Technical Papers
Sep 7, 2017

Detection of Stationary Markovian Zones in a Geologically Heterogeneous Area

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 3, Issue 4

Abstract

The stationary Markov process model is widely used to predict the geological conditions in tunnel excavation projects. However, the validity of the stationary assumption made in the model is questionable. The prediction error caused by the assumption has not been investigated in previous studies. In this study, the significance of a stationary Markovian zone detection is evaluated by comparing the predicted geological conditions with the real soil layer distributions in boreholes. A new method is proposed to detect the stationary Markovian zones in a tunnel-covered area. Borehole data from Perth, Australia are collected to illustrate the significance of the stationary Markovian zone detection and the effectiveness of the proposed method. The results show that the stationary assumption leads to considerable errors in the predicted number, location, and thickness of soil layers. The proposed method is robust with respect to the starting point of a detection.

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Acknowledgments

The authors gratefully acknowledge financial support from the Macau Science and Technology Development Fund (FDCT) 125/2014/A3 and the University of Macau Research Fund MYRG2015-00112-FST.

References

AGS (Australian Geomechanics Society). (1978). “Geotechnical borehole database, perth central business district, Western Australia.” ⟨https://australiangeomechanics.org/public-resources/downloads/⟩ (2015).
Anderson, T. W., and Goodman, L. A. (1957). “Statistical inference about Markov chains.” Ann. Math. Stat., 28(1), 89–110.
Bhat, U. N. (1972). Elements of applied stochastic processes, Wiley, New York.
Ching, J., and Phoon, K.-K. (2013). “Multivariate distribution for undrained shear strengths under various test procedures.” Can. Geotech. J., 50(9), 907–923.
Eisbacher, G. H. (1971). “Natural slope failure, northeastern Skeena mountains.” Can. Geotech. J., 8(3), 384–390.
Elfeki, A. M. M., and Dekking, F. M. (2001). “A Markov chain model for subsurface characterization: Theory and applications.” Math. Geol., 33(5), 569–589.
Elfeki, A. M. M., and Dekking, F. M. (2005). “Modelling subsurface heterogeneity by coupled Markov chains: Directional dependency, Walther’s law and entropy.” Geotech. Geol. Eng., 23(6), 721–756.
Elfeki, A. M. M., and Dekking, F. M. (2007). “Reducing geological uncertainty by conditioning on boreholes: The coupled Markov chain approach.” Hydrogeol. J., 15(8), 1439–1455.
Elkateb, T., Chalaturnyk, R., and Robertson, P. K. (2003). “An overview of soil heterogeneity: Quantification and implications on geotechnical field problems.” Can. Geotech. J., 40(1), 1–15.
Gates, P., and Tong, H. (1976). “On Markov chain modeling to some weather data.” J. Appl. Meteorol., 15(11), 1145–1151.
Halim, I. S. (1991). “Reliability of geotechnical systems considering geological anomaly.” Ph.D. dissertation, Univ. of Illinois at Urbana–Champaign, Champaign, IL.
Hu, Q., and Huang, H. (2007). “Risk analysis of soil transition in tunnel works.” Proc., 33rd ITA-AITES World Tunnel Congress—Underground Space—The 4th Dimension of Metropolises, Taylor & Francis, London, 209–215.
Ioannou, P. G. (1987). “Geologic prediction model for tunneling.” J. Constr. Eng. Manage., 569–590.
Ioannou, P. G. (1988). “Geologic exploration and risk reduction in underground construction.” J. Constr. Eng. Manage., 532–547.
Ioannou, P. G. (1989). “Evaluation of subsurface exploration programs.” J. Constr. Eng. Manage., 339–356.
Kohno, S., Ang, A. H. S., and Tang, W. H. (1992). “Reliability evaluation of idealized tunnel systems.” Struct. Saf., 11(2), 81–93.
Krumbein, W. C. (1968). “Statistical models in sedimentology.” Sedimentology, 10(1), 7–23.
Krumbein, W. C., and Dacey, M. F. (1969). “Markov chains and embedded Markov chains in geology.” J. Int. Assoc. Math. Geol., 1(1), 79–96.
Lee, S.-Y., Carle, S. F., and Fogg, G. E. (2007). “Geologic heterogeneity and a comparison of two geostatistical models: Sequential Gaussian and transition probability-based geostatistical simulation.” Adv. Water Resour., 30(9), 1914–1932.
Li, D.-Q., Qi, X.-H., Cao, Z.-J., Tang, X.-S., Phoon, K.-K., and Zhou, C.-B. (2016a). “Evaluating slope stability uncertainty using coupled Markov chain.” Comput. Geotech., 73, 72–82.
Li, J., Cassidy, M. J., Huang, J., Zhang, L., and Kelly, R. (2016b). “Probabilistic identification of soil stratification.” Géotechnique, 66(1), 16–26.
Park, E., Elfeki, A., and Dekking, M. (2005). “Characterization of subsurface heterogeneity: Integration of soft and hard information using multidimensional coupled Markov chain approach.” Developments in water science, T. Chin-Fu and A. A. John, eds., Elsevier, Amsterdam, Netherlands, 193–202.
Qi, X. H., and Zhou, W. H. (2017) “An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points.” Comput. Geotech., 85, 186–198.
Qi, X.-H., Li, D.-Q., Phoon, K.-K., Cao, Z.-J., and Tang, X.-S. (2016). “Simulation of geologic uncertainty using coupled Markov chain.” Eng. Geol., 207, 129–140.
Ruwanpura, J. Y., Abourizk, S. M., and Allouche, M. (2005). “An analytical method to predict soil types for underground construction operations.” Civil Eng. Environ. Syst., 22(1), 49–69.
Tang, W. H., Sidi, I., and Gilbert, R. B. (1989). “Average property in random two-state medium.” J. Eng. Mech., 131–144.
Ye, M., and Khaleel, R. (2008). “A Markov chain model for characterizing medium heterogeneity and sediment layering structure.” Water Resour. Res., 44(9), W09427.
Zhou, W. H., Yuen, K.-V., and Tan, F. (2013). “Estimation of maximum pullout shear stress of grouted soil nails using bayesian probabilistic approach.” Int. J. Geomech., 659–664.

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 3Issue 4December 2017

History

Received: Oct 3, 2016
Accepted: May 18, 2017
Published online: Sep 7, 2017
Published in print: Dec 1, 2017
Discussion open until: Feb 7, 2018

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Authors

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Xiao-Hui Qi [email protected]
Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, Faculty of Science and Technology, Univ. of Macau, Macau 999078, China. E-mail: [email protected]
Wan-Huan Zhou, M.ASCE [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Faculty of Science and Technology, Univ. of Macau, Macau 999078, China. E-mail: [email protected]
Ka-Veng Yuen [email protected]
Professor, Dept. of Civil and Environmental Engineering, Faculty of Science and Technology, Univ. of Macau, Macau 999078, China (corresponding author). E-mail: [email protected]

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