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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=373a7e068d1768bf86ed521a63133e5e3f556cc09e7cd1b07f9164c70c38cf3a&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=e164470b6c30071ac3eb8f9cea6f4b05aeae968e87b666a339b02724215053de&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=568a73ae845abb2b20db201bea5dffc13b4b3d2aee1a7ff47d91f61ef1ea2da1&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=133bb54d3893e04d746f0eda5928666cd2044a2edba99c7d43f1d276a73caaa9&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=6455895de4d7cd5f3ee3aed3cb9e2eb2e7720dee017a74b47dc210c9d565b828&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=d9c3548ee0a7ee4781fc8fa8e59d380f9eee225701ddd8de0b4b99b65a96a519&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=8a09811fb0b36cdc7fc296fead6e54f79c93f70f8caf562865b6fbdc8bd024b1&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=ASIA6AP2G7AKLV32NR4M%2F20260306%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260306T074145Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBQaDGV1LWNlbnRyYWwtMSJGMEQCIFLvPLXUG%2F3hts6lxVDeg0V1AyLGTBoh%2FZBJE03AWaW8AiAwCQNeUxguJ1o1Jitas%2BZ5SAhFKKSJ2QtON9553XiV0irGBQjd%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM9X3HGtQI2o7UO%2BS2KpoFxG7ar8PSEQAdM1CFVlXpyDrKaTO5gZJY%2Bb0H6B8LNfpVNgkJOuIe%2B9NLBis8%2Fprsn8bTeVYKPQnvOC41LHTWcNu00sat0gioJHkasLPSMcprw1BFnMAAIIkcI4JhITa4FDgPio7IFd4lhEz2ogrsBS779wlwdLrf1fi7VeAW5cMnqjc5PQVWYOWg80u6bguMBcCG1Mp81p2ra0MdUkI%2FPhw7gZ1WNUQvdI5U6bv10EKlr6JnmK0p8EbJTTEGUzgv%2Bx9DkcpBuy2jqZzEV1ZjNMAweN4ajHAwNjwH8oedNak7aeu57x1sxT3hBWpPvHzcq47OTuF%2BD1xpNlQoj1PDqKa9fpq4pogK8ya6gQiW6vzjFXA4nd7OCH3zFuh7On1kP8FPgbyxIhk1WG2PNbknoEkwc%2F3SgduubLF08fr%2FJQcICro3Euw9Vq3mUdCPOeYukkLR62eklM05iFPKMTf10Nl%2B4kwK5j86nubZ7dLrKrqZ3XTGcL5xSHyHK1SEVrSOtUwGmZaB4F4xbvAywifc53wCTZLLPx4vLOxaBNoAgiDwrCgCsGxuZ8w9l1WKjZDPwRAj0v7H4CRc6mtkKGyE4nhhnxMAjawduoK8Mb%2F3r6CsLyM6%2B29EVfqNynsGb%2BjloIyaEeJ3skvOZjSDEh5%2Fd8ol0VyUWP%2F4N5CjzRtch5k2hYBwPH02cHvRHj38IkcWDCMrffPATh41BYb2yNBwlkGvyIPZm35Kzzy8aTxQsTuVZjQ0eK4z4HVOpjGf3QWHqEwydzcwgo4lRI0YKO7wf3hd1iMCBEmZUwthCEciA4yYOw0ZjXjKTqt%2FMTfL%2BYlIc78YZ5fC6tlcfS%2FiiaeYzofJJ5BVhakioniADVcu9mKBeZvVsj6MrZdBMKSiqc0GOrIBQsAGShH29riYEgAfTNsytPCjtJUJZ2YAqie2KAtXMOfuiFj%2BTIMLuMSG6TUkCPo8cGb18oZOzaYqAhY4LDkJfc9%2FPTayNCqHCi6Dbl189%2BugY75PzavphSkQYus3ram8FWTa1E86pg9Kwf9Sh35aXUdyHJNKPe05zUqVxZqyynWUm%2FSxeJpsP3GvWtwtCMkUbJX0M0MQIk9QlnSniw%2FLQOcyarjiXs8eDDR0aYsEv%2Bpc0A%3D%3D&X-Amz-Signature=078b7a1a1fcf4a0d344132fabbdab991f919165ab7493575551cd44805eeee86&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_
| N [kN] | 0 | 145 | 289 | 432 | 576 | 720 | 863 | 1007 | 1150 | 1295 | 1438 | 1581 | 1726 | 1890 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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_
| N [kN] | 0 | 145 | 293 | 431 | 575 | 720 | 864 | 1006 | 1151 | 1294 | 1438 | 1582 | 1726 | 1896 | 2013 | 2156 | 2300 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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]_
| qc | svo | ID | Ic | qn | βq | Nm | Φ′ | C′ | Su(Cu) | M0 | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| [m] | [-] | [-] | [MPa] | [KPa] | [%] | [-] | [MPa] | [-] | [-] | [°] | [kPa] | [kPa] | [MPa] |
| 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_
| side EQ. (42) | Right side Eq.(42) | |
|---|---|---|
| Pile 1 | 0,83 | 0,803 |
| Pile 2 | 0,85 | 0,84 |