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Variability and Correlation of Strength Parameters Inferred from Direct Shear Tests

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Abstract

This paper presents a theoretical approach to evaluate the uncertainties and the correlation of the shear strength parameters c and t (cohesion and friction coefficient), obtained in direct shear tests. The analysis is based on the hypothesis that the soil is statistically homogeneous, with shear strength normally distributed having an expected resistance which is linearly dependent on the effective normal stress. With regard to the scatters of the population of the shear strength, two further statements have been formulated for the standard deviation: (1) a constant value, independent of the effective normal stresses and (2) a value which is linearly dependent on the normal effective stresses as a consequence of a constant coefficient of variation. The investigation shows that the strength parameters are negatively correlated and the coefficient of correlation and the coefficients of variation of cohesion and friction angle are highly dependent on the number of shear tests and the normal stresses used in the tests.

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References

  • Baecher GB, Marr WA, Lin JS, Consla J (1983) Critical parameters for mine tailings embankments. U.S. Bureau of Mines, Denver

    Google Scholar 

  • Baker R (2004) Nonlinear Mohr envelopes based on triaxial data. J Geotech Geoenviron Eng ASCE 130(5):498–506

    Article  Google Scholar 

  • Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10(12):1–54

    Article  Google Scholar 

  • Bhattacharya G, Jana D, Ojha S, Chakraborty S (2003) Direct search for minimum reliability index of earth slopes. Comp Geotech 30(6):455–462

    Article  Google Scholar 

  • Branco LP, Gomes AT, Cardoso AS, Pereira CS (2014) Natural variability of strength in a granite residual soil from Porto. Geotech Geol Eng 32:911–922

    Article  Google Scholar 

  • Cherubini C (1997) Data and considerations on the variability of geotechnical properties of soils. In: Proceedings of the international conference on safety reliability, vol 2, Lisbon, pp 1583–1591

  • Cherubini C (2000) Reliability evaluation of shallow foundation bearing capacity on c–φ soils. Can Geotech J 37(1):264–269

    Google Scholar 

  • Cho SE (2007) Effects of spatial variability of soil properties on slope stability. Eng Geol 92(3–4):97–109

    Article  Google Scholar 

  • Cho SE (2010) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron Eng ASCE 136(7):975–984

    Article  Google Scholar 

  • Cho SE, Park HC (2010) Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing. Int J Numer Anal Methods Geomech 34(1):1–26

    Google Scholar 

  • Chowdhury RN, Xu DW (1995) Geotechnical system reliability of slopes. Reliab Eng Syst Saf 47(3):141–151

    Article  Google Scholar 

  • Coulomb CA (1776) Essai sur une application des règles de maximis et minimis à quelques problèmes de statique, relatifs à l’architecture. Mémoires de mathématique & de physique, présentés à l’Académie Royale des Sciences par divers savans, vol 7, Tome VII, Paris, pp 343–382

  • De Mello VFB (1977) Reflections on the design decisions of practical significance of embankments dams. Géotechnique 27(3):279–355

    Article  Google Scholar 

  • Di Matteo L, Valigi D, Ricco R (2013) Laboratory shear strength parameters of cohesive soils: variability and potential effects on slope stability. Bull Eng Geol Environ 72(1):101–106

    Article  Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2003) Probabilistic stability analysis of a tailings dyke on presheared clay–shale. Can Geotech J 40(1):192–208

    Article  Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2006) Lodalen slide: a probabilistic assessment. Can Geotech J 43(9):956–968

    Article  Google Scholar 

  • Fenton GA, Griffiths DV (2003) Bearing capacity prediction of spatially random c–φ soils. Can Geotech J 40(1):54–65

    Article  Google Scholar 

  • Fisher RA (1921) On the `probable error’ of a coefficient of correlation deduced from a small sample. Metron 1(4):3–32

    Google Scholar 

  • Griffiths DV, Huang J, Fenton GA (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotech Geoenviron Eng ASCE 135(10):1367–1378

    Article  Google Scholar 

  • Hassan AM, Wolff TF (1999) Search algorithm for minimum reliability index of earth slopes. J Geotech Geoenviron Eng ASCE 125(4):301–308

    Article  Google Scholar 

  • Holtz RD, Krizek RJ (1972) Statistical evaluation of soil test data. In: Proceedings of the first international conference on applications of statistics and probability in civil engineering, Hong Kong, pp 229–266

