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Rock Stress Around Noncircular Tunnel: a New Simple Mathematical Method

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  28 November 2017

Wenlong Shen ,
Xiangyu Wang ,
Jianbiao Bai ,
Wenfeng Li  and
Yang Yu
Wenlong Shen*
Affiliation:
School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, Henan, China State Key Laboratory of Coal Resources and Mine Safety, China University of Mining & Technology, Xuzhou 221116, Jiangsu, China
Xiangyu Wang*
Affiliation:
State Key Laboratory of Coal Resources and Mine Safety, China University of Mining & Technology, Xuzhou 221116, Jiangsu, China
Jianbiao Bai
Affiliation:
State Key Laboratory of Coal Resources and Mine Safety, China University of Mining & Technology, Xuzhou 221116, Jiangsu, China
Wenfeng Li
Affiliation:
Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma, Norman, OK 73019, USA
Yang Yu
Affiliation:
School of Civil Engineering; Xuzhou Institute of Technology, Xuzhou 221008, Jiangsu, China
*
*Corresponding author. Email:wangxiangyu cumt@163.com (X. Y. Wang), shenwenlong.888@163.com (W. L. Shen)
*Corresponding author. Email:wangxiangyu cumt@163.com (X. Y. Wang), shenwenlong.888@163.com (W. L. Shen)
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Abstract

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.

Keywords

Rock stressmathematical modelnoncircular tunnelapplicable zonestress change ratenumerical simulation

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1330 - 1346
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Hasan, G., An elastic solution for stresses around tunnels with conventional shapes, Int. J.Mining Sci. Tech., 34 (1997).Google Scholar
[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. 3905–3913.Google Scholar
[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. 777–809.CrossRefGoogle Scholar
[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. 249–262.CrossRefGoogle Scholar
[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. 1407–1416.CrossRefGoogle Scholar
[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. 161–177.3.0.CO;2-B>CrossRefGoogle Scholar
[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. 365–390.CrossRefGoogle Scholar
[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. 1397–1404.CrossRefGoogle Scholar
[9] Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, Mathematical Gazette, 48 (1964), pp. 445–447.Google Scholar
[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. 616–622.CrossRefGoogle Scholar
[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. 78–85.CrossRefGoogle Scholar
[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. 59–68.CrossRefGoogle Scholar
[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. 2253–2259.Google Scholar
[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. 1475–1482.CrossRefGoogle Scholar
[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. 1131–1148.CrossRefGoogle Scholar
[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. 613–625.CrossRefGoogle Scholar
[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).CrossRefGoogle Scholar
[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. 339–354.CrossRefGoogle Scholar
[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. 1–5.Google Scholar
[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. 28–31.Google Scholar
[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. 340–346.Google Scholar
[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. 657–662.Google Scholar
[23] Xu, Z.-L., Elasticity, 4th ed. Beijing, China, Higher Education Press, (2006), pp. 73–77.Google Scholar
[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. 24–34.CrossRefGoogle Scholar
[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. 33–41.CrossRefGoogle Scholar
[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. 26–34.CrossRefGoogle Scholar
[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. 2447–2458.CrossRefGoogle Scholar