New approach of concrete tensile strength test

Journal Pre-proof New Approach of Concrete Tensile Strength Test Sa’ad Fahad Resan, Samir Mohammed Chassib, Sajid Kamil Zemam, Mr. Mustafa Jabar Madhi

PII:

S2214-5095(20)30019-X

DOI:

https://doi.org/10.1016/j.cscm.2020.e00347

Reference:

CSCM 347

To appear in:

Case Studies in Construction Materials

Received Date:

14 January 2020

Revised Date:

17 February 2020

Accepted Date:

19 February 2020

Please cite this article as: Resan SF, Chassib SM, Zemam SK, Madhi MMJ, New Approach of Concrete Tensile Strength Test, Case Studies in Construction Materials (2020), doi: https://doi.org/10.1016/j.cscm.2020.e00347

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New Approach of Concrete Tensile Strength Test Assist. Prof. Dr. Sa’ad Fahad Resan1, 2, Dr. Samir Mohammed Chassib1, Mr. Sajid Kamil Zemam1, and Mr. Mustafa Jabar Madhi1 1 Civil Engineering Department, Engineering College, University of Misan, Amarah, Iraq 2 Corresponding author; e-mail: [email protected]

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Abstract:. The study aims to develop a new approach of concrete tensile strength test characteristic by minimizing the traditional drawbacks such as load eccentricity, stress or strain non-uniformity and stress concentration in traditional test methods and of a distinguished gauge region which undergoes uniform tensile stress so the determination of the tensile stress-strain curve is simplified contrariwise of traditional methods. The elementary configuration of biaxial stress state is normalized into introduced model configuration under the effect of identical internal forces of specific alignment laid within specific compression and tension elements likewise a strut–tie model. Experimental program is considered to investigate the introduced model, flexural and Brazilian splitting tests are conducted to confirm its reliability. The obtained results are quite converged and show that the tensile strength determined by the proposed model is clearly higher than that of the Brazilian test with closer deviation and lower than that of the flexural test. Unique and sudden fracture is observed within assigned gauge length and led to separation of failed specimens without any deformation associated with loading mechanism.

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Notation The following symbols are considered: fcu cube concrete compressive strength, MPa Ec concrete modulus of elasticity, MPa fr concrete tensile strength or modulus of rupture determined using flexural test, MPa fs concrete tensile strength determined using splitting test, MPa ft concrete tensile strength determined using suggested model, MPa 𝜀 tensile strain measured within tensile gauge region a tensile gauge region height, mm b tensile gauge region width, mm At tensile gauge region area, mm2

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Keywords; concrete tensile strength, flexural test, Brazilian test, tensile test model, strut-tie model

1. Introduction

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The determination of concrete tensile strength and measuring of the tensile stress-strain curve using indirect tests are not a straight forward affair and become approximate hence there is a necessity for developing direct tensile strength evaluation of pure tensile stress state and encounters major drawbacks. The importance of concrete tensile strength is related to its rule in understanding concrete behaviour and pose challenges for concrete design because of the brittleness associated with influent parameters in failure criterion, in which the limiting tensile strain serves as a good reference of concrete strength under static loading and can be utilised as a failure indicator of concrete materials [1]. Concrete tensile strength could be determined using different test methods of various specimen models, such as direct pull [2-5], flexural, splitting, ring-tensile [6] and double-punch tests [7]. It is difficult to apply direct tension load to concrete specimens, the traditional tensile testing methods test suffer several major drawbacks associated with the identified challenges of loading mechanism, such as load eccentricity, stress or strain non-uniformity and stress concentration at the specimen ends, causing specimens’ end fracture. Considering these shortcomings of direct tension tests, tensile strength capacity is conveniently evaluated from the tensile fibres in a prism’s section of constant-moment using the flexural test [1]. The significant core related to direct tensile testing approaches were concerned with measuring concrete tensile strength by developed models provided by different means like embedded steel bars, lateral gripping, gluing, wings or truncated cones [1]. All these techniques create non pure tensile stresses and result in an uneven stress application to specimens [10]. Many experimental studies have attempted to overcome the drawbacks in concrete tensile strength determination [8-14]. Recently, several models were introduced to investigate concrete’s direct tensile strength. Mohammad Iqbal Khan proposed the direct tensile strength test shown in Figure 1.a and compared its results with compressive and flexural strengths. The obtained results were comparable, and the relationships were similar to those proposed in previous studies [15]. Vahab Sarfarazi et al. developed a compression-to-tensile load transformer device as a modern approach to determine the direct tensile strength of concrete, as shown in Figure 1.b. A Brazilian test was performed to compare the results of the two methods. The test results

