DOI QR코드

DOI QR Code

Physics-based reduced order model for computational geomechanics

  • Zhao, Hongbo (School of Civil and architectural Engineering, Shandong University of Technology) ;
  • Chen, Bingrui (Wuhan Institute of Rock and Soil mechanics, Chinese Academy of Sciences)
  • 투고 : 2020.05.17
  • 심사 : 2021.10.21
  • 발행 : 2021.11.25

초록

Numerical models are an essential tool in stability analysis, design, and construction for geotechnical engineering. Yet, numerical modeling is too time-consuming in practical engineering. In this study, a physics-based reduced order model (ROM) was developed to approximate the displacement and stress field of geotechnical structure by combining Latin hypercube sampling (LHS), a numerical method and proper orthogonal decomposition (POD). The set of design variables were constructed using LHS. A numerical model was used to generate the snapshots based on the design variables. POD was used to compute the eigenvalues and eigenvectors of a spatial Gram matrix, which was constructed based on snapshots. The first K eigenfunction vectors were determined based on eigenvalues and eigenvectors of the spatial Gram matrix. The interpolation matrix of elements was computed using a radial basin function (RBF), and then the vector of an element was determined by solving the penalized linear systems. To determine the new design variables, the coefficient of ROM was determined based on the RBF and the vector of elements, and the unknown field variables were predicted based on the ROM. The ROM was illustrated and verified for a circular tunnel. The results showed that the predicted displacement and stress field were in excellent agreement with both the analytical and numerical solutions. The physics-based ROM characterized well the deformation and failure mechanism of the surrounding rock mass and can be used to replace a numerical model for back analysis, optimal design, and uncertainty analysis of geotechnical engineering, thereby eliminating costly repetitive computations.

