The mechanical behavior of pipe umbrellas in loess tunnels

An analytical method is presented for the pipe umbrella in deep buried loess tunnels. The pipe umbrella is assumed to be an Euler–Bernoulli beam supported on a Pasternak foundation. The analytical formulas for the displacement and internal forces of the pipe umbrella were derived. The initial displacement is introduced into the model to characterize the influence of initial support stiffness, and the load transfer coefficient is used to evaluate the advanced support effect of the pipe umbrella. By analyzing and contrasting with existing research results and three-dimensional numerical simulation results of real-world engineering, the reliability of the proposed method is verified, and good agreements are observed. The grouting reinforcement effect on the mechanical behavior of the pipe umbrella in loess strata was discussed. The influence of pipe umbrella design parameters, loess surrounding rock stiffness, and excavation footage on the maximum displacement and load transfer coefficient was studied using analytical formulas. There exists an optimal excavation footage that can maximize the load-bearing capacity of the pipe umbrella. For the engineering case in this article, the optimal excavation footage is 1.0 m, and the load transfer coefficient reaches the minimum value of 0.46.