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

2. Introduced Model

58 59 60 61 62 63 64

2.1 Geometrical description

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The elementary configuration of biaxial stress state (illustrated in Figure .2) is normalized into introduced model configuration under the effect of identical internal forces of specific alignment laid within specific compression and tension elements likewise a strut–tie model. The developed stress trajectories within concrete element under compressive force ( shown in Figure .3) likewise splitting test unit (300x150 mm concrete specimen of cylindrical section) could be conjunction by alignment compressive and tensile forces within specific elements which are assigned as struts under compressive force and tie under uniform tension force to be consider as gauge length. The proposed model is derived from a splitting test model by removing limited parts and modifying the other parts, thereby allowing alignment with flow stress paths and creating a strut–tie model [17]. Struts are utilised as compression arms that transfer the applied load through relatively rigid nodal zones to a concrete tie, which is designed as a gauge region undergoing tension force. The similarity with that of strut-and-tie model is the presenting of actual truss model of compression and tension elements of specific force direction but not in stress complexity solving.

66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93

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were encouraging and showed that the direct tensile strength was clearly lower than that in the Brazilian test. The difference between the Brazilian and direct tensile strengths was approximately 33% [16]. The present study introduces a new and innovative testing approach of concrete tensile strength characteristics by controlled loading alignment and specific gauge length undergoing pure tensile stress so as to overcome conventional drawbacks associated with indirect tension tests.

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The suggested model is briefly described in Figure 4. In general, its characteristics are as follows. 1- The concrete tie part is utilised as a limited tensile gauge region to induce a pure tensile stress state (a x b). 2- Load is applied using a relatively rigid cylindrical fitting through a frictionless concrete contact surface by a smooth loading steel plate. The dimensions of loading cylindrical fitting (thickness 10 mm, Dia. 100mm) are selected so as to avoid any undesired deformation and so to eliminate any energy dissipation affect the accuracy of applied loading. 3- Loading, geometry and boundaries are symmetrical with respect to the x and y axes to eliminate any possible variation. 4- Tensile stress is developed within gauge length using a traditional loading machine in compression mode. 5- The nodal zone forces action under compression-tension-compression (C-T-C). Thus, steel reinforcement is provided for rigidity enhancement. 6- The region with applied load is likewise hinged to release model parts from one another except in the considered tensile gauge region and to avoid any energy dissipation. 7- No lateral boundary conditions exist.

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2.2 Force analysis

In accordance with the concept of static equilibrium, the free body diagram of loading fitting and the frictionless contact surface between loading fitting and concrete surface, the force component along the specimen wings is as follows:

𝑃

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𝑅 = 2 sin 𝜃

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Referring to free body diagram of loading fitting (Figure.4.a.i) and from equilibrium along y axis, ∑ 𝐹𝑦 = 0 , so; 𝑃 = 2 𝑅 sin 𝜃

…………..…..(1)

However, from the free body diagram of the considered model (Figure.4.a.ii) and under the effect of applied load (R) and from equilibrium in along x-axis, ∑ 𝐹𝑥 = 0; 𝑄 = 2𝑅 cos 𝜃

.….……………..(2)

Substituting Eq.1 into Eq.2 and remember that sin 𝜃 = cos 𝜃 for θ=45, we obtain the following; 𝑃

𝑄=2 cos 𝜃 …………………(3) 2 cos 𝜃 So, 𝑄 = 𝑃 Therefore, concrete tensile strength within the created pure tensile stress state could be determined as follows: 𝑃

