Probabilistic estimation of variogram parameters of geotechnical properties with a trend based on Bayesian inference using Markov chain Monte Carlo simulation

References

• Abdulla, M. B., R. L. Sousa, H. Einstein, and S. Awadalla. 2019. “Optimised Multivariate Gaussians for Probabilistic Subsurface Characterisation.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 303–312.
   Web of Science ®Google Scholar
• Al-Bittar, T., A. H. Soubra, and J. Thajeel. 2018. “Kriging-Based Reliability Analysis of Strip Footings Resting on Spatially Varying Soils.” Journal of Geotechnical and Geoenvironmental Engineering 144 (10): 04018071.
   Web of Science ®Google Scholar
• Bilgin, Ö., K. Arens, and A. Dettloff. 2019. “Assessment of Variability in Soil Properties from Various Field and Laboratory Tests.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 247–254.
   Web of Science ®Google Scholar
• Bogaert, P., and D. Russo. 1999. “Optimal Spatial Sampling Design for the Estimation of the Variogram Based on a Least Squares Approach.” Water Resources Research 35 (4): 1275–1289.
   Web of Science ®Google Scholar
• Bong, T., and A. W. Stuedlein. 2017. “Spatial Variability of CPT Parameters and Silty Fines in Liquefiable Beach Sands.” Journal of Geotechnical and Geoenvironmental Engineering 143 (12): 04017093.
   Web of Science ®Google Scholar
• Bong, T., and A. W. Stuedlein. 2018. “Effect of Cone Penetration Conditioning on Random Field Model Parameters and Impact of Spatial Variability on Liquefaction-Induced Differential Settlements.”.” Journal of Geotechnical and Geoenvironmental Engineering 144 (5): 04018018.
   Web of Science ®Google Scholar
• Cao, Z. J., and Y. Wang. 2013. “Bayesian Approach for Probabilistic Site Characterization Using Cone Penetration Tests.”.” Journal of Geotechnical and Geoenvironmental Engineering 139 (2): 267–276.
   Web of Science ®Google Scholar
• Cao, Z. J., and Y. Wang. 2014. “Bayesian Model Comparison and Selection of Spatial Correlation Functions for Soil Parameters.” Structural Safety 49: 10–17.
   Web of Science ®Google Scholar
• Cao, Z. J., Y. Wang, and D. Q. Li. 2016. “Quantification of Prior Knowledge in Geotechnical Site Characterization.” Engineering Geology 203: 107–116.
   Web of Science ®Google Scholar
• Chahbaz, R., S. Sadek, and S. Najjar. 2019. “Uncertainty Quantification of the Bond Stress – Displacement Relationship of Shoring Anchors in Different Geologic Units.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 276–283.
   Web of Science ®Google Scholar
• Cheng, Y., L. L. Zhang, J. H. Li, L. M. Zhang, J. H. Wang, and D. Y. Wang. 2017. “Consolidation in Spatially Random Unsaturated Soils Based on Coupled Flow-Deformation Simulation.” International Journal for Numerical and Analytical Methods in Geomechanics 41 (5): 682–706.
   Web of Science ®Google Scholar
• Ching, J. Y., and K. K. Phoon. 2017. “Characterizing Uncertain Site-Specific Trend Function by Sparse Bayesian Learning.” Journal of Engineering Mechanics 143 (7): 04017028.
   Web of Science ®Google Scholar
• Ching, J. Y., K. K. Phoon, J. L. Beck, and Y. Huang. 2017. “Identifiability of Geotechnical Site-Specific Trend Functions.” Asce-Asme Journal of Risk and Uncertainty in Engineering Systems Part a-Civil Engineering 3 (4): 04017021.
   Web of Science ®Google Scholar
• Ching, J. Y., K. K. Phoon, and S. H. Wu. 2016. “Impact of Statistical Uncertainty on Geotechnical Reliability Estimation.” Journal of Engineering Mechanics 142 (6): 04016027.
   Web of Science ®Google Scholar
• Corsten, L. C. A., and A. Stein. 1994. “Nested Sampling for Estimating Spatial Semivariograms Compared to Other Designs.” Appl. Stoch. Models & Data Anal 10 (2): 103–122.
   Google Scholar
• Cressie, N. A. C. 1987. “A Nonparametric View of Generalized Covariances for Kriging.” Mathematical Geology 19 (5): 425–449.
   Google Scholar
• Cressie, N. A. C. 1993. Statistics for Spatial Data. New York: John Wiley & Sons Ltd.
