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Retaining Wall Design : Ver W3.1.04 - 25 Apr 2019
Title : Cantilever wall example
C14
Input Data
Wall Dimensions Unfactored Live Loads General Parameters Design Parameters
H1 (m) 2.15 C (m) 0.35 W (kN/m²) 10 Soil frict (°) 30 SF Overt. 1.5
H2 (m) 1 F (m) 0 P (kN) 0 Fill slope (°) 0 SF Slip 1.5
H3 (m) 1.15 xf (m) 0 xp (m) 0 Wall frict (°) 20 ULS DL Factor 1.4
Hw (m) 0 At (m) 0.25 L (kN/m) 0 Conc kN/m3 25 ULS LL Factor 1.6
Hr (m) Ab (m) 0.25 xl (m) 0 Soil kN/m3 19 Pmax (kPa) 120
B (m) 0.625 Cov wall mm 75 Lh (kN/m) fc' (MPa) 28 Soil Poisson 0.5
D (m) 0.625 Cov base mm 75 x (m) 0 fy (MPa) 450 DLFac Slide/Ovt 1
Seepage not allowed
Active pressure applied on back of shear key for sliding
Theory : Coulomb
Wall type : Cantilever
SEISMIC ANALYSIS SETTINGS:
Seismic Analysis ON/OFF:ON
Hor Accel. (g) 0.02
Vert Accel. (g) 0.01
Include LL's Y
VALUES OF PRESSURE COEFFICIENTS:
Active Pressure coefficient Ka :0.297
Passive Pressure coefficient Kp :6.105
Seismic Active Pressure coefficient Kas :0.313
Seismic Passive Pressure coefficient Kps :5.934
Base frictional constant µ :0.577
FORCES ACTING ON THE WALL AT SLS:
All forces/moments are per m width
FORCES (kN ) and their LEVER ARMS (m )
Description F Horizontal Lever arm F Vertical Lever arm
left (+) down (+)
Destabilizing forces:
Total Active pressure Pa 2.794 0.347 1.017 0.875
Seismic component of Pa 0.140 0.600 0.051 0.875
As a result of surcharge w 2.912 0.500 1.060 0.875
Seismic wall inertia 0.483 0.671
Stabilizing forces:
Passive pressure on base Pp -56.378 0.326
Seismic component of Pp 1.623 0.600
Weight of the wall + base 24.131 0.750
Weight of soil on the base 15.283 0.750
UDL of 10.0 kPa 6.188 1.188
EQUILIBRIUM CALCULATIONS AT SLS
All forces/moments are per m width
1.Moment Equilibrium
Point of rotation: bottom front corner of base.
For Overturning moment Mo calculate as follows:
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Mo = Sum(hor. forces x l.a.) - Sum(vert. forces x l.a.)
For Stabilizing moment Mr calculate as follows:
Mr = -Sum(hor. forces x l.a.) + Sum(vert. forces x l.a.)
where l.a. = lever arm of each force.
Stabilizing moment Mr : 55.27 kNm
Destabilizing moment Mo : 0.93 kNm
Safety factor against overturning = Mr/Mo = 59.337
2.Force Equilibrium at SLS
Sum of Vertical forces Pv : 47.68 kN
Frictional resistance Pfric : 27.53 kN
Passive Pressure on shear key : 0.00 kN
Passive pressure on base : 56.38 kN
=> Total Horiz. resistance Fr : 83.91 kN
Horizontal sliding force on wall Fhw : 6.19 kN
Horizontal sliding force on shear key Fht : 0.00 kN
=> Total Horizontal sliding force Fh : 6.19 kN
Safety factor against overall sliding = Fr/Fh = 13.557
FORCES ACTING ON THE WALL AT ULS:
All forces/moments are per m width
FORCES (kN ) and their LEVER ARMS (m )
Description F Horizontal Lever arm F Vertical Lever arm
left (+) down (+)
Destabilizing forces:
Total Active pressure Pa 3.957 0.348 1.424 0.875
Seismic component of Pa 0.224 0.600 0.082 0.875
As a result of surcharge w 4.659 0.500 1.696 0.875
Seismic wall inertia 0.772 0.671
Stabilizing forces:
Passive pressure on base Pp -56.378 0.326
Seismic component of Pp 1.623 0.600
Weight of the wall + base 24.131 0.750
Weight of soil on the base 15.283 0.750
UDL of 10.0 kPa 6.188 1.188
EQUILIBRIUM CALCULATIONS AT ULS
All forces/moments are per m width
1.Moment Equilibrium
Point of rotation: bottom front corner of base.
For Overturning moment Mo calculate as follows:
Mo = Sum(hor. forces x l.a.) - Sum(vert. forces x l.a.)
