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1、Engineering Structures 33 (2011) 2120–2133Contents lists available at ScienceDirectEngineering Structuresjournal homepage: www.elsevier.com/locate/engstructA probabilistic approach for estimating the behavior of railway

2、tracksN. Rhayma b,a, Ph. Bressolette a,?, P. Breul a, M. Fogli a, G. Saussine ba Clermont Université, Université Blaise Pascal, EA 3867, LaMI, BP 10448, 63000 Clermont-Ferrand, Franceb I fax: +33 473 407 494.E-

3、mail addresses: philippe.bressolette@polytech.univ-bpclermont.fr,ph.bressolette@polytech.univ-bpclermont.fr (P. Bressolette).of knowledge of these heterogeneities and of their possible conse- quences on the track behavio

4、r, it is difficult to provide an optimized maintenance management.As a result, to describe in a realistic way the mechanicalbehavior of a railway track under dynamic loads, it is necessary to use a numerical model able t

5、o take into account the uncertain nature of some mechanical and geometrical parameters. Several numerical approaches based on the finite elements (FE) method have been developed in the last decades to describe the global

6、 or local behavior of railway tracks [9]. To take this random variability into consideration, the natural way is to use a stochastic finite elements (SFE) method [10–20]. It is the solution chosen in this paper, with the

7、 aim of analyzing the propagation of uncertainties through the numerical model describing the mechanical behavior of track sections. In this way, different maintenance solutions could be analyzed and compared by railway

8、managers.This paper is organized as follows. The next section deals withthe methodologies of diagnostics used by railway companies. In particular, the new devices used to collect the required mechanical and geometrical d

9、ata are described. Then, the deterministic FE track model is presented. Section 4 is focused on the probabilistic modeling of the uncertain data and on the choice of the control variables used in the probabilistic approa

10、ch. The proposed SFE method (based on the stochastic collocation method) is presented in Section 5. Some numerical applications of this method to the railway problem are detailed in Section 6 (influence of the distributi

11、on and of the correlations of the parameters, uncertainty propagation), and finally we explain how this approach can be used from a practical point of view by track managers to improve maintenance and draw some conclusio

12、ns in Section 7.0141-0296/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.02.0412122 N. Rhayma et al. / Engineering Structures 33 (2011) 2120–2133Fig. 2. Mauzin car and ex

13、ample of records.Fig. 3. Example of GPR test equipment deployed for track inspection [27].Fig. 4. Penetrometric (Panda type) test and geoendoscopy principle.estimation of the variability of the soil layers characteristic

14、s. More-over Elkateb et al. [36] have shown that this variability is often spe-cific to the site and to the property analyzed.From the in situ measurement carried out on 4 different realsites (2 sites on high-speed track

15、s and 2 sites on ‘‘classic’’ tracks),the variability of the thickness and of the modulus of each layerof the railway platform have been characterized. In this way, thefollowing strategy has been adopted:? Estimation of s

16、tatistical moments.? Homogeneity analysis of experimental samples by using a χ2test.? Adequacy test to theoretical distributions for the various sam-ples by using χ2 and Kolmogorov–Smirnov tests.? Analysis of correlation

17、s between parameters.The analysis for the various sites highlights the variabilityof the layers characteristics according to tracks and sites and the importance of the intermediate layer which has mechanical characterist

18、ics sharply superior to the other layers. Moreover, the study of the correlation between the parameters shows a weak correlation (often less than 50%). This kind of analysis was confronted with two types of problems:? th

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