SPH simulation and experimental investigation of fiber orientation in UHPC beams with different placements

Construction and Building Materials 233 (2020) 117372

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SPH simulation and experimental investigation of fiber orientation in UHPC beams with different placements Huanghuang Huang a, Xiaojian Gao a,b,⇑, Yifeng Li a, Anshuang Su c a

School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China c Heilongjiang Provincial Hydraulic Research Institute, Harbin 150080, China b

h i g h l i g h t s
SPH was used to model fiber orientation of UHPC with various casting methods.
Fiber orientation coefficient decreased with the flow distance.
Flexural properties of UHPC beams were notably affected by placement methods.

a r t i c l e

i n f o

Article history: Received 6 May 2019 Received in revised form 11 September 2019 Accepted 23 October 2019

Keywords: UHPC SPH simulation Placement Fiber orientation Flexural properties

a b s t r a c t Various placement methods can be applied to real ultra-high performance concrete (UHPC) structure elements. When placing fresh mixture at single or several target positions to fill the mold, the fiber orientation in the hardened specimen may be significantly variable with the flow distance. To investigate the influence of various placements on fiber orientation in UHPC beams, three casting methods, e.g., placing fresh mixture from one end, the middle position and two ends of the mold, respectively were simulated by the smoothed particle hydrodynamics (SPH) approach. Experimental investigations were also performed on fiber orientation and flexural properties of UHPC beams prepared by these three placements. Based on the modelling and experimental results, fiber orientation for each placement exhibited a descending tendency along the flow distance and was significantly reduced by the cooccurrence of two opposite flows. The variations of the number of fibers per unit area and fiber orientation coefficient reached 52.4% and 63.2%. Consequently, flexural strength, toughness and deflection at modulus of rupture tended to decrease with the flow distance and were notably aggravated by two opposite flow of mixtures. The variations of these three parameters along the beam specimen reached as high as 32.8%, 51.6% and 40.6%, respectively. Therefore, it is vital to control flow distance and direction of fresh mixture to manufacture UHPC elements with a high homogeneity. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Ultra-high performance concrete (UHPC) has become one of the research hotspots due to its excellent mechanical properties and durability in the latest decades [1,2]. The significant improvement on mechanical behaviors of UHPC is attributed to the dense microstructure with very low porosity. The w/b (water-to-binder ratio) adopted in UHPC production is much lower than that in ordinary concretes. Pozzolanic material such as silica fume (SF) is normally incorporated to refine the pore structure and coarse aggregates are excluded to reduce defects [3]. ⇑ Corresponding author at: School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China. E-mail address: [email protected] (X. Gao). https://doi.org/10.1016/j.conbuildmat.2019.117372 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

In addition, the enhancement of such mechanical properties can be obtained by the incorporation of a moderate volume of uniformly dispersed fibers. Stress existing in the matrix can be transferred to fibers, preventing cracks from propagation [4]. This improvement effect is strongly influenced by the fiber orientation. Generally, fibers are randomly distributed in all directions to achieve an isotropic behavior and such dispersed fibers behave a low efficiency of strengthening the matrix [5]. Pujadas et al. established a relation between mechanical properties and fiber orientation for fiber reinforced concrete and the fiber orientation was evaluated by a multidirectional double punch test [6,7]. Mansur found that fibers can behave the best efficiency in preventing cracks from propagating when the fiber orientation is parallel with the tensile stress [8].

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

Fig. 1. SPH algorithm used in this study.

Table 1 Chemical constituents of cementitious materials. Chemical analysis (wt%)

Cement

SF

CaO SiO2 Al2O3 Fe2O3 MgO Na2O K2O SO3

62.23 20.86 5.47 3.94 1.73 0.16 0.32 2.66

0.63 87.67 0.28 0.60 3.41 1.30 4.12 0.84

As reported, the fiber orientation is influenced by rheological performance and fluidity of fresh mixture [9,10], as well as the formwork shape or dimension [11,12]. Efforts have been also made to acquire the better fiber orientation using an extrusion forming

process to align fibers [13,14]. Besides, the magnetic orientation of steel fibers has been recently proposed and experimental results show that steel fibers can rotate to directions along magnetic field lines, generating higher flexural performance [15,16]. Since UHPC exhibits an adequate viscosity and high flowability, fiber orientation presents flow-dependent and is notably influenced by the flow path [17,18]. Therefore, flexural properties of UHPC will be strongly affected by the placement procedure. Currently, UHPC has gained wide applications in structural elements such as precast girders of highways or bridges [19], full-depth deck panels [20] and thin prefabricated panels [21]. In general, structural elements such as beams and panels may be manufactured using different casting methods, e.g., placing fresh mixture at one point or several target positions along the mold [22,23]. For mechanical design and related investigations of structural elements, UHPC is normally supposed as a homogeneous material. However, at the material

