Post on 24-Dec-2015
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1. C. WALL-002
Cantilever concrete wall
(EC2 EN1992-1-1:2004, EC0 EN1990-1-1:2002, EC7 EN1997-1-1:2004, EC8 EN1998-5:2004, )
1.1. Wall properties-Parameters-Code requirements
Dimensions
Height of wall h= 9.400 m
Transverse length of wall L=10.000 m
Steam thickness at top B1= 0.400 m
Steam thickness at bottom B2= 1.200 m
Width of wall base B= 6.500 m
Width of wall toe 0.800 m
Width of wall heel 4.500 m
Height of wall steam 8.200 m
Thickness of wall footing 1.200 m
Front thickness of wall toe 1.200 m
Back thickness of wall heel 1.200 m
Slope (batter) at frontface 0.000° (0:1)
Slope (batter) at backface 5.572° (1:10.3)
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Weight of wall
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Cross section area of wall A=14.360 m²
Self weight per meter of wall W= 14.360x25.000= 359.00 kN/m
Center of gravity of wall at x=-1.129 m, y=6.965 m (xo=2.329 m, yo=2.435 m)
Wall materials
Steam : Concrete-Steel class: C25/30-B500C (EN1992-1-1, §3)
: Concrete cover: Cnom=25 mm (EN1992-1-1, §4.4.1)
Footing : Concrete-Steel class: C25/30-B500C
: Concrete cover: Cnom=75 mm
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Weight of backfill
Weight of backfill per meter Ws=803.60 kN/m
Center of gravity of backfill x=-2.830 m, y=4.100 m
1.2. Partial factors for actions and soil properties (EC7 Tables A.1-A.4, EC8-5 §3.1)
Equilibrium limit state (EQU), Structural limit state (STR), Geotechnical limit state (GEO)
(EQU) (STR) (GEO) (SEISMIC)
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1.3. Properties of foundation soil
Bearing capacity of foundation soil qu=0.50 N/mm²
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Cohesion between wall footing and soil c=0.000 N/mm²
1.4. Seismic coefficients (EC8 EN1998-5:2004, §7.3.2)
Design ground acceleration ratio gh=axg, a=0.27 (EC8-5 §7.3.2)
Soil factor S=1.00 (EC8 §3.2.2.2)
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Reduction factor for seismic coefficient r=1.50 (EC8-5 Table 7.1)
Coefficient for horizontal seismic force kh=1.00x0.27x1.00/1.500=0.180 (EC8-5 Eq.7.1)
Coefficient for vertical seismic force kv=0.50x0.180=0.090 (EC8-5 Eq.7.2)
Forces due to seismic load (except from earth pressure)
Horizontal seismic force due to self weight Fwx=359.00x0.180= 64.62 kN/m
Vertical seismic force due to self weight Fwy=359.00x0.090= 32.31 kN/m
Horizontal seismic force of backfill Fwsx=803.60x0.180=144.65 kN/m
Vertical seismic force of backfill Fwsy=803.60x0.090= 72.32 kN/m
1.5. Computation of active earth pressure (Rankine theory)
1.5.1. Wall part from y=0.000 m to y=9.400 m, Hs=9.400 m
Top point A x=-5.300 m y= 0.000 m
Bottom point B x=-5.300 m y= 9.400 m
Soil properties
Soil type : Thin gravel
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Cohesion of ground c=0.000 N/mm²
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Earth pressure according to Coulomb theory
EQU STR GEO
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Coefficient of active earth pressure Ka= 0.361 0.271 0.361
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Permanent actions
EQU STR GEO
Earth pressure at the top (y=yA) qA= 0.00 0.00 0.00 kN/m²
Earth pressure at the bottom (y=yA+ 9.40m) qB= 67.87 50.95 67.87 kN/m²
Earth force Pa=½(qA+qB)H Pa=318.99 239.46 318.99 kN/m
