Spread Foundation EC7-Ex1+2
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Transcript of Spread Foundation EC7-Ex1+2
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Design approaches according to Eurocode 7
Structural Engineering Master program
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Geotechnical restriction
Ed
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For the GEO and STR limit states, the three possible design
approaches use different sets of partial safety factors:
Design approach 1 with two combinations: Combination 1: A1 + M1 (= 1) + R1 (= 1) safety factors on loads Combination 2: A2 (= 1) + M2 + R1 (= 1) safety factors on materials
(soil) for piles: Combination 1: A1 + M1 (= 1) + R1 (= 1) Combination 2: A2 (= 1) + (M1 (= 1) or M2) + R4 (M1 for pile resistance, M2 for unfavorable actions like negative skin friction or
transversal loads)
Design approach 2: A1 + M1 (= 1) + R2 safety factors on loads and resistances
Design approach 3: A2 (= 1) + M2 + R3 (= 1) (A1 for loads from the structure without influence of soil material parameters)
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Design example 1 spread foundation
Stiff till
Square pad foundation
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GEO ultimate limit state bearing resistance failure
Vd Rd
Vd design vertical load
Rd design bearing resistance
Short term safety undrained conditions for soil
Long term safety drained soil condition for soil
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partial safety factors on Actions - A
Actions A1 A2
Permanent loads, unfavorable 1.35 1.00
Permanent loads, favorable 1.00 1.00
Variable loads, unfavorable 1.50 1.30
Variable loads, favorable 0.00 0.00
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partial safety factors on Materials - M
Materials M1 M2
Angle of internal friction tan() 1.00 1.25
Cohesion c 1.00 1.25
Undrained cohesion cu 1.00 1.40
Unit weight 1.00 1.00
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partial safety factors on Resistances - R
Resistances R1 R2 R3 R4
Sliding resictance 1.00 1.40 1.00
Bearing capacity resistance 1.00 1.10 1.00
Passive earth pressure 1.00 1.40 1.00
End bearing for bore piles 1.25 1.10 1.00 1.60
Skin friction for bore piles, compress. 1.00 1.10 1.00 1.30
Skin friction for bore piles, tension 1.25 1.15 1.10 1.60
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Vertical loads
Vd = G (Gk + Gpad,k) + Q Qk= G (Gk + A c d) + Q Qk
Vd = G (900 + B2 x 24 x 0.8) + Q x 600
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Undrained condition short term safety
Rd/A = Rd/A = pcr = (( + 2) cu,d bc sc ic + qd) /R = (( + 2) cu,d sc + qd) /R
b base inclination factor, bc = 1.00
i load inclination factor, ic = 1.00
s shape factor, sc = 1.20
A = A, centric loading case
Rd = pcr x A = B2 x (( + 2) cu,d sc + qd)
/R = B2 (( +2)(200/M)+22 x 0.8)/ R
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DA1 combination 1
A1 + M1 (= 1) + R1 (= 1) safety
factors on loads
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x
600
Rd = B2 (( +2)(200/1.00)+22 x 0.8)/1.00
B = ?
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DA1 combination 2
A2 (= 1) + M2 + R1 (= 1) safety
factors on materials (soil)
Vd = 1.0 (900 + B2 x 24 x 0.8) + 1.3 x 600
Rd = B2 (( +2)(200/1.4)+22 x 0.8)/1.00
B = ?
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DA2
A1 + M1 (= 1) + R2 safety factors on
loads and resistances
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x 600
Rd = B2 (( +2)(200/1.00)+22 x 0.8)/1.40
B = ?
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DA3
A1 + M2 + R3 (= 1)
A1 for loads from the structure without influence of soil material parameters
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x 600
Rd = B2 (( +2)(200/1.40)+22 x 0.8)/1.00
B = ?
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Drained condition long term safety
Rd/A = c Nc bc sc ic + q Nq bq sq iq + 0.5 B N b s i
c = 0
q = 0.8 x ( - w) = 0.8 x (22 9.81) = 9.75kPa
A = A = B2; B = B
i = all 1.00
b = all 1.00
s = 0.7; sq = 1 + sin
Rd = A (q Nq sq + 0.5 B N 0.7) = B2 (9.75 x Nq x sq +
0.5 x 12.19 x B x N x 0.7
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DA1 combination 1 A1 + M1 (= 1) + R1 (= 1) safety factors on loads
Vd = 1.35 (900 + B2 x (24 9.81) x 0.8) + 1.5 x 600
Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x N x 0.7
Nq = e x tantan2(/4 + '/2) = etan35tan2(/4 + 35.0/2) =
33.30 N = 2(Nq - 1) tan' = 2(33.3 1) tan35 = 45.23 sq = 1 + sin' = 1 + sin35 = 1.57 Rd = B
2 (9.75 x 33.3 x 1.57 + 0.5 x 12.19 x B x 45.23 x 0.7)/1.00
B = ?
