Comptes Rendus
no. 8
Truth: non-additive measures for the determination of relative density of sands using CPT measurements
[Mesures a vérité non additive pour déterminer les densités relatives des sables utilisant les tests de pénétration du cone (tpc)]

Présenté par : Évariste Sanchez-Palencia

Chi Tran1
1 Faculty of science and technology, WM University of Olsztyn, 10-724 Olsztyn, Poland
Comptes Rendus. Mécanique, Volume 333 (2005) no. 8, pp. 605-611.

Dans cette Note, on développe une approche utilisant les intégrales floues afin d'analyser les corrélations utilisées communément pour déterminer la densité relative D à partir de mesures obtenues dans les Tests de Pénétration Conique (TPC). Dans ces données, les mesures non-additives sont traitées comme mesures floues afin de rendre compte de la relation existant entre la compressibilité évaluée grâce au rapport entre le frottement des sables et les corrélations de base. Les résultats relevant du cas étudié montrent que les mesures floues et les intégrales floues peuvent être utilisées dans une approche nouvelle au génie géotechnique.

In this Note, a fuzzy-integral based approach is developed for aggregating some of the available correlations that are commonly used for determining relative density Dr, from cone penetration test (CPT) data, in which non-additive measures are used as fuzzy measures to relate the actual compressibility measured by the friction ratio of sands to the base correlations. The results of the case studied show that fuzzy measures and the fuzzy integral can be utilized for a new approach in geo-technical engineering.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2005.07.020
Keywords: Soils, Relative density, Truth measure, Measurable function, Fuzzy integral
Mot clés : Sols, Densité relative, Mesures de verité, Fonctions mesurables, Intégrale floue
Chi Tran 1

1 Faculty of science and technology, WM University of Olsztyn, 10-724 Olsztyn, Poland 
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Chi Tran. Truth: non-additive measures for the determination of relative density of sands using CPT measurements. Comptes Rendus. Mécanique, Volume 333 (2005) no. 8, pp. 605-611. doi : 10.1016/j.crme.2005.07.020. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.07.020/

[1] W.C. Vilet; J.K. Mitchel Cone resistance, relative density and friction angle (G.N. Norris; R.D. Holtz, eds.), Proc. Session on Cone Penetration Testing and Experience, ASCE National Convention, ASCE, New York, 1981, pp. 178-208

[2] J.H. Schmertmann, Guidelines for cone penetration test. Performance and design, Rep. FHwA-TS-78-209, Fed. Hwy. Admin, Washington, DC, 1978

[3] G. Baldi; R. Bellotti; V. Ghionna; M. Jamiolkowski; E. Pasqualini Design parameters for sands from CPT, Proc. 2nd Euro Symp. on Penetration Test, vol. 2, Balkema, Rotterdam, The Netherlands, 1982, pp. 425-432

[4] F.H. Kulhawy, P.W. Mayne, Relative density, SPT and CPT interrelationships, in: Proc. Ist Int. Symp. on Calibration Chamber Testing, New York, 1991, pp. 197–211

[5] C.H. Juang; X.H. Huang; R.D. Holtz; J.W. Chen Determining relative density of sands from CPT using fuzzy sets, J. Geotech. Engrg., Volume 122 (1996), pp. 1-5

[6] R. Viertl Is it necessary to develop a fuzzy Bayesian inference?, Probability and Bayesian Statistics, Plenum Press, New York, 1987, pp. 471-475

[7] Z. Wang; G.J. Klir Fuzzy Measure Theory, Plenum Press, New York, 1992

[8] T. Chi A Theory of Geotechnical Uncertainty, Technical University of Gdańsk, 2000

[9] M. Sugeno Fuzzy measures and fuzzy integrals: a survey, Fuzzy Automata and Decision Processes, North-Holland, Amsterdam, 1977, pp. 89-102

[10] P.K. Robertson; R. Campanella Liquefaction potential of sands using the CPT, J. Geotech. Engrg. ASCE, Volume 109 (1985) no. 3, pp. 458-482

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