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Seismic bearing capacity of shallow strip footing embedded in slope resting on two-layered soil

Litan Debnath
Litan Debnath
   | 30 set 2021
Studia Geotechnica et Mechanica's Cover Image
INFORMAZIONI SU QUESTO ARTICOLO
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Article Category: Original Study
Pubblicato online: 30 set 2021
Pagine: 285 - 306
Ricevuto: 15 dic 2020
Accettato: 20 giu 2021
DOI: https://doi.org/10.2478/sgem-2021-0021
Parole chiave
© 2021 Litan Debnath, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Geometry of footing on two-layered soil profile.
Geometry of footing on two-layered soil profile.

Figure 2

Failure mechanism and wedges assumed in present analysis.
Failure mechanism and wedges assumed in present analysis.

Figure 3

Active wedge in Top layer.
Active wedge in Top layer.

Figure 4

Active wedge in Bottom layer.
Active wedge in Bottom layer.

Figure 5

Passive wedge in Top layer.
Passive wedge in Top layer.

Figure 6

Passive wedge in Bottom layer.
Passive wedge in Bottom layer.

Figure 7

Load spread mechanism.
Load spread mechanism.

Figure 8

Design chart of Bearing capacity coefficient at φ2 = 30°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.
Design chart of Bearing capacity coefficient at φ2 = 30°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.

Figure 9

Design chart of Bearing capacity coefficient at φ2 = 40°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 1, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8
Design chart of Bearing capacity coefficient at φ2 = 40°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 1, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8

Figure 10

Flowchart of PSO algorithm.
Flowchart of PSO algorithm.

Figure 11

Schematic structure of a particle in PSO (Kalatehjari 2013).
Schematic structure of a particle in PSO (Kalatehjari 2013).

Figure 12

Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, φ1/φ2 = 0.8, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.
Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, φ1/φ2 = 0.8, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.

Figure 13

Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1c2 = 0.8.
Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kv = kh/2, γ1/γ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1c2 = 0.8.

Figure 14

Variation of NγE with kh for φ2 = 300, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.
Variation of NγE with kh for φ2 = 300, δ2 = φ2/2, i = 150, δ1/δ2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.

Figure 15

Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, i = 15, δ1/δ2 = 0.8, kv = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, γ1/γ2 = 0.80, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.
Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2, i = 15, δ1/δ2 = 0.8, kv = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, γ1/γ2 = 0.80, 2c2/B0γ2 = 0.2, c1/c2 = 0.8.

Figure 16

Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2 i = 150, c2/c2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, γ1/γ2 = 0.8.
Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2 i = 150, c2/c2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, γ1/γ2 = 0.8.

Figure 17

Variation of NγE with kh for φ2 = 30, δ2 = φ2/2, Df/B0 = 0.5 i = 20°, h1/B0 = 0.25, γ1/γ2 = 0.8, δ1/δ2 = 0.8, φ1/φ2 = 0.8, 2c2/B0γ2 = 0, c1/c2 = 0.
Variation of NγE with kh for φ2 = 30, δ2 = φ2/2, Df/B0 = 0.5 i = 20°, h1/B0 = 0.25, γ1/γ2 = 0.8, δ1/δ2 = 0.8, φ1/φ2 = 0.8, 2c2/B0γ2 = 0, c1/c2 = 0.

Figure 18

Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2 i = 150, δ1/δ2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, γ1/γ2 = 0.8.
Variation of NγE with kh for φ2 = 30°, δ2 = φ2/2 i = 150, δ1/δ2 = 0.8, kV = kh/2, φ1/φ2 = 0.8, Df/B0 = 0.5, h1/B0 = 0.25, γ1/γ2 = 0.8.

Figure 19

Variation of NγE with kh for φ2 = 20°, δ2 = φ2/2, i = 20° δ1/δ2 = 1.1, kv = kh/2, γ1/γ2 = 1.1, Df/B0 = 0.50, 2c2/B0γ2, = 0, c1/c2 = 0.
Variation of NγE with kh for φ2 = 20°, δ2 = φ2/2, i = 20° δ1/δ2 = 1.1, kv = kh/2, γ1/γ2 = 1.1, Df/B0 = 0.50, 2c2/B0γ2, = 0, c1/c2 = 0.