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참고문헌

  1. Aksoy, O.C., Uyar, G.G., Utku, S., Safak, S. and Ozacar, V. (2019), "A new integrated method to design of rock structures", Geomech. Eng., 18(4), 339-352. https://doi.org/10.12989/gae.2019.18.4.339.
  2. Alipanahi, B., Delong, A., Weirauch, M.T. and Frey, B.J. (2015), "Predicting the sequence specificities of DNA- and RNAbinding proteins by deep learning", Nature Biotech., 33(8),831-838. https://doi.org/10.1038/nbt.3300.
  3. Audouze, C., Vuyst, F.De. and Nair, P.B. (2009), "Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis", J. Numerical Methods Eng., 80 (8),1025-1057. https://doi.org/10.1002/nme.2540.
  4. Bai, X.D., Cheng, W.C., Ong, D.E.L. and Li, G. (2021), "Evaluation of geological conditions and clogging of tunneling using machine learning", Geomech. Eng., 25(1),59-73. http://dx.doi.org/10.12989/gae.2021.25.1.059.
  5. Bhattacharjee, S. and Matous, K. (2020), "A nonlinear data-driven reduced order model for computational homogenization with physics/pattern-guided sampling", Comput. Methods Appl. Mech. Eng., 359, 112657. https://doi.org/10.1016/j.cma.2019.112657.
  6. Cardoso, J.B., Almeida, J.R., Dias, J.M. and Coelho, P.G. (2008), "Structural reliability analysis using Monte Carlo simulation and neural networks", Adv. Eng. Software, 39(6), 505-513. https://doi.org/10.1016/j.advengsoft.2007.03.015.
  7. Cizmas, G.A., Richardson, B.R., Brenner, T.A., O'Brien, T.J. and Breault, R.W. (2008), "Acceleration techniques for reducedorder models based on proper orthogonal decomposition", J. Comput. Phys, 227(16), 7791-7812. https://doi.org/10.1016/j.jcp.2008.04.036.
  8. Duncan, Fama. M.E. (1993). "Numerical modeling of yield zones in weak rocks", Comprehensive Rock Engineering Vol. 2, Oxford, Pergamon, 49-75.
  9. Feng, X.T., Zhao, H. and Li, S. (2004), "A new displacement back analysis to identify mechanical geo-material parameters based on hybrid intelligent methodology", Int. J. Numer. Analytical Methods Geomech., 28(11), 1141-1165. https://doi.org/10.1002/nag.381.
  10. Fic, A., Bialecki, R.A. and Kassab, A.J. (2006), "Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite element method", Numer. Heat Transfer B, 48(2), 102-124. https://doi.org/10.1615/ICHMT.2004.CHT-04.390.
  11. FLAC3D 3.1 (2009), FLAC3D 3.1: Verification Problems, Itasca, Minneapolis, USA.
  12. Freno, B.A. and Cizmas, P.G.A. (2014), "A proper orthogonal decomposition method for nonlinear flows with deforming meshes", Int. J. Heat Fluid Flow, 50, 145-159. https://doi.org/10.1016/j.ijheatfluidflow.2014.07.001.
  13. Gomes, H.M. and Awruch, A. M. (2004), "Comparison of response surface and neural network with other methods for structural reliability analysis", Struct. Safety, 26(1), 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5.
  14. Haghighat, E., Raissi, M., Moure, A., Gomez, H. and Juanes, R. (2021), "A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics", Comput. Methods Appl. Mech. Eng., 379, 113741. https://doi.org/10.1016/j.cma.2021.113741.
  15. Hamrouni, A., Dias, D and Sbartai, B. (2018), "Reliability analysis of a mechanically stabilized earth wall using the surface response methodology optimized by a genetic algorithm", Geomech. Eng., 15(4), 937-945. https://doi.org/10.12989/gae.2018.15.4.937.
  16. Hoek, E. (1999), "Putting numbers to geology-an engineer's viewpoint", Quarterly J. Eng. Geology Hydrogeology, 32(1), 1-19. https://doi.org/10.1144/GSL.QJEG.1999.032.P1.01.
  17. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", Int. J. Rock Mech. Mining Sci., 34(8), 1165-1186. https://doi.org/10.1016/S0148-9062(97)00305-7.
  18. Huys, Quentin. J.M., Maia, Tiago. V. and Frank, Michael. J. (2016), "Computational psychiatry as a bridge from neuroscience to clinical applications", Nature Neurosci., 19(3), 404-413. https://doi.org/10.1038/nn.4238.
  19. Jain, P. and Chakraborty, T. (2018), "Numerical analysis of tunnel in rock with basalt fiber reinforced concrete lining subjected to internal blast load", Comput. Concrete, 21(4), 399-406. https://doi.org/10.12989/cac.2018.21.4.399.
  20. Jing, L. and Hudson, J.A. (2002), "Numerical methods in rock mechanics", Int. J. Rock Mech. Mining Sci., 39(4),409-427. https://doi.org/10.1016/S1365-1609(02)00065-5.
  21. Kathirvel, P. and Kaliyaperumal, S.R.M. (2017), "Probabilistic modeling of geopolymer concrete using response surface methodology", Comput. Concrete, 19(6), 737-744. https://doi.org/10.12989/cac.2017.19.6.737.
  22. Kenneth, C., Hall, Jeffrey. P. Thomas., and Earl, H. Dowell. (2000), "Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows", AIAA J., 38(10),1853-1862. https://doi.org/10.2514/2.867.
  23. LeCun, Y., Bengio, Y. and Hinton, G. (2015), "Deep learning", Nature, 521, 436-444. https://doi.org/10.1038/nature14539.
  24. Li, D.Q., Zheng, D., Cao, Z.J., Tang, X.S. and Phoon, K.K. (2016), "Response surface methods for slope reliability analysis: Review and comparison", Eng. Geology, 203(25), 3-14. https://doi.org/10.1016/j.enggeo.2015.09.003.
  25. Li, Z., Liu, J., Xu, R., Liu, H. and Shi, W. (2021), "Study of grouting effectiveness based on shear strength evaluation with experimental and numerical approaches", Acta Geotechnica, https://doi.org/10.1007/s11440-021-01324-4.
  26. Liu, J., Jiang,Y., Zhang, Y. and Sakaguchi, O. (2021), "Influence of different combinations of measurement while drilling parameters by artificial neural network on estimation of tunnel support patterns", Geomech. Eng., 25(6), 439-454. http://dx.doi.org/10.12989/gae.2021.25.6.439.
  27. Lopes, P.A.M., Gomes H.M. and Awruch, A.M. (2010), "Reliability analysis of laminated composite structures using finite elements and neural networks", Compos. Structures, 92(7), 1603-1613. https://doi.org/10.1016/j.compstruct.2009.11.023.
