Question

A retaining wall has a stem height 8.5m and width is 0.5m from top and 1.4 from below. The base is 7.0x1.5m. the toe is 1.8m and the heel is 3.8m. the backfill is inclined by 15^o. Ɣ=18KN/m³ and Φ=25

Find if the given retaining wall is stable against sliding and overturning or not. Ɣ concrete = 24KN/m³. δ = 0.6 ɸ

Answer 1

Answer) Lets us calculate the earth pressure by using the below diagram

Height of inclined portion of the soil = 3.8 x tan 15 = 1.01m

Earth pressure coefficients ka=

force due to active earth pressure Pa=KaH2/2

where H= 8.5+1.5+1.01=11.01m

Pa= 0.47 x 18 x 11.012/2

Pa=512.16 KN(per m length of the wall)

Horizontal component = Pacos15 = 494.71kN

Vertical component = Pasin15 = 132.55kN

Calculation of the forces and the Moment about toe to proceed with factor of safety for stability check shown in figure below.

Check for stability against sliding

Factor of safety against sliding due inclined horizontal backfill is given by

Where u= coefficient of friction between slab and soil (assume 0.5)

W is the weight of the components of the retaining wall

Pacos=494.71 KN

<1.4 no safe

Shear key need to be provided

Check for stability against Overturning

Factor of safety against overturning due to inclined horizontal backfill is given by

Mo is the overturning moment which is given by PacosH/3

Mo=494.71 x 11.01/3

Mo=1813.01KNm

Where Mr is the stabalizing moment about toe

Wher x is the distance of vertical resultant force from heel

x=

x=1915.9/1062.02

x=1.80m

Mr=1062.02 x (7-1.8)

Mr=5522.504 KNm

F.S.=  

F.S=3.04>1.4 hence safe