# Solution of nonuniform and nonlinear axially symmetric problem on confining pressure in the presence of post-limiting zones using logarithmic strains

The article describes solution of nonlinear problems on the stress–strain behavior of enclosing rock mass around a long horizontal tunnel. The dedicated numerical method combines nonlinear programming and the explicit method of finite differences. The stress–strain behavior of rock mass governs the pressure and the radial displacement of the tunnel boundary, which in their turn depend on the size of post-limiting strain zone. The problem on the confining pressure is solved by search of values of post-limiting strain zone sizes. The nonuniformity of rock mass in the radial direction from the tunnel center, and the stress history are included. The methods to define the problem parameters for a weak rock mass are presented. A case-study of a real-life mine excavation is described. It is shown that there exists an optimal displacement zone of roof support with the preset load-bearing capacity. The simplified assumptions in the confining pressure problem are assessed. It is required to limit relative volumetric strain in the adjacent rock mass of the tunnel in the problems on confining pressure. The solutions obtained using logarithmic strains and the Cauchy strains are compared. The use of logarithmic strains considerably improves the stress–strain pattern in the presence of post-limiting zone.

Keywords: rock mass stress–strain behavior, logarithmic strains, elastic strain zone, post-limiting strain zone, explicit method of finite differences, stress history, physical nonlinearity, geometrical nonlinearity, long tunnel, confining pressure.
For citation:

Nemchin N. P., Vetrov S. V. Solution of nonuniform and nonlinear axially symmetric problem on confining pressure in the presence of post-limiting zones using logarithmic strains. MIAB. Mining Inf. Anal. Bull. 2021;(3):83-100. [In Russ]. DOI: 10.25018/0236-14932021-3-0-83-100.

Acknowledgements:
Issue number: 3
Year: 2021
Page number: 83-100
ISBN: 0236-1493
UDK: 622.02
DOI: 10.25018/0236-1493-2021-3-0-83-100
Article receipt date: 27.09.2019
Date of review receipt: 14.04.2020
Date of the editorial board′s decision on the article′s publishing: 10.02.2021

N.P. Nemchin1, Cand. Sci. (Eng.), Assistant Professor, e-mail: nemchin_np@mail.ru,
S.V. Vetrov1, Senior Lecturer, e-mail: eridani_alpha@hotmail.com,
1 Transbaikal State University, 672039, Chita, Russia.

For contacts:

N.P. Nemchin, e-mail: nemchin_np@mail.ru.

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