Abstract
The long-term stability control of surrounding rock of deep high-stress soft rock tunnel has always been the research hotspot and difficulty of underground engineering. With the continuous increase of the number of ultra-kilometer mines, reasonable support design has an important impact on the efficient and safe production and sustainable development of deep coal resources. In view of the above problems, the formation mechanism of surrounding rock deformation zoning of deep high-stress soft rock tunnel considering rock rheology is analyzed, a three-stage strain-softening model considering rock rheology is established, and the concept of elastic-creep modulus is proposed based on this model. Combined with the rheological influence of rock and the test method of long-term strength of surrounding rock, the elastic–plastic solutions of surrounding rock of deep tunnel based on Mohr–Coulomb and Drucker–Prager strength criteria are derived, and the formulas for solving the radius of deformation zones of tunnel-surrounding rock are calculated. Meanwhile, combined with an engineering example, the radius of deformation zones of tunnel-surrounding rock based on different strength criteria and rock rheology is calculated and compared, and the correctness and superiority of this theory are verified by the field measured results. In addition, the influence of rock mechanical parameters on the range of deformation zones of tunnel-surrounding rock under different mechanical models is assessed. This work can provide guidance for long-term stability evaluation, support design, and disaster prevention of deep soft rock tunnels.
Highlights
-
A novel three-stage strain softening model considering rock rheology was established.
-
Deformation mechanism of surrounding rock of deep roadway considering rheology.
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The elastic-plastic solution based on different strength criterion and rock rheology.
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Comparison and analysis of elastoplastic solutions under different strength criteria.
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The influences of rock mechanics parameters on the range of deformation zones.
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Abbreviations
- \(E_{{{\text{ec}}}}\) :
-
Elastic-creep modulus
- \(\sigma_{{{\text{ec}}}}\) :
-
Upper threshold of stable creep of tunnel-surrounding rock
- \(\varepsilon_{{{\text{ec}}}}\) :
-
Circumferential strain value corresponding to \(\sigma_{{{\text{ec}}}}\)
- \(e\) :
-
Elastic zone
- \(p\) :
-
Plastic-softening zone
- \(b\) :
-
Broken zone
- model 3S-R:
-
The three-stage strain-softening model of tunnel-surrounding rock considering rheological properties
- model 3S:
-
The three-stage strain-softening model of tunnel-surrounding rock without considering rheological properties
- model 4S-R:
-
The four-stage strain-softening model of tunnel-surrounding rock considering rheological properties
- \(R_{0}\) :
-
Tunnel radius
- \(q_{0}\) :
-
Original rock stress at infinity
- \(p_{{\text{s}}}\) :
-
Radial support resistance
- \(R_{{\text{b}}}\), \(R_{{\text{b}}}^{\prime }\) :
-
Radius of the broken zone
- \(R_{{\text{p}}}\), \(R_{{\text{p}}}^{\prime }\) :
-
Radius of the plastic-softening zone
- \(R_{{\text{e}}}\), \(R_{{\text{e}}}^{\prime }\) :
-
Radius of the elastic zone
- \({\left( {\sigma_{\theta } } \right)}_{{{\text{pk}}}}\) :
-
Peak stress of the rock
- \({\left( {\sigma_{\theta } } \right)}_{{\text{c}}}\) :
-
Long-term strength of surrounding rock
- \(L\) :
-
Upper threshold point of stable creep
- \(L_{0}\) :
-
Lower threshold point of stable creep
- \({\left( {\sigma_{{\rho {\text{e}}}} } \right)}_{{R_{{\text{p}}} }}\), \({\left( {\sigma_{{\rho {\text{e}}}} } \right)}_{{R_{{\text{p}}} }}^{\prime }\) :
-
Radial pressure at the boundary of elastic zone and plastic-softening zone
