Kriging-Based Reliability Analysis of Strip Footings Resting on Spatially Varying Soils
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 144, Issue 10
Abstract
The probabilistic analysis of geotechnical structures presenting spatial variability in the soil properties is generally performed using Monte Carlo simulation (MCS) methodology. Despite being robust and accurate, MCS has low efficiency when considering the small failure probabilities encountered in practice. This is because it is very time-expensive in such cases due to the large number of simulations required to calculate a small failure probability with a small value of the coefficient of variation of this failure probability. In order to reduce the number of calls of the mechanical model when performing a probabilistic analysis, this paper uses the active learning reliability method combining kriging and Monte Carlo simulation (AK-MCS). This method is shown to be very efficient because the obtained probability of failure is very accurate, needing only a small number of calls to the computationally expensive mechanical model compared with MCS methodology. This study involves a probabilistic analysis at the ultimate limit state of a strip footing resting on a spatially varying soil using the AK-MCS approach. The soil cohesion and angle of internal friction are considered as random fields. The mechanical model is based on numerical simulations using the finite-difference code . The obtained probabilistic numerical results are presented and discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Al-Bittar, T., and A. H. Soubra. 2013. “Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion.” Int. J. Numer. Anal. Methods Geomech. 37 (13): 2039–2060. https://doi.org/10.1002/nag.2120.
Al-Bittar, T., and A. H. Soubra. 2014a. “Efficient sparse polynomial chaos expansion methodology for the probabilistic analysis of computationally-expensive deterministic models.” Int. J. Numer. Anal. Methods Geomech. 38 (12): 1211–1230. https://doi.org/10.1002/nag.2251.
Al-Bittar, T., and A. H. Soubra. 2014b. “Probabilistic analysis of strip footings resting on spatially varying soils and subjected to vertical or inclined loads.” J. Geotech. Geoenviron. Eng. 38 (12): 04013043. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001046.
Al-Bittar, T., and A. H. Soubra. 2016. “Bearing capacity of spatially random rock masses obeying Hoek–Brown failure criterion.” Georisk: Assess. Manage. Risk Eng. Syst. Geohazards 11 (2): 215–229. https://doi.org/10.1080/17499518.2016.1232831.
Ching, J., Y. G. Hu, Z. Y. Yang, J. Q. Shiau, J. C. Chen, and Y. S. Li. 2011. “Reliability-based design for allowable bearing capacity of footings on rock masses by considering angle of distortion.” Int. J. Rock Mech. Min. Sci. 48 (5): 728–740. https://doi.org/10.1016/j.ijrmms.2011.05.005.
Ching, J. Y., X. W. Tong, and Y. G. Hu. 2016. “Effective Young’s modulus for a spatially variable soil mass subjected to a simple stress state.” Georisk 10 (1): 11–26. https://doi.org/10.1080/17499518.2015.1084426.
Cho, S. E., and H. C. Park. 2010. “Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing.” Int. J. Numer. Anal. Methods Geomech. 34 (1): 1–26. https://doi.org/10.1002/nag.791.
Der Kiureghian, A., and J. B. Ke. 1988. “The stochastic finite element method in structural reliability.” Probab. Eng. Mech. 3 (2): 83–91. https://doi.org/10.1016/0266-8920(88)90019-7.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
Fenton, G. A., and D. V. Griffiths. 2001. “Bearing capacity of spatially random soil: The undrained clay Prandtl problem revisited.” Géotechnique 51 (4): 351–359. https://doi.org/10.1680/geot.2001.51.4.351.
Fenton, G. A., and D. V. Griffiths. 2003. “Bearing-capacity prediction of spatially random soils.” Can. Geotech. J. 40 (1): 54–65. https://doi.org/10.1139/t02-086.
Griffiths, D. V., G. A. Fenton, and N. Manoharan. 2002. “Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study.” J. Geotech. Geoenviron. Eng. 128 (9): 743–755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743).
Li, C. C., and A. Der Kiureghian. 1993. “Optimal discretization of random fields.” J. Eng. Mech. 119 (6): 1136–1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
Li, J. H., M. J. Cassidy, Y. Tian, J. Huang, A. V. Lyamin, and M. Uzielli. 2016. “Buried footings in random soils: Comparison of limit analysis and finite element analysis.” Georisk 10 (1): 55–65. https://doi.org/10.1080/17499518.2015.1064141.
Li, J. L., M. J. Cassidy, and Y. Tian. 2015. “Failure mechanism and bearing capacity of footings buried at various depths in spatially random soil.” J. Geotech. Geoenviron. Eng. 141 (2): 04014099. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001219.
Lophaven, S. N., H. B. Nielsen, and J. Søndergaard. 2002. DACE—A Matlab Kriging toolbox, version 2.0. Lyngby, Denmark: Technical Univ. of Denmark.
Nataf, A. 1962. “Détermination des distributions de probabilités dont les marges sont données.” Comptes Rendus de l’Académie des Sciences 255: 42–43.
Phoon, K.-K., and F. H. Kulhawy. 1999. “Evaluation of geotechnical property variability.” Can. Geotech. J. 36 (4): 625–639. https://doi.org/10.1139/t99-039.
Popescu, R., G. Deodatis, and A. Nobahar. 2005. “Effects of random heterogeneity of soil properties on bearing capacity.” Probab. Eng. Mech. 20 (4): 324–341. https://doi.org/10.1016/j.probengmech.2005.06.003.
Sacks, J., W. J. Welch, T. J. Mitchell, and H. P. Wynn. 1989. “Design and analysis of computer experiments.” Stat. Sci. 4 (4): 409–423. https://doi.org/10.1214/ss/1177012413.
Santner, T. J., B. J. Williams, and W. I. Notz. 2003. The design and analysis of computer experiments. New York: Springer.
Sudret, B., and A. Der Kiureghian. 2000. Stochastic finite element methods and reliability: A state-of-the-art report. Berkeley, CA: Dept. of Civil and Environmental Engineering.
Vesic, A. S. 1973. “Analysis of ultimate loads of shallow foundations.” J. Soil Mech. Found. Div. 99 (1): 45–73. https://doi.org/10.1016/0148-9062(74)90598-1.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 27, 2017
Accepted: May 1, 2018
Published online: Jul 24, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 24, 2018
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.