Mechanical behavior of an FGM-type frozen soil wall: Theory and numerical analysis

Qinglong Wang; Han Wang; Junyuan Zhang; Dongyang Wu; Ruliang Zhao; Qinglong Wang; Han Wang; Junyuan Zhang; Dongyang Wu; Ruliang Zhao

doi:10.3934/mbe.2023694

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 15544-15567. doi: 10.3934/mbe.2023694

Previous Article Next Article

Research article Special Issues

Mechanical behavior of an FGM-type frozen soil wall: Theory and numerical analysis

1.
Yunnan Laman Expressway Co., Ltd. Xishuangbanna 666300, China
2.
School of Highway, Chang'an University, Xi'an 710064, China
3.
Bei Fang Investigation, Design & Research Co., Ltd. Tianjin 300223, China

Academic Editor: Yang Kuang

Received: 11 April 2023 Revised: 20 June 2023 Accepted: 29 June 2023 Published: 27 July 2023

With a laminate model foundation, we have used the complex variable function method to calculate the boundary displacement and stress of a frozen soil wall in a horizontal connecting passage. Using an actual engineering case, the effects of the number of divided layers of a functionally graded material-type frozen soil wall, the position of the freezing pipe and the section shape of the connecting passage on the displacements and tangential stresses of the frozen soil wall are discussed. The results indicate that the frozen soil wall as a temporary support structure exhibits a good supporting effect. With the increase of layers, the material strength of the frozen soil wall weakens, and the displacements and tangential stresses of the inner boundary increase. When the midline of the freezing pipe moves toward the inner boundary, the tensile area in the frozen soil wall begins to shift, and the displacements and tangential stresses of the inner boundary decrease differently. Thedistributions of internal boundary displacements and tangential stresses are significantly affected by the section shape of the frozen soil wall, and the internal boundary displacements and tangential stresses of the frozen soil wall of the small section are more uniform than those of the frozen soil wall of the large section.
- tunnel,
- connecting passage,
- frozen soil wall,
- complex variable function method,
- functionally graded material,
- laminated model
Citation: Qinglong Wang, Han Wang, Junyuan Zhang, Dongyang Wu, Ruliang Zhao. Mechanical behavior of an FGM-type frozen soil wall: Theory and numerical analysis[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 15544-15567. doi: 10.3934/mbe.2023694

Related Papers:

Abstract

With a laminate model foundation, we have used the complex variable function method to calculate the boundary displacement and stress of a frozen soil wall in a horizontal connecting passage. Using an actual engineering case, the effects of the number of divided layers of a functionally graded material-type frozen soil wall, the position of the freezing pipe and the section shape of the connecting passage on the displacements and tangential stresses of the frozen soil wall are discussed. The results indicate that the frozen soil wall as a temporary support structure exhibits a good supporting effect. With the increase of layers, the material strength of the frozen soil wall weakens, and the displacements and tangential stresses of the inner boundary increase. When the midline of the freezing pipe moves toward the inner boundary, the tensile area in the frozen soil wall begins to shift, and the displacements and tangential stresses of the inner boundary decrease differently. Thedistributions of internal boundary displacements and tangential stresses are significantly affected by the section shape of the frozen soil wall, and the internal boundary displacements and tangential stresses of the frozen soil wall of the small section are more uniform than those of the frozen soil wall of the large section.

