Earthquake Resistant Design of Retaining Structures

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EARTHQUAKE RESISTANT DESIGNOF RETAINING STRUCTURES



PREAMBLE AND BACKGROUND • Design of retaining walls under seismic condition is very

important in earthquake prone areas to reduce thedevastating effect of earthquake

• Evaluation of earth pressure under seismic condition isimportant

• Estimation of passive pressure under both static and seismicconditions are very important for the design of retainingwalls, anchors, foundations etc

• Research on static passive earth pressure is plenty whereasthe same under seismic condition is still lacking



RETAINING STRUCTURES

• A retaining wall is a

structure designed andconstructed to resist the

lateral pressure of soil

when there is a desired

change in ground elevation

that exceeds the angle of

repose of the soil



TYPES OF RETAINING WALLS Gravity Retaining Wall

• Provides stability by virtue of itsown weight

• Massive in size

•

Built in stone masonry and plainconcrete

• Thickness of the wall is governed

by the need to limit the resulting

tensile stress to its permissiblelimit

• Plain concrete gravity walls are

not used for heights exceeding

about 3 m, for economic reasons

Toe Heel

Retained

Earth



TYPES OF RETAINING WALLS Canti lever Wall

• Most common type of

retaining structure

• Economical for heights

up to about 8 m• Consists of a vertical

stem and a base slab,

made up of two distinct

regions, a heel slab and

a toe slab

Toe Heel

Retained

Earth



Canti lever Wall

• All three components behave as one-way cantilever slabs:

• The 'stem‘ acts as a vertical cantilever under the lateral

earth pressure

• The 'heel slab' acts as a horizontal cantilever under theaction of the weight of the retained earth

• The 'toe slab' also acts as a cantilever under the action of

the resulting soil pressure (acting upward).

• The stability of the wall is maintained essentially by the

weight of the earth on the heel slab plus the self weight

of the structure.

TYPES OF RETAINING WALLS



Counterfor t wall

• For large heights, in a

cantilever retaining wall,

the bending moments

developed become verylarge

• Bending moments can be

reduced by introducing

transverse supports,called counterforts

TYPES OF RETAINING WALLS Stem

Heel Slab

Counterfort

Earth retainedon this side



Counterfor t wall

• Counterforts interconnect the stem with the heel slab

• The counterforts are concealed within the retained earth

• Such a retaining wall structure is called the counterfort wall

• Economical for heights above 7 m

• Behave essentially as vertical cantilever beams of T-section

and varying depth

•The counterforts subdivide the vertical slab (stem) intorectangular panels

TYPES OF RETAINING WALLS



Buttr ess Wall

• The transverse stem supports,

called buttress are located in

the front side, interconnecting

the stem with the toe slab• Buttresses are structurally

more efficient (and more

economical) than counterforts

• The counterfort wall isgenerally preferred to the

buttress wall as it provides

free usable space (and better

aesthetics) in front of the wall.

TYPES OF RETAINING WALLS Stem

Heel Slab

Buttress

Earth retainedon this side



OTHER TYPES OF RETAINING STRUCTURE • Exterior walls in the

basement of a building

• Wall-type bridge abutments

Toe Heel

RetainedEarthFloor Slab

Wall

Toe Heel

Retained

EarthBridge Deck

Wall

Abutment

Approach

Pavement



LATERAL EARTH PRESSURE

Types of lateral earth pressure

• Active pressure due to earth fill

• Passive pressure due to earth fill

• Active Pressure Due to Uniform Surcharge

• Passive Pressure Due to Uniform Surcharge



ACTIVE PRESSURE DUE TO EARTH FILL

• The active pressure exerted against the wall shall be:

Pa = ½ wh2Ca

where

Pa - active earth pressure in kg/m length of wall

w - unit weight of soil in kg/m3

h - height of wall in m

Ca = (1± αv) cos2 (Φ-λ -α) 1cos λ cos2 α cos (δ+λ +α) 1 sin (Φ+δ) sin (Φ-λ -i)

cos (α– i) cos (δ+λ +α)

The maximum of the two bein the value for desi n

+

2

1

2

½




where

αv - vertical seismic coefficient - its direction being

taken consistent throughout the stability

analysis of wall and equal to (½) α h

Φ - angle of internal friction of soilλ - tan-1 αh / (1± αv)