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Earth force in x direction Pax=318.99 239.46 318.99 kN/m
Earth force in y direction Pay= 0.00 0.00 0.00 kN/m
Moment of earth force at top point (x=0,y=0) M =-1999.11-1500.70-1999.11 kNm/m
Point of application of earth force x= -5.300 m, y= 6.267 m
Total forces and moments
Forces and moments at bottom point B (x=-5.300 m, y=9.400 m)
Permanent actions
EQU STR GEO
Total horizontal earth force Fsx=318.99 239.46 318.99 kN/m
Total vertical earth force Fsy= 0.00 0.00 0.00 kN/m
Total moment of earth force Ms =999.40 750.23 999.40 kNm/m
Seismic loading (EC8 EN1998-1-1:2004, §7.3.2, Annex E)
Horizontal seismic coefficient kh=1.00x0.27x1.00/1.500=0.180 (EC8 Eq.7.1, T.7.1)
Vertical seismic coefficient kv=0.50x0.180=0.090 (EC8 Eq.7.2)
Soil above the water table (EC8 Annex E.5)
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Method Mononobe-Okabe (EC8 Annex E.4)
for active earth force during seismic loading
Coefficient of active earth pressure, Ke*= 0.475
Additional earth pressure due to seismic load
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Earth force due to seismic load (Permanent actions) Fx=1.753x239.46=419.77 kN/m
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1.6. Computation of passive earth pressure (Rankine theory)
1.6.1. Wall part from y=8.000 m to y=9.400 m, Hs=1.400 m
Top point A x= 1.200 m y= 8.000 m
Bottom point B x= 1.200 m y= 9.400 m
Soil properties
Soil type : Dense sand
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Cohesion of ground c=0.000 N/mm²
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Earth pressure according to Coulomb theory
EQU STR GEO
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Coefficient of passive earth pressure Kp= 2.770 3.690 2.770
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Permanent actions
EQU STR GEO
Earth pressure at the top (y=yA) qA= 0.00 0.00 0.00 kN/m²
Earth pressure at the bottom (y=yA+ 1.40m) qB=-65.93 -87.82 -65.93 kN/m²
Earth force Pa=½(qA+qB)H Pp= 46.15 61.47 46.15 kN/m
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Earth force in x direction Ppx=-46.15 -61.47 -46.15 kN/m
Earth force in y direction Ppy= 0.00 0.00 0.00 kN/m
Moment of earth force at top point (x=0,y=0) M =412.26 549.11 412.26 kNm/m
Point of application of earth force x= 1.200 m, y= 8.933 m
Total forces and moments
Forces and moments at bottom point B (x=1.200 m, y=9.400 m)
Permanent actions
EQU STR GEO
Total horizontal earth force Fsx=-46.15 -61.47 -46.15 kN/m
Total vertical earth force Fsy= 0.00 0.00 0.00 kN/m
Total moment of earth force Ms =-21.55 -28.71 -21.55 kNm/m
1.7. Checks of wall stability (EQU)
1.7.1. Forces (driving and resisting) on the wall (EQU)
Action y1 - y2 Fx Fy x y
[kN/m] [kN/m] [m] [m]
Active earth pressure Pa 0.00- 9.40 318.99 0.00 -5.300 6.267
Passive earth pressure Pp 8.00- 9.40 -46.15 0.00 1.200 8.933
Wall weight W 0.00 359.00 -1.129 6.965
Backfill weight Ws 0.00 803.60 -2.830 4.100
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1.7.2. Check of soil bearing capacity (EQU) (EC7 EN1997-1-1:2004, §6.5.2)
Check for 0.90x(self weight+top vertical dead load)+0.00x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.10 0.00- 9.40 350.89 0.00 6.500 3.133 1099.34
Wall weight W x0.90 0.00 323.10 2.329 2.435 -752.50
Backfill weight Wsx0.90 0.00 723.24 4.030 5.300 -2914.66
Sum= 1046.34 -2567.82
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Sum of vertical forces = 1046.34 kN/m
