Please wait a minute...
Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

Postal Subscription Code 80-968

2018 Impact Factor: 1.272

Front. Struct. Civ. Eng.    2022, Vol. 16 Issue (8) : 1017-1028    https://doi.org/10.1007/s11709-022-0871-8
RESEARCH ARTICLE
Effect of size on biaxial flexural strength for cement-based materials by using a triangular plate method
Hakan T TURKER()
Department of Civil Engineering, Bursa Uludag University, Bursa 16059, Turkey
 Download: PDF(3172 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The effect of size on the biaxial flexural strength (BFS) of Portland cement mortar was investigated by using the recently proposed triangular plate method (TPM). An experimental program was conceived to study the size effect by keeping a constant water-cement ratio of 0.485, cement-sand ratio of 1:2.75, and using unreinforced triangular mortar plates of five different thicknesses and seven different side lengths. The BFS of the produced specimens was tested, and variations of BFS depending on specimen thickness and side length were determined. The results indicated that increases in triangular plate specimen side length and specimen thickness led to a decrease in the BFS of Portland cement mortar. The effect of specimen length increase on BFS was more significant than on the effect of the specimen thickness. The variations in specimens’ thickness indicated a deterministic Type I size effect, while the variations in specimens’ length showed an energetic-statistical Type I size effect.

Keywords testing      apparatus & methods      plain concrete      tensile properties      biaxial flexural strength      triangular plate method     
Corresponding Author(s): Hakan T TURKER   
Just Accepted Date: 09 September 2022   Online First Date: 02 November 2022    Issue Date: 02 December 2022
 Cite this article:   
Hakan T TURKER. Effect of size on biaxial flexural strength for cement-based materials by using a triangular plate method[J]. Front. Struct. Civ. Eng., 2022, 16(8): 1017-1028.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0871-8
https://academic.hep.com.cn/fsce/EN/Y2022/V16/I8/1017
Fig.1  Geometry of the triangular plate specimen and loading base plate.
Fig.2  (a) Schematic demonstrations of testing configuration and (b) testing of a triangular plate.
Fig.3  Accepted failure mechanisms for ultimate load capacity.
Fig.4  Maximum stress fields in a triangular plate.
Fig.5  Maximum stresses along the yield line.
Fig.6  Normalized maximum stresses along the yield line.
Fig.7  Cracking pattern on tension surface at ultimate load.
first groupsecond group
thickness (cm)side length (cm)thickness (cm)side length (cm)
240420
440430
640440
840450
1040460
470
480
Tab.1  Dimensions of equilateral triangular specimens used for size effect
Fig.8  Failure pattern of a typical prism specimen under three-point bending test.
Fig.9  Failure patterns of samples of the equilateral triangular specimens. (a) Symmetric triple cracks; (b) symmetric triple cracks; (c) straight crack; (d) typical fracture pattern of a group of the tests.
