Bayesian Model Comparison and Characterization of Undrained Shear Strength
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 140, Issue 6
Abstract
This paper develops Bayesian approaches for facilitating the determination of characteristic (or nominal) values of geomaterial properties in geotechnical analysis and design when extensive testing cannot be performed, which is the case for a majority of geotechnical projects, particularly those of a small or medium size. These Bayesian approaches aim to characterize probabilistically the undrained shear strength, , of clay using a limited amount of liquidity index (LI) test data, and to provide a logical route to determine the characteristic values for analysis and design, particularly those using probability-based design codes. The proposed approaches include (1) a Bayesian model comparison approach that selects the most appropriate likelihood model, a key element in the Bayesian framework, using a limited number of LI data obtained from a specific project site, and (2) a Bayesian equivalent sample approach that uses the selected likelihood model, integrates the sound engineering judgment/local experience with the project-specific LI data, and transforms the integrated knowledge into a large number of equivalent samples using Markov chain Monte Carlo simulation. Conventional statistical analysis of the equivalent samples is subsequently performed to determine characteristic values of the profile. The proposed approaches use engineering judgment/local experience in a quantifiable and transparent manner and effectively tackle the difficulty of generating meaningful statistics and probability distributions of soil properties from a usually limited number of test data obtained during geotechnical site investigation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work described in this paper was supported by a grant (Project No. 9041550, CityU 110210) from the Research Grants Council of the Hong Kong Special Administrative Region, China, a Strategic Research Grant from City University of Hong Kong (Project No. 7004043), and a National Science Fund for Distinguished Young Scholars from China (Project No. 51225903). The financial support is gratefully acknowledged.
References
Ang, A. H.-S., and Tang, W. H. (2007). Probability concepts in engineering: Emphasis on applications to civil and environmental engineering, Wiley, New York.
Baecher, G. B., and Christian, J. T. (2003). Reliability and statistics in geotechnical engineering, Wiley, Hoboken, NJ.
Barker, R. M., Duncan, J. M., Rojiani, K. B., Ooi, P. S. K., Tan, C. K., and Kim, S. G. (1991). “Manuals for the design of bridge foundations, National Cooperative Highway Research Program (NCHRP).” Rep. 343, Transportation Research Board, National Research Council, Washington, DC.
Beck, J. L., and Au, S. K. (2002). “Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation.” J. Eng. Mech., 380–391.
Bjerrum, L. (1973). “Problems of soil mechanics and construction on soft clay.” Proc., 8th Int. Conf. on Soil Mechanics and Foundation Engineering, Vol. 3, Consultants Bureau, Division of Plenum Publishing, New York, 111–159.
Cao, Z., and Wang, Y. (2013). “Bayesian approach for probabilistic site characterization using cone penetration tests.” J. Geotech. Geoenviron. Eng., 267–276.
Cao, Z., Wang, Y., and Au, S. K. (2011). “CPT-based probabilistic characterization of effective friction angle of sand.” GeoRisk 2011: Geotechnical Risk Assessment and Management, Vol. 224, ASCE, Reston, VA, 403–410.
Ching, J., Phoon, K. K., and Chen, Y. C. (2010). “Reducing shear strength uncertainties in clays by multivariate correlations.” Can. Geotech. J., 47(1), 16–33.
Chiu, C. F., Yan, W. M., and Yuen, K.-V. (2012). “Reliability analysis of soil-water characteristics curve and its application to slope stability analysis.” Eng. Geol., 135–136, 83–91.
Choa, V., Chu, J., Bawajee, R., Win, M. B., and Arulrajah, A. (1996). “The strength and consolidation behavior of Singapore Marine Clay at Changi.” Proc., 12th Southeast Asian Geotechnical Conf., Institution of Engineers, Malaysia.
Christian, J. T. (2004). “Geotechnical engineering reliability: How well do we know what we are doing?” J. Geotech. Geoenviron. Eng., 985–1003.
