geotechnical engineering ecg 503 lecture · pdf file · 2011-05-04cantilever wall...

GEOTECHNICAL ENGINEERING

ECG 503

LECTURE NOTE 07

3.0 ANALYSIS AND DESIGN OF

RETAINING STRUCTURES

LEARNING OUTCOMES

Learning outcomes:

At the end of this lecture/week the students would

be able to:

Understand types of retaining walls

TOPIC TO BE COVERED

Types of Retaining Structures

LATERAL EARTH PRESSURE

Introduction & Overview

2.1 Introduction and overview

Retaining structures such as retaining walls, basement

walls, and bulkheads are commonly encountered in

foundation engineering, and they may support slopes

of earth mass.

Proper design and construction of these structures

require a thorough knowledge of the lateral forces that

act between the retaining structures and the soil mass

being retained.

• Retaining walls are used to prevent the retained material from assuming its natural slope. Wall structures are commonly use to support earth are piles. Retaining walls may be classified according to how they produce stability as reinforced earth, gravity wall, cantilever wall and anchored wall. At present, the reinforced earth structure is the most used particularly for roadwork

3 basic components of reinforced earth wall

• Facing unit – not necessary but usually used to

maintain appearance and avoid soil erosion

between the reinforces.

• Reinforcement – strips or rods of metal, strips

or sheets of geotextiles, wire grids, or chain link

fence or geogrids fastened to the facing unit

and extending into the backfill some distance.

• The earth fill – usually select granular material

with than 15% passing the no. 200 sieve.

Component of E.R. Wall

Types of Retaining Wall

Retaining Wall

Gravity Walls

Embedded walls

Reinforced and anchored earth

The various types of earth-retaining structures

fall into three broad groups.

EARTH RETAINING STRUCTURES

Gravity Walls

Gravity Walls

Masonry walls

Gabion walls

Crib walls

RC walls

Counterfort walls

Buttressed walls


Gravity Walls

Unreinforced masonry wall


Gravity Walls

Gabion wall


Gravity Walls

Crib wall


Gravity Walls

Types of RC

Gravity Walls


Embedded Walls

Embedded walls

Driven sheet-pile walls

Braced or propped walls

Contiguous bored-pile walls

Secant bored-pile walls

Diaphram walls


Embedded Walls

Types of embedded walls


Reinforced and Anchored Earth


Reinforced earth wall

Soil nailing

Ground anchors



Reinforced earth and soil nailing


Stability Criteria

Stability of Rigid Walls

Failures of the rigid gravity wall may occur

due to any of the followings:

Overturning failure

Sliding failure

Bearing capacity failure

Tension failure in joints

Rotational slip failure

In designing the structures at least the first three of the

design criteria must be analysed and satisfied.



Types of Lateral Pressure

Hydrostatic Pressure and Lateral Thrust

Earth Pressure at Rest

Active Earth Pressure

Passive Earth pressure

States of Equilibrium



Hydrostatic pressure and lateral thrust

Horizontal pressure due to a liquid



Earth pressure at rest


z

σv

σh = Ko σv

A

B

If wall AB remains static –

soil mass will be in a state

of elastic equilibrium –

horizontal strain is zero.

Ratio of horizontal stress to

vertical stress is called

coefficient of earth

pressure at rest, Ko, or

v

ho K

z K K ovoh

Unit weight of soil = γ

tan c f


Earth pressure at rest .. cont.




Active earth pressure


z

σv

σh

A

B

Plastic equilibrium in soil

refers to the condition

where every point in a soil

mass is on the verge of

failure.

If wall AB is allowed to move

away from the soil mass

gradually, horizontal stress

will decrease.

