A Case Study on the Numerical-Probability Approach for Deep Excavation Analysis

Authors: Komeil Valipourian

Abstract:

Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: Numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method, FDM.

References:

[1] Ghahramani, Z., Probabilistic machine learning and artificial intelligence. Nature, 2015. 521(7553): p. 452-459. https://doi.org/10.1038/nature14541
[2] Vanmarcke, E.H., Probabilistic modeling of soil profiles. Journal of the geotechnical engineering division, 1977. 103(11): p. 1227-1246.
[3] Jiangsheng, Y., Probabilistic Analysis and Randomized Algorithms. 2002.
[4] Lee, Y.-F., et al.., Reliability analysis of rock wedge stability: knowledge-based clustered partitioning approach. Journal of Geotechnical and Geoenvironmental Engineering, 2011. 138(6): p. 700-708. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000618
[5] Wu, T.H., et al.., Reliability of offshore foundations—State of the art. Journal of Geotechnical Engineering, 1989. 115(2): p. 157-178. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:2(157)
[6] Tang, W., M. Yucemen, and A.-S. Ang, Probability-based short term design of soil slopes. Canadian Geotechnical Journal, 1976. 13(3): p. 201-215. https://doi.org/10.1139/t76-024
[7] El-Ramly, H., N. Morgenstern, and D. Cruden, Probabilistic slope stability analysis for practice. Canadian Geotechnical Journal, 2002. 39(3): p. 665-683. https://doi.org/10.1139/t02-034
[8] Griffiths, D. and G.A. Fenton, Probabilistic slope stability analysis by finite elements. Journal of Geotechnical and Geoenvironmental Engineering, 2004. 130(5): p. 507-518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507)
[9] Cho, S.E., Probabilistic assessment of slope stability that considers the spatial variability of soil properties. Journal of geotechnical and geoenvironmental engineering, 2009. 136(7): p. 975-984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309
[10] Javankhoshdel, S. and R.J. Bathurst, Simplified probabilistic slope stability design charts for cohesive and cohesive-frictional (c-ϕ) soils. Canadian Geotechnical Journal, 2014. 51(9): p. 1033-1045. https://doi.org/10.1139/cgj-2013-0385
[11] Kitch, W.A., S.G. Wright, and R.B. Gilbert. Probabilistic analysis of reinforced soil slopes. in Engineering Mechanics. 1994. Citeseer.
[12] Luo, N., R.J. Bathurst, and S. Javankhoshdel, Probabilistic stability analysis of simple reinforced slopes by finite element method. Computers and Geotechnics, 2016. 77: p. 45-55. https://doi.org/10.1016/j.compgeo.2016.04.001
[13] de Araújo, J. and A.M. Awruch, Probabilistic finite element analysis of concrete gravity dams. Advances in Engineering Software, 1998. 29(2): p. 97-104. https://doi.org/10.1016/S0965-9978(98)00052-0
[14] McGuire, R.K., Probabilistic seismic hazard analysis: Early history. Earthquake Engineering & Structural Dynamics, 2008. 37(3): p. 329-338. https://doi.org/10.1002/eqe.765
[15] Cornell, C.A., Engineering seismic risk analysis. Bulletin of the seismological society of America, 1968. 58(5): p. 1583-1606.
[16] Gong, W., et al.., Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties. Tunnelling and Underground Space Technology, 2018. 73: p. 1-14. https://doi.org/10.1016/j.tust.2017.11.026
[17] Long, M., Database for retaining wall and ground movements due to deep excavations. Journal of Geotechnical and Geoenvironmental Engineering, 2001. 127(3): p. 203-224. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:3(203)
[18] Moormann, C., Analysis of wall and ground movements due to deep excavations in soft soil based on a new worldwide database. Soils and Foundations, 2004. 44(1): p. 87-98. https://doi.org/10.3208/sandf.44.87
[19] Leung, E.H. and C.W. Ng, Wall and ground movements associated with deep excavations supported by cast in situ wall in mixed ground conditions. Journal of geotechnical and geoenvironmental engineering, 2007. 133(2): p. 129-143. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:2(129)
[20] Castaldo, P., M. Calvello, and B. Palazzo, Probabilistic analysis of excavation-induced damages to existing structures. Computers and Geotechnics, 2013. 53: p. 17-30. https://doi.org/10.1016/j.compgeo.2013.04.008
[21] Hsiung, B.-C.B., et al.., Evaluation of the wall deflections of a deep excavation in Central Jakarta using three-dimensional modeling. Tunnelling and Underground Space Technology, 2018. 72: p. 84-96. https://doi.org/10.1016/j.tust.2017.11.013
