6.1 Fatigue validation 371
Validation of the model for fatigue results was made using the other half of the availed 372
population above described. Sixty-six specimens were used for validation purposes. The 373
validation of the model consisted in the comparison of fatigue life value (number of resisted 374
cycles) obtained from the test with respect to the achieved with the model, see Figure 21. As it is 375
32
possible to observe in the figure the data were well distributed along the line with slope 1, which 376
means that the model thrown similar values to experimental data.
377
378
In Figure 22, experimental and model data is compared. The pit depth characteristics upper and 379
lower bound limits defined with the statistical model are also represented. All the tested stress 380
range results were localized between the defined bounds. Taking into account the inner scatter 381
behaviour of fatigue very good agreement was observed for the corroded steel fatigue life value 382
estimation. It has to be noticed that for 150 MPa of stress range, the observed behaviour showed 383
higher scatter than the other tested stress ranges. More data would be required to perform a better 384
validation of the model for such low stress ranges.
385
33
386
6.2 Monotonic validation 387
Four different sets of experimental data were taken for the corroded steel tensile properties 388
validation. Set one consisted of 25 specimens, which include a wide range of corroded specimens 389
from very little degrees of corrosion about 2% up to very high degrees of corrosion 60%. The 390
34
second set of bars encompassed 23 specimens covering a closer range of degrees of corrosion 391
from 3% up to 16% [8]. The third set of specimens included 21 specimens also covering a full 392
range of degrees of corrosion from 1% to 50% [22]. Finally the most extended database of 393
specimens, which includes 54 specimens with two different bar diameter, ϕ10 mm and ϕ12 mm, 394
and covering corrosions levels from 7% up to 25% [21]. The results of the model validations are 395
presented in Figure 23, Figure 24, Figure 25 and Figure 26, in which are shown the experimental 396
fy or fmax compared to the model results, which include the upper and lower bounds. 397
Experimental and numerical data described very good agreement for yielding and ultimate 398
stresses. Almost all the experimental data were localized in between the confident bounds defined 399
with the presented statistical model. However, modulus of elasticity and maximum strain 400
estimations were not as accuracy as yielding stress and ultimate stress ones. It is necessary to 401
underline that the elastic modulus was obtained directly from the monotonic test not using the 402
code recommendations for this parameter; hence, it could present some dispersion. Regarding 403
maximum strain, it is subjected to other phenomena such as fracture mechanics due to pits in the 404
cross-section.
405
35
406
36
407
37
7. Conclusions 408
A mechanical model to evaluate the effect of steel reinforcement corrosion on σ-ε and fatigue 409
behaviour has been extended and presented. Corrosion phenomena has been implemented using 410
an idealized pitted cross-section.
411
The main conclusions of the presented work are described in the next points:
412
- The experimental study showed a non-uniform distribution of the material properties 413
throughout the steel cross-section. An increasing strength of the outer layers was 414
observed, where the outer martensitic layer achieved up to 806 MPa yielding stress. The 415
inner ferrite core achieved up to 435 MPa yielding stress. The effect of material properties 416
distribution is stated as relevant during a corrosion episode.
417
- The statistical model presented define different pit geometries with respect to the 418
expected corrosion level. That allows describing the upper and lower bound limits of the 419
pit geometry characteristics, ensuring that the real mechanical properties of the corroded 420
steel bar will be inside those bounds with a 90% of confident.
421
- Very good agreement was observed for yielding stress and ultimate stress within a 0% - 422
60% degree of corrosion. The model allows to describe quite well the average behaviour 423
of the corroded bars mechanical properties despite the experimental scatter values. Elastic 424
modulus and ductility presented more dispersion, likely because of the dispersion of these 425
parameters themselves, and the model did not adjusted the average behaviour as well as 426
for the other parameters. More detailed studies are needed to better calibrate the model 427
response for those values.
428
38
- The mechanical model can describe the fatigue behaviour under corrosion phenomenon 429
with a very good agreement with the experimental data. Then, the characteristic fatigue 430
curves with respect to the degree of corrosion can be defined.
431
As a general conclusion, the model leads to a good mechanical properties characterization for 432
corroded and uncorroded bars, necessary properties to carry out with enough accuracy analysis 433
and assessment of safety, serviceability and durability of deteriorated reinforced concrete 434
structures. However, more experimental work should be addressed to further calibrate and 435
validate the presented model for Low Cycle Fatigue, which is of interest in seismic zones.
436
Acknowledgments 437
The authors wish to acknowledge the financial support of The Ministry of Economy and 438
Competitiveness of the Government of Spain (MINECO) for providing funds for projects 439
BIA2009-11764, BIA2012-36848 and the European Regional Development Funds (ERDF). The 440
financial support of Infrastructures de Catalunya (ICAT) is also highly appreciated.
441
Acknowledgements are also extended to CIMNE to providing a license of the software GiD 442
necessary to develop the presented work.
443 444
39
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