29 Simple Retaining Walls

WHAT IS A RETAINING WALL ?

A structure introduced to achieve a step change in adjacent ground levels, or

A structure to hold an otherwise unstable bank of ground.

(Really the same definitions)

Old ground level

New ground levels

This is a simple retaining wall - there are many other types . . .

Building with basement

basement

Swimming pool

Bridge abutment

Some examples

Observation:

Retaining walls are really vertical slabs, with special configurations and loadings.

FREE-STANDING CANTILEVER RETAINING WALLIn this course, we’ll confine our attention to this simple wall:

Stem(may be tapered)

Base

Heel

Toe

Where there are no boundary constraints Where there are

boundary constraints

Boundary

No Heel

Boundary

No Toe

So how does the wall serve our purpose ?

Earth pressure on stem

May cause wall to

slide and/or

overturn

So there are two stability problems.

Resistance to sliding and overturning are offered by . . . .

Friction between base and soil

Passive earth pressure on face of toe

Weight of base and stem

Weight of soil above heel

Soil pressure acting on base

The base and stem bend, so there is also a strength problem to consider.

tension

tension

tension

So we need primary rebar thus:

So a design approach must address both stability (sliding and overturning) and strength . . .

DESIGN APPROACH

Design Steps suggested:

1. Estimate horizontal soil force on stem,

2. Select trial dimensions,

3. Check for sliding and overturning,

4. Check sub-soil pressures,

5. Estimate critical bending and shear,

6. Select concrete grade and rebar cover,

7. Select rebar, observing minimum requirements.

In the following example, we assume the soil is clean sand or gravel which is free-draining (no water pressure), backfill is horizontal (no slope) and there is no surcharge loading . . .

1. Estimate horizontal soil force on stem

Reasonably accurate to assume soil pressure increases linearly with depth. So lateral pressure at depth x : px = K γ x :

x

px = K γ x

po = 0

Three cases to consider:

At rest:

Ko = 0.4-0.6

Active :

Ka = 1 - sin φ1 + sin φ

Passive :

Kp = 1 + sin φ1 - sin φ

This is the case for our free-standing wall.

HP

So resultant force P acting on stem per unit length of wall

= 1/2 Ka γ H2

2. Select trial dimensions

Software packages are available to assist. The better packages consider practical, as well as structural aspects. Some guidance:

H

>= 200 mm

Stem thickness = H/8 to H/12

Base width = 0.4H to 0.7H

Width of toe = (0.25 to 0.4) * base width

Depth of toe = 1.2 * stem width

3. Check for sliding and overturning

These are stability concerns - so Disturbing forces are augmented, andRestoring forces are discounted.

The load factors are :Disturbing : 1.5 Restoring : 0.8

SLIDING

PA

WA

Ws

Pp

WbRestoring force = μ Σ W + PP

Disturbing force = PA

TEST 0.8 (μ Σ W + PP) >= 1.5 PA

OVERTURNING

PA

yA

ys

yg

yb

Restoring moment = Σ (Wy)

Disturbing moment = PA H/3

TEST 0.8 Σ (Wy) >= 1.5 PA H/3

4. Check sub-soil pressures

pmin

pmax

This force ΣW is the resultant of the soil pressures applied upwards on the base.

e = eccentricity from centroid

Assuming the pressure is linearly distributed:

pmax , min =

ΣW / D ( 1 ± 6e / D)

Two checks:

(1) Ensure that pmin is compressive, iethat resultant lies in middle-third of the base (emax=D/6)

. . . and

(2) Ensure that pmax < pall

e

5. Estimate critical bending and shear

P* = 1.5 1/2 Kγ H2

H/3

UBMD

M*max= P* H/3

USFD

V*max = P*

do

do

STEM :

V*max for design

HEEL :

dodo

UBMDM*max

USFD

V*max at faceof stem

TOE :

UBMDM*max

USFD

V*max at do from stem

Comment:

With the dimensions commonly encountered, shear is sometimes a problem, so always check !

6. Select concrete grade and rebar cover

Concrete Grade :

There are two exposure conditions to consider:

1. In contact with soil, and

2. Exposure to climate.

Select the most severe.

Cover to Rebar :

Different cover is usually required for each face. Make sure that this is clearly shown on drawings.

7. Select rebar, observing minimum requirements

The same procedures as for design of slabs :

P* = 1.5 1/2 Kγ H2

M*max= P* H/3

H/3

e.g. Stem: Ast = M* max / (0.8 * 0.9 * d * fsy)

Select dia. and spacing, observing Ast.min, and s max

Check that φ Vuc > V* max at do from base.

Similarly for heel and toe.

V*maxfor design

do

SUMMARY

• Retaining walls are used to achieve step changes in ground levels, and must therefore resist soil pressures stably and safely,

• Retaining walls are just like vertical slabs, with special configurations and loadings,

• Walls may form parts of structures, or may be free-standing,

• For free-standing walls, both sliding and overturning must be considered, using load factors of 1.5 for disturbing forces and 0.8 for restoring forces,