no.triangular plate method triangular specimen (b = 30 cm; t = 4 cm)tree point flexural test prism (4 cm × 4 cm × 16 cm)
P (kN)biaxial flexural strength σ (MPa)P (kN)flexural strength (MPa)
18.466.113.217.52
28.005.773.347.83
38.416.073.277.66
47.275.253.438.04
58.776.333.648.53
68.536.163.578.37
79.236.663.718.70
88.155.883.247.59
98.916.433.257.62
108.556.173.337.80
118.235.943.197.48
128.386.053.417.99
138.576.183.397.95
147.985.763.267.64
159.016.503.518.23
168.636.233.488.16
178.716.293.197.48
188.255.953.357.85
mean8.456.103.387.91
st. deviation0.440.320.160.36
variance0.190.100.020.13
Tab.2  Experimental test results for validation of TPM (given in Turker [13])
equilateral triangular plate specimenP (kN)biaxial flexural strength, σ (MPa)mean σ (MPa)standard deviationvariance
no.thickness, t (cm)side length (cm)
12402.246.476.790.620.38
22402.617.54
32402.136.14
42402.437.02
54408.406.065.880.160.02
64408.075.82
74408.225.93
84407.895.69
964017.645.665.540.190.04
1064016.765.38
1164016.545.3
1264017.405.58
1364017.965.76
1484030.445.495.310.160.03
1584028.795.19
1684029.165.24
17104046.395.365.250.370.13
18104047.695.51
19104040.784.71
20104046.945.42
Tab.3  Test results of first group
equilateral triangular plate specimenP (kN)biaxial flexural strength, σ (MPa)mean σ (MPa)standard deviationvariance
no.thickness, t (mm)side length (cm)
142012.629.19.250.210.04
242013.029.39
343010.287.597.830.330.11
443011.188.06
54409.486.847.150.270.07
644010.097.28
744010.147.32
84508.716.296.480.180.03
94509.046.52
104509.26.64
114707.625.495.760.370.14
124708.356.02
134807.015.065.370.340.11
144807.385.32
154807.945.73
Tab.4  Test results of second group
Fig.10  Mean nominal biaxial flexural strength. (a) Variation due to the specimen thickness; (b) percent reduction.
Fig.11  Predictive size effect curves and experimental results of biaxial flexural strength variation due to the specimen thickness.
Fig.12  Mean nominal biaxial flexural strength. (a) Variation due to the side length; (b) percent reduction.
Fig.13  Predictive size effect curves and experimental results of biaxial flexural strength variation due to the side length.
1 E Denneman, E P Kearsley, A T Visser. Splitting tensile test for fibre reinforced concrete. Materials and Structures, 2011, 44(8): 1441–1449
https://doi.org/10.1617/s11527-011-9709-x
2 A Mallat, A Alliche. A modified tensile test to study the behaviour of cementitious materials. Strain, 2011, 47(6): 499–504
https://doi.org/10.1111/j.1475-1305.2009.00717.x
3 D Li, L N Y Wong. The Brazilian disc test for rock mechanics applications: Review and new insights. Rock Mechanics and Rock Engineering, 2013, 46(2): 269–287
https://doi.org/10.1007/s00603-012-0257-7
4 R Felicetti, F Lo Monte, P Pimienta. A new test method to study the influence of pore pressure on fracture behaviour of concrete during heating. Cement and Concrete Research, 2017, 94: 13–23
https://doi.org/10.1016/j.cemconres.2017.01.002
5 E S Katsaragakis. A new tensile test for concrete. Materials and Structures, 1987, 20(6): 463–466
https://doi.org/10.1007/BF02472499
6 G Zi, H Oh, S K Park. A novel indirect tensile test method to measure the biaxial tensile strength of concretes and other quasibrittle materials. Cement and Concrete Research, 2008, 38(6): 751–756
https://doi.org/10.1016/j.cemconres.2008.02.002
7 O Ekincioglu. A discussion of paper “A novel indirect tensile test method to measure the biaxial tensile strength of concretes and other quasibrittle materials” by G. Zi, H. Oh, S.K. Cement and Concrete Research, 2010, 40(12): 1769–1770
https://doi.org/10.1016/j.cemconres.2010.08.008
