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Influence of Raft in the Analysis of Granular Piles

Ashish Solanki

Ashish Solanki

Department of Civil Engineering, Rajasthan Technical UniversityKota, India
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Solanki, Ashish
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Jitendra Kumar Sharma

Jitendra Kumar Sharma

Department of Civil Engineering, Rajasthan Technical UniversityKota, India
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Sharma, Jitendra Kumar
  
04 juin 2025
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Catégorie d'article: Original Study
Publié en ligne: 04 juin 2025
Pages: 145 - 166
Reçu: 17 déc. 2024
Accepté: 03 mars 2025
DOI: https://doi.org/10.2478/sgem-2025-0012
Mots clés
© 2025 Ashish Solanki et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

(a) Layout of a cluster consisting of four floating granular piles (GPs) arranged symmetrically. (b) Sectional elevation at X–X of a cluster comprising four symmetrically positioned floating GPs (Garg and c, 2019).
(a) Layout of a cluster consisting of four floating granular piles (GPs) arranged symmetrically. (b) Sectional elevation at X–X of a cluster comprising four symmetrically positioned floating GPs (Garg and c, 2019).

Figure 2:

Stresses on any ith element of the GP.
Stresses on any ith element of the GP.

Figure 3:

Four floating GPRs units
Four floating GPRs units

Figure 4:

Soil stresses in the four floating GPR units
Soil stresses in the four floating GPR units

Figure 5:

Numerical integration discretization scheme for GP.
Numerical integration discretization scheme for GP.

Figure 6:

Discretization scheme of solid raft (Solanki et al., 2022).
Discretization scheme of solid raft (Solanki et al., 2022).

Figure 7:

Variation of α2r, with Kgp, between 2GPs and 2GPRs—impact of s/d for L/d = 10 and D/d = 2.
Variation of α2r, with Kgp, between 2GPs and 2GPRs—impact of s/d for L/d = 10 and D/d = 2.

Figure 8:

Variation of α3r, with Kgp, between the 3GPs and 3GPRs—impact of s/d for L/d = 10 and D/d = 2.
Variation of α3r, with Kgp, between the 3GPs and 3GPRs—impact of s/d for L/d = 10 and D/d = 2.

Figure 9:

Variation of α4r, with Kgp, between 4GPs and 4GPRs—impact of s/d for L/d = 10 and D/d = 2.
Variation of α4r, with Kgp, between 4GPs and 4GPRs—impact of s/d for L/d = 10 and D/d = 2.

Figure 10:

Variation of α3GPRs, with Kgp, between the 3GPRs—impact of s/d for L/d = 10 and D/d = 2, R and S analyses.
Variation of α3GPRs, with Kgp, between the 3GPRs—impact of s/d for L/d = 10 and D/d = 2, R and S analyses.

Figure 11:

Variation of α3GPs, with Kgp, between 3GPs—impact of s/d for L/d = 10, R and S analyses.
Variation of α3GPs, with Kgp, between 3GPs—impact of s/d for L/d = 10, R and S analyses.

Figure 12:

Variation of α4GPRs, with Kgp, between 4GPRs—impact of s/d for L/d = 10 and D/d = 2, R and S analyses.
Variation of α4GPRs, with Kgp, between 4GPRs—impact of s/d for L/d = 10 and D/d = 2, R and S analyses.

Figure 13:

Variation of α4GPs, with Kgp, between 4GPs—impact of s/d for L/d = 10, R and S analyses.
Variation of α4GPs, with Kgp, between 4GPs—impact of s/d for L/d = 10, R and S analyses.

Figure 14: (a)

α2r v/s s/d, between 2GPRs and 2GPs—impact of Kgp for L/d = 10 and D/d=2.
α2r v/s s/d, between 2GPRs and 2GPs—impact of Kgp for L/d = 10 and D/d=2.

Figure. 14 (b):

α3r v/s s/d, between 3GPRs and 3GPs—impact of Kgp for L/d = 10 and D/d=2.
α3r v/s s/d, between 3GPRs and 3GPs—impact of Kgp for L/d = 10 and D/d=2.

Figure 14: (c)

α4r v/s s/d, between 4GPRs and 4GPs—impact of Kgp for L/d = 10 and D/d=2.
α4r v/s s/d, between 4GPRs and 4GPs—impact of Kgp for L/d = 10 and D/d=2.

Figure 15 (a):

Changes in PR, PP, and PB with respect to total load with Kgp for 2GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PR, PP, and PB with respect to total load with Kgp for 2GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Figure 15 (b):

Changes in PR, PP, and PB with respect to total load with Kgp for 3GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PR, PP, and PB with respect to total load with Kgp for 3GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Figure 15 (c):

Changes in PR, PP, and PB with respect to total load with Kgp for 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PR, PP, and PB with respect to total load with Kgp for 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Figure 16:

Changes in PP with respect to total load with Kgp for 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PP with respect to total load with Kgp for 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Figure 17:

Changes in PR with respect to total load with Kgp for 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PR with respect to total load with Kgp for 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Figure 18:

Changes in PB with respect to total load with Kgp, for groups of 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.
Changes in PB with respect to total load with Kgp, for groups of 2GPRs, 3GPRs, and 4GPRs—impact of s/d = 3 and 4 for L/d = 10 and D/d = 3.