Figure 20

Variation of NγE with kh for φ2 = 30°, i = 20°, δ2 = φ2/2, h1/B0 = 0.25, δ1/δ2 = 1.1, kv = kh/2, φ1/φ2 = 1.1, D/B0 = 0.50, 2c2/B0γ2 = 0, c1/c2 = 0.
Variation of NγE with kh for φ2 = 30°, i = 20°, δ2 = φ2/2, h1/B0 = 0.25, δ1/δ2 = 1.1, kv = kh/2, φ1/φ2 = 1.1, D/B0 = 0.50, 2c2/B0γ2 = 0, c1/c2 = 0.

Figure 21

Variation of NγE with kh for φ2 = 30°, i = 20°, δ2 = φ2/2, h1/B0 = 0.25, δ1/δ2 = 1.1, kv = kh/2, φ1/φ2 = 1.1, D/B0 = 0.50, γ1/γ2 = 1.1.
Variation of NγE with kh for φ2 = 30°, i = 20°, δ2 = φ2/2, h1/B0 = 0.25, δ1/δ2 = 1.1, kv = kh/2, φ1/φ2 = 1.1, D/B0 = 0.50, γ1/γ2 = 1.1.

Figure 22

Comparison of variation in static bearing capacity coefficients (NCS) with c1/c2 for i = 300.
Comparison of variation in static bearing capacity coefficients (NCS) with c1/c2 for i = 300.

Figure 23

Comparison of seismic bearing capacity coefficients (NcE) with kh for Df/B0 = 0, i = 30°, c1/c2 = 1.
Comparison of seismic bearing capacity coefficients (NcE) with kh for Df/B0 = 0, i = 30°, c1/c2 = 1.

Undrained seismic bearing capacity Ncs for strip footing placed adjacent to two layered slope with i=15°.

