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An Analytical Study of Annular Raft on Granular Piles

Ajay Pratap Singh Rathor

Ajay Pratap Singh Rathor

Civil Engineering Dept., Rajasthan Technical University, University DepartmentKota, India
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Rathor, Ajay Pratap Singh
, 
Jitendra Kumar Sharma

Jitendra Kumar Sharma

Civil Engineering Dept., Rajasthan Technical University, University DepartmentKota, India
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Sharma, Jitendra Kumar
 y 
Madhav Madhira

Madhav Madhira

Civil Engineering Dept., Jawaharlal Nehru Technological University & I.I.T.Hyderabad, India
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Madhira, Madhav
  
29 mar 2024
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Categoría del artículo: Original Study
Publicado en línea: 29 mar 2024
Páginas: 21 - 44
Recibido: 15 jul 2023
Aceptado: 30 ene 2024
DOI: https://doi.org/10.2478/sgem-2024-0002
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© 2024 Ajay Pratap Singh Rathor et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Schematic diagram of the annular raft over GPs.
Schematic diagram of the annular raft over GPs.

Figure 2:

Annular raft subdivisions into sectors
Annular raft subdivisions into sectors

Figure 3:

Discretization of (a) annular raft and (b) granular pile.
Discretization of (a) annular raft and (b) granular pile.

Figure 4:

Geometrical consideration in integration scheme.
Geometrical consideration in integration scheme.

Figure 5:

Spacing of group of four GPs in terms of Dr and Dg.
Spacing of group of four GPs in terms of Dr and Dg.

Figure 6:

Comparison of variation of SIF with Kgp for different spacing [45].
Comparison of variation of SIF with Kgp for different spacing [45].

Figure 7:

Variation of SIF (only annular raft without GPs) with Dr.
Variation of SIF (only annular raft without GPs) with Dr.

Figure 8:

Variation of Iagpr with Kgp for a group of four GPs having Dr=0.2 and L/d=10 (a) without the annular raft and (b) with the annular raft.
Variation of Iagpr with Kgp for a group of four GPs having Dr=0.2 and L/d=10 (a) without the annular raft and (b) with the annular raft.

Figure 9:

Variation of Iagpr with Kgp of the group of four GPs with and without raft for Dr=0.4 and L/d=10: (a) without annular raft and (b) with annular raft.
Variation of Iagpr with Kgp of the group of four GPs with and without raft for Dr=0.4 and L/d=10: (a) without annular raft and (b) with annular raft.

Figure 10:

Variation of Iagpr with Kgp of a group of four GPs with and without raft for Dr=0.6 and L/d=10: (a) without annular raft and (b) with annular raft.
Variation of Iagpr with Kgp of a group of four GPs with and without raft for Dr=0.6 and L/d=10: (a) without annular raft and (b) with annular raft.

Figure 11:

Variation of Iagpr with Kgp of a group of four GPs with and without raft for Dr=0.8 and L/d=10.
Variation of Iagpr with Kgp of a group of four GPs with and without raft for Dr=0.8 and L/d=10.

Figure 12:

Variation of Iagpr with Kgp - Effect of number of granular piles (Np).
Variation of Iagpr with Kgp - Effect of number of granular piles (Np).

Figure 13:

Variation of Iagpr with Kgp for Dg=2, with the effect of Dr and L/d: (a) Dr=0.2 and 0.4 (b) Dr=0.6 and Dr=0.8.
Variation of Iagpr with Kgp for Dg=2, with the effect of Dr and L/d: (a) Dr=0.2 and 0.4 (b) Dr=0.6 and Dr=0.8.

Figure 14:

Variation of Iagpr with Kgp for Dg=3 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.
Variation of Iagpr with Kgp for Dg=3 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.

Figure 15:

Variation of Iagpr with Kgp for Dg=4 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.
Variation of Iagpr with Kgp for Dg=4 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.

Figure 16:

Variation of Iagpr with Kgp for Dg=5 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.
Variation of Iagpr with Kgp for Dg=5 and with variation of Dr and L/d: (a) Dr=0.2 and Dr=0.4; (b) Dr=0.6 and Dr=0.8.

Figure 17:

Variation of Iagpr with Kgp, effect of Dr and Dg for L/d=10.
Variation of Iagpr with Kgp, effect of Dr and Dg for L/d=10.

Figure 18:

Variation of Iagpr with Kgp, effect of Dr and Dg.
Variation of Iagpr with Kgp, effect of Dr and Dg.

Figure 19:

Variation of the ratio of settlement of annular granular piled raft to the settlement of annular raft, Sr with Kgp – effect of Dg for L/d=10.
Variation of the ratio of settlement of annular granular piled raft to the settlement of annular raft, Sr with Kgp – effect of Dg for L/d=10.

Figure 20:

Variation of the ratio of settlement of annular granular piled raft to the settlement of annular raft, Sr with Kgp – effect of L/d for Dr=0.4, Dg=3.
Variation of the ratio of settlement of annular granular piled raft to the settlement of annular raft, Sr with Kgp – effect of L/d for Dr=0.4, Dg=3.

