Journal of Civil Engineering and Management ISSN 139-3730 / eissn 18-3605 018 Volume 4 Issue : 130 137 ttps://doi.org/10.3846/jcem.018.456 AIR-VOID-AFFECTED ZONE IN CONCRETE BEAM UNDER FOUR-POINT BENDING FRACTURE Cuancuan ZHANG 1, Xinua YANG 1, *, Hu GAO 1 1 Scool of Civil Engineering and Mecanics, Huazong University of Science and Tecnology, Wuan 430074, Cina Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, 1037 Luoyu Road, 430074 Wuan, Cina Received 16 November 017; accepted 15 February 018 Abstract. A series of numerical simulations were performed on prenotced four-point bending (FPB) concrete beams containing air voids of different sizes and locations by using te finite element metod combined wit te coesive crack model. Te void-affected zone was proposed for caracterizing te effect of a void on a fracture, and its size was determined by moving an air void orizontally until te crack pat canged. As a function of air void location and size, te dimensionless affected-zone radius was fitted according to te numerical results. Finally, te fracture processes of te prenotced FPB concrete beams wit randomly distributed voids were simulated numerically, and te affected-zone radius was used to explain te coice of crack pats to verify te prediction. It was found tat te prediction is accurate for an isolated affected zone and is rougly approximate for an overlapped one. Keywords: concrete, air void, fracture, affected-zone, coesive model, four-point bending. Introduction As a building material, concrete as been widely used in civil engineering, ydraulic engineering, and oter infrastructure construction. It is made of cement, water, sand, and coarse aggregates, and terefore, it usually contains natural defects suc as micro-cracks, weak interfaces, and air voids (Garbacz et al. 017; Qin et al. 016; Ren et al. 015; Xie et al. 015). Defects ave complicated effects. On te one and, tey can directly weaken material properties so tat te performance indicators of concrete suc as permeability, durability, and fracture resistance are usually lower tan teir design values. On te oter and, a crack trajectory is possibly deflected from rectilinearity owing to interactions between a crack and defects. Te crack pat deflection can be linked to an increase in material tougness by dissipating more fracture energy (Misseroni et al. 015). It is very useful for te design purposes of concrete structures to clarify effects of defects on crack propagation in concrete. In recent years, air voids in concrete material and construction ave attracted significant attention. Some nondestructive testing equipment, suc as scanning electron microscopes and X-ray computed tomograpy, combined wit te image analysis (IA) tecnique and ultrasonic scattering (US) tecnique, was used for air void detection. Using te IA tecnique, Nambiar and Ramamurty (007) analyzed te size distribution, sape parameter, and spacing factor of air voids in concrete, and Maoutian et al. (015) examined te effect of powdered activated carbon in fly as on te air void content and spacing factor of concrete. Wit te elp of te US tecnique, Guo et al. (016) measured te air void size distribution in ardened concrete, and Dong et al. (016) successfully quantified air voids in concrete-filled steel tubes. In addition, many studies were conducted on te effect of air voids on te performance of concrete by laboratory testing. Te experiments proved tat te volume fraction, size, and spacing of air voids all ave significant influence on te strengt and density of concrete (Nambiar, Ramamurty 007). Reder et al. (014) pointed out tat an increase in pore size leads to a reduction in te fracture resistance of pervious concrete. Hu et al. (016) found tat initial air voids ave a significant effect on te fatigue property of aspalt concrete. Nguyen et al. (017) quantitatively analyzed te influences of air void porosity, distri- *Corresponding autor. E-mail: yangxin@ust.edu.cn Copyrigt 018 Te Autor(s). Publised by VGTU Press Tis is an Open Access article distributed under te terms of te Creative Commons Attribution License (ttp://creativecommons.org/licenses/by/4.0/), wic permits unrestricted use, distribution, and reproduction in any medium, provided te original autor and source are credited.