𝑓𝑡 = 𝐴

𝑡

..….…………..(4)

2

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

which indicates that the tensile force within the gauge region is identical to the applied compression force. This force distribution is the same as that between pure shear and biaxial stress states relations as equivalent loading cases, Figure.2. 2.3 Standard test methods

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The following standard test methods are performed to compare the results of the suggested model with those of the following standard test methods: 1. Flexural test, which is coded as ASTM C348 – 18 and termed as Standard Test Method for Flexural Strength of Concrete Prism [18]; 2. Splitting test, which is coded as ASTM C 496 – 96 and termed as Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens [19]. Flexural test is conducted to estimate concrete modulus of rupture while splitting test is conducted to estimate the concrete tensile strength, the two test approaches are indirect tensile test and considered in this study for comparative analysis. Figure 3 illustrates the approaches’ descriptions, typical stress distribution along expected failure surface and the stress state of standard test methods beside the introduced model. The major difference among the various models presented in Figure 3 is the tensile stress states created within the failure surface. A simple stress distribution analysis for the considered model indicates that the stress state within the limited gauge region is pure tensile stress (Figure 5.a) without developing any compression stresses in nearby regions as occur in the other two models (Figures 5.b and 5.c) because of the free side boundaries of the considered model’s gauge region.

3. Experimental Program

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The experimental program aimed to investigate the proposed model’s reliability in predicting concrete tension strength. Twelve specimens were manufactured and tested. Maximum aggregate size and testing age were the variables to be investigated. 3.1 Construction materials

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Portland cement (Type I) was used; its physical and chemical characteristics conformed to ASTM C150-04 [20]. The natural fine aggregates used conformed to ASTM C33-03 [21], and the grading of the used washed crushed coarse gravel was within Iraqi specification requirements no. 45/1984 [22].

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3.2. Batch proportions

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Two series of samples were manufactured using two concrete batches and casted under different conditions to obtain the spectrum of compressive strength. Table 1 lists the material proportions of the used batches. Concrete cubes (B.S. 1881: Part 116) [23] were used to determine the compressive strength, whose results are listed in Table 2. The cubes were cured under the same moisture conditions as in the specimen curing.

113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

Wooden moulds were fabricated using 12 mm-thick plywood and stuffed with capsulated autoclaved aerated blocks to form the target model configuration shown in Figure 6. The fabricated specimens are shown in Figure 7. Steel reinforcement (2 ϕ 8 mm) was added along the struts and across the nodal zones for rigidity enhancement within the nodal zones to exclude any undesired failure mode especially that of expected shear mode in the nodal region of complex stresses.

149 150 151 152 153 154

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3.3. Samples details and fabrication

3.4. Apparatus and test arrangement

4. Results and Discussion

155 156 157 158 159

4.1 Comparative analysis

160

The relationships among the compressive, tensile and flexural strengths of concrete of various batches are evaluated and listed in Table 2. Comparative analysis is conducted between flexural and Brazilian splitting test results to confirm the

161 162

A seven Ton load capacity testing machine was used for testing. Static load was applied in controlled force mode. A portable data logger was used to assign tensile strains using 30 mm-long electrical strain gauges within the gauge area across the expected fracture line. Figures 8 and 9 show the test settings of the different approaches.

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considered approach’s reliability. The obtained results are quite converged and show that the tensile strength determined using the proposed model is higher than that of the Brazilian test (ft/fs always greater than 1) and lower than that of the flexural test (ft/fr always less than 1). The deviation from the Brazilian results is less than that obtained from the flexural test.

163 164 165 166

4.2 Compressive strength effect

167

The test results show that the specimens with high compressive strength have a low tensile–compressive strength ratio. The average determined tensile strengths are approximately 8% and 6.8% of the cubes’ compressive strength at 7 and 28 days, respectively. When the compressive strength is low, the corresponding values tend to be 11% and 8%, respectively. Figure 10 illustrates the variation of the determined tensile strengths versus the compressive strengths for the various considered test methods. The observed results stay within results domain of flexural test and splitting test and have a closer evaluation to those determined by splitting model where a small deviation is assigned in respect to the Brazilian test results. While the measured modulus of rupture assigned by flexural test indicated higher values than those determined by other models and this observation could be associated with known linear variation of tensile stress distribution along failure surface.

