effect of very low percentage of cycles above cafl
DESCRIPTION
Effect of very low percentage of cycles above CAFL in fatigue analysis of road bridgesTRANSCRIPT
1
Research Plan – Luca D’Angelo – Ecole Polytechnique Federale de Lausanne, ICOM
RESEARCH PLAN
Effect of very low percentages of cycles above fatigue limit on road bridges damaging process under variable amplitude loadings
Candidate: Luca D’Angelo
Thesis director: Professor Alain Nussbaumer
Thesis co-Director: ………….........
Program’s Director: Professor Michel Bierlaire
Date of immatriculation: 23/02/2012
Name of my mentor: Professor Christian Ludwig
Signatures:
Thesis Director: ………….........
Thesis co-Director: ………….........
Candidate: ……………….
Director of the doctoral program: ………….........
After signature by the thesis director, the co-director and the candidate, two copies of this research plan must be sent to the direction of the doctoral program Civil and Environmental Engineering. (without stapling)
2
Research Plan – Luca D’Angelo – Ecole Polytechnique Fédérale de Lausanne, ICOM
Personal Data / PhD Student
Date of submission (research plan): 11/12/2012
Prospective date of defense: November 2015
Name and first name: D’Angelo Luca
Date of birth: 09/05/1983
Place of birth: Naples, Italy
Private address: Passage F. Bocion 4, 1007 Lausanne
Diploma: Master of Science Year: 2008
Establishment: University of Naples “Federico II”
Thesis Director: Professor Alain Nussbaumer
Unit: Laboratory of Steel Construction (ICOM)
Envisaged collaborations:
Prof. Gilles Dumont, Traffic Facilities Laboratory, EPFL.
Prof. Mohammad Al-Emrani, Konstrutionsteknik, Chalmers University of Technology, Sweden
Prof. Tom Lassen, Fakultet for Teknologi og Realfag, Agder University, Norway
Source of financing: OFROU, Office federal des routes
Framework in which is the research is done: Project AGB 2010/003, “Traffic simulations with structural evaluation indexes computation”, Département fédéral de l’environnement, des transports, de l’énergie et de la communication DETEC, Office fédéral des routes OFROU.
Research Plan
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KeywordsMethods, D
2. State o
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Research Plan
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Research Plan
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Research Plan
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Research Plan
2.4.4. Fati
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Author
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rical evolution o
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or fatigue
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etime
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Reference
[1]
[6]
[7]
[4]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
to failure (N
7
(FLM) are he damage he damage
ibe fatigue yzed in Par. models is
N) and the
(8)
Research Plan
Where Y=
parameters
sum of sq
parameters
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The modeStatistics T
(
i
a
S
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Where S
used to est
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Finally, it that linearregion of and it is asthe averagvalue of Yvalue of Y
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tablish 100(
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8
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(10)
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(12)
Research Plan
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of freedom
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atigue test rutranslated atnconstancy 106 cycles.
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om the statives a larger approach isa). Assuminactile hyperbN Backgrou
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9
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10
Research Plan – Luca D’Angelo – Ecole Polytechnique Fédérale de Lausanne, ICOM
2.5.3. The Castillo and Fernandéz-Canteli model for S-N curves
In Chapter 2 of [18] Castillo and Canteli have proposed a general fatigue lifetime model for any constant stress range and level; few notes about this model are given in Paragraph 3.3.2, complete model derivation can be found in [18] (pp. 37-89).
2.5.4. The Lassen and Recho model
Lassen and Recho [15] have proposed a Semi-empirical Two Phases Model (TPM) that make it possible to build P-S-N curves directly based on physical parameters of welded joints. This approach is not presented in this work.
2.6. Weigh-in-Motion and traffic simulation
Weigh-in-motion (WIM) devices capture dynamic tire force of a moving truck to measure the correspondent static tire force; they are used for several purposes: 1) assessment of existing road and rail bridges 2) statistical studies 3) traffic simulations 4) calibration of codes [19].
