Arabian Journal of Geosciences

, 10:406 | Cite as

Determining optimum number of geotechnical testing samples using Monte Carlo simulations

  • Kerry Magner
  • Norbert Maerz
  • Ivan Guardiola
  • Adnan Aqeel
Original Paper


Knowing how many samples to test to adequately characterize soil and rock units is always challenging. A large number of tests decrease the uncertainty and increase the confidence in the resulting values of design parameters. Unfortunately, this large value also adds to project costs. This paper presents a method to determine the number of samples as a function of the coefficient of variation. If, as in the case of a reliability-based design, the resistance factors are a function of the coefficient of variation of the measurements, then lowering the coefficient of variation (COV) can result in lowering of the resistance factor resulting in a less conservative design. In this study, laboratory samples were isolated by specific unified soil classification system soil type and general site location. A distribution was fitted for each of the geotechnical parameters measured. For each scenario, groups of 2, 3, 4, 5, 10, 15, 20, 30, 50, and 100 random samples were generated by using Monte Carlo simulations from the fitted distributions. For each group, the variability was calculated in terms of the COV. In all cases, the COV decreased as the sample size increased. However, the rate of decrease for the COV was the greatest at a low number of samples; it becomes increasingly smaller at a higher number of samples.


Geotechnical tests Reliability Variance analysis Sampling Monte Carlo method 


  1. Baecher GB, Christian T (1972) Site exploration: a probabilistic approach. Dissertation, Massachusetts Institute of TechnologyGoogle Scholar
  2. Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. John Wiley & Sons Ltd, England, 605 ppGoogle Scholar
  3. Bardet JP (1997) Experimental soil mechanics. Prentice Hall, Upper SaddleGoogle Scholar
  4. Clarke KR, Green RH (1988) Statistical design and analysis for a “biological effects” study. Mar Ecol Prog Ser 46(1–3):213–226CrossRefGoogle Scholar
  5. Cochran WG (1963) Sampling techniques, 2nd edn. John Wiley & Sons Inc., New YorkGoogle Scholar
  6. Craig RF (2008) Craig’s soil mechanics. Spon Press, London/New YorkGoogle Scholar
  7. Dowdy S, Wearden S, Chilko D (2004) Statistics for research. John Wiley & Sons Inc., Hoboken, New YorkCrossRefGoogle Scholar
  8. Duncan M (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron:307–316Google Scholar
  9. Goldsworthy JS, Jaska MB, Fenton GA, Griffiths DV, Kaggwa WS, Poulos HG (2007) Measuring the risk of geotechnical site investigations. GeoDenver 2007: New Peaks in Geotechnics. American Society of Civil Engineers, GSP 170 Probabilistic Applications in Geotechincal Engineering 1–12Google Scholar
  10. Kachingan SK (1991) Multivariate statistical analysis: a conceptual introduction, 2nd edn. Radius Press, New YorkGoogle Scholar
  11. Kish L (1965) Survey sampling. John Wiley & Sons Inc., New YorkGoogle Scholar
  12. Krejcie RV, Morgan DW (1970) Determining the sample size for research activities. J Educ Psychol Meas 30(3):607–610CrossRefGoogle Scholar
  13. Kulhawy FH, Mayne PW (1990) Manual on estimating soil properties for foundation design. Electric Power Research Institute, Palo Alto, Calif., Report EL-6800: Research Project 1493–6Google Scholar
  14. Kulhawy FH, Phoon KK (2002) Observations on reliability-based design development in North America. Foundation design codes and soil investigation in view of international harmonization and performance. Balkema, Lisse, pp 31–48Google Scholar
  15. Magner KA (2010) Characterization of geotechnical variability based upon sampling frequency using a Monte Carlo simulation: a study of the KciCON project. M.Sc. Thesis, Missouri University of Science and TechnologyGoogle Scholar
  16. Miaoulis G, Michener RD (1976) An introduction to sampling. Kendall/Hunt Publishing Company, DubuqueGoogle Scholar
  17. Minitab Inc. (2010) Minitab statistical software (version 15). Minitab Inc. web. http://www.Minitab.Com. Accessed 1st June 2010
  18. MODOT: The Missouri Department of Transportation (2011) Procedures for estimation of geotechnical parameter values and coefficients of variation. IOP Publishing Engineering Policy Guide Web. Accessed 10th June 2010
  19. Owen LD, George EP (1957) Statistical methods in research production, with special reference to chemical industry, 3rd edn. Published for Imperial Chemical Industries by Oliver and Boyd, LondonGoogle Scholar
  20. Quesenberry CP (1993) The effect of sample size on estimated limits for sample mean and X control charts. J Qual Technol 25(4):237–237Google Scholar
  21. Schlager P, Schonhardt M (2008) Optimized site investigation and risk assessment strategies considering uncertain geotechnical parameters using Geo-AllStaR. GeoCongress 2008. Am Soc Civil Eng 573–580Google Scholar

Copyright information

© Saudi Society for Geosciences 2017

Authors and Affiliations

  • Kerry Magner
    • 1
  • Norbert Maerz
    • 2
  • Ivan Guardiola
    • 3
  • Adnan Aqeel
    • 4
  1. 1.NewFields Mining Design and Technical ServicesElkoUSA
  2. 2.Department of Geological Sciences and EngineeringMissouri University of Science and TechnologyRollaUSA
  3. 3.Department of Engineering ManagementMissouri University of Science and TechnologyRollaUSA
  4. 4.Department of GeologyTaibah UniversityMadinahSaudi Arabia

Personalised recommendations