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A Modified Stress-Displacement Solution for a Pressure Tunnel with a Permeable Liner in an Elastic Porous Medium Based on a New Model

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Abstract

Referring to previous literature, the elastic problem for a deep pressure tunnel with a permeable liner in a saturated elastic porous medium that obeys Terzaghi’s effective stress principle is further investigated. In the analysis, the influences of the changes of the pore water pressure around the opening, the construction sequence of the tunnel, and the interaction between the liner and the surrounding geomaterial on the mechanical response of the tunnel are appropriately considered. Also, the influences of the relative liner thickness and rigidity and the relative distance of the point under investigation from the tunnel axis on the stress-displacement fields for various combinations of the mechanical and geometric parameters are numerically evaluated and discussed. The results indicate that both the support pressure and displacement increase monotonically with increasing liner rigidity and thickness. The influence of the tunnel excavation upon the displacement field is significantly larger than upon the stress field. Either too high or too low values for the relative rigidity and thickness of the liner are unfavorable for structural stability.

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Abbreviations

a, b :

Inner and outer radii of liner

b″′, b″, b′:

Radii of the opening immediately after excavation, after the elastic deformation finishes, and before the liner is installed

E j :

Young’s modulus

G j , λ j :

Lamé’s elastic parameters

N s, M s, Q s :

Axial thrust, bending moment, and shear force of liner

p i :

Uniform internal pressure at the inner boundary of tunnel

p s :

Support pressure

r, θ :

Polar coordinates

u r :

Radial displacement in polar coordinates

\( u_{\text{s}}^{\text{r}} \) :

Support radial displacement in polar coordinates

x, y, z :

Cartesian coordinates

β :

Dimensionless variable defined by b/r

γ j :

Poisson’s ratio

Г:

Relative rigidity of liner

δ :

Elastic deformation rate

η :

Relative radius misfit between the surrounding geomaterial and the liner

σ :

Total normal stress

σ′:

Effective normal stress

σ r, σ θ :

Radial and tangential stresses in polar coordinates

\( \sigma_{\text{r}}^{\prime } ,\sigma_{\theta }^{\prime } \) :

Effective radial and tangential stresses in polar coordinates

\( \sigma_{\text{o}} ,\sigma_{\text{w}}^{\text{o}} \) :

Total stress and pore water pressure in geomaterial prior to excavation

σ w :

Pore water pressure

\( \sigma_{\text{w}}^{\text{b}} \) :

Pore water pressure at the outer boundary of liner

\( \sigma_{\text{w}}^{\text{e}} \) :

Uniform hydraulic pressure acting on the periphery of tunnel as the result of water inside tunnel

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Acknowledgments

The authors deeply appreciate the financial support by the Project of Shandong Province Higher Educational Science and Technology Program (grant no. J11LE03), the Natural Science Foundation of Shandong Province (grant no. ZR2012EEM010), the Natural Science Foundation of China (grant no. 51009086; 41002098), the Project supported by the Doctoral Foundation of Ludong University (grant no. LY2011013), the Research Award Fund for Outstanding Middle-Aged and Young Scientist of Shandong Province China (grant no. BS2010HZ015), and the Program for Changjiang Scholars and Innovative Research Team in University (grant no. IRT0843).

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Authors and Affiliations

  1. School of Civil Engineering, Ludong University, Yantai, 264025, People’s Republic of China

    M. B. Wang

  2. State Key Laboratory of Mine Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    G. Wang

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  1. M. B. Wang
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  2. G. Wang
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Correspondence to M. B. Wang.

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Wang, M.B., Wang, G. A Modified Stress-Displacement Solution for a Pressure Tunnel with a Permeable Liner in an Elastic Porous Medium Based on a New Model. Rock Mech Rock Eng 46, 259–268 (2013). https://doi.org/10.1007/s00603-012-0283-5

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