Abstract
Selecting suitable probability distributions (PDs) to describe cone tip resistance measurements (qc) obtained by a cone penetration test (CPT) is considered a crucial requirement to get a good solution for geotechnical problems solved by simulating the engineering properties of soil as a random field or for use in reliability-based design. This paper presents a statistical analysis of seven PDs proposed to model qc obtained through performing CPT for soil in Nasiriyah during the construction of a new refinery petrol station. Preliminary testing for suitability of the suggested distributions has used the method of moment ratio diagram (MRD) based on the Pearson system. It was found that the soil stratification has a large effect on the distance between every two points on MRD. The type of probability distribution was also affected, and changed, by increasing the number of data points for qc included in the analysis. Logistic and Weibull distributions are considered the best PDs that represent the qc of the first layer having thickness 12 m of clay soil, followed by the other distributions, while the logistic and normal distributions were considered the best PDs among the seven suggested distributions for the second layer of 8 m silty sand and clayey sand. All the suggested distribution can represent the given qc data approximately except the Rayleigh distribution.
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Abdulla F, Hossain M, Rahman M (2014) On the selection of samples in probability proportional to size sampling: cumulative relative frequency method. Math Theory Model 4(6):102
Aihua L, Feng M, Li Y, Liu Z (2016) Application of outlier mining in insider identification based on boxplot method. Proc Comput Sci 91:245–251
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19: 716–723. https://doi.org/10.1109/tac.1974.1100705, MR 0423716
Anderson TW, Darling DA (1952) Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes. Ann Math Stat 23:193–212. https://doi.org/10.1214/aoms/1177729437
Anderson T, Darling D (1954) A test of goodness-of-fit. J Am Stat Assoc 49:765–769
Bari MW (2015) Three-dimensional finite element analysis of spatially variable of PVD improved-ground. J Georisk Assess Manag Risk Eng Syst Geohazards 9(1):37–48
Chenari RJ, Kamyab Farahbakhsh H (2015) Generating non-stationary random fields of auto-correlated, normally distributed CPT profile by matrix decomposition method. J Georisk-Assess Manag Risk Eng Syst Geohazards 9:96–108
Chenari RJ, Seyedein MS, Faraji S, Kenarsari AE (2012) Investigation on inherent variability of soil properties from cone penetration test. In: Proceedings of the ISC4, XVI Brazilian Congress of Soil Mechanics and Geotechnical Engineering, 4th International Conference on Geotechnical and Geophysical Site Characterization, Porte de Galinhas, Brazil, 18–21 Sept 2012
Chenari RJ, Kamyab Farahbakhsh H, Heidarie Golfazani S, Eslami A (2018) Non-stationary realization of CPT Data considering lithological and inherent heterogeneity. J Georisk-Assess Manag Risk Eng Syst Geohazards. https://doi.org/10.1080/17499518.2018.1447675
Chow A, Edgar WW (2011) Use of Akaike information criterion for selection of flood frequency distribution. Can J Civ Eng 19:616–626. https://doi.org/10.1139/l92-071
Fenton GA (1999) Random field modeling of CPT data. J Geotech Geoenviron Eng 125:486–498
Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, New Jersey
Harr M (1987) Reliability-based design in civil engineering. McGraw-Hill, New York
Iliopoulou T, Aguilar C, Arheimer V, Bermúdez M, Bezak N, Andrea F, Koutsoyiannis D, Parajka J, Polo MJ, Guillaume T, Montanari A (2018) A large sample analysis of seasonal river flow correlation and its physical drivers. Hydrol Earth Syst Sci Dis. https://doi.org/10.5194/hess-2018-134
Jimenez R, Sitar N (2009) The importance of distribution types on finite element analyses of foundation settlement. Comput Geotech 36:474–483
Johnson N, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1. Wiley, New Jersey
Kenarsari AE, Chenari RJ, Eslami RA (2013) Characterization of the correlation structure of residual CPT profiles in sand deposits. Int J Civ Eng Trans B Geotech Eng 11(1):29–37
