Analytical study of ground responses induced by the excavation of quasirectangular tunnels at shallow depths

Abstract

Summary The construction of quasirectangular tunnels at shallow depths is becoming increasingly common in urban areas to efficiently utilize underground space and reduce the need for backfilling. To clarify the mechanical mechanism of the stresses and displacements around the tunnels, this study proposes analytical solutions that precisely account for quasirectangular tunnel shapes, the ground surface, the tunnel depth, and the ground's elastic/viscoelastic properties. The Schwarz alternating method combined with complex variable theory is employed to derive the elastic solution, and convergent and highly accurate solutions are obtained by superposing the solutions in the alternating iterations. Based on the solution and the extended corresponding principle for the viscoelastic problem, the time‐dependent analytical solutions for the displacement are obtained for the ground assuming any viscoelastic model. The analytical solutions agree well with the finite element method (FEM) numerical results for models that are completely consistent, and qualitatively agree with field data. Furthermore, based on the stress solution combined with the Mohr‐Coulomb failure criterion, the predicted initial plastic zone and propagation directions around the tunnels are qualitatively consistent with those determined by the limit analysis. A parametric study is performed to investigate the influences of the rectangular/quasirectangular tunnel shape, burial depth, and supporting pressure on the ground stresses and displacements.

An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole

“…The displacement of the anisotropic structure can be determined by substituting the calculated a 0 , c 0 , a k , b k , c k , and d k into equation (17).…”

“…However, for non-circular holes, the lack of a mapping function makes solving the boundary conditions exceedingly challenging. Wang and colleagues [16,17] combined the Schwarz alternating method with the complex variable function method to derive analytical solutions for stress and displacement of elliptical and square shallow-buried tunnels. Furthermore, Lu and colleagues [18,19] proposed a novel form of mapping function that can map a semi-infinite plane with a non-circular hole to a circular ring.…”

Solving Conformal Mapping Issues in Tunnel Engineering

“…From the definition of conformal mapping, it is obvious that the composite function of two conformal mapping functions is still a conformal mapping function. Thus, this transformation can satisfy the computing requirements for the mechanical analysis of multiple shallow cavities [109][110][111][112][113][114].…”

Soil Deformation around a Cylindrical Cavity under Drained Conditions: Theoretical Analysis

“…e soil estimation method can be adapted as a design guide for the initial displacement phase. Moreover, the proposed analytical solutions are classied into four categories: (1) solutions based on complex variables (Verruijt [5]; Strack and Verruijt [6]; Verruijt and Booker [7]; Verruijt and Strack [8]; Wang et al [9]; Fu et al [10]; Fu et al [11]; Zhang et al [12]; Zeng et al [13]), (2) closed-form analytical solution using the virtual image technique on the line sink (Sagaseta [14]; Verruijt and Booker [15]; Loganathan and Poulos [16]; Park [17]; Pinto and Whittle [18]), (3) the solution based on the exact prediction of the middle continues (Liu [19]; Yang et al [20]), and (4) the general solution under the form of the airy stress function in the cartesian and polar coordinates (Bobet [21]; Kooi and Verruijt [22]; Chou and Bobet [23]; Park [17,24]; Pinto [25]). ese analytical solutions focus on the deformation of soils at the boundary condition of underground structures and are obtained in the context of linear elasticity.…”