geotechnical engineering ecg 503 lecture note 07 topic : 3.0 analysis and design of retaining...

GEOTECHNICAL ENGINEERING

ECG 503

LECTURE NOTE 07

TOPIC : 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 natural slope and made engineered soil slope assessment which include rainfall induced failure and role of suction.

TOPIC TO BE COVERED

Types of Retaining Structures

Sheet Pile Wall – Cantilever and Anchored Sheet Pile

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 retaining structure • 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 States of Equilibrium



Hydrostatic pressure and lateral thrust

Horizontal pressure due to a liquid



Earth pressure at rest


zσv

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


zσv

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.


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

2a

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 :

c

zo

2


For cohesionless soil, c = 0

aava Kz K

z



K z a


Passive Earth Pressure

2.2.4 Passive earth pressure


zσv

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


PASSIVE EARTH PRESSURE (RANKINE’S)(in simple stress field for c=0 soil) – Fig. 2

σX = Ko σz

σz

σzKo σz σx’Pø


Sh

ear

stre

ss

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

2vp

K 2c Kz

)2

(45 tan 2c )2

(45 tan

sin 1

sin 1 )

2 (45 tan K 2

pv

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

Ea

rth

P

ress

ure

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 ''vaha K

cos ''vphp K

where)'cos - (cos cos

)'osc - (cos - cos

22

22

aK

a22

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


B6e

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 > 2.5Factor of safety against sliding > 1.5Maximum 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 mGWT

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 Analysis


Stability Analysis

OK is it thus 2.5, moment Disturbingmoment Resisting

83.350.336

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

34194180

9452

Thus it is not OK


Stability Analysis

B6e

B

R q V

b 1

2.10 452.9

336.5 - 1288.55

RMoment

xV

(iii) For base pressure

Now, Lever arm of base resultant

0.15 2.10 - 2.25 x - 2B

e

4.50.15 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 :

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 :

geotechnical engineering ecg 503 lecture note 07 topic : 3.0 analysis and design of retaining...

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