Sum of moments at front toe =-2567.82 kNm/m
Sum of moments at middle of base = 832.79 kNm/m
Eccentricity ec=832.79/1046.34=0.796m, ec<=6.500/6=1.083m
Soil pressure q1=0.279 N/mm² q2=0.043 N/mm²
Effective footing L=6.500-2x0.796= 4.908 m (EC7 Annex D)
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Bearing resistance check Vd=1046.34 < Rd=1752.86 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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Check for 1.10x(self weight+top vertical dead load)+1.50x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.10 0.00- 9.40 350.89 0.00 6.500 3.133 1099.34
Wall weight W x1.10 0.00 394.90 2.329 2.435 -919.72
Backfill weight Wsx1.10 0.00 883.96 4.030 5.300 -3562.36
Sum= 1278.86 -3382.74
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Sum of vertical forces = 1278.86 kN/m
Sum of moments at front toe =-3382.74 kNm/m
Sum of moments at middle of base = 773.55 kNm/m
Eccentricity ec=773.55/1278.86=0.605m, ec<=6.500/6=1.083m
Soil pressure q1=0.307 N/mm² q2=0.087 N/mm²
Effective footing L=6.500-2x0.605= 5.290 m (EC7 Annex D)
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Bearing resistance check Vd=1278.86 < Rd=1889.29 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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1.7.3. Failure check due to overturning (EQU) (EC7 EN1997-1-1:2004, §9.7.4)
Overturning with respect to the toe (xo=0,yo=0) (x=1.200,y=9.400 m)
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[kN/m] [kN/m] [m] [m] [kNm/m] [kNm/m]
Active earth pressure Pax1.10 0.00- 9.40 350.89 0.00 6.500 3.133 1099.34 0.00
Wall weight W x0.90 0.00 323.10 2.329 2.435 0.00 752.50
Backfill weight Wsx0.90 0.00 723.24 4.030 5.300 0.00 2914.66
Sum= 1099.34 3667.16
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Sum of overturning moments = 1099.34 kNm/m
Sum of moments resisting overturning = 3667.16 kNm/m
Overturning check Med=1099.34 < Mrd=3667.16 kNm/m, Check is verified
1.7.4. Failure check against sliding (EQU) (EC7 EN1997-1-1:2004, §9.7.3, §6.5.3)
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[kN/m] [kN/m] [kN/m]
Active earth pressure Pax1.10 0.00- 9.40 350.89 0.00 0.00
Passive earth pressure Ppx0.90 8.00- 9.40 0.00 41.53 0.00
Wall weight W x0.90 0.00 0.00 323.10
Backfill weight Wsx0.90 0.00 0.00 723.24
Sum= 350.89 41.531046.34
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(resisting forces from effective cohesion are neglected) (EC7 §6.5.3. 10)
Sum of driving forces = 350.89 kN/m
Sum of resisting forces (41.53+837.07) = 878.60 kN/m
Sliding resistance check Hd=350.89 < Rd=878.60 kN/m, Check is verified
1.8. Checks of wall stability (STR)
1.8.1. Forces (driving and resisting) on the wall (STR)
Action y1 - y2 Fx Fy x y
[kN/m] [kN/m] [m] [m]
Active earth pressure Pa 0.00- 9.40 239.46 0.00 -5.300 6.267
Passive earth pressure Pp 8.00- 9.40 -61.47 0.00 1.200 8.933
Wall weight W 0.00 359.00 -1.129 6.965
Backfill weight Ws 0.00 803.60 -2.830 4.100
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1.8.2. Check of soil bearing capacity (STR) (EC7 EN1997-1-1:2004, §6.5.2)
Check for 1.00x(self weight+top vertical dead load)+0.00x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.35 0.00- 9.40 323.27 0.00 6.500 3.133 1012.81
Wall weight W x1.00 0.00 359.00 2.329 2.435 -836.11
Backfill weight Wsx1.00 0.00 803.60 4.030 5.300 -3238.51
Sum= 1162.60 -3061.81