- \(E_{0}^{\prime }\) :
-
Internal boundary stress of the elastic zone when rheology is considered
- \(E_{0}\) :
-
Internal boundary stress of the elastic zone when rheology is not considered
- \(E_{1}^{\prime }\) :
-
Internal boundary stress of plastic-softening zone when rheology is considered
- \(E_{1}\) :
-
Internal boundary stress of plastic-softening zone when rheology is not considered
- \(E_{2}^{\prime }\) :
-
Internal boundary stress of the broken zone when rheology is considered
- \(E_{2}\) :
-
Internal boundary stress of the broken zone when rheology is not considered
- \(\sigma_{{\rho {\text{e}}}}\), \(\sigma_{{\rho {\text{e}}}}^{\prime }\) :
-
Radial stress of rock in the elastic zone
- \(\sigma_{{\theta {\text{e}}}}\), \(\sigma_{{\theta {\text{e}}}}^{\prime }\) :
-
Circumferential stress of rock in the elastic zone
- \(C_{0}^{{{\text{pk}}}}\) :
-
Initial cohesion
- \(\sigma_{{\text{f}}}^{{{\text{pk}}}}\) :
-
Uniaxial compressive strength
- \(\sigma_{{\text{f}}}^{{\text{c}}}\) :
-
Uniaxial compressive strength corresponding to the fitting line of long-term strength
- \(M_{C}\) :
-
Cohesive softening modulus
- \(C_{0}\) :
-
Initial cohesive stress of the rock at any position in the plastic-softening zone
- \(C_{{\text{b}}}\) :
-
Residual cohesive stress of the rock at any position in the plastic-softening zone
- \(C_{N}\) :
-
Cohesive stress of the rock at any position in the plastic-softening zone
- \(\left( {\varepsilon_{\theta } } \right)_{{R_{{\text{b}}} }}\) :
-
Circumferential strain at the inner boundary in the plastic-softening zone
- \(\left( {\varepsilon_{\theta } } \right)_{{R_{{\text{p}}} }}\) :
-
Circumferential strain at the outer boundary in the plastic-softening zone
- \(\left( {\varepsilon_{\theta } } \right)_{N}\) :
-
Circumferential strain at the any position in the plastic-softening zone
- \(\varepsilon_{{\theta {\text{p}}}}\), \(\varepsilon_{{\theta {\text{p}}}}^{\prime }\) :
-
Tangential strain in the plastic-softening zone of tunnel-surrounding rock
- \(P\) :
-
Constant
- \(E\) :
-
Elastic modulus of the elastic zone
- \(\mu\) :
-
Poisson's ratio
- \(i\) :
-
Zoning type of surrounding rock
- \(\psi\) :
-
Expansion angle
- \(\varphi\) :
-
Internal friction angle
- \(\Delta \varepsilon_{{\rho {\text{p}}}}\) :
-
Radial strain increments of the rock in the plastic-softening zone
- \(\Delta \varepsilon_{{\theta {\text{p}}}}\) :
-
Tangential strain increments of the rock in the plastic-softening zone
- \(\eta_{{\text{p}}}\), \(\eta_{{\text{b}}}\) :
-
Rock mass expansion parameter
- \(\Delta \varepsilon_{{\rho {\text{b}}}}\) :
-
Radial strain increments of the rock in the broken zone
- \(\Delta \varepsilon_{{\theta {\text{b}}}}\) :
-
Tangential strain increments of the rock in the broken zone
- \(\sigma_{{\theta {\text{p}}}}\), \(\sigma_{{\theta {\text{p}}}}^{\prime }\) :
-
Circumferential stress in the plastic-softening zone
- \(\sigma_{{\theta {\text{b}}}}\), \(\sigma_{{\theta {\text{b}}}}^{\prime }\) :
-
Circumferential stress of rock in the broken zone
- \(\sigma_{{\rho {\text{p}}}}\), \(\sigma_{{\rho {\text{p}}}}^{\prime }\) :
-
Radial stress of rock in the plastic-softening zone
- \(\sigma_{{\rho {\text{b}}}}\), \(\sigma_{{\rho {\text{b}}}}^{\prime }\) :
-
Radial stress of rock in the broken zone
- \(\sigma_{{{\text{fp}}}}\) :
-
Compressive strength of rock mass in plastic-softening zone
- \(\sigma_{{{\text{fb}}}}\) :
-
Compressive strength of rock mass in broken zone
- \(\varphi_{{\text{p}}}\) :
-
Internal friction angle of rock mass in plastic-softening zone
- \(\varphi_{{\text{b}}}\) :
-
Internal friction angle of rock mass in broken zone
- \(u\), \(u^{\prime}\) :
-
Radial displacement of rock
- \(\rho\) :
-
Distance from the rock to the tunnel center
- \(\sigma_{\rho }\), \(\sigma_{\rho }^{\prime }\) :
-
Radial stress of rock particles
- \(\sigma_{\theta }\), \(\sigma_{\theta }^{\prime }\) :
