Stability of Cantilever Retaining Walls Abdulrahman Alhabshi
Texas Tech University Units SI
Prepared by
Date June 5, 2021
Identification Cantilever Retaining Wall m
qs = 10 kPa
kN/m3
Input Data kN
Units of Measurement SI 0.6 b 5 kN-m
m2
Wall kN/m
Stem height 2m g conc 23.6
Footing thickness 0.8 m
Include Footing embedment, D 0.5 m 0.6 1 H' = 2.8 Fill Ka Kp
Stem thickness - top 0.6 m H =2 Pqs 12 Simple Rankine 0.376 2.663
Stem thickness - bottom 1m 2 Coulomb 0.376 2.663
Pa
Toe extension, btoe 0.5 m 0.4 48 Rankine with ba 0.588 2.577
Heel extension, bh 1.4 m 3 0.588 2.577
Base Length, B 2.9 m H' = 2.80
Backfill angle, b 0 deg D H3 = 0.00
4
Surcharge Load Yes Yes Include
qs 10 kPa h No Do Not Include
Base Key ? No Bt = 0.5 Bh = 1.4
0.6 qs = 10
Backfill Soil B = 2.9
g Fill 21 kN/m3
f' Fill 27 deg
c' Fill 0 kPa
Earth Pressure Theory Rankine with backslope h d
Ka 0.588 0 0 k = 2/3 0.7 0.7
Pa = 0.5 KagH' 2 48 kN/m ckB 29.0
Pqs = (qsKa) H 12 kN/m SV tan k f 35.9
Kp = tan2 (45+f/2) 2.04
Natural Soil at Base Pkey = 0.5 Kpgh2 7.7097134 0
g Soil 19.2 kN/m3 Reduce D= 0.5
f' soil 20 deg Yes PD = 0.5 KpgD2 5.4 5.4
c' Soil 15 kPa 2c sqrt(Kp) D 21.4
Allowable bearing pressure, qall 3000 kPa Pp 26.8
Forces & Moments Vertical Forces
Resisting Moment 239 kN-m Element Area Weight Mom. Arm Moment
Overturning Moment 80 kN-m m2 kN m kN-m
Net Moment 159 kN-m 1 2.8 58.8 2.20 129.4
Rz = SV + qs(Bh) 165 kN 2 1.2 28.3 0.80 22.7
Pp = Pkey + PpD 5 kN/m 3 0.4 9.4 0.77 7.2
SFR = SV tanf + Bc+Pp+Pkey 92 kN/m 4 2.32 54.8 1.45 79.4
SFSliding = Ph + Ph qs 60 kN/m
SV 151.3 SMR 238.6
Results Horizontal Forces
Pa 48.4 0.93 45.2
Sliding FS = 1.52 OK Pqs 11.8 3.00 35.3
Overturning FS = 3.00 OK PpD -5.4 0.17 -0.9
Resultant Location, x = MNet/Rz x= 0.96 m Pkey 0.0 0.30 0.0
e = |B/2 - x| e= 0.49 m SFd 54.8 SMo 79.6
B/6 = 0.48 m
No OK, e > B/6
Check Bearing Capcity
q max = (Rz/A)(1+(6e/B)) = 115 kPa
q min = (Rz/A)(1-(6e/B)) = -1 kPa
Bearing pressure OK? Yes
Backfill Soil
Rankines's Earth Pressure
f' 27 KaR KpR
1-sinf' 0.546 1-sinf' 0.546
1+sinf' 1.454 1+sinf' 1.454
KaR 0.376 KaR 2.66294
Coulomb's Earth Pressure
f' 27 KaC KpC
d 0
h 0 cos2(f'-h) 0.794 cos2(f'+h) 0.794
b 0 cos(h+d) 1.000 cos(h-d) 1.000
cos2h 1.000 cos2h 1.000
sin(f'+d) 0.454 sin(f'+d) 0.454
sin(f'-b) 0.454 sin(f'+b) 0.454
cos(h+d) 1.000 cos(h-d) 1.000
cos(h-b) 1.000 cos(h-b) 1.000
KaC = 0.376 KpC = 2.663
Rankines's Earth Pressure For a Sloping Backfill and a Sloping Wall Face
f' 27 KaR KpR
h 0
b 0 sinb 0.000 sinb 0.000
qa 58.50 sinf' 0.454 sinf' 0.454
qp 31.50 qa 58.500 qp 31.500
cos(b-h) 1.000 cos(b-h) 1.000
sin2f' 0.206 sin2f' 0.206
sin f' 0.454 sin f' 0.454
cos qa 0.522 cos qp 0.853
cos h 2
1.000 cos h 2
1.000
cos b 1.000 cos b 1.000
sin2b 0.000 sin2b 0.000
KaR 0.588 KpR = 2.577
Stem Desing of a Retaining Wall
Flexural Reinforcement
Top Stem Thickness 0.6 ft a 11.31
Bottom Stem Thickness 1 ft a= 1.47 As in
Stem Height 2 ft qs = 10 psf
Clear Cover 3 in
g 21 pcf
Ka 0.588
fy 60 ksi
fc 4 ksi
z Thichness d Mu Vu As As min As
of stem 0.0018bh
(ft) (ft) (in) (lbs-ft/ft) lbs (in2) (in2) (in2)
0 0.6 4.2 0.0 0.0 0.000 0.156 0.156
4 1.4 13.8 250.7 188.0 0.000 0.363 0.363
8 2.2 23.4 1,898.9 712.1 0.002 0.570 0.570
12 3 33 6,288.7 1,572.2 0.004 0.778 0.778
16 3.8 42.6 14,764.4 2,768.3 0.006 0.985 0.985
20 4.6 52.2 28,670.0 4,300.5 0.010 1.192 1.192
Mu, ft-lbs
Vu, lbs
0.0 5,000.0 10,000.0 15,000.0 20,000.0 25,000.0 30,000.0 35,000.0
0
4
Depth, z (ft)
10
12
14
16
18
20
Mu
Vu