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Sum of vertical forces = 1162.60 kN/m
Sum of moments at front toe =-3061.81 kNm/m
Sum of moments at middle of base = 716.64 kNm/m
Eccentricity ec=716.64/1162.60=0.616m, ec<=6.500/6=1.083m
Soil pressure q1=0.281 N/mm² q2=0.077 N/mm²
Effective footing L=6.500-2x0.616= 5.267 m (EC7 Annex D)
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Bearing resistance check Vd=1162.60 < Rd=2633.50 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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Check for 1.35x(self weight+top vertical dead load)+1.50x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.35 0.00- 9.40 323.27 0.00 6.500 3.133 1012.81
Wall weight W x1.35 0.00 484.65 2.329 2.435 -1128.75
Backfill weight Wsx1.35 0.00 1084.86 4.030 5.300 -4371.99
Sum= 1569.51 -4487.93
Sum of vertical forces = 1569.51 kN/m
Sum of moments at front toe =-4487.93 kNm/m
Sum of moments at middle of base = 612.98 kNm/m
Eccentricity ec=612.98/1569.51=0.391m, ec<=6.500/6=1.083m
Soil pressure q1=0.329 N/mm² q2=0.154 N/mm²
Effective footing L=6.500-2x0.391= 5.719 m (EC7 Annex D)
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Bearing resistance check Vd=1569.51 < Rd=2859.50 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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1.8.3. Failure check due to overturning (STR) (EC7 EN1997-1-1:2004, §9.7.4)
Overturning with respect to the toe (xo=0,yo=0) (x=1.200,y=9.400 m)
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[kN/m] [kN/m] [m] [m] [kNm/m] [kNm/m]
Active earth pressure Pax1.35 0.00- 9.40 323.27 0.00 6.500 3.133 1012.81 0.00
Wall weight W x1.00 0.00 359.00 2.329 2.435 0.00 836.11
Backfill weight Wsx1.00 0.00 803.60 4.030 5.300 0.00 3238.51
Sum= 1012.81 4074.62
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x0
Sum of overturning moments = 1012.81 kNm/m
Sum of moments resisting overturning = 4074.62 kNm/m
Overturning check Med=1012.81 < Mrd=4074.62 kNm/m, Check is verified
1.8.4. Failure check against sliding (STR) (EC7 EN1997-1-1:2004, §9.7.3, §6.5.3)
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[kN/m] [kN/m] [kN/m]
Active earth pressure Pax1.35 0.00- 9.40 323.27 0.00 0.00
Passive earth pressure Ppx1.00 8.00- 9.40 0.00 61.47 0.00
Wall weight W x1.00 0.00 0.00 359.00
Backfill weight Wsx1.00 0.00 0.00 803.60
Sum= 323.27 61.471162.60
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(resisting forces from effective cohesion are neglected) (EC7 §6.5.3. 10)
Sum of driving forces = 323.27 kN/m
Sum of resisting forces (61.47+1162.60) = 1224.07 kN/m
Sliding resistance check Hd=323.27 < Rd=1224.07 kN/m, Check is verified
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1.9. Checks of wall stability (GEO)
1.9.1. Forces (driving and resisting) on the wall (GEO)
Action y1 - y2 Fx Fy x y
[kN/m] [kN/m] [m] [m]
Active earth pressure Pa 0.00- 9.40 318.99 0.00 -5.300 6.267
Passive earth pressure Pp 8.00- 9.40 -46.15 0.00 1.200 8.933
Wall weight W 0.00 359.00 -1.129 6.965
Backfill weight Ws 0.00 803.60 -2.830 4.100
X
Y
Y
P
P X
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1.9.2. Check of soil bearing capacity (GEO) (EC7 EN1997-1-1:2004, §6.5.2)
Check for 1.00x(self weight+top vertical dead load)+0.00x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.00 0.00- 9.40 318.99 0.00 6.500 3.133 999.40
Wall weight W x1.00 0.00 359.00 2.329 2.435 -836.11