-
Circumferential stress of rock particles
- \(\varepsilon_{\rho }\), \(\varepsilon_{\rho }^{\prime }\) :
-
Radial strain of rock particles
- \(\varepsilon_{\theta }\), \(\varepsilon_{\theta }^{\prime }\) :
-
Circumferential strain of rock particles
- \(u_{{\text{e}}}\), \(u_{{\text{e}}}^{\prime }\) :
-
Radial displacement of rock mass in elastic zone
- \(\varepsilon_{{\rho {\text{e}}}}\), \(\varepsilon_{{\rho {\text{e}}}}^{\prime }\) :
-
Radial strain in the elastic zone of tunnel-surrounding rock
- \(\varepsilon_{{\theta {\text{e}}}}\), \(\varepsilon_{{\theta {\text{e}}}}^{\prime }\) :
-
Tangential strain in the elastic zone of tunnel-surrounding rock
- \(\varepsilon_{{\rho {\text{p}}}}\), \(\varepsilon_{{\rho {\text{p}}}}^{\prime }\) :
-
Radial strain in the plastic-softening zone of tunnel-surrounding rock
- \(\varepsilon_{{\rho {\text{p}}}}^{{\text{p}}}\), \(\varepsilon_{{{\rho {\text{p}}}}^{{{\prime }}}}^\text{p}\) :
-
Radial strain increments of any position in the plastic-softening zone during the plastic-softening process
- \(\varepsilon_{{{\theta p}}}^{{\text{p}}}\), \(\varepsilon_{{{{\theta p}}}^{{{\prime }}}}^\text{p}\) :
-
Circumferential strain increments of any position in the plastic-softening zone during the plastic-softening process
- \(\left( {\varepsilon_{\rho } } \right)_{{R_{{\text{p}}} }}\) :
-
Radial strain at the outer boundary in the plastic-softening zone
- \(u_{{\text{p}}}\), \(u_{{\text{p}}}^{\prime }\) :
-
Radial displacement of rock mass in plastic-softening zone
- \(u_{{\text{b}}}\), \(u_{{\text{b}}}^{\prime }\) :
-
Radial displacement of rock mass in broken zone
- \(\varepsilon_{{\rho {\text{b}}}}\), \(\varepsilon_{{\rho {\text{b}}}}^{\prime }\) :
-
Radial strain in the broken zone
- \(\varepsilon_{{\theta {\text{b}}}}\), \(\varepsilon_{{\theta {\text{b}}}}^{\prime }\) :
-
Tangential strain in the broken zone
- \(I_{1}\) :
-
The first stress tensor invariant
- \(J_{2}\) :
-
The second stress bias tensor invariant
- \(\alpha\), \(\beta\) :
-
Material parameters of D–P strength criterion
- \(V_{{R_{{\text{b}}} }}\) :
-
The reduction rate of the radius of broken zone based on D–P criterion and M–C criterion.
- \(V_{{R_{{\text{p}}} }}\) :
-
The reduction rate of the radius of plastic-softening zone based on D–P criterion and M–C criterion.
- \(u_{0}^{\prime }\) :
-
Tunnel wall displacement
- \(\xi\) :
-
Intermediate principal stress coefficient
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Acknowledgements
This study was supported by the Major Project Of Natural Science Research In Colleges And Universities Of Anhui Provincial Department of Education (KJ2021ZD0053), the National Natural Science Foundation of China (51904012), the Open Fund of State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mine (SKLMRDPC19KF02), the Project Supported By Scientific Research Activities Of Postdoctoral Researchers In Anhui Province (2022B640), the Research Project on Ningzheng Coal Mine Large Buried Deep Ultra-Thick Coal Seam Driving tunnel Along Goaf Floor Key Support Technology Of Huaneng Qingyang Coal Power Co., Ltd.(HNQMHTY-051-2022-JZ01), the Research Project On "Three Soft" Coal Seam Mining tunnel Support Technology Research Project Of Daliu Coal Mine Co., Ltd. (HNMYKJ19-04), and The Project Of Research On Large Deformation Mechanism And Control Technology Of Goaf Side Entry In **chuan Coal Mine With Complex Geological Conditions Of Huaneng Group Headquarters (HNKJ21-HF05).
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**g, W., Zhou, J., Yuan, L. et al. Deformation and Failure Mechanism of Surrounding Rock in Deep Soft Rock Tunnels Considering Rock Rheology and Different Strength Criteria. Rock Mech Rock Eng 57, 545–580 (2024). https://doi.org/10.1007/s00603-023-03565-z
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DOI: https://doi.org/10.1007/s00603-023-03565-z