Viscoelastic solution of optimal reserved deformation for deep soft rock tunnels with large deformation

Abstract

In the construction process of soft rock tunnels, determining a reasonable amount of reserved deformation is important to ensure the tunnel stability. This article presents the viscoelastic solution of reserved deformation for deep soft rock tunnels considering the support effects. Based on the analytical solution of the Burgers model, the expression of surrounding rock displacement was derived by considering reserved deformation and optimal reserved deformation. Subsequently, based on numerical simulation experiments, the variation laws and errors of the numerical and analytical solutions of the expressions of reserved deformation and surrounding rock displacement were analyzed. To gain a better understanding of the factors that affect reserved deformation, the factors influencing the expression of optimal reserved deformation were analyzed. The errors in the numerical simulation and analytical solution results were within 10%. This study could provide a theoretical basis for determining the amount of reserved deformation and analyzing the variation law of surrounding rock affected by the amount of reserved deformation.

Keywords

Reserved deformation / Circular cavity / Viscoelastic decomposition / Burgers model

Compliance with ethical standards

The authors declare compliance with ethical standards.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Declaration of competing interest

The authors declare no conflicts of interest.

Acknowledgements

This study is sponsored by the National Natural Science Foundation of China (Grants No. 42177158 and 11902249), Key Research and Development project of Shaanxi Province (No. 2022SF-412). Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology (Grants No. SKLGP2022K005). The financial support provided by this sponsor is greatly appreciated.

References

[1] L. Ming, Z. Ping, J. Yifan, et al., Numerical investigation on comprehensive control system of cooling and heat insulation for high geothermal tunnel: a case study on the highway tunnel with the highest temperature in China, Int. J. Therm. Sci. 173 (2022) 107385.

[2] H. Manchao, S. Qiru, L. Mengnan, et al., Compensation excavation method control for large deformation disaster of mountain soft rock tunnel, Int. J. Min. Sci. Technol. 32 (5) (2022) 951-963.

[3] Z. Nannan, S. Zhushan, B. Yuan, et al., Analytical approach to estimating the influence of friction slip contact between surrounding rock and concrete lining on mechanical response of deep rheological soft rock tunnels, Appl. Math. Model. 113 (2023) 287-308.

[4] S. Qiru, H. Manchao, S. Tingting, et al., Lateral damage mechanism of the doubletrack tunnel in the mountainous layered soft rock and NPR anchor cable control, Undergr. Space 12 (2023) 31-43.

[5] Z. Chengliang, L. Wenqian, L. Lei, et al., Study on reserved deformation of large section soft rock highway tunnel based on monitoring measurement, Mater. Sci. Eng. 452 (2) (2018) 022099.

[6] D. Huangshi, F. Helin, S. Yue, et al., Countermeasures against large deformation of deep-buried soft rock tunnels in areas with high geostress: a case study, Tunn. Undergr. Space Technol. 119 (2022) 104238.

[7] M. Lubo, L. Tianbin, J. Yun, et al., Characteristics and mechanisms of large deformation in the Zhegu mountain tunnel on the Sichuan-Tibet highway, Tunn. Undergr. Space Technol. 37 (2013) 157-164.

[8] W. Yaqiong, L. Yong, W. ZhiFeng, et al., Investigation on progressive failure process of tunnel lining induced by creep effect of surrounding rock: a case study, Eng. Fail. Anal. 144 (2023) 106946.

[9] L. Jiaqi, W. Zhifeng, W. Yaqiong, et al., Analysis and countermeasures of large deformation of deep-buried tunnel excavated in layered rock strata: a case study, Eng. Fail. Anal. 146 (2023) 107057.

[10] Z. Bo, T. Zhigang, G. Pengfei, et al., Model test on deformation and failure mechanism of tunnel support with layered rock mass under high ground stress, Eng. Fail. Anal. 150 (2023) 107296.

[11] L. Xiaohong, Tunnel New Austrian tunneling method and its measurement technology, China. Sci. Publishing & Mediz. Ltd, Beijing, 2002.

[12] L. Jiaqi, W. Zhifeng, W. Yaqiong, et al., Analysis and countermeasures of large deformation of deep-buried tunnel excavated in layered rock strata: a case study, Eng. Fail. Anal. 146 (139) (2023) 107057.