Backfill weight Wsx1.00 0.00 803.60 4.030 5.300 -3238.51
Sum= 1162.60 -3075.22
y0
x0
Sum of vertical forces = 1162.60 kN/m
Sum of moments at front toe =-3075.22 kNm/m
Sum of moments at middle of base = 703.23 kNm/m
Eccentricity ec=703.23/1162.60=0.605m, ec<=6.500/6=1.083m
Soil pressure q1=0.279 N/mm² q2=0.079 N/mm²
Effective footing L=6.500-2x0.605= 5.290 m (EC7 Annex D)
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Bearing resistance check Vd=1162.60 < Rd=1889.29 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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Check for 1.00x(self weight+top vertical dead load)+1.30x(top vertical live load)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.00 0.00- 9.40 318.99 0.00 6.500 3.133 999.40
Wall weight W x1.00 0.00 359.00 2.329 2.435 -836.11
Backfill weight Wsx1.00 0.00 803.60 4.030 5.300 -3238.51
Sum= 1162.60 -3075.22
Sum of vertical forces = 1162.60 kN/m
Sum of moments at front toe =-3075.22 kNm/m
Sum of moments at middle of base = 703.23 kNm/m
Eccentricity ec=703.23/1162.60=0.605m, ec<=6.500/6=1.083m
Soil pressure q1=0.279 N/mm² q2=0.079 N/mm²
Effective footing L=6.500-2x0.605= 5.290 m (EC7 Annex D)
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Bearing resistance check Vd=1162.60 < Rd=1889.29 kN/m, Check is verified (EC7 Eq.2.2, Eq.6.1)
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1.9.3. Failure check due to overturning (GEO) (EC7 EN1997-1-1:2004, §9.7.4)
Overturning with respect to the toe (xo=0,yo=0) (x=1.200,y=9.400 m)
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[kN/m] [kN/m] [m] [m] [kNm/m] [kNm/m]
Active earth pressure Pax1.00 0.00- 9.40 318.99 0.00 6.500 3.133 999.40 0.00
Wall weight W x1.00 0.00 359.00 2.329 2.435 0.00 836.11
Backfill weight Wsx1.00 0.00 803.60 4.030 5.300 0.00 3238.51
Sum= 999.40 4074.62
y0
x0
Sum of overturning moments = 999.40 kNm/m
Sum of moments resisting overturning = 4074.62 kNm/m
Overturning check Med=999.40 < Mrd=4074.62 kNm/m, Check is verified
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1.9.4. Failure check against sliding (GEO) (EC7 EN1997-1-1:2004, §9.7.3, §6.5.3)
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[kN/m] [kN/m] [kN/m]
Active earth pressure Pax1.00 0.00- 9.40 318.99 0.00 0.00
Passive earth pressure Ppx1.00 8.00- 9.40 0.00 46.15 0.00
Wall weight W x1.00 0.00 0.00 359.00
Backfill weight Wsx1.00 0.00 0.00 803.60
Sum= 318.99 46.151162.60
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(resisting forces from effective cohesion are neglected) (EC7 §6.5.3. 10)
Sum of driving forces = 318.99 kN/m
Sum of resisting forces (46.15+930.08) = 976.23 kN/m
Sliding resistance check Hd=318.99 < Rd=976.23 kN/m, Check is verified
1.10. Seismic design (EC8 EN1998-1-1:2004)Checks of wall stability (with seismic loading)
1.10.1. Forces (driving and resisting) on the wall
Action y1 - y2 Fx Fy x y
[kN/m] [kN/m] [m] [m]
Active earth pressure Pa 0.00- 9.40 239.46 0.00 -5.300 6.267
Passive earth pressure Pp 8.00- 9.40 -61.47 0.00 1.200 8.933
Wall weight W 0.00 359.00 -1.129 6.965
Backfill weight Ws 0.00 803.60 -2.830 4.100
X
Y
Y
P
P X
a
p 0
0
H
h
NeHe
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1.10.2. Additional forces due to seismic load
Action y1 - y2 Fx Fy x y
[kN/m] [kN/m] [m] [m]
Active earth pressure Pa 0.00- 9.40 180.31 -5.300 6.267
Wall weight W 64.62 -32.31-1.129 6.965
Backfill weight Ws 144.65 -72.32-2.830 4.100