kh Df/B0 c1/c2 c1/γB0 kh Df/B0 c1/c2 c1/γB0
1 2 4 6 1 2 4 6
0 0.25 0.25 5.52 5.54 5.56 5.56 0 0.50 0.25 4.54 4.60 4.62 4.64
0.5 5.52 5.54 5.56 5.56 0.5 4.52 4.60 4.61 4.63
0.75 5.42 5.37 5.43 5.46 0.75 4.52 4.60 4.60 4.62
1 4.74 4.40 4.41 4.42 1 4.36 4.42 4.44 4.47
1.5 3.05 3.17 3.22 3.22 1.5 3.32 3.45 3.52 3.54
2 2.4 2.52 2.58 2.6 2 1.55 2.82 2.90 2.92
3 - 1.80 1.85 1.88 3 – 2.12 2.22 2.24
4 - 0.6 1.51 1.53 4 – 0.91 1.84 1.90
5 - – 1.29 1.31 5 – – 1.61 1.64
0.75 0.25 4.50 4.46 4.25 4.49 1 0.25 4.40 4.49 4.52 4.53
0.5 4.5 4.48 4.53 4.59 0.5 4.39 4.49 4.52 4.53
0.75 4.4 4.4 4.54 4.58 0.75 4.38 4.49 4.52 4.53
1 4.35 4.2 4.45 4.49 1 4.38 4.44 4.47 4.48
1.5 4.05 3.84 3.93 3.96 1.5 3.88 4.2 4.3 4.33
2 3.45 3.24 3.36 3.4 2 1.87 3.62 3.76 3.82
3 - 2.44 2.62 2.68 3 – 2.7 3.07 3.13
4 - 1.12 2.20 2.28 4 – 1.38 2.64 2.71
5 - – 1.92 2.0 5 – – 2.27 2.42
1.25 0.25 4.42 4.46 4.50 4.52 1.5 0.25 4.44 4.50 4.52 4.53
0.5 4.41 4.43 4.48 4.51 0.5 4.41 4.49 4.52 4.53
0.75 4.40 4.42 4.47 4.50 0.75 4.41 4.49 4.52 4.54
1 4.39 4.41 4.45 4.48 1 4.38 4.44 4.47 4.48
1.5 4.01 3.59 3.74 3.85 1.5 4.17 4.49 4.52 4.44
2 3.67 3.2 3.42 3.45 2 2.34 4.18 4.31 4.37
3 - 2.64 2.92 2.97 3 – 3.1 3.54 3.74
4 - 1.67 2.59 2.67 4 – 1.92 3.3 3.43
5 - – 2.36 2.48 5 – – 2.87 3.12
0.1 0.25 0.25 4.84 4.79 4.8 4.81 0.1 0.5 0.25 4.12 4.2 4.23 4.24
0.5 4.82 4.78 4.8 4.81 0.5 4.13 4.2 4.24 4.24
0.75 4.64 4.79 4.8 4.81 0.75 4.13 4.2 4.24 4.24
1 4.12 4.15 4.2 4.21 1 4.06 4.15 4.19 4.21
1.5 - 3.03 3.09 3.11 1.5 – 3.37 3.46 3.5
2 - 2.42 2.49 2.51 2 – 2.76 2.87 2.91
3 - – 1.82 1.87 3 – – 2.21 2.25
4 - – 1.47 1.51 4 – – 1.85 1.89
5 - – – 1.28 5 – – – 1.65
0.75 0.25 4.11 4.14 4.18 4.2 1 0.25 4.06 4.15 4.18 4.19
0.5 4.08 4.13 4.18 4.19 0.5 4.05 4.14 4.19 4.19
0.75 4.06 4.14 4.18 4.19 0.75 4.04 4.13 4.18 4.19
1 4.04 4.15 4.2 4.21 1 4.02 4.11 4.14 4.17
1.5 - 3.74 3.85 3.89 1.5 – 4.07 4.18 4.2
2 - 3.13 3.31 3.36 2 – 3.48 3.71 3.79
3 - – 2.61 2.68 3 – – 3.01 3.1
4 - – 2.14 2.28 4 – – 2.34 2.67
5 - – – 2.02 5 – – – 2.38
1.25 0.25 4.08 4.14 4.18 4.19 1.5 0.25 4.05 4.14 4.18 4.19
0.5 4.06 4.14 4.18 4.2 0.5 4.04 4.14 4.18 4.19
0.75 4.05 4.13 4.18 4.19 0.75 4.05 4.14 4.18 4.19
1 4.04 4.15 4.2 4.21 1 4.06 4.14 4.19 4.2
1.5 - 4.14 4.19 4.2 1.5 – 4.14 4.19 4.2
2 - 3.84 4.07 4.16 2 – 3.95 4.18 4.2
3 - – 3.37 3.48 3 – – 3.67 3.82
4 - – 2.54 3.05 4 – – 2.72 3.38
5 - – – 2.68 5 – – – 2.98

Comparison of the variation in Ncs for i=15°.

