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An Analytical Study of Annular Raft on Granular Piles Cover

An Analytical Study of Annular Raft on Granular Piles

Studia Geotechnica et Mechanica
Volume 46 (2024): Issue 1 (March 2024)
By: Ajay Pratap Singh Rathor,  Jitendra Kumar Sharma and  Madhav Madhira  
Open Access
|Mar 2024

Figures & Tables

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)0.20.40.60.8
1.Al Sanad (1993) [49]0.8140.7090.5320.345
2.Egorov (1965) [50]0.790.800.820.90
3.Present analysis0.800.800.810.85

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

DrDgShear stresses of GPs without annular raftShear stresses of GPs with annular raftShear stresses reduction due to annular raft (%)
TopBottomTopBottomTopBottom
0.222.3244581.0792980.1235070.40375594.7062.65
32.2329641.0642190.1071690.32856795.2069.17
42.1697960.9742380.1004820.26314595.3872.99
52.1346030.9138770.0843270.20893796.0677.21
0.422.2488371.0797080.1064940.34918795.2867.66
32.1600450.9574850.0899820.26116195.8372.72
42.1205330.8927640.0740190.19404896.5178.26
52.1014520.8763110.0584830.14574397.2283.37
0.622.1471830.9351310.0874040.25968995.9372.23
32.1032370.8767950.0631820.17146897.0080.44
42.088330.8867770.0477830.1166897.7186.84
52.0825980.9079180.032320.0845298.4590.69
0.822.0854370.8950090.0334020.13209498.4085.24
32.0797230.9345510.0240730.08097698.8491.34
42.0792050.9544410.0201540.06005399.0393.71
52.0794280.9638230.0148680.04791799.2895.03

Parameters used in the study_

S. No.ParametersCorresponding values
1.Kgp10–400
2.Dr0.2, 0.4, 0.6, 0.8
3.Dg2, 3, 4, 5
4.L/d5–40
5.Np2–12
DOI: https://doi.org/10.2478/sgem-2024-0002 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 21 - 44
Submitted on: Jul 15, 2023
|
Accepted on: Jan 30, 2024
|
Published on: Mar 29, 2024
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
annular raft,
granular pile,
settlement influence factor,
ring footing,
shear stresses
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2024 Ajay Pratap Singh Rathor, Jitendra Kumar Sharma, Madhav Madhira, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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