Skip to main content
SpringerLink
Log in

Determination of isolation layer thickness for undersea mine based on differential cubature solution to irregular Mindlin plate

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The differential cubature solution to the problem of a Mindlin plate lying on the Winkler foundation with two simply supported edges and two clamped edges was derived. Discrete numerical technology and shape functions were used to ensure that the solution is suitable to irregular shaped plates. Then, the mechanical model and the solution were employed to model the protection layer that isolates the mining stopes from sea water in Sanshandao gold mine, which is the first subsea mine of China. Furthermore, thickness optimizations for the protection layers above each stope were conducted based on the maximum principle stress criterion, and the linear relations between the best protection layer thickness and the stope area under different safety factors were regressed to guide the isolation design. The method presented in this work provides a practical way to quickly design the isolation layer thickness in subsea mining.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. LI X, LI D, LIU Z, ZHAO G, WANG W. Determination of the minimum thickness of crown pillar for safe exploitation of a subsea gold mine based on numerical modeling [J]. International Journal of Rock Mechanics & Mining Sciences, 2013, 57(1): 42–56.

    Article  Google Scholar 

  2. NILSEN B, DAHLD T S. Stability and rock cover of hard rock subsea tunnels [J]. Tunnelling & Underground Space Technology, 1994, 9(2):151–158.

    Article  Google Scholar 

  3. NILSEN B. The optimum rock cover for subsea tunnels. Rock mechanics contributions and challenges [C]// Proceeding of the 31st US Symposium on Rock Mechanics. Golden, BALKEMA A A, Rotterdam Colorado: ASME, 1990: 1005–1012.

    Google Scholar 

  4. LI S C, LI S C, XU B S, WANG H P, DING W T. Study on determination method for minimum rock cover of subsea tunnel [J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(11): 2289–2295.

    Google Scholar 

  5. OU D Y, MAK C M, KONG P R. Free flexural vibration analysis of stiffened plates with general elastic boundary supports [J]. World Journal of Modelling and Simulation, 2012, 8(2): 96–102.

    Google Scholar 

  6. LI W L, ZHANG X, DU J, LIU Z. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports [J]. Journal of Sound and Vibration, 2009, 321(1): 254–269.

    Google Scholar 

  7. CIVALEK Ö. Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods [J]. Applied Mathematical Modelling, 2007, 31(3): 606–624.

    Article  MATH  Google Scholar 

  8. CATANIA G, SORRENTINO S. Spectral modeling of vibrating plates with general shape and general boundary conditions [J]. Journal of Vibration and Control, 2012,18(18):1607–1623.

    Article  MathSciNet  Google Scholar 

  9. CHEUNG Y K, THAM L G, LI W Y. Free vibration and static analysis of general plate by spline finite strip [J]. Computational Mechanics, 1988, 3(3): 187–197.

    Article  MATH  Google Scholar 

  10. SHI J, CHEN W, WANG C. Free vibration analysis of arbitrary shaped plates by boundary knot method [J]. Acta Mechanica Solida Sinica, 2009, 22(4): 328–336.

    Article  Google Scholar 

  11. KANG S W, ATLURI S N. Free vibration analysis of arbitrarily shaped polygonal plates with simply supported edges using a sub-domain method [J]. Journal of Sound and Vibration, 2009, 327(3): 271–284.

    Article  Google Scholar 

  12. SAADATPOUR M M, AZHARI M. The Galerkin method for static analysis of simply supported plates of general shape [J]. Computers & Structures, 1998, 69(1): 1–9.

    Article  MATH  Google Scholar 

  13. KHOV H, LI W L, GIBSON R F. An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions [J]. Composite Structures, 2009, 90(4): 474–481.

    Article  Google Scholar 

  14. QUINTANA M V, NALLIM L G. A general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports [J]. International Journal of Mechanical Sciences, 2013, 69: 1–9.

    Article  Google Scholar 

  15. LIEW K M, HAN J B, XIAO Z M, DU H. Differential quadrature method for Mindlin plates on Winkler foundations [J]. International Journal of Mechanical Sciences, 1996, 38(4): 405–421.

    Article  MATH  Google Scholar 

  16. REISSNER E. The effect of transverse shear deformation on the bending of elastic plates [J]. Journal of Applied Mechanics, 1945, 12(2): 69–77.

    MathSciNet  Google Scholar 

  17. REISSNER E. On bending of elastic plates [J]. Quarterly of Applied Mathematics, 1947, 5(1): 55–68.

    Article  MathSciNet  MATH  Google Scholar 

  18. MINDLIN R D. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates [J]. Journal of Applied Mechanics, 1951, 18: 31–38.

    MATH  Google Scholar 

  19. TSAI C C, WU E M Y. Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model [J]. Numerical Methods for Partial Differential Equations, 2012, 28(6): 1778–1793.

    Article  MathSciNet  MATH  Google Scholar 

  20. SETOODEH A R, MALEKZADEH P, VOSOUGHI A R. Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2012, 226(7): 1896–1906.

    Google Scholar 

  21. HOU G L, QI G W, XU Y N, CHEN A. The separable Hamiltonian system and complete biorthogonal expansion method of Mindlin plate bending problems [J]. Science China Physics: Mechanics and Astronomy, 2013, 56(5): 974–980.

    Article  Google Scholar 

  22. KOBAYASHI H, SONODA K. Rectangular Mindlin plates on elastic foundations [J]. International Journal of Mechanical Sciences, 1989, 31(9): 679–692.

    Article  MATH  Google Scholar 

  23. LIU F L, LIEW K M. Differential cubature method for static solutions of arbitrarily shaped thick plates [J]. International Journal of Solids and Structures, 1998, 35(28): 3655–3674.

    Article  MATH  Google Scholar 

  24. CIVAN F. Solving multivariable mathematical models by the quadrature and cubature methods [J]. Numerical Methods for Partial Differential Equations, 1994, 10(5): 545–567.

    Article  MathSciNet  MATH  Google Scholar 

  25. TIMOSHENKO S, WOINOWSKY-KRIEGER S. Theory of plates and shells [M]. New York: McGraw-Hill, 1959.

    MATH  Google Scholar 

  26. IYENGAR K T S R, CHANDRSHEKHARA K, SEBASTIAN V K. On the analysis of thick rectangular plates [J]. Ingenieur-Archive, 1974, 43(5): 317–330.

    Article  Google Scholar 

  27. PENG K, LI X B, WANG Z W. Hydrochemical characteristics of groundwater movement and evolution in the Xinli deposit of the Sanshandao gold mine using FCM and PCA methods [J]. Environmental Earth Sciences, 2015, 73(12): 7873–7888.

    Article  Google Scholar 

  28. PENG K, LI X B, WAN C C, PENG S Q, ZHAO G Y. Safe mining technology of undersea metal mine [J]. Transactions of Nonferrous Metals Society of China, 2012, 22(22): 740–746.

    Article  Google Scholar 

  29. KIM S M, MCCULLOUGH B F. Dynamic response of plate on viscous Winkler foundation to moving loads of varying amplitude [J]. Engineering Structures, 2003, 25(9): 1179–1188.

    Article  Google Scholar 

  30. GHAVANLOO E, DANESHMAND F, RAFIEI M. Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation [J]. Physica E: Lowdimensional Systems and Nanostructures, 2010, 42(9): 2218–2224.

    Article  Google Scholar 

  31. HARDEN C W, HUTCHINSON T C. Beam-on-nonlinear-Winklerfoundation modeling of shallow, rocking-dominated footings [J]. Earthquake Spectra, 2009, 25(2): 277–300.

    Article  Google Scholar 

  32. DALOGLU A T, VALLABHAN C V G. Values of k for slab on winkler foundation [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(5): 463–471.

    Article  Google Scholar 

  33. CHEN Y M, LI X B. Subsea large metal deposits safe and efficient mining technology [M]. Beijing: Press of Metallurgy Industry, 2013.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Kang Peng  (彭康) & Zhao-peng Liu  (刘照朋)

  2. State Key Laboratory of Resources and Safe Mining (CUMT), Xuzhou, 221116, China

    Kang Peng  (彭康)

  3. College of Resources and Environmental Science, Chongqing University, Chongqing, 400030, China

    Kang Peng  (彭康) & Zhao-peng Liu  (刘照朋)

  4. Automotive School, Qingdao Technological University, Qingdao, Shandong, 266520, China

    Yong-liang Zhang  (张永亮)

  5. School of Highway, Chang’an University, Xi’an, 710064, China

    Xiang Fan  (范祥)

  6. College of Resources and Metallurgy, Guangxi University, Nanning, 530004, China

    Qin-fa Chen  (陈庆发)

Authors
  1. Kang Peng  (彭康)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhao-peng Liu  (刘照朋)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong-liang Zhang  (张永亮)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiang Fan  (范祥)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qin-fa Chen  (陈庆发)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kang Peng  (彭康).

Additional information

Foundation item: Projects(51504044, 51204100) supported by National Natural Science Foundation of China; Project(14KF05) supported by the Research Fund of The State Key Laboratory of Coal Resources and Mine Safety, CUMT, China; Project(cstc2016jcyjA1861) supported by the Research Fund of Chongqing Basic Science and Cutting-Edge Technology Special Projects, China; Project(2015CDJXY) supported by the Fundamental Research Funds for the Central Universities; Project supported by the China Postdoctoral Science Foundation; Project(2011DA105287-MS201503) supported by the Independent Subject of State Key Laboratory of Coal Mine Disaster Dynamics and Control, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, K., Liu, Zp., Zhang, Yl. et al. Determination of isolation layer thickness for undersea mine based on differential cubature solution to irregular Mindlin plate. J. Cent. South Univ. 24, 708–719 (2017). https://doi.org/10.1007/s11771-017-3472-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-017-3472-2

Key words

Search

Navigation