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Mathematical Modeling of Stress-Strain Evolution in the Rock Mass around a Mine Opening. Evaluation of the Steps of First Roof Caving at Different Thicknesses of the Main Roof

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Abstract

Intensive mining activity has highlighted the need to study the dynamics of rock mass elements and to assess the degree of their nonequilibrium. The roof, floor, pillars, gateways, and so on are in a highly nonequilibrium state due to difficult mining conditions and high face advance rates. A good tool for predicting the mechanical behavior of the rock mass during mining is mathematical modeling, which is based on the solution of dynamic problems taking into account the nonequilibrium and nonstationary deformation and failure of rocks. In this paper, dynamic modeling has been performed within an evolutionary framework to investigate the steps of first caving in a model rock mass during face advance. All other things being equal, the thickness of the main coal seam roof is varied in the calculations. The steps of first caving are evaluated in the conditions of highly nonstationary deformation of the rock mass. The fluctuation statistics of the stress-strain parameters of the rock mass is analyzed. It is shown that the first roof caving is preceded by a fall in the slope of the amplitude-frequency curve of stress fluctuation.

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Abbreviations

ρ0, ρ:

reference and current densities of the material

V 0, V :

reference and current volumes of the material

v 0 :

velocity vector components

P :

pressure

σij :

stress tensor components

S ij :

deviatoric stress tensor components

F i :

mass force vector components

\({{\rm{\dot \omega}}_{ij}}\) :

velocity vector rotor

δij :

Kronecker symbol

\({\rm{\dot \lambda}}\) :

plastic factor

\({\rm{\dot \varepsilon}}_{ij}^{\rm{T}}\) :

strain rate tensor components

J 1 :

first invariant of the stress tensor

J 2 = 1/2 S ij S ij :

second invariant of the deviatoric stress tensor

\({\rm{\dot \varepsilon}}_{ij}^{\rm{p}}\) :

inelastic strain rate tensor components

\({{\rm{\dot \theta}}}^{\rm{T}}\) :

volumetric strain rate

\({{\rm{\dot \theta}}}^{\rm{p}}\) :

volumetric inelastic strain rate

K :

bulk modulus

μ:

shear modulus

α:

internal friction factor

Λ:

dilatancy factor

g(σij):

plastic potential

D :

damage measure

H(x):

Heaviside function

σi :

stress tensor intensity

\({\rm{\sigma}}_0^{\rm{c}}\), \({\rm{\sigma}}_0^{\rm{t}}\) :

initial stresses at the elastic stage after which the material accumulates damages in the compression and tension regions, respectively

μσ :

Lode parameter

σ0* :

parameter of the damage accumulation model

S 1, S 2, S 3 :

principal values of the deviatoric stress tensor

σzz :

stress tensor component, with the axis coincident with the gravity direction

σxx, σyy :

the other two diagonal stress tensor components

γ:

bulk specific gravity of rocks

H :

depth

ξ:

lateral pressure coefficient

σC :

relative Coulomb stress

Y :

cohesion-related constant

L g :

first caving step

L d :

damage dome height

H*:

main roof thickness.

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Funding

This work was granted by the Russian Science Foundation, grant No. 19-71-00083.

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Authors and Affiliations

  1. Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia

    M. O. Eremin & P. V. Makarov

  2. National Research Tomsk State University, Tomsk, 634050, Russia

    P. V. Makarov

Authors
  1. M. O. Eremin
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  2. P. V. Makarov
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Correspondence to M. O. Eremin.

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Russian Text © The Author(s), 2018, published in Fizicheskaya Mezomekhanika, 2018, Vol. 21, No. 2, pp. 80–88.

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Eremin, M.O., Makarov, P.V. Mathematical Modeling of Stress-Strain Evolution in the Rock Mass around a Mine Opening. Evaluation of the Steps of First Roof Caving at Different Thicknesses of the Main Roof. Phys Mesomech 22, 287–295 (2019). https://doi.org/10.1134/S1029959919040040

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