EQUATIONS OF THE TRAJECTORY OF THE HEAD'S MOTION IN THE GROUND WITH THE CONDITION OF ITS CORRECTION AND THEIR EXPERIMENTAL VERIFICATION

Abstract

DOI: https://doi.org/10.26565/2079-1747-2026-37-13

The primary limitation of the method is the deviation of the tool trajectory from the design path due to various factors, such as soil heterogeneity and positioning inaccuracies. This restricts the application of the method to short distances of up to 15–20 m.

To improve puncture accuracy, trajectory correction of the working body is proposed through adaptation of the tip (head) geometry.

In the event of deviation from the design trajectory, a tip with an asymmetric geometry is employed, generating a controlled imbalance of interaction forces with the soil. This enables purposeful control of the head motion during puncturing, allowing trajectory correction without interrupting the process and without additional intervention in the system.

The conducted research resulted in the development of a mathematical framework, including corresponding equations for trajectory correction of the working body. Key parameters such as soil type, its physical properties, and the inclination angle of the tip were taken into account. The obtained relationships allow prediction of system behavior and provide the capability to improve puncture accuracy under various operating conditions.

Analysis of experimental data showed that the largest trajectory deviations occur at smaller inclination angles of the tip, whereas with increasing angle this effect gradually decreases. In addition, clay soils exhibit the smallest deviations compared to other soil types. In particular, at a distance of 10 m and an inclination angle of 25°, the deviation in sandy loam was about 40 mm, while in clay it was approximately 20 mm. When the angle increases to 55°, these values decrease to 14 mm in sandy loam and 13 mm in clay, respectively. Further increase of the angle to 70° demonstrated that the influence of the inclination angle becomes negligible and no longer significantly affects trajectory deviation. At the same time, the discrepancy between experimental results and theoretical calculations does not exceed 15%, indicating sufficient accuracy of the proposed model and confirming its adequacy under real operating conditions.

The obtained results open new opportunities for improving the accuracy and efficiency of underground utility installation. In particular, they enable an increase in puncture length without loss of process controllability and expand the applicability of the static puncture method in complex engineering-geological conditions, ensuring more reliable and predictable execution of operations.