Abstract
This paper develops a Gaussian Mixture Model (GMM) method to produce the soil profile based on the cone penetration test results (CPT). The theoretical probabilistic model utilizes the Bayesian information criterion (BIC) and Akaike information criteria (AIC) to estimate the number of layers. The research analyzed the impact of four types of covariance matrices on soil classification. The proposed approach was applied to the real-life CPT data for the National Geotechnical Experimentation Site (NGES) at Texas, which was widely used for analysis and comparison. Evaluation of the proposed model with many previous classification systems indicated that the GMM could detect soil boundaries and types by clustering the data and employing Robertson chart. In addition to that, the clustering decision depended on the posterior probability of every soil unit to the corresponding clusters. The thickness of the thin layers and the location of boundaries rely on the type of covariance matrix. The study revealed that the four types of covariance give a range of layers from 5 to 7, corresponding to the minimum values of both BIC and AIC. The nonshared full covariance matrix reflected more layer boundaries and thin layers than the shared and diagonal covariance matrix. It is concluded that the proposed method did not require an experience-based decision to classify the soil and indicate the layer boundaries. Further, the proposed technique directly classified the soil in a fast process, expressed the results visually, and was more practical and familiar to geotechnical engineers. It was sensitive to detecting thin layers, which gives a chance to understand and interpret the CPT measurements.
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Abdulla MB, Sousa RL, Einstein H, Awadalla S (2019) Optimised multivariate Gaussians for probabilistic subsurface characterisation. Georisk 13(4):303–312. https://doi.org/10.1080/17499518.2019.1673441
Abu-Farsakh MY, Zhang Z, Tumay M, Morvant M (2008) Computerized Cone Penetration Test for Soil Classification: Development of MS-Windows Software. Transp Res Rec 2053(1):47–64. https://doi.org/10.3141/2053-07
ASTM D2487 (2006) Standard practice for classification of soils for engineering purposes. Unified Soil Classification System. ASTM International, West Conshohocken
Bilmes JA (1998) A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. Int Comput Sci Inst 10.1.1.119.4856
Briaud JL (2000) The national geotechnical experimentation sites at Texas A&M University: clay and sand. A summary. In National Geotechnical Experimentation Sites. Geotechnical Special Publication No. 93. ASCE, pp 26–51
Campanella RG, Robertson PK (1990) Current status of the piezocone test. Int J Rock Mech Min Sci Geomech Abstracts. https://doi.org/10.1016/0148-9062(90)95072-9
Cao ZJ, Wang Y (2013) Bayesian approach for probabilistic site characterization using cone penetration tests. J Geotech Geoenvironmental Eng 139(2):267–276. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000765
Cao ZJ, Zheng S, Li DQ, Phoon KK (2019) Bayesian identification of soil stratigraphy based on soil behaviour type index. Can Geotech J. https://doi.org/10.1139/cgj-2017-0714
Chenari J, Farahbakhsh K (2015) Georisk : assessment and management of risk for engineered systems and geohazards generating non-stationary random fields of auto- correlated , normally distributed CPT profile by matrix decomposition method (April):37–41. https://doi.org/10.1080/17499518.2015.1033429
Chenari RJ, Farahbakhsh HK, Heidarie S, Eslami A (2018) Georisk : assessment and management of risk for engineered systems and geohazards non-stationary realisation of CPT data : considering lithological and inherent heterogeneity. Georisk 0(0):1–14. https://doi.org/10.1080/17499518.2018.1447675
Ching J, Wang JS, Juang CH, Ku CS (2015) Cone penetration test (CPT)-based stratigraphic profiling using the Wavelet transform modulus maxima method. Can Geotech J 52(12):1993–2007. https://doi.org/10.1139/cgj-2015-0027
Collico S, Arroyo M, Deu A, Devincenzi M, Rodriguez A (2020) Semi-automated probabilistic soil profiling using CPTu. 6th International Conference on Geotechnical and Geophysical Site Charcterisation
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc: Ser B (methodol). https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
Deng Z, Jiang S, Niu J, Pan M, Liu L (2020) Stratigraphic uncertainty characterization using generalized coupled Markov chain stratigraphic uncertainty characterization using generalized coupled Markov chain, (June). https://doi.org/10.1007/s10064-020-01883-y
Depina I, Le TMH, Eiksund G, Strøm P (2016) Cone penetration data classification with Bayesian Mixture Analysis. Georisk 10(1):27–41. https://doi.org/10.1080/17499518.2015.1072637