h1/B0 Df/B0 c1/c2 Xiao et al. (2019) Present study
c1/γB0 c1/γB0
1 2 4 6 1 2 4 6
0.5 0.25 0.25 5.71 5.73 5.74 5.74 5.68 5.70 5.71 5.72
0.5 5.71 5.73 5.74 5.74 5.68 5.70 5.71 5.72
0.75 5.53 5.57 5.58 5.59 5.49 5.55 5.56 5.57
1 4.51 4.58 4.61 4.63 4.49 4.53 4.58 4.60
0.50 0.25 4.70 4.75 4.77 4.77 4.68 4.71 4.74 4.74
0.5 4.70 4.75 4.77 4.77 4.68 4.72 4.75 4.75
0.75 4.70 4.74 4.77 4.77 4.68 4.71 4.75 4.75
1 4.51 4.57 4.61 4.62 4.45 4.51 4.59 4.59
1 0.25 0.25 5.71 5.73 5.73 5.75 5.68 5.70 5.71 5.72
0.5 5.71 5.73 5.73 5.74 5.68 5.70 5.70 5.71
0.75 5.52 5.57 5.58 5.59 5.50 5.55 5.56 5.57
1 4.51 4.58 4.61 4.63 4.48 4.55 4.59 4.61
0.50 0.25 4.70 4.75 4.77 4.78 4.68 4.72 4.74 4.75
0.5 4.71 4.75 4.77 4.78 4.67 4.74 4.75 4.76
0.75 4.70 4.75 4.77 4.78 4.66 4.74 4.74 4.75
1 4.51 4.58 4.62 4.62 4.49 4.55 4.60 4.61
2 0.25 0.25 5.71 5.73 5.74 5.73 5.69 5.72 5.72 5.73
0.5 5.71 5.73 5.74 5.74 5.69 5.71 5.72 5.73
0.75 5.52 5.57 5.58 5.59 5.50 5.55 5.56 5.57
1 4.51 4.58 4.62 4.63 5.49 5.53 5.54 5.55
0.50 0.25 4.70 4.74 4.77 4.79 4.69 4.72 4.75 4.77
0.5 4.70 4.76 4.77 4.77 4.68 4.70 4.73 4.75
0.75 4.70 4.74 4.76 4.78 4.67 4.68 4.70 4.72
1 4.51 4.58 4.61 4.62 4.47 4.54 4.59 4.60
3 0.25 0.25 5.70 5.73 5.74 5.74 5.69 5.71 5.72 5.72
0.5 5.70 5.73 5.74 5.74 5.69 5.71 5.72 5.72
0.75 5.52 5.56 5.58 5.58 5.50 5.55 5.56 5.57
1 4.51 4.58 4.61 4.62 4.48 4.55 4.58 4.60
0.50 0.25 4.71 4.75 4.77 4.78 4.69 4.72 4.74 4.77
0.5 4.70 4.75 4.77 4.78 4.68 4.72 4.74 4.77
0.75 4.70 4.75 4.77 4.77 4.67 4.71 4.73 4.73
1 4.51 4.58 4.61 4.63 4.49 4.55 4.59 4.60

