Numerical simulation and visualization of motion and orientation of steel fibers in UHPC under controlling flow condition

Construction and Building Materials 199 (2019) 624–636

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Numerical simulation and visualization of motion and orientation of steel fibers in UHPC under controlling flow condition Huanghuang Huang a, Xiaojian Gao a,b,⇑, Ailian Zhang 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 School of Civil Engineering, Sichuan College of Architectural Technology, Deyang 618000, China b

h i g h l i g h t s
Motion and orientation of fibers in UHPC during flow was simulated by SPH.
The smaller channel height was better for improving the fiber orientation.
The predicted

gh showed an acceptable deviation from the measured one.


Visualization of fiber orientation under flow controlling was performed.

a r t i c l e

i n f o

Article history: Received 25 September 2018 Received in revised form 5 December 2018 Accepted 12 December 2018

Keywords: Ultra-high performance concrete (UHPC) Smoothed particle hydrodynamics Image analysis Visualization Fiber orientation Flow control

a b s t r a c t To improve fiber orientation in ultra-high performance concrete (UHPC), one L-shape device was developed to control the flow of fresh mixture. A smoothed particle hydrodynamics (SPH) method was used to analyze and simulate the motion of steel fibers in UHPC with flow through this L-shape apparatus. SPH simulation indicated that steel fibers tended to rotate to be parallel with local streamlines and most fibers were aligned in the horizontal channel of this L-shape device, inducing an improvement of fiber orientation in hardened specimens. This modification effect of fiber orientation can be a little strengthened with the decreasing height of the horizontal channel. On the other hand, a colorless, transparent and viscous concentrated suspension was obtained by adding super absorbent polymer (SAP) into water for representing fresh UHPC matrix and the visualization of fiber motion was achieved. This visualization approach, coupled with image analysis of steel fibers in hardened UHPC specimens, well verified the SPH numerical simulation results. Therefore, this type of L-shape apparatus provides a potential method to manually improve the steel fiber orientation in UHPC for better mechanical properties. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Ultra-high performance concrete (UHPC) has become one of the most promising building materials due to its superior mechanical properties and excellent durability [1,2]. Based on the packing density theory, UHPC is generally composed of large quantities of Portland cement, silica fume (SF) and fine aggregates with steel fibers for reinforcement and a high dosage of superplasticizer for fluidity at a very low water to binder ratio (w/b) [3,4]. Combined high performance concrete matrix with high strength steel reinforcement, a growing portion of civil structures have been constructed of UHPC, such as Mediterranean Culture Museum built in Marseille ⇑ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China. E-mail address: [email protected] (X. Gao). https://doi.org/10.1016/j.conbuildmat.2018.12.055 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

of France and Gärtnerplatz Bridge in Kassel of Germany [5]. One of the major advantages of utilizing short steel fibers is to improve flexural performance of UHPC. Stress can be transferred from the matrix to fibers because of fibers bridging at crack surfaces and resisting against crack propagation [6,7]. Many studies reported that flexural and tensile properties of UHPC are notably influenced by the fiber orientation [8–10]. It is well known that fibers are randomly dispersed in UHPC specimens when being prepared by a direct cast. The efficiency of randomly distributed fibers is not as high as expected [11], leading to a limited improvement on flexural performance. There is no doubt that flexural properties will be significantly enhanced if steel fibers are all aligned along the direction of tension. As reported by several researchers, fiber orientation is generally affected by rheological and fresh characteristics of mixtures [12–14], mixing and placing method [15–17] and the formwork shape and dimension [18,19].

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In previous literatures, extrusion processing and nozzle injection technique were employed to achieve a better fiber alignment in fiber reinforced cementitious composites [20,21]. Magnetic orientation of steel fibers was also studied in recent years, indicating that steel fibers tend to rotate to the direction of magnetic induction line (usually the direction of tension) [22,23]. In this paper, a flow control method performed by one L-shape device was developed to improve fiber orientation in UHPC. Flow of fresh UHPC mixture and motion of steel fibers along this Lshape apparatus were numerically simulated by Smoothed Particle Hydrodynamics (SPH) method. On the other hand, a novel fiber visualization approach was developed to observe the rotation of steel fibers in real time and image analysis technique was used to experimentally determine the fiber orientation in hardened UHPC specimens. Finally, both numerical simulation and experimental results verified the improvement effect of flow control on steel fiber orientation of UHPC. 2. Basic knowledge of SPH method SPH is a mesh free Lagrangian numerical method, which was firstly developed to simulate astrophysical fluid dynamics in 1977. It is relatively easy to incorporate complicated physical effects into SPH formulas, and thus SPH has been successfully applied to various fields such as dynamic material response [24], high velocity impact [25] and Newtonian or non-Newtonian flows [26]. As a particle-based method, the system is discretized into a limited number of smoothed particles that possess material properties, such as mass, position, velocity, etc. An interpolation process is employed to approximate values and derivatives of continuous field quantities by using smoothed particles in SPH. As shown in Fig. 1, the particle i interacts with the neighboring particles within the support domain X with a radius of jh settled by a smoothing function. Interpolation of variable A at any position r can be calculated by using SPH approximation [27]:

A ðr Þ ¼

X j

mj

Aj

qj

  W r  rj ; h

ð1Þ

where mj and qj are mass and density of particle j, respectively. W (r, h) is an interpolating kernel function and h is the radius of smoothing kernel. The gradient of the variable A is given by differentiating the interpolation Eq. (1) [27]:

r A ðr Þ ¼

X

mj

j

Aj

qj





r W r  rj ; h

ð2Þ

Based on Eq. (2), mechanical laws of discrete particles motion, being also called governing equations, can be presented in their SPH approximations. 2.1. Governing equations The governing equations that discrete particles should conform include the continuity equation and the momentum equation, which can be derived from mass conservation and Newton’s Second Law as follows [28]:

Dq ¼  q rv Dt

ð3Þ

Dv 1 rr þF ¼ Dt q

ð4Þ

D where Dt is the commoving time derivative, q is the density of particle, t is the time, v is the velocity of particle, r is the total stress tensor and F is the external forces such as gravity and magnetic force. The total stress tensor can be written as:

r ¼ PI þ S

ð5Þ

where P is the pressure, I is the unit matrix and S is the deviator stress tensor. 2.2. Kernel function The cubic spine function is utilized as a kernel in most simulations at present. There is a great computational advantage using this kernel function due to having a compact support, thus a relatively small number of neighboring particles are possibly taken into consideration in summations. The quartic spline and quintic spline interpolants were reported to have better stability properties and an increased computational cost. Therefore, in this study, cubic spine function in 3D is employed as the kernel function [29]:

8 > 1  32 q2 þ 34 q3 1 < 1 3 W ðjrj; hÞ ¼ > 4 ð2  qÞ ph3 : 0

0q1 1q2

ð6Þ

q2

where q ¼ jr j/h. Based on Eqs. (2) and (6), Eqs. (3) and (4) can be expressed in their SPH approximations [29]:

Dqi X mj ðv i  v j Þri W ij ¼ Dt j

ð7Þ

Dv i X ri rj mj ð 2 þ 2 Þri W ij þ F i ¼ Dt q qj i j

ð8Þ

where

  W ij ¼ Wðri  r j ; hÞ 2.3. Artificial compressibility

Fig. 1. SPH particle approximations using particles within the support domain of the smoothing function W for particle i.

Since the incompressible SPH method (ISPH) uses the actual equation of state, an extremely short time step is required and the whole solving process is very time-consuming. Therefore, an incompressible fluid is treated as weakly compressible to accelerate the solving process by means of introducing the artificial compressibility, called weakly compressible SPH method (WCSPH). Fresh concrete is considered to have weak compressibility due to the existence of entrapped air bubbles, part of which will escape

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during the fresh concrete flow. The equation of state when taking artificial compressibility into consideration can be written as below [30]:

q c2 P¼ 0 0 c



q q0

c

 1

ð9Þ

where q0 is the reference density of the fluid and c0 its speed of sound, c = 7 [27].

1 ðci þ cj Þ 2

ð12Þ



1 2

ð13Þ



1 ðhi þ hj Þ 2

ð14Þ

 c ij

¼

qij ¼ ðqi þ qj Þ hij ¼

2.4. Artificial viscosity To stabilize the simulating process, an additional viscosity (also called artificial viscosity) is utilized to overcome unreliable fluctuations in SPH method. The artificial viscosity adopted in this study was introduced by Monaghan as the following equations [31].

Y ij

¼

8  < a c ij £ij þb£2ij :

qij

0

v ij  rij < 0 v ij  rij  0

ð10Þ

hij v ij  r ij £ij ¼  2 rij  þ 0:01h2

ð11Þ

ij

Table 1 Chemical and physical properties of cementing materials.

