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An Attempt to Analytically Determine Course of the Continuous Q-S Curve in Case of Changed Pile Length or Diameter

Zygmunt Meyer
Zygmunt Meyer
 und 
Kamil Stachecki
Kamil Stachecki
   | 20. Juli 2023
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Online veröffentlicht: 20. Juli 2023
Seitenbereich: 119 - 126
Eingereicht: 15. Jan. 2023
Akzeptiert: 28. März 2023
DOI: https://doi.org/10.2478/acee-2023-0021
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© 2023 Zygmunt Meyer et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Example of M-K curves [12]
Example of M-K curves [12]

Figure 2.

Optimal values of M-K parameters for a pile 31–10L [1]
Optimal values of M-K parameters for a pile 31–10L [1]

Figure 3.

M-K curve for a pile 31–10L [1]
M-K curve for a pile 31–10L [1]

Figure 4.

Idea of curve conversion
Idea of curve conversion

Figure 5.

Plasticized zone under the pile toe [1]
Plasticized zone under the pile toe [1]

Figure 6.

Complete description of load-settlement relation of a pile 31–10L using the M-K method
Complete description of load-settlement relation of a pile 31–10L using the M-K method

Figure 7.

Comparison between load-settlement relation in case of decreased length and diameter
Comparison between load-settlement relation in case of decreased length and diameter

Figure 8.

Change of safety factor in cased of decreased length and diameter
Change of safety factor in cased of decreased length and diameter

Calculated and measured settlement for a pile 31 10L [1]

Ni [kN] si,test [mm] si,calc,opt [mm]
1600 1.2 1.575
2600 1.9 3.081
3200 2.4 4.308
3800 3.2 5.904
4100 4.1 6.892
4500 5.9 8.479
4750 7.1 9.668
4900 8.8 10.474
5100 9.4 11.673
5200 10 12.335
5800 14.6 17.492
6200 20 22.637
6500 24.9 28.011
6650 30 31.419
6800 35.2 35.482
6950 40 40.396
7100 45.2 46.435
7200 50 51.279
7300 60 56.964
7400 70 63.715
7500 80 71.837
7600 90 81.763

Parameters of analyzed piles

Pile H [m] D [m] HD {\boldsymbol {{H \over D}}} Ngr2 [kN] κ2 [−] C2 [mm/kN]
36N-10L 27.5 1 27.5 6590 0.61 0.00062
31-10L 27.5 2 13.75 8700 1.4 0.00077
38-10P 31.5 1.5 21 12500 0.65 0.00087
38-12P 33.5 1.5 22.33 11850 0.1 0.00064
38-12L 33.5 1.5 22.33 12200 0.5 0.00037

Calculated and measured values of maximum pile-bearing capacity

Pile D H/D Ngr2,test [kN] Ngr2,calc [kN] Ngr2,calcNgr2,test {\boldsymbol {{{{N_{gr2,calc}}} \over {{N_{gr2,test}}}}}}
36N-10L 1 27.5 6490 7127 1.09
31-10L 2 13.75 7700 8434 1.09
38-10P 1.5 21 11900 9984 0.84
21N-10L 2 13.75 8260 8434 1.02
25N-10L 1 27.5 6350 7126 1.12
38-12P 1.5 22.33 11780 11124 0.94
38-12L 1.5 22.33 12150 11124 0.92

Comparison between values of safety factor in case of decreased length and diameter

srec [mm] SF
Before conversion After conversion
1 7.89 4.84
1.2 6.77 4.23
1.4 5.97 3.79
1.6 5.37 3.47
1.8 4.90 3.21
2 4.53 3.01
2.2 4.22 2.84
2.4 3.97 2.70
2.6 3.75 2.58
2.8 3.57 2.48
3 3.41 2.39
3.2 3.26 2.31
3.4 3.14 2.24
3.6 3.03 2.18
3.8 2.93 2.13
4 2.84 2.08
4.2 2.76 2.03
4.4 2.69 1.99
4.6 2.62 1.95
4.8 2.56 1.92
5 2.50 1.89
5.2 2.45 1.86
5.4 2.40 1.83
5.6 2.35 1.80
5.8 2.31 1.78
6 2.27 1.76
6.2 2.23 1.74
6.4 2.20 1.72
6.6 2.17 1.70
6.8 2.14 1.68
7 2.11 1.67
7.2 2.08 1.65
7.4 2.05 1.64
7.6 2.03 1.62
7.8 2.00 1.61
8 1.98 1.60
8.2 1.96 1.58
8.4 1.94 1.57
8.6 1.92 1.56
8.8 1.90 1.55
9 1.89 1.54
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