Figure 21:

Variation of the ratio of settlement of the annular granular piled raft to the settlement of annular raft, Sr with Np – effect of L/d for Dr=0.4, Dg=3, Kgp=100.
Variation of the ratio of settlement of the annular granular piled raft to the settlement of annular raft, Sr with Np – effect of L/d for Dr=0.4, Dg=3, Kgp=100.

Figure 22:

Variation of normalized contact pressure distribution at raft–soil interface, Praft with normalized radial distance (R1) – effect of Np.
Variation of normalized contact pressure distribution at raft–soil interface, Praft with normalized radial distance (R1) – effect of Np.

Figure 23:

Variation of normalized contact pressure distribution at raft–soil interface, Praft, with normalized radial distance (R1) – effect of Kgp.
Variation of normalized contact pressure distribution at raft–soil interface, Praft, with normalized radial distance (R1) – effect of Kgp.

Figure 24:

Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without annular raft for Dr=0.2, L/d=10, and Kgp=100.
Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without annular raft for Dr=0.2, L/d=10, and Kgp=100.

Figure 25:

Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without annular raft for Dr=0.4, L/d=10, and Kgp=100.
Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without annular raft for Dr=0.4, L/d=10, and Kgp=100.

Figure 26:

Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without the annular raft for Dr=0.6, L/d=10, and Kgp=100.
Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without the annular raft for Dr=0.6, L/d=10, and Kgp=100.

Figure 27:

Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without the annular raft for Dr=0.8, L/d=10, and Kgp=100.
Comparison of normalized shear stress variation with the normalized depth for a group of four GPs with and without the annular raft for Dr=0.8, L/d=10, and Kgp=100.

Figure 28:

Variation of τ1 with Z1 – effect of number of GPs for Dr=0.4, Dg=3, L/d=10, and Kgp=50.
Variation of τ1 with Z1 – effect of number of GPs for Dr=0.4, Dg=3, L/d=10, and Kgp=50.

Figure 29:

Variation of τ1*τ1* with Z1 – effect of number of GPs for Dr=0.4, Dg=3, L/d=10, Kgp=50.
Variation of τ1*τ1* with Z1 – effect of number of GPs for Dr=0.4, Dg=3, L/d=10, Kgp=50.

Figure 30:

Variation of percentage load shared by GP (Pgp) and Raft with Kgp – effect of annular width, Dg.
Variation of percentage load shared by GP (Pgp) and Raft with Kgp – effect of annular width, Dg.

Figure 31:

Variation of percentage load shared by GP (Pgp) and raft with Kgp – effect of the annular width, Dg.
Variation of percentage load shared by GP (Pgp) and raft with Kgp – effect of the annular width, Dg.

Figure 32:

Variation of percentage load shared by GP (Pgp) and raft with Kgp – effect of L/d.
Variation of percentage load shared by GP (Pgp) and raft with Kgp – effect of L/d.

Validation of the SIF values_

S.No. Variable verified (Dr) 0.2 0.4 0.6 0.8
1. Al Sanad (1993) [49] 0.814 0.709 0.532 0.345
2. Egorov (1965) [50] 0.79 0.80 0.82 0.90
3. Present analysis 0.80 0.80 0.81 0.85

Shear stresses and its reduction due to the presence of an annular raft_

Dr Dg Shear stresses of GPs without annular raft Shear stresses of GPs with annular raft Shear stresses reduction due to annular raft (%)
Top Bottom Top Bottom Top Bottom
0.2 2 2.324458 1.079298 0.123507 0.403755 94.70 62.65
3 2.232964 1.064219 0.107169 0.328567 95.20 69.17
4 2.169796 0.974238 0.100482 0.263145 95.38 72.99
5 2.134603 0.913877 0.084327 0.208937 96.06 77.21
0.4 2 2.248837 1.079708 0.106494 0.349187 95.28 67.66
3 2.160045 0.957485 0.089982 0.261161 95.83 72.72
4 2.120533 0.892764 0.074019 0.194048 96.51 78.26
5 2.101452 0.876311 0.058483 0.145743 97.22 83.37
0.6 2 2.147183 0.935131 0.087404 0.259689 95.93 72.23
3 2.103237 0.876795 0.063182 0.171468 97.00 80.44
4 2.08833 0.886777 0.047783 0.11668 97.71 86.84
5 2.082598 0.907918 0.03232 0.08452 98.45 90.69
0.8 2 2.085437 0.895009 0.033402 0.132094 98.40 85.24
3 2.079723 0.934551 0.024073 0.080976 98.84 91.34
4 2.079205 0.954441 0.020154 0.060053 99.03 93.71
5 2.079428 0.963823 0.014868 0.047917 99.28 95.03

Parameters used in the study_

S. No. Parameters Corresponding values
1. Kgp 10–400
2. Dr 0.2, 0.4, 0.6, 0.8
3. Dg 2, 3, 4, 5
4. L/d 5–40
5. Np 2–12
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