Calcs by Checked by Date E-Mail : [email protected]
Retaining Wall Design : Cantilever wall example
C14
Input Data
Wall Dimensions Unfactored Live Loads General Parameters Design Parameters
H1 (m) 5.5 C (m) 0.5 W (kN/m²) 1.5 Soil frict φ (°) 20 SF Overt. 1.5
H2 (m) 0.5 F (m) 0.3 P (kN) 1 Fill slope β (°) 0 SF Slip 1.5
H3 (m) 0 xf (m) 2.40 xp (m) 1 Wall frict δ (°) 15 DL Factor 1.2
Hw (m) 5.5 At (m) 0.3 L (kN/m) 1 ρ Conc kN/m3 25 LL Factor 1.6
Hr (m) 0.36 Ab (m) 0.4 xl (m) 1 ρ Soil kN/m3 18 Pmax (kPa) 150
B (m) 0.5 Cov wall mm 50 Lh (kN/m) fcu (MPa) 30
D (m) 2.5 Cov base mm 50 x (m) 0 fy (MPa) 450
Seepage 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) Vert Accel. (g) Include LL's 0.02 0.01 Y
VALUES OF PRESSURE COEFFICIENTS:
Active Pressure coefficient Ka :0.442 Passive Pressure coefficient Kp :3.029 Seismic Active Pressure coefficient Kas :0.454 Seismic Passive Pressure coefficient Kps :1.345 Base frictional constant µ :0.364
FORCES ACTING ON THE WALL:
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 121.722 1.845 34.356 0.866 Siesmic component of Pa 2.973 3.300 0.861 0.840 Triangular W-table press Pw 85.328 1.878 0.000 0.872 Seismic component of Pw 2.597 3.300 0.000 0.844 Hydrostatic pressure on bot -16.510 1.700 of base: uniform portion
Hydrostatic pressure on bot -82.551 2.267 of base: triangular portion
As a result of surcharge w 3.560 2.750 1.031 0.855 As a result of Point load P 0.223 5.055 0.065 0.809 As a result of Line Load L 0.223 5.055 0.065 0.809 Siesmic wall inertia 1.767 1.582
Stabilizing forces:
Passive pressure on base Pp -2.592 -0.000 Siesmic component of Pp 3.791 0.300
Weight of the wall + base 88.358 1.228 Weight of soil on the base 103.378 2.125 Hydrostatic pressure on top 121.399 2.150 of rear portion of base
Hydrostatic pressure on top 0.000 0.250 of front portion of base
Calcs by Checked by Date E-Mail : [email protected]
Point load of 0.99 kN on backfill 0.090 1.500 Line load of 0.99 kN/m on backfill 0.990 1.500 UDL of 1.5 kPa 3.861 2.100
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:
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 : 598.93 kNm Destabilizing moment Mo : 583.24 kNm
Safety factor against overturning = Mr/Mo = 1.027
*** SAFETY FACTOR IS LOWER THAN SPECIFIED MINIMUM OF 1.5 ***
2.Force Equilibrium
Sum of Vertical forces Pv : 254.48 kN Frictional resistance Pfric : 92.62 kN Passive Pressure on shear key : 5.15 kN Passive pressure on base : 2.59 kN => Horizontal resistance Fr : 100.37 kN
Horizontal sliding force on wall Fhw : 212.64 kN Horizontal sliding force on shear key Fht : -23.28 kN => Total Horizontal sliding force Fh : 189.37 kN Safety factor against overall sliding = Fr/Fh = 0.530