8 S Wu, X Chen, J Zhou. Tensile strength of concrete under static and intermediate strain rates: Correlated results from different testing methods. Nuclear Engineering and Design, 2012, 250: 173–183
https://doi.org/10.1016/j.nucengdes.2012.05.004
9 P J F Wright, F Garwood. The effect of the method of test on the flexural strength of concrete. Magazine of Concrete Research, 1952, 4(11): 67–76
https://doi.org/10.1680/macr.1952.4.11.67
10 G Zi, J Kim, Z P Bažant. Size effect on biaxial flexural strength of concrete. ACI Materials Journal, 2014, 111(3): 319–326
https://doi.org/10.14359/51686576
11 J Kim, D J Kim, G Zi. Improvement of the biaxial flexure test method for concrete. Cement and Concrete Composites, 2013, 37: 154–160
https://doi.org/10.1016/j.cemconcomp.2012.11.001
12 H Kupfer, H K Hilsdorf, H Rusch. Behavior of concrete under biaxial stresses. Journal of the American Concrete Institute, 1969, 66(8): 656–666
13 H T Turker. A new test method for biaxial tensile strength of cement based materials: Triangular plate method. Journal of the Faculty of Engineering and Architecture of Gazi University, 2015, 30
https://doi.org/10.17341/gummfd.02170
14 Z P Bažant. Size effect on structural strength: A review. Archive of Applied Mechanics, 1999, 69(9−10): 703–725
https://doi.org/10.1007/s004190050252
15 C Rocco, G V Guinea, J Planas, M Elices. Size effect and boundary conditions in the Brazilian test: Experimental verification. Materials and Structures, 1999, 32(3): 210–217
https://doi.org/10.1007/BF02481517
16 T K Erdem. Specimen size effect on the residual properties of engineered cementitious composites subjected to high temperatures. Cement and Concrete Composites, 2014, 45: 1–8
https://doi.org/10.1016/j.cemconcomp.2013.09.019
17 D L Nguyen, G S Ryu, K T Koh, D J Kim. Size and geometry dependent tensile behavior of ultra-high-performance fiber-reinforced concrete. Composites. Part B, Engineering, 2014, 58: 279–292
https://doi.org/10.1016/j.compositesb.2013.10.072
18 A M Neville. Some aspects of the strength of concrete. Civil Engineering and Public Works Review, 1959, 54: 1153–1156
19 F David, K Dusan. Size effect in concrete. Journal of Engineering Mechanics, 1988, 114(4): 704–715
https://doi.org/10.1061/(ASCE)0733-9399(1988)114:4(704
20 A A Griffith. The phenomena of rupture and flow in solids. Philosophical transactions of the royal society of London. Series A, containing papers of a mathematical or physical character, 1921, 221(582–593): 163–198
21 R Ince, M Gör, M E Eren, K E Alyamaç. The effect of size on the splitting strength of cubic concrete members. Strain, 2015, 51(2): 135–146
https://doi.org/10.1111/str.12127
22 Z P Bažant. Size effect in blunt fracture: Concrete, rock, metal. Journal of Engineering Mechanics, 1984, 110(4): 518–535
https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518
23 C Carloni, G Cusatis, M Salviato, J L Le, C G Hoover, Z P Bažant. Critical comparison of the boundary effect model with cohesive crack model and size effect law. Engineering Fracture Mechanics, 2019, 215: 193–210
https://doi.org/10.1016/j.engfracmech.2019.04.036
24 Z P BažantP A Pfeiffer. Determination of fracture energy from size effect and brittleness number. ACI Materials Journal, 1987, 84(6)
25 Z P BažantJ Planas. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Boca Raton, FL: CRC press, 1998
26 Z P BažantJ L Le. Probabilistic Mechanics of Quasibrittle Structures. Cambridge: Cambridge University Press, 2017
27 Z P Bažant, Q Yu. Universal size effect law and effect of crack depth on quasi-brittle structure strength. Journal of Engineering Mechanics, 2009, 135(2): 78–84
https://doi.org/10.1061/(ASCE)0733-9399(2009)135:2(78
