PSI - Issue 10

G. Belokas / Procedia Structural Integrity 10 (2018) 120–128 G. Belokas / Structural Integrity Procedia 00 (2018) 000 – 000

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7. Conclusions

The determination of the uncertainties of the Mohr – Coulomb failure criterion constants c and tan φ can be treated by an error propagation technique, such as the FORM , applied to an appropriate transformation function. This is required because the variables of the M-C failure criterion are not directly measured. The FORM was applied to triaxial data and results were compared to various approaches. For the approaches considered, the FORM gave a lower uncertainty, since each single specimen was considered independent, which increased the sample size. These uncertainties together with the corresponding best estimates can be used for probabilistic analyses or to estimate the characteristic failure envelope. Regarding the characteristic failure envelope four different approaches were presented with different results. The FORM gave the more conservative results. In any case, engineering judgement on the results is necessary. The results were applied to a simple planar failure problem, in which it was observed that the maximum probability of having a SM <0 does not correspond to the minimum best estimate of the safety margin. This is attributed to a non – linear relationship of SM and u SM function and needs further exploring. The sensitivity analysis showed that the only influential uncertainty was that of cohesion, which generally happens to have the greater variability with regards to other soil constants. A sensitivity analysis is recommended in probabilistic analyses. Baecher, G., Christian, J., 2003. Reliability and Statistics in Geotechnical Engineering. Wiley, pp. 618. Duncan, J.M., 2000. Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering 126(4), 307-316. Fellin, W., 2005. Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design. Analyzing Uncertainty in Civil Engineering, Fellin, W., Lessmann, H., Oberguggenberger, M., Vieider, R. (eds.), Springer, 1-15. Frank, R., Bauduin, C., Driscoll, R., Kavvadas, M., Krebs Ovensen N., Orr, T., Schuppener, B., 2004. Designers' Guide to EN 1997-1 Eurocode 7: Geotechnical Design - General Rules. Thomas Telford, pp. 216. ISO/IEC Guide 98-3:2008. Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM: 1995). Kottegoda, N.T., Rosso, R., 2008. Applied Statistics for Civil and Environmental Engineers, 2nd Edition. Wiley-Blackwell, pp. 736. Kulhawy, H., 1992. On the evaluation of static soil properties. Stability and Performance of Slopes and Embankments – II, Proceedings of a Specialty Conference, Seed R.B. and Boulanger R.W. (eds), ASCE, 95-115. Orr, T., Breysse, D., 2008. Eurocode 7 and reliability-based design. Reliability-Based Design in Geotechnical Engineering. Computations and Applications, Kok-Kwang Phoon(edr), Taylor & Francis, 298-343. Pohl, C., 2011. Determination of characteristic soil values by statistical methods. ISGSR 2011 - Vogt, Schuppener, Straub & Bräu (eds), 427 -434. Schneider, H.R., 1997. Definition and determination of characteristic soil properties. Proceeding of the Fourteenth International Conference on Soil Mechanics and Foundation Engineering 4, 2271-2274. Schneider, H.R., Fitze, P., 2013. Characteristic shear strength values for EC7: Guidelines based on a statistical framework. Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering 4, 318-324. Tsiambaos, G., 1988. Technicogeological features of the Herakleion Crete Marls. PhD, University of Patras, pp. 358 (in Greek). Wu, T., 2008. Reliability analysis of slopes. Reliability-Based Design in Geotechnical Engineering, Computations and Applications, Kok-Kwang Phoon (ed), Taylor & Francis, 413-447. References