Explicit Approach for Reliability-Based Design of Lining Structures Subjected to Water Seepage Considering Spatial Correlation and Uncertainty
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 3
Abstract
With the rapid urbanization in this era, it has become an economic imperative to make use of underground space in many countries. Achieving long-term durability goals of lining structures is a challenging task to guarantee the normal serviceability of underground space, which may be affected by many threatening factors such as water seepage. In this paper, an explicit method is developed to guide the design of lining structure thickness against water seepage in a probability-based framework. For a two-dimensional surface, the mean value and variance of the average seepage scenario are first derived in a closed form, taking into account the spatial correlation and uncertainty of the lining structure thickness and water seepage depth. The gamma distribution is used to describe the probabilistic behavior of the average seepage scenario, based on which an explicit link is established between the lining structure thickness and structural failure probability. A numerical example is presented to demonstrate the accuracy and applicability of the proposed method.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research described in this paper was supported by the Vice-Chancellor’s Postdoctoral Research Fellowship from the University of Wollongong. This support is gratefully acknowledged. The author would like to acknowledge the thoughtful suggestions of two anonymous reviewers, which substantially improved the present paper.
References
Ahmad, S. 2003. “Reinforcement corrosion in concrete structures, its monitoring and service life prediction—A review.” Cem. Concr. Compos. 25 (4–5): 459–471. https://doi.org/10.1016/S0958-9465(02)00086-0.
Baji, H., C.-Q. Li, S. Scicluna, and J. Dauth. 2017. “Risk-cost optimised maintenance strategy for tunnel structures.” Tunnelling Underground Space Technol. 69 (Oct): 72–84. https://doi.org/10.1016/j.tust.2017.06.008.
Barg, S., F. Flager, and M. Fischer. 2018. “An analytical method to estimate the total installed cost of structural steel building frames during early design.” J. Build. Eng. 15 (Jan): 41–50. https://doi.org/10.1016/j.jobe.2017.10.010.
BTS/ICE (British Tunnelling Society and Institution of Civil Engineers). 2004. Tunnel lining design guide. London: Thomas Telford.
Carpinteri, A., G. Lacidogna, and S. Cammarano. 2014. “Conceptual design of tall and unconventionally shaped structures: A handy analytical method.” Adv. Struct. Eng. 17 (5): 767–783. https://doi.org/10.1260/1369-4332.17.5.767.
Castro, J., D. Bentz, and J. Weiss. 2011. “Effect of sample conditioning on the water absorption of concrete.” Cem. Concr. Compos. 33 (8): 805–813. https://doi.org/10.1016/j.cemconcomp.2011.05.007.
CEN (European Committee for Standardization). 2002. Basis of structural design. EN1990. Eurocode. Brussels, Belgium: CEN.
Deby, F., M. Carcassès, and A. Sellier. 2009. “Probabilistic approach for durability design of reinforced concrete in marine environment.” Cem. Concr. Res. 39 (5): 466–471. https://doi.org/10.1016/j.cemconres.2009.03.003.
Dejam, M., H. Hassanzadeh, and Z. Chen. 2017. “Pre-Darcy flow in porous media.” Water Resour. Res. 53 (10): 8187–8210. https://doi.org/10.1002/2017WR021257.
De Schutter, G., and K. Audenaert. 2004. “Evaluation of water absorption of concrete as a measure for resistance against carbonation and chloride migration.” Mater. Struct. 37 (9): 591. https://doi.org/10.1007/BF02483288.
Ellingwood, B. R. 2000. “LRFD: Implementing structural reliability in professional practice.” Eng. Struct. 22 (2): 106–115. https://doi.org/10.1016/S0141-0296(98)00099-6.
Govindaraju, R. S., R. Morbidelli, and C. Corradini. 2001. “Areal infiltration modeling over soils with spatially correlated hydraulic conductivities.” J. Hydrol. Eng. 6 (2): 150–158. https://doi.org/10.1061/(ASCE)1084-0699(2001)6:2(150).
Gravanis, E., L. Pantelidis, and D. Griffiths. 2014. “An analytical solution in probabilistic rock slope stability assessment based on random fields.” Int. J. Rock Mech. Min. Sci. 71 (Jan): 19–24. https://doi.org/10.1016/j.ijrmms.2014.06.018.
He, Z.-S., M. Akiyama, C. He, D. M. Frangopol, and S.-J. Liu. 2019. “Life-cycle reliability analysis of shield tunnels in coastal regions: Emphasis on flexural performance of deteriorating segmental linings.” Struct. Infrastruct. Eng. 15 (7): 851–871. https://doi.org/10.1080/15732479.2019.1578381.
Ho, D., and G. J. Chirgwin. 1996. “A performance specification for durable concrete.” Constr. Build. Mater. 10 (5): 375–379. https://doi.org/10.1016/0950-0618(95)00015-1.
