This article shows the mathematical method to determine the lateral stress on the shaft and toe resistance of pile using the new approach. The method was originally invented by Meyer and Kowalow for the static load test. The approximation curve was used for the estimation of both settlement curve and toe resistance curve of the pile. The load applied at the head of the pile is balanced by the sum of two components: the resistance under the toe of the pile and the skin friction. Therefore, the settlement curve is compilation of two factors: the skin friction curve and the resistance under toe curve. The analysis was based on the verification of the methods using laboratory experiments, that is, static load tests. The results of the research allowed to determine the relationship between parameters of the Meyer–Kowalow curve. On the basis of the relationships, it was possible to determine the skin friction and the toe resistance of the pile. Mathematical analysis of curve parameters allowed to determine the influence of the toe resistance on the settlement.

Foundation piles that are made by concrete 3D printers constitute a new alternative way of founding buildings constructed using incremental technology. We are currently observing very rapid development of incremental technology for the construction industry. The systems that are used for 3D printing with the application of construction materials make it possible to form permanent formwork for strip foundations, construct load-bearing walls and partition walls, and prefabricate elements, such as stairs, lintels, and ceilings. 3D printing systems do not offer soil reinforcement by making piles. The paper presents the possibility of making concrete foundation piles in laboratory conditions using a concrete 3D printer. The paper shows the tools and procedure for pile pumping. An experiment for measuring pile bearing capacity is described and an example of a pile deployment model under a foundation is described. The results of the tests and analytical calculations have shown that the displacement piles demonstrate less settlement when compared to the analysed shallow foundation. The authors indicate that it is possible to replace the shallow foundation with a series of piles combined with a printed wall without locally widening it. This type of foundation can be used for the foundation of low-rise buildings, such as detached houses. Estimated calculations have shown that the possibility of making foundation piles by a 3D printer will reduce the cost of making foundations by shortening the time of execution of works and reducing the consumption of construction materials.

Foundation piles transfer the applied vertical load to the surrounding soil by skin friction and base resistance. These two components induce stress in the soil. The load transfer is still not fully recognized, and some pile load tests analyses have raised many doubts. The present paper aimed to measure the stress levels during pile load tests in laboratory conditions. This research examined the possibilities of using thin, flexible sensors in measuring the stress in soil. Two sensors were used: tactile pressure sensor with mapping system and color film pressure sensors with digital analyzing. Calibration and preliminary tests of the sensors have been described. This calibration proved that this kind of sensor could measure the stress in the soil in laboratory conditions. The results of stress distribution in the soil, shown as pressure maps, have been presented. Significant stress changes were observed in pile load tests. Rough and smooth piles were compared in the analyses. Stress distribution was the result of simultaneous interaction of pile skin and base. The knowledge about stresses surrounding the pile allows us to carry out a deeper analysis of the pile–soil interaction.

The paper presents the results of static pile load test in laboratory conditions with additional measurement of vertical displacement of soil surrounding the shallow embedded pile. The main purpose of research to determine the pattern of soil displacement due to axial load of the pile. Although, the dimensions of pile are strongly differing from field pile used in practice, there are some phenomena which are similar to natural conditions. Tests were performed on a small precast concrete pile which was 7 cm in diameter and 25 cm long embedded in cohesionless soil. The measurements of the study were: applied load, resistance under the toe of the pile, settlement of the pile and vertical displacement of chosen points in the soil near to the toe of the pile. Performed test indicated that in small load the displacement in soil increase due to increasing load, but when the load was approaching the value of ultimate load, displacement stopped and at the limit load the direction of displacement vector changed to upward. The shape of the shear failure mechanism took the form of a logarithmic spiral which was widely described in literature. In this study an attempt at mathematical description has been made. In the proposed approach it was assumed that the displacement of the pile influenced the change of the sphere volume under the pile base which affects the displacement of the selected points of the soil. The research allowed to determine the size of ground space which was affected by the studied pile. The other studies indicate that the failure mechanism in deep piles and poorly compacted soils is caused by punching shear failure when only soil displacement down occurs, but in very compacted sands the mechanism of failure would be similar to obtained in laboratory test.

This paper investigates the effects of initial porosity index and load range on the shear strength of a sand sample using direct shear tests performed with a standard direct shear apparatus under varying densities, from loose to compacted. This study focuses on the distinction between the peak $\left({\varphi }_p\right)$ and critical $\left({\varphi }_{cv}\right)$ internal friction angles and their variation with stress level and initial porosity. Results show that the internal friction angle of sand depends on the stress state and initial porosity, reaching a peak value at maximum shear stresses and a critical value at constant sample volume. Higher initial compaction increases the peak friction angle, while higher effective stresses reduce the critical porosity index. The critical state line (CSL) defines the contraction and dilation behaviour of soils, with the critical porosity index varying with average soil stress. The analysis confirmed Bolton’s empirical relationship, linking the peak friction angle with the critical state angle and the dilation angle. This study emphasizes the importance of accurately defining the internal friction angle and considering the nonlinear relationship between shear strength and normal stresses. These findings are significant for geotechnical engineering, particularly in foundation bearing capacity, earth pressure, and slope stability analysis.

Transfer of axial force from the head of a pile to the surrounding soil by skin friction and toe resistance is still uncertain. The results of the static pile load test are usually presented as settlement curve. This curve can be divided into two components: skin friction curve and toe resistance curve according to the settlement. Laboratory research of pile load test was carried out in two schemes: with skin friction and without skin friction. The study proved that the toe resistance with and without skin friction is not the same. Skin friction influence on toe resistance due to settlement. This phenomenon is not usually taken into account, but very often has a significant impact on axially applied load transfer. In the paper results of laboratory pile load tests id, different schemes were presented. Transfer of axial force from the head of a pile to the surrounding soil by skin friction and toe resistance is still uncertain. The results of the static pile load test are usually presented as settlement curve. This curve can be divided into two components: skin friction curve and toe resistance curve according to the settlement. Laboratory research of pile load test was carried out in two schemes: with skin friction and without skin friction. The study proved that the toe resistance with and without skin friction is not the same. Skin friction influence on toe resistance due to settlement. This phenomenon is not usually taken into account, but very often has a significant impact on axially applied load transfer. In the paper results of laboratory pile load tests id, different schemes were presented.