References

[1]	T. Tsutomu, S. Kiriyama, T. Kato, Jointing of two tunnel shields using artificial underground freezing, Dev. Geotech. Eng., 13 (1979), 519–529. https://doi.org/10.1016/0013-7952(79)90054-1 doi: 10.1016/0013-7952(79)90054-1
[2]	H. L. Jessberger, Theory and application of ground freezing in civil engineering, Cold Reg. Sci. Technol., 3 (1980), 3–27. https://doi.org/10.1016/0165-232X(80)90003-8 doi: 10.1016/0165-232X(80)90003-8
[3]	X. S. Chen, Ground Freezing Method, Beijing: people's communications press, 2013.
[4]	H. Ding, F. Z. Li, H. Cui, Three-Dimensional Numerical Analysis on Freezing Temperature Field in Subway Cross-Passage, Mine Constr. Technol., 39 (2018), 54–57. https://doi.org/10.19458/j.cnki.cn11-2456/td.2018.01.013 doi: 10.19458/j.cnki.cn11-2456/td.2018.01.013
[5]	X. M. Zhou, M. S. Wang, L. G. Tao, Model test and prototype observation on artificial ground freezing and tunneling of Beijing subway, Chin. J. Geotech. Eng., 25 (2003), 676–679. https://doi.org/CNKI:SUN:YTGC.0.2003-06-006
[6]	X. Hu, T. Fang, J. Chen, H. Ren, W. Guo, A large-scale physical model test on frozen status in freeze-sealing pipe roof method for tunnel construction, Tunnelling Underground Space Technol., 72 (2018), 55–63. https://doi.org/10.1016/j.tust.2017.10.004 doi: 10.1016/j.tust.2017.10.004
[7]	F. T. Yue, P. Y. Qiu, G. X. Yang, G. X. Yang, R. J. Shi, Design and practice of freezing method applied to connected aisle in tunnel under complex conditions, Chin. J. Geotech. Eng., 28 (2006), 660–663. https://doi.org/10.1016/S1872-1508(06)60035-1 doi: 10.1016/S1872-1508(06)60035-1
[8]	I. S. Sokolnikoff, Mathematical theory of elasticity, New York: McGraw-Hill, 1956.
[9]	V. G. Ukadgaonker, P. Awasare, A novel method of stress analysis of an infinite plate with rounded corners of a rectangular hole under uniform edge loading, Indian J. Eng. Materialsences, 1 (1994), 17–25. https://doi.org/10.1109/96.296440 doi: 10.1109/96.296440
[10]	K. R. Y. Simha, S. S. Mohapatra, Stress concentration around irregular holes using complex variable method, Sadhana, 23 (1998), 393–412. https://doi.org/10.1007/BF02745750 doi: 10.1007/BF02745750
[11]	D. S. Sharma, Stress distribution around polygonal hole, Int. J. Mech. Sci., 65 (2012), 115–124. https://doi.org/10.1016/j.ijmecsci.2012.09.009 doi: 10.1016/j.ijmecsci.2012.09.009
[12]	Z. M. Chen, Analytical method for mechanical analysis of surrounding rock, China Coal Industry Publishing House, 1994.
[13]	G. E. Exadaktylos, M. C. Stavropoulou, A closed-form elastic solution for stresses and displacements around tunnels, Int. J. Rock Mech. Mining Sci., 39 (2002), 905–916. https://doi.org/10.1016/S1365-1609(02)00079-5 doi: 10.1016/S1365-1609(02)00079-5
[14]	G. E. Exadaktylos, P. A. Liolios, M. C. Stavropoulou, A semi-analytical elastic stress–displacement solution for notched circular openings in rocks, Int. J. Solids Struct., 40 (2003), 1165–1187. https://doi.org/10.1016/S0020-7683(02)00646-7 doi: 10.1016/S0020-7683(02)00646-7
[15]	P. Li, J. Liu, F. Su, X. Li, Analytical continuation method for solving stress and displacement of surrounding rock buried tunnel excavation with arbitrary shape section, J. Tongji Univ., 41 (2013), 1483–1489. https://doi.org/10.3969/j.issn.0253-374x.2013.10.006 doi: 10.3969/j.issn.0253-374x.2013.10.006
[16]	Q. Cheng, A. Lu, C. Yin, Analytical stress solutions for a deep buried circular tunnel under an unsteady temperature field, Rock Mech. Rock Eng., 54 (2021), 1355–1368. https://doi.org/10.1007/s00603-020-02316-8 doi: 10.1007/s00603-020-02316-8
[17]	A. Z. Lu, L. Q. Zhang, Complex function method for mechanical analysis of underground tunnel, China Science Press, 2007.
[18]	A. Z. Lu, N. Zhang, L. Kuang, Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay, Int. J. Rock Mech. Mining Sci., 70 (2014), 69–81. https://doi.org/10.1016/j.ijrmms.2014.04.008 doi: 10.1016/j.ijrmms.2014.04.008
[19]	A. Z. Lu, N. Zhang, Y. Qin, Analytical solutions for the stress of a lined non-circular tunnel under full-slip contact conditions, Int. J. Rock Mech. Mining Sci., 79 (2015), 183–192. https://doi.org/10.1016/j.ijrmms.2015.08.008 doi: 10.1016/j.ijrmms.2015.08.008
[20]	A. Z. Lu, N. Zhang, S. J. Wang, X. L. Zhang, Analytical solution for a lined tunnel with arbitrary cross sections excavated in orthogonal anisotropic rock mass, Int. J. Geomech., 17 (2017). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000912 doi: 10.1061/(ASCE)GM.1943-5622.0000912
[21]	N. Tutuncu, M. Ozturk, Exact solutions for stresses in functionally graded pressure vessels, Compos. Part B Eng., 32 (2001), 683–686. https://doi.org/10.1016/S1359-8368(01)00041-5 doi: 10.1016/S1359-8368(01)00041-5