168 169 170 171 172 173 174 175 176 177

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4.3 Maximum aggregate size effect

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Concrete cracking strength can be defined as the tensile strength of concrete subjected to pure tension stress [11] and due to the significant effect of particle size upon cracking forming, the particle size for the gravel is considered as variable to verify model reliability. Figure 11 clearly shows the effect of maximum aggregate size within the adopted concrete mixtures. The determined ratios of determined tensile strength using the proposed model compared with customary methods (flexural and splitting models) showed more divergent variation when the maximum aggregate size reduced to 9.6, the same variation is observed for both considered testing age (after 7 and after 28 days). The concrete mixture with the maximum aggregate size of 20 mm, which has well-graded aggregates and a uniform mixture and exhibits a small ratio variation. Generally, specimens of mixture (A) exhibited a relatively low tensile strength in spite of its compressive strength, which is higher than that of the specimens of mixture (B). A small maximum aggregate size translates to low resistance versus cracking, and vice versa.

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4.4 Test age effect

178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194

Beside the efficient of considered model to minimize of drawbacks associated with mention test methods, it has a distinguished region denoted as gauge region which undergoes uniform tensile stress so the determination of the tensile stress-strain curve is simplified contrariwise of traditional methods. The determined stress–strain responses are significantly affected by the considered approach, and thus, the applied stress state. Figures 12, 13 and 14 clearly illustrate the tensile stress–strain response for the different considered test methods. The tensile stress strain determined using the proposed approach demonstrates a shorter plastic portion than that of the flexural model and longer than that of the splitting model. The same opposite influence of compressive strength on tensile strength is confirmed upon tensile strain capacity. The determined tensile strain is approximately 30 μm/m for specimens with high compressive strength (mix type A) against about 55 μm/m for those with low compressive strength (mix type B). The measured tensile strain obtained by the flexure approach has a larger deviation, given that the concrete exhibits more ductile behaviour than other models, which have approximately equal strain capacities at identical stress levels. So, the measured modulus of rupture assigned by flexural test indicated higher values than tensile strengths determined by other models. This finding is confirmed by stress- strain behaviour (Figure.14) which exhibited sustainable trend more than those of other models while the stress- strain measured by suggested model succeeded to clarify concrete brittleness in comparing with other model as shown in Figure 12. Moreover, the tensile strains measured using the Brazilian test is significantly close to those determined by the proposed approach. 4.6 Failure mode

195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213

The specimens of the different test methods, which are of varied stress states, show different fracture mechanisms. The specimens of the considered approach exhibit rapid fracture as those of flexural test where sudden splitting aligned within gauge area without any developing initial cracks, it is extremely different from Brazilian test which characteristics by

214 215 216

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Figure 11 demonstrates the convergent ratios of the proposed approach in scope of testing ages with respect to the splitting and flexural models, where the indicated ratios tend to be closer as the concrete tends to have better compressive strength at 28 days than at 7 days. The convergence is logically and associates with bonding improvement of aggregate- mortar strength by time. 4.5 Tensile stress–strain response

4

developing initial cracks. The fashion of failure is definitely associated with the fraction crack across the specimen’s centre line. Figure 15 assigns a unique failure mode for the tested specimens, and Figure 16 denotes the failure surface textures of specimens with different maximum aggregate sizes for the three considered test approaches. The same failure plane textures are observed in the considered models. Deboning of coarse aggregate and mortar rupturing are denoted in the proposed model likewise in Brazilian or flexural test. Conclusions

