Experimental Testing of Statistical Size Effect in Civil Engineering Structures
The presented paper copes with an experimental evaluation of a model based on modified Weibull size effect theory. Classical statistical Weibull theory was modified by introducing a new parameter (correlation length lp) representing the spatial autocorrelation of a random mechanical properties of material. This size effect modification was observed on two different materials used in civil engineering: unreinforced (plain) concrete and multi-filament yarns made of alkaliresistant (AR) glass which are used for textile-reinforced concrete. The behavior under flexural, resp. tensile loading was investigated by laboratory experiments. A high number of specimens of different sizes was tested to obtain statistically significant data which were subsequently corrected and statistically processed. Due to a distortion of the measured displacements caused by the unstiff experiment device, only the maximal load values were statistically evaluated. Results of the experiments showed a decreasing strength with an increasing sample length. Size effect curves were obtained and the correlation length was fitted according to measured data. Results did not exclude the existence of the proposed new parameter lp.
<p>1] J. Kadˇerov´a, “Testov´an´ı statistick´eho vlivu velikosti pomoc´ı
ˇctyˇrbodov´eho ohybu (Experiments on statistical size effect in four point
bent specimens),” Bachelor’s thesis, Institute of Structural Mechanics,
Faculty of Civil Engineering, Brno University of Technology, Brno,
Czech Republic, 2009.
[2] “Multi-filament yarns testing for textile-reinforced concrete,”
Master’s thesis, Institute of Structural Mechanics, Faculty of Civil
Engineering, Brno University of Technology, Brno, Czech Republic,
2012.
[3] W. Weibull, “The phenomenon of rupture in solids,” Royal Swedish
Institute of Engineering Research (Ingenioersvetenskaps Akad. Handl.),
Stockholm, vol. 153, pp. 1–55, 1939.
[4] Z. P. Baˇzant, M. Voˇrechovsk´y, and D. Nov´ak, “Asymptotic prediction
of energetic-statistical size effect from deterministic finite element
solutions,” Journal of Engineering Mechanics (ASCE), vol. 133, no. 2,
pp. 153–162, 2007.
[5] Z. P. Baˇzant, S. D. Pang, M. Voˇrechovsk´y, and D. Nov´ak, “Energeticstatistical
size effect simulated by SFEM with stratified sampling and
crack band model,” International Journal for Numerical Methods in
Engineering (Wiley), vol. 71, no. 11, pp. 1297–1320, 2007.
[6] M. Voˇrechovsk´y, “Incorporation of statistical length scale into Weibull
strength theory for composites,” Composite Structures, vol. 92, no. 9,
pp. 2027–2034, 2010.
[7] M. Voˇrechovsk´y and R. Chudoba, “Stochastic modeling of multifilament
yarns: II. Random properties over the length and size effect,”
International Journal of Solids and Structures (Elsevier), vol. 43, no.
3-4, pp. 435–458, 2006.
[8] M. Voˇrechovsk´y, “Statistical alternatives of combined size effect on
nominal strength for structures failing at crack initiation,” in Probl´emy
lomov´e mechaniky IV (Problems of Fracture Mechanics IV), M. Stibor,
Ed. Academy of Sciences - Institute of physics of materials of
the ASCR: Brno University of Technology, 2004, pp. 99–106, invited
lecture.
[9] R. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related
Properties of Random Sequences and Processes, ser. Springer Series
in Statistics. Springer London, Limited, 2011. [Online]. Available:
http://books.google.cz/books?id=AGB9MQEACAAJ
[10] H. Koide, H. Akita, and M. Tomon, “Probability model of flexural
resistance on different lengths of concrete beams,” Applications of
Statistics and Probability, Melchers & Stewards (eds), pp. 1053–1057,
2000.
[11] H. Daniels, “The maximum of gaussian process whose mean path has
a maximum, with an application to the strength of bundles of fibres,”
Advances in Applied Probability, vol. 21, pp. 315–333, 1945.
[12] R. Smith, “The asymptotic distribution of the strength of the seriesparallel
system with equal load-sharing,” Annals of Probability, vol. 10,
no. 1, pp. 137–171, 1982.
[13] R. Chudoba, M. Voˇrechovsk´y, V. Eckers, and T. Gries, “Effect of twist,
fineness, loading rate and length on tensile behavior of multifilament
yarns (a multivariate study),” Textile Research Journal (Sage), vol. 77,
no. 11, pp. 880–891, 2007.</p>
<p>1] J. Kadˇerov´a, “Testov´an´ı statistick´eho vlivu velikosti pomoc´ı
ˇctyˇrbodov´eho ohybu (Experiments on statistical size effect in four point
bent specimens),” Bachelor’s thesis, Institute of Structural Mechanics,
Faculty of Civil Engineering, Brno University of Technology, Brno,
Czech Republic, 2009.