  28. Luat, N.V., Lee, K. and Thai, D.K. (2020), "Application of artificial neural networks in settlement prediction of shallow foundations on sandy soils", Geomech. Eng., 20(5), 385-397. http://dx.doi.org/10.12989/gae.2020.20.5.385.
  29. Luo, Z., Gao, J. and Xie, Z. (2015), "Reduced-order finite difference extrapolation model based on proper orthogonal decomposition for two-dimensional shallow water equations including sediment concentration", J. Math. Anal. Appl., 429(2), 901-923. https://doi.org/10.1016/j.apm.2012.10.051.
  30. Lv, Q. and Low, B.K. (2011), "Probabilistic analysis of underground rock excavations using response surface method and SORM", Comput. Geotech., 38(8),1008-1021. https://doi.org/10.1016/j.compgeo.2011.07.003.
  31. Mahdevari, S. and Torabi, S.R. (2012), "Prediction of tunnel convergence using Artificial Neural Networks", Tunnel Underground Space Technol., 28(1), 218-228. https://doi.org/10.1016/j.tust.2011.11.002.
  32. Mahdevari, S., Torabi, S.R. and Monjezi, M. (2012), "Application of artificial intelligence algorithms in predicting tunnel convergence to avoid TBM jamming phenomenon", Int. J. Rock Mech. Min. Sci, 55, 33-44. https://doi.org/10.1016/j.ijrmms.2012.06.005.
  33. Mathew, T.V., Prajith, P., Ruiz, R.O., Atroshchenko, E. and Natarajan, S. (2020), "Adaptive importance sampling based neural network framework for reliability and sensitivity prediction for variable stiffness composite laminates with hybrid uncertainties", Compos. Struct., 245, 112344. https://doi.org/10.1016/j.compstruct.2020.112344.
  34. Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009), Response Surface Methodology-Process and Product Optimization Using Designed Experiments 3rd edition, Wiley, New Jersey, USA.
  35. Oh, J., Moon, T., Canbulat, I. and Moon, J.S. (2019), "Design of initial support required for excavation of underground cavern and shaft from numerical analysis", Geomech. Eng., 17(6), 573-581. https://doi.org/10.12989/gae.2019.17.6.573.
  36. Pichler, B., Lackner, R. and Mang, H.A. (2003), "Back analysis of model parameters in geotechnical engineering by means of soft computing", J. Numer. Meth. Eng., 57(14), 1943-1978. https://doi.org/10.1002/nme.740.
  37. Rafiai, H. and Moosavi, M. (2012), "An approximate ANN-based solution for convergence of lined circular tunnels in elastoplastic rock masses with anisotropic stresses", Tunnel Underground Space Technol., 27(1), 52-59. https://doi.org/10.1016/j.tust.2011.06.008.
  38. Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J. and Carvalhais, N. (2019), "Deep learning and process understanding for data-driven earth system science", Nature, 566,195-203. https://doi.org/10.1038/s41586-019-0912-1.
  39. Saseendran, R. and Dodagoudar G.R. (2020), "Reliability analysis of slopes stabilised with piles using response surface method", Geomech. Eng., 21(6), 513-525. https://doi.org/10.12989/gae.2020.21.6.513.
  40. Severson, K. A., Attia, P. M., Jin, N., Perkins, N., Jiang, B., Yang, Z., Chen, M.H., Aykol, M., Herring, P.K., Fraggedakis, D., Bazant, M.Z., Harris, S.J., Chueh, W.C. and Braatz, R. D. (2019), "Data-driven prediction of battery cycle life before capacity degradation", Nature Energy, 4, 383-391. https://doi.org/10.1038/s41560-019-0356-8.
  41. Tang, M., Liu, Y. and Durlofsky, L.J. (2020), "A deep-learningbased surrogate model for data assimilation in dynamic subsurface flow problems", J. Comput. Physics, 413, 109456. https://doi.org/10.1016/j.jcp.2020.109456.
  42. Thakur, S.N., Chakraborty, S. and Ray, C. (2019), "Reliability analysis of laminated composite shells by response surface method based on HSDT", Struct. Eng. Mech., 72(2), https://doi.org/10.12989/sem.2019.72.2.203.
  43. Veer, L.J. and Bernards, R. (2008), "Enabling personalized cancer medicine through analysis of gene-expression patterns", Nature, 452, 564-570. https://doi.org/10.1038/nature06915.
  44. You, K. (2014), "A case study on the utilization of tunnel face mapping data for a back analysis based on artificial neural network", KSCE J. Civil Eng., 18, 751-759. https://doi.org/10.1007/s12205-014-0329-1.
  45. Zhang, B., Ma, Z., Wang, X., Zhang, J. and Peng, W. (2020), "Reliability analysis of anti-seismic stability of 3D pressurized tunnel faces by response surfaces method", Geomech. Eng., 20(1), 43-54. https://doi.org/10.12989/gae.2020.20.1.043.
  46. Zhao, H. (2008), "Slope reliability analysis using a support vector machine", Comput. Geotech., 35(3), 459-467. https://doi.org/10.1016/j.compgeo.2007.08.002.
  47. Zhao, H. (2021), "A reduced order model based on machine learning for numerical analysis: An application to geomechanics", Eng. Appl. Artificial Intelligent, 100, 104194. https://doi.org/10.1016/j.engappai.2021.104194.
  48. Zhao, H. and Yin, S. (2016), "Inverse analysis of geomechanical parameters by artificial bee colony algorithm and multi-output support vector machine", Inverse Problems Sci. Eng., 24(7), 1266-1281. https://doi.org/10.1080/17415977.2016.1178257.
  49. Zhao, H., Chen, B. and Li, S. (2021), "Determination of geomaterial mechanical parameters based on back analysis and reduced-order model", Comput. Geotech., 132, 104013. https://doi.org/10.1016/j.compgeo.2021.104013.
  50. Zhao, H., Chen, B., Li, S., Li, Z. and Zhu, C. (2021), "Updating models and the uncertainty of mechanical parameters for rock tunnels using Bayesian inference", Geosci. Frontiers, 12(5), 101198. https://doi.org/10.1016/j.gsf.2021.101198.
  51. Zhao, H.B. and Yin, S.D. (2009), "Geomechanical parameters identification by particle swarm optimization and support vector machine", Appl. Math Model, 33(10), 3997-4012. https://doi.org/10.1016/j.apm.2009.01.011.
  52. Zienkiewicz, O.Z., Taylor, R.L. and Zhu, J.Z. (2005), The Finite Element Method: Its Basis and Fundamentals, Sixth edition, Elsevier, Singapore, Singapore.