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Multivariate adaptive regression splines model for reliability assessment of serviceability limit state of twin caverns

  • Zhang, Wengang (School of Civil and Environmental Engineering, Nanyang Technological University) ;
  • Goh, Anthony T.C. (School of Civil and Environmental Engineering, Nanyang Technological University)
  • Received : 2013.10.10
  • Accepted : 2014.07.02
  • Published : 2014.10.25

Abstract

Construction of a new cavern close to an existing cavern will result in a modification of the state of stresses in a zone around the existing cavern as interaction between the twin caverns takes place. Extensive plane strain finite difference analyses were carried out to examine the deformations induced by excavation of underground twin caverns. From the numerical results, a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) has been used to relate the maximum key point displacement and the percent strain to various parameters including the rock quality, the cavern geometry and the in situ stress. Probabilistic assessments on the serviceability limit state of twin caverns can be performed using the First-order reliability spreadsheet method (FORM) based on the built MARS model. Parametric studies indicate that the probability of failure $P_f$ increases as the coefficient of variation of Q increases, and $P_f$ decreases with the widening of the pillar.

Keywords

References

  1. Aksoy, C.O., Ozacar, V. and Kantarci, O. (2010), "An example of estimating rock mass deformation around an underground opening using numerical modeling", Int. J. Rock Mech. Min., 47(2), 272-278. https://doi.org/10.1016/j.ijrmms.2009.12.001
  2. Attoh-Okine, N.O., Cooger, K. and Mensah, S. (2009), "Multivariate adaptive regression spline (MARS) and hinged hyper planes (HHP) for doweled pavement performance modeling", Constr. Build. Mater., 23(9), 3020-3023. https://doi.org/10.1016/j.conbuildmat.2009.04.010
  3. Barton, N., Loset, F., Lien, R. and Lunde, J. (1980), "Application of Q system in design decisions concerning dimensions and appropriate support for underground installations", Proceedings of the International Conference on Subsurface Space, Rockstore, Stockholm, June, Volume 2, pp. 553-561.
  4. Basarir, H. (2006), "Engineering geological studies and tunnel support design at Sulakyurt dam site, Turkey", Eng. Geol., 86(4), 225-237. https://doi.org/10.1016/j.enggeo.2006.05.003
  5. Bieniawski, Z.T. (1978), "Determining rock mass deformability: experience from case histories", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 15(5), 237-247. https://doi.org/10.1016/0148-9062(78)90956-7
  6. Bieniawski, Z.T. (1989), Engineering Rock Mass Classifications, John Wiley and Sons, New York, USA.
  7. Cornell, C.A. (1969), "A probability-based structural code", ACI, 66(12), 974-985.
  8. Friedman, J.H. (1991), "Multivariate adaptive regression splines", Ann. Stat., 19(1), 1-141. https://doi.org/10.1214/aos/1176347963
  9. Gandomi, A.H. and Roke, D.A. (2013), "Intelligent formulation of structural engineering systems", 7th M.I.T. Conference on Computational Fluid and Solid Mechanics-Focus: Multiphysics & Multiscale, Massachusetts Institute of Technology, Cambridge, MA, USA, June.
  10. Goh, A.T.C., Xuan, F. and Zhang, W.G. (2013), "Reliability assessment of diaphragm wall deflections in soft clays", Foundation Engineering in the Face of Uncertainty (GSP 229) ASCE, 487-496.
  11. Goh, A.T.C. and Zhang, W.G. (2012), "Reliability assessment of stability of underground rock caverns", Int. J. Rock Mech. Min., 55, 157-163.
  12. Goh, A.T.C. and Zhang, W.G. (2014), "An improvement to MLR model for predicting liquefaction-induced lateral spread using multivariate adaptive regression splines", Eng. Geol., 170, 1-10. https://doi.org/10.1016/j.enggeo.2013.12.003