α - angle which earth face of the wall makes with the

vertical

i - slope of earth fill

δ - angle of friction between the wall and earth fill

αh - horizontal seismic coefficient




i

h

Direction of horizontal

earthquake acceleration

Active earth pressure due to earthquake on retaining wall

δ

Po

α




Point of appl ication

• From the total pressure computed subtract the static active

pressure obtained by putting αh = αv = λ = 0 in the

expression (1) and (2)

•

The remainder is the dynamic increment• The static component of the total pressure shall be applied

at an elevation h/3 above the base of the wall

• The point of application of the dynamic increment shall be

assumed to be at mid-height of the wall



PASSIVE PRESSURE DUE TO EARTH FILL

The passive pressure against the walls shall be given by

P p = ½ wh2 C p

where

P p - passive earth pressure in kg/m length of wall

w - unit weight of soil in kg/m3 h - height of wall in m

CP = (1± αv) cos2 (Φ-λ +α) 1

cos λ cos2

α cos2

(δ+λ -α) 1 sin (Φ+δ) sin (Φ-λ +i)cos (α– i) cos (δ+λ -α)

The minimum of the two being the value for design

-

2

3

4

½




δ

i

α

h PP

Direction of horizontal

earthquake acceleration

Passive earth pressure due to earthquake on retaining wall





• From the total pressure computed subtract the total pressure

obtained by putting αh = αv = λ = 0 in the expression (1)

and (2)

•

The remainder is the dynamic decrement• The static component of the total pressure shall be applied

at an elevation h/3 above the base of the wall

• The point of application of the dynamic increment shall be

assumed to be at an elevation of 0.66h above the base of

the wall



Active Pressure Due to Uniform Surcharge

The active pressure against the wall due to a uniform

surcharge of intensity q per unit area of the inclined earth fillsurface shall be

(Pa)q = qh cos α Ca

cos (α – i)


•

The dynamic increment in active pressures due to uniformsurcharge shall be applied at an elevation of 0.66 h above

the base of the wall, while the static component shall be

applied at mid-height of the wall

5



Passive Pressure Due to Uniform Surcharge

The passive pressure against the wall due to a uniform

surcharge of intensity q per unit area of the inclined earth fillshall be

(Pa)q = qh cos α Ca

cos (α – i)


•

The dynamic decrement in passive pressures due to uniformsurcharge shall be applied at an elevation of 0.66 h above

the base of the-walls while the static component shall be

applied at mid-height of the wall.

6



EFFECT OF SATURATION

• For saturated earth fill, the saturated unit weight of the soil

shall be used• For submerged earth fill, the dynamic increment or

decrement in active and passive earth pressure during

earthquakes shall be found from expressions given in

equations 1,2,3 and 4 with the following modifications:

• The value of δ shall be taken as ½ the value of δ for dry

backfill

•Buoyant unit weight shall be adopted

• From the value of earth pressure found out, subtract the

value of earth pressure determined by putting

αh = αv = λ = 0 but using buoyant unit weight.

• The remainder shall be dynamic increment.



EFFECT OF SATURATION

• The value of λ shall be taken as follows:

λ = tan-1 ws αh

ws-1 ( 1 ± αv )

where

ws - saturated unit weight of soil in gm/cc

αh - horizontal seismic coefficient

αv - vertical seismic coefficient which is ½ αh

• Hydrodynamic pressure on account of water contained inearth fill shall not be considered separately as the effect of

acceleration on water has been considered indirectly



PARTIALLY SUBMERGED BACKFILL

• The ratio of the lateral dynamic increment in active

pressures to the vertical pressures at various depths alongthe height of wall may be taken

• The pressure distribution of dynamic increment in active

pressures may be obtained by multiplying the vertical

effective pressures by the coefficients in fig on next slide at

corresponding depths

• Similar procedure may be utilized for determining the

distribution of dynamic decrement in passive pressures



PARTIALLY SUBMERGED BACKFILL

h

h’

3(Ca - Ka )

3(C’a - K’a )h’/h

where

• Ca is computed for dry (moist) saturated

backfills

• C’a is computed for submerged backfills.

• K a is the value of Ca when αh = αv = λ = 0

• K’a is the value of C’a when αh = αv = λ = 0

• h’ is the height of submergence above the

base of the wall.

• h is the height of the retaining wall.

Distribution of the ratio Lateral dynamic increment with

Vertical effective pressure

height of the wall



REFERENCE

• IS 1893 : 1984

• Reinforced concrete design by S Unnikrishna Pillai &

Devdas Menon

Documents

Earthquake Resistant Design of Retaining Structures