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Bearing capacity of eccentrically loaded strip footing on spatially variable cohesive soil

Jędrzej Dobrzański
Jędrzej Dobrzański
 y 
Marek Kawa
Marek Kawa
   | 16 dic 2021
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Article Category: Original Study
Publicado en línea: 16 dic 2021
Páginas: 425 - 437
Recibido: 04 nov 2021
Aceptado: 15 nov 2021
DOI: https://doi.org/10.2478/sgem-2021-0035
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© 2021 Jędrzej Dobrzański et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

FE model scheme.
FE model scheme.

Figure 2

Reaction in displaced nodes (as a function of displacement) obtained in deterministic calculations. Maximum values (bearing capacities) are marked on the vertical axis.
Reaction in displaced nodes (as a function of displacement) obtained in deterministic calculations. Maximum values (bearing capacities) are marked on the vertical axis.

Figure 3

Distribution of vertical displacement in elements adjacent to the strip foundation.
Distribution of vertical displacement in elements adjacent to the strip foundation.

Figure 4

Exemplary realisation of random field modelling cohesion for θv = 1 m and θh = 10 m
Exemplary realisation of random field modelling cohesion for θv = 1 m and θh = 10 m

Figure 5

Cumulated equivalent plastic strain obtained for realisation of cohesion random field presented in Fig. 4 for a) e = 0.0 m, b) e = 0.5 m
Cumulated equivalent plastic strain obtained for realisation of cohesion random field presented in Fig. 4 for a) e = 0.0 m, b) e = 0.5 m

Figure 6

Estimated normal distributions of the bearing capacity obtained for θv = 1 m and θh = 10 m for different values of eccentricity e.
Estimated normal distributions of the bearing capacity obtained for θv = 1 m and θh = 10 m for different values of eccentricity e.

Figure 7

Influence of horizontal SOF θh on the mean value μQ for a) θv = 0.5 m and b) θv = 1.0 m.
Influence of horizontal SOF θh on the mean value μQ for a) θv = 0.5 m and b) θv = 1.0 m.

Figure 8

Influence of horizontal SOF θh on SD σQ for a) θv = 0.5 m and b) θv = 1.0 m.
Influence of horizontal SOF θh on SD σQ for a) θv = 0.5 m and b) θv = 1.0 m.

Figure 9

Influence of horizontal SOF θh on CoV δQ for a) θv = 0.5 m and b) θv = 1.0 m.
Influence of horizontal SOF θh on CoV δQ for a) θv = 0.5 m and b) θv = 1.0 m.

Figure 10

Influence of eccentricity e on SD σQ for a) θv = 0.5 m and b) θv = 1.0 m.
Influence of eccentricity e on SD σQ for a) θv = 0.5 m and b) θv = 1.0 m.

Figure 11

Influence of eccentricity e on CoV δQ for a) θv = 0.5 m and b) θv = 1.0 m.
Influence of eccentricity e on CoV δQ for a) θv = 0.5 m and b) θv = 1.0 m.

Comparison of semi-analytical and numerical values of bearing capacity.

Eccentricity e (m) 0 0.1 m 0.2 m 0.3 m 0.4 m 0.5 m
QFEM (kN/m) 217.28 197.43 176.81 156.12 135.44 114.68
B* = 2.000 m Qan (kN/m) 205.66 185.10 164.53 143.96 123.40 102.83
Relative difference (%) 5.65 6.66 7.46 8.45 9.76 11.52
B* = 2.113 m Qan (kN/m) 217.28 196.72 176.15 155.58 135.02 114.45
Relative difference (%) 0.00 0.36 0.38 0.34 0.31 0.20

Assumed model parameters.

Elasticity Mohr–Coulomb plasticity
Young's modulus, E Poisson's ratio, ν Cohesion mean value, μc Cohesion standard deviation, σc Internal friction angle, ϕ Dilation, angle, ψ
Soil 200 MPa 0.33 20 kPa 2 kPa 0° 0°
Footing 32 GPa 0.00 —

The values of β and pf calculated (based on Table 3) for θv = 1 m θh = 10 m and Q = 159.95 kN/m.

Eccentricity e (m)
0.00 0.01 0.02 0.10 0.20 0.30 0.4 0.5
β (−) 3.80 3.69 3.57 2.66 1.19 −0.53 −2.62 −5.27
pf (−) 7.2×10−5 1.1×10−4 1.8×10−4 3.9×10−3 1.2×10−1 7.0×10−1 ≈1.0 ≈1.0

Obtained and interpolated values of μQ and δQ.

θv (m) θh (m) μQ/δQ Eccentricity e (m)
0.00 0.01* 0.02* 0.10 0.20 0.30 0.4 0.5
0.5 2.0 μ Q(kN/m) 210.19 - - 194.21 173.95 153.71 133.45 113.14
δQ (%) 3.65 - - 4.08 4.33 4.63 4.99 5.42
5.0 μ Q(kN/m) 210.13 - - 193.88 173.78 153.66 133.52 113.29
δQ(%) 4.70 - - 5.24 5.51 5.81 6.17 6.60
10.0 μQ (kN/m) 210.24 - - 193.95 173.79 153.64 133.44 113.18
δQ (%) 5.27 - - 5.69 5.93 6.20 6.48 6.80
30.0 μQ (kN/m) 211.68 - - 194.51 174.27 154.02 133.72 113.33
δQ (%) 5.37 - - 5.67 5.90 6.16 6.47 6.85
1.0 2.0 μQ (kN/m) 209.72 - - 194.14 173.97 153.81 133.59 113.31
δQ (%) 4.51 - - 5.07 5.34 5.63 5.96 6.31
5.0 μQ (kN/m) 209.70 - - 194.03 173.92 153.78 133.60 113.33
δQ (%) 5.77 - - 6.13 6.38 6.65 6.95 7.25
10.0 μQ (kN/m) 209.88 208.32 206.75 194.25 174.18 154.07 133.89 113.60
δQ (%) 6.26 6.30 6.34 6.64 6.88 7.14 7.42 7.74
30.0 μQ (kN/m) 211.35 - - 194.66 174.53 154.38 134.19 113.90
δQ (%) 6.60 - - 6.86 7.06 7.27 7.52 7.79
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