Construction of a mathematical model of dynamic loads in a jib self-propelled crane when pulling a sheet pile out of the ground

The object of this study is the process of extracting sheet piles from the ground using a jib self-propelled crane for their repeated use. The task addressed was the extraction of steel sheet piles by a jib self-propelled crane, its interaction with the vibratory pile driver, and the determination of dynamic loads. The vibratory method significantly increases extraction efficiency; however, it also induces vibrational impacts on the crane, causing alternating stresses in the metal structure. This could lead to fatigue damage accumulation, cracks in weld seams, failure of base metal, and a decrease in the service life of the self-propelled crane. Furthermore, vibration negatively affects the working conditions of crane operators by causing fatigue, reducing performance, and compromising safety. Mathematical modeling methods were used, with the construction of calculation schemes that reflect all stages of sheet pile extraction: preliminary insertion, taking up slack in the lifting system, tensioning the lifting ropes, extraction with vibration over 2/3 of the pile’s length, and final extraction without vibration. Numerical modeling has shown that during static extraction, the dynamic coefficient may reach 4.76, while with vibration it decreases to 1.47. This confirms the effectiveness of the vibratory method, provided its adverse effects on the crane are minimized. The results could be applied to improve crane design, devise protective measures against vibration, and enhance operational efficiency and safety. Additionally, the findings could become a basis for optimizing the parameters of elastic ties and the interaction scheme between the crane and the ground, thereby expanding the potential for model’s practical application under more complex conditions