[雙語(yǔ)翻譯]--橋梁工程外文翻譯---建立在可靠性基礎(chǔ)上的對(duì)圬工拱橋的評(píng)估（英文）

1、Reliability-based assessment of masonry arch bridgesJoan R. Casas ?School of Civil Engineering, Universitat Politècnica de Catalunya (UPC), C/Jordi Girona 1-3, 08034 Barcelona, Spaina r t i c l e i n f oArticle hist

2、ory:Received 17 May 2010Received in revised form 30 September2010Accepted 23 October 2010Available online xxxxKeywords:MasonryArchReliabilityFatigueServiceabilitya b s t r a c tThe paper presents a methodology for the pr

3、obabilistic assessment of masonry arches at the serviceabil-ity and Ultimate Limit States. First, it explains the definition of the different failure modes andcorresponding limit state functions that may occur depending

4、on the type of masonry construction(single-ring and multi-ring). The most reported modes of failure are the four-hinge mechanism, the ringseparation in multi-ring arches and the slippage at the foundations. Because of th

5、e lack of reliable mate-rial data (in the statistic sense) or available response models, only those more prone to be analyzed usingreliability-based methods are shown in this paper: four-hinge mechanism and ring separati

6、on.The possibility of fatigue failure of masonry arch bridges under service loads and the proposal of reli-ability-based assessment methods at the ultimate level of the four-hinge mechanism are also analyzed.Finally, the

7、 proposed methodology is applied to an existing bridge.? 2010 Elsevier Ltd. All rights reserved.1. IntroductionOver the past 10 years there has been an extensive programme of research which considered some aspects of mas

8、onry arch behav- iour. A number of small and large scale tests have been carried out on masonry arches, most of them have been under static (mono- tonic) loading and considered mainly the arch ring itself. However, there

9、 has been very little work done on investigating the long-term effect of traffic (cyclic) loading and the effect of deteriorated masonry on the fatigue life of the bridge. Several semi-empirical and numerical methods exi

10、st to deter- mine the load carrying capacity of masonry arches: MEXE method, maximum stress analysis, limit analysis (mechanism) methods [1–3], solid mechanics methods (Castigliano’s non-linear analysis, finite element a

11、nalysis, discrete element analysis). Many com- puter-based applications of these methods also exist (Archie-M, RING, DIANA. . ..). Recently, the possibility of fatigue failure under cyclic loading at normal service level

12、 of loading, much lower than the ultimate load [4] has suggested a new approach to the assess- ment of masonry arches based upon the long-term performance of masonry subjected to cyclic loading [5,6]. Available assessmen

13、t methods of masonry arches are deterministic in nature. They can predict ultimate capacity provided that all variables involved in the response are assumed as deterministic values, what is not really the case due to unc

14、ertainties involved in geometry, materials and loads.Reliability-based assessment of structures and particularly bridges has been successfully implemented and performed in re- cent years. These methods assume the intrins

15、ic uncertainty of the variables involved. Most of the experiences have been done in the field of bridges either from structural concrete (reinforced and prestressed) or steel. Several experiences have shown the large amo

16、unt of money that can be saved by an efficient and accurate assessment based on a probabilistic approach [7–12]. However the application to masonry bridges has been almost negligible. One reason is the difficulty to defi

17、ne reliable failure criteria for this type of structures. Another reason is the lack of statistical data on material properties of masonry and filling material. The experi- mental tests show that normally the failure of

18、an arch is of a global nature more than due to the failure of a bridge component. In most cases, even the division of the bridge in different components is al- most impossible. For this reason, also the lack of accurate

19、theoret- ical models for the idealization of the behaviour of the masonry arch bridge as a system, including the interaction effects with the filling material, spandrel walls, etc., has been another difficulty not yet ov

20、ercome. Last, but not least, the absence of reliable data on the statistical definition of the material properties has been an- other issue that has limited the use of probability-based assess- ment techniques. Very few

21、data is available for the behaviour of the masonry under static loads. The lack of experimental data is even more dramatic in the case of cyclic loading. Estimation of ma- sonry strength from measurements may then be one

22、 of key issues of the assessment of existing structures [13,14]. However, some experiences have shown the potentiality of the use of reliability-based assessment in the capacity assessment of masonry structures in bendin

23、g and compression [15–18]. As an0950-0618/$ - see front matter ? 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.conbuildmat.2010.10.011? Tel.: +34 934016513; fax: +34 934054135.E-mail address: joan.ramon.casas@upc.