1.10.3. Check of soil bearing capacity (with seismic loading) (EC7 §6.5.2)
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[kN/m] [kN/m] [m] [m] [kNm/m]
Active earth pressure Pax1.00 0.00- 9.40 419.77 0.00 6.500 3.133 1315.15
Wall weight W x1.00 64.62 391.31 2.329 2.435 -603.51
Backfill weight Wsx1.00 144.65 875.92 4.030 5.300 -2180.42
Sum= 1267.23 -1468.78
Sum of vertical forces = 1267.23 kN/m
Sum of moments at front toe =-1468.78 kNm/m
Sum of moments at middle of base = 2649.72 kNm/m
Eccentricity ec=2649.72/1267.23=2.091m, ec>6.500/6=1.083m
Soil pressure q=0.729 N/mm² Bq=3.477 m
Effective footing L=6.500-2x2.091= 2.318 m (EC7 Annex D)
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Bearing resistance check Vd=1267.23 > Rd=1159.00 kN/m, Check is NOT verified
Soil bearing capacity exceeded (with seismic loading)
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1.10.4. Failure check due to overturning (with seismic loading) (EC7 §9.7.4)
Overturning with respect to the toe (xo=0,yo=0) (x=1.200,y=9.400 m)
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[kN/m] [kN/m] [m] [m] [kNm/m] [kNm/m]
Active earth pressure Pax1.00 0.00- 9.40 419.77 0.00 6.500 3.133 1315.15 0.00
Wall weight W x1.00 64.62 391.31 2.329 2.435 232.60 836.11*
Backfill weight Wsx1.00 144.65 875.92 4.030 5.300 1058.09 3238.51*
Sum= 2605.84 4074.62
(*moments of negative seismic vertical loads, are added to the overturning moments)
Sum of overturning moments = 2605.84 kNm/m
Sum of moments resisting overturning = 4074.62 kNm/m
Overturning check Med=2605.84 < Mrd=4074.62 kNm/m, Check is verified
1.10.5. Failure check against sliding (with seismic loading) (EC7 §9.7.3, §6.5.3)
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[kN/m] [kN/m] [kN/m]
Active earth pressure Pax1.00 0.00- 9.40 419.77 0.00 0.00
Passive earth pressure Ppx1.00 8.00- 9.40 0.00 61.47 0.00
Wall weight W x1.00 64.62 0.00 326.69
Backfill weight Wsx1.00 144.65 0.00 731.28
Sum= 629.04 61.471057.97
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(resisting forces from effective cohesion are neglected) (EC7 §6.5.3. 10)
Sum of driving forces = 629.04 kN/m
Sum of resisting forces (61.47+1057.97) = 1119.44 kN/m
Sliding resistance check Hd=629.04 < Rd=1119.44 kN/m, Check is verified
1.11. Design of wall steam (EC2 EN1992-1-1:2004)
1.11.1. Loading 1.35x(permanent unfavourable)+1.00x(permanent favourable)+1.50x(variable unfav.)
Forces (at cross section centroid) at wall steam
y h Fx Fy M
[m] [m] [kN/m] [kN/m] [kNm/m]
1.00 0.498 3.66 11.22 1.48
2.00 0.595 14.63 24.88 10.89
3.00 0.693 32.93 40.98 35.66
4.00 0.790 58.54 59.51 83.20
5.00 0.888 91.46 80.49 161.04
6.00 0.985 131.71 103.90 276.48
7.00 1.083 179.27 129.75 436.98
8.20 1.200 246.00 164.00 699.65
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1.11.2. Design of wall steam in bending (EC2 §9.6, §6.1)
Concrete-Steel class: C25/30-B500C, Concrete cover: Cnom=25 mm (§3, §4.4.1.1)
Vertical reinforcement minimum:0.26(fctm/fyk)d, 0.0013d, 0.0020Ac, maximum: 0.04Ac (EC2 §9.6.2)
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[m] [kN/m] [kN] [mm] [cm²/m] [cm²/m]
1.00 1.48 -11.22 468 23.58 0.01 0.2/20.0 2.31 0.00 ( 4.98)
2.00 10.89 -24.88 565 13.49 0.02 0.4/20.0 2.31 0.15 ( 7.64)
3.00 35.66 -40.98 663 9.50 0.03 0.6/20.0 2.32 0.76 ( 8.96)
4.00 83.20 -59.51 760 7.42 0.04 0.8/20.0 2.33 1.85 ( 10.28)
5.00 161.04 -80.49 858 6.15 0.05 1.0/20.0 2.34 3.44 ( 11.60)
