Sheet Job Number Job Title Client Calcs by Checked by Date Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]Retaining Wall Design : Ver W2.4.09 - 06 Aug 2009 Title : Cantilever wall example C14 Input Data Wall Dimensions Unfactored Live Loads General Parameters Design Parameters H1 (m) 5 C (m) 0.4 W (kN/m²) 1 Soil frict φ (°) 27 SF Overt. 1.5 H2 (m) 0.7 F (m) 0.70 P (kN) 10 Fill slope β (°) 9 SF Slip 1.5 H3 (m) 0.8 xf (m) 3.05 xp (m) 1.30 Wall frict δ (°) 20 ULS DL Factor 1.4 Hw (m) 2.8 At (m) 0.3 L (kN/m) 10 ρ Conc kN/m 3 25 ULS LL Factor 1.6 Hr (m) 0.36 Ab (m) 0.4 xl (m) 2.60 ρ Soil kN/m 3 18 Pmax (kPa) 400 B (m) 0.55 Cov wall mm 50 Lh (kN/m) fcu (MPa) 25 Soil Poisson υ 0.5 D (m) 2.5 Cov base mm 50 x (m) 0.45 fy (MPa) 450 DL Factor Ovt. 0.9 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 :0.343 Passive Pressure coefficient Kp :5.136 Seismic Active Pressure coefficient Kas :0.363 Seismic Passive Pressure coefficient Kps :5.006 Base frictional constant μ :0.510 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 55.568 1.464 15.566 1.072 Siesmic component of Pa 3.193 2.520 0.894 1.160 Triangular W-table press Pw 25.954 0.953 0.000 0.992 Seismic component of Pw 0.673 1.680 0.000 1.047 Hydrostatic pressure on bot -23.454 1.725 of base: uniform portion Hydrostatic pressure on bot -35.181 2.300 of base: triangular portion As a result of surcharge w 1.455 2.100 0.408 1.079 As a result of Point load P 0.364 3.204 -0.028 1.163 As a result of Line Load L 2.734 2.488 -0.208 1.109 Siesmic wall inertia 1.619 1.480 Stabilizing forces: Passive pressure on base Pp -12.419 0.229 Siesmic component of Pp 0.261 0.420 Weight of the wall + base 80.933 1.469 Weight of soil on the base 113.268 2.258 Hydrostatic pressure on top 58.271 2.200 of rear portion of base
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Retaining Wall Design : Ver W2.4.09 - 06 Aug 2009Title : Cantilever wall example
C14Input Data
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Wall Dimensions
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Unfactored Live Loads
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General Parameters
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Design Parameters
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H1 (m)
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5
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C (m)
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0.4
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W (kN/m²)
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1 Soil frict f (°)
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27
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SF Overt.
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1.5
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H2 (m)
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0.7
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F (m)
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0.70
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P (kN)
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10 Fill slope b (°)
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9
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SF Slip
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1.5
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H3 (m)
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0.8
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xf (m)
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3.05
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xp (m)
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1.30 Wall frict d (°)
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20
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ULS DL Factor
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1.4
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Hw (m)
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2.8
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At (m)
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0.3
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L (kN/m)
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10 r Conc kN/m3
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25
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ULS LL Factor
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1.6
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Hr (m)
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0.36
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Ab (m)
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0.4
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xl (m)
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2.60 r Soil kN/m3
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18
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Pmax (kPa)
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400
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B (m)
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0.55
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Cov wall mm
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50
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Lh (kN/m)
�
�
fcu (MPa)
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25 Soil Poisson u
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0.5
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D (m)
�
2.5
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Cov base mm
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50
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x (m)
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0.45
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fy (MPa)
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450
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DL Factor Ovt.