Comparison of the variation in Ncs for i=30°.

h1/B0 Df/B0 c1/c2 Xiao et al. (2019) Present study
c1/γB0 c1/γB0
1 2 4 6 1 2 4 6
0.5 0.25 0.25 5.15 5.20 5.23 5.23 5.11 5.16 5.21 5.21
0.5 5.15 5.20 5.22 5.23 5.11 5.16 5.21 5.20
0.75 4.86 4.95 5.00 5.01 4.81 4.88 4.91 4.96
1 3.88 4.01 4.07 4.09 3.82 4.01 4.03 4.05
0.50 0.25 4.09 4.18 4.23 4.24 4.05 4.16 4.20 4.21
0.5 4.09 4.18 4.23 4.24 4.02 4.14 4.18 4.20
0.75 4.09 4.18 4.23 4.24 4.01 4.12 4.16 4.18
1 3.88 4.00 4.07 4.09 3.84 3.95 4.02 4.05
1 0.25 0.25 5.15 5.20 5.22 5.23 5.10 5.15 5.20 5.21
0.5 5.15 5.20 5.22 5.23 5.09 5.13 5.19 5.20
0.75 4.85 4.95 5.00 5.01 4.80 4.85 4.90 4.93
1 3.83 3.99 4.06 4.08 3.80 3.92 3.99 4.01
0.50 0.25 4.10 4.19 4.24 4.25 4.07 4.11 4.20 4.22
0.5 4.10 4.19 4.23 4.25 4.05 4.10 4.19 4.20
0.75 4.10 4.19 4.23 4.25 4.04 4.10 4.18 4.19
1 3.83 3.99 4.06 4.08 3.80 3.95 4.04 4.06
2 0.25 0.25 5.15 5.20 5.22 5.23 5.11 5.17 5.20 5.21
0.5 5.15 5.20 5.22 5.23 5.10 5.17 5.20 5.21
0.75 4.85 4.95 5.00 5.01 4.82 4.90 4.96 4.99
1 3.83 3.99 4.06 4.08 3.81 3.95 4.01 4.04
0.50 0.25 4.09 4.19 4.23 4.25 4.07 4.15 4.20 4.22
0.5 4.09 4.19 4.23 4.25 4.05 4.14 4.20 4.21
0.75 4.09 4.19 4.23 4.25 4.05 4.14 4.20 4.21
1 3.82 3.98 4.05 4.07 3.80 3.94 4.01 4.04
3 0.25 0.25 5.16 5.20 5.22 5.23 5.11 5.18 5.20 5.21
0.5 5.16 5.20 5.22 5.23 5.11 5.17 5.20 5.21
0.75 4.85 4.95 5.00 5.01 4.81 4.92 4.99 5.00
1 3.83 3.99 4.06 4.08 3.80 3.96 4.03 4.06
0.50 0.25 4.10 4.19 4.23 4.25 4.07 4.15 4.20 4.23
0.5 4.09 4.19 4.23 4.24 4.06 4.14 4.20 4.22
0.75 4.10 4.19 4.23 4.24 4.05 4.12 4.18 4.20
1 3.83 3.99 4.06 4.08 3.80 3.93 4.03 4.06