Table 2 Details of the used steel fibers. Diameter, df (mm)

Length, lf (mm)

Aspect ratio (lf/df)

Density (g/cm3)

Tensile strength (MPa)

Elastic modulus (GPa)

0.22

13

59.1

7.9

2850

200

3

H. Huang et al. / Construction and Building Materials 233 (2020) 117372 Table 3 The mixing proportion of UHPC. w/b ratio

Cement (kg/ m3)

SF (kg/m3)

Fine sand (kg/m3)

Coarse sand (kg/m3)

Steel fibers (% by volume of mixture)

Superplasticizer (% by weight of binder)

0.2

920

276

202

810

2

2

several researchers to evaluate the orientation of fibers in UHPC and specimens will be destructed for preparing the observed samples [6,7,24,25]. As non-destructive methods, the electromagnetic field, conductivity and computed tomography analysis (CT) have also been applied to assess the fiber orientation in recent years [26–29]. In addition, several computational simulation strategies, such as the Finite Element Method [30], the Discrete Element Method [31] and the Lattice Boltzmann Technique [32] were employed to predict the distribution and orientation of fibers with the flow process of viscous fluid. Every modelling approach presents its merits and drawbacks for simulating the fiber orientation. The Smoothed Particle Hydrodynamics (SPH), as a mesh-free particle method, shows a great potential modelling the orientation of fibers with the flow of fresh concrete. With this simulation method, rheological properties of the mixture can be fully considered. The material is treated as a homogeneous viscous fluid consisting of different types of particles that can be tracked during the flow. Therefore, the SPH method has been employed to simulate the movement of coarse aggregates or orientation of steel fibers with the flow of self-compacting concrete [33,34]. Based on the simulation result of fiber orientation, it is possible to predict the mechanical strength of fiber reinforced concrete non-destructively [26,27]. This study intended to investigate the fiber orientation in UHPC beams with different placement methods. Steel fiber motion and orientation during these three placement procedures were numerically modelled using the SPH approach. Quantitative evaluation of fiber orientation along the cast beam specimens was also performed using image analysis. On the other hand, flexural properties of samples selected at different positions of the prepared beams were tested. The relationship between the flexural performance and fiber orientation was finally discussed. 2. SPH method The basic knowledge of SPH has been in detail introduced in one previous paper [24]. Interpolation calculation is performed to approximate field variables in SPH. By means of interpolation, the approximation of any variable D at position s can be expressed as Eq. (1):

DðsÞ ¼

X i

Fig. 2. Three placement methods: (a) placing UHPC at one end, (b) at the middle and (c) at two ends of the formwork.

scale, the fiber orientation and distribution in the element is significantly affected by the placement process which has been paid little attention in literatures. With respect to evaluation of the fiber orientation, several methods have been developed in published documents. Image analysis and multidirectional double punch test were utilized by

mi

Di

qi

K ðs  si ; hÞ

ð1Þ

where mi and qi are mass and density of particle i. K (s, h) is the kernel function and h is the smoothing kernel radius. The whole SPH modelling consists of a series of computation processes including governing equations, kernel function, artificial compressibility, artificial viscosity, boundary condition and time integration [35,36]. In this study, different placements were simulated in two-dimension, being a little different from the previous study [24]. Therefore, the two-dimensional kernel function is adopted as Eq. (2) [35]:

82 > 3  q2 þ 12 q3 0  q  1 15 < 1 K ðjsj; hÞ ¼ ð2  qÞ3 1  q  2 2 7ph > : 6 0 q2 where the scalar q ¼ jsj/h.