Figure 2-7 – Map of Swiss WIM stations
Measured WIM data give information on the frequency distribution of total gross weight, axles groups weight and axles distance; from 1990s there have been many probabilistic approaches to model the extrapolate the upper tail of the distribution of interest in order to find the rare extreme load events.
In 1996 Bailey [20] used a combined beta bimodal distribution to model the probability density function of axle weights measured by WIM devices; then a type Gumbel III Extreme Value Distribution is used to define the upper tail of the distribution. In 1997 Crespo-Minguillon and Casas [21] used the generalized Pareto distribution to extrapolate the upper tail of the distribution of interest given by their general continuous-flow traffic model for highway bridges. In 2006 Meystre [22] established a load model for “Swiss traffic” to evaluate existing roadway bridges with two lanes (bidirectional) and highway bridges with two lanes (unidirectional); the traffic simulation program is based on WIM measurements on different Swiss stations and it is used to validate SIA 261 [23] fatigue load model. 99.9% fractile is chosen in frequency distributions in order to get the rare load that has to be compared to SIA 261 model. SIA 261 model is updated using correction factors. In 2010 [24] Enright performed Monte Carlo simulations for
Research Plan
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17
Research Plan – Luca D’Angelo – Ecole Polytechnique Federale de Lausanne, ICOM
3.3.3. Application of R-code for evaluation of S-N curves from a CA fatigue test database
Experimental test results database [23] for a category 40 detail [table 8.4 EN 1993-1-9] has been considered. Figure 3-5 shows four RFL resistance curves based on four different confidence levels 1) Mean Curve 2) 95% C.I. on CAFL 3) 95% C.I. on CAFL and on log(N) 4) 95% C.I. on CAFL and on log(N) + 75% C.I. on CAFL distribution parameter estimators.
Figure 3-5 – Random Fatigue Limit S-N curves
Standard Deviations (SD) of model parameter estimators are determined by computing the diagonal elements of the inverted negative Hessian matrix.
Table 2 – RFL Model Parameter Estimators
EN standard double slope S-N curve, RFL Mean curve and RFL Confidence Level 1 curve have been compared for the damage calculation of a category 40 weld attachment; stress spectrum[30] has been considered. Total damage is calculated using linear Miner’s rule.
Model: ln(N)= 0 + 1 ln (S‐exp())
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1.66
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20.1
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Research Plan
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Table 3
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18
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19
Research Plan – Luca D’Angelo – Ecole Polytechnique Federale de Lausanne, ICOM
‐ Which probabilistic model does it give the most appropriate definition of the CAFL? (RFL Model, log-Gumbel Model, log-Weibull Model?)
‐ Which S-N curves have to be considered for the hot-spot stress approach? ‐ Which damage model has to be considered for VA loadings to get a better fatigue life
prediction with respect to linear Miner’s rule?
4.2. Objectives and scope
The main objectives of the research are as following:
1) Determination of realistic typical road bridges stress spectrum upper tails associated with infrequent loads.
2) Appropriate evaluation of hot-spot stress-based S-N curves by developing a probabilistic model that fit properly fatigue data issued by CA fatigue tests (comparison with EN standard S-N curves and proposition of modifications).
3) Evaluation of damaging effect of stress spectrum tails above the CAFL, for VA loadings.