For Stabilizing moment Mr calculate as follows:
Mr = -Sum(hor. forces x l.a.) + Sum(vert. forces x l.a.)
where l.a. = lever arm of each force.
Stabilizing moment Mr : 55.27 kNm
Destabilizing moment Mo : 1.50 kNm
Safety factor against overturning = Mr/Mo = 36.921
2.Force Equilibrium at ULS
Sum of Vertical forces Pv : 47.68 kN
Frictional resistance Pfric : 27.53 kN
Passive Pressure on shear key : 0.00 kN
Passive pressure on base : 56.38 kN
=> Total Horiz. resistance Fr : 83.91 kN
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Horizontal sliding force on wall Fhw : 9.39 kN
Horizontal sliding force on shear key Fht : 0.00 kN
=> Total Horizontal sliding force Fh : 9.39 kN
Safety factor against overall sliding = Fr/Fh = 8.937
SOIL PRESSURES UNDER BASE AT SLS
Maximum pressure : 88.21 kPa
Minimum pressure : 0 kPa at 0.42 m from left hand side of base.
Maximum pressure occurs at right hand side of base
WALL MOMENTS (ULS) AND REINFORCEMENT TO ACI 318 - 2014
Position from Moment Front Reinforcing Back Reinforcing Minimum
base top (m ) (kNm ) (mm²/m ) (mm²/m ) (mm²/m )
0.00 0.00 0.00 0.00 513.33
0.04 0.00 0.00 0.00 513.33
0.07 0.00 0.00 0.00 513.33
0.11 0.00 0.00 0.00 513.33
0.14 0.00 0.00 0.00 513.33
0.18 0.00 0.00 0.00 513.33
0.22 0.00 0.00 0.00 513.33
0.25 0.00 0.00 0.00 513.33
0.29 0.00 0.00 0.00 513.33
0.32 0.00 0.00 0.00 513.33
0.36 0.00 0.00 0.00 513.33
0.40 0.00 0.00 0.00 513.33
0.43 0.03 0.00 0.49 513.33
0.47 0.10 0.00 1.49 513.33
0.50 0.14 0.00 2.04 513.33
0.54 0.15 0.00 2.26 513.33
0.58 0.15 0.00 2.25 513.33
0.61 0.14 0.00 2.12 513.33
0.65 0.13 0.00 1.97 513.33
0.68 0.12 0.00 1.85 513.33
0.72 0.12 0.00 1.73 513.33
0.76 0.11 0.00 1.61 513.33
0.79 0.10 0.00 1.51 513.33
0.83 0.09 0.00 1.40 513.33
0.86 0.09 0.00 1.30 513.33
0.90 0.08 0.00 1.20 513.33
0.94 0.07 0.00 1.11 513.33
0.97 0.07 0.00 1.02 513.33
1.01 0.06 0.00 0.93 513.33
1.04 0.06 0.00 0.85 513.33
1.08 0.05 0.00 0.77 513.33
1.12 0.05 0.00 0.69 513.33
1.15 0.04 0.00 0.62 513.33
1.19 0.04 0.00 0.55 513.33
1.22 0.03 0.00 0.49 513.33
1.26 0.03 0.00 0.43 513.33
1.30 0.03 0.00 0.38 513.33
1.33 0.02 0.00 0.32 513.33
1.37 0.02 0.00 0.28 513.33
1.40 0.02 0.00 0.23 513.33
1.44 0.01 0.00 0.19 513.33
1.48 0.01 0.00 0.16 513.33
1.51 0.01 0.00 0.12 513.33
1.55 0.01 0.00 0.09 513.33
1.58 0.00 0.00 0.07 513.33
1.62 0.00 0.00 0.05 513.33
1.66 0.00 0.00 0.03 513.33
1.69 0.00 0.00 0.02 513.33
1.73 0.00 0.00 0.01 513.33
1.76 0.00 0.00 0.00 513.33
1.80 0.00 0.00 0.00 513.33
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Software Consultants (Pty) Ltd Client
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BASE MOMENTS (ULS) AND REINFORCEMENT TO ACI 318 - 2014
Position from Moment Top Reinforcing Bot Reinforcing Minimum
left (m ) (kNm ) (mm²/m ) (mm²/m ) (mm²/m )
0.00 0.00 0.00 0.00 824.44
0.03 0.01 0.10 0.00 824.44
0.06 0.04 0.42 0.00 824.44
0.09 0.10 0.94 0.00 824.44
0.12 0.18 1.67 0.00 824.44
0.14 0.28 2.61 0.00 824.44
0.17 0.40 3.77 0.00 824.44
