, Volume 54, Issue 1–2, pp 223–238 | Cite as

A new analytical approach for a shallow circular hydraulic tunnel

  • Aizhong Lu
  • Hui CaiEmail author
  • Shaojie Wang


An analytical solution is presented for a shallow circular hydraulic tunnel excavated in an elastic rock mass with gravity by a new approach. Through the stress boundary condition on the ground surface, the relationship between the two analytic functions can be directly given. Thus, only one analytic function should be considered in the solving process. Based on the stress boundary condition on the excavated boundary, the analytic function is solved by power series method. The solving process is much simpler than ever. The excavation process and unbalanced force system acting on the tunnel boundary are considered by a complex potential function with logarithmic term. Through the conformal mapping method in complex variable, the basic equations for solving the stresses and displacements are obtained according to the stress boundary condition on the tunnel boundary. The examples are presented under the different coefficients of horizontal stress, tunnel depths and water head heights.


New approach Shallow Hydraulic tunnel Stress Displacement 



This study was funded by the Natural Science Foundation of China (Grant Numbers 11172101; 11572126).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Hydroelectric and Geotechnical EngineeringNorth China Electric Power UniversityBeijingChina

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