Douglas BJ, Olsen RS (1981) Soil classification using electric cone penetrometer. In: Proceedings of Conference on Cone Penetration Testing and Experience, St. Louis, p 209–227
Facciorusso J, Uzielli M (2004) Stratigraphic Profiling by Cluster Analysis and Fuzzy Soil Classification from Mechanical Cone Penetration Tests. In: Viana da Fonseca A, Mayne PW (eds) Geotechnical and Geophysical Site Characterization. Millpress, Rotterdam, pp 905–912
Farhadi MS (2019) An integrated optimization-game theory model for CPT-based subground stratification. 29th European Safety and Reliability Conference Sep 22-26; Hannover, Germany
Gong W, Tang H, Wang H, Wang X, Juang H (2019) PT US. Eng Geol 105162. https://doi.org/10.1016/j.enggeo.2019.105162
Hegazy YA, Mayne PW (2002) Objective site characterization using clustering of piezocone data. J Geotech Geoenviron Eng. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:12(986)
Huang K, Cao Z, Wang Y (2014) CPT-based Bayesian identification of underground soil stratigraphy. In Geotechnical Safety and Risk IV—Proceedings of the 4th International Symposium on Geotechnical Safety and Risk, ISGSR 2013. https://doi.org/10.1201/b16058-14
Huang J, Zheng D, Li D, Kelly R, Sloan SW (2017) Probabilistic characterization of 2D soil profile by integrating CPT with MASW data. Canadian GeotechJ (December), cgj-2017–0429. https://doi.org/10.1139/cgj-2017-0429
Huang J, Griffiths DV (2010) One-dimensional consolidation theories for layered soil and coupled and uncoupled solutions by the finite-element method. Geotechnique 60:709–713. https://doi.org/10.1680/geot.08.P.038
Jiang SH, Papaioannou I, Straub D (2020) Optimization of site-exploration programs for slope-reliability assessment. ASCE-ASME J Risk Uncertain Eng Syst Part A: Civ Eng 6(1). https://doi.org/10.1061/AJRUA6.0001042
Jung B-C, Gardoni P, Biscontin G (2008) Probabilistic soil identification based on cone penetration tests. Géotechnique 58(7):591–603. https://doi.org/10.1680/geot.2007.00089
Jung BC, Gardoni P, Biscontin G (2007) Probabilistic soil classification based on cone penetration tests. In Applications of statistics and probability in civil engineering—Proceedings of the 10th International Conference on Applications of Statistics and Probability, ICASP10. https://doi.org/10.1680/geot.2007.00089
Kim T, Chen IR, Lin Y, Wang AYY, Yang JYH, Yang P (2019) Impact of similarity metrics on single-cell RNA-seq data clustering. Brief Bioinform. https://doi.org/10.1093/bib/bby076
Konkol J, Międlarz K, Bałachowski L (2019) Geotechnical characterization of soft soil deposits in Northern Poland. Eng Geol 259(June). https://doi.org/10.1016/j.enggeo.2019.105187
Kotzias PC, Stamatopoulos AC (2000) Statistical to fuzzy approach toward CPT soil classification. J Geotech Geoenviron Eng. https://doi.org/10.1061/(asce)1090-0241(2000)126:6(577)
Krogstad A, Depina I, Omre H (2018) Cone penetration data classification by Bayesian inversion with a Hidden Markov model. J Phys: Conf Ser. https://doi.org/10.1088/1742-6596/1104/1/012015
Lee KK, Cassidy MJ, Randolph MF (2013) Bearing capacity on sand overlying clay soils: experimental and finite-element investigation of potential punch-through failure. Geotechnique 63(15):1285–1297
Li J, Cassidy MJ, Huang J, Zhang L, Kelly R (2016) Probabilistic identification of soil stratification. Géotechnique 66(1):16–26. https://doi.org/10.1680/jgeot.14.P.242
Liao T, Mayne PW (2007) Stratigraphic delineation by three-dimensional clustering of piezocone data. Georisk 1:102–119
Lunne T, Eidsmoen T, Gillespie D, Howland JD (1986) Laboratory and field evaluation of cone penetrometers. In: Use of In-Situ Tests in Geotechnical Engineering (GSP 6). ASCE, Reston, pp 714–729
Milligan GW (1996) Clustering validation: results and implications for applied analyses. In: Arabie P, Hubert LJ, Soete GD (eds) Clustering and Classification. World Scientific, Singapore, pp 341–375
Phoon K-K, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36:612–624. https://doi.org/10.1139/t99-03
Qi Xiaohui, Pan X, Chiam K, Lim YS, Lau SG (2020) Comparative spatial predictions of the locations of soil-rock interface. Eng Geol 272(November 2019):105651. https://doi.org/10.1016/j.enggeo.2020.105651
Robertson PK (2009) Interpretation of cone penetration tests—A unified approach. Can Geotech J 46:1337–1355
Robertson PK (2010) Soil behaviour type from the CPT: An Update. In: 2nd International Symposium on Cone Penetration Testing, Huntington Beach, Vol. 2, p 575–583
Robertson PK (2016) Cone penetration test (CPT)-based soil behaviour type (SBT) classification system — an update. Can Geotech J 53(12):1910–1927. https://doi.org/10.1139/cgj-2016-0044
Shakir RR (2018) Spatial correlation of cone tip resistance for soil in Nasiriyah. Open Civ Eng J 12:413–29429