4.3. Methods
Objective Method
Determination of realistic typical bridges stress spectrum tails associated with infrequent loads
1) WIM data monitoring 2) Development of a ultra-realistic
traffic micro-simulation software (Par. 3.2)
3) Definition of realistic Load/Stress Transfer Functions through FE bridges modeling (Par. 3.1)
Appropriate evaluation of high-cycle region and CAFL of hot-spot stress-based curves
1) Development of a probabilistic model for the statistical evaluation of S-N curves and implementation of the model in a R-code (Par. 3.3)
2) Statistical validation of the model
Evaluation of damaging effect of stress spectrum tails above the CAFL, for VA loadings
1) Integration of the probabilistic model with a method for an appropriate evaluation of damage accumulation due to VA spectra
2) Validation of the model on existing VA fatigue test data
Table 4 – Project methods
20
Research Plan – Luca D’Angelo – Ecole Polytechnique Fédérale de Lausanne, ICOM
4.4. Tasks
In order to achieve the project objectives following steps have been planned:
4.4.1. Phase A: Literature review
The literature review phase is presented in section 2.
4.4.2. Phase B: Development of the traffic micro-simulation software (collaboration with LAVOC)
B1. Development of the traffic simulation tool prototype. Description of the prototype features is given in Par. 3.2.
B2. Upgrade of the traffic simulation tool prototype. Description of improvements provided for future versions of the tool are given in Par. 3.2.
4.4.3. Phase C: Development of a probabilistic model for the evaluation of hot-spot stress-based S-N curves
C1. Development of a R-code for the evaluation of S-N curves by statistical evaluation of CA fatigue test data. RFL model is implemented in the first version of the code and both failure and censored (run-outs) data are considered. (Par. 3.3)
C2. Improvement of the first version of the code: other statistical model will be considered and eventually included in the code.
C3. Statistical validation of the code and definition of the probabilistic model for the appropriate evaluation of hot-spot stress-based S-N curves.
4.4.4. Phase D: VA loadings: influence of cycles below the CAFL on damage sum
D1. Study of the cumulative damage mechanisms for VA loadings.
D2. Integration of the probabilistic model (C.3) with a method for the evaluation of effects of spectrum tail cycles on fatigue damage.
D3. Validation of the developed probabilistic model on existing VA Fatigue Test Data.
4.4.5. Phase E: Reporting and publication
Publication of at least two conference papers and two journal paper is planned. One conference paper on the subject “Fatigue life assessment of existing composite motorway bridge” is scheduled to be presented in September 2013 at Conference SEMC 2013 in Cape Town, South Africa. Abstract of the paper has been submitted and accepted.
4.4.6. Phase F: Writing thesis
Results of this research work will be published in the PhD thesis.
21
Research Plan – Luca D’Angelo – Ecole Polytechnique Federale de Lausanne, ICOM
5. Program of doctoral research up to thesis defense With reference to tasks presented in Par.4, time schedule of the project is presented in table 4.
2012 2013 2014 2015
Tasks T.1 T.2 T.3 T.4 T.1 T.2 T.3 T.4 T1. T.2 T.3 T.4 T.1 T.1 T.3 T.4
A X X X X
B1 X X
B2 X X X X
C1 X
C2 X X
C3 X X X X
D1 X X X X
D2 X X X X
D3 X X X X
E X X X X
F X X
Table 5 – Time-schedule of the project
22
Research Plan – Luca D’Angelo – Ecole Polytechnique Fédérale de Lausanne, ICOM
1. Wöhler, A., Theorie rechteckiger eiserner Brückenbalken mit Gitterwänden und mit Blechwänden. Zeitschrift für Bauwesen 1855. 5: p. 121-166.
2. Paris, P. and F. Erdogan, A Critical Analysis of Crack Propagation Laws. Trans.ASME, 1963: p. 528-534.
3. Niemi, E., W. Fricke, and S.J. Maddox, Fatigue Analysis of Welded Components, 2006. 4. Miner, M.A., Cumulative damage in fatigue. Journal of Applied Mechanics, 1945. 12: p. 159-164. 5. Gurney, T., Cumulative damage of welded joints. 2006. 6. Basquin, O.H., The exponential law of endurance tests. American Society for Testing and Materials
Proceedings, 1910. 10: p. 625-630. 7. Palmgren, A., Die Lebendauer von Kugellagern. Ver. Deut. Ingr, 1924. 68: p. 339-341. 8. Dixon, W.J. and A.M.M. . A method for obtaining and analyzing sensitivity data. Journal of the
American Statistical Association, 1948. 43: p. 109-126. 9. Bastenaire, F.A., New method for the statistica1 evaluation of constant stress amplitude fatigue-test
results. Probabilistic Aspects of Fatigue, American Society for Testing and Materials, 1972. ASTM STP 511: p. 3-28.
