An analytical design method for ductile support structures in squeezing tunnels
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(2020) 20:91
ORIGINAL ARTICLE
An analytical design method for ductile support structures in squeezing tunnels Kui Wu1,2 · Zhushan Shao1,2 · Su Qin1,2 Received: 23 April 2020 / Revised: 30 June 2020 / Accepted: 13 July 2020 © Wroclaw University of Science and Technology 2020
Abstract Ductile linings have been proved to be highly effective for tunnelling in heavy squeezing grounds. But there still has not been a well-established design method for them. In this paper, an investigation on an analytical design method for ductile tunnel linings is performed. Firstly, a solution in closed form for ground response of a circular tunnel within Burgers viscoelastic rocks is derived, accounting for the displacement release effect. Then based on the principle of equivalent deformation, the mechanical model of segmental shotcrete linings with yielding elements is established using the homogenization approach. Analytical prediction for behaviour of ductile tunnel linings is provided. Furthermore, the proposed design method for ductile tunnel linings is applied in Saint Martin La Porte access tunnel and the analytical prediction is in good agreement with field monitoring data. Finally, a parametric investigation on the influence of yielding elements on performance of ductile tunnel linings is conducted. Results show that the length of yielding elements poses a great influence on linings. It is feasible and effective to increase the length of yielding elements to obtain the pressure within the bearing capacity of linings. However, yield stress of yielding elements does not significantly affect the performance of the lining. It is suggested to apply yielding elements with relatively higher yield stress in linings for higher stability. Keywords Squeezing tunnel · Ductile lining · Analytical design method · Engineering application · Parametric investigation List of symbols 𝜎, 𝜎r , 𝜎𝜃 Compression stress, radial and tangential stresses, respectively 𝜎𝜃 Mean tangential stress 𝜎y Yield stress of yielding element 𝜀, 𝜀lim Strain and limit strain of yielding element, respectively sij Tensor of stress deviator eij Tensor of strain deviator G1 , G2 Elastic constants of Hookean spring 𝜂1 , 𝜂2 Viscous coefficients of Newtonian dashpot Electronic supplementary material The online version of this article (https://doi.org/10.1007/s43452-020-00096-0) contains supplementary material, which is available to authorized users. * Zhushan Shao [email protected] 1
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
Shaanxi Key Lab of Geotechnical and Underground Space Engineering (XAUAT), Xi’an University of Architecture and Technology, Xi’an 710055, China
2
𝜆 Lateral pressure coefficient Ak , Bk Coefficients in Burgers constitutive equation, respectively A, A1 , A2 Cross-sectional area, cross-sectional areas of segmental lining and steel pipes, respectively C1 , C2 , D1 , D2 Coefficients related with Poisson’s ratio of rock E1 , E2 , E∗ Elastic moduli of shotcrete, yielding
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