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Observations of the experimental data and their comparative analysis confirmed the reliability of the introduced approach to measure concrete tensile strength. The obtained results are quite converged and show that the tensile strength determined using the proposed model is clearly higher than that determined using the Brazilian test (ft/fs always greater than 1, with closer deviation) and lower than that determined using the flexural test (ft/fr always less than 1). The test results show that specimens with high compressive strength have a low tensile–compressive strength ratio, the average tensile strengths are approximately 8% and 6.8% of the cubes’ compressive strengths at 7 and 28 days, respectively; while for specimens of low compressive strength, the corresponding values tend to be 11% and 8%, respectively. The same finding, but of opposite influence is assigned upon tensile strain capacity. It is approximately 30 μm/m for specimens with relatively high compressive strength against about 55 μm/m for those with low compressive strength. The determined stress-strain responses are significantly affected by the considered approach, and thus, the applied stress state. The tensile- strain response measured by the flexure approach has a large deviation, given that concrete exhibits more ductile behaviour than in other models with approximately equal strain capacity at identical stress levels. The stress- strain response measured by suggested model succeeded to clarify concrete brittleness in comparing with other models, the specimens exhibit rapid fracture where sudden splitting aligned within the gauge area.

Conflict of Interest

217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240

paper.

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The authors declare that there is no conflict of interests regarding the publication of this

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1. T. H. Wee, H. R. Lu and S. Swaddiwudhipong, "Tensile strain capacity of concrete under various states of stress,” Magazine of Concrete Research, vol. 52, no. 3, pp. 185–193, June, 2000. 2. ASTM D2936-08, “Standard Test Method for Direct Tensile Strength of Intact Rock Core Specimens,” Annual Book of ASTM Standards, vol. 4, ASTM, West Conshohocken, PA, 2008. 3. A. Ghaffar, M. A. Chaudhry and M. Kamran Ali, “A new approach for measurement of tensile strength of concrete,” J. Res. Sci. Bahauddin Zakariya University, Multan, Pakistan, vol. 16, no. , pp.1-9, 2005. 4. N. X. Xie and W. Y. Liu, “Determining tensile properties of mass concrete by direct tensile test,” ACI Materials Journal, vol. 86, no.3, pp. 214–219, 1989. 5. W. Zheng, A. K. H. Kwan and P. K. K. Lee, “Direct tension test of concrete,” ACI Materials Journal, vol. 98, no.1, pp. 63-71, 2001. 6. D. J. Hannant, “The tensile strength of concrete: a review paper,” Structure Engineering, vol. 50, no. 7, pp. 253-257, 1972. 7. W. F. Chen and B. E. Trumbauer, “Double-punch test and tensile strength of concrete,” J. Mater., ASTM , vol. 7 , no. 2, 148-154, 1972. 8. P. C. Aitcin and A. Neville, “High performance concrete demystified,” Concrete Int., vol. 15, pp. 21-26, 1993. 9. J. T. Gomez, A. Shukla and A. Sharma, “Static and dynamic behavior of concrete and granite in tension with damage,” Theor. Appl. Fract. Mech. Vol. 36, pp.37–49, 2001. 10. M. I. Khan, “Direct tensile strength measurement of concrete,” Applied Mechanics and Materials, vol. 117-119, pp. 9-14, 2012, https://doi.org/10.4028/www. scientific. net/AMM.117-119.9. 11. J. Kim and M. R., Taha, “Experimental and numerical evaluation of direct tension test for cylindrical concrete specimens,” Advances in Civil. Engineering, pp. 1–8, 2014, http://dx.doi.org/10.1155/2014/156926. 12. S. Li, H. Wang, Y. Li, Q. Li, B. Zhang and H. Zhu, “A new mini-grating absolute displacement measuring system for static and dynamic geomechanical model tests,” Measurement, vol. 82, pp. 421-431, 2016. 13. J. G. M. Mier and M. R. A. Vliet, “Uniaxial tension test for the determination of fracture parameters of concrete, Engineering Fracture Mechanics, vol. 69, pp. 235–247, 2002. 14. S. Swaddiwudhipong, H. R. Lu and T. H. Wee, “Direct tension test,” Cem. Concr. Res., vol. 33, pp. 2077-2084, 2003. 15. I. K. Mohammad,“Direct tensile strength measurement of concrete, Applied Mechanics and Materials, ISSN: 1662-7482, vols. 117–119, pp 9–14, 2011. doi:10.4028/www.scientific.net/AMM.117-119.9 16. V. Sarfarazi, A. Ghazvinian, W. Schubert, H. R. Nejati, Raouf, Hadei, “A new approach for measurement of tensile strength of concrete,” Periodica Polytechnica Civil Engineering, vol. 60, no. 2, pp. 199–203, 2016. 17. ACI Committee 318, “Building code requirements for structural concrete and commentary,” ACI 318–14/ACI 318R–14, American Concrete Institute, Detroit, Michigan, 2015. 18. ASTM C348-18, Standard Test Method for Flexural Strength of concrete prism, American Standard Test Method, West Conshohocken, Penn, USA, 2018. 19. ASTM C 496-96, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, American Standard Test Method, West Conshohocken, Penn, USA, 1996. 20. ASTM C150-04, Standard Specification for Portland Cement, vol. 4.1, pp. 1−8, American Standard Test Method, West Conshohocken, Penn, USA, 2004. 21. ASTM C33-03, Standard Specification for Concrete Aggregates, vol. 4.2, pp. 1−11, American Standard Test Method, West Conshohocken, Penn, USA, 2003. 22. Iraqi Standard No. 45/1984, “Aggregate from Natural Sources for Concrete and Construction,” Ministry of Housing and Construction, Baghdad, 2004. 23. B.S. 1881: Part 116: 1983, “Methods for Determination of Compressive Strength of Concrete Cubes”, pp. 1−8, January 1983. 24. American Concrete Associate, “Guide for Consolidation of Concrete Reported by ACI Committee 309”, 2005.