ð2Þ

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

Fig. 3. The left specimen (LS), the center specimen (CS) and the right specimen (RS) cut from the cast beam.

Fig. 1 gives the SPH algorithm. The modelling process can be divided into three main steps. Firstly, UHPC matrix particles, fiber particles, virtual particles were generated and the neighboring particles searching was proceeded. Virtual particles with repulsive force were utilized to prohibit UHPC particles including matrix and fibers from penetrating the boundary regions. Secondly, the change rates of density and velocity were calculated to address continuity and momentum equations. Lastly, the change rates of density and velocity were updated for the given time step and iteratively marched till the final step. 3. Materials and methods 3.1. Materials Fig. 4. Rheology of fresh UHPC.

Two cementing materials including ordinary Portland cement and silica fume (SF) were used in this paper. The cement

Fig. 5. SPH simulation results of placing UHPC at one end of the formwork at (a) t = 0 s, (b) t = 0.5 s and (c) t = 2 s.

H. Huang et al. / Construction and Building Materials 233 (2020) 117372

conforming to GB 175–2007 [37] has a strength grade of 42.5 with apparent density and specific surface area of 3.10 g/m3 and 0.36 m2/g, respectively. The main ingredient of the utilized SF is amorphous silicon dioxide with the pozzolanic reactivity index of 108.6%. The apparent density and specific surface area are 2.25 g/ m3 and 17.30 m2/g, respectively. Table 1 shows the chemical constituents of these two cementitious materials measured by X-Ray Fluorescence method. Quartz sands used in this paper included fine particles with diameters of 0.109–0.212 mm and coarse ones with diameters of 0.212–0.380 mm. Steel fibers utilized in the experiment had length of 13 mm and diameter of around 0.22 mm. More details about steel fibers are given in Table 2. A polycarboxylate-based superplasticizer (SP) was incorporated to improve the fluidity of fresh mixture and it has a water reduction rate of above 30% [38–40]. The mixing proportion of UHPC was designed according to GB/T 31387-2015 [41] as given in Table 3. A planetary mixer was employed to prepare the fresh UHPC mixture. Firstly, all solid materials excluding steel fibers were premixed for 4 min to achieve a uniform blend. Then, the water-reducing agent was premixed with water and incorporated into the blend in two halves with an interval of 6 min. Finally, steel fibers were slowly added into the flowable mixture in 10 min to gain a homogeneous distribution state. Based on preliminary experiments, specimens prepared by this mixture proportion behaved compressive strength of 140.8 MPa and flexural strength of 30.6 MPa. On the other hand, fresh mixture was also prepared without addition of steel fibers to test the rheological properties. The rheological performance of fresh mixture was measured by the RheoCAD400 rheometer in accordance with the testing regime given in Ref. [24].

5

3.2. Experimental methods As shown in Fig. 2, beam specimens were prepared by three placement methods: (1) placing UHPC at one end of the formwork, (2) placing UHPC at the middle of the formwork and (3) placing UHPC at two ends of the formwork. The fresh mixture was firstly poured into the vertical container to reach the height of 320 mm. Then, the baffle plate was rapidly lifted up. Two plates were simultaneously lifted up when beams were cast by placing UHPC at the middle and two ends of the formwork. The mixture was consolidated by gravity and beam specimens with sizes of 630 mm  70 mm  70 mm were finally fabricated. For each placement method, three specimens were prepared. All the beams were subsequently covered with plastic sheets to prevent moisture evaporation and stored in a curing room with 20 ± 2 and relative humidity above 90% for 2 days [42–44]. Then the specimens were demolded and cured in a steam container with temperature of 90 for 3 days. For measuring flexural properties of UHPC samples along the prepared beams, each beam was cut into three equal sections with sizes of 70 mm  70 mm  210 mm (b  h  l) as the left (LS), the center (CS) and the right specimen (RS) as indicated in Fig. 3. Flexural load–deflection curves were obtained by the three-point bending test at a loading rate of 0.4 mm/min [45]. Flexural strength and toughness can be calculated from the load–deflection curve as described in previous studies [25,46]. The fiber orientation was quantitatively accessed by image analysis. As proposed in Reference [24], slice samples were cut at the position around 40 mm from the primary cracks by a diamond saw to reduce the influence of fiber pull-out and then polished to

Fig. 6. SPH simulation results of placing UHPC at the middle of the formwork at (a) t = 0 s, (b) t = 0.5 s and (c) t = 2 s.