El-Ramly, H., Morgenstern, N. R., and Cruden, D. M. (2003). “Probabilistic stability analysis of a tailings dyke on presheared clay-shale.” Can. Geotech. J., 40(1), 192–208.
European Committee for Standardization (CEN). (2010). “Geotechnical design—Part 1: General rules.” Eurocode 7, Brussels, Belgium.
Griffiths, D. V., and Fenton, G. A. (2004). “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. Eng., 507–518.
Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, 57(1), 97–109.
Jaksa, M. B. (1995). “The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay.” Ph.D. thesis, Univ. of Adelaide, Adelaide, Australia.
Juang, C. H., Luo, Z., Atamturktur, S., and Huang, H. W. (2013). “Bayesian updating of soil parameters for braced excavations using field observations.” J. Geotech. Geoenviron. Eng., 395–406.
Kulhawy, F. H., and Mayne, P. W. (1990). “Manual on estimating soil properties for foundation design.” Rep. EL-6800, Electric Power Research Institution, Palo Alto, CA.
Lacasse, S., and Nadim, F. (1996). “Uncertainties in characterizing soil properties.” Uncertainty in the Geologic Environment: From Theory to Practice, Geotechnical Special Publication, Vol. 58(I), ASCE, Reston, VA, 49–75.
Ladd, C. C., Foote, R., Ishihare, K., Schlosser, F., and Poulos, H. G. (1977). “Stress-deformation and strength characteristics.” Proc., 9th Int. Conf. on Soil Mechanics and Foundation Engineering, Vol. 2, Japanese Society of Soil Mechanics and Foundation Engineering, Tokyo, 421–494.
Lumb, P. (1966). “The variability of natural soils.” Can. Geotech. J., 3(2), 74–97.
Luo, Z., Atamturktur, S., Cai, Y., and Juang, C. H. (2012). “Simplified approach for reliability-based design against basal-heave failure in braced excavations considering spatial effect.” J. Geotech. Geoenviron. Eng., 441–450.
Mayne, P. W., Christopher, B. R., and DeJong, J. (2002). “Subsurface investigations—geotechnical site characterization.” No. FHWA NHI-01-031, Federal Highway Administration, DOT, Washington, DC.
Mesri, G. (1975). “Discussion of ‘New design procedure for stability of soft clays’ by Charles C. Ladd and Roger Foott.” J. Geotech. Engrg. Div., 101(4), 409–412.
Mesri, G. (1989). “A re-evaluation of using laboratory shear tests.” Can. Geotech. J., 26(1), 162–164.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., and Teller, A. (1953). “Equations of state calculations by fast computing machines.” J. Chem. Phys., 21(6), 1087–1092.
Mitchell, J. K., and Soga, K. (2005). Fundamentals of soil behavior, Wiley, Hoboken, NJ.
Najjar, S. S., and Gilbert, R. B. (2009). “Importance of lower-bound capacities in the design of deep foundations.” J. Geotech. Geoenviron. Eng., 890–900.
Phoon, K. K. (2008). “Numerical recipes for reliability analysis—A primer.” Chapter 1, Reliability-based design in geotechnical engineering: Computations and applications, Taylor & Francis, London, 1–75.
Phoon, K. K., and Kulhawy, F. H. (1999). “Characterization of geotechnical variability.” Can. Geotech. J., 36(4), 612–624.
Phoon, K. K., Kulhawy, F. H., and Grigoriu, M. D. (2003a). “Development of a reliability-based design framework for transmission line structure foundations.” J. Geotech. Geoenviron. Eng., 798–806.
Phoon, K. K., Kulhawy, F. H., and Grigoriu, M. D. (2003b). “Multiple resistance factor design for shallow transmission line structure foundations.” J. Geotech. Geoenviron. Eng., 807–818.
Sivia, D. S., and Skilling, J. (2006). Data analysis: A Bayesian tutorial, Oxford University Press, New York.