Journal of Civil Engineering and Management, 018, 4(): 130 137 131 Figure 1. Prenotced FPB concrete beam bution, and microstructure on te compressive beavior of concrete. However, owing to difficulties in controlling air void size and position, it is nearly impossible to assess te impact of air voids on concrete properties systematically by experiments. Numerical simulation is a powerful investigation tool. Over te past several decades, computer performance as improved significantly, so tat it became reality to simulate fracture beaviors of eterogeneous concrete at te mesoscale level. Many numerical metods, suc as te digital image processing (DIP) metod (Barbosa et al. 011; Başyiğit et al. 01) and te parameterization modeling (PM) metod (Qin et al. 013; Xu, Cen 016; Yin et al. 015; Zang et al. 016), were developed for modeling eterogeneous concrete wit aggregates and mortar matrix. Recently, air voids were also contained in some numerical models created wit te DIP (Huang et al. 016) and PM (Ren, Sun 017; Wang et al. 015, 016) metods to assess te effects of te caracteristic parameters of air voids on te fracture properties of concrete. A coesive crack model wit a bilinear constitutive law, quadratic nominal stress cracking criterion, and linear damage evolution criterion was introduced to simulate te fracture processes (Yang et al. 009; Yin et al. 014). As is well known, a crack would rater initiate and propagate in a weak zone. Accordingly, wen a crack approaces an air void, it is probably attracted by te void, and canges its pat. How does an air void affect crack propagation in concrete? How does a crack coose its pat in concrete wit a lot of randomly distributed voids? To answer tese questions, te effects of air voids on fractures in concrete sould be quantitatively studied. In tis paper, a series of two-dimensional (D) numerical simulations will be performed on a prenotced four-point bending (FPB) concrete beam wit a single air void, and te effects of te void size and location on te fracture will be evaluated. Teir fracture-affecting zones will be determined, and dimensionless zone sizes will be given as functions of air void size and location. Finally, tis function will be used to explain te crack propagation in FPB multi-void concrete beams wit randomly distributed voids. 1. Numerical model As sown in Figure 1, a series of D concrete beam models wit a eigt of and a lengt of 5 are created. Tese models are subjected to a symmetrical FPB load. Tere is a distance of 4.5 between te two supports, and a distance of 1.5 between te two loading points. A crack wit a dept of 5 mm and a widt of 0. mm is located at te mid-span of te beam. In te center of te beam, a zone wit a widt of is considered. In tis zone, an air void is arranged to measure its effect on te fracture. As sown in Figure 1, a rectangular coordinate system wit te crack mout as te origin, te beam bottom as te orizontal axis, and te axle wire as te vertical axis, is created. An air void wit a diameter of d as its center at a point of (X, Y). To simplify te calculations, te concrete beam is treated as a omogeneous material (Hassani, Hinton 1998; Ren et al. 015). Bot te triangular and quadrilateral plane stress solid elements are employed for discretization of te computation model. In order to simulate crack initiation and propagation, coesive elements (Yin et al. 01) are inserted in te central zone of te beam. Figure exibits te finite element mes wit red coesive elements. Te mes is refined in te central zone. Te material parameters are as follows (Dong et al. 017). For te triangular Figure. Finite element mes wit red coesive elements
13 C. Zang et al. Air-void-affected zone in concrete beam under four-point bending fracture Table 1. Number of nodes, numbers of elements, and computing time for different mes densities Element size (mm) 1.00 0.75 0.50 Void size (mm) 1 3 5 1 3 5 1 3 5 Number of nodes 1196 1043 019 3347 3471 3387 6969 68046 67445 Number of triangular elements 5649 5496 535 9407 9093 9065 0931 0547 033 Number of quadrilateral elements 417 4140 4140 5190 5131 5131 6449 6449 6449 Number of coesive elements 8363 8076 7873 13967 13454 13438 31164 30655 3058 Computing time (min) 3 19 53 49 47 560 530 518 and quadrilateral plane stress solid elements, te density is 600 kg/m 3, Young s modulus is 8.0 GPa, and Poisson s ratio ν is 0.18. For te coesive elements, te elastic stiffness k is 10 6 MPa/mm (Wang et al. 015), te critical tensile strengt f t is.54 MPa, and te fracture energy G f is 138.6 N/m (Dong et al. 017). Te sear parameters are assumed to be te same as te corresponding normal ones. Wen te fracture process is simulated, a linearly increasing displacement is loaded at te two loading points until te displacement reaces 1 mm or te beam is completely torn apart.. Results and discussion.1. Mes dependence Te fracture pat generally depends on te mes density