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

enhance the color contrast [47]. One ultra-depth threedimensional microscope was applied to aquire images of the section surface of slice samples. The view field was kept at 3.5 mm  3.5 mm with a resolution of 500  500 and 256 pictures were captured for each cross section and then synthesized into one final image (RGB). About 30 pixels represented the cross section area of each fiber. For further increasing the color contrast to distinguish steel fibers from the background, the binary image was converted from the RGB one by setting an appropriate threshold using the Image Pro Plus software [25]. In addition, other two thresholds related to the minimum and maximum areas of fiber cross section were adopted to more precisely detect fibers and remove other doubtful objects. Bright areas smaller and larger than the preset thresholds or not exhibiting an elliptical geometry were deleted during this process [48]. After that, the number of fibers per unit area, nf (number/mm2), can be calculated by Eq. (3):

nf ¼

Nf A

ð3Þ

where N f is the total number of fibers, A is the counted area. The inclined angles between longitudinal directions of steel fibers and the specimen cross sections can be computed by Eq. (4):

h ¼ cos1

df a

Z

gh ¼

hmax

pðhÞcos2 hdh

where pðhÞ is the distribution function. gh ¼ 1 means that all fibers are perpendicular to the cutting section, and gh ¼ 0 means that all fibers are parallel to the cutting section. 4. Results and discussion 4.1. SPH modelling It is widely known that fresh cement and concrete mixture behaves as the Bingham fluid, being expressed by two basic rheological parameters, i.e., yield stress s0 and plastic viscosity l [49]. Usually, plastic viscosity is regarded as the slope and yield stress is the intercept in the fitted line between shear stress s and shear rate c_ . As shown in Fig. 4, l and s0 of the fresh UHPC mixture in this experiment were 11.88 Pas and 42.63 Pa, respectively. In the SPH simulation, however, a regularized Bingham model was employed according to Kulasegaram et al. [50]:



s ¼ lc_ þ s0 1  emc_



5

ð4Þ

where h,df and a are the inclined angle, fiber diameter and major axis length, respectively. On the other hand, after obtaining the distribution function of fiber orientation angles through Eq. (4), the fiber orientation coefficient gh can be calculated by Eq. (5):

ð5Þ

hmin

ð6Þ

where m = 10 . During the SPH modelling, fibers were treated as rigid bodies and only underwent rotational and translational motions. A fiber was simplified as a couple of particles and the fiber mass was equally shared by this couple of particles. The initial positions of fiber particles were generated, then randomly dispersed and orientated by means of the Shuffle algorithm [51]. Each couple of fiber

Fig. 7. SPH simulation results of placing UHPC at two ends of the formwork at (a) t = 0 s, (b) t = 0.5 s and (c) t = 2 s.

H. Huang et al. / Construction and Building Materials 233 (2020) 117372

particles was kept at an invariable distance, equaling to the length of fiber. Besides the mass, both UHPC matrix and fiber particles had the same properties of continuity. The positions of fiber particles were mainly controlled by the matrix particles surrounding them and the orientation of fibers during each placement process was determined by the flow of UHPC rather than the mass of fiber particles [34]. A total number of 3192 particles and 200 couples of marked particles were employed to simulate 3.136 L fresh mixture of matrix and steel fibers, respectively. 338 virtual particles were used to provide repulsive force and guarantee the simulation stability. In addition, the mold surface was assumed to be smooth, thus the frictional action between the mixture and surface of mold was neglected in this simulation [34]. Each placement method was simulated for 2 s to reach the final static state. SPH modelling results of these three placement methods are given at t = 0 s, 0.5 s and 2 s in Figs. 5–7. It can be found that steel fibers were randomly distributed at the initial stage. With the modelling time, fibers were orientated under the effect of flow induction for each placement method. When placing UHPC at one end of the formwork, most fibers were aligned to parallel with the flow direction in the LS sample, generating the best fiber orientation. The fiber orientation became weaker in the CS and RS parts because more fibers behaved larger inclined angles against the flow direction along the flow distance. When placing UHPC at the middle of the formwork, the CS part presented a better fiber orientation than the other two parts of LS and RS. This is because more fibers were induced to the direction of flow in the middle space of the mold. LS and RS exhibited similar fiber orientations being