   Google Scholar
• Dasaka, S. M., and L. M. Zhang. 2012. “Spatial Variability of in situ Weathered Soil.” Géotechnique 62 (5): 375–384.
   Web of Science ®Google Scholar
• Fenton, G. A., F. Naghibi, and M. A. Hicks. 2018. “Effect of Sampling Plan and Trend Removal on Residual Uncertainty.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 12 (4): 253–264.
   Web of Science ®Google Scholar
• Folle, D., J. F. C. Leite Costa, D. Renard, J. C. Koppe, and A. C. Zingano. 2008. “3-D Soil-Resistance Maps in the Presence of a Strong Vertical Trend.” Engineering Geology 102 (1–2): 46–53.
   Web of Science ®Google Scholar
• Gringarten, E., and C. V. Deutsch. 2001. “Teacher’s Aide Variogram Interpretation and Modeling.” Mathematical Geology 33 (4): 507–534.
   Google Scholar
• Huang, J. S., C. Zeng, and R. Kelly. 2019. “Back Analysis of Settlement of Teven Road Trial Embankment Using Bayesian Updating.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 320–325.
   Web of Science ®Google Scholar
• Ibsen, C. C. 2019. “On the Use of Bayesian Networks as a Meta-Modelling Approach to Analyse Uncertainties in Slope Stability Analysis.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (1): 53–65.
   Google Scholar
• Journel, A. G. 1986. “Geostatistics: Models and Tools for the Earth Sciences.” Mathematical Geology 18 (1): 119–140.
   Google Scholar
• Journel, A. G., and M. E. Rossi. 1989. “When do We Need a Trend Model in Kriging?” Mathematical Geology 21 (7): 715–739.
   Google Scholar
• Kenarsari, A. E., R. J. Chenari, and A. Eslami. 2013. “Characterization of the Correlation Structure of Residual CPT Profiles in Sand Deposits.” International Journal of Civil Engineering 11 (1B): 29–37.
   Web of Science ®Google Scholar
• Knuuti, M., and T. Länsivaara. 2019. “Variation of CPTu-Based Transformation Models for Undrained Shear Strength of Finnish Clays.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 262–270.
   Web of Science ®Google Scholar
• Lark, R. M. 2000a. “Estimating Variograms of Soil Properties by the Method-of-Moments and Maximum Likelihood.” European Journal of Soil Science 51 (4): 717–728.
   Web of Science ®Google Scholar
• Lark, R. M. 2000b. “A Comparison of Some Robust Estimators of the Variogram for Use in Soil Survey.” European Journal of Soil Science 51 (1): 137–157.
   Web of Science ®Google Scholar
• Lark, R. M., and B. R. Cullis. 2004. “Model-Based Analysis Using REML for Inference from Systematically Sampled Data on Soil.” European Journal of Soil Science 55 (4): 799–813.
   Web of Science ®Google Scholar
• Lark, R. M., and R. Webster. 2006. “Geostatistical Mapping of Geomorphic Variables in the Presence of Trend.” Earth Surface Processes & Landforms 31 (7): 862–874.
   Web of Science ®Google Scholar
• Li, J., M. J. Cassidy, J. Huang, L. Zhang, and R. Kelly. 2016. “Probabilistic Identification of Soil Stratification.” Géotechnique 66 (1): 16–26.
   Web of Science ®Google Scholar
• Lin, Y. P., T. K. Chang, and T. P. Teng. 2001. “Characterization of Soil Lead by Comparing Sequential Gaussian Simulation, Simulated Annealing Simulation and Kriging Methods.” Environmental Geology 41 (1–2): 189–199.
   Google Scholar
• Liu, C. N., and C. H. Chen. 2010. “Estimating Spatial Correlation Structures Based on CPT Data.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 4 (2): 99–108.
   Google Scholar
• Liu, W. F., and Y. F. Leung. 2015. “Analyzing Spatial Variability of Geologic Profiles for Four Sites in Hong Kong.” Paper presented at the 5th International Symposium on Geotechnical Safety and Risk (ISGSR), Rotterdam, Netherlands, Oct 13–16, 2015.
   Google Scholar
• Liu, W. F., Y. F. Leung, and M. K. Lo. 2017. “Integrated Framework for Characterization of Spatial Variability of Geological Profiles.” Canadian Geotechnical Journal 54 (1): 47–58.
   Web of Science ®Google Scholar
• Luo, N., and R. J. Bathurst. 2018. “Probabilistic Analysis of Reinforced Slopes Using RFEM and Considering Spatial Variability of Frictional Soil Properties due to Compaction.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 12 (2): 87–108.
