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An Analytical Study of Annular Raft on Granular Piles

Ajay Pratap Singh Rathor
Ajay Pratap Singh Rathor
, 
Jitendra Kumar Sharma
Jitendra Kumar Sharma
 and 
Madhav Madhira
Madhav Madhira
   | Mar 29, 2024
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Article Category: Original Study
Published Online: Mar 29, 2024
Page range: 21 - 44
Received: Jul 15, 2023
Accepted: Jan 30, 2024
DOI: https://doi.org/10.2478/sgem-2024-0002
Keywords
© 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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