7

attributed to the symmetry of this casting method. With respect to the placement at two ends of the formwork, most of steel fibers were induced to be perpendicular to the flow direction in the middle zone with flow distance of around 0.3 m, indicating that the worst fiber orientation and flexural strength may be generated in this region. Both LS and RS parts showed a similar fiber orientation which was better than that of the CS part. For a couple of fiber particles, the positions of both ends lsi and lei are described as Eq. (7):

lsi ¼ ðxsi ; ysi Þ; lei ¼ ðxei ; yei Þ

ð7Þ

where i is the ith couple of fiber particles. The orientation angle h can be computed by Eq. (8): 1

h ¼ cos

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðysi  yei Þ2 ðxsi  xei Þ2 þ ðysi  yei Þ2

ð8Þ

In the direction of x-axis, the center of gravity (lcxi ) of a fiber can be calculated as the average value of both ends of fiber particles:

lcxi ¼

xsi þ xei 2

ð9Þ

The fiber orientation angle distributions of specimens prepared by these three placement methods are demonstrated in Fig. 8. Fiber orientation angle less than 20° was reported to be more beneficial for flexural properties [14]. The number of fibers with the orientation angle of below 20° was in accordance with the sequence of LS > CS > RS when placing UHPC at one end of the mold. Almost

Fig. 8. The fiber orientation angle distribution of specimens cast by (a) placing UHPC at one end, (b) at the middle and (c) at two ends of the formwork.

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

all fibers in the LS part had orientation angles of lower than 20° and fewer fibers presented orientation angles of less than 20° in the other two parts. The number of fibers with the orientation angle of under 20° in the CS part reached the most when casting UHPC at the middle of the mold. Finally, the CS part behaved the worst state when UHPC was simultaneously placed at two ends. Therefore, the horizontal orientation of steel fibers in the beam specimen behaved a degrading tendency with the flow distance and also aggravated by the opposite flow of fresh mixtures. 4.2. Fiber orientation Figs. 9–11 exhibit binary images of specimens prepared by three placements. It can be observed that Fig. 9(a), Fig. 10(b), Fig. 11(a) and (c) showed better fiber orientations than other samples. The fiber orientation tended to gradually decrease along the flow distance, because more ellipses were observed in images. On the other hand, the number of fibers in the section also presented a decreasing tendency along the flow distance. As revealed by previous study, flexural properties of UHPC are significantly influenced by both the fiber orientation and the number of fibers

per unit area [52]. Therefore, it is necessary to quantitatively evaluate the fiber orientation and the number of fibers per unit area for every specimen. Based on image analysis, distribution curves of the fiber orientation angle for every specimen was obtained as given in Fig. 12. It is obvious that the distribution curve of specimen prepared by placing UHPC at one end of the formwork transferred from leftskewed to right-skewed with the section changing from LS to RS. The orientation angle at the peak point in the curve increased from 27.5° to 47.5°. For the placement at the middle and two ends of the formwork, the CS specimen exhibited left-skewed and rightskewed distribution curves, respectively, with orientation angles of 37.5° and 52.5° at peak points. The LS and RS specimens for these two methods presented opposite distribution curves, being rightskewed and left-skewed and the related orientation angles at the peak points reached 47.5° and 32.5°, respectively. Table 4 presents the number of fibers per unit area and fiber orientation coefficient of each specimen. The LS specimen with the placement at one end of the formwork presented the highest nf and gh , while the CS one prepared by placing UHPC at two ends had the lowest ones. The largest difference reached 52.4% and

Fig. 9. Binary images of (a) LS, (b) CS and (c) RS for placing UHPC at one end of the formwork.

H. Huang et al. / Construction and Building Materials 233 (2020) 117372

9

Fig. 10. Binary images of (a) LS, (b) CS and (c) RS for placing UHPC at the middle of the formwork.