6.00 276.48 -103.90 955 5.30 0.05 1.2/20.0 2.34 5.58 ( 12.92)
7.00 436.98 -129.75 1053 4.69 0.06 1.3/20.0 2.35 8.26 ( 14.24)
8.20 699.65 -164.00 1170 4.15 0.07 1.6/20.0 2.36 12.24 ( 15.82)
1.11.3. Loading 1.00x(permanent unfav.)+1.00x(permanent favour.)+1.00x(variable)+1.00x(seismic)
Forces (at cross section centroid) at wall steam (with seismic loading)
y h Fx Fy M
[m] [m] [kN/m] [kN/m] [kNm/m]
1.00 0.498 22.97 11.22 10.94
2.00 0.595 55.88 24.88 50.50
3.00 0.693 98.73 40.98 128.71
4.00 0.790 151.52 59.51 255.64
5.00 0.888 214.25 80.49 441.48
6.00 0.985 286.92 103.90 696.09
7.00 1.083 369.54 129.75 1029.61
8.20 1.200 481.79 164.00 1548.30
Y
X
Mx
yh
1.11.4. Design of wall steam in bending (with seismic loading) (EC2 §9.6, §6.1)
Concrete-Steel class: C25/30-B500C, Concrete cover: Cnom=25 mm (§3, §4.4.1.1)
Vertical reinforcement minimum:0.26(fctm/fyk)d, 0.0013d, 0.0020Ac, maximum: 0.04Ac (EC2 §9.6.2)
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[m] [kN/m] [kN] [mm] [cm²/m] [cm²/m]
1.00 10.94 -11.22 468 12.78 0.02 0.4/20.0 2.32 0.41 ( 6.32)
2.00 50.50 -24.88 565 7.48 0.04 0.8/20.0 2.33 1.78 ( 7.64)
3.00 128.71 -40.98 663 5.57 0.05 1.1/20.0 2.34 4.06 ( 8.96)
4.00 255.64 -59.51 760 4.56 0.06 1.4/20.0 2.35 7.22 ( 10.28)
5.00 441.48 -80.49 858 3.94 0.08 1.7/20.0 2.37 11.25 ( 11.60)
6.00 696.09 -103.90 955 3.50 0.09 2.0/20.0 2.38 16.14 ( 12.92)
7.00 1029.61 -129.75 1053 3.18 0.10 2.3/20.0 2.39 21.93 ( 14.24)
8.20 1548.30 -164.00 1170 2.89 0.12 2.7/20.0 2.41 30.07 ( 15.82)
1.11.5. Reinforcement of wall steam
Reinforcement at back steam face (y=0 wall top)
(y= 0.00 ~ y= 4.10m) Ø25/40.0 (12.27cm²/m)
(y= 4.10 ~ y= 8.20m) Ø25/40.0 + Ø32/40.0 (32.37cm²/m) Secondary transverse reinforcement Ø 8/40.0 ( 1.26cm²/m)
Reinforcement at front steam face Ø16/16.5 (12.18cm²/m)
Secondary transverse reinforcement Ø 8/40.0 ( 1.26cm²/m)
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1.11.6. Anchorage of wall steam reinforcement (EC2 §8.4)
Basic required anchorage length (EC2 Eq.8.3)
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ıVG ������[��������� ���03D�IEG ����[����[�IFWN�����ȖF� �����03D� (EC2 §8.4.2)
Design anchorage length lbd=1.00x1569=1569mm, Cnom=25mm<3Ø=75mm (EC2 §8.4.4, T.8.2)
Minimum anchorage length lb,min=max(0.30lbrqd,10Ø,100mm)=471mm
Necessary bend 445mm at lower bar end for anchorage
1.11.7. Shear check of wall steam (EC2 EN1992-1-1:2004, §6.2.2)
Concrete-Steel class: C25/30-B500C, Concrete cover: Cnom=25 mm (§3, §4.4.1.1)
The earth pressure load variation is linear, so the variation of shear
force is parabolic. The variation of steam cross section is linear.
The most unfavourable place for shear check is the base of the steam.
Ved=180.93 kN/m, Ved (+seismic)=372.34 kN/m, Ned=-130.61 kN/m
Shear capacity without shear reinforcement Vrdc (EC2 §6.2.2)
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·Öfck = 0.29N/mm² (EC2 Eq.6.3N)
Vrd,c(min)=0.001x(0.29+0.15x0.11)x1000x1170=358.61kN/m
Vrdc=0.001x[0.120x1.41x(0.28x25.00) ����+0.15x0.11]x1000x1170=398.00kN/m
Ved=372.34 kN/m <= Vrdc=398.00 kN/m, shear OK
1.12. Design of wall footing and reinforcement (EC2 EN1992-1-1:2004)
1.12.1. Design of back heel x=-5.300 m to x=-0.800 m
Sum of vertical forces = 1569.51 kN/m
Sum of moments at middle of base = 612.98 kNm/m
q1= 0.275 N/mm², q2= 0.154 N/mm², w= 4.500 m
pressure from backfill and self weight q3= 0.209 N/mm²
M= -145.90 kNm/m, V= 25.55 kN/m