Hojjati, A., I. Jefferson, N. Metje, and C. D. Rogers. 2017. “Embedding sustainability criteria into pre-appraisal of underground utility for future cities.” Proc. Inst. Civ. Eng. Urban Des. Plann. 170 (6): 258–271. https://doi.org/10.1680/jurdp.17.00023.
Huang, J., A. Lyamin, D. Griffiths, K. Krabbenhoft, and S. Sloan. 2013. “Quantitative risk assessment of landslide by limit analysis and random fields.” Comput. Geotech. 53 (Sep): 60–67. https://doi.org/10.1016/j.compgeo.2013.04.009.
Inokuma, A., and S. Inano. 1996. “Road tunnels in Japan: Deterioration and countermeasures.” Tunnelling Underground Space Technol. 11 (3): 305–309. https://doi.org/10.1016/0886-7798(96)00026-0.
Jang, J., G. A. Narsilio, and J. C. Santamarina. 2011. “Hydraulic conductivity in spatially varying media—A pore-scale investigation.” Geophys. J. Int. 184 (3): 1167–1179. https://doi.org/10.1111/j.1365-246X.2010.04893.x.
Jiang, X., Y. Yuan, and X. Liu. 2014. “Multivariate probabilistic modelling for seepage risk assessment in tunnel segments.” Int. J. Reliab. Saf. 8 (2–4): 228–249. https://doi.org/10.1504/IJRS.2014.069507.
Li, Q., K. Li, X. Zhou, Q. Zhang, and Z. Fan. 2015. “Model-based durability design of concrete structures in Hong Kong–Zhuhai–Macau sea link project.” Struct. Saf. 53 (8): 1–12. https://doi.org/10.1016/j.strusafe.2014.11.002.
Li, Q., and X. Ye. 2018. “Surface deterioration analysis for probabilistic durability design of RC structures in marine environment.” Struct. Saf. 75 (Nov): 13–23. https://doi.org/10.1016/j.strusafe.2018.05.007.
Lin, W., and T. Yoda. 2017. Bridge engineering: Classifications, design loading, and analysis methods. Oxford, UK: Butterworth-Heinemann.
Liu, P.-L., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Lockington, D., C. Leech, J. Parlange, and P. Dux. 2002. “The sorptivity test and predicting resistance to water absorption in concrete.” In Proc., Int. Conf. held at the Univ. of Dundee, Scotland, UK, September 9–11, 2002, 315–324. London: Thomas Telford.
Mathai, A., P. Moschopoulos, and G. Pederzoli. 1999. “Random points associated with rectangles.” Rend. Circolo Matematico di Palermo 48 (1): 163–190. https://doi.org/10.1007/BF02844387.
Melchers, R. E., and A. T. Beck. 2018. Structural reliability analysis and prediction. Hoboken, NJ: Wiley.
Metwaly, M., M. Khalil, E.-S. Al-Sayed, and S. Osman. 2006. “A hydrogeophysical study to estimate water seepage from northwestern Lake Nasser, Egypt.” J. Geophys. Eng. 3 (1): 21–27. https://doi.org/10.1088/1742-2132/3/1/003.
Montes, F., and L. Haselbach. 2006. “Measuring hydraulic conductivity in pervious concrete.” Environ. Eng. Sci. 23 (6): 960–969. https://doi.org/10.1089/ees.2006.23.960.
Muhammad, N. Z., A. Keyvanfar, M. Z. A. Majid, A. Shafaghat, and J. Mirza. 2015. “Waterproof performance of concrete: A critical review on implemented approaches.” Constr. Build. Mater. 101 (Dec): 80–90. https://doi.org/10.1016/j.conbuildmat.2015.10.048.
Murata, J., Y. Ogihara, S. Koshikawa, and Y. Itoh. 2004. “Study on watertightness of concrete.” ACI Mater. J. 101 (2): 107–116.
National Standard. 2008. Unified standard for reliability design of engineering structures. GB50153. Beijing, China: Ministry of Housing and Urban-Rural Construction of the People’s Republic of China.
Neithalath, N., J. Weiss, and J. Olek. 2006. “Characterizing enhanced porosity concrete using electrical impedance to predict acoustic and hydraulic performance.” Cem. Concr. Res. 36 (11): 2074–2085. https://doi.org/10.1016/j.cemconres.2006.09.001.
Pan, X., Z. Shi, C. Shi, T.-C. Ling, and N. Li. 2017. “A review on surface treatment for concrete—Part 2: Performance.” Constr. Build. Mater. 133 (Feb): 81–90. https://doi.org/10.1016/j.conbuildmat.2016.11.128.
Panthi, K. K., and B. Nilsen. 2010. “Uncertainty analysis for assessing leakage through water tunnels: A case from Nepal Himalaya.” Rock Mech. Rock Eng. 43 (5): 629–639. https://doi.org/10.1007/s00603-009-0075-8.
Phoon, K.-K. 2006. “Serviceability limit state reliability-based design.” In New generation design codes for geotechnical engineering practice. Singapore: World Scientific.
