Analytical solutions of vertical load on deep rectangular jacked pipe considering tunnelling-induced ground loss

Abstract

Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force, especially for deep-buried pipes. To better reflect the soil arching effect resulting from the excavation of rectangular jacked pipes and the distribution of the earth pressure on jacked pipes, we present an analytical solution for predicting the vertical earth pressure on deep-buried rectangular pipe jacking tunnels, incorporating the tunnelling-induced ground loss distribution. Our proposed analytical model consists of the upper multi-layer parabolic soil arch and the lower friction arch. The key parameters (i.e., width and height of friction arch B and height of parabolic soil arch H1) are determined according to the existing research, and an analytical solution for Kl is derived based on the distribution characteristics of the principal stress rotation angle. With consideration for the transition effect of the mechanical characteristics of the parabolic arch zone, an analytical solution for soil load transfer is derived. The prediction results of our analytical solution are compared with tests and simulation results to validate the effectiveness of the proposed analytical solution. Finally, the effects of different parameters on the soil pressure are discussed.

1. Introduction

The development of underground transportation infrastructure has emerged as a critical solution to reconcile the conflict between urban economic expansion and traffic congestion challenges [1−4]. Among modern trenchless technologies, rectangular pipe jacking has gained prominence in constructing utility tunnels and subsurface passageways due to its superior spatial efficiency, economic viability, and rapid construction timelines [5−7]. A fundamental requirement in rectangular pipe jacking operations is maintaining sufficient jacking force to overcome both frictional resistance along the pipe periphery and face resistance at the excavation front, thereby ensuring continuous advancement. Notably, frictional resistance, predominantly governed by the circumferential earth pressure distribution along the pipe-soil interface, constitutes the primary component of total jacking force consumption [8, 9]. This underscores the critical importance of accurate earth pressure prediction for reliable jacking force estimation and equipment selection in engineering practice [10, 11].

Scholars have conducted model tests and numerical studies to determine the earth pressure above tunnels [12−19]. These studies offer valuable insights into the soil-tunnel interaction and serve as a solid foundation for establishing theoretical models. Based on model tests, TERZAGHI [20] built a widely used model for predicting vertical earth pressure on shallow tunnels. However, some key parameters in Terzaghi’s formula, such as loosened zone width and lateral pressure coefficient, are empirical and challenging to determine. As a result, many researchers have modified these parameters based on model tests and numerical analysis [21, 22]. While improvements have been made to Terzaghi’s theory for shallow-buried tunnels, the focus has mainly been on tunnels where the loosened soil zone extends to the ground surface. In contrast, JACOBSZ [23] discovered that a damage zone exists in the soil without extending to the surface in deep-buried tunnels. Consequently, researchers have further studied the damage zone height based on the existing research for shallow-buried tunnels to accurately calculate soil load on deep-buried tunnels. For example, according to simulation results, the damage region height is considered 0.75 times the tunnel diameter [24]. In fact, the damage region height is determined by several parameters, including ground loss and volume bulking factors. ZHANG et al [25] derived an equation to calculate the height of the shearing bands caused by circular pipe jacking machine.