Analytical Solutions for Long Tunnels Under Arbitrary Dynamic Loadings

Haitao Yu, Chuang Cai, Zhengwei Zhang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Assuming the long lined tunnel as an infinite homogeneous beam resting on a Pasternak foundation, the governing equation of the dynamic problem can be established based on Euler-Bernoulli beam theory. Integration transform and Residue theorem are applied to solve the differential equation, thus the analytical solutions of displacement, velocity, acceleration, bending moment, shear force for long lined tunnels subjected to arbitrary dynamic loads are obtained. The specified solutions for harmonic line loads, moving line loads and travelling loads are discussed and compared with the exiting solutions, and therefore, the validation of the presented generic form of solutions is verified. Taking travelling loads as an example, parametric analyses are performed to investigate the influence of the velocity and frequency of travelling loads and the shear modulus of foundation on the tunnel dynamic responses. The proposed solution is of value for seismic design of long line tunnel.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalTongji Daxue Xuebao/Journal of Tongji University
Issue number1
StatePublished - 1 Jan 2018
Externally publishedYes


  • Analytical solution
  • Dynamic loads
  • Integration transform
  • Long lined tunnel
  • Longitudinal response


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