For the cantilever retaining wall shown below, calculate the factor of safety with respect to: (a)overturning and (b) sliding (use yeoncrete = 23.58 kN/m², 8' = (2/3) 'and ca'= (2/3) c').Wall: H= 6.5 m, x/ = 0.3 m, x2 = 0.6 m, x3 = 0.8 m, x4 = 2 m, xs = 0.8 m, D = 1.5 m, a = 0°Soil: y, = 18.08 kN/m², ¢,'= 36°, y2 = 19.65 kN/m², 62'= 15°, c;'= 0, c;'= 30 kN/m?.Ta

The given values are: γ(concrete)=23.58 KN/m3 ∂'=(2*36)/3 =24° Cu=(2*30)/3 =20 KN/m2 The wall is vertical and backfill is horizontal: Applying Rankine theory Now we calculate Pa: Pa=(1*γ'*H2*Ka)/2 Ka=Tan2(45-(ϕ/2)) Ka=0.2596 Pa=(1*18.08*6.52*0.2596/2) =99.15 KN Now for the location of Pa will be=H/3 =6.5/3 =2.166 m Therefore overturning moment ,MOT=Pa*(H/3) =99.15*2.166 KN-m =214.758 KNmNow to calculate MR we divided the soil and the concrete into rectangles and triangles to find the area easily and to find the arm from the center of each area to point O as prepared in the following table: Now FOSoT=MR/MOT =745.54/214.758 =3.47>2 OKNow check for sliding: FOSs=FR/Pa ≥ 2 It is preferable to consider passive force in this check. Applying Rankine theory on the soil in the left (draw vertical line tillreaching the soil surface). kP is calculated for the soil using rankine theory without considering any iniclination of the wall, because it is calculated for the soil below the base. Kp=Tan2(45+ϕ2/2) =Tan2(45+7.5) =1.69 P1=AREA OF RECTANGLE P1=2*30*squareroot(1.69)*1.5=122.9=123 KN P2=AREA OF TRIANGLE P2=(1*19.65*1.5*1.69/2)=24.9=25 KN Now Pp=P1+P2 Pp=123+25=148 KN FR=∑V*tan k1ϕ2 +K2c2B+Pp ∑V=∑A*γ FR =368.15*tan(2*15/3)*30*3.4+148=280.9 KN FS=280.9/Pa FS=281/99.15 =2.83 >2 OK