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The Longitudinal Deformation Profile of a Rock Tunnel: An Elastic Analysis

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  • Yonghong Wang
  • Wen Du
  • Guohui Zhang
  • Yang Song

Abstract

The longitudinal deformation profile (LDP) is the profile of wall displacement versus the distance from the tunnel face. To develop LDP equations, numerical methods and in situ experiments have been used to obtain the deformation of a tunnel in three-dimensional space. However, extant approaches are inadequate in terms of explaining the mechanical relation between the wall displacement and the conditions of a tunnel (e.g., properties of rock). In this paper, an analytical approach is proposed to develop a new LDP equation. First, on the basis of the axisymmetric elastic model of a tunnel, a closed-form solution of wall displacement is derived. Then, a new LDP equation is presented according to the solution developed above; the coefficient β , defined as the ratio of the effective range of the “face effect” to the radius of the tunnel, is proposed for the first time. Finally, a case study is proposed to validate the practicability of this equation.

Suggested Citation

  • Yonghong Wang & Wen Du & Guohui Zhang & Yang Song, 2021. "The Longitudinal Deformation Profile of a Rock Tunnel: An Elastic Analysis," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, April.
    • Handle: RePEc:hin:jnlmpe:6684035
    DOI: 10.1155/2021/6684035
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