Figure 1.
![Example of M-K curves [12]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64b9094864573c28bc2b890f/j_acee-2023-0021_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHYOMBSH6%2F20251215%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251215T011620Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEHQaDGV1LWNlbnRyYWwtMSJIMEYCIQDK5%2B8eYyV5Vk5QP5UEmr22ttGpJCjKMqvCSEya7w%2BIPAIhANh1BGSm4JKH4EyvuL8EyZYlPBU6LIE3EDCO6KnOMWaKKr0FCD4QAhoMOTYzMTM0Mjg5OTQwIgwQo6iIWpGy7Xqlvz8qmgVFUJ1k3m%2FQQ%2F5c9Ujvn6uhdAI4Roe5ZYJEUUDhh0BZOjqdKjAi0GOJe8FTkhLIbKYL9Q%2FdbRIFQs6maP%2B7i1aabDDajKf0V%2Fm9rSeOjI3UXC0gAHeMG0YA1w6VSb43H%2B8B2HBVDilSBHof3PXOO%2F%2BmUWrmP%2BJchs4WcMKLcpAiBI3MQzL%2FOhjTTS%2BV4sp69UMrSjJmvTZ%2B0B34RL%2Bb4hvUB08DGDupsqq7tkaQd0NtaPsrI0pkghjngg7%2BoInOC%2F3txUc4M8DYfxny6pzYoQGMIiwSoY3Bpe3Qj6I9pE35RA8yTufhw%2FJqN6U9ktnXiDgXSRUXbsBwFGph%2BjUNm6u66JZmR6OwRUSMiioBiSsgSzqt3IGJ3OdpD7%2BY6J5GGW%2FGj3QSIoeCJ03JnEJzeNMXN%2Fb4ZRt5uz2Hmmkio0mGn%2F49BQSWBbi6sFrpbIYXTNTGI0%2BqxZ8uuAj0WATql%2FBl0IStQXMUcP3DI1eqTV8u2IB7if0%2FH5oFY%2B3s6EJ2vA5esCGxzSHzl4wUxLbf0kOSBxGzlqN2G7%2F2xWhxS7JSJ3KsyEE%2FwnXwdq7CWyejsksrGdRnGmu54asVLGfKY7UlivYhRQBmlar0U66uP52N07vPBqM%2Bucx1rWdtJggGfEVCtN608q6AtmKQnBUjTC80uzBgwklviOljKCzzGv7V9QEFu1Y6Si8dEuDfYVeuOGjKtZRb8HlEhIKYWEV4KXKG1xxGu%2Bb7HURg31KLL1sMb2owjLOZB6IL4AcuL35dc83tU5xu3VZOcpMXNCoEiwPZUPAcoVeHpSqZD0rgpiVKlBA9PWJ34SbcddLP8%2B48iCVAuQmYg3M8iFa30QYadaOrIOIdDV%2B%2BNn6Xo1y99cQbYsFV1H676pjBQo8wlLr8yQY6sAH3ecj%2FSUOs23qB3T6jb85ee3g3xlm2dcZB3JbK5zHfr5y7TU2B%2BlqFHBRWA1DmtkeoKFIE5FsppLSVToMxAZHLksziVBP9EQdCv4%2B3ft84yAk%2FnMRMkuGaAMebNDPMnBlRHZZm4TbqnN1QicGoWiS5nUUw9FHidPxKsXoGlUfLNG7UPfl%2BYUfASj7pck9tTlnkcoQdOnXYyfn8j0ibnifZdGRTRCHT2yU%2BBQBQMD857Q%3D%3D&X-Amz-Signature=9681a4a01217958d374d67a91085be25f0b0368f6bce968675e3f7ce22312a0a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2.