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DA1 combination 2 A2 (= 1) + M2 + R1 (= 1) safety factors on materials
(soil)
Vd = 1.0 (900 + B2 x (24 9.81) x 0.8) + 1.3 x 600
Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x N x 0.7
'd = tan-1(tan 'k)/M = tan
-1(tan35/1.25) = 29.30 Nq = e
x tantan2(/4 + '/2) = etan29.3tan2(/4 + 29.3/2) = 16.92
N = 2(Nq - 1) tan' = 2(16.92 1) tan29.3 = 17.84 sq = 1 + sin' = 1 + sin29.3 = 1.49
Rd = B2 (9.75 x 16.92 x 1.49 + 0.5 x 12.19 x B x 17.84 x
0.7)/1.00
B = ?
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DA2
A1 + M1 (= 1) + R2 safety factors on loads and resistances
Vd = 1.35 (900 + B2 x (24-9.81) x 0.8) + 1.5 x 600
Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x N x 0.7
Nq = e x tantan2(/4 + '/2) = etan35tan2(/4 + 35.0/2) =
33.30 N = 2(Nq - 1) tan' = 2(33.3 1) tan35 = 45.23 sq = 1 + sin' = 1 + sin35 = 1.57 Rd = B
2 (9.75 x 33.3 x 1.57 + 0.5 x 12.19 x B x 45.23 x 0.7)/1.40
B = ?
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DA3A1 + M2 + R3 (= 1)
A1 for loads from the structure without influence of soil material parameters
Vd = 1.35 (900 + B2 x (24 - 9.81) x 0.8) + 1.5 x 600
Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x N x 0.7
'd = tan-1(tan 'k)/M = tan
-1(tan35/1.25) = 29.30 Nq = e
x tantan2(/4 + '/2) = etan29.3tan2(/4 + 29.3/2) = 16.92 N = 2(Nq - 1) tan' = 2(16.92 1) tan29.3 = 17.84 sq = 1 + sin' = 1 + sin29.3 = 1.49
Rd = B2 (9.75 x 16.92 x 1.49 + 0.5 x 12.19 x B x 17.84 x 0.7)/1.00
B = ?
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Design widths for different Design
Approaches and Design conditions
Design Approach Foundation width (m) OFS = Ruk/VkUndrained Drainedcondition condition
DA1 (Combination 1)
DA1 (Combination 2)
DA2
DA3
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Design example 2
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GEO ultimate limit state bearing resistance failure
Vd RdVd design vertical load
Rd design bearing resistance
Short term safety undrained conditions for soil
Long term safety drained soil condition for soil
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partial safety factors on Actions - A
Actions A1 A2
Permanent loads, unfavorable 1.35 1.00
Permanent loads, favorable 1.00 1.00
Variable loads, unfavorable 1.50 1.30
Variable loads, favorable 0.00 0.00
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partial safety factors on Materials - MMaterials M1 M2
Angle of internal friction tan() 1.00 1.25
Cohesion c 1.00 1.25
Undrained cohesion cu 1.00 1.40
Unit weight 1.00 1.00
partial safety factors on Resistances - R
Resistances R1 R2 R3
Sliding resictance 1.00 1.10 1.00
Bearing capacity resistance 1.00 1.40 1.00
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about vertical loads
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Nq = etan ' tan2(45 + '/2)
Nc = (Nq - 1) cot'
N = 2 (Nq - 1) tan
sq = 1 + sin' for a square or circular shape
s = 1 - 0.3(B'/L') for a rectangular shape
s = 0.7 for a square or circular shape
sc = (sqNq - 1)/(Nq - 1)
ic = iq (1 - iq)/N c tan'
iq = [1 - H/(V + A c cot')]m
i = [1 - H/(V + A c cot')]m + 1
m = [2 + (B'/L')]/[1+(B'/L')] when H acts in the direction of B'
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about resistances
Values to determine, based on the B value