Advance Design of RC Structure 1 - Islamic …site.iugaza.edu.ps/btayeh/files/2013/11/Retaining-Wall.pdfLecture 11 Advance Design of RC Structure Cantilever Retaining Walls 15 External

Lecture 11 Advance Design of RC Structure

1 Advance Design of RC Structure

Retaining Wall


2 Retaining Walls

What are retaining walls

Retaining walls are soil-structure systems

intended to support earth backfills.

Type of retaining walls

Gravity retaining wall

gravity walls rely on their own weight to

provide static equilibrium.

typically made of plain (unreinforced)

concrete or stone blocks.

Cantilever retaining walls

cantilever walls derive a portion of their

stabilizing forces and moments from the

backfill soil above the heel.

require the use of steel reinforcement to

resist the large moments and shear stresses.


3


4


5 Retaining Walls MSE walls

Mechanically Stabilized Earth (MSE) walls derive their stability

from the internal stresses developing at the interface between the

soil and the reinforcement elements.

MSE walls are constructed by compacting the soil in layers

separated by reinforcement strips or sheets. Reinforcement strips are

attached to facing units, and extend far enough into the backfill to

ensure adequate pullout resistance.

Soil-Nailed walls


6 Retaining Walls Reinforced Earth Walls

Geotextile-Reinforced Walls

Cantilever Sheet Piles

Reinforced Earth Walls


7

Cantilever Sheet Piles


8


9 Cantilever Retaining Walls

Basic Principles

Cantilever walls are made of reinforced concrete, & come in different

geometries.

Rely on their self-weight to resist sliding & overturning, but derive part

of their stability from the weight of the backfill above the heel of the

wall.


10



Typical Dimensions of retaining walls


12


13



Basic Design Principles

In addition to the external stability, cantilever walls must also satisfy

internal structural.

The wall section should be able to withstand the shear stresses and

bending moments resulting from the lateral earth pressure as well as the

difference in pressure between the top and bottom faces of the base.



External stability

In analyzing or designing for external stability, all the forces acting on

the structure are considered. These forces include lateral earth

pressures, the self-weight of the structure, & the reaction from the

foundation soil.

The stability of the wall is then evaluated by considering the relevant

forces for each potential failure mechanism.

The wall has to be stable against:

Sliding

Overturning

Bearing capacity

max

1allBC

qFS

q



Design Example

Given data

As shown in the figure

Design the retaining wall

' 25cf MPa

420yf MPa2150 /allq kN m


17 Design Example Step 1: Check for overturning

Calculate the weight per unit width (Wi)

(per meter) 1 23.5 0.5 0.7 8.23W kN

2 23.5 5 0.5 58.75W kN

3 23.5 0.5 1.4 16.45W kN

4 (17 2.5 19 0.2)1.4 112.7W kN

Moment arm (xi)

1 0.35x m

2 0.95x m

3 1.9x m

4 1.9x m


18 Design Example Calculate the active earth pressure & the water pressure

1' 17 2.5 0.271 11.52h kPa

2' (17 2.5 (19 9.8) 2.5) 0.271 17.75h kPa

9.8 2.5 24.5u kPa

4 (17 2.5 19 0.2)1.4 112.7W kN

The active forces P1 to P4 per unit width

1 0.5 11.52 2.5 14.4P kN

2 17.75 2.5 44.38P kN

3 0.5 (17.75 11.52) 2.5 7.79P kN

4 0.5 24.5 2.5 30.63P kN

Moment arm (yi)

1 2.5 2.5 / 3 3.33y m

2 2.5 / 2 1.25y m

3 2.5 / 3 0.83y m

4 0.83y m

1 sin350.27

1 sin35aK


19 Design Example Calculate the active earth pressure & the water pressure

i iRoverturning

O i i

W xMFS

M P y

8.23 0.35 58.75 0.95 16.45 1.9 112.7 1.9

14.4 3.33 44.38 1.25 7.79 0.83 30.63 0.83

Step 2: Check for bearing capacity

The eccentricity on the wall base

0.5 ( ) /R Oe B M M W

OK304.1

2.2 1.5135.3

0.5(2.6) (304.1 135.3) /196.1

0.42 / 6 0.43e m B OK

The maximum & minimum soil pressures at the toe & heel of the base are

2

max 2

196.1 196.1 0.42 6148.5 /

2.6 2.6

xtoe

x

F Mq q y kN m

A I

2

min 2

196.1 196.1 0.42 62.3 /

2.6 2.6heelq q kN m


20 Design Example

max

1501.01 1

148.5

allBC

qFS

q

Step 3: Check for shear strength at critical section

The ultimate shear on the base at a distance d from the face of the wall is

0.5 .075 0.02 0.405d m

OK

2(148.5 2.3) 2.2952.3 131.3 /

2.6dq kN m

2

max 148.5 /q kN m

Effective depth of base

1.6 (0.7 )uV qb d

148.5 131.3

1.6 1 0.7 0.405 662

kN

Pressure at distance d from the face of the wall

00.17 'cV fc b d

0.17 0.85 30 1 0.405 293 ukN V OK

At the TOE


21 Design Example

2(148.5 2.3) 0.9952.3 58.2 /

2.6dq kN m

2

min 2.3 /q kN m

1.6 (1.4 )uV qb d

58.2 2.3

1.6 1 1.4 0.405 502

kN

Pressure at distance d from the face of the wall

00.17 'cV fc b d

0.17 0.85 30 1 0.405 293 ukN V OK

At the HEEL

Step 3: Flexural reinforcement

At the HEEL

2 21.4 1.4

1.6 1.6 2.3 81 2.32 6

u heelM M

44.8 .uM kN m

Case I


22 Design Example 3

2

0.85 ' 2.61 101 1

'

c u

y c

f M

f bd f

3

min2

0.85 25 2.61 10 (44.8)1 1 0.0007 0.0018

420 1(0.405) 25

20.0018(100)(40.5) 7.3sA cm

Use 12mm @ 15cm

W3 + W4

1.6 1.6 16.45 112.7 0.7 144.6u heelM M kN

Case II

3

2

0.85 25 2.61 10 (144.6)1 1 0.0024

420 1(0.405) 25

20.0024(100)(40.5) 9.7sA cm

Use 14mm @ 15cm


23 Design Example At the TOE

2 20.7 0.7

1.6 1.6 109.1 148.5 109.12 3

u toeM M

53.1 .uM kN m

3

min2

0.85 25 2.61 10 (53.1)1 1 0.0009 0.0018

420 1(0.405) 25

20.0018(100)(40.5) 7.3sA cm

Use 12mm @ 15cm

At the STEM

1.6 1.6 86.7 138.7 .u stemM M kN m

3

2

0.85 25 2.61 10 (148.7)1 1 0.0023

420 1(0.405) 25

14.4 2.83 44.38 0.75 7.79 0.33 30.63 0.33stemM

86.7 .stemM kN m


24 Design Example 20.0023(100)(40.5) 9.3sA cm

Use 14mm @ 15cm

Step 4: Shrinkage reinforcement

20.0018(100)(40.5) 7.3sA cm

Use 12mm @ 15cm


25 Design Example

14mm @ 15cm

14mm @ 15cm

12mm @ 15cm

12mm @ 15cm

12mm @ 15cm

Flexural reinforcement

Shrinkage reinforcement

12mm @ 15cm

12mm @ 15cm

Documents

Advance Design of RC Structure 1 - Islamic …site.iugaza.edu.ps/btayeh/files/2013/11/Retaining-Wall.pdfLecture 11 Advance Design of RC Structure Cantilever Retaining Walls 15 External