Stas, C. V., and Kulhawy, F. H. (1984). “Critical evaluation of design methods for foundations under axial uplift and compression loading.” Rep. EL-3771, Electric Power Research Institute, Palo Alto, CA.
Suchomel, R., and Mašín, D. (2010). “Comparison of different probabilistic methods for predicting stability of a slope in spatially variable soil.” Comput. Geotech., 37(1–2), 132–140.
Tan, T. S., et al. (1999). “Characterization of Singapore lower marine clay by in-situ and laboratory tests.” Proc., Dr. Tan Swan Beng Memorial Symposium, A. A. Balkema, Rotterdam, Netherlands, 181–190.
Tan, T. S., Phoon, K. K., Lee, F. H., Tanaka, H., Locat, J., and Chong, P. T. (2003). “A characterisation study of Singapore Lower Marine Clay.” Characterisation and engineering properties of natural soils, Vol. 1, Swets & Zeitlinger, Lisse, Netherlands, 429–454.
Terzaghi, K., Peck, R. B., and Meris, G. (1996). Soil mechanics in engineering practice, Wiley, New York.
Wang, Y., Au, S. K., and Cao, Z. (2010). “Bayesian approach for probabilistic characterization of sand friction angles.” Eng. Geol., 114(3-4), 354–363.
Wang, Y., and Cao, Z. (2013). “Probabilistic characterization of Young’s modulus of soil using equivalent samples.” Eng. Geol., 159, 106–118.
Wang, Y., Huang, K., and Cao, Z. (2013). “Probabilistic identification of underground soil stratification using cone penetration tests.” Can. Geotech. J., 50, 1–11.
Wang, Y., Huang, K., and Cao, Z. (2014). “Bayesian identification of soil strata in London clay.” Geotechnique, 64(3), 239–246.
Whittle, A. J., and Davis, R. V. (2006). “Nicoll Highway collapse: Evaluation of geotechnical factors affecting design of excavation support system.” Proc., Int. Conf. on Deep Excavations, Land Transport Authority of Singapore, Association of Consulting Engineers, and Tunneling and Underground Construction Society, Singapore.
Win, B. M., Arulrajah, A., Choa, V., and Chang, M. F. (1998). “Site characterization for a land reclamation project at Changi in Singapore.” Proc., 1st Int. Conf. on Site Characterization (ISC 98), P. K. Robertson and P. W. Mayne, eds., A. A. Balkema, Rotterdam, Netherlands, 333–338.
Wood, D. M. (1990). Soil behaviour and critical state soil mechanics, Cambridge University Press, New York.
Wroth, C. P. (1984). “The interpretation of in-situ soil tests.” Geotechnique, 34(4), 449–489.
Zhang, J., Tang, W. H., Zhang, L. M., and Huang, H. W. (2012). “Characterising geotechnical model uncertainty by hybrid Markov Chain Monte Carlo simulation.” Comput. Geotech., 43, 26–36.
Zhang, J., Zhang, L. M., and Tang, W. H. (2009). “Bayesian framework for characterizing geotechnical model uncertainty.” J. Geotech. Geoenviron. Eng., 932–940.
Zhang, L. L., Zhang, J., Zhang, L. M., and Tang, W. H. (2010). “Back analysis of slope failure with Markov chain Monte Carlo simulation.” Comput. Geotech., 37(7-8), 905–912.
Zhang, L. L., Zuo, Z. B., Ye, G. L., Jeng, D. S., and Wang, J. H. (2013). “Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope.” Comput. Geotech., 48, 72–81.
Zhang, L. M., Tang, W. H., Zhang, L. L., and Zheng, J. G. (2004). “Reducing uncertainty of prediction from empirical correlations.” J. Geotech. Geoenviron. Eng., 526–534.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 140 • Issue 6 • June 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 7, 2013
Accepted: Feb 6, 2014
Published online: Mar 10, 2014
Published in print: Jun 1, 2014
Discussion open until: Aug 10, 2014
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.