Abstract
Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n n = E h / E v and m m = G v h / E v have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.
Highlights
Due to the complexity of metro projects, many metro shields use varying cross-sectional shapes for the shield, such as rectangular [1], quasi-rectangular [2, 3], elliptical, horseshoe-shaped, and double-O-tube [4]
Numerical methods can identify the elastic solution for an underground excavation, analytical methods provide important information
Elasticity problems can be solved by combining the complex variable method with numerous theorems arising from analytical functions, such as Cauchy’s integral theorem, Laurent’s theorem, and theorems on conformal mapping [6, 7]. ese theories are widely used for the first fundamental problem of deep tunnels
Summary
Due to the complexity of metro projects, many metro shields use varying cross-sectional shapes for the shield, such as rectangular [1], quasi-rectangular [2, 3], elliptical, horseshoe-shaped, and double-O-tube [4]. Research on tunnels with arbitrary cross sections can guide engineers in predicting ground displacement and underground deformation. Zhang and Sun [10] derived an analytical solution for the radial displacement of an unlined deep tunnel with an arbitrary cross section in transversely isotropic rock using Kolosov–Muskhelishvili complex potentials [11]. Advances in Civil Engineering [12] and Manh [13] proposed closed-form solutions for the stress and displacement around an unlined deep tunnel with an arbitrary cross section in elastic isotropic and anisotropic ground, respectively. Analytical solutions have been developed for ground movements induced by tunnels with a circular cross section in clay by using the complex variable method. Full-plane elastic solutions are proposed for an unlined tunnel with an arbitrary cross section subjected to certain deformation modes. Analytical solutions of displacements in half plane are obtained by using a virtual image technique. e effect of stiffness parameters, n and m, on the distribution of the predicted displacement for an unlined elliptical tunnel is analyzed
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