Moment

Vu can be calculated a distance ‘d’ from face of wall since there is a compressive reaction with the wall.

Mu is computed at the face of the wall.

Flexural Steel extends a

development length into

the heel and should

develop within the

length of the toe.

Add T&S Steel

HeelHeel

Shear

Moment

Design Shear

Design Moment

Vu must be calculated at the face of wall since there is a tensile reaction with the wall.

Mu is computed at the face of the wall.

Flexural Steel extends a

development length into the toe and

should develop

within the length of the

heel.

Add T&S Steel

The Design ProcessThe Design Process Select the overall dimensions (height, embedment, Select the overall dimensions (height, embedment,

footing length and position, and estimated footing & footing length and position, and estimated footing & wall thicknesses) based on stability (sliding and wall thicknesses) based on stability (sliding and overturning) and soil strength (max/min bearing overturning) and soil strength (max/min bearing pressures) using service level loads.pressures) using service level loads.

Check slab (wall and footing) thicknesses using shear Check slab (wall and footing) thicknesses using shear criteria and factored loads. Adjust thicknesses as criteria and factored loads. Adjust thicknesses as necessary, rechecking stability and soil strength of the necessary, rechecking stability and soil strength of the values change.values change.

Select the flexural steel for the three cantilever slab Select the flexural steel for the three cantilever slab elements using factored loads.elements using factored loads.

Select the temperature and shrinkage steel for wall Select the temperature and shrinkage steel for wall and footing.and footing.

Draw the resulting wall cross section (to scale!)Draw the resulting wall cross section (to scale!)