DESIGN OF Reverse L Shaped Cantilever RETAINING WALL        
   
   
1 Preliminary Data    
i) Height of Retaining Wall h 3.00 meters
ii) Height of Plinth Fill hp 0.50 meters
iii) Soil Density γs 18 KN/cum
iv) SBC qo 250 KN/sqm
v) Angle of repose Ø 30 degrees
  0.524 radians
vi) Surcharge Angle Ө 0 degrees
  0.000 radians
vii) Coefficient of friction µ 0.5
vii) Surcharge Load Ws 4 KN/sqm
2 Pressure Coefficients    
i) Active Pressure Coefficients Ca 0.333
=(cosӨ-√(cos2Ө-cos2Ø)*cosӨ) / (cosӨ+√(cos2Ө-cos2Ø))  
ii) Passive Pressure Coefficients Cp 3.000
= (1+SinØ) / (1+SinØ)  
3 Preliminary Dimensions    
Proposed Adopted
i) Thickness of Stem ts min 200mm 0.20 meters
ii) Thickness of footing base slab tb = 0.08 * (h + hs) 0.24 meters 0.45 meters
iii) Length of base slab if sloped backfill α = 1 – (q0/2.7*γs*H) -0.60 meters 2.45 meters
L = H*sqrt((Ca*cosβ)/((1-α)*(1+3α)) 0.00 meters
if horizontal backfill α = 1 – (q0/2.2*γs*H) -0.96 meters
L = 0.95*H*sqrt((Ca)/((1-α)*(1+3α)) 0.00 meters
L = 0.6h to 0.65h 2.09 meters
 
iv) Extra Height of Retaining Wall due to Surcharge hs = Ws/γs 0.22 meters
v) Total Height of Retaining Wall due to Surcharge Hs = h+hs 3.22 meters
 
vi) Extra Height of RW due to inclined back fill hi = (L-ts)* tanӨ 0.00 meters
vii) Total Height of RW due to inclined back fill Hi = h+hi 3.00 meters
 
viii) Design Height of RW considered H = Max of H1 & H2 3.22 meters
 
 
4 Stability against Overturning      
i) Active pressure due Surcharge Load PHS = Ca*Ws*h 4 KN
ii) Active pressure due Backfill Load PH = Ca*γs*h2 / 2 31 KN
iii) Total Load on stem (Force) Pa = PHS + PH 35 KN
iv) Overturning Moment due to Imposed load MOIL = PHS*h/2 7 KN
v) Overturning Moment due to Backfill load MODL = PH*h/3 33 KN
vi) Overturning Moment Mo = (1.2*MDIL) + (1.4*MOIL) 50 KN
 
v) Load     Lever arm at start of heel Moment
W1 Front fill Load = (L-ts)*(hp-tb)*γs 2 KN ((L-ts) / 2) 1.13 meters 2 KNm
W3 Stem self weight = ts*(h-tb)*γconc 14 KN (ts/2) + (L-ts) 2.35 meters 33 KNm
W4 Base self weight = L*tb*γconc 28 KN L / 2 1.23 meters 34 KNm
W5 Other Load PT Beam Load 0 KN  
∑W 43 KN ∑Mw 69 KNm
viii) Mw not less than (1.2*MODL) +(1.4*MOIL) Safe against Overturning    
-clause 20.1 page 33 of IS 456 2000      
5 Stability against Sliding    
i) Sliding Force Pa = PHS + PH 35 KN
ii) Resisting Force F = µ*∑W 22 KN
iii) (FS)SL= (0.9*F)/(Pa) 0.55 < 1.4 Unsafe against Sliding  
-clause 20.2 page 33 of IS 456 2000
 
5a Shear key Design
a) Shear Key Size x 0.30 meters
y 0.30 meters
b) Distance from stem z 0.30 meters
c) Heigth of exacavation h1 0.60 meters
d) Heigth of earth mobilization h2 = h1 + y + (z * tanØ) 1.07 meters
e) Passive Pressure Pp = Cp*γs*(h12-h22) / 2 21 KN
v) Revised Factor of Safety against SLIDING
(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ)) 1.09 > 1.4
Unsafe against Sliding. Shear Key Required
6 Soil Pressures at footing base      
i) Net Moment at toe Mn = Mw – (MOIL+MODL) 28 KN
ii) Point of application of Resultant R x = Mn/W 0.65 meters
iii) Eccentricity e = (L/2) – x 0.58 meters L/6= 0.41
e>L6 Eccentricity lies outside the middle third of the base. Revise the base dimensions
iv) Pressure Distridution on soil qmax = W/L * (1+(6*e/L)) 43 KN/sqm
qmin = W/L * (1-(6*e/L)) -7 KN/sqm
Max Pressure qmax<SBC hence pressure on base is OK
     
v) Pressure at junction of stem and heel qsh=qmax-((qmax-qmin)/L)*ts) 39 KN/sqm
   
7 Constants for Working Stress Method    
       
  Design Constants    
  i) Grade of concrete 20 MPa
  ii) Grade of steel 415 MPa
     
iii) Compr stress in concrete c 7.0 table 21 page 81 IS 456
iv) Tensile stress in steel t 230
v) Modular ratio m = 280/3c 13.33
vi) Neutral axis depth factor k=mc/(mc+t) 0.289
vii) Lever arm j = 1 – k/3 0.904
viii) Factor R= cjk / 2 0.913
8 Design  
     
A) Stem
i) Beanding Moment at base of stem M = MODL + MOIL 40 KN/m    
 
ii) Thickness required dreq=√(Ms/(R*b) 0.01 meters
iii) Thickness provided ts 0.20 meters
Thickness of Stem is OK
iv) Ast required Ast = M/(t*j*tse) 1387 sqmm
v) Ast provided 16 mm dia @ 120 mm c/c 1676 sqmm
vi) Percentage of Steel pt = Ast/(b*d) 0.99 %  
Steel OK  
B) Base Slab
Force     Lever arm from end of stem Moment
i) Force due to Frontfill = (L-ts)*(hp-tb)*γs 2 (L-ts) / 2 1.13 meters 2 KNm
iii) Self Weight of base slab = L* tb * γconc 28 L / 2 1.23 meters 34 KNm
∑Ws 30 Md 36 KNm
vi) Upward soil pressure Nup = ((qsh+qmin)/2)*(L-ts) 35 ((qsh+(2*qmin))/(qsh+qmin)) / ((L-ts)/3) 1.03 meters 36 KNm
Upward Pressure is greater Mu 36 KNm
   
v) Bending Moment Msh = Mu-Md 0      
           
vi) Thickness required dreq=√(Ms/(R*b) 0.01 meters Thickness of Stem is OK
vii) Thickness provided ts 0.45 meters  
 
viii) Ast required Ast = M/(t*j*tse) 2 sqmm
ix) Ast provided 12 mm dia @ 150 mm c/c 754 sqmm
x) Percentage of Steel pt = Ast/(b*d) 0.00 %
Steel OK
         
         
C) Reinforcement Details