STUDY ON THE SETTLEMENT OF TUNNEL BOTTOM AND PRESSURE OF ROCK MASS BASED ON CURVED BEAM ON ELASTIC FOUNDATION THEORY
DOI:
https://doi.org/10.14311/CEJ.2018.04.0038Keywords:
Tunnel invert Curved beam Elastic foundation Displacement equation P ressure of rock massAbstract
Tunnel invert is
a weak section of curved beam on tunnel foundation, and it is easy to break
down. Based on the curved beam theory on elastic foundation, the curved beam model of tunnel
invert was established, the displacement equation of tunnel invert under external load was deduced,
and the formula of settlement of tunnel bottom and the pressure of rock mass was presented. By
means of the calculating formula, the distribution law of settlement of tunnel bottom and pressure of
rock mass w ere obtained when tunnel bottom was strengthened and not strengthened by high
pressure jet grouting pile. The final formula in the paper is precise to predict the settlement of tunnel
bottom and pressure of rock mas s, so it is of great value for tunnel design and construction.
Downloads
References
S. Chakraborty, S. K. Sarkar, “Analysis of a curved beam on uncertain elastic foundation”,
Finite Elements
in Analysis and Design , vol. 36, no. 1, pp. 73 82, 2000.
A. M. Talmon, A. Bezuijen, “Analytical model for the beam action of a tunnel lining during construction”,
International Journal for Numerical & Analytical Methods in Geomechan ics , vol. 37, no. 2, pp. 181 200,
L. Zhang, M. H. Zhao, C. J. Shi, H. Zhao, “Settlement Calculation of Composite Foundation Reinforced
with Stone Columns”, International Journal of Geomechanics , vol. 13, no. 3, pp. 248 256, 2013.
W.
Wang, R. A. Shenoi, “Delamination modelling of a curved composite beam subjected to an opening
bending moment”, J ournal of Strain Analysis for Engineering Design , vol. 38, no. 5, pp. 453 457, 2003.
E. L. Tan, B. Uy, “Experimental study on straight composite beams subjected to combined flexure and
torsion”, Journal of Constructional Steel Research vol. 65, no. 8, pp. 1855 1863, 2009.
N. J. Pagano, “Analysis of The Flexure Test of Bidirectional Composites”, Journal of Composite Material s ,
vol. 1, no. 4, p p. 336 342 ,
N. J. Pagano NJ, “Exact solution for composite laminates in cylindrical bending”, Solid Mechanics & Its
Applications , vol. 3, no. 3, pp. 398 411, 1969.
R. D. Chien, C. S. Chen, “Nonlinear vibration of laminated plates on a nonlin ear elastic foundat ion”,
Composite Structures , vol. 70, no. 1, pp. 606 615 , 2005.
H. S. Shen, F. Lin, Y. Xiang, “Nonlinear vibration of functionally graded graphene reinforced composite
laminated beams resting on elastic foundations in thermal environ ments”, Nonlinear Dynamics , vol. 90,
no. 2, pp. 899 914, 2017.
F. Tornabene, N. Fantuzzi, M. Bacciocchi, J. N. Reddy, “A posteriori stress and strain recovery procedure
for the static analysis of laminated shells resting on nonlinear elastic founda tion”, Composites Part
B Engineering , vol. 126, pp. 162 191, 2017.
S. G. Lekhnitskii, “Bending of a curved rod by moments and a force applied at the ends, theory of
elasticity of an anisotropic body”, Moscow: Mir. Pub ,
ASTMD6415/D6415M 06 a, “Standard test method for measuring the curved beam strength of a
fiber reinforced polymermatrix composite”, West Conshohocken: American Society for Testing and
Materials ,
R. A. Shenoi, W. Wang, “Flexural behaviour of a curved ort hotropic beam on an elastic foundation”,
Journal of Strain Analysis for Engineering Design , vol. 36, no. 1, pp. 1 15, 2001.
M. Arici, M. F. Granata, “Generalized curved beam on elastic foundation solved by transfer matrix
method”, Structural Enginee ring and Mechanics , vol. 40, no. 2, pp. 279 295, 2011.
K. H. Lo, R. M. Christensen, E. M. Wu, “Stress solution determination for high order plate theory”,
International Journal of Solids & Structures , vol. 14, no. 8, pp. 655 662, 1978.
J. N. R eddy, “A Simple Higher Order Theory for Laminated Composite Plates”, Journal of Applied
Mechanics , vol. 51, no. 4, pp. 745 752, 1984.
A. Y. Aköz, F. Kadioğlu, “The mixed finite element solution of circular beam on elastic foundation”,
Computers & Str uctures , vol. 60, no. 4, pp. 643 651, 1996.
M. R. Banan, G. Karami, M. Farshad, “Finite element analysis of curved beams on elastic foundations”,
Computers & Structures , vol. 32, no. 1, pp. 45 53, 1989.
F. F. Çalım, F. G. Akkurt, “Static and fre e vibration analysis of straight and circular beams on elastic
foundation”, Mechanics Research Communications , vol. 38, no. 2, pp. 89 94, 2011.
F. F. Çalım, “Forced vibration of curved beams on two parameter elastic foundation”, Applied
Mathematical Mo delling , vol. 36, no. 3, pp. 964 973, 2012.
T. M. Wang, W. F. Brannen, “Natural frequencies for out of plane vibrations of curved beams on elastic
foundations”, Journal of Sound & Vibration , vol. 84, no. 2, pp. 241 246, 1982.
H.R.Öz, M. Pakdemirl i, E. Özkaya, “Non linear vibrations of a slightly curved beam resting on a non linear
elastic foundation”, Journal of Sound & Vibration , vol. 212, no. 2, pp. 295 309, 1998.
C. S. Chen, A. H. Tan, R. D. Chien, “Non linear oscillations of orthotropic p lates on a non linear elastic
foundation”, Journal of Reinforced Plastics and Composites , vol. 28, no. 7, pp. 851 867, 2009.
P. Malekzadeh, M. R. G. Haghighi, M. M. Atashi, “Out of plane free vibration of functionally graded
circular curved beams in t hermal environment”, International Journal of Applied Mechanics , vol. 2, no. 3,
pp. 635 652, 2010.
C. L. Wei, C. S. Chen, C. S. Shih, Y. C. Chang, Nonlinear vibration of initially stressed hybrid composite
plates on elastic foundations , Mechanics of C omposite Materials , vol. 48, no. 4, pp. 467 482, 2012.
J. Zhong, Y. Fu, Y. Chen, Y. Li, “Analysis of nonlinear dynamic responses for functionally graded beams
resting on tensionless elastic foundation under thermal shock”, Composite Structures , vol. 1 42, pp.
277, 2016.
M. Adineh, M. Kadkhodayan, “Three dimensional thermo elastic analysis and dynamic response of a
multi directional functionally graded skew plate on elastic foundation”, Composites Part B Engineering ,
vol. 125, pp. 227 240, 2017.
P. H. Cong, P. T. N. An, N. D. Duc, “Nonlinear stability of shear deformable eccentrically stiffened
functionally graded plates on elastic foundations with temperature dependent properties”, Science and
Engineering of Composite Materials , vol. 24, no . 3, pp. 455 469, 2017.
N. D. Duc, P. D. Nguyen, N. D. Khoa, “Nonlinear dynamic analysis and vibration of eccentrically stiffened
S FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments”,
Thin walled structures , v ol. 117, pp. 178 189, 2017.
N. D. Duc, V. D. Quang, V. T. T. Anh, “The nonlinear dynamic and vibration of the S FGM shallow
spherical shells resting on an elastic foundations including temperature effects”, International Journal of
Mechanical Sciences , vol. 123, pp. 54 63, 2017.
D. V. Dung, P. M. Vuong, “Analytical investigation on buckling and postbuckling of FGM toroidal shell
segment surrounded by elastic foundation in thermal environment and under external pressure using
TSDT”, Acta Mechanica vol. 228, no. 10, pp. 3511 3531, 2017.
C. Q. Dai, L. Wang, Y. J. Wang, “Deformation study of Lining on Overlap Tunnels Based on Elastic
Foundation Beam”, Applied Mechanics & Materials , vol. 94, no. 10, pp. 1875 1878, 2011.
F. X. Sun, X. H. Cai, Y. H. Zhu, “Analytical solution of internal force and displacement in multi center
circular arc tunnel lining based on initial parameter method”, Rock & Soil Mechanics , vol. 30, no. 4, pp.
1130, 2009. (in Chinese)
J. Z. Wen, Y. X. Zhang, C. Wang, “Back analysis of internal force of initial support in tunnel based on
touch stress”, Rock & Soil Mechanics , vol. 32, no. 8, pp. 2467 2472, 2011. (in Chinese)
Z. Li, S. Y. Chen, “Calculation and analysis of longitudinal settlement join t of shield tunnel based on dual
elastic foundation beam”, World Automation Congress. IEEE , pp. 1 6, 2012.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).