![Optimal values of M-K parameters for a pile 31–10L [1]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64b9094864573c28bc2b890f/j_acee-2023-0021_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHYOMBSH6%2F20251215%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251215T011620Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEHQaDGV1LWNlbnRyYWwtMSJIMEYCIQDK5%2B8eYyV5Vk5QP5UEmr22ttGpJCjKMqvCSEya7w%2BIPAIhANh1BGSm4JKH4EyvuL8EyZYlPBU6LIE3EDCO6KnOMWaKKr0FCD4QAhoMOTYzMTM0Mjg5OTQwIgwQo6iIWpGy7Xqlvz8qmgVFUJ1k3m%2FQQ%2F5c9Ujvn6uhdAI4Roe5ZYJEUUDhh0BZOjqdKjAi0GOJe8FTkhLIbKYL9Q%2FdbRIFQs6maP%2B7i1aabDDajKf0V%2Fm9rSeOjI3UXC0gAHeMG0YA1w6VSb43H%2B8B2HBVDilSBHof3PXOO%2F%2BmUWrmP%2BJchs4WcMKLcpAiBI3MQzL%2FOhjTTS%2BV4sp69UMrSjJmvTZ%2B0B34RL%2Bb4hvUB08DGDupsqq7tkaQd0NtaPsrI0pkghjngg7%2BoInOC%2F3txUc4M8DYfxny6pzYoQGMIiwSoY3Bpe3Qj6I9pE35RA8yTufhw%2FJqN6U9ktnXiDgXSRUXbsBwFGph%2BjUNm6u66JZmR6OwRUSMiioBiSsgSzqt3IGJ3OdpD7%2BY6J5GGW%2FGj3QSIoeCJ03JnEJzeNMXN%2Fb4ZRt5uz2Hmmkio0mGn%2F49BQSWBbi6sFrpbIYXTNTGI0%2BqxZ8uuAj0WATql%2FBl0IStQXMUcP3DI1eqTV8u2IB7if0%2FH5oFY%2B3s6EJ2vA5esCGxzSHzl4wUxLbf0kOSBxGzlqN2G7%2F2xWhxS7JSJ3KsyEE%2FwnXwdq7CWyejsksrGdRnGmu54asVLGfKY7UlivYhRQBmlar0U66uP52N07vPBqM%2Bucx1rWdtJggGfEVCtN608q6AtmKQnBUjTC80uzBgwklviOljKCzzGv7V9QEFu1Y6Si8dEuDfYVeuOGjKtZRb8HlEhIKYWEV4KXKG1xxGu%2Bb7HURg31KLL1sMb2owjLOZB6IL4AcuL35dc83tU5xu3VZOcpMXNCoEiwPZUPAcoVeHpSqZD0rgpiVKlBA9PWJ34SbcddLP8%2B48iCVAuQmYg3M8iFa30QYadaOrIOIdDV%2B%2BNn6Xo1y99cQbYsFV1H676pjBQo8wlLr8yQY6sAH3ecj%2FSUOs23qB3T6jb85ee3g3xlm2dcZB3JbK5zHfr5y7TU2B%2BlqFHBRWA1DmtkeoKFIE5FsppLSVToMxAZHLksziVBP9EQdCv4%2B3ft84yAk%2FnMRMkuGaAMebNDPMnBlRHZZm4TbqnN1QicGoWiS5nUUw9FHidPxKsXoGlUfLNG7UPfl%2BYUfASj7pck9tTlnkcoQdOnXYyfn8j0ibnifZdGRTRCHT2yU%2BBQBQMD857Q%3D%3D&X-Amz-Signature=330c9f8ac57240a6ebeafe4c0a8b943f1a9c6a7721163181f006ca02bad72295&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3.
![M-K curve for a pile 31–10L [1]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64b9094864573c28bc2b890f/j_acee-2023-0021_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHYOMBSH6%2F20251215%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251215T011620Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEHQaDGV1LWNlbnRyYWwtMSJIMEYCIQDK5%2B8eYyV5Vk5QP5UEmr22ttGpJCjKMqvCSEya7w%2BIPAIhANh1BGSm4JKH4EyvuL8EyZYlPBU6LIE3EDCO6KnOMWaKKr0FCD4QAhoMOTYzMTM0Mjg5OTQwIgwQo6iIWpGy7Xqlvz8qmgVFUJ1k3m%2FQQ%2F5c9Ujvn6uhdAI4Roe5ZYJEUUDhh0BZOjqdKjAi0GOJe8FTkhLIbKYL9Q%2FdbRIFQs6maP%2B7i1aabDDajKf0V%2Fm9rSeOjI3UXC0gAHeMG0YA1w6VSb43H%2B8B2HBVDilSBHof3PXOO%2F%2BmUWrmP%2BJchs4WcMKLcpAiBI3MQzL%2FOhjTTS%2BV4sp69UMrSjJmvTZ%2B0B34RL%2Bb4hvUB08DGDupsqq7tkaQd0NtaPsrI0pkghjngg7%2BoInOC%2F3txUc4M8DYfxny6pzYoQGMIiwSoY3Bpe3Qj6I9pE35RA8yTufhw%2FJqN6U9ktnXiDgXSRUXbsBwFGph%2BjUNm6u66JZmR6OwRUSMiioBiSsgSzqt3IGJ3OdpD7%2BY6J5GGW%2FGj3QSIoeCJ03JnEJzeNMXN%2Fb4ZRt5uz2Hmmkio0mGn%2F49BQSWBbi6sFrpbIYXTNTGI0%2BqxZ8uuAj0WATql%2FBl0IStQXMUcP3DI1eqTV8u2IB7if0%2FH5oFY%2B3s6EJ2vA5esCGxzSHzl4wUxLbf0kOSBxGzlqN2G7%2F2xWhxS7JSJ3KsyEE%2FwnXwdq7CWyejsksrGdRnGmu54asVLGfKY7UlivYhRQBmlar0U66uP52N07vPBqM%2Bucx1rWdtJggGfEVCtN608q6AtmKQnBUjTC80uzBgwklviOljKCzzGv7V9QEFu1Y6Si8dEuDfYVeuOGjKtZRb8HlEhIKYWEV4KXKG1xxGu%2Bb7HURg31KLL1sMb2owjLOZB6IL4AcuL35dc83tU5xu3VZOcpMXNCoEiwPZUPAcoVeHpSqZD0rgpiVKlBA9PWJ34SbcddLP8%2B48iCVAuQmYg3M8iFa30QYadaOrIOIdDV%2B%2BNn6Xo1y99cQbYsFV1H676pjBQo8wlLr8yQY6sAH3ecj%2FSUOs23qB3T6jb85ee3g3xlm2dcZB3JbK5zHfr5y7TU2B%2BlqFHBRWA1DmtkeoKFIE5FsppLSVToMxAZHLksziVBP9EQdCv4%2B3ft84yAk%2FnMRMkuGaAMebNDPMnBlRHZZm4TbqnN1QicGoWiS5nUUw9FHidPxKsXoGlUfLNG7UPfl%2BYUfASj7pck9tTlnkcoQdOnXYyfn8j0ibnifZdGRTRCHT2yU%2BBQBQMD857Q%3D%3D&X-Amz-Signature=a1f785a37cc1f06aad38ecf329a3b6d50523a63ede377cd36b07d1e8f8ae84e9&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4.