0.20 0.55 5.13 0.00 824.44
0.23 0.72 6.70 0.00 824.44
0.26 0.91 8.47 0.00 824.44
0.29 1.12 10.46 0.00 824.44
0.32 1.36 12.66 0.00 824.44
0.35 1.62 15.07 0.00 824.44
0.38 1.90 17.69 0.00 824.44
0.40 2.20 20.51 0.00 824.44
0.43 2.53 23.55 0.00 824.44
0.46 2.87 26.80 0.00 824.44
0.49 3.24 30.26 0.00 824.44
0.52 3.64 33.93 0.00 824.44
0.55 4.05 37.81 0.00 824.44
0.58 4.49 41.90 0.00 824.44
0.61 4.95 46.20 0.00 824.44
0.63 5.43 0.00 0.00 824.44
0.66 5.94 0.00 0.00 824.44
0.69 6.47 0.00 0.00 824.44
0.72 7.02 0.00 0.00 824.44
0.75 7.30 0.00 0.00 824.44
0.78 -15.23 0.00 0.00 824.44
0.81 -13.50 0.00 0.00 824.44
0.84 -12.39 0.00 0.00 824.44
0.87 -11.34 106.06 0.00 824.44
0.89 -10.33 96.60 0.00 824.44
0.92 -9.37 87.59 0.00 824.44
0.95 -8.46 79.03 0.00 824.44
0.98 -7.59 70.91 0.00 824.44
1.01 -6.77 63.23 0.00 824.44
1.04 -6.00 56.00 0.00 824.44
1.07 -5.27 49.20 0.00 824.44
1.10 -4.59 42.85 0.00 824.44
1.12 -3.96 36.94 0.00 824.44
1.15 -3.37 31.47 0.00 824.44
1.18 -2.83 26.44 0.00 824.44
1.21 -2.34 21.85 0.00 824.44
1.24 -1.90 17.69 0.00 824.44
1.27 -1.50 13.98 0.00 824.44
1.30 -1.15 10.70 0.00 824.44
1.33 -0.84 7.86 0.00 824.44
1.36 -0.59 5.46 0.00 824.44
1.38 -0.37 3.49 0.00 824.44
1.41 -0.21 1.96 0.00 824.44
1.44 -0.09 0.87 0.00 824.44
1.47 -0.02 0.22 0.00 824.44
1.50 0.00 0.00 0.00 824.44
SHEAR CHECK AT WALL-BASE JUNCTION TO ACI 318 - 2014
Shear force at bottom of wall V = 2.3 kN
Shear stress at bottom of wall v = 0.01 MPa OK
Allowable shear stress vc = 0.64 MPa (based on Wall tensile reinf.)
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Sketch of Wall
Design code: ACI 318 - 2014
0.25
1.15
20.00°
2.15
10.00
kh =0.02g
0.00° kv =0.01g
1.00
0.62 0.25 0.62
0.35
Kas=0.31
Kps=5.93
µ=0.58
V= 2.3kN
88.2kPa v= 0.01MPa
Wall type: Cantilever SFslip = 13.56 vc= 0.64MPa
Theory: Coulomb SFslip (ULS) = 8.94
SFovt = 59.34
SFovt (ULS) = 36.92
Wall Bending Moments
Wall Moments
1.80
Moment max = .1513kNm @ .550m
1.60
1.40
1.20
1.00
Height (m)
.800
.600
.400
.200
.200
.400
.600
.800
1.00
-.200
Bending moment (kNm)
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Base Bending Moments
Base Moments Moment max = -15.23kNm @ .754m
8.00
6.00
4.00
2.00
Bending moment (kNm)
.100
.200
.300
.400
.500
.600
.700
.800
.900
1.00
1.10
1.20
1.30
1.40
1.50
-2.00
-4.00
-6.00
-8.00
-10.0
-12.0
-14.0
Position (m)
Wall Reinforcement
Wall Reinforcement
1.80
Reinf. max = 513.3mm²/m @ 1.80m
1.60
Nominal
1.40
1.20
1.00
Height (m)
Back
.800
.600
.400 Front
.200
100
200
300
400
500
Reinforcement (mm²/m)
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Base Reinforcement
Base Reinforcement Reinf. max = 0.000mm²/m @ 0.00m
800 Nominal
700
600
Reinforcement (mm²/m)
500
400
300
200
100
.100
.200
.300
.400
.500
.600
.700
.800
.900
1.00
1.10
1.20
1.30
1.40
1.50
Top
Bottom
Position (m)
Schematic Reinforcement
Y12@150 (Hor)
Y12@150 (Hor)
Y12@150 (NF)
Y12@150 (FF)
Y12@150 starters
FRONT Y12@150 starters
Y16@150 (T1)
Y16@150 (B1)
Y16@150 (T2)
Y16@150 (B2)
SECTION
