Numerical modeling of seismic wave impact on enclosing rock mass surrounding underground structures

Currently Hanoi, the capital city of Vietnam, is solving the problem connected with traffic congestion thanks to the designed and built metro system. Some infrastructure objects of the metro are situated at a depth down to 20 m below ground surface. In order to ensure safe and reliable operation of underground structures, it is required to estimate impact of seismic waves induced by earthquakes. Modern Vietnam occupies the north and northeast of the Sunda Plate which is a seismically active structure. In the mid-1980s many Richter magnitude 5–8 earthquakes were recorded within the boundaries of the city agglomeration of Hanoi, which damaged some buildings and structures on ground surface. It is important and relevant to undertake and compare in-situ measurement and numerical modeling of seismic wave impacts on underground structures of the Hanoi Metro. Solution of such geodynamic problem at a certain confidence of the result uses the developed and approved numerical-and-analytical approach (modification of a known method) which includes influence of junctions in the metro tunnel lining in calculation. Mathematical modeling describes the behavior of the main stress state parameters in the tunnel lining in the Hanoi Metro, and enables justification of the choice of both lining material and lining parameters with regard to the impact of seismic waves generated by earthquakes. Drilling in mines also induces adverse seismic waves which can cause deformation and disintegration in enclosing rock mass surrounding various-purpose underground openings. For instance, surface mine operations at the Hanoi apatite–nepheline deposit involves drilling and blasting connected with high energy release. The latter provokes considerable stresses and straining which directly affect safety and stability of underground openings. In this respect, it is necessary to develop and improve universal methods of numerical and mathematical modeling and to create computing systems on this basis. This article describes the developed mathematical modeling of blasting-induced seismic wave impact on a nonuniform enclosing rock mass surrounding an underground tunnel. Application of Godunov’s splitting using the authors’ numerical algorithm made it possible to design a computer program for the numerical modeling of geodynamic processes towards safety and integrity of underground structures during drilling and blasting.

Keywords: stress state, Hanoi Metro, drilling and blasting, seismic waves, in-situ measurements, numerical modeling, computation program, prediction of blasting-induced and seismic wave impact on underground structures.
For citation:

Gospodarikov A. P., Zatsepin M. A., Ya.N. Vykhodtsev, Nguen C. T. Numerical modeling of seismic wave impact on enclosing rock mass surrounding underground structures. MIAB. Mining Inf. Anal. Bull. 2022;(7):116-130. [In Russ]. DOI: 10.25018/0236_1493_ 2022_7_0_116.


The study was supported under the state contract for scientific research in 2021, Contract No. FSRW-2020-0014.

Issue number: 7
Year: 2022
Page number: 115-130
ISBN: 0236-1493
UDK: 622.235.535.2
DOI: 10.25018/0236_1493_2022_7_0_115
Article receipt date: 24.12.2021
Date of review receipt: 20.04.2022
Date of the editorial board′s decision on the article′s publishing: 10.06.2022
About authors:

A.P. Gospodarikov1, Dr. Sci. (Eng.), Head of Chair, e-mail:, ORCID ID: 0000-0003-1018-6841,
M.A. Zatsepin1, Cand. Sci. (Phys. Mathem.), Assistant Professor, e-mail:, ORCID ID: 0000-0002-6304-8349,
Ya.N. Vykhodtsev, Cand. Sci. (Eng.), Senior Engineer Programmer, T-Systems Multimedia Solutions, Saint-Petersburg, Russia, e-mail:,
C.T. Nguen, Cand. Sci. (Eng.), Assistant Professor, Institute of Marine Geology and Geophysics, Hanoi University of Mining and Geology, Hanoi, Vietnam, e-mail:,
1 Saint-Petersburg Mining University, 199106, Saint-Petersburg, Russia.


For contacts:

Zatsepin M.A., e-mail:


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