[22]	T. Akis, A. N. Eraslan, The stress response and onset of yield of rotating FGM hollow shafts, Acta Mech., 187 (2006), 169–187. https://doi.org/10.1007/s00707-006-0374-z doi: 10.1007/s00707-006-0374-z
[23]	Y. Z. Chen, X. Y. Lin, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Comput. Mater. Sci., 44 (2008), 581–587. https://doi.org/10.1016/j.commatsci.2008.04.018 doi: 10.1016/j.commatsci.2008.04.018
[24]	P. Das, M. A. Islam, S. Somadder, M. A. Hasib, Analytical and numerical analysis of functionally graded (FGM) axisymmetric cylinders under thermo-mechanical loadings, Mater. Today Commun., 33 (2022), 104405. https://doi.org/10.1016/j.mtcomm.2022.104405 doi: 10.1016/j.mtcomm.2022.104405
[25]	C. G. Zhang, B. X. Gao, T. B. Li, Z. P. Shan, An elastic-plastic solution for frost heaving force of cold region tunnels considering transversely isotropic frost heave and displacement release, Rock Soil Mech., 42 (2021), 2967–2976. https://doi.org/10.16285/j.rsm.2021.0635 doi: 10.16285/j.rsm.2021.0635
[26]	Z. Y. Guo, H. N. Wang, M. J. Jiang, Elastoplastic analytical investigation of wellbore stability for drilling in methane hydrate-bearing sediments, J. Nat. Gas Sci. Eng., 79 (2020), 103344. https://doi.org/10.1016/j.jngse.2020.103344 doi: 10.1016/j.jngse.2020.103344
[27]	X. Y. Cao, J. H. Zhao, C. G. Zhang, Elastoplastic stress analysis of frozen soil wall based on unified strength theory, Rock Soil Mech., 38 (2017), 769–774. https://doi.org/10.16285/j.rsm.2017.03.020 doi: 10.16285/j.rsm.2017.03.020
[28]	X. D. Hu, Y. Wang, Analytical solution of three-row-piped frozen temperature field by means of superposition of potential function, Chin. J. Rock Mech. Eng., 31 (2012), 1071–1080.
[29]	X. D. Hu, S. Chang, Stress field analysis of functionally graded material frozen soil wall in doublerow-pipe shaft freezing, Eng. Mech., 31 (2014), 145–153. https://doi.org/10.6052/j.issn.1000-4750.2012.09.0651 doi: 10.6052/j.issn.1000-4750.2012.09.0651
[30]	L. Xiang, F. Ye, X. Liang, Multi-tube freezing temperature field considering range of influence of freezing tubes, Tunnel Constr., 41 (2021), 52–59.
[31]	Z. M. Chen, Analytical method for mechanical analysis of surrounding rock, China Coal Industry Publishing House, 1994.
[32]	J. Dryden, K. Jayaraman, Effect of Inhomogeneity on the Stress in Pipes, J. Elasticity, 83 (2006), 179–189. https://doi.org/10.1007/s10659-005-9043-z doi: 10.1007/s10659-005-9043-z
[33]	M. Mohammadi, J. R. Dryden, Influence of the spatial variation of Poisson's ratio upon the elastic field in nonhomogeneous axisymmetric bodies, Int. J. Solids Struct., 46 (2009), 788–795. https://doi.org/10.1016/j.ijsolstr.2008.09.030 doi: 10.1016/j.ijsolstr.2008.09.030
[34]	M. Mohammadi, J. R. Dryden, L. Y. Jiang, Stress concentration around a hole in a radially inhomogeneous plate, Int. J. Solids Struct., 48 (2011), 83–491. https://doi.org/10.1016/j.ijsolstr.2010.10.013 doi: 10.1016/j.ijsolstr.2010.10.013
[35]	Z. W. Wu, W. Ma, C. Q. Zhang, L. Y. Jiang, Strength characteristics of frozen sandy soil, J. Glaciol. Geol., 16 (1994), 15–20. https://doi.org/10.13247/j.cnki.jcumt.000611 doi: 10.13247/j.cnki.jcumt.000611
[36]	G. M. Xi, G. S. Yang, L. Pang, X. T. Lv, L. Fang, Experimental study on basic mechanical behaviors of sandy mudstone under low freezing temperature, J. China Coal Soc., 39 (2014), 1262–1268. https://doi.org/10.13225/j.cnki.jccs.2014.0533 doi: 10.13225/j.cnki.jccs.2014.0533
[37]	G. S. Yang, Y. Wei, Y. J. Shen, L. Wang, H. Liu, X. H. Dong, et al., Mechanical behavior and strength forecast model of frozen saturated sandstone under triaxial compression, Chin. J. Rock Mech. Eng., 38 (2019), 683–694. https://doi.org/10.13722/j.cnki.jrme.2018.1417 doi: 10.13722/j.cnki.jrme.2018.1417
[38]	R. S. Yang, Q. X. Wang, S. Z. Chen, Elastic analysis of irregular inclined shaft lining subjected to water pressure, J. China Univ. Mining Technol., 46 (2017), 48–57. https://doi.org/10.13247/j.cnki.jcumt.000611 doi: 10.13247/j.cnki.jcumt.000611
[39]	Q. X. Wang, Research on deformation law and design method of inclined shaft frozen wall, China University of Mining and Technology, 2017.
[40]	P. Yang, J. M. Ke, J. G. Wang, Y. K. Chow, F. B. Zhu, Numerical simulation of frost heave with coupled water freezing, temperature and stress fields in tunnel excavation, Comput. Geotech., 33 (2006), 330–340. https://doi.org/10.1016/j.compgeo.2006.07.006 doi: 10.1016/j.compgeo.2006.07.006

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)