63.2%, respectively. It is obvious that both nf and gh presented a decreasing tendency along the flow distance for each placement method. Both nf and gh were also significantly declined by the occurrence of two opposite flows. Adopting electrical resistivity and X-ray CT techniques, Barnett et al. found similar results that fibers were aligned to be perpendicular to the flow direction of fresh concrete [28]. It should be noted that the SPH simulation in this work was carried out in two dimensions and it was difficult to calculate nf and gh at a certain cross section. However, it is feasible to compare the tendency of fiber orientation measured by image analysis with the simulation results along the flow distance. These modelling results present significant consistency with the experimental ones, indicating the two-dimensional SPH approach is appropriate to simulate the fiber orientation during the placement of UHPC. 4.3. Flexural properties Flexural load–deflection curves for different specimens are presented in Fig. 13. As suggested by Yoo et al., the first cracking behavior and post-cracking peak point can be described using limit of proportionality (LOP) and modulus of rupture (MOR),

respectively [53]. It was easily found that LOPs for all measured samples were almost the same. This is reasonable that the first cracking behavior largely depends on the matrix strength, mainly determined by the mix proportion and w/b ratio rather than nf and gh [54]. Therefore, the loads and deflections at LOPs showed no evident difference. With respect to MORs, notable differences can be observed among variable placement methods and sampling sections. Such difference in the flexural behavior is largely ascribed to the variation of fiber orientation as being widely reported in other investigations [14–16]. Fig. 14 shows flexural strength, toughness and deflection at MOR (SMOR) of all the tested specimens. It can be easily observed that the LS sample for the placement at one end of the formwork exhibited the highest flexural strength, toughness and SMOR, while the CS sample cast by placing UHPC at two ends of the formwork presented the lowest ones. The maximum difference reached 44.0%, 103.5% and 47.4% for flexural strength, toughness and deflection at MOR (SMOR), respectively. Both SPH modelling and image analysis results can be used to account for these flexural test results. Most of steel fibers in the LS sample for the one end placement were nearly parallel to the flow direction (direction of tension), showing the highest nf and gh . However, most of steel

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

Fig. 11. Binary images of (a) LS, (b) CS and (c) RS for placing UHPC at two ends of the formwork.

fibers in the CS part prepared by placing UHPC at two ends tended to be perpendicular to the flow direction, presenting the lowest nf and gh . Moreover, as revealed by Mansur et al., steel fibers exhibit the best efficiency in resisting cracks from propagation when fibers are parallel to the direction of tension, resulting in the best flexural properties [8]. It can be concluded that flexural strength, toughness and SMOR tended to decrease with the flow distance or notably reduced by two opposite flow of mixtures. Flexural strength, toughness and SMOR of the LS sample were 32.8%, 39.9% and 20.7% higher than those of the RS sample, respectively for the one end placement method. The CS sample presented the highest flexural strength, toughness and SMOR with the largest enhancement of 9.4%, 15.1% and 4.1% when compared with those of the LS and RS samples for the placement at the middle of the formwork. For the third placement method at two ends of the formwork, the middle part in the beam showed the lowest flexural strength, toughness and SMOR. Both LS and RS samples presented better flexural strength, toughness and SMOR, being up to 31.6%, 51.6% and 40.6% more than those of the CS sample, respectively.

As reported, flexural strength of UHPC is strongly affected by the fiber bridging strength rb ðdÞ, being given as Eq. (10) [55]:

rb ðdÞ ¼

4V f

pd2f

Z 0

p 2

Z

l 2

Pðh; le ; dÞpðle ÞpðhÞcoshdle dh

ð10Þ

0

where V f is the fiber volume, le is the insert length of fiber, d is the opening displacement of the crack, P ðh; le ; dÞ is the resistance force against fiber pull-out, pðle Þ is the probability density distribution for le . It is indicated that rb ðdÞ increases with the higher fiber orientation coefficient (gh ) as a result of the higher pðhÞcosh, indicating that more fibers will orientate to the tensile direction and the higher flexural strength is induced. On the other hand, the higher number of fibers per unit area (nf ) is also beneficial for improving the flexural strength. rb ðdÞ is increased with more fibers per unit area as a result of more fibers embedding at crack surfaces. This is attributed to the enlarged bond area between fibers and the surrounding matrix [54]. Moreover, the higher flexural strength is undoubtedly beneficial for enhancing toughness and SMOR.

