About this article
Article Category: Original Study
Published Online: Jun 22, 2024
Page range: 164 - 175
DOI: https://doi.org/10.2478/sgem-2024-0010
Keywords
© 2024 Paweł Siemaszko, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Figure 1:
![Graphical description of the loads acting on a pile in the presented approach. D – Pile diameter [m]; h – Pile length [m]; N2 – Load acting on the head of the pile [N]; N1 – Soil reaction at the toe [N]; T – Pile skin resistance [N]; s2,1 – Settlement value of the head and base of the pile [mm]; σ1 – Stress under the base of the pile [Pa]; τ – Stress acting on the skin of the pile, representing the skin resistance [Pa]; l – Arm of the soil deformation according to Kirchhoff's principle [m].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=1a1d751c6b48026bf469a3bed5e2c2e2bd92c3ad7f29490036a3771b04d421b9&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2:

Figure 3:

Figure 4:

Figure 5:
![Distribution of the axial force along the pile shaft and deformation of the pile shaft measured during the static load test with extensometers [36].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=f0f6ed7051668afa5cb5e7562fc215766fb038157bb824d32efe6d1033050996&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 6:

Figure 7:
![CPTu investigation results for Pile 1 [27].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_007.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=1e251c92e80df75bf9356316a229690fb9992b3052e5bd0612c074057218d817&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 8:
![CPTu investigation results for Pile 2 [27].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_008.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=f259445ed51bf5fa95492ec5a0af486a12d4c4b94a65c9f4922dc001b6158b2a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 9:
![Example of the M–K curve graph [20].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_009.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=3b80ad910527879eeade0044cfa34064bab3f4316d170db55c5ee09c9a0c7c82&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 10:

Figure 11:
![Relationship between the load acting on the head of the pile and the shear stress at the head level (τ2) and base level (τ1) for the pile taken from Heyki 1 [by author].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_011.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=b148126804ec50190c3a45d3c5421e8a55ebeda8d2412d0f796de17817d46f96&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 12:
![Relationship between the load acting on the head of the pile and the shear stress at the head level (τ2) and base level (τ1) for the pile taken from Heyki 2 [by author].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_012.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=4c99aeabeac1954c76d92b9a6ad0e6de53b4122964dfac73561eb801f68b1f1c&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 13:
![Soil under and around the pile base forming a sphere, where the parameters vary significantly [22, 28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a3e4e662f30ba53f8da/j_sgem-2024-0010_fig_013.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20250920%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20250920T135731Z&X-Amz-Expires=3600&X-Amz-Signature=042dae5630b905e28441f89e32afc568571c1f00a3ce0d6a54a60b007ed246ff&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 14:

Load–settlement values obtained from the static load test; Pile Heyki 1_
s [mm] | 0,00 | 0,57 | 1,14 | 1,86 | 2,64 | 3,69 | 4,82 | 6,54 | 8,38 | 10,83 | 13,38 | 16,41 | 20,28 | 26,08 |
Load–settlement values obtained from static load test for Pile Heyki 2_
s [mm] | 0,00 | 0,71 | 1,27 | 1,88 | 2,57 | 3,49 | 4,48 | 6,04 | 7,77 | 10,24 | 13,24 | 16,13 | 19,59 | 23,20 | 27,14 | 31,73 | 36,42 |
Geotechnical parameters of the soil profile [27]_
0,0 | |||||||||||||
1,8 | Mg(hgrcFSa) | nN(Pd+H+c+ż) | 2,20 | 35 | 20 | - | 2,19 | 0,02 | - | 29° 30′ | - | - | 9,5 |
2,3 | Mg(grchclSa) | nN(Pg+H+c+ż) | 1,30 | 42 | - | 0,54 | 1,27 | 0,01 | 11,1 | 22° 10′ | 6 | 98 | 9,2 |
2,5 | Mg(grchFSa) | nN(Pd+H+c+ż) | 2,20 | 57 | 15 | - | 2,14 | 0,00 | - | 29° | - | - | 9,4 |
3,8 | Or(Nm) | Nm | 0,45 | 92 | - | 0,50 | 0,38 | 0,04 | 3,7 | 13° 10′ | 3 | 20 | 1,1 |
6,6 | Or(Nm) | Nm | 0,65 | 117 | - | 0,60 | 0,58 | 0,12 | 5,1 | 15° 50′ | 4 | 31 | 2,5 |
7,0 | Or(Nmp)/HFSa | Nmp/PdH | 1,10 | 133 | - | 0,44 | 1,00 | 0,01 | 6,8 | 18° 50′ | 5 | 71 | 7,9 |
8,2 | FSa | Pd | 3,30 | 149 | 20 | - | 3,18 | 0,00 | - | 29° 20′ | - | - | 14,2 |
8,6 | FSa | Pd/Ps | 6,40 | 177 | 40 | - | 6,25 | 0,00 | - | 32° 10′ | - | - | 28,4 |
11,1 | FSa | Pd | 13,20 | 208 | 65 | - | 13,03 | 0,00 | - | 35° 10′ | - | - | 64,9 |
11,8 | FSa | Pd | 7,30 | 220 | 40 | - | 7,12 | 0,00 | - | 32° 20′ | - | - | 32,4 |
12,4 | saSi | Πp | 2,60 | 236 | - | 0,74 | 2,40 | 0,00 | 11,1 | 22° 10′ | 7 | 171 | 21,8 |
13,3 | FSa | Pd | 7,00 | 250 | 35 | - | 6,80 | 0,00 | - | 31° 50′ | - | - | 31,1 |
13,8 | FSa | Pd | 11,10 | 268 | 55 | - | 10,88 | 0,00 | - | 33° 50′ | - | - | 54,6 |
15,2 | saSi/siSa | Πp/Pπ | 3,40 | 292 | - | 0,82 | 3,17 | 0,00 | 12,2 | 22° 50′ | 7 | 226 | 28,5 |
16,2 | FSa/MSa | Pd/Ps | 14,00 | 320 | 60 | - | 13,74 | 0,00 | - | 34° 30′ | - | - | 70,3 |
18,0 | FSa | Pd | 7,00 | 342 | 30 | - | 6,73 | 0,00 | - | 31° | - | - | 31,2 |
18,4 | FSa | Pd | 10,50 | 353 | 45 | - | 10,22 | 0,00 | - | 33° | - | - | 51,8 |
19,1 | FSa/MSa | Pd/Ps | 15,40 | 400 | 60 | - | 15,08 | 0,00 | - | 34° 30′ | - | - | 75,9 |
Equation (42) results, left side and right side_
Pile 1 | 0,83 | 0,803 |
Pile 2 | 0,85 | 0,84 |