  • Hong HP, Roh G (2008) Reliability evaluation of earth slopes. J Geotech Geoenviron Eng ASCE 134(12):1700–1705

    Article  Google Scholar 

  • Jiang SH, Li DQ, Zhang LM, Zhou CB (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168(January):120–128

    Article  Google Scholar 

  • Kutner MH, Nachtsheim CJ, Neter J, Li W (2005) Applied linear statistical model, 5th edn. MGraw-Hill, New York

    Google Scholar 

  • Lefebvre G (1981) Strength and slope stability in Canadian soft clay deposits. Can Geotech J 18(3):420–442

    Article  Google Scholar 

  • Li D, Chen Y, Lu W, Zhou C (2011) Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables. Comp Geotech 38(1):58–68

    Article  Google Scholar 

  • Liang RY, Nusier OK, Malkawi AH (1999) A reliability based approach for evaluating the slope stability of embankment dams. Eng Geol 54(3–4):271–285

    Article  Google Scholar 

  • Low BK (2007) Reliability analysis of rock slopes involving correlated nonnormals. Int J Rock Mech Min Sci 44(6):922–935

    Article  Google Scholar 

  • Low BK (2008) Efficient probabilistic algorithm illustrated for a rock slope. Rock Mech Rock Eng 41(5):715–734

    Article  Google Scholar 

  • Lumb P (1966) The variability of natural soils. Can Geotech J 3(2):74–97

    Article  Google Scholar 

  • Lumb P (1970) Safety factors and the probability distributions of soil strength. Can Geotech J 7(3):225–242

    Article  Google Scholar 

  • Luo X, Cheng T, Li X, Zhou J (2012) Slope safety factor search strategy for multiple sample points for reliability analysis. Eng Geol 129–130(March):27–37

    Article  Google Scholar 

  • Maksimovic M (1989) Nonlinear failure envelope for soils. J Geotech Eng ASCE 115(4):581–586

    Article  Google Scholar 

  • Maksimovic M (1996) A family of nonlinear failure envelopes. Electron J Geotech Eng 1

  • Massih DSYA, Soubra AH, Low BK (2009) Reliability-based analysis and design of strip footings against bearing capacity failure. J Geotech Geoenvironal Eng ASCE 134(7):917–928

    Article  Google Scholar 

  • Matyas EL (1977) Probabilistic analysis of predicted and measured settlements: discussion. Can Geotech J 14(1):159–163

    Article  Google Scholar 

  • Morgenstern NR, Price VE (1965) The analysis of the stability of general slip surfaces. Géotechnique 15(1):79–93

    Article  Google Scholar 

  • Most T, Knabe T (2010) Reliability analysis of the bearing failure problem considering uncertain stochastic parameters. Comp Geotech 37(3):299–310

    Article  Google Scholar 

  • Papoulis A (1979) Probability, random variables and stochastic processes, 3rd edn. McGraw-Hill, New York

    Google Scholar 

  • Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624

    Article  Google Scholar 

  • Rahardjo H, Satyanaga A, Leong EC, Ng YS, Pang HTC (2012) Variability of residual soil properties. Eng Geol 141–142(July):124–140

    Article  Google Scholar 

  • Rankine W (1857) On the stability of loose earth. Philos Trans R Soc Lond 147:9–27

    Article  Google Scholar 

  • Schultze E (1972) Frequency distribution and correlation of soil properties. In: Proceedings of the first international conference on applications of statistics and probability in civil engineering, Hong Kong, pp 371–387

  • Schultze E (1975) Some aspects concerning the application of statistics and probability to foundations structures. In: Proceedings of the 2nd international conference on applications of statistics and probability in civil engineering, Aachen, Germany, pp 457–494

  • Sevaldson RA (1954) The slide in Lodalen, October 6th 1954. Géotechnique 6(4):167–182

    Article  Google Scholar 

  • Shahin MA, Cheung EM (2011) Probabilistic analysis of bearing capacity of strip footings. In: Proceedings of the 3rd international symposium on geotechnical risk safety, Munich, Germany, pp 225–230

  • Shou KJ, Chen YL (2005) Spatial risk analysis of Li-shan landslide in Taiwan. Eng Geol 80(3–4):199–213