24、eduConstruction and Building Materials xxx (2010) xxx–xxxContents lists available at ScienceDirectConstruction and Building Materialsjournal homepage: www.elsevier.com/locate/conbuildmatPlease cite this article in press

25、as: Casas JR. Reliability-based assessment of masonry arch bridges. Constr Build Mater (2010), doi:10.1016/j.conbuildmat.2010.10.011The failure mechanism by ring separation normally appears un- der cyclic loading conditi

26、ons, although also a monotonic extreme load may cause the separation. In the case of static loading, ring separation can occur between the 1=4 point and the nearest abut- ment and the failure is considered as an Ultimate

27、 Limit State. For cyclic loading, the separation occurs between the 1=4 and 3=4 point. In the case of the ring separation under cyclic loading, the failure should be considered a Fatigue Limit State, or, again, as a Perm

28、issi- ble Limit State [4,6].3. Limit state functionsDepending on the criteria adopted to define the failure of the bridge, different limit state functions and different levels of assess- ment can be formulated. According

29、 to the failure mechanisms defined in Section 2, the possible levels of assessment and corre- sponding limit state functions are described below. Despite a sig- nificant uncertainty exists on the ability of the used mode

30、ls to characterize the behaviour of masonry structures, even for the most advanced ones, model uncertainty has not been considered explicitly in the definition of the limit state functions. The mean reason is that, at th

31、e present moment, not sufficient experimental data is available to statistically define such uncertainty. It is clear that this should be corrected as more comparisons between exper- imental and numerical results will be

32、come available. Neglecting the model uncertainty in the limit state function can be compen- sated by requiring a higher target reliability level in the structure than in the case where model uncertainty is considered. At

33、 least, three assessment levels exist, with increasing level of complexity and accuracy depending on the failure criteria and ana- lytical model used. They are summarized in the diagram in Fig. 4 jointly with the failure

34、 modes and limit states considered, and fully described below.3.1. First level of assessment: local failure3.1.1. Monotonic loading This failure occurs when an extreme load causes excessive bending moments/shear forces c

35、ombined with important axial loads resulting in the failure either because tension stress appears or excessive compression in the material provokes crushing of the masonry. The failure criteria can be based on the Ultima

36、te Limit State (ULS) formulation. The lowest capacity level will be obtained considering the failure of the bridge when any fibre at any cross- section is in tension or it reaches the maximum allowable com- pression of t

37、he material. The corresponding LS function is:G ¼ rminG ¼ fc ? rmax ð1Þwhere rmin and rmax are the lowest and highest stress at any pointof the bridge and fc is the compressive strength of masonry. Th

38、e va- lue of the internal forces (bending moment, normal force) and thedistribution of stresses in the cross-section are derived assuming a linear behaviour of the structure and the material. Of course, thisis an extreme

39、ly restrictive and over-conservative failure criterion. However, if the bridge passes this level of assessment, that requiresvery simple modelling tools, it may be assured that the bridge is in very good shape.3.1.2. Cyc

40、lic loading (fatigue) The few available high cycle fatigue tests either in small speci- mens [23] or full laboratory models [4] have shown that the fatigue strength of brick masonry subject to compressive-bending state d

41、epends upon the induced stress range, the mean or maximum induced stress and the quasi-static compressive strength of the masonry under similar loading conditions. Considering that a set of experimental points in the S–N

42、 plane is provided, then the fatigue capacity from a probabilistic point of view can be analysed in a similar way as in the case of concrete or steel [24]. The limit state function in the case of several number of cycles

43、 of different load intensity, assuming that Miner’s rule is of application [6], can be written in the following way:G ¼ 1 ? XDrini Ni ð2Þni = number of cycles of load level Dri due to external loads (ran-

44、dom variable) and Ni = number of cycles of load level Dri that thebridge can support (random variable). ni as a random variable will be obtained via a structural analysis taking into account the randomness in the live-lo

45、ads acting on the bridge or, alternatively, by extrapolation of measurements taken in the bridge. Also the variability of the bridge properties should be considered in the definition of ni as the stress increment will al

46、so depend on these properties. At the present stage and despite some preliminary tests [6], there is not yet a clear evidence that the Miner’s rule is applicable to masonry material as it seems to be for steel. In this s

47、ense, there is still a limitation for a fully appraisal of the results obtained by the application of the proposed assessment method. The way to derive the statistics of random variable ni is by sim- ulation of traffic e

48、ffects jointly with simulation of geometric and material properties of the structure [24,25]. In the case of railway traffic and taking into account that the stress increments due to bridge dynamics will be very low for

49、this type of bridges (the infill mitigates the vibration level), one may consider the passage of each convoy as a cycle of loading. The statistical definition of Ni can be done in the following way. Different works have

50、shown that the Weibull distribution function agrees very well with the expected physical criteria of progressive fatigue deterioration [26,27]. On the basis of physi- cally valid assumption, sound experimental verificati

51、on, relative ease in its use and better developed statistics, the Weibull distri- bution has been widely used for the fatigue analysis of metals. It is also well-suited for certain procedures of statistical extrapola- ti

52、on of large systems [26]. In [27,28], the distribution of fatigue life of concrete was found also to approximately follow the Wei- bull distribution. Some theoretical and experimental works[29,30] have shown also the fea

53、sibility of the Weibull distribu- tion regarding the statistical model for steel wires and strands to fatigue.Ring separation Fig. 3. Failure by ring separation in a multi-ring arch. Test carried out at theUniversity of

54、Salford (UK) [4].J.R. Casas / Construction and Building Materials xxx (2010) xxx–xxx 3Please cite this article in press as: Casas JR. Reliability-based assessment of masonry arch bridges. Constr Build Mater (2010), doi:1