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Creep Failure of Roof Stratum Above Mined-Out Area

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Abstract

By taking into account the rheological behavior of the rock mass, the creep failure of a roof stratum seated on pillars in mined-out area is analyzed through a newly developed visco-elastic model. The time-dependent deflection of the roof stratum is obtained by numerical inversion of Laplace transform. The study shows that when creep properties of both the pillars and roof stratum are considered, the expected deflection in the roof stratum increases with time. Consequently, the roof would fail when the critical tensile stress is reached as the result of the increased deflection. To demonstrate the present analytical procedure, the failure time of roof stratum of the Xingtai Gypsum Mine in China was estimated, and the results obtained agreed with the observation. The case study indicates that the analytic approach provides a new way to assess the potential impact of the time-dependence of the roof stratum deformation and is useful in predicting its stability above a mined-out area.

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Abbreviations

a, b, h :

Half of length, half of width, and thickness of the roof stratum

α, β:

Coefficients of regression

A, H, D :

Area of the

δ:

Plastic constraint

Ep, Er :

Young’s modulus of the pillar and the roof

η1, η2, k1, k2 :

Coefficients viscosity and elasticity modulus for Burgers model

P, Q, P1, Q1, P2, Q2 :

Linear operators with respect to time

Pr1(s), Qr1(s), Pr2(s), Qr2(s):

Linear operators with respect to Laplace variable for associated with the roof

p 0, p 1, p 2, q 0, q 1, q 2,:

Material constants

s :

Transform variable

σ p :

Critical strength of the pillar

σ:

Average strength of the pillar

w 0, w 0 :

Deflection at the center of the plate in terms of time and transform variable respectively

ζ:

Ratio of the accumulated cross area of pillars to total mined out area

\(\hat{\sigma },\hat{\varepsilon }\) :

Transformed stress and strain

σ ii , ε ii , s ij, d ij :

Spherical stress, spherical strain, deviatoric stress, and deviatoric strain respectively

[σt], σc :

Tensile strength and uniaxial compressive strength of the rock mass

σ xmax :

Maximum stress in x-direction

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Acknowledgments

The presented work has been financially supported by the State Key Foundation Research (973 Project) granted by the Ministry of China Science and Technology (No. 2010CB731500). Prof. M. Kwaśniewski from the Silesian Technical University, Poland, and Prof. Lin Jeen-Shan from the University of Pittsburgh, USA, have provided their kind help in modification of the manuscript, which are gratefully acknowledged.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, University of Science and Technology Beijing, Xueyuan Road 30, Haidian District, Beijing, 100083, China

    J. -A. Wang

  2. Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    D. Z. Li

  3. School of Applied Science, University of Science and Technology Beijing, Xueyuan Road 30, Haidian District, Beijing, 100083, China

    X. C. Shang

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  1. J. -A. Wang
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Wang, J.A., Li, D.Z. & Shang, X.C. Creep Failure of Roof Stratum Above Mined-Out Area. Rock Mech Rock Eng 45, 533–546 (2012). https://doi.org/10.1007/s00603-011-0216-8

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