This is represented by

Mohr’s circle in the

subsequent slide.


tan c f

ACTIVE EARTH PRESSURE (RANKINE’S)

(in simple stress field for c=0 soil) – Fig. 1

σX = Ko σz

σz

σzKo σzσx’A

ø


Based on the diagram :

pressure earthactive sRankine' of tcoefficien Ratiov

a

aK (Ka is the ratio of the effective stresses)

Therefore :

sin 1

sin -1 )

2 (45 -tan K

2

v

aa

It can be shown that :

aa

2

a

K 2c -Kz

)2

(45 - tan 2c -)2

(45 -tanz



aa K 2c -Kz

z

zo

aK 2c-

Active pressure distribution


aK 2c-

K z a




Based on the previous slide, using

similar triangles show that :

a

oK

cz

2 where zo is depth of tension

crack

For pure cohesive soil, i.e. when = 0 :

czo

2


For cohesionless

soil, c = 0

aava Kz K

z



K z a


Passive Earth Pressure

2.2.4 Passive earth pressure


z

σv

σh

A

B

If the wall is pushed into the

soil mass, the principal

stress σh will increase. On

the verge of failure the

stress condition on the soil

element can be expressed

by Mohr’s circle b.

The lateral earth pressure,

σp, which is the major

principal stress, is called

Rankine’s passive earth

pressure


tan c f

PASSIVE EARTH PRESSURE (RANKINE’S)

(in simple stress field for c=0 soil) – Fig. 2

σX = Ko σz

σz

σzKo σz σx’P

ø


Shear

str

ess

Normal stress

tan c f

C

D

D’

OA σpKoσv

b

a

σv

c

Mohr’s circle

representing

Rankine’s

passive state.



For cohesionless soil :

Referring to previous slide, it can be shown that :


pp

2

vp

K 2c Kz

)2

(45 tan 2c )2

(45 tan

sin 1

sin 1 )

2 (45 tan K

2

p

v

p


For cohesionless soil,

Passive pressure distribution


z

Kz ppK2c

ppvp Kz K


In conclusion

Earth Pressure

Wall tilt

Passive pressure

At-rest pressure

Active pressure

Eart

h

Pre

ssu

re

Wall tilt



Rankine’s Theory

Assumptions :

Vertical frictionless wall

Dry homogeneous soil

Horizontal surface

Initial work done in 1857

Develop based on semi infinite “loose granular” soil

mass for which the soil movement is uniform.

Used stress states of soil mass to determine lateral

pressures on a frictionless wall



Active pressure for cohesionless soil



Effect of a stratified soil

Effect of surcharge



Effect of sloping surface



Active pressure,

Passive pressure,

cos ''

vahaK

cos ''

vphpK

where)'cos - (cos cos

)'osc - (cos - cos

22

22

aK

a

22

22

p

1

)'cos - (cos cos

)'osc - (cos cos

KK

and



Tension cracks in cohesive soils



Effect of surcharge (undrained)



Passive resistance in undrained clay


The stability of the retaining wall should be checked against :

(ii) FOS against sliding (recommended FOS = 2.0)

(i) FOS against overturning (recommended FOS = 2.0)

Stability Criteria

moment Disturbing

momentResisting FOS

H

wpV

R

Bc P 0.7) -(0.5 tan RFOS


Stability Analysis

Pp

Ph

∑ V

A

The stability of the retaining wall should

be checked against :

2.3.1 FOS against overturning

(recommended FOS = 2.0)

moment Disturbing

momentResisting FOS

.. overturning about A


2.3.2 FOS against sliding

(recommended FOS = 2.0)

Stability Criteria

H

wpV

R

Bc P 0.7) -(0.5 tan RFOS

Ph

∑ V

Pp

Friction & wall base adhesion


B

6e

B

R q V

b 1

2.3.3 For base pressure (to be compared against the

bearing capacity of the founding soil. Recommended

FOS = 3.0)

Now, Lever arm of base resultant

Thus eccentricity

R

Moment x

V

x - 2

B e

Stability Criteria


Stability Analysis

Pp

Ph

∑ V

Base pressure on the founding soil

Stability Analysis


Figure below shows the cross-section of a reinforced concrete

retaining structure. The retained soil behind the structure and

the soil in front of it are cohesionless and has the following

properties:

SOIL 1 : u = 35o, d = 17 kN/m3,

SOIL 2 : u = 30o, = 25o , d = 18 kN/m3,

sat = 20 kN/m3

The unit weight of concrete is 24 kN/m3. Taking into account the

passive resistance in front of the wall, determine a minimum value

for the width of the wall to satisfy the following design criteria:

Factor of safety against overturning > 2.5

Factor of safety against sliding > 1.5

Maximum base pressure should not exceed 150 kPa

Worked example :

Stability Analysis


SOIL 2

2.0 m

0.5 m

0.6 m

2.9 m

2.0 m

GWT

4.5 m

SOIL 1

SOIL 2

30 kN/m2

4.0 m

THE PROBLEM


Stability Analysis

P1P3

SOIL 2

2.0 m

0.5 m

0.6 m

2.9 m

2.0 m

GWT

4.5 m

SOIL 1

SOIL 2

30 kN/m2

4.0 m

P2P4

PP

W41

W3

W2

W1

P5

THE SOLUTION

P6


Stability Analysis

271.035sin1

35sin -1

sin1

sin1o

o

1

aK

333.030sin1

30sin -1

sin1

sin1o

o

2

aK

00.330sin1

30sin 1

sin1

sin1o

o

2

pK

Determination of the Earth Pressure Coefficients


Stability AnalysisELEM. FORCE (kN/m) TOTAL

L. ARM

(m)

MOMENT

(kNm/m)

HORIZONTAL

Active

P1 0.271 x 30 x 2 16.26 4.5 73.17

P2 0.333 x 30 x 3.5 34.97 1.75 61.20

P3 0.5 x 0.271 x 17 x 2 x 2 9.21 4.17 38.41

P4 0.333 x 17 x 2 x 3.5 39.63 1.75 69.35

P5 0.5 x .333 x (20-9.81) x 3.5 x 3.5 20.78 1.167 24.25

P6 0.5 x 9.81 x 3.5 x 3.5 60.09 1.167 70.13

SUM 180.94 336.50

Passive

Pp 0.5 x 3 x 18 x 1.5 x 1.5 60.75 0.5 30.38

VERTICAL

W1 0.5 x 4.9 x 24 58.8 1.75 102.90

W2 0.6 x 4.5 x 24 64.8 2.25 145.80

W3 2 x 2.5 x 17 + 2.9 x 2.5 x 20 + 30 x 2.5 305 3.25 991.25

W4 0.9 x 1.5 x 18 24.3 0.75 18.23

SUM 452.9 1288.55


Stability Analysis

OK is it thus 2.5, moment Disturbing

moment Resisting 83.3

50.336

55.1288FOS

To check for stability of the retaining wall

(i) FOS against overturning > 2.5

(ii) FOS against sliding > 1.5

1.5 ..

60.75x 0.5 25tan .

R

P0.5 tan RFOS

o

H

pV

341

94180

9452

Thus it is not OK


Stability Analysis

B

6e

B

R q V

b 1

2.10 452.9

336.5 - 1288.55

R

Moment x

V

(iii) For base pressure

Now, Lever arm of base resultant

0.15 2.10 - 2.25 x - 2

B e

4.5

0.15 x 6

4.5

452.9 qb 1

Thus eccentricity

Therefore

Stability Analysis


qb = 120.8 and 80.5 kPa

Since maximum base pressure is less than the bearing pressure of the

soil, the foundation is stable against base pressure failure.

DISTRIBUTION OF BASE PRESSURE

80.5 kPa120.8 kPa

In conclusion the retaining wall is not safe against sliding. To

overcome this the width of the base may be increased or a

key constructed at the toe.

Group assignment NO. 1:

Form a group of 6 members in each group. Your task is to

write up a case study which involve a dam case failure in

Malaysia and a slope failure in Malaysia. Your report shall

consists of the history of each case, as examples;

amount of dam in Malaysia, their purpose, operation, etc.

Make sure your case study are not the same as others

groups. Penalties will be given accordingly for those who

ignore the warnings.

Date of submission : 08 October 2009

Group assignment NO. 2:

Form a group of 6 members in each group. Your task is to

write up a case study which involve a ground

improvement technique. Your shall selected a real project

which will consists of real soil problems and technique to

overcome the problems.

Make sure your case study are not the same as others

groups. Penalties will be given accordingly for those who

ignore the warnings.

Date of submission : 15 October 2009

geotechnical engineering ecg 503 lecture · pdf file · 2011-05-04cantilever wall...

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