10. Spindel, J.E. and E. Haibach, Some consideration in the statistical determination of the shape of S-N curves. Statistical Analysus of Fatigue Data, ASTM,STP 74, 1981. 4: p. 89-113.
11. Pascual, F.G. and W.Q. Meeker, Estimating fatigue curves with the random fatigue-limit modeé. Technometrics 1999. 41: p. 277-302.
12. Castillo, E. and A.F. Canteli, A general regression model for lifetime evaluation and prediction. International Journal of Fatigue, 2001. 107: p. 117-137.
13. Kohout, J. and S. Vechet, A new function for fatigue curves characterization and its multiple merits. International Journal of Fatigue, 2001. 23: p. 175-183.
14. Castillo, E. and A.F. Canteli, A parametric lifetime model for the prediction of high-cycle fatigue based on stress level and amplitude. Fatigue Fracture Engineering Material Structure, 2006. 29: p. 1031-1038.
15. Lassen, T. and N. Recho, Proposal for a more accurate physically based S-N curve for welded steel joints. International Journal of Fatigue, 2008. 3: p. 70-78.
16. Brozzetti, J., et al., Eurocode No.3 Part 1 - Background Documentation - Chapter - Document 9.01, 1989.
17. Team, R.C., R: A language and environment for statistical computing., ed. R.F.f.S. Computing. 2012, Vienna, Austria.
18. Castillo, E. and A.F. Canteli, A Unified Statistical Methodology for Modeling Fatigue Damage. 2009. 19. Znidaric, A., Bridge-WIM as an efficient tool for optimised bridge assessment, in ENEA2010: Rome. 20. Bailey, S.F., Basic Principles and load models for the structural safety evaluation of existing road
bridges, in ENAC ICOM1996, EPFL: Lausanne. 21. Crespo-Minguillon, C. and J.R. Casas, A comprehensive traffic load model for bridge safety
checking. Structural Safety, 1997. 19: p. 339-359. 22. Meystre, T., Evaluation de ponts routiers existants avec un modèle de charge de trafic actualisé,
Mandat de recherhe AGB 2002/2005, 2006, EPFL-ICOM: Lausanne. 23. Swiss Norm SIA 261, Actions on Structures. 24. Enright, B., Simulation of traffic loading on highway bridges, in School of Architecture, Landscape
and Civil Engineering2010, University College Dublin Ireland: Dublin, Ireland. 25. Treacy, M. and E. Bruhwiler, Fatigue loading estimation for road bridges using long term WIM
monitoring, in ESREL 20112011: London. p. 1870-1875. 26. Nelson, W., Fitting of Fatigue Curves with NonConstant Standard Deviation to Data with Runouts.
Journal of Testing and Evaluation 1984. 12: p. 69-77. 27. Ostrouchov, G. and W. Meeker, Accuracy of Approximate Confidence Bounds Computed from
Interval Censored Weibull and Lognormal Data. Journal of Statistical Computing and Simulation, 1988. 29: p. 43-76.
28. Wackerly, D., W.Mendehall, and R.L. Scheaffer, Mathematical Statistics Brooks/Coole, Editor. 2008.
29. Bertrand, J., Sur l'homogéneté dans les formules de physique". Comptes rendus, 1878. 86: p. 916-920.
30. Estimate fatigue damage of the 83'-0'' deck truss spans of the Mukoka river bridge, 1981, CN Rail, Office of the Chief Engineer: Montreal.