Study on Dynamic Characteristics of Circular Tunnel Lining in Fractional Derivative Viscoelastic Radially Inhomogeneous Soil

Abstract

Considering the heterogeneous and viscoelastic characteristics of the soil around the tunnel, the dynamic characteristics of circular tunnel lining in fractional derivative viscoelastic radially inhomogeneous soil are studied. To accurately describe the viscoelasticity of the soil around the circular tunnel, the fractional derivative viscoelastic model is used to describe the stress-strain relationship of the soil. To consider the heterogeneous characteristics of the soil around the circular tunnel caused by construction and in situ stress, the soil around the tunnel lining is divided into undisturbed area and disturbed area, and the disturbed area is divided into multiple thin concentric rings. A dynamic interaction model of fractional derivative viscoelastic radially inhomogeneous soil-circular tunnel lining is established. By solving the vibration of the soil in undisturbed area and each circle and considering the continuity conditions of the radial displacement and radial stress of the soil at the junction of each circle, the transfer matrix of the radial displacement and radial stress of the soil at the outer and inner boundaries of disturbed area is obtained. Based on the transfer matrix of the radial displacement and radial stress of soil in the disturbed area and considering the boundary conditions and continuity conditions of the problem, the solution of the dynamic response of circular tunnel lining in fractional derivative viscoelastic radially inhomogeneous soil is obtained in the frequency domain. The results show that the fractional derivative viscoelastic inhomogeneous soil-circular tunnel lining system also has resonance under the action of simple harmonic internal pressure, and the curves of the radial displacement and radial stress of soil varying with frequency obtained by the fractional derivative viscoelastic model fluctuate greatly. When studying the dynamic response of circular tunnel lining in inhomogeneous soil, the influence of viscoelasticity of the soil around the tunnel should not be ignored. The shear modulus ratio of soil in the affected area around the tunnel has a great influence on the dynamic characteristics of circular tunnel lining in fractional derivative viscoelastic radial inhomogeneous soil, and the inhomogeneous characteristics of soil should not be ignored. The greater the thickness and shear modulus of the tunnel lining, the greater the stiffness of tunnel lining and the smaller the radial stress and radial displacement of the soil.