Chemical analysis (wt%) CaO SiO2 Al2O3 Fe2O3 MgO Na2O K2O SO3 Physical properties Apparent density (g/m3) Blaine (BET) SSA (m2/g) Pozzolanic activity index

Cement

SF

63.64 20.65 4.26 3.58 2.14 0.16 0.96 4.10

0.63 87.67 0.28 0.60 3.41 1.30 4.12 0.84

3.10 0.36 –

2.25 17.30 108.6

Fig. 3. Geometry of the L-shape apparatus.

Table 2 Geometrical and physical properties of steel fibers. Diameter, df (mm)

Length, lf (mm)

Aspect ratio (lf/df)

Density (g/cm3)

Tensile strength (MPa)

Elastic modulus (GPa)

0.2

13.0

65.0

7.9

2850.0

200.0

Table 3 Mix proportions 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)

SP (% by weight of binder)

0.22‘

920

276

202

810

2

1.8

Fig. 2. Mixing procedure of UHPC.

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Fig. 4. Rheological parameters measurement (a) RheoCAD400 rheometer and (b) testing protocol.

where D is decided by numerical problem which generally has the same magnitude with the square of maximum particle speed, r 0 is the cut-off radius which equals to the initial particle spacing, the values of n1 and n2 are 12 and 4 [31], respectively. xij is the relative position of particle i and particle j at every dimension. 2.6. Time integration Being similar to other explicit hydrodynamic methods, SPH equations can be integrated with standard methods such as Leap-Frog (LF), predictor-corrector and Runge-Kutta (RK) schemes. LF scheme is employed in this study considering its low memory storage and the field variables are updated after every step as follows [33].

Fig. 5. Positions of slices cut from the L-shape specimen.

v ij ¼ v i  v j ; rij ¼ ri  rj

ð15Þ

where a and b are two constants that are typically set around 1.0 [31], v ij and r ij are relative velocity and position vectors between particle i and particle j. 2.5. Boundary condition

  Dp Dt Dt n

ð17Þ

v nþ1=2

¼

  Dv Dt Dt n

ð18Þ

xn

¼ xn þ

þ 1

v n1=2 þ

v n þ 1=2 Dt

ð19Þ

For stability, the time step Dt is chosen according to the relevant Courant-Friedrichs-Lewy condition, additional constraints and viscous diffusion. Therefore, the time step can be decided by Eq. (20) [34].

sffiffiffiffi ! 2 h h h q ; 0:125 Dt ¼ min ; 0:25 c fi l

ð20Þ

where f i is the particle acceleration and l is the plastic viscosity.

Repulsive boundary condition was used to prevent particles from unphysical penetration while particles are approaching to the boundary improving the accuracy of SPH method in boundary region. Virtual particles are distributed around the boundary. If virtual particle j becomes the neighboring particle of particle i, a repulsive force will be exerted to i along the center line between i and j. The calculation of the repulsive force is similar with the Lennard-Jones potential function [32].

8  n1  n2  jxij j > r0 : 0

qnþ1=2 ¼ qn1=2 þ

r0

1

r0 jrij j

>1

jrij j

ð16Þ

3. Materials and methods 3.1. Materials Ordinary Portland cement with strength grade of 52.5 in accordance with GB 175-2007 [35] was used in this study. SF powder employed was mainly composed of amorphous silicon dioxide, with particle size ranging from 0.1 lm to 1 lm. Its pozzolanic reactivity index was measured in accordance with GB/T 12957-2005 [36]. Chemical components measured by X-Ray Fluorescence and physical properties of these two cementing materials are given in Table 1.

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Fig. 6. Image analysis procedure for determining fiber orientation.

Fig. 7. Rheology of (a) fresh UHPC and (b) SAP suspension.