   Web of Science ®Google Scholar
• Minasny, B., and A. B. McBratney. 2005. “The Matérn Function as a General Model for Soil Variograms.” Geoderma 128 (3–4): 192–207.
   Web of Science ®Google Scholar
• Minasny, B., J. A. Vrugt, and A. B. McBratney. 2011. “Confronting Uncertainty in Model-Based Geostatistics Using Markov Chain Monte Carlo Simulation.” Geoderma 163 (3): 150–162.
   Web of Science ®Google Scholar
• Montoya-Noguera, S., T. Zhao, Y. Hu, Y. Wang, and K. K. Phoon. 2019. “Simulation of Non-Stationary Non-Gaussian Random Fields From Sparse Measurements Using Bayesian Compressive Sampling and Karhunen-Loève Expansion.” Structural Safety 79: 66–79.
   Web of Science ®Google Scholar
• Morris, M. D. 1991. “On Counting the Number of Data Pairs for Semivariogram Estimation.” Mathematical Geology 23 (7): 929–943.
   Google Scholar
• Möttönen, M., E. Järvinen, T. J. Hokkanen, T. Kuuluvainen, and R. Ohtonen. 1999. “Spatial Distribution of Soil Ergosterol in the Organic Layer of a Mature Scots Pine (Pinus Sylvestris L.) Forest.” Soil Biology & Biochemistry 31 (4): 503–516.
   Web of Science ®Google Scholar
• Murakami, S., K. Yasuhara, K. Suzuki, and H. Komine. 2006. “Reliable Land Subsidence Mapping Using a Spatial Interpolation Procedure Based on Geostatistics.” Soils and Foundations 46 (2): 123–134.
   Web of Science ®Google Scholar
• Nikellis, A., K. O. Eshun, M. Dyanati, D. A. Roke, Q. D. Huang, A. Chandra, and K. Sett. 2018. “Effect of Site-Specific Soil Nonlinearities and Uncertainties on Ground Motion Intensity Measures and Structural Demand Parameters.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 7: 1–18.
   Google Scholar
• Nobre, M. M., and J. F. Sykes. 1992. “Application of Bayesian Kriging to Subsurface Characterization.” Canadian Geotechnical Journal 29 (4): 589–598.
   Web of Science ®Google Scholar
• Oh, S. H., and B. D. Kwon. 2001. “Geostatistical Approach to Bayesian Inversion of Geophysical Data: Markov Chain Monte Carlo Method.” Earth, Planets and Space 53 (8): 777–791.
   Web of Science ®Google Scholar
• Oliver, M. A., and R. Webster. 2014. “A Tutorial Guide to Geostatistics: Computing and Modelling Variograms and Kriging.” Catena 113: 56–69.
   Web of Science ®Google Scholar
• Pardo-Iguzquiza, E., and P. A. Dowd. 2013. “Comparison of Inference Methods for Estimating Semivariogram Model Parameters and Their Uncertainty: The Case of Small Data Sets.” Computers & Geosciences 50: 154–164.
   Web of Science ®Google Scholar
• Phoon, K. K., and F. H. Kulhawy. 1999. “Characterization of Geotechnical Variability.” Canadian Geotechnical Journal 36 (4): 612–624.
   Web of Science ®Google Scholar
• Phoon, K. K., S. T. Quek, and P. An. 2003. “Identification of Statistically Homogeneous Soil Layers Using Modified Bartlett Statistics.” Journal of Geotechnical and Geoenvironmental Engineering 129 (7): 649–659.
   Web of Science ®Google Scholar
• Phoon, K. K., and C. Tang. 2019. “Characterisation of Geotechnical Model Uncertainty.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (2): 101–130.
   Web of Science ®Google Scholar
• Pyrcz, M. J., and C. V. Deutsch. 2014. Geostatistical Reservoir Modeling, 2nd ed. New York: Oxford University Press.
   Google Scholar
• Remy, N., A. Boucher, and J. Wu. 2009. Applied Geostatistics with SGeMS: A User’s Guide. New York: Cambridge University Press.
   Google Scholar
• Reza, J. C., K. F. Hassan, H. G. Sara, and E. Abolfazl. 2018. “Non-stationary Realisation of CPT Data: Considering Lithological and Inherent Heterogeneity.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 12 (4): 265–278.
   Google Scholar
• Russo, D., and W. A. Jury. 1987. “A Theoretical Study of the Estimation of the Correlation Scale in Spatially Variable Fields: 1. Stationary Fields.” Water Resources Research 23 (7): 1257–1268.