V at distance d=1125mm from the face of the steam = 31.68 kN/m
Med= -145.90k Nm/m, Vsd= 31.68 kN/m
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q q
W
q
1.12.2. Design of back heel x=-5.300 m to x=-0.800 m (with seismic loading)
Sum of vertical forces = 1267.23 kN/m
Sum of moments at middle of base = 2649.72 kNm/m
q1= 0.310 N/mm², q2= 0.000 N/mm², w= 4.500 m
pressure from backfill and self weight q3= 0.209 N/mm²
M= -1657.04 kNm/m, V= 711.81 kN/m
V at distance d=1125mm from the face of the steam = 641.78 kN/m
Med= -1657.04k Nm/m, Vsd= 641.78 kN/m
1.12.3. Design of wall footing in bending (EC2 EN1992-1-1:2004, §6.1)
Concrete-Steel class: C25/30-B500C, Concrete cover: Cnom=75 mm (§3, §4.4.1.1)
0HG ������N1P�P��G ����PP��.G ������[�G �����İF��İV� ���������NV ����� As=*cm²/m
0HG ��������N1P�P��G ����PP��.G ������[�G �����İF��İV� ����������NV ����� As=35.96cm²/m
Minimum reinforcement As>=0.26bd·fctm/fyk (As=15.10cm²/m) (EC2 §9.3.1)
Minimum reinforcement Ø16/13.0(15.46cm²/m)
1.12.4. Reinforcement of wall footing
Footing reinforcement at bottom Ø16/13.0 (15.46cm²/m)Footing reinforcement at top Ø20/8.5 (36.94cm²/m)Secondary transverse reinforcement Ø16/40.0 ( 5.02cm²/m)
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1.12.5. Anchorage of footing reinforcement (EC2 EN1992-1-1:2004, §9.8.2.2, §8.4)
x=h/2=0.600m, R=1000x0.310x0.600=186.00 kN/m
e=0.15b=0.180m ze=4.380 m, zi=0.900d=1.005m
Fs=R·ze/zi=186.00x4.380/1.005=810.38 kN/m
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Basic required anchorage length (EC2 Eq.8.3)
lb,rqd=(Ø/4)�ıVG�IEG� ������[���������� ���PP
IEG ����[����[�IFWN�����ȖF� �����03D� (EC2 §8.4.2)
Design anchorage length (EC2 §8.4.4, T.8.2)
lbd=0.70x476=333mm, Cnom=75mm>3Ø=60mm
Minimum anchorage length lb,min=max(0.30lbrqd,10Ø,100mm)=200mm
Necessary anchorage length of longitudinal reinforcement Lbd=340mm =0.340m
lbd=340mm<(x-Cnom)=525.00. Sufficient length is available
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1.12.6. Design of wall footing for shear and punching shear (EC2 EN1992-1-1:2004, §6.2.2)
Concrete-Steel class: C25/30-B500C, Concrete cover: Cnom=75 mm (§3, §4.4.1.1)
Punching shear capacity without shear reinforcement Vrdc (EC2 §6.4.4)
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Vrdc>=[vmin·2d/a]·bw·d, d=dm=1117mm, a=1117mm
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k=1+Ö(200/d) <=2, k=1.42
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vmin=0.035·k ����·Öfck = 0.30N/mm² (EC2 Eq.6.3N)Vrd,c(min)=0.001x(0.30x2x1117/1117)x1000x1117=670.20kN/m
Vrdc=0.001x[0.120x1.42x(0.14x25.00) ����x2x1117/1117]x1000x1117=577.97, Vrdc=Vrdc(min)=670.20kN/
Ved=641.78 kN/m <= Vrdc=670.20 kN/m, shear and punching shear OK
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d45o dm
1.13. Material estimate
Concrete per meter of wall length 14.360 m³/m
Reinforcing steel per meter of wall 616.540 kg/m
Total concrete of wall 10.000x 14.360= 143.598 m³
Total reinforcing steel of wall 10.000x 616.540= 6165.400 kg
1.14. Reinforcing bar schedule
Num type reinforcing bar [mm] items g/m [kg/m]
length[m]
weight [kg]
4509270
250 1 1 25 25 3.850 9.970 959.61
4505680
2 2 25 32 6.310 6.130 967.01
4509270
160 3 4 61 16 1.580 9.880 952.23
10000 4 9 42 8 0.395 10.000 165.90
6330 5 7 77 16 1.580 6.330 770.11
6330 6 8 118 20 2.470 6.330 1844.94
10000 7 10 32 16 1.580 10.000 505.60
Total weight [kg] 6165.40
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