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References

6

291 292 293 294 295

b. Sarfarazi’s proposed model[16]

a.Khan’s proposed model[15]

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Figure 1. Proposed tensile strength determination models

296 297

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Figure 2. Equivalence insight between considered model and biaxial stress state

Compressive stress Tensile stress

298 299 300 301 302 303

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Figure 3. Typical stress trajectories within concrete element of compression field

Relatively rigid fitting

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Frictionless contact surface Hinge

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Tensile gauge region Free boundaries

a.

304 305 306 307 308

Geometrical description

7

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Strut–tie simulation and elementary detail

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b.

309 310 311 312

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313 314 315 316 317

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c. Free body force diagrams Figure 4. Introduced model of concrete tensile strength prediction

318 319 320

a. Introduced model

8

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b. Splitting model

321 322 323 324

325 326 327 328 329 330 331

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a. Flexural test model

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Figure 5. Different model configurations and typical stress distributions

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Figure 6. Wooden mould and poured sample setting

332 333

Figure 7. Fabricated specimens

9

334 335 336

Splitting test

337 338 339 340

b. Flexural test

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a.

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Figure 8. Test setup of proposed approach

Figure 9. Test setup of customary method 5.00

5.00

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4.00

3.00

2.00

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ft, Mpa

1.00

0.00

Tensile strength, Mpa

fs, Mpa

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Tensile strength, Mpa

fr, Mpa

4.00

fr, Mpa fs, Mpa ft, Mpa

3.00

2.00

1.00

0.00

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24.00 26.00 28.00 30.00 34.00 38.00 Compressive strength (fcu), Compressive strength (fcu), MPa MPa (i. 7 days) (ii. 28 days) a. Concrete mixing batch (A)

341 342 343

10

5.00

5.00

fr, Mpa

fs, Mpa

4.00

ft, Mpa 3.00

2.00

1.00

4.00

fs, Mpa ft, Mpa

3.00

2.00

1.00

0.00 17.00

18.00

25.00

Compressive strength (fcu), MPa

26.00

27.00

Compressive strength (fcu), MPa

(i. 7 days)

344 345 346 347 348

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0.00 16.00

Tensile strength, Mpa

Tensile Strength, Mpa

fr, Mpa

(ii. 28 days)