Figure 5.
![Plasticized zone under the pile toe [1]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64b9094864573c28bc2b890f/j_acee-2023-0021_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHYOMBSH6%2F20251215%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251215T011620Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEHQaDGV1LWNlbnRyYWwtMSJIMEYCIQDK5%2B8eYyV5Vk5QP5UEmr22ttGpJCjKMqvCSEya7w%2BIPAIhANh1BGSm4JKH4EyvuL8EyZYlPBU6LIE3EDCO6KnOMWaKKr0FCD4QAhoMOTYzMTM0Mjg5OTQwIgwQo6iIWpGy7Xqlvz8qmgVFUJ1k3m%2FQQ%2F5c9Ujvn6uhdAI4Roe5ZYJEUUDhh0BZOjqdKjAi0GOJe8FTkhLIbKYL9Q%2FdbRIFQs6maP%2B7i1aabDDajKf0V%2Fm9rSeOjI3UXC0gAHeMG0YA1w6VSb43H%2B8B2HBVDilSBHof3PXOO%2F%2BmUWrmP%2BJchs4WcMKLcpAiBI3MQzL%2FOhjTTS%2BV4sp69UMrSjJmvTZ%2B0B34RL%2Bb4hvUB08DGDupsqq7tkaQd0NtaPsrI0pkghjngg7%2BoInOC%2F3txUc4M8DYfxny6pzYoQGMIiwSoY3Bpe3Qj6I9pE35RA8yTufhw%2FJqN6U9ktnXiDgXSRUXbsBwFGph%2BjUNm6u66JZmR6OwRUSMiioBiSsgSzqt3IGJ3OdpD7%2BY6J5GGW%2FGj3QSIoeCJ03JnEJzeNMXN%2Fb4ZRt5uz2Hmmkio0mGn%2F49BQSWBbi6sFrpbIYXTNTGI0%2BqxZ8uuAj0WATql%2FBl0IStQXMUcP3DI1eqTV8u2IB7if0%2FH5oFY%2B3s6EJ2vA5esCGxzSHzl4wUxLbf0kOSBxGzlqN2G7%2F2xWhxS7JSJ3KsyEE%2FwnXwdq7CWyejsksrGdRnGmu54asVLGfKY7UlivYhRQBmlar0U66uP52N07vPBqM%2Bucx1rWdtJggGfEVCtN608q6AtmKQnBUjTC80uzBgwklviOljKCzzGv7V9QEFu1Y6Si8dEuDfYVeuOGjKtZRb8HlEhIKYWEV4KXKG1xxGu%2Bb7HURg31KLL1sMb2owjLOZB6IL4AcuL35dc83tU5xu3VZOcpMXNCoEiwPZUPAcoVeHpSqZD0rgpiVKlBA9PWJ34SbcddLP8%2B48iCVAuQmYg3M8iFa30QYadaOrIOIdDV%2B%2BNn6Xo1y99cQbYsFV1H676pjBQo8wlLr8yQY6sAH3ecj%2FSUOs23qB3T6jb85ee3g3xlm2dcZB3JbK5zHfr5y7TU2B%2BlqFHBRWA1DmtkeoKFIE5FsppLSVToMxAZHLksziVBP9EQdCv4%2B3ft84yAk%2FnMRMkuGaAMebNDPMnBlRHZZm4TbqnN1QicGoWiS5nUUw9FHidPxKsXoGlUfLNG7UPfl%2BYUfASj7pck9tTlnkcoQdOnXYyfn8j0ibnifZdGRTRCHT2yU%2BBQBQMD857Q%3D%3D&X-Amz-Signature=a45732022d322d723241f05c3feda7f160b77c9ef164c81a342f2bdfb8bc7310&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 6.

Figure 7.

Figure 8.

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] |
| 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] |
|
|---|---|---|---|---|---|
| 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 |