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

Fig. 12. Distribution curves of the fiber orientation angle for specimens cast by (a) placing UHPC at one end, (b) at the middle and (c) at two ends of the formwork.

Table 4 Summary of number of fibers per unit area and fiber orientation coefficients of specimens. Placement methods

Sections

nf (number/ mm2)

gh

Placing UHPC at one end of the formwork

LS CS RS LS CS RS LS CS RS

0.314 0.281 0.258 0.282 0.291 0.269 0.310 0.206 0.295

0.62 0.54 0.45 0.48 0.53 0.47 0.56 0.38 0.59

Placing UHPC at the middle of the formwork Placing UHPC at two ends of the formwork

4.4. Relations between flexural properties and fiber orientation It is indicated from the above results that specimens with the larger nf and gh exhibited the better flexural behaviors. Therefore, to establish the relation between flexural behavior and fiber orientation, a scalar descriptor, k ¼ nf  gh was proposed to characterize the steel fiber orientation. Fig. 15 shows the relationship between flexural behavior and the descriptor k. All these three parameters related to flexural properties were enhanced by the higher k value. Similar relations were also found in previous studies [25]. Flexural strength and toughness exhibited better linear relationships with the parameter k than the SMOR. Coefficients of determination (R2) reached 0.95 for the former two flexural parameters and only 0.74 for the third parameter. When taking the rule of mixture of composites into consideration, the linear relationship can be also built between flexural strength and fiber orientation as given in Eq. (11) [56]:

fs ¼ agl gh V f rfu þ

a b

rmft V m

ð11Þ

where a and b are the sample dimensional parameters, gl is the fiber length efficiency factor, rfu and rmft are tensile strength of the fiber and matrix, V m is the volumetric content of matrix. With the given mixing proportion and curing regime, tensile strength of the matrix is invariable. As a consequence, the flexural strength exhibited a linear increase tendency with the fiber orientation. This was in well agreement with the experimental results.

5. Conclusions Based on the above modelling and experimental results, some conclusions can be obtained as below.
Two-dimensional SPH approach was successfully employed to simulate motion and orientation of steel fibers in UHPC beams under three placement procedures.
Both SPH modelling and image analysis indicated that the fiber orientation tended to decrease along the flow distance in beam specimens and also reduced significantly by the occurrence of two opposite flows.
Flexural strength, toughness and SMOR presented a degrading tendency with the flow distance and also aggravated by the opposite flow of mixtures. The induced variation of these parameters for one beam specimen reached as high as 32.8%, 51.6% and 40.6%, respectively.
Flexural strength and toughness of UHPC presented good linear relations with the steel fiber parameter k with R2 of 0.95.

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H. Huang et al. / Construction and Building Materials 233 (2020) 117372

Fig. 13. Load-deflection curves of specimens cast by (a) placing UHPC at one end, (b) at the middle and (c) at two ends of the formwork.

Fig. 14. (a) Flexural strength, (b) toughness and (c) SMOR of specimens cast by these three placement methods.

H. Huang et al. / Construction and Building Materials 233 (2020) 117372

13

Fig. 15. Relationships between (a) flexural strength, (b) toughness, (c) SMOR and the parameter k.


The SPH approach behaved a great potential in simulating the fiber orientation of UHPC during different placement methods. Nevertheless, three–dimensional simulations with a higher efficiency should be further investigated and the interaction among fibers and frictional effect between UHPC and the mold surface should be considered.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Acknowledgments This work was supported by the National Key Research and Development Program of China (No. 2017YFC0404805) and the National Natural Science Foundation of China (No. 51578193). References [1] K. Habel, M. Viviani, E. Denarié, E. Brühwiler, Development of the mechanical properties of an ultra-high performance fiber reinforced concrete (UHPFRC), Cem. Concr. Res. 36 (7) (2006) 1362–1370. [2] J.S. Zhang, Y.H. Zhao, The mechanical properties and microstructure of ultrahigh-performance concrete containing various supplementary cementitious materials, J. Sustain. Cement-Based Mater. 6 (4) (2017) 254–266. [3] P. Richard, M. Cheyrezy, Composition of reactive powder concretes, Cem. Concr. Res. 25 (7) (1995) 1501–1511.

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