[22] Luo, Z., et al.., Effects of vertical spatial variability on supported excavations in sands considering multiple geotechnical and structural failure modes. Computers and Geotechnics, 2018. 95: p. 16-29. https://doi.org/10.1016/j.compgeo.2017.11.017
[23] Clough, G.W. and T.D. O'Rourke. Construction induced movements of insitu walls. in Design and performance of earth retaining structures. 1990. ASCE.
[24] Peck, R.B., Deep excavations and tunneling in soft ground. Proc. 7th Int. Con. SMFE, State of the Art, 1969: p. 225-290.
[25] Hashash, Y.M. and A.J. Whittle, Ground movement prediction for deep excavations in soft clay. Journal of geotechnical engineering, 1996. 122(6): p. 474-486. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:6(474)
[26] Finno, R.J. and M. Calvello, Supported excavations: observational method and inverse modeling. Journal of Geotechnical and Geoenvironmental Engineering, 2005. 131(7): p. 826-836. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:7(826)
[27] Poulos, H. and L. Chen, Pile response due to excavation-induced lateral soil movement. Journal of Geotechnical and Geoenvironmental Engineering, 1997. 123(2): p. 94-99. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:2(94)
[28] Kung, G.T., et al.., Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays. Journal of Geotechnical and Geoenvironmental Engineering, 2007. 133(6): p. 731-747. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(731)
[29] Hashash, Y.M., et al.., Novel approach to integration of numerical modeling and field observations for deep excavations. Journal of Geotechnical and Geoenvironmental Engineering, 2006. 132(8): p. 1019-1031. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:8(1019)
[30] McKay, M.D., R.J. Beckman, and W.J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979. 21(2): p. 239-245.
[31] Hänninen, S., M. Lehtonen, and U. Pulkkinen, A probabilistic method for detection and location of very high resistive earth faults. Electric Power Systems Research, 2000. 54(3): p. 199-206. https://doi.org/10.1016/S0378-7796(99)00084-X
[32] Robert, C.P., Casella: Monte Carlo Statistical Methods. Springerverlag, New York, 2004. 3. https://doi.org/10.1007/978-1-4757-4145-2
[33] Wang, W. and J. Fu, Global assessment of predictability of water availability: a bivariate probabilistic Budyko analysis. Journal of Hydrology, 2017.
[34] Zhao, H., C. Zhao, and Y. Ruan, A probabilistic soft alert method for abnormal glycemic event by quantitative analysis of prediction uncertainty for type 1 diabetes. Chemometrics and Intelligent Laboratory Systems, 2018. https://doi.org/10.1016/j.chemolab.2018.01.010
[35] Choi, S.-K., R.A. Canfield, and R.V. Grandhi, Probabilistic Analysis. Reliability-based Structural Design, 2007: p. 51-80.
[36] Hubbard, D.W., How to measure anything: Finding the value of intangibles in business. 2014: John Wiley & Sons.
[37] Rübenkönig, O., The finite difference method (FDM)-an introduction. Albert Ludwigs University of Freiburg, 2006: p. 139.
[38] Chen, J., et al.., Numerical study on the movement of existing tunnel due to deep excavation in Shanghai. Geotechnical Engineering Journal of the SEAGS & AGSSEA, 2011. 42(3): p. 30-40.
[39] Chang, C.-T., et al.., Response of a Taipei Rapid Transit System (TRTS) tunnel to adjacent excavation. Tunnelling and Underground Space Technology, 2001. 16(3): p. 151-158. https://doi.org/10.1016/S0886-7798(01)00049-9
[40] Svoboda, T. and D. Masin, Comparison of displacement field predicted by 2D and 3D finite element modelling of shallow NATM tunnels in clays. geotechnik, 2011. 34(2): p. 115-126. https://doi.org/10.1002/gete.201000009
[41] Janin, J., et al.., Numerical back-analysis of the southern Toulon tunnel measurements: a comparison of 3D and 2D approaches. Engineering Geology, 2015. 195: p. 42-52. https://doi.org/10.1016/j.enggeo.2015.04.028
[42] Do, N.A. and D. Dias, A comparison of 2D and 3D numerical simulations of tunnelling in soft soils. Environmental Earth Sciences, 2017. 76(3): p. 102. https://doi.org/10.1007/s12665-017-6425-z
[43] Likitlersuang, S., et al.., Finite element analysis of a deep excavation: A case study from the Bangkok MRT. Soils and foundations, 2013. 53(5): p. 756-773. https://doi.org/10.1016/j.sandf.2013.08.013