Undrained seismic bearing capacity Ncs for strip footing placed adjacent to two layered slope with i=30°.

kh Df/B0 c1/c2 c1/γB0 kh Df/B0 c1/c2 c1/γB0
1 2 4 6 1 2 4 6
0 0.25 0.25 5.12 5.16 5.18 5.19 0 0.5 0.25 4.06 4.14 4.21 4.23
0.5 5.12 5.16 5.18 5.19 0.5 4.05 4.13 4.19 4.22
0.75 4.82 4.91 4.96 4.97 0.75 4.03 4.11 4.17 4.20
1 3.8 3.96 4.03 4.05 1 3.8 3.96 4.06 4.08
1.5 2.23 2.81 2.9 2.93 1.5 2.32 3.01 3.10 3.12
2 – 2.18 2.3 2.33 2 – 2.45 2.61 2.65
3 – 1.25 1.68 1.72 3 – 1.44 2 2.06
4 – – 1.33 1.38 4 – – 1.65 1.72
5 – – 1 1.17 5 – – 1.24 1.5
0.75 0.25 3.82 3.97 4.06 4.09 1 0.25 3.80 3.92 4.04 4.06
0.5 3.83 3.97 4.06 4.09 0.5 3.80 3.92 4.04 4.06
0.75 3.82 3.97 4.07 4.09 0.75 3.80 3.91 4.04 4.06
1 3.8 3.96 4.06 4.09 1 3.82 3.96 4.03 4.05
1.5 2.51 3.25 3.37 3.41 1.5 2.64 3.44 3.59 3.64
2 – 2.73 2.9 2.95 2 – 2.96 3.17 3.23
3 – 1.67 2.31 2.38 3 – 1.86 2.56 2.67
4 – – 1.92 2.05 4 – – 2.17 2.34
5 – – 1.5 1.8 5 – – 1.74 2.07
1.25 0.25 3.83 3.96 4.03 4.06 1.5 0.25 3.8 3.96 4.03 4.05
0.5 3.83 3.96 4.03 4.05 0.5 3.79 3.96 4.02 4.04
0.75 3.83 3.96 4.03 4.05 0.75 3.8 3.96 4.03 4.05
1 3.83 3.96 4.03 4.05 1 3.8 3.96 4.03 4.05
1.5 2.74 3.65 3.84 3.9 1.5 2.8 3.84 4.01 4.04
2 – 3.2 3.45 3.53 2 – 3.41 3.71 3.8
3 – 2.1 2.9 3.02 3 – 2.33 3.18 3.32
4 – – 2.43 2.64 4 – – 2.69 2.94
5 – – 2.02 2.35 5 – – 2.28 2.64
0.1 0.25 0.25 4.25 4.31 4.34 4.34 0.1 0.5 0.25 3.57 3.68 3.74 3.76
0.5 4.25 4.31 4.34 4.35 0.5 3.57 3.69 3.74 3.76
0.75 4.25 4.31 4.33 4.33 0.75 3.57 3.69 3.74 3.76
1 3.44 3.6 3.67 3.7 1 3.44 3.61 3.68 3.71
1.5 – 2.6 2.7 2.73 1.5 – 2.82 2.94 2.97
2 – 2.03 2.15 2.19 2 – 2.29 2.46 2.5
3 – – 1.57 1.61 3 – – 1.89 1.95
4 – – 1.23 1.3 4 – – 1.48 1.64
5 – – – 1.1 5 – – – 1.4
0.75 0.25 3.45 3.61 3.68 3.7 1 0.25 3.44 3.61 3.68 3.7
0.5 3.45 3.61 3.68 3.7 0.5 3.44 3.61 3.68 3.7
0.75 3.45 3.61 3.68 3.7 0.75 3.45 3.61 3.68 3.71
1 3.45 3.61 3.68 3.7 1 3.45 3.61 3.68 3.7
1.5 – 3.04 3.18 3.22 1.5 – 3.23 3.44 3.5
2 – 2.55 2.75 2.81 2 – 2.78 3.04 3.12
3 – – 2.2 2.28 3 – – 2.5 2.62
4 – – 1.74 1.96 4 – – 2.03 2.27
5 – – – 1.74 5 – – – 1.97
1.25 0.25 3.45 3.61 3.68 3.67 1.5 0.25 3.44 3.61 3.68 3.7
0.5 3.44 3.61 3.68 3.67 0.5 3.44 3.61 3.68 3.7
0.75 3.44 3.61 3.68 3.67 0.75 3.44 3.61 3.68 3.7
1 3.45 3.61 3.68 3.7 1 3.45 3.62 3.68 3.7
1.5 – 3.47 3.68 3.71 1.5 – 3.61 3.68 3.7
2 – 2.95 3.3 3.38 2 – 3.13 3.59 3.68
3 – – 2.76 2.91 3 – – 3.06 3.24
4 – – 2.18 2.54 4 – – 2.33 2.86
5 – – – 2.22 5 – – – 2.53

Comparison of the variation in Ncs for i=45°.