Khaled H, Ramachandro R (1999) Flood frequency analysis. CRC Press, Boca Raton
Kotz S, Vicari D (2005) Survey of developments in the theory of continuous skewed distributions. Metron LXIII:225–261
Laufer I (2013) Statistical analysis of CPT tip resistances. Period Polytech Civ Eng 57:45–61. https://doi.org/10.3311/ppci.2141
Law AM, Kelton WD (2000) Simulation modelling and analysis, 3rd edn. McGraw-Hill, New York
Li DQ, Tang X-S, Phoon KK (2015) Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability. Reliab Eng Syst Saf 140:99–106
McGill R, Tukey JW, Larsen WA (1978) Variations of box plots. Am Stat 32(1):12–16. https://doi.org/10.1080/00031305.1978.10479236
Nour A, Slimani A, Laouami N (2002) Foundation settlement statistics via finite element analysis. Comput Geotech 29:641–672
Okeniyi J, Okeniyi E (2012) Implementation of Kolmogorov–Smirnov p-value computation in visual basic for implication for Microsoft Excel® library function. J Stat Comput Simul 82:1727–1741
Okeniyi J, Loto C, Popopla A (2015) Electrochemical performance of Anthocleista djalonensis on steel reinforcement corrosion in concrete immersed in saline/marine stimulating environment. Trans Indian Inst Met. https://doi.org/10.1007/s1266601404245
Ouarda TBMJ, Charron C, Chebana F (2016) Review of criteria for the selection of probability distributions for wind speed data and introduction of the moment and L-moment ratio diagram methods, with a case study. Energy Convers Manag. https://doi.org/10.1016/jenconman201607012
Phoon KK, Kulhawy FH (1996) On quantifying inherent soil variability. In: Uncertainty in the Geologic Environment, ASCE specialty conference. Madison, WI. ASCE, Reston, VA, pp 326–340
Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36:612–624
Podladchikova O, Lefebvre B, Krasnoselskikh V, Podladchikov V (2003) Classification of probability densities on the basis of Pearson’s curves with application to coronal heating simulations. Nonlinear Process Geophys 10(4/5):323–333
Popescu R, Prevost JH, Deodatis G (1997) Effects of spatial variability on soil liquefaction: some design recommendations. Geotechnique 47:1019–1036
Popescu R, Prevost JH, Deodatis G (2005) 3D effects in seismic liquefaction of stochastically variable soil deposits. Géotechnique 55:21–31
Rahman AS, Rahman A, Zaman AM, Haddad K, Ahsan A, Imteaz M (2013) A study on selection of probability distributions for at-site flood frequency analysis in Australia. Nat Hazards. https://doi.org/10.1007/s11069-013-0775-y
Robertson PK (1990) Soil classification using the cone penetration test. Can Geotech J 27(1):151–158
Robertson PK (2009) CPT interpretation—a unified approach. Can Geotech J 46:1–19
Robertson PK (2010) Soil behaviour type from the CPT: An Update. In: 2nd international symposium on cone penetration
Robertson PK (2016) CPT-based soil behaviour type (SBT) classification system—an update. Can Geotech J 53:1910–1927. https://doi.org/10.1139/cgj-2016-0044
Seyedein MS, Chinari RJ, Eslami A (2012) Investigation on probability density function for cone penetration test data. In: The 2012 world congress on advances in civil, environmental, and materials research (ACEM’12), Seoul, Korea, pp 26–30
Uzielli M, Vannucchi G, Phoon KK (2005) Random field characterization of stress-normalized cone penetration testing parameters. Géotechnique 55:3–20. https://doi.org/10.1680/geot.55.1.3.58591
Zhou W, Hong H, Shang JQ (1999) Probabilistic design method of prefabricated vertical drains for soil improvement. J Geotech Geoenviron Eng 125:659–664
Acknowledgements
The author highly appreciates the support adopted by the college of engineering in the University of Thi-Qar to complete this research and also to the engineering consultant bureau in this college to make data available for performing this research.
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Shakir, R.R. Selecting the Probability Distribution of Cone Tip Resistance Using Moment Ratio Diagram for Soil in Nasiriyah. Geotech Geol Eng 37, 1703–1728 (2019). https://doi.org/10.1007/s10706-018-0716-3
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DOI: https://doi.org/10.1007/s10706-018-0716-3