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An Analytical Study of Partially Strengthened Single End-Bearing Granular Pile Near the Top and Bottom

Vaibhaw Garg
Vaibhaw Garg
, 
Jitendra Kumar Sharma
Jitendra Kumar Sharma
 and 
Ashish Solanki
Ashish Solanki
   | Jun 30, 2021
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Article Category: Original Study
Published Online: Jun 30, 2021
Page range: 99 - 115
Received: Nov 05, 2020
Accepted: Apr 22, 2021
DOI: https://doi.org/10.2478/sgem-2021-0010
Keywords
© 2021 Vaibhaw Garg et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

(a) Plan of strengthened end bearing GP (b) Sectional elevation at 1–1 of a single strengthened end bearing GP, subjected to load F, revealing strengthening effect. (c) Problem description sketch, development of interfacial shear stresses on soil due to a single strengthened end-bearing GP.
(a) Plan of strengthened end bearing GP (b) Sectional elevation at 1–1 of a single strengthened end bearing GP, subjected to load F, revealing strengthening effect. (c) Problem description sketch, development of interfacial shear stresses on soil due to a single strengthened end-bearing GP.

Figure 2

Basic mirror image methodology for GP.
Basic mirror image methodology for GP.

Figure 3

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP(Lg/Dg=10, ηt or ηb=10%).
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP(Lg/Dg=10, ηt or ηb=10%).

Figure 4

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=20%).
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=20%).

Figure 5

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=30%).
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=30%).

Figure 6

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).

Figure 7

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess =100).
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess =100).

Figure 8

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt or strengthening factor for the bottom, χb, such that χt=χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess =100)
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt or strengthening factor for the bottom, χb, such that χt=χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess =100)

Figure 9

Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative length of GP, Lg/Dg; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Kp=50, ηt=ηb=20%)
Variation of displacement affecting component for the top of GP, DT, with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative length of GP, Lg/Dg; PLST of GP, ηt; PLSB of GP, ηb; and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Kp=50, ηt=ηb=20%)

Fig. 10

Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=10%)
Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=10%)

Figure 11

Variation of PLTB of GP, (Fb/F) ×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=20%).
Variation of PLTB of GP, (Fb/F) ×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=20%).

Figure 12

Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=30%).
Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb. Impact of the relative stiffness of GP, Kp, and relative stiffness of bearing stratum, Ebs/Ess, on a single partially strengthened GP (Lg/Dg=10, ηt or ηb=30%).

Figure 13

Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).
Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).

Figure 14

Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).
Variation of PLTB of GP, (Fb/F)×100 with strengthening factor for the top, χt, or strengthening factor for the bottom, χb, such that χt= χb. Impact of the relative stiffness of GP, Kp; PLST of GP, ηt; PLSB of GP, ηb; on a single partially strengthened GP (Lg/Dg=10, Ebs/Ess=100).

Figure 15

Variation of NSS, τ*E= τ(πDgLg)/F with normalized depth, z*g=zg/Lg. Impact of strengthening factor for the top, χt, or strengthening factor for bottom, χb, on a single partially strengthened GP (Lg/Dg=10, Kp=100, ηt=20%, ηb=20%, Ebs/Ess=100).
Variation of NSS, τ*E= τ(πDgLg)/F with normalized depth, z*g=zg/Lg. Impact of strengthening factor for the top, χt, or strengthening factor for bottom, χb, on a single partially strengthened GP (Lg/Dg=10, Kp=100, ηt=20%, ηb=20%, Ebs/Ess=100).

Figure 16

Variation of NSS, τ*E= τ(πDgLg)/F with normalized depth, z*g=zg/Lg. Impact of strengthening factor for the top, χt, or strengthening factor for bottom, χb, on a single partially strengthened GP (Lg/Dg=10, Kp=100, ηt=30%, ηb=30%, Ebs/Ess=100).
Variation of NSS, τ*E= τ(πDgLg)/F with normalized depth, z*g=zg/Lg. Impact of strengthening factor for the top, χt, or strengthening factor for bottom, χb, on a single partially strengthened GP (Lg/Dg=10, Kp=100, ηt=30%, ηb=30%, Ebs/Ess=100).

Validation of results.

Variables verified Lg/Dg Kp and Ebs/Ess Results of Poulos and Mattes [20] Present analysis with (χt=χb=1)
DACT (DT) of GP 25 100 and 10 0.54 0.539
25 100 and 100 0.51 0.508
25 100 and 1000 0.49 0.489
20 100 and 100000 0.09 0.0899
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