Two kinds of quartz sand, i.e. fine sand with size between 0.109 mm and 0.212 mm and coarse sand ranging from 0.212 mm to 0.380 mm, were utilized as aggregates. The grading and physical properties of these two types of sand can be found in a previous study [37]. The employed steel fiber was copper coated, with a high tensile strength of 2850 MPa. More details about the geometrical and physical properties of steel fibers are given in Table 2. A polycarboxylate-based superplasticizer (SP) with water-reducing range of more than 30% and solid content of about 40% by weight was applied to improve the flowability of fresh mixture. The mix proportion of UHPC is presented in Table 3. All the raw materials were blended using a Hobart mixer according to the mixing procedure given in Fig. 2. The low speed and high speed were 198 rpm and 361 rpm. Firstly, solid materials except for steel fibers were premixed at low speed for 4 min to obtain a homogeneous mixture. Then, the mixing water containing SP was added in two halves prior to Step 2 and 3. When a homogeneous mixture formed with a good flowability, steel fibers were slowly incorporated into the mixture in 10 min to achieve a uniform distribution. Hardened specimens prepared with this mix had compressive strength of 135.1 MPa and flexural strength of 26.4 MPa as reported in our previous study [8].

3.2. Experimental methods The L-shape device was made of transparent organic glass, consisting of a vertical container and a horizontal channel. As presented in Fig. 3, the vertical container had a size of 100 mm  100 mm  250 mm. The height (h) of the horizontal channel was adjustable with sizes of 75 mm  100 mm  10 mm, 75 mm  100 mm  20 mm and 75 mm  100 mm  30 mm, respectively. The vertical container and horizontal channel were connected by a curved surface with height of 15 mm and length of 30 mm. The fresh mixture was poured from the top entrance of the vertical container and then flows out from the horizontal channel due to its gravity. In this study, the fresh UHPC had a fluidity of 240 mm, behaving a good workability for this flow control cast. Based on previous experiments, a very low fluidity possibly leads to the blockage of mixture in the narrow channel of this apparatus and the sedimentation of steel fibers occasionally occurs for very high fluidity mixtures. For visualizing fiber motion in the L-shape device, a colorless, transparent and viscous concentrated suspension obtained by adding super absorbent polymer (SAP) into water was utilized as a replacement of fresh UHPC. The fluidity of SAP suspension was also adjusted to around 240 mm, being similar to fresh UHPC mixture.

H. Huang et al. / Construction and Building Materials 199 (2019) 624–636

(a) original state

629

(b) front view

(c) top view Fig. 8. (a) Original state, (b) front view and (c) top view of SPH simulation results of UHPC flow and fiber motion in the L-shape apparatus with h = 10 mm (t = 2 s).

Rheological parameters were also measured to more precisely reproduce the behavior of actual UHPC. To increase color contrast, steel fibers were sprayed red by aerosol paint. According to other studies, the effects of fiber content and shape on fiber orientation are negligible with this visualization method and the fiber orientation becomes more difficult to observe as the fiber fraction increases [19,38]. Therefore, steel fibers were incorporated by 0.5% in volume into SAP suspension to facilitate the observation of fiber orientation along flow in the study. For testing yield stress and plastic viscosity of fresh mixture and SAP concentrated suspension, a RheoCAD400 rheometer with a 3 L container was employed in this paper, as presented in Fig. 4 (a). Fresh mixture or SAP suspension was transferred into this container in 1 min after the completion of mixing procedure, and then operated the measurement by the testing protocol as shown in Fig. 4 (b). The rotational speed was kept at 0.1 rpm for 40 s at the beginning. Then, the rotational speed increased to 150 rpm by 9 steps in 144 s. After being kept constant at 150 rpm for 80 s, the rotational speed was decreased to zero by 10 steps in 160 s.

The fresh mixture was continuously poured in the L-shape device, exit of horizontal channel was initially blocked until the height of mixture in the vertical container reached 210 mm. The mixture subsequently flowed out from the channel for around 2 s. Then the exit was blocked again. L-shape specimens with horizontal channel height of 10 mm, 20 mm and 30 mm were prepared. As shown in Fig. 5, to quantitatively evaluate the fiber orientation at different positions in the apparatus, slices P1, P2 and P3 were cut at  = 40 mm, 70 mm and 150 mm, respectively. The height of slices at  = 40 mm and 70 mm was 50 mm. For  = 150 mm, the height equaled to that of exit (10/20/30 mm). Slice samples were treated by coarse grinding, fine grinding and ultrasonic wave cleaning successively to obtain smooth surfaces and increase color contrast between fibers and matrix. After this treatement, one microscopy digital camera, Olympus DSX500 with 5/0.15BD lens, was employed to aquire high resolution images of the cross sections of specimens. To achieve a good color contrast for distinguishing steel fibers from the surrounding cementitious matrix, the acquired image (called RGB image) was disposed using an Image Pro Plus software and converted into a binary image

