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Rock Stress Around Noncircular Tunnel: a New Simple Mathematical Method

  • Wenlong Shen (a1) (a2), Xiangyu Wang (a2), Jianbiao Bai (a2), Wenfeng Li (a3) and Yang Yu (a4)...

A new simple mathematical method has been proposed to predict rock stress around a noncircular tunnel and the method is calibrated and validated with a numerical model. It can be found that the tunnel shapes and polar angles affect the applicable zone of the theoretical model significantly and the applicable zone of a rectangular tunnel was obtained using this method. The method can be used to predict the values of the concentrated stress, and to analyze the change rate of rock stress and back to calculate the mechanical boundary condition in the applicable zone. The results of the stress change rate indicate that the horizontal stress is negatively related to the vertical boundary load and positively related to the horizontal boundary load. The vertical stress is negatively related to the horizontal boundary load and positively related to the vertical boundary load. These findings can be used to explain the evolution of the vertical increment in stress obtained with field-based borehole stress monitoring.

Corresponding author
*Corresponding author. Email: wangxiangyu (X. Y. Wang), (W. L. Shen)
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[1] Hasan, G., An elastic solution for stresses around tunnels with conventional shapes, Int. J.Mining Sci. Tech., 34 (1997).
[2] Huangfu, P. P., Zhang, L. Q. and Wu, F. Q., Research on analytical solution of stress field of surrounding rock of single hole with arbitrary shape based on highly-efficient conformal mapping, Chinese J. Rock Mech. Eng., S2 (2011), pp. 39053913.
[3] Carranza-Torres, C. and Fairhurst, C., The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion, Int. J. Rock Mech. Mining Sci., 36 (1999), pp. 777809.
[4] Islam, M. R. and Shinjo, R., Numerical simulation of stress distributions and displacements around an entry roadway with igneous intrusion and potential sources of seam gas emission of the Barapukuria coal mine, NW Bangladesh, Int. J. Coal Geology, 78 (2009), pp. 249262.
[5] Hosseini, N., Oraee, K., Shahriar, K. and Goshtasbi, K., Studying the stress redistribution around the longwall mining panel using passive seismic velocity tomography and geostatistical estimation, Arabian J. Geosci., 6 (2011), pp. 14071416.
[6] Hefny, A. M. and Lo, K. Y., Analytical solution for stresses and displacements around tunnels driven in cross-anisotropic rocks, Int. J. Numer. Anal. Methods Geomech., 23 (1999), pp. 161177.
[7] Lee, K. M., Hou, X. Y., Ge, X.W. and Tang, Y., An analytical solution for a jointed shield-driven tunnel lining, Int. J. Numer. Anal. Methods Geomech., 25 (2001), pp. 365390.
[8] Lu, Y.-E. and Yang, W., Analytical solutions of stress and displacement in strain softening rock mass around a newly formed cavity, J. Central South University, 20 (2013), pp. 13971404.
[9] Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, Mathematical Gazette, 48 (1964), pp. 445447.
[10] Park, K.-H. and Kim, Y.-J., Analytical solution for a circular opening in an elastic-brittle-plastic rock, Int. J. Rock Mech. Mining Sci., 43 (2006), pp. 616622.
[11] Sharan, S. K., Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock, Int. J. Rock Mech. Mining Sci., 45 (2008), pp. 7885.
[12] Feng, Q., Jiang, B.-S., Zhang, Q. and Wang, L. P., Analytical elasto-plastic solution for stress and deformation of surrounding rock in cold region tunnels, Cold Regions Sci. Tech., 108 (2014), pp. 5968.
[13] Han, K.-H., Zhang, C.-P. and Wang, M.-S., Explicit analytical solutions for stress and displacement of surrounding rock in shallow tunnels, Chinese J. Geotechnical Eng., 36 (2014), pp. 22532259.
[14] Kargar, A. R., Rahmannejad, R. and Hajabasi, M. A., A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method, Int. J. Solids Struct., 51 (2014), pp. 14751482.
[15] Vrakas, A. and Anagnostou, G., A finite strain closed-form solution for the elastoplastic ground response curve in tunnelling, Int. J. Numer. Anal. Methods Geomech., 38 (2014), pp. 11311148.
[16] Huo, H., Bobet, A., Fernández, G. and Ramírez, J., Analytical solution for deep rectangular structures subjected to far-field shear stresses, Tunnelling and Underground Space Technology, 21 (2006), pp. 613625.
[17] Lu, A. Z., Zhang, N., Zhang, X. L., Lu, D. H. and Li, W. S., Analytic method of stress analysis for an orthotropic rock mass with an arbitrary-shaped tunnel, Int. J. Geomech., 15 (2015).
[18] Ukadgaonker, V. G. and Rao, D. K. N., A general solution for stresses around holes in symmetric laminates under inplane loading, Compos. Struct., 49 (2000), pp. 339354.
[19] Liu, C.-W., Cao, L. and Liu, S.-X., Method of equivalent radius for the analyzing rock stress of high-buried non-circular underground chambers, Chinese J. Copper Eng., (2010), pp. 15.
[20] Shen, W.-L., Bai, J.-B., Yu, Y., Liu, F. and Huang, Z.-F., Research on floor heave mechanism and control technology of muddy floor roadway under dynamic pressure, Chinese J. Coal Sci. Tech., 42 (2014), pp. 2831.
[21] Yu, Y., Bai, J., Wang, X., Shen, W. and Lian, C., Study on asymmetric distortion and failure characteristics and stability control of soft rock roadway, J. Mining Safety Eng., 31 (2014), pp. 340346.
[22] Zha, W.-H., Hua, X.-Z. and Chen, D.-H., QuantitativeAnalysis of plastic region in deep buried tunnel based on in-situ stress test, Chinese J. Experimental Mech., 28 (2013), pp. 657662.
[23] Xu, Z.-L., Elasticity, 4th ed. Beijing, China, Higher Education Press, (2006), pp. 7377.
[24] Shabanimashcool, M. and Li, C. C., Numerical modelling of longwall mining and stability analysis of the gates in a coal mine, Int.J. Rock Mech. Mining Sci., 51 (2012), pp. 2434.
[25] Yan, S., Bai, J., Wang, X. and Huo, L., An innovative approach for gateroad layout in highly gassy longwall top coal caving, Int. J. Rock Mech. Mining Sci., 59 (2013), pp. 3341.
[26] Shen, W. L., Bai, J. B., Wang, X. Y. and Yu, Y., Response and control technology for entry loaded by mining abutment stress of a thick hard roof, Int. J. Rock Mech. Mining Sci., 90 (2016), pp. 2634.
[27] Bai, J. B., Shen, W. L., Guo, G. L., Wang, X. Y. and Yu, Y., Roof deformation, failure characteristics, and preventive techniques of gob-side entry driving heading adjacent to the advancing working face, Rock Mech. Rock Eng., 48 (2015), pp. 24472458.
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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
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