   Web of Science ®Google Scholar
• Samui, P., and T. G. Sitharam. 2010. “Site Characterization Model Using Artificial Neural Network and Kriging.” International Journal of Geomechanics 10 (5): 171–180.
   Web of Science ®Google Scholar
• Skøien, J. O., and G. Blöschl. 2006. “Scale Effects in Estimating the Variogram and Implications for Soil Hydrology.” Vadose Zone Journal 5 (1): 153–167.
   Web of Science ®Google Scholar
• Somarathna, P., B. Minasny, B. P. Malone, U. Stockmann, and A. B. Mcbratney. 2018. “Accounting for the Measurement Error of Spectroscopically Inferred Soil Carbon Data for Improved Precision of Spatial Predictions.” Science of the Total Environment 631–632: 377–389.
   PubMed Web of Science ®Google Scholar
• Srivastava, A., and G. L. S. Babu. 2009. “Effect of Soil Variability on the Bearing Capacity of Clay and in Slope Stability Problems.” Engineering Geology 108 (1–2): 142–152.
   Web of Science ®Google Scholar
• Sun, X. L., S. C. Wu, H. L. Wang, Y. G. Zhao, G. L. Zhang, Y. B. Man, and M. H. Wong. 2013. “Dealing with Spatial Outliers and Mapping Uncertainty for Evaluating the Effects of Urbanization on Soil: A Case Study of Soil pH and Particle Fractions in Hong Kong.” Geoderma 195: 220–233.
   Web of Science ®Google Scholar
• Tang, C., and K. K. Phoon. 2018. “Statistics of Model Factors in Reliability-Based Design of Axially Loaded Driven Piles in Sand.” Canadian Geotechnical Journal 55 (11): 1592–1610.
   Web of Science ®Google Scholar
• Uzielli, M., and P. W. Mayne. 2019. “Probabilistic Assignment of Effective Friction Angles of Sands and Silty Sands FROM CPT Using Quantile Regression.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 13 (4): 271–275.
   Web of Science ®Google Scholar
• Van der Krogt, M. G., T. Schweckendiek, and M. Kok. 2018. “Uncertainty in Spatial Average Undrained Shear Strength with a Site-Specific Transformation Model.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards. doi:10.1080/17499518.2018.1554820.
   Google Scholar
• Vrugt, J. A., C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson. 2008. “Treatment of Input Uncertainty in Hydrologic Modeling: Doing Hydrology Backward with Markov Chain Monte Carlo Simulation.” Water Resources Research 44: W00B09.
   Web of Science ®Google Scholar
• Wang, Y., S. K. Au, and Z. J. Cao. 2010. “Bayesian Approach for Probabilistic Characterization of Sand Friction Angles.” Engineering Geology 114 (3–4): 354–363.
   Web of Science ®Google Scholar
• Wang, Y., Z. J. Cao, and D. Q. Li. 2016. “Bayesian Perspective on Geotechnical Variability and Site Characterization.” Engineering Geology 203: 117–125.
   Web of Science ®Google Scholar
• Wang, Y., K. Huang, and Z. J. Cao. 2013. “Probabilistic Identification of Underground Soil Stratification Using Cone Penetration Tests.” Canadian Geotechnical Journal 50 (7): 766–776.
   Web of Science ®Google Scholar
• Wang, Y., K. Huang, and Z. J. Cao. 2014. “Bayesian Identification of Soil Strata in London Clay.” Géotechnique 64 (3): 239–246.
   Web of Science ®Google Scholar
• Wang, Y., and T. Zhao. 2017. “Statistical Interpretation of Soil Property Profiles From Sparse Data Using Bayesian Compressive Sampling.” Géotechnique 67 (6): 523–536.
   Web of Science ®Google Scholar
• Wang, Y., T. Y. Zhao, and Z. J. Cao. 2015. “Site-Specific Probability Distribution of Geotechnical Properties.” Computers and Geotechnics 70: 159–168.
   Web of Science ®Google Scholar
• Wang, Y., T. Zhao, Y. Hu, and K. K. Phoon. 2019. “Simulation of Random Fields with Trend From Sparse Measurements Without Detrending.” Journal of Engineering Mechanics. ASCE 145 (2): 04018130.
   Web of Science ®Google Scholar
• Wang, Y., T. Zhao, and K. K. Phoon. 2018. “Direct Simulation of Random Field Samples From Sparsely Measured Geotechnical Data with Consideration of Uncertainty in Interpretation.” Canadian Geotechnical Journal 55 (6): 862–880.
   Web of Science ®Google Scholar
• Warrick, A. W., and D. E. Myers. 1987. “Optimization of Sampling Locations for Variogram Calculations.” Water Resources Research 23 (3): 496–500.