    Article  Google Scholar 

  • Sing A (1972) How reliable is the factor of safety in foundation engineering? In: Proceedings of the first international conference on applications of statistics and probability in civil engineering, Hong Kong, pp 389–424

  • Sivakumar Babu GL, Srivastava A (2007) Reliability analysis of allowable pressure on shallow foundation using response surface method. Comp Geotech 34(3):187–194

    Article  Google Scholar 

  • Sivakumar Babu GL, Srivastava A, Sahana V (2007) Analysis of stability of earthen dams in kachchh region, Gujarat, India. Eng Geol 94(3–4):123–136

    Article  Google Scholar 

  • Sokolowski VV (1965) Statics of granular media. Pergamon, Oxford

    Google Scholar 

  • Soubra AH, Mao N (2012) Probabilistic analysis of obliquely loaded strip foundations. Soils Founds 52(3):524–538

    Article  Google Scholar 

  • Spencer E (1967) A method of analysis of the stability of embankments assuming parallel forces. Geotechnique 17(1):11–26

    Article  Google Scholar 

  • Suchomel R, Mašin D (2010) Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c–ϕ soil. Comp Geotech 37(1–2):132–140

    Article  Google Scholar 

  • Tan CP, Donald IB, Melchers RE (1993) Probabilistic slip circle analysis of earth and rockfill dams. In: Proceedings of the conference on probabilistic methods in geotechnical engineering, Canberra, Australia, pp 281–288

  • Tobutt DC, Richards EA (1979) Reliability of earth slopes. Int J Numer Anal Methods Geomech 3(4):323–354

    Article  Google Scholar 

  • Vesic AS (1973) Analysis of ultimate loads of shallow foundations. J Soil Mech Found Div ASCE 99(SM1):45–73

    Google Scholar 

  • White DJ, Yang H, Schaefer VR, Thompson MJ (2005) Innovative solutions for slope stability reinforcement and characterization: vol. I, Final report CTRE Project 03-127. Center for Transportation Research and Education Iowa State University

  • Wolff TH (1985) Analysis and design of embankment dam slopes: a probabilistic approach. Ph.D. thesis, Purdue University, Lafayette, Ind

  • Xue JF, Gavin K (2007) Simultaneous determination of critical slip surface and reliability index for slopes. J Geotech Geoenviron Eng ASCE 133(7):878–886

    Article  Google Scholar 

  • Yan X, Su XG (2009) Linear regression analysis: theory and computing. World Scientific, Singapore

    Book  Google Scholar 

  • Yucemen MS, Tang WH (1975) Long term stability of soil slopes. A reliability approach. In: Proceedings of the second international conference on applications of statistics and probability in civil engineering, Aachen, Germany, pp 215–229

  • Yucemen MS, Tang WH, Ang AHS (1973) A probabilistic study of safety and design of earth slopes. Civil Engineering Studies, Structural Research Series 402, University of Illinois, Urbana

  • Zekkos DP (2005) Evaluation of static and dynamic properties of municipal solid waste. Ph.D. thesis, Department of Civil and Environmental Engineering, University of California, Berkeley

  • Zhang J, Tang WH, Hon M, Zhang LM (2010) Efficient probabilistic back-analysis of slope stability model parameters. J Geotech Geoenviron Eng ASCE 136(1):99–109

    Article  Google Scholar 

  • Zhang J, Zhang LM, Tang WH (2011) New methods for system reliability analysis of soil slopes. Can Geotech J 48(7):1138–1148

    Article  Google Scholar 

  • Zhang J, Huang HW, Juang CH, Li DQ (2013) Extension of Hassan and Wolff method for system reliability analysis of soil slopes. Eng Geol 160(June):81–88

    Article  Google Scholar 

  • Zhou G, Esaki T, Mitani Y, **e M, Mori J (2003) Spatial probabilistic modeling of slope failure using an integrated GIS Monte Carlo simulation approach. Eng Geol 68(3–4):373–386

    Article  Google Scholar 

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  1. Department of Environmental Engineering and Chemical Engineering, University of Calabria, 87036, Rende, Italy

    Venanzio R. Greco

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Greco, V.R. Variability and Correlation of Strength Parameters Inferred from Direct Shear Tests. Geotech Geol Eng 34, 585–603 (2016). https://doi.org/10.1007/s10706-015-9968-3

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