and tus a fine mes is necessary for accurate computation. However, too fine a mes will lead to a ig computational cost. Terefore, it is necessary to realize te balance between mes density and computational efficiency. For tis purpose, tree 50-mm-eigt concrete beam models are used to evaluate te mes dependence. Tey ave a void wit different diameters of 1 mm, 3 mm, and 5 mm at te points (1.9 mm, 0 mm), (4.9 mm, 0 mm), and (7.0 mm, 0 mm), respectively. Tree different element sizes of 1.00 mm, 0.75 mm, and 0.50 mm are considered in te central zones of te beams, but te element size of.00 mm is kept at te left and rigt sides. Te fracture processes are simulated by using te ABAQUS/Explicit solver and parallel computation system wit 8 Inter(R) Core (TM) i7-4790 CPUs @ 3.60 GHz. Te corresponding number of nodes, numbers of triangular and quadrilateral elements, number of coesive elements, and computing time are listed in Table 1. By comparison, it can be found tat as te element lengt canges from 1.00 mm to 0.75 mm and 0.50 mm, te number of nodes, te number of triangular elements, and te number of coesive elements all increase rapidly, and te computing time also increases very quickly. Figure 3. Load-displacement curves and dissipated fracture energy vs. displacement curves for different void and mes sizes: (a) load-displacement; (b) dissipated fracture energy
Journal of Civil Engineering and Management, 018, 4(): 130 137 133 Figure 4. Crack pats for different void and mes sizes: (a) element size of 1.00 mm; (b) element size of 0.75 mm; (c) element size of 0.50 mm Figure 3 sows te load-displacement curves and dissipated fracture energy vs. displacement curves for different void and mes sizes. Tere is a sligt difference between te load-displacement curves sown in Figure 3(a), and te same is observed between te dissipated fracture energy vs. displacement curves sown in Figure 3(b). Furter, te crack pats for different void and mes sizes are compared. For cleanness, te central zones of te beams are cut out for all of te crack pat pictures, as sown in Figure 4. Obviously, te crack goes troug te void bot in Figures 4(b) and 4(c), but it does not in Figure 4(a), and tere are very similar crack pats in Figures 4(b) and 4(c). Tis indicates tat 0.75 mm can be regarded as te element size for equilibrating computational accuracy and efficiency even for a void diameter of 1 mm. troug te void, as sown in Figure 5(a). However, wen te X coordinate is larger tan tis critical value, te void as almost no effect on te crack pat, as sown in Figure 5(b). Accordingly, as a new concept for caracterizing te effect of an air void on a fracture, te air-void-affected zone can be introduced. If we assume tat te affected zone is circular, ten its radius is 4.9 mm for te above void wit a diameter of 3 mm and Y coordinate of 0 mm. It is possible tat te affected zone size depends on te diameter and Y coordinates of te void..3. Effect of air void diameter In tis section, te Y coordinate of te air void is fixed at 0 mm, but its diameter is canged from 1 to, 3, 4, and.. Air-void-affected zone Witout loss of generality, for an air void wit a diameter of 3 mm located in te central zone of te beam wit = 50 mm, wile its Y coordinate is fixed at 0 mm, its X coordinate is gradually canged from small to large in order to observe its effect on te crack pat. Figure 5 sows te crack pats for te void at different X coordinates. It is found tat its X coordinate as a critical value of about 4.9 mm. Wen te X coordinate is less tan or equal to tis critical value, te crack pat will be attracted and go Figure 5. Crack pat of concrete beams wit different X coordinates of te void: (a) X = 4.9 mm; (b) X = 7.8 mm
134 C. Zang et al. Air-void-affected zone in concrete beam under four-point bending fracture Figure 6. Variation of affected-zone radius wit void diameter 5 mm (Guo et al. 016) in a concrete beam wit a eigt of 50 mm to evaluate te effects of te air void diameter on te affected zone size. Figure 6 sows te variation curve of te affected-zone radius wit te void diameter. It is obvious tat te affected-zone radius monotonously increases wit an increasing void diameter. For a pure Mode-I fracture in a semi-infinite brittle body wit a void, Valentini et al. (1999) derived an asymptotic closed-form formula for te crack pat. According to tis formula, for a circular void, te deflection of te crack pat from te vertical axis H can be expressed as a function of l, wic is te Y coordinate of te new crack tip: were ( 1 ν ) d H( l ) = t( + t t ) 8X, (1) t = 0 Y 0 l 0 0 ( ) X + Y l, and X 0 and Y 0 are te orizontal and vertical coordinates of te void center. d Wen H( Y0) = X0, te crack just goes troug te void. Accordingly, as te affected-zone radius, te critical value of X 0 can be obtained. It is found tat te affectedzone radius depends linearly on te void diameter, namely: ( ) 1+ 1+ 41 ν r = d = 0.8017d. () 4 For comparison, tis is also plotted in Figure 6 as a dased line. Clearly, te predictions from Eqn () are always lower tan te above numerical results. Tis can be attributed to te fact tat te asymptotic model is only for a semi-infinite brittle body under simple tension, and is based on te assumptions of a small ratio between te void diameter and its distance to te unperturbed crack pat. Misseroni et al. (015) studied te fracture beavior of ceramics wit voids experimentally and analytically. Tey found tat wen te void diameter is in close proximity to te distance from te void center to te crack pat, tere is an obvious difference between te asymptotic model prediction and te experimental crack pat, altoug te prediction can still provide a good approximation of te initial crack deviation. Figure 7. Radius of affected zone vs. Y coordinate of void center for different void diameters.4. Effect of air void location In tis section, te effect of te air void location on a fracture is investigated by canging te Y coordinate of te void center wen te beam eigt is fixed at 50 mm. Figure 7 sows te variation of te affected-zone radius wit canges in te Y coordinate for different void sizes. It is clear tat tere is a common tendency in te dependency of te affected-zone radius on te Y coordinate of te void center. Te affected-zone radius increases sligtly wit an increasing Y coordinate in te initial stage, but decreases gradually soon afterward. As te void size increases, te range of te affected-zone radius is extended. Obviously, compared wit te void size, te void location as a sligt influence on te radius of te affected zone..5. Numerical fitting In order to exclude te effect of te beam size, te radius of te affected zone, void size, and Y coordinate of te void center are all divided by te beam eigt. Compared wit te Y coordinate of te void center, te void size as a large effect on te radius of te affected zone. Accordingly, te relation of te dimensionless radius of te affected zone to te dimensionless void size and Y coordinate of te void center is fitted by te following expressions, wit te dimensionless void size as te dominating variable: 0 1, r Y Y d Y d = f + f + f were: Y Y Y f0 P00 P01 P0 = + + + 3 4 Y Y 03 + P04 ; P 3 Y Y Y Y 1 = 01 + 11 + 1 + 13 ; f P P P P (3) (4) (5)
Journal of Civil Engineering and Management, 018, 4(): 130 137 135 Table. Fitting parameters in Eqn (3) P 00 P 10 P 01 P 0 P 11 P 0 P 1 P 1 P 03 P P 13 P 04 0.0191 0.563 0.3760 0.5835 9.18 1.656 5.14 17.65.766 3.3 8.310 1.534 Y Y Y = 0 + 1 +. f P P P Te fitting parameters P ij are given in Table. All of te data are redrawn in Figure 8 as blue dots, and te fitting surface is indicated in green. For comparison, te predictions from Eqn (3) are plotted in Figure 6 and Figure 7 as solid lines. It is found tat tere is a good consistency between te data points and te predictions. Te coefficient of determination of 0.9946 indicates tat te dependency of te affected-zone radius on te void diameter and location can be well caracterized wit Eqn (3). In order to ceck te applicability of Eqn (3), some numerical simulations are conducted on a 75-mm-eigt beam wit a void of, 3, 4, or 5 mm in diameter, and a 100-mm-eigt beam wit a void of 3 or 5 mm in diameter. All voids are located at Y = 0 mm. Te obtained data are also plotted in Figure 8 as red tetraedrons. Clearly, tey can be covered by te prediction of Eqn (3). (6) Figure 8. Variation of dimensionless radius of affected zone wit dimensionless void diameter and Y coordinate of void center 3. Rationality test In tis section, two types of D beam models wit a eigt of 50 mm, randomly distributed circular voids, and a notc at te mid-span are built, and teir FPB fracture processes are numerically simulated by using te finite element metod combined wit a coesive crack model. All of te voids ave te same diameter of 3 mm in te two Type-1 models sown in Figure 9, but te void diameter lies in a range from 1 to 5 mm in te Type- model sown in Figure 10. Bot types ave te same volume fraction of %. In order to test te legitimacy of Eqn (3), te void-affected-zone radius prediction is used to explain te coice of crack pats in tese models. 3.1. Fracture in multi-void beams wit te same void diameter Figure 9 sows te crack pats in te two Type-1 models wit different void distributions, namely Distributions 1 and. Te crack pats are marked as black lines, and te boundaries of te void-affected zones predicted by Eqn (3) are marked as colored circles. In Figure 9(a) for Distribution 1, it is found tat only one void (namely, Void A) as a considerable influence on te fracture pat. Te oter voids ave almost no influence owing to teir great distances from te fracture pat. Wen te crack enters te affected zone of Void A predicted by Eqn (3) at Site 1, te pat begins to deviate to Figure 9. Crack pats in Type-1 models: (a) distribution 1; (b) distribution
