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Instability and pillar burst mechanism in roof-pillar system with rock beam embedded in elastic foundation

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Abstract

Pillar burst depends not only on the pillar itself but also on other components of the roof-pillar system. Instability theory is applied to optimize the critical condition of pillar instability, thus minimizing the likelihood of a pillar burst event. The instability mechanism and evolution process of a pillar burst for a rock beam embedded in an elastic foundation (EF) are investigated. The unmined orebody (UMO) is considered to be an EF; the pillar’s strain-softening behavior is described by a Weibull distribution. Pillar burst events occur in the post-peak strain-softening stage of the pillar and are mainly dependent on the pillar strength and stiffness ratio rK of the UMO-roof-pillar system. The EF coefficient kf reflecting the UMO property is an important factor affecting rK. The maximum deviation of rK reaches up to 198% when the UMO is regarded as a rigid foundation (RF), which emphasizes the importance of kf in terms of overall system instability. A typical case of partial pillar recovery is simulated to demonstrate that EF hypothesis accurately reflects the UMO response in such a system. The instability conditions obtained by simulation analysis are consistent with the theoretical results. The instability of the UMO-roof-pillar system is the result of many factors, among which the thickness hb and span l of the rock beam are extremely sensitive. The lateral pressure coefficient does not significantly affect pillar instability and can be neglected to some extent. The pillar burst evolution process can be divided into a stability stage, subcritical instability stage, instability stage, and post-instability stage.

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Abbreviations

EF:

Elastic foundation

RF:

Rigid foundation

UMO:

Unmined orebody

k f :

Elastic foundation coefficient

E b, I :

Young’s modulus and inertia moment of beam, respectively

w o :

Width of open stope (or room)

w p, h :

Width and height of pillar, respectively

h b, l :

Thickness and span of rock beam (or hard roof), l = wo + wp/2

q :

Uniform load acting on beam

λ:

Lateral pressure coefficient

P :

Horizontal force acting on roof, P = λqhb

F :

Force of roof acting on pillar

R :

Pillar supporting force against roof

M A, R A :

Bending moment and shear force of beam at point A, respectively

E :

Young’s modulus of pillar

k :

Initial stiffness of pillar

A :

Cross-sectional area of pillar

σ,ε :

Stress and strain

ε 0 :

Average strain

m :

Shape parameter of pillar

u :

Deformation of pillar

u 0 :

Deformation value corresponding to pillar peak strength when m = 1

u t = 2u 0 :

Deformation value at inflection point of F–u curve.

y 1, y 2 :

Deflections of beam when x < 0 and 0 < x < l respectively (Fig. 1b)

C 1 ~C 6 :

Undetermined coefficients defined in Eq. (5)

α, β, γ :

Parameters defined as Eq. (6)

K, b :

Parameters defined in Eq. (11), K is local stiffness of beam midpoint

u j, u s :

Starting point and ending point of sudden jump (instability)

\( {u}_s^{\prime } \) :

Previously reported ending point of sudden jump

W st :

Elastic strain energy stored in pre-peak range of the pillar

W sf1 :

Pillar dissipated energy between peak point and instability starting point

W sf2 :

Dissipated energy during pillar instability process

W cf :

Rockburst energy index

ΔW :

External work acting on pillar during pillar instability process

ΔE :

Excess energy not completely dissipated during pillar instability process

K C :

Post-peak stiffness of pillar

r K :

Stiffness ratio of system defined as Eq. (12)

PFS:

Panel factor of stability, PFS = rK

FOS:

Factor of safety

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Funding

This study was supported by China Postdoctoral Science Foundation (No. 2018M641706), National Science Foundation of China (No. 51904057), Fundamental Research Funds for Central Universities of China (No.170104026), and Zhejiang Collaborative Innovation Center for Prevention and Control of Mountain Geological Hazards (No. PCMGH-2017-Y-04).

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Authors and Affiliations

  1. Center for Rock Instability and Seismicity Research, School of Resource and Civil Engineering, Northeastern University, Shenyang, 110819, China

    Xinrong Wang, Kai Guan & Xige Liu

  2. Department of Civil Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang, 312000, China

    Jie Liu

  3. Zhejiang Collaborative Innovation Center for Prevention and Control of Mountain Geological Hazards, 508 Huancheng West Road, Shaoxing, Zhejiang, 312000, China

    Jie Liu

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  1. Xinrong Wang
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Correspondence to Xige Liu.

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Wang, X., Guan, K., Liu, J. et al. Instability and pillar burst mechanism in roof-pillar system with rock beam embedded in elastic foundation. Bull Eng Geol Environ 80, 2447–2459 (2021). https://doi.org/10.1007/s10064-020-01991-9

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