Analytical method for structural analysis of segmental lining interaction with nonlinear surrounding soil and its application in physical test interpretation

Abstract

The bedding beam method, in which a series of springs are employed to simulate the interaction between the segmental lining and surrounding soils, is efficient and widely used in the preliminary design of tunnel linings. Existing methods for determining the stiffness of the springs are linearly elastic or empirical. Soils exhibit significant nonlinear behavior, and their nonlinearity has been extensively described based on laboratory tests using nonlinear stiffness curves degraded with the shear strain. However, the influence of the nonlinear behavior of the surrounding soil has been rarely considered in analytical solutions, and the application of the nonlinear soil stiffness curves in the bedding beam method is somewhat limited. The aim of this study is to develop a calculation method combined with nonlinear soil stiffness curves for describing the lining–surrounding soil interaction in tunnel lining analysis and design. First, a multilayer-annulus model with strain-dependent soil stiffness was established. The cavity expansion theory was then applied to derive the relationship between the lining deformation and the strain field of soil using a typical nonlinear soil stiffness curve. An explicit equation for the spring stiffness coefficient of the soil was derived and introduced into the well-established state-space method for segmental linings. The responses of the segmental lining interacting with the nonlinear surrounding soil were solved. Finally, the analytical solution was verified through comparison with the results obtained using other methods, and also used to interpret the results of both laboratory model test and field test. The main advantages of the proposed method include high calculation efficiency, rapid convergence, and a more realistic lining–soil interaction.