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(a) original state

(b) front view

(c) top view Fig. 9. (a) Original state, (b) front view and (c) top view of SPH simulation results of UHPC flow and fiber motion in the L-shape apparatus with h = 20 mm (t = 2 s).

through setting a threshold value [39]. The whole image analysis procedure is given in Fig. 6. On the basis of obtained binary image, the inclined angle of single fiber against the specimen cross section can be calculated as:

h ¼ cos1

df a

ð21Þ

where h; df ; and a are the inclined angle of fiber, the diameter of fiber and the major axis length of the fiber image, respectively. The fiber orientation coefficient gh can be computed by Eq. (22).

gh ¼

Z

hmax

hmin

pðhÞcos2 hdh

ð22Þ

where pðhÞ is the probability density distribution of fiber orientation angle. gh ¼ 1 indicates that every fiber is aligned perpendicular to the cross section, and gh ¼ 0 indicates that every fiber is aligned parallel to the cross section.

4. Results and discussion 4.1. Rheology of fresh UHPC and SAP suspension The rheological behaviors of fresh UHPC and SAP suspension are presented in Fig. 7. In this study, the rheology of UHPC was measured on plain mixture without steel fibers. Both plastic viscosity and yield stress can be obtained by fitting the relation between shear stress and shear rate. For fresh UHPC mixture, plastic viscosity and yield stress reached 7.45 Pas and 25.86 Pa. In another investigation, UHPC mixture presented plastic viscosity of 13.3 Pas and yield stress of 127.0 Pa when the same w/b and a lower dosage of SP (1.6%) were adopted [40]. The higher dosage of SP increased the fluidity of fresh mixture as expected. As acknowledged, most of polymer solutions behave as pseudoplastic fluids. The SAP suspension behaved a slightly shear thinning as observed from Fig. 7 (b). Plastic viscosity and yield stress for this SAP suspension presented 4.32 Pas and 85.03 Pa, respectively. Actually, it is very difficult to accurately simulate the rheology of fresh UHPC using the SAP suspension or other transparent fluids. However, the SAP suspension

H. Huang et al. / Construction and Building Materials 199 (2019) 624–636

(a) original state

631

(b) front view

(c) top view Fig. 10. (a) Original state, (b) front view and (c) top view of SPH simulation results of UHPC flow and fiber motion in the L-shape apparatus with h = 30 mm (t = 2 s).

behaves a similar Bingham model to fresh UHPC. Therefore, it provides a feasibility to replace fresh UHPC mixture for performing the visualization of steel fibers. 4.2. SPH modelling In this study, a regularized Bingham model is employed in SPH simulation from a practical computational point of view [41]:



s ¼ le_ þ s0 1  eme_



ð23Þ

where s is shear stress, e_ is shear rate, s0 is yield stress and m = 105. e_ is generally defined by the second invariant of the rate of deformation d:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 trd e_ ¼ 2

 1

rv f þ rv Tf 2

where the superscript T denotes transpose.

P

mj W ij

qi ¼ P j m  j

ð24Þ

The rate of deformation is usually expressed as:

d¼

It is assumed that fibers are rigid bodies with only rotation and translation. Both ends for a fiber are represented by a pair of particles and the mass of a fiber is equally divided by them. The initial positions of pairs of particles representing fibers are generated randomly and distributed by the Knuth-Durstenfeld Shuffle algorithm. The distance between each pair of particles is maintained constant as the fiber length. Both the fluid and fiber particles have the same continuum properties except for their masses. To keep the mass conservation equation well satisfying mi ¼ qi V i and improve the density precision between the fluid and fiber particles, the density field is corrected during SPH calculation as:

ð25Þ

j

qj

W ij

ð26Þ

A total number of 17460, 18,060 and 18,660 fluid particles were utilized to represent fresh UHPC mixture in the L-shape device with corresponding channel heights of 10 mm, 20 mm and 30 mm. 400 pairs of tagged particles were adopted to represent steel fibers and 6502 virtual particles were employed to prevent particles from penetrating the boundaries by applying repulsive

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force. For simplicity of observation, these fiber particles were only distributed in the vertical container. The flow of UHPC and motion of steel fibers in the L-shape apparatus with these three channel heights were simulated for 2 s. The SPH simulation results for three horizontal channel heights are presented Figs. 8–10. It is well acknowledged that the flow velocity of UHPC mixture becomes higher with the increasing channel height of this device. Therefore, the flow distance increased with the higher channel height. As observed in these figures, steel fibers are originally dispersed at random. With the flow

of fresh UHPC, steel fibers starts to orientate to the flow direction of mixture, generating a modified fiber orientation. For every channel height, most of steel fibers presents parallel orientation to the flow direction in the horizontal container. Little difference can be easily observed among them. For a pair of fiber particles, the coordinates of two ends lsi and lei can be expressed as:.

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

ð27Þ

th

where i means the i pair of fiber particles. The average fiber orientation angle h is calculated by:

1 XN h¼ cos1 i¼1 N

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxsi  xei Þ2 þ ðysi  yei Þ2 ðxsi  xei Þ2 þ ðysi  yei Þ2 þ ðzsi  zei Þ2

ð28Þ

where N is the total number of fiber particle pairs. The average fiber orientation angles in sample P1, P2 and P3 for every channel height are demonstrated in Fig. 11. It can be observed that the average fiber orientation angle decreases with the position changing from P1 to P3. The average fiber orientation angle reduction reaches 61.8%, 54.1% and 19.9% for h = 10 mm, 20 mm and 30 mm, respectively, indicating that the improvement effect of flow control on fiber orientation decreases with the higher channel height. Therefore, a better modification of fiber orientation can be obtained by a smaller channel height. At arbitrary instant time t, the velocity of a pair of fiber particles, v si and v ei can be resolved to three directions in 3D dimensions as:







v si ¼ v xsi ; v ysi ; v zsi ; v ei ¼ v xei ; v yei ; v zei Fig. 11. Average fiber orientation angles at three positions calculated by SPH for h = 10 mm, 20 mm and 30 mm.



ð29Þ

In x-axis direction, the gravity center lcxi and its velocity v cxi of a fiber can be expressed as averages of the pair of fiber particles:

Fig. 12. Velocity distribution of fiber center in the x-axis direction for h = (a) 10 mm, (b) 20 mm and (c) 30 mm (t = 2 s).

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Fig. 13. Binary images of different positions in the L-shape apparatus with h = (a) 10 mm, (b) 20 mm and (c) 30 mm.

lcxi ¼

xsi þ xei v xsi þ v xei ; v cxi ¼ 2 2

ð30Þ

As analyzed above, the fiber has a tendency to rotate to the direction of local streamlines in the flow controlling device, leading to a larger fiber velocity in x-axis. Fig. 12 presents the velocity distribution of fiber centers in the x-axis direction for h = 10 mm, 20 mm and 30 mm at t = 2 s. It can be easily found that the fiber velocity in x-axis increases with the higher x-coordinate of fiber center (lcx ), especially when lcx surpasses 0.1 m. It is reasonably understood that the enhancement of fiber velocity under 0.1 m is slighter due to the restriction of right boundary. With pairs of fiber particles rotating to the direction of local streamlines and flowing

into the horizontal channel (lcx > 0.1 m), the dominate direction of fiber velocity becomes x-axis, indicating that most of fibers are aligned parallel to the flow direction. 4.3. Image analysis on fiber orientation The improvement of steel fibers on flexural properties of UHPC is mainly attributed to the fiber bridging strength which increases with the better fiber orientation [8,42,43]. Therefore, the controlling flow method was motivated in this study to improve fiber orientation. Binary images were obtained for slice samples P1, P2 and P3 as shown in Fig. 13. For every channel height, sample P3

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Fig. 14. Probability density distribution of fiber orientation angle at different positions for h = (a) 10 mm, (b) 20 mm and (c) 30 mm.

Fig. 15. Fiber orientation coefficients at three positions calculated by image analysis and SPH for h = 10 mm, 20 mm and 30 mm.

behaved better fiber orientation than sample P1. On the other hand, more ellipses are observed in P3 with the increasing height of horizontal channel, indicating that the modification effect of flow control on fiber orientation becomes a little weaker. The probability density distribution of fiber orientation angle for each slice is shown in Fig. 14. It can be easily found that the distribution curve for each channel height transfers from rightskewed to left-skewed with the position migrating from P1 to P3. Taking h = 10 mm as an example, the inclined angle corresponding to the peak probability density decreases from 52.5° to 27.5° with the position changing from P1 to P3, indicating a significant

improvement on fiber orientation induced by the flow control. Most of steel fibers in P3 have a lower inclined angle, implying a higher tendency to be parallel to the flow direction. A comparison was performed for fiber orientation coefficients obtained by image analysis and calculated by the SPH method as given in Fig. 15. It can be clearly observed that fiber orientation coefficients are obviously improved with the position migrating from P1 to P3, indicating that the fiber orientation is significantly modified by this flow control method. This is attributed to the tendency of steel fibers to gradually rotate to direction of local streamlines. For example, the image analysis obtained fiber orientation coefficients at P1, P2 and P3 for h = 10 mm are 0.42, 0.69 and 0.78 and those calculated by the SPH method reach 0.59, 0.81 and 0.88, respectively. This improvement effect decreases with the increasing channel height. Moreover, specimens prepared by the L-shape device forms at the position of P3. Based on theoretical analysis on specimen without the flow control influence [44], fiber orientation coefficients at position P3 for h = 10 mm, 20 mm and 30 mm reached 0.89, 0.57 and 0.54, being much lower than those obtained by this study. It is once again proved that a significant improvement on orientation of steel fibers can be easily achieved using this suggested approach. The fiber orientation coefficient calculated by image analysis presents an acceptable deviation of less than 15% from that calculated by SPH for most of samples (except P1 for h = 10 mm and 20 mm). With respect to P1 for h = 10 mm and 20 mm, the deviation is more than 15% and this may be attributed to influence of the formwork structure or sampling operation. 4.4. Fiber motion and orientation visualization Visualization results of steel fibers motion at t = 2 s in the apparatus with different horizontal channel heights are presented in

H. Huang et al. / Construction and Building Materials 199 (2019) 624–636

635

Fig. 17. Load-deflection curves of UHPC samples prepared by a direct cast and the flow control method.

ter orientation distribution along the flow direction. From results shown in Fig. 16, it can be also observed by naked eyes that steel fibers in the apparatus with a lower channel height present a better orientation along the flow direction. This is consistent with SPH simulation results. 4.5. Mechanical properties The flexural load–deflection curves of UHPC samples prepared by a direct cast and this flow control method (h = 10 mm) are presented in Fig. 17. It is obviously seen that the maximum load of samples prepared by the flow control method is higher than that of samples prepared by a direct cast. Flexural strength, toughness and deflection at modulus of rupture (SMOR) can be obtained from the load-deflection curves [8]. Compressive strength, flexural strength, toughness and SMOR of specimens fabricated by these types of casting are summarized in Table 4. For measurement of compressive strength, the load direction is perpendicular to the fiber orientation. It can be found that there is only a slight increase for compressive strength induced by the orientation of steel fibers. With this flow control method, flexural strength, toughness and SMOR was improved by 35.2%, 61.2% and 31.8%, respectively. Therefore, the designed L-shape device provides a potential method for improving the flexural performance of UHPC through controlling the flow path. On the other hand, this method could not be directly applied to practical construction at present. It can be possibly achieved by installing an L-shape outlet to the traditional concrete pouring system. In this case, the pouring efficiency may be significantly reduced. Therefore, the field application of this approach should be further investigated in the future. Fig. 16. Visualization of steel fibers motion at t = 2 s in the L-shape apparatus with h = (a) 10 mm, (b) 20 mm and (c) 30 mm.

Fig. 16. As mentioned above, the exit of horizontal channel was firstly blocked until the height of SAP suspension in the vertical container reached 210 mm and it was blocked again when the SAP suspension flowed out from the channel for 2 s. In this test, SAP suspension in the vertical container drops faster for the higher horizontal channel due to the higher flow velocity. As expected, steel fibers asymptotically rotate to the direction of local streamlines as illustrated by the red arrows, generating a bet-

5. Conclusions 1) SPH method was applied to numerically model the motion and orientation of steel fibers in UHPC mixture during the flow through the L-shape device. Steel fibers tend to rotate to the direction of local streamlines, leading to an improvement in fiber orientation. 2) Based on SPH modelling results, most of steel fibers are aligned along the mixture flowing into the horizontal channel. The better modification of fiber orientation is obtained by the smaller channel height.

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Table 4 Mechanical properties of UHPC samples prepared by a direct cast and the flow control method. Method

Compressive strength (MPa)

Flexural strength (MPa)

Toughness (kNmm)

SMOR (mm)

Without steel fibers Direct cast Flow control

113.2 135.1 139.8

11.5 26.4 35.7

4.3 64.9 104.6

0.559 1.295 1.707

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