Shakir RR (2020) Thajeel Jawad, and Al-umar Mohammad “Soil profile stratification based on cone penetration test results using k-means and hierarchical clustering” 3RD conference of the Arabian Journal Geoscience (CAJG), 2–5 November 2020, Sousse, Tunisia (In press)
Shirkhorshidi AS, Aghabozorgi S, Ying Wah T (2015) A comparison study on similarity and dissimilarity measures in clustering continuous data. PLoS ONE. https://doi.org/10.1371/journal.pone.0144059
Uzielli M, Vannucchi G, Phoon KK (2005) Random field characterisation of stress-normalised cone penetration testing parameters. Géotechnique 55(1):3–20. https://doi.org/10.1680/geot.55.1.3.58591
Vessia G, Curzio D. Di, Castrignanò A (2020) Science of the total environment modeling 3D soil lithotypes variability through geostatistical data fusion of CPT parameters. Sci Total Environ 698:134340. https://doi.org/10.1016/j.scitotenv.2019.134340
Wang H (2020a) Finding patterns in subsurface using Bayesian machine learning approach. Underground Space (china) 5(1):84–92. https://doi.org/10.1016/j.undsp.2018.10.006
Wang X (2020b) Uncertainty quantification and reduction in the characterization of subsurface stratigraphy using limited geotechnical investigation data. Undergr Space (china) 5(2):125–143. https://doi.org/10.1016/j.undsp.2018.10.008
Wang Y, Cao Z (2013) CPT-based probabilistic site characterization in geotechnical engineering. In Safety, reliability, risk and life-cycle performance of structures and infrastructures—Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. https://doi.org/10.1201/b16387-82
Wang Yu, Huang K, Cao Z (2013) Probabilistic identification of underground soil stratification using cone penetration tests. Can Geotech J 50(7):766–776. https://doi.org/10.1139/cgj-2013-0004
Wang Y, Cao Z, Li D (2016a) Bayesian perspective on geotechnical variability and site characterization. Eng Geol 203:117–125
Wang H, Wellmann JF, Li Z, Wang X, Liang RY (2016b) A segmentation approach for stochastic geological modeling using hidden Markov random fields. Math Geosci 49(2):145–177. https://doi.org/10.1007/s11004-016-9663-9
Wang H, Wang X, Wellmann F (2018a) A Bayesian unsupervised learning approach for identifying soil stratification using cone penetration data (October). https://doi.org/10.1139/cgj-2017-0709
Wang X, Wang H, Liang RY (2018b) A method for slope stability analysis considering subsurface stratigraphic uncertainty. Landslides 15. https://doi.org/10.1007/s10346-017-0925-5
Wang X, Wang H, Liang RY, Zhu H, Di H (2018c) A hidden Markov random field model based approach for probabilistic site characterization using multiple cone penetration test data. Struct Saf. https://doi.org/10.1016/j.strusafe.2017.10.011
Wang X, Wang H, Liu Y (2018d) A semi-supervised clustering-based approach for stratification identification using borehole and cone penetration test data a semi-supervised clustering-based approach for stratification identification using borehole and cone penetration test data (November). https://doi.org/10.1016/j.enggeo.2018.11.014
Wang H, Wang X, Wellmann JF, Liang RY (2019) A Bayesian unsupervised learning approach for identifying soil stratification using cone penetration data. Can Geotech J 56(8):1184–1205
Wang H, Wang X, Liang R (2020) Study of AI based methods for characterization of geotechnical site investigation data. FHWA/OH-2020-3. Ohio Department of Transportation
Wen J, Zheng N, Yuan J, Gong Z, Chen C (2019) Bayesian uncertainty matching for unsupervised domain adaptation. Proc 28th Int Joint Conf Artif Intell 3849-3855
Xiao T, Zhang LM, Li X (2017) Probabilistic stratification modeling in geotechnical site characterization probabilistic stratification modeling in geotechnical site characterization (July). https://doi.org/10.1061/AJRUA6.0000924
Zhang Z, Tumay MT (1999) Statistical to fuzzy approach toward cpt soil classification. J Geotech Geoenviron Eng. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:3(179)
Zhao T, Wang Y (2020b) Non-parametric simulation of non-stationary non-Gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo. Reliability Eng Syst Saf 107087. https://doi.org/10.1016/j.ress.2020.107087
Zhao T, Wang Y (2020) Interpolation and stratification of multilayer soil property profile from sparse measurements using machine learning methods. Eng Geol 265(October 2019):105430. https://doi.org/10.1016/j.enggeo.2019.105430
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Shakir, R.R., Wang, H. Estimation of probabilistic CPT-based soil profile using an unsupervised Gaussian mixture model. Arab J Geosci 16, 218 (2023). https://doi.org/10.1007/s12517-023-11283-7
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DOI: https://doi.org/10.1007/s12517-023-11283-7