h1/B0 Df/B0 c1/c2 Xiao et al. (2019) Present study
c1/γB0 c1/γB0
1 2 4 6 1 2 4 6
0.5 0.25 0.25 4.57 4.63 4.66 4.67 4.54 4.60 4.62 4.64
0.5 4.57 4.64 4.66 4.68 4.53 4.60 4.61 4.63
0.75 4.23 4.34 4.40 4.41 4.21 4.31 4.37 4.40
1 3.44 3.57 3.63 3.65 3.41 3.53 3.55 3.59
0.50 0.25 3.49 3.62 3.67 3.70 3.45 3.58 3.62 3.67
0.5 3.49 3.61 3.67 3.70 3.44 3.59 3.60 3.67
0.75 3.49 3.61 3.68 3.70 3.43 3.56 3.59 3.66
1 3.44 3.57 3.63 3.65 3.42 3.53 3.56 3.64
1 0.25 0.25 4.57 4.63 4.66 4.67 4.55 4.60 4.63 4.65
0.5 4.57 4.63 4.66 4.68 4.54 4.58 4.62 4.64
0.75 4.13 4.28 4.35 4.37 4.11 4.25 4.33 4.35
1 3.16 3.41 3.51 3.54 3.11 3.38 3.50 3.52
0.50 0.25 3.49 3.61 3.68 3.69 3.45 3.59 3.64 3.67
0.5 3.49 3.61 3.68 3.69 3.44 3.58 3.63 3.67
0.75 3.49 3.61 3.68 3.69 3.43 3.57 3.63 3.67
1 3.16 3.41 3.51 3.54 3.12 3.38 3.50 3.52
2 0.25 0.25 4.58 4.64 4.66 4.68 4.54 4.60 4.62 4.66
0.5 4.58 4.63 4.67 4.68 4.53 4.60 4.61 4.64
0.75 4.11 4.28 4.35 4.38 4.10 4.25 4.32 4.32
1 3.15 3.41 3.50 3.54 3.11 3.40 3.48 3.50
0.50 0.25 3.49 3.61 3.67 3.69 3.44 3.58 3.62 3.64
0.5 3.49 3.61 3.68 3.69 3.42 3.56 3.61 3.63
0.75 3.49 3.61 3.67 3.69 3.41 3.54 3.58 3.61
1 3.15 3.41 3.51 3.54 3.10 3.36 3.52 3.52
3 0.25 0.25 4.58 4.64 4.67 4.67 4.55 4.62 4.64 4.65
0.5 4.58 4.63 4.67 4.68 4.54 4.60 4.62 4.64
0.75 4.11 4.28 4.35 4.37 4.08 4.24 4.31 4.35
1 3.15 3.40 3.51 3.54 3.12 3.36 3.41 3.48
0.50 0.25 3.49 3.61 3.67 3.69 3.44 3.60 3.62 3.65
0.5 3.48 3.61 3.67 3.69 3.43 3.60 3.61 3.63
0.75 3.49 3.61 3.67 3.67 3.42 3.58 3.60 3.63
1 3.15 3.40 3.51 3.54 3.13 3.38 3.49 3.51

Comparison of variation of seismic bearing capacity (quE) KN/m2 with γ (KN/m3) for the case of φ = 30°, c = 9.8KN/m2, i = 20°, B0 = 10m.

Sawada et al. (1994) Askari and Farzaneh (2003) Yamamoto (2010) Present Analysis
kh γ=9.8 γ=19.8 γ=9.8 γ=19.8 γ=9.8 γ=19.8 γ=9.8 γ=19.8
0.1 1798 3321 1066 1856 1013 1795 1614.14 3139.92
0.2 1770 3269 829 1307 755 1283 654 1167

Comparison of the variation in Ncs with different kh and c1/c2 for i=0° and Df/B0.

kh Ncs (Present study) Ncs (Jahani et al. 2019)
c1/c2=0.25 c1/c2=0.50 c1/c2=0.75 c1/c2=0.25 c1/c2=0.50 c1/c2=0.75
0 5.62 3.94 3.06 5.67 4 3.1
0.1 5.20 3.48 2.75 5.25 3.58 2.73
0.2 4.04 3.04 2.37 4.44 3.12 2.4
0.3 3.38 2.65 2.12 3.47 2.7 2.15

Comparison of the variation in Ncs with different cu/γB0, Df/B0, c1/c2 for i=30°.

cu/γB0 Ncs (Present study) Ncs (Wu et al. 2020)
Df/B0=0.5, c1/c2=0.5 Df/B0=1.5, c1/c2=0.5 Df/B0=1.5, c1/c2=1.5 Df/B0=0.5, c1/c2=1.5 Df/B0=0.5, c1/c2=0.5 Df/B0=1.5, c1/c2=0.5 Df/B0=1.5, c1/c2=1.5 Df/B0=0.5, c1/c2=1.5
1 4.06 3.78 2.78 2.34 4.05 3.79 2.8 2.34
2 4.15 3.92 3.05 2.95 4.16 3.96 3.01 3.01
4 4.20 4.02 3.11 3.04 4.19 4.02 3.12 3.12
6 4.22 4.04 3.22 3.10 4.2 4.04 3.15 3.15
8 4.24 4.06 3.23 3.14 4.21 4.05 3.17 3.17
10 4.25 4.08 3.24 3.16 4.22 4.6 3.17 3.17
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