# Experimental Study on the Damage Evolution of Gas-Bearing Coal and Its Electric Potential Response

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## Abstract

Previous studies indicate that an electric potential (EP) signal is generated during the loading process of coal and that the EP response is related to the damage evolution. When coupled with gas, EP changes the pore structure and mechanical properties of a coal mass, promoting crack generation and growth and accelerating damage evolution. To study the EP response characteristics and investigate the damage of gas-bearing coal, a triaxial test was carried out with a gas-controlled confining pressure, and multiple types of data were measured and analyzed. The results show that with the change in stress, the EP response increases and fluctuates. This response reflects the stress and reveals the damage evolution, which could be verified with the variation in the acoustic emission response. For the mechanism analyses, the failure of the sample is caused by crack expansion and propagation under the coupling action of stress and gas. Consequently, microscopic charge separation and electron emission are the dominant mechanisms controlling the EP response. Furthermore, the constitutive damage equation of gas-bearing coal is established based on the EP response in view of continuous damage theory and the stress intensity distribution hypothesis. The calculation results of damage and stress based on the EP response are utilized for verification; the results indicate that the damage expressed by the EP response is reasonable and useful. This finding is helpful for understanding the damage evolution mechanism of gas-bearing coal.

## Keywords

Gas-bearing coal Electric potential response Damage evolution Constitutive equation## List of symbols

- \(U_{P}\)
EP on Point

*P*(mV)- \(Q_{i}\)
Charge quantity of the

*i*-th point charge (*C*)- \(r_{i}\)
Distance from

*i*-th point charge to Point*P*(m)- \(\varepsilon_{\text{r}}\)
Dielectric constant of dielectric medium

- \(n\)
Charges number

- \(q_{i}\)
Charge quantity of the

*i*-th charge body (C/m^{3})- \(m^{\prime }\)
Boundary number

- \(\Delta S_{j,t}\)
Area of

*j*-th area element of*m*-th boundary (m^{2})- \(\rho_{j,t}\)
Average surface charge density on \(\Delta S_{j,t}\) (C/m

^{2})- \(r_{si}\)
Distance from

*P*to*i*-th free charged body (m)- \(r_{\text{b,j,t}}\)
Distance from

*P*to center of \(\Delta S_{\text{j,t}}\) (m)- \(S_{j}\)
*j*-th Boundary- \(\sigma_{1}\)
First principal stress (MPa)

- \(\sigma_{2}\)
Second principal stress (MPa)

- \(\sigma_{3}\)
Third principal stress (MPa)

- \(\sigma_{0}\)
Critical stress of material failure (MPa)

- \(P\)
Gas pressure (MPa)

- \(\varepsilon\)
Strain of \(\sigma_{0}\)

- \(\varepsilon_{1}\)
Strain of \(\sigma_{1}\)

- \(\varphi \left( \varepsilon \right)\)
Probability density

*m*Constants

*β*Constants

*σ*_{p}Peak stress value (MPa)

- \(\varepsilon_{\text{p}}\)
Strain of \(\sigma_{\text{p}}\)

*D*Damage

- \(\upsilon\)
Poisson ratio

- \(N_{\text{m}}\)
Cumulative value of EP intensity completely (mV)

*N*Cumulative value of EP intensity of ε (mV)

*E*Elastic modulus (Pa)

*σ*Stress (MPa)

*D*_{E}Damage value base on EP

- \(\sigma_{\text{E}}\)
Stress value base on EP (MPa)

- \(D_{\sigma }\)
Constitutive damage value

- \(\sigma^{\prime }\)
Constitutive stress value (MPa)

- \(\sigma_{\text{r}}\)
Residual stress

## Notes

### Acknowledgements

This work is supported by the General Program of National Natural Science Foundation of China (51674254, 51574231), State Key Research Development Program of China (2016YFC0801401, 2016YFC0801404), State Key Laboratory of Coal Resources and Safe Mining, CUMT (SKLCRSM15X03), A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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