Selecting the Probability Distribution of Cone Tip Resistance Using Moment Ratio Diagram for Soil in Nasiriyah

  • Ressol R. ShakirEmail author
Original Paper


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.


Probability distribution Cone tip resistance Moment ratio diagram The Nasiriyah soil 



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.

Compliance with Ethical Standards

Conflict of interest

The corresponding author states that there is no conflict of interest.


  1. 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):102Google Scholar
  2. Aihua L, Feng M, Li Y, Liu Z (2016) Application of outlier mining in insider identification based on boxplot method. Proc Comput Sci 91:245–251CrossRefGoogle Scholar
  3. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19: 716–723., MR 0423716CrossRefGoogle Scholar
  4. Anderson TW, Darling DA (1952) Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes. Ann Math Stat 23:193–212. CrossRefGoogle Scholar
  5. Anderson T, Darling D (1954) A test of goodness-of-fit. J Am Stat Assoc 49:765–769CrossRefGoogle Scholar
  6. 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):37–48CrossRefGoogle Scholar
  7. 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 9:96–108CrossRefGoogle Scholar
  8. 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 2012Google Scholar
  9. 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. CrossRefGoogle Scholar
  10. Chow A, Edgar WW (2011) Use of Akaike information criterion for selection of flood frequency distribution. Can J Civ Eng 19:616–626. CrossRefGoogle Scholar
  11. Fenton GA (1999) Random field modeling of CPT data. J Geotech Geoenviron Eng 125:486–498CrossRefGoogle Scholar
  12. Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, New JerseyCrossRefGoogle Scholar
  13. Harr M (1987) Reliability-based design in civil engineering. McGraw-Hill, New YorkGoogle Scholar
  14. 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. CrossRefGoogle Scholar
  15. Jimenez R, Sitar N (2009) The importance of distribution types on finite element analyses of foundation settlement. Comput Geotech 36:474–483CrossRefGoogle Scholar
  16. Johnson N, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1. Wiley, New JerseyGoogle Scholar
  17. 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):29–37Google Scholar
  18. Khaled H, Ramachandro R (1999) Flood frequency analysis. CRC Press, Boca RatonGoogle Scholar
  19. Kotz S, Vicari D (2005) Survey of developments in the theory of continuous skewed distributions. Metron LXIII:225–261Google Scholar
  20. Laufer I (2013) Statistical analysis of CPT tip resistances. Period Polytech Civ Eng 57:45–61. CrossRefGoogle Scholar
  21. Law AM, Kelton WD (2000) Simulation modelling and analysis, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  22. 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 140:99–106CrossRefGoogle Scholar
  23. McGill R, Tukey JW, Larsen WA (1978) Variations of box plots. Am Stat 32(1):12–16. CrossRefGoogle Scholar
  24. Nour A, Slimani A, Laouami N (2002) Foundation settlement statistics via finite element analysis. Comput Geotech 29:641–672CrossRefGoogle Scholar
  25. 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 82:1727–1741CrossRefGoogle Scholar
  26. 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. CrossRefGoogle Scholar
  27. 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. CrossRefGoogle Scholar
  28. 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 326–340Google Scholar
  29. Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36:612–624CrossRefGoogle Scholar
  30. 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):323–333CrossRefGoogle Scholar
  31. Popescu R, Prevost JH, Deodatis G (1997) Effects of spatial variability on soil liquefaction: some design recommendations. Geotechnique 47:1019–1036CrossRefGoogle Scholar
  32. Popescu R, Prevost JH, Deodatis G (2005) 3D effects in seismic liquefaction of stochastically variable soil deposits. Géotechnique 55:21–31CrossRefGoogle Scholar
  33. 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. CrossRefGoogle Scholar
  34. Robertson PK (1990) Soil classification using the cone penetration test. Can Geotech J 27(1):151–158CrossRefGoogle Scholar
  35. Robertson PK (2009) CPT interpretation—a unified approach. Can Geotech J 46:1–19CrossRefGoogle Scholar
  36. Robertson PK (2010) Soil behaviour type from the CPT: An Update. In: 2nd international symposium on cone penetrationGoogle Scholar
  37. Robertson PK (2016) CPT-based soil behaviour type (SBT) classification system—an update. Can Geotech J 53:1910–1927. CrossRefGoogle Scholar
  38. 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 26–30Google Scholar
  39. Uzielli M, Vannucchi G, Phoon KK (2005) Random field characterization of stress-normalized cone penetration testing parameters. Géotechnique 55:3–20. CrossRefGoogle Scholar
  40. Zhou W, Hong H, Shang JQ (1999) Probabilistic design method of prefabricated vertical drains for soil improvement. J Geotech Geoenviron Eng 125:659–664CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Civil Engineering Department, College of EngineeringUniversity of Thi-QarNasiriyahIraq

Personalised recommendations