28 J L Le, Z P Bažant, M Z Bazant. Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling. Journal of the Mechanics and Physics of Solids, 2011, 59(7): 1291–1321
https://doi.org/10.1016/j.jmps.2011.03.002
29 R Danzer, W Harrer, P Supancic, T Lube, Z Wang, A Börger. The ball on three balls test—Strength and failure analysis of different materials. Journal of the European Ceramic Society, 2007, 27(2−3): 1481–1485
https://doi.org/10.1016/j.jeurceramsoc.2006.05.034
30 P C Aitcin, B Miao, W D Cook, D Mitchell. Effects of size and curing on cylinder compressive strength of normal and high-strength concrete. ACI Materials Journal, 1994, 91(4): 349–355
https://doi.org/10.14359/4044
31 W Weibull. A statistical distribution function of wide applicability. Journal of Applied Mechanics, 1951, 18: 293–297
32 G D Quinn. Weibull strength scaling for standardized rectangular flexure specimens. Journal of the American Ceramic Society, 2003, 86(3): 508–510
https://doi.org/10.1111/j.1151-2916.2003.tb03329.x
33 Z P Bažant, S D Pang, M Vořechovský, D Novák, R Pukl. Statistical size effect in quasibrittle materials: Computation and extreme value theory. Fracture Mechanics of Concrete Structures, 2004, 1: 189–196
[1] Tarek Uddin MOHAMMED, Aziz Hasan MAHMOOD, Mohammad Zunaied-Bin-HARUN, Jamil Ahmed JOY, Md. Asif AHMED. Destructive and non-destructive evaluation of concrete for optimum sand to aggregate volume ratio[J]. Front. Struct. Civ. Eng., 2021, 15(6): 1400-1414.
[2] Yi YANG, Dalong JIN, Xinggao LI, Weilin SU, Xuyang WANG. Probabilistic analysis of secant piles with random geometric imperfections[J]. Front. Struct. Civ. Eng., 2021, 15(3): 682-695.
[3] Mohammad Reza AZADI KAKAVAND, Ertugrul TACIROGLU. An enhanced damage plasticity model for predicting the cyclic behavior of plain concrete under multiaxial loading conditions[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1531-1544.
[4] Sawan KUMAR, Ajitanshu VEDRTNAM, S. J. PAWAR. Effect of wood dust type on mechanical properties, wear behavior, biodegradability, and resistance to natural weathering of wood-plastic composites[J]. Front. Struct. Civ. Eng., 2019, 13(6): 1446-1462.
[5] Sunghwan KIM, Halil CEYLAN, Kasthurirangan GOPALAKRISHNAN. Finite element modeling of environmental effects on rigid pavement deformation[J]. Front. Struct. Civ. Eng., 2014, 8(2): 101-114.
[6] Qiangong CHENG,Jiujiang WU,Dongxue ZHANG,Fengping MA. Field testing of geosynthetic-reinforced and column-supported earth platforms constructed on soft soil[J]. Front. Struct. Civ. Eng., 2014, 8(2): 124-139.
[7] Kaoshan DAI, Zhenhua HUANG. Novel sensing techniques for full-scale testing of civil structures[J]. Front Struc Civil Eng, 2012, 6(3): 240-256.
[8] Cheng CHEN, James M. RICLES. A model reference adaptive control based method for actuator delay estimation in real-time testing[J]. Front. Struct. Civ. Eng., 2010, 4(3): 277-286.
[9] Hanlong LIU, Xuanming DING. Propagation characteristics of transient waves in low-strain integrity testing on cast-in-situ concrete thin-wall pipe piles[J]. Front Arch Civil Eng Chin, 2009, 3(2): 180-186.
[10] Weiming GONG, Guoliang DAI, Haowen ZHANG. Experimental study on pile-end post-grouting piles for super-large bridge pile foundations[J]. Front Arch Civil Eng Chin, 2009, 3(2): 228-233.
[11] ZHUANG Haiyang, CHEN Guoxing, ZHU Dinghua. Dynamic visco-plastic memorial nested yield surface model of soil[J]. Front. Struct. Civ. Eng., 2008, 2(1): 49-55.
[12] HU Kexu, HE Guisheng, LU Fan. Experimental study on fire protection methods of reinforced concrete beams strengthened with carbon fiber reinforced polymer[J]. Front. Struct. Civ. Eng., 2007, 1(4): 399-404.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed