Theoretical Analysis of the Jacking Force During the Vertical Pipe Jacking Process

With the growing scarcity of surface space, underground development has become essential for expanding human living space. Among various tunneling methods, pipe jacking stands out due to its economic advantages and minimal environmental impact. Recently, vertical pipe jacking has been explored as an innovative technique for constructing shafts that connect horizontal tunnels to the ground surface. However, the evolution of jacking force during vertical pipe jacking with increasing jacking distance remains poorly understood. Understanding this evolution is critical for selecting jacking equipment, designing the horizontal tunnel lining against reaction forces, and preventing construction failures. Unlike horizontal pipe jacking where self-weight is negligible, the proposed model reveals that in vertical pipe jacking the self-weight of the pipe and machine above the excavation face increases with jacking distance while the overburden pressure decreases, resulting in a parabolic-like jacking force trend—a novel finding not reported in previous pipe jacking literature. This paper proposes theoretical formulas to quantify the three components constituting the jacking force: face resistance at the cutting head, frictional resistance along the pipe surface, and the dead weight of the machine and pipe above. The influence of jacking distance on each component is systematically analyzed. Parametric studies under standard and varied conditions reveal that under standard conditions, jacking force follows a parabolic trend—rapid initial increase, followed by slower growth, and eventually a slight decrease. The maximum jacking force consistently occurs at L = L0 − 1 m, identifying the most unfavorable construction stage where special attention to tunnel lining deformation is required. Increasing outer diameter transitions the force curve from quasi-parabolic to “half diamond” shape, while doubling the friction coefficient approximately doubles the jacking force. These findings provide practical guidelines for vertical pipe jacking design and construction, including equipment capacity selection, friction reduction strategies, and monitoring priorities.