136 C. Zang et al. Air-void-affected zone in concrete beam under four-point bending fracture Void A. As te crack furter comes near Void A, it is strongly attracted, so tat a larger deflection occurs at Site. After te crack passes troug Void A, te crack pat seems to ave a trend to return to te initial pat. Wen te crack leaves te affected zone of Void A at Site 3, a sarp deviation of te pat occurs again. It is sown tat te numerical crack pat can be well explained by te void-affected-zone radius prediction from Eqn (3). For Distribution, tree voids affect te crack pat considerably, as sown in Figure 9(b). Te affected zone of Void A partly overlaps tat of Void B. Te crack begins to enter te affected zone of Void A at Site 1. After te crack passes troug Void A, it directly moves toward Void B owing to teir overlapping affected zones, and leaves te affected zone of Void B at Site. Ten, te crack reaces te affected zone of Void C at Site 3, and leaves near Site 4. It is found tat te pat as an obvious deviation close to Sites 3 and 4 wen te crack enters or leaves te affected zone of Void C. However, it seems tat a sudden deviation occurs before te crack enters te predicted affected zone of Void A. Apparently, te prediction is accurate for Void C but is rougly approximate for Void A. Tis occurs because te interaction between voids is not considered in Eqn (3). 3.. Fracture in multi-void beams wit different void diameters Figure 10 sows te crack pat in te Type- model wit different void diameters. Compared wit te Type-1 models sown in Figure 9, te Type- model is obviously more complex. Owing to different void diameters, tere is a wide size range of te void-affected zone in tis model. As a result, overlapping frequently occurs between neigboring void-affected zones suc as te affected zones of Voids B and D, Voids C and D, and Voids D and E, and even te affected zone of Void C is completely covered by tat of Void B. It can be seen from Figure 10 tat Void A is too distant to affect te crack pat. Te crack goes forward near te affected zone of Void A, and enters te affected zone of Void B at Site 1. An obvious deviation in te crack pat occurs Figure 10. Crack pat in Type- model ere. Owing to overlap between te affected zones of Voids B, C, D, and E, after te crack passes troug Void B, it almost directly goes troug Voids C, D, and ten E. Te pat-deviation penomenon can also be observed wen te crack leaves Voids C and D at Sites and 3, respectively. However, a pat perturbation seems to occur in advance wen te crack leaves Void E at Site 4. Tis indicates tat te crack pat could be well explained in most cases by te void-affected-zone radius prediction from Eqn (3), altoug te interactions between neigboring void-affected zones are not involved. Conclusions Te fracture beaviors of FPB concrete beams wit random air voids were numerically simulated wit te elp of te finite element metod combined wit a coesive crack model. Te dependence of te void-affected-zone size on te air void size and location was carefully investigated. Te following conclusions are drawn: (1) Te void-affected-zone size was determined by moving an air void orizontally until te crack pat canged. Its relation to te air void size and location was given by nonlinear numerical fitting, and te effect of te void size is dominant. () Te affected-zone radius prediction from te fitting equation was used to explain te coice of crack pats in multi-void beams wit te same or different void diameters. It was found tat te prediction is accurate for an isolated affected zone but is rougly approximate for an overlapped one. In addition, it is conceivable tat te void-affectedzone size is very dependent on diverse void sapes and loading formats. Tis will be our direction of researc in te future. Acknowledgements Tis work is supported by te National Basic Researc Program of Cina [973 Program: 011CB013800]. References Barbosa, F. S.; Beaucour, A. L.; Farage, M. C. R.; Ortola, S. 011. Image processing applied to te analysis of segregation in ligtweigt aggregate concretes, Construction and Building Materials 5: 3375 3381. ttps://doi.org/10.1016/j.conbuildmat.011.03.08 Başyiğit, C.; Çomak, B.; Kılınçarslan, Ş.; Serkan Üncü, İ. 01. Assessment of concrete compressive strengt by image processing tecnique, Construction and Building Materials 37: 56 53. ttps://doi.org/10.1016/j.conbuildmat.01.07.055 Dong, W.; Wu, Z.; Zou, X.; Dong, L.; Kastiukas, G. 017. FPZ evolution of mixed mode fracture in concrete: Experimental and numerical, Engineering Failure Analysis 75: 54 70. ttps://doi.org/10.1016/j.engfailanal.017.01.017 Dong, W.; Wu, Z.; Zou, X.; Tan, Y. 016. Experimental studies on void detection in concrete-filled steel tubes using ultrasound, Construction and Building Materials 18: 154 16. ttps://doi.org/10.1016/j.conbuildmat.016.10.061
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