1.60

1.40

1.40

-p

1.60

Ratio variation

1.20 1.00 0.80

ft/fr

0.60

ft/fs

0.20 0.00

1.00 0.80

ft/fr

0.60

ft/fs

0.40

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0.40

1.20

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Ratio variation

b. Concrete mixing batch (B) Figure 10. Variation of determined tensile strengths versus compressive strengths for various tensile test methods

0.20 0.00 7 28 Time (days)

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7 28 Time (days)

349 350 351

(A ) ( B) Figure 11. Variation of determined tensile strength with respect to customary methods for different concrete mixes

1.5

1

Tensil stress, Mpa

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Tensil stress, Mpa

2

0.5

3

3

2.5

2.5

Tensil stress, MPa

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2.5

2 1.5 1 0.5

0 0.02

0.04

Tensile strain x 10-3

1 0.5

A6

0 0

1.5

A5

A4 -0.02

2

0.06

-0.02

0 0

0.02

0.04

Tensile strain x 10-3

0.06

-0.02

0

0.02

0.04

0.06

Tensile strain x 10-3

352 11

2.5

2

2

2

1.5

1

Tensil stress, MPa

2.5

Tensil stress, MPa

Tensil stress, MPa

2.5

1.5

1

0.5

0.5

B5

0

B6

0 0

0.02

0.04

1

0.5

B4 -0.02

1.5

0.06

-0.02

0 0

Tensile strain x 10-3

0.02

0.04

0.06

-0.02

Tensile strain x 10-3

0

0.02

0.04

0.06

Tensile strain x 10-3

353 354

Figure 12. Tensile strain determined using proposed approach 2.5

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4.5 4

2

1

3 2.5 2 1.5

Group A

0.5

Group B

1 0.5

0

0 0

0.02

0.04

0.06

-0.06

0

Group A

0.06 0.12 0.18 0.24 0.3 0.36 0.42 0.48 0.54 0.6 0.66 0.72

Tensile strain x 10-3

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Tensile strain x 10-3

355 356

Figure 14. Flexural test

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Figure 13. Splitting test

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1.5

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Tensil stress, MPa

Tensil stress, MPa

3.5

357 358

Figure 15. Unique failure mode

12

359 360 361 362

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(A) (B) Figure 16. Fracture surface textures

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No.

Mix type

Cement, kg/m3

Sand, kg/m3

Gravel, kg/m3

1

A

444.75

667

1334

2

B

444.75

667

1334

Table 1 Batch Material Proportions Gravel Water, W/C, max. Cement:Sand:Gravel kg/m3 % size 9.6 186.8 42 1:1.5:3 20

186.8

42

1:1.5:3

363

90

Mixture workability [24] Plastic

95

Plastic

Slump, mm

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364

14

365 fr, Mpa

fs, Mpa

ft, Mpa

ft/fr

ft/fs

25.42 26.34 27.59 26.45 32.00 36.70 38.10 35.60 16.71 16.97 17.23 16.97 25.70 26.10 26.50 26.10

2.50 2.59 2.69 2.59 4.08 4.27 4.47 4.27 2.38 2.57 2.78 2.58 3.37 3.41 3.97 3.58

1.33 1.50 1.50 1.44 2.00 2.00 2.40 2.13 1.51 1.67 1.82 1.67 1.82 1.92 2.01 1.92

1.75 2.11 2.46 2.11 2.27 2.39 2.56 2.41 1.67 1.90 2.14 1.90 1.92 2.08 2.23 2.08

0.70 0.81 0.92 0.81 0.56 0.56 0.57 0.56 0.70 0.74 0.77 0.74 0.57 0.61 0.56 0.58

1.31 1.40 1.64 1.46 1.14 1.20 1.07 1.13 1.11 1.14 1.18 1.14 1.06 1.08 1.11 1.08

ro of

fcu, MPa

366

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na

lP

re

-p

Table 2 Result Comparison Batch Test age, Specimen type days code A1 A2 7 A3 Average A A4 A5 28 A6 Average B1 B2 7 B3 Average B B4 B5 28 B6 Average

15