  13. Hasofer, A.M. and Lind, N. (1974), "An exact & invariant first-order reliability format", J. Eng. Mech. ASCE, 100(1), 111-121.
  14. Hastie, T., Tibshirani, R. and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference and Prediction, (2nd Ed.), Springer.
  15. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", J. Rock Mech. Min., 34(8), 1165-1186. https://doi.org/10.1016/S1365-1609(97)80069-X
  16. Itasca Consulting Group (2005), FLAC-3D, User's Guide: Fast-Lagrangian Analysis of Continua in 3 Dimensions-Version 3.0, Minneapolis, MN, USA.
  17. Jekabsons, G. (2010), VariReg: A Software Tool for Regression Modeling using Various Modeling Methods, Riga Technical University, Latvia, URL: http://www.cs.rtu.lv/jekabsons/.
  18. Lashkari, A. (2012), "Prediction of the shaft resistance of non-displacement piles in sand", Int. J. Numer. Anal. Met., 38(7), 904-931.
  19. Low, B.K. (1996), "Practical probabilistic approach using spreadsheet", Uncertainty in the Geologic Environment (GSP 58) ASCE, Reston, VA, USA, pp. 1284-1302.
  20. Low, B.K. and Tang, W.H. (2004), "Reliability analysis using object-oriented constrained optimization", Struct. Saf., 26(1), 69-89 https://doi.org/10.1016/S0167-4730(03)00023-7
  21. Low, B.K. and Tang, W.H. (2007), "Efficient spreadsheet algorithm for first-order reliability method", J. Eng. Mech. ASCE, 133(12), 1378-1387. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378)
  22. Meguid, M.A. and Rowe, R.K. (2006), "Stability and D-shaped tunnels in a Mohr-Coulomb material under anisotropic stress conditions", Can. Geotech. J., 43(3), 273-281. https://doi.org/10.1139/t06-004
  23. Mirzahosseinia, M., Aghaeifarb, A., Alavic, A., Gandomic, A. and Seyednour, R. (2011), "Permanent deformation analysis of asphalt mixtures using soft computing techniques", Expert Syst. Appl., 38(5), 6081-6100. https://doi.org/10.1016/j.eswa.2010.11.002
  24. Palmstrom, A. (2000), "On classification systems", Proceedings GeoEng2000, Melbourne, Vic, Australia, November.
  25. Samui, P. (2011), "Determination of ultimate capacity of driven piles in cohesionless soil: a multivariate adaptive regression spline approach", Int. J. Numer. Anal. Met., 36(11), 1434-1439.
  26. Samui, P. and Karup, P. (2011), "Multivariate adaptive regression spline and least square support vector machine for prediction of undrained shear strength of clay", IJAMC, 3(2), 33-42.
  27. Serafim, J.L. and Pereira, J.P. (1983), "Considerations of the geomechanics classification of Bieniawski", Proceedings of the International Symposium on Engineering Geology and Underground Construction, Lisbon, Portugal, Volume 1, pp. 1133-1142.
  28. Tugrul, A. (1998), "The application of rock mass classification systems to underground excavation in weak lime stone, Ataturk dam", Turk. Eng. Geol., 50(3-4), 337-345. https://doi.org/10.1016/S0013-7952(98)00034-9
  29. Zarnani, S., El-Emam, M. and Bathurst, R.J. (2011), "Comparison of numerical and analytical solutions for reinforced soil wall shaking table tests", Geomech. Eng., Int. J., 3(4), 291-321. https://doi.org/10.12989/gae.2011.3.4.291
  30. Zhang, W.G. and Goh, A.T.C. (2012), "Reliability assessment on ultimate and serviceability limit states and determination of critical factor of safety for underground rock caverns", Tunn. Undergr. Sp. Tech., 32, 221-230. https://doi.org/10.1016/j.tust.2012.07.002
  31. Zhang, W.G. and Goh, A.T.C. (2013), "Multivariate adaptive regression splines for analysis of geotechnical engineering systems", Comput. Geotech., 48, 82-95. https://doi.org/10.1016/j.compgeo.2012.09.016

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