Search

In this paper, we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results. [ABSTRACT FROM AUTHOR]

In this paper, a novel numerical simulation approach based on the finite element method for dynamically modeling the excavation process of shield tunneling is proposed, with the shield-ground interactions well captured. This method is capable of mimicking the alternating modes of advancing and stopping of a shield boring machine during underground construction, with the important effects of the cutterhead rotation and slurry support pressure considered. Under the cutting action, the soil at the excavation face would experience irreversible deformation and damage, such that additional support needs to be provided by the cutterhead blades and slurry to maintain stability. The impacts of key construction parameters are examined, including cutterhead rotary speed, advance rate, and slurry support pressure, on shield tunneling operations and ground responses. The numerical model is rigorously validated against physical model experiments. This work provides useful insights into the mechanistic processes in the stratum during shield tunneling, including the spatiotemporal evolution of ground deformation patterns and stress redistributions. The results offer valuable guidance for optimizing shield tunneling operations and enhancing tunneling safety and efficiency. [ABSTRACT FROM AUTHOR]