*** SAFETY FACTOR IS LOWER THAN SPECIFIED MINIMUM OF 1.50 ***
SOIL PRESSURES UNDER BASE
Maximum pressure :2750.33 kPa
Minimum pressure : 0 kPa at 3.21 m from right hand side of base. Maximum pressure occurs at left hand side of base
*** MAXIMUM PRESSURE EXCEEDS SPECIFIED ALLOWABLE PRESSURE BY 2600.3 kPa ***
WALL MOMENTS (ULS) AND REINFORCEMENT TO BS8110 - 1997
Position from Moment Front Reinforcing Back Reinforcing Nominal (0.13%) base top (m ) (kNm ) (mm²/m ) (mm²/m ) (mm²/m ) 0.00 366.56 0.00 2901.92 522.60 0.10 346.82 0.00 2740.12 520.00 0.20 326.82 0.00 2576.72 517.40 0.30 307.61 0.00 2421.20 514.80 0.40 289.16 0.00 2273.15 512.20 0.50 271.47 0.00 2132.20 509.60 0.60 254.51 0.00 1998.00 507.00 0.70 238.27 0.00 1870.24 504.40 0.80 222.74 0.00 1748.64 501.80 0.90 207.90 0.00 1632.93 499.20 1.00 193.74 0.00 1522.88 496.60 1.10 180.23 0.00 1418.24 494.00 1.20 167.37 0.00 1318.81 491.40 1.30 155.13 0.00 1224.39 488.80 1.40 143.50 0.00 1134.79 486.20 1.50 132.47 0.00 1049.83 483.60
Calcs by Checked by Date E-Mail : [email protected] 1.60 122.02 0.00 969.35 481.00 1.70 112.14 0.00 896.48 478.40 1.80 102.80 0.00 827.21 475.80 1.90 94.00 0.00 761.34 473.20 2.00 85.71 0.00 698.82 470.60 2.10 77.93 0.00 639.58 468.00 2.20 70.63 0.00 583.57 465.40 2.30 63.80 0.00 530.70 462.80 2.40 57.42 0.00 480.93 460.20 2.50 51.49 0.00 434.18 457.60 2.60 45.98 0.00 390.37 455.00 2.70 40.87 0.00 349.44 452.40 2.80 36.16 0.00 311.31 449.80 2.90 31.82 0.00 275.90 447.20 3.00 27.85 0.00 243.14 444.60 3.10 24.21 0.00 212.94 442.00 3.20 20.91 0.00 185.23 439.40 3.30 17.92 0.00 159.90 436.80 3.40 15.23 0.00 136.88 434.20 3.50 12.82 0.00 116.08 431.60 3.60 10.68 0.00 97.40 429.00 3.70 8.79 0.00 80.74 426.40 3.80 7.13 0.00 66.00 423.80 3.90 5.69 0.00 53.09 421.20 4.00 4.46 0.00 41.89 418.60 4.10 3.41 0.00 32.30 416.00 4.20 2.54 0.00 24.20 413.40 4.30 1.82 0.00 17.48 410.80 4.40 1.24 0.00 12.02 408.20 4.50 0.79 0.00 7.70 405.60 4.60 0.44 0.00 4.38 403.00 4.70 0.22 0.00 2.14 400.40 4.80 0.09 0.00 0.87 397.80 4.90 0.02 0.00 0.20 395.20 5.00 0.00 0.00 0.01 392.60
BASE MOMENTS (ULS) AND REINFORCEMENT TO BS8110 - 1997
Position from Moment Top Reinforcing Bot Reinforcing Nominal (0.13%) left (m ) (kNm ) (mm²/m ) (mm²/m ) (mm²/m ) 0.07 -0.00 0.00 0.00 650.00 0.14 -1.90 0.00 10.64 650.00 0.20 -7.61 0.00 42.57 650.00 0.27 -17.12 0.00 95.78 650.00 0.34 -30.43 0.00 170.28 650.00 0.41 -47.54 0.00 266.06 650.00 0.48 -68.46 0.00 383.13 650.00 0.54 -93.19 0.00 521.49 650.00 0.61 -121.71 0.00 681.13 650.00 0.68 -154.04 0.00 862.05 650.00 0.75 -190.18 0.00 1064.26 650.00 