Qian, Q. 2016. “Present state, problems and development trends of urban underground space in China.” Tunnelling Underground Space Technol. 55 (May): 280–289. https://doi.org/10.1016/j.tust.2015.11.007.
Schneider, S., D. Mallants, and D. Jacques. 2012. “Determining hydraulic properties of concrete and mortar by inverse modelling.” MRS Online Proc. Lib. 1475 (1): 367–372. https://doi.org/10.1557/opl.2012.601.
Serrano, S. E. 1995. “Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity.” Water Resour. Res. 31 (11): 2733–2742. https://doi.org/10.1029/95WR02038.
Smyl, D., F. Ghasemzadeh, and M. Pour-Ghaz. 2016. “Modeling water absorption in concrete and mortar with distributed damage.” Constr. Build. Mater. 125 (Oct): 438–449. https://doi.org/10.1016/j.conbuildmat.2016.08.044.
Solomon, H. 1978. Geometric probability. Philadelphia: Society for Industrial and Applied Mathematics.
Sterling, R., H. Admiraal, N. Bobylev, H. Parker, J.-P. Godard, I. Vähäaho, C. D. Rogers, X. Shi, and T. Hanamura. 2012. “Sustainability issues for underground space in urban areas.” Proc. Inst. Civ. Eng. 165 (4): 241–254. https://doi.org/10.1680/udap.10.00020.
Stewart, M. G., and J. A. Mullard. 2007. “Spatial time-dependent reliability analysis of corrosion damage and the timing of first repair for RC structures.” Eng. Struct. 29 (7): 1457–1464. https://doi.org/10.1016/j.engstruct.2006.09.004.
Vu, K. A., and M. G. Stewart. 2005. “Predicting the likelihood and extent of reinforced concrete corrosion-induced cracking.” J. Struct. Eng. 131 (11): 1681–1689. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:11(1681).
Wang, C. 2020. “Reliability-based design of lining structures for underground space against water seepage.” Underground Space 2020 (Apr): 12. https://doi.org/10.1016/j.undsp.2020.03.004.
Wang, C. 2021. Structural reliability and time-dependent reliability. Berlin: Springer.
Wang, C., Q. Li, and B. R. Ellingwood. 2016. “Time-dependent reliability of ageing structures: An approximate approach.” Struct. Infrastruct. Eng. 12 (12): 1566–1572. https://doi.org/10.1080/15732479.2016.1151447.
Wang, L., and T. Ueda. 2011. “Mesoscale modeling of water penetration into concrete by capillary absorption.” Ocean Eng. 38 (4): 519–528. https://doi.org/10.1016/j.oceaneng.2010.12.019.
Wang, X., Q. Shi, W. Fan, R. Wang, and L. Wang. 2019. “Comparison of the reliability-based and safety factor methods for structural design.” Appl. Math. Modell. 72 (Aug): 68–84. https://doi.org/10.1016/j.apm.2019.03.018.
Yang, W., C.-Q. Li, and H. Baji. 2019. “Design for service life of underground space based on water seepage criterion.” Tunnelling Underground Space Technol. 93 (8): 103066. https://doi.org/10.1016/j.tust.2019.103066.
Yoo, J.-H., H.-S. Lee, and M. A. Ismail. 2011. “An analytical study on the water penetration and diffusion into concrete under water pressure.” Constr. Build. Mater. 25 (1): 99–108. https://doi.org/10.1016/j.conbuildmat.2010.06.052.
Yuan, Y., Y. Bai, and J. Liu. 2012. “Assessment service state of tunnel structure.” Tunnelling Underground Space Technol. 27 (1): 72–85. https://doi.org/10.1016/j.tust.2011.07.002.
Yuan, Y., X. Jiang, and Q. Ai. 2017. “Probabilistic assessment for concrete spalling in tunnel structures.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 3 (4): 04017011. https://doi.org/10.1061/AJRUA6.0000912.
Zhang, J., G. Ma, R. Ming, X. Cui, L. Li, and H. Xu. 2018. “Numerical study on seepage flow in pervious concrete based on 3D CT imaging.” Constr. Build. Mater. 161 (Feb): 468–478. https://doi.org/10.1016/j.conbuildmat.2017.11.149.
Zhang, Y., D. Zhang, Q. Fang, L. Xiong, L. Yu, and M. Zhou. 2020. “Analytical solutions of non-Darcy seepage of grouted subsea tunnels.” Tunnelling Underground Space Technol. 96 (Feb): 103182. https://doi.org/10.1016/j.tust.2019.103182.
Zhou, Y., and J. Zhao. 2016. “Assessment and planning of underground space use in Singapore.” Tunnelling Underground Space Technol. 55 (Aug): 249–256. https://doi.org/10.1016/j.tust.2015.12.018.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 3 • September 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 14, 2020
Accepted: Apr 18, 2021
Published online: Jul 15, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 15, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.