Validation and comparison of α for groups of two, three, and four GP–GPR systems_

PARAMETERS SETTLEMENT INTERACTION FACTOR, α REFERENCES
L/d=10, s/d=3, νs= 0.5, Kgp=10000 0.494 Present analysis for 2GPs
L/d=10, s/d=3, νs= 0.5, Kgp=∞ 0.493 Poulos (1968)
L/d=25, s/d=3, νs= 0.5, Kgp=10000 0.584 Present analysis for 2GPs
L/d=25, s/d=3, νs= 0.5, Kgp=∞ 0.582 Poulos (1968)
L/d=25, s/d=3, νs= 0, Kgp=10000 0.631 Present analysis for 2GPs
L/d=25, s/d=3, νs= 0, Kgp=∞ 0.630 Poulos (1968)
L/d=25, s/d=10, νs=0.5, Kgp=10000 0.299 Present analysis for 2GPs
L/d=25, s/d=10, νs=0.5, Kgp=1000 0.26 Kitiyodom and Matsumoto (2003)
L/d=25, s/d=10, νs=0.5, Kgp=1000 0.265 Present analysis for 2GPs
L/d=25, s/d=10, νs= 0.5, Kgp=∞ 0.31 Poulos (1968)
L/d=25, s/d=10, νs=0.5, Kgp=10000 0.596 Present analysis for 3GPs
L/d=25, s/d=10, νs= 0.5, Kgp=∞ 0.589 Poulos (1968)
L/d=25, s/d=10, νs=0.5, Kgp=10000 0.829 Present analysis for 4GPs
L/d=25, s/d=10, νs= 0.5, Kgp=∞ 0.81 Poulos (1968)
L/d=10, D/d=2, s/d=4, νs=0.5, Kgp=10000 0.42 Present analysis for 2GPRs
L/d=10, D/d=2, s/d=4, νs=0.5, Kgp=∞ 0.41 Davis and Poulos (1972)
L/d=10, D/d=2, s/d=6, νs=0.5, Kgp=10000 0.311 Present analysis for 2GPRs
L/d=10, D/d=2, s/d=6, νs=0.5, Kgp=∞ 0.31 Davis and Poulos (1972)
L/d=25, D/d=2, s/d=4, νs=0.5, Kgp=10000 0.51 Present analysis for 2GPRs
L/d=25, D/d=2, s/d=4, νs=0.5, Kgp=∞ 0.50 Davis and Poulos (1972)
L/d=25, D/d=2, s/d=6, νs=0, Kgp=10000 0.471 Present analysis for 2GPRs
L/d=25, D/d=2, s/d=6, νs=0, Kgp=∞ 0.47 Davis and Poulos (1972)

Calculated α Values for 2GPR, 3GPR, and 4GPR at Different Kgp Values_

Kgp Ssingle GPR S2GPRs α2 S3GPRs α3 S4GPRs α4
10 0.28896019 0.44372244 0.5354 0.57710092 0.9974 0.66499219 1.3012
20 0.24921961 0.37804292 0.517 0.4909663 0.9707 0.57116472 1.2923
40 0.21146596 0.32215436 0.5237 0.42253469 0.9977 0.49794194 1.3545
60 0.19295914 0.29693231 0.5392 0.3930989 1.037 0.46686672 1.4202
80 0.18191326 0.28252547 0.5527 0.37668362 1.0703 0.44965581 1.4722
100 0.17456244 0.27319766 0.5653 0.36620857 1.0974 0.43871883 1.5138
200 0.15786745 0.25275908 0.6007 0.34367319 1.1776 0.41531357 1.6311
300 0.15160321 0.24534996 0.6177 0.33564417 1.2138 0.40701624 1.6848
400 0.14831981 0.24152163 0.6284 0.33152454 1.2357 0.40276757 1.7154
500 0.14629833 0.23918332 0.6355 0.32901799 1.2489 0.40018538 1.7365
600 0.1449285 0.23760681 0.6402 0.32733219 1.2588 0.39844994 1.7517
700 0.14393894 0.23647197 0.6434 0.32612074 1.2667 0.39720341 1.7627
800 0.1431906 0.23561598 0.6455 0.3252081 1.2727 0.3962647 1.7703
900 0.14260485 0.23494732 0.6468 0.32449587 1.2774 0.39553232 1.7757
1000 0.14213391 0.23441055 0.6476 0.32392456 1.2811 0.39494498 1.7797
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Géosciences, Géosciences, autres, Sciences des matériaux, Matériaux composites, Matériaux poreux, Physique, Mécanique et dynamique des fluides
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