Earthquake Resistant Design of Retaining Structures

 

EARTHQUAKE RESISTANT DESIGN OF RETAINING STRUCTURES

 

PREAMBLE AND BACKGROUND  •

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Design of retaining walls under seismic condition is very important in earthquake prone areas to reduce the devastating effect of earthquake Evaluation of earth pressure under seismic condition is important Estimation of passive pressure under both static and seismic conditions are very important for the design of retaining walls, anchors, foundations etc Research on static passive earth pressure is plenty whereas the same under seismic condition is still lacking

 

RETAINING RET AINING STRUCTURES •

A retaining wall is a structure designed and constructed 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 TYPE S OF RET RETAIN AINING ING WALLS   Gr avi avi ty Re Retaini tai ni n g Wall  •

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Provides stability by virtue of its own weight Massive in size

Retained

Built in stone masonry and plain concrete

Earth

Thickness of the wall is governed  by the need to limit the resulting tensile stress to its permissible limit

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Plain concrete gravity walls are not used for heights exceeding

Toe

Heel

about 3 m, for economic reasons  

TYPES TYPE S OF RET RETAIN AINING ING WALLS   Canti l ever ver Wal all  l  •

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Most common type of  retaining structure

Retained Earth

Economical for heights up to about 8 m Consists of a vertical stem  and a base slab, made up of two distinct regions, a h eel sl ab and a t oe sl ab  Toe

Heel

 

TYPES TYPE S OF RETAIN RETAINING ING WALL ALLS S  Canti l ever ver Wal all  l  •

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

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The 'stem‘ acts as a vertical cantilever under the lateral earth pressure The 'heel slab' acts as a horizontal cantilever under the action of the weight of the retained earth

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

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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 TYPE S OF RETAIN RETAINING ING WALL ALLS S  Coun Co unte terr f or t wal wal l  •

For large heights, in a cantilever retaining wall, the bending moments

Stem

Earth retained on this side

developed become very large •

Bending moments can be reduced by introducing transverse supports, called counterforts 

Heel Slab Counterfort

 

TYPES TYPE S OF RETAIN RETAINING ING WALL ALLS S  Coun Co unte terr f or t wal wal l  •

Counterforts interconnect the stem with the heel slab

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The counterforts are concealed within the retained earth

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Such a retaining wall structure is called the counterfort wall

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Economical for heights above 7 m

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Behave essentially as vertical cantilever beams of T-section and varying depth The counterforts subdivide the vertical slab (stem) into rectangular panels

 

TYPES TYPE S OF RETAIN RETAINING ING WALL ALLS S  B u ttr ess Wal all  l  •

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Stem Earth retained on this side

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 is generally preferred to the  buttress wall as it provides free usable space (and better 

Heel Slab Buttress

aesthetics) in front of the wall.  

OTHER TYPES OF RETAINING STRUCTURE  •

Exterior walls in the  basement of a building

Floor Slab

Retained Earth

Wall

Toe

Heel Approach Pavement

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Wall-type bridge abutments Bridge Deck 

Retained Earth

Wall Abutment

Toe

Heel

 

LATERAL EARTH PRESSURE Types Type s of llate aterr al ear earth th pre pr essu r e  •

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Active pressure due to earth fill Passive pressure due to earth fill

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Active Pressure Due to Uniform Surcharge

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Passive Pressure Due to Uniform Surcharge

 

ACTIVE PRESSURE DUE TO EARTH FILL •

The active pressure exerted against the wall shall be: Pa = ½ wh2Ca 

1

where P - active earth pressure in kg/m length of wall a

w - unit weight of soil in kg/m3  h - height of wall in m 2

Ca =

(1± αv) cos2 (Φ-λ -α) cos λ  cos2 α cos  (δ+λ +α) 1

1 ½

+

sin (Φ+δ) sin (Φ-λ -i) -i) α– 

cos (

δ λ  α

i) cos ( + + )

2

 

Thee m Th max axim imum um of th thee tw two o be bein in th thee va valu luee fo forr d des esii n

ACTIVE PRESSURE DUE TO EARTH FILL 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 soil

λ  -

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 fr iction between the wall and earth fill

αh

- horizontal seismic coefficient

 

ACTIVE PRESSURE DUE TO EARTH FILL Direction of horizonta horizontall earthquake acceleratio acc eleration n

i

α  h

δ  Po 

 Active earth pressure pressure due to earthquake on retaining retaining wall 

 

ACTIVE PRESSURE DUE TO EARTH FILL Poii nt of appl Po ppl i cation  •

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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

3

where P p -  passive earth pressure in kg/m length of wal walll w - unit weight of soil in kg/m3  h - height of wall in m CP =

(1± αv) cos2 (Φ-λ +α) cos λ  cos2 α cos2 (δ+λ -α)

2

1 1 - sin (Φ+δ) sin (Φ-λ +i) +i)

½

cos (α– i) i) cos (δ+λ -α) The minimum of the two being the value for design

4

 

PASSIVE PRESSURE DUE TO EARTH FILL Direction of horizonta horizontall earthquake acceleratio acc eleration n

α  i

h

δ  PP 

 Passive earth pressure pressure due to earthquake on retaining wall 

 

PASSIVE PRESSURE DUE TO EARTH FILL Poii nt of appl Po ppl i cation  •

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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  per unit area of the inclined earth fill surface shall be (Pa)q = qh cos α Ca cos (α  –  i)

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Poii nt of appl Po ppl i cation  •

The dynamic increment in active pressures due to uniform surcharge 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

 

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 fill shall be (Pa)q = qh cos α Ca cos (α  –  i)

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Poii nt of app Po appl i cation  ti on  •

The dynamic decrement in passive pressures due to uniform surcharge 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.

 

EFFECT EFF ECT OF SATUR SATURA ATION TION •

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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: •

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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.

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The remainder shall be dynamic increment.

 

EFFECT EFF ECT OF SATUR SATURA ATION TION •

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 α

α

- vertical seismic coefficient which is ½ h Hydrodynamic pressure on account of water contained in earth fill shall not be considered separately as the effect of  acceleration on water has been considered indirectly  v

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- horizontal seismic coefficient

 

PARTIALLY SUBMERGED BACKFILL •

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The ratio of the lateral dynamic increment in active  pressures to the vertical pressures at various depths along the 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 3(Ca - Ka )

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3(C’a - K’a )h’/h 

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h

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where C is computed for dry (moist) saturated a  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.

h’ 

Distribution of the ratio

Lateral dynamic increment Vertical effective pressure

height of the wall  

with

 

REFERENCE •

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IS 1893 : 1984 Reinforced concrete design by S Unnikrishna Pillai & Devdas Menon