[2] “Multi-filament yarns testing for textile-reinforced concrete,”
Master’s thesis, Institute of Structural Mechanics, Faculty of Civil
Engineering, Brno University of Technology, Brno, Czech Republic,
2012.
[3] W. Weibull, “The phenomenon of rupture in solids,” Royal Swedish
Institute of Engineering Research (Ingenioersvetenskaps Akad. Handl.),
Stockholm, vol. 153, pp. 1–55, 1939.
[4] Z. P. Baˇzant, M. Voˇrechovsk´y, and D. Nov´ak, “Asymptotic prediction
of energetic-statistical size effect from deterministic finite element
solutions,” Journal of Engineering Mechanics (ASCE), vol. 133, no. 2,
pp. 153–162, 2007.
[5] Z. P. Baˇzant, S. D. Pang, M. Voˇrechovsk´y, and D. Nov´ak, “Energeticstatistical
size effect simulated by SFEM with stratified sampling and
crack band model,” International Journal for Numerical Methods in
Engineering (Wiley), vol. 71, no. 11, pp. 1297–1320, 2007.
[6] M. Voˇrechovsk´y, “Incorporation of statistical length scale into Weibull
strength theory for composites,” Composite Structures, vol. 92, no. 9,
pp. 2027–2034, 2010.
[7] M. Voˇrechovsk´y and R. Chudoba, “Stochastic modeling of multifilament
yarns: II. Random properties over the length and size effect,”
International Journal of Solids and Structures (Elsevier), vol. 43, no.
3-4, pp. 435–458, 2006.
[8] M. Voˇrechovsk´y, “Statistical alternatives of combined size effect on
nominal strength for structures failing at crack initiation,” in Probl´emy
lomov´e mechaniky IV (Problems of Fracture Mechanics IV), M. Stibor,
Ed. Academy of Sciences - Institute of physics of materials of
the ASCR: Brno University of Technology, 2004, pp. 99–106, invited
lecture.
[9] R. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related
Properties of Random Sequences and Processes, ser. Springer Series
in Statistics. Springer London, Limited, 2011. [Online]. Available:
http://books.google.cz/books?id=AGB9MQEACAAJ
[10] H. Koide, H. Akita, and M. Tomon, “Probability model of flexural
resistance on different lengths of concrete beams,” Applications of
Statistics and Probability, Melchers & Stewards (eds), pp. 1053–1057,
2000.
[11] H. Daniels, “The maximum of gaussian process whose mean path has
a maximum, with an application to the strength of bundles of fibres,”
Advances in Applied Probability, vol. 21, pp. 315–333, 1945.
[12] R. Smith, “The asymptotic distribution of the strength of the seriesparallel
system with equal load-sharing,” Annals of Probability, vol. 10,
no. 1, pp. 137–171, 1982.
[13] R. Chudoba, M. Voˇrechovsk´y, V. Eckers, and T. Gries, “Effect of twist,
fineness, loading rate and length on tensile behavior of multifilament
yarns (a multivariate study),” Textile Research Journal (Sage), vol. 77,
no. 11, pp. 880–891, 2007.</p>
@article{"International Journal of Architectural, Civil and Construction Sciences:65319", author = "Jana Kaděrová and Miroslav Vořechovský", title = "Experimental Testing of Statistical Size Effect in Civil Engineering Structures", abstract = "The presented paper copes with an experimental evaluation of a model based on modified Weibull size effect theory. Classical statistical Weibull theory was modified by introducing a new parameter (correlation length lp) representing the spatial autocorrelation of a random mechanical properties of material. This size effect modification was observed on two different materials used in civil engineering: unreinforced (plain) concrete and multi-filament yarns made of alkaliresistant (AR) glass which are used for textile-reinforced concrete. The behavior under flexural, resp. tensile loading was investigated by laboratory experiments. A high number of specimens of different sizes was tested to obtain statistically significant data which were subsequently corrected and statistically processed. Due to a distortion of the measured displacements caused by the unstiff experiment device, only the maximal load values were statistically evaluated. Results of the experiments showed a decreasing strength with an increasing sample length. Size effect curves were obtained and the correlation length was fitted according to measured data. Results did not exclude the existence of the proposed new parameter lp.
", keywords = "Statistical size effect, concrete, multi filaments yarns, experiment, autocorrelation length.", volume = "7", number = "10", pages = "730-8", }