0.82 -209.67 0.00 1173.35 650.00 0.88 273.79 1542.19 0.00 650.00 0.95 253.88 1423.55 0.00 650.00 1.02 241.03 1348.83 0.00 650.00 1.09 228.51 1278.77 0.00 650.00 1.16 216.32 1210.58 0.00 650.00 1.22 204.47 1144.26 0.00 650.00 1.29 192.96 1079.81 0.00 650.00 1.36 181.77 1017.22 0.00 650.00 1.43 170.92 956.51 0.00 650.00 1.50 160.41 897.66 0.00 650.00 1.56 150.23 840.68 0.00 650.00 1.63 140.38 785.57 0.00 650.00 1.70 130.86 732.33 0.00 650.00 1.77 121.68 680.95 0.00 650.00 1.84 112.84 631.44 0.00 650.00 1.90 104.32 583.81 0.00 650.00
Calcs by Checked by Date E-Mail : [email protected] 1.97 96.14 538.04 0.00 650.00 2.04 88.30 494.13 0.00 650.00 2.11 80.79 452.10 0.00 650.00 2.18 73.61 411.93 0.00 650.00 2.24 66.77 373.64 0.00 650.00 2.31 60.26 337.21 0.00 650.00 2.38 54.08 302.64 0.00 650.00 2.45 48.24 269.95 0.00 650.00 2.52 42.73 239.13 0.00 650.00 2.58 37.56 210.17 0.00 650.00 2.65 32.72 183.08 0.00 650.00 2.72 28.21 157.86 0.00 650.00 2.79 24.04 134.51 0.00 650.00 2.86 20.20 113.02 0.00 650.00 2.92 16.69 93.41 0.00 650.00 2.99 13.52 75.66 0.00 650.00 3.06 10.68 59.78 0.00 650.00 3.13 8.18 45.77 0.00 650.00 3.20 6.01 33.63 0.00 650.00 3.26 4.17 23.35 0.00 650.00 3.33 2.67 14.95 0.00 650.00 3.40 1.50 8.41 0.00 650.00
SHEAR CHECK AT WALL-BASE JUNCTION TO BS8110 - 1997
Shear force at bottom of wall V = 259.7 kN
Shear stress at bottom of wall v = 0.76 MPa INADEQUATE
Allowable shear stress vc = 0.66 MPa (based on Wall tensile reinf.)
Sketch of Wall
5
.5
0
0.99kN
0.99kN/m
0
.3
0
0
.5
0
5
.5
0
0
.5
0
0.00°
0.50
0.30
0.40
2.50
1.00
1.00
1.49
2.40
1
5
.0
0
°
20.00°
kh =0.02g
kv =0.01g
Wall type: Cantilever
Theory: Coulomb
Design code: BS8110 - 1997
SFovt = 1.03
SFslip = 0.53
Kas=0.45
Kps=1.34
V=259.7kN
v= 0.76MPa
vc= 0.66MPa
µ=0.36
2750.3kPa
Calcs by Checked by Date E-Mail : [email protected]
Wall Bending Moments
Wall Moments M o m e n t m a x = 3 6 7 k N m @ -.5 0 0 m .500 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 0 .0 0 5 0 .0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 H e ig h t (m ) Bending moment (kNm)
Calcs by Checked by Date E-Mail : [email protected]
Base Bending Moments
Base Moments
Moment max = 274 kNm @ .703m
-200
-150
-100
-50.0
50.0
100
150
200
250
300
.2
0
0
.4
0
0
.6
0
0
.8
0
0
1
.0
0
1
.2
0
1
.4
0
1
.6
0
1
.8
0
2
.0
0
2
.2
0
2
.4
0
2
.6
0
2
.8
0
3
.0
0
3
.2
0
3
.4
0
B
e
n
d
in
g
m
o
m
e
n
t
(k
N
m
)
Position (m)
Wall Reinforcement
Wall Reinforcement R e in f. m a x = 2 9 0 0 m m ²/ m @ 0 .0 0 m .500 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 H e ig h t (m ) Reinforcement (mm²/m) Front Nominal BackCalcs by Checked by Date E-Mail : [email protected]