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0.9
Seepage allowedActive pressure applied on back of shear key for sliding
Theory : Coulomb Wall type : Cantilever
SEISMIC ANALYSIS SETTINGS:
Seismic Analysis ON/OFF:ON
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Hor Accel. (g)
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Vert Accel . (g)
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Include LL's
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0.02
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0.01
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Y
VALUES OF PRESSURE COEFFICIENTS:
Active Pressure coefficient Ka :0.343 Passive Pressure coefficient Kp :5.136 Seismic Active Pressure coefficient Kas :0.363 Seismic Passive Pressure coefficient Kps :5.006 Base frictional constant µ :0.510
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 55.568 1.464 15.566 1.072 Siesmic component of Pa 3.193 2.520 0.894 1.160 Triangular W-table press Pw 25.954 0.953 0.000 0.992 Seismic component of Pw 0.673 1.680 0.000 1.047 Hydrostatic pressure on bot -23.454 1.725 of base: uniform portion Hydrostatic pressure on bot -35.181 2.300 of base: triangular portion As a result of surcharge w 1.455 2.100 0.408 1.079 As a result of Point load P 0.364 3.204 -0.028 1.163 As a result of Line Load L 2.734 2.488 -0.208 1.109 Siesmic wall inertia 1.619 1.480
Stabilizing forces: Passive pressure on base Pp -12.419 0.229 Siesmic component of Pp 0.261 0.420 Weight of the wall + base 80.933 1.469 Weight of soil on the base 113.268 2.258 Hydrostatic pressure on top 58.271 2.200 of rear portion of base
Hydrostatic pressure on top 1.602 0.275 of front portion of base Point load of 10.00 kN on backfill 1.190 2.300 UDL of 1.0 kPa 2.128 2.375
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 : 513.88 kNm Destabilizing moment Mo : 224.03 kNm
Safety factor against overturning = Mr/Mo = 2.294
2.Force Equilibrium at SLS
Sum of Vertical forces Pv : 214.48 kN Frictional resistance Pfric : 109.28 kN Passive Pressure on shear key : 75.89 kN Passive pressure on base : 12.42 kN => Total Horiz. resistance Fr : 197.59 kN
Horizontal sliding force on wall Fhw : 87.69 kN Horizontal sliding force on shear key Fht : 34.91 kN => Total Horizontal sliding force Fh : 122.60 kN
Safety factor against overall sliding = Fr/Fh = 1.612
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 78.816 1.473 21.792 1.072 Siesmic component of Pa 5.109 2.520 1.431 1.160 Triangular W-table press Pw 36.550 0.955 0.000 0.992 Seismic component of Pw 0.942 1.680 0.000 1.047 Hydrostatic pressure on bot -32.836 1.725 of base: uniform portion Hydrostatic pressure on bot -49.254 2.300 of base: triangular portion As a result of surcharge w 2.329 2.100 0.652 1.079 As a result of Point load P 0.582 3.204 -0.044 1.163 As a result of Line Load L 4.375 2.488 -0.333 1.109 Siesmic wall inertia 2.590 1.480
Stabilizing forces: Passive pressure on base Pp -11.177 0.229 Siesmic component of Pp 0.235 0.420 Weight of the wall + base 72.839 1.469 Weight of soil on the base 101.941 2.258 Hydrostatic pressure on top 52.444 2.200 of rear portion of base Hydrostatic pressure on top 1.442 0.275 of front portion of base Point load of 9.00 kN on backfill 1.071 2.300 UDL of 0.9 kPa 1.916 2.375
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 : 462.49 kNm Destabilizing moment Mo : 318.74 kNm
Safety factor against overturning = Mr/Mo = 1.451
2.Force Equilibrium at ULS
Sum of Vertical forces Pv : 193.04 kN Frictional resistance Pfric : 98.36 kN Passive Pressure on shear key : 68.30 kN Passive pressure on base : 11.18 kN => Total Horiz. resistance Fr : 177.83 kN
Horizontal sliding force on wall Fhw : 93.83 kN Horizontal sliding force on shear key Fht : 31.42 kN => Total Horizontal sliding force Fh : 125.24 kN
Safety factor against overall sliding = Fr/Fh = 1.420
SOIL PRESSURES UNDER BASE AT SLS
Maximum pressure :102.56 kPa Minimum pressure : 21.77 kPa Maximum pressure occurs at left hand side of base
WALL MOMENTS (ULS) AND REINFORCEMENT TO ACI 318 - 2005
Position from Moment Front Reinforcing Back Reinforcing Nominal (0.13%) base top (m ) (kNm ) (mm²/m ) (mm²/m ) (mm²/m )
SHEAR CHECK AT WALL-BASE JUNCTION TO ACI 318 - 2005
Shear force at bottom of wall V = 108.4 kN Shear stress at bottom of wall v = 0.32 MPa OK Allowable shear stress vc = 0.43 MPa (based on Wall tensile reinf.)