[13] Q. Liu, R. Li, W. Tian, et al., Monitoring and support optimization analysis of surrounding rock pressure and initial supporting stress in deep-buried soft rock tunnel, Revista. Int. de. M_etodos. Num_ericos. Para. C_alculo. Y. Dise-no. En. Ingeniería. 37 (2) (2021).

[14] G. Baoshu, Key points for tunnel engineering construction, China Communications Press, Beijing, 2003.

[15] A. Lallit, A. Ozgur, A.C. Shawn, A large-deformation gradient theory for elastic-plastic materials, Int. J. Plast.30-31 (2012) 116-143.

[16] C. Feng, Y. Liangliang, M. Hongling, et al., Subsidence above gas storage in salt caverns predicted with viscoelastic theory, J. Nat. Gas Sci. Eng. 103 (2022) 104620.

[17] W. Junbao, Z. Qiang, L. Xiao, et al., Creep properties and constitutive model for salt rock subjected to uniaxial trapezoidal cyclic loading, J. Energy Storage 52 (2) (2022) 105023.

[18] H. Xiongyu, M. Gutierrez, Viscoelastic Burger's model for tunnels supported with tangentially yielding liner, J. Rock Mech. Geotech. Eng. 15 (4) (2023) 826-837.

[19] F. Ahmad, M.T. Farshad, H. Ahmadreza, et al., Analytical solution for the excavation of circular tunnels in a visco-elastic Burger's material under hydrostatic stress field, Tunn. Undergr. Space Technol. 25 (4) (2010) 297-304.

[20] G. Kirsch, Die theorie der elastizitaet und die deduerfnisse der festigkeitlehre, Veit. Ver. Deut. Ing. 42 (1898) 797-807.

[21] P.F. Gnirk, R.E. Johnson, The deformational behavior of a circular mine shaft situated in a viscoelastic medium under hydrostatic stress, in: Proceedings of 6th US rock mechanics symposium, University of Missouri, Rolla, 28-30 October 1964, pp. 231-259.

[22] M. Panet, A. Guenot, Analysis of convergence behind the face of a tunnel, Int. J. Rock. Mech. Min. Sci & Geos. Abstracts. (1982) 197-202.

[23] B.H.G. Brady, E.T. Brown, Rock mechanics for underground mining, Springer Neth, 2006.

[24] O. Hamza, R. Stace, Creep properties of intact and fractured muddy siltstone, Int. J. Rock Mech. Min. Sci. 106 (2018) 109-116.

[25] M. Zhaoyang, Z. Chenpeng, G.P. Ranjith, et al., Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation, Int. J. Min. Sci. Technol. 32 (2) (2022) 283-294.

[26] L. Li, Study on squeezing large deformation mechanism and control technology of phyllite tunnel, Dissertation, Beijing jiaotong University, 2017.

[27] Y. Zhenwei, J. Aibing, Z. Yu, et al., Parametric analysis of Burgers model and creep properties of rock with particle flow code, Rock Soil Mech. 36 (1) (2015) 240-248.

[28] M.I. _Alvarez-Fern_andez, C. Gonz_alez-Nicieza A.E. _Alvarez-Vigil, et al., Numerical modelling and analysis of the influence of local variation in the thickness of a coal seam on surrounding stresses: application to a practical case, Int. J. Coal Geol. 79 (4) (2009) 157-166.

[29] L. Ning, L. Niafei, L. Guofeng, New method for stability evaluation of soil and soft rock tunnels, Chin. J. Rock Mech. Eng. 33 (9) (2014) 1812-1821.

[30] J. Housheng, W. Yinwei, L. Shaowei, et al., Experimental study on double cuneiform reamed anchorages for cable bolt boreholes in soft rock, Int. J. Rock Mech. Min. Sci. 158 (2022) 105198.

[31] Y. Kaigang, G. Deli, Numerical simulation of hydraulic fracturing process with consideration of fluid-solid interaction in shale rock, J. Nat. Gas Sci. Eng. 102 (2022) 104580.

[32] A.G. Mikhail, Chapter 3 - non-Euclidean model of rock masses. Model, Geotech. Eng. (2021) 61-77.

[33] J. Huilin, W. Eeyuan, S. Xiaoyan, et al., Correlation of electromagnetic radiation emitted from coal or rock to supporting resistance, Min. Sci. Technol. China. 19 (3) (2009) 317-320.