# Mechanism of Zonal Disintegration Phenomenon (ZDP) Around Deep Roadway Under Dynamic Excavation

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## Abstract

Due to the exhaustion of shallow resources, the underground roadway used for coal mining has reached the depth of 1000 m. The zonal disintegration phenomenon (ZDP) in deep rock mass will appear with the increase of depth which is widely different from shallow failure mode.In order to reveal the formation mechanism of ZDP, a new theoretical model is proposed. Based on the strain gradient theory and the deformation theory of plasticity, an elastoplastic damage softening model considering of dynamic excavation is put forward. The dynamic equations and boundary equations are expressed through the Runge–Kutta method. The numerical analysis of rock mass failure induced by blast loading and transient release of in-situ stress after blasting excavation is compiled by Matlab program. Taking the deep tunnel of Dingji coal mine in Huainan mine area as engineering background, the theoretical solutions of radial displacement and stresses present an oscillating mode. The theoretical values are in good agreement with the field measured results in terms of magnitude and change law. The applicability of the elastoplastic damage softening model for ZDP is confirmed and the model can be used to provide theoretical support for the deformation and failure of surrounding rock in deep underground engineering.

## Keywords

Zonal disintegration phenomenon (ZDP) Strain gradient Deformation theory of plasticity Dynamic excavation Numerical analysis Oscillating mode## List of symbols

- \(\ddot{u_{k}}\)
Two order derivative of the displacement on time

- \(\varDelta r\)
The space step

- \(\delta\)
Modification parameter of the damage variable

- \(\delta _{ij}\)
Kronecker symbol

- \(\eta _{ijk}\)
High order strain tensor

- \(\gamma\)
Isentropic exponent of explosives

- \(\lambda\)
Lame constant

- \(\rho _{0}\)
The density of the rock mass

- \(\rho _{e}\)
The density of explosives

- \(\sigma _1\)
The first principal stress

- \(\sigma _{0}\)
Residual stress

- \(\sigma _{\theta \theta }\)
Tangential stress

- \(\sigma _{\theta \theta }^{*}\)
The generalized tangent stress

- \(\sigma _{c}\)
Uniaxial compressive strength

- \(\sigma _{f}\)
Peak stress

- \(\sigma _{ij}\)
Two order Cauchy stress tensor

- \(\sigma _{rr}\)
Radial stress

- \(\sigma _{rr}^{*}\)
The generalized radial stress

- \(\sigma _{s}\)
Yield stress

- \(\sigma _{t}\)
The tensile strength

- \(\sigma _{zz}\)
Axial stress

- \(\sigma _{zz}^{*}\)
The generalized axial stress

- \(\tau\)
The time step

- \(\tau _{ijk}\)
Three order stress

- \(\tilde{\sigma }\)
Equivalent stress

- \(\tilde{\varepsilon }\)
Equivalent strain

- \(\upsilon\)
Poisson ratio

- \(\varepsilon _1\)
The first principal strain

- \(\varepsilon _{0}\)
Residual strain

- \(\varepsilon _{\theta \theta }\)
Tangential strain

- \(\varepsilon _{f}\)
Peak strain

- \(\varepsilon _{ij}\)
Eulerian strain tensor

- \(\varepsilon _{rr}\)
Radial strain

- \(\varepsilon _{s}\)
Yield strain

- \(\varepsilon _{u}\)
Ultimate strain

- \(\varepsilon _{z0}\)
Initial axis strain

- \(\varphi\)
Internal friction angle

*a*Theoretical excavating radius

*b*Radius of disturbed zone

- \(C_{f}\)
The average speed of expansion

- \(C_{u2}\)
The reflected wave velocity spread

- \(d_{b}\)
Diameter of blast hole

- \(d_{c}\)
Diameter of cartridge

- \(D_{e}\)
Detonation velocity of explosives

- \(D_{i}\)
Surface gradient operator

*E*Elastic modulus

*G*Lame constants

- \(k_{1},\, k_{2}\)
Small parameter perturbation terms

- \(L_{1}\)
Length of the charging section

- \(L_{2}\)
Length of the blockage section

- \(n_{i}\)
Surface normal vector

*P*(*t*)Dynamic pressure on inner wall

- \(P_{0}\)
In-situ stress

- \(P_{a}\)
The pressure on the inner wall of the cylinder

- \(P_{b}\)
The pressure on the outer wall of the cylinder

- \(P_{eb}\)
Equivalent peak load of the blasting load

- \(P_{z}\)
Axial stress

- \(r_{p}\)
Radius of plastic zone

*S*Distance of adjacent blast holes

- \(t_{b}\)
Start time of in-situ stress transient release

- \(t_{d}\)
Time of positive pressure

- \(t_{r}\)
Time of the basting load rising

- \(u_{i}\)
Macroscopic displacement of material

- \(u_{r}\)
Radial displacement

- \(u_{z}\)
Axial displacement

## Notes

### Acknowledgements

This study was financially supported by the National Key Research and Development Program of China (No. 2016YFC0401804-03), the Project of Taishan scholar Engineering, the National Natural Science Foundation of China (No. 41772282), the Preliminary Research Project of the Underground Experimental Project for the Geological Disposal of High-level Radioactive Waste (No. YKKY-J-2015-25). The authors are deeply grateful for the support.

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