   Web of Science ®Google Scholar
• Webster, R. 2015. “Technological Developments for Spatial Prediction of Soil Properties, and Danie Krige’s Influence on It.” Journal of the Southern African Institute of Mining and Metallurgy 115 (2): 165–172.
   Web of Science ®Google Scholar
• Western, A. W., and G. Blöschl. 1999. “On the Spatial Scaling of Soil Moisture.” Journal of Hydrology 217 (3–4): 203–224.
   Web of Science ®Google Scholar
• Xiong, X., S. Grunwald, D. B. Myers, J. S. Kim, W. G. Harris, and N. Bliznyuk. 2015. “Assessing Uncertainty in Soil Organic Carbon Modeling Across a Highly Heterogeneous Landscape.” Geoderma 251–252: 105–116.
   Web of Science ®Google Scholar
• Yáñez-Godoy, H., A. Mokeddem, and S. M. Elachachi. 2017. “Influence of Spatial Variability of Soil Friction Angle on Sheet Pile Walls’ Structural Behaviour.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 11 (4): 299–314.
   Web of Science ®Google Scholar
• Yang, H. Q., L. L. Zhang, and D. Q. Li. 2018. “Efficient Method for Probabilistic Estimation of Spatially Varied Hydraulic Properties in a Soil Slope Based on Field Responses: A Bayesian Approach.” Computers and Geotechnics 102: 262–272.
   Web of Science ®Google Scholar
• Yong, R., J. Ye, B. Li, and S. G. Du. 2018. “Determining the Maximum Sampling Interval in Rock Joint Roughness Measurements using Fourier Series.” International Journal of Rock Mechanics and Mining Sciences 101: 78–88.
   Web of Science ®Google Scholar
• Zhang, J., H. W. Huang, and K. K. Phoon. 2013. “Application of the Kriging-Based Response Surface Method to the System Reliability of Soil Slopes.” Journal of Geotechnical and Geoenvironmental Engineering 139 (4): 651–655.
   Web of Science ®Google Scholar
• Zhang, L. L., W. H. Tang, and L. M. Zhang. 2009. “Bayesian Model Calibration Using Geotechnical Centrifuge Tests.” Journal of Geotechnical and Geoenvironmental Engineering 135 (2): 291–299.
   Web of Science ®Google Scholar
• Zhang, L. L., F. Wu, Y. F. Zheng, L. H. Chen, J. Zhang, and X. Li. 2018. “Probabilistic Calibration of a Coupled Hydro-Mechanical Slope Stability Model with Integration of Multiple Observations.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 12 (3): 169–182.
   Web of Science ®Google Scholar
• Zhang, J., L. M. Zhang, and W. H. Tang. 2009. “Bayesian Framework for Characterizing Geotechnical Model Uncertainty.” Journal of Geotechnical and Geoenvironmental Engineering 135 (7): 932–940.
   Web of Science ®Google Scholar
• Zhang, L. L., Y. F. Zheng, L. M. Zhang, X. Li, and J. H. Wang. 2014. “Probabilistic Model Calibration for Soil Slope Under Rainfall: Effects of Measurement Duration and Frequency in Field Monitoring.” Géotechnique 64 (5): 365–378.
   Web of Science ®Google Scholar
• Zhao, T., and Y. Wang. 2018. “Simulation of Cross-Correlated Random Field Samples From Sparse Measurements Using Bayesian Compressive Sensing.” Mechanical Systems and Signal Processing 112: 384–400.
   Web of Science ®Google Scholar
• Zhao, Y. C., X. H. Xu, B. Huang, W. X. Sun, X. X. Shao, X. Z. Shi, and X. L. Ruan. 2007. “Using Robust Kriging and Sequential Gaussian Simulation to Delineate the Copper- and Lead-Contaminated Areas of a Rapidly Industrialized City in Yangtze River Delta, China.” Environmental Geology 52 (7): 1423–1433.
   Google Scholar
• Zhu, H., L. M. Zhang, L. L. Zhang, and C. B. Zhou. 2013. “Two-Dimensional Probabilistic Infiltration Analysis with a Spatially Varying Permeability Function.” Computers and Geotechnics 48: 249–259.
   Web of Science ®Google Scholar
• Zou, H. F., S. Y. Liu, G. J. Cai, T. V. Bheemasetti, and A. J. Puppala. 2017. “Mapping Probability of Liquefaction Using Geostatistics and First Order Reliability Method Based on CPTU Measurements.” Engineering Geology 218: 197–212.
   Web of Science ®Google Scholar