Indices

Equation for evaluation

Determination graph

Bursting liability category

1) Elastic Strain energy index W_ET

(Kidybinski 1981)

$W_{ET}=E_e/E_p$

where is E_e Elastic strain energy and E_p is plastic strain energy ε₁ and ε₀ are the strain at the equivalent unloading level, and the residual strain when the stress is unloaded to 0.

W_ET < 2.0 none

2.0 ≤ W_ET < 5 Weak,

W_ET ≥ 5

2) Impact energy index or bursting index K_E

(TAN Y A. 1992)

$K_E=U_o/U_a$

where U_o is the pre-peak and U_a is the post-peak, ε₁ is the strain at peak strength, and ε₂ is the maximum strain of the coal specimen during UCS tests

K_E < 1.5 none

1.5 ≤ K_E < 5 Weak,

K_E ≥ 5

3) Dynamic Failure time DT

(W.B. Zhang,

S.K. Wang, Y.K. Wu, X.C. Qu 1986)

$DT=T_2-T_1$

When T₁ is the duration from ultimate strength, T₂ is the duration to complete damage of coal specimens

DT > 500, none,

50 < DT ≤ 500, Weak,

DT ≤ 50, strong

4) Uniaxial Compressive Strength (R_C) (K. ZCzeczeńska

D. K. Zuo 1986)

$R_C=P/A$

Where P is the maximum breaking load N, A is the cross-sectional area of the sample

R_C < 7, none,

7 ≤ R_C < 14, weak,

R_C ≥ 14, strong

5) Modulus index

Kλ (Dai et al. 2019)

$K\lambda =\lambda /E$ ,

where λ is the softening modulus of stress-strain curve after peak stress, and E is the elastic modulus before peak stress

Kλ ≥ 3.51, strong,

1.11 < Kλ < 3.51, Weak, Kλ ≤ 1.11, none

6) Residual elastic strain energy index C_EF (F. Gong, J. Yan, X. Li 2018)

$C_{EF}=U^e-U^a$

where C_EF is the residual elastic energy index, U^a is the failure energy density and U^e is elastic strain energy density, U^d is dissipated energy density (ε₁) is the axial strain at its maximum strength, and (ε₂) is the coal specimen’s ultimate strain.

C_EF 1< 15 kJ/m³

15 ≤ C_EF ≤ 30 kJ/m³, weak, C_EF > 30 kJ/m³