Earthquake Engineering and Engineering Vibration

, Volume 19, Issue 1, pp 179–188 | Cite as

Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes

  • Thanh Nguyen ChiEmail author
  • Gospodarikov Alexandr


Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some improvements to the use of the Hyperstatic Reaction Method-HRM for analysing tunnels with horseshoe-shaped cross-sections when these tunnels operate under the influence of earthquakes, particularly in cases when the tunnel lining is a continuous lining. The analysis used parameters of a tunnel from the Hanoi metro system, as well as parameters of the strongest earthquake that may occur in the central Hanoi area in the improved HRM and 2D numerical methods using the ABAQUS software. On the basis of the results obtained, the paper gives conclusions about the HRM methodology when it is used to calculate tunnels that have horseshoe cross-sections operating under the influence of earthquakes.


hyperstatic reaction method earthquake horseshoe cross-section impact tunnel 


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This work was supported by the Saint Petersburg Mining University. We thank two anonymous reviewers for their comments that were very valuable for revising the manuscript.


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration 2020

Authors and Affiliations

  1. 1.Saint Petersburg Mining UniversitySaint PetersburgRussian Federation
  2. 2.Faculty of Civil EngineeringHanoi University of Mining and GeologyHanoiVietnam

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