On the Hole Effect in Soil Spatial Variability
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
A hole-effect autocorrelation function is one that is non-monotonic or pseudo-periodic as defined in the geostatistics literature. This paper shows that such an autocorrelation function (ACF) can influence the probability of failure of some geotechnical structures. As such, it is relevant to ask whether this hole effect does exist and is identifiable from the cone penetration test data. For this purpose, a novel hole-effect ACF model, called the cosine Whittle-Matérn (CosWM) model, is proposed to simultaneously identify the scale of fluctuation (SOF), sample path smoothness, and hole effect. Based on simulation examples and two real case histories, it is found that the hole effect is identifiable only if the hole effect is significant and the data record is of sufficient length. One real case history exhibits a significant hole effect, and this hole effect is successfully identified by the CosWM model. It is also found that if a monotonic ACF is adopted in place of the CosWM model for this case history, not only can the hole effect not be identified (as is to be expected) but also the SOF will be overestimated significantly.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abramowitz, M., and I. Stegun. 1970. Handbook of mathematical functions. New York: Dover.
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Bong, T., and A. W. Stuedlein. 2017. “Spatial variability of CPT parameters and silty fines in liquefiable beach sands.” J. Geotech. Geoenviron. Eng. 143 (12): 04017093. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001789.
Box, G. E. P., and G. M. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden-Day.
Cami, B., S. Javankhoshdel, K. K. Phoon, and J. Ching. 2020. “Scale of fluctuation for spatially varying soils: Estimation methods and values.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 6 (4): 03120002. https://doi.org/10.1061/AJRUA6.0001083.
Ching, J., and K. K. Phoon. 2019. “Impact of auto-correlation function model on the probability of failure.” J. Eng. Mech. 145 (1): 04018123. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001549.
Ching, J., K. K. Phoon, A. W. Stuedlein, and M. Jaksa. 2019. “Identification of sample path smoothness in soil spatial variability.” Struct. Saf. 81: 101870. https://doi.org/10.1016/j.strusafe.2019.101870.
Dasaka, S. M., and L. M. Zhang. 2012. “Spatial variability of in situ weathered soil.” Géotechnique 62 (5): 375–384. https://doi.org/10.1680/geot.8.P.151.3786.
DeGroot, D. J., and G. B. Baecher. 1993. “Estimating autocovariances of in-situ soil properties.” J. Geotech. Eng. 119 (1): 147–166. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147).
DeGroot, D. J., and A. J. Lutenegger. 2005. “Characterization by sampling and in situ testing—Connecticut valley varved clay.” Stud. Geotech. Mech. 27 (3–4): 107–120.
Dolloff, J., B. Lofy, A. Sussman, and C. Taylor. 2006. “Strictly positive definite correlation functions.” In Vol. 6235 of Proc., Signal Processing, Sensor Fusion, and Target Recognition XV, Defense and Security Symp. Bellingham, WA: International Society for Optics and Photonics.
Firouzianbandpey, S., D. V. Griffiths, L. B. Ibsen, and L. V. Anderson. 2014. “Spatial correlation length of normalized cone data in sand: Case study in the north of Denmark” Can. Geotech. J. 51 (8): 844–857. https://doi.org/10.1139/cgj-2013-0294.
Hristopulos, D. T., and M. Žukovič. 2011. “Relationships between correlation lengths and integral scales for covariance models with more than two parameters.” Stochastic Environ. Res. Risk Assess. 25 (1): 11–19. https://doi.org/10.1007/s00477-010-0407-y.
Jaksa, M. 1995. “The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Adelaide.
Jaksa, M. B., W. S. Kaggwa, and P. I. Brooker. 1999. “Experimental evaluation of the scale of fluctuation of a stiff clay.” In Proc., 8th Int. Conf. on Application of Statistics and Probability, 415–422. Rotterdam, Netherlands: A.A. Balkema.
Journel, A. G., and R. Froidevaux. 1982. “Anisotropic hole-effect modeling.” Math. Geol. 14 (3): 217–239. https://doi.org/10.1007/BF01032885.
Lumb, P. 1974. “Applications of statistics in soil mechanics.” In Soil mechanics: New horizons, edited by I. K. Lee. New York: Elsevier.
Ma, Y. Z., and T. A. Jones. 2001. “Teacher’s aid: Modeling hole-effect variograms of lithology-indicator variables.” Math. Geol. 33 (5): 631–648. https://doi.org/10.1023/A:1011001029880.
Nelder, J. A., and R. Mead. 1965. “A simplex method for function minimization.” Comput. J. 7 (4): 308–313. https://doi.org/10.1093/comjnl/7.4.308.
Phoon, K. K., and J. Ching. 2021. “Project deepGeo—Data-driven 3D subsurface mapping.” J. GeoEng. 16 (2): 61–73.
Rasmussen, C. E., and C. K. I. Williams. 2006. Gaussian processes for machine learning. Cambridge, MA: MIT Press.
Schwarz, G. E. 1978. “Estimating the dimension of a model.” Ann. Stat. 6 (2): 461–464. https://doi.org/10.1214/aos/1176344136.
Spanos, P. D., M. Beer, and J. Red-Horse. 2007. “Karhunen-Loeve expansion of stochastic processes with a modified exponential covariance kernel.” J. Eng. Mech. 133 (7): 773–779. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(773).
Uzielli, M., G. Vannucchi, and K. K. Phoon. 2005. “Random field characterisation of stress-normalised cone penetration testing parameters.” Géotechnique 55 (1): 3–20. https://doi.org/10.1680/geot.2005.55.1.3.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. Div. 103 (11): 1227–1246. https://doi.org/10.1061/AJGEB6.0000517.
Vanmarcke, E. H. 1983. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Xiao, T., D. Q. Li, Z. J. Cao, and L. M. Zhang. 2018. “CPT-based probabilistic characterization of three-dimensional spatial variability using MLE.” J. Geotech. Geoenviron. Eng. 144 (5): 04018023. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001875.
Yue, Q. X., J. R. Yao, A. H.-S. Ang, and P. D. Spanos. 2018. “Efficient random field modeling of soil deposits properties.” Soil Dyn. Earthquake Eng. 108 (May): 1–12. https://doi.org/10.1016/j.soildyn.2018.01.036.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Nov 20, 2020
Accepted: Apr 29, 2021
Published online: Jul 16, 2021
Published in print: Dec 1, 2021
Discussion open until: Dec 16, 2021
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